text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
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using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace LionFire.Referencing
{
// If inheriting this, also consider inheriting from IReferencable
public interface IReferencable<out TReference> : IReferencable // REVIEW - IReferencable? Helps for Save(). Having it separate results in ambiguous resolution of Reference.
where TReference : IReference
{
new TReference Reference { get; }
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
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Agriculture & chemicals in Nashik: agriculture & agro chemicals are usually defined as pesticides, fertilizers and seed products. The US environmental protection agency defines pesticides as any materials manufactured or formulated to kill a pest. This means that herbicides, fungicides, insecticides and miticides are pesticides. Find the sources of agriculture & chemicals suppliers in Nashik, agriculture & chemicals dealers in Nashik, agriculture & chemicals distributors in Nashik and agriculture & chemicals manufacturers. The quality-tested variety of agriculture & chemicals provided by trusted and reliable sources listed into myinfoline in Nashik market. Find agriculture & chemicals providers in Nashik earch information of agriculture & chemicals providers services, offices and shops. Find phone numbers, addresses, map, email id, my offers, see ratings & reviews of agriculture & chemicals in Nashik, for best search of agriculture & chemicals in Nashik. Submit your details and get Best price quotes and deals instantly! | {
"redpajama_set_name": "RedPajamaC4"
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ACCEPTED
#### According to
The Catalogue of Life, 3rd January 2011
#### Published in
null
#### Original name
Streptocalyx biflorus L.B.Sm.
### Remarks
null | {
"redpajama_set_name": "RedPajamaGithub"
} | 2,168 |
› KPMG launches Digital Ledger Services
KPMG launches Digital Ledger Services to help companies implement blockchain technology
KPMG launches Digital Ledger Services
Collaborates with Microsoft to offer blockchain as a service.
KPMG in Singapore has announced the introduction of its Digital Ledger Services. This is a comprehensive suite of services designed to help companies, especially those in regulated sectors such as financial services, to realise the potential of blockchain capabilities such as providing faster and more secure transactions, streamlining and automating back office operations, and reducing costs by utilising blockchain-based technologies.
Blockchain is an alternative ledger database that maintains a continuously growing list of transaction records that are considered permanent and unchangeable, and is increasingly becoming the destination platform for financial services companies.
As a service offered through the KPMG Digital Village, KPMG's Digital Ledger Services include full lifecycle support – from ideation, market needs validation, business case development and the building of prototypes – to systems and operations integration, and ongoing management of a company's blockchain infrastructure.
The lifecycle support will involve management consulting and risk consulting proficiency in financial processes with regulatory requirements in mind. KPMG's specialised in-house coding and development will also be part of the services offered to clients.
"Blockchain has the potential to replace all business intermediaries and ensures distributed trust. Imagine a process where we on-board clients via their blockchain identities just like you would use your own social media credentials to log-in to any application or device," said Jan Reinmueller, Head of Digital Village, KPMG in Singapore.
Expanding alliance with Microsoft
In addition, KPMG will expand its strategic alliance with Microsoft to work on blockchain initiatives – with Microsoft providing blockchain as a service platform and KPMG providing its comprehensive suite of services – which will help clients efficiently and securely move to the cloud for storage, while adopting disruptive blockchain technologies.
"To make it truly meaningful, we need to work with industry partners such as Microsoft to offer digital ledger technology as a service. Its accessibility via cloud infrastructure enables us to scale up and support our clients operating in Singapore and the region," said Lyon Poh, Head of Digital + Innovation, KPMG in Singapore.
"We're excited to be expanding our efforts with KPMG to develop blockchain services," said Marley Gray, Principal Program Manager of Azure Blockchain Engineering at Microsoft. "The global availability of Microsoft Azure, with its hybrid cloud capabilities, extensive compliance certification portfolio, and enterprise-grade security help to enable blockchain adoption, especially in highly regulated industries like financial services, healthcare and government. With the availability of KPMG's Digital Ledger Services in Singapore, built on Microsoft's Blockchain as a Service platform, we hope to empower companies in Asia Pacific to build technology systems of the future."
True to KPMG Digital Village's vision of collaborative innovation, it is also actively working with one of its portfolio start-ups, Bluzelle, to offer blockchain-powered applications to clients in the finance and healthcare industry.
Already, clients of KPMG are seeing the benefits of blockchain technology. Bob Crozier, Associate Director of AIA Edge's Innovation Team in Asia Pacific, shared how KPMG Digital Village has helped identify opportunities and address challenges associated with blockchain and distributed ledger technology.
"Blockchain presents a tremendous opportunity for the insurance industry. Understanding its value is key, and the only way to do that is to get your hands dirty. To this end, we've worked with partners such as KPMG Digital Village to build prototypes and pilots to learn how they can add value to our business. These could be solutions that solve pain points for customers, such as purchasing, claims, KYC and AML, or other back office functions," he said.
Across its member firms worldwide, KPMG has dedicated more than 80 partners and executives to focus on blockchain, including its industry leading Data and Analytics services that will focus on coding and development in support of proof of concept, prototyping and integration of blockchain capabilities.
In addition to increasing the speed and security of transactions worldwide by using cryptology, blockchain technology also can be used to reduce costs by leveraging cloud technology and improve regulatory compliance by offering detailed factual evidence and a solid audit trail of transactions for auditors and regulators.
Currently, KPMG is working with clients worldwide on a range of global blockchain projects. Among these projects is the qualification of a blockchain solution for a major bank's global payments and the development and prototyping of smart contracts in insurance.
Digital Ledger Services will also be similarly available to clients in Indonesia, with KPMG Digital Village extending its presence in the market this month.
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© 2020 KPMG Services Pte. Ltd. (Registration No: 200003956G), a Singapore incorporated company and a member firm of the KPMG network of independent member firms affiliated with KPMG International Cooperative ("KPMG International"), a Swiss entity. All rights reserved. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
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Q: I am not able to run my flutter app beacause of this error of Jitsi meet package for FLUTTER Launching lib\main.dart on CPH2381 in debug mode...
Running Gradle task 'assembleDebug'...
WARNING: [Processor] Library 'C:\Users\Yusuf Ansari\.gradle\caches\modules-2\files-2.1\com.facebook.react\react-native-webrtc\1.89.1-jitsi-7097494\2eba38ea6be677eccbf67760c601f477edaf08dd\react-native-webrtc-1.89.1-jitsi-7097494.aar' contains references to both AndroidX and old support library. This seems like the library is partially migrated. Jetifier will try to rewrite the library anyway.
Example of androidX reference: 'androidx/core/view/ViewCompat'
Example of support library reference: 'android/support/annotation/Nullable'
e: C:\Users\Yusuf Ansari\AppData\Local\Pub\Cache\hosted\pub.dartlang.org\jitsi_meet-4.0.0\android\src\main\kotlin\com\gunschu\jitsi_meet\JitsiMeetPlugin.kt: (66, 42): Type mismatch: inferred type is Activity? but Activity was expected
FAILURE: Build failed with an exception.
* What went wrong:
Execution failed for task ':jitsi_meet:compileDebugKotlin'.
> A failure occurred while executing org.jetbrains.kotlin.compilerRunner.GradleCompilerRunnerWithWorkers$GradleKotlinCompilerWorkAction
> Compilation error. See log for more details
I tried changing the Kotlin version but it's still not resolving this issue
| {
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Sciades botelensis är en skalbaggsart som först beskrevs av J. Linsley Gressitt 1951. Sciades botelensis ingår i släktet Sciades och familjen långhorningar.
Artens utbredningsområde är Taiwan. Inga underarter finns listade i Catalogue of Life.
Källor
Långhorningar
botelensis | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,809 |
{"url":"https:\/\/math.stackexchange.com\/questions\/2206805\/factoring-1x-dots-xn-into-a-product-of-polynomials-with-positive-coefficie","text":"Factoring $1+x+\\dots +x^n$ into a product of polynomials with positive coefficients\n\nCan the polynomial $1+x+x^2+\\dots +x^n$ be factored, for some $n\\ge 1$, into a product of two non-constant polynomials with positive coefficients?\n\nThoughts\n\nIt is easy to factor it into polynomials with non-negative coefficients e.g. $$1+x+x^2+x^3 = (1+x)(1+0x + x^2),$$ but I have no example with positive coefficients. I believe this should be possible for large $n$, since there are so many (something like $2^{\\lceil n\/2\\rceil-1}$) ways to factor $1+x + x^2 +\\dots + x^n$ into a product of two monic polynomials with real coefficients.\n\nSome motivation from probability theory\n\nThe question is motivated by Can the sum of two independent r.v.'s with convex support be uniformly distributed?\n\nNamely, we can ask ourselves a discrete counterpart:\n\nWhether a discrete uniform random variable (i.e. the one taking values $0,1,\\dots,n$ with equal probabilities) can be decomposed into a sum of independent non-constant random variables, each ranging over a set of consecutive integers?\n\nThe link is provided by the probability generating function (pgf): $$m_Y(x) = \\mathbb E[x^{Y}].$$ If the random variable $Y$ takes values $0,1,\\dots,k$ with positive probabilities, then its pgf is a polynomial with positive coefficients: $$m_Y(x) = \\sum_{i=0}^k \\mathbb{P}(Y=i) x^i;$$ in particular, for a random variable $U_n$, uniformly distributed on $\\{0,1,\\dots,n\\}$, $$m_{U_n}(x) = \\frac1{n+1}\\bigl(1+x+x^2+\\dots + x^n\\bigr).$$\n\nSince for independent random variables, the pgf of sum if a product of pgfs: $$m_{Y'+Y''}(x) = \\mathbb E[x^{Y'+Y''}] = \\mathbb E[x^{Y'}]\\mathbb E[x^{Y''}] = m_{Y'}(x)m_{Y''}(x),\\tag{1}$$ these two questions are equivalent$^*$.\n\n$^*$Note that in general $(1)$ does not imply the independence of $Y'$ and $Y''$. Nevertheless, if $m_Y$ factors, say, into $m_{Y'}$ and $m_{Y''}$, then $Y$ has the same distribution as the sum of independent copies of $Y'$ and $Y''$, and, indeed, we have the desired decomposition.\n\n\u2022 Comments are not for extended discussion; this conversation has been moved to chat. \u2013\u00a0user642796 Mar 30 '17 at 6:40\n\nCan the polynomial $1+x+x^2+\\dots +x^n$ be factored, for some $n\\ge 1$, into a product of two non-constant polynomials with positive coefficients?\n\n$$x^n+\\cdots +x+1=\\frac{x^{n+1}-1}{x-1}=\\frac{\\prod_{1\\le k\\le n+1}(x - e^{2i\\pi k\/(n+1)})}{x-1}=\\prod_{1\\le k\\lt n+1}(x - e^{2i\\pi k\/(n+1)})$$ For a factorization $x^n+\\dots +x+1=g(x)h(x)$, $g$ and $h$ are products of some $x-\\zeta^k$ where $\\zeta$ is nth root of unity (up to units (in this case multiplying by positive real numbers) however any such factorization implies one without units). The leading term of both polynomials must be $1$ because it is the product of leading terms that are always $1$. The constant term is also one because it is the product of root of unity so its absolute value is $1$ and it must be real and positive.\n\n$$(x^p+\\cdots +1)(x^q+\\cdots+1)=x^n+\\cdots +x+1$$ Assume without loss of generality that $p\\ge q$. Take the constant term of the first polynomial and multiply it with the leading term of the second and you get $x^q$. \\begin{align} (x^p+\\cdots+ ax^q +\\cdots +1)(x^q+\\cdots+1) &=\\cdots +ax^q1+ \\cdots +1x^q +\\cdots\\\\ &= \\cdots +(\\cdots+a+1)x^q \\\\ \\end{align} All other terms must be positive and they can only add to $x^q$, the coefficient should be equal $1$. Therefore all other coefficients of $x^q$ must be zero and $a$ is zero.\n\n\u2022 Wow. Ridiculously easy. Half of the words in your answer are not needed, but +1 from me. \u2013\u00a0zhoraster Mar 30 '17 at 19:53\n\u2022 @zhoraster Yeah I was surprised too, and it is indeed two-linear but I wanted to explain things that might not be obvious immediately. I have few good follow up questions I hadn't thought about yet: 1) What is the minimal amount of zero coefficients for each $n$ 2) What if allow the factorization to only be a multiplication of cyclotomic polynomials? 3) What is the minimal product of zero coefficients in each polynomial for each $n$? \u2013\u00a0i9Fn Mar 30 '17 at 20:05\n\nI believe this should be possible for large $n$, since there are so many (something like $2^{\\lceil n\/2\\rceil-1}$) ways to factor $1+x + x^2 +\\dots + x^n$ into a product of two monic polynomials with real coefficients.\n\nNice exercise :): show that $1+x+\\cdots+x^n$ can be factored into $2$ polynomials of degree at least $1$ with non-negative coefficients if and only if $n+1$ is not prime.\n\nProbabilistic reformulation: Let $n \\geq 2$ be an integer, $X$ a random variable following the uniform distribution on $\\{1,2,\\ldots,n\\}$. Show that there exist two independent nonnegative integer-valued independent random variables $Y$ and $Z$ such that $X$ and $Y+Z$ have the same distribution if and only if $n$ is not prime.","date":"2021-03-02 23:34:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 1, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9562749862670898, \"perplexity\": 152.79745286784933}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-10\/segments\/1614178364932.30\/warc\/CC-MAIN-20210302221633-20210303011633-00598.warc.gz\"}"} | null | null |
{"url":"http:\/\/memolamadrid.es\/ioyps\/f3126e-mahalanobis-distance-distribution","text":"The MD can be used to detect outliers. point cloud), the Mahalanobis distance (to the new origin) appears in place of the \" x \" in the expression exp (\u221212x2) that characterizes the probability density of the standard Normal distribution\u2026 :) What is the explanation which justify this threshold ? I think the Mahalanobis metric is perhaps best understood as a weighted Euclidean metric. And finally, for each vertex v \\in V, we also have a multivariate feature vector r(v) \\in \\mathbb{R}^{1 \\times k}, that describes the strength of connectivity between it, and every region l \\in L. I\u2019m interested in examining how \u201cclose\u201d the connectivity samples of one region, l_{j}, are to another region, l_{k}. Cortical regions do not have discrete cutoffs, although there are reasonably steep gradients in connectivity. Rick is author of the books Statistical Programming with SAS\/IML Software and Simulating Data with SAS. In statistics, we sometimes measure \"nearness\" or \"farness\" in terms of the scale of the data. The set of empirically estimated Mahalanobis distances of a dataset is in the first step a random vector with exchangable but dependent entries. I need to calculate the mahalanobis distance for a numerical dataset of 500 independent observations grouped in 12 groups (species). (AB)-1 = B-1A-1, and (A-1)T = (AT)-1. Theory of Mahalanobis Distance Assume data is multivariate normally distributed (d dimensions) Appl. It reduces to the familiar Euclidean distance for uncorrelated variables with unit variance. For many distributions, such as the normal distribution, this choice of scale also makes a statement about probability. All the distribution correspond to the distribution under the Null-Hypothesis of multivariate joint Gaussian distribution of the dataset. Pingback: How to compute Mahalanobis distance in SAS - The DO Loop. Ways to measure distance from multivariate Gaussian (Mahalanobis distance) 5. After transforming the data, you can compute the standard Euclidian distance from the point z to the origin. If the data reveals, the MD value is 12 SD\u2019s away from a standardized residual of 2.14. goodness-of-fit tests for whether a sample can be modeled as MVN. The Mahalanobis distance can be used to compare two groups (or samples) because the Hotelling T\u00b2 statistic defined by: T\u00b2 = [(n1*n2) \u2044 (n1 + n2)] dM. 2) what is the difference between PCA and MD? Then, as a confirmation step to ensure that our empirical data actually follows the theoretical \\chi_{p}^{2} distribution, I\u2019ll compute the location and scale Maximumim Likelihood(MLE) parameter estimates of our d^{2} distribution, keeping the d.o.f. I actually wonder when comparing 10 different clusters to a reference matrix X, or to each other, if the order of the dissimilarities would differ using method 1 or method 2. For X1, substitute the Mahalanobis Distance variable that was created from the regression menu (Step 4 above). However, as measured by the z-scores, observation 4 is more distant than observation 1 in each of the individual component variables. It seems to be related to the MD. The estimated LVEFs based on Mahalanobis distance and vector distance were within 2.9% and 1.1%, respectively, of the ground truth LVEFs calculated from the 3D reconstructed LV volumes. Other approaches [17][18][19] use the Mahalanobis distance to the mean of the multidimensional Gaussian distribution to measure the goodness of \ufb01t between the samples and the statistical model, resulting in ellipsoidal con\ufb01dence regions. Theoretically, your approach sounds reasonable. There are other T-square statistics that arise. In my case, I have normally-distributed random variables which are highly correlated with each other. For example, a student might be moderately short and moderately overweight, but have basketball skills that put him in the 75th percentile of players. I do not see it in any of the books on my reference shelf, nor in any of my multivariate statistics textbooks (eg, Johnson & Wichern), although the ideas are certainly present and are well known to researchers in multivariate statistics. Mahalanobis Distance: Mahalanobis distance (Mahalanobis, 1930) is often used for multivariate outliers detection as this distance takes into account the shape of the observations. I want to flag cases that are multivariate outliers on these variables. See http:\/\/en.wikipedia.org\/wiki\/Euclidean_distance. Look at the Iris example in PROC CANDISC and read about the POOL= option in PROC DISCRIM. In both of these applications, you use the Mahalanobis distance in conjunction with the chi-square distribution function to draw conclusions. Figure 2. From: Data Science (Second Edition), 2019 Statements like Mahalanobis distance is an example of a Bregman divergence should be fore-head-slappingly obvious to anyone who actually looks at both articles (and thus not in need of a reference). It would be great if you can add a plot with Standardised quantities too. Results seem to work out (that is, make sense in the context of the problem) but I have seen little documentation for doing this. As stated in your article 'Testing data for multivariate normality', the squared Mahalanobis distance has an approximate chi-squared distribution when the data are MVN. p) fixed. \"However, for this distribution, the variance in the Y direction is LESS than the variance in the X direction, so in some sense the point (0,2) is \"more standard deviations\" away from the origin than (4,0) is.\". The multivariate generalization of the -statistic is the Mahalanobis Distance: where the squared Mahalanobis Distance is: where is the inverse covariance matrix. Some of the points towards the centre of the distribution, seemingly unsuspicious, have indeed a large value of the Mahalanobis distance. If you change the scale of your variables, then the covariance matrix also changes. If we were to include samples that were considerably far away from the the rest of the samples, this would result in inflated densities of higher d^{2} values. As to \"why,\" the squared MD is just the sum of squares from the mean. The Mahalanobis distance from a vector x to a distribution with mean \u03bc and covariance \u03a3 is d = ( x \u2212 \u03bc ) \u2211 \u2212 1 ( x \u2212 \u03bc ) ' . All this sense is because of your clear and great explanation of the method. The higher it gets from there, the further it is from where the benchmark points are. Can you please help me to understand how to interpret these results and represent graphically. I have read that Mahalanobis distance theoretically requires input data to be Gaussian distributed. Distribution of the Mahalanobis distance between two samples from a Gaussian distribution. The purpose of data reduction is two-fold, it identities relevant commonalities among the raw data variables and gives a better sense of anatomy, and it reduces the number of variables sothat the within-sample cov matrices are not singular due to p being greater than n. Is this appropriate? If we define a specific hyper-ellipse by taking the squared Mahalanobis distance equal to a critical value of the chi-square distribution with p degrees of freedom and evaluate this at $$\u03b1$$, then the probability that the random value X will fall inside the ellipse is going to be equal to $$1 - \u03b1$$. The MD to the second center is based on the sample mean and covariance of the second group. I do have a question regarding PCA and MD. Thanks. If I plot two of them, the data points lie somehow around a straight line. The Mahalanobis distance is a measure between a sample point and a distribution. Using Principal Component & 2. using Hat Matrix. [1 2 3 3 2 1 2 1 3] using the formula available in the literature. Need your help.. Sure. Thank you for sharing this great article! Very desperate, trying to get an assignment in and don't understand it at all, if someone can explain please? between the 12 species. By solving the 1-D problem, I often gain a better understanding of the multivariate problem. To measure the Mahalanobis distance between two points, you first apply a linear transformation that \"uncorrelates\" the data, and then you measure the Euclidean distance of the transformed points. = zT z Finally, let\u2019s have a look at some brains! The Mahalanobis distance and its relationship to principal component scores The Mahalanobis distance is one of the most common measures in chemometrics, or indeed multivariate statistics. In both contexts, we say that a distance is \"large\" if it is large in any one component (dimension). Generate random variates that follow a mixture of two bivariate Gaussian distributions by using the mvnrnd function. Notice that if \u03a3 is the identity matrix, then the Mahalanobis distance reduces to the standard Euclidean distance between x and \u03bc. We\u2019ve gone over what the Mahalanobis Distance is and how to interpret it; the next stage is how to calculate it in Alteryx. R. \u2026 Whenever I am trying to figure out a multivariate result, I try to translate it into the analogous univariate problem. It seems that PCA will remove the correlation between variables, so is it the same just to calculate the Euclidean distance between mean and each point? Here, larger d^{2} values are in red, and smaller d^{2} are in black. In the graph, two observations are displayed by using red stars as markers. So any distance you compute in that k-dimensional space is an approximation of distance in the original data. In this fragment, should say \"...the variance in the Y direction is MORE than the variance ....\"? Pingback: The best of SAS blogs for 2012 - SAS Voices, Pingback: 12 Tips for SAS Statistical Programmers - The DO Loop. Pingback: The curse of dimensionality: How to define outliers in high-dimensional data? As long as the data are non-degenerate (that is, the p RVs span p dimensions), the distances should follow a chi-square(p) distribution (assuming MVN). You can generalize these ideas to the multivariate normal distribution. The point (0,2) is located at the 90% prediction ellipse, whereas the point at (4,0) is located at about the 75% prediction ellipse. In SAS, you can use PROC CORR to compute a covariance matrix. Sorry, but I do not understand your question. To detect outliers, the calculated Mahalanobis distance is compared against a chi-square (X^2) distribution with degrees of freedom equal to the number of dependent (outcome) variables and an alpha level of 0.001. we expect the Mahalanobis distances to be characterised by a chi squared distribution. But now, I am quite excited about how great was the idea of mahalanobis distance and how beautiful is it! Likewise, we also made the distributional assumption that our connectivity vectors were multivariate normal \u2013 this might not be true \u2013 in which case our assumption that d^{2} follows a \\chi^{2}_{p} would also not hold. The squared distance Mahal2(x,\u03bc) is The result is approximately true (see 160) for a finite sample with estimated mean and covariance provided that n-p is large enough. (2012). The heavier tail of the upper quantile could probability be explained by acknowledging that our starting cortical map is not perfect (in fact there is no \u201cgold-standard\u201d cortical map). A Q-Q plot can be used to picture the Mahalanobis distances for the sample. This doesn\u2019t necessarily mean they are outliers, perhaps some of the higher principal components are way off for those points. This measures how far from the origin a point is, and it is the multivariate generalization of a z-score. What makes MD useful is that IF your data are MVN(mu, Sigma) and also you use Sigma in the MD formula, then the MD has the geometric property that it is equivalent to first transforming the data so that they are uncorrelated, and then measuring the Euclidean distance in the transformed space. And then asked the same question again. For a standardized normal variable, an observation is often considered to be an outlier if it is more than 3 units away from the origin. The more interesting image is the geometry of the Cholesky transformation, which standardizes and \"uncorrelates\" the variables. MD units apart? The default threshold is often arbitrarily set to some deviation (in terms of SD or MAD) from the mean (or median) of the Mahalanobis distance. And based on the analysis I showed above, we know that the data-generating process of these distances is related to the \\chi_{p}^{2} distribution. This is going to be a good one. I have one question: the data set is 30 by 4. If not, can you please let me know any workaround to classify the new observation? Next, as described in the article 'Detecting outliers in SAS: Part 3: Multivariate location and scatter', I would base my outlier detection on the critical values of the chi-squared distribution. Last revised 30 Nov 2013. Therefore if you divide by k you get a \"mean squared deviation.\" \u03a3_X=LL^T The Mahalanobis distance is a measure between a sample point and a distribution. The second option assumes that each cluster has it's own covariance. Thx for the reply. For multivariate normal data with mean \u03bc and covariance matrix \u03a3, you can decorrelate the variables and standardize the distribution by applying the Cholesky transformation z = L-1(x - \u03bc), where L is the Cholesky factor of \u03a3, \u03a3=LLT. A Mahalanobis Distance of 1 or lower shows that the point is right among the benchmark points. ? (e.g. It's not a simple yes\/no answer. This article is referenced by Wikipedia, so it is suitable as a reference: Can you elaborate that a little bit more? In many books, they explain that this scaling\/dividing by 'k' term will read out the MD scale as the mean square deviation (MSD) in multidimensional space. You choose any covariance matrix, and then measure distance by using a weighted sum of squares formula that involves the inverse covariance matrix. Do you have some sample data and a tutorial somewhere on how to generate the plot with the ellipses? I guess both, only in the latter, the centroid is not calculated, so the statement is not precise... . Maybe you could find it in a textbook that discusses Hotelling's T^2 statistic, which uses the same computation. By using a chi-squared cumulative probability distribution the D 2 values can be put on a common scale, such \u2026 follows a Hotelling distribution, if the samples are normally distributed for all variables. The degree of freedom in this case equals to the number of predictors (independent variables). However, the regions with connectivity profiles most different than our target region are not only contiguous (they\u2019re not noisy), but follow known anatomical boundaries, as shown by the overlaid boundary map. I got 20 values of MD [2.6 10 3 -6.4 9.5 0.4 10.9 10.5 5.8,6.2,17.4,7.4,27.6,24.7,2.6,2.6,2.6,1.75,2.6,2.6]. Mahalanobis distance is only defined on two points, so only pairwise distances are calculated, no? Figure 2. You can use the \"reference observations\" in the sample to estimate the mean and variance of the normal distribution for each sample. Inference concerning \u03bc when \u03a3 is known is based, in part, upon the Mahalanobis distance N(X\u0305\u2212\u03bc)\u03a3 \u22121 (X\u0305\u2212\u03bc)\u2032 which has a \u03c7 N 2 distribution when X 1,\u2026 X N is a random sample from N(\u03bc, \u03a3). def gaussian_weights(bundle, n_points=100, return_mahalnobis=False): \"\"\" Calculate weights for each streamline\/node in a bundle, based on a Mahalanobis distance from the mean of the bundle, at that node Parameters ----- bundle : array or list If this is a list, assume that it is a list of streamline coordinates (each entry is a 2D array, of shape n by 3).","date":"2021-02-25 05:17:56","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8400517702102661, \"perplexity\": 540.0399616061541}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-10\/segments\/1614178350717.8\/warc\/CC-MAIN-20210225041034-20210225071034-00593.warc.gz\"}"} | null | null |
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| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,906 |
Changes to zoning of Valemount's 5th Avenue
Published on : June 22, 2017 June 18, 2017 Published by : The Goat
Village of Valemount office. / RMG FILE PHOTO
by EVAN MATTHEWS
Select properties on Valemount's 5th Avenue have been rezoned for indefinite residential use — but make no mistake — the area is still zoned for commercial use.
Just following its May. 23 meeting, Council held a public hearing before giving third reading to the zoning bylaw's changes. The bylaw changes amend the area's "C1 designation," meaning the Village will allow property owners with existing homes "indefinite residential use," with no obligation or pressure to ever own a business.
The affected properties sit between Ash and Cedar Street.
"These properties will be permitted to continue residential use until such time there is commercial use on the subject property for a period of six or more consecutive months," said the Village's Corporate Services Clerk Carleena Shepherd.
There are instances of commercial businesses with a residential space in the same building, such as Home Hardware.
"Residential use can't outweigh commercial use in commercial zones… We're going to see similar (changes) around the Village in the near future with the infusion of more interests," — Gord Simmons, Village's subdivision approving officer
Council's rationale for re-evaluating 5th Avenue Zoning involved a resident who expressed concern over the (potential) loss of their home due to a fire, and not being able to re-build because of commercial zoning, according to Councillor Peter Reimer.
Reimer says Council has addressed the issue, in that if a person has owned a residence on one of the properties, they can continue to live in the commercially zoned space as long as they'd like.
Local business owner Joseph Nusse owns one of the affected properties, and expressed concern regarding residential use taking precedent over commercial development in the future.
Nusse says within five years he intends to construct a bigger commercial building on the property, with residential space above.
"I have absolutely no issue being surrounded by residential neighbours," says Nusse.
"However, I want it clarified that these changes come only with the explicit understanding that concerns of a residential nature will in no way affect — or even delay consideration — for development of a commercial building," he says.
Nusse listed potential concerns from neighbours including the height of the building, (tree) falling within pre-existing commercial guidelines, ease of parking due to increased traffic, and noise.
The Village's Subdivision Approving Officer Gord Simmons responded to Nusse, saying, "It's commercially zoned property already. The residential use is secondary.
"Residential use can't outweigh commercial use in commercial zones… We're going to see similar (changes) around the Village in the near future with the infusion of more interests," he said, making note of undeveloped commercially zoned areas.
Simmons said even a new Council would have to support commercial development in a commercial zone — such as Nusse's property — unless they changed the zoning all together through public process.
"I would suggest that may allay some of Mr. Nusse's concerns," said Simmons. "It's what it's zoned for."
Council gave the third reading to the proposed zoning changes and closed the public hearing.
Swift Creek Motel now a housing unit
New rules for property owners with revamped Zoning Bylaw
Robson Valley property values a mixed bag: rural Valemount…
Valemount Council - VCF/VIP appointments, lift station, roof…
Valemount Council: Capping expenses, new equipment, rezoning…
Categorized in : Business Editor's Pick News and Views
CBT helps to preserve Robson Valley heritage
Local man publishes Robson Valley anthology | {
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} | 9,568 |
Apply to win a $25,000 Scholarship – Summer 2014 Brightest Minds MBA Scholarship Contest
Home/Opportunities, Rise Networks Community, Youth Speak/Apply to win a $25,000 Scholarship – Summer 2014 Brightest Minds MBA Scholarship Contest
The Brightest Minds MBA scholarship contest 2014 is now open for applications. The Economist GMAT Tutor is pleased to announce the launch of the Summer 2014 Contest, which will award one winner a $25,000 scholarship to business school.
The scholarship competition is open to all prospective MBA and EMBA students. The winner will be the student who scores the highest on the Economist GMAT Tutor simulation test. The winning student will be awarded a $25,000 scholarship to one of the premiere business school sponsors. Five randomly selected runners-up will each receive a free iPad Air.
The simulation test will require the completion of a 75-minute Verbal section and a 75-minute Quant section. Please ensure you have the available time to complete the test all at once. You will not be able to pause once you begin.
The prize is a USD $25,000 tuition scholarship to a business school of the winner's choice from among the business schools that are sponsoring this Contest.
The contest is open to all prospective MBA or Executive MBA students worldwide.
Contest open only to college graduates who are age 18 or over.
The $25,000 scholarship will be awarded to the person who scores the highest on our GMAT simulation exam.
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The winner will be announced on November 17th. Five randomly selected runners-up will receive a free iPad mini. Ready to enter the contest for your chance to win? View the contest rules.
"Opinion pieces of this sort published on RISE Networks are those of the original authors and do not in anyway represent the thoughts, beliefs and ideas of RISE Networks."
By RISE NETWORKS|2014-08-14T17:10:24+01:00August 14, 2014|Opportunities, Rise Networks Community, Youth Speak|0 Comments
About the Author: RISE NETWORKS
"Nigeria's Leading Private Sector and Donor funded Social Enterprise with deliberate interest in Technology and its relevance to Youth and Education Development across Africa. Our Strategic focus is on vital human capital Development issues and their relationship to economic growth and democratic consolidation." Twitter: @risenetworks || Facebook - RISE GROUP || Google Plus - Rise Networks | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,944 |
\section{Introduction}
\label{sec:introduction}
Since its introduction, Einstein's theory in three dimensions has been a very
useful toy model to study properties of gravitational theories. Even if it lacks some
features compared to its higher dimensional versions, like gravitational
waves, it still possesses dynamical objects \cite{Deser1984} and black-holes
\cite{Banados1992,Banados1993}.
This theory is particularly interesting in the context
of AdS/CFT. In their seminal work \cite{Brown1986}, Brown and Henneaux showed that the algebra of
the conserved charges of asymptotically $AdS_3$ space-times is given by two
copies of the Virasoro algebra with non-zero central charge. This lead
to many interesting results, for instance:
Strominger was able to reproduce the Bekenstein-Hawking entropy of the BTZ
black-holes using the Cardy formula \cite{strominger1998}. Since then, this
framework has been extended: either by
relaxing the original asymptotic conditions of Brown-Henneaux
\cite{Porfyriadis2010,Troessaert2013} or introducing new asymptotics with
different boundary dynamics \cite{Compere2013,Avery2014}. We now have a few
different sets of boundary conditions available but it is reasonable to say
that a lot more possibilities should exist.
Using the Chern-Simons description of 3D gravity, one can solve the
constraints and obtain the reduced theory describing the dynamics of the
boundary gravitons. For Brown-Henneaux boundary conditions, this procedure
leads to a Liouville theory on the boundary
\cite{Coussaert1995,Henneaux2000,Rooman2001,Barnich2013}. On the other hand, for chiral
boundary conditions, one obtains a chiral Liouville theory on the boundary
\cite{Compere2013}. All these results rely
heavily on the fact that one can solve the constraints and are difficult
to generalize in different contexts.
\vspace{5mm}
In this work, we use the hamiltonian framework to provide a unified
description of the previously introduced boundary conditions. The idea is to
start with very general asymptotic fall-off conditions and use the results obtained in
\cite{Troessaert2013a}. In the process, we will build a description of the
reduced theory living on the boundary at infinity without explicitly solving
the constraints.
In the first section, we study the asymptotic structure of 3D gravity with a
negative cosmological constant. We introduce our asymptotic fall-off
conditions and
study the structure of the reduced phase-space. More precisely, we build
quantities parametrizing the boundary gravitons and compute the induced
poisson structure.
In the second section, we describe all possible boundary conditions on the
lagrange multipliers. These boundary conditions are responsible for the
dynamical part of the theory. In particular, they are in one to one
correspondence with the induced hamiltonian on the phase-space of the boundary gravitons.
In the last section, we use our formalism to describe some of the boundary
conditions previously obtained in the literature. We study both the conformaly
symmetric boundary conditions \cite{Troessaert2013,Brown1986} and the chiral
boundary conditions \cite{Avery2014,Compere2013}
\vspace{5mm}
In \cite{Apolo2014}, the authors conjectured that all the previously
introduced asymptotic conditions for 3D gravity are dual to Polyakov 2D gravity
with different gauge choices for the metric. It would be interesting to see how
their approach can be extended to the most general asymptotic conditions introduced
here.
\vspace{5mm}
In this paper, we use the notation $O(r^n)$ to describe functions with the
following behavior in the limit $r\rightarrow \infty$:
\begin{equation}
f(r,x^A) = O(r^n) \quad \Rightarrow \quad \lim_{r\rightarrow \infty}
\frac{f}{r^n} = \bar f(x^A).
\end{equation}
We will also ask for a compatible behavior with as many partial derivatives as
needed:
\begin{gather}
f(r,x^A) = O(r^n) \quad \Rightarrow \quad \d^k_r f(r,x^A) = O(r^{n-k})\quad \text{and} \quad \d^k_A f = O(r^n).
\end{gather}
\section{Asymptotic structure}
\label{sec:AsymptoticStructure}
The bulk hamiltonian action for gravity in 3 dimension is given by:
\begin{eqnarray}
\label{eq:bulkaction}
S[N,N^i,g_{ij},\pi^{ij}] & = & \frac{1}{16\pi G}\int dt \int_\Sigma d^2x\, \left\{\pi^{ij} \d_t
g_{ij} - N \mathcal{R} - N^i \mathcal{R}_i\right\},\\
\mathcal{R} & =& - \sqrt{g} \left[ R - 2\Lambda + \frac{1}{g} \left(
\pi^2 - \pi^{ij} \pi_{ij} \right)\right], \\
\mathcal{R}_i & = & -2 \nabla_j\pi^{\phantom{i}j}_i,
\end{eqnarray}
where $g_{ij}$ is a 2 dimensional metric and $\pi^{ij}$ is a
density. In order to apply the formalism of \cite{Troessaert2013a},
we need boundary conditions on the dynamical variables
$(g_{ij},\pi^{ij})$. As, we want to study the
asymptotic structure, we need fall-off conditions in order to have
generators given by finite quantities. The most common choice is the
one used in \cite{Brown1986} but there have been other propositions
\cite{Porfyriadis2010,Compere2013,Troessaert2013,Avery2014}. Following the
results of \cite{Troessaert2013a}, we expect these boundary
conditions to share the same reduced phase-space, the differences
being in the choice of the Hamiltonian.
We will start with general fall-off conditions on the phase-space
containing all of the previously proposed boundary conditions. The
analysis of the boundary conditions on the lagrange multipliers will
be posponed to the study of the hamiltonian generators starting in
section \ref{sec:conf}. We will consider the following asymptotic behavior:
\begin{gather}
\label{eq:assympg}
g_{rr} = \frac{l^2}{r^2} + O(r^{-4}), \quad g_{r\phi} = O(r^{-1}),
\quad g_{\phi\phi} = r^2 \bar \gamma(t, \phi) + O(1),\\
\pi^{rr} = O(r),\quad \pi^{r\phi} = O(r^{-2}), \quad \pi^{\phi\phi} = O(r^{-5}),
\label{eq:assympp}
\end{gather}
where $\Lambda = -\frac{1}{l^2}$ and $\bar \gamma$ is a dynamical
field which is always positive. In \cite{Brown1986}, the authors
showed that such fall-off conditions are not enough for a hamiltonian
analysis of the problem. We also have to impose the constraints asymptotically:
\begin{equation}
\label{eq:assympR}
\mathcal{R} = O(r^{-n}), \quad \mathcal{R}_i = O(r^{-n}) \qquad \forall n\in \mathbb{N}.
\end{equation}
With this set of fall-off conditions, the bulk part of the action
\eqref{eq:bulkaction} is finite whenever the lagrange multipliers
satisfy
\begin{equation}
\exists m \in \mathbb{N}\quad \text{s.t.}\quad N = O(r^m), \quad N^i = O(r^m).
\end{equation}
The additional conditions on the constraints \eqref{eq:assympR} have
some useful consequences. In particular, we have:
\begin{equation}
\label{eq:asymppirr}
\pi^{rr} = \frac{r}{2 l} P(t, \phi) + O(r^{-1}),
\end{equation}
and
\begin{equation}
\label{eq:asympK}
\d_r \left(r^2 (K + \frac{1}{l}) \right) = O(r^{-3}),
\end{equation}
where $K$ is the trace of the extrinsic curvature of the circles $r$
equals constant (see appendix \ref{sec:ADMspa}).
\subsection{Differentiable gauge transformations}
\label{sec:inf-diff-gauge-gener}
Gauge-like transformations are given by:
\begin{equation}
g_{ij} = \frac{\delta ( \xi\mathcal{R} + \xi^k\mathcal{R}_k)}{\delta
\pi^{ij}}, \quad \pi^{ij} =-
\frac{\delta (\xi \mathcal{R} + \xi^k \mathcal{R}_k)}{\delta g_{ij}},
\end{equation}
where the gauge parameters $\xi, \xi^i$ can depend on the fields. We
will restrict our analysis to gauge parameters with the following
asymptotic behavior:
\begin{equation}
\label{eq:inf-paramgauge}
\xi = O(r), \qquad \xi^r = O(r), \qquad \xi^\phi = O(1).
\end{equation}
In this case, using \eqref{eq:assympR}, the explicit form of the
gauge-like transformations is worked out to be:
\begin{eqnarray}
\label{eq:gaugeg}
\delta_\xi \pi^{ij} & = & -\sqrt{g} \xi
\Lambda g^{ij} + \sqrt{g} \left(
\nabla^i\nabla^j \xi - g^{ij} \nabla^k\nabla_k\xi\right)\nonumber\\
&& - 2\frac{\xi}{\sqrt{g}}\left( \pi^{ik}\pi_k^j -
\pi\pi^{ij} \right) -
\frac{\xi}{\sqrt{g}}\frac{g^{ij}}{2}\left(\pi^2 -
\pi^{kl}\pi_{kl} \right),\nonumber\\
&& +\d_k \left( \xi^k \pi^{ij}\right) - \d_k\xi^i \pi^{kj} - \d_k\xi^j \pi^{ki}+ O(r^{-n}),\\
\label{eq:gaugep}
\delta_\xi g_{ij} & = & 2
\frac{\xi}{\sqrt{g}} \left( \pi_{ij} - \pi g_{ij}\right) +
\xi^k \d_k g_{ij} +
\d_i \xi^k g_{kj} + \d_j \xi^k g_{ki} + O(r^{-n}),
\end{eqnarray}
for all $n \in \mathbb{R}$.
\vspace{5mm}
A differentiable gauge transformation is a gauge-like transformation $\delta_\xi$
for which we can associate a differentiable generator. This requires two
conditions to be met: the transformation $\delta_\xi$ preserves the boundary conditions
and the generator $\Gamma_\xi$ satisfies
\begin{equation}
\delta \Gamma_\xi = \int_\Sigma d^2x \left(\frac{\delta
\Gamma_\xi}{\delta g_{ij}} \delta g_{ij} + \frac{\delta
\Gamma_\xi}{\delta \pi^{ij}} \delta \pi^{ij}\right).
\end{equation}
To compute the set of differentiable gauge transformations, we will
start by computing the set of gauge-like transformations
\eqref{eq:gaugeg}-\eqref{eq:gaugep} preserving the boundary conditions.
The variations of the constraints under a gauge-like transformation are
given by:
\begin{eqnarray}
\delta_\xi \mathcal{R} = \d_i (\xi^i \mathcal{R}) - \d_i (\xi g^{ij}\mathcal{R}_j) - \d_i \xi
g^{ij} \mathcal{R}_j + O(r^{-n}), \qquad \forall n \in \mathbb{R},\\
\delta _\xi \mathcal{R}_k = \d_k \xi \mathcal{R} + \d_i(\xi^i \mathcal{R}_k) + \d_k \xi^i
\mathcal{R}_i+ O(r^{-n}),\qquad \forall n \in \mathbb{R}.
\end{eqnarray}
We see that any transformation of the form \eqref{eq:inf-paramgauge} will
preserve the fall-off conditions on the constraints. Computing the
variation of the metric and using the fall-off conditions, we obtain:
\begin{eqnarray}
\delta_\xi g_{rr} & = & 2 \frac{l^2}{r^2}(\d_r \xi^r-\frac{1}{r}\xi^r )
+ 2 \d_r \xi^\phi g_{r\phi} + O(r^{-4}),\\
\delta_\xi g_{r\phi} & = & r^2 \sigma \d_r \xi^\phi + O(r^{-1}),\\
\delta_\xi g_{\phi\phi} & = & -2 \xi \sqrt{g} \pi^{rr} + \xi^r
\d_rg_{\phi\phi} + \xi^\phi \d_\phi g_{\phi\phi} + 2 \d_\phi \xi^\phi
g_{\phi\phi} + O(1).
\end{eqnarray}
The preservation of the fall-off conditions for $g_{rr}$ and
$g_{r\phi}$ leads to
\begin{equation}
\xi^r = r \psi + O(r^{-1}), \quad \xi^\phi = Y + O(r^{-2}),
\end{equation}
where $\psi$ and $Y$ are arbitrary functions independant of $r$.
Taking this into account
and using the spatial 1+1 decomposition of the metric described in
appendix \ref{sec:ADMspa}, the variations of the momenta become
\begin{eqnarray}
\delta_\xi \pi^{rr} & = & - \sqrt{\sigma}
\frac{r^3}{l^3}(\d_r \xi - \frac{1}{r} \xi)+ O(r),\\
\delta_\xi \pi^{r\phi} & = & \frac{1}{l\sqrt{\sigma}} (\d_\phi+\frac{r}{l^2} \lambda_\phi )(\d_r \xi-\frac{1}{r} \xi)+ O(r^{-2}),\\
\delta_\xi \pi^{\phi\phi} &=& - \frac{1}{\sqrt{g}} \left( \d_r^2 \xi - \frac{\lambda^2
}{l^2} \xi - \frac{\d_r \lambda}{\lambda}\d_r
\xi + \frac{r}{l^2} \lambda_\phi \lambda^\phi (\d_r \xi-\frac{1}{r} \xi)\right. \nonumber \\ && \qquad
\left. -(3\frac{\lambda^\phi}{r} +\d_r \lambda^\phi) \d_\phi
\xi\right) + O(r^{-5}) \label{eq:varpiphiphiI}
\end{eqnarray}
where $\lambda_\phi = O(r^{-1})$ and $\lambda = \frac{l}{r} + O(r^{-3})$. The preservation of the fall-off
conditions for $\pi^{rr}$ and $\pi^{r\phi}$ then imply
\begin{equation}
\xi = r f + \kappa,\qquad \kappa = O(r^{-1}),
\end{equation}
where $f$ is another arbitrary function independent of $r$. Using this
and the asymptotic form of $\pi^{rr}$ given in \eqref{eq:asymppirr},
the variation of $g_{\phi\phi}$ automatically preserves the fall-off
condition \eqref{eq:assympg}.
The only condition we still need to check is the preservation of
$\pi^{\phi\phi}=O(r^{-5})$.
Using the expansion $\lambda = \frac{l}{r} + \tilde \lambda$
with $\tilde \lambda = O(r^{-3})$, we can simplify the variation \eqref{eq:varpiphiphiI} to:
\begin{equation}
\label{eq:varfinalpiphiphi}
\delta_\xi \pi^{\phi\phi}
= - \frac{r^{-2}}{\sqrt{g}} \d_r\left[r^2\left( \d_r\kappa -
\frac{1}{r}\kappa - \frac{\tilde \lambda}{l} rf -\lambda^\phi
r\d_\phi f\right)\right] + O(r^{-5}).
\end{equation}
Any possible transformation satisfying this condition will also
preserve the more constrained form of $\pi^{rr}$ given in equation
\eqref{eq:asymppirr}. Computing the variation of $\pi^{rr}$ taking
the gap into account leads to:
\begin{equation}
\label{eq:varfinalpirr}
\delta_\xi \pi^{rr} = \frac{\gamma}{\lambda l}\left( \d_r \kappa
-\frac{1}{r} \kappa - \frac{\tilde \lambda}{l} r f - \lambda^\phi r\d_\phi f - l( K+
\frac{1}{l}) f\right) + \omega r + O(r^{-1}),
\end{equation}
where $\omega$ is a function independent of $r$ encoding part
of the variation of $P$. In order to preserve the asymptotic form
of $\pi^{rr}$, the function $\kappa$ must be of the form
\begin{eqnarray}
\kappa &=& - \frac{l^2}{2r} \chi - r\int_r^\infty dr' j(r') + O(r^{-3}), \\
j &=& \frac{\tilde \lambda}{l} f + \lambda^\phi\d_\phi f + \frac{l}{r}( K+
\frac{1}{l}) f = O(r^{-3}),\label{eq:fuckingj}
\end{eqnarray}
where $\chi$ is an arbitrary function independent of $r$. Combining
equation \eqref{eq:varfinalpirr} with \eqref{eq:asympK}, we see that
such a $\kappa$ induces a variation \eqref{eq:varfinalpiphiphi} that
automatically preserves the fall-off of $\pi^{\phi\phi}$.
We have shown the following:
\begin{theorem}
The set of gauge-like transformations preserving the asymptotic
conditions \eqref{eq:assympg}-\eqref{eq:assympR} is given by:
\begin{eqnarray}
\label{eq:allowed}
\xi & = & r f - \frac{l^2}{2r} \chi - r\int_r^\infty dr' j(r') +
O(r^{-3}),\\
\xi^r & = & r \psi + O(r^{-1}),\\
\xi^\phi & = & Y + O(r^{-2}),
\end{eqnarray}
where the function $j$ is given in equation \eqref{eq:fuckingj} and the
four functions $f, \chi, \psi$ and $Y$ are independent of $r$.
\end{theorem}
The second condition for a gauge-like transformation to be differentiable is
the existance of a differentiable generator.
The bulk part of the generator of a gauge-like transformation is given
by the smeared constraints:
\begin{equation}
\tilde \Gamma_{\xi} = \frac{1}{16\pi G}\int_\Sigma d^2x \left( \xi \mathcal{R} + \xi^i \mathcal{R}_i\right).
\end{equation}
The boundary term coming from a general variation is then easily
computed:
\begin{eqnarray}
\label{eq:nonintegI}
\delta \tilde \Gamma_\xi &=& \int_\Sigma d^2x \, \left( \frac{\delta \tilde
\Gamma_\xi}{\delta g_{ij}} \delta g_{ij} + \frac{\delta \tilde
\Gamma_\xi }{\delta \pi^{ij}} \delta \pi^{ij}
\right)\nonumber \\
&& + \frac{1}{16\pi G}\oint_{\d \Sigma} (d^1x)_k \, \left\{-2 \xi^i \delta \pi^k_{\phantom k i}
+\xi^k \pi^{ij} \delta g_{ij} - \xi \sqrt{g} \left(g^{ij}\delta \Gamma^k_{ij} -
g^{ki}\delta \Gamma^j_{ji}\right)\right. \nonumber\\
&& \qquad \left. + \d_l \xi \sqrt{g}
\left(g^{ki}g^{lj} - g^{kl} g^{ij} \right) \delta g_{ij} + \Theta^k(\mathcal{R}, \mathcal{R}_i)\right\}.
\end{eqnarray}
The function $\Theta$ is coming from the variation of the gauge
parameters $\xi, \xi^i$: it is a local function of the constraints and
their derivatives. In this case, as we have imposed the
constraints asymptotically, it will always be zero. Inserting our
fall-off conditions, the asymptotic form of the gauge parameters and
evaluating at the boundary $r\rightarrow \infty$,
the boundary term becomes:
\begin{multline}
\label{eq:nonintegII}
-\frac{1}{16\pi G} \oint_{\d \Sigma} d\phi\, \lim_{r \rightarrow \infty}\left\{2Y \delta
\pi^r_\phi +l \psi \, \delta P +2 r^2 f \delta\left( \sqrt{\bar\gamma} (K +
\frac{1}{l})\right) \right. \\ \left. + 2 \left(
r^2 (K + \frac{1}{l})f +l\, \chi\right) \delta
\sqrt{\bar\gamma}\right\}.
\end{multline}
Let's introduce the fields:
\begin{equation}
J(t, \phi) \equiv \frac{2}{l}\lim_{r\rightarrow \infty} \pi^r_\phi,
\qquad M(t, \phi) \equiv
\frac{ 2 \sqrt{\bar\gamma}}{l} \lim_{r\rightarrow \infty} \left(r^2 ( K +
\frac{1}{l})\right), \qquad Q(t, \phi) \equiv 2 \sqrt{\bar\gamma}.
\end{equation}
The boundary term \eqref{eq:nonintegII} is integrable if and only if there
exists a functional on the circle
\begin{equation}
\frac{l}{16\pi G} \oint_{\d \Sigma}
d\phi\, k_\xi( P, J, M, Q),
\end{equation}
such that:
\begin{gather}
Y = \frac{\bar \delta k_\xi}{\delta J},\qquad
\psi = \frac{\bar \delta k_\xi}{\delta P},\label{eq:asymparamkI}\\
f = \frac{\bar \delta k_\xi}{\delta M},\qquad
\tilde \chi \equiv \chi + \frac{ M}{ Q} f = \frac{\bar \delta k_\xi}{\delta Q},
\label{eq:asymparamkII}
\end{gather}
where the Euler-Lagrange derivative $\frac{\bar \delta}{\delta}$ is the one
defined on the circle only:
\begin{equation}
\frac{\bar \delta k}{\delta M} = \sum_k (-\d_\phi)^k
\frac{\d k}{\d \d^k_\phi M}.
\end{equation}
If such a functional exists, the differentiable generator of the transformation is given by:
\begin{equation}
\Gamma_\xi = \frac{1}{16\pi G}\int_\Sigma d^2x \left( \xi \mathcal{R} + \xi^i \mathcal{R}_i\right) + \frac{l}{16\pi G} \oint_{\d \Sigma}
d\phi\, k_\xi(P, J, M, Q).
\end{equation}
On the constraints, we obtain
\begin{equation}
\Gamma_\xi \approx \frac{l}{16\pi G} \oint_{\d \Sigma}
d\phi\, k_\xi(P, J, M, Q).
\end{equation}
The transformations for which $\Gamma_\xi \approx 0$ are called proper
gauge transformations. They are the true gauge freedom of the system
as they are generated by constraints and always comute with the
differentiable Hamiltonian \cite{Troessaert2013a}. In the following,
we will denote the parameters of proper gauge transformations by
$\eta$ and $\eta^i$.
The set differentiable gauge transformations form an algebra under the
Poisson bracket for which the set of proper gauge transformations is
an ideal. We have proved that
\begin{theorem}
The quotient of the differentiable gauge transformation by the proper
gauge transformations is parametrized by the functionals of $P,
J, M$ and $Q$ defined on the circle:
\begin{equation}
\frac{l}{16\pi G} \oint_{\d \Sigma} d\phi\, k_\xi(P, J, M, Q).
\end{equation}
\end{theorem}
\noindent The induced Poisson bracket on the quotient will be computed
in section \ref{sec:dirac-brack-bound}.
\subsection{Boundary gravitons}
\label{sec:boundary-gravitons}
We expect the quantities $P, J, M$ and $Q$ that we defined
in the previous section to encode all the information about the
boundary gravitons. More specifically, we expect them to be gauge
invariant and to completely characterize the configuration up to proper
gauge transformations.
The parameters of proper gauge transformations $\Gamma_\eta$ have the following fall-off
\begin{equation}
\eta = O(r^{-3}), \qquad \eta^r = O(r^{-1}), \qquad \eta^\phi = O(r^{-2}).
\end{equation}
We easily show that the associated transformations on the relevant canonical
fields are given by:
\begin{equation}
\delta_\eta \pi^{rr} = O(r^{-1}), \qquad \delta_\eta \pi^{r\phi} =
O(r^{-4}), \qquad \delta_\eta g_{\phi\phi} = O(1).
\end{equation}
This means that $P$, $J$ and $Q$ are gauge invariant quantities. For
$M$, we need the transformation law of $K$ (see eq \eqref{eq:transfoK}). A straightforward computation gives
\begin{equation}
\delta_\eta K = O(r^{-4}),
\end{equation}
which means that $M$ is also gauge invariant.
In order to analyse the structure of the reduced phase-space, it is
easier to fix the gauge. The simplest choice is the Fefferman-Graham
gauge which is given by:
\begin{equation}
g_{rr} = \frac{l^2}{r^2}, \qquad g_{r\phi} = 0, \qquad \pi^{\phi\phi}
= 0.
\end{equation}
This gauge can always reached by a proper gauge transformation (more details
are given in appendix \ref{sec:FGfixing}).
With the gauge fixed, the constraints simplify
drastically:
\begin{eqnarray}
\label{eq:gaugefixconstrr}
\mathcal{R}_r & = & -2 \frac{l^2}{r^2} \left( \d_r \pi^{rr} - \frac{1}{r}
\pi^{rr} + \d_\phi \pi^{r\phi} \right),\\
\label{eq:gaugefixconstrphi}
\mathcal{R}_\phi & = & -2 \gamma\frac{l}{r}\left( \frac{r}{l}\d_r \pi^{r\phi} + \frac{2}{l}
\pi^{r\phi} - 2\pi^{r\phi} (K + \frac{1}{l})\right),\\
\label{eq:gaugefixconstrperp}
\mathcal{R} & = & -2 \frac{l}{r}\sqrt{\gamma}\left( \frac{r}{l} \d_r K - K^2 -
(\pi^{r\phi})^2 + \frac{1}{l^2}\right),
\end{eqnarray}
where the extrinsic curvature is given by $K = -\frac{r}{2l}
\gamma^{-1} \d_r \gamma$ (see appendix \ref{sec:ADMspa}). This gives us a set of four differential
equation in $r$ for which $P, J, M$ and $Q$ are the
corresponding four integration constants. This can be seen easily
as this system is solvable explicitly.
In term of $L_\pm = K +
\frac{1}{l} \pm \pi^{r\phi}$, we can rewrite the constraints
\eqref{eq:gaugefixconstrphi} and \eqref{eq:gaugefixconstrperp} as
\begin{equation}
\frac{r}{l}\d_r L_\pm + \frac{2}{l} L_\pm - L_\pm^2=0.
\end{equation}
This gives
\begin{equation}
L_{\pm}= \frac{2}{l}\frac{ A_\pm}{ A_\pm + \frac{r^2}{l^2}} = 2l\frac{A_\pm}{r^2}+O(r^{-4}),
\end{equation}
where $A^\pm$ are two integration constants.
We can then solve
for $\pi^{rr}$ and $\gamma$:
\begin{eqnarray}
\pi^{rr} &=& r \frac{P}{2l} + \frac{r}{2l}\left(\frac{\d_\phi
A_+}{ A_+
+ \frac{r^2}{l^2}} -\frac{\d_\phi A_-}{A_-
+ \frac{r^2}{l^2}} \right) = r \frac{P}{2l}+O(r^{-1}),\\
\gamma & = & \bar \gamma r^{2}\left(1 + \frac{l^2}{r^2}A_+ \right)\left(1 +
\frac{l^2}{r^2}A_- \right) = \bar\gamma r^{2} + O(1),
\end{eqnarray}
with the last two integration constants $\bar\gamma = \frac{Q^2}{4}$ and
$P$. The functions $A_\pm$ are related to
$M$ and $J$ by:
\begin{equation}
J = 2 \bar\gamma (A_+ - A_-), \qquad M = 2 \sqrt{\bar\gamma}(A_+ + A_-).
\end{equation}
\begin{theorem}
The four functions $P, J, M$ and $Q>0$ completely determine
the configuration asymptotically up to gauge transformations. They parametrize the only degrees of freedom of the
theory: the boundary gravitons.
\end{theorem}
\noindent The above analysis was only done asymptotically. For specific values of $P, J, M$ and $Q$, we have no guaranty
that the configuration will be regular everywhere in the bulk.
The BTZ black-holes \cite{Banados1992,Banados1993} are given by:
\begin{equation}
\label{eq:BTZinf}
P=0, \qquad J = 8 G \,\frac{j}{l}, \qquad M = 8 G \,m,\qquad Q = 2,
\end{equation}
where $m$ and $j$ are the mass and angular momentum of
black-hole. Let's remark that we are only talking about a
configuration at fixed $t$. To have the full 3D black-hole, we also
need the right time evolution: the right Hamiltonian. This will be
studied in section \ref{sec:brown-henn-bound}.
\subsection{Dirac bracket for the boundary gravitons}
\label{sec:dirac-brack-bound}
The Poisson bracket of two differentiable functionals
$F[g_{ij},\pi^{ij}]$ and $G[g_{ij},\pi^{ij}]$ is given by
\begin{equation}
\left\{F[g_{ij},\pi^{ij}], G[g_{ij},\pi^{ij}] \right\} = 16 \pi G\int_{\Sigma}
d^2x \, \left( \frac{\delta F}{\delta g_{ij}}\frac{\delta G}{\delta \pi^{ij}} -\frac{\delta G}{\delta g_{ij}}\frac{\delta F}{\delta \pi^{ij}} \right).
\end{equation}
For differentiable gauge generators, a straightforward computation gives
\begin{eqnarray}
\label{eq:constalge}
\left\{ \Gamma_\xi, \Gamma_\zeta\right\} & = & \tilde G \left[ [\xi,\zeta]_g\right]\\ && +\frac{1}{16\pi G}
\oint_{\d \Sigma} (d^{n-1}x)_k \left\{ 2(\zeta^k \nabla_i\xi_j
-\xi^k\nabla_i\zeta_j) \pi^{ij}+ 2 \left[ \xi, \zeta \right]^j_{SD} \pi^k_j\right. \nonumber\\ &&\quad \left. +2\sqrt{g}\left(
\nabla_i \xi^k \nabla^i\zeta - \nabla_i \xi^i \nabla^k\zeta -
\nabla_i \zeta^k \nabla^i\xi + \nabla_i \zeta^i \nabla^k\xi\right)
\right.\nonumber\\ &&\quad \left. -
(\zeta\xi^k-\xi\zeta^k) (2 \Lambda \sqrt{g} -
\frac{1}{\sqrt{g}}(\pi^2 - \pi^{ij}\pi_{ij})) + \Theta^k(\mathcal{R}, \mathcal{R}_i)\right\},\nonumber\\
\left[ \xi, \zeta \right]^a_{g} & = & \left[ \xi, \zeta \right]^a_{SD} +
\delta_\zeta \xi^a - \delta_\xi \zeta^a + \Xi^a(\mathcal{R}, \mathcal{R}_i),
\end{eqnarray}
where $\xi^a=(\xi, \xi^i)$ and the functions $\Theta$ and $\Xi$ are
local functions of the contraints and their derivatives. The surface deformation bracket is given by:
\begin{eqnarray}
\left[ \xi, \zeta \right]_{SD}&=&\xi^i\d_i \zeta - \zeta^i \d_i \xi,\\
\left[ \xi, \zeta \right]^i_{SD}& = & \xi^j\d_j \zeta^i - \zeta^j\d_j \xi^i + g^{ij}
\left( \xi \d_j \zeta - \zeta \d_j \xi\right).
\end{eqnarray}
Differentiable gauge generators are first-class functionals,
evaluating their Poisson bracket will also give us their Dirac bracket
when evaluated on the reduced phase-space. Let's consider two
differentiable gauge generators $\Gamma_1$ and $\Gamma_2$ associated
to the functionals
\begin{equation}
\frac{l}{16\pi G} \oint_{\d \Sigma}d\phi\, k_1(P, J, M, Q) \qquad \text{and} \qquad \frac{l}{16\pi G} \oint_{\d \Sigma}d\phi\, k_2(P, J, M, Q).
\end{equation}
The corresponding gauge parameters $\xi_1$ and $\xi_2$ are given, up to
proper gauge transformations, by the identifications \eqref{eq:asymparamkI} and
\eqref{eq:asymparamkII}. By construction, we then have the following
\begin{equation}
\left\{ \frac{l}{16\pi G} \oint_{\d \Sigma}d\phi\, k_1(P, J, M, Q), \frac{l}{16\pi G} \oint_{\d
\Sigma}d\phi\, k_2(P, J, M, Q)\right\}^* \approx \left\{ \Gamma_1,
\Gamma_2\right\},
\end{equation}
where the LHS is the bracket on the reduced phase space. On the
constraints surface, the RHS reduces to the boundary term of
\eqref{eq:constalge}. It is a gauge invariant quantity, it is easier
to evaluate it when the gauge is fixed. Using the Fefferman-Graham
gauge described in the previous section, we obtain
\begin{eqnarray}
\left\{ \Gamma_1, \Gamma_2\right\} & \approx & \frac{l}{16\pi G} \oint_{\d \Sigma} d\phi \,
\left\{P (Y_1 \d_\phi \psi_2 +f_1 \tilde \chi_2) + JY_1 \d_\phi Y_2 +
\frac{4 J}{Q^2} f_1 \d_\phi f_2 \right. \nonumber \\ && \qquad +M (Y_1 \d_\phi f_2 + \psi_1 f_2) + Q (Y_1 \d_\phi \tilde
\chi_2 - \psi_1 \tilde \chi_2) \nonumber \\ && \qquad \left. + \frac{4}{Q} \d_\phi \psi_1 \d_\phi
f_2 - (1 \leftrightarrow 2) \right\}.
\end{eqnarray}
If we replace, $Y, f, \psi$ and $\tilde \chi$ by their values in term
of the Euler-Lagrange derivatives of $k_1$ and $k_2$ using
\eqref{eq:asymparamkI} and \eqref{eq:asymparamkII}, we obtain the
induced Dirac bracket as
\begin{multline}
\label{eq:asympboundbracket}
\left\{ \Gamma_1, \Gamma_2\right\} \approx \frac{l}{16\pi G} \oint_{\d \Sigma} d\phi \,
\left\{P \left(\frac{\bar \delta k_1}{\delta J} \d_\phi \frac{\bar \delta k_2}{\delta P} +\frac{\bar \delta k_1}{\delta M} \frac{\bar \delta k_2}{\delta Q}\right)
\right. \\
+ M \left (\frac{\bar \delta k_1}{\delta J} \d_\phi \frac{\bar \delta k_2}{\delta M} + \frac{\bar \delta k_1}{\delta P}\frac{\bar \delta k_2}{\delta M}\right)
+ Q \left(\frac{\bar \delta k_1}{\delta J} \d_\phi \frac{\bar \delta k_2}{\delta Q} - \frac{\bar \delta k_1}{\delta P} \frac{\bar \delta k_2}{\delta Q}\right) \\
\left. + J\left( \frac{\bar \delta k_1}{\delta J}\d_\phi \frac{\bar \delta k_2}{\delta J} +
\frac{4}{Q^2}\frac{\bar \delta k_1}{\delta M} \d_\phi \frac{\bar \delta
k_2}{\delta M}\right)+ \frac{4}{Q} \d_\phi \frac{\bar \delta k_1}{\delta P} \d_\phi
\frac{\bar \delta k_2}{\delta M} - (1 \leftrightarrow 2) \right\}.
\end{multline}
\section{Boundary hamiltonian}
\label{sec:boundcondlagr}
As shown in \cite{Troessaert2013a}, the differentiable Hamiltonian is given by the
boundary conditions on the Lagrange multipliers. More precisely, the
Hamiltonian for 3D gravity is given by the differentiable gauge
generator associated to the gauge parameters $N$ and $N^i$. We saw in
section \ref{sec:inf-diff-gauge-gener} that, on the constraints surface, it is given by a boundary term
\begin{equation}
H[g_{ij}, \pi^{ij}] \approx \frac{l}{16\pi G} \oint_{\d \Sigma} k_H(M, J, P, Q),
\end{equation}
with
\begin{gather}
f_H \equiv \lim_{r\rightarrow \infty} \frac{N}{r} = \frac{\bar \delta
k_H}{\delta M}, \qquad \psi_H \equiv \lim_{r\rightarrow
\infty} \frac{N^r}{r} = \frac{\bar \delta k_H}{\delta P},\\
Y_H \equiv \lim_{r\rightarrow \infty} N^\phi= \frac{\bar \delta
k_H}{\delta J}, \qquad \tilde\chi_H \equiv \lim_{r\rightarrow
\infty} \frac{r}{l} \left( \frac{1}{\lambda} \d_r N - \frac{1}{l} N
- \frac{r}{l}\lambda^\phi \d_\phi N\right)= \frac{\bar \delta
k_H}{\delta Q}.
\end{gather}
Tuning these boundary conditions we can build any
functional $k_H$ on the boundary. This is our main result:
\begin{theorem}
If we assume that the canonical variables have the following asymptotic
behavior:
\begin{gather}
g_{rr}=\frac{l^2}{r^2} + O(r^{-4}), \quad g_{r\phi}=O(r^{-1}),
\quad g_{\phi\phi}=r^2\bar\gamma(t,\phi)+O(1),\\
\pi^{rr} = O(r), \quad\pi^{r\phi} = O(r^{-2}), \quad \pi^{\phi\phi}
=O(r^{-5},\\
\mathcal{R} = O(r^{-n}),\quad \mathcal{R}_i = O(r^{-n})\qquad \forall n \in \mathbb{R}.
\end{gather}
then the set of possible boundary conditions at spatial infinity on the lagrange multipliers $(N,
N^i)$ is in one to one correspondance with the functionals
$\oint_{\d\Sigma}k_H(M, J, P, Q)$ (modulo the constant
functionals) where the boundary
fields are defined by:
\begin{eqnarray}
P(t, \phi) \equiv 2l \lim_{r\rightarrow \infty} \frac{
\pi^{rr}}{r}, \quad
J(t, \phi) \equiv \frac{2}{l}\lim_{r\rightarrow \infty} \pi^r_\phi,
\\ M(t, \phi) \equiv
\frac{ 2 \sqrt{\bar\gamma}}{l} \lim_{r\rightarrow \infty} \left(r^2 ( K +
\frac{1}{l})\right), \qquad Q(t, \phi) \equiv 2 \sqrt{\bar\gamma},
\end{eqnarray}
wich $\bar \gamma >0$.
On the constraint's surface, we obtain a theory on the boundary $\d\Sigma$
with a phase-space parametrized by $(M, J, P, Q)$ with a
bracket given in equation \eqref{eq:asympboundbracket} and an Hamiltonian given by
\begin{equation}
H[g_{ij}, \pi^{ij}] \approx \frac{l}{16\pi G} \oint_{\d \Sigma} k_H(M, J, P, Q),
\end{equation}
\end{theorem}
\noindent This analysis only concerns the differentiable structure at infinity, we
didn't treat any of the possible obstruction coming from the bulk structure of
the space-time.
A surprising feature is the need for 4 functions in order to completely
describe the asymptotic phase-space. When written in term of Chern-Simons
theory, one needs 6 functions to describe the corresponding asymptotic phase-space. Since
one adds 3 gauge degrees of freedom in the bulk, one would have expected to have
three more asymptotic functions in the Chern-Simons description compared to
the metric description.
\vspace{5mm}
We will now study the different type of boundary conditions
that appeared in the literature. We will start with the sets of boundary
conditions that have the conformal algebra in two dimensions as a
symmetry algebra.
\section{Some examples of boundary conditions}
\subsection{Conformal}
\label{sec:conf}
Let's consider the boundary conditions presented in
\cite{Troessaert2013}. With the coordinates $x^A=t, \phi$, they are given by:
\begin{eqnarray}
\label{eq:bcconfextI}
g_{rr} & = & \frac{l^2}{r^2} + C_{rr}r^{-4} + o(r^{-4}),\\
g_{rA} & = & C_{rA}r^{-3} + o(r^{-3}),\\
g_{AB} & = & r^2 e^{2\varphi}\eta_{AB} + C_{AB} + o(1),\\
\label{eq:confaddcond}
0 & = & e^{-2\varphi}\eta^{AB}C_{AB} + \frac{1}{l^2}C_{rr},
\end{eqnarray}
where $\eta_{AB}dx^Adx^B = -\frac{1}{l^2}dt^2 + d\phi^2$ is a fixed
metric on the cylinder and $\eta^{AB}$ is its inverse. In term of
those fields, our quantities describing the boundary gravitons are
given by:
\begin{gather}
Q=2e^\varphi, \qquad M=\frac{2}{l^2}e^\varphi \left( e^{-2\varphi}
C_{\phi\phi} + \frac{1}{2l^2} C_{rr}\right),\\
P = -2l \dot \varphi, \qquad J = \frac{2}{l}C_{t\phi}.
\end{gather}
The lagrange multipliers take the following form:
\begin{equation}
N= \frac{r}{l} e^\varphi - \frac{l}{2}C_{tt}
e^{-\varphi}r^{-1}+o(r^{-1}), \quad N^r = O(r^{-1}), \quad N^\phi = O(r^{-2}),
\end{equation}
which leads to
\begin{equation}
f_H =\frac{Q}{2l}, \quad \tilde\chi_H = \frac{M}{2l}, \quad \psi_H = 0, \quad Y_H = 0.
\end{equation}
The associated differentiable Hamiltonian is then easily computed
\begin{equation}
\label{eq:hamiltEBH}
H_{EBH} \approx \frac{1}{16\pi G}\oint_{\d \Sigma} d\phi \, \frac{1}{2}
M Q.
\end{equation}
For the BTZ Black-hole \eqref{eq:BTZinf}, we have $H_{EBH} \approx m$
as expected. Using the equation of motion for $Q$, one can check that the
condition $Q>0$ is preserved under time evolution.
This set of boundary conditions possesses an asymptotic symmetry group
given by two Virasoros in semi-direct product with two current
algebras. As we have already computed the induced bracket on the boundary gravitons, we
just need to find the boundary generators in terms of $Q, P, J$ and
$M$ that are symmetry generators for the Hamiltonian $H_{EBH}$.
Let's define
\begin{gather}
\label{eq:definfcLcP}
\mathcal{L}^\pm(\phi) = \frac{l}{32 \pi G} \left(\frac{1}{2} M Q \pm J\right), \qquad
\mathcal{P}^\pm(\phi) = \frac{l}{32\pi G}\left( -P \pm \frac{2}{Q} \d_\phi
Q\right), \\
\label{eq:definfcQ}
\mathcal{Q} = \frac{-l}{16\pi G}\oint_{\d\Sigma} d\phi \log Q.
\end{gather}
They have the following bracket
\begin{eqnarray}
\left\{ \mathcal{L}^\pm(\phi), \mathcal{L}^\pm(\phi')\right\}^* &\approx&
\pm\mathcal{L}^\pm(\phi) \,\d_\phi \delta(\phi - \phi')\mp\mathcal{L}^\pm(\phi')\, \d_{\phi'} \delta(\phi' - \phi),\\
\left\{ \mathcal{L}^\pm(\phi), \mathcal{P}^\pm(\phi')\right\}^* &\approx & \pm\mathcal{P}^\pm(\phi)
\,\d_\phi \delta(\phi - \phi') - \frac{l}{16\pi G} \, \d_\phi^2 \delta(\phi - \phi'),\\
\left\{ \mathcal{P}^\pm(\phi), \mathcal{P}^\pm(\phi')\right\}^* &\approx& \mp \frac{l}{16\pi G} \, \d_\phi \delta(\phi - \phi'),
\end{eqnarray}
\begin{equation}
\left\{ \mathcal{L}^\pm(\phi), \mathcal{Q} \right\}^*
\approx \frac{1}{2} \mathcal{P}^\pm (\phi), \qquad\qquad
\left\{ \mathcal{P}^\pm(\phi), \mathcal{Q}\right\}^* \approx -\frac{l}{32\pi G},
\end{equation}
where the rest gives zero.
If we expand them in modes,
\begin{equation}
\mathcal{L}^\pm_m = \oint_{\d\Sigma} d\phi\, e^{\pm im \phi} \mathcal{L}^\pm(\phi),
\qquad \mathcal{P}^\pm_m = \oint_{\d\Sigma} d\phi\, e^{\pm im \phi} \mathcal{P}^\pm(\phi),
\end{equation}
we recover the algebra obtained in
\cite{Troessaert2013}:
\begin{equation}
\label{eq:adsextalgebra}\begin{array}{rclcrcl}
i\left\{\mathcal{L}^\pm_m,\mathcal{L}^\pm_n\right\}^*&=&(m-n)\mathcal{L}^\pm_{m+n}, & \qquad & i\{\mathcal{L}^+_m,\mathcal{L}^-_n\}^*&=&0, \\
i\left\{\mathcal{L}^\pm_m,\mathcal{P}^\pm_n\right\}^*&=&-n \mathcal{P}^\pm_{m+n} + \frac{l}{8G} im^2\delta_{m+n,0}, & \qquad & i\{\mathcal{L}^\pm_m,\mathcal{P}^\mp_n\}^*&=&0, \\
i\left\{\mathcal{P}^\pm_m,\mathcal{P}^\pm_n\right\}^*&=&-\frac{l}{8G} m\delta_{m+n,0}, &
\qquad & i\{\mathcal{P}^+_m,\mathcal{P}^-_n\}^*&=&0, \\
i\left\{\mathcal{L}^\pm_m, \mathcal{Q}\right\}^*& = & \frac{i}{2}\mathcal{P}^\pm_m, &\qquad &
i\left\{\mathcal{P}^\pm_m, \mathcal{Q} \right\}^* & = & -i\frac{l}{16 G}\delta_{m,0}.
\end{array}
\end{equation}
The identification $\mathcal{P}^+_0=\mathcal{P}^-_0$ is also present here:
\begin{equation}
\oint_{\d \Sigma} d\phi \,\mathcal{P}^+ = \oint_{\d \Sigma}d\phi\, \mathcal{P}^- =
\frac{-l}{32\pi G}\oint_{\d \Sigma} d\phi \, P.
\end{equation}
\vspace{5mm}
From this algebra, we can easily reconstruct the conserved quantities
$\mathcal{L}^\pm_m(t), \mathcal{P}^\pm_m(t)$ and $\mathcal{Q}(t)$ where the quantities defined
in \eqref{eq:definfcLcP}-\eqref{eq:definfcQ} are their values at $t=0$. A conserved quantity $F(t)$
satisfies
\begin{equation}
\frac{\d}{\d t} F + \left\{F , H\right\}^* \approx 0,
\end{equation}
where $\frac{\d}{\d t}$ only hits the explicit dependence on
time. Using $H_{EBH} = \frac{1}{l}(\mathcal{L}^+_0 + \mathcal{L}^-_0)$, we
obtain:
\begin{equation}
\mathcal{L}^\pm_m(t)=e^{i m \frac{t}{l}} \mathcal{L}^\pm_m, \qquad \mathcal{P}^\pm_m(t)=e^{i m
\frac{t}{l}} \mathcal{P}^\pm_m, \qquad \mathcal{Q}(t)=\mathcal{Q} + \frac{2}{l}\mathcal{P}_0 t.
\end{equation}
By construction, the algebra \eqref{eq:adsextalgebra} is time
independent.
These conserved quantities are
associated to asymptotic symmetries using the dictionary given in
\eqref{eq:asymparamkI}-\eqref{eq:asymparamkII}. For instance, the
angular momentum is
\begin{equation}
\mathcal{L}^+_0 - \mathcal{L}^-_0 = \frac{l}{16 \pi G} \oint_{\d \Sigma} d\phi \,J.
\end{equation}
It leads to
\begin{equation}
f=0, \qquad Y = 1, \qquad \psi = 0, \qquad \chi = 0,
\end{equation}
and then
\begin{equation}
\xi = O(r^{-3}), \qquad \xi^r = O(r^{-1}), \qquad \xi^\phi = 1 + O(r^{-2}),
\end{equation}
which is the expected rotation in $\frac{\d}{\d \phi}$ at infinity.
\subsection{Brown-Henneaux}
\label{sec:brown-henn-bound}
The original Brown-Henneaux (BH) boundary conditions are a sub-set of the
boundary conditions presented in the previous section where part of the boundary degrees of freedom are
frozen. We saw in \cite{Troessaert2013a} that such additional
boundary conditions on the phase-space can be imposed through residual
constraints on the boundary.
The BH boundary conditions are given by
\begin{eqnarray}
g_{rr} & = & \frac{l^2}{r^2} + C_{rr}r^{-4} + o(r^{-4}),\\
g_{rA} & = & C_{rA}r^{-3} + o(r^{-3}),\\
g_{AB} & = & r^2 \eta_{AB} + C_{AB} + o(1).
\end{eqnarray}
Our boundary variables are then easily computed. We have
\begin{gather}
Q=2, \qquad M=\frac{2}{l^2} \left(
C_{\phi\phi} + \frac{1}{2l^2} C_{rr}\right),\\
P = 0, \qquad J = \frac{2}{l}C_{t\phi},
\end{gather}
and, for the lagrange multipliers,
\begin{equation}
N= \frac{r}{l} - \frac{l}{2}C_{tt} r^{-1}+o(r^{-1}), \quad N^r = O(r^{-1}), \quad N^\phi = O(r^{-2}).
\end{equation}
We see that the phase-space is smaller in this case: we have to impose
both $Q=2$ and $P=0$. The boundary gravitons are then completely
parametrized by the boundary fields $M$ and $J$.
In order to describe this
phase-space, we will treat the two additional boundary conditions on the
boundary variables as constraints. This can be done by relaxing the
boundary conditions on the corresponding lagrange multipliers: we have
to relax both $\chi_H$ and $\psi_H$. Looking at the asymptotic form of
$N$, we see that $\tilde\chi_H$ is already relaxed: we have
\begin{equation}
\tilde\chi_H = \frac{1}{l} C_{tt} - \frac{1}{2l^5}C_{rr},
\end{equation}
but, this time, $C_{tt}$ is not related to $M$. Let's consider
the following relaxed asymptotics for the lagrange multipliers:
\begin{gather}
N= \frac{r}{l} - (\frac{l^2}{2}\tilde \chi_H + \frac{1}{4l^3}C_{rr})r^{-1}+o(r^{-1}), \\ N^r
= \psi_H +O(r^{-1}), \qquad N^\phi = O(r^{-2}),
\end{gather}
where both $\tilde \chi_H$ and $\psi_H$ are free to vary. The
corresponding differentiable Hamiltonian generating the additionary boundary
constraints $P=0$ and $Q=2$ is then given by:
\begin{multline}
H_{BH} =\frac{1}{16\pi G} \int_\Sigma d^2x \, \left( N \mathcal{R} + N^i
\mathcal{R}_i\right) \\+ \frac{1}{16 \pi G}\oint_{\d \Sigma} d\phi \, \Big(
M + l \psi_H P
+ l \tilde\chi_H (Q-2) \Big),
\end{multline}
The variation of the action then gives
\begin{multline}
\delta S = \int dt \int_{\Sigma}d^2x \, \left(\frac{\delta S}{\delta
g_{ij}} \delta g_{ij} + \frac{\delta S}{\delta \pi^{ij}} \delta
\pi^{ij} - \delta N \mathcal{R} - \delta N^i \mathcal{R}_i \right)\\
+ \frac{l}{16 \pi G}\oint_{\d \Sigma} d\phi \, \Big(
\delta\psi_H P
+ \delta\tilde\chi_H (Q-2) \Big),
\end{multline}
which is what we wanted: $\psi_H$ and $\tilde \chi_H$ are playing the
role of lagrange multipliers enforcing $Q=2$ and $P=0$.
We can now do our analysis of the boundary dynamics using the full
boundary phase-space described in section \ref{sec:dirac-brack-bound} with the
Hamiltonian:
\begin{eqnarray}
H_{BH} &\approx& \frac{1}{16 \pi G}\oint_{\d \Sigma} d\phi \,
M + \frac{l}{16 \pi G}\oint_{\d \Sigma} d\phi \, \Big(\psi_H P
+\tilde \chi_H (Q-2) \Big),\\
&\approx& H_{EBH}+ \frac{l}{16 \pi G}\oint_{\d \Sigma} d\phi \, \Big(\psi_H P
+\tilde \chi_H (Q-2) \Big).
\end{eqnarray}
In the second line, we used the constraints $Q=2$ to recover the Hamiltonian of the
previous section \eqref{eq:hamiltEBH}. We see that the theory corresponding to the
Brown-Henneaux boundary conditions is a constrained version of the
theory associated to the boundary conditions \eqref{eq:bcconfextI}-\eqref{eq:confaddcond}.
The boundary constraints are second-class:
\begin{equation}
\left\{P(\phi), Q(\phi')-2\right\}^* \approx -\frac{16 \pi G}{l}\Big(Q(\phi)-2\Big)
\delta (\phi-\phi') - \frac{32\pi G}{l} \delta(\phi - \phi'),
\end{equation}
the other brackets being zero. It is then straightforward to compute
the induced bracket on the fully reduced phase-space. In term of $M$
and $J$, we have
\begin{eqnarray}
\left\{ M(\phi), M(\phi')
\right\}^{**} &\approx& \frac{16 \pi G}{l}\Big(J(\phi) \,\d_\phi
\delta(\phi - \phi') -J(\phi')\, \d_{\phi'} \delta(\phi' - \phi)\Big),\\
\left\{M(\phi), J(\phi') \right\}^{**} &\approx& \frac{16 \pi G}{l}\Big(M(\phi) \,\d_\phi
\delta(\phi - \phi') -M(\phi')\, \d_{\phi'} \delta(\phi' -
\phi)\Big)\nonumber\\
&& \qquad \qquad-\frac{32 \pi G}{l}\d^3_\phi \delta (\phi - \phi'),\\
\left\{J(\phi), J(\phi') \right\}^{**} &\approx& \frac{l}{16 \pi G}\Big(J(\phi) \,\d_\phi
\delta(\phi - \phi') - J(\phi')\, \d_{\phi'} \delta(\phi' - \phi)\Big),
\end{eqnarray}
where $\approx$ means in this case that we have imposed all
constraints: from both the bulk and the boundary. On this fully
reduced phase-space, the Hamiltonian is simply given by
\begin{equation}
H_{BH} \approx \frac{1}{16 \pi G}\oint_{\d \Sigma} d\phi \, M.
\end{equation}
The two Virasoro algebras of conserved charges can be
recovered easily. Defining
\begin{equation}
\xbar \mathcal{L}^\pm(\phi) = \frac{l}{32 \pi G} \Big(M(\phi) \pm J(\phi)\Big), \qquad \xbar \mathcal{L}^\pm_m = \oint_{\d \Sigma}d\phi
\, e^{\pm i m \phi}\xbar\mathcal{L}^\pm(\phi),
\end{equation}
we obtain the usual result
\begin{equation}
\label{eq:BHvirasoro}
i\left\{ \xbar\mathcal{L}^\pm_m, \xbar\mathcal{L}^\pm_n\right\}^{**} \approx (m-n) \xbar\mathcal{L}^\pm_{m+n} + \frac{l}{8G}
m^3 \delta_{m+n,0}, \quad i\left\{ \xbar\mathcal{L}^+_m,
\xbar\mathcal{L}^-_n\right\}^{**} \approx 0.
\end{equation}
The Virasoro generators $\xbar\mathcal{L}^\pm_m$ are the generators defined on
the previous section $\mathcal{L}^\pm_m$ evaluated on the constraint's surface
$Q=2$ and $P=0$. The central charge in \eqref{eq:BHvirasoro} appeared
due to the correction coming from the Dirac bracket $\{ \,,
\,\}^{**}$. The conserved charges $\mathcal{L}^\pm_m(t)$ are easily computed:
\begin{equation}
\xbar\mathcal{L}^\pm_m(t) = e^{im\frac{t}{l}} \xbar\mathcal{L}^\pm_m.
\end{equation}
The algebra obtained here is of course just the current algebra of the
dual Liouville theory living on the boundary \cite{Coussaert1995,Henneaux2000,Rooman2001,Barnich2013}.
\subsection{Chiral}
\label{sec:chir-bound-cond}
In \cite{Compere2013}, the authors proposed a set of chiral
boundary conditions for $AdS_3$ that was extended in
\cite{Avery2014}. We will first find the Hamiltonian for the
extended version and then obtain the additional boundary constraints
corresponding to the original chiral boundary conditions. For the
extended case, the asymptotic behavior of the metric in the Fefferman-Graham
gauge can be written as
\begin{eqnarray}
g_{rr} & = & \frac{l^2}{r^2},\\
g_{r\phi} & = & 0,\\
g_{\phi\phi} & = & r^2 (1 + F) + C_{\phi\phi} + o(1),\\
g_{rt} & = & 0,\\
g_{t\phi} & = &\frac{F}{l} r^2 + C_{t\phi} + o(1),\\
g_{tt} & = & \frac{r^2}{l^2} (-1 + F) + \Delta- l^{-2} C_{\phi\phi} + 2 l^{-1} C_{t\phi} + o(1),
\end{eqnarray}
where $F$ is a function of $t$ and $\phi$ and $\Delta$ is a fixed constant. As
we assumed $\bar \gamma>0$, this
means that we are studying the case $F>-1$ only. A straighforward
computation leads to the following values for our quantities
describing the boundary gravitons:
\begin{gather}
Q = 2 \sqrt{1+F}, \qquad M= \frac{2}{l^2}\frac{C_{\phi\phi}}{\sqrt{1+F}}+\frac{1}{l^4}C_{rr}\sqrt{1+F}, \\
P = -l \d_t F + \frac{2+F}{1+F}\d_\phi F, \qquad
J=\frac{2}{l}C_{t\phi}(1+F) - \frac{2}{l^2}C_{\phi\phi}F,
\end{gather}
associated to the lagrange multipliers:
\begin{gather}
N = \frac{r}{l}\frac{1}{\sqrt{1+F}} +
\frac{l}{2r}\sqrt{1+F}\left(-\Delta
+\frac{C_{\phi\phi}}{l^2}\frac{1+2F}{(1+F)^2}
-\frac{2}{l}\frac{C_{t\phi}}{1+F}\right)+o(r^{-1}),\\
N^\phi = \frac{1}{l}\frac{F}{(1+F)}+O(r^{-2}), \qquad N^r = O(r^{-1}).
\end{gather}
This leads to
\begin{gather}
f_H=\frac{2}{l} \frac{1}{Q}, \qquad Y_H=\frac{1}{l} - \frac{4}{l} \frac{1}{Q^2},
\qquad \Psi_H=0,\\
\chi_H = \frac{\Delta}{2l} Q + \frac{8}{l}\frac{J}{Q^3} - \frac{2}{l}
\frac{M}{Q^2},
\end{gather}
and to the Hamiltonian:
\begin{equation}
\label{eq:HamilChiral}
H_{EC} \approx \frac{1}{16 \pi G}\oint_{\d \Sigma} d\phi \, \left(J -
4\frac{J}{Q^2} +
2 \frac{M}{Q} +\Delta \frac{Q^2}{4}\right).
\end{equation}
The equation of motion for $F$ is given by
\begin{equation}
\Delta\frac{\d }{\d x^-} F+ \left(\frac{\d}{\d x^-}\right)^3F = 0.
\end{equation}
where $x^- = \frac{t}{l} - \phi$. In general, we cannot expect the time
evolution to preserve the condition $F>-1$. The breaking of this condition
means that the surfaces of constant $t$ are not space-like and
our ADM split is not valid anymore. However, if the initial conditions
satisfy $F>-1$ then it will stay valid close to $t_0$ and, in this
neighborhood, we can still apply our analysis.
\vspace{5mm}
In \cite{Avery2014}, the authors showed that, for $\Delta<0$,
the algebra of the charges is given by the semi-direct product of a
Virasoro algebra with a $sl(2,\mathbb{R})$ current algebra. Functionals
of the boundary gravitons reproducing this result are built from
\begin{gather}
L_C(\phi) =\frac{l}{16\pi G}J - \d_\phi\mathcal{P}^+, \quad
T^0_C(\phi) = \mathcal{P}^+,\\
T^+_C(\phi) = \frac{l}{4\pi G}\left(\frac{M}{Q}- 2 \frac{J}{Q^2}\right), \quad
T^-_C(\phi) =\frac{l}{16\pi G}\frac{-Q^2}{8},
\end{gather}
where $\mathcal{P}^+(\phi)$ was defined in \eqref{eq:definfcLcP}. The brackets
of these new quantities are given by:
\begin{eqnarray}
\left\{L_C(\phi), L_C(\phi') \right\}^* & \approx & L_C(\phi)
\d_\phi \delta(\phi - \phi') - L_C(\phi')
\d_\phi' \delta(\phi' - \phi) \nonumber \\ && \qquad- \frac{l}{16 \pi G} \d_\phi^3
\delta(\phi - \phi'),\\
\left\{L_C(\phi), T_C^a(\phi') \right\}^* & \approx & T_C^a(\phi)
\d_\phi \delta(\phi - \phi'),\\
\left\{T^a_C(\phi), T^b_C(\phi') \right\}^* & \approx &f^{ab}_c
T_C^c(\phi) \delta (\phi-\phi') +\frac{l }{16\pi G}\eta^{ab} \d_\phi
\delta (\phi-\phi'),
\end{eqnarray}
where $a,b,c=+,-,0$. The current algebra is characterized by
\begin{equation}
f^{0+}_+=-1, \quad f^{0-}_-=1, \quad f^{+-}_0=2, \quad
\eta^{00}=-1, \quad \eta^{+-}=2,
\end{equation}
with all the other components equal to zero.
If we develop in modes:
\begin{gather}
L_{m} = \oint_{\d\Sigma}d\phi \, e^{im\phi} L_C(\phi),\quad T^a_{m} =
\oint_{\d\Sigma}d\phi \, e^{im\phi} T^a_C(\phi),
\end{gather}
we recover the algebra of the charges found in \cite{Avery2014}
\begin{eqnarray}
\label{eq:ChiralChargeI}
i \left\{ L_{m}, L_{n}\right\} & = & (m-n)L_{m+n} +\frac{l}{8 G}m^3
\delta_{m+n, 0},\\
i \left\{ L_{m}, T^a_{n}\right\} & = & -n T^a_{m+n},\\
\label{eq:CHiralChargeIII}
i \left\{ T^a_{m}, T^b_{n}\right\} & = & i f^{ab}_c
T^c_{m+n}+\frac{l }{8 G}\eta^{ab} m \delta_{m+n,0}.
\end{eqnarray}
In terms of these generators, the Hamiltonian is given by,
\begin{equation}
H =\frac{1}{l}(L_0 + \frac{1}{2} T^+_0 - 2\Delta T^-_0).
\end{equation}
The conserved quantities are easily built by adding an explicit time
dependence to each mode. If $\Delta =- \alpha^2$, we get
\begin{eqnarray}
\tilde L_m(t) &=& L_m e^{im\frac{t}{l}}, \\
\tilde T^0_m(t) &=&T^0_m e^{im\frac{t}{l}} \cos(2\alpha \frac{t}{l}) +
\frac{1}{4\alpha}T^+_m e^{im\frac{t}{l}} \sin(2\alpha \frac{t}{l})\nonumber \\ &&
\qquad-\alpha T^-_m e^{im\frac{t}{l}} \sin(2\alpha \frac{t}{l}),\\
\tilde T^+_m(t) &=& T^+_m e^{im\frac{t}{l}}\cos^2(\alpha \frac{t}{l})+
4\alpha^2 T^-_m e^{im\frac{t}{l}}\sin^2(\alpha \frac{t}{l})\nonumber\\ && \qquad-
2\alpha T^0_m e^{im\frac{t}{l}} \sin(2\alpha \frac{t}{l}),\\
\tilde T^-_m(t) &=& \frac{1}{4\alpha^2}T^+_m e^{im\frac{t}{l}}\sin^2(\alpha \frac{t}{l}) +
T^-_me^{im\frac{t}{l}}\cos^2(\alpha \frac{t}{l})\nonumber
\\ && \qquad + \frac{1}{2\alpha} T^0_m e^{im\frac{t}{l}} \sin(2\alpha \frac{t}{l}).
\end{eqnarray}
The cases $\Delta=0$ and $\Delta <0$ can be obtained in a similar way.
The charges we obtained here are not the one obtained in
\cite{Avery2014}. However, we built these because the are well adapted to the
constraints analysis that we will do in the next section.
\subsection{Constrained Chiral}
\label{sec:constr-chir-bound}
The original chiral boundary conditions introduced in
\cite{Compere2013} are a subset of the one introduced in the
previous section with the additional condition
\begin{equation}
\d_t F - \frac{1}{l} \d_\phi F = 0.
\end{equation}
A good point here is that this extra condition garanties the preservation of
$F>-1$ under time evolution.
This can easily be rewritten as
\begin{equation}
\label{eq:chiralconstraint}
T^0_C=\mathcal{P}^+ = \frac{l}{32 \pi G} \left(-P + \frac{2}{Q}\d_\phi
Q\right) = 0.
\end{equation}
The boundary theory associated to these restricted boundary conditions can be
described by
a theory built from the Hamiltonian
\eqref{eq:HamilChiral} with the constraint $T^0_C\approx 0$.
For simplicity, the rest of the analysis will be done using Fourier modes. The
primary constraints are $T^0_m\approx 0$ for all $m$. They lead to secondary
constraints:
\begin{gather}
\left\{ T^0_{m}, lH\right\} = -imT^0_m
-\frac{1}{2}T^+_m-2\Delta T^-_m,\\
\Rightarrow K^+_m \equiv \frac{1}{2}T^+_m+2\Delta T^-_m\approx 0.
\end{gather}
With these extra constraints, the set is complete:
\begin{equation}
\left\{K^+_m, lH \right\} = -imK^+_m -4\Delta T^0_m \approx 0.
\end{equation}
Their algebra is complicated and it is difficult to form the Dirac bracket. However, when $\Delta \ne
0$, $L_m$ and $K^-_m\equiv \frac{1}{2}T^+_m-2\Delta T^-_m$
form a complete set
of gauge-invariant quantities.
The reduced phase-space is parametrized by $L_m$ and $K^-_m$ with
\begin{eqnarray}
i\left\{L_m, L_n \right\} &=& (m-n)L_{m+n} + \frac{l}{8G}
m^3\delta_{m+n,0},\\
i\left\{L_m, K^-_n \right\} &=& -n K^-_{m+n},\\
i\left\{K^-_m, K^-_n \right\} &=& -\frac{\Delta l}{2G} m\delta_{m+n,0},
\end{eqnarray}
and the Hamiltonian given by
\begin{equation}
H = \frac{1}{l}(L_0 + K^-_0).
\end{equation}
To make the link with the charges obtained in equations (2.15) and (2.16) of
\cite{Compere2013}, we define
\begin{equation}
\hat L_m=L_m + \frac{1}{2}K_m^--\frac{l\Delta}{16G}\delta_{m,0},\qquad \hat
P_m=\frac{1}{2}K_m^--\frac{l\Delta}{16G}\delta_{m,0}.
\end{equation}
which leads to the following algebra
\begin{eqnarray}
i\left\{\hat L_m, \hat L_n \right\} &=& (m-n)\hat L_{m+n} + \frac{l}{8G}
m^3\delta_{m+n,0},\\
\label{eq:extchiralCompII}
i\left\{\hat L_m, \hat P_n \right\} &=& -n \hat
P_{m+n}
-\frac{\Delta l}{16G} m\delta_{m+n,0},\\
i\left\{\hat P_m, \hat P_n\right\} &=& -\frac{\Delta l}{8G} m\delta_{m+n,0}.
\end{eqnarray}
The algebra we obtain here is the algebra of the generators
written in equations (2.15) and (2.16) of
\cite{Compere2013}. However, the difference between the extension obtained
here and the one written in equations (2.17)-(2.19) of \cite{Compere2013} is a
redefiniton of the zero mode $\hat P_0 \rightarrow \hat P_0
-\frac{l\Delta}{16G}\delta_{m,0}$.
This change of basis absorbs the extension in \eqref{eq:extchiralCompII} and brings back the algebra to the canonical form
with the following central charge and level
\begin{equation}
c_R=\frac{3l}{2G}, \qquad k_{KM}=-\frac{l\Delta}{4G}.
\end{equation}
\section*{Acknowledgements}
\label{sec:acknowledgements}
I would like to thank G. Barnich, H. Gonz\'alez, P. Ritter and D. Tempo for
useful discussions. This work is founded by the fundecyt postdoctoral grant
3140125. The Centro de Estudios Cient\'ificos (CECs) is funded by the Chilean
Government through the Centers of Excellence Base Financing Program of
Conicyt.
\newpage
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,039 |
Сэр Ке́вин Ви́ктор А́ндерсон (; ) — австралийский юрист. Судья Верховного суда Виктории (1969—1984). Автор Комиссии по расследованию саентологии (1963—1965).
Биография
В 1929 году окончил в Мельбурне и работал судебным секретарём в .
В 1937 году заочно окончил Мельбурнского университета, получив бакалавра права.
Во время Второй мировой войны служил в оперативной и военно-морской разведке Королевского Австралийского военно-морского флота. К концу войны стал офицером связи в штаб-квартире генерала Дугласа Макартура в Маниле и присутствовал при капитуляции Японии в Токийском заливе в сентябре 1945 года.
24 ноября 1945 года был принят в . В 1965—1967 годах был её председателем.
14 августа 1962 года стал королевским адвокатом.
29 апреля 1969 года избран судьёй Верховного суда Виктории, пробыв в этой должности до 31 августа 1984 года. Будучи набожным католиком и после выхода на пенсию выступал за сохранение традиционного приведения в суде на Библии.
Жена — Клара Андерсон, умерла раньше него. Отец шести дочерей и двадцати внуков и внучек.
Награды
Рыцарь-бакалавр (14 июня 1980)
Труды
Anderson K. V. Landlord and tenant : Landlord and Tenant (Control) Act 1957 No. 6098 rules and regulations, Landlord and Tenant Act 1928 No. 3710 part V. — Sydney: Butterworths, 1958. — 197 p.
Anderson K. V. Landlord and tenant. — Sydney: Butterworths, 1959. — 324 p.
Anderson K. V., Rendit P. Workers compensation. — Melbourne: Butterworths, 1966. — 430 p.
Anderson K. V. The law of stamp duties in Victoria. — Sydney: Butterworths, 1968. — 412 p.
Anderson K. V. Some aspects of the hearsay rule. Adress delivered by Mr. Kevin Anderson, Q.C. at the Annual Conference of the Stipendiary Magistrates' of Victoria, held at Melbourne on 25th July, 1968. — Melbourne: Butterworths, 1968. — 25 p.
Anderson K. V. Community Justice Centres: an experiment in mediated dispute settlement. The Sixth National Convention of Civil Liberties in Australia, 1980. — 13 p.
Anderson K. V. Fossil in the Sandstone: The Recollecting Judge. — Melbourne: Spectrum Publications, 1986. — 287 pp.
Anderson K. V. Oaths are as old as a belief in God. // Law Institute Journal. — May 1987. — P. 502—503.
Примечания
Литература
Юристы Австралии
Судьи Австралии
Выпускники Мельбурнского университета
Критики саентологии | {
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{"url":"https:\/\/proxieslive.com\/tag\/small\/","text":"## Interview q: Small possible length of stick from an array of stick lengths\n\nI was asked this question in a phone interview recently and I bombed it completely. Zero clue how to approach it. I wasn\u2019t able to find any similar patterns on google-ing. Thought maybe folks here might be able to help?\n\nStatement: Given `m` sticks with different lengths. Combine these sticks to form longer sticks with the same length. What\u2019s the smallest possible length of these newly unified sticks?\n\nConditions:\n\n\u2022 Must use all sticks\n\u2022 `m < 50`\n\u2022 max length of single stick less than 20\n\nExample:\n\n``Input: 5 2 1 5 2 1 5 2 1 Output: 6 (Process: 1+5, 1+5, 1+5, 2+2+2) ``\n\n``Input: 3 3 3 2 2 5 Output: 9 (Process: 3+3+3, 2+2+5) ``\n\n``Input: 1 2 3 4 5 Output: 5 (Process: 2+3, 1+4, 5) ``\n\n``Input: 1 3 4 5 Output: 13 (Process: 1+3+4+5) ``\n\n## Does the ability score modifier go in the large box or the small oval?\n\nWhen filling in the ability scores section of the standard character sheet as used in the D&D 5e Player\u2019s Handbook, I\u2019ve seen a lot of people put each ability score in the large box, and the corresponding ability score modifier in the small oval below it. This makes sense to some because that\u2019s the order you\u2019re writing it from top to bottom.\n\nHowever, it seems more practical to put the ability score modifier in the large box, since that\u2019s almost always the number you need to look at, and the ability score in the small oval.\n\nIs there any official ruling on this, or other evidence to suggest which approach (if either) is official, standard, or more correct?\n\n## Attempt to merge 2 small fresh projects leads to freeze of GSA SER\n\nHello Sven,\nI have tried several times, to make all projects Inactive, GSA SER is Stopped, no Threads is recognized on the status bar. I have also reset the Submitted records, and projects just keeps Options and Verified (105 and 130) to make projects for merge smaller. No matter what, anytime I try it, GSA SER got frozen. At the moment of trying is running only GSA SEO Indexer,\u00a0 CapMonster, GSA Proxy Scraper and DropBox application, that feeds GSA SER by fresh lists.\nBeyond mentioned apps is yet ran. I have set in all GSA apps count of threads to 20, however neither like that it have no possitive impact.\n\nIs there anything else I can do, not to make GSA SER freezing all the time? That leads me to kill it in Task Manager and start it again.\n\nMy HW config is following: Intel i3-7130U @2,70GHz, 12GB RAM DDR4, 1TB M2 NvMe, 500Gbps WAN\nSystem resources are following: 12%CPU, 35%RAM, 0%HDD, 0%LAN.\nMy OS is MS Windows 10 PRO 64-bit. The machine is completely dedicated just for purpose of link-building.\n\nRegards,\nMichal\n\n## Is there any way to gain the endless special quality without carrying around a small necromantic magic item?\n\nDragon Magazine #354 has a fairly well-known special quality called endless, which prevents aging and all its normal effects, but is unfortunately not actually granted by its associated feat, Wedded to History. Within the pages of this magazine, the only way to gain the quality (DM fiat aside) is to have someone cast kissed by the ages on you, and then to forevermore give up a magical item body slot and risk taking a penalty if you ever lose the item\u2013which also radiates enough necromancy to make many NPCs very uneasy.\n\nBut what about methods outside the pages of the magazine? Is there any sort of feat, feature, or other special means by which someone can gain this extraordinary special quality, without needing to go around holding a pseudo-phylactery?\n\n## Large Creature Overrun of a Meduim and Small Creature\n\nA halfling and a human are blocking a group of winter wolves (large) on a 10\u2032 wide ledge. Can the wolves just squeeze through the halfling\u2019s space that is two sizes smaller; at 1\/2 speed or 1\/4 speed? Do the wolves need\/get to overrun both at advantage since they only take up two squares a winter wolves take up 4? Playing G2 from Tales from the Yawning Portal.\n\n## Minimum spanning tree with small set of possible edge weights\n\nGiven a undirected graph which only has two different edge weights $$x$$ and $$y$$ is it possible to make a faster algorithm than Prim\u2019s algorithm or Kruskal\u2019s algorithm?\n\nI saw on Kruskal\u2019s algorithm that it already assumes that the edges can be sorted in linear time with count sort, so then can we gain any benefit by knowing the weights of all of the edges ahead of time?\n\nI don\u2019t think there is any benefit, but I am not sure\u2026\n\n## How do you determine constraint length,k is small value or large value?\n\n[For small values of k, this is done with a widely used algorithm developed by Viterby(Forney, 1973]\n\nMy question is how do they determine k value is considered small or big? What is the threshold value for k? For example, length of this code is 7 and they considered it as small value. How about 10? or how about 20? Are they considered as small value or large value? I\u2019m curious about the threshold value of k.\n\nThis is an excerpt from Computer Network Book by Andrew S. Tanenbaum\n\nThe data link layer(chapter 3), Page 208, Fifth edition.\n\n## Does a small race do extra damage when enlarged by the Enlarge\/Reduce spell?\n\nMe and a friend were discussing gnome barbarians, and the fact that small creatures have disadvantage on an attack when using a weapon with the heavy property. I brought up that the \u201cEnlarge\/Reduce\u201d spell would negate this disadvantage by making the gnome size class medium temporarily.\n\nThough, the \u201cEnlarge\/Reduce\u201d spell also causes creatures to do 1d4 extra damage with weapons they use. If a gnome\/kobold\/halfling\/goblin were to hold a greatsword, and have a wizard enlarge them, it appears that, not only would the disadvantage imposed by being a small race be removed, but they would also do 1d4 damage more than any normally medium character using the weapon. This makes no sense to me though, am I reading everything correctly?\n\n## Problems for which a small change in the statement causes a big change in time complexity\n\nI know that there are several problems for which a small change in the problem statement would result in a big change in its (time) complexity, or even in its computability.\n\nAn example: The Hamiltonian path problem defined as\n\nGiven a graph, determine whether a path that visits each vertex exactly once exists or not.\n\nis NP-Complete while the Eulerian path problem defined as\n\nGiven a graph, determine whether a trail that visits every edge exactly once exists or not.\n\nis solvable in linear time with respect to the number of edges and nodes of the graph.\n\nAnother example is 2-SAT (polynomial complexity) vs K-SAT (NP-complete) although someone could argue that 2-SAT is just a specific case of K-SAT.\n\nWhat do you call this kind of problems \u2013if they even have a name? Can someone provide a list of other examples or some references?","date":"2020-08-15 13:24:58","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 2, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2918614149093628, \"perplexity\": 1802.781265391708}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-34\/segments\/1596439740848.39\/warc\/CC-MAIN-20200815124541-20200815154541-00217.warc.gz\"}"} | null | null |
I help people who truly want to want to grow beyond their past, to nurture who they are today and embrace who they can be tomorrow.
Do you feel anchored to your past yet want to launch forward beyond your experiences? You may have been through therapy and realize you still have growth potential. You may recognize the future is the place you want to be. If you genuinely want to expand beyond your past, you are in the right place. If you are motivated and want to move forward with change, you are in the right place. We cannot change the past, but we do not have to live in it. You can thrive, and not just survive.
I am a professional life coach, working in the Raleigh area, who helps people advance and grow. I practiced as a therapist for many years in the UK, after training at the University of Cambridge, before relocating to the US and transforming into a life coach. I am, therefore, uniquely experienced in working with people with diverse challenges, transitioning from therapy and wanting to move beyond their past. I am passionate about life coaching as a way to make a positive impact in the development of my clients. I am an ICF (International Coach Federation) Global Member.
Have you worked with Laura? Tell your friends!
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Coaching or Therapy - Which is Right for You?
Resilience is key to thriving through life's periods of transition and change. Coaching can provide a space to discover what you truly want. | {
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Q: Is Ariana Dumbledore's death different in the movies compared to the books? I can't find any mention of this in 'Behind the scenes' in the HP fandom.
What I understand is:
*
*In books: There was a 3-way duel (or 2v1 ?) and then Ariana was caught in the cross fire. More info here: What exactly happened to Ariana when Dumbledore and Grindelwald fought?
*In movies, specifically Fantastic Beasts 3: The Secrets of Dumbledore: Albus and Grindelwald planned to run away together. Aberforth didn't approve. Both Albus and Aberforth drew their wands, and Grindelwald laughed.
Or perhaps they're actually the same:
Grindelwald still pulls out a wand. And in the movie version, Albus just omits mention of the other details like how Grindelwald used Cruciatus curse on Aberforth.
| {
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James Gandolfini's Death at 51 Destroys "The Sopranos Movie" Hopes – Who Can Play Tony Soprano?
BY Kristine Francis on June 19, 2013 | Comments: one comment
Related : Celebrity Death, James Gandolfini, The Sopranos
James Gandolfini passed away today due to a possible heart attack. He leaves behind a wife and son. Primarily known for his role as the brutal mob boss Tony Soprano in The Sopranos, he was both brutal in his role but a hell of a character and role model to every male who didn't need adult supervision! Those who watched, primarily my dad, loved the show yet forbade me to watch it. James manged to turned a ruthless philandering killer into the semi-lovable guy you want to share a pizza with. In everyday life the self-titled "260-pound Woody Allen" was known for being gentle and humble.
But damn! My dad was really waiting for the Sopranos Movie and the show ended six years ago. Jamie-Lynn Sigler, his TV daughter, hasn't even had her baby yet. I would have liked to hear his congratulations on that. But no matter what could have been I don't think New Jersey should have been hit with this. Haven't they've been through enough. That state will mourn this man like no one else.
Some of us have decided to dedicate this coming weekend to a non-stop Soprano Weekend. All seasons. As for myself I have to build my stamina for this weekend but as of right now, I'm watching.
R.I.P. James Gandolfini – Tony Soprano
Photo Credit: FameFlynet
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Sopranos stars salute two of their own now starring in the Broadway Last Night
Gandolfini is no Tony Soprano – Punching Little Photogs With Their Moms Present Is A NO NO!
Rue McClanahan dies at 76
Whitney Houston's Final Autopsy Report Implies Fatal Cocaine Overdose (Report)
Hollywood Reacts to Nora Ephron's Passing
'Cosmopolitan' Magazine Editor Helen Gurley Brown Dies at age 90 | {
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Q: Same dbGetQuery() call via odbc connection gives "Invalid Descriptor Index" error on some PCs but script runs fine on others I have an R script that works fine on my PC. I have sent it to a colleague to use as a source for Power BI, however it does not run (even from base R without Power BI) on their PC.
The issue seems to be with DBI::GetQuery via an odbc connection, and the script is as such (I've changed the names of intellectual property and shortened the very long case_when statements):
Database_connection <- dbConnect(drv = odbc::odbc(),
Driver = "SQL Server",
server = "addressofserver.database.windows.net",
database = "database",
uid = "UserName",
pwd = "UserPassword")
events_typed<- dbGetQuery(Database_connection, "
SELECT
--- FIELDS: ---
ThemeEvents.Id as EventId,
[ThemeEvents].[VisitedStoreCode] AS Store_Unique_Number,
CONCAT([dbo].Stores.PostCodeOuter, ' ', [dbo].Stores.PostCodeInner) as Postcode,
Themes.[Name] AS Theme_Name,
ProductCategories.Type As Type,
ProductCategories.ProductType AS ProductType,
CASE -- flag whether Store has been Visited in both Themes (will only work after Themes filter added)
WHEN ThemeEvents.VisitedStoreCode IN (SELECT VisitedStoreCode FROM dbo.ThemeEvents JOIN [dbo].Themes on [dbo].ThemeEvents.Theme_Id = [dbo].Themes.Id WHERE [Themes].[name] = 'Theme One')
AND ThemeEvents.VisitedStoreCode IN (SELECT VisitedStoreCode FROM dbo.ThemeEvents JOIN [dbo].Themes on [dbo].ThemeEvents.Theme_Id = [dbo].Themes.Id WHERE [Themes].[name] = 'Theme Two')
THEN 'TRUE'
ELSE 'FALSE'
End AS Visited_In_Both_Themes,
Sum(ThemeEventSalesLines.[Qty]) as PacksSold
Sum(ThemeEventSalesLines.[SalesSubTotal]) as SalesSubTotal --
FROM [dbo].ThemeEvents
-- JOINS: ----
LEFT JOIN [dbo].Themes on [dbo].ThemeEvents.Theme_Id = [dbo].Themes.Id
LEFT JOIN [dbo].Stores on [dbo].ThemeEvents.VisitedStoreCode = [dbo].Stores.StoreCode
LEFT JOIN ThemeEventSales on ThemeEventSales.EventId = ThemeEvents.Id
LEFT JOIN ThemeEventSalesLines on ThemeEventSalesLines.ThemeEventSale_Id = ThemeEventSales.Id
LEFT JOIN ThemeProducts on ThemeProducts.Id = ThemeEventSalesLines.ProductId
LEFT JOIN ( --put the code for the product categories output here:
SELECT [Id]
,[Name]
,[StandardSKUCode]
,[TypeVariantGroupCode]
,[IsActive]
,[PriceSectorCode]
,CASE
WHEN [Name] like '%Apple%' THEN 'Fruit'
WHEN [Name] like '%Banana%' THEN 'Fruit'
WHEN [Name] like '%Carrot%' THEN 'Vegetable'
WHEN [Name] like '%Tablecloth%' THEN 'Accessory'
WHEN [Name] like '%Candlestick%' THEN 'Accessory'
WHEN [TypeVariantGroupCode] = 00071 THEN 'Fruit'
ELSE 'False Product/Not Mapped' END AS [Type],
CASE
WHEN [Name] like '%Apple%' THEN 'Food'
WHEN [Name] like '%Banana%' THEN 'Food'
WHEN [Name] like '%Carrot%' THEN 'Food'
WHEN [Name] like '%Tablecloth%' THEN 'Non-Edible'
WHEN [Name] like '%Candlestick%' THEN 'Non-Edible'
WHEN [TypeVariantGroupCode] = 00071 THEN 'Food'
ELSE 'False Product/Not Mapped' END AS ProductType,
CASE
WHEN [Name] like '%Multipack%' THEN 'TRUE'
ELSE 'FALSE' END AS IsMultipack,
CASE
WHEN [Name] like '%Apple%' AND [Name] like '%British%' THEN 'British Fruit'
WHEN [Name] like '%Carrot%' AND [Name] like '%British%' THEN 'British Vegetable'
WHEN [Name] like '%Carrot%' THEN 'Irish Vegetable'
WHEN [Name] like '%Banana%' AND [Name] like '%Jamaican%' THEN 'Jamaican Fruit'
WHEN [TypeVariantGroupCode] = 00071 THEN 'Unidentified Fruit'
WHEN [Name] like '%Apple%' THEN 'Unidentified Fruit'
ELSE NULL END as TypeLocation
FROM [dbo].[Products]
) AS ProductCategories
ON ProductCategories.Id = ThemeProducts.ProductId --- join to Theme products table not to products table here
--- CONDITIONS & GROUPING: ---
where VisitedStoreCode NOT LIKE '%p%'
and ([Themes].[name] = 'Theme One' -- I have checked and the names are correct
or [Themes].[name] = 'Theme Two')
group by ThemeEvents.Id, VisitedStoreCode, Themes.[Name], CONCAT([dbo].Stores.PostCodeOuter, ' ', [dbo].Stores.PostCodeInner), Type, ProductType, RebateGiven, ThemeEvents.PacksSold
order by EventId
")
Which returns the error message (in Power BI):
Error in result_fetch(res@ptr, n) :
nanodbc/nanodbc.cpp:2966: 07009: [Microsoft][ODBC SQL Server Driver]Invalid Descriptor Index
Calls: dbGetQuery ... dbGetQuery -> .local -> dbFetch -> dbFetch -> result_fetch
Execution halted
Warning message:
In dbClearResult(rs) : Result already cleared
And when ran in Base R:
Error in result_fetch(res@ptr, n) :
nanodbc/nanodbc.cpp:2966: 07009: [Microsoft][ODBC SQL Server Driver]Invalid Descriptor Index
The SQL script itself runs fine when used to read from the database directly in Power BI (this is not useful as the rest of the R script modifies it considerably after import), but it does not run within the R script/dbGetQuery call on their computer. However as stated it runs fine on my own PC. We have installed all the required libraries for the script and checked that they are installed.
Additionally, a more basic query such as:
test<- dbGetQuery(Database_connection, "SELECT TOP 10 * FROM dbo.ThemeEvents")
works perfectly fine.
All the previous questions about this error message imply it's something to do with the structure of the query or SQL database, or the order of columns in the output, but both of us are running the same query against the same database in the same R script, using the same credentials. Does anyone know why it might generate an error on one computer but not another? I can't work out how to fix it because it already runs fine on my own PC, but I want it to be capable of being ran by other colleagues so that they can use it in their Power BI reports (they do not code in R themselves).
A: Underneath the [R]/package:odbc layer, there sits an ODBC driver that is responsible for the ODBC API implementation.
To answer your question re: why you might be seeing an error on one machine, but not on another, it could be the case that on different machines package:odbc is paired with different drivers (that come with their own idiosyncrasies). For example, the SQL Server driver from Microsoft is known to throw the error you logged, however other ones (I believe, including the open source FreeTDS driver) do not.
odbc::odbcListDrivers() can give you an idea which drivers are available on the machine you are using.
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{"url":"http:\/\/mathhelpforum.com\/algebra\/2277-another-problem-almost-done.html","text":"# Math Help - Another problem, almost done :)\n\n1. ## Another problem, almost done :)\n\nSolve: 1\/(x-2) less then or equal to 0\n\nAlso having trouble with: \"Suppose that a polynomial function of degree 4 with rational coefficients has -4, -5, -4, -i as zeros. Find the other zeros.\nA)4,5,-4,i\nB)4 + i\nC)-4 + i\nD) -4, -i\n\nThank you captain black!\n\n2. Originally Posted by kharris82\nSolve: 1\/(x-2) less then or equal to 0\n\nAlso having trouble with: \"Suppose that a polynomial function of degree 4 with rational coefficients has -4, -5, -4, -i as zeros. Find the other zeros.\nA)4,5,-4,i\nB)4 + i\nC)-4 + i\nD) -4, -i\n\nThank you captain black!\nHello,\n\nI can offer you some help with your first problem. But I don't know what to do with your 2nd problem: The given list of zeros looks a little bit funny to me (for instance why is the (-4) listed twice?).\n\nto 1.: You're looking for negative quotient with a positive numerator. That is only possible if the nominator is negative:\n$\\frac{1}{x-2}\\leq 0\\ \\Longrightarrow \\ x-2<0 \\ \\Longrightarrow \\ x<2$\n\nGreetings\n\nEB\n\n3. Originally Posted by kharris82\nSolve: 1\/(x-2) less then or equal to 0\n\nAlso having trouble with: \"Suppose that a polynomial function of degree 4 with rational coefficients has -4, -5, -4, -i as zeros. Find the other zeros.\nA)4,5,-4,i\nB)4 + i\nC)-4 + i\nD) -4, -i\n\nThank you captain black!\nAs to the second problem, if the polynomial (with rational coefficients) is of degree 4 then it has at most 4 distinct roots. In addition, if a complex root of a polynomial function with rational coefficients exists, then the complex conjugate of that root is also a root. For that reason, \"i\" must also be a root of this polynomial. But that means your polynomial is of degree 5, not 4.\n\nI don't understand what they mean by \"find the other zeros.\" You've already got four listed!\n\nSomething's fishy here.\n\n-Dan","date":"2015-11-26 08:22:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 1, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7750357985496521, \"perplexity\": 667.9838709131127}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-48\/segments\/1448398446535.72\/warc\/CC-MAIN-20151124205406-00047-ip-10-71-132-137.ec2.internal.warc.gz\"}"} | null | null |
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-webkit-transition: 0.2s ease-in-out all;
-moz-transition: 0.2s ease-in-out all;
-o-transition: 0.2s ease-in-out all;
transition: 0.2s ease-in-out all;
-webkit-transform: scale(0.95);
-moz-transform: scale(0.95);
-ms-transform: scale(0.95);
-o-transform: scale(0.95);
transform: scale(0.95);
}
.iview-caption > .caption-contain:hover .box-hover {
opacity: 1;
-webkit-transform: scale(1);
-moz-transform: scale(1);
-ms-transform: scale(1);
-o-transform: scale(1);
transform: scale(1);
}
.iview-video-show {
background: #000000;
position: absolute;
width: 100%;
height: 100%;
z-index: 101;
}
.iview-video-show .iview-video-container {
position: relative;
width: 100%;
height: 100%;
}
.iview-video-show .iview-video-container a.iview-video-close {
position: absolute;
right: 10px;
top: 10px;
background: #222222;
color: #ffffff;
height: 20px;
width: 20px;
text-align: center;
line-height: 29px;
font-size: 22px;
font-weight: bold;
overflow: hidden;
}
.iview-video-show .iview-video-container a.iview-video-close:hover {
background: #444444;
}
.iview-caption.caption1 {
font-size: 100px;
font-weight: 900;
}
.iview-caption.caption2 {
font-size: 40px;
}
.iview-caption.caption3 {
font-size: 17px;
line-height: 18px;
}
.iview-caption.btn-more {
font-size: 14px;
width: 142px;
height: 50px;
text-align: center;
-webkit-transition: all 100ms ease-in-out;
-moz-transition: all 100ms ease-in-out;
-o-transition: all 100ms ease-in-out;
-ms-transition: all 100ms ease-in-out;
transition: all 100ms ease-in-out;
}
.iview-caption.btn-more > .caption-contain {
display: table-cell;
vertical-align: middle;
background-color: #035a85;
-webkit-transition: all 100ms ease-in-out;
-moz-transition: all 100ms ease-in-out;
-o-transition: all 100ms ease-in-out;
-ms-transition: all 100ms ease-in-out;
transition: all 100ms ease-in-out;
}
.iview-caption.btn-more a {
color: #ffffff;
text-decoration: none;
}
.iview-caption.btn-more > .caption-contain:hover {
cursor: pointer;
background-color: #003a57;
}
.iview-caption.btm-bar > .caption-contain {
padding: 15px 30px;
background-color: #e65a4c;
}
.iview-caption.btm-bar > .caption-contain h1 {
font-size: 25px;
color: #ffffff;
margin-top: 0px;
margin-bottom: 5px;
}
.iview-caption.btm-bar > .caption-contain p {
line-height: 18px;
font-size: 13px;
color: #ffffff;
}
.iview-caption.btm-bar > .caption-contain a {
text-decoration: none;
color: #ffffff;
}
.iview-caption.metro-heading h1 {
display: block;
text-align: right;
color: #ffffff;
text-transform: uppercase;
font-size: 23px;
font-weight: 900;
width: 330px;
}
.iview-caption.metro-heading span {
display: block;
color: #ffffff;
font-size: 13px;
line-height: 20px;
text-align: right;
width: 330px;
}
.iview-caption.metro-box1 a {
color: #ffffff;
text-decoration: none;
}
.iview-caption.metro-box1 a > i {
font-size: 50px;
width: 100%;
text-align: center;
vertical-align: middle;
line-height: 100px;
}
.iview-caption.metro-box1 a > span {
line-height: 75px;
font-size: 14px;
}
.iview-caption.metro-box1 > .caption-contain {
height: 163px;
width: 163px;
padding: 10px;
}
.iview-caption.metro-box2 a {
color: #ffffff;
text-decoration: none;
}
.iview-caption.metro-box2 a > i {
font-size: 50px;
width: 100%;
text-align: center;
vertical-align: middle;
line-height: 100px;
}
.iview-caption.metro-box2 a > img {
top: 0px;
right: 0px;
}
.iview-caption.metro-box2 span {
line-height: 10px;
font-size: 14px;
font-weight: bold;
position: absolute;
bottom: 0px;
right: 0px;
padding: 10px;
background: rgba(255, 255, 255, 0.67);
color: #000000;
z-index: 10;
}
.iview-caption.metro-box2 .monthlydeals .fa {
font-size: 25px;
line-height: 163px;
opacity: 0.2;
}
.iview-caption.metro-box2 .monthlydeals .fa:hover {
opacity: 1;
}
.iview-caption.metro-box2 .monthlydeals .carousel-control {
text-shadow: none;
background-image: none;
}
.iview-caption.metro-box2 > .caption-contain {
background-image: linear-gradient(rgba(255, 255, 255, 0.2), rgba(255, 255, 255, 0));
height: 163px;
width: 335px;
}
.monthlydeals .active.left,
.monthlydeals .active.right {
left: 0;
opacity: 0;
z-index: 2;
}
.monthlydeals .next,
.monthlydeals .prev {
left: 0;
opacity: 1;
z-index: 1;
}
.monthlydeals .item {
-webkit-transition: opacity 1s;
-moz-transition: opacity 1s;
-ms-transition: opacity 1s;
-o-transition: opacity 1s;
transition: opacity 1s;
}
.iview-caption.orange {
background-color: #d35400;
}
.iview-caption.blue {
background-color: #2980b9;
}
.iview-caption.purple {
background-color: #8e44ad;
}
.iview-caption.dark-blue {
background-color: #2c3e50;
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,372 |
package types
// MappingLimitSettingsNestedObjects type.
//
// https://github.com/elastic/elasticsearch-specification/blob/4ca0cc05d3ae3fa06c2cd7be91905b656a474334/specification/indices/_types/IndexSettings.ts#L446-L453
type MappingLimitSettingsNestedObjects struct {
// Limit The maximum number of nested JSON objects that a single document can contain
// across all nested types. This limit helps
// to prevent out of memory errors when a document contains too many nested
// objects.
Limit *int `json:"limit,omitempty"`
}
// NewMappingLimitSettingsNestedObjects returns a MappingLimitSettingsNestedObjects.
func NewMappingLimitSettingsNestedObjects() *MappingLimitSettingsNestedObjects {
r := &MappingLimitSettingsNestedObjects{}
return r
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,647 |
package com.keystone.server.config.parser;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import javax.servlet.ServletException;
import com.keystone.server.contexts.KeystoneAppContext;
import com.keystone.server.contexts.container.HttpContainer;
import com.keystone.support.common.CommonUtils;
import com.keystone.support.common.IOUtils;
import com.keystone.support.common.NumberUtils;
import com.keystone.support.common.StringUtils;
import com.keystone.support.utils.XmlElement;
/**
*
* @author wuqq
*
*/
public class HttpWebAppParser {
/**
*
* @param httpContainer
* @throws FileNotFoundException
* @throws ServletException
*/
public static void parseWebXml(KeystoneAppContext appContext) throws FileNotFoundException, ServletException {
String namepath = IOUtils.mergePaths(appContext.getContextConfig().getContextRoot(), "WEB-INF", "web.xml") ;
File file = new File(namepath) ;
if(file.exists())
{
XmlElement webXml = XmlElement.read(new FileInputStream(file)) ;
HttpContainer httpContainer = appContext.getHttpContainer() ;
//1. parse filter
HttpFilterParser.parse(webXml, httpContainer) ;
//2. parse servlet
HttpServletParser.parse(webXml, httpContainer) ;
//3. parse error page
parseErrorPages(webXml, httpContainer) ;
}
}
/**
*
* @param element
* @return
*/
public static Map<String, String> parseInitParams(XmlElement element) {
Map<String, String> params = new HashMap<String, String>() ;
List<XmlElement> paramList = element.elements("init-param") ;
if(!CommonUtils.isEmpty(paramList))
{
for(XmlElement param : paramList) {
String paramName = param.element("param-name").getElementText() ;
String paramValue = param.element("param-value").getElementText();
params.put(paramName, paramValue) ;
}
}
return params ;
}
/**
*
* @param webXml
* @param httpContainer
*/
private static void parseErrorPages(XmlElement webXml, HttpContainer httpContainer) {
List<XmlElement> list = webXml.elements("error-page") ;
if(!CommonUtils.isEmpty(list))
{
for(XmlElement n : list)
{
int errorCode = NumberUtils.parseInt(n.elementText("error-code"), -1);
String location = n.elementText("location") ;
if(errorCode > 0 && !StringUtils.isEmpty(location))
{
httpContainer.getErrorPages().put(errorCode, location);
}
}
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,330 |
Q: Getting data from PHP file using Ajax and JQuery Im trying to get data from my php file using success function(data)
When im using console.log(data) i get; true/false/exists
But i cant make a if statement, if i do it dosent alert!!
Heres my js file
function ajaxCall(username, email, password){
$.ajax({
type: 'POST',
url: '../register.php',
data: {
'username' : username,
'email' : email,
'password' : password,
},
success: function(data) {
if(data === "exists")
alert("user exists");
}
});
}
heres my .php file
<?php
$servername = "#";
$username = "#";
$password = "#";
$dbname = "#";
$regusername = $_POST['username'];
$email = $_POST['email'];
$regpassword = $_POST['password'];
$mysqli = new mysqli($servername, $username, $password, $dbname);
$selectQuery = "SELECT username FROM users WHERE username = '$regusername'";
$select = $mysqli->query($selectQuery);
// var_dump($select->num_rows);
if( $select->num_rows == 0) {
$insertQuery = "INSERT INTO users (username, password, email) VALUES ('$regusername','$regpassword','$email');";
$insert = $mysqli->query($insertQuery);
if( $insert == true) {
echo "true";
}else {
echo "false";
}
}else {
echo "exists";
}
?>
A: Use a properly structured data format, such as json:
php:
$data=['exists'=>false];
if( $select->num_rows == 0) {
$insertQuery = "INSERT INTO users (username, password, email) VALUES ('$regusername','$regpassword','$email');";
$data['inserted'] = (bool) $mysqli->query($insertQuery);
}else {
$data['exists']=true;
}
header('Content-Type: application/json');
echo json_encode($data);
die();
JS
$.ajax({
type: 'POST',
url: '../register.php',
data: {
'username' : username,
'email' : email,
'password' : password,
},
success: function(data) {
if(data.exists){
alert("user exists");
}elseif(data.inserted){
alert("inserted");
}else{
alert("did not insert");
}
});
A: Chances are there is extra whitespace in the response
Try:
if($.trim(data) === "exists")
A: You are not responding with an answer to the front, you just echoing 'exist' word in your php handler.
Try using json_encode, because the dataType is "json" by default not "html"
Lets's say
if($insert) {
$response['exist_status'] = 'exist'
}else{
$response['exist_status'] = 'do not exist'
}
echo json_encode($response);
In your jquery
success: function(response) {
if(response.exist_status && response.exist_status == 'exist') {
alert(1);
}
}
A: I think its better to work with HTTP-Status codes like 404 or 403 (https://en.wikipedia.org/wiki/List_of_HTTP_status_codes) instead of retuning a string. This can by done with PHP (http://php.net/manual/de/function.http-response-code.php) and use the error callback of your ajax call (http://api.jquery.com/jquery.ajax/ --> StatusCode)
A: if(data == "exists") instead of if(data === "exists")
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,013 |
With the latest early adopter release of the SQL Developer, it's possible to browse your NoSQL datastores.We will use the BigData lite virtualbox appliance, and the latest early adopter SQL Developer, to demonstrate this feature.
Follow the instructions to assemble the bits of the virtualbox into one single "ova" file. Import this file into your virtualbox installation, create the BigData lite VM and start it.
I used the "Other Platforms" distribution (see below image). Download the Java 8 JDK (see below image).
3) Upload the SQL developer and the jdk to the virtualbox BigData Lite VM.
4) Install the jdk8 and the SQL Developer 4.1 into their own directories (I created a stage directory into an Oracle user home directory).
Start your SQL Developer 4.1 EA2 instance, from your installation directory.
Then in the right tab on the NoSQL connection, right click the link NoSQL connections.
Then provide all the connectivity information to your NoSQL store. In our case, the out-of-the box NoSQL installation is using the 5000 port, so we just accept the settings.
Enjoy the rest of your developments on NoSQL with this new feature of the SQL developer.
Using Oracle NoSQL Database (4 days).
Explore all of the available training for Big Data appliance products.
Eugene Simos is based in France and joined Oracle through the BEA-Weblogic Acquisition, where he worked for the Professional Service, Support and Education for major accounts across the EMEA Region. He worked in the banking sector, ATT and Telco companies giving him extensive experience on production environments. Eugene currently specializes in Oracle Fusion Middleware, teaching an array of courses on Weblogic/Webcenter, Content,BPM /SOA/Identity-Security/GoldenGate/Virtualisation/Unified Comm Suite) throughout the EMEA region.
Is it possible to connect to the NoSQL database from outside the virtual box. I am running the Big Data lite appliance on an other laptop.
Yes its possible if your BigData lite is having its own ip ie you should be able either to assign a static or a dchp ip,pingable from your other laptop, then your NoSql databases will use the BigData lite ip, and this is the ip that you should enter to the "host" ip of the NoSql connection.
Free Live Webinar! Oracle Database: to 18c and Beyond! | {
"redpajama_set_name": "RedPajamaC4"
} | 4,949 |
French garrison. This is but a glimpse at what is to see at Fort Ticonderoga. For if you are a reader of this blog, then you know I had a calamity while there - lost my phone. That unfortunately distracted me from a thorough enjoyment of my visit. Perhaps on my ride up to Vermont I will stop by and do it justice. There is a lot of history there to take in. And the ride from Lake George along 9N is beautiful.
So back to what was seen. Lots of canon and mortars on site. In addition there is what appears to be a fine cafe. The Fort Cafe features casual dining with stunning views of Lake Champlain and the Green Mountains of Vermont.
And yes, the kitchen was making some kind of porridge and cornbread in the dirt oven.
fort to overlook and protect the river that connected Lake George and Lake Champlain. Remember there were no roads then and everything had to be transported by waterways or carried overland.
Ticonderoga to Boston. Placed on the high ground of Dorchester Heights forcing the British to abandon Boston. Lots of history here and a must see if in the area.
later in the week. Off to Hamburg, NY for the annual BMWMOA rally.. If you see me on the road - Wave!
This is the time of year when many of us are looking at maps, dreaming of destinations near and far and planning our routes and rides for the year. We want to personally invite you to include "DAS RALLY" in Hamburg in your plans.
We were thrilled when we first learned that the BMW MOA 44th International Rally was coming to Hamburg, New York, as there is so much to see and do in the Western New York and the Great Lakes Regions. A short ride in any direction will net a wonderful destination. To the west, beautiful Woodlawn beach on the shores of Lake Erie beckons. To the north is Niagara Falls (need we say more?) and the revitalized city of Buffalo with its beautiful new waterfront, theatre district, renowned dining and fabulous architecture. Venture east and visit the charming village of East Aurora on your way to the scenic Finger Lakes region and Letchworth State Park. Just to the south are roads that will take you through the picturesque ski areas of Ellicottville and Springville.
Then there is the Rally site itself. Situated in a mostly residential area, it offers rally goers a quiet, tranquil setting with close proximity to shops, restaurants, and services. Easily accessed from both interstate and major secondary roads, the first thing to greet attendees as they enter the Fairgrounds is a large water feature with a fountain. There is plenty of asphalt to support the center stand as you register in the Event Center. Campers will be pleased with the tree-lined, spacious, grass-covered tenting areas. For the adventure enthusiast, be it rider or spectator, this site also offers an incredible off-road competition area with great exposure to the camp grounds. If you like a little variety in your entertainment, the Fairgrounds also has a casino and a horse racing track on site.
When we had a chance to visit the Rally site at the Hamburg Fairgrounds, we could immediately see how the layout would lend itself to a beautiful 'Rally Central' area. There are several impressive, parklike gardens sporting gazebos, picnic tables, and Adirondack chairs, a pedestrian thoroughfare for the food vendors, beer and wine gardens, an entertainment area, and so much more.
We are convinced that all of this will make the 2016 Rally in Hamburg absolutely fantastisch!
Looking forward to it. As always will be a great ride and a fun time.
I love the Steam Locomotives! They are alive. You can hear them breathe and snort, roar and rumble!
Strassburg Railroad is a short ride from where I live. Short yes, but it will take you back to yesteryear.
screaming whistle, for I peed my pants. I guess at that moment I was drawn to the steam locomotives.
My father would take me to Griffith Park Live Steamers often. There I could climb on the locomotives, and cars. Then go watch the wonderfully crafted locomotives built by hand. Truly a labor of love. Most of these as you can see below, you could ride on.
Images from the Griffith Park Live Steam website.
off the 134, in Burbank.
place to visit year round.
in the snow and ice!
Over the years I have ridden to Durango to ride the DRGRR. My first ride on this train was when I was about ten years old. My father rode it back in 1941 when it was still a work train. The train was moving sheep from Durango to Silverton. Someday I will convert the 16mm film he shot on that trip. The film runs about twelve minutes. Couple of years ago rode to do a shoot on the Western Maryland Railroad. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,724 |
\section{Introduction}
Since its original conception, the two-atom Fermi problem
\cite{fermi} has been the subject of an intense academic debate.
Stated in very simple terms, this {\itshape gedanken} experiment
goes as follows: suppose there are two two-level atoms (qubits),
say $A$ and $B$, spatially separated by a distance $r$ and
interacting independently with a the (multi-mode) quantized
electromagnetic field, initially in the vacuum state. The atom
$A$ is in an excited state $|e\rangle$ whereas the atom $B$ is in
its ground state $|g\rangle$. At some time $t_{0}$ the atom $A$
emits a photon. The original question by Fermi was then the
following: as long as the two atoms are causally disconnected, is
the excitation probability of $B$ independent on the presence of
$A$? This question points at the very foundations of quantum
mechanics: do quantum mechanical probabilities respect
micro-causality? Over the past years a considerable amount of
literature has dealt with this problem and several perturbative
solutions have been proposed
\cite{biswas,heger,buch,power,milonni}, sometimes even presenting
opposite conclusions. Recently, in Ref.\cite{carlos1}, a
non-perturbative proof of strict causality in the Fermi problem
has been finally given along with an explanation of why the
existence of correlations outside the light-cone connecting the
two atoms is not in contrast with micro-causality. In fact, in a
previous paper \cite{carlos2}, some of the same authors had
already studied the dynamics of concurrence \cite{concurrence} and
found that it starts increasing just before $(t-t_{0})=r/c$ by a
very tiny amount.
In this paper, motivated by such results, we take a step further
and investigate the dynamics of other types of atom-atom
correlations. In particular, besides extending the analysis of
entanglement dynamics, we study the time evolution of geometric
quantum discord and (classical) connected correlation functions.
Quantum discord was first introduced by Ollivier and Zurek
\cite{zurek,anvedi} as a novel measure of the quantumness of
correlations. The idea behind it is conceptually very simple.
Quantum discord is indeed defined as the discrepancy, in the
quantum regime, between two classically equivalent definitions of
mutual information. It is believed to capture a more general type of
quantum correlation than entanglement, in the sense that quantum
states with zero entanglement but non-zero quantum discord do exist
(see e.g.~\cite{ferraro,piani,streltsov,plastica,gerardo,pianinew}).
Unfortunately, the computation of quantum discord implies solving
a rather complicated minimization problem and, although
considerable improvements have been made over the last years
\cite{reviewmodi}, analytical results are available for very few
cases only \cite{luo,davide,discordgaussiano}. In order to
overcome such computational issues, alternative indicators of
general quantum correlations have been recently introduced, mostly
based on distance-based approaches \cite{vedral,kavan}. On the
other hand, connected correlation functions provide a statistical
quantifier of the (classical) correlations extractable during a
joint measurement of the two atoms
\cite{localizable1,localizable2,arealaw}.
The results reported in this article have a double merit: on one
hand they give a more complete picture of the dynamics of
correlations in the two-atom Fermi problem. In fact, to the best
of our knowledge, this is the first study of quantum discord and
more general correlation dynamics in such a physical model, where
an exact solution of the dynamics is still missing. As it turns out, all the
types of correlations we consider have a nice physical
interpretation in terms of a few relevant physical processes of
the dynamics. On the other hand our results suggest a way to
detect atom-atom correlations outside the light cone, that is,
when the two atoms are causally disconnected. It is important to
remark that our calculations are performed in the framework of
time-dependent perturbation theory and they are exact and
consistent up to the second order in the coupling constant.
However, this is certainly not a problem since, as stated above,
strict causality in the model has been analytically proven with no
usage of perturbation theory \cite{carlos1}. Moreover, the time
interval under scrutiny falls within the limits of validity of our
approach provided the two atoms are not that distant.
\section{The Model}
\label{model}
We will consider a one-dimensional physical setup. A pair of
two-level superconducting qubits (artificial atoms) $A$ and $B$,
separated by a fixed distance $r$, interact with an
electromagnetic field propagating along the open transmission line
connecting them. We name the atomic levels as
$\{|g\rangle,|e\rangle\}$ and we assume the following multimode
structure for the field
\begin{equation}
V(x)=\int dk \sqrt{N\omega_{k}}\left[e^{ikx}a_{k}+e^{-ikx}a^{\dagger}_{k}\right]
\label{field}
\end{equation}
where $N$ is a normalization factor which may accommodate
different circuit QED architectures, the dispersion relation is
linear $\omega_{k}=\upsilon |k|$, and $a_{k}, a^{\dagger}_{k}$ are
the usual annihilation and creation operator satisfying boson
commutation relations $[a_{k},a^{\dagger}_{k'}]=\delta_{k,k'}$. We
define $\Omega_J=\omega_{Je}-\omega_{Jg}$ ($J=A,B$) the energy
separations between the qubit levels and we assume the qubits to
be much smaller than the relevant wavelengths $\lambda_J=
\upsilon/(\Omega_J/(2\pi))$, $\upsilon$ being the propagation
velocity of the field quanta which in this scheme depends on the
microscopic details of the model. Specifically,
$\upsilon=1/\sqrt{cl}$, $c$ and $l$ being the capacitance and
inductance per unit length respectively. A typical value is
$\upsilon=1.2\cdot10^8 m/s$ \cite{casimirwilson}. Under these
conditions the Hamiltonian, $H = H_0 + H_I,$ splits into a free
part for the qubits and the field
\begin{equation}
H_0 = \frac{1}{2}\hbar(\Omega_A\sigma^z_A + \Omega_A\sigma^z_A) + \int_{-\infty}^{\infty}dk\, \hbar\omega_k a^{\dagger}_ka_k \label{h0}
\end{equation}
and a point-like interaction between them
\begin{equation}
H_I = - \sum_{J=A,B} d_J\,V(x_J)\,\sigma_J^x\label{c}
\end{equation}
Here $x_J$ are the fixed positions of the atoms, and $d_J\,
\sigma^x_J$ comes from a dimensional reduction of the matter-
radiation interaction hamiltonian with two-level atoms and the
electromagnetic field. We will consider the following initial
state
\begin{equation}
|\psi(0)\rangle = |eg0\rangle,\label{eq:initialstate}
\end{equation}
where only qubit $A$ is excited, while $B$ and the field remain in
their ground and vacuum states, respectively. We use the formalism
of perturbation theory up to the second order and beyond Rotating
Wave Approximation \cite{carlos2} and trace over the field
degrees of freedom to obtain the corresponding two-qubit reduced
density matrix $\rho_{\rm X}$ evaluated at $t$.
In the interaction picture with respect to the free Hamiltonian
$H_0,$ the system evolves during a lapse of time $t$ into the
state
\begin{equation}
\ket{\psi(t)} = {\cal T}[e^{-i \int_0^tdt' H_I(t')/\hbar}]\ket{eg}\otimes\ket{0},\label{c}
\end{equation}
${\cal T}$ being the time ordering operator. Up to second order in perturbation theory the final state can be written as
\begin{eqnarray}
\ket{\psi(t)} &= & \left[(1+A)\ket{eg} + X\ket{ge}\right]\otimes\ket{0} +
\label{wavefunction} \nonumber \\
&& (U_A\ket{gg} + V_B\ket{ee})\otimes\ket{1} \nonumber \\ && + (F\ket{eg} + G \ket{ge})\otimes\ket{2} + {\cal O}(d^3).
\end{eqnarray}
The coefficients for the vacuum, single-photon, and two-photon states,
are computed using the action $(\alpha=A,B)$
\begin{eqnarray}
\mathcal{S}^+_\alpha \! = \! - \frac{i}{\hbar}
\int_0^t
e^{i\Omega t'}\braket{e_\alpha|d\sigma^x_\alpha|g_\alpha} V(x_\alpha,t') dt'
= -(\mathcal{S}^{-}_\alpha)^\dagger\label{f}
\end{eqnarray}
among different photon number states $\ket{n}, n=0,1,2\ldots$,
being $\ket{n}\bra{n}=\frac{1}{n!}\int dk_1....\int
dk_n\ket{k_1...k_n}\bra{k_1...k_n}$ and
$\ket{k}=a_k^{\dagger}\ket{0}$. Among the various terms present
here, the only one containing an effective coupling between $A$
and $B$ is
\begin{equation}
X = \langle0|T(\mathcal{S}^+_B \mathcal{S}^-_A)|0\rangle . \label{exchange}
\end{equation}
This includes photon exchange only inside the light cone, $vt>r,$
and vacuum fluctuations for all values of $t$ and $r$, being
$r=x_B-x_A$ the distance between the qubits. The remaining terms
are
\begin{eqnarray}
A & \!\! = \!\! & \frac{1}{2}\bra{0}T(\mathcal{S}_A^+ \mathcal{S}_A^- +
\mathcal{S}_B^-\mathcal{S}_B^+)\ket{0}\label{e}\\
U_A & \!\! = \!\! & \bra{1}\mathcal{S}^-_A\ket{0},
V_B = \bra{1}\mathcal{S}^+_B\ket{0} , \nonumber\\
F & \!\! = \!\! & \frac{1}{2}\bra{2}T(\mathcal{S}_A^+ \mathcal{S}_A^-
+\mathcal{S}_B^-\mathcal{S}_B^+)\ket{0} \! , \, G = \bra{2}T(\mathcal{S}^+_B \mathcal{S}^-_A)\ket{0}.\nonumber
\end{eqnarray}
Here, $A$ describes intra-qubit radiative corrections, while $U_A,
V_B, F$ and $G$ correspond to single-photon emission events by one
or more qubits.
The coefficients in Eq.~(\ref{wavefunction}) will be computed
analytically as a function of two dimensionless parameters, $\xi$
and $K$. The first one, $\xi=\upsilon t/r$, is a dimensionless
time variable; the time $\xi=1$ corresponds to the light-cone,
which separates two different spacetime regions, before and after
photons can be exchanged. The second parameter is a dimensionless
coupling strength
\begin{equation}
K=\frac{4d^2N}{\hbar^2 \upsilon} =
2\left(\frac{g}{\Omega}\right)^2\label{g}.
\end{equation}
Note that the qubit-line coupling $g=d\sqrt{N\Omega}/\hbar$
corresponds to the qubit-cavity coupling that appears by taking
the same transmission line and cutting it in order to have a
length $L=\lambda$ (thus creating a resonator). This formulation
has the advantage of being valid both for inductive and capacitive
coupling, the details being hidden in the actual expressions for
$d$ and $N$.
Tracing over the states of the field, we arrive at the following
reduced density matrix
\begin{eqnarray}
\rho_{\rm X}=\frac{1}{c}\left( \begin{array}{c c c c}
\rho_{11}&0&0&\rho_{14} \\
0&\rho_{22}&\rho_{23}&0\\
0&\rho_{23}^*&\rho_{33}&0\\
\rho_{14}^*&0&0&\rho_{44}
\end{array}\right) , \label{state}
\end{eqnarray}
representing the two-qubit state in the basis formed by $\ket{ee},$
$\ket{eg},$ $\ket{ge},$ and $\ket{gg}.$ The coefficients with the
leading order of neglected contributions are
\begin{eqnarray}
\rho_{11}&=&|V|_B^2+\mathcal{O}(d^4),~
\rho_{22}=1+2\mathrm{Re}(A)+\mathcal{O}(d^4)\nonumber\\
\rho_{33}&=&|X|^2+|G|^2+\mathcal{O}(d^6),~
\rho_{44}=|U|_A^2+\mathcal{O}(d^4) \nonumber\\
\rho_{14}&=&U_A^*V_B+\mathcal{O}(d^4)=\langle0|\mathcal{S}_A^+ \mathcal{S}_B^+|0\rangle +\mathcal{O}(d^4)\label{j}\\
\rho_{23} &=& X^*+\mathcal{O}(d^4) , \nonumber
\end{eqnarray}
and the state is normalized, $c=\sum_i \rho_{ii}.$
\section{Dynamics of Correlations}
\label{correlations}
In this section we report our results
regarding the dynamics of correlations between the two
(artificial) atoms. We investigate the time evolution of the
square root of geometric quantum discord $\sqrt{D}$ \cite{vedral},
of the entanglement as measured by the negativity $N$ \cite{neg},
and of the maximum connected correlation function $C$
\cite{localizable2} in the state $\rho_{\rm X}$. We have chosen
these three specific types of correlations (whose definitions and
properties are reported below) for four reasons:
\begin{itemize}
\item[(i)] to best relate our results with the ones reported in \cite{carlos2} by using a different measure of entanglement;
\item[(ii)] to have a more complete description of the time evolution of general quantum correlations;
\item[(iii)] to compare quantum correlations with correlations having also a classical nature;
\item[(iv)] to issue a comprehensive comparative analysis among {\it compatible} measures of different types of correlations.
\end{itemize}
The meaning of the latter point can be clarified in connection
with our choice of using $\sqrt{D}$. One might in fact question
why we are comparing different powers of geometric discord and
entanglement. The reason for this is that we want to be consistent
in the order of expansion of the perturbative analysis we have
performed. A good test to check whether this is true is provided
by a hierarchy-type relationship that exists between the three
chosen quantities for arbitrary states $\rho$ of two qubits, namely
\begin{equation}\label{hierardy}
C(\rho) \geq \sqrt{D}(\rho) \ge N(\rho)\,.
\end{equation}
The rightmost inequality in (\ref{hierardy}) was proven
analytically in \cite{gerardo}, while the leftmost one has been
verified numerically in \cite{unpube}. Notice that for pure
two-qubit states both inequalities are saturated and
(\ref{hierardy}) becomes a chain of equalities.
In our analysis, we have found no violation of the hierarchy
(\ref{hierardy}) for any range of the relevant physical parameters
characterizing the states $\rho_{\rm X}$, which serves as a
validating indication that our results are consistent up to the
second order. As a general remark, we can conclusively state that
all correlations whose time evolution we have looked at, start increasing
before the time at which the two atoms become causally connected.
However, the rate of increase changes a lot from one type of
correlation to another.
Let us now introduce the measures of correlations of interest and
then discuss the main aspects of their dynamical behavior. To this
end, the Bloch representation of generic two-qubit states $\rho$
will be useful \cite{luo}. Namely,
\begin{eqnarray}\label{blopix}
\rho &= \frac14 \sum_{i,j=0}^3 R_{ij} \sigma_i \otimes \sigma_j \\
&= \frac 14\left(\textrm{I}_{1}\otimes\textrm{I}_{2}+\sum_{i=1}^3 x_i\sigma_i \otimes \textrm{I}_{2} +\sum_{j=1}^3 y_j \textrm{I}_{1}\otimes \sigma_j+\sum_{i,j=1}^3 t_{ij} \sigma _i\otimes\sigma_j\right)\,, \nonumber
\end{eqnarray}
where $R_{ij}=\textrm{Tr}[\rho(\sigma_i\otimes \sigma_j)]$,
$\sigma_0=\textrm{I}$, $\sigma _i$ ($i=1,2,3$) are the Pauli
operators; $\vec{x}=\{x_i\}$ and $\vec{y}=\{y_i\}$ represent the
three-dimensional Bloch column vectors associated to the qubits
$A$ and $B$, respectively; and $t_{ij}$ are the elements of the
$3 \times 3$ correlation matrix $T$.
\subsection{Geometric discord}
The geometric measure of quantum discord was first introduced in
\cite{vedral} and further investigations for two-qubit systems
have been reported in \cite{luofu,gerardo,gprl}. Given a general
bipartite $d_A\otimes d_B$ quantum state $\rho$, the (normalized)
geometric discord is defined as
\begin{equation}
D(\rho)\doteq\frac{d_A}{d_A-1}
\min_{\chi\in\Omega_{0}}||\rho-\chi||_{2}^{2}
\label{gd}
\end{equation}
where $\chi$ is a so-called classical-quantum state belonging to
the set of zero-discord states $\Omega_{0}$, $\chi= \sum_i p_i
|i\rangle\langle i| \otimes \varrho_{i B}$ and
$||P-Q||_2^{2}=\textrm{Tr}(P-Q)^{2}$ is the squared
Hilbert-Schmidt distance between a pair of operators $P, Q$. We
can look at geometric discord as the minimum disturbance that
would be induced in the system after a projective measurement on
one of the two parties (say $A$ in the above definition)
\cite{luofu}. It is important to remark that its value is
dependent on the choice of the party to be measured \cite{notepiani}. Although in
principle this expression can be very complicated to evaluate
explicitly as it involves a minimization problem over the set of
zero-discord states, an analytical formula exists for the general
two-qubit case \cite{vedral,luofu,gprl}. In terms of the Bloch
picture [Eq.~(\ref{blopix})], one has
\[
D(\rho)=2\textrm{Tr}[S]-2\lambda_{\max}(S)\,,
\] where $\lambda_{\max}$ stands for `maximum eigenvalue', and the matrix $S$ is defined as $S=\frac14 (\vec{x} \vec{x}^T + T T^T)$.
The (square root of) geometric discord of $\rho_{\rm X}$ is then
\begin{equation}
\sqrt{D(\rho_{\rm X})}=\sqrt{[\textrm{Re}(U_{A}^{*}V_{B})]^{2}+|X|^{2}}\,.
\label{gdos}
\end{equation}
The above formula is correct up to the second order and it has an
immediate physical interpretation. The two terms in
Eq.(\ref{gdos}) come indeed from first and second order
contributions to the time evolution of the state. In particular
the $X$ term accounts for photon-exchange between the two atoms
and carries all the information available about causal propagation
and atom state dressing. Interestingly, the processes which
contribute to non-zero quantum discord are 0 and 1-photon
processes and even though the (square root of) geometric quantum
discord has a continuous evolution starting from $t=0$, it is well
sensitive to light-cone crossing, showing a peak at $t=r/c$.
\subsection{Negativity}
Negativity \cite{neg} is a well-known and easily computable
measure of entanglement for bipartite systems which is based on
the positivity of the partial transposition (PPT) criterion
\cite{ppt}. Given a general $d\otimes d$ quantum bipartite state
$\rho$, the (normalized) negativity is defined as
\begin{equation}
N(\rho)\doteq\frac{1}{d-1}||\rho^{T_{A}}-\textrm{I}_{AB}||_{1}
\label{neg}
\end{equation}
where the $T_{x}$ refers to the partial transposition operation
with respect to the $x$ party ($x=A,B$), $\textrm{I}_{AB}$ is the
identity operator in the composed Hilbert space
$\mathcal{H}_{A}\otimes\mathcal{H}_{B}$ and
$||M||_{1}=\textrm{Tr}|M|=\sum_{i}|m_{i}|$ is the trace norm for a
matrix $M$ with eigenvalues $\{m_{i}\}$. As in the case of
geometric discord we can easily compute the negativity of
$\rho_{\rm X}$ up to the second order in time-dependent
perturbation theory and we obtain the following expression
\begin{equation}
N(\rho_{\rm X})=\max\left\{0,\,\sqrt{(|U_{A}|^{2}-|V_{B}|^{2})^{2}+4|X|^{2}}-|U_{A}|^{2}-|V_{B}|^{2}\right\}\,.
\label{negus}
\end{equation}
The three physical processes contributing to entanglement are
exactly the same as for geometric discord. However, in this case
there is a time-dependent condition for entanglement to start
increasing. Indeed it is easy to check that as long as the
following condition is fulfilled
\begin{equation}
\frac{|X|^{2}}{|U_{A}|^{2}|V_{B}|^{2}}\le 1
\label{entacond}
\end{equation}
entanglement will be zero. Intuitively, this means that for
entanglement to be non-zero, second-order processes must dominate
over first-order ones. It is worth noticing that such a kind of
constraint is absent in the case of the (square root of) geometric
discord, which amounts simply to the sum of two positive and
continuous functions.
\subsection{Maximum connected correlation function}
Geometric discord and entanglement are quantities which are
strictly connected to the quantum character of a system and,
indeed, they miss a classical analogue. In this respecr, they are
key quantities when it comes to understanding the interplay
between the foundations of quantum mechanics and micro-causality,
one of the postulates of relativity theory. However, one might
also be interested in correlations arising from observable
quantities such as, for instance, angular momenta and in general
spin-like operators. We thus study the atom-atom (classical)
connected correlation functions \cite{arealaw}, to reveal the
highest level of sensitivity at which the Bloch vectors of the two
atoms perceive each other outside and inside the light cone. Given
a bipartite state $\rho$ of a pair of two-level quantum systems,
we define the maximum connected correlation function $C(\rho)$ as
follows
\begin{equation}
C(\rho)\doteq \max_{n,n'}\left\{\langle(\vec{\sigma} \cdot\hat{n})_{A}\otimes(\vec{\sigma} \cdot\hat{n}')_{B}\rangle_{\rho}-\langle(\vec{\sigma} \cdot\hat{n})_{A}\rangle_{\rho}\langle(\vec{\sigma} \cdot\hat{n}')_{B}\rangle_{\rho}\right\}\,,
\label{spin}
\end{equation}
where $\vec{\sigma}$ is the three-component Pauli-operator
vector and $(\vec{\sigma} \cdot\hat{n})$ is the projection of
such a spin vector along the direction pointed by $\hat{n}$. For
generic two-qubit states $\rho$ decomposed in Bloch form as in
Eq.~(\ref{blopix}), the maximum in Eq.~(\ref{spin}) can be
computed in closed form and reads \cite{localizable2,unpube}
\[
C(\rho)=\sqrt{\lambda_{\max}(W^T W)}\,,
\]
where $W=T-\vec{x}\, \vec{y}^T$. We have computed $C(\rho)$ for
the state $\rho_{\rm X}$ and obtained an exact expression up to
the second order,
\begin{equation}
C(\rho_{\rm X})=\max\left\{ |U_{A}|^{2}+|V_{B}|^{2}+2\textrm{Re}(A),2(|X|+|L|)\right\}
\label{spinus}
\end{equation}
where $L=U_{A}^{*}V_{B}$. Once again, in this case only 0 and
1-photon processes contribute to the above correlation function.
Moreover, with $C(\rho_{\rm X})$ being dependent on $X$, it shows
sensitivity to the light-cone crossing.
\begin{figure*}[t]
\begin{center}
\subfigure[]
{\includegraphics[height=3.8cm]{plot_disc.pdf}\label{geodisc}}
\hspace*{0.2cm} \subfigure[]
{\includegraphics[height=3.8cm]{plot_neg.pdf}\label{negat}}
\hspace*{0.2cm} \subfigure[]
{\includegraphics[height=3.8cm]{plot_corr.pdf}\label{corr}}
\center{\caption{(Color online) Time-evolution of (a) the square root of
geometric quantum discord $\sqrt{D(\rho_{\rm X})}$, (b) the
negativity $N(\rho_{\rm X})$ and (c) the maximum connected
correlation function $C(\rho_{\rm X})$, for $r = \upsilon \pi / 4
\Omega$ and three different choices of the coupling strength:
$Z=50$ (dotted green), $Z=200$ (dashed red), $Z=400$ (continuous
blue).}}
\end{center}
\label{figures}
\end{figure*}
\subsection{Results and Discussion}
In the following we analyze the time evolution of the above
correlations and compare their behavior qualitatively and
quantitatively. We remark that all of the above quantities depend
on the three terms $U_{A}, V_{B}$ and $X$, while the maximum
connected correlation function displays an $A$-dependence as well.
Fig.\ref{geodisc} shows the behavior of the square root of
geometric discord $\sqrt{D(\rho_{\rm X})}$ as a function of the
re-scaled time $\xi=rt/\upsilon$ for different choices of the
atom-field coupling constant, spanning from a weak to a strong
coupling regime, and for a fixed distance $ r = \upsilon \pi / 4
\Omega$ between the qubits.
The first feature we notice, which is perhaps the most interesting
one, is the relatively slow but continuous increase that the
(square root of) geometric discord shows prior to the light-cone
crossing. A similar behavior had been previously found by one of
the present authors in \cite{carlos2} when studying the time
evolution of entanglement measured by the concurrence
\cite{concurrence} in the same model. However, unlike concurrence
which started increasing within a very short time interval just
before $\xi=1$, the (square root of) geometric discord reaches
finite values for a much longer time interval inside the
space-like region $J_S\equiv\{0\le\xi\le1\}$. If we recall the
interpretation of geometric discord mentioned above, we may argue
that a one-party measurement performed at any time inside $J_S$
will always induce a disturbance on the composite system.
Secondly, we observe a peak at $\xi=1$ which is independent of the
interaction regime. The height of such a peak, and more generally
the global magnitude of the (square root of) geometric discord,
increases as we increase the coupling. These latter features are
easily understood by looking at Eq.(\ref{gdos}). As we said above
the (square root of) geometric discord is the sum of a first order
term, which does not carry any causality-related information, and
a second order term, which instead does carry that kind of
information. Hence, the stronger the interaction is, the bigger
this second order term becomes.
In Fig.\ref{negat} we show the time evolution of the negativity
for the same three choices of coupling strengths and the same
atom-atom separation. In this case we find essentially the same
behavior as reported in \cite{carlos2} for concurrence. By
comparing Fig.\ref{geodisc} and \ref{negat}, we may conclude that
quantum discord is more sensitive to vacuum fluctuations, which
are responsible for creating correlations between the two atoms
outside the light cone. This behavior is well understood again
when one looks at Eq.(\ref{gdos}). The proportionality to $X$,
which is a second-order 0-photon term, incorporates exactly this
kind of trait.
Fig.\ref{corr} shows the time evolution of the maximum connected
correlation function $C(\rho_{\rm X})$ for the same choice of
parameters as in the previous plots. In this case we find
something very interesting and not at all easily predictable.
Indeed, like geometric discord, the maximum connected correlation
function starts increasing significantly inside $J_S$ and it shows
a peak at $\xi=1$. The maximum connected correlation function
$C(\rho)$ is not {\itshape a priori} a fully quantum quantity, and it
determines how, on average, the Bloch vectors of the two atoms influence each
other. The present results seem to suggest that this might be the
key quantity to measure when it comes to an experimental detection
of the dynamics of correlations, provided that a simultaneous set
of optimal measurements on the two qubits can be efficiently
performed in the laboratory frame.
It is worth noticing here that the optimal ``measurement
directions'' $\hat n, \hat n'$ are completely different in the
space-like region $J_S$ and on the light cone. Indeed, for $\xi <
1$, the correlation between the two Bloch vectors is best
highlighted by measuring the effective spin projections in the
equatorial $x-y$ plane. On the light cone, on the other hand, the
best choice is to measure $\sigma_z$ for both qubits. This appears
to be related to the fact that no excitation can reach the atom
$B$ before $\xi =1$ and that, as demonstrated in \cite{carlos2},
it is only after this time that the excited state population of
atom $B$ starts depending on the presence of atom $A$. The vacuum
fluctuations, thus, are able to correlate essentially transversal
observables for $\xi <1$, while for a longitudinal ($z-z$)
correlation, one has to wait the arrival of the light signal.
Finally, in Fig. \ref{all} reports a visual comparison of all the
three indicators of correlations considered in the present analysis,
as functions of $Z$ and $\xi$. As anticipated, there is no
violation of the general hierarchy (\ref{hierardy}), thus
confirming that the perturbative analysis we have performed is
consistent up to the present expansion order.
\begin{figure}[tb]
\begin{center}
\includegraphics[width=10cm]{all3d.pdf}
\caption{(Color online) Comparative plot displaying the maximum
connected correlation function $C$ (topmost surface, blue online),
the square root $\sqrt{D}$ of the geometric discord (middle
surface, red online), and the negativity $N$ (bottommost surface,
green online), calculated for the state $\rho_X$ as functions of
the dimensionless time $\xi$ and of the coupling strength $Z$, for
$r = \upsilon \pi / 4 \Omega$.} \label{all}
\end{center}
\end{figure}
\section{Non-locality}\label{inequality}
One may wonder what the above results mean in term of
non-locality. In this respect, a key quantity to investigate
non-local effects in the dynamics of two two-level systems is the
Bell parameter \cite{bell}, resulting from well-known inequalities
that local classical hidden variable theories cannot violate. To
make a long story short, one identifies a set of joint
measurements to be performed on the composite system. Then, based
on the outcomes of such measurements, it is possible to define a
statistical parameter $\cal{B}$ for which a classical threshold
value $\cal{B}_{C}$ exists. Whenever the inequality
$$
\cal{B}<\cal{B}_{C}
$$
is violated, the state of the system under scrutiny is not
reproducible by means of local classical hidden variable theories.
Unfortunately, the other way around is not true: some mixed
entangled states exist that do not violate any Bell inequality
\cite{werner}. In the case of two two-level system, it is well
known that $\cal{B}_{C}=$ 2, whereas the maximum violation allowed
by quantum mechanics is given by the so-called Tsirelson bound,
$\cal{B}_{\max}=$ 2$\sqrt{2}$, which is saturated by maximally
entangled states. Hence, if for a given bipartite quantum state
$\rho$ we find $2<\cal{B}(\rho)\leq 2\sqrt{2}$, such a state is
not classically reproducible. We have considered two different
Bell parameters in the present analysis: the conventional CHSH one
\cite{chsh} and its optimized version for ``X''-shaped states such
as $\rho_{\rm X}$, given in \cite{bellomo}. The former, for the
states in Eq.~(\ref{state}), reads as follows (up to the second
perturbative order)
\begin{equation}
{\cal B}_{CHSH}(\rho_{\rm
X})=-\sqrt{2}(\rho_{11}+\rho_{44}-\rho_{22}-\rho_{33}+2\textrm{Re}\rho_{23}+2\textrm{Re}\rho_{14})
\, , \label{chsh}
\end{equation}
whereas the latter is \cite{bellomo}
\begin{equation}
{\cal B}_{OPT}(\rho_{\rm
X})=2\sqrt{u_{1}+\max[u_{2},u_{3}]}\, , \label{bello}
\end{equation}
where
$$
u_{1}=4(|\rho_{14}|+|\rho_{23}|)^{2}\qquad u_{3}=4(|\rho_{14}|-|\rho_{23}|)^{2}
$$
$$
u_{2}=(\rho_{11}+\rho_{44}-\rho_{22}-\rho_{33})^{2} \, .
$$
The above quantities correspond to two different choices of the
Bell parameters, that is, different choices of the angles along
which we project the effective spin operators in a
joint-measurement experiment. The main difference between them is
that ${\cal B}_{OPT}$ is optimal in the sense that it
maximizes the violation of the related Bell inequality, whenever
such a violation is present. We report in Fig.\ref{bell} the time
evolution of the the Bell parameter ${\cal B}_{CHSH}$. It is clear
from these plots that, in order to observe a violation of the Bell
inequality, a very strong coupling is required ($Z\approx 1000$).
However, such a violation is witnessed only in the surroundings of
the light cone crossing $\xi=1$. Fig.\ref{opt} shows, instead, the
time evolution of ${\cal B}_{OPT}$. Some qualitative and
quantitative differences between these quantities, especially for
$\xi>1$ and very strong coupling, are present. First of all we
notice that, as expected, the optimized Bell parameter ${\cal B}_{OPT}$ is greater than ${\cal B}_{CHSH}$ for all
couplings and times. Secondly, the latter is clearly more
sensitive to the strong-coupling regime. This result makes perfectly
sense if we look at the entanglement dynamics as a function of the
coupling constant: the bigger $Z$ is, the more entanglement is
present in the system, pushing up the Bell parameters' value.
These last two features are best enlightened in the third plot
\ref{confr} where the dynamics of the two Bell parameters we
considered, is compared in the case of very strong coupling
$Z=1000$.
\begin{figure*}[t]
\begin{center}
\subfigure[]
{\includegraphics[width=5.7cm]{bchsh.pdf}\label{bell}}
\hspace*{0.2cm} \subfigure[]
{\includegraphics[width=5.7cm]{bopt.pdf}\label{opt}}
\hspace*{0.2cm} \subfigure[]
{\includegraphics[width=5.7cm]{confr.pdf}\label{confr}}
\caption{(Color online) (a) Bell-CHSH parameter ${\cal B}_{CHSH}$ and (b) its optimized version ${\cal B}_{\textrm{OPT}}$, plotted for $Z =
100$ (dotted green), $Z = 400$ (dashed red) and $Z =
800$ (continuous blue), as a function of $\xi$. The straight line at ${\cal B}=2$ gives the limit for
a local realistic description.
As one can see, in both cases, a very strong
coupling is needed in order to have a clear violation of the
inequality, occurring, however, only very close to the light cone
crossing point.
(c) Comparison between
${\cal B}_{CHSH}$ (red dashed) and ${\cal B}_{\textrm{OPT}}$ (blue dotted) for strong coupling $Z=1000$. In all these plots $r = \upsilon \pi / 4
\Omega$.
} \label{chsh}
\end{center}
\label{figures}
\end{figure*}
\section{Experimental implementation}
\label{expeimple} Now we will focus on the particular experimental
set-up that we propose to test the results above. Clearly, we need
the ability of fast on-off switching of the qubit-field
interaction. We should be able to prepare the initial state Eq.
(\ref{eq:initialstate}) and let the interaction be active only
during a finite time. We can conceive several circuit QED schemes
in order to achieve these goals. As commented before our general
formalism can accommodate several architectures; in particular, it
is valid both for inductive and capacitive couplings. We can
choose for instance a pair of three-junction flux qubits
galvanically coupled to the center conductor of an open
transmission line. In Ref. \cite{carlos1} it is shown how the
desired initial state can be prepared with high fidelity by
varying an external magnetic flux adiabatically for qubit $B$ and
non-adiabatically for qubit $A$. After that, the interaction has
to be switched on and kept constant during a given time interval.
In Ref. \cite{peropadre} several modifications of the
three-junction scheme are proposed in order to achieve couplings
tunable in strength up to the ultra-strong regime. In particular,
a specific set-up featuring an intermediate superconducting loop
has been described in details in Ref. \cite{carlos3}, where an
effective interaction Hamiltonian between a qubit and a
transmission line has been derived, that reads
\begin{equation}
H_I \propto \cos(f)\sigma_x\,V(x), \label{effhamilt}
\end{equation}
$f$ being related with an external magnetic flux $\Phi$ threading
the SQUID: $f=2\pi\Phi/\Phi_0$ (where $\Phi_0=h/2e$ is the flux
unit). By a suitable modulation of the flux $\Phi$, thus, the
interaction can be activated and switched off at will. State of
the art circuit-QED technology allows variations of the magnetic
flux at frequencies of about $10\,\mbox{GHz}$ \cite{casimirwilson}
and larger values are expected for the future \cite{guille}. As a
result, switching times of the order of $0.1\, ns$ and even
shorter can be safely considered. Taking the values that we have
considered in our plots, and typical circuit-QED parameters, such
as $\upsilon=1.2\cdot10^8\, \mbox{m/s}$ and $\Omega=10^9 \,
\mbox{m/s}$, the point $\xi=1$ is equivalent to an interaction
time $t \simeq 1\, \mbox{ns}$. Thus, the region around $\xi=1$ is
well within experimental reach. In particular the strongest value
that we considered for the adimensional coupling $Z$ is
equivalent to $g/\Omega \simeq 0.3$, which is quite similar to the
ones in cutting-edge experiments investigating the ultra-strong
coupling regime \cite{forn-diaz10,niemczyk10}.
Once the interaction is switched off, quantum state tomography
\cite{tomographycircuits} may be performed in order to quantify
the degree of correlations, using for instance the magnitudes that
we have considered in this work. The dynamics is effectively
frozen and the system remains in the state $\rho_{\rm X} (t)$, so
measurements can take as much time as required. In particular, it
would be interesting to run the experiment for different
interaction times inside and outside the light cone, in order to
test both the peak at $\xi=1$ and the correlations for $\xi<1$.
\section{Concluding Remarks}
\label{conclu} To summarize, using second order perturbation
theory we have discussed the dynamics of quantum correlations in
the Fermi problem, which can be experimentally tested in a
one-dimensional set-up involving two artificial atoms coupled to
the electromagnetic field of an open ended transmission line. We
have compared the time behavior of the entanglement, as measured
by the negativity, and of more general quantum correlations such
as the (square root of) geometric discord, and the maximum
connected correlation function. All of these correlations display
a peak at the light cone crossing point, $\xi =1$, which
corresponds to the time at which a signal from atom $A$ arrives at
$B$. The geometric discord and the connected correlation, however,
have a substantially non-zero value also in the space-like region.
This is due to the fact that electromagnetic vacuum fluctuations
can induce (transverse) correlations that are signalled by these
functions. As the light-cone is crossed, these correlations change
their character and become longitudinal as a result of the fact
that the excited state population of the second atom starts to
depend on the presence of the first one. We have briefly
investigated non-local effects in this model as encoded in
possible violations of Bell inequalities. We have found that a
violation can occur in the neighborhood of the light-cone crossing
and only for strong couplings between the atoms and the
propagating field. We
believe that both geometric discord and maximum connected
correlations, which are found to be sensitive to causal
propagation, are suitable candidates for understanding and testing
experimentally the role of micro-causality in the dynamics of
quantum correlations.
\section*{Acknowledgments}{We acknowledge the University of Nottingham
(ECRKTA/2011), the U.K. EPSRC [Grants EP/J016349/1 and EP/J016314/1 (subcode RDF/BtG/0612b/31)], the Finnish Cultural Foundation [Science Workshop on Entanglement], and the Emil Aaltonen foundation [Non-Markovian Quantum Information] for financial support. GA thanks D Girolami and M Piani for discussions.}
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,518 |
Virginia Slims of Indianapolis 1972 — жіночий тенісний турнір, що проходив на закритих кортах з килимовим покриттям Indiana State Fairgrounds Coliseum в Індіанаполісі (США). Належав до Virginia Slims Circuit 1972. Турнір відбувся вперше і тривав з 3 до 6 травня 1972 року. Кваліфікаційні змагання до одиночного розряду відбулись 1 і 2 травня 1972 в Indianapolis Racquet Club. Перша сіяна Біллі Джин Кінг здобула титул в одиночному розряді й отримала за це 4 тис. доларів США.
Фінальна частина
Одиночний розряд
Біллі Джин Кінг — Ненсі Гюнтер 6–3, 6–3
Парний розряд
Розмарі Касалс / Карен Крантцке — Джуді Далтон / Франсуаза Дюрр 6–3, 6–2
Розподіл призових грошей
Примітки
Virginia Slims of Indianapolis
Virginia Slims of Indianapolis
Virginia Slims of Indianapolis | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,741 |
What Proof Is There That God Loves Me?
There have been moments these past months that I've wanted to give up on God. I'm simply being honest.
As one who grew up in a severely alcoholic home, I witnessed more violence as a child than I care to remember. As a full-time pastor now for some 30 years, I've had, on occasion, the unfortunate opportunity to see the very ugly side of what some have otherwise called "Christianity." But those pale in comparison to the events of May 13th, when my world caved in around me.
THIS is the unstoppable, indefensible, indisputable love of God is Christ Jesus. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,104 |
Q: How to pass ID (Primary Key) in ListView in OnItemClickListener to get data from SQLite Database in Android app? I need to pass ID, which is a primary key in SQLite Database in android app, to get the data from the Database related to the list item in ListView. When the data is received, it is then passed to another activity using intent.
Everything else is working properly but I am not able to get the ID of the row in the Database according to list item clicked.
Following is the DatabaseHandler.java:
package com.Its_Kush.comety_new;
import android.content.ContentValues;
import android.content.Context;
import android.database.Cursor;
import android.database.sqlite.SQLiteDatabase;
import android.database.sqlite.SQLiteOpenHelper;
public class DatabaseHandler extends SQLiteOpenHelper {
public DatabaseHandler(Context context) {
super(context, DATABASE_NAME, null, DATABASE_VERSION);
// TODO Auto-generated constructor stub
}
// MainActivity
public static final String dbID = "ID";
public static final String dbNAME = "Name";
public static final String dbEMI = "Emi";
public static final String dbMONTHLY_EXP = "Monthly_Exp";
public static final String dbMEMBERS = "Members";
//
public static final String DATABASE_NAME = "Comety_Database.db";
public static final String TABLE_NAME = "Comety_Database_Table";
public static final int DATABASE_VERSION = 1;
SQLiteDatabase db;
//
@Override
public void onCreate(SQLiteDatabase db) {
// TODO Auto-generated method stub
db.execSQL("CREATE TABLE " + TABLE_NAME + "(" + dbID
+ " INTEGER PRIMARY KEY AUTOINCREMENT, " + dbNAME + " TEXT, "
+ dbEMI + " REAL, " + dbMONTHLY_EXP + " REAL, " + dbMEMBERS
+ " INTEGER " + ")");
}
@Override
public void onUpgrade(SQLiteDatabase db, int oldVersion, int newVersion) {
// TODO Auto-generated method stub
db.execSQL("DROP TABLE IF EXIST " + TABLE_NAME);
onCreate(db);
}
public boolean insertData(String name, double emi, double monthly_exp,
int members) {
SQLiteDatabase db = this.getWritableDatabase();
ContentValues content = new ContentValues();
content.put(dbNAME, name);
content.put(dbEMI, emi);
content.put(dbMONTHLY_EXP, monthly_exp);
content.put(dbMEMBERS, members);
long result = db.insert(TABLE_NAME, null, content);
if (result == -1)
return false;
else
return true;
}
public Cursor viewOne(String id){
SQLiteDatabase db = this.getWritableDatabase();
Cursor dataShow = db.rawQuery("SELECT * FROM " + TABLE_NAME + " WHERE ID = " + id, null);
return dataShow;
}
public Cursor viewAll(){
SQLiteDatabase db = this.getWritableDatabase();
Cursor dataShow = db.rawQuery("SELECT * FROM " + TABLE_NAME, null);
return dataShow;
}
public boolean updateData(String id, String name, double emi, double monthly_exp, int members){
SQLiteDatabase db = this.getWritableDatabase();
ContentValues content = new ContentValues();
content.put(dbID, id);
content.put(dbNAME, name);
content.put(dbEMI, emi);
content.put(dbMONTHLY_EXP, monthly_exp);
content.put(dbMEMBERS, members);
db.update(TABLE_NAME, content, "id = ?", new String[] { id });
return true;
}
public int deleteData(String id){
SQLiteDatabase db = this.getWritableDatabase();
return db.delete(TABLE_NAME, "ID = ?", new String[] { id });
}
public void deleteAll(){
SQLiteDatabase db = this.getWritableDatabase();
db.execSQL("DELETE FROM " + TABLE_NAME);
}
public void resetId(){
SQLiteDatabase db = this.getWritableDatabase();
db.execSQL("delete from sqlite_sequence where name = '" + TABLE_NAME + "'");
}
}
Following is the class containing ListView:
package com.Its_Kush.comety_new;
import java.util.ArrayList;
import android.app.AlertDialog;
import android.content.DialogInterface;
import android.content.Intent;
import android.database.Cursor;
import android.os.Bundle;
import android.support.v7.app.AppCompatActivity;
import android.view.Menu;
import android.view.MenuItem;
import android.view.View;
import android.widget.AdapterView;
import android.widget.AdapterView.OnItemClickListener;
import android.widget.AdapterView.OnItemLongClickListener;
import android.widget.ArrayAdapter;
import android.widget.Button;
import android.widget.EditText;
import android.widget.ListView;
import android.widget.TextView;
import android.widget.Toast;
public class ShowActivity extends AppCompatActivity {
DatabaseHandler dbComety = new DatabaseHandler(this);
ArrayList<String> listItems = new ArrayList<String>();
ArrayAdapter<String> adapter;
ListView list1;
Button submit, delete;
EditText id;
String name, str;
double monthly_exp, emi;
short members;
@Override
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.activity_show);
list1 = (ListView) findViewById(R.id.list1);
show_all();
list1.setOnItemClickListener(new OnItemClickListener() {
@Override
public void onItemClick(AdapterView<?> parent, View v,
int position, long id) {
// TODO Auto-generated method stub
str = (String) ((TextView) v).getText();
Cursor dataOneView = dbComety.viewOne(str.substring(0, 2));
if (dataOneView.moveToFirst()) {
name = dataOneView.getString(1);
emi = dataOneView.getDouble(2);
monthly_exp = dataOneView.getDouble(3);
members = dataOneView.getShort(4);
}
// showMessage("Value", "Name: " + name + "\nemi:" + emi
// + "\nm_exp" + monthly_exp + "\nmembers: " + members);
// id.setText("");
Intent submit = new Intent(ShowActivity.this,
MainActivity.class);
submit.putExtra("name", name);
submit.putExtra("emi", emi);
submit.putExtra("members", members);
submit.putExtra("monthly_exp", monthly_exp);
//
startActivity(submit);
}
});
list1.setOnItemLongClickListener(new OnItemLongClickListener() {
@Override
public boolean onItemLongClick(AdapterView<?> arg0, View v,
int arg2, long arg3) {
// TODO Auto-generated method stub
str = (String) ((TextView) v).getText();
showMessage("Delete", "Are you sure?");
return true;
}
});
}
DialogInterface.OnClickListener cancelClickListner = new DialogInterface.OnClickListener() {
@Override
public void onClick(DialogInterface arg0, int arg1) {
// TODO Auto-generated method stub
finish();
}
};
public void show_all() {
Cursor dataView = dbComety.viewAll();
if (dataView.getCount() == 0) {
AlertDialog.Builder builder = new AlertDialog.Builder(this);
builder.setTitle("Error");
builder.setCancelable(false);
builder.setMessage("No data found.").setPositiveButton("Back", cancelClickListner).show();
dbComety.resetId();
} else {
String buffer = null;
if (dataView.moveToFirst()) {
do {
buffer = dataView.getString(0) + "\t\t"
+ dataView.getString(1);
listItems.add(buffer);
} while (dataView.moveToNext());
}
}
adapter = new ArrayAdapter<String>(this, R.layout.textview_listitems,
listItems);
list1.setAdapter(adapter);
}
DialogInterface.OnClickListener dialogClickListener = new DialogInterface.OnClickListener() {
@Override
public void onClick(DialogInterface dialog, int which) {
switch (which) {
case DialogInterface.BUTTON_POSITIVE:
// Yes button clicked
int deletedRows = dbComety.deleteData(str.substring(0, 2));
if (deletedRows > 0) {
Toast.makeText(ShowActivity.this, R.string.deleted,
Toast.LENGTH_SHORT).show();
adapter.clear();
show_all();
adapter.notifyDataSetChanged();
} else
Toast.makeText(ShowActivity.this, R.string.not_deleted,
Toast.LENGTH_SHORT).show();
break;
case DialogInterface.BUTTON_NEGATIVE:
// No button clicked
break;
}
}
};
public void showMessage(String title, String message) {
AlertDialog.Builder builder = new AlertDialog.Builder(this);
builder.setTitle(title);
builder.setMessage(message)
.setPositiveButton("Yes", dialogClickListener)
.setNegativeButton("No", dialogClickListener);
builder.show();
}
DialogInterface.OnClickListener deleteAllClickListener = new DialogInterface.OnClickListener() {
@Override
public void onClick(DialogInterface dialog, int which) {
switch (which) {
case DialogInterface.BUTTON_POSITIVE:
// Yes button clicked
dbComety.deleteAll();
adapter.clear();
show_all();
adapter.notifyDataSetChanged();
break;
case DialogInterface.BUTTON_NEGATIVE:
// No button clicked
break;
}
}
};
@Override
public boolean onCreateOptionsMenu(Menu menu) { // Inflate the menu; this
// adds items to the action
// bar if it is present.
getMenuInflater().inflate(R.menu.show, menu);
return true;
}
@Override
public boolean onOptionsItemSelected(MenuItem item) {
AndroidManifest.xml.
int id = item.getItemId();
if (id == R.id.delete_all) {
AlertDialog.Builder builder = new AlertDialog.Builder(this);
builder.setTitle("Delete all");
builder.setMessage("Are you sure?")
.setPositiveButton("Yes", deleteAllClickListener)
.setNegativeButton("No", deleteAllClickListener);
builder.show();
return true;
}
return super.onOptionsItemSelected(item);
}
}
I am currently using a String to store the list item TextView data and then getting the id using the substring method. How can I directly get the ID of the row in Database?
A: Create a list of row id and make sure that the id and content are stored in the same index of both the lists.
buffer = dataView.getString(1);
idItems.add(dataView.getString(0));
listItems.add(buffer);
and in onitemclicklistener:
Cursor dataOneView = dbComety.viewOne(idItems.get(position));
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,170 |
Galaktao - debiutancki album duetu hip-hopowego Paresłów. Wydawnictwo ukazało się 24 marca 2001 roku nakładem wytwórni muzycznej Baza Lebel w dystrybucji Pomaton EMI. Płytę poprzedził singel do utworu tytułowego.
Lista utworów
Opracowano na podstawie materiału źródłowego.
"Intro" (prod. Wielki Brat, scratche: DJ Deszczu Strugi) - 01:11
"Wyścig" (prod. Wielki Brat) - 04:32
"W miejskim tłoku ginąc" (gościnnie: Dizkret, Pezet, Wujrock, prod. Wielki Brat, scratche: DJ Romek) - 05:38
"Rano" (perkusja, gitara, prod. Wielki Brat) - 00:42
"Mikrofon dla paresłów" (prod. Wielki Brat) - 04:59
"A mi to na tym" (instrumenty klawiszowe, prod. Wielki Brat) - 05:29
"Delektuj się" (gościnnie: CNE, WSZ, prod. Wielki Brat) - 04:41
"Hip Hop na wagę" (gościnnie: G. Frontczak) - 00:50
"Nie rozumiem" (gitara, instrumenty klawiszowe, gitara basowa, prod. Wielki Brat, scratche: DJ Romek) - 04:11
"Ekspresja" (prod. Wielki Brat, scratche: JMI) - 04:13
"Galaktao" (prod. Wielki Brat, scratche: DJ Romek) - 03:50
"W samo południe" (prod. Wielki Brat) - 00:21
"Ja?" (instrumenty klawiszowe, gitara, prod. Wielki Brat) - 04:27
"Kiepski kawałek" (gitara, prod., instrumenty klawiszowe: Wielki Brat) - 05:19
"Nie tym tonem (mówiłeś do mnie)" (trąbka: Korzeń, śpiew: Single Asa, prod. Wielki Brat) - 04:08
"Wieczorem" (prod. Wielki Brat, scratche: DJ Romek) - 00:54
"Fenomen ps" (gitara, instrumenty klawiszowe, prod. Wielki, scratche: JMI) - 04:10
"Na marsie skit" (prod. Wielki Brat) - 01:05
"Spławiłam Cię już w zeszłym roku" (gościnnie: Ginger, instrumenty klawiszowe, prod. Wielki Brat) - 03:51
"Outro" (prod. Wielki Brat) - 01:22
Przypisy
Linki zewnętrzne
Okładka
Albumy hip-hopowe
Albumy muzyczne wydane w roku 2001 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,562 |
Biobateriile sunt surse chimice de curent electric bazate pe biomateriale cum ar fi carbohidrați. Reacția de la anod poate fi oxidarea glucozei la gluconolactonă.
Biobateriile pot fi construite cu lămâi, cartofi, etc.
Sony a dezvoltat o biobaterie cu o putere electrică de 50 mW, suficientă pentru alimentarea unui MP3-player.
Note
Vezi și
Pilă de combustie
Pilă de combustie enzimatică
Bioreactor electrochimic
Bioelectrochimie
Conversia electrochimică a energiei
Hidrogenază
Legături externe
World's most powerful biobattery 50 mW
Electrochimie | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,259 |
She will most likely be catholic, beautiful, serene and calm even in the time of chaos, yes, just as you see in the soap operas. She will have a chubby, cherubic face, a baby face, one that will stay young for a long time. And she will most likely be well brought up, with the values of respect and dignity engraved in her heart. What is not to love about the Filipino women? If you ask me, there are more than ten reasons to love these gorgeous women, but then, ten is all you need.
Eyes never lie if they see something they like. The irresistible beauty of Filipino women is something you cannot ignore. The Filipinos are different from ladies from other backgrounds. There is no way you can confuse them for some other women even if they are biracial Filipino singles. Their long silky hair, flawless skin and petite bodies cannot go unmentioned. Of course, beauty is not the only factor that attracts you to Filipino women dating. There are many more good things about them as you will see here.
If you are looking for someone to commit to among the Asian race, then go for Filipino women. Whenever a Filipino woman decides that you are the right one, she is focused on you. Therefore, do not make the mistake of being a player or having fun with a Filipino woman. It does not augur so well with ladies from this country.
A strong belief system is another feature of Filipino singles. You have heard of stories from Philippines where people are even crucified on Good Friday. It simply shows how strong their religious beliefs are; not that you will be crucified. Therefore, if you are the religious type, then Filipino dating is the kind of thing that you want to try out. If you are catholic, you stand a better chance because it has most followers in Philippines. If you are not religious, then you need to respect her religion. If she asks you to attend mass with her, do not decline. You should never deny your woman what she asks if you love her. Make her happy. If you value yourself more than her, you will not get along well.
Philippines dating guarantees you a great homemaker. Filipino women are wired to be hospitable and they do know how to make a home comfortable. Whether you are dating one or you consider marrying a Filipino woman, you will always feel welcome at her house. You do not want to date or have a chaotic, disorganized woman as a wife. You need someone who can make your friends, visitors and even business partners comfortable whenever they visit you at home. A Filipino woman will ensure they live happy and impressed.
Self-respect is a very important aspect in life. You would like to date a woman who is not 'loose' in morals if you are serious. Dating is part of development in your life. Yes, have all the fun but remember; you do not want to write a history that you will hate or regret later in life. You may not see the sense now, but one day you will. Put your life in order. Date a woman who you can proudly introduce to your business partners at dinner, family and friends. You do not want a situation where you go to a party with this lady you believe is yours, only for people to look at you with giggles because of the 'encounter' they had with her.
If you do not value family, you then you need to change that attitude; it might cost you your thriving relationship with a Filipino. Filipino women love their families to the soul. This is attributed to their strong religious beliefs, which attest to the fact that family is essential in life, and there ought to be a peaceful co-existence and care amongst members. Expect to be invited to family dinners when you date Filipino singles, being introduced to any member of the family however distant. It is all about recognizing other members as important people in a Filipino woman's life.
Filipino women are humble and naïve in a nice way; even their looks portray humility. Have you ever met ladies from other backgrounds and all you see on their faces is: being outspoken? However, humility does not mean being quiet but talking whenever necessary, being composed. You do not want a woman who shouts across the tables at dinner in a restaurant. You are better than that and Filipino women will spare you such trouble. Besides, there are those looks you cannot ignore. For example, when a Philippine single woman you are dating looks at you with these lazy, shy eyes, you cannot resist but do whatever she asks you to. You almost wish she acts that way the whole day.
Filipino women understand the difference between submission and oppression. Given what their religion stands for, submission is not being oppressed, forget about the dictionary meaning. Someone who loves a Filipino woman cannot oppress her or make her a slave. Submission has a lot to do with respect and speaking out one's mind. Oppression on the other hand is about mistreating someone and never letting him or her speak out.
When you go for Philippines dating, you will experience the beauty of simplicity. At times, all you need is a simple woman; it does not mean that such a woman is not sophisticated. There is a lot of sophistication in simplicity. Filipino women dress in a simple manner, talk gently, act humble and value relationships. But there is class, dignity and beauty in this simplicity. For instance, if you want to buy a gift for a simple Filipino woman, you need to think hard and at the same time think simple. Gifts need to impress the receiver and that is not easy. The best way to prove that is by dating a woman from Philippines.
You will not believe it, but the truth about Filipina women is that they are quiet, dignified and they have a classiness that cannot be explained. You have to date one to experience what we mean here. They add a sense of dignity to any macabre situation, even to any delirium. They are brought up in such a way they can be choosy, expressive of taste without appearing too overbearing.
If you want to date Philippines girls, go and start your exotic love adventure to our post of the best Filipino dating sites.
Hey! I'm Peter Wang, the founder of LovelyPandas. My dream is for a world full of love and romance. I seek to help people find love and build amazing relationships. You can find useful online dating tips and honest dating site reviews here. Feel free to write to us if you have any comments.
Hi Guys! We create Lovely Pandas to help men and women like you find love and build amazing relationships. Hope you you like our site and feel free to write to us if you have any comments.
© 2019 Lovely Pandas. All rights reserved. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,645 |
James Green (4 July 1879 – 1940) was an English footballer who played in the Football League for Preston North End.
References
1879 births
1940 deaths
English footballers
Association football forwards
English Football League players
Preston North End F.C. players
Chorley F.C. players | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,348 |
{"url":"https:\/\/opus4.kobv.de\/opus4-zib\/frontdoor\/index\/index\/docId\/1117","text":"## The Steiner Connectivity Problem\n\nPlease always quote using this URN: urn:nbn:de:0297-zib-11171\n\u2022 The Steiner connectivity problem is a generalization of the Steiner tree problem. It consists in finding a minimum cost set of simple paths to connect a subset of nodes in an undirected graph. We show that polyhedral and algorithmic results on the Steiner tree problem carry over to the Steiner connectivity problem, namely, the Steiner cut and the Steiner partition inequalities, as well as the associated polynomial time separation algorithms, can be generalized. Similar to the Steiner tree case, a directed formulation, which is stronger than the natural undirected one, plays a central role.\n\n$Rev: 13581$","date":"2016-07-27 01:14:13","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7921419143676758, \"perplexity\": 511.16373563125484}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-30\/segments\/1469257825125.30\/warc\/CC-MAIN-20160723071025-00095-ip-10-185-27-174.ec2.internal.warc.gz\"}"} | null | null |
Q: Razor - Variable in Foreach In this code, I use variable num like a flag if equal 0 I use
td class="row_grid_Par" else if equal 1 I use td class="text-row_grid_Dis.
Why this code doesn't work ?
<tbody>
@{int num = 0};
@foreach (var CodRis in Model)
{
<tr>
<td>
@CodRis.CodRis
</td>
@if (num == 0)
{
<td class="row_grid_Par">
@CodRis.DescRis
</td>
@{num = 1};
}
else
{
<td class="text-row_grid_Dis">
@CodRise.DescRis
</td>
@{num = 0};
}
</tr>
}
</tbody>
A: <tbody>
@{int num = 0};
@foreach (var CodRis in Model)
{
<tr>
<td>
@CodRis.CodRis
</td>
<td class='@(num==0?"row_grid_Par":"text-row_grid_Dis")'>
@CodRis.DescRis
</td>
</tr>
num=num==0?1:0;
}
</tbody>
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,689 |
Зображення сторінки
0 Рецензії/відгукиНаписати рецензію
Principles of Political Economy, with Some of Their Applications to ..., Том 1
За John Stuart Mill
Докладніше про цю книгу
social employment of their leisure hours not disagreeable.
§ 4. These two cases, of slave labour and of domestic manufactures, exemplify the conditions under which low wages enable a country to sell its commodities cheaper in foreign markets, and consequently to undersell its rivals, or to avoid being undersold by them. But no such advantage is conferred by low wages when common to all branches of industry. General low wages never caused any country to undersell its rivals, nor did general high wages ever hinder it from doing so.
To demonstrate this, we must return to an elementary principle which was discussed in a former chapter.* General low wages do not cause low prices, nor high wages high prices, within the country itself. General prices are not raised by a rise of wages, any more than they would be raised by an increase of the quantity of labour required in all production. Expenses which affect all commodities equally, have no influence on prices. If the maker of broadcloth or cutlery, and nobody else, had to pay higher wages, the price of his commodity would rise, just as it would if he had to employ more labour; because otherwise he would gain less profit than other producers, and nobody would engage in the employment. But if everybody has to pay higher wages, or everybody to employ more labour, the loss must be submitted to ; as it affects everybody alike, no one can hope to get rid of it by a change of employment, each therefore resigns himself to a diminution of profits, and prices remain as they were. In like manner, general low wages, or a general increase in the productiveness of labour, does not make prices low, but profits high. If wages fall (meaning here by wages the cost of labour), why, on that account, should the producer lower his price? He will be forced, it may be said, by the competition of other capitalists who will crowd into his employment. But other capitalists are also paying lower wages, and by entering into competition with him they would gain nothing but what * Supra, book iii. ch. It.
they are gaining already. The rate then at which labour is paid, as well as the quantity of it which is employed, affects neither the value nor the price of the commodity produced, except in so far as it is peculiar to that commodity, and not common to commodities generally.
Since low wages are not a cause of low prices in the country itself, so neither do they cause it to offer its commodities in foreign markets at a lower price. It is quite true that if the cost of labour is lower in America than in England, America could sell her cottons to Cuba at a lower price than England, and still gain as high a profit as the English manufacturer. But it is not with the profit of the English manufacturer that the American cotton spinner will make his comparison; it is with the profits of other American capitalists. These enjoy, in common with himself, the benefit of a low cost of labour, and have accordingly a high rate of profit. This high profit the cotton spinner must alsoliave: he will not content himself with the English profit. It is true he may go on for a time at that lower rate, rather than change his employment; and a trade may be carried on, sometimes for a long period, at a much lower profit than that for which it would have been originally engaged in. Countries which have a low cost of labour, and high profits, do not for that reason undersell others, but they do oppose a more obstinate resistance to being undersold, because the producers can often submit to a diminution of profit without being unable to live, and even to thrive, by their business. But this is all which their advantage does for them: and in this resistance they will not long persevere, when a change of times, which may give them equal profits with the rest of their countrymen, has become manifestly hopeless.
§ 5. There is a class of trading and exporting communities, on which a few words of explanation seem to be required. These are hardly to be, looked upon as countries, carrying on an exchange of commodities with other countries, but more properly as outlying agricultural or manufacturing establishments belonging to a larger community. Our West India colonies, for example, cannot be regarded as countries, with a productive capital of their own. If Manchester, instead of being where it is, were on a rock in the North Sea (its present industry nevertheless continuing), it would still be but a town of England, not a country trading with England; it would be merely, as now, a place where England finds it convenient to carry on her cotton manufacture. The West Indies, in like manner, are the place where England finds it convenient to carry on the production of sugar, coffee, and a few other tropical commodities. All the capital employed is English capital; almost all the industry is carried on for English uses; there is little production of anything except the staple commodities, and these are sent to England, not to be exchanged for things exported to the colony and consumed by its inhabitants, but to be sold in England for the benefit of the proprietors there. The trade with the West Indies is therefore hardly to be considered as external trade, but more resembles the traffic between town and country, and is amenable to the principles of the home trade. The rate of profit in the colonies will be regulated by English profits: the expectation of profit must be about the same as in England, with the addition of compensation, for the disadvantages attending the more distant and hazardous employment: and after allowance is made for those disadvantages, the value and price of West India produce in the English market must be regulated (or rather must have been regulated formerly), like that of any English commodity, by the cost of production. For the last twelve or fifteen years this principle has been in abeyance: the price was first kept up beyond the ratio of the cost of production by deficient supplies, which could not, owing to the deficiency of labour, be increased; and more recently the admission of foreign competition has introduced another
element, and some of the West India Islands are undersold, not so much because wages are higher than in Cuba and Brazil, as because they are higher than in England: for were they not so, Jamaica could sell her sugars at Cuban prices, and still obtain, though not a Cuban, an English rate of profit.
It is worth while also to notice another class of small, but in this case mostly . independent communities, which have supported and enriched themselves almost without any productions of their own, (except ships and marine equipments,) by a mere carrying trade, and commerce of entrepot; by buying the produce of one country, to sell it at a profit in another. Such were. Venice and the Hanse Towns. The case of these communities is very simple. They made themselves and their capital the instruments, not of production, but of accomplishing exchanges between the productions of other countries. These exchanges are attended with an advantage to those countries—an increase of the aggregate returns to industry—part of which went to indemnify the agents, for the necessary expense of transport, and another part to remunerate the use of their capital and mercantile skill. The countries themselves had not capital disposable for the operation. When the Venetians became the agents of the general commerce of Southern Europe, they had scarcely any competitors: the thing would not have been done at all without them, and there was really no limit to their profits except the limit to what the ignorant feudal nobility could and would give for the unknown luxuries then first presented to their sight. At a later period competition arose, and the profit of this operation, like that of others, became amenable to natural laws. The carrying trade was taken up by Holland, a country with productions of its own and a large accumulated capital. The other nations of Europe also had now capital to spare, and were capable of conducting their foreign trade for themselves: but Holland, having, from a variety of circumstances, a lower rate of profit at home, could afford to carry for other countries at a smaller advance on the original cost of the goods, than would have been required by their own capitalists; and Holland, therefore, engrossed the
greatest part of the carrying trade cf all those countries which did not keep it to themselves by Navigation Laws, constructed, like those of England, for that express purpose.
CHAPTER XXVI.
OP DISTRIBUTION, AS AFFECTED BY EXCHANGE.
§ 1. We have now completed, as far as is compatible with our purposes and limits, the exposition of the machinery through which the produce of a country is apportioned among the different classes of its inhabitants; which is no other than the machinery of Exchange, and has for the exponents of its operation, the laws of Value and of Price. We shall now avail ourselves of the light thus acquired, to cast a retrospective glance at the subject of Distribution. The division of the produce among the three classes, Labourers, Capitalists, and Landlords, when considered without any reference to Exchange, appeared to depend on certain general laws. It is fit that we should now consider whether these same laws still operate, when the distribution takes place through the complex mechanism of exchange and money; or whether the properties of the mechanism interfere with and modify the presiding principles.
The primary division of the produce of human exertion and frugality is, as we have seen, into three shares, wages, profits, and rent; and these shares are portioned out to the persons entitled to them, in the form of money, and by a process of exchange; or rather, the capitalist, with whom in the usual arrangements of society the produce remains, pays in money, to the other two sharers, the market value of their labour and land. If we examine, on what the pecuniary value of labour, and the pecuniary value of the use of land, depend, we shall find that it is on the very same causes by which we found that wages and rent would be
regulated if there were no money and no exchange of commodities.
It is evident, in the first place, that the law of Wages is not affected by the existence or non-existence of Exchange or Money. Wages depend on the ratio between population and capital ; and would do so if all the capital in the world were the property of one association, or if the capitalists among whom it is shared maintained each an establishment for the production of every article consumed in the community, exchange of commodities having no existence. As the ratio between capital and population, in all old countries, depends on the strength of the checks by which the too rapid increase of population is restrained, it may be said, popularly speaking, that wages depend on the checks to population; that when the check is not death, by starvation or disease ,wages depend on the prudence of the labouring people; and that wages in any country are habitually at the lowest rate, to which in that country the labourer will suffer them to be depressed rather than put a restraint upon multiplication.
What is here meant, however, by wages, is the labourer's real scale of comfort; the quantity he obtains of the things which nature or habit has made necessary or agreeable to him: wages in the sense in which they are of importance to the receiver. In the sense in which they are of importance to the payer, they do not depend exclusively on such simple principles. Wages in the first sense, the wages on which the labourer's comfort depends,
we will call real wages, or wages in kind. Wages in the second sense, we may be permitted to call, for the present, money wages; assuming, as it is allowable to do, that money remains for the time an invariable standard, no alteration taking place in the conditions under which the circulating medium itself is produced or obtained. If money itself undergoes no variation in cost, the money price of labour is an exact measure of the Cost of Labour, and may be made use of as a convenient symbol to express it.
The money wages of labour are a compound result of two elements: first, real wages, or wages in kind, or in other words, the quantity which the labourer obtains of the ordinary articles of consumption; and secondly, the money prices of those articles. In all old countries—all countries in which the increase of population is in any degree checked by the difEculty of obtaining subsistence—the habitual money price of labour is that which .will just enable the labourers, one with another, to purchase the commodities without which they either cannot or will not keep up the population at its customary rate of increase. Their standard of comfort being given, (and by the standard of comfort in a labouring class, is meant that, rather than forego which, they will abstain from multiplication), money wages depend on the money price, and therefore on the cost of production, of the various articles which the labourers habitually consume: because if their wages cannot procure them a given quantity of these, their increase will slacken, and their wages rise. Of these articles, food and other agricultural produce are so much the principal, as to leave little influence to anything else.
It is at this point that we are enabled to invoke the aid of the principles which have been laid down in this Third Part. The cost of production of food and agricultural produce has been analyzed in a preceding chapter. It depends on the productiveness of the least fertile land, or of the least productively employed portion of capital, which the necessities of r.E.
society have as yet put in requisition for agricultural purposes. The cost of production of food grown in these least advantageous circumstances, determines, as we have seen, the exchange value and money price of the whole. In any given state, therefore, of the labourers' habits, their money wages depend on the productiveness of the least fertile land, or least productive agricultural capital; on the point which cultivation has reached in its downward progress—in its encroachments on the barren lands, and its gradually increased strain upon the powers of the more fertile. Now, the force which urges cultivation in this downward course, is the increase of people; while the counter-force which checks the descent, is the improvement of agricultural science and practice, enabling the same soil to yield to the same labour more ample returns. The costliness of the most costly part of the produce of cultivation, is an exact expression of the state, at any given moment, of the race which population and agricultural skill are always running against each other.
§ 2. It is well said by Dr. Chalmers, that many of the most important lessons in political economy are to be learnt at the extreme margin of cultivation, the last point which the culture of the soil has reached in its contest with the spontaneous agencies of nature. The degree of productiveness of this extreme margin, is an index to the existing state of the distribution of the produce among the three classes, of labourers, capitalists, and landlords.
When the demand of an increasing population for more food cannot be satisfied without extending cultivation to less fertile land, or incurring additional outlay, with a less proportional return, on land already in cultivation, it is a necessary condition of this increase of agricultural produce, that the value and price of that produce must first rise. But as soon as the price has risen sufficiently to give to the additional outlay of capital the ordinary profit, the rise will not go on still further for the purpose of enabling the new land, or the new expenditure on old land, to yield rent as well as profit. The land or capital last put in requisition, and occupying what Dr. Chalmers calls the margin of cultivation, will yield, and continue to yield, no rent. But if this yields no rent, the rent afforded by all other land or agricultural capital will be exactly so much as it produces more than this. The price of food will always on the average be such, that the worst land, and the least productive instalment of the capital employed on the better lands, shall just replace the expenses with the ordinary profit. If the least favoured land and capital just do thus much, all other land and capital will yield an extra profit, equal to the proceeds of the extra produce due to their superior productiveness; and this extra profit becomes, by competition, the prize of the landlords. Exchange, and money, therefore, make no difference in the law of rent: it is the same as we originally found it. Bent is the extra return made to agricultural capital when employed with peculiar advantages; the exact equivalent of what those advantages enable the producers to economize in the cost of production: the value and price of the produce being regulated by the cost of production to those producers who have no advantages; by the return to that portion of agricultural capital, the circumstances of which are the least favourable.
§ 3. Wages and Rent being thus regulated by the same principles when paid in money, as they would be if apportioned in kind, it follows that Profits are so likewise. For the surplus, after replacing wages and paying rent, constitutes Profits.
We found in the last chapter of the Second Book, that the advances of the capitalist, when analyzed to their ultimate elements, consist either in the purchase or maintenance of labour, or in the profits of former capitalists; and that therefore profits in the last resort, depend upon the Cost of Labour, falling as that rises, and rising as it falls. Let
us endeavour to trace more minutely the operation cf this law.
There are two modes in which the Cost of Labour, which is correctly represented (money being supposed invariable) by the money wages of the labourer, may be increased. The labourer may obtain greater comforts; wages in kind—real wages—may rise. Or the progress of population may force down cultivation to inferior soils, and more costly processes; thus raising tie cost of production, the value, and the price, of the chief articles of the labourer's consumption. On either of these suppositions, the rate of profit will fall.
If the labourer obtains more abundant commodities, only by reason of their greater cheapness; if he obtains a greater quantity, but not on the whole a greater cost; real wages will be increased, but not money wages, and there will be nothing to affect the rate of profit. But if he obtains a greater quantity of commodities of which the cost of production is not lowered, he obtains a greater cost; his money wages are higher. The expense of these increased money wages falls wholly on the capitalist. There are no conceivable means by which he can shake it off. It may be said—it used formerly to be said—that he will get rid of it by raising his price. But this opinion we have already, and more than once, fully refuted.*
The doctrine, indeed, that a rise of wages causes an equivalent rise of prices, is, as we formerly observed, selfcontradictory: for if it did so, it would not be a rise of wages; the labourer would get no more of any commodity than he had before, let his money wages rise ever so much; a rise of real wages would be an impossibility. This being equally contrary to reason and to fact, it is evident that a rise of money wages does not raise prices; that high wages are not a cause of high prices. A rise of general wages falls on profits. There is no possible alternative.
Having disposed of the case in which the increase of money wages, and of
* Supra, book iii. ch. Iv. § 2, and eta. Xzt. 5 4.
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La più giovane vincitrice di American Idol, ha pubblicato quattro album in studio, vendendo oltre 12 milioni di copie, vincendo due BET Awards, un American Music Award, un NAACP Image Award e venendo candidata ai Grammy Award per la collaborazione No Air con Chris Brown.
Grazie alla vittoria del programma ha pubblicato il suo album di debutto, Jordin Sparks (2007), che ha ottenuto ampio successo internazionale, sostenuto dai singoli esordienti nella top ten della Billboard Hot 100 Tattoo e No Air. Quest'ultimo, in collaborazione con Chris Brown, è divenuto il maggior successo internazionale della cantante, facendole ottenere un Teen Choice Award, un People Choice Awards e venendo candidata al Grammy Award alla miglior collaborazione vocale pop.
Il secondo album in studio di Sparks, Battlefield (2009), ha esordito alla posizione numero 7 della classifica Billboard 200. Il singolo che dà il titolo all'album ha raggiunto la posizione numero 10 della Billboard Hot 100, rendendo Sparks l'unica concorrente di American Idol ad avere i suoi primi cinque singoli nella top 20 degli Stati Uniti. I successivi progetti dell'artista, Right Here Right Now (2015) e Cider & Hennessy (2020) ottengono un successo inferiore in termini di vendite, venendo tuttavia apprezzati dalla critica musicale.
Parallelamente alla carriera musicale, Sparks si è cimentata nella recitazione, dedicandosi alla televisione, apparendo nel corso degli anni in numerosi programmi e serie televisive, tra cui Big Time Rush, CSI - Scena del crimine, The View, RuPaul's Drag Race e The Masked Dancer. Ha inoltre recitato in film e cortometraggi, tra in Sparkle - La luce del successo (2012), The Inevitable Defeat of Mister and Pete (2013) e Left Behind - La profezia (2014), e a Broadway, nei musical In the Heights (2010) e in Waitress (2019).
Biografia
Jordin è nata a Phoenix, Arizona, da Philippi Sparks, giocatore di football afroamericano nella NFL e Jodi Wiedmanne, di origine tedesca-inglese. È cresciuta nei sobborghi di Ridgewood, nel New Jersey, mentre il padre giocava per i New York Giants. Sparks ha frequentato la Northwest Community Christian School di Phoenix fino alla terza media. Ha frequentato la Sandra Day O'Connor High School fino al 2006, dopodiché è stata educata a casa dalla nonna, Pam Wiedmann, per potersi concentrare meglio sul canto. Per tre anni consecutivi ha vinto il premio come miglior giovane artista dell'anno in Arizona.
2006-2010: American Idol, Jordin Sparks e Battlefield
Jordin ha partecipato e vinto la sesta edizione di American Idol. Dalle prime audizioni a Seattle, Washington, il suo percorso è stato lineare, con giudizi dei giudici per la maggior parte positivi.
Dopo la breve parentesi di un mini-album per iTunes, il primo album di Jordin è stato pubblicato negli Stati Uniti il 20 novembre 2007, dall'etichetta discografica della giovane, la 19 Recordings/Jive Records. L'album si intitola Jordin Sparks e contiene il singolo Tattoo, vero e proprio successo negli States e la hit a livello mondiale, No Air in collaborazione con la stella dell'hip-hop-R'n'B Chris Brown è il secondo singolo, ed è un altro grande successo. L'album debutta nella top ten americana e finora ha venduto poco più di 1 milione di copie. Segue il terzo singolo One Step At Time, che dona a Jordin la sua terza top 10 consecutiva in USA. In seguito a questi grandi successi, Jordin Sparks viene premiata come "Best New Artist" agli MTV Video Music Awards. Nel 2008 la cantante ha inoltre l'opportunità di esibirsi al Super Bowl con l'inno nazionale statunitense.
Nel 2009 inoltre apre il
The Circus: Starring Britney Spears, tour di Britney Spears. Precedentemente aveva aperto anche lAs I Am Tour di Alicia Keys e portato avanti un joint tour in compagnia di Jesse McCartney. Sempre nel 2009, Jordin Sparks ha l'opportunità di esibirsi davanti all'allora presidente degli USA Barack Obama.
Sempre nel 2009, Jordin Sparks pubblica il singolo Battlefield e riesce ad ottenere la quarta top 10 consecutiva in USA, piazzandosi alla numero 10 della Billboard Hot 100. Nelle settimane successive viene pubblicato l'album omonimo, il secondo nella carriera dell'artista. Il singolo ottiene un ottimo successo internazionale, tuttavia l'album non riesce ad ottenere alcuna certificazione. Seguono altri singoli ed un tour intitolato per l'appunto "Battlefield Tour". In questo stesso periodo, Jordin Sparks apre il Jonas Brothers World Tour 2009 dei Jonas Brothers e collabora con il cantante australiano Guy Sebastian nel brano "Like It Like That", che ottiene un buon successo in Nuova Zelanda e Australia. Successivamente, Jordin Sparks incide una cover del classico "Beauty And The Beast" e pubblica i singoli "The World I Knew", "Count On You" con i Big Time Rush e "I Am A Woman". Nel corso dell'anno partecipa all'evento VH1 Divas 2012 al fianco di Adele, Leona Lewis, Kelly Clarkson e Jennifer Hudson.
2011 - 2016: Cambio casa discografica e la carriera da attrice
Nel 2011, Sparks passa sotto il controllo della RCA Records a causa del fallimento della casa discografica precedente. Nello stesso periodo, la Sparks prende parte al remix ufficiale di It Girl, singolo dell'allora fidanzato Jason Derulo. Nell'autunno del 2011, Sparks ricopre il ruolo da protagonista nella sua prima pellicola cinematografica Sparkle - La luce del successo, diretta da Salim Akil, ispirata alla storia delle The Supremes, recitando al fianco di Derek Luke, Carmen Ejogo, Tika Sumpter e Whitney Houston. Nel corso delle riprese del film, Sparks e Houston interpretano numerosi brani, tra cui il brano Celebrate, registrata otto giorni prima della morte della Houston. La collaborazione viene successivamente riconosciuta con il Soul Train Music Award alla miglior interpretazione gospel e ai Black Reel Awards alla miglior canzone originale.
Successivamente alla partecipazione all'evento VH1 Divas 2012, al fianco di Kelly Rowland, Ciara e Miley Cyrus, Sparks recita al fianco di Jennifer Hudson, Anthony Mackie e Jeffrey Wright nel film The Inevitable Defeat of Mister and Pete, diretto da George Tillman Jr. e prodotto dalla casa di produzione di Alicia Keys. Nel 2013 Jordin torna a collaborare con Jason Derulo nel brano Vertigo ed appare inoltre nel video di Marry Me: Derulo dichiara di aver scritto sia questo brano che The Other Side dedicandole proprio alla Sparks. Nel medesimo anno, Jordin Sparks annuncia su Twitter la fine dei rapporti fra lei e la RCA Records: per tale ragione, il terzo album di Jordin Sparks non verrà mai rilasciato sebbene la cantante avesse annunciato che il progetto fosse stato ultimato.
Nel 2014 viene scelta nel cast del film Left Behind - La profezia con Nicolas Cag, recitando con Nicolas Cage, Lea Thompson e Nicky Whelan. Dopo aver pubblicato il brano I Wish We'd All Been Ready per la colonna sonora del film, Jordin Sparks pubblica un mixtape intitolato Left Felicia sulla piattaforma Soundcloud. Viene successivamente annunciato che Jordin Sparks sarebbe entrata a far parte della casa discografica fondata dal produttore Salaam Remi, restando dunque all'interno della Sony Music.
Il 25 novembre 2014 viene annunciata la pubblicazione dell'album Right Here Right Now, prevista per il 2015. Il 24 febbraio 2015 viene pubblicato il singolo Double Tap in collaborazione con 2 Chainz. L'album, pubblicato il 21 agosto 2015, viene accolto tiepidamente dalle classifiche, esordendo alla posizione numero 161 della Billboard 200 e 11 della US R&B/Hip-Hop Albums. Successivamente alla sua pubblicazione Sparks lascia anche la casa discografica di Remi.
2017–presente: Broadway e il quarto album in studio
Nel maggio 2018, Sparks e il marito Dana hanno iniziato la produzione dello speciale televisivo riguardo alla loro famiglia, denominato Jordin Sparks: A Baby Story per Lifetime. Nell'agosto 2018, KIN Network ha pubblicato una serie web, Heart of Batter with Jordin Sparks, incentrata sull'amore di Sparks per la pasticceria.
Tra settembre ed ottobre 2019 Sparks torna a recitare a Broadway nello spettacolo Waitress, ideato dalla cantante e compositrice Sara Bareilles. Nel corso dello stesso anno ha pubblicato un EP congiunto con il cantante R&B Elijah Blake intitolato 1990 Forever. Successivamente l'artista partecipa al brano House Party insieme ai New Kids On The Block, Naughty By Nature, Big Freedia, Boyz II Men.
Il 2 giugno 2020, dopo oltre cinque anni di assenza come artista solista, Sparks pubblica il singolo "Unknown". Il 31 luglio 2020 ha pubblicato unsecondo singolo, "Red Sangria", attraverso la Red Bull Records. Il 14 agosto 2020 viene pubblicato l'EP Sounds Like Me, che include i due singoli precedenti. Nel dicembre 2020 pubblica il quarto album in studio di musica natalizia, intitolato Cider & Hennessy.
Nel 2021, Sparks ha partecipato al programma The Masked Dancer, interpretando il personaggio Exotic Bird, classificandosi al quinto posto. Nello stesso anno torna a recitare nel film televisivo A Christmas Treasure e doppia il personaggio di Tabitha nella serie animata I Rugrats.
Vita privata
Nel 2011 Sparks si è legata sentimentalmente con il cantante e ballerino Jason Derulo. La cantante ha affermato che la sua scelta di fidanzarsi con Derulo portò a diversi scontri con la sua famiglia, soprattutto sul piano religioso, in quanto associati alla Chiesa Evangelica. La relazione termina nel 2014.
Nel 2017, Jordin Sparks ha sposato il modello Dana Isaiah. I due hanno dato alla luce il loro primo figlio, Dana Isaiah Thomas Jr., nel 2018.
Filantropie e controversie
Organizzazioni umanitarie e prevenzione alle malattie
Nel febbraio 2008, Sparks si è recata in Ghana con l'associazione Malaria No More, un'organizzazione fondata da George W. Bush, con l'obiettivo di porre fine alle morti per malaria in Africa entro il 2015. Nel corso della missione si è esibita con il brano Amazing Grace di fronte alla delegazione dei capi tribù ganesi, riuniti per accogliere la first lady degli Stati Uniti Laura Bush. Sempre nel 2008, Sparks ha sostenuto la campagna Do Something 101 di Dosomething.org filmando un annuncio di servizio pubblico che spiegava il progetto di raccolta di materiale scolastico a livello nazionale.
Nel febbraio 2010, Sparks è stata una dei tanti artisti che hanno contribuito a We Are the World 25 for Haiti, un singolo di beneficenza per le vittime del terremoto di Haiti del 2010. Per la stessa causa Sparks ha collaborato con il creatore e designer di Pennyroyal Silver, Tim Foster, per creare il suo personale design di collane per la collezione firmata dell'azienda, il cui ricavato finanzia le unità mediche predisposte per aiutare la popolazione haitiana.
Nel 2018, successivamente alla morte della sorellastra Bryanna Jackson-Frias per la falcemia all'età di sedici anni, Sparks ha collaborato con la compagnia assicurativa Aflac, associazione che finanzia le ricerche scientifiche per i tumori infantili e le malattie del sangue come l'anemia drepanocitica.
Diritti civili
Sparks è sostenitrice dei diritti civili, sostenendo le organizzazioni che si oppongono al razzismo negli Stati Uniti d'America, tra cui il movimento Black Lives Matter. In una discussione al Time 100 Talks, con il direttore esecutivo della rivista Time Dan Macsai, Spark ha dichiarato:
La cantante sostiene la comunità LGBT, sostenendo i diritti LGBT negli Stati Uniti d'America, esibendosi nel corso di numerose parate del Pride.
Influenze musicali
Sparks ha raccontato di essere stata influenzata dalla musica R&B degli anni '90, in particolar modo da artisti quali Mariah Carey, Céline Dion, Christina Aguilera, Brandy, Boyz II Men, Babyface e Whitney Houston. La cantante ha citato tra le influenze musicali anche Nat King Cole, Martina McBride.
Successivamente alla morte di Whitney Houston, avvenuta tre mesi dopo la fine delle riprese del film Sparkle - La luce del successo in cui le due artiste recitavano assieme, Sparks ha raccontato l'influenza che ha avuto nella sua carriera:
Discografia
Album in studio
2007 - Jordin Sparks
2009 - Battlefield
2015 - Right Here, Right Now
2020 - Cider & Hennessy
EP
2006 - For Now
2007 - Jordin Sparks
2020 - Sounds Like Me
Mixtape
2014 - #ByeFelicia
Singoli
2007 - This Is My Now
2007 - Tattoo
2008 - No Air (featuring Chris Brown)
2008 - One Step at a Time
2009 - Battlefield
2009 - S.O.S. (Let the Music Play)
2010 - Don't Let It Go to Your Hand
2011 - I Am Woman
2012 - Celebrate (con Whitney Houston)
2014 - It Ain't You
2015 - Double Tap
2015 - Right Here Right Now
2015 - They Don't Give
2020 - Unknown
2020 - Red Sangria
Collaborazioni
Count On You - Big Time Rush ft. Jordin Sparks
Filmografia
Cinema
2012 - Sparkle - La luce del successo (Sparkle), regia di Salim Akil
2013 - The Inevitable Defeat of Mister and Pete (The Inevitable Defeat of Mister & Pete), regia di George Tillman Jr.
2014 - Left Behind - La profezia (Left Behind), regia di Vic Armstrong
2018 - Show Dogs - Entriamo in scena (Show Dogs), regia di Raja Gosnell - voce
Televisione
2007 - American Idol - programma televisivo, vincitrice stagione 6
2009 - Zack e Cody sul ponte di comando (The Suite Life on Deck) - serie TV, episodio 2x10
2010 - Big Time Rush - serie TV, episodio 1x16
2013 - Dear Secret Santa - film TV
2013 - CSI - Scena del crimine (CSI: Crime Scene Investigation) - serie TV, episodio 14x09
2015 - America's Next Drag Queen (RuPaul's Drag Race) - programma televisivo, giudice stagione 7
2017 - The Real O'Neals - serie TV, episodio 2x13
2018 - Jordin Sparks: A Baby Story - speciale TV, 1 episodio
2021 - A Christmas Treasure - film TV
2021 - I Rugrats - serie animata, voce
Webserie
2018 - Heart of Batter with Jordin Sparks - speciale TV, 3 episodi
Teatro
Broadway
2010 - In the Heights, musiche e testi di Lin-Manuel Miranda
2019 - Waitress, musiche e testi di Sara Bareilles
Riconoscimenti
American Music Award
2008 – Miglior artista adult contemporary
BET Awards
2008 – Miglior canzone d'amore per No Air
2008 – Candidatura al Viewer's Choice Award per No Air
2008 – Beautiful Face Award
Grammy Award
2009 – Candidatura alla miglior collaborazione vocale pop per No Air
MTV Video Music Awards
2008 - Candidatura al miglior video di un'artista femminile per No Air
2008 – Candidatura al miglior artista esordiente
NAACP Image Award
2008 – Miglior artista esordiente
2009 – Candidatura alla miglior collaborazione per No Air
People's Choice Awards
2009 – Miglior collaborazione per No Air
2009 – Candidatura alla canzone preferita per No Air
Soul Train Music Award
2013 – Miglior interpretazione gospel per Celebrate
Teen Choice Award
2007 – Candidatura al miglior personaggio di un reality televisivo
2008 – Miglior canzone per un appuntamento romantico per No Air
2008 – Candidatura alla miglior canzone d'amore per No Air
2008 – Candidatura al miglior artista esordiente
Note
Altri progetti
Collegamenti esterni
American Idol
Personaggi televisivi statunitensi
Attori afroamericani
Vincitori di talent show
Attori teatrali statunitensi | {
"redpajama_set_name": "RedPajamaWikipedia"
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Q: Retrieving data from URL fails I have been trying different ways to get data from the following link:
http://www.ensembl.org/Danio_rerio/Export/Output/Location?db=core;flank3_display=300;flank5_display=300;output=fasta;r=18:19408965-19409049;strand=feature;coding=yes;cdna=yes;peptide=yes;utr3=yes;exon=yes;intron=yes;genomic=unmasked;utr5=yes;_format=Text
Copy paste the link to a web browser works for me but I cannot get to it programmatically in java.
It seems that it doesn't follow the get protocol as the separation of parameters is not as expected.
I tried to use URL but it separates the link above into server path and query and results in HTTP 500.
I tried to use sockets but again failed.
I believe that what I need is a way to simply send the complete string unaltered and then read the result.
Any ideas?
A: This code reads first line from that URL successfully:
URL u = new URL("http://www.ensembl.org/Danio_rerio/Export/Output/Location?db=core;flank3_display=300;flank5_display=300;output=fasta;r=18:19408965-19409049;strand=feature;coding=yes;cdna=yes;peptide=yes;utr3=yes;exon=yes;intron=yes;genomic=unmasked;utr5=yes;_format=Text");
DataInputStream ds = new DataInputStream(u.openStream());
String s = ds.readLine();
System.out.println(s);
It prints out: >18 dna:chromosome chromosome:Zv9:18:19408665:19409349:1
| {
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Are you an experienced temps Recruiter looking for a fresh start? Perhaps you'd like greater work / life balance or to join a firm where you can gain long term progression? Maybe you would just like to work somewhere where your efforts are truly appreciated and rewarded. If so, a shining light in the world of finance recruitment is now expanding their team and would love to meet you.
With the backing of a true entrepreneur this firm enjoys modern leadership with the Directors believing in leading by example and being very hands on in terms of their support for their team. You won't find KPI management here - just a proactive, modern and highly consultative approach with clients and candidates in an environment where everyone if encouraged to be themselves and recruit in their own style.
Working closely with the business Director and as part of a wider team of c15, you will have access to their impressive client base spanning FS (not corporate, PSL led clients), industry & commerce and NFP/charities. You will be responsible for temp and interim placements mainly into the C&I clients. The Director here manages the permanent positions across these clients and will instantly pass over all temp/interim requirements to you which you will earn full commission on.
Renowned for their really unique recruitment strategies and smart matching technologies, this business enjoy a high level of repeat business and extremely valuable candidate referrals - so the set up here is really different to a typical accountancy & finance agency!
Team work and a high degree of collaboration is really important to this business, so you will have a steady stream of leads and candidates being passed over from your co-workers - so in order to fit in here, you must be somebody who is prepared to work as part of a wider team and also be prepared to have a lot of fun in the office!
So if it's time for you to make a move into a more progressive, rewarding and quality orientated firm in London, this opportunity will offer you greater autonomy AND greater work/life balance.
For more information or to arrange a time to confidentially explore this career enhancing opportunity please get in touch with Tara Lescott today. | {
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Q: Jmeter-Webdriver Webdriver Sampler - How to execute a script in HtmlUnitDriver? My Jmeter-webdriver webdriver sampler script is executed finely on chrome browser, whereas when same script is executed the on htmlunitdriver it throws an error.
To configure a HtmlUnitdriver followed the steps:-
Thread Group > Add > Listener > jp@gc- HtmlUnitDriver Config
2016/12/23 14:26:51 ERROR - com.googlecode.jmeter.plugins.webdriver.sampler.WebDriverSampler: com.gargoylesoftware.htmlunit.ScriptException: TypeError: Cannot find function addEventListener in object [object Window]. (https://test.html
Build info: version: '2.52.0', revision: '4c2593d28', time: '2016-02-11 11:22:43'
System info: host: 'EN09', ip: '192.168.254.2', os.name: 'Windows 7', os.arch: 'amd64', os.version: '6.1', java.version: '1.8.0_111'
Driver info: driver.version: HtmlUnitDriver
Please let me know how to run Webdriver sampler script on Htmlunitdriver successfully
A: Quick checklist:
*
*Are you able to run something "minimal" successfully, i.e.:
WDS.sampleResult.sampleStart()
WDS.browser.get('http://example.com')
WDS.sampleResult.sampleEnd()
If the answer is "No" - it may be installation issue, I would recommend reinstalling the Selenium/WebDriver Support plugins bundle via JMeter Plugins Manager:
*Are you able to execute your test using HtmlUnitDriver from Java code (without JMeter)?
If the answer is "No" - check if the issue is present here: https://sourceforge.net/p/htmlunit/bugs/ and if not - report it.
*If you can run your test scenario from Java and not able to run it with JMeter - report it to JMeter Plugins forum
The viable workaround for headless Selenium tests execution using JMeter is PhantomJS Driver
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,223 |
'use strict';
module.exports = object => {
const result = {};
for (const [key, value] of Object.entries(object)) {
result[key.toLowerCase()] = value;
}
return result;
};
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,309 |
{"url":"https:\/\/nathanpjones.com\/2016\/02\/remote-debug-gpio-on-raspberry-pi\/","text":"# Remote Debug GPIO on Raspberry Pi\n\nRecently I\u2019ve been getting into embedded Linux, particularly the Raspberry Pi and have consequently been learning Python. I really don\u2019t like programming directly on these small devices since the environment is typically spare and slow.\n\nAt first I used Cyberduck to open and update files along with a text editor. That became exhausting particularly as my project began to grow and span multiple directories. It was also a lot of Alt+Tabbing back and forth between Cyberduck, the text editor, and PuTTY.\n\nWhat I really needed was something that I could work on in my main dev environment but deploy and execute on the RPi. This is particularly important to me since my RPi is way out in the garage. It also needed to be able to run as root because all RPi GPIO requires root privileges.\n\nI decided on PyCharm, since I have a JetBrains Toolbox subscription and I\u2019m familiar with CLion which uses the same base IDE framework. Most importantly, PyCharm has a remote debugging feature which coupled with automatic deployment makes everything super easy.\n\n### Setting Up Remote Debugging\n\nBelow is how I set up my environment. Much of this is found in the PyCharm help documentation. You can find how to set up remote debugging particularly the section on setting up a remote interpreter via SSH.\n\n#### Automatic Deployment\n\nFirst we need to setup automatic deployment of our files to the RPi. This part isn\u2019t strictly required but if you don\u2019t do it you\u2019ll have to manage uploading your changes.\n\n1. Create a new project called RemoteDebugEx.\n2. Click on File -> Settings. Then go to Editor -> Code Style and change line endings to \u201cUnix and OS X (\\n)\u201d. You want this since your target environment is Linux and different line endings may cause issues.\n\n3. Click on Tools -> Deployment -> Configuration.\n4. Add a new SFTP connection called \u201cMy RPi\u201d. This will use SSH to copy files to and from the Pi.\n5. Provide connection settings. You can use a server name or IP address.\n6. Press the \u201cTest SFTP connection\u2026\u201d button to make sure everything is correct. You may be prompted to accept the new fingerprint. Click Yes.\n7. Set paths to say where we want to keep this on our remote. You can choose temporary or permanent locations. (I use temporary, but PyCharm\u2019s sync features allow you to make changes on the RPi and download them back to your computer.)\n8. Now click Tools -> Deployment -> Automatic Upload. This makes it so files will automatically upload whenever you save.\n\n#### Remote Interpreter\n\nThe next task is to set up a remote interpreter. In this section I\u2019ll also show you how to download changes you make on the Pi.\n\n1. Now we need a virtual environment on the remote. Create an empty requirements.txt file. Save and it should be uploaded automatically. This also creates the remote debug folder.\n2. Log into the Pi using SSH (I like PuTTY but there are other options). We should be able to see our newly uploaded file.\n[shell]ls \/home\/pi\/remote_debug\/remote_debug_ex[\/shell]\n3. Create the virtual environment. First make sure virtualenv is installed.\n[shell]sudo pip install virtualenv[\/shell]\nThen navigate to your project root folder on the remove and create the virtual environment.\n[shell linenumbers=\"false\"] cd \/home\/pi\/remote_debug\/remote_debug_ex virtualenv venv source venv\/bin\/activate pip install RPi.GPIO pip freeze > requirements.txt [\/shell]\n4. Now you want to get the updated requirements.txt file back to your computer. Right click the file and choose \u201cSync with Deployed to My RPi\u2026\u201d. You\u2019ll see a compare dialog that allows you to copy the file back to your computer.\n\n5. The next step is to add the virtual environment as a project interpreter. Click on File -> Settings.\n6. Then go to Project: RemoteDebugEx -> Project Interpreter. Click the gear icon and choose Add Remote.\n7. Choose to use SSH credentials and enter your host and login information. For \u201cPython interpreter path\u201d, choose the \u201cpython\u201d file within your virtual environment folder.\n\nImportant: The login you use here is the credentials that the remote process will be run as. You can use the \u201cpi\u201d user, as we have another way of gaining root privileges to access GPIO detailed below.\n\n#### Run Configuration\n\nStill with me? Now that we\u2019ve got deployment set up and an interpreter that will use our remote virtual environment, the final step is to create a run configuration to actually run a script.\n\n1. Create a simple python script and call it hello_world.py. Give it the following contents.\n[python linenumbers=\"false\"] import RPi.GPIO print \"hello world!\" [\/python]\n2. Click in the upper right of the main window and choose \u201cEdit Configurations\u2026\u201d.\n3. Click the plus button and choose Python.\n4. Give the new configuration the name \u201chello_world (remote)\u201d. For the script, choose the script we just created. For Python interpreter, choose the remote interpreter we created in the last section.\n5. Now add a path mapping to map from your local project path to the remote path. This lets the interpreter find the source file for what\u2019s executing remotely.\n\n6. Save the new configuration and click the run button. You should see PyCharm connect and the hello world print on the debug console.\n\n#### Running as Root\n\nRather than enabling logging in as root over SSH, there\u2019s another approach that will work without opening that security hole. Using permissions, we can cause our python interpreter to simply run as root.\n\n1. Reconnect using PuTTY and navigate to the project root folder.\n[shell]cd \/home\/pi\/remote_debug\/remote_debug_ex[\/shell]\n2. Change ownership of the python interpreter to root and cause it to be executed as its owner whenever it\u2019s run.\n[shell linenumbers=\"false\"] sudo chown -v root:root venv\/bin\/python sudo chmod -v u+s venv\/bin\/python [\/shell]\n\nThis will cause pip to act a bit funny when you want to install anything later on so just reverse the above changes from step 2 as needed. Just use the same commands but with pi instead of root and with u-s.\n\nI have a couple of scripts that I keep in the project root for just this purpose. You can download them here.\n\n### Conclusion\n\nNow you have a way to remote debug your RPi with the interpreter running as root, allowing access to the Pi\u2019s GPIO. You can do this with multiple projects and even have multiple projects or instances of projects open and debugging remotely.\n\nPyCharm is a great IDE and I encourage you to look into using it to improve your development environment. For example, check out Zeal and the Dash plugin that will cause PyCharm to perform a documentation lookup when you press Ctrl+Shift+D. There are also plugins to provide support for Markdown and bash scripts.\n\n## 12 thoughts on \u201cRemote Debug GPIO on Raspberry Pi\u201d\n\n1. Very helpful. Thank you so much..\n\n2. Mike Knoblock\n\nThis is a great post; but I got lost along the way. I had to back up to where pip failed to install RPi.GPIO:\n\nsudo pip uninstall RPi.GPIO\n\nthen install python-dev (I am running debian jessie lite):\n\nsudo apt-get update\nsudo apt-get install -t jessie python-dev\n\nthen the install for GPIO was successful. However, when I ran it remotely from PyCharm, the console said \u2018no module named RPi.GPIO\u2019. I ran SSH into the pi and I ran hello_world.py without a problem. Seems PyCharm is trying to run this script from a different location (venv\/bin), and sure enough, the script does not work from there over SSH for me either.\n\nI\u2019m fuzzy on this virtual env thing. Do you need it?\n\nthanks for any help!!!\n\nMike\n\n3. Nathan Jones\n\n@Mike: Thanks for the question. There are a lot of details to the setup so you do have to be careful. When you\u2019re setting up the remote interpreter you have to make sure you set the interpreter path correctly. Look closely again at the last step in the \u201cRemote Interpreter\u201d section. It\u2019s also possible that I missed something in the instructions so let me know if you still have problems.\n\nYou don\u2019t technically need to run using virtual environments but many people use them as a matter of course. It\u2019s an alternative to installing all dependencies globally. You have one place where you can see all the dependencies for the project including which version of python. This makes sure things will run correctly when you have several projects that may need different versions of the same package. It also makes it easy to uninstall a project since it and all of its dependencies are co-located.\n\n4. Mr. Jones:\n\nOn this part of your instructions you never mentioned WHERE do I create this file: requirements.txt? in Pycharm or in RPi using putty? also in which folder? Inside or outside RemoteDebugEx?\n\nYOU WROTE:\nRemote Interpreter\nThe next task is to set up a remote interpreter. In this section I\u2019ll also show you how to download changes you make on the Pi.\n\nNow we need a virtual environment on the remote. Create an empty requirements.txt file. Save and it should be uploaded automatically. This also creates the remote debug folder\n\n5. Nathan Jones\n\nPut it in the root folder of the project. It\u2019s a python convention. You pip freeze your list of packages into requirements.txt and then pip later consumes that file to restore your packages in the virtual environment.\n\n6. Nathan\n\nQuick question: Can you do this just using a Python2.7 on RPI? I have a GUI python script and I am having difficulty running it as root. Is this why you are using a virtual environment? Please, let em know.\n\n7. Nathan Jones\n\nThe virtual environment is so you can set just that project\u2019s copy of python to automatically run as root. You wouldn\u2019t want your system\u2019s python to always run as root.\n\nThere\u2019s not really any magic to this setup. All that\u2019s really going on in the background is PyCharm is logging in via SSH, uploading some debugging helpers, and executing Python in debug mode.\n\nI\u2019m not sure you could remote debug a GUI app though since that would need to be started in a context where the GUI could be shown. Unless your UI is web-based there aren\u2019t any easy options.\n\n8. Ren\u00e9 R.\n\nWhat a great tutorial, without any pitfalls! It works like a charm and is fun to follow them. Thanks a lot!\n\n9. reza\n\nhi Nathan you write an awesome tutorial.\nthank you\n\nafter all works, when i want to run the programm remotely , i get an bellow error,\n\u201c\u201d\u201d\u201d\u201d\u201d\u201d\u201d\u201d\u201d\u201d\u201d\nError running \u2018hello_world(remote)\u2019: Cannot run program \u201cssh:\\pi@192.168.43.25:22\\home\\pi\\remote_debug\\remote_debug_ex\\venv\u201d (in directory \u201cC:\\Users\\reza\\PycharmProjects\\RemoteDebugEx\u201d): CreateProcess error=2, The system cannot find the file specified\n\u201c\u201d\u201d\u201d\u201d\u201d\u201d\u201d\u201d\u201d\u201d\u201d\n\n10. reza\n\nin section \u201cRemote Interpreter\u201d and step 7\nwhen i set the \u201cPython interpreter path\u201d to \u201c\/home\/pi\/remote_debug\/remote_debug_ex\/venv\u201d\nit shows me an error and said : \u201c\u201dCan\u2019t create python SDK, Interpreter \u2018\/home\/pi\/remote_debug\/remote_debug_ex\/venv\u2019 doesn\u2019t exist on remote server\u201d\n\n11. Max\n\nHi, thanks for the great tutorial!\n\nI have a question about module usage though, how do I import modules so that they are available in pycharm as well? I tried to install an adafruit DHT module, and I couldn\u2019t get it to work but the next day somehow pycharm could find it.\n\nBut now that I need another module, I just can\u2019t get it to work.\n\nIt seems that smbus is available on the pi, but not when I\u2019m in pycharm :\nhttps:\/\/i.imgur.com\/0ohmz0F.png\n\nI tried to make it available via :\n\ncd \/home\/pi\/remote_debug\/remote_debug_ex\nsource venv\/bin\/activate\nsudo apt-get install python-smbus\npip freeze > requirements.txt\n\nBut as you can see in the image, it was already installed.\nHow would you sync dependencies and make them available both to pycharm and the pi?\n\nThanks again\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed.","date":"2021-06-13 17:02:37","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2421654313802719, \"perplexity\": 3340.6317186676524}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623487610196.46\/warc\/CC-MAIN-20210613161945-20210613191945-00468.warc.gz\"}"} | null | null |
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Marriage Going Boom Among Boomers?
On behalf of The Marks Law Firm, L.L.C. posted in Divorce on Wednesday, March 14, 2012
One Baby Boom generation anthem declares that they were born to be wild. Another shouts that they can't get no satisfaction. Both statements might be true when it comes to Boomers and marriage, a new study indicates.
Divorce rates among people aged 50 and over doubled between the years 1990 and 2009, according to "The Gray Divorce Revolution" study.
In 2009, one in four U.S. divorces involved couples over the age of 50.
One family law attorney interviewed for a news article on the study noted that because people are getting married and having families later in life, they're also getting divorced later in life.
"If they are marrying at 35 and divorcing once the kids are almost out of the house, that means a divorce at 50. When people were getting married in their 20s, it used to mean a divorce at 35 or 40," she said.
She also said that for people who are bored with their partner, the internet makes romantic possibilities outside of marriage "just a couple of clicks away," making divorce among older couples more likely.
The two main factors in most divorces, regardless of the couple's age, are children and finances, she said.
Older couples are typically past the age of difficult child custody disputes, but often have financial ties that can be difficult to untangle in a divorce.
"You've often got real estate, a 401(k), an IRA, perhaps a business started during the marriage, and more. Sorting it out and ensuring that both parties are set up equally for retirement can be difficult."
That's exactly why it's wise for a person considering divorce to contact as soon as possible an experienced family law firm in order to discuss their legal options.
Source: Fox Business: "The Boomer's Guide to Divorce," Kathryn Tuggle, March 7, 2012
PrevPreviousPost-divorce daters beware: Online scams booming
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MOVE IN READY $4000. in closing costs (with preferred lender and attorney) Beautiful Roanoke plan! Walk in to your open 2 story foyer, and walk out in to your relaxing covered patio. This home has Stainless steel appliances, tile backsplash, granite countertops, and smart home technology. Home includes Merv 11 Hvac for exquisite air filtration. You will LOVE this home! Incentive with the use of preferred lender and attorney. See docs for incentive details.
Please have an Agent contact me about MLS#: 2216232 44 Jonalker Court, Clayton. | {
"redpajama_set_name": "RedPajamaC4"
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Leclerc reveals secret of qualifying approach tweak
After qualifying nearly seven-tenths adrift of his team mate Sebastian Vettel's pole time at the Canadian Grand Prix, Ferrari's Charles Leclerc fronted up about his need to improve his Q3 performances. And having put himself third on the grid as the fastest Ferrari last time out at Paul Ricard, Leclerc revealed the small qualifying tweak he'd made that could be a game changer for his Saturdays.
In France, Leclerc was the only driver to get within a second of the two Mercedes runners – albeit over six-tenths adrift of Lewis Hamilton's pole time – before converting his third place grid slot to the same position in the race, and harrying second-placed Valtteri Bottas in a thrilling final lap chase between the pair.
READ MORE: The favourites for pole, points and victory in Austria
So, what had been the key to that impressive qualifying performance at Paul Ricard?
"Overall, I think [I changed] the approach for the set-up to try and anticipate the track evolution," said Leclerc. "On some tracks, it's bigger than others, and I think most of the time when the track evolution was quite big, I was not in the best place, or not in the place I wanted to be for Q3. I felt quite good in Q1, Q2 was worse, Q3 was even worse. So now I just tried to analyse that to understand what I have to live with in Q1 to have the car I wanted in Q3, and it worked."
I love the Red Bull Ring. It's one of my favourite tracks actually
France represented the first time Leclerc had qualified ahead of his team mate since securing his maiden career pole in Bahrain back in March. And the Monegasque revealed that he was looking forward to putting his newfound qualifying mind-set into practice around one of his favourite tracks this weekend, having been on pole and won at the Red Bull Ring in both GP3 and Formula 2 during his junior career.
"I love it," said Leclerc of the Spielberg circuit, where last year he finished P9 for Sauber. "It's one of my favourite tracks, actually. I really enjoy having the short track – it reminds me a little bit of the karting days… I just enjoy driving here."
Leclerc's affection for the Red Bull Ring could pay particular dividends this weekend, with Ferrari expected to be far more competitive relative to Mercedes than they were at Paul Ricard, given that the short, power-rewarding Austrian track should play to the SF90's straight-line speed advantage and medium-speed corner ability.
Alfa Romeo to replace Technical Director Resta with Head of Aero
Sainz: McLaren need low-speed performance gains to keep Renault at bay
Tickets for the 2020 Vietnam Grand Prix on sale now! | {
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John Price (29 August 1918 – 18 April 2013) was an English professional footballer born in Horden, County Durham, who played in the Football League in the 1930s for Hartlepools United and York City. He played as a forward.
References
1918 births
2013 deaths
People from Horden
Footballers from County Durham
English footballers
Association football forwards
Portsmouth F.C. players
Wolverhampton Wanderers F.C. players
Hartlepool United F.C. players
York City F.C. players
English Football League players | {
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Q: How to fix "TypeError: unsupported operand type(s) for &: 'list' and 'list'" using numpy.where() with python? I have a csv table with many columns, including a column named "blend" and a column named "hires."
Blend has elements like 'N', 'Y unpub NAME', and 'Y? unnpub NAME.'
Hires has elements like 'N', 'redo;NAME OF TELESCOPE', and 'NAME OF TELESCOPE.'
I want a list (called 'known_binary') where the following conditions are true: blend=='Y' & hires!='N' & hires!='redo'.
(I'll be making other lists with other combinations of those possibilities like a list where: blend=='Y?' & (hires=='N' | hires=='redo').
I know how to have python just look at either the first letter of the element, or first four letters, etc..
(for example, this works without error):
redo = np.where([x[0:4]=='redo' for x in hires])[0]
But, when I put multiple things in np.where() it doesn't work:
file = pandas.read_csv('file location')
blend = file["blend"]
hires = file["hires"]
known_binary = np.where(([x[0]=='Y' for x in blend]) & ([x[0]!='N' for x in hires]) & ([x[0:4]!='redo' for x in hires]))[0]
I get the error: "TypeError: unsupported operand type(s) for &: 'list' and 'list'"
I just want a list of indices (might be the wrong wording, sorry) where the conditions I stated are true.
If the elements in the hires column (for example) were just "redo" and not "redo;name of specific telescope" I wouldn't be having any issue.
I know how to do some specific stuff in python for astronomy, but overall I have VERY little understanding of how all of this stuff works.
Thanks in advance!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,944 |
Taylor Aitken | Banks – Do they do their best for SMEs ?
They thought they got away with it ! Owed Money ?
Are you getting what you require from your Bank or are they causing issues for SMEs? A recent article in the Insolvency News cites that RBS may potentially have a huge claim against them from SMEs. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,392 |
{"url":"https:\/\/ee.gateoverflow.in\/923\/gate2018-ga-4","text":"0 votes\n\nFor what values of $k$ given below is \u00a0$\\dfrac{(k + 2)^2}{(k - 3)}$ an integer?\n\n1. $4 , 8 , 18$\n2. $4 , 10 , 16$\n3. $4 , 8 , 28$\n4. $8 , 26 , 28$\n\nedited\n\n## 1 Answer\n\n0 votes\n\nWe'll try and eliminate the\u00a0wrong options\n\nwhen K = 4\u00a0 ==>\u00a0 \u00a0$\\dfrac{(4 + 2)^2}{(4 - 3)}$ = 36 (integer)\n\nwhen K = 8\u00a0 ==>\u00a0 \u00a0$\\dfrac{(8 + 2)^2}{(8 - 3)}$ = $\\dfrac{(100)}{(5)}$ = 20 (integer)\n\nwhen K = 10\u00a0 ==>\u00a0 \u00a0$\\dfrac{(10 + 2)^2}{(10 - 3)}$ = $\\dfrac{(144)}{(7)}$ = 20.57 (not an integer)\n\nwhen K = 16\u00a0 ==>\u00a0 \u00a0$\\dfrac{(16 + 2)^2}{(16 - 3)}$ = $\\dfrac{(324)}{(13)}$ = 24.92 (not an integer)\n\nwhen K = 18\u00a0 ==>\u00a0 \u00a0$\\dfrac{(18 + 2)^2}{(18 - 3)}$ = $\\dfrac{(400)}{(15)}$ = 26.66 (not an integer)\n\nwhen K = 26\u00a0 ==>\u00a0 \u00a0$\\dfrac{(26 + 2)^2}{(26 - 3)}$ = $\\dfrac{(784)}{(23)}$ = 34.08 (not an integer)\n\nwhen K = 28\u00a0 ==>\u00a0 \u00a0$\\dfrac{(28 + 2)^2}{(28 - 3)}$ = $\\dfrac{(900)}{(25)}$ = 36 (integer)\n\nBy Verifying all the options we found out the correct option as C) 4, 8, 28\n\nby (720 points)\nAnswer:","date":"2019-12-13 16:11:49","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6578617691993713, \"perplexity\": 11176.803152112412}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-51\/segments\/1575540564599.32\/warc\/CC-MAIN-20191213150805-20191213174805-00226.warc.gz\"}"} | null | null |
\section{Introduction}\label{introduction}
The Internet has emerged as an integral part of our lives, which has gone far beyond its original use for connecting computers, and now also inter-connects mobile phones, devices, and everything. The traffic from wireless and mobile devices will exceed that from wired devices by 2019 \cite{cisco2015cisco}. By the same year, WiFi and mobile devices will account for 66\% of IP traffic. According to \cite{Ericsson2013report}, we spend 90\% of our time indoor and 80\% of the mobile Internet access traffic happens indoor \cite{Alcatel2015inbuilding,Cisco2015service}. This percentage will only increase as 54\% of the cellular traffic is expected to be offloaded to WiFi by 2019 \cite{index2015global}. It is expected that 87\% of the companies would switch providers by 2019 for better indoor coverage \cite{Alcatel2015inbuilding}.
Relying on cellular networks alone to satisfy such demand is not a viable solution, because the size of the cell can not be decreased in an arbitrary fashion due to the backhaul challenge \cite{chia2009next} and the increased cost of building and maintaining the system. This fact puts pressure on indoor networks to support the insatiable demand for wireless Internet access.
To alleviate the problems of system construction and maintenance, and to enhance spectrum reusability, innovative approaches need to be adopted, among which visible light communication (VLC) is an excellent candidate. The emergence and the commercialization of power line communication concept \cite{tsuzuki2012feasibility,tonello2008challenges}, makes it easy and attractive to add a driver circuit to perform modulation functionality between the light source and the power cables and utilize VLC with very small one-time cost based on the available indoor infrastructure. Benefiting from the short transmission range and unlicensed wide bandwidth, VLC technology provided with LED devices is characterized by high area spectral efficiency. As a complementary approach to the existing wireless RF solutions, VLC is poised to overcome the crowded radio spectrum and become a promising broadband wireless access candidate to resolve the ``spectrum crunch" problem \cite{hanchard2010fcc}.
For indoors environment, whenever communication is needed, {\it lighting is also needed most of the time}. According to \cite{lindsay2012what}, energy consumption of lighting represents about 15\% of the worlds total energy consumption. Therefore, by jointly performing lighting and Internet access, VLC can operate on a very small energy budget.
For upper layers in multi-user scenarios, \cite{li2012vico} and \cite{tao2015scheduling} consider link scheduling algorithms to serve multiple users based on multiple VLC links with no power efficiency guarantees. The work in \cite{li2012vico} relies on a simple impractical assumption to measure the illumination using the average SNR distribution. The work in \cite{din2014energy} proposes an energy-efficient brightness control and data transmission scheme for VLC. However, the scheme can only be applied to the single user scenario and only the optical power is taken into account when minimizing the power consumption.
In this paper, we investigate the problem of {\it optimizing total power consumption of a general multi-user VLC indoor network while satisfying the traffic demands and illumination requirements}. A novel algorithm is proposed to efficiently obtain a practical $\epsilon$-bounded solution. Our contributions are summarized as follows:
\begin{itemize}
\item {\bf Minimizing the total power consumption for a general multi-user VLC indoor network:} Taking the users' traffic demand and the illumination requirement of entire horizontal space into account, the total power consumption of a general multi-user VLC indoor network is optimized via a novel efficient and practical algorithm.
\item {\bf Effectively model the level of interference among VLC links:} Based on the proposed algorithm, an effective interference management approach is verified by extensive simulation results.
\item {\bf Design of a novel structure of light source:} An innovative configuration of light source is proposed and analyzed, and compared with two other common configurations in terms of total power consumption.
\item {\bf Validating the power efficiency and illumination satisfaction:} Extensive simulation results reveal that, our proposed link scheduling algorithm can provide around 60\% and 80\% saving in power consumption compared to two VLC-based solutions, and the illumination distribution obtained by our proposed algorithm can always satisfy the requirements.
\end{itemize}
\section{System Model}\label{system_model}
\subsection{Access system model}
Consider a visible light access system model (Fig.~\ref{fig_system_model}) comprising of $\mathcal{V}=\{1,2,...,i,...,V\}$ VLC APs, $\mathcal{M}=\{1,2,...,j,...,M\}$ user terminals (UTs), and $\mathcal{W}=\{1,2,...,b,...,W\}$ available channels with different bandwidths. The bandwidth of channel $b$ is denoted by $B^{b}$. We also denote the set of transmitters on VLC AP $i\in\mathcal{V}$ by $Tx_{i}=\{1,2,...,m,...,|Tx_{i}|\}$, where $|Tx_{i}|$ is the number of transmitters on VLC AP $i$, and the set of receivers on UT $j\in\mathcal{M}$ by $Rx_{j}=\{1,2,...,n,...,|Rx_{j}|\}$, where $|Rx_{j}|$ is the number of receivers on UT $j$. We assume the UT $j$ has a throughput requirement $\mathcal{R}_{j}$.
A recent measurement study \cite{ding2013characterizing} on traces of 3785 smart phone users from 145 countries over a four-month period shows that the ratio of WiFi download traffic to its upload traffic is 20:1. Therefore, in this work, we mainly consider the power consumption for the downlink data transmission. Regarding the uplink issue in VLC network, a hybrid WiFi-VLC Internet access system (VLC downlink and WiFi uplink) is presented in our earlier work \cite{shao2014indoor,shao2015analysis,shao2015design}.
\begin{figure}
\centering
\includegraphics[width=0.37\textwidth]{system_model.eps}
\caption{System model for multi-user VLC indoor network}
\vspace{-12pt}
\label{fig_system_model}
\end{figure}
\subsection{Communication}
Optical modulation is performed by varying the forward current of the light source. The output optical power changes proportionally to the modulated forward current. The increase in total power consumption (including the power consumed by modulator) is mainly due to the switching loss in the driver circuitry at high speed (AC current for modulation). Such behavior is observed in our preliminary experimental results and the results in \cite{hsu2005optimization}. Here, we denote a peak-to-peak optical signal strength (generated from AC current) by $P_{AC}$ and its average value by $P_{AC,Avg}$.
\subsection{Illuminance}
Consider a horizontal user plane comprising of $\mathcal{K}=\{1,2,...,k,...,K\}$ positions and each position requires an illumination level in the range of $E_{k}^{L}$ and $E_{k}^{U}$. The illumination level of ambient light at position $k$ is denoted by $E_{k}^{Am}$.
The illumination level at a given location depends on the average optical power received. This can be generated by both the DC and the AC current. We denote an optical DC power (generated from DC current) by $P_{DC}$, which is responsible for compensating the average AC power in order to meet the illumination demands.
The DC component does not require a current switching process. This switching process reduces the efficiency of the driver circuit and light source by consuming more power. Thus, for the transmitter $m$ of the $i^{th}$ VLC AP, we denote $\eta_{AC}^{i,m}$ and $\eta_{DC}^{i,m}$ as the wall plug efficiency factors (i.e. the ratio of the optical power consumption to the electrical power consumption) for AC and DC optical power, respectively, where $\eta_{AC}^{i,m}$ is generally smaller than $\eta_{DC}^{i,m}$.
The illuminance represents the level of brightness of the illuminated surface. A horizontal illuminance $E_{k}$ [lux] at position $k$, can be given \cite{din2014energy} as $E_{k}=\sum_{i\in\mathcal{V}}\sum_{m\in Tx_{i}}(P_{DC}^{i,m}g_{i,k,m}^{DC}+P_{AC,Avg}^{i,m}g_{i,k,m}^{AC})\rho$, where $P_{DC}^{i,m}$ and $P_{AC,Avg}^{i,m}$ denote the generated DC and average AC optical power from the transmitter $m$ of the $i^{th}$ VLC AP, respectively, $\rho$ [lm/W] is the luminosity efficacy, and $g_{i,k,m}^{DC}$ and $g_{i,k,m}^{AC}$ are given as follows
\begin{align}
g_{i,k,m}^{DC}&=\frac{ml_{DC}+1}{2\pi D^{2}}cos^{ml_{DC}}(\theta_{DC})cos(\psi)\nonumber\\
g_{i,k,m}^{AC}&=\frac{ml_{AC}+1}{2\pi D^{2}}cos^{ml_{AC}}(\theta_{AC})cos(\psi)\nonumber
\end{align}
where $ml$ is the Lambertian order ($ml=-ln2/ln(cos\theta_{1/2})$, $\theta_{1/2}$ is the semi-angle at half power), (in Fig.~\ref{fig_system_model}) $D$ is the distance between VLC AP $i$ and position $k$, $\theta$ is the radiance angle, and $\psi$ is the incidence angle. Note that, the $ml$ and $\theta$ of the DC and AC powered source could be different, which will be discussed in detail in Section~\ref{pracitcal_issues}.
\subsection{Channel capacity, interference and noise}
From \cite{komine2004fundamental}, the received optical intensity via a line-of-sight (LOS) path is about 30 times higher than that via the first reflective path. Since LOS paths are typically feasible, in this paper, we only consider the LOS links. The LOS channel gain between VLC AP $i$, using transmitter $m$, and UT $j$, using receiver $n$, denoted by $H_{ij,mn}$, is illustrated in \cite{komine2004fundamental}.
It is worth noticing that, the gain of VLC channel highly depends on the strict alignment between VLC transceivers. In contrast to the omnidirectional WiFi channel, the potential motion of users will lead to severe degradation of VLC channel gain. Nevertheless, according to \cite{Cisco2015service}, most of the Internet access traffic will happen indoor at fixed locations. Thus, we focus on scenarios that the users' location are fixed, where the channel gain of VLC is more stable than that of WiFi \cite{zhang2015dancing}.
The Gaussian noise of the optical wireless channel consists of the shot noise (stems from the received optical power) and the thermal noise (stems from the receiver's circuitry). Increasing the transmitted optical power increases the noise level at the receiver. However, if the modulation bandwidth is large (above 50 MHz) and the optical power level is low (below 20 W) as is the case with most VLC APs and VLC front-ends \cite{langer2013optoelectronics}, the thermal noise would dominate the shot noise \cite{komine2004fundamental}. With fixed gain of the receiver, the thermal noise is essentially independent of the ambient light and signal strength while the shot noise is not. Our experimental results \cite{shao2015analysis,shao2015design} have validated this behavior even in outdoor settings. Therefore, a constant variance of Gaussian noise can be assumed.
Typically, there are two major interference models for the wireless networks \cite{gupta2000capacity}: Physical Model and Protocol Model. Under Physical Model, the link capacity depends on the signal-to-interference-plus-noise ratio (SINR) at the receiver side. It is a very accurate representation of real scenarios, but it is computationally difficult to work with. On the other hand, Protocol Model only considers the pairwise interference relationship among the links. With Protocol Model, the interference among individual VLC links can be modeled through the use of a conflict graph \cite{diestel2005graph}. The approach works as follows. Each receiver on a UT or each transmitter on a VLC AP is represented by a vertex in a graph. If a transmitter can transmit to a receiver on a given channel, an edge is drawn between the two vertices representing the transmitter and the receiver. The conflict graph is then constructed, such that each edge in the original graph is represented by a vertex in the conflict graph. An edge in the conflict graph is drawn between two vertices, if the corresponding edges in the original graph interfere with each other. An interference constraint (addressed in details in the next section) represents the fact that for a successful transmission (i.e. vertex in the conflict graph), none of those vertices (i.e. links in the original graph) connected by an edge in the conflict graph are active at the same time. Based on this interference constraint, the link capacity depends on the signal-to-noise ratio (SNR) under Protocol Model.
Given a link with bandwidth $B^{b}$, based on Shannon-Hartley theorem \cite{cover2012elements}, the maximum link capacity $C$ when VLC AP $i$, using transmitter $m$, transmits data to UT $j$, using receiver $n$, on channel $b$, in two interference models are given \cite{stefan2014hybrid} by
\begin{align}
&C_{ij,mn}^{b}(Protocol)=B^{b}\times log_{2}(1+\frac{(\gamma H_{ij,mn}P_{AC}^{i,m})^{2}}{N})\\
&C_{ij,mn}^{b}(Physical)=B^{b}\times log_{2}(1+\frac{(\gamma H_{ij,mn}P_{AC}^{i,m})^{2}}{(\gamma P_{I})^{2}+N})
\end{align}
where $\gamma$ is the detector responsivity, $P_{I}$ is the summation of interference optical power and $N$ is the variance of noise.
\section{Problem Formulation}\label{problem_formulation}
We investigate the minimum power consumption problem for a multi-user VLC indoor network by joint link scheduling and illuminating. For a conflict graph under Protocol Model, an {\it independent set} (IS) $\mathcal{I}$ is defined as a set of vertices in the conflict graph (i.e. links in the original graph) such that none of them are connected by an edge \cite{diestel2005graph}.
Suppose all the ISs are known and the set of all ISs is denoted as $\mathcal{Q}=\{\mathcal{I}_{1},\mathcal{I}_{2},...,\mathcal{I}_{q},...,\mathcal{I}_{|\mathcal{Q}|}\}$. In order to ensure the successful transmissions in each IS, at any given time, only one IS should be active. We define $\omega_{q}$ as the fraction of the time during which the $q^{th}$ IS is active. Therefore, we have
\begin{align}
&\sum_{1\leq q\leq|\mathcal{Q}|}\omega_{q}\leq 1,~\omega_{q}\geq 0
\end{align}
An integer variable is defined as follows: $x_{ij,mn}^{q,b}$ is equal to 1 if VLC AP $i$, using transmitter $m$, transmits to UT $j$, using receiver $n$, on channel $b$, in $\mathcal{I}_{q}$, and equal to 0 otherwise.
Recall that the $j^{th}$ UT's throughput requirement is $\mathcal{R}_{j}$. In order to meet the traffic demands of users, the following set of constraints need to be satisfied
\begin{align}
\sum_{1\leq q\leq|\mathcal{Q}|}\omega_{q}\sum_{i\in\mathcal{V}}\sum_{b\in\mathcal{W}}\sum_{m\in Tx_{i}}\sum_{n\in Rx_{j}}\mathcal{C}_{ij,mn}^{b}x_{ij,mn}^{q,b}\geq \mathcal{R}_{j}\nonumber\\
(\forall j\in\mathcal{M})
\end{align}
where $\mathcal{C}_{ij,mn}^{b}$ is calculated by (1).
Denote $P_{DC}^{i,q,m}$ as the $i^{th}$ VLC AP's DC optical power consumption of the transmitter $m$ in the $q^{th}$ IS and $P_{AC}^{i,m}$ as the fixed peak-to-peak signal strength of $i^{th}$ VLC AP's transmitter $m$. For one VLC transmitter, the summation of $P_{AC}$ and $P_{DC}$ can not exceed the maximum optical power $P_{max}$. Thus we have
\begin{align}
P_{DC}^{i,q,m}+\sum_{j\in\mathcal{M}}\sum_{b\in\mathcal{W}}\sum_{n\in Rx_{j}}P_{AC}^{i,m}x_{ij,mn}^{q,b}\leq P_{max}^{i,m}\nonumber\\
(\forall i\in\mathcal{V}, \forall m\in Tx_{i}, 1\leq q\leq|\mathcal{Q}|)
\end{align}
Recall that, at position $k$, the minimum and maximum illuminance thresholds are $E_{k}^{L}$ and $E_{k}^{U}$, respectively, and the illuminance level of ambient light is $E_{k}^{Am}$. The summation of the LED lighting and the ambient lighting needs to be within the range [$E_{k}^{L}$,$E_{k}^{U}$]. Therefore, we have the following illumination constraints
\begin{align}
&E_{k}^{U}\geq\sum_{i\in\mathcal{V}}\sum_{j\in\mathcal{M}}\sum_{b\in\mathcal{W}}\sum_{m\in Tx_{i}}\sum_{n\in Rx_{j}}(P_{AC,Avg}^{i,m}x_{ij,mn}^{q,b}g_{i,k,m}^{AC,q}+\nonumber\\
&P_{DC}^{i,q,m}g_{i,k,m}^{DC})\rho+E_{k}^{Am}\geq E_{k}^{L}~(\forall k\in\mathcal{K}, 1\leq q\leq|\mathcal{Q}|)
\end{align}
The reason for adding the superscript $q$ to the AC optical power gain is that, the Lambertian order or the radiance angle of the AC powered source on each VLC transmitter may be varied in different IS. This condition will be demonstrated in details in Section~\ref{pracitcal_issues}.
Given the link scheduling in each IS, the illuminance distribution from the average AC optical power can be obtained. Therefore, to satisfy the maximum power constraint (5) and the illumination constraint (6), we can compute the optimal $P_{DC}^{i,q,m}$ for each VLC transmitter in each IS. Denote $P_{AC,Avg}(\mathcal{I}_{q})$ and $P_{DC}(\mathcal{I}_{q})$ as the total AC and DC power consumption of the $q^{th}$ IS, respectively. The optimal solution of our algorithm might result in $\sum_{1\leq q\leq|\mathcal{Q}|}\omega_{q}<1$, this means that the data transmission will be completed within the $\sum_{1\leq q\leq|\mathcal{Q}|}\omega_{q}$ fraction of time. However, the illumination is always needed. Let $P_{illumi}^{min}$ represent the minimum total power consumption when all the VLC APs only perform illumination. This means that during the $(1-\sum_{1\leq q\leq|\mathcal{Q}|}\omega_{q})$ fraction of time, the power consumption is $P_{illumi}^{min}$. Therefore, the total power consumption optimization problem can be formulated as follows
\begin{align}
\min_{\omega_{q}}~&\sum_{1\leq q\leq|\mathcal{Q}|}\omega_{q}[P_{AC,Avg}(\mathcal{I}_{q})+P_{DC}(\mathcal{I}_{q})]\nonumber\\
&\qquad\qquad\qquad\qquad+(1-\sum_{1\leq q\leq|\mathcal{Q}|}\omega_{q})P_{illumi}^{min}\nonumber\\
s.t.~&(3),(4)\nonumber
\end{align}
Given that all the ISs satisfying constraints (5) and (6), the formulated optimization problem is a linear programming problem. We call this problem the {\it master problem} (MP). The solution to the MP is to find the optimal values of $\omega_{q}$ ($1\leq q\leq|\mathcal{Q}|$). In the next section, we will introduce the challenges of solving the MP and our solution methodology.
\section{Solution Methodology}\label{solution_methodology}
\subsection{Challenges of Solving MP}
To efficiently solve the MP, there are two main challenges: i) Although the MP is a linear programming problem if all the ISs are given, the IS decision problem itself is NP-complete \cite{diestel2005graph} and hence it is believed that there is no efficient algorithm for solving it. ii) Even if all the ISs are given, the number of ISs and corresponding variables increases exponentially as the number of links increases. Therefore, the complexity of solving the MP will be extremely high when the network is very large. We propose a column generation based $\epsilon$-bounded approximation algorithm to resolve these challenges.
\subsection{Column Generation}
Column generation \cite{bertsimas1997introduction} is an efficient algorithm for solving large scale (i.e. the number of variables is large) linear programming problem. Even though the MP has a large number of variables, only a small subset of them will be non-zero (basis variables) in the optimal solution. Based on this observation, rather than adding all the variables in the MP, column generation only generates the variables with the highest potential to enhance the objective function. In particular, the large MP is split into two smaller and simpler problems: {\it restricted master problem} (RMP) and {\it pricing problem} (PP). The RMP only includes an initial subset of variables in the MP, and the PP is a new optimization problem assigned to find a variable or a column (i.e. independent set) that has the most negative reduced cost (i.e. decrease of the objective value). The process works iteratively as follows: the RMP is solved and its optimal and dual optimal solutions are obtained; the PP utilizes the dual optimal solution of the RMP to identify the column with the most negative reduced cost and adds it into RMP to re-optimize RMP. The process continues until the objective value of PP is non-negative. If the PP returns a non-negative solution, the solution of RMP is the optimal solution to the MP.
Instead of considering the set $\mathcal{Q}$ of all the ISs, RMP starts with an initial set $\tilde{\mathcal{Q}}$ of ISs (called observed ISs). A simple method of selecting the initial ISs is to place only one active link in each of them. Hence, the RMP is formulated as follows
\begin{align}
&\min_{\omega_{q}}~\sum_{1\leq q\leq|\tilde{\mathcal{Q}}|}\omega_{q}[P_{AC,Avg}(\mathcal{I}_{q})+P_{DC}(\mathcal{I}_{q})]\nonumber\\
& \qquad\qquad\qquad\qquad\qquad+(1-\sum_{1\leq q\leq|\tilde{\mathcal{Q}|}}\omega_{q})P_{illumi}^{min}\nonumber\\
s.t.~&\sum_{1\leq q\leq|\tilde{\mathcal{Q}}|}\omega_{q}\sum_{i\in\mathcal{V}}\sum_{b\in\mathcal{W}}\sum_{m\in Tx_{i}}\sum_{n\in Rx_{j}}\mathcal{C}_{ij,mn}^{b}x_{ij,mn}^{q,b}\geq R_{j}\nonumber\\
&\qquad\qquad\qquad \qquad\qquad\qquad\qquad\qquad\qquad (\forall j\in\mathcal{M})\nonumber\\
&\sum_{1\leq q\leq|\tilde{\mathcal{Q}}|}\omega_{q}\leq 1,~\omega_{q}\geq 0\nonumber
\end{align}
where $P_{DC}(\mathcal{I}_{q})$ ($1\leq q\leq|\tilde{\mathcal{Q}}|$) can be computed optimally by satisfying the maximum power constraint (5) and the illumination constraint (6).
After solving the RMP, the primal optimal solution and the Lagrangian dual optimal solution can be obtained. Since the ISs in RMP is only a subset of the ISs in MP (i.e. $\tilde{\mathcal{Q}}\subseteq\mathcal{Q}$), the primal optimal solution of RMP can be regarded as an upper bound of the optimal solution of MP. Adding another column, which does not exist in RMP, may reduce the upper bound and improve the objective function. Therefore, the PP is responsible for generating a column with the most negative reduced cost.
For a IS that has not been observed (i.e. included in the RMP), the PP needs to determine whether the reduced cost of the IS is negative or not. Referring to \cite{bertsimas1997introduction}, the reduced cost of $\mathcal{I}_{q}$ can be calculated as $c_{r}(\mathcal{I}_{q})-P_{illumi}^{min}$, where
\begin{align}
c_{r}(\mathcal{I}_{q})=\sum_{i\in\mathcal{V}}\sum_{j\in\mathcal{M}}\sum_{b\in\mathcal{W}}\sum_{m\in Tx_{i}}\sum_{n\in Rx_{j}}(\frac{1}{\eta_{AC}^{i,m}} P_{AC,Avg}^{i,m}x_{ij,mn}^{b}+\nonumber\\
\frac{1}{\eta_{DC}^{i,m}}P_{DC}^{i,m})-\sum_{j\in\mathcal{M}}\lambda_{j}\sum_{i\in\mathcal{V}}\sum_{b\in\mathcal{W}}\sum_{m\in Tx_{i}}\sum_{n\in Rx_{j}}\mathcal{C}_{ij,mn}x_{ij,mn}^{b}\nonumber
\end{align}
where $\lambda_{j}$ is the Lagrangian dual optimal solution for the $j^{th}$ UT. To find the $\mathcal{I}_{q}$ with the most negative reduced cost, the objective of PP is to minimize $c_{r}(\mathcal{I}_{q})-P_{illumi}^{min}$.
Regarding the constraints of PP, under Protocol Model, we denote $\mathcal{T}_{ij,mn}^{b}$ as the set of links that interfere with the transmission from the $i^{th}$ AP, using transmitter $m$, to the $j^{th}$ UT, using receiver $n$, on channel $b$. Thus, we have
\begin{align}
x_{ij,mn}^{b}+\sum_{pq,uv\in\mathcal{T}_{ij,mn}}x_{pq,uv}^{b}\leq 1\nonumber\\
(\forall i\in\mathcal{V}, \forall j\in\mathcal{M}, \forall m\in Tx_{i}, \forall n\in Rx_{j})
\end{align}
In addition, the total number of transmitting links at VLC AP $i$ and receiving links at UT $j$ should be no larger than $|Tx_{i}|$ and $|Rx_{j}|$, respectively, which means
\begin{align}
&\sum_{j\in\mathcal{M}}\sum_{b\in\mathcal{W}}\sum_{m\in Tx_{i}}\sum_{n\in Rx_{j}}x_{ij,mn}^{b}\leq |Tx_{i}|~(\forall i\in\mathcal{V})\\
&\sum_{i\in\mathcal{V}}\sum_{b\in\mathcal{W}}\sum_{m\in Tx_{i}}\sum_{n\in Rx_{j}}x_{ij,mn}^{b}\leq |Rx_{j}|~(\forall j\in\mathcal{M})
\end{align}
Besides, a transmitter of a VLC AP can not transmit to multiple UTs and a receiver of a UT can not receive from multiple VLC APs due to interference. Therefore, we get
\begin{align}
&\sum_{j\in\mathcal{M}}\sum_{b\in\mathcal{W}}\sum_{n\in Rx_{j}}x_{ij,mn}^{b}\leq1~(\forall i\in\mathcal{V}, \forall m\in Tx_{i})\\
&\sum_{i\in\mathcal{V}}\sum_{b\in\mathcal{W}}\sum_{m\in Tx_{i}}x_{ij,mn}^{b}\leq1~(\forall j\in\mathcal{M}, \forall n\in Rx_{j})
\end{align}
It is worth noticing that, in contrast to RF communication, the optical signal propagation may not be isotropic from the perspective of UTs plane (e.g. the central luminous flux is not vertical to the horizontal UTs plane), and also the orientation and filed of view (FOV) of VLC receiver can be tuned in order to receive signals from a specific direction and a small range. Thus, using the same channel, a transmitter of a VLC AP can transmit to multiple UTs, and a UT can receive from multiple VLC APs.
Assembling together the constraints of power and brightness control with the above constraints, the PP can be formulated as follows:
\begin{align}
&\min_{\mathcal{I}_{q}\in\mathcal{Q}\backslash\tilde{\mathcal{Q}}}c_{r}(\mathcal{I}_{q})-P_{illumi}^{min}\nonumber\\
s.t.~&(7),(8),(9),(10),(11)\nonumber\\
&P_{DC}^{i,m}+\sum_{j\in\mathcal{M}}\sum_{b\in\mathcal{W}}\sum_{n\in Rx_{j}}P_{AC}^{i,m}x_{ij,mn}^{b}\leq P_{max}^{i,m}\nonumber\\
&\qquad\qquad\qquad\qquad\qquad(\forall i\in\mathcal{V}, \forall m\in Tx_{i})\nonumber\\
&E_{k}^{U}\geq\sum_{i\in\mathcal{V}}\sum_{j\in\mathcal{M}}\sum_{b\in\mathcal{W}}\sum_{m\in Tx_{i}}\sum_{n\in Rx_{j}}(P_{DC}^{i,m}g_{i,k,m}^{DC}+\nonumber\\
&\qquad P_{AC,Avg}^{i,m}x_{ij,mn}^{b}g_{i,k,m}^{AC})\rho+E_{k}^{Am}\geq E_{k}^{L}~(\forall k\in\mathcal{K})\nonumber
\end{align}
where $P_{DC}^{i,m}$ and $x_{ij,mn}^{b}$ are the variables.
RMP and PP are solved in an iterative way, until PP returns a non-negative reduced cost. However, since the size of $\mathcal{Q}$ could be huge, it might take long time to reach the optimal solution. Therefore, instead of finding the optimal solution, we propose an $\epsilon$-bounded approximation approach to find a satisfactory $\epsilon$-bounded solution.
\subsection{$\epsilon$-Bounded Approximation Approach}
Let $z^{\ast}$ denote the optimal result of MP and $z^{u}$ denote the optimal result of RMP (upper bound on $z^{\ast}$), when $\kappa\geq\sum_{1\leq q\leq|\mathcal{Q}|}\omega_{q}$ holds for the optimal solution of MP, the $z^{u}$ can not be reduced more than $\kappa$ times the most negative reduced cost $c_{r}^{\ast}$ \cite{desrosiers2005primer} :
\begin{align}
&z^{u}+\kappa c_{r}^{\ast}\leq z^{\ast}\leq z^{u}\nonumber
\end{align}
Denote $z^{l}=z^{u}+\kappa c_{r}^{\ast}$ as the lower bound on $z^{\ast}$ and the following lemma can be proved.
\begin{lemma}
Define $\epsilon$ as $0\leq\epsilon<1$. The optimal solution of RMP $z^{u}\leq(1+\epsilon)z^{\ast}$, if $z^{u}/z^{l}\leq 1+\epsilon$.
\end{lemma}
\begin{IEEEproof}
If $z^{u}/z^{l}\leq 1+\epsilon$, then $z^{u}\leq(1+\epsilon)z^{l}\leq(1+\epsilon)z^{\ast}$. Hence, $z^{u}$ is the $\epsilon$-bounded solution of MP.
\end{IEEEproof}
Based on the $\epsilon$-bounded approximation approach, the iteration of column generation can be terminated when $c_{r}^{\ast}\geq0$ or $z^{u}/z^{l}\leq 1+\epsilon$.
\subsection{Reality Check}
Although the column generation based $\epsilon$-bounded approximation algorithm is capable of efficiently finding the $\epsilon$-bounded solution of MP, the feasibility of the Protocol Model solution is doubtful. Under the Protocol Model, the impact of some non-zero interfering links are neglected, which may lead to overestimation of the achievable link capacity. Thus the power consumption solution (under the Protocol Model) of MP may be lower than the real power consumption in practice. To investigate the practical objective value of MP, a validation process called ``reality check" is introduced in \cite{shi2013bridging}. Note that, in \cite{shi2013bridging}, the ``reality check" process is neither integrated with the column generation algorithm nor applied to evaluate the real power consumption.
Since the Protocol Model solution of RMP includes all the ISs with non-zero $\omega_{q}$, the link scheduling (i.e. which link is active and which link is idle) of each of those ISs can be known. Hence, the actual achievable capacity of each active link can be recomputed by equation (2). The ``reality check" process consists of two steps: i) Recompute the actual link capacity by equation (2) for the Protocol Model solution of RMP; ii) Substitute the recomputed link capacity into RMP and re-optimize the RMP to obtain a feasible solution of power consumption. The column generation based $\epsilon$-bounded approximation algorithm with reality check is summarized in Algorithm~\ref{algorithm}.
\begin{algorithm}
\caption{Column generation based $\epsilon$-bounded approximation algorithm with reality check}\label{algorithm}
\begin{algorithmic}[1]
\REQUIRE~Initial independent sets $\tilde{\mathcal{Q}}$, traffic demands $\mathcal{R}_{j}$, interference set of each link $\mathcal{T}^{b}_{ij,mn}$, Protocol Model link capacity $\mathcal{C}^{b}_{ij,mn}$, optical signal strength $P_{AC}^{i,m}$, maximum power consumption $P_{max}^{i,m}$, approximation factor $\epsilon$, gains of AC and DC optical power $g^{AC}_{i,k,m}$ and $g^{DC}_{i,k,m}$, wall plug efficiency factors $\eta_{AC}^{i,m}$ and $\eta_{DC}^{i,m}$, illuminance lower and upper bounds $E_{k}^{l}$ and $E_{k}^{u}$, ambient lighting level $E_{k}^{Am}$, $c_{r}^{\ast}=-\infty$, $\kappa=1$, $z^{l}=-\infty$ and $z^{u}=\infty$.\\
\ENSURE~Time fraction (out of one time unit) $\omega_{q}$ and solution of RMP $z^{u}$.\\
\STATE Compute $P_{AC,Avg}(\mathcal{I}_{q})$ and $P_{DC}(\mathcal{I}_{q})$ for $\tilde{\mathcal{Q}}$, and compute $P_{illumi}^{min}$;
\WHILE {$z^{u}/z^{l}>1+\epsilon$ and $c_{r}^{\ast}<0$}
\STATE Solve RMP and obtain its optimal result $z^{u}$ and dual optimal solution $\lambda_{j}$;
\STATE Solve PP with $\lambda_{j}$ and obtain a IS $\mathcal{I}_{q}$ with $c_{r}^{\ast}$ and the corresponding optimal $P_{DC}^{i,q,m}$;
\STATE Update $c_{r}^{\ast}$ and $\tilde{\mathcal{Q}}=\tilde{\mathcal{Q}}\bigcup\mathcal{I}_{q}$, and compute the new $P_{AC,Avg}(\mathcal{I}_{q})$ and $P_{DC}(\mathcal{I}_{q})$;
\STATE $z_{l}=z^{u}+c_{r}^{\ast}$;
\ENDWHILE
\STATE Update the link capacity in RMP by reality check;
\STATE Re-optimize RMP and obtain its optimal result $z^{u}$;
\end{algorithmic}
\end{algorithm}
\section{Practical Issues}\label{pracitcal_issues}
\subsection{Three Configurations of Light Source}
Typically, a light source operates with fixed beamangle (i.e. formed by the central luminous flux and the central vertical line) and beamwidth (i.e. semi-angle at half power $\theta_{1/2}$). This configuration is capable of efficiently providing sufficient illumination. However, its weak competitiveness manifest on the communication functionality, due to the high inter-link interference and non-uniform distribution of optical signal strength, which will lead to severe degradation of channel gain when the transceivers are not strictly aligned. To mitigate the interference and enhance the channel gain, mechanically steering the beamangle and beamwidth is introduced in \cite{tronghop2012modeling} and \cite{li2012vico}. In this paper, we further explore the impact of tuning the beamangle and beamwidth on the power consumption of multi-user VLC indoor networks. Although adjustable beamangle can be implemented by traditional {\it mechanical steering} method, the energy cost of tuning the orientation of light source is considerable \cite{nakhkoob2009multi}, and even worse, the time it takes to change the direction is inevitable, which will bring a significant negative-impact on the network delay and capacity. To circumvent these problems, a new structure of light source is proposed. Multiple chips with different beamangles and beamwidths are installed on one light source and the diversity of orientation of light source can be implemented by activating any of those chips. This configuration is motivated by the ``{\it electronic steering}" concept introduced in \cite{nakhkoob2009multi}. Since the new structure of light source needs to be specified before being evaluated by the optimization algorithm, we outline an implementable design of such light source based on the assumption of uniformly distributed UTs. In summary, three configurations\footnote{In order to distinguish the difference among three configurations, it is assumed that, in the first and the second configurations, the beamangle of all the transmitters on one VLC AP are the same.} (shown in Fig.~\ref{fig_three_configurations}) of light source are investigated: i) fixed beamangle and beamwidth; ii) mechanically adjustable beamangle and beamwidth; iii) electronically selectable beamangle and beamwidth.
\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{Three_configurations.eps}
\caption{Three different configurations: a) fixed beamangle and beamwidth; b) mechanically adjustable beamangle and beamwidth; c) electronically selectable beamangle and beamwidth}
\vspace{-5pt}
\label{fig_three_configurations}
\end{figure}
As shown in Fig.~\ref{fig_three_configurations}, for Config. a, the beamwidth and beamangle are fixed regardless of the location of UT. The orientation of all VLC APs are vertical to the horizontal UTs plane. The semi-angle at half power $\theta_{1/2}$ (i.e. beamwidth) of AC and DC powered sources are the same. For Config. b, the beamwith and beamangle are tunable. For the purpose of concentrating the optical signal, the $\theta_{1/2}$ of AC powered source is set to be smaller than that of DC powered source. By adjusting the beamangle, the transmitter can directly point to the receiver. It can be seen that, for Config. b, the radiance angle of each link is always zero. For Config. c, multiple chips are installed on one VLC AP. The beamangle and beamwidth of each chip are fixed. Nevertheless, the VLC AP can selectively activate any of those chips and ``electronically steering" the beamangle and beamwidth. Notice that, since the beamangle of each chip (for Config. c) is fixed, the transmitter might not be able to directly point to the receiver, such as for Config. b. Next, we specify the new structure of light source for Config. c.
\subsection{New Structure of Light Source}
\begin{wrapfigure}{r}{0.21\textwidth}
\vspace{-5pt}
\begin{center}
\includegraphics[width=0.21\textwidth]{grid_structure_VLC.eps}
\end{center}
\vspace{-10pt}
\caption{Grid structure of multi-user VLC indoor network}
\vspace{-5pt}
\label{fig_grid_structure_VLC}
\end{wrapfigure}
As shown in Fig.~\ref{fig_grid_structure_VLC}, the VLC APs are mounted on the ceiling in grid structure. To maximize the capacity of each link, each UT\footnote{To focus on the configuration of light source and make it easier to understand, it is assumed here and also in the simulation that, each UT is equipped with only one receiver. It means that each UT can connect to only one VLC AP at a time.} chooses the nearest VLC AP to associate with, thus the served area of each VLC AP can be modeled as a square. In Fig.~\ref{fig_acr_shaped_general}, a new structure of light source is shown. It can be seen from Fig.~\ref{fig_acr_shaped_general} (a) that, one VLC AP is equipped with $(n\times n)+1$ chips, including $n\times n$ (n is a multiple of 2) peripheral chips and one central chip, which is mainly responsible for illuminating. In Fig.~\ref{fig_acr_shaped_general} (c), a square area served by a VLC AP is equally divided into $n\times n$ small square regions. Each peripheral chip is assigned to serve one region. The star (i.e. center of coverage) in each region is the intersection of the central luminous flux of the corresponding peripheral chip and the horizontal UT plane. Each star is located at the center of each square region. Denote the side length of a square area served by a VLC AP as $l$, the maximum distance $d_{max}$ between a UT and its corresponding center of coverage satisfy $d_{max}\leq \frac{\sqrt{2}l}{2n}$.
\begin{figure}
\centering
\includegraphics[width=0.40\textwidth]{arc_shaped_general.eps}
\caption{New structure of light source}
\vspace{-5pt}
\label{fig_acr_shaped_general}
\end{figure}
\subsection{Constructing conflict graph}
In this section, we also introduce an effective approach to construct the conflict graph for multi-user VLC indoor networks. Traditionally, in Protocol Model, whether or not a transmission is being interfered by another transmission is determined by the distance between the receiver and the non-intended transmitter \cite{gupta2000capacity,shi2013bridging,shi2007optimal}. In VLC network, this standard is not always applicable, since the optical signal propagation may not be isotropic from the perspective of UTs plane. In \cite {tao2015scheduling}, the orientation of each VLC AP is fixed and vertical to the horizontal UTs plane, such that the conflict graph, constructed by using the interference range \cite{gupta2000capacity} as in RF networks, is valid. However, if the orientation of VLC APs is tunable, then interference range is not a reliable measure to accurately model the level of interference. As such, we propose a new criterion, according to which, if one of the pairwise signal-to-interference ratio (SIR) measurement of two links is lower than a threshold $SIR_{th}$, those two links can not be scheduled in the same IS.
Under Protocol Model, we define a maximum SIR threshold as $SIR_{th}^{max}$ such that if $SIR_{th}\geq SIR_{th}^{max}$, then when any link is active, other links on the same channel can not be active. A minimum SIR threshold $SIR_{th}^{min}$ is 1, since if $SIR_{th}<1$, the interference signal will be stronger than the transmission signal. For a wireless network with high traffic load, there could exist an upper bound $SIR_{th}^{U}$ for SIR threshold such that if $SIR_{th}>SIR_{th}^{U}$, the Protocol Model solution is infeasible (i.e. $\sum_{1\leq q\leq|\mathcal{Q}|}\omega{q}>1$). For a dense wireless network, there could exist a lower bound $SIR_{th}^{L}$ such that if $SIR_{th}<SIR_{th}^{L}$, even though the Protocol Model solution is feasible (i.e. $\sum_{1\leq q\leq|\mathcal{Q}|}\omega{q}\leq1$), the reality check result is infeasible. Therefore, we need to select the $SIR_{th}$ within the range $[SIR_{th}^{L}, SIR_{th}^{U}]$. In the next section, we study the $SIR_{th}^{U}$ and the $SIR_{th}^{L}$ for a VLC indoor network with three different configurations of light source through simulations.
\section{Numerical Results}\label{numerical_analysis}
In this section, we conduct extensive simulations to evaluate our proposed algorithm integrated with the practical issues. The simulations are conducted under Matlab R2013b and CPLEX 12.6.1 \cite{cplex2014v12} on a computer with 2.0 GHz and 4 GB RAM. We study the cost of solving the MP under different values of $\epsilon$. Our proposed algorithm is compared with two other recent schemes \cite{li2012vico,tao2015scheduling} in terms of power consumption and running time. In \cite{li2012vico}, the VICO framework does not consider the illumination constraints in the algorithm. Let $P_{total}$ represent the total power consumption of a given scheme, since the illumination is always needed, the power consumption evaluated in the numerical analysis is $P_{total}-P_{illumi}^{min}$.
The room size is 6.0 m $\times$ 6.0 m $\times$ 3.0 m. The height of desk is 0.8 m and the UTs are randomly distributed on the desk according to uniform distribution. There are 36 (6$\times$6) VLC APs in grid structure installed on the ceiling and each VLC AP is equipped with one chip\footnote{It means that each VLC AP can serve only one UT at a time.} (i.e. transmiter) filled with 625 (25$\times$25) white light LEDs. Note that, for the new structure of light source (Fig.~\ref{fig_acr_shaped_arch}), each VLC AP is equipped with 5 such chips\footnote{In order to fairly evaluate the three configurations, for Config. c, it is assumed that only one of the peripheral chips can be active for data transmission at a time, and the total optical power generated from one VLC AP can not exceed the $P_{max}$ of a single chip.}. The distances between two neighboring VLC APs and two neighboring LEDs are 1 m and 1 cm, respectively. The maximum transmitted optical power of each LED is 20 mW. The value of $P_{AC}$ of each VLC AP is set to 0.1 W. $P_{AC,Avg}$ is set to be half of $P_{AC}$. The channel bandwidth of each VLC link is 100 MHz and we assume all the VLC APs use the same channel in the simulation. The constant Gaussian noise is calculated from the parameters in \cite {komine2004fundamental} and set to be 4.7$\times$10$^{-14}$ A$^{2}$. The receiver parameters (i.e. FOV of receiver, detector area of a photodiode, gain of optical filter, refractive index of lens and O/E conversion efficiency) are the same with those in \cite {komine2004fundamental}. The required illuminance range is 300-500 lux. For Config. a, the semi-angle at half power $\theta_{1/2}$ of AC and DC powered sources are both set to 70$^\circ$. For Config. b, $\theta_{1/2}$ of AC powered source is set to 30$^\circ$, while that of DC powered source is set to 70$^\circ$. For Config. c, as shown in Fig.~\ref{fig_acr_shaped_arch}, $\theta_{1/2}$ of the central chip is set to 70$^\circ$, and $\theta_{1/2}$ of the peripheral chips are all set to 30$^\circ$. The wall plug efficiency factors $\eta_{AC}$ and $\eta_{DC}$ for all the VLC transmitters are set to 0.02 and 0.1, respectively.
\begin{figure}
\centering
\includegraphics[width=0.30\textwidth]{arc_shaped_arch.eps}
\caption{A sample new structure light source}
\label{fig_acr_shaped_arch}
\end{figure}
\begin{figure*}
\centering
\begin{minipage}[t]{.329\linewidth}
\includegraphics[width=1.0\textwidth]{SIR_sample.eps}
\vspace{-10pt}
\caption{Protocol Model solutions and corresponding reality check results}
\vspace{-2pt}
\label{fig_SIR_sample}
\end{minipage}
\begin{minipage}[t]{.329\linewidth}
\includegraphics[width=1.0\textwidth]{effective_SIR.eps}
\vspace{-10pt}
\caption{$SIR_{th}^{L}$ and $SIR_{th}^{U}$ for three configurations}
\vspace{-2pt}
\label{fig_effective_SIR}
\end{minipage}
\begin{minipage}[t]{.329\linewidth}
\includegraphics[width=1.0\textwidth]{user_three_cases.eps}
\vspace{-10pt}
\caption{Real power consumption under different number of UTs for three configurations}
\vspace{-2pt}
\label{fig_user_three_cases}
\end{minipage}
\end{figure*}
\subsection{Cost of solving MP}
For a 30-UTs VLC indoor network, Table~\ref{table_complexity} shows the number of iterations and the total running time needed to achieve an $\epsilon$-bounded solution. It can be seen that, it takes 14 iterations and 9.33 seconds to obtain 1\%-bounded results, and 44 iterations and 17.84 seconds to get a near-optimal result (i.e. $\epsilon\approx0$). For the following numerical results, we use $\epsilon=0.01$.
\begin{table}
\centering
\caption{Iteration Number and Running Time for an $\epsilon$-bounded solution}
\begin{tabular}{|c|c|c|}
\hline
$\epsilon$&Number of Iterations&Running Time (s)\\\hline
0.01&14&9.33\\
0.005&22&11.56\\
1$\times$10$^{-14}$&44&17.84\\
\hline
\end{tabular}
\label{table_complexity}
\end{table}
\subsection{Constructing Conflict Graph}
For a 30-UTs VLC indoor network under Config. a, the traffic demand of each UT is 20 Mbps, we show the Protocol Model solutions and the corresponding reality check results in Fig.~\ref{fig_SIR_sample}. The upper bound for SIR threshold $SIR_{th}^{U}$ is 3, and if $SIR_{th}>3$, the Protocol Model solution will be infeasible. The lower bound for SIR threshold $SIR_{th}^{L}$ is 2, and if $SIR_{th}<2$, the reality check solution will be infeasible. When $2\leq SIR_{th}\leq3$, although the Protocol Model solution is almost the same, a lower $SIR_{th}$ will lead to a higher reality check result, which is due to neglecting the non-zero interference in Protocol Model. Thus, choosing $SIR_{th}^{U}$ as the SIR threshold will minimize the total power consumption while satisfying the traffic demands.
In Fig.~\ref{fig_effective_SIR}, we show the $SIR_{th}^{U}$ and the $SIR_{th}^{L}$ for a VLC indoor network under the three configurations. As the number of UTs increases, the $SIR_{th}^{U}$ will decrease and the $SIR_{th}^{L}$ will increase. And when the $SIR_{th}^{U}$ and the $SIR_{th}^{L}$ converge to one value, this indicates that the traffic load reaches up to the system capacity. From Fig.~\ref{fig_effective_SIR}, we can observe that, the system capacity of Config. b and Config. c is around double that of Config. a. And the feasible region of Config. b and Config. c is larger than that of Config. a, which shows the superiority of the new structure of light source (i.e. Config.~c).
\subsection{Power Consumption Evaluation}
In the following, we evaluate the objective value (i.e. power consumption) for the three configurations, in terms of different number of UTs. From Fig.~\ref{fig_user_three_cases} , it can be observed that, the real power consumption (after reality check) for Config. a is more than double that for Config. b and Config. c. More to the point, the real power consumption for Config. c, which is much more practical than Config. b, is almost the same as that for Config. b. In summary, the new structure of light source (i.e. Config. c) is a practical design and capable to provide excellent power-saving performance.
\begin{figure*}
\centering
\begin{minipage}[t]{.327\linewidth}
\includegraphics[width=1.0\textwidth]{user_three_algorithms.eps}
\vspace{-10pt}
\caption{Real power consumption under different number of UTs for three algorithms}
\vspace{-2pt}
\label{fig_user_three_algorithms}
\end{minipage}
\begin{minipage}[t]{.327\linewidth}
\includegraphics[width=1.0\textwidth]{throughput_three_algorithms.eps}
\vspace{-10pt}
\caption{Real power consumption under different throughput requirement for three algorithms}
\vspace{-2pt}
\label{fig_throughput_three_algorithms}
\end{minipage}
\begin{minipage}[t]{.327\linewidth}
\includegraphics[width=1.0\textwidth]{complexity_three_algorithms.eps}
\vspace{-10pt}
\caption{Algorithm running time under different number of UTs for three algorithms}
\vspace{-2pt}
\label{fig_complexity_three_algorithms}
\end{minipage}
\end{figure*}
We also compare the $\epsilon$-bounded solution obtained by column generation (CG) with the results obtained by a random link scheduling introduced in VICO \cite{li2012vico} and a link scheduling based on maximum weighted independent set (MWIS) introduced in \cite{tao2015scheduling}. The real power consumption under the three algorithms are simulated in terms of different number of UTs and different throughput requirement of each UT. As shown in Fig.~\ref{fig_user_three_algorithms}, the traffic demand of each UT is 5 Mbps, the real power consumption under VICO and MWIS becomes much higher than that under CG, as the number of UTs increases. For a 35-UTs network, the CG algorithm cuts the power consumption of VICO by 60\%. Although the MWIS algorithm can achieve a better objective value under Protocol Model than random scheduling, after reality check its power consumption is much worse than that of VICO due to neglecting the non-zero interference from other links. The results shown in Fig.~\ref{fig_throughput_three_algorithms} are consistent with the above analysis. For a 20-UTs VLC network, as the throughput requirement of each UT increases, there is almost no changes in the gaps between the real power consumption obtained by three algorithms.
\subsection{Illumination Evaluation}
Regarding the illuminance satisfaction, in our proposed algorithm, since the illuminance level for the entire horizontal space is conditioned to be within the specified range (300-500 lux), the illuminance distribution always meets the requirements. In Fig.~\ref{fig_CG_illumination}, we show a sample distribution of illuminance under our proposed algorithm. We also show a sample illuminance distribution under VICO framework in Fig.~\ref{fig_VICO_illumination}. Around 70\% of the horizontal space do not meet the illumination requirements, because VICO framework does not take the illumination constraints into account when performing the optimization algorithm.
\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{CG_illumination.eps}
\caption{A sample distribution of illuminance created by our proposed algorithm with the entire horizontal space illumination constraints}
\vspace{-7pt}
\label{fig_CG_illumination}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{VICO_illumination.eps}
\caption{A sample distribution of illuminance under the VICO framework}
\vspace{-7pt}
\label{fig_VICO_illumination}
\end{figure}
\subsection{Cost of three algorithms}
The running time costs by minimizing the power consumption under three algorithms are shown in Fig.~\ref{fig_complexity_three_algorithms}. We can observe that, the CG algorithm costs around 5.2 seconds more than that of the random link scheduling under VICO. Nevertheless, the optimization algorithm can be run with one-time cost in the centralized controller and no extra operations are needed until the network environment changes. This extra overhead is acceptable, given that our algorithm can achieve a 60\% power-saving performance while satisfying the illumination requirements.
\section{Related Work}\label{related_work}
Many efforts have been paid on the VLC indoor network, however, most of them do not provide comprehensive consideration on the illumination and communication, or only focus on limited aspects. Even though one of them \cite{li2012vico} proposes a framework for configuring the VLC indoor networks with adjustable LEDs' beamangle and beamwidth, the link scheduling algorithm has no power efficiency guarantees and the framework relies on a simple impractical assumption to measure the illumination using the average SNR distribution.
The LED angle tuning issue is also studied in \cite{tronghop2012modeling}, which only presents the heuristic simulation results of the average SNR distribution without considering illumination. For the cooperation among VLC cells, the work in \cite{li2015cooperative} presents an elaborative study on the bandwidth efficiency of four different VLC cell formations. However, in the cooperative load balancing approach, the users' traffic demand is not concerned. The merging VLC cell approach is also studied in \cite{tao2015scheduling}, which has not taken the illumination into account. In \cite{wu2014cellular}, an optimal Lambertian order algorithm is proposed. To maximize the VLC cell boundary signal strength, an optimal Lambertian order can be found by calculating the first order derivative of the VLC path loss model. Whereas the illumination and multiple users scenario are not considered in this work. The work in \cite{rahaim2013sinr} introduces the concept of DC and AC optical power without considering overall power consumption optimization and the distribution of illumination. In \cite{din2014energy}, the authors investigate the energy-efficiency for only optical power with brightness control and data transmission in VLC networks. Three power levels of the sub-carrier pulse position modulation scheme are utilized as the variables to perform the power consumption optimization. Nonetheless, in their optimization constraints, the brightness control is only applied to the location of user, which is not practicable. A multi-transceiver optical wireless spherical structure is proposed in \cite{nakhkoob2009multi}. The spherical optical antenna is tessellated with multiple LEDs, to enable the beamangle diversity. However, this design does not carefully consider the illumination functionality of LEDs. The transverse line-of-sight of the spherical optical antenna may produce glaring in some specific scenarios. Several brightness control methods have been introduced in \cite{sugiyama2007brightness}. The PWM and DC bias are two predominant approaches for dimming control. A room division multiplexing-based VLC network is proposed in \cite{huang2013design}, while in our work, the concept of space division multiplex is manifested by adjusting the Lambertian order.
\section{Conclusion}\label{conclusion}
In this paper, we investigate the problem of minimizing the total power consumption of a general multi-user VLC indoor network while satisfying the traffic demands and providing acceptable level of illumination. A column generation based $\epsilon$-bounded approximation algorithm with reality check is proposed. Regarding the light source, three configurations are considered and one of them (i.e. a new structure of light source) is proposed. For constructing the conflict graph, an effective range of SIR threshold is evaluated by extensive simulation results. The power consumption of the three configurations are evaluated by simulations and the results reveal that the new structure light source is practical and provides power-efficient solutions. Compared to two other VLC link scheduling algorithms, our proposed algorithm can achieve a better performance of power consumption, especially in crowded scenarios, while satisfying the illumination requirements on the entire horizontal plane.
\section*{Acknowledgment}
This work was supported in part by the NSF grant ECCS-1331018.
\bibliographystyle{IEEEtran}
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} | 6,859 |
Thauria lathy är en fjärilsart som beskrevs av Hans Fruhstorfer 1902. Thauria lathy ingår i släktet Thauria och familjen praktfjärilar. Inga underarter finns listade i Catalogue of Life.
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require 'json'
require 'rest-client'
require 'yaml'
module Bracket
# SC2BC API wrapper
class API
PREFIX = "https://beta.sc2bc.com/api"
LOGIN = "https://beta.sc2bc.com/user/sign/in?do=signInForm-submit"
class << self
def instance
@instance ||= self.new
end
def method_missing(method, *args)
instance.send(method, *args)
end
end
# Load and parse YML config
def load_config
config = YAML.load_file(File.dirname(File.expand_path(__FILE__)) +
"/../../config/sc2bc.yml")
@username = config[:username]
@token = config[:token]
@auth = { username: @username, token: @token }.freeze
end
def initialize
# TODO - add some kind of validation API for the login credentials
load_config
end
# Authenticate to the API for given credential
def login_via_form
RestClient.post(LOGIN, { username: @username, password: @password })
end
# Create a new tournament and return it's ID
#
# {
# name: "SCV Rush BSG #20",
# begin: "2011-07-07T18:05:00+00:00",
# end: "-0001-11-30T00:00:00+00:00",
# registration_begin: "2011-07-05T13:05:00+00:00",
# registration_end: "2011-07-07T17:30:00+00:00",
# confirmation_begin: "2011-07-07T17:30:00+00:00",
# confirmation_end: "2011-07-07T17:55:00+00:00"
# }
def create_tournament(options)
response = RestClient.post "#{PREFIX}/tournament", @auth.merge(options)
end
# Set players for a given tournament
#
# tournament - id of the tournament
# players - an Array of players, such as
# [{
# email: "foobar@example.com",
# code: 222,
# name: "foobar"
# }, ...]
def set_players(tournament, players)
data = {
players: players.to_json,
username: @username,
token: @token,
id: tournament
}
RestClient.post "#{PREFIX}/tournament/set_players", data
end
# Delete a tournament for a given ID
def destroy_tournament(id)
RestClient.delete "#{PREFIX}/tournament/#{id}"
end
# Start a given tournament
def start
RestClient.post "#{PREFIX}/tournament/start"
end
# Returns a parsed JSON response
def parse(response)
JSON.parse(response)
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,406 |
\section{Introduction}
In recent years, with the rapid development of Internet technology, the amount of information on the Internet has shown explosive growth. To obtain valuable information from massive data information more quickly and effectively, ``recommender systems''\cite{bobadilla2013recommender} came into being and quickly gained extensive attention and practical application in academia and industry. Recommender algorithms mine the content that the user is interested in from a large amount of data by using information such as user behavior and item characteristics and presenting it to the user in a list\cite{himeur2022blockchain}. Their superiority and commercial background make them widely used in various industries \cite{lian2020geography, bobadilla2013recommender,chevalier2006effect}.
However, the recommender system also faces the test of severe security problems while providing convenience for our lives. Since the collaborative filtering method works based on user profile information, it is easily affected by false user profile information. Studies \cite{wu2021triple,li2016data,lin2020attacking} have long shown that
recommender systems, especially those in the field of sales
and scoring, systematically interfere with the user ratings
included in the system, which will also impact users' purchase
behavior and system recommendation results \cite{chevalier2006effect}. And even if attackers do not know the algorithm or implementation details used by the recommendation system, only using small-scale misleading data, can also have obvious interference effects on the normal recommendation behavior of the system, (e.g., in 2002, after receiving a complaint, Amazon found that when a website recommends a Christian classic, another irrelevant book will be recommended simultaneously, which is caused by malicious users using deceptive means \cite{liu2014new}).
Two main defense methods against poisoning attacks are data-processing-based defense and model-based defense \cite{wu2021fight,deldjoo2021survey}. Data-based defense tries to study the characteristics of poisoning attacks, strip fake profiles, and purify datasets before the training of recommender systems. However, to pursue high recall, these methods will inevitably delete normal data, which will lead to biased recommendations. Model-based defense improves the robustness of the recommendation algorithm itself, and adversarial training \cite{madry2017towards} is recognized as the most popular and effective model-based defense method to enhance recommendation robustness \cite{wu2021fight}. This method maximizes recommendation error while minimizing the model's empirical risk by adding adversarial perturbations to the model parameters, eventually building robust models in adversarial games. Although adversarial training can significantly improve the robustness of the recommender system, it is difficult to control the strength of adversarial noise, which results in reducing the generalization of the recommendation to a certain extent. Besides, a recent study has shown that adversarial training with perturbations added to model parameters cannot well resist poisoning attacks \cite{wu2021fight}. Therefore, it is very needed to design a suitable means to integrate them and make use of their strengths and avoid weaknesses.
Based on the shortcomings mentioned above, we propose a novel defense method that integrates data processing and model robustness boosting, Triple Cooperative Defense(TCD), to enhance the robustness of recommender systems. Specifically, in each round of training, we sequentially use the high-confidence prediction ratings (consistent ratings) of any two models as auxiliary training data for the remaining models, and the three models cooperatively improve recommendation robustness. The proposed strategy is based on the following considerations. In the recommender system, extremely sparse user-item interactions are difficult to support good model training, leading to models that are easily misled by malicious profiles. Besides, recent work also emphasizes that the model's robustness requires more real data\cite{wu2021fight}. Therefore, we make reasonable use of cheap pseudo-labels. Obviously, pseudo-labels must be guaranteed by high-confidence ratings, but in the explicit feedback-based recommender system that we focus on, the predicted value is the rating, not the confidence. To this end, we suggest training with three models and any two models' consistent prediction ratings as auxiliary training data for the third model. Model robustness is improved in data augmentation and co-training of the three models. Notably, we do not cull the data nor modify the individual model structure, which can overcome the shortcomings of existing defense methods. Through
extensive experiments with five poisoning attacks on three real-world datasets, the results show that the robustness improvement
of TCD significantly outperforms baselines. It is worth mentioning that TCD also improves model generalization.
The main contributions of this work are summarized as follows:
\begin{itemize}
\item the proposal of a novel robust training strategy, named
Triple Cooperative Defense, by generating pseudo labels into the recommender system for eliminating the damage of malicious profiles to models, and training three models cooperatively for improving model robustness. It is noteworthy that this is the first algorithm to combine data-processing-based defense and model-based defense in recommender systems.
\item an extensive study of co-training (defensive) methods to robustify the recommendation performance through the analysis of five attacks and three recommendation datasets. The results verify that our method enhances the robustness of the recommendation while ensuring generalization.
\end{itemize}
\section{Related Work}
\subsection{Security of Recommender Systems}
Many issues about security and privacy have been studied in recommender systems, which suggest that recommender systems are vulnerable \cite{du2018enhancing, si2020shilling}, which leads to developing a toolkit for evaluating robustness \cite{ovaisi2022rgrecsys}.
Earlier attacks injected malicious profiles manually generated with little knowledge about the recommender system,
so it could not achieve satisfactory attack performance, e.g., random
attack\cite{lam2004shilling} and average attack \cite{lam2004shilling}.
The training of model-based recommendation algorithms usually
used backpropagation \cite{guo2017deepfm, he2017neural}, so perturbations were added along
the gradient direction to perform the attack \cite{fang2020influence, fang2018poisoning,li2016data,tang2020revisiting}. Inspired
by the GAN's application \cite{jin2020sampling} in the recommendation, some work\cite{christakopoulou2019adversarial, lin2020attacking} used GAN to generate real-like fake ratings to bypass the
detection. With
the development of optimization algorithms, many works focused on attack specific types of recommender systems and turned attacks into optimization problems of deciding appropriate rating scores for users \cite{lam2004shilling,li2016data,yang2017fake,fang2018poisoning, oh2022robustness}. Moreover, some works \cite{fan2021attacking,song2020poisonrec}treated the items' ratings as actions and used reinforcement learning to generate real-like fake ratings. Such optimization-based methods have strong attack performance, so defense is needed to mitigate the harm of attack.
\subsection{Defense against Poisoning Attacks}
According to the defense objective, a defense can be (i) reactive attack detection\cite{deldjoo2021survey} or (ii) proactive robust model construction, which will be listed below.
Many researchers used KNN, C4.5, and SVM \cite{burke2006classification}to supervise the statistical attributes to detect attacks. In most practical recommendation systems, due to the small number of labeled users and the lack of prior knowledge, unsupervised learning \cite{zhang2018ud,zhang2014detection}and
semi-supervised learning \cite{cao2013shilling} were used to detect attacks. However, to pursue high recall, these methods inevitably delete normal data, which lead to biased recommendations. Conversely, for our proposed TCD to enrich high-confidence data rather than remove outliers, it can avoid cleaning normal data and train a more accurate and robust model.
Athalye et al.\cite{athalye2018obfuscated} proposed defenses based on gradient masking produce models containing smoother gradients that hinder
optimization-based attack algorithms from finding the wrong directions in space\cite{machado2021adversarial}. More recently,
many works\cite{du2018enhancing,he2018adversarial,li2020adversarial,park2019adversarial,tang2019adversarial} have focused on adversarial
training. Assuming that each instance may be the target of attacks
\cite{machado2021adversarial}, adversarial training adds perturbations to the inputs or model
parameters that force the model to learn fragile perturbations. Although adversarial training can significantly improve the robustness of recommender systems, it is difficult to control the strength of adversarial data, which results in reducing the generalization of the recommendation. Instead, the proposed TCD does not need to add sensitive noise and is trained cooperatively to facilitate generalization, and we will prove it in section 4.
\section{Methodology}
\subsection{Threat Model}
\subsubsection{Attack goal}
Different shilling attacks may have different intents, but the eventual goal of an attacker may be one of several alternatives. We can divide the attack intents into three types, including push attacks, nude attacks, and random vandalism \cite{si2020shilling}. The push attack (nude attack) typically aims to increase (decrease) the popularity of the target item. For the random vandalism, the attacker combines push attack and null attack to maximize the error of the recommendation making users stop trusting the recommendation model and finally stop using it. We mainly focus on the defense against push attack, while nude attacks can be achieved by increasing the popularity
of non-target items until the target item is not in the user's recommendation list \cite{yang2017fake}, which in a sense is equivalent to push
attacks.
\subsubsection{Attack knowledge-cost}
Attacker's knowledge-cost can be divided into high-knowledge attacks and low-knowledge
attacks\cite{si2020shilling}. The former requires the attackers to know detailed knowledge of the
rating distribution in a recommender system's database, such as the algorithm used, specific parameter
settings, and even the users' historical behavior, the latter only knows system-independent knowledge such as knowledge
might be obtained by consulting public information sources. Obviously, low-knowledge attacks are more practical because it is difficult for attackers to obtain detailed data and models. Therefore, we study the robust defense against low-knowledge attacks.
\subsubsection{Attack size}
Attack size is the number of fake profiles injected into the system by the attackers \cite{wu2014survey}. Obviously, the model
robustness and attack size cannot be decoupled. Considering that most users only rate a small number of items, the greater the attack intensity, the more likely it is to be detected \cite{mobasher2007toward}. Similar to \cite{wu2021fight}, we limit the attacker size to 5\%, and the limit of the number of ratings for each attacker is the average number of ratings.
\subsection{Triple Cooperative Defense}
\begin{figure}[h]
\centering
\includegraphics[width=1\columnwidth]{framework.pdf}
\captionsetup{font=scriptsize}
\caption{The training of model $h_{i}$ in each round. a: The other two models use the same collaborative training. b: The labels predicted the same by the two models are taken as consistent samples. c: Model i is trained on labeled samples $D_{L}$ and consistent samples.}
\label{fig:framework}
\end{figure}
As discussed in section 1, data-processing-based defense inevitably removes normal data altogether to achieve high recall rates, while model-based defense is difficult to enjoy both robustness and generalization\cite{zhang2020attacks}. Therefore, it is crucial to combine them effectively and design a defense algorithm that maximizes their strengths and circumvents their weaknesses. Recent studies\cite{deldjoo2021survey} demonstrated that robust models require more labeled data\cite{wu2021fight}. Besides, the recommender system is extremely sparse, that is, there is little interactive information about users and items, making a small amount of normal data difficult to support good training of the model, and maybe misled easily by malicious data and produce biased recommendations. This finding makes us reasonably believe that the vulnerability of the recommendation system is largely due to the lack of data. However, it takes a lot of manpower and material resources to get labeled data, and using a small number of ``expensive'' labeled data instead of a large number of ``cheap'' unlabeled data is a huge waste of data resources. Considering the reasons mentioned above, we constructively propose adding pseudo ratings with high confidence improves the recommender robustness.
Unfortunately, in the implicit recommendation system concerned in this paper, it is challenging to obtain high confidence pseudo scores. This is because the output of recommender systems is prediction scores, not confidence, unlike other areas of machine learning(e.g., in the image field, the output is the prediction probability). So we develop TCD, which uses three models and takes the prediction consistency ratings of any two models as the high confidence pseudo ratings of the remaining model. Moreover, the use of three models can not only provide confidence scores but also improve the robustness of the model through the collaborative training of three models. The framework is shown in Fig.1. In theory, more models with majority votes are more beneficial to obtain high-confidence data. However, the training of the model is linearly positively related to the number of models. We found that the performance of the three models is satisfactory and the training delay is tolerable. Now we provide details of the proposed TCD
for defending against poisoning attacks.
Let $D$ denote the dataset, $D_{L}$ denotes the scoring samples of $D$, where each sample $(u,i,r_{i,j})$ denotes that the user $u$'s rating on item $i$ is $r_{i,j}$, and $D_{U}$ denotes the no scoring samples of $D$, where each sample is like $(u,i)$. The goal of the recommendation system $h$ is to predict accurate scores $\hat{r}_{u,i}=h(u,i)$ of each sample $(u,i)\in D_U$.
In TCD, we denote the three models as $h_0$, $h_1$, and $h_2$, respectively. For any model,
if the predicted scores of the other two models are consistent, then we have reason to believe that the predicted scores are high-confident and reliable to be added to the training set which addresses the difficulty to measure rating confidence. For instance, if $h_{0}$ and $h_{1}$ agree on the
labeling $r_{i,j}$ of $(u,i)$ in $D_{U}$, then $(u,i,r_{i,j})$ will be put into the training set for $h_{2}$ as auxiliary training data. It
is obvious that in such a scheme if the prediction of $h_{0}$ and $h_{1}$
on $(u,i)$ is correct, then $h_{2}$ will receive a new sample with high confidence for
further training. This strategy takes into account that it is difficult for attackers to learn the real rating distribution, causing the poisoning profiles to deviate from the real data \cite{lin2020attacking}, which is reflected in the instability of their training. Therefore, cooperative training will magnify the influence of real profiles and relatively weaken the harm of false profiles.
Besides, the predicted ratings are floating points, making it impractical to judge based on the consistent rating. So we define a projection function $\Pi(\cdot)$ to project continuous scores onto reasonable discrete scores. In this way, only when two models give the same rating on $(u,i)$ after projection, do we take the rating as the pseudo label and put $(u, i, \Pi(\hat{h_{j}}(u,i)))$ into the training set $D_{L}^{(k)}$.
\begin{algorithm}
\caption{Triple Cooperative Defense
\LinesNumbered
\KwIn{The epochs of training $T$, the epochs of pre-training $T_{pre}$, three models $h_{1}(u,i), h_{2}(u,i), h_{3}(u,i)$, labeled data $D_{L}$, unlabeled data $D_{U}$, projection function $\Pi(x)$}
\For{$T_{pre}$ epochs}{
\For{$j \in [0,1,2]$}{
Train $h_{j} $ based on the training set $D_{L}$
}
}
\For{$T-T_{pre}$ epochs}{
\For{$j \in [0,1,2]$}{
$D_{L}^{(j)} \gets D_{L}$\\
\For{every $(u,i) \in D_{U}$}{
\If{$\Pi(\hat{h}_{(j+1)mod 3}(u,i)) = \Pi(\hat{h}_{(j+2)mod 3}(u,i))$}
{$D_{L}^{(j)} \gets D_{L}^{(j)} \cup \{(u, i, \Pi(\hat{h}_{(j+1)mod 3}(u,i)))\}$\\
}
}
Train $h_{j} $ based on training set $D_{L}^{(j)}$
}
}
\end{algorithm}
The algorithm of TCD is shown in Alg. 1. Each model is pre-trained from lines 1 to 5. Then, for each round of training for each model, an unlabeled prediction will be labeled if any two models agree on the labeling, as shown in lines 6 through 10. These pseudo labels with high confidence will be put into the third model's training dataset to reduce the harm that poisoning data do to the model, as shown in lines 11 through 16. After the training, we can perform the recommendation task using any model. Since the structure of each model is unchanged, the proposed strategy does not have inference delay, which is of more concern to practical applications.
It is worth noting that in the pre-training phase, we used the same dataset $D_{L}$ for all models. Theoretically, we need to choose different training subsets to ensure the diversity of the model. This is necessary for other domains, such as computer version, because the number of parameters in a classifier is independent of the number of samples. However, in the recommender systems with extremely sparse data, selecting a subset means that a large number of users are cold-start users, and the parameters of these users cannot be trained, which directly leads to unsatisfactory recommendation performance. Therefore, all label data are selected for pre-training, while the models' diversity is guaranteed by different pseudo-labels in collaborative training.
\section{EXPERIMENT}
\subsection{Settings}
\subsubsection{Datasets}
We use three real-world datasets commonly used
in the security studies \cite{christakopoulou2019adversarial,yuan2019adversarial} of the recommender system, including FilmTrust\footnote{https://www.librec.net/datasets/flmtrust.zip}, ML-100K\footnote{https://grouplens.org/datasets/movielens}
(MovieLens-100K), and ML-1M\footnote{https://grouplens.org/datasets/movielens}(MovieLens-1M). ML-100K includes 943 users who
have rated 1,682 movies for 100,000 ratings. ML-1M comprises 6,040
users who have rated 3,706 movies about one million times. For
FilmTrust, the same pretreatment as \cite{lin2020attacking} is used to filter cold-start
users who seriously affect the recommender system (the rating
number is less than 15), leaving 796 users with trust ratings for
2011 movies. Table 1 lists the detailed statistics of these datasets. All
ratings are from 1 to 5, and we normalized them to [0, 1] in the
experiments. For each dataset, we randomly select a positive sample
from each user for testing, and the rest are used as the training set
and verification set in a 9:1 ratio.
\begin{table}[htbp]
\centering
\caption{Statistics of datasets}
\setlength{\tabcolsep}{5mm}{
\begin{tabular}{ccccc}
\toprule
Dataset&users&items&ratings&sparsity \\
\midrule
FilmTrust&796&2011&30880&98.07\\
ML-100K&943&1682&100000&93.70\\
ML-1M&6040&3706&1000209&95.53\\
\bottomrule
\end{tabular}}
\end{table}
\subsubsection{Attack Methods}
In the low-knowledge attacks studied in this paper, the attacker uses captured partial data to rebuild a local simulator which is similar to the target model. Then, the attacker take the local simulator as a white box for attacking. The validity of this setting is guaranteed by the transferability of the attack. Here we use the following attacks for robustness validation:
\begin{itemize}
\item \textbf{Random Attack} \cite{lam2004shilling}: This attack assigns the maximum rating
to the target item and rates selected items according to the normal
distribution of all user ratings at random.
\item \textbf{Average Attack} \cite{lam2004shilling}: The only difference from Random Attack
is that the non-target selected item is randomly rated with the
normal rating distribution of items.
\item \textbf{AUSH Attack} \cite{lin2020attacking}: This attack uses GAN to generate fake
users to carry out attacks imperceptibly and assigns the highest
rating to the target item.
\item \textbf{PGA Attack} \cite{li2016data}: This attack builds an attack objective and uses
SGD to update the poisoned user's ratings to optimize the objective.
Finally, the first items with the largest ratings are selected as
the fake user's filler items.
\item \textbf{TNA Attack} \cite{fang2020influence}: This attack selects a subset of the most influential users in the dataset and optimizes the rating gap between the
target item and top-K items in the user subset. Here we use S-TNA.
\end{itemize}
\subsubsection{Baselines}
We compare the proposed TCD with the following
robust algorithms:
\begin{itemize}
\item \textbf{Adversarial Training(AT)}\cite{he2017neural}: In each training step, it first uses SGD to optimize the inner objective to generate small perturbations, adds them to the parameters, and then performs training.
\item \textbf{Random Adversarial Training(RAT)}\cite{he2017neural}: In each training step, it first uses the truncated normal distribution N(0,0.01) to generate small perturbations, adds them to the parameters, and then performs training.
\end{itemize}
These methods cannot enjoy both generalization and robustness. The larger the noise is, the better the robustness will be, but the generalization will decrease significantly. Therefore, 0.03 is selected as a compromise.
\subsubsection{Evaluation Metric}
We first use HR@50 (Hit Ratio), just like \cite{wu2021fight}, which
calculates the proportion of test items that appear in the user's top-50 recommendation list. Setting a large K helps make apparent comparisons between
defense methods and collaborative filtering is often used for candidate selection in practical recommendations, so it is more instructive to select a larger K to ensure a high recall \cite{he2018adversarial}. Besides, we use robustness improvement
$RI = 1- (HR_{defense} - HR_{orgin})/(HR_{attack} - HR_{orgin})$ defined in \cite{wu2021fight}. The closer
the value is to 1, the better the robustness. We report the average
results of 30 independent repeated experiments and perform paired
t-test to judge the statistical significance when necessary.
\subsubsection{Parameters Setting}
We concern with the MF-based collaborative filtering method, and we set the latent factor
dimension $d$ to 128, the batch size to 2048, and the regularization parameter to 0.005. In FilmTrust, ML-100K, and ML-1M, $Tpre$ is set to 1, 4, 2, respectively. The model is trained for 40 epochs, the results are based on the choice of the smallest MSE, and the
Adam optimizer is used for training. Besides, we set the attacker knowledge-cost to 0.4, the attack size to 3\%, and the pseudo-label rate of ML-1M to 0.2. For the target items of
attacks, we learn two types of items: (1) random items randomly
selected from all items, and (2) unpopular items randomly selected
from items with the number of rates less than 5. In each attack,
we set the number of target items to 5 and set the number of filler items $m '$ to the average number of ratings per user. The source
code of TCD is available at https://github.com/greensun0830/TCD.
\begin{table}[htbp]
\centering
\caption{Attack performance under different attack knowledge-cost.}
\begin{adjustbox}{width=1\textwidth}
\small
\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c|c}
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{3}[3]{*}{Dataset} & \multicolumn{7}{c|}{Random Items} & \multicolumn{6}{c}{Unpopular Items} \\
\noalign{\smallskip} \cline{2-14} \noalign{\smallskip}
& \multirow{2}[2]{*}{Attack} &\multirow{2}[2]{*}{Origin} & \multicolumn{5}{c|}{Attack Knowledge-cost} & \multirow{2}[2]{*}{Origin} & \multicolumn{5}{c}{Attack Knowledge-cost} \\
\noalign{\smallskip} \cline{4-8} \cline{10-14}\noalign{\smallskip}
& & & 0.2 & 0.4 & 0.6 & 0.8 & 1 & & 0.2 & 0.4 & 0.6 & 0.8 & 1 \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{5}[0]{*}{Filmtrust} & Average & 0.1617 & 0.0889 & 0.1005 & 0.1612 & 0.1222 & 0.1303 & 0.0000 & 0.0016 & 0.0022 & 0.0013 & 0.0017 & 0.0024 \\
& Random & 0.1702 & 0.1376 & 0.1213 & 0.1622 & 0.1214 & 0.1404 & 0.0000 & 0.0034 & 0.0019 & 0.0012 & 0.0028 & 0.0023 \\
& AUSH & 0.1629 & 0.1132 & 0.1403 & 0.1625 & 0.2540 & 0.2675 & 0.0000 & 0.0152 & 0.0296 & 0.0285 & 0.0283 & 0.0461 \\
& PGA & 0.1574 & 0.0983 & 0.1031 & 0.1625 & 0.1471 & 0.1396 & 0.0000 & 0.0028 & 0.0013 & 0.0040 & 0.0049 & 0.0080 \\
& TNA & 0.1628 & 0.5619 & 0.5463 & 0.1446 & 0.5435 & 0.3380 & 0.0000 & 0.3054 & 0.4059 & 0.1839 & 0.0899 & 0.0807 \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{5}[0]{*}{ML-100K} & Average & 0.0233 & 0.1829 & 0.1579 & 0.2193 & 0.2237 & 0.2209 & 0.0000 & 0.0255 & 0.1572 & 0.5094 & 0.5943 & 0.4694 \\
& Random & 0.0234 & 0.0519 & 0.0956 & 0.0812 & 0.1099 & 0.0870 & 0.0000 & 0.1101 & 0.1056 & 0.1186 & 0.0906 & 0.0874 \\
& AUSH & 0.0233 & 0.1676 & 0.2819 & 0.3112 & 0.3667 & 0.3013 & 0.0000 & 0.0756 & 0.2320 & 0.7809 & 0.7942 & 0.8150 \\
& PGA & 0.0237 & 0.0855 & 0.1583 & 0.1673 & 0.1194 & 0.1667 & 0.0000 & 0.4558 & 0.2828 & 0.3912 & 0.3113 & 0.2809 \\
& TNA & 0.0244 & 0.0735 & 0.2355 & 0.2786 & 0.2512 & 0.2714 & 0.0000 & 0.6925 & 0.3934 & 0.6932 & 0.5628 & 0.7511 \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{5}[0]{*}{ML-1M} & Average & 0.0000 & 0.1829 & 0.2390 & 0.2812 & 0.2674 & 0.3116 & 0.0000 & 0.9029 & 0.9326 & 0.9261 & 0.9408 & 0.9434 \\
& Random & 0.0000 & 0.0519 & 0.0568 & 0.0563 & 0.0596 & 0.0608 & 0.0000 & 0.7213 & 0.7184 & 0.6471 & 0.7014 & 0.7588 \\
& AUSH & 0.0000 & 0.1676 & 0.2829 & 0.3145 & 0.3061 & 0.3278 & 0.0000 & 0.9680 & 0.9712 & 0.9767 & 0.9759 & 0.9803 \\
& PGA & 0.0000 & 0.0855 & 0.1027 & 0.1036 & 0.0418 & 0.0336 & 0.0000 & 0.9569 & 0.9433 & 0.9243 & 0.9034 & 0.9118 \\
& TNA & 0.0000 & 0.0735 & 0.2622 & 0.3046 & 0.3114 & 0.3406 & 0.0000 & 0.9068 & 0.9325 & 0.9395 & 0.9508 & 0.9496 \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\end{tabular}%
\end{adjustbox}
\label{tab:addlabel}%
\end{table}%
\subsection{Result Analysis}
In this section, we compare the robustness and generalization of
the model configured with TCD and other defense methods.
\subsubsection{Attack Threat}
Different attack knowledge-cost leads to different attack performances, as shown in Table 2. We can find that a larger attack knowledge-cost does not have better attack performance, even when attackers only know 20\% of the model knowledge, they can achieve a good attack effect, and in most cases, 40\% attack knowledge performs well. Moreover, considering practical application scenarios, attacks cannot get full knowledge about recommender systems. So we choose to set the attack knowledge-cost to 0.4 to ensure its practicability while achieving a good attack performance. However, we also found that not all attacks are effective. For example, heuristic Random Attack and Average Attack are ineffective in FilmTrust and even reduce the exposure rate of target items, which emphasizes the significance of studying optimization-based attacks.
\subsubsection{Robustness}
We evaluate the hit ratio of target items in attack
and defense, as shown in Table 3. The Origin denotes the unperturbed model, and the Attack represents the perturbed model with
no defense. Consistent with the findings in Table 3,
We have the following finds:
\begin{table*}[htbp]
\centering
\caption{The performance in target items (robustness). *, ** and *** indicate that the improvements over the best results of baselines are statistically significant for $ p<0.05, p<0.01 $ and $ p<0.001 $, respectively.}
\begin{adjustbox}{width=1\textwidth}
\small
\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c}
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{2}[2]{*}{Dataset} & \multirow{2}[2]{*}{Attack} & \multicolumn{5}{c|}{Random Items} & \multicolumn{5}{c}{Unpopular Items} \\
\noalign{\smallskip} \cline{3-12} \noalign{\smallskip}
& & Origin & Attack & AT & RAT & TCD & Origin & Attack & AT & RAT & TCD \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{5}[0]{*}{FilmTrust\newline{}} & Average & 0.1617 & 0.1005 & 0.0961 & 0.1001 & \textbf{0.1093**} & 0.0000 & 0.0016 & 0.0010 & 0.0008 & \textbf{0.0009***} \\
& Random & 0.1702 & 0.1213 & 0.1187 & 0.1257 & 0.1123 & 0.0000 & 0.0016 & 0.0020 & 0.0019 & \textbf{0.0016***} \\
& AUSH & 0.1629 & 0.1403 & 0.1345 & 0.1454 & 0.2204 & 0.0000 & 0.0323 & 0.0284 & 0.0330 & \textbf{0.0024***} \\
& PGA & 0.1574 & 0.1031 & 0.1008 & 0.1075 & \textbf{0.1101**} & 0.0000 & 0.0012 & 0.0015 & 0.0016 & \textbf{0.0009***} \\
& TNA & 0.1628 & 0.5463 & 0.5346 & 0.5489 & \textbf{0.4086***} & 0.0000 & 0.4276 & 0.4251 & 0.4444 & \textbf{0.0416***} \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{5}[0]{*}{ML-100K\newline{}} & Average & 0.0233 & 0.1579 & 0.1741 & 0.1525 & \textbf{0.0340***} & 0.0000 & 0.1694 & 0.1796 & 0.1421 & \textbf{0.0009***} \\
& Random & 0.0234 & 0.0956 & 0.0932 & 0.0889 & \textbf{0.0353***} & 0.0000 & 0.1105 & 0.1277 & 0.0965 & \textbf{0.0010***} \\
& AUSH & 0.0233 & 0.2819 & 0.2665 & 0.2773 & \textbf{0.0355***} & 0.0000 & 0.1478 & 0.1869 & 0.1714 & \textbf{0.0009***} \\
& PGA & 0.0237 & 0.1583 & 0.1654 & 0.1471 & \textbf{0.0385***} & 0.0000 & 0.3486 & 0.4656 & 0.4108 & \textbf{0.0015***} \\
& TNA & 0.0244 & 0.2355 & 0.2411 & 0.2369 & \textbf{0.0334***} & 0.0000 & 0.3011 & 0.3624 & 0.2986 & \textbf{0.0015***} \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{5}[0]{*}{ML-1M} & Average & 0.0000 & 0.2390 & 0.1547 & 0.2364 & \textbf{0.0048***} & 0.0000 & 0.8604 & 0.8593 & 0.8633 & \textbf{0.0309***} \\
& Random & 0.0000 & 0.0568 & 0.0455 & 0.0517 & \textbf{0.0072***} & 0.0000 & 0.6513 & 0.6450 & 0.6064 & \textbf{0.0254***} \\
& AUSH & 0.0000 & 0.2829 & 0.1395 & 0.2518 & \textbf{0.0031***} & 0.0000 & 0.9056 & 0.8845 & 0.8999 &\textbf{0.0353***} \\
& PGA & 0.0000 & 0.1027 & 0.0832 & 0.0968 & \textbf{0.0191***} & 0.0000 & 0.8577 & 0.8501 & 0.8498 & \textbf{0.0236***} \\
& TNA & 0.0000 & 0.2622 & 0.1663 & 0.2403 & \textbf{0.0042***} & 0.0000 & 0.8654 & 0.8525 & 0.8650 &\textbf{0.0269***} \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\end{tabular}%
\end{adjustbox}
\end{table*}%
\begin{figure*}[h]
\centering
\subfloat[FilmTrust]{\includegraphics[width=0.5\linewidth]{filmtrust.pdf}}
\hfill
\subfloat[ML-100K]{\includegraphics[width=0.5\linewidth]{ml100k.pdf}}
\hfill
\caption{The distribution of rank shift. In FilmTrust and Ml-100k, top: TNA attack; middle: AT on TNA attack; bottom:
TCD on TNA attack; boxplot: statistical distributions of rank shift. The closer the rank shift is to 0,
the smaller the damage of the attack}
\label{fig:ri}
\end{figure*}
\begin{itemize}
\item These defense methods are positive in weakening
the attack's damage concerning HR in most cases.
\item The
proposed TCD achieves remarkable defense results, almost close
to the unperturbed model performance. On average, we reduce
the impact of attacks on random items by over 88\% and unpopular
items by over 82\%, which effortlessly outperforms baselines.
\item We notice that the performance of TCD against Average and Random on FilmTrust's unpopular items is slightly
inferior when compared with the defense against other attacks while almost every performance of TCD on ML-100k and ML-1M is better than that of baselines. We
suspect that Filmtrust is too small to represent real data, making it easier for adversarial training to
discover and learn adversary data non-robust features while making it more formidable for TCD to find data's non-robust features.
\end{itemize}
Besides, Fig. 2 shows the Rank shift distribution of target items (unpopular items) under the TNA attack. The attack significantly promotes the target item's
rank among all users. After using adversarial training, the rank change caused by the attack can be eased, but it is only slight. On
the contrary, TCD impels the distribution of rank shift obviously
tends to 0, which means that applying TCD can produce more stable
recommendations in a disturbed environment.
In conclusion, these results confirm the positive effect of TCD in
boosting recommendation robustness against poisoning attacks.
\subsubsection{Generalization}
\begin{table*}[htbp]
\centering
\caption{The performance in test set (generalization). *, ** and *** indicate that the improvements over the unperturbed model are statistically significant for $ p<0.05, p<0.01 $ and $ p<0.001 $, respectively.}
\begin{adjustbox}{width=1\textwidth}
\small
\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c}
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{2}[2]{*}{Dataset} & \multirow{2}[2]{*}{Attack} & \multicolumn{5}{c|}{Random Items} & \multicolumn{5}{c}{Unpopular Items} \\
\noalign{\smallskip} \cline{3-12} \noalign{\smallskip} & & Origin & Attack & AT & RAT & TCD & Origin & Attack & AT & RAT & TCD \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{5}[0]{*}{Filmtrust}& Average & 0.8253 & 0.8196 & 0.8086 & 0.8187 & \textbf{0.8640***} & 0.8273 & 0.8258 & 0.8096 & 0.8160 & \textbf{0.8648***} \\
& Random & 0.8266 & 0.8245 & 0.8010 & 0.8179 & \textbf{0.8635***} & 0.8275 & 0.8221 & 0.8085 & 0.8185 & \textbf{0.8651***} \\
& AUSH & 0.8252 & 0.8240 & 0.8170 & 0.8193 & \textbf{0.8660***} & 0.8256 & 0.8196 & 0.8053 & 0.8184 & \textbf{0.8639***} \\
& PGA & 0.8257 & 0.8222 & 0.8046 & 0.8181 & \textbf{0.8643***} & 0.8266 & 0.8212 & 0.8088 & 0.8205 & \textbf{0.8636***} \\
& TNA & 0.8264 & 0.8079 & 0.7840 & 0.8021 & \textbf{0.8639***} & 0.8273 & 0.8054 & 0.7824 & 0.8002 &\textbf{0.8622***} \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{5}[0]{*}{ML-100K} & Average & 0.2006 & 0.1985 & 0.1907 & 0.1995 & \textbf{0.2875***} & 0.2020 & 0.1998 & 0.1924 & 0.1970 &\textbf{0.2836***} \\
& Random & 0.1988 & 0.2025 & 0.2003 & 0.2005 & \textbf{0.2898***} & 0.1969 & 0.2058 & 0.1973 & 0.2003 & \textbf{0.2804***} \\
& AUSH & 0.1998 & 0.1978 & 0.1894 & 0.1940 & \textbf{0.2824***} & 0.2007 & 0.1971 & 0.1904 & 0.1951 & \textbf{0.2797***} \\
& PGA & 0.2005 & 0.1960 & 0.1872 & 0.1920 & \textbf{0.2851***} & 0.2022 & 0.1887 & 0.1848 & 0.1905 & \textbf{0.2858***} \\
& TNA & 0.1995 & 0.1990 & 0.1933 & 0.1967 & \textbf{0.2897***} & 0.2003 & 0.1970 & 0.1873 & 0.1911 & \textbf{0.2785***} \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\multirow{5}[0]{*}{ML-1M} & Average & 0.0834 & 0.0748 & 0.0542 & 0.0718 & \textbf{0.1097***} & 0.0843 & 0.0718 & 0.0519 & 0.0695 & \textbf{0.1094***} \\
& Random & 0.0844 & 0.0877 & 0.0850 & 0.0860 & \textbf{0.1097***} & 0.0833 & 0.0827 & 0.0816 & 0.0830 & \textbf{0.1097***} \\
& AUSH & 0.0837 & 0.0733 & 0.0523 & 0.0689 & \textbf{0.1105***} & 0.0832 & 0.0685 & 0.0448 & 0.0639 & \textbf{0.1103***} \\
& PGA & 0.0837 & 0.0842 & 0.0805 & 0.0818 & \textbf{0.1092***} & 0.0831 & 0.0774 & 0.0731 & 0.0767 & \textbf{0.1105***} \\
& TNA & 0.0827 & 0.0748 & 0.0540 & 0.0713 & \textbf{0.1101***} & 0.0846 & 0.0743 & 0.0539 & 0.0719 & \textbf{0.1096***} \\
\noalign{\smallskip} \hline \noalign{\smallskip}
\end{tabular}%
\end{adjustbox}
\label{tab:ex:cref}
\end{table*}%
It is meaningless to improve the robustness
at the cost of apparently sacrificing the generalization of standard
recommendations. Table 4 records the HR of various defense methods in the holdout test set. We have the following finds:
\begin{itemize}
\item TCD surprisingly improves the generalization of the three datasets and the improvement is above 0.02 in terms of HR.
These results confirm that TCD effectively guarantees the model's
generalization while performing high-quality defense.
\end{itemize}
\subsection{Parameter Analysis}
\subsubsection{Performance under Different Attack knowledge-cost}
We conduct the robustness improvement test of TCD under different
attack knowledge-cost, as illustrated in Fig. 3. On the one hand, the overall
defense performance of TCD remains at a high level, although there
will be individual cases on FilmTrust where it performs not that well. On the other hand, as the
attack intensity increases, the robustness against attacks is still satisfactory. Especially in ML-100K and ML-1M, RI is almost clear 100\%!
\begin{figure}[h]
\centering
\includegraphics[width=1.\columnwidth]{inject_rate3.pdf}
\caption{Robustness improvement under different attack knowledge-cost
}
\label{fig:knowledge cost}
\end{figure}
\subsubsection{Performance under Different Pseudo-label Ratios}
The training time of TCD is directly proportional to the training set. Considering the size and sparsity of ML-1M, we decide to put only part of pseudo labels into the training set, and we denote the pseudo labels rate as the proportion of the pseudo labels which is put into the training set. We conduct the robustness test of TCD under different
pseudo-label ratios, as illustrated in Fig. 4. With the injected pseudo-label ratio increases, the robustness of the model is improved accordingly, and 0 on the abscissa means attack without any defense. When the pseudo-label ratio is only 0.2, TCD can significantly improve the robustness of the model, which emphasizes its practicality in large datasets.
\begin{figure}[h]
\centering
\includegraphics[width=0.9\columnwidth]{dele-rate.pdf}
\caption{The defense performance of the target items on ML-1M under different injected pseudo-label ratio}
\label{fig:pseudo labels rate}
\end{figure}
\section{Conclusion and Outlook}
In this paper, we proposed the TCD method to defend against attacks on recommender systems. It is noteworthy that TCD is the first algorithm to combine data-processing-based defense with model-based defense in recommender systems. Specifically, we sequentially use the high-confidence prediction ratings of any two models as auxiliary training data for the remaining models. Since TCD enhances data by adding pseudo labels instead of deleting abnormal data, it can avoid cleaning normal data and train a more accurate and robust model. Moreover, the cooperative training of the three models makes it beneficial for model generalization. Moreover, TCD is a general framework, so it can be combined with other defense methods. In the future, we plan to apply TCD in non-recommendation fields.
\renewcommand{\bibsection}{\section*{References}}
\bibliographystyle{splncsnat}
\begingroup
\microtypecontext{expansion=sloppy}
\small
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,983 |
title : Coinspeaker April 8, 2016
publishedBy : Coinspeaker
publishedOn : April 8, 2016
link : https://www.coinspeaker.com/2016/04/08/storj-labs-joins-the-microsoft-azure-blockchain-ecosystem/
weight: 215
articleName : Storj Labs Joins the Microsoft Azure Blockchain Ecosystem
class : pressArticle
---
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,764 |
"use strict";
Object.defineProperty(exports, "__esModule", {
value: true
});
exports.default = void 0;
var _index = _interopRequireDefault(require("./_lib/formatDistance/index.js"));
var _index2 = _interopRequireDefault(require("./_lib/formatLong/index.js"));
var _index3 = _interopRequireDefault(require("./_lib/formatRelative/index.js"));
var _index4 = _interopRequireDefault(require("./_lib/localize/index.js"));
var _index5 = _interopRequireDefault(require("./_lib/match/index.js"));
function _interopRequireDefault(obj) { return obj && obj.__esModule ? obj : { default: obj }; }
/**
* @type {Locale}
* @category Locales
* @summary Dutch locale.
* @language Dutch
* @iso-639-2 nld
* @author Jorik Tangelder [@jtangelder]{@link https://github.com/jtangelder}
* @author Ruben Stolk [@rubenstolk]{@link https://github.com/rubenstolk}
* @author Lode Vanhove [@bitcrumb]{@link https://github.com/bitcrumb}
* @author Edo Rivai [@edorivai]{@link https://github.com/edorivai}
* @author Niels Keurentjes [@curry684]{@link https://github.com/curry684}
* @author Stefan Vermaas [@stefanvermaas]{@link https://github.com/stefanvermaas}
*/
var locale = {
code: 'nl',
formatDistance: _index.default,
formatLong: _index2.default,
formatRelative: _index3.default,
localize: _index4.default,
match: _index5.default,
options: {
weekStartsOn: 1
/* Monday */
,
firstWeekContainsDate: 4
}
};
var _default = locale;
exports.default = _default;
module.exports = exports.default; | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,786 |
Jelendol je naselje u slovenskoj Općini Škocjanu. Jelendol se nalazi u pokrajini Dolenjskoj i statističkoj regiji Jugoistočnoj Sloveniji.
Stanovništvo
Prema popisu stanovništva iz 2002. godine naselje je imalo 34 stanovnika.
Izvor
Naselja u Općini Škocjan | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,493 |
Bei der Fernsehshow Ca$hman (engl. "Geldmann") handelt es sich um eine Spielshow des Senders RTL 2, die sich im deutschen Fernsehen nicht etablieren konnte.
Konzept
Auf offener Straße wurden Passanten vom sogenannten Cashman gefragt, ob sie für Geld eine Aufgabe erledigen würden. Diese Aufgaben bestanden beispielsweise darin, mit dem Gesicht Tischtennis-Bälle aus einem Ketchup-Eimer zu angeln, einen Rolltreppenhandlauf mit der Zunge abzulecken oder Sekt aus getragenen Schuhen zu schlürfen. Für eine erfolgreich absolvierte Aufgabe bekam der Spieler einen 500-Mark-Schein.
Das Konzept der Sendung kam ursprünglich aus den Niederlanden, konnte sich in Deutschland jedoch nicht durchsetzen. Bereits nach zwei Monaten wurde die Sendung wegen schwacher Quoten wieder abgesetzt.
Kritik
Die Frankfurter Allgemeine Zeitung sah in einer Nachbetrachtung in der Spielshow Ca$hman eine weitere Stufe des Fernsehens, den Anspruch an den guten Geschmack zu verlieren. Ca$hman wurde zudem als frühe Stufe des heutigen Ekelfernsehens in Deutschland eingeordnet.
Einzelnachweise
RTL II
Fernsehsendung der 1990er Jahre
Spielshow | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 106 |
\section*{Introduction}
The importance of quantum information processing is beyond doubt due to its spectacular applications.
Nowadays there is some evidence of quantum processors capable of executing certain tasks greatly improving classical processors \cite{Aru} which increases the interest in tools for the proper functioning of quantum computers such as the quantum error-correcting codes (QECCs). QECCs are mainly designed for protecting quantum information from quantum noise and decoherence. Notice that, despite quantum information cannot be cloned \cite{8AS, 26RBC}, quantum error correction works \cite{23RBC, 95kkk}. These facts explain why many researchers are interested in obtaining QECCs with good parameters (which measure the behaviour of the codes) and the literature contains a large quantity of papers devoted to finding QECCs with better parameters than others previously obtained.
Let $q$ be a prime power, a $q$-ary QECC of length $n$ is a subspace of the Hilbert space $\mathcal{H}=\mathbb{C}^{q^n}$. The most used class of quantum codes are stabilizer quantum codes. They are obtained as the intersection of the eigenspaces, corresponding to the eigenvalue $1$, of the elements of some subgroup of the error group generated by a suitable error basis of the Hilbert space $\mathcal{H}$. The parameters of a QECC, length, dimension and minimum distance, are usually denoted by $((n,K,d))_q$, where errors with weight less than $d$ either can be detected or have no effect on $C$ but some error with weight $d$ cannot be detected. We are only interested in $q^k$-dimensional subspaces of $\mathcal{H}$ and, abusing of notation and when no confusion arises, we say that these QECCs have dimension $k$; in this case, the parameters are usually written as $[[n,k,d]]_q$.
QECCs were firstly introduced in the binary case, where one finds the seminal papers on the subject \cite{20kkk, 38kkk, 18kkk, 19kkk, 45kkk, 7kkk, 8kkk}. Later QECCs were studied for the general $q$-ary case (see \cite{BE, 71kkk, AK, 35kkk, opt, kkk, Akk, lag3, lag1, jin, lag2, SLLG, galindo-hernando, gal-her-rua, QINP2, traza, cao-cui2, cao-cui} among many other articles). The general case is particularly interesting for fault-tolerant computing \cite{FTShor, FTKnill, FTPres, FTGot, FTSte, FTCam, luol}.
One of the main advantages of stabilizer codes is that their existence is equivalent to that of self-orthogonal additive codes with respect to certain trace-symplectic form (see \cite{AK} or \cite[Theorem 13]{kkk}). This trace-symplectic form is not very used but the above result allows us to deduce that many stabilizer quantum codes can be derived from self-orthogonal classical codes with respect to the Hermitian or the Euclidean inner product. Usually one finds good stabilizer codes over $\mathbb{F}_q$ by considering Hermitian self-orthogonal codes over $\mathbb{F}_{q^2}$. The specific result, Theorem \ref{La1}, shows that an $[[n,n-2k, \geq d^{\perp_h}]]_q$ quantum code can be constructed from a Hermitian self-orthogonal $[n,k]_{q^2}$ linear code $C$ over $\mathbb{F}_{q^2}$, where $d^{\perp_h}$ stands for the minimum distance of the Hermitian dual code $C^{\perp_h}$. This result has been extensively used in many papers to give many good QECCs \cite{lag3, lag2, jin, zh}.
In the present paper we recall that Theorem \ref{La1} can be regarded as a special case of a more general result by considering linear codes over certain extensions of $\mathbb{F}_{q}$. Indeed, Theorem \ref{Elbueno} states that if $C$ is a linear code over $\mathbb{F}_{q^{2 m}}$, $m \geq 1$, with parameters $[n,k]_{q^{2 m}}$ which is self-orthogonal with respect to the Hermitian inner product, then there exists an $[[m n, m n - 2 m k, \geq d^{\perp_h}]]_q$ stabilizer quantum code. Theorem \ref{Elbueno} is a straightforward consequence of \cite[Lemma 76]{kkk} which seems to have gone unnoticed by many researchers because, in the literature, we have not found new quantum codes considering $m>1$.
We expect that many good quantum codes can be established by this result. Our goal is to give some evidence by stating (and proving) Theorem \ref{elH} which combined with Theorem \ref{Elbueno} gives rise to a number of stabilizer quantum codes with good parameters. Theorem \ref{elH} derives from \cite{jin} and gives an easy way to find Hermitian self-orthogonal codes. The above mentioned combination produces, in the binary case, new QECCs which are records according to \cite{codet}. Here, the word record means we provide codes for entries in \cite{codet} whose constructions were missing. There is no collection of tables as \cite{codet} for non-binary QECCs but one can find many papers in the literature about them. Most of these papers are devoted to quantum MDS codes which have relatively small length \cite{chen, refer, zh}. Since we are able to construct long QECCs, we use recent articles \cite{SLLG, cao-cui, LV} for comparison and show that with our method we can improve the parameters of a number of codes therein.
Section \ref{secuno} of the paper is devoted to recall Theorem \ref{Elbueno} for obtaining QECCs from linear codes. Theorem \ref{elH} and parameters (some of them displayed in tables) of new QECCs can be found in Section \ref{secdos}. As mentioned all the provided parameters correspond to QECCs obtained by applying Theorems \ref{elH} and \ref{Elbueno}. In the binary case, our results together with propagation rules determine $91$ new QECCs which are records according to \cite{codet}. We use the rules that state that the existence of an $[[n,k, d]]_q$ quantum code implies that of an $[[n+1,k, \geq d]]_q$ quantum code (lengthening) and, also, that of an $[[n,k-1, d]]_q$ quantum code (subcode-construction) \cite[Lemmas 69 and 71]{kkk}.
\section{A construction of stabilizer quantum codes}
\label{secuno}
Let $q=p^r$, where $p$ is a prime and $r$ a positive integer. Many good stabilizer quantum codes over the finite field with $q$ elements $\mathbb{F}_q$ are obtained from linear codes over the finite field $\mathbb{F}_{q^2}$ which are self-orthogonal under the Hermitian inner-product. Recall that given two vectors $\boldsymbol{x} = (x_1, x_2, \ldots, x_n)$ and $\boldsymbol{y} = (y_1, y_2, \ldots, y_n)$ in $\mathbb{F}_{q^2}^n$, $n \geq 1$, their {\it Hermitian inner product} is defined by
\[
\boldsymbol{x} \cdot_h \boldsymbol{y} := \sum_{i=1}^n x_i y_i^q \in \mathbb{F}_{q^2},
\]
and the specific result to construct stabilizer quantum codes is the following (see \cite[Corollary 16 and Lemma 18]{kkk}).
\begin{teo}
\label{La1}
Let $C$ be an $\mathbb{F}_{q^2}$-linear code of length $n$ and dimension $k$. Assume that $C$ is Hermitian self-orthogonal, i.e.
\[
C \subseteq C^{\perp_h} := \left\{ \boldsymbol{x} \in \mathbb{F}_{q^2}^n \; | \; \boldsymbol{x} \cdot_h \boldsymbol{y} =0 \mbox{ for all $\boldsymbol{y}$ in $C$} \right\}.
\]
Then, there exists a stabilizer quantum code over $\mathbb{F}_{q}$ with parameters $[[n,n-2k, \geq d^{\perp_h}]]_q$, where $d^{\perp_h}$ stands for the minimum distance of the code $C^{\perp_h}$.
\end{teo}
Next we recall a generalization of Theorem \ref{La1} allowing the use of codes over extension fields of $\mathbb{F}_{q^2}$. We will prove that one can obtain long stabilizer codes with good parameters over $\mathbb{F}_{q}$ by considering linear codes over fields $\mathbb{F}_{q^{2 m}}$, $m >0$, which are self-orthogonal with respect to the Hermitian inner product.
\begin{teo}
\label{Elbueno}
Let $C$ be an $\mathbb{F}_{q^{2m}}$-linear code of length $n$ and dimension $k$, $m>0$. Suppose that $C \subseteq C^{\perp_h}$, where
\[
C^{\perp_h} := \left\{ \boldsymbol{x} \in \left(\mathbb{F}_{q^{2 m}}\right)^n \; | \; \boldsymbol{x} \cdot_h \boldsymbol{y} := \sum_{i=1}^n x_i y_i^{q^{m}} = 0 \mbox{ for all $\boldsymbol{y}$ in $C$}
\right\}.
\]
Then, there exists an $\mathbb{F}_{q}$-stabilizer quantum code with parameters
\[
\big[\big[ m n, mn - 2 m k, \geq d^\perp_h \big]\big]_q,
\]
where $d^\perp_h$ is the minimum distance of the code $C^{\perp_h}$.
\end{teo}
This result can be deduced from Lemma 76 in \cite{kkk} (see also \cite{AK}) which states that the existence of an $((n,K,d))_{q^m}$ stabilizer code implies that of an $((mn,K, \geq d))_q$ stabilizer code. Then, to deduce Theorem \ref{Elbueno}, it suffices to consider the above code $C$ to obtain an $[[n, n- 2k, \geq d^{\perp_h}]]_{q^m}$ stabilizer code by applying Theorem \ref{La1} and by \cite[Lemma 76]{kkk} there exists a $q$-ary stabilizer code as in the statement.
Surprisingly we have not found in the literature new quantum codes obtained from Theorem \ref{Elbueno}, $m>1$. We think that this result goes unnoticed by many researchers. We learned it when a reviewer pointed out to us the existence of \cite[Lemma 76]{kkk} after a first version of this paper where, in a different way, we proved Theorem \ref{Elbueno} for the particular case where $m=2^{\ell -1}$, $\ell \geq 1$.
\section{Hermitian self-orthogonal codes and examples}
\label{secdos}
We devote this section to show that some very good stabilizer quantum codes can be derived from Theorem \ref{Elbueno}.
\subsection{A useful result}
Next we state and prove a result derived from \cite[Theorem 2.5]{jin} which provides suitable linear codes to apply Theorem \ref{Elbueno}. This procedure gives some binary stabilizer quantum codes which are records according to \cite{codet} (in the sense explained in the introduction) and also some $q$-ary stabilizer quantum codes, $q \neq 2$, improving the parameters of codes in the recent literature.
We start by recalling Theorem 2.5 in \cite{jin}.
\begin{teo}
\label{elF}
Let $e$ be a prime power and set $Q=e^2$. Consider an integer $2 \leq n \leq Q$ and write
$n=n_1 + n_2 + \cdots + n_t$, where $1 \leq t \leq e$ and $2 \leq n_i \leq e$ for all $1 \leq i \leq t$. Then, for any positive integer
\[
1 \leq k \leq \frac{\min\{n_1, n_2, \ldots, n_t\}}{2},
\]
there exists an $[n,k]_Q$ linear code $\mathcal{C}$ over the field $\mathbb{F}_Q$ which is Hermitian self-orthogonal and the minimum distance of $\mathcal{C}^{\perp_h}$ is $k+1$.
\end{teo}
Next we state a new result which will be useful.
\begin{teo}
\label{elH}
Let $e>2$ be a prime power and set $Q:= e^2$. Consider an integer $2 \leq n \leq Q$ and write $n$ as $n=a e + b$, where $0 \leq a < e$ and $0 \leq b < e$, i.e. the $e$-adic expression of $n$, and include the case $a=e$ and $b=0$.
Define $K_n$ as follows: $K_n:= \lfloor e/2 \rfloor$ when $b=0$. $K_n:= \lfloor n/2 \rfloor$ when $a=0$. $K_n:= \lfloor (e-1) /2 \rfloor $ when $a \neq 0$, $b \neq 0$ and $a + b \geq e$. Otherwise,
\[
K_n := \left\lfloor \frac{\max \left\{ \lfloor n/(a+1) \rfloor, a +b \right\} }{2} \right\rfloor.
\]
Then, for each $1 \leq k \leq K_n$, there exists an $[n,k]_Q$ linear code $\mathcal{C}$ which is self-orthogonal for the Hermitian inner product and such that the minimum distance of the Hermitian dual code $\mathcal{C}^{\perp_h}$ is $k+1$.
\end{teo}
\begin{proof}
Assume $b=0$, then the result holds by setting $n_1=n_2 = \cdots = n_a = e$ and applying Theorem \ref{elF}. When $a=0$, the same theorem with $n_1=n$ proves the result.
Suppose $a \neq 0 \neq b$ and $a + b \geq e$. Let us see that there exist non-negative integers $i, j$ such that $i+j=a$ and positive integers $n_1 = \cdots = n_i = e$, $n_{i+1} = \cdots =n_{i+j}=e -1$ and $n_{a+1}= e -1$ that are suitable to apply Theorem \ref{elF}, which concludes the result in this case. Indeed,
\[
ie + j(e -1) + e -1 = (i+j) e + e -1 -j = a e + e -1 -j =n,
\]
for some $j$ because the fact that $a+b \geq e$ proves the existence of such a $j$ with $0 \leq j \leq e-1$.
Finally, assume $a +b < e$. Then, on the one hand, setting $n_1=n_2 = \cdots = n_a = e -1$ and $n_{a+1} = a +b$, we find the second bound for $k$, $\lfloor (a+b)/2 \rfloor$, by Theorem \ref{elF}. With respect to the first one, it is clear that
\[
(a+1) \left\lfloor \frac{n}{a+1} \right\rfloor \leq n \leq (a+1) \left( \left\lfloor \frac{n}{a+1} \right\rfloor +1 \right).
\]
This implies that a set $\{n_i\}_{i=1}^{a+1}$ as in Theorem \ref{elF} can be constructed for values $n_i$ which are either $\left\lfloor \frac{n}{a+1} \right\rfloor$ or $\left\lfloor \frac{n}{a+1} \right\rfloor + 1$. This concludes the proof because we can choose the best bound.
\end{proof}
\subsection{Examples}
In this subsection we determine parameters of some (constructible) stabilizer quantum codes over finite fields of small cardinality.
\subsubsection{Binary stabilizer quantum codes} We start with binary codes. In this case we give a number of quantum codes which are records according to \cite{codet}, that is we give codes for entries in \cite{codet} whose constructions were missing. We explain in detail how we get our first binary code.
We start with the values $e = 16$ and $Q=16^2 = 256$. By Theorem \ref{elH}, we can consider the value $n=63$ because $2 \leq 63 \leq 256$ and $63=n= 3 \cdot 16 + 15$. Thus $a=3$ and $b=15$. Since $a+b \geq 16$, $K_{63}= \lfloor 15 / 2 \rfloor =7$. Then, by Theorem \ref{elH}, there exists a suitable linear code $\mathcal{C}$ over $\mathbb{F}_Q$ with length $n=63$, dimension $k=6$ and $d(\mathcal{C}^{\perp_h}) =7$. Now $Q=q^{2m}$ for $q=2$ and $m=4$. Applying Theorem \ref{Elbueno}, we get a
$\mathbf{[[252,204, \geq 7]]_2}$ quantum code which is a record. If we pick $n=62$ and $k=7$, then a new record is obtained: $\mathbf{[[248,192, \geq 8]]_2}$.
With an analogous procedure we obtain new records according to \cite{codet}. By using either lengthening or subcode-construction (the two propagation rules described at the end of the introduction) we get more records. All of them are grouped in Table \ref{tabla1}, where the parameters obtained without propagation rules are marked with a * and those obtained by lengthening (respectively, subcode-construction) are marked with an $L$ (respectively, $S$).
\begin{table}
\begin{center}
\begin{tabular}{||c|c|c||c|c|c||c|c|c||c|c|c||}
\hline
$n$ & $k$ & $ \geq d$ & $n$ & $k$ & $\geq d$ & $n$ & $k$ & $\geq d$ & $n$ & $k$ & $\geq d$\\
\hline
252* & 204 & 7 & 252* & 196 & 8 & 248* & 200 & 7 & 248* & 192 & 8\\
\hline
244* & 196 & 7 & 244* & 188 & 8 & 240* & 192 & 7 & 240* & 184 & 8\\
\hline
$252^S$ & 203 & 7 & $252^S$ & 195 & 8 & $251^L$ & 200 & 7 & $251^S$ & 199 & 7\\
\hline
$251^S$ & 198 & 7 & $251^L$ & 192 & 8 & $251^S$ & 191 & 8 & $251^S$ & 190 & 8\\
\hline
$250^L$ & 200 & 7 & $250^S$ & 199 & 7 & $250^S$ & 198 & 7 & $250^S$ & 197 & 7\\
\hline
$250^L$ & 196 & 7 & $250^L$ & 192 & 8 & $250^S$ & 191 & 8 & $250^S$ & 190 & 8\\
\hline
$249^L$ & 200 & 7 & $249^S$ & 199 & 7 & $249^S$ & 198 & 7 & $249^S$ & 197 & 7\\
\hline
$249^S$ & 196 & 7 & $249^S$ & 195 & 7 & $249^L$ & 192 & 8 & $249^S$ & 191 & 8\\
\hline
$249^S$ & 190 & 8 & $249^S$ & 189 & 8 & $248^S$ & 199 & 7 & $248^S$ & 198 & 7\\
\hline
$248^S$ & 197 & 7 & $248^S$ & 196 & 7 & $248^S$ & 195 & 7 & $248^S$ & 194 & 7\\
\hline
$248^S$ & 191 & 8 & $248^S$ & 190 & 8 & $248^S$ & 189 & 8 & $248^S$ & 188 & 8\\
\hline
$247^L$ & 196 & 7 & $247^S$ & 195 & 7 & $247^S$ & 194 & 7 & $247^S$ & 193 & 7\\
\hline
$247^L$ & 188 & 8 & $247^S$ & 187 & 8 & $246^L$ & 196 & 7 & $246^S$ & 195 & 7\\
\hline
$246^S$ & 194 & 7 & $246^S$ & 193 & 7 & $246^S$ & 192 & 7 & $246^L$ & 188 & 8\\
\hline
$246^S$ & 187 & 8 & $246^S$ & 186 & 8 & $245^L$ & 196 & 7 & $245^S$ & 195 & 7\\
\hline
$245^S$ & 194 & 7 & $245^S$ & 193 & 7 & $245^S$ & 192 & 7 & $245^S$ & 191 & 7\\
\hline
$245^L$ & 188 & 8 & $245^S$ & 187 & 8 & $245^S$ & 186 & 8 & $245^S$ & 185 & 8\\
\hline
$244^S$ & 195 & 7 & $244^S$ & 194 & 7 & $244^S$ & 193 & 7 & $244^S$ & 192 & 7\\
\hline
$244^S$ & 191 & 7 & $244^S$ & 187 & 8 & $244^S$ & 186 & 8 & $244^S$ & 185 & 8\\
\hline
$244^S$ & 184 & 8 & $243^L$ & 192 & 7 & $243^S$ & 191 & 7 & $243^L$ & 184 & 8\\
\hline
$243^S$ & 183 & 8 & $242^L$ & 192 & 7 & $242^S$ & 191 & 7 & $242^L$ & 184 & 8\\
\hline
$242^S$ & 183 & 8 & $241^L$ & 192 & 7 & $241^S$ & 191 & 7 & $241^L$ & 184 & 8\\
\hline
$241^S$ & 183 & 8 & $240^S$ & 191 & 7 & $240^S$ & 183 & 8 & - & - & -\\
\hline
\end{tabular}
\end{center}
\caption{Binary stabilizer quantum records}
\label{tabla1}
\end{table}
\subsubsection{Non-binary stabilizer quantum codes}
As we did in the binary case, we explain in detail the construction of some families of good stabilizer quantum codes over $\mathbb{F}_4$. We will only show the parameters of the remaining stabilizer codes which can be obtained in a similar way.
Set $e=16$, $Q=16^2 = 256$ and, applying Theorem \ref{elH}, pick $n=76$, which accomplishes $2 \leq 76 \leq 256$. Now $n=76=4 \cdot 16 + 12$, then under the notation of that theorem $a=4$ and $b=12$. Since $a + b \geq 16$, $K_{76} = 7$, and there exists a linear code over $\mathbb{F}_Q$ which is self-orthogonal for the Hermitian inner product, where $Q=q^{2m}$ for $q=4$ and $m=2$. Applying Theorem \ref{Elbueno} we find the stabilizer quantum codes over $\mathbb{F}_4$ showed in Table \ref{tabla2}.
\begin{table}
\begin{center}
\begin{tabular}{||c|c|c||c|c|c||}
\hline
$n$ & $k$ & $\geq d$ & $n$ & $k$ & $\geq d$ \\
\hline
152 &148 &2&152 &144 &3 \\ \hline
152 &140 &4&152 &136 &5 \\ \hline
152 &132 &6&152 &128 &7 \\ \hline
152 &124 &8&- &- &- \\
\hline
\end{tabular}
\end{center}
\caption{Stabilizer quantum codes over $\mathbb{F}_4$ }
\label{tabla2}
\end{table}
By lengthening, we obtain quantum codes with parameters $$[[153,140,\geq 4]]_4,[[153,136,\geq 5]]_4, \;\; [[153,132, \geq 6]]_4 \;\; [[153,128,\geq 7]]_4$$
improving some codes in (and adding a new one to) \cite[Table 3]{SLLG}.
Looking for more $4$-ary stabilizer codes, set $q=4$ and $m=3$. Write $Q=q^{2m}$ and $e=q^m=64$. Pick $n=255$ which gives $a=3$ and $b=63$ with the notation of Theorem \ref{elH}. Then $K_{255}=31$ and applying Theorems \ref{elH} and \ref{Elbueno} one gets a family of stabilizer codes with parameters
\[
\left\{ [[765, 765 - 6j, \geq 1+j]]_4 \right\}_{18 \leq j \leq 31}.
\]
These codes improve a lot some given in \cite[Table 2]{SLLG} whose minimum distance $d$ satisfies $19 \leq d \leq 32$. For instance we give codes with parameters $[[765, 657, \geq 19]]_4$, $[[765, 651, \geq 20]]_4$ and $[[765, 645, \geq 21]]_4$ while the parameters of the corresponding codes in \cite{SLLG} are $[[765, 643, \geq 19]]_4$, $[[765, 639, \geq 20]]_4$ and $[[765, 631, \geq 21]]_4$.
We conclude this section by giving some more families of stabilizer quantum codes obtained with our procedure.
We start with a $3$-ary stablizer quantum code with parameters $[[110,98, \geq 4]]_3$ which improves the quantum code with parameters $[[110,96, \geq 4]]_3$ given in \cite{LV}. Our code is obtained by setting, with the previous notation, $n=55$, $q=3$ and $m=2$.
Similarly, considering $n=234$, we get stabilizer quantum codes over $\mathbb{F}_5$ with parameters as in Table \ref{tabla3}.
\begin{table}
\begin{center}
\begin{tabular}{||c|c|c||c|c|c||}
\hline
$n$ & $k$ & $\geq d$ & $n$ & $k$ & $\geq d$ \\ \hline
468 &452 &5&468 &448 &6 \\ \hline
468 &444 &7&468 &440 &8 \\ \hline
468 &436 &9&468 &432 &10 \\ \hline
468 &428 &11&468 &424 &12 \\
\hline
\end{tabular}
\end{center}
\caption{Stabilizer quantum codes over $\mathbb{F}_5$ }
\label{tabla3}
\end{table}
Notice that these codes make a great improvement to some ones in \cite[Table 4]{SLLG}.
Now we provide the parameters of a family of QECCs over $\mathbb{F}_7$. Consider $Q=2401 = 7^4$ and $n=196$, again by Theorems \ref{elH} and \ref{Elbueno} we get a family of stabilizer quantum codes with parameters
\[
\Big\{[[392, 388 - 4j, \geq 2 +j]]_7 \Big\}_{j=3}^{23}.
\]
Comparing with \cite[Table 3]{cao-cui}, we obtain many more $7$-ary quantum codes of length $392$. For $j=3, 4$ our parameters coincide with those in \cite{cao-cui} and we get a $[[392,368, \geq 7]]_7$ code which improves the $[[392,364, \geq 7]]_7$ code in \cite{cao-cui}.
Our next family corresponds to the field $\mathbb{F}_8$. Theorems \ref{elH} and \ref{Elbueno} for $Q=8^4= 4096$ and $n=283$ give rise to a new family of QECCs with parameters
\[
\Big\{[[566, 562 - 4j, \geq 2 +j]]_8 \Big\}_{j=5}^{27}.
\]
After lengthening, one gets a set of QECCs with parameters
\[
\Big\{[[567, 562 - 4j, \geq 2 +j]]_8 \Big\}_{j=5}^{27}.
\]
As before, we add many new codes to those $8$-ary ones in \cite[Table 1]{cao-cui} of length $567$ and obtain a code with parameters $[[567,542, \geq 7]]_8$ improving the $[[567,539, \geq 7]]_8$ code in \cite{cao-cui}.
To end, set $Q=6561=9^4$. As above
\begin{itemize}
\item Picking $n=200$, we get a family of stabilizer quantum codes over $\mathbb{F}_9$ with parameters:
$$ \Big\{[[400, 396 - 4j, \geq 2 +j]]_9 \Big\}_{j=3}^{32}.$$
\item Setting $n=400$, we obtain: $$ \Big\{[[800, 796 - 4j, \geq 2 +j]]_9 \Big\}_{j=3}^{39}.$$
\item With $n=405$, we obtain: $$ \Big\{[[810, 806 - 4j, \geq 2 +j]]_9 \Big\}_{j=3}^{39}.$$
\item Finally, with $n=162$, we get: $$ \Big\{[[324, 320 - 4j, \geq 2 +j]]_9\Big\}_{10 \neq j=7}^{39}.$$
\end{itemize}
With respect to Tables 1, 3, 5 and 8 in \cite{cao-cui} we add quite a few new codes. In addition we obtain several codes with better parameters than those given in \cite{cao-cui}: $[[400,376, \geq 7]]_9$, $[[800,776, \geq 7]]_9$, $[[800,772, \geq 8]]_9$, $[[810,786, \geq 7]]_9$, $[[810,782, \geq 8]]_9$, $[[810,778, \geq 9]]_9$, $[[324,276, \geq 13]]_9$ and $[[324,260, \geq 17]]_9$.
Notice that, when providing our families of codes over $\mathbb{F}_4$, $\mathbb{F}_7$, $\mathbb{F}_8$ and $\mathbb{F}_9$, we have considered different values for the indices $j$ in order to get parameters which are either new or better than or equal to those in \cite{SLLG, cao-cui}. Finally it is worth pointing out that, when comparison is possible, our codes improve (in general, a lot) those in \cite{edel}.
\begin{rem}
{\rm
We have explained how to get $q$-ary stabilizer codes with length $nm$ by considering a class of Hermitian self-orthogonal codes of length $n$ over the field $\mathbb{F}_{q^{2m}}$, where $2 \leq n \leq q^{2m}$. Dimensions and minimum distances of the stabilizer codes depend on the $q^m$-adic expression of $n$. In certain cases, one gets better quantum codes taking Hermitian self-orthogonal codes over fields $\mathbb{F}_{q^{2m'}}$ with $m' <m$. Indeed, when the length of the quantum codes we are looking for is less than or equal to $m' q^{2m'}$ and if there exists $n' \leq q^{2m'}$ such that $nm =n'm'$, then, for distances $d \leq \min \{K_n +1, K_{n'}+1\}$ ($K_n$ and $K_{n'}$ defined as in Theorem \ref{elH} for suitable values $e=q^m$ and $e'=q^{m'}$), we obtain stabilizer codes with parameters $[[nm, nm-2m(d-1), \geq d]]_q$ if we use the extension field $\mathbb{F}_{q^{2m}}$ and better stabilizer codes with parameters $[[n'm'=nm, nm-2m'(d-1), \geq d]]_q$ when using the extension field $\mathbb{F}_{q^{2m'}}$.
}
\end{rem}
\section*{Acknowledgments}
We thank the anonymous reviewers for their careful reading of our manuscript. We especially thank one of the reviewers for pointing out to us the existence of \cite[Lemma 76]{kkk}.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,250 |
package io.finch.benchmarks.service
import com.twitter.finagle.httpx.{Request, Response}
import com.twitter.finagle.{Service, SimpleFilter}
import com.twitter.util.Future
import io.finch.request._
import io.finch.response._
import io.finch.route._
import io.finch.{Endpoint => _}
class FinchUserService(implicit
userDecoder: DecodeRequest[User],
newUserInfoDecoder: DecodeRequest[NewUserInfo],
userEncoder: EncodeResponse[User],
usersEncoder: EncodeResponse[List[User]]
) extends UserService {
def getUser(id: Long): Future[User] = db.get(id).flatMap {
case Some(user) => Future.value(user)
case None => Future.exception[User](UserNotFound(id))
}
val allUsers: Service[Request, List[User]] = Service.mk(_ => db.all)
val createUser: Service[Request, Response] = Service.mk { req =>
for {
NewUserInfo(name, age) <- body.as[NewUserInfo].apply(req)
id <- db.add(name, age)
} yield Created.withHeaders("Location" -> s"/users/$id")()
}
val updateUser: Service[Request, Response] = Service.mk { req =>
body.as[User].apply(req).flatMap(db.update).map(_ => NoContent())
}
val deleteUsers: Service[Request, Response] =
Service.mk(_ => db.delete().map(count => Ok(s"$count users deleted")))
val users: Service[Request, Response] = (
get("users" / long) /> getUser :+:
get("users") /> allUsers :+:
post("users") /> createUser :+:
put("users") /> updateUser :+:
delete("users") /> deleteUsers
).toService
val handleExceptions = new SimpleFilter[Request, Response] {
def apply(req: Request, service: Service[Request, Response]): Future[Response] =
service(req).handle {
case notFound @ UserNotFound(_) => BadRequest(notFound.getMessage)
case _ => InternalServerError()
}
}
val backend = handleExceptions andThen users
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,577 |
Q: Reading Settings -> Front Page displays "Static Page" being reset Every day my WordPress blog is going from a static page, back to "your latest posts".
I am not setting this setting, something is doing this automatically!
Any ideas what to check for? Is there any audit log that shows what is making this change?
I am using WordPress 3.9.2 and haven't had issues till recently, no changes to any plugins that i can think of that could cause this.
We are using a custom theme which hasn't been changed for the past year.
The plugins installed are below:
BackWPup
Version 3.1.2 | By Inpsyde GmbH
Select Display Widgets
Version 2.03 | By Strategy11
Select Image Widget
Version 4.1 | By Modern Tribe, Inc.
Select JJ NextGen JQuery Carousel
Version 1.1.8 | By JJ Coder
Select NextGEN Gallery by Photocrati
Version 2.0.66.27 | By Photocrati Media
Select NextGEN Scroll Gallery
Version 1.8.2 | By Benedikt Morschheuser
Select Redirection
Version 2.3.6 | By John Godley
Select RSS Multi Importer
Version 3.13 | By Allen Weiss
Select Wordfence Security
Version 5.2.4 | By Wordfence
A: I would suggest first to update your Wordpress, so that if there's any error in any of the files for it to get sorted out.
Once you update Wordpress, do set the Page to Static page, and check if it fixes your issue..
NOTE: Dont worry about the custom theme.. When you update wordpress, the theme doesnt get affected. But to be on safer sides do take a backup of your theme and DB before you update :)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,834 |
Babel 7 comes after more than 2 years of active development and four thousand commits. The main advantage of the new version is the speed optimizations and configuration flexibility. In this tutorial we'll see how to upgrade our React boilerplate application to support Babel 7.
The main change compared to the older version is Babel's switch to scoped packages. To summarize, from now on most of the packages named with the prefix babel- will now be named @babel/.
Next step will be to replace our .babelrc with babel.config.js. You can read more about why it's recommended to use a project wide babel.config.js here.
This post is a follow up on the previous post where we prepared a ReactJS application from scratch in order to use Babel 7. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,489 |
The Sports Club Council (SCC) was created through a Resolution of the 35th Student Senate in the Spring Semester of 2003. The SCC was created as an agency of the Student Government Association (SGA) to provide funding, training, facilities, and other administrative services to all eligible sport clubs that are members of the agency. Following the creation of the SCC as an agency, the Recreation and Wellness Center (RWC) partnered with the SCC under the programs department of the RWC. The RWC Associate Director of Programs also serves as the program advisor to the SCC. Although the Sport Club Council's budget is requested directly from the Activity and Service Fee Committee (much like the RWC), the RWC provides facilities, administrative support, and the Sport Club Coordinator.
The University of Central Florida (UCF) Sport Club Program is an agency of the UCF Student Government Association (SGA) and is advised by the Sport Club Staff at the UCF Recreation & Wellness Center (RWC). Each sport club is a Registered Student Organization (RSO) with the Office of Student Involvement (OSI). The Sport Club program at UCF exists to provide students opportunities to promote and develop interest in particular sports activities that are predominantly physical in nature and understanding, supports healthy lifestyles and is in alignment with the RWC's mission and values. Interests may be competitive, recreational, instructional or any combination of the three. The Sport Club staff of the RWC believes that involvement in the Sport Club Program enhances development, leadership, and the overall college experience for students by supplementing skills learned in the educational realm. It is the mission of the program to provide diverse sports opportunities for all students across a broad range of skill levels and experiences.
Get involved with Sport Clubs! The SCC supports a variety of organizations that are organized and lead by students.
Membership in any student organization is limited to any student who is currently paying activity and service fees and is enrolled with the University of Central Florida. Employees at the University of Central Florida may advise sport clubs but may not participate as a member.
In order to join a sport club, fill out this interest form and a club representative will contact you. You can find more information about different clubs by joining KnightSync and looking at the clubs' individual websites. Many clubs have tryouts at the start of each semester, while other offer open enrollment throughout the year.
Looking to start a club that doesn't already exist? All sport clubs are required to be Registered Student Organizations through the Office of Student Involvement (OSI). Students may form new clubs through OSI at any time. There are specific steps and guidelines that clubs must follow through the Office of Student Involvement before applying to be part of the Sport Club Council. To start a club, students should visit Student Organizations.
After a club is registered with the Office of Student Involvement, they can apply to be part of the Sport Club Council. All steps and forms are outlined in the New Club Application. In order to understand the requirements placed on sport clubs, look at the tier requirements. Among other things, sport clubs are required to fundraise and fulfill community service requirements. The first step towards becoming a sport club is to meet with the Sport Club Council President. | {
"redpajama_set_name": "RedPajamaC4"
} | 457 |
Many leaders also serve as parents, happily balancing a daily workload with ball games and family dinners. Along the way, most of these leader-parents also realize the influence they have over young minds. Today's children are tomorrow's leaders, especially if those children have parents who are leaders.
While leadership skills can come naturally, children learn lessons along the way that significantly impacts them later in life. The right words at the right time can make all the difference.
I see many children in our karate classes that are going to make great leaders and then I see others who always try to take shortcuts and/or only want to try at the things they like to do.
Being a leader is not easy, but it can be learned. Leaders do their very best all the time and they have probably learned this from their parents. They see you and will emulate everything you do.
Here are some tips that can help you to get your children headed in the direction of becoming a leader rather than a follower.
As a leader, you realize the importance of setting a good example for your team. This is even truer of your role as a parent. By allowing your children to see how well you balance your work and personal roles, you'll teach them accountability through effective leadership.
2. Participation in organized activities.
Early on, identify your children's interests and encourage their participation in organized activities. Whether it's joining a scouting troop, karate classes, participation in sports or joining the school band, children learn valuable lessons about being disciplined, working hard to improve and working with others.
3. Help them understand perseverance.
The best leaders learn to handle failure as gracefully as they handle success. It's important to expose future leaders to disappointment rather than protecting them from it. Children need to learn to handle the loss and move forward when the other team wins or someone else is elected class president.
4. Learning how to compromise.
Every good leader knows the art of compromise. Instead of giving your children a firm "yes" or "no" to a request, make an offer and allow them to counter that offer by providing solid points. While you don't need to negotiate everything, it is important to teach them how to work together and find a compromise.
Children should learn how to make good decisions as early in life as possible. Because children become overwhelmed by too many choices, narrow down the options to two or three, whether a child is deciding on afternoon activities or a movie to watch. Help them to understand the decisions that they are making and how they will affect them. This will help them to make correct decisions in everyday life.
6. Give them chores to do.
Chores are an important part of growing up. Children need to learn and understand responsibility for the tasks you give them. Help them understand that this is their role to help their family. These early jobs can be essential to building leadership skills in children.
When your child works on a project or activity, it can be tempting to jump in and help, especially if you see your child struggling. Instead, consider stepping back and letting your children work through it themselves. If they ask you for help, guide them in the right direction but don't do the work for them. Let them learn to problem solve with some guidance from you.
Help your children understand how important goals are, and even more importantly, completing them. Have them set challenging but realistic goals. Walk them through how to set goals, the importance of following through, and the fulfillment when they complete a goal. This is an invaluable tool to becoming a leader among their peers.
Studies have shown the benefits of reading for fun in childhood, with children who read having greater intellectual progress in a variety of subjects. Young readers tend to learn more about the world, even when the reading is of a frivolous nature. Reading helps to create a greater vocabulary, a better imagination and exposure to many new and different ideas.
Use these tips and ideas to help your child become a leader for tomorrow. There are so many things that can distract your child from what is important. Helping your child to become a leader will be huge for them as they grow into teens and beyond. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,963 |
Christoffer Dybvad (o. 1578–1622) var en dansk matematiker, søn af dr. Jørgen Dybvad, var født i København 1577 eller 1578 og blev student i en meget ung alder, da han allerede 1594 og følgende år findes anført som respondens ved faderens disputatser.
Udlandsrejser
Tidlig betrådte han også forfatterbanen, og 1599 drog han
udenlands, støttet af det kongelige rejsestipendium for en mediciner. På denne rejse erhvervede han omkring 1601 doktorgraden i Caen i Normandiet, ligesom han en tid lang studerede i Leiden, hvor han 1602
på dansk udgav sit første matematiske skrift,
«Decarithmia»
, der er mærkeligt ved de forsøg,
det indeholder på at erstatte de sædvanlige græske kunstord i matematikken med tilsvarende danske ord.
Jobsøgning i Danmark
Det var hans ønske at finde ansættelse
ved Københavns Universitet; men skønt han tit nok
søgte derom, ville det dog aldrig lykkes, da noget af
den uvilje, der næredes mod faderen, også synes at
have ramt sønnen, hvis karakter heller ikke var af de
tiltalende. Indtil videre blev han derfor i Holland,
hvor han udgav flere for deres tid vistnok værdifulde
matematiske skrifter.
Opholdet i Holland
synes at have haft blivende indflydelse på hans
politiske og religiøse anskuelser. Det nøje kendskab
til Nederlandenes ejendommelige politiske forhold
måtte åbne hans øjne for manglerne ved Danmarks
udpræget aristokratiske forfatning; og i religiøs
henseende blev han stærkt påvirket af arminianismen,
en rationalistisk retning inden for den Reformerte kirke,
der blev herskende ved universitetet i Leiden
netop i de år, da han studerede her.
Efter syv års ophold i udlandet kom Dybvad hjem 1606 og
søgte nu ved udgivelsen af et matematisk skrift,
som han tilegnede universitetets professorer, at
vinde deres gunst; men da hans forsøg på at opnå
en ansættelse atter var mislykket, drog han efter
faderens afsættelse på ny ud og færdedes nu igen
en række år i udlandet, især i Frankrig og Italien.
Ligesom han i Holland var blevet påvirket i retninger,
der stod i strid med de bestående forhold i hans
fædreland, således blev også opholdet særlig i
Frankrig skæbnesvangert for ham, ikke blot fordi han
gjorde fortroligere bekendtskab med de løse franske
sæder, men også fordi han tilegnede sig de politiske
grundsætninger om den enevældige kongemagts betydning,
der af den tids fremskridtsmænd betragtedes som den
bedste lægedom mod de sociale brøst, fejl og mangler.
1612: Hjemme igen
Henimod slutningen af året 1612 synes Dybvad atter at
være kommen hjem. Skønt rygtet om hans lærdom gik
forud for ham, måtte han dog for fjerde gang forgæves
ansøge om en akademisk lærerplads.
Under disseforhold groede der i hans i forvejen vistnok irritable
sind en bitterhed op, der bragte ham til omkring 1615
at forfatte en række til kongen stilede «politiske
Observationer», der i de stærkeste udtryk angreb den
i Danmark bestående forfatning og anbefale indførelse
af arvelig kongemagt og enevælde. Vi ved ikke, om
dette mærkelige skriftstykke – hvori mange af de i
Christian 4.'s tid trufne regeringsforanstaltninger
på det skarpeste dadles, men under den form, at
skylden tillægges kongens rådgivere – virkelig er
kommet kongen i hænde; men endelig opnåede Dybvad 1618
at blive udnævnt til Kongelig Mathematicus, idet han
som løn aflagdes med et kanonikat i Lund.
Kongelig Mathematicus og horoskopstiller
Som kongelig mathematicus havde Dybvad den opgave at
stille nativiteter, horoskoper, og udføre andre derhen hørende
kunster og beregninger, der for en videnskabsmand
måtte have lidet tilfredsstillende ved sig, da
de mere klarsynede havde begyndt at få øjnene
op for, at slige beregninger og forudsigelser
kun var videnskabelig humbug.
Misfornøjelse med
stillingen i forbindelse med bitre erindringer om
tidligere tilsidesættelser og nye stridigheder, hvori
Dybvad indvikledes med kapitlet i Lund, bragte atter hans
heftige sind i kog.
1619: Bergen
I november 1619 rejste han til Bergen,
uvist i hvilken anledning. Her henledte han snart
opmærksomheden på sig ved sine dristige ytringer om
forskellige statssager.
Især gik han løs på adelen
og udtalte det som sin bestemte forventning, at inden
få år skulle dens magt være forbi og kongen være
i besiddelse af de syv majestætsrettigheder, som
den franske forfatter Jean Bodin
omtaler. Der behøvedes
kun en passende åreladning – et par læster blod –,
for at adelsvældet skulle være knækket. Tillige lod
han antydninger falde om, at han allerede havde givet
kongen ideen til, hvorledes han skulle gribe sagen an,
og han pralede af at have udkastet
planen til vigtige foranstaltninger, som
kongen for nylig havde begyndt at sætte i værk,
såsom oprettelsen af Holmens faste stok og det
ostindiske kompagni. I selskaber, hvortil han som
anset videnskabsmand blev indbudt, hos biskoppen i Bergen, dr. Niels Paaske,
og hos lensmanden, Knud Gyldenstjerne
, lod han sin tunge frit løb og udtalte i
manges påhør sine ønsker og forventninger med hensyn
til en omvæltning i den bestående statsforfatning.
1620 Undersøgelser mod Dybvad
Da disse hans ytringer kom regeringen for øre, udgik
der i marts 1620 kongelige befaling til den ovennævnte
lensmand om at anstille undersøgelser om «alle
Haande sælsomme ord og letfærdig Tale om disse
Landes Regering og Højhed», som Dybvad sagdes at have
ladet falde.
Han var imidlertid selv draget ned til
Danmark uden at ane nogen fare. Men da de i Bergen
optagne vidnesbyrd indløb, blev han underkastet
et forhør af kansler Christian Friis til Kragerup og
to medlemmer af rigsrådet, hvilket førte til
hans anholdelse.
Samtidig blev der lagt beslag på
hans papirer, blandt hvilke der fandtes adskilligt
af graverende art, særlig en del notitser, kaldet
«Joci aulici», hof-vitser, der selv for et velvilligt øje
måtte tage sig ud som kåd spot over den kristne
religion og en uren fantasis leg med det obskøne.
Proces og dom 1620
Universitetets rektor og professorer fik nu befaling til at dømme i Dybvads sag, idet den kongelige sekretær Axel Arenfeldt optrådte som aktor imod ham. Dommen, der faldt 22. december 1620, gik ud på,
«at efterdi Dybvad befindes at have grovelig forgrebet sig imod Gud,
imod den kristelige Religion og Kirkeceremonier,
imod kongelig Majestæt, imod Riget, Rigens Raad, endog
imod den døde (Kansler), imod menige Adelskab og
andre Rigens Stænder, da bør han være berøvet alle
akademiske Privilegier og Værdigheder og med Vanære
udstødes af vor Orden, i det han for øvrigt overgives
til kongelig Majestæts, som en kristelig Ørigheds, Naade og Unaade».
At flere af Dybvads politiske projekter i og for sig var meget vel grundede og forstandige, kom ham ikke til gode, da hele vægten blev lagt på det formentlig revolutionære i hans færd. Efter nogen
tids betænkning bestemte regeringen da hans straf til livsvarigt fængsel, og 27. januar 1621 førtes Dybvad fra Blåtårn til Kalundborg Slot, hvor han indesluttedes
i det bekendte tårn «Folen». Her døde han 1622 efter henved to års fangeliv.
En morgen, da fangevogteren kom ind i hans kammer, fandt han ham liggende livløs i sengen, omkommen, som man antog, ved en kulilteforgiftning, som var opstået derved, at han af uforsigtighed om aftenen, da han slukkede lyset, havde henkastet den endnu brændende tande, og at denne var faldet i en revne mellem stenfliserne og havde antændt noget trækul, som man i gamle dage havde brugt til at fylde hvælvingen under kammeret med.
Foruden flere trykte skrifter efterlod Dybvad adskillige i håndskrift, deriblandt et vistnok nu tabt værk «De mensuris et ponderibus, tam medicis quam civilibus», der ifølge dr. Thomas Bartholins dom var affattet med utrolig flid og lærdom og med en høj grad af matematisk nøjagtighed, hvorfor broderen dr. Rasmus Bartholin havde til hensigt at udgive det, noget, der dog ikke er sket. Dybvad var ugift.
Danske Magasin 4. R. II, 211 ff. V, 40 ff.
H.F. Rørdam, 1830–1906, teolog og kirkehistoriker
Noter
Se også
Til kampen mod de sidste "kryptocalvinister" i begyndelsen af 1600-tallet se afsnittene "Sagen mod Oluf Kock" og "Oluf Kock" i artiklerne om de to biskopper Jesper Rasmussen Brochmand og Hans Poulsen Resen
Kryptocalvinisme – Calvinisme – Jean Calvin – Lille ordliste med kort beskrivelse af tilknyttede ord, vendinger og begreber
Litteratur
Kornerup, Bjørn (1928, 1968). Biskop Hans Poulsen Resen. Bind 1 fra 1928 (disputats), bind 2 fra 1968. København: Gad. DK5=99.4 Resen
Bind 2, afsnittet "Sagen mod Christoffer Dybvad", side 137
Aage Heinberg, Fantaster, Skandinavisk Bogforlag, 1950.
Morten Fink-Jensen: "De lærde Dybvader. Bogtryk og samfundskritik i det 16. og 17. århundrede". Fund og Forskning, bd. 44, 2005, s. 63-106.
Morten Fink-Jensen: "Enevældens ensomme fortrop. Christoffer Dybvads systemkritik under Christian 4". I Morten Petersen (red.): Oprørere. Skæbnefortællinger om danmarkshistoriens tolv største rebeller, København: Aschehoug 2006, s. 37-62.
Kilder
Mindeside om Christoffer Dybvad fra Astrologisk Museum
Christoffer Dybvad astrolog og Kgl. Mathematicus, (pdf-fil), Informationsbrev fra Astrologisk Museum , SOPHIE nr. 19 [december 2006] side 7 [9], Faghistorie ved Claus Houlberg (for visning som html-fil prøv Google)
I et afsnit om geometriske lærebøger på en side fra Ribe Katedralskole kan man læse at Christoffer Dybvad skulle have været den første dansker der publicerede en udgave af Euklids Elementer i 1603-05
Matematikere fra Danmark
Danskere i 1600-tallet
Personer fra København | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,081 |
{"url":"https:\/\/www.physicsforums.com\/threads\/chemical-potential-vs-pressure-and-temperature-difficulty-with-fermi-gases.600603\/","text":"# Chemical potential vs pressure and temperature; difficulty with Fermi gases\n\n1. ### jfizzix\n\n394\nFor any system where the thermodynamic limit exists, we know that the internal energy U, the entropy \u03c3, the total particle number N and the total volume V are all extensive. Because of this, we know that the Euler relation holds true\n\nU = -PV + $\\tau$\u03c3 + $\\mu$N\n\nand that the chemical potential is just the Gibbs free energy per particle.\n\nG = $\\mu$ N\n\nWe can use the differential relation of the Gibbs free energy\n\ndG = V dP -\u03c3 d$\\tau$ + $\\mu$ dN\n\nto find expressions for the derivatives of the chemical potential.\nd$\\mu$\/d$\\tau$ = 1\/N * dG\/d$\\tau$ =-\u03c3\/N\nd$\\mu$\/dP = 1\/N * dG\/dP = V\/N\n\nSince N, $\\sigma$, and V are all positive, it appears that the chemical potential must increase with pressure at constant temperature, and decrease with temperature at constant pressure.\n\nMy question is this:\nthe 1D fermi gas is a case where the chemical potential actually increases with temperature for small temperatures, though we would think in all cases the chemical potential should be decreasing with temperature.\n\nHow do we reconcile this result with the previous assumptions about the chemical potential?\n\n-James\n\n2. ### DrDu\n\n4,349\nI don't have this stuff in mind. Could you please for our convenience write down some formula that shows this?\nI suspect you are considering a Fermi gas with fixed particle number instead of fixed pressure or equivalently U.\n\n3. ### Blwderkik\n\n1\nExcuse me,but I don't very understand how it is done with this:\nd\u03bc\/d\u03c4 = 1\/N * dG\/d\u03c4 =-\u03c3\/N\nd\u03bc\/dP = 1\/N * dG\/dP = V\/N\n\nI am a little confused.\n\n4. ### DrDu\n\n4,349\nHe is using e.g.\n$(\\partial \\mu\/\\partial T)_{P,N}=-(\\partial S\/\\partial N)_{T,P}=-S\/N$\nThe first equality is a Maxwell relation, the second one follows from S(N,p,T) being an extensive function whence it must be proportional to N.\n\n5. ### jfizzix\n\n394\n\nFor the 1D (or 2D or 3D) Fermi gas we can calculate the chemical potential in the following way. In a nutshell, we say that the number of particles is constant whether the temperature is zero or not.\n\nFirst, we can find the number of particles at zero temperature in terms of the Fermi energy. Starting at the ground state, we put in fermions at each successive orbital until all N fermions have been placed. The highest energy (that of the final fermion) is the Fermi energy.\n\nNext we can calculate the number of particles at nonzero temperature by integrating over the density of states. For a nonzero temperature, the integral is harder to evaluate, but can be carried out for small temperatures with what is known as the Sommerfeld expansion\/approximation.\n\nSetting these two expressions for the number of particles equal to each other, we can calculate the chemical potential in terms of the Fermi energy.\n\nfor small temperatures the chemical potential of the 1D Fermi gas increases in the following way with temperature:\n$\\frac{\\mu}{E_{F}}$ \u2248 1 + $\\frac{\\pi^{2}}{12}$*($\\frac{k_{b}T}{E_{F}})^{2}$\n\nIn the 2D case, the chemical potential is just the Fermi energy at low temperatures, and in the 3D case, the chemical decreases with temperature in the same way that it increases for the 1D gas. Kittel and Kroemer has a nice derivation, as well as Schroeder's book.\n\nLast edited: Apr 27, 2012\n6. ### jfizzix\n\n394\nThe natural variables for the Gibbs free energy are G(P,T,N), just as for the internal energy\nU=U(S,V,N)\nH=H(S,P,N) (for the enthalpy)\nF=F(T,V,N) (for the Helmholtz free energy)\n\nSince P and T are intensive, and G is extensive, we can write G as N times some other function of P and T.\nTaking the derivative of G with respect to N, we get that $\\mu$ is that same function of P and T.\n\n7. ### jfizzix\n\n394\nNow that I think about it, the maxwell relation here says it all.\n\nin 1-D, the density of states decreases with increasing energy as $1\/\\sqrt{\\epsilon}$. This means the number of accessible states decreases with increasing particle number (and hence increasing Fermi energy).\n\nAs such, the entropy must decrease with the addition of more fermions, which means that the chemical potential increases with increasing temperature.\n\nI'm satisfied as to why the chemical potential decreases using the maxwell relations, but why then can we not say G = $\\mu$*N.\n\nThanks to all who helped,\n\n-James\n\n8. ### DrDu\n\n4,349\nBut this equation holds true!\n\n9. ### DrDu\n\n4,349\nWhat you need is mu(P,T), so you should eliminate E_F in terms of P and T.\n\n10. ### DrDu\n\n4,349\nOk,\nI think I understand it now:\nTo lowest order in the Sommerfeld expansion independent of dimension $\\mu(T,P)=E_F(T,P)$\nso\n$\\partial \\mu \/\\partial T|_P=\\partial E_F \/\\partial T|_P=- (\\partial P\/\\partial T)_{E_F}(\\partial E_F\/\\partial P)_T$\nAs the Fermi energy is a monotonously increasing function of the density, only, in the first derivative on the right we can alternatively keep the density constant. But P always increases with increasing temperature at constant density, so this term is positive. Considering the second derivative, the density (and E_F) increases with p at constant T, so this term is also positive. So to lowest order, the change of mu with T is always negative as it should be. The small higher order corrections will not change this.\n\nOr stated differently, when T is increasing, density or E_F has to disminish for P to remain constant.\n\nLast edited: May 11, 2012\n11. ### jfizzix\n\n394\n\nThe Fermi energy $E_{f}$ does not depend explicitly on temperature; only on particle number $N$ and the space in which the particles are contained (i.e. in 1-D, the length; in 2D, the area; in 3D, the volume).\n\nOne can express the Fermi energy in terms of N and length and get the chemical potential in terms of N, length, and temperature.\nIntegrating this with respect to N gives you the Helmholtz free energy $F(T,V,N)$ since $\u03bc(T,V,N)=(\u2202F\/\u2202N)_{T,V}$. we can then take the derivative of F with respect to volume to get the pressure $P(T,V,N)=-(\u2202F\/\u2202V)_{T,N}$. We can also take the derivative of F with respect to temperature to get the entropy $S(T,V,N)=-(\u2202F\/\u2202T)_{V,N}$. With the state equation of the pressure, we can substitute this into our expression for the entropy to get the entropy in terms of N,P, and T.\nIf you take the derivative of this entropy with respect to N, you find it is negative.. which means that where\n$(\u2202\u03bc\/\u2202T)_{P,N}=\u2212(\u2202S\/\u2202N)_{T,P}$\n\nthe chemical potential must increase with temperature for the 1D degenerate Fermi gas.\n\nNow, in 2D and 3D (taking higher order terms) the chemical potential decreases with temperature, but the question persistently remains...\n\nHow do we say that G is not \u03bc*N? Is G no longer extensive for a 1D Fermi gas?\n\nThanks again,\n\n-James\n\n12. ### DrDu\n\n4,349\nThat is not generally true but depends on the parametrization. E_F can be written as a function of only N\/L but this is not what is needed in your question as you are taking the derivative at constant P and N and not at constant L and N.\nThink of the ideal gas equation which is also the limit of the Fermi equation of state at low densities or high temperature: N\/V=P\/RT.\n\n13. ### jfizzix\n\n394\nPoint taken..\n\nWe start with the Fermi energy of a 1D Fermi gas.\n\n$E_{f} = (\\frac{\\hbar^2 \\pi^2}{8m})(\\frac{N}{L})^2 = \\alpha_{1} (\\frac{N}{L})^2$\n\nand the formula for the chemical potential at low temperature where the Fermi energy has already been substituted\n\n$\\mu(\\tau , L, N) \u2248 \\alpha_{1} (\\frac{N}{L})^2 + \\frac{\\pi^2 \\tau^2}{12 \\alpha_{1}}(\\frac{L}{N})^2$\n\nWe integrate the chemical potential with respect to N from 0 to N to obtain the Helmholtz free energy F. Recall that in 1D...\n$dF = - P dL - \\sigma d\\tau + \\mu dN$\nso that\n\n$F( \\tau, L, N) = \\int_{0}^{N}{\\mu (\\tau, L, N) dN} = \\frac{\\alpha_{1}}{3}\\frac{N^3}{L^2} - \\frac{\\pi^2 \\tau^2}{12 \\alpha_{1}} \\frac{L^2}{N}$\n\nNow we take the derivative of the Helmholtz free energy with respect to length to find the pressure in 1D\n\n$P = -(\\frac{\\partial F}{\\partial L})_{\\tau,N} = \\frac{2 \\alpha_{1}}{3}\\frac{N^3}{L^3} + \\frac{\\pi^2 \\tau^2}{6 \\alpha_{1}} \\frac{L}{N} \u2248 \\frac{2 \\alpha_{1}}{3}\\frac{N^3}{L^3}$\n\nSubstituting this expression for the pressure into our original expression for the chemical potential, we find\n\n$\\mu(\\tau , P, N) \u2248 \\alpha_{1} (\\frac{3 P}{2 \\alpha_{1}})^{2\/3}+ \\frac{\\pi^2 \\tau^2}{12 \\alpha_{1}}(\\frac{2 \\alpha_{1}}{3 P})^{2\/3}$\n\nIn short, for small temperatures, and in one dimension, the chemical potential does increase with temperature at constant pressure and particle number. I could have made a mistake with the math, but I think it's all there.\n\n-James\n\n14. ### DrDu\n\n4,349\nMethinks you deliberately dropped an infinity from the second term at N=0 on integration!\nObviously what is happening here is that at small N and fixed L and T the Sommerfeld expansion breaks down.\n\nLast edited: May 16, 2012\n15. ### jfizzix\n\n394\nNever attribute to malice, that which can be attributed to stupidity.\n\nI actually forgot that infinity there.. I'll have to get back to you on how to do it right.\n\n-James\n\n16. ### DrDu\n\n4,349\nYou really should calculate the Sommerfeld expansion of p in terms of E_F and T.\n\n17. ### jfizzix\n\n394\nI think you're right.\n\nI just substitute the Fermi pressure along with factors of N and $\\tau$ into the expression, and that should do the trick..\n\nmore to follow...\n\n-James\n\n18. ### jfizzix\n\n394\nSo.. in 1D,\n\nThe fermi energy $E_{f}$ can be expressed in terms of the Fermi pressure $P_{f}$ using the expression for the internal energy $U$ at absolute zero. If we differentiate the internal energy $U$ with respect to the length of the 1D box $L$ and add a negative sign, we have an expression for the pressure.\n\n$P = -(\\frac{\\partial U}{\\partial L})_{\\sigma,N}$\n\nIn 1D at absolute zero...\n\n$U = \\frac{1}{3} N E_{f}$ where $E_{f} = \\frac{\\hbar^{2}}{8 m}(\\frac{N \\pi}{L})^{2}$\n\nFrom these expressions, we can express the Fermi energy in terms of the pressure at absolute zero.\n\n$E_{f} = (\\frac{3 \\pi}{2})^{\\frac{2}{3}}(\\frac{\\hbar^{2}}{8 m})^{\\frac{1}{3}} P^{\\frac{2}{3}} = C_{1} P^{\\frac{2}{3}}$\n\nThen the expression for the chemical potential becomes\n\n$\\mu \u2248 C_{1} P^{\\frac{2}{3}} + \\frac{\\pi^{2}}{12} \\frac{\\tau^{2}}{C_{1} P^{\\frac{2}{3}}}$\n\nWith this as our form for the chemical potential, we see that it does decrease with temperature at constant pressure and particle number.\n\nI'm pretty sure I've got it right this time, but feel free to correct me. Does this make sense?\n\n-James\n\n19. ### DrDu\n\n4,349\nNo, you need the expansion of U or P in T in the same order as that for mu.\nCome on, it's not so difficult...\n\n20. ### DrDu\n\n4,349\n$E_F \\approx C_1 P^{2\/3}(1-\\frac{\\pi^2 k^2T^2}{9 (C_1P^{2\/3})^2})$\nSufficient to render the dependence of mu on T negative.\n\nLast edited: May 21, 2012\nKnow someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook\n\nHave something to add?","date":"2015-07-01 17:04:44","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8612765073776245, \"perplexity\": 496.5990656283231}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-27\/segments\/1435375095183.13\/warc\/CC-MAIN-20150627031815-00249-ip-10-179-60-89.ec2.internal.warc.gz\"}"} | null | null |
Q: How to print table with one header someFile = open("komad_namestaja.txt", "r")
for linija in someFile.readlines():
code, name, color, quantity, price, category = linija.split("|")
print("---------------------------------------------------------------------+")
print("Code |Name |Color |Quantity|Price |category |") #Header print("-------+-------------+-----------+--------+-----------+-------------+")
print("{0:8.8}|{1:14.14}|{2:10.10}|{3:8.8}|{4:11.11}|{5:13.6}|".format(code, name, color, quantity, price, category))
This is my code for making table of information from file.
Problem is, code print for every line in file new header.
What am doing wrong?
A: Just move your header before your loop, and print info inside the loop:
someFile = open("komad_namestaja.txt", "r")
print("-------------------------------------------------------------------+")
print("Code |Name |Color |Quantity|Price |category |")
print("-------+-------------+-----------+--------+------------+-----------+")
for linija in someFile.readlines():
code, name, color, quantity, price, category = linija.split("|")
print("{0:8.8}|{1:14.14}|{2:10.10}|{3:8.8}|{4:11.11}|{5:13.6}|".format(code, name, color, quantity, price, category))
| {
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Crackdown 3 Gets Rated By Brazilian Board Suggesting That Its Release Is Near
Usually when a game is rated, it suggests that its release will soon follow.
Posted By Ashish Isaac | On 23rd, Apr. 2018 Under News
Crackdown 3's release has been delayed multiple times but some new information suggests that the game may be releasing quite soon. Some recent rumors predicted that the game would release on June 29, but this hasn't been confirmed yet. Now, the Brazilian classification board has rated the game, and when games are rated, it usually signals that it will release quite soon.
This is certainly not the first time that such information has been leaked due to ratings given by classification boards. The Brazilian board rated the game as "not recommended for children under sixteen." It's likely that we'll get to learn more about the game, including its release date at this year's E3. After the multiple delays that the game has seen, it is about time for a release date to be confirmed.
Crackdown 3 will release for the Xbox One and PC, with it being available on day one for Xbox Game Pass subscribers.
Tagged With: Crackdown 3, Microsoft, pc, Xbox One
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15 Years Later, Splinter Cell: Chaos Theory is Still a Stealth Masterclass | {
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\subsection{Electron population at the QD sites}
\label{population}
The populations at each dot site can be written in terms of the electronic Green's functions $G_{ij}(\tau,\tau')$ as
\begin{eqnarray}
n_{j} &\equiv & \langle c^{\dagger}_{j} c_{j} \rangle = -i \int \frac{d\omega}{2 \pi} G^{<}_{jj}(\omega) \nonumber \\
&=& -i \sum_{kl} \int \frac{d\omega}{2 \pi} G^r_{jk}(\omega) \Sigma^{<,tot}_{kl}(\omega) G^a_{lj}(\omega)\,\, j=1,2
\end{eqnarray}
The population is related to the lesser component of the Green's function. In the second line we make use of the Keldysh equation for $G_{ij}^{<}(\omega)$.
\end{comment}
1. Extend axes in contour plots. (epsilon_1 and epsilon_2)
2. Do we understand Fig. 5? Why does finite bias leads to |t|>1 how does F'' behave with bias?
does it flip sign?
F'' changes sign. Do we understand the meaning?
If we understand the behavior of F'' we get the gain medium clarified!
3 .Do we understnad scaling relation in Lehur Schiro PRB 2014? DOI: 10.1103/PhysRevB.89.195127
cavity photons and electronic nanocircuit
Add
Nori
Petta
Hauk
Lev lab stanford
Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems
Ze-Liang Xiang, Sahel Ashhab, J. Q. You, and Franco Nori
Rev. Mod. Phys. 85, 623 � Published 9 April 2013
Write somewhere how the detuning epsilon is selected
hybrid systems comprising mesoscopic quantum dot devices coupled to an electromagnetic resonator
highlight that in model 1 there is no direct direct tunnel and electrostatic couplings between dots
Engineering the interaction between light and mattter couple two quantum dot circuit
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,023 |
As of May 1st, we will begin seeing clients in our new art therapy space in East Austin. When we first walked into the space, we loved it. It was creative, interesting, and not at all the traditional therapy space that we were trying so hard to steer clear of. And so, we signed the lease and started thinking of what we would do with the space.
Change is not many people's forte. There are the logistical problems that go along with any new venture and the need to adapt to new surroundings. When we say yes to a new beginning, we might also need to keep an eye on the emotions that arise from something else ending.
A therapy office can often times feel like a very sacred space. We become accustomed to the set up, the smell, the art work ... and our bodies inherently begin to associate all of those things with the notion of safety. Our brain makes the connection and allows us to be vulnerable. For the therapist, the room is the container for all that is shared with us. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,039 |
What is the correct spelling for REAGAE?
This word (Reagae) may be misspelled. Below you can find the suggested words which we believe are the correct spellings for what you were searching for. If you click on the links, you can find more information about these words.
rake She went across to the fire and began to rake it out, he watching her in silence, still with that sombre look in his dark eyes.
riga Drilled through and through by the fire of the Riga, she fought and suffered until the Lancaster foundered; then, with all guns out of action, but with still intact engine-power, she left the line, not to run, but to ram. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,264 |
class PuppetX::Coi::Jboss::Functions
class << self
# PRIVATE INTERNAL FUNCTION.
#
# @param method_name [String] a method name
# @param args [Array] an array of args
# @param block [Block] a yeild block that should return description of args and condition
def validate_method_parameters(method_name, args)
info = yield
raise_puppet_error(method_name, args.size, info[:desc]) if info[:condition]
end
private
def raise_puppet_error(method_name, arg_size, arg_desc)
raise(
Puppet::ParseError,
"#{method_name}(): Wrong number of arguments given (#{arg_size} for #{arg_desc})"
)
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,070 |
{"url":"https:\/\/socratic.org\/questions\/562c981a11ef6b336c4474d7","text":"Question #474d7\n\nOct 25, 2015\n\n$1 \\text{g}$ helium contains the most particles.\n\nExplanation:\n\nThe relative atomic mass in grams of an element contains the number of particles equal to the Avogadro Constant $= 6.02 \\times {10}^{23} {\\text{mol}}^{- 1}$\n\nSo $\\frac{m}{A} _ r$ $\\times 6.02 \\times {10}^{23}$ will give you the number of particles, in this case atoms, which are present.\n\nUsing approx. ${A}_{r}$ values:\n\nFor $A l$ $n = \\frac{1}{27} \\times 6.02 \\times {10}^{23} = 2.23 \\times {10}^{22}$\n\nFor $C$ $n = \\frac{1}{12} \\times 6.02 \\times {10}^{23} = 5 \\times {10}^{22}$\n\nFor $H e$ $n = \\frac{1}{4} \\times 6.02 \\times {10}^{23} = 15 \\times {10}^{22}$\n\nFor $F e$ $n = \\frac{1}{56} \\times 6.02 \\times {10}^{23} = 1.07 \\times {10}^{22}$\n\nSo you can see from these data that 1g of He contains the most atoms.","date":"2020-09-18 21:13:18","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 13, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5598815083503723, \"perplexity\": 578.7464281642788}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-40\/segments\/1600400188841.7\/warc\/CC-MAIN-20200918190514-20200918220514-00606.warc.gz\"}"} | null | null |
FOUNDATION_EXPORT double Pods_Xcode7GenericArchiveVersionNumber;
FOUNDATION_EXPORT const unsigned char Pods_Xcode7GenericArchiveVersionString[];
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,760 |
NCTCPServer::NCTCPServer()
: socket_descriptor_(0), port_(0)
{
::memset(&socket_address_, 0, sizeof(socket_address_));
}
NCTCPServer::~NCTCPServer()
{
this->close();
}
void NCTCPServer::open(int port)
{
port_ = port;
socket_descriptor_ = socket(AF_INET, SOCK_STREAM, 0);
if (socket_descriptor_ == -1) {
// TODO(2/8):perrorではなくExceptionをthrowすべき
perror("socket");
return;
}
socket_address_.sin_family = AF_INET;
socket_address_.sin_port = htons(port_);
socket_address_.sin_addr.s_addr = htonl(INADDR_ANY);
if (bind( socket_descriptor_,
(struct sockaddr*)(&socket_address_),
sizeof(socket_address_)) == -1) {
perror("bind");
this->close();
return;
}
if (listen(socket_descriptor_, CONNECTION_QUEUE_MAX) == -1) {
perror("listen");
this->close();
return;
}
}
NCConnection& NCTCPServer::waitForConnection()
{
int descriptor = accept(socket_descriptor_, NULL, NULL);
if (descriptor == -1) {
perror("accept");
this->close();
}
NCTCPConnection* connection = new NCTCPConnection();
connection->connection_descriptor_ = descriptor;
connections_.push_back(connection);
return *connection;
}
void NCTCPServer::close()
{
std::vector<NCConnection*>::iterator itr = connections_.begin();
while (itr != connections_.end()) {
(*(itr))->close();
itr++;
}
::close(socket_descriptor_);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,688 |
\section{Introduction}
The strong openness property of multiplier ideal sheaves \cite{GZSOC}, i.e. $\mathcal{I}(\varphi)=\mathcal{I}_+(\varphi):=\mathop{\cup} \limits_{\epsilon>0}\mathcal{I}((1+\epsilon)\varphi)$
(conjectured by Demailly \cite{DemaillySoc}) is an important feature of multiplier ideal sheaves and has opened the door to new types of approximation technique (see e.g. \cite{GZSOC,McNeal and Varolin,K16,cao17,cdM17,FoW18,DEL18,ZZ2018,GZ20,ZZ2019,ZhouZhu20siu's,FoW20,KS20,DEL21}),
where the multiplier ideal sheaf $\mathcal{I}(\varphi)$ is the sheaf of germs of holomorphic functions $f$ such that $|f|^2e^{-\varphi}$ is locally integrable (see e.g. \cite{Tian,Nadel,Siu96,DEL,DK01,DemaillySoc,DP03,Lazarsfeld,Siu05,Siu09,DemaillyAG,Guenancia}),
and $\varphi$ is a plurisubharmonic function on a complex manifold $M$ (see \cite{Demaillybook}).
Guan-Zhou \cite{GZSOC} proved the strong openness property (the 2-dimensional case was proved by Jonsson-Musta\c{t}\u{a} \cite{JonssonMustata}).
After that, using the strong openness property, Guan-Zhou \cite{GZeff} proved a conjecture posed by Jonsson-Musta\c{t}\u{a} (Conjecture J-M for short, see \cite{JonssonMustata}),
which is about the volumes growth of the sublevel sets of quasi-plurisubharmonic functions.
Recall that the 2-dimensional case of Conjecture J-M was proved by Jonsson-Musta\c{t}\u{a} \cite{JonssonMustata},
which deduced the 2-dimensional strong openness property.
It is natural to ask
\begin{Question}
\label{Q:JM-SOC}
Can one obtain a proof of Conjecture J-M \textbf{independent} of the strong openness property?
\end{Question}
In \cite{BGY-boundary}, Bao-Guan-Yuan gave a positive answer to Question \ref{Q:JM-SOC} by establishing a concavity property of the minimal $L^2$ integrals related to modules at boundary points of the sublevel sets of plurisubharmonic functions on pseudoconvex domains.
After that, Guan-Mi-Yuan \cite{GMY-boundary2} considered the minimal $L^2$ integrals on weakly pseudoconvex K\"{a}hler manifolds with Lebesgue measurable gain,
and established a concavity property of the minimal $L^2$ integrals,
which deduced a necessary condition for the concavity degenerating to linearity,
a concavity property related to modules at inner points of the sublevel sets,
an optimal support function related to the modules,
a strong openness property of the modules and a twisted version,
an effectiveness result of the strong openness property of the modules.
In this article, we consider a modified version of the minimal $L^2$ integrals in \cite{GMY-boundary2}, and obtain a concavity property of the modified version.
As an application, we give a characterization for the concavity degenerating to linearity on open Riemann surfaces.
\subsection{Main result: minimal $L^2$ integrals and concavity property}\label{sec:Main result}
Let $M$ be a complex manifold. Let $X$ and $Z$ be closed subsets of $M$. We call that a triple $(M,X,Z)$ satisfies condition $(A)$, if the following two statements hold:
$\uppercase\expandafter{\romannumeral1}.$ $X$ is a closed subset of $M$ and $X$ is locally negligible with respect to $L^2$ holomorphic functions; i.e., for any local coordinated neighborhood $U\subset M$ and for any $L^2$ holomorphic function $f$ on $U\backslash X$, there exists an $L^2$ holomorphic function $\tilde{f}$ on $U$ such that $\tilde{f}|_{U\backslash X}=f$ with the same $L^2$ norm;
$\uppercase\expandafter{\romannumeral2}.$ $Z$ is an analytic subset of $M$ and $M\backslash (X\cup Z)$ is a weakly pseudoconvex K\"ahler manifold.
Let $M$ be an $n-$dimensional complex manifold.
Assume that $(M,X,Z)$ satisfies condition $(A)$. Let $K_M$ be the canonical line bundle on $M$.
Let $dV_M$ be a continuous volume form on $M$. Let $F$ be a holomorphic function on $M$.
Assume that $F$ is not identically zero. Let $\psi$ be a plurisubharmonic function on $M$.
Let $\varphi$ be a Lebesgue measurable function on $M$ such that $\varphi+\psi$ is a plurisubharmonic function on $M$.
Let $T\in [-\infty,+\infty)$.
Denote that
$$\Psi:=\min\{\psi-2\log|F|,-T\}.$$
For any $z \in M$ satisfying $F(z)=0$,
we set $\Psi(z)=-T$.
Note that for any $t\ge T$,
the holomorphic function $F$ has no zero points on the set $\{\Psi<-t\}$.
Hence $\Psi=\psi-2\log|F|=\psi+2\log|\frac{1}{F}|$ is a plurisubharmonic function on $\{\Psi<-t\}$.
\begin{Definition}
We call that a positive measurable function $c$ (so-called ``\textbf{gain}") on $(T,+\infty)$ is in class $\tilde{P}_{T,M,\Psi}$ if the following two statements hold:
\par
$(1)$ $c(t)e^{-t}$ is decreasing with respect to $t$;
\par
$(2)$ For any $t_0> T$, there exists a closed subset $E_0$ of $M$ such that $E_0\subset Z\cap \{\Psi(z)=-\infty\}$ and for any compact subset $K\subset M\backslash E_0$, $e^{-\varphi}c(-\Psi)$ has a positive lower bound on $K\cap \{\Psi<-t_0\}$ .
\end{Definition}
\begin{Remark}
Recall that \cite{GMY-boundary2} a positive measurable function $c(t)$ on $(T,+\infty)$ is in class $P_{T,M,\Psi}$ if the following two statements hold:
\par
$(1)$ $c(t)e^{-t}$ is decreasing with respect to $t$;
\par
$(2)$ There exist $T_1> T$ and a closed subset $E$ of $M$ such that $E\subset Z\cap \{\Psi(z)=-\infty\}$ and for any compact subset $K\subset M\backslash E$, $e^{-\varphi}c(-\Psi_1)$ has a positive lower bound on $K$, where $\Psi_1:=\min\{\psi-2\log|F|,-T_1\}$.
Let $T_2>T$ be any real number and denote $\Psi_2:=\min\{\psi-2\log|F|,-T_2\}$.
We note that $c(t)$ is positive on $[T_1,T_2]$(or $[T_2,T_1]$) and has positive lower bound and upper bound on $[T_1,T_2]$(or $[T_2,T_1]$). Hence $\frac{c(-\Psi_2)}{c(-\Psi_1)}$ has a positive lower bound on $M$. Then we know that for any compact subset $K\subset M\backslash E$, $e^{-\varphi_\alpha}c(-\Psi_2)$ has a positive lower bound on $K$.
Then it is clear that $P_{T,M,\Psi}\subseteq\tilde{P}_{T,M,\Psi}$.
Let $M=\Delta\subset \mathbb{C}$ and $Z=X=\emptyset$. Let $\psi=2\log|z|+2\log|z-\frac{1}{2}|$, $\varphi=-2\log|z-\frac{1}{2}|$ and $F=z-\frac{1}{2}$. Let $T=4\log 2$. Then $\Psi=\min\{\psi-2\log|F|,-T\}=\min\{2\log|z|,-4\log 2\}$. Then we know that $c(t)\equiv 1 \in \tilde{P}_{T,M,\Psi}$ and $c(t)\equiv 1$ is not in $P_{T,M,\Psi}$. Hence $P_{T,M,\Psi}$ is a proper subset of $\tilde{P}_{T,M,\Psi}$.
\end{Remark}
Let $z_0$ be a point in $M$. Denote that $\tilde{J}(\Psi)_{z_0}:=\{f\in\mathcal{O}(\{\Psi<-t\}\cap V): t\in \mathbb{R}$ and $V$ is a neighborhood of $z_0\}$. We define an equivalence relation $\backsim$ on $\tilde{J}(\Psi)_{z_0}$ as follows: for any $f,g\in \tilde{J}(\Psi)_{z_0}$,
we call $f \backsim g$ if $f=g$ holds on $\{\Psi<-t\}\cap V$ for some $t\gg T$ and open neighborhood $V\ni o$.
Denote $\tilde{J}(\Psi)_{z_0}/\backsim$ by $J(\Psi)_{z_0}$, and denote the equivalence class including $f\in \tilde{J}(\Psi)_{z_0}$ by $f_{z_0}$.
If $z_0\in \cap_{t>T} \{\Psi<-t\}$, then $J(\Psi)_{z_0}=\mathcal{O}_{M,z_0}$ (the stalk of the sheaf $\mathcal{O}_{M}$ at $z_0$), and $f_{z_0}$ is the germ $(f,z_0)$ of holomorphic function $f$. If $z_0\notin \cap_{t>T} \overline{\{\Psi<-t\}}$, then $J(\Psi)_{z_0}$ is trivial.
Let $f_{z_0},g_{z_0}\in J(\Psi)_{z_0}$ and $(h,z_0)\in \mathcal{O}_{M,z_0}$. We define $f_{z_0}+g_{z_0}:=(f+g)_{z_0}$ and $(h,z_0)\cdot f_{z_0}:=(hf)_{z_0}$.
Note that $(f+g)_{z_0}$ and $(hf)_{z_0}$ ($\in J(\Psi)_{z_0}$) are independent of the choices of the representatives of $f,g$ and $h$. Hence $J(\Psi)_{z_0}$ is an $\mathcal{O}_{M,z_0}$-module.
For $f_{z_0}\in J(\Psi)_{z_0}$ and $a,b\ge 0$, we call $f_{z_0}\in I\big(a\Psi+b\varphi\big)_{z_0}$ if there exist $t\gg T$ and a neighborhood $V$ of $z_0$,
such that $\int_{\{\Psi<-t\}\cap V}|f|^2e^{-a\Psi-b\varphi}dV_M<+\infty$.
Note that $I\big(a\Psi+b\varphi\big)_{z_0}$ is an $\mathcal{O}_{M,z_0}$-submodule of $J(\Psi)_{z_0}$.
If $z_0\in \cap_{t>T} \{\Psi<-t\}$, then $I_{z_0}=\mathcal{O}_{M,z_0}$, where $I_{z_0}:=I\big(0\Psi+0\varphi\big)_{z_0}$.
Let $Z_0$ be a subset of $\cap_{t>T} \overline{\{\Psi<-t\}}$. Let $f$ be a holomorphic $(n,0)$ form on $\{\Psi<-t_0\}\cap V$, where $V\supset Z_0$ is an open subset of $M$ and $t_0\ge T$
is a real number.
Let $J_{z_0}$ be an $\mathcal{O}_{M,z_0}$-submodule of $J(\Psi)_{z_0}$ such that $I\big(\Psi+\varphi\big)_{z_0}\subset J_{z_0}$,
where $z_0\in Z_0$.
Let $J$ be the $\mathcal{O}_{M,z_0}$-module sheaf with stalks $J_{z_0}$, where $z_0\in Z_0$.
Denote the \textbf{minimal $L^{2}$ integral} related to $J$
\begin{equation}
\label{def of g(t) for boundary pt}
\begin{split}
\inf\Bigg\{ \int_{ \{ \Psi<-t\}}|\tilde{f}|^2e^{-\varphi}c(-\Psi): \tilde{f}\in
H^0(\{\Psi<-t\},\mathcal{O} (K_M) ) \\
\&\, (\tilde{f}-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0},\text{for any } z_0\in Z_0 \Bigg\}
\end{split}
\end{equation}
by $G(t;c,\Psi,\varphi,J,f)$, where $t\in[T,+\infty)$, $c$ is a nonnegative function on $(T,+\infty)$ and $|f|^2:=\sqrt{-1}^{n^2}f\wedge \bar{f}$ for any $(n,0)$ form $f$.
Without misunderstanding, we denote $G(t;c,\Psi,\varphi,J,f)$ by $G(t)$ for simplicity. For various $c(t)$, we denote $G(t;c,\Psi,\varphi,J,f)$ by $G(t;c)$ respectively for simplicity.
In this article, we obtain the following concavity property of $G(t)$.
\begin{Theorem}
\label{main theorem}
Let $c\in\tilde{P}_{T,M,\Psi}$. If there exists $t \in [T,+\infty)$ satisfying that $G(t)<+\infty$, then $G(h^{-1}(r))$ is concave with respect to $r\in (\int_{T_1}^{T}c(t)e^{-t}dt,\int_{T_1}^{+\infty}c(t)e^{-t}dt)$, $\lim\limits_{t\to T+0}G(t)=G(T)$ and $\lim\limits_{t \to +\infty}G(t)=0$, where $h(t)=\int_{T_1}^{t}c(t_1)e^{-t_1}dt_1$ and $T_1 \in (T,+\infty)$.
\end{Theorem}
When $M$ is a pseudoconvex domain $D$ in $\mathbb{C}^n$, $\varphi\equiv0$, $c(t)\equiv 1$ and $T=0$, Theorem \ref{main theorem} degenerates to the concavity property in \cite{BGY-boundary}. When $c(t)\in P_{T,M,\Psi}$, Theorem \ref{main theorem} degenerates to the concavity property in \cite{GMY-boundary2} (Theorem 1.2 in \cite{GMY-boundary2}).
\begin{Remark} It follows from Theorem 1.2 and Remark 1.8 in \cite{GMY-boundary2} that the assumption ``$\{\psi<-t\}\backslash Z_0$ is a weakly pseudoconvex K\"ahler manifold for any $t\in\mathbb{R}$'' in \cite{BGMY7} can be removed.
\end{Remark}
\begin{Remark}
\label{infty2}Let $c\in\tilde{P}_{T,M,\Psi}$. If $\int_{T_1}^{+\infty}c(t)e^{-t}dt=+\infty$ and $f_{z_0}\notin
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$ for some $ z_0\in Z_0$, then $G(t)=+\infty$ for any $t\geq T$. Thus, when there exists $t \in [T,+\infty)$ satisfying that $G(t)\in(0,+\infty)$, we have $\int_{T_1}^{+\infty}c(t)e^{-t}dt<+\infty$ and $G(\hat{h}^{-1}(r))$ is concave with respect to $r\in (0,\int_{T}^{+\infty}c(t)e^{-t}dt)$, where $\hat{h}(t)=\int_{t}^{+\infty}c(l)e^{-l}dl$.
\end{Remark}
Let $c(t)$ be a nonnegative measurable function on $(T,+\infty)$. Denote that
\begin{equation}\nonumber
\begin{split}
\mathcal{H}^2(t;c):=\Bigg\{\tilde{f}:\int_{ \{ \Psi<-t\}}|\tilde{f}|^2e^{-\varphi}c(-\Psi)<+\infty,\ \tilde{f}\in
H^0(\{\Psi<-t\},\mathcal{O} (K_M) ) \\
\& (\tilde{f}-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0},\text{for any } z_0\in Z_0 \Bigg\},
\end{split}
\end{equation}
where $t\in[T,+\infty)$.
As a corollary of Theorem \ref{main theorem}, we give a necessary condition for the concavity property degenerating to linearity.
\begin{Corollary}
\label{necessary condition for linear of G}
Let $c\in\tilde{P}_{T,M,\Psi}$.
Assume that $G(t)\in(0,+\infty)$ for some $t\ge T$, and $G(\hat{h}^{-1}(r))$ is linear with respect to $r\in[0,\int_T^{+\infty}c(s)e^{-s}ds)$, where $\hat{h}(t)=\int_{t}^{+\infty}c(l)e^{-l}dl$.
Then there exists a unique holomorphic $(n,0)$ form $\tilde{F}$ on $\{\Psi<-T\}$
such that $(\tilde{F}-f)_{z_0}\in\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$ holds for any $z_0\in Z_0$,
and $G(t)=\int_{\{\Psi<-t\}}|\tilde{F}|^2e^{-\varphi}c(-\Psi)$ holds for any $t\ge T$.
Furthermore
\begin{equation}
\begin{split}
\int_{\{-t_1\le\Psi<-t_2\}}|\tilde{F}|^2e^{-\varphi}a(-\Psi)=\frac{G(T_1;c)}{\int_{T_1}^{+\infty}c(t)e^{-t}dt}
\int_{t_2}^{t_1}a(t)e^{-t}dt
\label{other a also linear}
\end{split}
\end{equation}
holds for any nonnegative measurable function $a$ on $(T,+\infty)$, where $T\le t_2<t_1\le+\infty$ and $T_1 \in (T,+\infty)$.
\end{Corollary}
\begin{Remark}
\label{rem:linear}
If $\mathcal{H}^2(t_0;\tilde{c})\subset\mathcal{H}^2(t_0;c)$ for some $t_0\ge T$, we have
\begin{equation}
\begin{split}
G(t_0;\tilde{c})=\int_{\{\Psi<-t_0\}}|\tilde{F}|^2e^{-\varphi}\tilde{c}(-\Psi)=
\frac{G(T_1;c)}{\int_{T_1}^{+\infty}c(t)e^{-t}dt}
\int_{t_0}^{+\infty}\tilde{c}(s)e^{-s}ds,
\label{other c also linear}
\end{split}
\end{equation}
where $\tilde{c}$ is a nonnegative measurable function on $(T,+\infty)$ and $T_1 \in (T,+\infty)$. Thus, if $\mathcal{H}^2(t;\tilde{c})\subset\mathcal{H}^2(t;c)$ for any $t>T$, then $G(\hat{h}^{-1}(r);\tilde c)$ is linear with respect to $r\in[0,\int_T^{+\infty}c(s)e^{-s}ds)$.
\end{Remark}
\subsection{An application: a characterization for the concavity degenerating to linearity on open Riemann surfaces}
In this section, we give a characterization for the concavity degenerating to linearity on open Riemann surfaces.
Let $\Omega$ be an open Riemann surface, and let $K_{\Omega}$ be the canonical (holomorphic) line bundle on $\Omega$. Let $dV_{\Omega}$ be a continuous volume form on $\Omega$. Let $\psi$ be a subharmonic function on $\Omega$, and let $\varphi$ be a Lebesgue measurable function on $\Omega$ such that $\varphi+\psi$ is subharmonic on $\Omega$. Let $F$ be a holomorphic function on $\Omega$. Let $T\in[-\infty,+\infty)$ such that $-T\le\sup\{\psi(z)-2\log|F(z)|:z\in\Omega \,\&\,F(z)\not=0\}$. Denote that
$$\Psi:=\min\{\psi-2\log|F|,-T\}.$$
For any $z\in \Omega$ satisfying $F(z)=0$, we set $\Psi(z)=-T$. Note that $\Psi$ is subharmonic function on $\{\Psi<-T\}$.
Let $Z_0$ be a subset of $ \cap_{t>T}\overline{\{\Psi<-t\}}$. Denote that $Z_1:=\{z\in Z_0:v(dd^c(\psi),z)\ge2ord_{z}(F)\}$ and $Z_2:=\{z\in Z_0:v(dd^c(\psi),z)<2ord_{z}(F)\},$ where $d^c=\frac{\partial-\bar\partial}{2\pi\sqrt{-1}}$ and $v(dd^c(\psi),z)$ is the Lelong number of $dd^c(\psi)$ at $z$ (see \cite{Demaillybook}). Assume that $Z'_1:=\{z\in Z_0:v(dd^c(\psi),z)>2ord_{z}(F)\}$ is a finite subset of $\Omega$. Note that $\{\Psi<-t\}\cup Z'_1$ is an open Riemann surface for any $t\ge T.$
Let $c(t)$ be a positive measurable function on $(T,+\infty)$ such that
$c(t)e^{-t}$ is decreasing on $(0,+\infty)$,
$c(t)e^{-t}$ is integrable near $+\infty$,
and $e^{-\varphi}c(-\Psi)$ has a positive lower bound on $K\cap\{\Psi<-T\}$ for any compact subset $K$ of $\Omega\backslash E$,
where $E\subset\{\Psi=-\infty\}$ is a discrete subset of $\Omega$.
Let $f$ be a holomorphic $(1,0)$ form on $\{\Psi<-t_0\}\cap V$, where $V\supset Z_0$ is an open subset of $\Omega$ and $t_0>T$
is a real number.
Let $J_{z}$ be an $\mathcal{O}_{\Omega,z}$-submodule of $H_{z}$ such that $I(\Psi+\varphi)_{z}\subset J_{z}$,
where $z\in Z_0$ and $H_{z}:=\{h_{z}\in J(\Psi)_{z}:\int_{\{\Psi<-t\}\cap U}|h|^2e^{-\varphi}c(-\Psi)dV_{\Omega}<+\infty$ for some $t>T$ and some neighborhood $U$ of $z\}$.
Denote
\begin{equation}
\label{def of g(t) for boundary pt}
\begin{split}
\inf\Bigg\{ \int_{ \{ \Psi<-t\}}|\tilde{f}|^2&e^{-\varphi}c(-\Psi): \tilde{f}\in
H^0(\{\Psi<-t\},\mathcal{O} (K_{\Omega}) ) \\
&\&\, (\tilde{f}-f)_{z}\in
\mathcal{O} (K_{\Omega})_{z} \otimes J_{z}\text{ for any } z\in Z_0 \Bigg\}
\end{split}
\end{equation}
by $G(t;c,\Psi,\varphi,J,f)$, where $t\in[T,+\infty)$ and $|f|^2:=\sqrt{-1}f\wedge \bar{f}$ for any $(1,0)$ form $f$.
Without misunderstanding, we denote $G(t;c,\Psi,\varphi,J,f)$ by $G(t)$ for simplicity.
Recall that $G(h^{-1}(r))$ is concave with respect to $r$ (Theorem \ref{main theorem}), where $h(t)=\int_{t}^{+\infty}c(s)e^{-s}ds$ for any $t\ge T$.
We obtain a characterization for $G(h^{-1}(r))$ degenerating to linearity.
\begin{Theorem}
\label{thm:linearity1}
For any $z\in Z_1$, assume that one of the following two conditions holds:
$(A)$ $\varphi+a\psi$ is subharmonic near $z$ for some $a\in[0,1)$;
$(B)$ $(\psi-2p_z\log|w|)(z)>-\infty$, where $p_z=\frac{1}{2}v(dd^c(\psi),z)$ and $w$ is a local coordinate on a neighborhood of $z$ satisfying that $w(z)=0$.
If there exists $t_1\ge T$ such that $G(t_1)\in(0,+\infty)$, then $G(h^{-1}(r))$ is linear with respect to $r\in(0,\int_T^{+\infty}c(s)e^{-s}ds)$ if and only if the following statements hold:
$(1)$ $\varphi+\psi=2\log|g|+2\log|F|$ on $\{\Psi<-T\}\cup Z'_1$, $J_{z}=I(\varphi+\Psi)_z$ for any $z\in Z'_1$ and there exists a holomorphic $(1,0)$ form $f_1$ on $(\{\Psi<-t_0\}\cap V)\cup Z'_1$ such that $f_1=f$ on $\{\Psi<-t_0\}\cap V$, where $g$ is a holomorphic function on $\{\Psi<-T\}\cup Z'_1$ such that $ord_z(g)=ord_z(f_1)+1$ for any $z\in Z'_1$;
$(2)$ $Z'_1\not=\emptyset$ and $\psi=2\sum_{ z\in Z'_1}p_zG_{\Omega_t}(\cdot, z)+2\log|F|-t$ on $\Omega_t$ for any $t>T$, where $\Omega_t=\{\Psi<-t\}\cup Z'_1$ and $G_{\Omega_t}(\cdot, z)$ is the Green function on $\Omega_t$;
$(3)$ $\frac{p_z}{ord_{z}(g)}\lim_{z'\rightarrow z}\frac{dg(z')}{f(z')}=c_0$ for any $z\in Z'_1$, where $c_0\in\mathbb{C}\backslash\{0\}$ is a constant independent of $z\in Z'_1$.
\end{Theorem}
When $F\equiv1$, $\psi(z)=-\infty$ for any $z\in Z_0=Z'_1$ and condition $(B)$ holds, Theorem \ref{thm:linearity1} can be referred to \cite{GY-concavity3} (see also Theorem \ref{thm:m-points} and Remark \ref{r:equivalent}).
\section{preparations}
In this section, we do some preparations.
\subsection{$L^2$ method}
Let $M$ be an $n-$dimensional weakly pseudoconvex K\"ahler manifolds. Let $\psi$ be a plurisubharmonic function on $M$. Let $F$ be a holomorphic function on $M$. We assume that $F$ is not identically zero. Let $\varphi$ be a Lebesgue measurable function on $M$ such that $\varphi+\psi$ is a plurisubharmonic function on $M$.
Let $\delta$ be a positive integer. Let $T_1$ be a real number. Denote
$$\varphi_1:=(1+\delta)\max\{\psi+T_1,2\log|F|\},$$
and
$$\Psi_1:=\min\{\psi-2\log|F|,-T_1\}.$$
If $F(z)=0$ for some $z \in M$, we set $\Psi_1(z)=-T_1$.
Let $c(t)$ be a positive measurable function on $[T_1,+\infty)$ such that $c(t)e^{-t}$ is decreasing with respect $t$. We have the following lemma.
\begin{Lemma}[see \cite{GMY-boundary2}]
\label{L2 method}
Let $B\in(0,+\infty)$ and $t_0>T_1$ be arbitrarily given. Let $f$ be a holomorphic $(n,0)$ form on $\{\Psi_1<-t_0\}$ such that
$$\int_{\{\Psi_1<-t_0\}\cap K}|f|^2<+\infty,$$
for any compact subset $K\subset M$, and
$$\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi_1<-t_0\}}|f|^2e^{-\varphi-\Psi}<+\infty.$$
Then there exists a holomorphic $(n,0)$ form $\tilde{F}$ on $M$ such that
\begin{equation*}
\begin{split}
& \int_{M}|\tilde{F}-(1-b_{t_0,B}(\Psi_1))fF^{1+\delta}|^2e^{-\varphi-\varphi_1+v_{t_0,B}(\Psi_1)-\Psi_1}c(-v_{t_0,B}(\Psi_1)) \\
\le & (\frac{1}{\delta}c(T_1)e^{-T_1}+\int_{T_1}^{t_0+B}c(s)e^{-s}ds)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|f|^2e^{-\varphi-\Psi_1},
\end{split}
\end{equation*}
where $b_{t_0,B}(t)=\int^{t}_{-\infty}\frac{1}{B} \mathbb{I}_{\{-t_0-B< s < -t_0\}}ds$,
$v_{t_0,B}(t)=\int^{t}_{-t_0}b_{t_0,B}(s)ds-t_0$.
\end{Lemma}
Let $T\in[-\infty,+\infty)$. Denote $$\Psi:=\min\{\psi-2\log|F|,-T\}.$$
If $F(z)=0$ for some $z \in M$, we set $\Psi(z)=-T$. Let $c(t)\in \tilde{P}_{T,M,\Psi}$.
Let $T_1>T$ be a real number. Denote
$$\varphi_1:=(1+\delta)\max\{\psi+T_1,2\log|F|\},$$
and
$$\Psi_1:=\min\{\psi-2\log|F|,-T_1\}.$$
If $F(z)=0$ for some $z \in M$, we set $\Psi_1(z)=-T_1$.
It follows from Lemma \ref{L2 method} that we have the following lemma.
\begin{Lemma}
Let $(M,X,Z)$ satisfy condition $(A)$. Let $B \in (0, +\infty)$ and $t_0> T_1>T$ be arbitrarily given.
Let $f$ be a holomorphic $(n,0)$ form on $\{\Psi< -t_0\}$ such that
\begin{equation}
\int_{\{\Psi<-t_0\}} {|f|}^2e^{-\varphi}c(-\Psi)<+\infty,
\label{condition of lemma 2.2}
\end{equation}
Then there exists a holomorphic $(n,0)$ form $\tilde{F}$ on $M$ such that
\begin{equation}
\begin{split}
&\int_{M}|\tilde{F}-(1-b_{t_0,B}(\Psi_1))fF^{1+\delta}|^2e^{-\varphi-\varphi_1-\Psi_1+v_{t_0,B}(\Psi_1)}c(-v_{t_0,B}(\Psi_1))\\
\le & \left(\frac{1}{\delta}c(T_1)e^{-T_1}+\int_{T_1}^{t_0+B}c(t)e^{-t}dt\right)\int_M \frac{1}{B} \mathbb{I}_{\{-t_0-B< \Psi_1 < -t_0\}} {|f|}^2
e^{{-}\varphi-\Psi_1},
\end{split}
\end{equation}
where $b_{t_0,B}(t)=\int^{t}_{-\infty}\frac{1}{B} \mathbb{I}_{\{-t_0-B< s < -t_0\}}ds$ and
$v_{t_0,B}(t)=\int^{t}_{-t_0}b_{t_0,B}(s)ds-t_0$.
\label{L2 method for c(t)}
\end{Lemma}
\begin{proof} We note that $\{\Psi<-t_0\}=\{\Psi_1<-t_0\}$ and $\Psi_1=\Psi$ on $\{\Psi<-t_0\}$. It follows from inequality \eqref{condition of lemma 2.2} and $c(t)e^{-t}$ is decreasing with respect to $t$ that
$$\int_M \frac{1}{B} \mathbb{I}_{\{-t_0-B< \Psi_1 < -t_0\}} {|f|}^2
e^{{-}\varphi-\Psi}<+\infty.$$
As $c(t)\in \tilde{P}_{T,M,\Psi}$, $\{\Psi<-t_0\}=\{\Psi_1<-t_0\}$ and $\Psi_1=\Psi$ on $\{\Psi<-t_0\}$, there exists a closed subset $E\subset Z\cap \{\Psi=-\infty\}$ such that for any compact subset $K\subset M\backslash E$, $e^{-\varphi}c(-\Psi)$ has a positive lower bound on $K\cap \{\Psi_1<-t_0\} $.
It follows from inequality \eqref{condition of lemma 2.2} that we have
\begin{equation}\nonumber
\int_{K\cap \{\Psi_1<-t_0\}}|f|^2<+\infty.
\end{equation}
As $(M,X,Z)$ satisfies condition $(A)$, $M\backslash (Z\cup X)$ is a weakly pseudoconvex K\"ahler manifold. It follows from Lemma \ref{L2 method} that there exists a holomorphic $(n,0)$ form $\tilde{F}_Z$ on $M\backslash (Z\cup X)$ such that
\begin{equation*}
\begin{split}
& \int_{M\backslash (Z\cup X)}|\tilde{F}_Z-(1-b_{t_0,B}(\Psi_1))fF^{1+\delta}|^2e^{-\varphi-\varphi_1+v_{t_0,B}(\Psi_1)-\Psi_1}c(-v_{t_0,B}(\Psi_1)) \\
\le & (\frac{1}{\delta}c(T_1)e^{-T_1}+\int_{T_1}^{t_0+B}c(s)e^{-s}ds)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi_1<-t_0\}}|f|^2e^{-\varphi-\Psi_1}<+\infty.
\end{split}
\end{equation*}
For any $z\in \left((Z\cup X)\backslash E\right)$, there exists an open neighborhood $V_z$ of $z$ such that $V_z\Subset M\backslash E$.
It follows from inequality \eqref{condition of lemma 2.2} and $c(t)\in \tilde{P}_{T,M,\Psi}$ that we have $\int_{V_z\cap \{\Psi_1<-t_0\}}|f|^2<+\infty$.
Note that $\varphi+\varphi_1+\Psi$ is a plurisubharmonic function on $M$. As $c(t)e^{-t}$ is decreasing with respect to $t$ and $v_{t_0,B}(\Psi_1)\ge -t_0-\frac{B}{2}$, we have $c(-v_{t_0,B}(\Psi_1))e^{v_{t_0,B}(\Psi_1)}\ge c(t_0+\frac{B}{2})e^{-t_0-\frac{B}{2}}>0$. Denote $C:=\inf\limits_{V_z}e^{-\varphi-\varphi_1+v_{t_0,B}(\Psi_1)-\Psi_1}c(-v_{t_0,B}(\Psi_1))$, we know $C>0$. Then we have
\begin{equation*}
\begin{split}
&\int_{V_z\backslash (Z\cup X)}|\tilde{F}_Z|^2\\
\le & 2\int_{V_z\backslash (Z\cup X)}|\tilde{F}_Z-(1-b_{t_0,B}(\Psi_1))fF^{1+\delta}|^2
+2\int_{V_z\backslash (Z\cup X)}|(1-b_{t_0,B}(\Psi_1))fF^{1+\delta}|^2
\\
\le &
\frac{2}{C}\bigg(\int_{M\backslash (Z\cup X)}|\tilde{F}_Z-(1-b_{t_0,B}(\Psi_1))fF^{1+\delta}|^2e^{-\varphi-\varphi_1+v_{t_0,B}(\Psi_1)-\Psi_1}c(-v_{t_0,B}(\Psi_1))\bigg)\\
&+\sup_{V_z}|F^{1+\delta}|^2\int_{\{\Psi_1<-t_0\}\cap V_z}|f|^2\\
<&+\infty.
\end{split}
\end{equation*}
As $Z\cup X$ is locally negligible with respect to $L^2$ holomorphic function, we can find a holomorphic extension $\tilde{F}_E$ of $\tilde{F}_Z$ from $M\backslash (Z\cup X)$ to $M\backslash E$ such that
\begin{equation*}
\begin{split}
& \int_{M\backslash E}|\tilde{F}_E-(1-b_{t_0,B}(\Psi_1))fF^{1+\delta}|^2e^{-\varphi-\varphi_1+v_{t_0,B}(\Psi_1)-\Psi_1}c(-v_{t_0,B}(\Psi_1)) \\
\le & (\frac{1}{\delta}c(T_1)e^{-T_1}+\int_{T_1}^{t_0+B}c(s)e^{-s}ds)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi_1<-t_0\}}|f|^2e^{-\varphi-\Psi}.
\end{split}
\end{equation*}
Note that $E\subset\{\Psi=-\infty\}\subset\{\Psi<-t_0\}$ and $\{\Psi<-t_0\}$ is open, then for any $z\in E$, there exists an open neighborhood $U_z$ of $z$ such that $U_z\Subset\{\Psi<-t_0\}=\{\Psi_1<-t_0\}$.
As $v_{t_0,B}(t)\ge -t_0-\frac{B}{2}$, we have $c(-v_{t_0,B}(\Psi_1))e^{v_{t_0,B}(\Psi_1)}\ge c(t_0+\frac{B}{2})e^{-t_0-\frac{B}{2}}>0$. Note that $\varphi+\varphi_1+\Psi_1$ is plurisubharmonic on $M$. Thus we have
\begin{equation*}
\begin{split}
& \int_{U_z\backslash E}|\tilde{F}_E-(1-b_{t_0,B}(\Psi))fF^{1+\delta}|^2 \\
\le & \frac{1}{C_1}\int_{U_z\backslash E}|\tilde{F}_E-(1-b_{t_0,B}(\Psi_1))fF^{1+\delta}|^2e^{-\varphi-\varphi_1+v_{t_0,B}(\Psi_1)-\Psi_1}c(-v_{t_0,B}(\Psi_1))
<+\infty,
\end{split}
\end{equation*}
where $C_1$ is some positive number.
As $U_z\Subset\{\Psi<-t_0\}$, we have
\begin{equation*}
\begin{split}
\int_{U_z\backslash E}|(1-b_{t_0,B}(\Psi))fF^{1+\delta}|^2
\le
\left(\sup_{U_z}|F^{1+\delta}|^2\right)\int_{U_z}|f|^2 <+\infty.
\end{split}
\end{equation*}
Hence we have
$$\int_{U_z\backslash E}|\tilde{F}_E|^2<+\infty. $$
As $E$ is contained in some analytic subset of $M$, we can find a holomorphic extension $\tilde{F}$ of $\tilde{F}_E$ from $M\backslash E$ to $M$ such that
\begin{equation}
\begin{split}
&\int_{M}|\tilde{F}-(1-b_{t_0,B}(\Psi_1))fF^{1+\delta}|^2e^{-\varphi-\varphi_1-\Psi_1+v_{t_0,B}(\Psi_1)}c(-v_{t_0,B}(\Psi_1))\\
\le & \left(\frac{1}{\delta}c(T_1)e^{-T_1}+\int_{T_1}^{t_0+B}c(t)e^{-t}dt\right)\int_M \frac{1}{B} \mathbb{I}_{\{-t_0-B< \Psi_1 < -t_0\}} {|f|}^2
e^{{-}\varphi-\Psi_1}.
\end{split}
\end{equation}
Lemma \ref{L2 method for c(t)} is proved.
\end{proof}
Let $T\in[-\infty,+\infty)$. Let $c(t)\in \tilde{P}_{T,M,\Psi}$.
Using Lemma \ref{L2 method for c(t)}, we have the following lemma, which will be used to prove Theorem \ref{main theorem}.
\begin{Lemma}
\label{L2 method in JM concavity}
Let $(M,X,Z)$ satisfy condition $(A)$. Let $B \in (0, +\infty)$ and $t_0>t_1> T$ be arbitrarily given.
Let $f$ be a holomorphic $(n,0)$ form on $\{\Psi< -t_0\}$ such that
\begin{equation}
\int_{\{\Psi<-t_0\}} {|f|}^2e^{-\varphi}c(-\Psi)<+\infty,
\label{condition of JM concavity}
\end{equation}
Then there exists a holomorphic $(n,0)$ form $\tilde{F}$ on $\{\Psi<-t_1\}$ such that
\begin{equation*}
\begin{split}
& \int_{\{\Psi<-t_1\}}|\tilde{F}-(1-b_{t_0,B}(\Psi))f|^2e^{-\varphi+v_{t_0,B}(\Psi)-\Psi}c(-v_{t_0,B}(\Psi)) \\
\le & \left(\int_{t_1}^{t_0+B}c(s)e^{-s}ds\right)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|f|^2e^{-\varphi-\Psi},
\end{split}
\end{equation*}
where $b_{t_0,B}(t)=\int^{t}_{-\infty}\frac{1}{B} \mathbb{I}_{\{-t_0-B< s < -t_0\}}ds$,
$v_{t_0,B}(t)=\int^{t}_{-t_0}b_{t_0,B}(s)ds-t_0$.
\end{Lemma}
\begin{proof}[Proof of Lemma \ref{L2 method in JM concavity}]
Denote that
$$\tilde{\varphi}:=\varphi+(1+\delta)\max\{\psi+t_1,2\log|F|\}$$
and
$$\tilde{\Psi}:=\min\{\psi-2\log|F|,-t_1\}.$$
As $t_0>t_1>T$, we have $\{\tilde{\Psi}<-t_0\}=\{\Psi<-t_0\}$. It follows from inequality \eqref{condition of JM concavity} and Lemma \ref{L2 method for c(t)} that there exists a holomorphic function $\tilde{F}_{\delta}$ on $M$ such that
\begin{equation*}
\begin{split}
& \int_{M}|\tilde{F}_{\delta}-(1-b_{t_0,B}(\tilde\Psi))fF^{1+\delta}|^2e^{-\tilde \varphi+v_{t_0,B}(\tilde \Psi)-\tilde \Psi}c(-v_{t_0,B}(\tilde \Psi)) \\
\le & \left(\frac{1}{\delta}c(t_1)e^{-t_1}+\int_{t_1}^{t_0+B}c(s)e^{-s}ds\right)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\tilde\Psi<-t_0\}}|f|^2e^{-\varphi-\tilde\Psi}.
\end{split}
\end{equation*}
Note that on $\{\Psi<-t_1\}$, we have $\Psi=\tilde{\Psi}=\psi-2\log|F|$ and $\tilde{\varphi}=\varphi+\varphi_1=\varphi+(1+\delta)2\log|F|$. Hence
\begin{equation}\label{1st formula in L2 method JM concavity}
\begin{split}
& \int_{\{\Psi<-t_1\}}|\tilde{F}_{\delta}-(1-b_{t_0,B}(\Psi))fF^{1+\delta}|^2
e^{-\varphi-\varphi_1+v_{t_0,B}(\Psi)-\Psi}c(-v_{t_0,B}(\Psi)) \\
= & \int_{\{\Psi<-t_1\}}|\tilde{F}_{\delta}-(1-b_{t_0,B}(\tilde\Psi))fF^{1+\delta}|^2
e^{-\tilde\varphi+v_{t_0,B}(\tilde\Psi)-\tilde\Psi}c(-v_{t_0,B}(\tilde\Psi))\\
\le &
\int_{M}|\tilde{F}_{\delta}-(1-b_{t_0,B}(\tilde\Psi))fF^{1+\delta}|^2
e^{-\tilde\varphi+v_{t_0,B}(\tilde\Psi)-\tilde\Psi}c(-v_{t_0,B}(\tilde\Psi))\\
\le & \left(\frac{1}{\delta}c(t_1)e^{-t_1}+\int_{t_1}^{t_0+B}c(s)e^{-s}ds\right)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\tilde\Psi<-t_0\}}|f|^2e^{-\varphi-\tilde\Psi}\\
=&
\left(\frac{1}{\delta}c(t_1)e^{-t_1}+\int_{t_1}^{t_0+B}c(s)e^{-s}ds\right)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|f|^2e^{-\varphi-\Psi}<+\infty.
\end{split}
\end{equation}
Let $F_{\delta}:=\frac{\tilde{F}_{\delta}}{F^{\delta}}$ be a holomorphic function on $\{\Psi<-t_1\}$. Then it follows from \eqref{1st formula in L2 method JM concavity} that
\begin{equation}\label{2nd formula in L2 method JM concavity}
\begin{split}
& \int_{\{\Psi<-t_1\}}|F_{\delta}-(1-b_{t_0,B}(\Psi))fF|^2
e^{-\varphi+v_{t_0,B}(\Psi)-\psi}c(-v_{t_0,B}(\Psi)) \\
\le&
\bigg(\frac{1}{\delta}c(t_1)e^{-t_1}+\int_{t_1}^{t_0+B}c(s)e^{-s}ds\bigg)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|f|^2e^{-\varphi-\Psi}.
\end{split}
\end{equation}
Let $K$ be any compact subset of $M$. Note that $\inf_{K}e^{-\varphi+v_{t_0,B}(\Psi)-\psi}c(-v_{t_0,B}(\Psi))\ge \left(c(t_0+\frac{2}{B})e^{-t_0-\frac{2}{B}}\right)\inf_{K}e^{-\varphi-\psi}>0$. It follows from inequality \eqref{2nd formula in L2 method JM concavity} that we have
$$\sup_{\delta} \int_{\{\Psi<-t_1\}\cap K}|F_{\delta}-(1-b_{t_0,B}(\Psi))fF|^2<+\infty.$$
We also note that
$$\int_{\{\Psi<-t_1\}\cap K}|(1-b_{t_0,B}(\Psi))fF|^2\le
\left(\sup_{K}|F|^2\right)\int_{\{\Psi<-t_0\}\cap K}|f|^2<+\infty.$$
Then we know that
$$\sup_{\delta} \int_{\{\Psi<-t_1\}\cap K}|F_{\delta}|^2<+\infty,$$
and there exists a subsequence of $\{F_\delta\}$ (also denoted by $F_\delta$) compactly convergent to a holomorphic $(n,0)$ form $\tilde{F}_1$ on $\{\Psi<-t_1\}$.
It follows from Fatou's Lemma and inequality \eqref{2nd formula in L2 method JM concavity} that we have
\begin{equation}\label{3rd formula in L2 method JM concavity}
\begin{split}
& \int_{\{\Psi<-t_1\}}|\tilde{F}_1-(1-b_{t_0,B}(\Psi))fF|^2
e^{-\varphi+v_{t_0,B}(\Psi)-\psi}c(-v_{t_0,B}(\Psi)) \\
\le &\liminf_{\delta\to +\infty} \int_{\{\Psi<-t_1\}}|F_{\delta}-(1-b_{t_0,B}(\Psi))fF|^2
e^{-\varphi+v_{t_0,B}(\Psi)-\psi}c(-v_{t_0,B}(\Psi)) \\
\le&\liminf_{\delta\to +\infty}
\bigg(\frac{1}{\delta}c(t_1)e^{-t_1}+\int_{t_1}^{t_0+B}c(s)e^{-s}ds\bigg)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|f|^2e^{-\varphi-\Psi}\\
\le &\left(\int_{t_1}^{t_0+B}c(s)e^{-s}ds\right)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|f|^2e^{-\varphi-\Psi}.
\end{split}
\end{equation}
Denote $\tilde{F}:=\frac{\tilde{F}_1}{F}$. Note that on $\{\Psi<-t_1\}$, we have $\Psi=\psi-2\log|F|$. It follows from inequality \eqref{3rd formula in L2 method JM concavity} that we have
\begin{equation}\nonumber
\begin{split}
& \int_{\{\Psi<-t_1\}}|\tilde{F}-(1-b_{t_0,B}(\Psi))f|^2
e^{-\varphi+v_{t_0,B}(\Psi)-\Psi}c(-v_{t_0,B}(\Psi)) \\
\le &\left(\int_{t_1}^{t_0+B}c(s)e^{-s}ds\right)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|f|^2e^{-\varphi-\Psi}.
\end{split}
\end{equation}
Lemma \ref{L2 method in JM concavity} is proved.
\end{proof}
\subsection{Properties of $\mathcal{O}_{M,z_0}$-module $J_{z_0}$}
\label{sec:properties of module}
In this section, we present some properties of $\mathcal{O}_{M,z_0}$-module $J_{z_0}$.
Since the case is local, we assume that $F$ is a holomorphic function on a pseudoconvex domain $D\subset \mathbb{C}^n$ containing the origin $o\in \mathbb{C}^n$. Let $\psi$ be a plurisubharmonic function on $D$. Let $\varphi$ be a Lebesgue measurable function on $D$ such that $\psi+\varphi$ is plurisubharmonic. Let $T\in [-\infty,+\infty)$. Denote $$\Psi:=\min\{\psi-2\log|F|,-T\}.$$
If $F(z)=0$ for some $z \in M$, we set $\Psi(z)=-T$. Let $T_1>T$ be a real number.
Denote
$$\varphi_1:=2\max\{\psi+T_1,2\log|F|\},$$
and
$$\Psi_1:=\min\{\psi-2\log|F|,-T_1\}.$$
If $F(z)=0$ for some $z \in M$, we set $\Psi_1(z)=-T_1$. We also note that by definition $I(\Psi_1+\varphi)_o=I(\Psi+\varphi)_o$.
Let $c(t)$ be a positive measurable function on $(T,+\infty)$ such that $c(t)\in\tilde{P}_{T,D,\Psi}$.
Denote that $H_o:=\{f_o\in J(\Psi)_o:\int_{\{\Psi<-t\}\cap V_0}|f|^2e^{-\varphi}c(-\Psi)dV_M<+\infty \text{ for some }t>T \text{ and } V_0 \text{ is an open neighborhood of o}\}$ and
$\mathcal{H}_o:=\{(F,o)\in \mathcal{O}_{\mathbb{C}^n,o}:\int_{U_0}|F|^2e^{-\varphi-\varphi_1}c(-\Psi_1)dV_M<+\infty \text{ for some open neighborhood} \ U_0 \text{ of } o\}$.
As $c(t)\in\tilde{P}_{T,D,\Psi}$, hence $c(t)e^{-t}$ is decreasing with respect to $t$ and we have $I(\Psi_1+\varphi)_o=I(\Psi+\varphi)_o\subset H_o$.
We also note that $\mathcal{H}_o$ is an ideal of $\mathcal{O}_{\mathbb{C}^n,o}$.
\begin{Lemma}\label{construction of morphism} For any $f_o\in H_o$, there exist a pseudoconvex domain $D_0\subset D$ containing $o$ and a holomorphic function $\tilde{F}$ on $D_0$ such that $(\tilde{F},o)\in \mathcal{H}_o$ and
$$\int_{\{\Psi_1<-t_1\}\cap D_0}|\tilde{F}-fF^2|e^{-\varphi-\varphi_1-\Psi_1}<+\infty,$$
for some $t_1>T_1$.
\end{Lemma}
\begin{proof}It follows from $f_o\in H_o$ that there exists $t_0>T_1>T$ and a pseudoconvex domain $D_0\Subset D$ containing $o$ such that
\begin{equation}\label{construction of morphism formula 1}
\int_{\{\Psi<-t_0\}\cap D_0}|f|^2e^{-\varphi}c(-\Psi)<+\infty.
\end{equation}
Then it follows from Lemma \ref{L2 method for c(t)} that there exists a holomorphic function $\tilde F$ on $D_0$ such that
\begin{equation*}
\begin{split}
& \int_{D_0}|\tilde{F}-(1-b_{t_0}(\Psi_1))fF^{2}|^2e^{-\varphi-\varphi_1+v_{t_0}(\Psi_1)-\Psi_1}c(-v_{t_0}(\Psi_1)) \\
\le & \left(c(T_1)e^{-T_1}+\int_{T_1}^{t_0+1}c(s)e^{-s}ds\right)
\int_{D_0}\mathbb{I}_{\{-t_0-1<\Psi_1<-t_0\}}|f|^2e^{-\varphi-\Psi_1},
\end{split}
\end{equation*}
where $b_{t_0}(t)=\int^{t}_{-\infty} \mathbb{I}_{\{-t_0-1< s < -t_0\}}ds$,
$v_{t_0}(t)=\int^{t}_{-t_0}b_{t_0}(s)ds-t_0$. Denote $C:=c(T_1)e^{-T_1}+\int_{T_1}^{t_0+B}c(s)e^{-s}ds$, we note that $C$ is a positive number.
As $v_{t_0}(t)>-t_0-1$, we have $e^{v_{t_0}(\Psi)}c(-v_{t_0}(\Psi))\ge c(t_0+1)e^{-(t_0+1)}>0$. As $b_{t_0}(t)\equiv 0$ on $(-\infty,-t_0-1)$, we have
\begin{equation}\label{construction of morphism formula 2}
\begin{split}
&\int_{D_0\cap\{\Psi_1<-t_0-1\}}|\tilde{F}-fF^2|^2e^{-\varphi-\varphi_1-\Psi_1} \\
\le & \frac{1}{c(t_0+1)e^{-(t_0+1)}}
\int_{D_0}|\tilde{F}-(1-b_{t_0}(\Psi_1))fF^2|^2e^{-\varphi-\varphi_1-\Psi_1+v_{t_0}(\Psi_1)}c(-v_{t_0}(\Psi_1))\\
\le &\frac{C}{c(t_0+1)e^{-(t_0+1)}}
\int_{D_0}\mathbb{I}_{\{-t_0-1<\Psi_1<-t_0\}}|f|^2e^{-\varphi-\Psi_1}<+\infty.
\end{split}
\end{equation}
Note that on $\{\Psi_1<-t_0\}$, $|F|^4e^{-\varphi_1}=1$. As $v_{t_0}(\Psi_1)\ge \Psi_1$, we have $c(-v_{t_0}(\Psi_1))e^{v_{t_0}(\Psi_1)}\ge c(-\Psi_1)e^{-\Psi_1}$. Hence we have
\begin{equation}\nonumber
\begin{split}
&\int_{D_0}|\tilde{F}|^2e^{-\varphi-\varphi_1}c(-\Psi_1) \\
\le & 2\int_{D_0}|\tilde{F}-(1-b_{t_0}(\Psi_1))fF^2|^2e^{-\varphi-\varphi_1}c(-\Psi_1)\\
+&2\int_{D_0}|(1-b_{t_0}(\Psi_1))fF^2|^2e^{-\varphi-\varphi_1}c(-\Psi_1)\\
\le&
2\int_{D_0}|\tilde{F}-(1-b_{t_0}(\Psi_1))fF^2|^2e^{-\varphi-\varphi_1-\Psi_1+v_{t_0}(\Psi_1)}c(-v_{t_0}(\Psi_1))\\
+&2\int_{D_0\cap\{\Psi<-t_0\}}|f|^2e^{-\varphi}c(-\Psi)\\
< &+\infty.
\end{split}
\end{equation}
Hence we know that $(\tilde{F},o)\in \mathcal{H}_o$.
\end{proof}
For any $(\tilde{F},o)\in\mathcal{H}_o$ and $(\tilde{F}_1,o)\in\mathcal{H}_o$ such that $\int_{D_1\cap\{\Psi_1<-t_1\}}|\tilde{F}-fF^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$ and
$\int_{D_1\cap\{\Psi_1<-t_1\}}|\tilde{F}_1-fF^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$, for some open neighborhood $D_1$ of $o$ and $t_1> T_1$, we have
$$\int_{D_1\cap\{\Psi_1<-t_1\}}|\tilde{F}_1-\tilde{F}|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty.$$
As $(\tilde{F},o)\in\mathcal{H}_o$ and $(\tilde{F}_1,o)\in\mathcal{H}_o$, there exists a neighborhood $D_2$ of $o$ such that
\begin{equation}\label{construction of morphism formula 3}
\int_{D_2}|\tilde{F}_1-\tilde{F}|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty.
\end{equation}
Note that we have $c(-\Psi_1)e^{\Psi_1}\ge c(t_1)e^{-t_1}$ on $\{\Psi\ge-t_1\}$. It follows from inequality \eqref{construction of morphism formula 3} that we have
$$\int_{D_2\cap \{\Psi\ge-t_1\}}|\tilde{F}_1-\tilde{F}|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty.$$
Hence we have $(\tilde{F}-\tilde{F}_1,o)\in \mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$.
Thus it follows from Lemma \ref{construction of morphism} that there exists a map $\tilde{P}:H_o\to \mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$ given by
$$\tilde{P}(f_o)=[(\tilde{F},o)]$$
for any $f_o\in H_o$, where $(\tilde{F},o)$ satisfies $(\tilde{F},o)\in \mathcal{H}_o$ and
$\int_{D_1\cap\{\Psi_1<-t_1\}}|\tilde{F}-fF^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty,$
for some $t_1>T_1$ and some open neighborhood $D_1$ of $o$, and $[(\tilde{F},o)]$ is the equivalence class of $(\tilde{F},o)$ in $\mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$.
\begin{Proposition}\label{proposition of morphism}
$\tilde{P}$ is an $\mathcal{O}_{\mathbb{C}^n,o}$-module homomorphism and $Ker(\tilde{P})=I(\varphi+\Psi_1)_o$.
\end{Proposition}
\begin{proof}For any $f_o,g_o\in H_o$. Denote that $\tilde{P}(f_o)=[(\tilde{F},o)]$, $\tilde{P}(g_o)=[(\tilde{G},o)]$ and $\tilde{P}(f_o+g_o)=[(\tilde{H},o)]$.
Note that there exists an open neighborhood $D_1$ of $o$ and $t> T_1$ such that $\int_{D_1\cap\{\Psi_1<-t\}}|\tilde{F}-fF^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$,
$\int_{D_1\cap\{\Psi_1<-t\}}|\tilde{G}-gF^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$, and
$\int_{D_1\cap\{\Psi_1<-t\}}|\tilde{H}-(f+g)F^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$. Hence we have
$$\int_{D_1\cap\{\Psi_1<-t\}}|\tilde{H}-(\tilde{F}+\tilde{G})|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty.$$
As $(\tilde{F},o),(\tilde{G},o)$ and $(\tilde{H},o)$ belong to $ \mathcal{H}_o$, there exists an open neighborhood $\tilde{D}_1\subset D_1$ of $o$ such that
$\int_{\tilde{D}_1}|\tilde{H}-(\tilde{F}+\tilde{G})|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty$.
As $c(t)e^{-t}$ is decreasing with respect to $t$, we have $c(-\Psi_1)e^{\Psi_1}\ge c(t)e^{-t}$ on $\{\Psi_1\ge -t\}$. Hence we have
$$\int_{\tilde{D}_1\cap\{\Psi_1\ge -t\}}|\tilde{H}-(\tilde{F}+\tilde{G})|^2e^{-\varphi-\varphi_1-\Psi_1}
\le\frac{1}{c(t)e^{-t}}\int_{\tilde{D}_1\cap\{\Psi_1\ge -t\}}|\tilde{H}-(\tilde{F}+\tilde{G})|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty.$$
Thus we have $\int_{\tilde{D}_1}|\tilde{H}-(\tilde{F}+\tilde{G})|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$, which implies that $\tilde{P}(f_o+g_o)=\tilde{P}(f_o)+\tilde{P}(g_o)$.
For any $(h,o) \in \mathcal{O}_{\mathbb{C}^n,o}$. Denote $\tilde{P}((hf)_o)=[(\tilde{F}_h,o)]$. Note that there exists an open neighborhood $D_2$ of $o$ and $t> T_1$ such that $\int_{D_2\cap\{\Psi_1<-t\}}|\tilde{F}_h-(hf)F^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$. It follows from $\int_{D_2\cap\{\Psi_1<-t\}}|\tilde{F}-fF^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$ and $h$ is holomorphic on $\overline{D_2}$ (shrink $D_2$ if necessary) that $\int_{D_2\cap\{\Psi_1<-t\}}|h\tilde{F}-hfF^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$. Then we have
$$\int_{D_2\cap\{\Psi_1<-t\}}|\tilde{F}_h-h\tilde{F}|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty.$$
Note that $(h\tilde{F},o) $ and $(\tilde{F}_h,o)$ belong to $ \mathcal{H}_o$, we have
$\int_{D_2}|\tilde{F}_h-h\tilde{F}|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty$.
As $c(t)e^{-t}$ is decreasing with respect to $t$, we have $c(-\Psi_1)e^{\Psi_1}\ge c(t)e^{-t}$ on $\{\Psi_1\ge -t\}$. Hence we have
$$\int_{D_2\cap\{\Psi_1\ge -t\}}|\tilde{F}_h-h\tilde{F}|^2e^{-\varphi-\varphi_1-\Psi_1}
\le\frac{1}{c(t)e^{-t}}\int_{D_2\cap\{\Psi_1\ge -t\}}|\tilde{F}_h-h\tilde{F}|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty.$$
Thus we have $\int_{D_2}|\tilde{F}_h-h\tilde{F}|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$, which implies that $\tilde{P}(hf_o)=(h,o)\tilde{P}(f_o)$.
Now we have proved that $\tilde{P}$ is an $\mathcal{O}_{\mathbb{C}^n,o}$-module homomorphism.
Next, we prove $Ker(\tilde{P})=I(\varphi+\Psi_1)_o$.
If $f_o\in I(\varphi+\Psi_1)_o$. Denote $\tilde{P}(f_o)=[(\tilde{F},o)]$. It follows from Lemma \ref{construction of morphism} that $(\tilde{F},o)\in \mathcal{H}_o$ and there exists an open neighborhood $D_3$ of $o$ and a real number $t_1>T_1$ such that
$$\int_{\{\Psi_1<-t_1\}\cap D_3}|\tilde{F}-fF^2|e^{-\varphi-\varphi_1-\Psi_1}<+\infty.$$
As $f_o\in I(\varphi+\Psi_1)_o$, shrink $D_3$ and $t_1$ if necessary, we have
\begin{equation}\label{proposition of morphism formula 1}
\begin{split}
&\int_{\{\Psi_1<-t_1\}\cap D_3}|\tilde{F}|^2e^{-\varphi-\varphi_1-\Psi_1}\\
\le &2\int_{\{\Psi_1<-t_1\}\cap D_3}|\tilde{F}-fF^2|^2e^{-\varphi-\varphi_1-\Psi_1}
+2\int_{\{\Psi_1<-t_1\}\cap D_3}|fF^2|^2e^{-\varphi-\varphi_1-\Psi_1}\\
\le &2\int_{\{\Psi_1<-t_1\}\cap D_3}|\tilde{F}-fF^2|^2e^{-\varphi-\varphi_1-\Psi_1}
+2\int_{\{\Psi_1<-t_1\}\cap D_3}|f|^2e^{-\varphi-\Psi_1}\\
<&+\infty.
\end{split}
\end{equation}
As $c(t)e^{-t}$ is decreasing with respect to $t$, $c(-\Psi_1)e^{\Psi_1}\ge C_0>0$ for some positive number $C_0$ on $\{\Psi_1\ge-t_1\}$. Then we have
\begin{equation}\label{proposition of morphism formula 1'}
\begin{split}
\int_{\{\Psi_1\ge-t_1\}\cap D_3}|\tilde{F}|^2e^{-\varphi-\varphi_1-\Psi_1}
\le\frac{1}{C_0}\int_{\{\Psi_1\ge-t_1\}\cap D_3}|\tilde{F}|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty.
\end{split}
\end{equation}
Combining inequality \eqref{proposition of morphism formula 1} and inequality \eqref{proposition of morphism formula 1'}, we know that $\tilde{F}\in \mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$, which means $\tilde{P}(f_o)=0$ in $\mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$. Hence we know $I(\varphi+\Psi_1)_o\subset Ker(\tilde{P})$.
If $f_o\in Ker(\tilde{P})$, we know $\tilde{F}\in \mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$.
We can assume that $\tilde{F}$ satisfies $\int_{D_4}|\tilde{F}|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty$ for some open neighborhood $D_4$ of $o$. Then we have
\begin{equation}\label{proposition of morphism formula 2'}
\begin{split}
&\int_{ \{\Psi_1<-t_1\}\cap D_4}|f|^2e^{-\varphi-\Psi_1}\\
=&\int_{\{\Psi_1<-t_1\}\cap D_4}|fF^2|^2e^{-\varphi-\varphi_1-\Psi_1}\\
\le & \int_{\{\Psi_1<-t_1\}\cap D_4}|\tilde{F}|^2e^{-\varphi-\varphi_1-\Psi_1}+\int_{\{\Psi_1<-t_1\}\cap D_4}|\tilde{F}-fF^2|e^{-\varphi-\varphi_1-\Psi_1}\\
< &+\infty.
\end{split}
\end{equation}
By definition, we know $f_o\in I(\varphi+\Psi_1)_o$. Hence $ Ker(\tilde{P})\subset I(\varphi+\Psi_1)_o$.
$ Ker(\tilde{P})= I(\varphi+\Psi_1)_o$ is proved.
\end{proof}
Now we can define an $\mathcal{O}_{\mathbb{C}^n,o}$-module homomorphism $P:H_o/I(\varphi+\Psi_1)_o\to \mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$ as follows,
$$P([f_o])=\tilde{P}(f_o)$$
for any $[f_o]\in H_o/I(\varphi+\Psi_1)_o$, where $f_o\in H_o$ is any representative of $[f_o]$. It follows from Proposition \ref{proposition of morphism} that $P([f_o])$ is independent of the choices of the representatives of $[f_o]$.
Let $(\tilde{F},o)\in \mathcal{H}_o$, i.e. $\int_{U}|\tilde{F}|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty$ for some neighborhood $U$ of $o$. Note that $|F|^4e^{-\varphi_1}\equiv 1$ on $\{\Psi_1<-T\}$. Hence we have $\int_{U\cap \{\Psi_1<-t\}}|\frac{\tilde{F}}{F^2}|^2e^{-\varphi}c(-\Psi_1)<+\infty$ for some $t>T$, i.e. $(\frac{\tilde{F}}{F^2})_o\in H_o$. And if $(\tilde{F},o)\in \mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$, it is easy to verify that $(\frac{\tilde{F}}{F^2})_o\in I(\varphi+\Psi_1)_o$. Hence we have an $\mathcal{O}_{\mathbb{C}^n,o}$-module homomorphism $Q:\mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o\to H_o/I(\varphi+\Psi_1)_o$ defined as follows,
$$Q([(\tilde{F},o)])=[(\frac{\tilde{F}}{F^2})_o].$$
The above discussion shows that $Q$ is independent of the choices of the representatives of $[(\tilde{F},o)]$ and hence $Q$ is well defined.
\begin{Proposition}\label{module isomorphism}$P:H_o/I(\varphi+\Psi_1)_o\to \mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$ is an $\mathcal{O}_{\mathbb{C}^n,o}$-module isomorphism and $P^{-1}=Q$.
\end{Proposition}
\begin{proof} It follows from Proposition \ref{proposition of morphism} that we know $P$ is injective.
Now we prove $P$ is surjective.
For any $[(\tilde{F},o)]$ in $\mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$. Let $(\tilde{F},o)$ be any representatives of $[(\tilde{F},o)]$ in $\mathcal{H}_o$. Denote that $[(f_1)_o]:=[(\frac{\tilde{F}}{F^2})_o]=Q([(\tilde{F},o)])$. Let $(f_1)_o:=(\frac{\tilde{F}}{F^2})_o\in H_o$ be the representative of $[(f_1)_o]$. Denote $[(\tilde{F}_1,o)]:=\tilde{P}((f_1)_o)=P([(f_1)_o])$. By the construction of $\tilde{P}$, we know that $(\tilde{F}_1,o)\in \mathcal{H}_o$ and
$$\int_{D_1\cap\{\Psi_1<-t\}}|\tilde{F}_1-f_1F^2|e^{-\varphi-\varphi_1-\Psi_1}<+\infty,$$
where $t>T$ and $D_1$ is some neighborhood of $o$. Note that $(f_1)_o:=(\frac{\tilde{F}}{F^2})_o$. Hence we have
$$\int_{D_1\cap\{\Psi_1<-t\}}|\tilde{F}_1-\tilde{F}|e^{-\varphi-\varphi_1-\Psi_1}<+\infty.$$
It follows from $(\tilde{F},o)\in \mathcal{H}_o$ and $(\tilde{F}_1,o)\in \mathcal{H}_o$ that there exists a neighborhood $D_2\subset D_1$ of $o$ such that
$$\int_{D_2}|\tilde{F}-\tilde{F}_1|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty.$$
Note that on $\{\Psi_1\ge -t\}$, we have $c(-\Psi_1)e^{\Psi_1}\ge c(t)e^{-t}>0$. Hence we have
$$\int_{D_2\cap \{\Psi_1\ge-t\}}|\tilde{F}-\tilde{F}_1|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty.$$
Thus we know that $(\tilde{F}_1-\tilde{F},o) \in \mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$, i.e. $[(\tilde{F},o)]=[(\tilde{F}_1,o)]$ in $ \mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$. Hence we have $P\circ Q([(\tilde{F},o)])=[(\tilde{F},o)]$, which implies that $P$ is surjective.
We have proved that $P:H_o/I(\varphi+\Psi_1)_o\to \mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$ is an $\mathcal{O}_{\mathbb{C}^n,o}$-module isomorphism and $P^{-1}=Q$.
\end{proof}
We recall the following property of closedness of holomorphic functions on a neighborhood of $o$.
\begin{Lemma}[see \cite{G-R}]
\label{closedness}
Let $N$ be a submodule of $\mathcal O_{\mathbb C^n,o}^q$, $1\leq q<+\infty$, let $f_j\in\mathcal O_{\mathbb C^n}(U)^q$ be a sequence of $q-$tuples holomorphic in an open neighborhood $U$ of the origin $o$. Assume that the $f_j$ converge uniformly in $U$ towards a $q-$tuples $f\in\mathcal O_{\mathbb C^n}(U)^q$, assume furthermore that all germs $(f_{j},o)$ belong to $N$. Then $(f,o)\in N$.
\end{Lemma}
\begin{Lemma}[see \cite{GY-concavity}]
\label{l:converge}
Let $M$ be a complex manifold. Let $S$ be an analytic subset of $M$.
Let $\{g_j\}_{j=1,2,...}$ be a sequence of nonnegative Lebesgue measurable functions on $M$, which satisfies that $g_j$ are almost everywhere convergent to $g$ on $M$ when $j\rightarrow+\infty$, where $g$ is a nonnegative Lebesgue measurable function on $M$. Assume that for any compact subset $K$ of $M\backslash S$, there exist $s_K\in(0,+\infty)$ and $C_K\in(0,+\infty)$ such that
$$\int_{K}{g_j}^{-s_K}dV_M\leq C_K$$
for any $j$, where $dV_M$ is a continuous volume form on $M$.
Let $\{F_j\}_{j=1,2,...}$ be a sequence of holomorphic $(n,0)$ form on $M$. Assume that $\liminf_{j\rightarrow+\infty}\int_{M}|F_j|^2g_j\leq C$, where $C$ is a positive constant. Then there exists a subsequence $\{F_{j_l}\}_{l=1,2,...}$, which satisfies that $\{F_{j_l}\}$ is uniformly convergent to a holomorphic $(n,0)$ form $F$ on $M$ on any compact subset of $M$ when $l\rightarrow+\infty$, such that
$$\int_{M}|F|^2g\leq C.$$
\end{Lemma}
The following lemma shows the closedness of submodules of $H_o$.
\begin{Lemma}\label{closedness of module}Let $D$ be a pseudoconvex domain containing $o$. Let $c(t)\in \tilde{P}_{T,D,\Psi}$.
Let $U_0\Subset D$ be a Stein neighborhood of $o$.
Let $J_o$ be an $\mathcal{O}_{\mathbb{C}^n,o}$-submodule of $H_o$ such that $I(\varphi+\Psi)_o\subset J_o$. Assume that $f_o\in J(\Psi)_o$. Let $\{f_j\}_{j\ge 1}$ be a sequence of holomorphic functions on $U_0\cap \{\Psi<-t_j\}$ for any $j\ge 1$, where $t_j>T$. Assume that $t_0:=\lim_{j\to +\infty}t_j\in[T,+\infty)$,
\begin{equation}\label{convergence property of module}
\limsup\limits_{j\to+\infty}\int_{U_0\cap\{\Psi<-t_j\}}|f_j|^2e^{-\varphi}c(-\Psi)\le C<+\infty,
\end{equation}
and $(f_j-f)_o\in J_o$. Then there exists a subsequence of $\{f_j\}_{j\ge 1}$ compactly convergent to a holomorphic function $f_0$ on $\{\Psi<-t_0\}\cap U_0$ which satisfies
$$\int_{U_0\cap\{\Psi<-t_0\}}|f_0|^2e^{-\varphi}c(-\Psi)\le C,$$
and $(f_0-f)_o\in J_o$.
\end{Lemma}
\begin{proof}
It follows from $c(t)\in\tilde{P}_{T,D,\Psi}$ that there exists an analytic subset $Z$ of $D$ and for any compact subset $K\subset D\backslash Z$, $e^{-\varphi}c(-\Psi)$ has a positive lower bound on $K\cap \{\Psi<-t_j\}$.
It follows from inequality \eqref{convergence property of module}, Lemma \ref{l:converge} and diagonal method that there exists a subsequence of $\{f_j\}_{j\ge 1}$ (also denoted by $\{f_j\}_{j\ge 1}$) compactly convergent to a holomorphic function $f_0$ on $\{\Psi<-t_0\}\cap U_0$. It follows from Fatou's Lemma that
$$\int_{U_0\cap\{\Psi<-t_0\}}|f_0|^2e^{-\varphi}c(-\Psi)\le \liminf\limits_{j\to+\infty}\int_{U_0\cap\{\Psi<-t_j\}}|f_j|^2e^{-\varphi}c(-\Psi)\le C.$$
Now we prove $(f_0-f)_o\in J_o$. We firstly recall some constructions in Lemma \ref{construction of morphism}.
As $t_0:=\lim_{j\to +\infty}t_j\in[T,+\infty)$. We can assume that $\{t_j\}_{j\ge 0}$ is upper bounded by some real number $T_1+1$. Denote $\Psi_1:=\min\{\psi-2\log|F|,-T_1\}$, and
if $F(z)=0$ for some $z \in M$, we set $\Psi_1(z)=-T_1$. We note that \begin{equation}\nonumber
\limsup\limits_{j\to+\infty}\int_{U_0\cap\{\Psi<-T_1-1\}}|f_j|^2e^{-\varphi}c(-\Psi)\le C<+\infty.
\end{equation}
It follows from $c(t)\in\tilde{P}_{T,D,\Psi}$ and Lemma \ref{L2 method for c(t)} that there exists a holomorphic function $\tilde{F}_j$ on $U_0$ such that
\begin{equation}\label{convergence property of module formula 1}
\begin{split}
& \int_{U_0}|\tilde{F}_j-(1-b_{1}(\Psi_1))f_jF^{2}|^2e^{-\varphi-\varphi_1+v_{1}(\Psi_1)-\Psi_1}c(-v_{1}(\Psi_1)) \\
\le & \left(c(T_1)e^{-T_1}+\int_{T_1}^{T_1+2}c(s)e^{-s}ds\right)
\int_{U_0}\mathbb{I}_{\{-T_1-2<\Psi_1<-T_1-1\}}|f_j|^2e^{-\varphi-\Psi_1},
\end{split}
\end{equation}
where $b_{1}(t)=\int^{t}_{-\infty} \mathbb{I}_{\{-T_1-2< s < -T_1-1\}}ds$,
$v_{1}(t)=\int^{t}_{-T_1-1}b_{1}(s)ds-(T_1+1)$. Denote $C_1:=c(T_1)e^{-T_1}+\int_{T_1}^{T_1+1}c(s)e^{-s}ds$.
Note that $v_{1}(t)>-T_1-2$. We have $e^{v_{1}(\Psi_1)}c(-v_{1}(\Psi))\ge c(T_1+2)e^{-(T_1+2)}>0$. As $b_{1}(t)\equiv 0$ on $(-\infty,-T_1-2)$, we have
\begin{equation}\label{convergence property of module formula 2}
\begin{split}
&\int_{U_0\cap\{\Psi<-T_1-2\}}|\tilde{F}_j-f_jF^2|^2e^{-\varphi-\varphi_1-\Psi_1} \\
\le & \frac{1}{c(T_1+2)e^{-(T_1+2)}}
\int_{U_0}|\tilde{F}_j-(1-b_{1}(\Psi_1))f_jF^2|^2e^{-\varphi-\varphi_1-\Psi_1+v_{1}(\Psi_1)}c(-v_{t_j}(\Psi_1))\\
\le &\frac{C_1}{c(T_1+2)e^{-(T_1+2)}}
\int_{U_0}\mathbb{I}_{\{-T_1-2<\Psi_1<-T_1-1\}}|f_j|^2e^{-\varphi-\Psi_1}<+\infty.
\end{split}
\end{equation}
Note that $|F^2|^2e^{-\varphi_1}=1$ on $\{\Psi_1<-T_1-1\}$. As $v_{t_j}(\Psi_1)\ge \Psi_1$, we have $c(-v_{t_j}(\Psi_1))e^{v_{t_j}(\Psi_1)}\ge c(-\Psi_1)e^{-\Psi_1}$. Hence we have
\begin{equation}\label{convergence property of module formula 3}
\begin{split}
&\int_{U_0}|\tilde{F}_j|^2e^{-\varphi-\varphi_1}c(-\Psi_1) \\
\le & 2\int_{U_0}|\tilde{F}_j-(1-b_{1}(\Psi_1))f_jF^2|^2e^{-\varphi-\varphi_1}c(-\Psi_1)\\
+&2\int_{U_0}|(1-b_{1}(\Psi_1))f_jF^2|^2e^{-\varphi-\varphi_1}c(-\Psi_1)\\
\le&
2\int_{U_0}|\tilde{F}_j-(1-b_{1}(\Psi_1))f_jF^2|^2e^{-\varphi-\varphi_1-\Psi_1+v_{1}(\Psi_1)}c(-v_{1}(\Psi_1))\\
+&2\int_{U_0\cap\{\Psi_1<-T_1-1\}}|f_j|^2e^{-\varphi}c(-\Psi_1)\\
< &+\infty.
\end{split}
\end{equation}
Hence we know that $(\tilde{F}_j,o)\in \mathcal{H}_o$.
It follows from inequality \eqref{convergence property of module}, $\sup_{j\ge1}\left(\int_{U_0}\mathbb{I}_{\{-T_1-2<\Psi<-T_1-1\}}|f_j|^2e^{-\varphi-\Psi}\right)<+\infty$ and inequality \eqref{convergence property of module formula 3} that we actually have \begin{equation}\label{closedness of module formula 1}
\sup_j\left(\int_{U_0}|\tilde{F}_j|^2e^{-\varphi-\varphi_1}c(-\Psi_1)\right)<+\infty.
\end{equation}
Note that $c(t)e^{-t}$ is decreasing with respect to $t$ and there exists an analytic subset $S$ of $D$ and for any compact subset $K\subset D\backslash S$, $e^{-\varphi}c(-\Psi_1)$ has a positive lower bound on $K\cap \{\Psi<-T_1\}$. Let $K\subset U_0\backslash S\subset D\backslash S$ be any compact set, since $\varphi_1$ and $\varphi+\varphi_1+\Psi_1$ are plurisubharmonic, we have
\begin{equation}\label{closedness of module formula 2}
\begin{split}
\int_K \frac{1}{e^{-\varphi-\varphi_1}c(-\Psi_1)}& =\int_{K\cap\{\Psi_1<-T_1\}} \frac{e^{\varphi_1}}{e^{-\varphi}c(-\Psi_1)}+\int_{K\cap\{\Psi_1\ge-T_1\}} \frac{1}{e^{-\varphi-\varphi_1}c(-\Psi_1)} \\
&\le M_K\int_{K\cap\{\Psi_1<-T_1\}} e^{\varphi_1}+\tilde{M}_K \int_{K\cap\{\Psi_1\ge-T_1\}} e^{\varphi+\varphi_1+\Psi_1}\\
&\le M_K\int_{K} e^{\varphi_1}+\tilde{M}_K \int_{K} e^{\varphi+\varphi_1+\Psi_1}\\
&<+\infty,
\end{split}
\end{equation}
where $M_K=\sup_{K\cap\{\Psi<-T_1\}}\frac{1}{e^{-\varphi}c(-\Psi_1)}$ and $\tilde{M}_K=\frac{1}{c(-T_1)e^{T_1}}$.
It follows from inequality \eqref{closedness of module formula 1}, inequality \eqref{closedness of module formula 2} and Lemma \ref{l:converge} that there exists a subsequence of $\{\tilde{F}_j\}_{j\ge 1}$ (also denoted by $\{\tilde{F}_j\}_{j\ge 1}$) compactly convergent to a holomorphic function $\tilde{F}_0$ on $U_0$ and
\begin{equation}\label{convergence property of module formula 4}
\int_{U_0}|\tilde{F}_0|^2e^{-\varphi-\varphi_1}c(-\Psi_1)\le
\liminf_{j\to +\infty}\int_{U_0}|\tilde{F}_j|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty.
\end{equation}
As $f_j$ converges to $f_0$, it follows from Fatou's Lemma and inequality \eqref{convergence property of module formula 1} that
\begin{equation}\nonumber
\begin{split}
&\int_{U_0}|\tilde{F}_0-(1-b_{1}(\Psi))f_0F^{2}|^2e^{-\varphi-\varphi_1+v_{1}(\Psi_1)-\Psi_1}c(-v_{1}(\Psi_1)) \\
\le & \liminf_{j\to+\infty} \int_{U_0}|\tilde{F}_j-(1-b_{1}(\Psi))f_jF^{2}|^2e^{-\varphi-\varphi_1+v_{1}(\Psi)-\Psi}c(-v_{1}(\Psi_1)) \\
< &+\infty,
\end{split}
\end{equation}
which implies that
\begin{equation}\label{convergence property of module formula 5}
\begin{split}
\int_{U_0\cap\{\Psi<-T_1-2\}}|\tilde{F}_0-f_0F^2|^2e^{-\varphi-\varphi_1-\Psi_1}<+\infty.
\end{split}
\end{equation}
It follows from inequality \eqref{convergence property of module formula 2}, inequality \eqref{convergence property of module formula 3}, inequality \eqref{convergence property of module formula 4}, inequality \eqref{convergence property of module formula 5} and definition of $P:H_o/I(\varphi+\Psi_1)_o\to \mathcal{H}_o/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o$ that for any $j\ge 0$, we have
$$P([(f_j)_o])=[(\tilde{F}_j,o)].$$
Note that $I(\Psi_1+\varphi)_o=I(\Psi+\varphi)_o\subset J_o$. As $(f_j-f)_o\in J_o$ for any $j\ge 1$, we have $(f_j-f_1)_o\in J_o$ for any $j\ge 1$.
It follows from Proposition \ref{module isomorphism} that there exists an ideal $\tilde{J}$ of $\mathcal{O}_{\mathbb{C}^n,o}$ such that $\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o\subset \tilde{J}\subset \mathcal{H}_o$ and $\tilde{J}/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o=\text{Im}(P|_{J_o/I(\varphi+\Psi_1)_o})$. It follows from $(f_j-f_1)_o\in J_o$ and $P([(f_j)_o])=[(F_j,o)]$ for any $j\ge 1$ that we have
$$(\tilde{F}_j-\tilde{F}_1)\in \tilde{J},$$
for any $j\ge 1$.
As $\tilde{F}_j$ compactly converges to $\tilde{F}_0$, using Lemma \ref{closedness}, we obtain that $(\tilde{F}_0-\tilde{F}_1,o)\in\tilde{J}$. Note that $P$ is an $\mathcal{O}_{\mathbb{C}^n,o}$-module isomorphism and $\tilde{J}/\mathcal{I}(\varphi+\varphi_1+\Psi_1)_o=\text{Im}(P|_{J_o/I(\varphi+\Psi_1)_o})$. We have $(f_0-f_1)_o\in J_o$, which implies that $(f_0-f)_o\in J_o$.
Lemma \ref{closedness of module} is proved.
\end{proof}
\subsection{Properties of $G(t)$}
Following the notations in Section \ref{sec:Main result}, we present some properties of the function $G(t)$ in this section.
For any $t\ge T$, denote
\begin{equation}\nonumber
\begin{split}
\mathcal{H}^2(t;c,f):=\Bigg\{\tilde{f}:\int_{ \{ \Psi<-t\}}|\tilde{f}|^2e^{-\varphi}c(-\Psi)<+\infty,\ \tilde{f}\in
H^0(\{\Psi<-t\},\mathcal{O} (K_M) ) \\
\& (\tilde{f}-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0},\text{for any } z_0\in Z_0 \Bigg\},
\end{split}
\end{equation}
where $f$ is a holomorphic $(n,0)$ form on $\{\Psi<-t_0\}\cap V$ for some $V\supset Z_0$ is an open subset of $M$ and some $t_0\ge T$ and $c(t)$ is a positive measurable function on $(T,+\infty)$.
For any $t\ge T$, denote
\begin{equation}\nonumber
\begin{split}
\mathcal{H}^2(t;c,f,H):=\Bigg\{\tilde{f}:\int_{ \{ \Psi<-t\}}|\tilde{f}|^2e^{-\varphi}c(-\Psi)<+\infty,\ \tilde{f}\in
H^0(\{\Psi<-t\},\mathcal{O} (K_M) ) \\
\& (\tilde{f}-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes (J_{z_0}\cap H_{z_0}),\ \text{for any } z_0\in Z_0 \Bigg\},
\end{split}
\end{equation}
where $f$ is a holomorphic $(n,0)$ form on $\{\Psi<-t_0\}\cap V$ for some $V\supset Z_0$ is an open subset of $M$ and some $t_0\ge T$, $c(t)$ is a positive measurable function on $(T,+\infty)$ and $H_{z_0}=\{f_o\in J(\Psi)_o:\int_{\{\Psi<-t\}\cap V_0}|f|^2e^{-\varphi}c(-\Psi)<+\infty \text{ for some }t>T_0 \text{ and } V_0 \text{ is an open neighborhood of}\ z_0\}$ (the definition of $H_{z_0}$ can be referred to Section \ref{sec:properties of module}).
If $G(t_1;c,\Psi,\varphi,J,f)<+\infty$, then there exists a holomorphic $(n,0)$ form $\tilde{f}_0$ on $\{\Psi<-t_1\}$ such that $(\tilde{f}_0-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0},\text{for any } z_0\in Z_0$ and $$\int_{ \{ \Psi<-t_1\}}|\tilde{f}_0|^2e^{-\varphi}c(-\Psi)<+\infty.$$
\begin{Lemma}
\label{module in def of G(t)}If $G(t_1;c,\Psi,\varphi,J,f)<+\infty$ for some $t_1\ge T$, we have $\mathcal{H}^2(t;c,f)=\mathcal{H}^2(t;c,\tilde{f}_0)=\mathcal{H}^2(t;c,\tilde{f}_0,H)$ for any $t\ge T$.
\end{Lemma}
\begin{proof}
As $(\tilde{f}_0-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0},\text{for any } z_0\in Z_0$, we have $\mathcal{H}^2(t;c,f)=\mathcal{H}^2(t;c,\tilde{f}_0)$ for any $t\ge T$.
Now we prove $\mathcal{H}^2(t;c,\tilde{f}_0)=\mathcal{H}^2(t;c,\tilde{f}_0,H)$ for any $t\ge T$. It is obviously that $\mathcal{H}^2(t;c,\tilde{f}_0)\supset\mathcal{H}^2(t;c,\tilde{f}_0,H)$. We only need to show $\mathcal{H}^2(t;c,\tilde{f}_0)\subset\mathcal{H}^2(t;c,\tilde{f}_0,H)$.
Let $\tilde{f}_1\in \mathcal{H}^2(t_2;c,\tilde{f}_0)$ for some $t_2\ge T$. As $\int_{ \{ \Psi<-t_2\}}|\tilde{f}_1|^2e^{-\varphi}c(-\Psi)<+\infty$, denote $t=\max\{t_1,t_2\}$, we know that
$$\int_{ \{ \Psi<-t\}}|\tilde{f}_1-\tilde{f}_0|^2e^{-\varphi}c(-\Psi)<+\infty,$$
which implies that $(\tilde{f}_1-\tilde{f}_0)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes H_{z_0},\ \text{for any } z_0\in Z_0$. Hence $(\tilde{f}_1-\tilde{f}_0)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes (J_{z_0}\cap H_{z_0}),\ \text{for any } z_0\in Z_0$, which implies that $\tilde{f}_1\in \mathcal{H}^2(t;c,\tilde{f}_0, H)$. Hence $\mathcal{H}^2(t;c,\tilde{f}_0)=\mathcal{H}^2(t;c,\tilde{f}_0,H)$.
\end{proof}
\begin{Remark}
\label{module equivalence in def of G}
If $G(t_1;c,\Psi,\varphi,J,f)<+\infty$ for some $t_1\ge T$, we can always assume that $J_{z_0}$ is an $\mathcal{O}_{M,z_0}$-submodule of $H_{z_0}$ such that $I\big(\Psi+\varphi\big)_{z_0}\subset J_{z_0}$, for any $z_0\in Z_0$ in the definition of $G(t;c,\Psi,\varphi,J,f)$, where $t\in[T,+\infty)$.
\end{Remark}
\begin{proof} If $G(t_1;c,\Psi,\varphi,J,f)<+\infty$ for some $t_1\ge T$, it follows from Lemma \ref{module in def of G(t)} that $\mathcal{H}^2(t;c,f)=\mathcal{H}^2(t;c,\tilde{f}_0)=\mathcal{H}^2(t;c,\tilde{f}_0,H)$ for any $t\ge T$. By definition, we have $G(t;c,\Psi,\varphi,J,f)=G(t;c,\Psi,\varphi,J,\tilde{f}_0)=G(t;c,\Psi,\varphi,J\cap H,\tilde{f}_0)$.
Hence we can always assume that $J_{z_0}$ is an $\mathcal{O}_{M,z_0}$-submodule of $H_{z_0}$ such that $I\big(\Psi+\varphi\big)_{z_0}\subset J_{z_0}$, for any $z_0\in Z_0$.
\end{proof}
In the following discussion, we assume that $J_{z_0}$ is an $\mathcal{O}_{M,z_0}$-submodule of $H_{z_0}$ such that $I\big(\Psi+\varphi\big)_{z_0}\subset J_{z_0}$, for any $z_0\in Z_0$.
Let $c(t)\in \tilde{P}_{T,M,\Psi}$.
The following lemma will be used to discuss the convergence property of holomorphic forms on $\{\Psi<-t\}$.
\begin{Lemma}\label{global convergence property of module}
Let $f$ be a holomorphic $(n,0)$ form on $\{\Psi<-\hat{t}_0\}\cap V$, where $V\supset Z_0$ is an open subset of $M$ and $\hat{t}_0>T$
is a real number. For any $z_0\in Z_0$, let $J_{z_0}$ be an $\mathcal{O}_{M,z_0}$-submodule of $H_{z_0}$ such that $I\big(\Psi+\varphi\big)_{z_0}\subset J_{z_0}$.
Let $\{f_j\}_{j\ge 1}$ be a sequence of holomorphic $(n,0)$ forms on $\{\Psi<-t_j\}$. Assume that $t_0:=\lim_{j\to +\infty}t_j\in[T,+\infty)$,
\begin{equation}\label{global convergence property of module 1}
\limsup\limits_{j\to+\infty}\int_{\{\Psi<-t_j\}}|f_j|^2e^{-\varphi}c(-\Psi)\le C<+\infty,
\end{equation}
and $(f_j-f)_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$. Then there exists a subsequence of $\{f_j\}_{j\in \mathbb{N}^+}$ compactly convergent to a holomorphic $(n,0)$ form $f_0$ on $\{\Psi<-t_0\}$ which satisfies
$$\int_{\{\Psi<-t_0\}}|f_0|^2e^{-\varphi}c(-\Psi)\le C,$$
and $(f_0-f)_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$.
\end{Lemma}
\begin{proof}
It follows from $c(t)\in\tilde{P}_{T,M,\Psi}$ that there exists an analytic subset $Z$ of $D$ and for any compact subset $K\subset D\backslash Z$, $e^{-\varphi}c(-\Psi)$ has a positive lower bound on $K\cap \{\Psi<-t_j\}$.
It follows from inequality \eqref{global convergence property of module 1}, Lemma \ref{l:converge} and diagonal method that there exists a subsequence of $\{f_j\}_{j\ge 1}$ (also denoted by $\{f_j\}_{j\ge 1}$) compactly convergent to a holomorphic function $f_0$ on $\{\Psi<-t_0\}\cap U_0$. It follows from Fatou's Lemma that
$$\int_{U_0\cap\{\Psi<-t_0\}}|f_0|^2e^{-\varphi}c(-\Psi)\le \liminf\limits_{j\to+\infty}\int_{U_0\cap\{\Psi<-t_j\}}|f_j|^2e^{-\varphi}c(-\Psi)\le C.$$
Next we prove $(f_0-f)_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$.
Let $z_0\in Z_0$ be a point. As $\limsup\limits_{j\to+\infty}\int_{\{\Psi<-t_j\}}|f_j|^2e^{-\varphi}c(-\Psi)\le C<+\infty$,
there exists an open Stein neighborhood $U_{z_0}\Subset M$ of $z_0$ such that
$$\limsup\limits_{j\to+\infty}\int_{U_{z_0}\cap\{\Psi<-t_j\}}|f_j|^2e^{-\varphi}c(-\Psi)\le C<+\infty.$$
Note that we also have $(f_j-f)_{z_0}\in J_{z_0}$.
It follows from Lemma \ref{closedness of module} and the uniqueness of limit function that $(f_0-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$ for any $z_0\in Z_0$.
Lemma \ref{global convergence property of module} is proved.
\end{proof}
\begin{Lemma}
\label{characterization of g(t)=0} Let $t_0>T$.
The following two statements are equivalent,\\
(1) $G(t_0)=0$;\\
(2) $f_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$.
\end{Lemma}
\begin{proof}If $f_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$, then take $\tilde{f}\equiv 0$ in the definition of $G(t)$ and we get $G(t_0)\equiv 0$.
If $G(t_0)=0$, by definition, there exists a sequence of holomorphic $(n,0)$ forms $\{f_j\}_{j\in\mathbb{Z}^+}$ on $\{\Psi<-t_0\}$ such that
\begin{equation}\label{estimate in G(t)=0}
\lim_{j\to+\infty}\int_{\{\Psi<-t_0\}}|f_j|^2e^{-\varphi}c(-\Psi)=0,
\end{equation}
and $(f_j-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$ and $j\ge 1$. It follows from Lemma \ref{global convergence property of module} that there
exists a subsequence of $\{f_j\}_{j\in \mathbb{N}^+}$ compactly convergent to a holomorphic $(n,0)$ form $f_0$ on $\{\Psi<-t_0\}$ which satisfies
$$\int_{\{\Psi<-t_0\}}|f_0|^2e^{-\varphi}c(-\Psi)=0$$
and
$(f_0-f)_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$. It follows from $\int_{\{\Psi<-t_0\}}|f_0|^2e^{-\varphi}c(-\Psi)=0$ that we know $f_0\equiv 0$. Hence we have $f_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$. Statement (2) is proved.
\end{proof}
The following lemma shows the existence and uniqueness of the holomorphic $(n,0)$ form related to $G(t)$.
\begin{Lemma}
\label{existence of F}
Assume that $G(t)<+\infty$ for some $t\in [T,+\infty)$. Then there exists a unique
holomorphic $(n,0)$ form $F_t$ on $\{\Psi<-t\}$ satisfying
$$\ \int_{\{\Psi<-t\}}|F_t|^2e^{-\varphi}c(-\Psi)=G(t)$$ and
$\ (F_t-f)\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$.
\par
Furthermore, for any holomorphic $(n,0)$ form $\hat{F}$ on $\{\Psi<-t\}$ satisfying
$$\int_{\{\Psi<-t\}}|\hat{F}|^2e^{-\varphi}c(-\Psi)<+\infty$$ and $\ (\hat{F}-f)\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$. We have the following equality
\begin{equation}
\begin{split}
&\int_{\{\Psi<-t\}}|F_t|^2e^{-\varphi}c(-\Psi)+
\int_{\{\Psi<-t\}}|\hat{F}-F_t|^2e^{-\varphi}c(-\Psi)\\
=&\int_{\{\Psi<-t\}}|\hat{F}|^2e^{-\varphi}c(-\Psi).
\label{orhnormal F}
\end{split}
\end{equation}
\end{Lemma}
\begin{proof} We firstly show the existence of $F_t$. As $G(t)<+\infty$, then there exists a sequence of holomorphic $(n,0)$ forms $\{f_j\}_{j\in \mathbb{N}^+}$ on $\{\Psi<-t\}$ such that $$\lim\limits_{j \to +\infty}\int_{\{\Psi<-t\}}|f_j|^2e^{-\varphi}c(-\Psi)=G(t)$$ and $(f_j-f)\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$ and any $j\ge 1$.
It follows from Lemma \ref{global convergence property of module} that there
exists a subsequence of $\{f_j\}_{j\in \mathbb{N}^+}$ compactly convergent to a holomorphic $(n,0)$ form $F$ on $\{\Psi<-t\}$ which satisfies
$$\int_{\{\Psi<-t\}}|F|^2e^{-\varphi}c(-\Psi)\le G(t)$$
and
$(F-f)_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$. By the definition of $G(t)$, we have $\int_{\{\Psi<-t\}}|F|^2e^{-\varphi}c(-\Psi)= G(t)$. Then we obtain the existence of $F_t(=F)$.
We prove the uniqueness of $F_t$ by contradiction: if not, there exist
two different holomorphic $(n,0)$ forms $f_1$ and $f_2$ on $\{\Psi<-t\}$
satisfying $\int_{\{\Psi<-t\}}|f_1|^2e^{-\varphi}$ $c(-\Psi)=
\int_{\{\Psi<-t\}}|f_2|^2e^{-\varphi}c(-\Psi)=G(t)$, $(f_1-f)_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$ and $(f_2-f)_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$. Note that
\begin{equation}\nonumber
\begin{split}
\int_{\{\Psi<-t\}}|\frac{f_1+f_2}{2}|^2e^{-\varphi}c(-\Psi)+
\int_{\{\Psi<-t\}}|\frac{f_1-f_2}{2}|^2e^{-\varphi}c(-\Psi)\\
=\frac{1}{2}(\int_{\{\Psi<-t\}}|f_1|^2e^{-\varphi}c(-\Psi)+
\int_{\{\Psi<-t\}}|f_1|^2e^{-\varphi}c(-\Psi))=G(t),
\end{split}
\end{equation}
then we obtain that
\begin{equation}\nonumber
\begin{split}
\int_{\{\Psi<-t\}}|\frac{f_1+f_2}{2}|^2e^{-\varphi}c(-\Psi)
< G(t)
\end{split}
\end{equation}
and $(\frac{f_1+f_2}{2}-f)_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$, which contradicts to the definition of $G(t)$.
Now we prove equality \eqref{orhnormal F}. Let $h$ be any holomorphic $(n,0)$ form on $\{\Psi<-t\}$
such that $\int_{\{\Psi<-t\}}|h|^2e^{-\varphi}c(-\Psi)<+\infty$ and $h \in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$. It is clear that for any complex
number $\alpha$, $F_t+\alpha h$ satisfying $((F_t+\alpha h)-f) \in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$ and
$\int_{\{\Psi<-t\}}|F_t|^2e^{-\varphi}c(-\Psi) \leq \int_{\{\Psi<-t\}}|F_t+\alpha
h|^2e^{-\varphi}c(-\Psi)$. Note that
\begin{equation}\nonumber
\begin{split}
\int_{\{\Psi<-t\}}|F_t+\alpha
h|^2e^{-\varphi}c(-\Psi)-\int_{\{\psi<-t\}}|F_t|^2e^{-\varphi}c(-\Psi)\geq 0
\end{split}
\end{equation}
(By considering $\alpha \to 0$) implies
\begin{equation}\nonumber
\begin{split}
\mathfrak{R} \int_{\{\Psi<-t\}}F_t\bar{h}e^{-\varphi}c(-\Psi)=0,
\end{split}
\end{equation}
then we have
\begin{equation}\nonumber
\begin{split}
\int_{\{\Psi<-t\}}|F_t+h|^2e^{-\varphi}c(-\Psi)=
\int_{\{\Psi<-t\}}(|F_t|^2+|h|^2)e^{-\varphi}c(-\Psi).
\end{split}
\end{equation}
\par
Letting $h=\hat{F}-F_t$, we obtain equality \eqref{orhnormal F}.
\end{proof}
The following lemma shows the lower semicontinuity property of $G(t)$.
\begin{Lemma}$G(t)$ is decreasing with respect to $t\in
[T,+\infty)$, such that $\lim \limits_{t \to t_0+0}G(t)=G(t_0)$ for any $t_0\in
[T,+\infty)$, and if $G(t)<+\infty$ for some $t>T$, then $\lim \limits_{t \to +\infty}G(t)=0$. Especially, $G(t)$ is lower semicontinuous on $[T,+\infty)$.
\label{semicontinuous}
\end{Lemma}
\begin{proof}By the definition of $G(t)$, it is clear that $G(t)$ is decreasing on
$[T,+\infty)$. If $G(t)<+\infty$ for some $t>T$, by the dominated convergence theorem, we know $\lim\limits_{t\to +\infty}G(t)=0$. It suffices
to prove $\lim \limits_{t \to t_0+0}G(t)=G(t_0)$ . We prove it by
contradiction: if not, then $\lim \limits_{t \to t_0+0}G(t)<
G(t_0)$.
By using Lemma \ref{existence of F}, for any $t>t_0$, there exists a unique holomorphic $(n,0)$ form
$F_t$ on $\{\Psi<-t\}$ satisfying
$\int_{\{\Psi<-t\}}|F_t|^2e^{-\varphi}c(-\Psi)=G(t)$ and $(F_t-f) \in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$. Note that $G(t)$ is decreasing with respect to $t$. We have $\int_{\{\Psi<-t\}}|F_t|^2e^{-\varphi}c(-\psi)\leq \lim
\limits_{t \to t_0+0}G(t)$ for any $t>t_0$. If $\lim\limits_{t \to t_0+0}G(t)=+\infty$, the equality $\lim \limits_{t \to t_0+0}G(t)=G(t_0)$ obviously holds, thus it suffices to prove the case $\lim\limits_{t \to t_0+0}G(t)<+\infty$. It follows from $\int_{\{\Psi<-t\}}|F_t|^2e^{-\varphi}c(-\Psi)\le \lim\limits_{t \to t_0+0}G(t)<+\infty$ holds for any $t\in (t_0,t_1]$ (where $t_1>t_0$ is a fixed number) and Lemma \ref{global convergence property of module} that there exists a subsequence of $\{F_t\}$ (denoted by $\{F_{t_j}\}$) compactly convergent to a holomorphic $(n,0)$ form $\hat{F}_{t_0}$ on $\{\Psi<-t_0\}$ satisfying
$$\int_{\{\Psi<-t_0\}}|\hat{F}_{t_0}|^2e^{-\varphi}c(-\Psi)\le \lim\limits_{t \to t_0+0}G(t)<+\infty$$
and $(\hat{F}_{t_0}-f)_{z_0} \in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$.
Then we obtain that $G(t_0)\leq
\int_{\{\Psi<-t_0\}}|\hat{F}_{t_0}|^2e^{-\varphi}c(-\Psi)
\leq \lim \limits_{t\to t_0+0} G(t)$,
which contradicts $\lim \limits_{t\to t_0+0} G(t) <G(t_0)$. Thus we have $\lim \limits_{t \to t_0+0}G(t)=G(t_0)$.
\end{proof}
We consider the derivatives of $G(t)$ in the following lemma.
\begin{Lemma}
\label{derivatives of G}
Assume that $G(t_1)<+\infty$, where $t_1\in (T,+\infty)$. Then for any $t_0>t_1$, we have
\begin{equation}\nonumber
\begin{split}
\frac{G(t_1)-G(t_0)}{\int^{t_0}_{t_1} c(t)e^{-t}dt}\leq
\liminf\limits_{B \to
0+0}\frac{G(t_0)-G(t_0+B)}{\int_{t_0}^{t_0+B}c(t)e^{-t}dt},
\end{split}
\end{equation}
i.e.
\begin{equation}\nonumber
\frac{G(t_0)-G(t_1)}{\int_{T_1}^{t_0}
c(t)e^{-t}dt-\int_{T_1}^{t_1} c(t)e^{-t}dt} \geq
\limsup \limits_{B \to 0+0}
\frac{G(t_0+B)-G(t_0)}{\int_{T_1}^{t_0+B}
c(t)e^{-t}dt-\int_{T_1}^{t_0} c(t)e^{-t}dt}.
\end{equation}
\end{Lemma}
\begin{proof}
It follows from Lemma \ref{semicontinuous} that $G(t)<+\infty$ for any $t>t_1$. By Lemma \ref{existence of F}, there exists a holomorphic $(n,0)$ form $F_{t_0}$ on $\{\Psi<-t_0\}$, such that $(F_{t_0}-f)\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$ and $G(t_0)=\int_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)$.
It suffices to consider that $\liminf\limits_{B\to 0+0} \frac{G(t_0)-G(t_0+B)}{\int_{t_0}^{t_0+B}c(t)e^{-t}dt}\in [0,+\infty)$ because of the decreasing property of $G(t)$. Then there exists $1\ge B_j\to 0+0$ (as $j\to+\infty$) such that
\begin{equation}
\label{derivatives of G c(t)1}
\lim\limits_{j\to +\infty} \frac{G(t_0)-G(t_0+B_j)}{\int_{t_0}^{t_0+B_j}c(t)e^{-t}dt}=\liminf\limits_{B\to 0+0} \frac{G(t_0)-G(t_0+B)}{\int_{t_0}^{t_0+B}c(t)e^{-t}dt}
\end{equation}
and $\{\frac{G(t_0)-G(t_0+B_j)}{\int_{t_0}^{t_0+B_j}c(t)e^{-t}dt}\}_{j\in\mathbb{N}^{+}}$ is bounded. As $c(t)e^{-t}$ is decreasing and positive on $(t,+\infty)$, then
\begin{equation}\label{derivatives of G c(t)2}
\begin{split}
\lim\limits_{j\to +\infty} \frac{G(t_0)-G(t_0+B_j)}{\int_{t_0}^{t_0+B_j}c(t)e^{-t}dt}
=&\big(\lim\limits_{j\to +\infty} \frac{G(t_0)-G(t_0+B_j)}{B_j})(\frac{1}{\lim\limits_{t\to t_0+0}c(t)e^{-t}}\big)\\
=&\big(\lim\limits_{j\to +\infty} \frac{G(t_0)-G(t_0+B_j)}{B_j})(\frac{e^{t_0}}{\lim\limits_{t\to t_0+0}c(t)}\big).
\end{split}
\end{equation}
Hence $\{\frac{G(t_0)-G(t_0+B_j)}{B_j}\}_{j\in\mathbb{N}^+}$ is uniformly bounded with respect to $j$.
As $t \leq v_{t_0,j}(t)$, the decreasing property of $c(t)e^{-t}$ shows that
\begin{equation}\nonumber
e^{-\Psi+v_{t_0,B_j}(\Psi)}c(-v_{t_0,B_j}(\Psi))\geq c(-\Psi).
\end{equation}
\par
It follows from Lemma \ref{L2 method in JM concavity} that, for any $B_j$, there exists holomorphic
$(n,0)$ form $\tilde{F}_j$ on $\{\Psi<-t_1\}$ such that
\begin{flalign}
&\int_{\{\Psi<-t_1\}}|\tilde{F}_j-(1-b_{t_0,B_j}(\Psi))F_{t_0}|^2e^{-\varphi}c(-\Psi)\nonumber\\
\leq &
\int_{\{\Psi<-t_1\}}|\tilde{F}_j-(1-b_{t_0,B_j}(\Psi))F_{t_0}|^2e^{-\varphi}e^{-\Psi+v_{t_0,B_j}(\Psi)}c(-v_{t_0,B_j}(\Psi))\nonumber\\
\leq &
\int^{t_0+B_j}_{t_1}c(t)e^{-t}dt\int_{\{\Psi<-t_1\}}\frac{1}{B_j}
\mathbb{I}_{\{-t_0-B_j<\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi-\Psi}\nonumber\\
\leq &
\frac{e^{t_0+B_j}\int^{t_0+B_j}_{t_1}c(t)e^{-t}dt}{\inf
\limits_{t\in(t_0,t_0+B_j)}c(t)}\int_{\{\Psi<-t_1\}}\frac{1}{B_j}
\mathbb{I}_{\{-t_0-B_j<\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)\nonumber\\
= &
\frac{e^{t_0+B_j}\int^{t_0+B_j}_{t_1}c(t)e^{-t}dt}{\inf
\limits_{t\in(t_0,t_0+B_j)}c(t)}\times
\bigg(\int_{\{\Psi<-t_1\}}\frac{1}{B_j}\mathbb{I}_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)\nonumber\\
&-\int_{\{\Psi<-t_1\}}\frac{1}{B_j}\mathbb{I}_{\{\Psi<-t_0-B_j\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)\bigg)\nonumber\\
\leq &
\frac{e^{t_0+B_j}\int^{t_0+B_j}_{t_1}c(t)e^{-t}dt}{\inf
\limits_{t\in(t_0,t_0+B_j)}c(t)} \times
\frac{G(t_0)-G(t_0+B_j)}{B_j}<+\infty.
\label{derivative of G 1}
\end{flalign}
Note that $b_{t_0,B_j}(t)=0$ for $t\le-t_0-B_j$, $b_{t_0,B_j}(t)=1$ for $t\ge t_0$, $v_{t_0,B_j}(t)>-t_0-B_j$ and $c(t)e^{-t}$ is decreasing with respect to $t$. It follows from inequality \eqref{derivative of G 1} that $(F_j-F_{t_0})_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes I(\Psi+\varphi)_{z_0} \subset \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$.
Note that
\begin{equation}\label{derivative of G 2}
\begin{split}
&\int_{\{\Psi<-t_1\}}|\tilde{F}_j|^2e^{-\varphi}c(-\Psi)\\
\le&2\int_{\{\Psi<-t_1\}}|\tilde{F}_j-(1-b_{t_0,B_j}(\Psi))F_{t_0}|^2e^{-\varphi}c(-\Psi)
+2\int_{\{\Psi<-t_1\}}|(1-b_{t_0,B_j}(\Psi))F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
\le&2
\frac{e^{t_0+B_j}\int^{t_0+B_j}_{t_1}c(t)e^{-t}dt}{\inf
\limits_{t\in(t_0,t_0+B_j)}c(t)} \times
\frac{G(t_0)-G(t_0+B_j)}{B_j}
+2\int_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi).
\end{split}
\end{equation}
We also note that $B_j\le 1$, $\frac{G(t_0)-G(t_0+B_j)}{B_j}$ is uniformly bounded with respect to $j$ and $G(t_0)=\int_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)$. It follows from inequality \eqref{derivative of G 2} that we know $\int_{\{\Psi<-t_1\}}|\tilde{F}_j|^2e^{-\varphi}c(-\Psi)$ is uniformly bounded with respect to $j$.
It follows from Lemma \ref{global convergence property of module} that there exists a subsequence of $\{\tilde{F}_j\}_{j\in \mathbb{N}^+}$ compactly convergent to a holomorphic $(n,0)$ form $\tilde{F}_{t_1}$ on $\{\Psi<-t_1\}$ which satisfies
$$\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}|^2e^{-\varphi}c(-\Psi)\le \liminf_{j\to+\infty} \int_{\{\Psi<-t_1\}}|\tilde{F}_j|^2e^{-\varphi}c(-\Psi)<+\infty,$$
and $(\tilde{F}_{t_1}-F_{t_0})_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$.
Note that
$\lim_{j\to+\infty}b_{t_0,B_j}(t)=\mathbb{I}_{\{t\ge -t_0\}}$ and
\begin{equation}\nonumber
v_{t_0}(t):=\lim_{j\to+\infty}v_{t_0,B_j}(t)=\left\{
\begin{aligned}
&-t_0 &\text{ if } & x<-t_0, \\
&\ t &\text{ if } & x\ge t_0 .
\end{aligned}
\right.
\end{equation}
It follows from inequality \eqref{derivative of G 1} and Fatou's lemma that
\begin{flalign}
\label{derivative of G 3}
&\int_{\{\Psi<-t_0\}}|\tilde{F}_{t_1}-F_{t_0}|^2e^{-\varphi}c(-\Psi)
+\int_{\{-t_0\le\Psi<-t_1\}}|\tilde{F}_{t_1}|^2e^{-\varphi}c(-\Psi)\nonumber\\
\leq &
\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}-\mathbb{I}_{\{\Psi< -t_0\}}F_{t_0}|^2e^{-\varphi}e^{-\Psi+v_{t_0}(\Psi)}c(-v_{t_0}(\Psi))\nonumber\\
\le&\liminf_{j\to+\infty}\int_{\{\Psi<-t_1\}}|\tilde{F}_j-(1-b_{t_0,B_j}(\Psi))F_{t_0}|^2e^{-\varphi}c(-\Psi)\nonumber\\
\leq &\liminf_{j\to+\infty}
\bigg(\frac{e^{t_0+B_j}\int^{t_0+B_j}_{t_1}c(t)e^{-t}dt}{\inf
\limits_{t\in(t_0,t_0+B_j)}c(t)} \times
\frac{G(t_0)-G(t_0+B_j)}{B_j}\bigg).
\end{flalign}
It follows from Lemma \ref{existence of F}, equality \eqref{derivatives of G c(t)1}, equality \eqref{derivatives of G c(t)2} and inequality \eqref{derivative of G 3} that we have
\begin{equation}
\label{derivative of G 4}
\begin{split}
&\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}|^2e^{-\varphi}c(-\Psi)
-\int_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
\le&\int_{\{\Psi<-t_0\}}|\tilde{F}_{t_1}-F_{t_0}|^2e^{-\varphi}c(-\Psi)
+\int_{\{-t_0\le\Psi<-t_1\}}|\tilde{F}_{t_1}|^2e^{-\varphi}c(-\Psi)\\
\leq &
\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}-\mathbb{I}_{\{\Psi< -t_0\}}F_{t_0}|^2e^{-\varphi}e^{-\Psi+v_{t_0}(\Psi)}c(-v_{t_0}(\Psi))\\
\le&\liminf_{j\to+\infty}\int_{\{\Psi<-t_1\}}|\tilde{F}_j-(1-b_{t_0,B_j}(\Psi))F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
\leq &\liminf_{j\to+\infty}
\big(\frac{e^{t_0+B_j}\int^{t_0+B_j}_{t_1}c(t)e^{-t}dt}{\inf
\limits_{t\in(t_0,t_0+B_j)}c(t)} \times
\frac{G(t_0)-G(t_0+B_j)}{B_j}\big)\\
\le &\bigg(\int^{t_0}_{t_1}c(t)e^{-t}dt\bigg)\liminf\limits_{B\to 0+0} \frac{G(t_0)-G(t_0+B)}{\int_{t_0}^{t_0+B}c(t)e^{-t}dt}.
\end{split}
\end{equation}
Note that $(\tilde{F}_{t_1}-F_{t_0})_{z_0}\in \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$. It follows from the definition of $G(t)$ and inequality \eqref{derivative of G 4} that we have
\begin{equation}
\label{derivative of G 5}
\begin{split}
&G(t_1)-G(t_0)\\
\le&\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}|^2e^{-\varphi}c(-\Psi)
-\int_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
\le&\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}-\mathbb{I}_{\{\Psi< -t_0\}}F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
\leq &
\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}-\mathbb{I}_{\{\Psi< -t_0\}}F_{t_0}|^2e^{-\varphi}e^{-\Psi+v_{t_0}(\Psi)}c(-v_{t_0}(\Psi))\\\
\le &\big(\int^{t_0}_{t_1}c(t)e^{-t}dt\big)\liminf\limits_{B\to 0+0} \frac{G(t_0)-G(t_0+B)}{\int_{t_0}^{t_0+B}c(t)e^{-t}dt}.
\end{split}
\end{equation}
Lemma \ref{derivatives of G} is proved.
\end{proof}
The following property of concave
functions will be used in the proof of Theorem \ref{main theorem}.
\begin{Lemma}[see \cite{G16}]
Let $H(r)$ be a lower semicontinuous function on $(0,R]$. Then $H(r)$ is concave
if and only if
\begin{equation}\nonumber
\begin{split}
\frac{H(r_1)-H(r_2)}{r_1-r_2} \leq
\liminf\limits_{r_3 \to r_2-0}
\frac{H(r_3)-H(r_2)}{r_3-r_2}
\end{split}
\end{equation}
holds for any $0<r_2<r_1 \leq R$.
\label{characterization of concave function}
\end{Lemma}
\subsection{Some required results}
We recall the following two well-known results about Lelong numbers.
\begin{Lemma}[\cite{skoda1972}\label{l:skoda}]
Let $u$ be a plurisubharmonic function on $\Delta^n\subset\mathbb{C}^n$. If $v(dd^cu,o )<1$, then $e^{-2u}$ is $L^1$ on a neighborhood of $o$, where $o\in\Delta^n$ is the origin.
\end{Lemma}
\begin{Lemma}
\label{l:1d-MIS}Let $\varphi$ be a subharmonic function on the unit disc $\Delta\subset\mathbb{C}$. Then we have $\mathcal{I}(\varphi)_o=(w^k)_o$ if and only if $v(dd^c(\varphi),o)\in[2k,2k+2)$.
\end{Lemma}
\begin{proof}
For convenience of the readers, we give a proof of this lemma by using Lemma \ref{l:skoda} and Siu's Decomposition Theorem. It follows from Siu's Decomposition Theorem that $\varphi=v(dd^c(\varphi),o)\log|w|+\varphi_1$, where $\varphi_1$ is subharmonic function on $\Delta$ satisfying $v(dd^c(\varphi_1),o)=0$.
For any positive integer $m$, if $v(dd^c(\varphi),o)<2m$, then there exists $p>1$ such that $pv(dd^c(\varphi),o)<2m$. Note that $2pm-2p-pv(dd^c(\varphi),o)\ge 2m-2-pv(dd^c(\varphi),o)>-2$. Using Lemma \ref{l:skoda} and H\"older inequality, we get that there exists a neighborhood $V$ of $o$ such that
\begin{displaymath}
\begin{split}
\int_{V}|w^{m-1}|^{2}e^{-\varphi}&\le\int_{V}|w|^{2m-2-v(dd^c(\varphi),o)}e^{-\varphi_1}\\
&\le\left(\int_{V}|w|^{2pm-2p-pv(dd^c(\varphi),o)}\right)^{\frac{1}{p}}\left(\int_{V}e^{-q\varphi_1}\right)^{\frac{1}{q}}\\
&<+\infty,
\end{split}
\end{displaymath}
where $\frac{1}{p}+\frac{1}{q}=1$. Then we have $(w^{m-1},o)\in\mathcal{I}(\varphi)_o$.
For any positive integer $m$, if $v(dd^c(\varphi),o)\ge 2m$, then there exists a constant $C$ such that $\varphi\le 2m\log|w|+C$ near $o$, which implies that $(w^{m-1},o)\not\in\mathcal{I}(\varphi)_o$.
Thus, we have $\mathcal{I}(\varphi)_o=(w^k)_o$ if and only if $v(dd^c(\varphi),o)\in[2k,2k+2)$.
\end{proof}
We recall some basic properties of Green functions. Let $\Omega$ be an open Riemann surface, which admits a nontrivial Green function $G_{\Omega}$, and let $z_0\in\Omega$.
\begin{Lemma}[see \cite{S-O69}, see also \cite{Tsuji}] \label{l:green-sup}Let $w$ be a local coordinate on a neighborhood of $z_0$ satisfying $w(z_0)=0$. $G_{\Omega}(z,z_0)=\sup_{v\in\Delta_{\Omega}^*(z_0)}v(z)$, where $\Delta_{\Omega}^*(z_0)$ is the set of negative subharmonic function on $\Omega$ such that $v-\log|w|$ has a locally finite upper bound near $z_0$. Moreover, $G_{\Omega}(\cdot,z_0)$ is harmonic on $\Omega\backslash\{z_0\}$ and $G_{\Omega}(\cdot,z_0)-\log|w|$ is harmonic near $z_0$.
\end{Lemma}
\begin{Lemma}[see \cite{GY-concavity}]\label{l:G-compact}
For any open neighborhood $U$ of $z_0$, there exists $t>0$ such that $\{G_{\Omega}(z,z_0)<-t\}$ is a relatively compact subset of $U$.
\end{Lemma}
\subsection{Inner points on open Riemann surfaces}
Let $\Omega$ be an open Riemann surface, which admits a nontrivial Green function $G_{\Omega}$. Let $\psi$ be a negative subharmonic function on $\Omega$, and let $\varphi$ be a Lebesgue measurable function on $\Omega$ such that $\varphi+\psi$ is subharmonic on $\Omega$.
Let $Z_0\subset\{\psi=-\infty\}$ be a discrete subset of $\Omega$, and Let $\mathcal{F}_{z}\supset\mathcal{I}(\varphi+\psi)_{z}$ be an ideal of $\mathcal{O}_{z}$ for any $z\in Z_0$.
Let $f$ be a holomorphic $(1,0)$ form on a neighborhood of $Z_0$. Let $c(t)$ be a positive measurable function on $(0,+\infty)$ satisfying $c(t)e^{-t}$ is decreasing on $(0,+\infty)$, $\int_{0}^{+\infty}c(s)e^{-s}ds<+\infty$ and $e^{-\varphi}c(-\psi)$ has a positive lower bound on any compact subset of $\Omega\backslash E$, where $E\subset\{\psi=-\infty\}$ is a discrete point subset of $\Omega$.
Denote the minimal $L^{2}$ integrals (see \cite{GY-concavity}, see also \cite{GMY-concavity2})
\begin{equation*}
\begin{split}
\inf\Bigg\{\int_{\{\psi<-t\}}|\tilde{f}|^{2}e^{-\varphi}c(-\psi):(\tilde{f}-f,z)\in(\mathcal{O}(K_{\Omega})&)_{z}\otimes\mathcal{F}_{z} \text{ for any } z\in Z_0 \\&\&{\,}\tilde{f}\in H^{0}(\{\psi<-t\},\mathcal{O}(K_{\Omega}))\Bigg\}
\end{split}
\end{equation*}
by $G(t;c)$ (without misunderstanding, we denote $G(t;c)$ by $G(t)$), where $t\in[0,+\infty)$ and
$|f|^{2}:=\sqrt{-1}f\wedge\bar{f}$ for any $(1,0)$ form $f$.
Theorem \ref{main theorem} shows that $G(h^{-1}(r))$ is concave with respect to $r\in(0,\int_0^{+\infty}c(s)e^{-s}ds)$ (see also \cite{GY-concavity,GMY-concavity2,GMY-boundary2}), where $h(t)=\int_t^{+\infty}c(s)e^{-s}ds$. In this section, we discuss the case that the concavity degenerates to linearity.
We recall the following two lemmas, which will be used in the following discussion.
\begin{Lemma}[see \cite{GY-concavity}]
\label{l:cu}
Let $T$ be a closed positive $(1,1)$ current on $\Omega$. For any open set $U\subset\subset \Omega$ satisfying $U\cap SuppT\not=\emptyset$, there exists a subharmonic function $\Phi<0$ on $\Omega$, which satisfies the following properties:
$(1)$ $i\partial\bar\partial\Phi\leq T$ and $i\partial\bar\partial\Phi\not\equiv0$;
$(2)$ $\lim_{t\rightarrow0+0}\left(\inf_{\{G_{\Omega}(z,z_0)\geq-t\}}\Phi(z)\right)=0$;
$(3)$ $Supp(i\partial\bar\partial\Phi)\subset U$ and $\inf_{\Omega\backslash U}\Phi>-\infty$.
\end{Lemma}
Denote that
\begin{displaymath}
\begin{split}
\mathcal{H}^2(c,\varphi,t):=\Bigg\{\tilde f\in H^0(\{\psi<-t\}&,\mathcal{O}(K_{\Omega})):\int_{\{\psi<-t\}}|\tilde f|^2e^{-\varphi}c(-\psi)<+\infty \\&\&{\,}(\tilde{f}-f,z)\in(\mathcal{O}(K_{\Omega}))_{z}\otimes\mathcal{F}_{z} \text{ for any }z\in Z_0\Bigg\}.
\end{split}
\end{displaymath}
\begin{Lemma}
[\cite{GY-concavity}]
\label{l:n} Assume that there exists $t_0\geq0$ such that $G(t_0)\in(0,+\infty)$.
If $G(\hat{h}^{-1}(r))$ is linear with respect to $r$, then there is no Lebesgue measurable function $\tilde \varphi\geq\varphi$ such that $\tilde\varphi+\psi$ is subharmonic function on $M$ and satisfies:
$(1)$ $\tilde\varphi\not=\varphi$ and $\mathcal{I}(\tilde\varphi+\psi)=\mathcal{I}(\varphi+\psi)$;
$(2)$ $\lim_{t\rightarrow 0+0}\sup_{\{\psi\geq-t\}}(\tilde\varphi-\varphi)=0$;
$(3)$ there exists an open subset $U\subset\subset\Omega$ such that $\sup_{\Omega\backslash U}(\tilde\varphi-\varphi)<+\infty$, $e^{-\tilde\varphi}c(-\psi)$ has a positive lower bound on $U$ and $\int_{U}|F_1-F_2|^2e^{-\varphi}c(-\psi)<+\infty$ for any $F_1\in\mathcal{H}^2(c,\tilde\varphi,t)$ and $F_2\in\mathcal{H}^2(c,\varphi,t)$, where $t\ge 0$ such that $U\subset\subset\{\psi<-t\}$.
\end{Lemma}
We recall some notations (see \cite{OF81}, see also \cite{guan-zhou13ap,GY-concavity,GMY-concavity2}). Let $p:\Delta\rightarrow\Omega$ be the universal covering from unit disc $\Delta$ to $\Omega$. we call the holomorphic function $f$ on $\Delta$ a multiplicative function,
if there is a character $\chi$, which is the representation of the fundamental group of $\Omega$, such that $g^{\star}f=\chi(g)f$,
where $|\chi|=1$ and $g$ is an element of the fundamental group of $\Omega$.
It is known that for any harmonic function $u$ on $\Omega$,
there exist a $\chi_{u}$ (the character associate to $u$) and a multiplicative function $f_u\in\mathcal{O}^{\chi_{u}}(\Omega)$,
such that $|f_u|=p^{*}(e^{u})$.
Let $z_0\in \Omega$.
Recall that for the Green function $G_{\Omega}(z,z_0)$,
there exist a $\chi_{z_0}$ and a multiplicative function $f_{z_0}\in\mathcal{O}^{\chi_{z_0}}(\Omega)$, such that $|f_{z_0}(z)|=p^{*}\left(e^{G_{\Omega}(z,z_0)}\right)$ .
Firstly, we consider the case that $Z_0$ is finite. Let $Z_0=\{z_1,z_2,\ldots ,z_m\}\subset\Omega$ be a finite subset of $\Omega$ satisfying that $z_j\not=z_k$ for any $j\not=k$.
The following Theorem gives a characterization of the concavity of $G(h^{-1}(r))$ degenerating to linearity.
\begin{Theorem}[see \cite{GY-concavity3}]
\label{thm:m-points}
Assume that $G(0)\in(0,+\infty)$ and $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)>-\infty$ for $j\in\{1,2,\ldots,m\}$, where $p_j=\frac{1}{2}v(dd^c(\psi),z_j)>0$. Then $G(h^{-1}(r))$ is linear with respect to $r$ if and only if the following statements hold:
$(1)$ $\psi=2\sum_{1\le j\le m}p_jG_{\Omega}(\cdot,z_j)$;
$(2)$ $\varphi+\psi=2\log|g|+2\sum_{1\le j\le m}G_{\Omega}(\cdot,z_j)+2u$ and $\mathcal{F}_{z_j}=\mathcal{I}(\varphi+\psi)_{z_j}$ for any $j\in\{1,2,\ldots,m\}$, where $g$ is a holomorphic function on $\Omega$ such that $ord_{z_j}(g)=ord_{z_j}(f)$ for any $j\in\{1,2,\ldots,m\}$ and $u$ is a harmonic function on $\Omega$;
$(3)$ $\prod_{1\le j\le m}\chi_{z_j}=\chi_{-u}$, where $\chi_{-u}$ and $\chi_{z_j}$ are the characters associated to the functions $-u$ and $G_{\Omega}(\cdot,z_j)$ respectively;
$(4)$ $\lim_{z\rightarrow z_k}\frac{f}{gp_*\left(f_u\left(\prod_{1\le j\le m}f_{z_j}\right)\left(\sum_{1\le j\le m}p_{j}\frac{d{f_{z_{j}}}}{f_{z_{j}}}\right)\right)}=c_0$ for any $k\in\{1,2,\ldots,m\}$, where $c_0\in\mathbb{C}\backslash\{0\}$ is a constant independent of $k$, $f_{u}$ is a holomorphic function $\Delta$ such that $|f_u|=p^*(e^u)$ and $f_{z_j}$ is a holomorphic function on $\Delta$ such that $|f_{z_j}|=p^*\left(e^{G_{\Omega}(\cdot,z_j)}\right)$ for any $j\in\{1,2,\ldots,m\}$.
\end{Theorem}
\begin{Remark}\label{r:equivalent}
The statements $(2)$, $(3)$ and $(4)$ hold if and only if the following statements hold:
$(1)'$ $\varphi+\psi=2\log|g_1|$ and $\mathcal{F}_{z_j}=\mathcal{I}(\varphi+\psi)_{z_j}$ for any $j\in\{1,2,\ldots,m\}$, where $g_1$ is a holomorphic function on $\Omega$ such that $ord_{z_j}(g_1)=ord_{z_j}(f_1)+1$ for any $j\in\{1,2,\ldots,m\}$;
$(2)'$ $\frac{ord_{z_j}(g_1)}{p_j}\lim_{z\rightarrow z_j}\frac{f}{dg_1}=c_0$ for any $j\in\{1,2,\ldots,m\}$, where $c_0\in\mathbb{C}\backslash\{0\}$ is a constant independent of $j$;
\end{Remark}
\begin{proof}
If statements $(2)$ and $(3)$ in Theorem \ref{thm:m-points} hold, following from the definitions of $\chi_{z_j}$ and $\chi_{-u}$, we know that there exists a (single-value) holomorphic function $g_2$ on $\Omega$ such that $g_2=p_*\left(f_u\prod_{1\le j\le m}f_{z_j} \right)$ on $\Omega$. Let $g_1=gg_2$ on $\Omega$, thus $$\varphi+\psi=2\log|g_1|$$ and $ord_{z_j}(g_1)=ord_{z_j}(g)+ord_{z_j}(g_2)=ord_{z_j}(f)+1$ for any $j\in\{1,2,\ldots,m\}$. Note that $ord_{z_k}(g)=ord_{z_k}(dg_1)$ and
\begin{equation}
\label{eq:0319a}
\begin{split}
&\lim_{z\rightarrow z_k}\frac{dg_1}{gp_*\left(f_u\left(\prod_{1\le j\le m}f_{z_j}\right)\left(\sum_{1\le j\le m}p_{j}\frac{d{f_{z_{j}}}}{f_{z_{j}}}\right)\right)}\\
=&\lim_{z\rightarrow z_k}\frac{d\left(gp_*\left(f_u\prod_{1\le j\le m}f_{z_j} \right)\right)}{gp_*\left(f_u\left(\prod_{1\le j\le m}f_{z_j}\right)\left(p_{k}\frac{d{f_{z_{k}}}}{f_{z_{k}}}\right)\right)}\\
=&\frac{ord_{z_k}(g_1)}{p_k}
\end{split}
\end{equation}
for any $k\in\{1,2,\ldots,m\}$. Furthermore, if statement $(4)$ in Theorem \ref{thm:m-points} holds, following from equality \eqref{eq:0319a}, we have $\frac{ord_{z_j}(g_1)}{p_j}\lim_{z\rightarrow z_j}\frac{f}{dg_1}=c_0$ for any $j\in\{1,2,\ldots,m\}$. Thus, the statements $(2)$, $(3)$ and $(4)$ in Theorem \ref{thm:m-points} implies the statements $(1)'$ and $(2)'$.
If statement $(1)'$ holds, it follows from Weierstrass Theorem on open Riemann surface (see \cite{OF81}) that there exists a holomorphic function $g$ on $\Omega$ such that $$ord_{z_j}(g)=ord_{z_j}(g_1)-1=ord_{z_j}(f)$$ for any $j\in\{1,2,\ldots,m\}$ and $g_2:=\frac{g_1}{g}$ is a holomorphic function on $\Omega$ satisfying $g_2(z)\not=0$ for any $z\in\Omega\backslash\{z_1,z_2,\dots,z_m\}$. Thus, there exists a harmonic function $u$ on $\Omega$ such that $$2u=2\log|g_2|-\sum_{1\le j\le m}2G_{\Omega}(\cdot,z_j)=\varphi+\psi-2\log|g|-2\sum_{1\le j\le m}G_{\Omega}(\cdot,z_j).$$
Note that
$g_2=c_1p_*\left(f_u\prod_{1\le j\leq m}f_{z_j} \right)$
and
\begin{equation}\label{eq:0319b}
\begin{split}
&\lim_{z\rightarrow z_k}\frac{dg_1}{gp_*\left(f_u\left(\prod_{1\le j\le m}f_{z_j}\right)\left(\sum_{1\le j\le m}p_{j}\frac{d{f_{z_{j}}}}{f_{z_{j}}}\right)\right)}\\
=&\lim_{z\rightarrow z_k}\frac{d\left(c_1gp_*\left(f_u\prod_{1\le j\le m}f_{z_j} \right)\right)}{gp_*\left(f_u\left(\prod_{1\le j\le m}f_{z_j}\right)\left(p_{k}\frac{d{f_{z_{k}}}}{f_{z_{k}}}\right)\right)}\\
=&c_1\frac{ord_{z_k}(g_1)}{p_k},
\end{split}
\end{equation}
where $c_1\in\mathbb{C}$ is a constant satisfying $|c_1|=1$.
Furthermore, if statement $(2)'$ holds, it follows from equality \eqref{eq:0319b} that $\lim_{z\rightarrow z_k}\frac{f}{gp_*\left(f_u\left(\prod_{1\le j\le m}f_{z_j}\right)\left(\sum_{1\le j\le m}p_{j}\frac{d{f_{z_{j}}}}{f_{z_{j}}}\right)\right)}=c_0c_1$ for any $k\in\{1,2,\ldots,m\}$. Thus, the statements $(1)'$ and $(2)'$ implies the statements $(2)$, $(3)$ and $(4)$ in Theorem \ref{thm:m-points}.
\end{proof}
We give a generalization of Theorem \ref{thm:m-points}, which will be used in the proof of Proposition \ref{p:n-linearity1}.
\begin{Proposition}
\label{p:inner1}
Let $G(0)\in(0,+\infty)$ and $p_j=\frac{1}{2}v(dd^c(\psi),z_j)>0$ for any $j\in\{1,2,\ldots,m\}$. For any $j\in\{1,2,\ldots,m\}$, assume that one of the following conditions holds:
$(A)$ $\varphi+a\psi$ is subharmonic near $z_j$ for some $a\in[0,1)$;
$(B)$ $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)>-\infty$.
Then $G(h^{-1}(r))$ is linear with respect to $r$ if and only if the following statements hold:
$(1)$ $\psi=2\sum_{1\le j\le m}p_jG_{\Omega}(\cdot,z_j)$;
$(2)$ $\varphi+\psi=2\log|g|+2\sum_{1\le j\le m}G_{\Omega}(\cdot,z_j)+2u$ and $\mathcal{F}_{z_j}=\mathcal{I}(\varphi+\psi)_{z_j}$ for any $j\in\{1,2,\ldots,m\}$, where $g$ is a holomorphic function on $\Omega$ such that $ord_{z_j}(g)=ord_{z_j}(f)$ for any $j\in\{1,2,\ldots,m\}$ and $u$ is a harmonic function on $\Omega$;
$(3)$ $\prod_{1\le j\le m}\chi_{z_j}=\chi_{-u}$, where $\chi_{-u}$ and $\chi_{z_j}$ are the characters associated to the functions $-u$ and $G_{\Omega}(\cdot,z_j)$ respectively;
$(4)$ $\lim_{z\rightarrow z_k}\frac{f}{gp_*\left(f_u\left(\prod_{1\le j\le m}f_{z_j}\right)\left(\sum_{1\le j\le m}p_{j}\frac{d{f_{z_{j}}}}{f_{z_{j}}}\right)\right)}=c_0$ for any $k\in\{1,2,\ldots,m\}$, where $c_0\in\mathbb{C}\backslash\{0\}$ is a constant independent of $k$.
\end{Proposition}
\begin{proof}
The sufficiency follows from
Theorem \ref{thm:m-points}. Thus, we just need to prove the necessity.
It follows from Theorem \ref{thm:m-points} that it suffices to prove $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)>-\infty$ for any $j\in\{1,2,\ldots,m\}$.
We prove $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)>-\infty$ for any $j\in\{1,2,\ldots,m\}$ by contradiction: if not, there exists
$j\in\{1,2,\ldots,m\}$ such that $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)=-\infty$, then we have $\varphi+a\psi$ is subharmonic near $z_j$ for some $a\in[0,1)$. As $\psi$ is subharmonic function on $\Omega$, it follows from Siu's Decomposition Theorem that $\psi=2p_jG_{\Omega}(\cdot,z_j)+\psi_1$ such that $v(dd^c(\psi_1),z_j)=0$ and $\psi_1(z_j)=-\infty$. Note that $\psi_1$ is subharmonic and not harmonic near $z_j$.
There exists a closed positive $(1,1)$ current $T\not\equiv0$, such that $SuppT\subset\subset V$ and $T\leq \frac{1-a}{2}i\partial\bar\partial\psi_1$ on $V$, where $V\Subset\Omega$ is an open neighborhood of $z_j$ satisfying that $\varphi+a\psi$ is subharmonic on a neighborhood of $\overline{V}$. Without loss of generality, assume that $\{z\in \overline{V}:\mathcal{I}(\varphi+\psi)_z\not=\mathcal{O}_z\}=\{z\in \overline{V}:v(dd^c(\varphi+\psi),z)\ge2\}=\{z_j\}$.
By Lemma \ref{l:cu}, there exists a subharmonic function $\Phi<0$ on $\Omega$, which satisfies the following properties: $i\partial\bar\partial\Phi\leq T$ and $i\partial\bar\partial\Phi\not\equiv0$; $\lim_{t\rightarrow0+0}(\inf_{\{G_{\Omega}(\cdot,z_j)\geq-t\}}\Phi(z))=0$; $Supp(i\partial\bar\partial\Phi)\subset V$ and $\inf_{\Omega\backslash V}\Phi>-\infty$. It follows from Lemma \ref{l:green-sup}, $v(dd^{c}\psi,z_j)>0$ and $\psi<0$ on $\Omega$ that $\lim_{t\rightarrow0+0}(\inf_{\{\psi\geq-t\}}\Phi(z))=0$.
Set $\tilde\varphi=\varphi-\Phi$, then $\tilde\varphi+\psi=\varphi+a\psi+2(1-a)p_jG_{\Omega}(\cdot,z_j)+(1-a)\psi_1-\Phi$ on $V$. As $(1-a)\psi_1-\Phi$ is subharmonic on $V$, we have $\tilde\varphi+\psi$ is subharmonic on $V$. It is clear that $\tilde\varphi\geq\varphi$ and $\tilde\varphi\not=\varphi$. It follows from $SuppT\subset\subset V$ and $i\partial\bar\partial\Phi\leq T\le i\partial\bar\partial\psi_1$ that $\tilde\varphi+\psi$ is subharmonic on $\Omega$ and $\mathcal{I}(\tilde\varphi+\psi)=\mathcal{I}(\varphi+\psi)$.
It follows from Remark \ref{rem:linear} that we can assume that $c(t)>e^{\frac{(1+a)t}{2}}$ for any $t>0$. $T\leq \frac{1-a}{2}i\partial\bar\partial\psi_1$ on $V$ and $i\partial\bar\partial\Phi\subset\subset V$ show that $\frac{1-a}{2}\psi-\Phi$ is subharmonic on $\Omega$, which implies that
$e^{-\tilde\varphi}c(-\psi)\geq e^{-\varphi-a\psi}e^{\Phi-\frac{1-a}{2}\psi}$
has positive lower bound on $V$. Notice that $\inf_{\Omega\backslash V}(\varphi-\tilde\varphi)=\inf_{\Omega\backslash V}\Phi>-\infty$ and $\int_{V}|F_1-F_2|^2e^{-\varphi}c(-\psi)\leq C\int_{V}|F_1-F_2|^2e^{-\varphi-\psi}<+\infty$ for any $F_1\in\mathcal{H}^2(c,\tilde\varphi,t)$ and $F_2\in\mathcal{H}^2(c,\varphi,t)$, where $V\subset\subset\{\psi<-t\}$, then $\tilde\varphi$ satisfies the conditions in Lemma \ref{l:n}, which contradicts to the result of Lemma \ref{l:n}. Thus $\psi_1(z_j)>-\infty$.
Thus, Proposition \ref{p:inner1} holds.
\end{proof}
Now, we consider the case that $Z_0$ is infinite. Let $Z_0=\{z_j:j\in\mathbb{Z}_{\ge1}\}\subset\Omega$ be a discrete set of infinite points satisfying $z_j\not=z_k$ for any $j\not=k$.
The following result gives a necessary condition for $G(h^{-1}(r))$ is linear.
\begin{Proposition}[\cite{GY-concavity3}] \label{p:infinite}
Assume that $G(0)\in(0,+\infty)$ and $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)>-\infty$ for $j\in\mathbb{Z}_{\ge1}$, where $p_j=\frac{1}{2}v(dd^c(\psi),z_j)>0$. Assume that $G(h^{-1}(r))$ is linear with respect to $r$. Then the following statements hold:
$(1)$ $\psi=2\sum_{j\in\mathbb{Z}_{\ge1}}p_jG_{\Omega}(\cdot,z_j)$;
$(2)$ $\varphi+\psi=2\log|g|$ and $\mathcal{F}_{z_j}=\mathcal{I}(\varphi+\psi)_{z_j}$ for any $j\in\mathbb{Z}_{\ge1}$, where $g$ is a holomorphic function on $\Omega$ such that $ord_{z_j}(g)=ord_{z_j}(f)+1$ for any $j\in\mathbb{Z}_{\ge1}$;
$(3)$ $\frac{p_j}{ord_{z_j}(g)}\lim_{z\rightarrow z_j}\frac{dg}{f}=c_0$ for any $j\in\mathbb{Z}_{\ge1}$, where $c_0\in\mathbb{C}\backslash\{0\}$ is a constant independent of $j$;
$(4)$ $\sum_{j\in\mathbb{Z}_{\ge1}}p_j<+\infty$.
\end{Proposition}
We give a generalization of Proposition \ref{p:infinite}, which will be used in the proof of Proposition \ref{p:n-linearity1}.
\begin{Proposition}
\label{p:inner2} Let $G(0)\in(0,+\infty)$ and $p_j=\frac{1}{2}v(dd^c(\psi),z_j)>0$ for any $j\in\mathbb{Z}_{\ge1}$. For any $j\in\mathbb{Z}_{\ge1}$, assume that one of the following conditions holds:
$(A)$ $\varphi+a\psi$ is subharmonic near $z_j$ for some $a\in[0,1)$;
$(B)$ $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)>-\infty$.
If $G(h^{-1}(r))$ is linear with respect to $r$, then the following statements hold:
$(1)$ $\psi=2\sum_{j\in\mathbb{Z}_{\ge1}}p_jG_{\Omega}(\cdot,z_j)$;
$(2)$ $\varphi+\psi=2\log|g|$ and $\mathcal{F}_{z_j}=\mathcal{I}(\varphi+\psi)_{z_j}$ for any $j\in\mathbb{Z}_{\ge1}$, where $g$ is a holomorphic function on $\Omega$ such that $ord_{z_j}(g)=ord_{z_j}(f)+1$ for any $j\in\mathbb{Z}_{\ge1}$;
$(3)$ $\frac{p_j}{ord_{z_j}(g)}\lim_{z\rightarrow z_j}\frac{dg}{f}=c_0$ for any $j\in\mathbb{Z}_{\ge1}$, where $c_0\in\mathbb{C}\backslash\{0\}$ is a constant independent of $j$;
$(4)$ $\sum_{j\in\mathbb{Z}_{\ge1}}p_j<+\infty$.
\end{Proposition}
\begin{proof} The proof of Proposition \ref{p:inner2} is similar to Proposition \ref{p:inner1}.
It follows from Proposition \ref{p:infinite} that it suffices to prove $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)>-\infty$ for any $j\in\mathbb{Z}_{\ge1}$.
We prove $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)>-\infty$ for any $j\in\mathbb{Z}_{\ge1}$ by contradiction: if not, there exists
$j\in\mathbb{Z}_{\ge1}$ such that $(\psi-2p_jG_{\Omega}(\cdot,z_j))(z_j)=-\infty$, then we have $\varphi+a\psi$ is subharmonic near $z_j$ for some $a\in[0,1)$. As $\psi$ is subharmonic function on $\Omega$, it follows from Siu's Decomposition Theorem that $\psi=2p_jG_{\Omega}(\cdot,z_j)+\psi_1$ such that $v(dd^c(\psi_1),z_j)=0$ and $\psi_1(z_j)=-\infty$. Note that $\psi_1$ is subharmonic and not harmonic near $z_j$.
There exists a closed positive $(1,1)$ current $T\not\equiv0$, such that $SuppT\subset\subset V$, $T\leq \frac{1-a}{2}i\partial\bar\partial\psi_1$ on $V$, where $V\Subset\Omega$ is an open neighborhood of $z_j$ satisfying that $\varphi+a\psi$ is subharmonic on a neighborhood of $\overline{V}$. Without loss of generality, assume that $\{z\in \overline{V}:\mathcal{I}(\varphi+\psi)_z\not=\mathcal{O}_z\}=\{z\in \overline{V}:v(dd^c(\varphi+\psi),z)\ge2\}=\{z_j\}$.
Using Lemma \ref{l:cu}, there exists a subharmonic function $\Phi<0$ on $\Omega$, which satisfies the following properties: $i\partial\bar\partial\Phi\leq T$ and $i\partial\bar\partial\Phi\not\equiv0$; $\lim_{t\rightarrow0+0}(\inf_{\{G_{\Omega}(\cdot,z_j)\geq-t\}}\Phi(z))=0$; $Supp(i\partial\bar\partial\Phi)\subset V$ and $\inf_{\Omega\backslash V}\Phi>-\infty$. It following from Lemma \ref{l:green-sup}, $v(dd^{c}\psi,z_j)>0$ and $\psi<0$ on $\Omega$ that $\lim_{t\rightarrow0+0}(\inf_{\{\psi\geq-t\}}\Phi(z))=0$.
Set $\tilde\varphi=\varphi-\Phi$, then $\tilde\varphi+\psi=\varphi+a\psi+2(1-a)p_jG_{\Omega}(\cdot,z_j)+(1-a)\psi_1-\Phi$ on $V$. As $(1-a)\psi_1-\Phi$ is subharmonic on $V$, we have $\tilde\varphi+\psi$ is subharmonic on $V$. It is clear that $\tilde\varphi\geq\varphi$ and $\tilde\varphi\not=\varphi$. It follows from $SuppT\subset\subset V$ and $i\partial\bar\partial\Phi\leq T\le i\partial\bar\partial\psi_1$ that $\tilde\varphi+\psi$ is subharmonic on $\Omega$ and $\mathcal{I}(\tilde\varphi+\psi)=\mathcal{I}(\varphi+\psi)$.
It follows from Remark \ref{rem:linear} that we can assume that $c(t)>e^{\frac{(1+a)t}{2}}$ for any $t>0$. $T\leq \frac{1-a}{2}i\partial\bar\partial\psi_1$ on $V$ and $i\partial\bar\partial\Phi\subset\subset V$ show that $\frac{1-a}{2}\psi-\Phi$ is subharmonic on $\Omega$, which implies that
$e^{-\tilde\varphi}c(-\psi)\geq e^{-\varphi-a\psi}e^{\Phi-\frac{1-a}{2}\psi}$
has positive lower bound on $V$. Notice that $\inf_{\Omega\backslash V}(\varphi-\tilde\varphi)=\inf_{\Omega\backslash V}\Phi>-\infty$ and $\int_{V}|F_1-F_2|^2e^{-\varphi}c(-\psi)\leq C\int_{V}|F_1-F_2|^2e^{-\varphi-\psi}<+\infty$ for any $F_1\in\mathcal{H}^2(c,\tilde\varphi,t)$ and $F_2\in\mathcal{H}^2(c,\varphi,t)$, where $V\subset\subset\{\psi<-t\}$, then $\tilde\varphi$ satisfies the conditions in Lemma \ref{l:n}, which contradicts to the result of Lemma \ref{l:n}. Thus $\psi_1(z_j)>-\infty$.
Thus, Proposition \ref{p:inner2} holds.
\end{proof}
\section{Proofs of Theorem \ref{main theorem}, Remark \ref{infty2}, Corollary \ref{necessary condition for linear of G} and Remark \ref{rem:linear}}
We firstly prove Theorem \ref{main theorem}.
\begin{proof} We firstly show that if $G(t_0)<+\infty$ for some $t_0> T$, then $G(t_1)<+\infty$ for any $T< t_1<t_0$. As $G(t_0)<+\infty$, it follows from Lemma \ref{existence of F} that there exists a unique
holomorphic $(n,0)$ form $F_{t_0}$ on $\{\Psi<-t\}$ satisfying
$$\ \int_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)=G(t_0)<+\infty$$ and
$\ (F_{t_0}-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$.
It follows from Lemma \ref{L2 method in JM concavity} that there exists a holomorphic $(n,0)$ form $\tilde{F}_1$ on $\{\Psi<-t_1\}$ such that
\begin{equation}\label{main theorem 1}
\begin{split}
& \int_{\{\Psi<-t_1\}}|\tilde{F}_1-(1-b_{t_0,B}(\Psi))F_{t_0}|^2e^{-\varphi+v_{t_0,B}(\Psi)-\Psi}c(-v_{t_0,B}(\Psi)) \\
\le & (\int_{t_1}^{t_0+B}c(s)e^{-s}ds)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi-\Psi}<+\infty.
\end{split}
\end{equation}
Note that $b_{t_0,B}(t)=0$ on $\{\Psi<-t_0-B\}$ and $v_{t_0,B}(\Psi)> -t_0-B$. We have $e^{v_{t_0,B}(\Psi)}c(-v_{t_0,B}(\Psi))$ has a positive lower bound. It follows from inequality \eqref{main theorem 1} that
we have $\ (\tilde{F}_{1}-F_{t_0})_{z_0}
\in \mathcal{O} (K_M)_{z_0}\otimes I(\Psi+\varphi)_{z_0} \subset \mathcal{O} (K_M)_{z_0}\otimes J_{z_0}$ for any $z_0\in Z_0$, which implies that
$(\tilde{F}_{1}-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$. As $v_{t_0,B}(\Psi)\ge\Psi$ and $c(t)e^{-t}$ is decreasing with respect to $t$, it follows from inequality \eqref{main theorem 1} that we have
\begin{equation}\label{main theorem 2}
\begin{split}
& \int_{\{\Psi<-t_1\}}|\tilde{F}_1-(1-b_{t_0,B}(\Psi))F_{t_0}|^2e^{-\varphi}c(-\Psi)
\\
\le&\int_{\{\Psi<-t_1\}}|\tilde{F}_1-(1-b_{t_0,B}(\Psi))F_{t_0}|^2e^{-\varphi+v_{t_0,B}(\Psi)-\Psi}c(-v_{t_0,B}(\Psi)) \\
\le & (\int_{t_1}^{t_0+B}c(s)e^{-s}ds)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi-\Psi}<+\infty.
\end{split}
\end{equation}
Then we have
\begin{equation}\label{main theorem 3}
\begin{split}
&\int_{\{\Psi<-t_1\}}|\tilde{F}_1|^2e^{-\varphi}c(-\Psi)\\
\le & 2\int_{\{\Psi<-t_1\}}|\tilde{F}_1-(1-b_{t_0,B}(\Psi))F_{t_0}|^2e^{-\varphi}c(-\Psi)
+2\int_{\{\Psi<-t_1\}}|(1-b_{t_0,B}(\Psi))F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
\le & 2(\int_{t_1}^{t_0+B}c(s)e^{-s}ds)
\int_{M}\frac{1}{B}\mathbb{I}_{\{-t_0-B<\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi-\Psi}
+2\int_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
<&+\infty.
\end{split}
\end{equation}
Hence we have $G(t_1)\le \int_{\{\Psi<-t_1\}}|\tilde{F}_1|^2e^{-\varphi}c(-\Psi)<+\infty$.
Now, it follows from Lemma \ref{semicontinuous}, Lemma \ref{derivatives of G} and Lemma \ref{characterization of concave function} that we know $G(h^{-1}(r))$ is concave with respect to $r$. It follows from Lemma \ref{semicontinuous} that $\lim\limits_{t\to T+0}G(t)=G(T)$ and $\lim\limits_{t\to+\infty}G(t)=0$.
Theorem \ref{main theorem} is proved.
\end{proof}
Now we prove Remark \ref{infty2}.
\begin{proof}Note that if there exists a positive decreasing concave function $g(t)$ on $(a,b)\subset\mathbb{R}$ and $g(t)$ is not a constant function, then $b<+\infty$.
Assume that $G(t_0)<+\infty$ for some $t_0\geq T$. As $f_{z_0}\notin
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$ for some $ z_0\in Z_0$, Lemma \ref{characterization of g(t)=0} shows that $G(t_0)\in(0,+\infty)$. Following from Theorem \ref{main theorem} we know $G({h}^{-1}(r))$ is concave with respect to $r\in(\int_{T_1}^{T}c(t)e^{-t}dt,\int_{T_1}^{+\infty}c(t)e^{-t}dt)$ and $G({h}^{-1}(r))$ is not a constant function, therefore we obtain $\int_{T_1}^{+\infty}c(t)e^{-t}dt<+\infty$, which contradicts to $\int_{T_1}^{+\infty}c(t)e^{-t}dt=+\infty$. Thus we have $G(t)\equiv+\infty$.
When $G(t_2)\in(0,+\infty)$ for some $t_2\in[T,+\infty)$, Lemma \ref{characterization of g(t)=0} shows that $f_{z_0}\notin
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$. Combining the above discussion, we know $\int_{T_1}^{+\infty}c(t)e^{-t}dt<+\infty$. Using Theorem \ref{main theorem}, we obtain that $G(\hat{h}^{-1}(r))$ is concave with respect to $r\in (0,\int_{T}^{+\infty}c(t)e^{-t}dt)$, where $\hat{h}(t)=\int_{t}^{+\infty}c(l)e^{-l}dl$.
Thus, Remark \ref{infty2} holds.
\end{proof}
Now we prove Corollary \ref{necessary condition for linear of G}.
\begin{proof} As $G(h^{-1}(r))$ is linear with respect to $r\in[0,\int_T^{+\infty}c(s)e^{-s}ds)$, we have $G(t)=\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{t}^{+\infty}c(s)e^{-s}ds$ for any $t\in[T,+\infty)$ and $T_1 \in (T,+\infty)$.
We follow the notation and the construction in Lemma \ref{derivatives of G}. Let $t_0>t_1> T$ be given. It follows from $G(h^{-1}(r))$ is linear with respect to $r\in[0,\int_T^{+\infty}c(s)e^{-s}ds)$ that we know that all inequalities in \eqref{derivative of G 5} should be equalities, i.e., we have
\begin{equation}
\label{necessary condition for linear of G 1}
\begin{split}
&G(t_1)-G(t_0)\\
=&\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}|^2e^{-\varphi}c(-\Psi)
-\int_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
=&\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}-\mathbb{I}_{\{\Psi< -t_0\}}F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
= &
\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}-\mathbb{I}_{\{\Psi< -t_0\}}F_{t_0}|^2e^{-\varphi}e^{-\Psi+v_{t_0}(\Psi)}c(-v_{t_0}(\Psi))\\
= &\big(\int^{t_0}_{t_1}c(t)e^{-t}dt\big)\liminf\limits_{B\to 0+0} \frac{G(t_0)-G(t_0+B)}{\int_{t_0}^{t_0+B}c(t)e^{-t}dt}.
\end{split}
\end{equation}
Note that $G(t_0)=\int_{\{\Psi<-t_0\}}|F_{t_0}|^2e^{-\varphi}c(-\Psi)$. Equality \eqref{necessary condition for linear of G 1} shows that $G(t_1)=\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}|^2e^{-\varphi}c(-\Psi)$.
Note that on $\{\Psi\ge -t_0\}$, we have $e^{-\Psi+v_{t_0}(\Psi)}c(-v_{t_0}(\Psi))=c(-\Psi)$. It follows from
\begin{equation}\nonumber
\begin{split}
&\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}-\mathbb{I}_{\{\Psi< -t_0\}}F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
= &
\int_{\{\Psi<-t_1\}}|\tilde{F}_{t_1}-\mathbb{I}_{\{\Psi< -t_0\}}F_{t_0}|^2e^{-\varphi}e^{-\Psi+v_{t_0}(\Psi)}c(-v_{t_0}(\Psi))\\
\end{split}
\end{equation}
that we have (note that $v_{t_0}(\Psi)=-t_0$ on $\{\Psi< -t_0\}$)
\begin{equation}
\begin{split}
\label{necessary condition for linear of G 2}
&\int_{\{\Psi<-t_0\}}|\tilde{F}_{t_1}-F_{t_0}|^2e^{-\varphi}c(-\Psi)\\
= &
\int_{\{\Psi<-t_0\}}|\tilde{F}_{t_1}-F_{t_0}|^2e^{-\varphi}e^{-\Psi-t_0}c(t_0).\\
\end{split}
\end{equation}
As $\int_{T}^{+\infty}c(t)e^{-t}dt<+\infty$ and $c(t)e^{-t}$ is decreasing with respect to $t$, we know that there exists $t_2>t_0$ such that $c(t)e^{-t}<c(t_0)e^{-t_0}-\epsilon$ for any $t\ge t_2$, where $\epsilon>0$ is a constant. Then equality \eqref{necessary condition for linear of G 2} implies that
\begin{equation}
\begin{split}
\label{necessary condition for linear of G 3}
&\epsilon\int_{\{\Psi<-t_2\}}|\tilde{F}_{t_1}-F_{t_0}|^2e^{-\varphi-\Psi}\\
\le &
\int_{\{\Psi<-t_2\}}|\tilde{F}_{t_1}-F_{t_0}|^2e^{-\varphi}(e^{-\Psi-t_0}c(t_0)-c(-\Psi))\\
\le &
\int_{\{\Psi<-t_0\}}|\tilde{F}_{t_1}-F_{t_0}|^2e^{-\varphi}(e^{-\Psi-t_0}c(t_0)-c(-\Psi))\\
= &0.
\end{split}
\end{equation}
Note that $e^{-\varphi-\Psi}\ge e^{-(\varphi+\psi)}|F|^2$, $\varphi+\psi$ is a plurisubharmonic function and the integrand in \eqref{necessary condition for linear of G 3} is nonnegative, we must have $\tilde{F}_{t_1}|_{\{\Psi<-t_0\}}=F_{t_0}$.
It follows from Lemma \ref{existence of F} that for any $t>T$, there exists a unique holomorphic $(n,0)$ form $F_t$ on $\{\Psi<-t\}$ satisfying
$$\ \int_{\{\Psi<-t\}}|F_t|^2e^{-\varphi}c(-\Psi)=G(t)$$ and
$\ (F_t-f)\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$. By the above discussion, we know $F_{t}=F_{t'}$ on $\{\Psi<-\max{\{t,t'\}}\}$ for any $t\in(T,+\infty)$ and $t'\in(T,+\infty)$. Hence combining $\lim_{t\rightarrow T+0}G(t)=G(T)$, we obtain that there exists a unique holomorphic $(n,0)$ form $\tilde{F}$ on $\{\Psi<-T\}$ satisfying $(\tilde{F}-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$ for any $z_0\in Z_0$ and $G(t)=\int_{\{\Psi<-t\}}|\tilde{F}|^2e^{-\varphi}c(-\Psi)$ for any $t\ge T$.
Secondly, we prove equality \eqref{other a also linear}.
As $a(t)$ is a nonnegative measurable function on $(T,+\infty)$, then there exists a sequence of functions $\{\sum\limits_{j=1}^{n_i}a_{ij}\mathbb{I}_{E_{ij}}\}_{i\in\mathbb{N}^+}$ $(n_i<+\infty$ for any $i\in\mathbb{N}^+)$ satisfying that $\sum\limits_{j=1}^{n_i}a_{ij}\mathbb{I}_{E_{ij}}$ is increasing with respect to $i$ and $\lim\limits_{i\to +\infty}\sum\limits_{j=1}^{n_i}a_{ij}\mathbb{I}_{E_{ij}}=a(t)$ for any $t\in(T,+\infty)$, where $E_{ij}$ is a Lebesgue measurable subset of $(T,+\infty)$ and $a_{ij}\ge 0$ is a constant for any $i,j$. It follows from Levi's Theorem that it suffices to prove the case that $a(t)=\mathbb{I}_{E}(t)$, where $E\subset\subset (T,+\infty)$ is a Lebesgue measurable set.
Note that $G(t)=\int_{\{\Psi<-t\}}|\tilde{F}|^2e^{-\varphi}c(-\Psi)=\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}
\int_{t}^{+\infty}c(s)e^{-s}ds$ where $T_1 \in (T,+\infty)$, then
\begin{equation}\label{linear 3.4}
\int_{\{-t_1\le\Psi<-t_2\}}|\tilde{F}|^2e^{-\varphi}c(-\Psi)=\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}
\int_{t_2}^{t_1}c(s)e^{-s}ds
\end{equation}
holds for any $T\le t_2<t_1<+\infty$. It follows from the dominated convergence theorem and equality \eqref{linear 3.4} that
\begin{equation}\label{linear 3.5}
\int_{\{z\in M:-\Psi(z)\in N\}}|\tilde{F}|^2e^{-\varphi}=0
\end{equation}
holds for any $N\subset\subset (T,+\infty)$ such that $\mu(N)=0$, where $\mu$ is the Lebesgue measure on $\mathbb{R}$.
As $c(t)e^{-t}$ is decreasing on $(T,+\infty)$, there are at most countable points denoted by $\{s_j\}_{j\in \mathbb{N}^+}$ such that $c(t)$ is not continuous at $s_j$. Then there is a decreasing sequence of open sets $\{U_k\}$, such that
$\{s_j\}_{j\in \mathbb{N}^+}\subset U_k\subset (T,+\infty)$ for any $k$, and $\lim\limits_{k \to +\infty}\mu(U_k)=0$. Choosing any closed interval $[t'_2,t'_1]\subset (T,+\infty)$, then we have
\begin{equation}\label{linear 3.6}
\begin{split}
&\int_{\{-t'_1\le\Psi<-t'_2\}}|\tilde{F}|^2e^{-\varphi}\\
=&\int_{\{z\in M:-\Psi(z)\in(t'_2,t'_1]\backslash U_k\}}|\tilde{F}|^2e^{-\varphi}+
\int_{\{z\in M:-\Psi(z)\in[t'_2,t'_1]\cap U_k\}}|\tilde{F}|^2e^{-\varphi}\\
=&\lim_{n\to+\infty}\sum_{i=0}^{n-1}\int_{\{z\in M:-\Psi(z)\in I_{i,n}\backslash U_k\}}|\tilde{F}|^2e^{-\varphi}+
\int_{\{z\in M:-\Psi(z)\in[t'_2,t'_1]\cap U_k\}}|\tilde{F}|^2e^{-\varphi},
\end{split}
\end{equation}
where $I_{i,n}=(t'_1-(i+1)\alpha_n,t'_1-i\alpha_n]$ and $\alpha_n=\frac{t'_1-t'_2}{n}$. Note that
\begin{equation}\label{linear 3.7}
\begin{split}
&\lim_{n\to+\infty}\sum_{i=0}^{n-1}\int_{\{z\in M:-\Psi(z)\in I_{i,n}\backslash U_k\}}|\tilde{F}|^2e^{-\varphi}\\
\le&\limsup_{n\to+\infty}\sum_{i=0}^{n-1}\frac{1}{\inf_{I_{i,n}\backslash U_k}c(t)}\int_{\{z\in M:-\Psi(z)\in I_{i,n}\backslash U_k\}}|\tilde F|^2e^{-\varphi}c(-\Psi).
\end{split}
\end{equation}
It follows from equality \eqref{linear 3.4} that inequality \eqref{linear 3.7} becomes
\begin{equation}\label{linear 3.8}
\begin{split}
&\lim_{n\to+\infty}\sum_{i=0}^{n-1}\int_{\{z\in M:-\Psi(z)\in I_{i,n}\backslash U_k\}}|\tilde F|^2e^{-\varphi}\\
\le&\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}
\limsup_{n\to+\infty}\sum_{i=0}^{n-1}\frac{1}{\inf_{I_{i,n}\backslash U_k}c(t)}\int_{I_{i,n}\backslash U_k}c(s)e^{-s}ds.
\end{split}
\end{equation}
It is clear that $c(t)$ is uniformly continuous and has positive lower bound and upper bound on $[t'_2,t'_1]\backslash U_k$. Then we have
\begin{equation}\label{linear 3.9}
\begin{split}
&\limsup_{n\to+\infty}\sum_{i=0}^{n-1}\frac{1}{\inf_{I_{i,n}\backslash U_k}c(t)}\int_{I_{i,n}\backslash U_k}c(s)e^{-s}ds \\
\le&\limsup_{n\to+\infty}\sum_{i=0}^{n-1}\frac{\sup_{I_{i,n}\backslash U_k}c(t)}{\inf_{I_{i,n}\backslash U_k}c(t)}\int_{I_{i,n}\backslash U_k}e^{-s}ds\\
=&\int_{(t'_2,t'_1]\backslash U_k}e^{-s}ds.
\end{split}
\end{equation}
Combining inequality \eqref{linear 3.6}, \eqref{linear 3.8} and \eqref{linear 3.9}, we have
\begin{equation}\label{linear 3.10}
\begin{split}
&\int_{\{-t'_1\le\Psi<-t'_2\}}|\tilde{F}|^2e^{-\varphi}\\
=&\int_{\{z\in M:-\Psi(z)\in(t'_2,t'_1]\backslash U_k\}}|\tilde{F}|^2e^{-\varphi}+
\int_{\{z\in M:-\Psi(z)\in[t'_2,t'_1]\cap U_k\}}|\tilde{F}|^2e^{-\varphi}\\
\le&\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{(t'_2,t'_1]\backslash U_k}e^{-s}ds+
\int_{\{z\in M:-\Psi(z)\in[t'_2,t'_1]\cap U_k\}}|\tilde{F}|^2e^{-\varphi}.
\end{split}
\end{equation}
Let $k\to +\infty$, following from equality \eqref{linear 3.5} and inequality \eqref{linear 3.10}, then we obtain that
\begin{equation}\label{linear 3.11}
\begin{split}
\int_{\{-t'_1\le\Psi<-t'_2\}}|\tilde{F}|^2e^{-\varphi}
\le\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{t'_2}^{t'_1}e^{-s}ds.
\end{split}
\end{equation}
Following from a similar discussion we can obtain that
\begin{equation}\nonumber
\begin{split}
\int_{\{-t'_1\le\Psi<-t'_2\}}|\tilde{F}|^2e^{-\varphi}
\ge\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{t'_2}^{t'_1}e^{-s}ds.
\end{split}
\end{equation}
Then combining inequality \eqref{linear 3.11}, we know
\begin{equation}\label{linear 3.12}
\begin{split}
\int_{\{-t'_1\le\Psi<-t'_2\}}|\tilde{F}|^2e^{-\varphi}
=\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{t'_2}^{t'_1}e^{-s}ds.
\end{split}
\end{equation}
Then it is clear that for any open set $U\subset (T,+\infty)$ and compact set $V\subset (T,+\infty)$,
$$
\int_{\{z\in M;-\Psi(z)\in U\}}|\tilde{F}|^2e^{-\varphi}
=\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{U}e^{-s}ds,
$$
and
$$
\int_{\{z\in M;-\Psi(z)\in V\}}|\tilde{F}|^2e^{-\varphi}
=\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{V}e^{-s}ds.
$$
As $E\subset\subset (T,+\infty)$, then $E\cap(t_2,t_1]$ is a Lebesgue measurable subset of $(T+\frac{1}{n},n)$ for some large $n$, where $T\le t_2<t_1\le+\infty$. Then there exists a sequence of compact sets $\{V_j\}$ and a sequence of open subsets $\{V'_j\}$ satisfying $V_1\subset \ldots \subset V_j\subset V_{j+1}\subset\ldots \subset E\cap(t_2,t_1]\subset \ldots \subset V'_{j+1}\subset V'_j\subset \ldots\subset V'_1\subset\subset (T,+\infty)$ and $\lim\limits_{j\to +\infty}\mu(V'_j-V_j)=0$, where $\mu$ is the Lebesgue measure on $\mathbb{R}$. Then we have
\begin{equation}\nonumber
\begin{split}
\int_{\{-t'_1\le\Psi<-t'_2\}}|\tilde{F}|^2e^{-\varphi}\mathbb{I}_E(-\Psi)
=&\int_{z\in M:-\Psi(z)\in E\cap (t_2,t_1]}|\tilde{F}|^2e^{-\varphi}\\
\le&\liminf_{j\to+\infty}\int_{\{z\in M:-\Psi(z)\in V'_j\}}|\tilde{F}|^2e^{-\varphi}\\
\le&\liminf_{j\to+\infty}\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{V'_j}e^{-s}ds\\
\le&\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{E\cap(t_2,t_1]}e^{-s}ds\\
=&\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{t_2}^{t_1}e^{-s}\mathbb{I}_E(s)ds,
\end{split}
\end{equation}
and
\begin{equation}\nonumber
\begin{split}
\int_{\{-t'_1\le\Psi<-t'_2\}}|\tilde{F}|^2e^{-\varphi}\mathbb{I}_E(-\Psi)
\ge&\liminf_{j\to+\infty}\int_{\{z\in M:-\Psi(z)\in V_j\}}|\tilde{F}|^2e^{-\varphi}\\
\ge&\liminf_{j\to+\infty}\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{V_j}e^{-s}ds\\
=&\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{t_2}^{t_1}e^{-s}\mathbb{I}_E(s)ds,
\end{split}
\end{equation}
which implies that
$$\int_{\{-t'_1\le\Psi<-t'_2\}}|\tilde{F}|^2e^{-\varphi}\mathbb{I}_E(-\Psi)=
\frac{G(T_1)}{\int_{T_1}^{+\infty}c(s)e^{-s}ds}\int_{t_2}^{t_1}e^{-s}\mathbb{I}_E(s)ds.$$
Hence we know that equality \eqref{other a also linear} holds.
Corollary \ref{necessary condition for linear of G} is proved.
\end{proof}
Now we prove Remark \ref{rem:linear}.
\begin{proof}[Proof of Remark \ref{rem:linear}]
By the definition of $G(t;\tilde{c})$, we have $G(t_0;\tilde{c})\le\int_{\{\Psi<-t_0\}}|\tilde{F}|^2e^{-\varphi}\tilde{c}(-\Psi)$, where $\tilde{F}$ is the holomorphic $(n,0)$ form on $\{\Psi<-T\}$ such that $G(t)=\int_{\{\Psi<-t\}}|\tilde{F}|^2e^{-\varphi}c(-\Psi)$ for any $t\ge T$. Hence we only consider the case $G(t_0;\tilde{c})<+\infty$.
By the definition of $G(t;\tilde{c})$, we can choose a holomorphic $(n,0)$ form $F_{t_0,\tilde{c}}$ on $\{\Psi<-t_0\}$ satisfying $\ (F_{t_0,\tilde{c}}-f)_{z_0}\in
\mathcal{O} (K_M)_{z_0} \otimes J_{z_0}$, for any $ z_0\in Z_0$ and $\int_{ \{ \Psi<-t_0\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\tilde{c}(-\Psi)<+\infty$. As $\mathcal{H}^2(\tilde{c},t_0)\subset \mathcal{H}^2(c,t_0)$, we have $\int_{ \{ \Psi<-t_0\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}c(-\Psi)<+\infty$. Using
Lemma \ref{existence of F}, we obtain that
\begin{equation}\nonumber
\begin{split}
\int_{ \{ \Psi<-t\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}c(-\Psi)
=&\int_{ \{ \Psi<-t\}}|\tilde{F}|^2e^{-\varphi}c(-\Psi)\\
+&\int_{ \{ \Psi<-t\}}|F_{t_0,\tilde{c}}-\tilde{F}|^2e^{-\varphi}c(-\Psi)
\end{split}
\end{equation}
for any $t\ge t_0,$ then
\begin{equation}\label{linear 3.13}
\begin{split}
\int_{ \{-t_3\le \Psi<-t_4\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}c(-\Psi)
=&\int_{ \{-t_3\le \Psi<-t_4\}}|\tilde{F}|^2e^{-\varphi}c(-\Psi)\\
+&\int_{\{-t_3\le \Psi<-t_4\}}|F_{t_0,\tilde{c}}-\tilde{F}|^2e^{-\varphi}c(-\Psi)
\end{split}
\end{equation}
holds for any $t_3>t_4\ge t_0$. It follows from the dominated convergence theorem, equality \eqref{linear 3.13}, \eqref{linear 3.5} and $c(t)>0$ for any $t>T$, that
\begin{equation}\label{linear 3.14}
\begin{split}
\int_{ \{z\in M:-\Psi(z)=t\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}
=\int_{\{z\in M:-\Psi(z)=t\}}|F_{t_0,\tilde{c}}-\tilde{F}|^2e^{-\varphi}
\end{split}
\end{equation}
holds for any $t>t_0$.
Choosing any closed interval $[t'_4,t'_3]\subset (t_0,+\infty)\subset (T,+\infty)$. Note that $c(t)$ is uniformly continuous and have positive lower bound and upper bound on $[t'_4,t'_3]\backslash U_k$, where $\{U_k\}$ is the decreasing sequence of open subsets of $(T,+\infty)$, such that $c$ is continuous on $(T,+\infty)\backslash U_k$ and $\lim\limits_{k \to +\infty}\mu(U_k)=0$. Take $N=\cap_{k=1}^{+\infty}U_k.$ Note that
\begin{equation}\label{linear 3.15}
\begin{split}
&\int_{ \{-t'_3\le\Psi<-t'_4\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\\
=&\lim_{n\to+\infty}\sum_{i=0}^{n-1}\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}
+\int_{\{z\in M:-\Psi(z)\in(t'_4,t'_3]\cap U_k\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\\
\le&\limsup_{n\to+\infty}\sum_{i=0}^{n-1}\frac{1}{\inf_{S_{i,n}}c(t)}\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}c(-\Psi)\\
&+\int_{\{z\in M:-\Psi(z)\in(t'_4,t'_3]\cap U_k\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi},
\end{split}
\end{equation}
where $S_{i,n}=(t'_4-(i+1)\alpha_n,t'_3-i\alpha_n]$ and $\alpha_n=\frac{t'_3-t'_4}{n}$.
It follows from equality \eqref{linear 3.13},\eqref{linear 3.14}, \eqref{linear 3.5} and the dominated convergence theorem that
\begin{equation}\label{linear 3.16}
\begin{split}
&\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}c(-\Psi)\\
=&\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|\tilde F|^2e^{-\varphi}c(-\Psi)
+\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi}c(-\Psi).
\end{split}
\end{equation}
As $c(t)$ is uniformly continuous and have positive lower bound and upper bound on $[t'_3,t'_4]\backslash U_k$, combining equality \eqref{linear 3.16}, we have
\begin{equation}\label{linear 3.17}
\begin{split}
&\limsup_{n\to+\infty}\sum_{i=0}^{n-1}\frac{1}{\inf_{S_{i,n}\backslash U_k}c(t)}\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}c(-\Psi)\\
=&\limsup_{n\to+\infty}\sum_{i=0}^{n-1}\frac{1}{\inf_{S_{i,n}\backslash U_k}c(t)}(\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|\tilde F|^2e^{-\varphi}c(-\Psi)\\
&+\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi}c(-\Psi))\\
\le & \limsup_{n\to+\infty}\sum_{i=0}^{n-1}\frac{\sup_{S_{i,n}\backslash U_k}c(t)}{\inf_{S_{i,n}\backslash U_k}c(t)}(\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|\tilde F|^2e^{-\varphi}\\
&+\int_{\{z\in M:-\Psi(z)\in S_{i,n}\backslash U_k\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi})\\
=&\int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\backslash U_k\}}|\tilde F|^2e^{-\varphi}
+\int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\backslash U_k\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi}.
\end{split}
\end{equation}
If follows from inequality \eqref{linear 3.15} and \eqref{linear 3.17} that
\begin{equation}\label{linear 3.18}
\begin{split}
&\int_{ \{-t'_3\le\Psi<-t'_4\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\\
\le & \int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\backslash U_k\}}|\tilde F|^2e^{-\varphi}
+\int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\backslash U_k\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi}\\
&+\int_{ \{z\in M: -\Psi(z)\in(t'_4,t'_3]\cap U_k\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}.
\end{split}
\end{equation}
It follows from $F_{t_0,\tilde{c}}\in\mathcal{H}^2(c,t_0)$ that $\int_{ \{-t'_3\le\Psi<-t'_4\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}<+\infty$. Let $k\to+\infty,$ by equality \eqref{linear 3.5}, inequality \eqref{linear 3.18} and the dominated theorem, we have
\begin{equation}\label{linear 3.19}
\begin{split}
&\int_{ \{-t'_3\le\Psi<-t'_4\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\\
\le & \int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\}}|\tilde F|^2e^{-\varphi}
+\int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\backslash N\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi}\\
&+\int_{ \{z\in M: -\Psi(z)\in(t'_4,t'_3]\cap N\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}.
\end{split}
\end{equation}
By similar discussion, we also have that
\begin{equation}\nonumber
\begin{split}
&\int_{ \{-t'_3\le\Psi<-t'_4\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\\
\ge & \int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\}}|\tilde F|^2e^{-\varphi}
+\int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\backslash N\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi}\\
&+\int_{ \{z\in M: -\Psi(z)\in(t'_4,t'_3]\cap N\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}.
\end{split}
\end{equation}
then combining inequality \eqref{linear 3.19}, we have
\begin{equation}\label{linear 3.20}
\begin{split}
&\int_{ \{-t'_3\le\Psi<-t'_4\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\\
= & \int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\}}|\tilde F|^2e^{-\varphi}
+\int_{\{z\in M:-\Psi(z)\in (t'_4,t'_3]\backslash N\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi}\\
&+\int_{ \{z\in M: -\Psi(z)\in(t'_4,t'_3]\cap N\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}.
\end{split}
\end{equation}
Using equality \eqref{linear 3.5}, \eqref{linear 3.14} and Levi's Theorem, we have
\begin{equation}\label{linear 3.21}
\begin{split}
&\int_{ \{z\in M:-\Psi(z)\in U\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\\
= & \int_{\{z\in M:-\Psi(z)\in U\}}|\tilde F|^2e^{-\varphi}
+\int_{\{z\in M:-\Psi(z)\in U\backslash N\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi}\\
&+\int_{ \{z\in M: -\Psi(z)\in U\cap N\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}
\end{split}
\end{equation}
holds for any open set $U\subset\subset (t_0,+\infty)$, and
\begin{equation}\label{linear 3.22}
\begin{split}
&\int_{ \{z\in M:-\Psi(z)\in V\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\\
= & \int_{\{z\in M:-\Psi(z)\in V\}}|\tilde F|^2e^{-\varphi}
+\int_{\{z\in M:-\Psi(z)\in V\backslash N\}}|F_{t_0,\tilde{c}}-\tilde F|^2e^{-\varphi}\\
&+\int_{ \{z\in M: -\Psi(z)\in V\cap N\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}
\end{split}
\end{equation}
holds for any compact set $V\subset (t_0,+\infty)$. For any measurable set $E\subset\subset (t_0,+\infty)$, there exists a sequence of compact set $\{V_l\}$, such that $V_l\subset V_{l+1}\subset E$ for any $l$ and $\lim\limits_{l\to +\infty}\mu(V_l)=\mu(E)$, hence by equality \eqref{linear 3.22}, we have
\begin{equation}\label{linear 3.23}
\begin{split}
\int_{ \{\Psi<-t_0\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\mathbb{I}_E(-\Psi)
\ge&\lim_{l \to +\infty} \int_{ \{\Psi<-t_0\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\mathbb{I}_{V_j}(-\Psi)\\
\ge&\lim_{l \to +\infty} \int_{ \{\Psi<-t_0\}}|\tilde F|^2e^{-\varphi}\mathbb{I}_{V_j}(-\Psi)\\
=& \int_{ \{\Psi<-t_0\}}|\tilde F|^2e^{-\varphi}\mathbb{I}_{V_j}(-\Psi).
\end{split}
\end{equation}
It is clear that for any $t>t_0$, there exists a sequence of functions $\{\sum_{j=1}^{n_i}\mathbb{I}_{E_{i,j}}\}_{i=1}^{+\infty}$ defined on $(t,+\infty)$, satisfying $E_{i,j}\subset\subset (t,+\infty)$, $\sum_{j=1}^{n_{i+1}}\mathbb{I}_{E_{i+1,j}}(s)\ge \sum_{j=1}^{n_{i}}\mathbb{I}_{E_{i,j}}(s)$ and $\lim\limits_{i\to+\infty}\sum_{j=1}^{n_i}\mathbb{I}_{E_{i,j}}(s)=\tilde{c}(s)$ for any $s>t$. Combining Levi's Theorem and inequality \eqref{linear 3.23}, we have
\begin{equation}\label{linear 3.24}
\begin{split}
\int_{ \{\Psi<-t_0\}}|F_{t_0,\tilde{c}}|^2e^{-\varphi}\tilde{c}(-\Psi)
\ge\int_{ \{\Psi<-t_0\}}|\tilde F|^2e^{-\varphi}\tilde{c}(-\Psi).
\end{split}
\end{equation}
By the definition of $G(t_0,\tilde{c})$, we have $G(t_0,\tilde{c})=\int_{ \{\Psi<-t_0\}}|\tilde F|^2e^{-\varphi}\tilde{c}(-\Psi).$ Equality \eqref{other c also linear} is proved.
\end{proof}
\section{A necessary condition for $G(h^{-1}(r))$ is linearity on open Riemann surfaces}\label{sec:n}
Let $\Omega$ be an open Riemann surface, and let $K_{\Omega}$ be the canonical (holomorphic) line bundle on $\Omega$. Let $dV_{\Omega}$ be a continuous volume form on $\Omega$. Let $\psi$ be a subharmonic function on $\Omega$, and let $\varphi$ be a Lebesgue measurable function on $\Omega$ such that $\varphi+\psi$ is subharmonic on $\Omega$. Let $F$ be a holomorphic function on $\Omega$. Let $T\in[-\infty,+\infty)$ such that $-T\le\sup\{\psi(z)-2\log|F(z)|:z\in\Omega \,\&\,F(z)\not=0\}$. Denote that
$$\Psi:=\min\{\psi-2\log|F|,-T\}.$$
For any $z\in \Omega$ satisfying $F(z)=0$, we set $\Psi(z)=-T$. Note that $\Psi$ is subharmonic function on $\{\Psi<-T\}$.
Let $Z_0$ be a subset of $ \cap_{t>T}\overline{\{\Psi<-t\}}$. Denote that $Z_1:=\{z\in Z_0:v(dd^c(\psi),z)\ge2ord_{z}(F)\}$ and $Z_2:=\{z\in Z_0:v(dd^c(\psi),z)<2ord_{z}(F)\}$. Denote that $Z'_1:=\{z\in Z_0:v(dd^c(\psi),z)>2ord_{z}(F)\}$. Note that $Z'_1\backslash\{\Psi<-t\}\subset\{z\in\Omega:F(z)=0\}$ and $\{\Psi<-t\}\cup Z'_1$ is an open Riemann surface for any $t\ge T$. Assume that $Z'_1$ is a discrete subset of $\{\Psi<-T\}\cup Z'_1$.
Let $c(t)$ be a positive measurable function on $(T,+\infty)$ satisfying $c(t)e^{-t}$ is decreasing on $(0,+\infty)$, $c(t)e^{-t}$ is integrable near $+\infty$, and $e^{-\varphi}c(-\Psi)$ has a positive lower bound on $K\cap\{\Psi<-T\}$ for any compact subset $K$ of $\Omega\backslash E$, where $E\subset\{\Psi=-\infty\}$ is a discrete subset of $\Omega$.
Let $f$ be a holomorphic $(1,0)$ form on $\{\Psi<-t_0\}\cap V$, where $V\supset Z_0$ is an open subset of $\Omega$ and $t_0>T$
is a real number.
Let $J_{z}$ be an $\mathcal{O}_{\Omega,z}$-submodule of $H_{z}$ such that $I(\Psi+\varphi)_{z}\subset J_{z}$,
where $z\in Z_0$ and $H_{z}:=\{h_{z}\in J(\Psi)_{z}:\int_{\{\Psi<-t\}\cap U}|h|^2e^{-\varphi}c(-\Psi)dV_{\Omega}<+\infty$ for some $t>T$ and some neighborhood $U$ of $z\}$.
Denote
\begin{equation*}
\begin{split}
\inf\Bigg\{ \int_{ \{ \Psi<-t\}}|\tilde{f}|^2&e^{-\varphi}c(-\Psi): \tilde{f}\in
H^0(\{\Psi<-t\},\mathcal{O} (K_{\Omega}) ) \\
&\&\, (\tilde{f}-f)_{z}\in
\mathcal{O} (K_{\Omega})_{z} \otimes J_{z}\text{ for any } z\in Z_0 \Bigg\}
\end{split}
\end{equation*}
by $G(t;c,\Psi,\varphi,J,f)$, where $t\in[T,+\infty)$ and $|f|^2:=\sqrt{-1}^{n^2}f\wedge \bar{f}$ for any $(1,0)$ form $f$.
Note that there exists a subharmonic function $\psi_1$ on $\Omega_1:= \{\Psi<-T\}\cup Z'_1$ such that $\psi_1+2\log|F|=\psi$. Let $K_{\Omega_1}$ be the canonical (holomorphic) line bundle on $\Omega_1$. For any $z\in \Omega_1$, if $F(z)=0$, we know that $e^{-\varphi}c(-\Psi)=e^{-\varphi}c(-\psi_1)$ has a positive lower bound on $V'\backslash\{z\}$, where $V'\Subset \Omega_1$ is a neighborhood of $z$. Combining $e^{-\varphi}c(-\psi_1)\le Ce^{-\varphi-\psi_1}=Ce^{-\varphi-\psi+2\log|F|}$ on $V'$, we have $v(dd^c(\varphi+\psi),z_0)\ge 2ord_{z_0}(F)$. Hence we have $\varphi+\psi_1$ is a subharmonic function on $\Omega_1$.
For any $z\in Z'_1$, if $F(z)\not=0$, we know that $J_{z}$ and $I(\varphi+\Psi)_z=\mathcal{I}(\varphi+\psi_1)_z$ are ideals of $\mathcal{O}_{\Omega_1,z}$, and we denote $J_{z}$ by $\mathcal{F}_{z}$. For any $z\in Z'_1$, if $F(z)=0$, we know that $e^{-\varphi}c(-\Psi)$ has a positive lower bound on $V'\backslash\{z\}$, where $V'\subset \Omega$ is a neighborhood of $z$, hence $I(\varphi+\Psi)_z\subset J_{z}\subset H_{z}$ shows that for any $h_z\in J(\Psi)_z$, $h_{z}\in I(\varphi+\Psi)_z$ if and only if there exists a holomorphic extension $\tilde h$ of $h$ near $z$ such that $(\tilde h,z)\in \mathcal{I}(\varphi+\psi_1)_z$, and we get that there exists an ideal $\mathcal{F}_{z}$ of $\mathcal{O}_{\Omega_1,z}$ such that for any $h_z\in J(\Psi)_z$, $h_{z}\in J_{z}$ if and only if there exists a holomorphic extension $\tilde h$ of $h$ near $z$ such that $(\tilde h,z)\in\mathcal{F}_{z}$.
Let $f_1$ be a holomorphic $(1,0)$ form on $V_1$, where $V_1\supset Z'_1$ is an open subset of $\Omega_1$. Denote
\begin{equation*}
\begin{split}
\inf\Bigg\{ \int_{ \{ \psi_1<-t\}}|\tilde{f}|^2e^{-\varphi}c(-\psi_1): \tilde{f}\in
H^0(\{\psi_1<-t\},\mathcal{O} (K_{\Omega_1}) ) \\
\&\, (\tilde{f}-f_1,z)\in
\mathcal{O} (K_{\Omega_1})_{z} \otimes \mathcal{F}_{z},\text{ for any } z\in Z'_1 \Bigg\}
\end{split}
\end{equation*}
by $G_{f_1}(t)$, where $t\in[T,+\infty)$.
Note that $e^{-\varphi}c(-\psi_1)$ has a positive lower bound on any compact subset of $\Omega_1\backslash(E\cup Z'_1)$. Let $f_2$ be a holomorphic $(1,0)$ form on $V\cap(\{\Psi<-t_0\}\cup Z'_1)=V\cap\{\psi_1<-t_0\}$ satisfying that $(f_2)_z\in
\mathcal{O} (K_{\Omega})_{z} \otimes H_{z}$ for any $z\in Z_0$, where $V\supset Z_0$ is an open subset of $\Omega$ and $t_0>T$
is a real number. Theorem \ref{main theorem} shows that
$G(h^{-1}(r);c,\Psi,\varphi,J,f_2)$ and $G_{f_2}(h^{-1}(r))$ are concave with respect to $r$, where $h(t)=\int_{t}^{+\infty}c(s)e^{-s}ds$. We give a relationship between $G(h^{-1}(r);c,\Psi,\varphi,J,f_2)$ and $G_{f_2}(h^{-1}(r))$, which will be used in the proof of Proposition \ref{p:n-linearity1}.
\begin{Lemma}\label{l:inner}
If $H_z=I(\varphi+\Psi)_z$ for any $z\in Z_0\backslash Z'_1$, then $G(t;c,\Psi,\varphi,J,f_2)=\tilde G_{f_2}(t)$ for any $t\ge T$.
\end{Lemma}
\begin{proof}
$H_z=I(\varphi+\Psi)_z$ for any $z\in Z_0\backslash Z'_1$ shows that $J_{z_0}=H_z=I(\varphi+\Psi)_z$ for any $z\in Z_0\backslash Z'_1$. For any $t\ge T$ and holomorphic $(1,0)$ form $\tilde f$ on $\{\psi_1<-t\}$ satisfying $(\tilde f-f_2,z)\in
\mathcal{O} (K_{\Omega_1})_{z} \otimes \mathcal{F}_{z}$ for any $z\in Z'_1$ and $\int_{\{\psi_1<-t\}}|\tilde f|^2e^{-\varphi}c(-\psi_1)<+\infty$, it follows from $(f_2)_z\in
\mathcal{O} (K_{\Omega})_{z} \otimes H_{z}$ for any $z\in Z_0$ and the definition of $H_z$ that $(\tilde f-f_2)_z\in
\mathcal{O} (K_{\Omega})_{z} \otimes J_{z}$ for any $z\in Z_0$.
As $\mu(Z'_1)=0$, where $\mu$ is the Lebesgue measure on $\Omega$, the definitions of $G(h^{-1}(r);c,\Psi,\varphi,J,f_2)$ and $G_{f_2}(h^{-1}(r))$ show that $G(t;c,\Psi,\varphi,J,f_2)\le\tilde G_{f_2}(t)$ for any $t\ge T$.
For any $t\ge T$, let $\tilde f$ be a holomorphic $(1,0)$ form on $\{\Psi<-t\}$ satisfying $(\tilde f-f_2)_{z}\in\mathcal{O}(K_{\Omega})_z\otimes J_z$ for any $z\in Z_0$ and $\int_{\{\Psi<-t\}}|\tilde f|^2e^{-\varphi}c(-\Psi)<+\infty$. For any $z_0\in Z'_1\backslash\{\Psi<-t\}$, we have $F(z_0)=0$. Note that $v(dd^c(\psi),z_0)>2ord_{z_0}(F)$, then $e^{-\varphi}c(-\Psi)$ has a positive lower bound on $V'\backslash\{z_0\}\subset\{\Psi<-t\}$, where $V'\Subset\Omega_1$ is a neighborhood of $z_0$. Following from $\int_{\{\Psi<-t\}}|\tilde f|^2e^{-\varphi}c(-\Psi)<+\infty$, we get that there exists a holomorphic $(1,0)$ form $\tilde f_1$ on $\{\psi_1<-t\}=\{\Psi<-t\}\cup Z'_1$ such that $\tilde f_1=\tilde f$ on $\{\Psi<-t\}$, which implies that $(\tilde f_1-f_2,z)\in\mathcal{O}(K_{\Omega})_z\otimes \mathcal{F}_z$ for any $z\in Z'_1$ and $\int_{\{\psi_1<-t\}}|\tilde f_1|^2e^{-\varphi}c(-\psi_1)=\int_{\{\Psi<-t\}}|\tilde f|^2e^{-\varphi}c(-\Psi)$. By the definitions of $G(h^{-1}(r);c,\Psi,\varphi,J,f_2)$ and $G_{f_2}(h^{-1}(r))$, we have $G(t;c,\Psi,\varphi,J,f_2)\ge\tilde G_{f_2}(t)$ for any $t\ge T$.
Thus, Lemma \ref{l:inner} holds.
\end{proof}
We give a necessary condition for the concavity of $G(h^{-1}(r))$ degenerating to linearity.
\begin{Proposition}
\label{p:n-linearity1}
For any $z\in Z_1$, assume that one of the following conditions holds:
$(A)$ $\varphi+a\psi$ is subharmonic near $z$ for some $a\in[0,1)$;
$(B)$ $(\psi-2p_z\log|w|)(z)>-\infty$, where $p_z=\frac{1}{2}v(dd^c(\psi),z)$ and $w$ is a local coordinate on a neighborhood of $z$ satisfying that $w(z)=0$.
If there exists $t_1\ge T$ such that $G(t_1)\in(0,+\infty)$ and $G(h^{-1}(r))$ is linear with respect to $r\in(0,\int_T^{+\infty}c(s)e^{-s}ds)$, then the following statements hold:
$(1)$ $\varphi+\psi=2\log|g|+2\log|F|$ on $\{\Psi<-T\}\cup Z'_1$, $J_{z}=I(\varphi+\Psi)_z$ for any $z\in Z'_1$ and there exists a holomorphic $(1,0)$ form $f_1$ on $(\{\Psi<-t_0\}\cap V)\cup Z'_1$ such that $f_1=f$ on $\{\Psi<-t_0\}\cap V$, where $g$ is a holomorphic function on $\{\Psi<-T\}\cup Z'_1$ such that $ord_z(g)=ord_z(f_1)+1$ for any $z\in Z'_1$;
$(2)$ $\{z\in Z_1:v(dd^c(\psi),z)>2ord_z(F)\}\not=\emptyset$ and $\psi=2\sum_{ z\in Z'_1}p_zG_{\Omega_t}(\cdot, z)+2\log|F|-t$ on $\{\Psi<-t\}\cup Z'_1$ for any $t>T$, where $\Omega_t=\{\Psi<-t\}\cup Z'_1$ and $G_{\Omega_t}(\cdot, z)$ is the Green function on $\Omega_t$;
$(3)$ $\frac{p_z}{ord_{z}(g)}\lim_{z'\rightarrow z}\frac{dg(z')}{f(z')}=c_0$ for any $z\in Z'_1$, where $c_0\in\mathbb{C}\backslash\{0\}$ is a constant independent of $z\in Z'_1$.
$(4)$ $\sum_{z\in Z'_1}p_z<+\infty$.
\end{Proposition}
\begin{proof}
It follows from Remark \ref{rem:linear} that
we can assume that $c(t)\ge \frac{e^t}{t^2}$ near $+\infty$.
We prove Proposition \ref{p:n-linearity1} in three steps.
\
\emph{Step 1. $H_z=I(\varphi+\Psi)_z$ for any $z\in Z_2$.}
\
Fixed any $z_0\in Z_2$, the following remark shows that we can assume that $v(dd^c(\psi),z_0)+v(dd^c(\varphi+\psi),z_0)\not\in\mathbb{Z}$ and $c(t)\ge1$ near $+\infty$.
\begin{Remark}
\label{r:not integer}
Let $a\in(0,1)$. Let $\tilde\varphi=\varphi+a(\psi-2\log|F|)$ and $\tilde\psi=(1-a)\psi+2a\log|F|$. Denote that $\tilde\Psi:=\min\{\tilde\psi-2\log| F|,(1-a)T\}=(1-a)\Psi$.
Let $\tilde c(t)=c\left(\frac{t}{1-a}\right)e^{-\frac{at}{1-a}}$ be a function on $((1-a)T,+\infty)$, and we have $\tilde c(t)\ge 1$ near $+\infty$. It is clear that $\tilde\psi$ and $\tilde\varphi+\tilde\psi=\varphi+\psi$ are subharmonic functions.
Note that $e^{-\tilde\varphi}\tilde c(-\tilde\Psi)=e^{-\varphi-a(\psi-2\log|F|)}c(-\Psi)e^{a\Psi}=e^{-\varphi}c(-\Psi)$ on $\{\Psi<-T\}$, $\varphi+\Psi=\tilde\varphi+\tilde\Psi$ on $\{\Psi<-t\}$ and $\tilde c(t)e^{-t}=c\left(\frac{t}{1-a}\right)e^{-\frac{t}{1-a}}$.
As $z_0\in Z_2=\{z\in Z_0:2ord_{z}(F)>v(dd^c(\psi),z)\}$, we can choose $a\in(0,1)$ such that $v(dd^c(\tilde\psi),z_0)+v(dd^c(\tilde\varphi+\tilde\psi),z_0)=v(dd^c(\psi),z_0)+v(dd^c(\varphi+\psi),z_0)+a(2ord_{z_0}(F)-v(dd^c(\psi),z_0))\not\in \mathbb{Z}$.
\end{Remark}
Denote that $\Psi_1:=\min\{\Psi,T_0\}$ and $\varphi_1:=2\max\{\psi+T_0,2\log|F|\}$, where $T_0>T$. Note that $I(\varphi+\Psi)_{z_0}=I(\varphi+\Psi_1)_{z_0}$ and $\frac{1}{2}\varphi_1+\Psi=\psi$. It follows from Proposition \ref{module isomorphism} that $H_{z_0} =I(\varphi+\Psi_1)_{z_0}$ if and only if $\mathcal{H}_{z_0}=\mathcal{I}(\varphi+\Psi_1+\varphi_1)_{z_0}$, where $\mathcal{H}_{z_0}:=\{(h,z_0)\in\mathcal{O}_{\Omega,z_0}:|h|^2e^{-\varphi-\varphi_1}c(-\Psi_1)$ is integrable near $z_0\}$.
Now, we prove $\mathcal{H}_{z_0}=\mathcal{I}(\varphi+\Psi_1+\varphi_1)_{z_0}$. Without loss of generality, we can assume that $\Omega=\Delta$ (the unit disc in $\mathbb{C}$) and $z_0=o$ (the origin). As $c(t)e^{-t}$ is decreasing, we have $\mathcal{I}(\varphi+\Psi_1+\varphi_1)_{o}\subset \mathcal{H}_{o}$. For any $(h,o)\in \mathcal{H}_o$, there exists $r_1>0$ such that $\int_{\Delta_{r_1}}|h|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty$, which implies that
\begin{equation}
\label{eq:0316a}\int_{\Delta_{r_1}}|h|^2e^{-\varphi-\varphi_1}<+\infty,
\end{equation}
where $\Delta_{r_1}=\{z\in\mathbb{C}:|z|<r_1\}$.
Denote that $x_1:=v(dd^c(\psi),o)$ and $x_2:=v(dd^c(\varphi+\psi),o)$. It follows from Siu's Decomposition Theorem that
\begin{equation}
\label{eq:0316b}\psi=x_1\log|w|+\tilde\psi,
\end{equation}
where $\tilde\psi$ is a subharmonic function on $\Delta$ satisfying that $v(dd^c(\tilde\psi),o)=0$. As $v(dd^c(\psi),o)<2ord_o(F)$, we have
\begin{equation}
\label{eq:0316c}\psi\le\frac{1}{2}\varphi_1=\max\{\psi+T_0,2\log|F|\}\le x_1\log|w|+C_1
\end{equation}
near $o$, where $C_1$ is a constant, which implies that $v(dd^c(\frac{1}{2}\varphi_1),o)=x_1$. As $x_2=v(dd^c(\varphi+\psi),o)$, we have
\begin{equation}
\label{eq:0316d}\varphi+\psi\le x_2\log|w|+C_2
\end{equation}
near $o$, where $C_2$ is a constant. Denote that $k:=ord_o(h)$.
Combining inequality \eqref{eq:0316a}, equality \eqref{eq:0316b}, inequality \eqref{eq:0316c} and inequality \eqref{eq:0316d}, we get that there exists $r_2\in(0,r_1)$ such that
\begin{equation}
\label{eq:0316e}
\begin{split}
&\int_{\Delta_{r_2}}|w|^{2k-x_1-x_2}e^{\tilde\psi}\\
\le &C_3\int_{\Delta_{r_2}}|h|^2e^{-\frac{1}{2}\varphi_1-\varphi-\psi+\tilde\psi}\\
=&C_3\int_{\Delta_{r_2}}|h|^2e^{-\frac{1}{2}\varphi_1-\varphi-x_1\log|w|}\\
\le&C_3e^{C_1}\int_{\Delta_{r_2}}|h|^2e^{-\varphi-\varphi_1}\\
<&+\infty.
\end{split}
\end{equation}
For any $p>1$, as $v(dd^c(\tilde\psi),o)=0$, it follows from lemma \ref{l:skoda} that there exists $r_3\in(0,r_2)$ such that $\int_{\Delta_{r_3}}e^{-\frac{q}{p}\tilde\psi}<+\infty$, where $\frac{1}{p}+\frac{1}{q}=1$.
It follows from inequality \eqref{eq:0316e} and H\"older inequality that
\begin{equation}
\label{eq:0316f}
\begin{split}
&\int_{\Delta_{r_3}}|w|^{\frac{2k-x_1-x_2}{p}}\\
\le&\left(\int_{\Delta_{r_3}}|w|^{2k-x_1-x_2}e^{\tilde\psi}\right)^{\frac{1}{p}}\left(\int_{\Delta_{r_3}}e^{-\frac{q}{p}\tilde\psi}\right)^{\frac{1}{q}}\\
<&+\infty,
\end{split}
\end{equation}
which shows that $|w|^{\frac{2k-x_1-x_2}{p}}$ is integrable near $o$ for any $p>1$.
As $x_1+x_2=v(dd^c(\psi),o)+v(dd^c(\varphi+\psi),o)\not\in \mathbb{Z}$, we have $|w|^{2k-x_1-x_2}$ is integrable near $o$. Note that $v(dd^c(\varphi+\Psi_1+\varphi_1),o)=v(dd^c(\varphi+\psi+\frac{1}{2}\varphi_1),o)=x_1+x_2$. It follows from Lemma \ref{l:1d-MIS} that $(w^k,o)\in\mathcal{I}(\varphi+\Psi_1+\varphi_1)_o$, which shows that $(h,o)\in\mathcal{I}(\varphi+\Psi_1+\varphi_1)_o$. We obtain that $\mathcal{H}_{o}=\mathcal{I}(\varphi+\Psi_1+\varphi_1)_{o}.$
Thus, we have $H_z=I(\varphi+\Psi)_z$ for any $z\in Z_2$.
\
\emph{Step 2. $H_z=I(\varphi+\Psi)_z$ for any $z\in Z_1\backslash Z'_1$.}
\
Let $z_0\in Z_1\backslash Z'_1$, where $Z'_1=\{z\in Z_0:v(dd^c(\psi),z)>2ord_{z}(F)\}$. We have $v(dd^c(\psi),z_0)=2ord_{z_0}(F)$. Denote that $\Psi_1:=\min\{\Psi,T_0\}$ and $\varphi_1:=2\max\{\psi+T_0,2\log|F|\}$, where $T_0>T$. Note that $I(\varphi+\Psi)_{z_0}=I(\varphi+\Psi_1)_{z_0}$ and $\frac{1}{2}\varphi_1+\Psi=\psi$. It follows from Proposition \ref{module isomorphism} that $H_{z_0} =I(\varphi+\Psi_1)_{z_0}$ if and only if $\mathcal{H}_{z_0}=\mathcal{I}(\varphi+\Psi_1+\varphi_1)_{z_0}$, where $\mathcal{H}_{z_0}:=\{(h,z_0)\in\mathcal{O}_{\Omega,z_0}:|h|^2e^{-\varphi-\varphi_1}c(-\Psi_1)$ is integrable near $z_0\}$. As $c(t)e^{-t}$ is decreasing, we have $\mathcal{I}(\varphi+\Psi_1+\varphi_1)_{z_0}\subset \mathcal{H}_{z_0}$.
Thus, it suffices to prove $\mathcal{H}_{z_0}\subset \mathcal{I}(\varphi+\Psi_1+\varphi_1)_{z_0}$.
Without loss of generality, we can assume that $\Omega=\Delta$ (the unit disc in $\mathbb{C}$) and $z_0=o$ (the origin). Denote that $x_1:=v(dd^c(\psi),o)$ and $x_2:=v(dd^c(\varphi+\psi),o)$.
Firstly, we prove $\mathcal{H}_{o}\subset \mathcal{I}(\varphi+\Psi_1+\varphi_1)_{o}$ under condition $(A)$ ($\varphi+a\psi$ is subharmonic near $o$ for some $a\in[0,1)$). For any $(h,o)\in\mathcal{H}_o$, as $c(t)\ge e^{at}$ near $+\infty$, we get that there exists $r_1\in(0,1)$ such that
\begin{equation}
\label{eq:0317a}\int_{\Delta_{r_1}}|h|^2e^{-\varphi-a\Psi_1-\varphi_1}\le C\int_{\Delta_{r_1}}|h|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty.
\end{equation}
Note that $\varphi+a\Psi_1+\varphi_1=\varphi+a\psi+(2-a)\max\{\psi,2\log|F|\}$ and $v(dd^c(\varphi+a\psi),o)=v(dd^c(\varphi+\psi),o)-(1-a)v(dd^c(\psi),o)=x_2-(1-a)x_1$. As $v(dd^c(\psi),o)=2ord_{o}(F)$, we have $v(dd^c(\varphi+a\Psi_1+\varphi_1),o)=x_2-(1-a)x_1+(2-a)x_1=x_2+x_1$. Denote that $k:=ord_o(h)$. Note that $v(dd^c(\varphi+\Psi_1+\varphi_1),o)=x_1+x_2$. It follows from inequality \eqref{eq:0317a} and Lemma \ref{l:1d-MIS} that $(h,o)\in\mathcal{I}(\varphi+\Psi_1+\varphi_1)_{o}$. Thus, $\mathcal{H}_{o}\subset \mathcal{I}(\varphi+\Psi_1+\varphi_1)_{o}$ holds under condition $(A)$.
Now, we prove $\mathcal{H}_{o}\subset \mathcal{I}(\varphi+\Psi_1+\varphi_1)_{o}$ under condition $(B)$ $\big((\psi-x_1\log|w|)(o)>-\infty\big)$. For any $(h,o)\in \mathcal{H}_o$, there exists $r_2>0$ such that $\int_{\Delta_{r_2}}|h|^2e^{-\varphi-\varphi_1}c(-\Psi_1)<+\infty$, which implies that
\begin{equation}
\label{eq:0317b}\int_{\Delta_{r_2}}|h|^2e^{-\varphi-\varphi_1}<+\infty.
\end{equation} It follows from Siu's Decomposition Theorem that
\begin{equation*}
\psi=x_1\log|w|+\tilde\psi,
\end{equation*}
where $\tilde\psi$ is a subharmonic function on $\Delta$ satisfying that $v(dd^c(\tilde\psi),o)=0$.
Note that $\tilde\psi(o)>-\infty$ and $\varphi+\varphi_1\le \varphi+2x_1\log|w|+C_1=\varphi+\psi-\tilde\psi+x_1\log|w|\le (x_1+x_2)\log|w|-\tilde\psi+C_2$ near $o$, where $C_1$ and $C_2$ are constants. Denote that $k:=ord_o(h)$. Note that $e^{\tilde\psi}$ is subharmonic, then it follows from inequality \eqref{eq:0317b} and the sub-mean value inequality that there exists $r_3\in(0,r_2)$ such that
\begin{equation}
\label{eq:0317c}
\begin{split}
&\int_{\Delta_{r_3}}|w|^{2k-x_1-x_2}\\
=&2\pi\int_0^{r_3}r^{2k+1-x_1-x_2}dr\\
\le& \frac{1}{e^{\tilde\psi(o)}}\int_0^{r_3}\int_{0}^{2\pi}r^{2k+1-x_1-x_2}e^{\tilde\psi(re^{i\theta})}d\theta dr\\
=&\frac{1}{e^{\tilde\psi(o)}}\int_{\Delta_{r_3}}|w|^{2k-x_1-x_2}e^{\tilde\psi}\\
\le&\frac{C}{e^{\tilde\psi(o)}}\int_{\Delta_{r_3}}|h|^2e^{-\varphi-\varphi_1}\\
<&+\infty.
\end{split}
\end{equation}
As $v(dd^c(\varphi+\Psi_1+\varphi_1),o)=x_1+x_2$, it follows from inequality \eqref{eq:0317c} and Lemma \ref{l:1d-MIS} that $(h,o)\in\mathcal{I}(\varphi+\Psi_1+\varphi_1)_{o}$. Thus, $\mathcal{H}_{o}\subset \mathcal{I}(\varphi+\Psi_1+\varphi_1)_{o}$ holds under condition $(B)$.
\
\emph{Step 3. The four statements hold.}
\
It follows from Lemma \ref{characterization of g(t)=0} that there exists a holomorphic $(1,0)$ form $f_{t_1}$ on $\{\Psi<-t_1\}$ such that $(f_{t_1}-f)_{z}\in\mathcal{O}(K_{\Omega})_z\otimes J_z$ for any $z\in Z_0$ and $\int_{\{\Psi<-t_1\}}|f_{t_1}|^2e^{-\varphi}c(-\Psi)<+\infty$, which implies that $(f_{t_1})_{z}\in\mathcal{O}(K_{\Omega})_z\otimes H_z$ for any $z\in Z_0$.
Note that $\{\Psi<-t\}\cup Z'_1$ is an open Riemann surface for any $t\ge T$ and there exists a subharmonic function $\psi_1$ on $\Omega_1=\{\Psi<-T\}\cup Z'_1$ such that $\psi_1+2\log|F|=\psi$.
For any $z_0\in Z'_1\backslash\{\Psi<-t_1\}$, we have $F(z_0)=0$. Note that $v(dd^c(\psi),z_0)>2ord_{z_0}(F)$, then $e^{-\varphi}c(-\Psi)$ has a positive lower bound on $V'\backslash\{z_0\}\subset\{\Psi<-t\}$, where $V'\Subset\Omega_1$ is a neighborhood of $z_0$. Following from $\int_{\{\Psi<-t_1\}}| f_{t_1}|^2e^{-\varphi}c(-\Psi)<+\infty$, we get that there exists a holomorphic $(1,0)$ form $\tilde f_{t_1}$ on $\{\psi_1<-t_1\}=\{\Psi<-t_1\}\cup Z'_1$ such that $\tilde f_{t_1}= f_{t_1}$ on $\{\Psi<-t_1\}$, which implies that $(\tilde f_{t_1}-f,z)\in\mathcal{O}(K_{\Omega})_z\otimes \mathcal{F}_z$ for any $z\in Z'_1$ and $(\tilde f_{t_1}-f)_z\in\mathcal{O}(K_{\Omega})_z\otimes J_z$ for any $z\in Z_0$. By the definition of $G(h^{-1}(r);c,\Psi,\varphi,J,f)$, we have $G(t;c,\Psi,\varphi,J,f)=G(t;c,\Psi,\varphi,J,\tilde f_{t_1})$ for any $t\ge T$. It follows from Lemma \ref{l:inner} and $H_z=I(\varphi+\Psi)_z$ for any $z\in Z_0\backslash Z'_1$ that $G_{\tilde f_{t_1}}(t)=G(h^{-1}(r);c,\Psi,\varphi,J,\tilde f_{t_1})$ for any $t\ge T$, which implies that $G_{\tilde f_{t_1}}(h^{-1}(r))$ is linear with respect to $r$.
As $G(t_1;c,\Psi,\varphi,J,\tilde f_{t_1})=G_{\tilde f_{t_1}}(t_1)\in(0,+\infty)$, we have $Z'_1=\{z\in Z_0:v(dd^c(\psi),z)>2ord_{z}(F)\}\not=\emptyset$. It follows from Proposition \ref{p:inner1}, Remark \ref{r:equivalent} and Proposition \ref{p:inner2} (replace $\Omega$, $\psi$ and $c(\cdot)$ by $\{\psi_1<-t\}=\{\Psi<-t\}\cup Z'_1$, $\psi_1+t$ and $c(\cdot+t)$ respectively, where $t>T$) that the following statements hold:
$(a)$ $\varphi+\psi_1=2\log|g|$ and $\mathcal{F}_z=\mathcal{I}(\varphi+\psi_1)_z$ for any $z\in Z'_1$, where $g$ is a holomorphic function on $\Omega_1= \{\Psi<-T\}\cup Z'_1$ such that $ord_z(g)=ord_z(\tilde f_{t_1})+1$ for any $z\in Z'_1$;
$(b)$ $\psi_1+t=2\sum_{z\in Z'_1}p_zG_{\Omega_t}(\cdot,z)$ on $\{\psi_1<-t\}$ for any $t>T$;
$(c)$ $\frac{p_z}{ord_z(g)}\lim_{z'\rightarrow z}\frac{dg(z')}{f_{\tilde t_1}(z')}=c_0$ for any $z\in Z'_1$, where $c_0\in\mathbb{C}\backslash\{0\}$ is a constant independent of $z\in Z'_1$;
$(d)$ $\sum_{z\in Z'_1}p_z<+\infty$.
It follows from $\mathcal{F}_z=\mathcal{I}(\varphi+\psi_1)_z$ for any $z\in Z'_1$ and $H_z=I(\varphi+\Psi)_z$ for any $z\in Z_0\backslash Z'_1$ that $J_z=I(\varphi+\Psi)_z$ for any $z\in Z_0$. Note that for any $z\in Z'_1$ and any $h_z\in H_z$, there exists a holomorphic extension $\tilde h$ of $h$ near $z$. As $(f_{t_1}-f)_z\in\mathcal{O}(K_{\Omega})_z\otimes J_z$ for any $z\in Z_0$ and $\tilde f_{t_1}$ is a holomorphic $(1,0)$ form on $\{\psi_1<-t_1\}$ such that $\tilde f_{t_1}=f_{t_1}$ on $\{\Psi<-t_1\}$, then there exists a holomorphic $(1,0)$ form $f_1$ on $(\{\Psi<-t_1\}\cap V)\cup Z'_1$ such that $f_1=f$ on $\{\Psi<-t_1\}\cap V$, which shows that $(\tilde f_{t_1}-f_1,z)\in\mathcal{O}(K_{\Omega})_z\otimes\mathcal{I}(2\log|g|)_z$ for any $z\in Z'_1$. $ord_z(g)=ord_z(\tilde f_{t_1})+1$ for any $z\in Z'_1$ implies that $ord_z(g)=ord_z(\tilde f_{1})+1$ for any $z\in Z'_1$.
Thus, the four statements in Proposition \ref{p:n-linearity1} hold.
\end{proof}
\section{Proof of Theorem \ref{thm:linearity1}}
The necessity of Theorem \ref{thm:linearity1} follows from Proposition \ref{p:n-linearity1}. In the following, we prove the sufficiency.
As $\psi=2\sum_{z\in Z'_1}p_zG_{\Omega_t}(\cdot,z)+2\log|F|-t$ on $\{\Psi<-t\}$, it follows from Lemma \ref{l:G-compact} that $$Z_0=Z_0\cap(\cap_{s>T}\overline{\{\Psi<-s\}})=Z'_1.$$ Note that $\{\Psi<-t\}\cup Z'_1$ is an open Riemann surface for any $t\ge T$ and there exists a subharmonic function $\psi_1$ on $\Omega_1=\{\Psi<-T\}\cup Z'_1$ such that $\psi_1=\psi-2\log|F|=2\sum_{z\in Z'_1}p_zG_{\Omega_t}(\cdot,z)-t$ for any $t>T$. Note that $f_1$ is a holomorphic $(1,0)$ form on $(\{\Psi<-t_0\}\cap V)\cup Z'_1$ such that $f_1=f$ on $\{\Psi<-t_0\}\cap V$. Following the definition of $G_{f_1}(t)$ in Section \ref{sec:n}, Lemma \ref{l:inner} shows that
$$G_{f_1}(t)=G(t)$$
for any $t\ge T$. It follows from Theorem \ref{thm:m-points} and Remark \ref{r:equivalent} (replace $\Omega$, $c(\cdot)$ and $\psi$ by $\{\psi_1<-t\}=\{\Psi<-t\}\cup Z'_1$, $c(\cdot+\tilde{t})$ and $\psi_1+\tilde{t}$ respectively, where $\tilde{t}>T$) that $G_{f_1}(h_{\tilde{t}}^{-1}(r)+\tilde{t})$ is linear with respect to $r\in (0,\int_{0}^{+\infty}c(s+\tilde{t})e^{-s}ds)$ for any $\tilde{t}> T$, where $h_{\tilde{t}}(t)=\int_t^{+\infty}c(s+\tilde{t})e^{-s}ds=e^{\tilde{t}}\int_{t+\tilde{t}}^{+\infty}c(s)e^{-s}ds=e^{\tilde{t}}h(t+\tilde{t})$. Note that $G(h^{-1}(r))=G_{f_1}(h^{-1}(r))=G_{f_1}(h_{\tilde{t}}^{-1}(e^{\tilde{t}}r)+\tilde{t})$ for any $r\in(0,\int_{\tilde{t}}^{+\infty}c(s)e^{-s}ds)$. Hence we have $G(h^{-1}(r))$ is linear with respect to $r\in (0,\int_{0}^{+\infty}c(s)e^{-s}ds)$.
Thus, Theorem \ref{thm:linearity1} holds.
\vspace{.1in} {\em Acknowledgements}.
The first author was supported by NSFC-11825101, NSFC-11522101 and NSFC-11431013.
\bibliographystyle{references}
| {
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} | 2,213 |
Вита́лий Андре́евич Соро́кин (25 ноября 1921, Орск, РСФСР — 14 ноября 1985, Орск, СССР) — советский военный лётчик, Герой Советского Союза.
Биография
Родился в семье служащего. Закончил десять классов. Учился в аэроклубе. В 1940 году призван в Красную Армию.
Учился в Оренбургской военно-авиационной школе пилотов, где освоил самолёт Пе-2.
На фронт в ходе Великой Отечественной войны попал в мае 1943 года. Служил в 24-м бомбардировочном авиаполку (241-я бомбардировочная авиационная дивизия). Первый боевой вылет совершил 10 июля 1943 года, успешно отбомбившись по вражеской технике.
Уже через два месяца за боевые заслуги был награждён орденом Красной Звезды. Виталий Сорокин вместе с полком участвовал в Орловско-Курской, Севской, Речицко-Гомельской, Калинковичско-Мозырьской и Бобруйской боевых операциях. Стал командиром звена.
11 марта 1945 года вместе со всем полком получил приказ — разбомбить хорошо защищённый опорный пункт обороны противника в районе Штеттина. Для Сорокина это был 74-й боевой вылет. При подлёте к цели в его самолёт попал снаряд, осколками Виталий был ранен: один из осколков попал в правую ногу, другим перебило ладонь правой руки, лишив лётчика трёх пальцев. Однако Сорокин не вышел из боя, довёл самолёт до заданной цели и отбомбился.
Управляя одной рукой и истекая кровью, с помощью штурмана 40 минут Виталий вёл самолёт до аэродрома и успешно его посадил, после этого потерял сознание. После выхода из госпиталя в 1946 году по состоянию здоровья уволился из вооружённых сил.
Вернувшись в Орск, закончил Орский нефтяной техникум, работал в заводоуправлении нефтеперерабатывающего завода имени Чкалова. За трудовые заслуги был награждён орденом.
Умер 14 ноября 1985 года. Его именем названа одна из улиц Орска.
Награды
Герой Советского Союза № 6148 (15 мая 1946 года);
орден Ленина (15 мая 1946);
орден Красного Знамени
орден Отечественной войны 1 степени;
орден Красной Звезды (1943);
орден «Знак Почёта»;
девять медалей.
Литература
Лукерченко М. Орск. Челябинск, Южно-Уральское книжное издательство, 1968. — 161 с. Стр. 98-102.
Секрет М. Г. Золотые Звёзды орчан. Орск. 1973. 52 стр. с ил. Стр 39.
Ссылки
История Орска: Сорокин Виталий Андреевич.
Лётчики Великой Отечественной войны
Почётные граждане Орска
Награждённые медалью «За взятие Берлина» | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,075 |
// [VexFlow](http://vexflow.com) - Copyright (c) Mohit Muthanna 2010.
/* eslint-disable key-spacing */
import { ArticulationStruct } from './articulation';
import { Fonts } from './font';
import { Fraction } from './fraction';
import { Glyph } from './glyph';
import { RuntimeError } from './util';
// Custom note heads
const customNoteHeads: Record<string, { code: string }> = {
/* Diamond */
D0: { code: 'noteheadDiamondWhole' },
D1: { code: 'noteheadDiamondHalf' },
D2: { code: 'noteheadDiamondBlack' },
D3: { code: 'noteheadDiamondBlack' },
/* Triangle */
T0: { code: 'noteheadTriangleUpWhole' },
T1: { code: 'noteheadTriangleUpHalf' },
T2: { code: 'noteheadTriangleUpBlack' },
T3: { code: 'noteheadTriangleUpBlack' },
/* Cross */
X0: { code: 'noteheadXWhole' },
X1: { code: 'noteheadXHalf' },
X2: { code: 'noteheadXBlack' },
X3: { code: 'noteheadCircleX' },
/* Square */
S1: { code: 'noteheadSquareWhite' },
S2: { code: 'noteheadSquareBlack' },
/* Rectangle */
R1: { code: 'vexNoteHeadRectWhite' }, // no smufl code
R2: { code: 'vexNoteHeadRectBlack' }, // no smufl code
};
const RESOLUTION = 16384;
const durations: Record<string, number> = {
'1/2': RESOLUTION * 2,
1: RESOLUTION / 1,
2: RESOLUTION / 2,
4: RESOLUTION / 4,
8: RESOLUTION / 8,
16: RESOLUTION / 16,
32: RESOLUTION / 32,
64: RESOLUTION / 64,
128: RESOLUTION / 128,
256: RESOLUTION / 256,
};
const accidentals: Record<string, { code: string; parenRightPaddingAdjustment: number }> = {
'#': { code: 'accidentalSharp', parenRightPaddingAdjustment: -1 },
'##': { code: 'accidentalDoubleSharp', parenRightPaddingAdjustment: -1 },
b: { code: 'accidentalFlat', parenRightPaddingAdjustment: -2 },
bb: { code: 'accidentalDoubleFlat', parenRightPaddingAdjustment: -2 },
n: { code: 'accidentalNatural', parenRightPaddingAdjustment: -1 },
'{': { code: 'accidentalParensLeft', parenRightPaddingAdjustment: -1 },
'}': { code: 'accidentalParensRight', parenRightPaddingAdjustment: -1 },
db: { code: 'accidentalThreeQuarterTonesFlatZimmermann', parenRightPaddingAdjustment: -1 },
d: { code: 'accidentalQuarterToneFlatStein', parenRightPaddingAdjustment: 0 },
'++': { code: 'accidentalThreeQuarterTonesSharpStein', parenRightPaddingAdjustment: -1 },
'+': { code: 'accidentalQuarterToneSharpStein', parenRightPaddingAdjustment: -1 },
'+-': { code: 'accidentalKucukMucennebSharp', parenRightPaddingAdjustment: -1 },
bs: { code: 'accidentalBakiyeFlat', parenRightPaddingAdjustment: -1 },
bss: { code: 'accidentalBuyukMucennebFlat', parenRightPaddingAdjustment: -1 },
o: { code: 'accidentalSori', parenRightPaddingAdjustment: -1 },
k: { code: 'accidentalKoron', parenRightPaddingAdjustment: -1 },
bbs: { code: 'vexAccidentalMicrotonal1', parenRightPaddingAdjustment: -1 },
'++-': { code: 'vexAccidentalMicrotonal2', parenRightPaddingAdjustment: -1 },
ashs: { code: 'vexAccidentalMicrotonal3', parenRightPaddingAdjustment: -1 },
afhf: { code: 'vexAccidentalMicrotonal4', parenRightPaddingAdjustment: -1 },
accSagittal5v7KleismaUp: { code: 'accSagittal5v7KleismaUp', parenRightPaddingAdjustment: -1 },
accSagittal5v7KleismaDown: { code: 'accSagittal5v7KleismaDown', parenRightPaddingAdjustment: -1 },
accSagittal5CommaUp: { code: 'accSagittal5CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal5CommaDown: { code: 'accSagittal5CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal7CommaUp: { code: 'accSagittal7CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal7CommaDown: { code: 'accSagittal7CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal25SmallDiesisUp: { code: 'accSagittal25SmallDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal25SmallDiesisDown: { code: 'accSagittal25SmallDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal35MediumDiesisUp: { code: 'accSagittal35MediumDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal35MediumDiesisDown: { code: 'accSagittal35MediumDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal11MediumDiesisUp: { code: 'accSagittal11MediumDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal11MediumDiesisDown: { code: 'accSagittal11MediumDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal11LargeDiesisUp: { code: 'accSagittal11LargeDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal11LargeDiesisDown: { code: 'accSagittal11LargeDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal35LargeDiesisUp: { code: 'accSagittal35LargeDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal35LargeDiesisDown: { code: 'accSagittal35LargeDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp25SDown: { code: 'accSagittalSharp25SDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat25SUp: { code: 'accSagittalFlat25SUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp7CDown: { code: 'accSagittalSharp7CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat7CUp: { code: 'accSagittalFlat7CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp5CDown: { code: 'accSagittalSharp5CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat5CUp: { code: 'accSagittalFlat5CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v7kDown: { code: 'accSagittalSharp5v7kDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v7kUp: { code: 'accSagittalFlat5v7kUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp: { code: 'accSagittalSharp', parenRightPaddingAdjustment: -1 },
accSagittalFlat: { code: 'accSagittalFlat', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v7kUp: { code: 'accSagittalSharp5v7kUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v7kDown: { code: 'accSagittalFlat5v7kDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp5CUp: { code: 'accSagittalSharp5CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat5CDown: { code: 'accSagittalFlat5CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp7CUp: { code: 'accSagittalSharp7CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat7CDown: { code: 'accSagittalFlat7CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp25SUp: { code: 'accSagittalSharp25SUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat25SDown: { code: 'accSagittalFlat25SDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp35MUp: { code: 'accSagittalSharp35MUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat35MDown: { code: 'accSagittalFlat35MDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp11MUp: { code: 'accSagittalSharp11MUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat11MDown: { code: 'accSagittalFlat11MDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp11LUp: { code: 'accSagittalSharp11LUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat11LDown: { code: 'accSagittalFlat11LDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp35LUp: { code: 'accSagittalSharp35LUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat35LDown: { code: 'accSagittalFlat35LDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp25SDown: { code: 'accSagittalDoubleSharp25SDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat25SUp: { code: 'accSagittalDoubleFlat25SUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp7CDown: { code: 'accSagittalDoubleSharp7CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat7CUp: { code: 'accSagittalDoubleFlat7CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp5CDown: { code: 'accSagittalDoubleSharp5CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat5CUp: { code: 'accSagittalDoubleFlat5CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp5v7kDown: { code: 'accSagittalDoubleSharp5v7kDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat5v7kUp: { code: 'accSagittalDoubleFlat5v7kUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp: { code: 'accSagittalDoubleSharp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat: { code: 'accSagittalDoubleFlat', parenRightPaddingAdjustment: -1 },
accSagittal7v11KleismaUp: { code: 'accSagittal7v11KleismaUp', parenRightPaddingAdjustment: -1 },
accSagittal7v11KleismaDown: { code: 'accSagittal7v11KleismaDown', parenRightPaddingAdjustment: -1 },
accSagittal17CommaUp: { code: 'accSagittal17CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal17CommaDown: { code: 'accSagittal17CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal55CommaUp: { code: 'accSagittal55CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal55CommaDown: { code: 'accSagittal55CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal7v11CommaUp: { code: 'accSagittal7v11CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal7v11CommaDown: { code: 'accSagittal7v11CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal5v11SmallDiesisUp: { code: 'accSagittal5v11SmallDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal5v11SmallDiesisDown: { code: 'accSagittal5v11SmallDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v11SDown: { code: 'accSagittalSharp5v11SDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v11SUp: { code: 'accSagittalFlat5v11SUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp7v11CDown: { code: 'accSagittalSharp7v11CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat7v11CUp: { code: 'accSagittalFlat7v11CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp55CDown: { code: 'accSagittalSharp55CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat55CUp: { code: 'accSagittalFlat55CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp17CDown: { code: 'accSagittalSharp17CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat17CUp: { code: 'accSagittalFlat17CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp7v11kDown: { code: 'accSagittalSharp7v11kDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat7v11kUp: { code: 'accSagittalFlat7v11kUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp7v11kUp: { code: 'accSagittalSharp7v11kUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat7v11kDown: { code: 'accSagittalFlat7v11kDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp17CUp: { code: 'accSagittalSharp17CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat17CDown: { code: 'accSagittalFlat17CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp55CUp: { code: 'accSagittalSharp55CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat55CDown: { code: 'accSagittalFlat55CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp7v11CUp: { code: 'accSagittalSharp7v11CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat7v11CDown: { code: 'accSagittalFlat7v11CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v11SUp: { code: 'accSagittalSharp5v11SUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v11SDown: { code: 'accSagittalFlat5v11SDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp5v11SDown: { code: 'accSagittalDoubleSharp5v11SDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat5v11SUp: { code: 'accSagittalDoubleFlat5v11SUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp7v11CDown: { code: 'accSagittalDoubleSharp7v11CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat7v11CUp: { code: 'accSagittalDoubleFlat7v11CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp55CDown: { code: 'accSagittalDoubleSharp55CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat55CUp: { code: 'accSagittalDoubleFlat55CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp17CDown: { code: 'accSagittalDoubleSharp17CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat17CUp: { code: 'accSagittalDoubleFlat17CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp7v11kDown: { code: 'accSagittalDoubleSharp7v11kDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat7v11kUp: { code: 'accSagittalDoubleFlat7v11kUp', parenRightPaddingAdjustment: -1 },
accSagittal23CommaUp: { code: 'accSagittal23CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal23CommaDown: { code: 'accSagittal23CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal5v19CommaUp: { code: 'accSagittal5v19CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal5v19CommaDown: { code: 'accSagittal5v19CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal5v23SmallDiesisUp: { code: 'accSagittal5v23SmallDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal5v23SmallDiesisDown: { code: 'accSagittal5v23SmallDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v23SDown: { code: 'accSagittalSharp5v23SDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v23SUp: { code: 'accSagittalFlat5v23SUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v19CDown: { code: 'accSagittalSharp5v19CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v19CUp: { code: 'accSagittalFlat5v19CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp23CDown: { code: 'accSagittalSharp23CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat23CUp: { code: 'accSagittalFlat23CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp23CUp: { code: 'accSagittalSharp23CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat23CDown: { code: 'accSagittalFlat23CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v19CUp: { code: 'accSagittalSharp5v19CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v19CDown: { code: 'accSagittalFlat5v19CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v23SUp: { code: 'accSagittalSharp5v23SUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v23SDown: { code: 'accSagittalFlat5v23SDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp5v23SDown: { code: 'accSagittalDoubleSharp5v23SDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat5v23SUp: { code: 'accSagittalDoubleFlat5v23SUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp5v19CDown: { code: 'accSagittalDoubleSharp5v19CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat5v19CUp: { code: 'accSagittalDoubleFlat5v19CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp23CDown: { code: 'accSagittalDoubleSharp23CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat23CUp: { code: 'accSagittalDoubleFlat23CUp', parenRightPaddingAdjustment: -1 },
accSagittal19SchismaUp: { code: 'accSagittal19SchismaUp', parenRightPaddingAdjustment: -1 },
accSagittal19SchismaDown: { code: 'accSagittal19SchismaDown', parenRightPaddingAdjustment: -1 },
accSagittal17KleismaUp: { code: 'accSagittal17KleismaUp', parenRightPaddingAdjustment: -1 },
accSagittal17KleismaDown: { code: 'accSagittal17KleismaDown', parenRightPaddingAdjustment: -1 },
accSagittal143CommaUp: { code: 'accSagittal143CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal143CommaDown: { code: 'accSagittal143CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal11v49CommaUp: { code: 'accSagittal11v49CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal11v49CommaDown: { code: 'accSagittal11v49CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal19CommaUp: { code: 'accSagittal19CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal19CommaDown: { code: 'accSagittal19CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal7v19CommaUp: { code: 'accSagittal7v19CommaUp', parenRightPaddingAdjustment: -1 },
accSagittal7v19CommaDown: { code: 'accSagittal7v19CommaDown', parenRightPaddingAdjustment: -1 },
accSagittal49SmallDiesisUp: { code: 'accSagittal49SmallDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal49SmallDiesisDown: { code: 'accSagittal49SmallDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal23SmallDiesisUp: { code: 'accSagittal23SmallDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal23SmallDiesisDown: { code: 'accSagittal23SmallDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal5v13MediumDiesisUp: { code: 'accSagittal5v13MediumDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal5v13MediumDiesisDown: { code: 'accSagittal5v13MediumDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal11v19MediumDiesisUp: { code: 'accSagittal11v19MediumDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal11v19MediumDiesisDown: { code: 'accSagittal11v19MediumDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal49MediumDiesisUp: { code: 'accSagittal49MediumDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal49MediumDiesisDown: { code: 'accSagittal49MediumDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal5v49MediumDiesisUp: { code: 'accSagittal5v49MediumDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal5v49MediumDiesisDown: { code: 'accSagittal5v49MediumDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal49LargeDiesisUp: { code: 'accSagittal49LargeDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal49LargeDiesisDown: { code: 'accSagittal49LargeDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal11v19LargeDiesisUp: { code: 'accSagittal11v19LargeDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal11v19LargeDiesisDown: { code: 'accSagittal11v19LargeDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittal5v13LargeDiesisUp: { code: 'accSagittal5v13LargeDiesisUp', parenRightPaddingAdjustment: -1 },
accSagittal5v13LargeDiesisDown: { code: 'accSagittal5v13LargeDiesisDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp23SDown: { code: 'accSagittalSharp23SDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat23SUp: { code: 'accSagittalFlat23SUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp49SDown: { code: 'accSagittalSharp49SDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat49SUp: { code: 'accSagittalFlat49SUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp7v19CDown: { code: 'accSagittalSharp7v19CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat7v19CUp: { code: 'accSagittalFlat7v19CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp19CDown: { code: 'accSagittalSharp19CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat19CUp: { code: 'accSagittalFlat19CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp11v49CDown: { code: 'accSagittalSharp11v49CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat11v49CUp: { code: 'accSagittalFlat11v49CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp143CDown: { code: 'accSagittalSharp143CDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat143CUp: { code: 'accSagittalFlat143CUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp17kDown: { code: 'accSagittalSharp17kDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat17kUp: { code: 'accSagittalFlat17kUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp19sDown: { code: 'accSagittalSharp19sDown', parenRightPaddingAdjustment: -1 },
accSagittalFlat19sUp: { code: 'accSagittalFlat19sUp', parenRightPaddingAdjustment: -1 },
accSagittalSharp19sUp: { code: 'accSagittalSharp19sUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat19sDown: { code: 'accSagittalFlat19sDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp17kUp: { code: 'accSagittalSharp17kUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat17kDown: { code: 'accSagittalFlat17kDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp143CUp: { code: 'accSagittalSharp143CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat143CDown: { code: 'accSagittalFlat143CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp11v49CUp: { code: 'accSagittalSharp11v49CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat11v49CDown: { code: 'accSagittalFlat11v49CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp19CUp: { code: 'accSagittalSharp19CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat19CDown: { code: 'accSagittalFlat19CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp7v19CUp: { code: 'accSagittalSharp7v19CUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat7v19CDown: { code: 'accSagittalFlat7v19CDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp49SUp: { code: 'accSagittalSharp49SUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat49SDown: { code: 'accSagittalFlat49SDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp23SUp: { code: 'accSagittalSharp23SUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat23SDown: { code: 'accSagittalFlat23SDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v13MUp: { code: 'accSagittalSharp5v13MUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v13MDown: { code: 'accSagittalFlat5v13MDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp11v19MUp: { code: 'accSagittalSharp11v19MUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat11v19MDown: { code: 'accSagittalFlat11v19MDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp49MUp: { code: 'accSagittalSharp49MUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat49MDown: { code: 'accSagittalFlat49MDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v49MUp: { code: 'accSagittalSharp5v49MUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v49MDown: { code: 'accSagittalFlat5v49MDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp49LUp: { code: 'accSagittalSharp49LUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat49LDown: { code: 'accSagittalFlat49LDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp11v19LUp: { code: 'accSagittalSharp11v19LUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat11v19LDown: { code: 'accSagittalFlat11v19LDown', parenRightPaddingAdjustment: -1 },
accSagittalSharp5v13LUp: { code: 'accSagittalSharp5v13LUp', parenRightPaddingAdjustment: -1 },
accSagittalFlat5v13LDown: { code: 'accSagittalFlat5v13LDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp23SDown: { code: 'accSagittalDoubleSharp23SDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat23SUp: { code: 'accSagittalDoubleFlat23SUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp49SDown: { code: 'accSagittalDoubleSharp49SDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat49SUp: { code: 'accSagittalDoubleFlat49SUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp7v19CDown: { code: 'accSagittalDoubleSharp7v19CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat7v19CUp: { code: 'accSagittalDoubleFlat7v19CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp19CDown: { code: 'accSagittalDoubleSharp19CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat19CUp: { code: 'accSagittalDoubleFlat19CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp11v49CDown: { code: 'accSagittalDoubleSharp11v49CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat11v49CUp: { code: 'accSagittalDoubleFlat11v49CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp143CDown: { code: 'accSagittalDoubleSharp143CDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat143CUp: { code: 'accSagittalDoubleFlat143CUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp17kDown: { code: 'accSagittalDoubleSharp17kDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat17kUp: { code: 'accSagittalDoubleFlat17kUp', parenRightPaddingAdjustment: -1 },
accSagittalDoubleSharp19sDown: { code: 'accSagittalDoubleSharp19sDown', parenRightPaddingAdjustment: -1 },
accSagittalDoubleFlat19sUp: { code: 'accSagittalDoubleFlat19sUp', parenRightPaddingAdjustment: -1 },
accSagittalShaftUp: { code: 'accSagittalShaftUp', parenRightPaddingAdjustment: -1 },
accSagittalShaftDown: { code: 'accSagittalShaftDown', parenRightPaddingAdjustment: -1 },
accSagittalAcute: { code: 'accSagittalAcute', parenRightPaddingAdjustment: -1 },
accSagittalGrave: { code: 'accSagittalGrave', parenRightPaddingAdjustment: -1 },
accSagittal1MinaUp: { code: 'accSagittal1MinaUp', parenRightPaddingAdjustment: -1 },
accSagittal1MinaDown: { code: 'accSagittal1MinaDown', parenRightPaddingAdjustment: -1 },
accSagittal2MinasUp: { code: 'accSagittal2MinasUp', parenRightPaddingAdjustment: -1 },
accSagittal2MinasDown: { code: 'accSagittal2MinasDown', parenRightPaddingAdjustment: -1 },
accSagittal1TinaUp: { code: 'accSagittal1TinaUp', parenRightPaddingAdjustment: -1 },
accSagittal1TinaDown: { code: 'accSagittal1TinaDown', parenRightPaddingAdjustment: -1 },
accSagittal2TinasUp: { code: 'accSagittal2TinasUp', parenRightPaddingAdjustment: -1 },
accSagittal2TinasDown: { code: 'accSagittal2TinasDown', parenRightPaddingAdjustment: -1 },
accSagittal3TinasUp: { code: 'accSagittal3TinasUp', parenRightPaddingAdjustment: -1 },
accSagittal3TinasDown: { code: 'accSagittal3TinasDown', parenRightPaddingAdjustment: -1 },
accSagittal4TinasUp: { code: 'accSagittal4TinasUp', parenRightPaddingAdjustment: -1 },
accSagittal4TinasDown: { code: 'accSagittal4TinasDown', parenRightPaddingAdjustment: -1 },
accSagittal5TinasUp: { code: 'accSagittal5TinasUp', parenRightPaddingAdjustment: -1 },
accSagittal5TinasDown: { code: 'accSagittal5TinasDown', parenRightPaddingAdjustment: -1 },
accSagittal6TinasUp: { code: 'accSagittal6TinasUp', parenRightPaddingAdjustment: -1 },
accSagittal6TinasDown: { code: 'accSagittal6TinasDown', parenRightPaddingAdjustment: -1 },
accSagittal7TinasUp: { code: 'accSagittal7TinasUp', parenRightPaddingAdjustment: -1 },
accSagittal7TinasDown: { code: 'accSagittal7TinasDown', parenRightPaddingAdjustment: -1 },
accSagittal8TinasUp: { code: 'accSagittal8TinasUp', parenRightPaddingAdjustment: -1 },
accSagittal8TinasDown: { code: 'accSagittal8TinasDown', parenRightPaddingAdjustment: -1 },
accSagittal9TinasUp: { code: 'accSagittal9TinasUp', parenRightPaddingAdjustment: -1 },
accSagittal9TinasDown: { code: 'accSagittal9TinasDown', parenRightPaddingAdjustment: -1 },
accSagittalFractionalTinaUp: { code: 'accSagittalFractionalTinaUp', parenRightPaddingAdjustment: -1 },
accSagittalFractionalTinaDown: { code: 'accSagittalFractionalTinaDown', parenRightPaddingAdjustment: -1 },
accidentalNarrowReversedFlat: { code: 'accidentalNarrowReversedFlat', parenRightPaddingAdjustment: -1 },
accidentalNarrowReversedFlatAndFlat: {
code: 'accidentalNarrowReversedFlatAndFlat',
parenRightPaddingAdjustment: -1,
},
accidentalWilsonPlus: { code: 'accidentalWilsonPlus', parenRightPaddingAdjustment: -1 },
accidentalWilsonMinus: { code: 'accidentalWilsonMinus', parenRightPaddingAdjustment: -1 },
};
export const Tables = {
STEM_WIDTH: 1.5,
STEM_HEIGHT: 35,
STAVE_LINE_THICKNESS: 1,
RESOLUTION: RESOLUTION,
/**
* Customize this to choose a different music font.
* For example: Vex.Flow.DEFAULT_FONT_STACK = [Fonts.Petaluma(), Fonts.Custom()];
*/
DEFAULT_FONT_STACK: [Fonts.Bravura(), Fonts.Gonville(), Fonts.Custom()],
DEFAULT_NOTATION_FONT_SCALE: 39,
DEFAULT_TABLATURE_FONT_SCALE: 39,
SLASH_NOTEHEAD_WIDTH: 15,
STAVE_LINE_DISTANCE: 10,
// HACK:
// Since text origins are positioned at the baseline, we must
// compensate for the ascender of the text. Of course, 1 staff space is
// a very poor approximation.
//
// This will be deprecated in the future. This is a temporary solution until
// we have more robust text metrics.
TEXT_HEIGHT_OFFSET_HACK: 1,
/* Kerning (DEPRECATED) */
IsKerned: true,
clefProperties: (clef: string): { line_shift: number } => {
const values: Record<string, { line_shift: number }> = {
treble: { line_shift: 0 },
bass: { line_shift: 6 },
tenor: { line_shift: 4 },
alto: { line_shift: 3 },
soprano: { line_shift: 1 },
percussion: { line_shift: 0 },
'mezzo-soprano': { line_shift: 2 },
'baritone-c': { line_shift: 5 },
'baritone-f': { line_shift: 5 },
subbass: { line_shift: 7 },
french: { line_shift: -1 },
};
if (!clef) throw new RuntimeError('BadArgument', 'Invalid clef: ' + clef);
const props = values[clef];
if (!props) throw new RuntimeError('BadArgument', 'Invalid clef: ' + clef);
return props;
},
/*
Take a note in the format "Key/Octave" (e.g., "C/5") and return properties.
The last argument, params, is a struct the currently can contain one option,
octave_shift for clef ottavation (0 = default; 1 = 8va; -1 = 8vb, etc.).
*/
// eslint-disable-next-line
keyProperties(key: string, clef?: string, params?: any): any {
const noteValues: Record<
string,
{
index: number;
int_val?: number;
accidental?: string;
rest?: boolean;
octave?: number;
code?: string;
shift_right?: number;
}
> = {
C: { index: 0, int_val: 0 },
CN: { index: 0, int_val: 0, accidental: 'n' },
'C#': { index: 0, int_val: 1, accidental: '#' },
'C##': { index: 0, int_val: 2, accidental: '##' },
CB: { index: 0, int_val: 11, accidental: 'b' },
CBB: { index: 0, int_val: 10, accidental: 'bb' },
D: { index: 1, int_val: 2 },
DN: { index: 1, int_val: 2, accidental: 'n' },
'D#': { index: 1, int_val: 3, accidental: '#' },
'D##': { index: 1, int_val: 4, accidental: '##' },
DB: { index: 1, int_val: 1, accidental: 'b' },
DBB: { index: 1, int_val: 0, accidental: 'bb' },
E: { index: 2, int_val: 4 },
EN: { index: 2, int_val: 4, accidental: 'n' },
'E#': { index: 2, int_val: 5, accidental: '#' },
'E##': { index: 2, int_val: 6, accidental: '##' },
EB: { index: 2, int_val: 3, accidental: 'b' },
EBB: { index: 2, int_val: 2, accidental: 'bb' },
F: { index: 3, int_val: 5 },
FN: { index: 3, int_val: 5, accidental: 'n' },
'F#': { index: 3, int_val: 6, accidental: '#' },
'F##': { index: 3, int_val: 7, accidental: '##' },
FB: { index: 3, int_val: 4, accidental: 'b' },
FBB: { index: 3, int_val: 3, accidental: 'bb' },
G: { index: 4, int_val: 7 },
GN: { index: 4, int_val: 7, accidental: 'n' },
'G#': { index: 4, int_val: 8, accidental: '#' },
'G##': { index: 4, int_val: 9, accidental: '##' },
GB: { index: 4, int_val: 6, accidental: 'b' },
GBB: { index: 4, int_val: 5, accidental: 'bb' },
A: { index: 5, int_val: 9 },
AN: { index: 5, int_val: 9, accidental: 'n' },
'A#': { index: 5, int_val: 10, accidental: '#' },
'A##': { index: 5, int_val: 11, accidental: '##' },
AB: { index: 5, int_val: 8, accidental: 'b' },
ABB: { index: 5, int_val: 7, accidental: 'bb' },
B: { index: 6, int_val: 11 },
BN: { index: 6, int_val: 11, accidental: 'n' },
'B#': { index: 6, int_val: 12, accidental: '#' },
'B##': { index: 6, int_val: 13, accidental: '##' },
BB: { index: 6, int_val: 10, accidental: 'b' },
BBB: { index: 6, int_val: 9, accidental: 'bb' },
R: { index: 6, rest: true }, // Rest
X: {
index: 6,
accidental: '',
octave: 4,
code: 'noteheadXBlack',
shift_right: 5.5,
},
};
if (clef === undefined) {
clef = 'treble';
}
let options = { octave_shift: 0 };
if (typeof params === 'object') {
options = { ...options, ...params };
}
const pieces = key.split('/');
if (pieces.length < 2) {
throw new RuntimeError('BadArguments', `Key must have note + octave and an optional glyph: ${key}`);
}
const k = pieces[0].toUpperCase();
const value = noteValues[k];
if (!value) throw new RuntimeError('BadArguments', 'Invalid key name: ' + k);
if (value.octave) pieces[1] = value.octave.toString();
let octave = parseInt(pieces[1], 10);
// Octave_shift is the shift to compensate for clef 8va/8vb.
octave += -1 * options.octave_shift;
const base_index = octave * 7 - 4 * 7;
let line = (base_index + value.index) / 2;
line += Tables.clefProperties(clef).line_shift;
let stroke = 0;
if (line <= 0 && (line * 2) % 2 === 0) stroke = 1; // stroke up
if (line >= 6 && (line * 2) % 2 === 0) stroke = -1; // stroke down
// Integer value for note arithmetic.
const int_value = typeof value.int_val !== 'undefined' ? octave * 12 + value.int_val : undefined;
/* Check if the user specified a glyph. */
const code = value.code;
const shift_right = value.shift_right;
let extraProps = {};
if (pieces.length > 2 && pieces[2]) {
const glyph_name = pieces[2].toUpperCase();
extraProps = customNoteHeads[glyph_name] || {};
}
return {
key: k,
octave,
line,
int_value,
accidental: value.accidental,
code,
stroke,
shift_right,
displaced: false,
...extraProps,
};
},
integerToNote(integer?: number): string {
const table: Record<number, string> = {
0: 'C',
1: 'C#',
2: 'D',
3: 'D#',
4: 'E',
5: 'F',
6: 'F#',
7: 'G',
8: 'G#',
9: 'A',
10: 'A#',
11: 'B',
};
if (typeof integer === 'undefined') {
throw new RuntimeError('BadArguments', 'Undefined integer for integerToNote');
}
if (integer < -2) {
throw new RuntimeError('BadArguments', `integerToNote requires integer > -2: ${integer}`);
}
const noteValue = table[integer];
if (!noteValue) {
throw new RuntimeError('BadArguments', `Unknown note value for integer: ${integer}`);
}
return noteValue;
},
tabToGlyph(fret: string, scale = 1.0): { text: string; code?: string; getWidth: () => number; shift_y: number } {
let glyph = undefined;
let width = 0;
let shift_y = 0;
if (fret.toUpperCase() === 'X') {
const glyphMetrics = new Glyph('accidentalDoubleSharp', Tables.DEFAULT_TABLATURE_FONT_SCALE).getMetrics();
glyph = 'accidentalDoubleSharp';
if (glyphMetrics.width == undefined || glyphMetrics.height == undefined)
throw new RuntimeError('InvalidMetrics', 'Width and height required');
width = glyphMetrics.width;
shift_y = -glyphMetrics.height / 2;
} else {
width = Tables.textWidth(fret);
}
return {
text: fret,
code: glyph,
getWidth: () => width * scale,
shift_y,
};
},
textWidth(text: string): number {
return 7 * text.toString().length;
},
articulationCodes(artic: string): ArticulationStruct {
const articulations: Record<string, ArticulationStruct> = {
'a.': { code: 'augmentationDot', between_lines: true }, // Staccato
av: {
aboveCode: 'articStaccatissimoAbove',
belowCode: 'articStaccatissimoBelow',
between_lines: true,
}, // Staccatissimo
'a>': {
aboveCode: 'articAccentAbove',
belowCode: 'articAccentBelow',
between_lines: true,
}, // Accent
'a-': {
aboveCode: 'articTenutoAbove',
belowCode: 'articTenutoBelow',
between_lines: true,
}, // Tenuto
'a^': {
aboveCode: 'articMarcatoAbove',
belowCode: 'articMarcatoBelow',
between_lines: false,
}, // Marcato
'a+': { code: 'pluckedLeftHandPizzicato', between_lines: false }, // Left hand pizzicato
ao: {
aboveCode: 'pluckedSnapPizzicatoAbove',
belowCode: 'pluckedSnapPizzicatoBelow',
between_lines: false,
}, // Snap pizzicato
ah: { code: 'stringsHarmonic', between_lines: false }, // Natural harmonic or open note
'a@': { aboveCode: 'fermataAbove', belowCode: 'fermataBelow', between_lines: false }, // Fermata
'a@a': { code: 'fermataAbove', between_lines: false }, // Fermata above staff
'a@u': { code: 'fermataBelow', between_lines: false }, // Fermata below staff
'a|': { code: 'stringsUpBow', between_lines: false }, // Bow up - up stroke
am: { code: 'stringsDownBow', between_lines: false }, // Bow down - down stroke
'a,': { code: 'pictChokeCymbal', between_lines: false }, // Choked
};
return articulations[artic];
},
accidentalMap: accidentals,
accidentalCodes(acc: string): { code: string; parenRightPaddingAdjustment: number } {
return accidentals[acc];
},
accidentalColumnsTable: {
1: {
a: [1],
b: [1],
},
2: {
a: [1, 2],
},
3: {
a: [1, 3, 2],
b: [1, 2, 1],
second_on_bottom: [1, 2, 3],
},
4: {
a: [1, 3, 4, 2],
b: [1, 2, 3, 1],
spaced_out_tetrachord: [1, 2, 1, 2],
},
5: {
a: [1, 3, 5, 4, 2],
b: [1, 2, 4, 3, 1],
spaced_out_pentachord: [1, 2, 3, 2, 1],
very_spaced_out_pentachord: [1, 2, 1, 2, 1],
},
6: {
a: [1, 3, 5, 6, 4, 2],
b: [1, 2, 4, 5, 3, 1],
spaced_out_hexachord: [1, 3, 2, 1, 3, 2],
very_spaced_out_hexachord: [1, 2, 1, 2, 1, 2],
},
} as Record<number, { [name: string]: number[] }>,
ornamentCodes(acc: string): { code: string } {
const ornaments: Record<string, { code: string }> = {
mordent: { code: 'ornamentShortTrill' },
mordent_inverted: { code: 'ornamentMordent' },
turn: { code: 'ornamentTurn' },
turn_inverted: { code: 'ornamentTurnSlash' },
tr: { code: 'ornamentTrill' },
upprall: { code: 'ornamentPrecompSlideTrillDAnglebert' },
downprall: { code: 'ornamentPrecompDoubleCadenceUpperPrefix' },
prallup: { code: 'ornamentPrecompTrillSuffixDandrieu' },
pralldown: { code: 'ornamentPrecompTrillLowerSuffix' },
upmordent: { code: 'ornamentPrecompSlideTrillBach' },
downmordent: { code: 'ornamentPrecompDoubleCadenceUpperPrefixTurn' },
lineprall: { code: 'ornamentPrecompAppoggTrill' },
prallprall: { code: 'ornamentTremblement' },
scoop: { code: 'brassScoop' },
doit: { code: 'brassDoitMedium' },
fall: { code: 'brassFallLipShort' },
doitLong: { code: 'brassLiftMedium' },
fallLong: { code: 'brassFallRoughMedium' },
bend: { code: 'brassBend' },
plungerClosed: { code: 'brassMuteClosed' },
plungerOpen: { code: 'brassMuteOpen' },
flip: { code: 'brassFlip' },
jazzTurn: { code: 'brassJazzTurn' },
smear: { code: 'brassSmear' },
};
return ornaments[acc];
},
keySignature(spec: string): { type: string; line: number }[] {
const keySpecs: Record<string, { acc?: string; num: number }> = {
C: { num: 0 },
Am: { num: 0 },
F: { acc: 'b', num: 1 },
Dm: { acc: 'b', num: 1 },
Bb: { acc: 'b', num: 2 },
Gm: { acc: 'b', num: 2 },
Eb: { acc: 'b', num: 3 },
Cm: { acc: 'b', num: 3 },
Ab: { acc: 'b', num: 4 },
Fm: { acc: 'b', num: 4 },
Db: { acc: 'b', num: 5 },
Bbm: { acc: 'b', num: 5 },
Gb: { acc: 'b', num: 6 },
Ebm: { acc: 'b', num: 6 },
Cb: { acc: 'b', num: 7 },
Abm: { acc: 'b', num: 7 },
G: { acc: '#', num: 1 },
Em: { acc: '#', num: 1 },
D: { acc: '#', num: 2 },
Bm: { acc: '#', num: 2 },
A: { acc: '#', num: 3 },
'F#m': { acc: '#', num: 3 },
E: { acc: '#', num: 4 },
'C#m': { acc: '#', num: 4 },
B: { acc: '#', num: 5 },
'G#m': { acc: '#', num: 5 },
'F#': { acc: '#', num: 6 },
'D#m': { acc: '#', num: 6 },
'C#': { acc: '#', num: 7 },
'A#m': { acc: '#', num: 7 },
};
const keySpec = keySpecs[spec];
if (!keySpec) {
throw new RuntimeError('BadKeySignature', `Bad key signature spec: '${spec}'`);
}
if (!keySpec.acc) {
return [];
}
const accidentalList: Record<string, number[]> = {
b: [2, 0.5, 2.5, 1, 3, 1.5, 3.5],
'#': [0, 1.5, -0.5, 1, 2.5, 0.5, 2],
};
const notes = accidentalList[keySpec.acc];
const acc_list = [];
for (let i = 0; i < keySpec.num; ++i) {
const line = notes[i];
acc_list.push({ type: keySpec.acc, line });
}
return acc_list;
},
unicode: {
// ♯ accidental sharp
sharp: String.fromCharCode(0x266f),
// ♭ accidental flat
flat: String.fromCharCode(0x266d),
// ♮ accidental natural
natural: String.fromCharCode(0x266e),
// △ major seventh
triangle: String.fromCharCode(0x25b3),
// ø half-diminished
'o-with-slash': String.fromCharCode(0x00f8),
// ° diminished
degrees: String.fromCharCode(0x00b0),
// ○ diminished
circle: String.fromCharCode(0x25cb),
},
// Used to convert duration aliases to the number based duration.
// If the input isn't an alias, simply return the input.
//
// example: 'q' -> '4', '8' -> '8'
sanitizeDuration(duration: string): string {
const durationAliases: Record<string, string> = {
w: '1',
h: '2',
q: '4',
// This is the default duration used to render bars (BarNote). Bars no longer
// consume ticks, so this should be a no-op.
//
// TODO(0xfe): This needs to be cleaned up.
b: '256',
};
const alias = durationAliases[duration];
if (alias !== undefined) {
duration = alias;
}
if (durations[duration] === undefined) {
throw new RuntimeError('BadArguments', `The provided duration is not valid: ${duration}`);
}
return duration;
},
// Convert the `duration` to an fraction
durationToFraction(duration: string): Fraction {
return new Fraction().parse(Tables.sanitizeDuration(duration));
},
// Convert the `duration` to an number
durationToNumber(duration: string): number {
return Tables.durationToFraction(duration).value();
},
// Convert the `duration` to total ticks
durationToTicks(duration: string): number {
duration = Tables.sanitizeDuration(duration);
const ticks = durations[duration];
if (ticks === undefined) {
throw new RuntimeError('InvalidDuration');
}
return ticks;
},
// Return a glyph given duration and type. The type can be a custom glyph code from customNoteHeads.
getGlyphProps(
duration: string,
type?: string
): // eslint-disable-next-line
any {
// eslint-disable-next-line
const duration_codes: Record<string, any> = {
'1/2': {
common: {
stem: false,
stem_offset: 0,
flag: false,
stem_up_extension: -Tables.STEM_HEIGHT,
stem_down_extension: -Tables.STEM_HEIGHT,
tabnote_stem_up_extension: -Tables.STEM_HEIGHT,
tabnote_stem_down_extension: -Tables.STEM_HEIGHT,
dot_shiftY: 0,
line_above: 0,
line_below: 0,
},
type: {
n: {
// Breve note
code_head: 'noteheadDoubleWhole',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadDoubleWhole', scale).getMetrics().width;
},
},
h: {
// Breve note harmonic
code_head: 'unpitchedPercussionClef1',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('unpitchedPercussionClef1', scale).getMetrics().width;
},
},
m: {
// Breve note muted -
code_head: 'vexNoteHeadMutedBreve',
stem_offset: 0,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('vexNoteHeadMutedBreve', scale).getMetrics().width;
},
},
r: {
// Breve rest
code_head: 'restDoubleWhole',
rest: true,
position: 'B/5',
dot_shiftY: 0.5,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('restDoubleWhole', scale).getMetrics().width;
},
},
s: {
// Breve note slash -
// Drawn with canvas primitives
getWidth: () => Tables.SLASH_NOTEHEAD_WIDTH,
position: 'B/4',
},
},
},
1: {
common: {
stem: false,
stem_offset: 0,
flag: false,
stem_up_extension: -Tables.STEM_HEIGHT,
stem_down_extension: -Tables.STEM_HEIGHT,
tabnote_stem_up_extension: -Tables.STEM_HEIGHT,
tabnote_stem_down_extension: -Tables.STEM_HEIGHT,
dot_shiftY: 0,
line_above: 0,
line_below: 0,
},
type: {
n: {
// Whole note
code_head: 'noteheadWhole',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadWhole', scale).getMetrics().width;
},
},
h: {
// Whole note harmonic
code_head: 'noteheadDiamondWhole',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadDiamondWhole', scale).getMetrics().width;
},
},
m: {
// Whole note muted
code_head: 'noteheadXWhole',
stem_offset: -3,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadXWhole', scale).getMetrics().width;
},
},
r: {
// Whole rest
code_head: 'restWhole',
rest: true,
position: 'D/5',
dot_shiftY: 0.5,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('restWhole', scale).getMetrics().width;
},
},
s: {
// Whole note slash
// Drawn with canvas primitives
getWidth: () => Tables.SLASH_NOTEHEAD_WIDTH,
position: 'B/4',
},
},
},
2: {
common: {
stem: true,
stem_offset: 0,
flag: false,
stem_up_extension: 0,
stem_down_extension: 0,
tabnote_stem_up_extension: 0,
tabnote_stem_down_extension: 0,
dot_shiftY: 0,
line_above: 0,
line_below: 0,
},
type: {
n: {
// Half note
code_head: 'noteheadHalf',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadHalf', scale).getMetrics().width;
},
},
h: {
// Half note harmonic
code_head: 'noteheadDiamondHalf',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadDiamondHalf', scale).getMetrics().width;
},
},
m: {
// Half note muted
code_head: 'noteheadXHalf',
stem_offset: -3,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadXHalf', scale).getMetrics().width;
},
},
r: {
// Half rest
code_head: 'restHalf',
stem: false,
rest: true,
position: 'B/4',
dot_shiftY: -0.5,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('restHalf', scale).getMetrics().width;
},
},
s: {
// Half note slash
// Drawn with canvas primitives
getWidth: () => Tables.SLASH_NOTEHEAD_WIDTH,
position: 'B/4',
},
},
},
4: {
common: {
stem: true,
stem_offset: 0,
flag: false,
stem_up_extension: 0,
stem_down_extension: 0,
tabnote_stem_up_extension: 0,
tabnote_stem_down_extension: 0,
dot_shiftY: 0,
line_above: 0,
line_below: 0,
},
type: {
n: {
// Quarter note
code_head: 'noteheadBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadBlack', scale).getMetrics().width;
},
},
h: {
// Quarter harmonic
code_head: 'noteheadDiamondBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadDiamondBlack', scale).getMetrics().width;
},
},
m: {
// Quarter muted
code_head: 'noteheadXBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadXBlack', scale).getMetrics().width;
},
},
r: {
// Quarter rest
code_head: 'restQuarter',
stem: false,
rest: true,
position: 'B/4',
dot_shiftY: -0.5,
line_above: 1.5,
line_below: 1.5,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('restQuarter', scale).getMetrics().width;
},
},
s: {
// Quarter slash
// Drawn with canvas primitives
getWidth: () => Tables.SLASH_NOTEHEAD_WIDTH,
position: 'B/4',
},
},
},
8: {
common: {
stem: true,
stem_offset: 0,
flag: true,
beam_count: 1,
code_flag_upstem: 'flag8thUp',
code_flag_downstem: 'flag8thDown',
stem_up_extension: 0,
stem_down_extension: 0,
tabnote_stem_up_extension: 0,
tabnote_stem_down_extension: 0,
dot_shiftY: 0,
line_above: 0,
line_below: 0,
},
type: {
n: {
// Eighth note
code_head: 'noteheadBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadBlack', scale).getMetrics().width;
},
},
h: {
// Eighth note harmonic
code_head: 'noteheadDiamondBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadDiamondBlack', scale).getMetrics().width;
},
},
m: {
// Eighth note muted
code_head: 'noteheadXBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadXBlack', scale).getMetrics().width;
},
},
r: {
// Eighth rest
code_head: 'rest8th',
stem: false,
flag: false,
rest: true,
position: 'B/4',
dot_shiftY: -0.5,
line_above: 1.0,
line_below: 1.0,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('rest8th', scale).getMetrics().width;
},
},
s: {
// Eight slash
// Drawn with canvas primitives
getWidth: () => Tables.SLASH_NOTEHEAD_WIDTH,
position: 'B/4',
},
},
},
16: {
common: {
beam_count: 2,
stem: true,
stem_offset: 0,
flag: true,
code_flag_upstem: 'flag16thUp',
code_flag_downstem: 'flag16thDown',
stem_up_extension: 0,
stem_down_extension: 0,
tabnote_stem_up_extension: 0,
tabnote_stem_down_extension: 0,
dot_shiftY: 0,
line_above: 0,
line_below: 0,
},
type: {
n: {
// Sixteenth note
code_head: 'noteheadBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadBlack', scale).getMetrics().width;
},
},
h: {
// Sixteenth note harmonic
code_head: 'noteheadDiamondBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadDiamondBlack', scale).getMetrics().width;
},
},
m: {
// Sixteenth note muted
code_head: 'noteheadXBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadXBlack', scale).getMetrics().width;
},
},
r: {
// Sixteenth rest
code_head: 'rest16th',
stem: false,
flag: false,
rest: true,
position: 'B/4',
dot_shiftY: -0.5,
line_above: 1.0,
line_below: 2.0,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('rest16th', scale).getMetrics().width;
},
},
s: {
// Sixteenth slash
// Drawn with canvas primitives
getWidth: () => Tables.SLASH_NOTEHEAD_WIDTH,
position: 'B/4',
},
},
},
32: {
common: {
beam_count: 3,
stem: true,
stem_offset: 0,
flag: true,
code_flag_upstem: 'flag32ndUp',
code_flag_downstem: 'flag32ndDown',
stem_up_extension: 9,
stem_down_extension: 9,
tabnote_stem_up_extension: 8,
tabnote_stem_down_extension: 5,
dot_shiftY: 0,
line_above: 0,
line_below: 0,
},
type: {
n: {
// Thirty-second note
code_head: 'noteheadBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadBlack', scale).getMetrics().width;
},
},
h: {
// Thirty-second harmonic
code_head: 'noteheadDiamondBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadDiamondBlack', scale).getMetrics().width;
},
},
m: {
// Thirty-second muted
code_head: 'noteheadXBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadXBlack', scale).getMetrics().width;
},
},
r: {
// Thirty-second rest
code_head: 'rest32nd',
stem: false,
flag: false,
rest: true,
position: 'B/4',
dot_shiftY: -1.5,
line_above: 2.0,
line_below: 2.0,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('rest32nd', scale).getMetrics().width;
},
},
s: {
// Thirty-second slash
// Drawn with canvas primitives
getWidth: () => Tables.SLASH_NOTEHEAD_WIDTH,
position: 'B/4',
},
},
},
64: {
common: {
beam_count: 4,
stem: true,
stem_offset: 0,
flag: true,
code_flag_upstem: 'flag64thUp',
code_flag_downstem: 'flag64thDown',
stem_up_extension: 13,
stem_down_extension: 13,
tabnote_stem_up_extension: 12,
tabnote_stem_down_extension: 9,
dot_shiftY: 0,
line_above: 0,
line_below: 0,
},
type: {
n: {
// Sixty-fourth note
code_head: 'noteheadBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadBlack', scale).getMetrics().width;
},
},
h: {
// Sixty-fourth harmonic
code_head: 'noteheadDiamondBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadDiamondBlack', scale).getMetrics().width;
},
},
m: {
// Sixty-fourth muted
code_head: 'noteheadXBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadXBlack', scale).getMetrics().width;
},
},
r: {
// Sixty-fourth rest
code_head: 'rest64th',
stem: false,
flag: false,
rest: true,
position: 'B/4',
dot_shiftY: -1.5,
line_above: 2.0,
line_below: 3.0,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('rest64th', scale).getMetrics().width;
},
},
s: {
// Sixty-fourth slash
// Drawn with canvas primitives
getWidth: () => Tables.SLASH_NOTEHEAD_WIDTH,
position: 'B/4',
},
},
},
128: {
common: {
beam_count: 5,
stem: true,
stem_offset: 0,
flag: true,
code_flag_upstem: 'flag128thUp',
code_flag_downstem: 'flag128thDown',
stem_up_extension: 22,
stem_down_extension: 22,
tabnote_stem_up_extension: 21,
tabnote_stem_down_extension: 18,
dot_shiftY: 0,
line_above: 0,
line_below: 0,
},
type: {
n: {
// Hundred-twenty-eight note
code_head: 'noteheadBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadBlack', scale).getMetrics().width;
},
},
h: {
// Hundred-twenty-eight harmonic
code_head: 'noteheadDiamondBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadDiamondBlack', scale).getMetrics().width;
},
},
m: {
// Hundred-twenty-eight muted
code_head: 'noteheadXBlack',
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('noteheadXBlack', scale).getMetrics().width;
},
},
r: {
// Hundred-twenty-eight rest
code_head: 'rest128th',
stem: false,
flag: false,
rest: true,
position: 'B/4',
dot_shiftY: -2.5,
line_above: 3.0,
line_below: 3.0,
getWidth(scale = Tables.DEFAULT_NOTATION_FONT_SCALE): number | undefined {
return new Glyph('rest128th', scale).getMetrics().width;
},
},
s: {
// Hundred-twenty-eight rest
// Drawn with canvas primitives
getWidth: () => Tables.SLASH_NOTEHEAD_WIDTH,
position: 'B/4',
},
},
},
};
duration = Tables.sanitizeDuration(duration);
type = type || 'n'; // default type is a regular note
// Lookup duration for default glyph head code
const code = duration_codes[duration];
if (code === undefined) {
return;
}
// Get glyph properties for 'type' from duration string (note, rest, harmonic, muted, slash)
let glyphTypeProperties = code.type[type];
// If this isn't a standard type, then lookup the custom note head map.
if (glyphTypeProperties === undefined) {
// Try and get it from the custom list of note heads
const customGlyphTypeProperties = customNoteHeads[type.toUpperCase()];
// If not, then return with nothing
if (customGlyphTypeProperties === undefined) {
return;
}
// Otherwise set it as the code_head value
glyphTypeProperties = {
code_head: customGlyphTypeProperties.code,
...customGlyphTypeProperties,
};
}
// Merge duration props for 'duration' with the note head properties.
return { ...code.common, ...glyphTypeProperties };
},
validTypes: {
n: { name: 'note' },
r: { name: 'rest' },
h: { name: 'harmonic' },
m: { name: 'muted' },
s: { name: 'slash' },
} as Record<string, Record<string, string>>,
// Default time signature.
TIME4_4: {
num_beats: 4,
beat_value: 4,
resolution: RESOLUTION,
},
};
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,199 |
\section{Introduction}
Difficult causal questions, such as \emph{`does eating meat cause cancer'} or \emph{`would increasing the minimum wage lead to a fall in employment'} are fundamental to decisions around how our society is structured and our understanding of the world. The development of Causal Graphical Models (CGMs) and the do-calculus \cite{pearl1995causal,pearl2009} has given us an extremely rich and powerful framework with which to formalise and approach such questions. This framework is presented as fundamentally extra-statistical - Pearl has argued forcefully that (Bayesian) probability theory alone is not sufficient for solving causal problems \cite{pearl2001bayesianism}.
The notion that causality fundamentally requires new mathematics and that causal questions cannot be solved within existing paradigms for probabilistic inference has led to extensive controversy and debate, eg \cite{gelman2009blog,gelman2019blog}. This debate has been particularly intense between proponents of causal modelling and Bayesian modellers, perhaps not surprisingly, since the Bayesian approach to combining assumptions with data is typically presented as sufficiently general to tackle \emph{any} probabilistic inference problem (although computational constraints may make it impractical).
In this paper, we demonstrate how the assumptions encoded by causal graphical models can be represented with a probabilistic graphical model (PGM). The advantage of doing so is mostly conceptual: it allows Bayesian practitioners to represent and reason about the modelling assumptions required for causal inference in a framework with which they are familiar. However, there may also be practical benefits in cases where causal queries are not identifiable via the do-calculus. In such cases, it is fundamentally impossible to infer the exact outcome of an intervention, even given infinite pre-interventional data without additional assumptions. Modelling such problems within a standard Bayesian inference setting allows us to leverage a vast body of existing research on combining assumptions with data to obtain finite sample estimates for distributions of interest. While the posterior distribution will always remain sensitive to the prior (unless we add assumptions about the functional form of the relationships between variables) we may still obtain useful bounds. The disadvantage of modelling causal questions explicitly as a single PGM is that it is more cumbersome and computationally expensive (unless we use the machinery of the do-calculus to identify appropriate re-parameterisations).
\subsection{Representing a Causal Problem with a Probabilistic graphical model}
In the following sections we show how a causal query can be represented with a PGM and how to do causal inference via this approach. For the necessary background on probabilistic and causal graphical models, we refer readers to the appendix.
To represent an intervention with an ordinary Probabilistic graphical model, we must explicitly model the pre and post intervention systems and the relationship between them. Algorithm 1 constructs a probabilistic graphical model for a specific intervention in a causal graphical model.
\paragraph*{Algorithm 1: CausalBayesConstruct}\label{Alg:causebayesconstruct}~\\ \emph{Input}: Causal graph $G$ and intervention $do(T=t)$. ~\\\emph{Output}: Probabilistic graphical model representing this intervention
\begin{enumerate}
\item Draw the original causal graph $G$ inside a plate indexed from $1, ... M$ to represent the data generating process.
\item For each variable $V\in G$, parameterize $P(V|parents(V))$ by adding a parameter $\theta_V$ with a link into $V$.
\item Draw the graph after the intervention by setting $T=t$ and
removing all links into it.
Rename each of the variables to distinguish them from the variables in the original graph, e.g. $X$ becomes $X^*$.
\item Connect the two graphs linking $\theta_V$ to the corresponding variable $V^*$ in the post-interventional graph, for each $V$ excluding $T$.
\end{enumerate}
\begin{figure}
\centering
\tikz{
\node[obs] (Zm) {$Z$} ;
\node[obs, below left=of Zm] (Xm) {$T$} ;
\node[obs, below right=of Zm] (Ym) {$Y$} ;
\edge {Zm} {Xm} ;
\edge {Zm} {Ym} ;
\edge {Xm} {Ym} ;
} \hspace{1cm}
\tikz{
\node[obs] (Zm) {$Z$} ;
\node[obs, below left=of Zm] (Xm) {$T$} ;
\node[obs, below right=of Zm] (Ym) {$Y$} ;
\edge {Zm} {Ym} ;
\edge {Xm} {Ym} ;
}
\caption{A CGM of Case 1: Left observational, Right: mutilated}
\label{fig:cgm1}
\end{figure}
\begin{figure}
\centering
\tikz{
\node[obs] (Zm) {$Z_m$} ;
\node[obs, below left=of Zm] (Xm) {$T_m$} ;
\node[obs, below right=of Zm] (Ym) {$Y_m$} ;
\edge {Zm} {Xm} ;
\edge {Zm} {Ym} ;
\edge {Xm} {Ym} ;
\plate[inner sep=0.25cm, xshift=-0.12cm, yshift=0.12cm] {plate1} {(Xm) (Zm) (Ym)} {m=1..M};
\node[latent, right=3.5cm of Zm] (Zn) {$Z^*$} ;
\node[obs, below left=of Zn] (Xn) {$T^*$} ;
\node[latent, below right=of Zn] (Yn) {$Y^*$} ;
\edge {Zn} {Yn} ;
\edge {Xn} {Yn} ;
\node[latent, right=1.5cm of Zm] (gamma) {$\gamma$};
\node[latent, left=of Xm] (phi) {$\phi$};
\node[latent, below=.3cm of Xn] (theta) {$\psi$};
\edge {gamma} {Zm,Zn};
\edge {phi} {Xm};
\edge {theta} {Ym,Yn};
}
\caption{A PGM of Case 1}
\label{fig:pgm1}
\end{figure}
A PGM constructed with Algorithm 1 represents exactly the same assumptions about a specific intervention as the corresponding CGM, see Figures~\ref{fig:cgm1} and \ref{fig:pgm1} for an example. We have just explicitly created a joint model over the system pre and post-intervention, which allows the direct application of standard statistical inference, rather than requiring additional notation and operations that map from one to the other - as the do-calculus does. The Bayesian model is specified by the parameterization of the conditional distribution of variables given their parents, and priors may be placed on the parameters $\params$. The fact that the parameters are shared for all pairs of variables $(V,V^*)$ excluding $T$, captures the assumption that all that is changed by the intervention is the way $T$ takes its value - the conditional distributions for all other variables given their parents are invariant.
Despite its simplicity we are unaware of a direct statement of Algorithm 1, it is related to twin networks \cite{pearl2009} and augmented directed acyclic graphs \cite{dawid2015statistical} but is distinct from both.
\subsection{Causal Inference with Probabilistic graphical models}
The result of Algorithm 1 is a Probabilistic graphical model on which we can do inference with standard probability theory rather than the do-calculus, and which has properties such as arrow reversal (by the use of Bayes rule). To infer causal effects we compute a predictive distribution for the quantity of interest in the post-intervention graph using Bayes rule, integrating out all parameters, latent variables and any observed variables that are not of interest, for each setting of the treatment $T=t^*$.
\newcommand{\Dpost}{\boldsymbol{v^*}}
\newcommand{\Dpre}{\boldsymbol{v}}
To make this procedure clearer, let $\boldsymbol{V}$ be the set of variables in the original causal graph $\G$, excluding the variable we intervene on, $T$, and $\boldsymbol{V^*}$ be the corresponding variables in the post-interventional graph. We have: $\params$: the set of model parameters, $\Dpre$: a matrix of the $M$ observations of variables $\boldsymbol{V}$, $(\boldsymbol{v}_1,...,\boldsymbol{v}_M)$ collected pre-intervention,
$\bt$: a vector of the $M$ observed values of the treatment variable $T$, $t_1,..t_M$,
$\Dpost$: The variables of the system post-intervention,
$t^*$: the value that the intervened on variable $T$ is set to,
$Y^*\in {\Dpost}$: the variable of interest post-intervention.
The goal is to infer the value of the unobserved post-interventional
distribution over $\Dpost$, given the observed data and $(\Dpre,\bt)$
and a selected treatment $t^*$. By construction, conditional on the
parameters $\params$, the post-interventional variables $\Dpost$ are
independent of data collected pre-intervention $(\Dpre,\bt)$. The
value of the intervention $t^*$ is set exogenously\footnote{Also $t^*$
has no marginal distribution - it is a constant set by the
intervention} - so is independent of both $\params$ and
$(\Dpre,\bt)$. This ensures joint distribution over
$(\Dpre,\bt,\Dpost,\params)$ factorize into three terms: a prior over
the parameters $\P{\params}$, the likelihood for the original system
$\P{\Dpre,\bt|\params}$, and a predictive distribution for the
post-interventional variables given parameters and intervention
$\P{\Dpost|\params,t^*}$:
\eq{
\P{\Dpre,\bt,\Dpost,\params|t^*} = \P{\params}\P{\Dpre,\bt|\params}\P{\Dpost|\params,t^*}
}
We then marginalize out $\params$,
\eqn{
\P{\Dpre,\bt,\Dpost|t^*} = \int_{\params}\P{\params}\P{\Dpre,\bt|\params}\P{\Dpost|\params,t^*}d\params
}
and condition on the observed data $(\Dpre,\bt)$,
\eqn{
\P{\Dpost|\Dpre,\bt,t^*} &= \frac{\P{\Dpre,\bt,\Dpost|t^*}}{\P{\Dpre,\bt|t^*}} \nonumber \\
&= \int_{\params}\frac{\P{\params}\P{\Dpre,\bt|\params}}
{\P{\Dpre,\bt}}\P{\Dpost|\params,t^*}d\params \nonumber \\
&= \int_{\params}\P{\params|\Dpre,\bt}\P{\Dpost|\params,t^*}d\params.
\label{eqn:post_given_observed_general}
}
Finally, if the goal is to infer mean treatment effects\footnote{We could also compute conditional treatment effects by first conditioning on selected variables in $\Dpost$.} on a specific variable post-intervention $Y^*$, we can marginalize out the remaining variables in $\boldsymbol{V^*}$,
\eqn{
\P{Y^*|\Dpre,\bt,t^*}
&= \int_{\params}\P{\params|\Dpre,\bt}\sum_{\boldsymbol{V^*}\backslash Y^*}\P{\Dpost|\params,t^*}d\params.
\label{eqn:post_given_observed_general}
}
If there are no latent variables in $\G$, assuming positive density over the domain of $(\Dpre,\bt)$ and a well defined prior $\P{\params}$, the likelihood $\P{\Dpre,\bt|\params}$ will dominate, and the posterior over the parameters $\P{\params|\Dpre,\bt}$ will become independent of the prior at the infinite data limit. The term $\P{\Dpost|\params,t^*}$ can be expanded into a product of terms of the form $\P{V^*|parents(V^*),\params}$ following the factorization implied by the post-interventional graph. From step (3) of Algorithm 1 each of these terms are equal to the corresponding terms $\P{V|parents(V),\params}$, giving results equivalent to Pearl's truncated product formula \cite{pearl2009}. \citet{lattimore2019replacing} demonstrate the equivalence of this approach with the do-calculus on a number of worked examples.
\section{Conclusion}
The paper shows that it is possible to arrive at the same solution for
causal problems using both the do-calculus and Bayesian theory, the
key insight required for the Bayesian formulation is that the probabilistic
graphical model must jointly model both the pre-intervention and post
intervention worlds. Our conclusion is similar to that of \cite{lindley1981role}, however we provide an explicit mechanism by which we can encode the assumptions implied by a causal graphical model, formalising the notion of exchangability in this context.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,918 |
Новые левые () — польская новая левая социал-демократическая политическая партия, основанная в 2021 году членами бывших партий Союз демократических левых сил и Wiosna. Входит в коалицию «Левые» с более радикальной партией «Левые вместе».
История
Союз демократических левых сил и Wiosna приняли решение объединиться в конце 2019 года после парламентских выборов.
9 ноября 2019 лидер Национальный совет СЛДС утвердил изменения в уставе партии, создающие правовую основу для объединения с другими политическими партиями.
14 декабря 2019 года было объявлено, что новообразования партия, созданная после объединения СЛДС и «Весны» получит название «Новые левые».
27 января 2020 была формально зарегистрирована партия «Новые левые», созданная путём переименования СЛДС.
11 июня 2021 прекратила свое существование партия «Весна» Роберта Бедроня и её члены присоединились к «Новым левым». 9 октября того же года состоялся объединительный съезд, на котором были избраны два сопредседателя: Влодзимеж Чажастый (от СЛДС) и Роберт Бедронь (от «Весны»).
14 декабря 2021 из фракции партии в парламенте покинули несколько депутатов Сейма и членов Сената, создавшие собственную депутатскую группу «Польская социалистическая партия».
Представительство в органах власти
Депутаты Сейма IX созыва
Бывшие депутаты Сейма от«Новых левых»
Роберт Квятковский
Йоанна Сенишин
14 декабря 2021 они присоединились к депутатской группе ППС
Члены Сената (до декабря 2021)
Габриэла Моравская-Станецкая (14 декабря 2021 покинула «Новах Левых» и перешла в группу ППС)
Депутаты Европарламента
Марек Балт
Роберт Бедронь
Лукаш Кохут
Богуслав Либерацкий
Депутаты Воеводских сеймиков
Депутаты избранные на Местных выборах 2018 года
Депутаты по состоянию на 2022 год
Адам Цукер
Агнешка Гжеховяк
Мария Яворская
Тадеуш Енджейчак
Кристина Кубицкая-Штуль
Хенрик Милцаж
Станислав Павляк
Станислав Взёнтек
Примечания
Ссылки
Политические партии Польши
Социал-демократические партии
Новые левые | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 321 |
Today I am opening up something fun that will become a series about THE EMPOWERED WOMAN.
Who is she? What does she look like?
Let's begin with a definition from the Oxford Dictionaries.
I was so struck when I read this message. Particularly the last sentence which places all the power in our own hands and requiring, as all true miracles do, simply a shift in our perception. Same body, same person, same problems - different experience.
I could be strong, simply by seeing myself in the most favourable light I could imagine?!
I felt like I had again discovered "the secret" that I continually find myself learning, forgetting & rediscovering over and over again.
Life becomes a different experience, simply in the way we perceive it!
And with that I hope it lands that everything I write from here on is available to you, simply with a shift in perception.
So, what does empowerment mean to me?
Empowerment means living & embracing the full extent of our power. Finding our inner strength to live & consciously create the life & experiences we desire.
To show up fully & authentically as ourselves.
The Empowered Woman lives as a full expression of her truth.
She embraces all aspects of herself.
She takes responsibility for her life.
She is confident in herself, she knows her power.
She sets boundaries that support her.
She speaks her mind & embodies her truth.
She uses her voice as inspired & expresses herself fully.
She prioritises her health & fulfilment above all else.
She embodies love, facing fear head on with courage.
She decides, she knows her strength.
She feels her feelings fully, listening to the wisdom they provide her.
She communicates consciously and confidently.
She expresses herself emotionally, spiritually, sexually, physically.
She partners with people who respect her, who uplift her, who value her and she them.
She does not fear time or age.
She is connected to herself & trusts the inner wisdom she receives.
She knows what she wants and she creates it.
She honours her body & her cyclical nature.
She believes in her equality.
She is love, kindness & compassion.
She is grounded & flowing.
She belongs, because she accepts herself completely.
She is centred, in alignment with her higher self.
She recognises her limitations & ensures she is supported as she needs.
She asks & receives without guilt.
She loves without reservation, without games, without scarcity.
She sees her beauty inside and out.
She is connected to her body, her heart & understands her mind.
She gives without diminution of her power.
She draws from her masculine & feminine energy as she needs.
She does what she loves.
She follows her passions, her curiosities, her inspirations. She takes them seriously.
She stands up for what she believes.
She supports, empowers & inspires others.
She is a conscious creator.
She knows who she is, what she needs & she moves through life in that power.
The power of knowing who she is.
She is not a victor because she holds no prisoners. And she certainly is not a victim because she is not imprisoned.
The Empowered Woman represents freedom.
Take a moment to breath that in. To taste it, to feel it - The Empowered Woman is FREE to be herself.
Isn't that what we are searching for? Freedom to live the life we want to live. Freedom to feel the way we feel. Freedom to express ourselves fully. Freedom to show up completely as ourselves and to be accepted.
Remember the shift in perception. This freedom is available to you at any given moment - all it takes is a conscious shift in your perception. I'm a prisoner or I'm free.
The Empowered Woman lies in every single one of us. How would it feel to embody this part of yourself? How would you life look? What would you change?
I like to see my inner Empowered Woman as a part of myself that I can call on & align with at any time. What would my inner Empowered Woman do?
And now I would love for you to explore your own definition of The Empowered Woman.
Who is she and what does she embody for you? Share with us in the comments below! Let's draw a picture together!
Stay up to date with The Empowered Woman Series and all my latest content & offerings by subscribing for my newsletter below.
Are you ready to embody your Empowered Woman? I invite you to check out my signature online program, Embrace Your Feminine Essence: this is my online course to Embrace Your Feminine Power & Live As the Empowered Woman You Truly Are. Check out this page to find out what we cover.
Want to go even deeper? I'm also excited to be offering 6 month 1-1 coaching packages - 6 months of 1-1 coaching to help you step into your power & show up for the life you truly desire - you can find all the details here. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,308 |
Q: How to serialize an IEnumerable? I wrote a simple custom JsonConverter class for serializing the DateOnly, but I have no idea how to apply the converter to a collection like IEnumerable.
A: nothing on top needed, just serialize your IEnumerable:
var list = new List<DateOnly>() { new DateOnly(1,2,3), new DateOnly(4, 5, 6) };
IEnumerable<DateOnly> x = list.Where( x => x.Day<100 );
var options = new JsonSerializerOptions
{
Converters = { new DateConverter() }
};
var json = System.Text.Json.JsonSerializer.Serialize( x, options);
Console.WriteLine(json);
generates
["0001-02-03","0004-05-06"]
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,689 |
Mark Hannesson – A Moment Is a Window (2017) - Duration: 18 minutes.
Anna Höstman – What Her Friend Said (2009) - Duration: 4 minutes, 45 seconds.
Performed by Gina Adorno (soprano) and Lorna Krier (piano) at the Extradition Series, Portland, Oregon, USA, January 12, 2019.
Matt Hannafin – Variations on a Picture of Snow by Evan Cordes (2016/18) - Duration: 19 minutes.
John Cage – Two (1987) - Duration: 10 minutes.
Performed by John C. Savage (flute) and Matt Carlson (piano) at the Extradition Series, Portland, Oregon, USA, January 12, 2019.
Morgan Evans-Weiler – Constructed Objects (2016) - Duration: 12 minutes.
Antoine Beuger – Does Beauty Say Adieu? (2017) - Duration: 52 minutes.
Unboxing Danny Clay's "Correspondences I & 2" - Duration: 11 minutes.
Become a Supporter of the Extradition Series - Duration: 103 seconds.
G. Douglas Barrett – A Few Silence (Portland, Oregon - October 20, 2018 - 7:45–7:55pm) - Duration: 10 minutes.
Daniel Brandes – Other Echoes Inhabit the Garden (2013) - Duration: 25 minutes.
Cornelius Cardew – The Tiger's Mind (Nightpiece) (1967) - Duration: 22 minutes.
Ryoko Akama – Tada No (2013/14) - Duration: 12 minutes.
Glenn Sogge – Gestures (2017) - Duration: 20 minutes.
Recorded live at the Extradition Series, Portland, OR, USA – September 15, 2018.
Matthias Kaul – Two Together (2014) - Duration: 14 minutes.
Performed by Loren Chasse & Matt Hannafin (percussion, voices).
Matt Hannafin – Post Box Music (2018) - Duration: 18 minutes.
Michael Pisaro – A Drum Acted Upon by Friction, Gravity, and Electricity (2011) - Duration: 15 minutes.
Mark So – (idle.) – 51 THINGS TO DO WITH 2 HANDS. for Eileen Myles (2010) - Duration: 18 minutes.
Manfred Werder – 2009(4) - Duration: 18 minutes.
Kristin Bolstad – Silence Come Closer Wait Expect (2014) - Duration: 20 minutes.
Performed by Branic Howard (electronics & percussion) at the Extradition Series, Portland, Oregon, USA, July 21, 2018.
James Saunders – Surfaces (2010/11) - Duration: 24 minutes.
Performed by Loren Chasse & Matt Hannafin (surfaces & objects) at the Extradition Series, Portland, Oregon, USA, July 21, 2018.
Matt Hannafin – Honor Roll (2017) - Duration: 14 minutes.
Recorded live at the Extradition Series in Portland, Oregon, USA, July 21, 2018.
Christian Wolff – Play (1969) - Duration: 15 minutes.
Toshi Ichiyanagi – The Field (1966) - Duration: 20 minutes.
Mark So – a tepid atmosphere (bedroom near the sky) (2007) - Duration: 23 minutes.
Jürg Frey – Floating Categories (2015) - Duration: 18 minutes.
Catherine Lamb – Nodes, Various (2009/10) - Duration: 17 minutes.
Michael Pisaro – Entre-Moments (2005/6) - Duration: 32 minutes.
Antoine Beuger – Now Is the Moment to Learn Hope (2018) - Duration: 47 minutes.
Markus Trunk – Slightly Ajar (1993) - Duration: 14 minutes.
Performed by Loren Chasse, Branic Howard, Juniana Lanning, Catherine Lee, and Rebecca Olason (doors, speakers, lights).
Stefan Thut – Five and Three Boxes (2012) - Duration: 27 minutes.
Performed by Lee Elderton (clarinet), Branic Howard (boxes + recordings), Catherine Lee (oboe), Gina Adorno Lunde (soprano), and Rebecca Olason (horn).
Alvin Lucier – Carbon Copies (1989) - Duration: 20 minutes.
Patrick Farmer – Camera Silenta: Two Eggs in a Cup to Stand in for Reality (2014) - Duration: 15 minutes.
Hanna Hartman – Message from the Lighthouse (2009/2016) - Duration: 15 minutes.
Antoine Beuger – Now Is the Moment to Learn Hope (2018) - Duration: 24 minutes.
Gordon Mumma – 7/5 à Pauline Oliveros (1978) / Tom Johnson – Chain II + Chain III (1967) - Duration: 9 minutes, 56 seconds.
Pauline Oliveros – Two for T - Duration: 12 minutes.
Dana Reason – Folded Subjects: Olive Rose (2017) - Duration: 20 minutes.
Antoine Beuger – Cantor Quartets (2003) - Duration: 34 minutes.
Daniel Brandes – A Dwelling Place for You (2014) - Duration: 19 minutes.
Christopher Hobbs – Two Compositions, 21 May 1969 (#2) - Duration: 22 minutes.
Loren Chasse – Silver Blood (2016) - Duration: 29 minutes.
Recorded live at the inaugural Extradition Series, Portland, Oregon, USA, January 27, 2016.
Branic Howard – Room Source (2016) - Duration: 25 minutes.
Extradition Series Mini-Documentary, Summer 2017 - Duration: 7 minutes, 56 seconds.
Anastassis Philippakopoulos - Two Piano Pieces (2006–2008) - Duration: 4 minutes, 54 seconds.
Anastassis Philippakopoulos - Onissia (2002) - Duration: 4 minutes, 56 seconds.
Samuel Vriezen - The Weather Riots (2002) - Duration: 11 minutes.
Giacinto Scelsi - Ko-Tha: Three Dances of Shiva (1967) - Duration: 7 minutes, 34 seconds.
Nomi Epstein - Combine, Juxtapose, Delayed Overlap (2013) - Duration: 14 minutes.
G. Douglas Barrett - Two Voices (2008) - Duration: 10 minutes.
Alvin Lucier - Wind Shadows (1994) - Duration: 15 minutes. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,889 |
South Africa: Out of Desperation, Zuma Pledges to 'Give Life' to the Poor
Posted: April 6, 2017 at 9:41 am / by Caracal Reports / comments (0)
Under fire, South African leader Jacob Zuma is pledging to 'redistribute wealth' among poor South Africans as part of measures to 'radically transform' the ailing economy- with the poor bearing most of the brunt.
In a speech on Thursday, Zuma said the new drive to redistribute wealth in the economy to poor black people was part of a policy he calls "radical socio-economic transformation".
He said the policy means a total and fundamental change in the structure, systems, institutions, and patterns of ownership, management and control of the economy in favor of South Africans, especially the poor.
Jacob Zuma's cabinet reshuffle has earned him a no-confidence vote by South Africa's opposing parties on Monday.
The parties had threatened to organize mass protests against Zuma as well as continue to lobby for the vote of 'no confidence.'
Respected finance minister Pravin Gordhan was fired in a late-night cabinet reshuffle exercise last Thursday that opposition felt was used to purge growing numbers of the president's critics.
Malusi Gigaba, the home affairs minister who has been Mr. Zuma's close ally, was named as the replacement.
"I have decided to make changes to the National Executive in order to improve efficiency and effectiveness," Mr. Zuma was quoted saying last Thursday, adding that he would direct the new ministers to work tirelessly with their colleagues to bring about radical socio-economic transformation.
Mmusi Maimane, the leader of the main opposition Democratic Alliance (DA), was quoted as saying:
"Opposition parties are fully behind the motion of no confidence in Jacob Zuma. The President has once again shown that he has no interest in our beloved country's future."
"He has bowed to the whims of those who are determined to enrich themselves at the expense of the poor and jobless," Maimane said.
Although the South African Parliament is currently in recess, the DA and the third-largest opposition party, the leftist Economic Freedom Fighters Party (EFF), have sent letters to the national assembly speakers requesting an urgent sitting to debate the no-confidence motion.
There are widespread concerns for investors who think the economy is in terrible shape.
Ademola George for Caracal Reports | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,596 |
"There have been a few incidents of steering wheels becoming loose, but there have been no accidents," he added.
The remainder of the global recall affects the Cube, produced in Japan between 2002-2006. The Cube is not on sale in the UK. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,011 |
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You are here: Home / Community / 90 Seconds to Change a Life: Ford Partners with the Salvation Army + Dallas Cowboys to Honor North Texas Veteran
90 Seconds to Change a Life: Ford Partners with the Salvation Army + Dallas Cowboys to Honor North Texas Veteran
Community· Drive #DSMDrive· Drive News· Lifestyle· Single Mom Life
Editorial note: The season of giving is in full swing. We love a feel-good story. Here's a beautiful one happening right now through the combined efforts of Sam Pack Ford, the Dallas Cowboys, the Salvation Army coming together to honor a local veteran.
There are few things as American as football and coming together to share in this season of Giving.
Mr. James Brown, North Texas Veteran.
MEET MR. BROWN
More than meets the eye, the man that you see to above is Mr. James Brown. Both humble and proud, he is a father and fellow North Texan. He is also an Air Force veteran that joined the service back in 1985, and has combatted a season of complex and difficult times that have spun his course into something he never had imagined or foreseen as the child of a military family.
As such, Mr. Brown has experienced direct effects of homelessness and as he battled a dependence alcohol and pain medication. That all being said, also served this country with honor and quiet grace.
STARTING A NEW CHAPTER
During a dark chapter in his journey, Mr. Brown came across the path of The Salvation Army where they gave him a warm and safe home through their Homor Sweet Home program. The community-based initiative helps the newly homeless get their legs back under them and gain long-term stability. While engaged in this program, Mr. Brown was afforded the opportunity to focus on securing and creating the tools he needs to pass through this season and get on to the next with the comfort of stability and the innate power of self-sufficiency.
90 SECONDS to CHANGE A LIFE
Every year millions of Americans enjoy the NFL's Thanksgiving Day coverage. It is also an opportunity brands use to share their message and products with viewers nationwide. This year, Ford has chosen to spend the valuable :90s spot to share the surprise with us and honor veteran Mr. James Brown.
"At Ford, we've remained committed to strengthening the communities where we live and work for more than for 118 years, and our commitments will only continue to grow. For example, Ford is investing $90-million in Texas training centers over the next five years… and provide jobs…. In addition, by leveraging the power and expertise of the Ford Motor Company network – our employees, Ford dealers and community partners, as well as our philanthropic arm the Ford Motor Company Fund (Ford Fund) – we provide resources and opportunities that make life better."
Debra Hotaling, Ford Regional Communications
Frederiek Toney, Ford President, Global Ford Customer Service Division and Dallas Cowboys players, Ceedee Lamb & Trevon Diggs. Credit: Ford via Direct Impact
Using the talents of Dallas Cowboys players Ceedee Lamb and Trevon Diggs, the do-good, feel-good of the Salvation Army and Ford's President of the Global Ford Customer Service Division Frederiek Toney to deliver in the fun, the collective unit surprised James Brown with life changing news.
About the Surprise
Mr. Brown will be awarded a full two-year scholarship to the Ford Automotive Student Service Educational Training (ASSET) program. Once he completes the program, he will have earned an Associate's Degree in of Applied Science in Automotive Service Technology (ASSET). He will graduate with a guaranteed a job at Sam Pack's Five Star Ford of Carrolton where he can apply his newly honed skills to keep vehicles in service including the new electrics that are coming off the line. He also was gifted with 2 tickets to the Cowboys Thanksgiving Day Game.
"Our team interviewed James and we thought that he was highly qualified, so we made an offer. He will be involved in the ASSET program now. He represented our country. He has experience in the service, he was a drug and dog bomb handler. Not unlike other veterans, returning home and trying to come back can be a challenge. Like many veterans, perhaps they experience things you and I have never experienced. It's important for us to honor our responsibilities and make a better experience in quality of life, not just for veterans, but anyone we can touch."
Sam Pack of Sam Pack Ford.
When asked about why Mr. Brown, Sam Pack said, "He has a son. That's very important to him. In our view of things, we're going to do everything we can for him and for his family. If you look what the Salvation Army has done and continues to do over the years, it's been an incredible organization and we offer financial assistance to that organization."
To Learn More About the Home Sweet Home Program, visit here
To learn more about what Ford is doing in North Texas Communities, visit here.
About Teia Collier
Teia Collier shares about her daily adventures and offers ways for Dallas' single moms lead their best lives through education, encouragement, inspiration and active engagement in their lives despite life transitions. She is a mother of three, longtime editor, educator, speaker and lifestyle consultant. Her focus at the Dallas Single Mom is to highlight the best in Dallas-Fort Worth area resources that encourage a full well-lived life including family travel, single and preemie parenting, dating, divorce, inspiration, lifestyle management and best life now coaching.
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Australand becomes Frasers Property Australia
Robert Harley
Aug 31, 2015 — 6.11pm
The Singapore-based Frasers Centrepoint has stamped its mark on the Australand Property Group – the local business which it acquired a year ago – rebranding the operation as Frasers Property Australia.
Frasers Property Australia chief executive, Rod Fehring, said the new brand aligned the group with its international parent and stressed the integration within the Australian business.
Mr Fehring noted "a remarkably consistent alignment of values", between the global and local operations, summed up in the idea "real places for real people".
Frasers Property Australia chief executive Rod Fehring says the business has "very good momentum". Robert Rough
He added that under the new brand, Frasers Property Australia would broaden its market reach, create opportunities to develop supplementary asset classes and build alignment with Frasers' Singapore-based Real Estate Investment Trust platform.
One Melbourne tower, 357 Collins Street, has already be sold to the Frasers Commercial Office Trust and other projects can be sold to the Frasers Centrepoint Trust, which holds retail, and the Frasers Hospitality Trust.
"Its a very powerful model; to grow assets, stabilise the earnings, and then recycle the capital," Mr Fehring said.
Frasers has also considered floating an Australian REIT. Mr Fehring acknowledged it was an option but stressed that "we don't need to create trusts for the sake of them."
All the Frasers Centrepoint real estate operations in China, New Zealand, Thailand, the United Kingdom and Vietnam, operate under the Frasers Property banner. Total assets under management are around $23 billion.
Mr Fehring said the Australian business was trading "very strongly", with 167,500 square metres of commercial and industrial space under development, a portfolio of investment properties valued at $2.7 billion and unrecognised residential revenue of $1.5 billion.
Under the Frasers control it has expanded the development business buying a mixed use site in the Brisbane suburb of Cooparoo, a land project at Grampian Way near Ipswich in south east Queensland and last week the Edmondson Park Town Centre site in Sydney's south west for around $100 million.
"We have very good momentum, and we have a significantly larger backing than before, but we have to take a disciplined approach because most segments of the market are so strong," he said. | {
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About the TIR
TIR System
TIR Convention
Resolution and Recommendations
TIR Secretariat
TIR In Figures
TIR Carnets
Authorized Transport Operators
Safe TIR Statistics
ITDB
TIRExB
Example Authorization and Example Agreement
Restricted Documents *
Focal Points *
Geneva – Switzerland - 2018
Dushanbe - Tajikistan - 2015
Helsinki - Finland - 2013
Issyk-Kul - Kyrgyzstan - 2012
Sarajevo – Bosnia and Herzegovina - 2011
Tunis - Tunisia - 2009
Belgrade – Serbia - 2006
Sofia – Bulgaria - 2006
Beijing - China - 2005
Moscow - Russia - 2003
Riga - Latvia - 2002
Baku - Azerbaijan - 2001
Amman - Jordan - 2000
TIR Publications
TIR Handbook
TIR Carnet Prices
A Review Conference convened in November 1975 under the auspices of the United Nations Economic Commission for Europe (UNECE) produced the TIR Convention of 1975 that came into force in 1978. Since that time the TIR Convention has proved that it is one of the most successful international transport conventions and is in fact so far the only universal Customs transit system in existence. The idea behind the TIR Convention and its transit regime has formed the basis for many regional transit systems and has thus, directly and indirectly, contributed to the facilitation of international transport, especially international road transport, not only in Europe and the Middle East, but also in other parts of the world, such as Africa and Latin America.
Anyone who has ever travelled on European roads will recognize the familiar blue and white TIR plate borne by thousands of lorries and semi-trailers using the TIR Customs transit system. For the driver, the transport operator and the shipper, this plate stands for fast and efficient international transportation by road.
Work on the TIR transit system started soon after the Second World War under the auspices of the United Nations Economic Commission for Europe (UNECE). The first TIR Agreement was concluded in 1949 between a small number of European countries. The success of this limited scheme led to the negotiation of a TIR Convention which was adopted in 1959 by the UNECE Inland Transport Committee and entered into force in 1960. This first TIR Convention was revised in 1975 to take account of practical experience in operating the system and to give effect to technical advances and changing Customs and transportation requirements.
The experience gained in the first 10 to 15 years of operating the system was thus used to make the TIR system more efficient, less complex and at the same time more Customs secure. Another reason why the original TIR system had to be modified was that in the early 1960's a new transport technique emerged: the maritime container. That was followed a little later by the inland container used by the European railways and by the swap-body introduced for improving the efficiency of road/rail transport.
These new combined or multimodal transport techniques necessitated the acceptance of the container, under certain conditions, as a Customs secure loading unit. It meant also that the TIR regime no longer only covered road transport, but was extended to rail, inland waterways and even maritime transport, although at least one part of the total transport operation still has to be made by road.
Upon its entry into force the new Convention terminated and replaced the old Convention of 1959. However, the former Convention is still in force for various reasons, one of which is that one of the Contracting Parties to the old Convention (Japan) has not yet acceded to the TIR Convention of 1975.
The TIR Convention has proved to be one of the most effective international instruments prepared under the auspices of the United Nations Economic Commission for Europe (UNECE). To date, it has 76 Contracting Parties, including the European Union. It covers the whole of Europe and reaches out to North Africa and the Near and Middle East. Countries in Asia have been informed about the facilities of this global Customs transit system and their interest has shown that they may well join the TIR Convention in the not too distant future. Already today, the United States of America and Canada are Contracting Parties as well as Chile and Uruguay in South America (see "Contracting Parties of the TIR Convention, 1975").
The success of the TIR system may also be attested by the number of TIR Carnets distributed and issued every year. Whilst in 1952 only a little over 3,000 TIR Carnets were issued, this number increased steadily reaching 100,000 in 1960, then 800,000 in 1970. During the seventies and eighties the demand for TIR Carnets floated between around 500,000 and 900,000. This can be explained by the enlargement of the European Union which utilizes its own Community Transit System within its territory. Thus, TIR Carnets are not used for Customs transit operations within its member countries.
As a result of the expanding East-West European trade, particularly since 1989, and the corresponding tremendous increase in international road transport, the number of TIR Carnets issued exceeded one million in 1992 and even reached 3 million in 2013, representing the start of nearly 10,000 TIR transports every day in 62 countries and well over 50,000 TIR border crossing procedures daily. The number of transport companies authorized by national Customs authorities to utilize TIR Carnets amounts to more than 34,000 (2017) (see "Number of TIR Carnets issued by IRU to different national associations from 2001 to 2017"). Further to ongoing problems in the implementation of the TIR Convention in the Russian Federation since 2013, the number of TIR Carnets issued has dropped to 1,5 million in 2015.
The success of the TIR Customs transit system can be explained by the special features of the TIR regime which offer transport operators and Customs authorities a simple, flexible, cost-effective and secure Customs regime for the international transport of goods across frontiers.
OBJECTIVE AND ADVANTAGES
Customs transit systems are devised to facilitate to the greatest possible extent the movement of goods under Customs seals in international trade and to provide the required Customs security and guarantees. For such a system to function satisfactorily, it is essential that any formalities involved are neither too burdensome for the Customs officials nor too complex for the transport operators and their agents. Therefore, a balance needs to be struck between the requirements of the Customs authorities on the one hand and those of the transport operators on the other.
Traditionally when goods crossed the territory of one or more States in the course of an international transport of goods by road, the Customs authorities in each State applied national controls and procedures. These varied from State to State, but frequently involved the inspection of the load at each national frontier and the imposition of national security requirements (guarantee, bond, deposit of duty, etc.) to cover the potential duties and taxes at risk while the goods were in transit through each territory. These measures, applied in each country of transit, led to considerable expenses, delays and interferences with international transport.
In an attempt to reduce these difficulties experienced by transport operators and, at the same time, to offer Customs administrations an international system of control replacing traditional national procedures, whilst effectively protecting the revenue of each State through which goods were carried, the TIR system was devised.
(a) Advantages for Customs administrations
As regards Customs control measures at frontiers, the TIR system clearly has advantages for Customs administrations as it reduces the normal requirements of national transit procedures. At the same time the system avoids the need - expensive in manpower and facilities - for physical inspection in countries of transit other than checking seals and the external conditions of the load compartment or container. It also dispenses with the need to operate national guarantees and national systems of documentation.
In addition, advantages arise from the fact that the international transit operation is covered by a single transit document, the TIR Carnet, which reduces the risk of presenting inaccurate information to Customs administrations.
In case of doubt, Customs authorities have the right to inspect the goods under Customs seal at any time and, if necessary, to interrupt the TIR transport and/or to take adequate measures in accordance with national legislation. In view of the strict provisions of the TIR Convention and the interest of all Customs authorities and transport operators to apply these provisions, such interventions should remain exceptional. Customs authorities can therefore reduce routine administrative Customs procedures to a minimum and devote their limited resources to specific control measures based on risk assessment and intelligence information.
The TIR Executive Board (TIRExB), as an inter-governmental organ, ensures that each of the actors in the TIR procedure adequately applies the provisions of the Convention. In case of difficulties in the application of the TIR Convention at the international level, Customs authorities may wish to address the TIRExB for guidance and support. The TIRExB is also at the disposal of all Contracting Parties to coordinate and foster the exchange of intelligence and other information.
(b) Advantages for the transport industry
The advantages of the TIR Convention to commerce and to transport interests are also obvious. Goods may travel across national frontiers with a minimum of interference by Customs administrations. By easing traditional impediments to the international movement of goods, the TIR system encourages the development of international trade. By reducing delays in transit, it enables significant economies to be made in transport costs.
The TIR Convention also provides, through its international guarantee chain, relatively simple access to the required guarantees which are a sine qua non for the transport and trade industry to benefit from the facilities of Customs transit systems.
Finally, in reducing the impediments to international traffic by road caused by Customs controls, it enables exporters and importers to select more easily the form of transport most suitable for their needs.
FUTURE DEVELOPMENT OF THE TIR SYSTEM
(a) World-wide application of the TIR System
The TIR system is promoted under the auspices of the United Nations to make it as widely available as possible for all countries wishing to make use of it. In 1984, the Economic and Social Council of the United Nations (ECOSOC) adopted a Resolution (1984/79) which recommends that countries world-wide examine the possibility of acceding to the Convention and introducing the TIR system. Furthermore, it recommends that international, intergovernmental and non-governmental organizations, and in particular the Regional Commissions of the United Nations, promote the introduction of the TIR system as a universal Customs transit system.
In accordance with this ECOSOC Resolution, activities have been undertaken to promote the application of the TIR Convention beyond the present 76 Contracting Parties. Several regional and sub-regional seminars and workshops have already been organized in Europe, Asia and the Middle East to familiarize Governments, trade and the transport industry with the facilities of the Convention.
Currently work is under way to extend the scope of the TIR system to Asia and to the Middle East. This work is undertaken in particular by the secretariats of the UNECE and the United Nations Economic and Social Commissions for Asia and the Pacific (UN ESCAP) and Western Asia (ESCWA) which promote the TIR system as one of the cornerstones for efficient international land transport in Asia and the Middle East. These efforts are supported by various international bodies and banks, such as the European Commission and the World Bank which see the TIR system as an important element in facilitating road transport along the historic Silk route or in the Greater Mekong sub-region in Far-East Asia.
(b) The TIR System and electronic data processing
World-wide, the replacement of paper documents by electronic data processing is an ongoing process which will continue to gain further importance, also for Customs administrations and transport operators. This trend will increasingly affect Customs procedures and the documents used by Customs authorities.
The reasons are that Customs administrations are confronted with an enormous dilemma. On the one hand they are governed by laws which oblige them to collect and account for revenues in an effective and efficient manner and to prevent fraud and smuggling of contraband. On the other hand they are increasingly criticized by trading parties (importers, exporters, transport operators, freight forwarders) for not facilitating the speedy throughput of cargo.
Taking into account the limitations of Customs manpower and the increasingly sophisticated methods of Customs fraud and smuggling, there seems to be no other way than to increase productivity and Customs control by adapting national and international administrative procedures, making use of the latest technologies and electronic data processing.
The Contracting Parties to the TIR Convention have included the computerization of the TIR procedure into Phase III of the TIR revision process. They recognized that computerization of the TIR procedure was inevitable in the light of:
- today's extremely rapid technological developments, based on Internet and Smart Card technologies, particularly affecting international transport and trade;
- the ever increasing need for improved efficiency of Customs procedures and trade practices; and
- the fight against fraudulent activities which must be conducted with the most appropriate and effective means.
Given the large number and the diversified administrative structure of the more than 70 Contracting Parties to the TIR Convention, any computerized system must be able to function in a very decentralized and flexible manner on the basis of only a few internationally accepted standard features, such as the establishment of an international centralized database under Customs control and the management by Customs of data on guarantees. This is a difficult, but challenging task which will have to be realized with an appropriate level of connectivity with the existing TIR related IT systems. But there can be no doubt: The TIR system must be kept in line with the latest developments in electronic data processing techniques which have already and increasingly will change all related Customs, transport and trade activities. If not, the TIR system, particularly the paper-based TIR Carnet, will become an obstacle to efficient international transport and trade and will jeopardize effective national Customs procedures and controls.
This challenge will have to be met by all Contracting Parties to the TIR Convention, by national and international organizations as well as by the transport industry involved.
The TIR system, created more than 60 years ago and the TIR Convention, have proved to be a very effective international Customs transit system and have played an important role in facilitating international trade and transport, primarily within Europe, but more recently also between Europe and neighbouring areas.
With the rapid increase of East-West European traffic and with the emergence of many newly independent countries in Central and Eastern Europe, the TIR system is today faced with new and, to this extent, unprecedented challenges. At the same time Customs authorities are faced with an unparalleled amount of Customs fraud and smuggling as a result of changing political, economic and social situations in many countries in the region and due to often heavily increasing Customs duties and taxes.
Furthermore, the management and the control of the TIR system pose problems for national Customs authorities which, mainly in newly independent countries, sometimes still have to acquire the necessary experience and often do not have sufficient and adequately trained personnel.
To counter some of these unwanted developments, Governments and other actors in the TIR system sometimes impose unilateral measures, such as the requirement of additional guarantees for TIR transit operations or the exclusion of certain categories of goods which are not in line with the provisions and the spirit of the TIR Convention.
While such measures may provide some temporary relief, they will induce in the long run not only other countries to introduce similar measures, but they will also make international trade and transport more expensive and, eventually, may lead to a total collapse of the TIR transit system - with no viable alternative in sight.
The TIR Convention itself provides already a number of measures to safeguard the legitimate interests of Customs authorities, such as the requirement for escort services, prescription of transit routes and reduced transit times. Other measures may be prepared if Contracting Parties to the TIR Convention so wish.
Stable and long-term solutions can only be found in joint and concerted action by all concerned Contracting Parties to the TIR Convention. The TIR Executive Board (TIRExB) as well as the UNECE and its Working Party on Customs Questions affecting Transport (WP.30) provide a forum for such cooperation and coordination. Experience has shown that solutions to many recently emerged problems in the application of the TIR Convention have been found within the organs and bodies established in the framework of the TIR Convention and the UNECE.
It is the aim of the UNECE and the TIR secretariat to continue to work in this direction and to provide a well-functioning international machinery to further improve cooperation and coordination among Contracting Parties to the TIR Convention and the transport industry. It is essential to continuously improve the legal framework within which the TIR transit system operates and to streamline its operation so that the TIR transit system is always in line with the requirements of the transport industry and of the Customs authorities.
The United Nations, as a universal organization, is the depositary of the TIR Convention and provides the framework and the services to administer and, where necessary, adapt the TIR Convention to changing requirements. Past experience has shown that the TIR Convention, as part of the transport facilitation work undertaken within the UNECE, has served the interests of all concerned, Customs authorities and transport operators alike, and there is every reason to believe that it will continue to do so in the future. | {
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Our book 'Aspirasi Angkasawan' is No.7 on MPH Best sellers list for week ending 24th October 2010
MPH Non-fiction best sellers list (local) for week ending 24th October 2010:
1. Bila Allah Menduga Kita Author : Syed Alwi Alatas
2. Di Mana Dia Di Hatiku? Author : Pahrol Mohd Juoi
3. Jadi 'Cool + Positif: Psikologi Suka-Suka (Kompilasi Ruangan Psikologi Majalah Remaja)
4. Indahnya Amalan Doa Author : Dato Ismail Kamus
5. Location, Timing & Branding Author : Ho Chin Soon
6. Rojak: Bite-Sized Stories Author : Amir Muhammad
7. Aspirasi Angkasawan: Catatan Pengalaman calon Angkasawan Negara Author : Persatuan Astronautik Malaysia; Mohammed Faiz Kamaludin
8. Hadiah Cinta Untuk Ilahi Author : Muhammad Rashidi Hj Wahab
9. What Your Teacher Didn't Tell You: The Annexe Lectures (Vol. 1) Author : Farish A. Noor
10. Get Into Gold: How to Invest in Gold Profitably While Avoiding the Traps Author : Azizi Ali
Get a copy of our book today at MPH bookstores nationwide...
Thank you for all your support!!!
Inspiring the young to know more about space
KUCHING: The younger generation needs more exposure to the field of space exploration so that they could understand the subject better, Universiti Malaysia Sarawak (Unimas) vice-chancellor Prof Dr Khairuddin Hamid said yesterday.
SHARING: Owen (left) relating his experience to the crowd. Also seen are Mario (second right) and Richard.
He said although there was a booming interest in the field since Datuk Dr Sheikh Muszaphar Shukor became the country's first astronaut in 2007, he was concerned the enthusiasm might fade once the hype was over.
As such, he called for continuous programmes on the subject so that the younger generation would be inspired to learn more about the field and its benefits to mankind.
He believed that through such efforts, the country could one day be the regional centre for space exploration and achieve greater progress in science and technological area.
"I really hope that with the exposure to science, technologies and the future of space travel, we can increase the interest among Malaysians.
"With advanced and modern science and technological expertise here in Malaysia, it is not impossible to promote our country as a possible hub for research and education on space technologies," he said when speaking during the 'Campus Space Walk' talk at Unimas near here.
Three astronauts from the United States, father and son Owen Garriot and Richard Garriot, and Mario Runco Jr were invited for the talk held in connection with the XXIII Planetary Congress of Association of Space Explorers (ASE).
The talk was attended by students of Unimas and selected schools.
Owen, who went to Skylab in 1973 and Spacelab-1 in 1983, was the first of six scientist astronauts selected by Nasa, and he operated the world's first amateur radio station from space.
Richard on the other hand was not qualified to become an astronaut, according to Nasa, but paid US$30 million and became the sixth space tourist.
A video game developer and entrepreneur, Richard took part in several education outreach programmes during his time at the SOYUZ TMA-13 in October 2008 and operated an amateur radio operator from the International Space Station (ISS).
Mario, who went to STS-44 Atlantis in 1991, STS-54 Endeavour 1003 and STS-77 Endeavour in May 1996 spent most of his space journey attending numerous experiments such as earth observation experiments, radiation monitoring experiments and life sciences experiments in support of long duration space flights.
The ASE congress in Kuala Lumpur was the first to be held in Malaysia and the second after Japan.
ASE, which was formed in 1985, has 350 members and it aims at providing a forum for dialogue and to promote education on space science and technology.
by Saiful Bahari. Posted on October 8, 2010, Friday
Taken from http://www.theborneopost.com/?p=67346
Posted by M.Faiz at 7:09 PM No comments:
Malaysia On Right Track In Developing Aerospace Sector
MELAKA, Oct 8 (Bernama) -- Malaysia is on the right track in developing the aerospace sector by organising various programmes, hence placing itself at par with other developing countries which have the same mission.
Former astronaut from Russia, Alexander Ivanchenkov, 60, regards the cooperation between the Malaysian and Russian governments in sending Malaysia's first astronaut Datuk Dr Sheikh Muszaphar Shukor into space in October 2007 as apt in developing the field.
"Malaysia needs more such cooperation where it can encourage transfer of technology in aerospace to the country," he said through an interpreter after delivering a talk on space exploration at Universiti Teknikal Malaysia Melaka (UTeM), here, Thursday.
Also present was another Russian foremer astronaut Alexander Poleshchuk, 57, and former astronaut from the United States, Henry Hartsfield, 77.
They are in Malaysia with over 60 other astronauts and cosmonauts from 17 countries for the XXIII International Association of Space Explorers Planetary Congress themed "1Planet, 1Hope, 1Future", from Oct 5 to 10 in Kuala Lumpur.
Ivanchenkov who went into space for the first time on July 15, 1975, hoped Malaysia's aerospace sector development would be a continuous one by cultivating interest in aerospace among its young generation.
Meanwhile, Hartsfield said the development of the aerospace sector was not only limited to the technical aspects, but the development of human capital too, especially involving the young generation.
"The future of aerospace is in the hands of young people. They must master science and technology in order to carry on this effort (developing the sector), besides having a high level of discipline," he said.
Hartsfield who first went into space in June 1982, has been involved in many development programmes by the National Aeronautics and Space Administration (Nasa) since 1969.
The Malaysian Multimedia University in Bukit Beruang here also held a similar programme attended by over 1,000 university and school students who listened to talks given by six foreign astronauts.
Taken from BERNAMA
Pictures taken at Universiti Pertahanan Nasional Malaysia, one of the 11 participating universities during the Campus Space Walk community programme...
The crowd in UPNM
NASA Astronaut Richard Richards
I have a question...
Photo with the kids
Posted by M.Faiz at 2:20 AM No comments:
23rd ASE Planetary Congress officially launched in KL
The 23rd Planetary Congress for the Association of Space Explorers (ASE) was successfully launched in Istana Hotel, Kuala Lumpur this morning. Dato' Dr. Sheikh Muszaphar Shukor, Malaysia's first angkasawan is playing host to this year's congress with the theme of One Planet, One Hope, One Future. The event was kicked off by the Deputy Minister of the Ministry of Higher Education, Dato' Saifuddin Abdullah followed by the first technical session on human exploration titled perspectives of language and culture chaired by astronaut Gerhard Thiele. The congress serves as a forum for astronaut members to interact professionally and develop ASE programmes, importantly motivational talks that will be carried out in 11 universities throughout Malaysia this Thursday 7th of October 2010. The event is a first of it's kind in South East Asia whereby 61 participating astronauts from 17 countries are gathering to encourage international cooperation and essentially promote education in space science and engineering.
Children with flags from participating nations
Go for Launch!!!
ASE members
Campus Space Walk: Association of Space Explorers XXIII Planetary Congress Kuala Lumpur, Malaysia 2010
A group of astronauts will conduct presentations for students in selected educational institutions nationwide in conjunction with the 23rd Planetary Congress for the Association of Space Explorers. The sessions will begin from 10am to 1230pm respectively in each campus.
Participating universities:
National University of Malaysia (UKM)
Astronauts: Dato' Sheikh Muszaphar (Malaysia), Alexei Leonov (Russia), Yang Liwei (China), Sultan Al Saud (Saudi Arabia), Soyeon Yi (Korea)
Universiti Pertahanan Nasional Malaysia (UPNM)
Astronauts: Leroy Chiao (USA), Fei Junlong (China), Richard Richards (USA), Rusty Schweickart (USA), Chiaki Mukai (Japan), Yuri Baturin (Russia)
Politeknik Ungku Omar Perak (PUO)
Astronauts: John Fabian (USA), Aleksandar Aleksandrov (Bulgaria), Franz Viehbock (Austria), Pam Melroy (USA)
Nilai University College (NILAI UC)
Astronauts: Klaus-Dietrich Flade (Germany), Vladimir-Lyakhov (Russian), Don Williams (USA), Miroslaw Hermaszewski (Poland), Sergei Treschev (USA)
University of Technical Malaysia Melaka (UTeM)
Astronauts: Hank Hartsfield (USA), Alexander Poleshchuk (Russia), Ulrich Walter (Germany), Alexander Ivanchenkov (Russia), Alexander Lazutkin (Russia)
Multimedia University Malacca (MMU)
Astronauts: Elena Kondakova (Russia), Jon McBride (USA), Valeri Ryumin (Russia), Charlie Walker (USA), Jim Voss (USA), Karol "Bo" Bobko (USA)
Universiti Utara Malaysia (UUM)
Astronauts: Chris Heidfield (Canada), Claude Nicollier (Switzerland), Anousheh Ansari (USA)
University of Malaysia Perlis (UniMAP)
Astronauts: Soichi Noguchi (Japan), Dirk Frimout (Belgium), Bonnie Dunbar (USA), Bertalan Farkas (Hungary)
Universiti Darul Iman Malaysia (UNISZA)
Astronauts: Toyohiro Akiyama (Japan), Anatoli Berezovoi (Russia), Patrick Baudry (France), Yuri Gidzenko (Russia)
Astronauts: John Phillips (USA), Pavel Vinogradov (Russia), Gerhard Thiele (Germany), Sergei Avdeev (Russia), Oleg Kotov (Russia)
Universiti Malaysia Sarawak (UNIMAS)
Astronauts: Richard Garriott (USA), Owen Garriott (USA), Mario Runco (USA)
Hope to see you all there...
Astrophysicist to be named UN's alien ambassador
If an alien ever says "take me to your leader", where would you take them?
Pretty soon the answer will be a Malaysian astrophysicist named Mazlan Othman, who's expected to be appointed as the United Nation's space ambassador for extraterrestrial contact affairs. That gives her the right to make the first official response to any travelling aliens.
Othman was Malaysia's first astrophysicist, became the head of the country's national planetarium (Negara) and launched the first Malaysian astronaut, Sheikh Muszaphar Shukor, to the International Space Station in October 2007.
Now, Othman is the director of the UN's Office for Outer Space Affairs (UNOOSA); a branch of the General Assembly, established in 1962. The office is responsible for promoting international co-operation and peace in dealing with outer space, and includes topics such as satellite navigation and space debris.
If approved, her latest role would place her as the go-to contact in the event of aliens making contact with earth. She's got to pitch her new job title at a scientific conference at the Royal Society's Kavli conference centre in Buckinghamshire next week, then if the idea is backed by the UN scientific advisory committees, it'll be passed to General Assembly.
Othman recently gave a talk to fellow scientists, where she said that the continued search sustains the hope that "some day humankind will receive signals from extraterrestrials. When we do, we should have in place a coordinated response that takes into account all the sensitivities related to the subject".
Stephen Hawking suggested earlier this year that aliens almost certainly exist, but cautioned humanity against making contact. He warned that extraterrestrial nomads could be "looking to conquer and colonise whatever planets they can reach."
By Mark Brown |27 September 2010
Taken from: http://www.wired.co.uk/news/archive/2010-09/27/alien-ambassador
Posted by M.Faiz at 10:01 AM No comments:
Aerospace Club members take turns at the controls
NOAH Aiman Mohd Faiz, 10, and Jonathan Ang Kwang Siong, 10, were captaining a Boeing 737-400 confidently, sending the aircraft soaring into the sky.
Suddenly, the clear, blue sky turned into complete darkness. Before they could react, soft lights illuminated the horizon and dawn had arrived.
The kids did not panic. They kept their hands on the yoke while the aircraft flew steadily onward.
Smooth landing: Capt Mohd Radzi giving some advice to the children when they were on the simulator.
Behind them, Malaysia Airlines (MAS) flight operations manager Captain Mohd Radzi Mohamad Alias was choosing the scenes from a touch screen.
There were also buttons to customise the weather conditions. When the turbulence setting was activated, everyone in the cockpit felt the instability.
Noah and Jonathan were in a flight simulator with equipment identical to that of the original aircraft at MAS Flight Crew Training Centre in Sultan Abdul Aziz Shah Airport, Subang.
Organised by Astronautical Association of Malaysia and Aerospace Education Services, the visit gave about 10 kids and teenagers a unique flying experience right in the centre that produces pilots for the national carrier.
They were given a briefing before they toured the building to visit the computer-based training centre and a number of other simulators.
Hands-on: Mohammed Faiz (right) helping Suhaimi Abdul Rahman to put on an oxygen mask.
When Mohd Radzi put on his epaulettes, jacket and hat, the kids looked at him with great admiration.
The three-hour experience fuelled Fariz Izlan Feizal's dream of becoming a pilot one day.
"I have wanted to be a pilot since I was six," the 15-year-old said.
Ahmad Helmi Abu Kassim, 23, a student from Universiti Kuala Lumpur's Malaysian Institute of Aviation Technology (MIAT), saluted MAS Captain Mohammed Faiz Kamaludin animatedly after his attempt in the simulator.
"It is difficult for us on the aircraft engineering side, and today, I realised that it is just as hard for the pilots to steer an aircraft, especially to perform a landing," he said.
Mohammed Faiz, who was one of the final four candidates to be Malaysia's astronaut in 2006, said the Astronautical Association of Malaysia was founded last year, comprising of the former top 59 astronaut candidates.
It involves in talks and programmes to promote aerospace and science to the younger generation.
"Aerospace Education, on the other hand, organises space camps, astronomy nights, classes on aerospace and so on.
"The kids who are here today are its Aerospace Club members," he said.
From the Star Online by Tho Xin Yi
Malaysia Airlines Flight Simulator Centre Visit
Today, the association together with 10 schoolchildren and a few engineering students made a visit to the Malaysia Airlines Flight Simulator Centre in Subang. After an informative briefing by Capt. Mohd Radzi, we were given the chance to fly a full-motion Boeing 737-400 simulator. The aspiring pilots took turns at the flight controls and found out that it wasn't really easy to land a jet aircraft..hehe! Nonetheless everyone had fun and we truly enjoyed ourselves. We were also given a tour of the state of the art CBT (computer based training) centre and other simulators within the complex such as the F50, A330, B777, B747 and the latest Airbus 380. In the end, we had a great day and would like to thank Malaysia Airlines for letting us visit their Flight Simulator Centre.
Capt. Mohd Radzi giving us a briefing
Can't wait for our turn to fly...
Ok ..what do I do now???
Thank you MAS!!!!
Career Talk @ Kolej Matrikulasi Selangor, Banting, 7th August 2010
From Left: Haizam, Harridon, Shafini, Norisham and Yusfi
Promoting 'Aspirasi Angkasawan' on MHI TV3
Our Book 'Aspirasi Angkasawan' Launched
Our book 'Aspirasi Angkasawan' was officially launched today in conjunction with PM's visit to the Karangkraf HQ in Shah Alam. It will be available in all major book stores such as MPH and Popular or you can purchase it on-line at eBay.com.my. Search categories for Books > Non-English Books or just type in 'Aspirasi Angkasawan'. For a limited time only we are offering free postage via 'pos ekspres' to anywhere within Malaysia...so grab a copy today!!!
Successful Soft Launch of 'Aspirasi Angkasawan' Book
We had a successful soft launch of our book 'Aspirasi Angkasawan' today at the Kompleks PKNS, Shah Alam with a simple ceremony. Our books are available at a special 20% discount during the Pesta Buku Selangor 2010 until the 5th of July 2010. So come down to the BukuPrima booth and get your copy today. Our official launch by Dato' Dr. Sheikh Muszaphar Shukor will be held on the 6th of July 2010. We would like to thank everyone that came by today to witness our event. Do enjoy the pics...
Giving my speech
On stage with the publisher and association members
Ok cut it gently now...
Signings for schoolchildren
On stage with family members
Soft Launch of our book 'Aspirasi Angkasawan' 25th June 2010
In conjunction with the 'Pesta Buku Selangor 2010' we will be having a soft launch of our book 'Aspirasi Angkasawan' from 4 to 6pm next Friday 25th of June 2010 at the foyer of Kompleks PKNS, Shah Alam. So come one, come all to our book launch and purchase it at a super discounted price. Our authors/members will be there to personally sign copies of your book. Hope to see everyone there...
Aerospace Adventure Workshops & Bernam River Fly-in
I recently gave a talk to the pupils of SJKC Sungai Buloh, Selangor to promote our aerospace adventure workshops catered for schoolchildren. The first workshop was successfully conducted last Friday on the 11th of June 2010 followed by our involvement with the Bernam River Fly-in which was held at the Bernam River Airfield the following day on the 12th of June 2010. It was a great double event for us and do look out for our next event, which is the launch of our book 'Aspirasi Angkasawan'. Until then enjoy some pictures of the Bernam River Fly-in.
Dune buggy rides for kids
Water rocket launches by Sam
The Pitts Special going off for some aerobatics
Some inverted action
A low fly-pass
The Pitts Special produced some great aerobatics
Cessna Caravan
Heli landing
With Hozay
Sam was the MC too
Flagging off the air race
Pleasure flights with the Cessna
Aerial view of Bernam River Airfield
Some of the vintage cars on display
The crowd at Bernam River Airfield
Our book 'Aspirasi Angkasawan' is No.7 on MPH Best...
Malaysia On Right Track In Developing Aerospace Se...
23rd ASE Planetary Congress officially launched in...
Campus Space Walk: Association of Space Explorers ...
Career Talk @ Kolej Matrikulasi Selangor, Banting,...
Successful Soft Launch of 'Aspirasi Angkasawan' Bo...
Soft Launch of our book 'Aspirasi Angkasawan' 25th...
Aerospace Adventure Workshops & Bernam River Fly-i... | {
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Raj Bhavsar (né le à Houston) est un gymnaste artistique américain.
Biographie
Raj Bhavsar intègre l'équipe nationale américaine en 1999. Il remporte aux Jeux olympiques d'été de 2008 à Pékin la médaille de bronze du concours général par équipe. Il participe aussi au concours des anneaux, des barres parallèles, du cheval d'arçons et du sol, sans dépasser le stade des qualifications.
Palmarès
Jeux olympiques
Pékin 2008
médaille de bronze au concours général par équipes.
Championnats du monde
Gand 2001
médaille d'argent au concours général par équipes.
Anaheim 2003
médaille d'argent au concours général par équipes.
Jeux panaméricains
Winnipeg 1999
médaille d'argent au concours général par équipes.
Notes et références
Liens externes
Gymnaste artistique masculin américain
Gymnaste artistique masculin aux Jeux olympiques d'été de 2008
Naissance en septembre 1980
Naissance à Houston
Médaillé de bronze olympique américain
Étudiant de l'université d'État de l'Ohio | {
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{"url":"http:\/\/mathhelpforum.com\/advanced-statistics\/65169-stats-multiple-probabilities.html","text":"# Math Help - Stats: Multiple Probabilities\n\n1. ## Stats: Multiple Probabilities\n\n2. Peter is a door-to-door sales representative who makes a sale at only 8% of his house calls. If Peter makes 219 house calls today, what is the probability that:\n(a) he makes a sale at 12 or fewer houses?\n\nSomeone was trying to help me and said 12 x 100\/219 = 5.6% but I have no idea where the 100\/219 comes into play.\n\n(b) he makes a sale at 20 or fewer houses?\n\n(c) he makes a sale at 15 to 25 houses?\n\n2. Originally Posted by JeanetteR\n2. Peter is a door-to-door sales representative who makes a sale at only 8% of his house calls. If Peter makes 219 house calls today, what is the probability that:\n(a) he makes a sale at 12 or fewer houses?\n\nSomeone was trying to help me and said 12 x 100\/219 = 5.6% but I have no idea where the 100\/219 comes into play. Mr F says: This is wrong.\n\n(b) he makes a sale at 20 or fewer houses?\n\n(c) he makes a sale at 15 to 25 houses?\nLet X be the random variable number of sales made.\n\nX ~ Binomial(n = 219, p = 0.08)\n\n(a) Calculate $\\Pr(X \\leq 12)$.\n\n(b) Calculate $\\Pr(X \\leq 20)$.\n\nA normal approximation to the binomial distribution would be valid here.\n\n3. For part C\n\nYou have to calculate\n\nP(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)\n\nX ~ Binomial(n = 219, p = 0.08)\nto find P(x=15) = ( 219 C 15 )(0.08)^15(1-0.08)^204\n\nNow you have to calculate the rest and add them together.","date":"2015-08-30 04:55:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 2, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5008981227874756, \"perplexity\": 734.0866566153104}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-35\/segments\/1440644064869.18\/warc\/CC-MAIN-20150827025424-00236-ip-10-171-96-226.ec2.internal.warc.gz\"}"} | null | null |
For: Arcade, Atari ST, Commodore 64, IBM PC/Compatibles
Main Genre:
Sub-Genre:
3rd-Person
Visual Presentation:
Scrolling (Horizontal or Vertical)
Arcade version of Road Runner
Road Runner is an action game originally released in arcades by Atari Games in 1986 and later ported to several home computers including the Atari ST, Commodore 64, IBM PC, and more. The game is inspired by the famous Warner Brothers cartoon series; as the titular Road Runner, players need to eat bird seed found along a winding desert road while evading Wile E. Coyote who is in constant pursuit. The game features a graphical style along with music and sound effects which remain faithful to the original cartoons.
The game screen in Road Runner scrolls from right to left and depicts a desert road similar to the ones often found in the cartoon series. As the Road Runner, players run along the road and can eat the piles of bird seed that are found. Players need to make sure the Road Runner's energy is kept up; if five bird seed piles are skipped, the Road Runner becomes faint and a life is lost (A meter at the top of the screen shows the current bird seed level). Throughout the game Wile E. Coyote is constantly chasing the Road Runner, and players lose a life if caught. While the coyote often just runs, he can't keep up to the Road Runner at full speed so he'll frequently use a variety of gadgets and inventions (usually from the Acme Corporation) in an attempt to capture the road runner (especially if players are able to get far ahead of him). Rockets, roller skates, giant springs, dynamite, helicopters, and many more inventions inspired by the cartoon will give the coyote an advantage (such as extra speed or the ability to jump off of the road instead of having to stay on it). This can make it trickier for the player to avoid capture, however the inventions often backfire so if players can evade long enough they'll have a brief moment before the coyote is able to recover.
The desert landscape can also present obstacles; While the road begins fairly wide and straight, it soon turns narrow with lots of turns making navigating more difficult (since the Road Runner has to stay on the road, the narrow roads provide less room to avoid the coyote). Other obstacles such as oncoming traffic and falling boulders appear in some levels too; these will cost the player a life if hit, however they also provide an opportunity to provide cover for an escape. Players begin the game with a limited number of lives and they game ends when all are lost to either being caught by the coyote or being hit by an obstacle. Bonus lives can be earned for crossing certain point thresholds throughout the game.
Platform: Arcade
Produced by: Norm Avellar, Greg Rivera
Directed by: Mike Hally
Backgrounds by: Sam Comstock, Mark West
Animation by: Susan G. McBride
Audio by: Hal Canon, Earl Vickers
Location Tech: Rob Rowe
Support: Jack Aknin, Brad Fuller, Rich Moore, Mike Albaugh, Pat McCarthy, Don Paauw
Special Thanks to: Ed Logg, Chris Drobny, Gary Stempler, Dennis Harper, Synthia Petroka, Dave Pettigrew, et al
Platform: IBM PC/Compatibles
IBM Conversion by: John Siegesmund
Click on a picture below to view a larger version.
Arcade Version
© 2020 PixelatedArcade | {
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NGC 3426 is een spiraalvormig sterrenstelsel in het sterrenbeeld Leeuw. Het hemelobject werd op 23 maart 1887 ontdekt door de Amerikaanse astronoom Lewis A. Swift.
Synoniemen
UGC 5975
MCG 3-28-20
ZWG 95.46
ARAK 262
PGC 32577
Zie ook
Lijst van NGC-objecten
Externe links
NASA/IPAC Extragalactic Database
SIMBAD Astronomical Database
SEDS
NGC-object in Leeuw
Sterrenstelsel in Leeuw | {
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\section{INTRODUCTION}
The molecular weight distribution and architecture are two important characteristics of a system of polymer chains \cite{RubinsteinColby2003}. They strongly affect material properties such as dynamic moduli, fracture toughness, glass transition temperature, and viscosity \cite{RubinsteinColby2003, Nunes1982, Suneel2002}. Experimental methods for an accurate determination of molecular weight distributions are thus of great interest \cite{Suneel2002, Mead1994, Williamson2016}. Theoretically, it is also highly desirable if the molecular weight distribution of a polymer can be predicted \textit{a priori} based on the knowledge of the polymerization reaction without even synthesizing the polymer. Such a theoretical method will be a valuable tool not only useful for understanding experimental measurements but also beneficial for other theories and models aiming to predict polymer properties. For example, Nichetti and Manas-Zloczower proposed a theoretical model to predict viscosity of a polymer melt based on its molecular weight distribution that was determined by fitting the gel permeation chromatography data to statistical distribution functions \cite{Nichetti1998}. A method to quickly generate molecular weight distributions before polymers are synthesized thus might be able to advance the predictive capability of such theories.
A theory on the constitution and molecular size distribution of a step-growth polymer was proposed by Flory and Stockmayer many years ago \cite{Flory1941, Flory1941a, Flory1941b, Stockmayer1943, Stockmayer1944, Stockmayer1952} and has been frequently used to determine the gel point. Flory studied the polymerization of bifunctional monomers mixed with trifunctional and tetra functional branching units and made two fundamental assumptions. First, the same functional group has the same probability to react with another group and this probability is not affected by the length of the polymer to which the functional group belongs as well as the position of the functional group on that polymer. Secondly, ring polymers are not formed. Stockmayer extended the theory to branching units with arbitrary functionalities and derived the Stockmayer formula for the number of a polymer with a given composition, though ring structures were still excluded. The predictions of the Flory-Stockmayer theory, including the gel point and the average molecular weight, have been tested experimentally \cite{Peebles1971, Matsumoto1995, Matsumoto1999, Bannister2006, GaoHaifeng2007, Schultz2009, Rosselgong2009}. However, the entire distribution is hard to probe experimentally and often only some average molecular weight is measured. Practically, it is also difficult to directly predict the molecular weight distribution using the Flory-Stockmayer theory because of mathematical complexity of computing the numbers of all possible molecules in a branched polymer system. Furthermore, the Flory-Stockmayer theory is only expected to be valid below the gel point. Beyond the gel point, the formation of cyclics and closed loops in network structures (i.e., branching) becomes significant and the theory may fail \cite{Lyu2018, Lyu2018a}.
Monte Carlo (MC) methods are a class of techniques based on random sampling to numerically solve problems that have a probabilistic interpretation \cite{Landau2005}. MC methods have broad applications in polymer science \cite{Hsu2011, Brandao2015}, especially in polymer reaction engineering \cite{Brandao2015}. Johnson and O'Driscoll used MC simulation to study sequence distributions in step-growth copolymerization \cite{Johnson1984}. Tobita applied MC simulation to a wide range of polymerization problems, including free-radical cross-linking copolymerization \cite{Tobita1993}, emulsion polymerization \cite{Tobita1995}, the modification of polymer via crosslinking and degradation \cite{Tobita1995b}, long-chain branching and random scission \cite{Tobita2001}, and living radical polymerization \cite{Tobita2006b, Tobita2007}. Hadicke and Stutz used an amine-cured epoxy as an example to compare the structure of step-growth networks obtained by MC simulation to that predicted by a branching theory \cite{Hadicke2002}. He \textit{et al.} applied a MC method to simulate self-condensing vinyl polymerization in the presence of multifunctional initiators and probed the role of reactive rate constants \cite{HeXuehao2001, HeXuehao2003}. Rouault and Milchev \cite{Rouault1997} and He \textit{et al.} \cite{HeJunpo1997} performed MC simulations to study the kinetics and chain length distributions in living polymerization. Prescott used a MC model to show that chain-length dependent termination plays a significant role in living/controlled free-radical polymerization systems containing reversible transfer agents \cite{Prescott2003}. In a series of papers, Al-Harthi \textit{et al.} used dynamic MC simulations to study atom-transfer radical polymerizations \cite{Al-Harthi2006, Al-Harthi2007, Al-Harthi2009, Al-Harthi2009a}. Polanowski \textit{et al.} \cite{Polanowski2010, Polanowski2011} and Bannister \textit{et al.} \cite{Bannister2009} used MC methods to study the branching and gelation in living copolymerization of vinyl and divinyl monomers. Recently, Lyu \textit{et al.} used a similar model to study the atom transfer radical and the conventional free radical polymerization of divinyl monomers and checked the applicability of the Flory-Stockmayer theory in such systems \cite{Lyu2018, Lyu2018a}. Gao \textit{et al.} used kinetic MC methods to simulate free radical copolymerization processes and discussed how to accelerate such simulations using scaling approaches \cite{GaoHanyu2015, GaoHanyu2017}. Meimaroglou \textit{et al.} proposed a MC algorithm to calculate the molecular weight distribution for linear polymers and the bivariate molecular weight-long chain branching distribution for highly branched polymers \cite{Meimaroglou2007}. They also used MC simulation to investigate the molecular, topological, and solution properties of highly branched low-density polyethylene \cite{Meimaroglou2011} and the ring-opening homopolymerization of L,L-Lactide \cite{Meimaroglou2017}. Iedema \textit{et al.} developed a MC simulation model including both branching and random scission to calculate the molecular weight and branching distributions and compared their calculations to experimental measurements on high-density polyethylene \cite{Iedema2013}. Yaghini and Iedema compared the results on low-density polyethylene from such MC simulations to the predictions of a multiradical model based on a Galerkin finite element approach \cite{Yaghini2015}.
One important application of MC simulations is to quickly compute molecular weight distributions \cite{Tobita1993, Tobita1995, Tobita1995b, Tobita2001, Tobita2006b, Tobita2007, Rouault1997, Milchev2000, HeJunpo1997, GaoZehui2015, Maafa2007, Soares2007, Hsu2011, Hamzehlou2013, Iedema2013, Yaghini2015, GaoHanyu2015, GaoHanyu2017, Lyu2018, Lyu2018a}. In MC simulations, all structures including rings and networks allowed by a polymerization reaction can be produced \cite{Fawcett1995}, no matter the system is below or beyond the gel point \cite{Tripathi2014}. Various schemes can also be implemented for the kinetics of the polymerization, which thus allows us to test the specific assumptions made by a theory. The Gillespie algorithm can be used to speed up the kinetics of a reaction \textit{in silico} and enable a reactive system to quickly reach a steady state \cite{Gillespie1977, Gillespie2007}. In this paper, we develop a MC simulation model based on the Gillespie algorithm to study the polymerization of polyetherimides (PEIs) in the presence of chain terminators and branching agents. The results from the MC simulations are used to test the Flory-Stockmayer theory including its assumption on the reaction rates.
This paper is organized as follows. In Sec.~\ref{sec:stockmayer} the Flory-Stockmayer theory is introduced, the technical challenge of computing molecular weight distributions with this theory is discussed, and an approximation method is proposed. In Sec.~\ref{sec:MC} we describe the MC model of the polymerization process of branched PEIs in detail. In Sec.~\ref{sec:results}, MC results are compared to the predictions of the Flory-Stockmayer theory. Practically, computations of molecular weight distributions can be only be executed for a small system either with the Flory-Stockmayer theory or the MC model. We thus include a discussion on the effect of finite system size in this section. Although the emphasis is on stoichiometric, fully reacted systems, those that are only partially reacted and/or nonstoichiometric are also discussed in Sec.~\ref{sec:results}. Finally, a brief summary is provided in Sec.~\ref{sec:conclusions}.
\section{Flory-Stockmayer Theory of Step-Growth Polymers} \label{sec:stockmayer}
Flory and Stockmayer considered a general step-growth polymer that consists of two types of monomers, $A$ and $B$. All reactions occur between $A$ and $B$. There are $i$ type-$A$ monomers denoted as $A_1$, $A_2$, ..., $A_i$. To simplify notation, we also use $A_q$ with $q\in \{1, 2, ..., i\}$ to denote the number of $A_q$ monomers. Similarly, there are $j$ type-$B$ monomers and the corresponding numbers are $B_1$, $B_2$, ..., $B_j$, respectively. The symbol $f_q$ denotes the functionality of an $A_q$ monomer, where $q\in \{1, 2, ..., i\}$, i.e., there are $f_q$ functional groups on an $A_q$ monomer that can form bonds with the corresponding functional groups on a $B_h$ monomer, where $h\in \{1, 2, ..., j\}$. The functionality of a $B_h$ monomer is denoted as $g_h$. The Flory-Stockmayer theory can be applied to a polymerized state where a fraction $p_A$ of all the functional groups on the type-$A$ monomers have reacted with a fraction $p_B$ of all the functional groups on the type-$B$ monomers. Therefore,
\begin{align}
\label{eq:constraint}
p_A\sum_{q=1}^i f_qA_q=p_B\sum_{h=1}^j g_hB_h.
\end{align}
In this paper, we call the systems with $\sum_{q=1}^i f_qA_q=\sum_{h=1}^j g_hB_h$ and thus $p_A = p_B$ as stoichiometric systems while those with $\sum_{q=1}^i f_qA_q \neq\sum_{h=1}^j g_hB_h$ and $p_A \neq p_B$ as nonstoichiometric. The systems with $p_A$ or $p_B$, or both, equal to 1 are fully reacted.
We use $N\{m,n\}$ to denote the number of molecules formed by $m_q$ monomers of sub-type $A_q$ and $n_h$ monomers of sub-type $B_h$, with $q$ running from 1 to $i$ and $h$ running from 1 to $j$. Here $\{m,n\}$ is a shorthand of $\{m_1, m_2., ..., m_i, n_1, n_2, ..., n_j\}$, which denotes the monomer composition of a given molecule. The Flory-Stockmayer theory predicts that
\begin{align}
\label{eq:stockmayer_dist}
\begin{split}
N\{m,n\}&=K\frac{\left(\sum_{q=1}^i f_q m_q-\sum_{q=1}^i m_q\right)!}{\left(\sum_{q=1}^i f_q m_q-\sum_{q=1}^i m_q-\sum_{h=1}^j n_h+1\right)!}\\
&\times \frac{\left(\sum_{h=1}^j g_h n_h-\sum_{h=1}^j n_h\right)!}{\left(\sum_{h=1}^j g_h n_h-\sum_{h=1}^j n_h-\sum_{q=1}^i m_q+1\right)!} \\
&\times \prod_{q=1}^i \frac{x_q^{m_q}}{m_q!}\prod_{h=1}^j \frac{y_h^{n_h}}{n_h!}
\end{split}
\end{align}
with
\begin{align}
x_q&=\frac{f_qA_q}{\sum_{l=1}^i f_lA_l}\frac{p_B\left(1-p_A\right)^{f_q-1}}{(1-p_B)}~,\\
y_h&=\frac{g_hB_h}{\sum_{l=1}^j g_lB_l}\frac{p_A\left(1-p_B\right)^{g_h-1}}{1-p_A}~,\\
K&=\frac{\left(1-p_A\right)\left(1-p_B\right)}{p_B }\sum_{q=1}^i f_qA_q \nonumber \\
&= \frac{\left(1-p_A\right)\left(1-p_B\right)}{p_A} \sum_{h=1}^jg_hB_h~.
\end{align}
Equation (\ref{eq:stockmayer_dist}) is called the Stockmayer formula, which gives the number of molecules of any monomer compositions. However, practically it is difficult to compute the molecular weight distribution from the Stockmayer formula, as all the possible combinations for $\{m_1, m_2., ..., m_i, n_1, n_2, ..., n_j\}$ have to be taken into account. Since $m_q$ runs from 1 to $A_q$ for $q\in \{1, 2, ..., i\}$ and $n_h$ runs from 1 to $B_h$ for $h\in \{1, 2, ..., j\}$, the total number of possible molecules is $\prod_{q=1}^i A_q!\times \prod_{h=1}^j B_h!$. This number is huge when there are many sub-types (i.e., large $i$ and $j$) and/or large numbers (i.e., large $A_q$ and $B_h$) of monomers involved in a polymerization.
For a molecule with composition $\{m,n\}$, the total number of monomers is $\sum_{q=1}^i m_q + \sum_{h=1}^j n_h$. Since the Flory-Stockmayer theory does not consider rings, the total number of bonds in this molecule must be $\sum_{q=1}^i m_q + \sum_{h=1}^j n_h-1$. When $p_A=p_B=1$, all the functional groups have reacted and in a given molecule the total number of the functional groups on all the type-$A$ monomers is equal to the total number of the functional groups on all the type-$B$ monomers. This number must also be equal to the total number of bonds in that molecule. Namely, for $p_A=p_B=1$ there are two identities,
\begin{align}
\sum_{q=1}^i f_q m_q=\sum_{q=1}^i m_q+\sum_{h=1}^j n_h-1
\label{eq:fully_reacted_constraint_1}
\end{align}
and
\begin{align}
\sum_{h=1}^j g_h n_h=\sum_{h=1}^j n_h+\sum_{q=1}^i m_q-1.
\label{eq:fully_reacted_constraint_2}
\end{align}
These two identities can help us simplify the Stockmayer formula for stoichiometric, fully reacted systems. Note that the terms in Eq.~(\ref{eq:stockmayer_dist}) involving $\left(1-p_A\right)$ and $\left(1-p_B\right)$ appear as
$$\left(1-p_A\right)^{\sum_{q=1}^i f_q m_q-\sum_{q=1}^i m_q-\sum_{h=1}^j n_h+1}$$
and
$$\left(1-p_B\right)^{\sum_{h=1}^j g_h n_h-\sum_{h=1}^j n_h-\sum_{q=1}^i m_q+1}~.$$
These terms can be dropped out because of Eqs.~(\ref{eq:fully_reacted_constraint_1}) and (\ref{eq:fully_reacted_constraint_2}). As a result, for fully reacted stoichiometric systems with $p_A=p_B=1$ the Stockmayer formula is simplified as
\begin{align}
\label{eq:stockmayer_dist_simp}
N\{m,n\}&=K\left(\sum_{q=1}^i f_q m_q-\sum_{q=1}^i m_q\right)!\nonumber \\
&\times \left(\sum_{h=1}^j g_h n_h-\sum_{h=1}^j n_h\right)!
\prod_{q=1}^i \frac{x_q^{m_q}}{m_q!}\prod_{h=1}^j \frac{y_h^{n_h}}{n_h!}
\end{align}
with
\begin{align}
x_q&=\frac{f_qA_q}{\sum_{l=1}^i f_lA_l}~,\\
y_h&=\frac{g_hB_h}{\sum_{l=1}^jg_lB_l}~,\\
K&=\sum_{q=1}^i f_qA_q =\sum_{h=1}^jg_hB_h~.
\end{align}
Computing $N\{m,n\}$ is not easy as it contains many factorials. The calculation can be expedited using the Stirling approximation,
\begin{align}
\label{eq:logstirling}
\log n!\approx \log\left(\sqrt{2\pi n}\right)+ n\log \left(\frac{n}{e}\right)+\log\left(1+\frac{1}{12n}\right)~.
\end{align}
Then for fully reacted stoichiometric systems, the Stockmayer formula can be approximated logarithmically as
\begin{align}
\label{eq:logN}
\log N\{m,n\} & \approx \log K+ \log \left(\sum_{q=1}^i f_q m_q-\sum_{q=1}^i m_q\right)! \nonumber \\
& +
\log\left(\sum_{h=1}^j g_h n_h-\sum_{h=1}^j n_h\right)! \nonumber \\
&+\sum_{q=1}^i \left(m_q\log x_q -\log m_q ! \right) \nonumber \\
&+\sum_{h=1}^j \left(n_h\log y_h -\log n_h !\right)~.
\end{align}
The computation of the molecular weight distribution from $N\{m,n\}$ can be further accelerated by noting that not all the combinations $\{m,n\}$ will yield a molecule. For a fully reacted stoichiometric system where $p_A=p_B=1$, Eqs.~(\ref{eq:constraint}), (\ref{eq:fully_reacted_constraint_1}), and (\ref{eq:fully_reacted_constraint_2}) can be used to reduce the total number of $\{m,n\}$. For the branched PEIs considered in this paper (see Sec.~\ref{sec:MC}), $f_1=1$, $f_2=2$, $g_1=2$ and $g_2=3$. The constraints become
\begin{align}
\label{eq:constrain_PEI_1}
m_1+2m_2&=2n_1+3n_2~,
\end{align}
and
\begin{align}
\label{eq:constrain_PEI_2}
m_2 = n_1+n_2-1~.
\end{align}
Combining Eqs.~(\ref{eq:constrain_PEI_1}) and (\ref{eq:constrain_PEI_2}), we get
\begin{align}
\label{eq:constrain_PEI_3}
m_1= n_2+2~.
\end{align}
Equations (\ref{eq:constrain_PEI_2}) and (\ref{eq:constrain_PEI_3}) indicate that $m_1$ and $m_2$ are totally constrained by $n_1$ and $n_2$ in an allowed composition. Furthermore, since $m_2\geq 0$, $n_1$ and $n_2$ cannot be zero at the same time. The time complexity to enumerate all possible molecules is thus $\mathcal{O}(B_1B_2)$, which is about $\mathcal{O}(Z^2)$ with $Z$ being the system size (i.e., the total number of monomers prior to polymerization). This time complexity is acceptable for small systems. However, if there are more sub-types of monomers, then the time complexity will increase exponentially as $\mathcal{O}(Z^w)$, where $w$ is the number of monomer sub-types. For not fully reacted or nonstoichiometric systems where $p_A$ or $p_B$ are less than 1, we lose the constrains that help reduce the number of possible $\{m,n\}$ and then computing the molecular weight distribution from $N\{m,n\}$ has to rely on Eq.~(\ref{eq:stockmayer_dist}) and will become more challenging, even though the Stirling approximation may still be used. In these situations, the MC model described below will serve as a solution as it does not suffer from such limitations and the time complexity of computing the molecular weight distribution with MC simulations is always $\mathcal{O}(Z)\times k$, where $k$ is the number of MC runs needed to obtain desired statistics. Usually, $k$ is about $10^3$ to $10^4$.
\section{Monte Carlo Model of Polymerization of Branched Polyetherimides}
\label{sec:MC}
\begin{figure}[h]
\includegraphics[width = 0.48\textwidth]{{Figure1.reaction.scheme-eps-converted-to}.pdf}
\caption{(a)-(d): The representation of the four types of monomers of branched PEIs in the MC simulation model. Each functional group containing one amine is mapped to a $B$ bead. Each functional group containing one carboxylic anhydride is mapped to an $A$ bead. (e): Each $A$ bead can form a bond with a $B$ bead, mimicking the condensation reaction between an amine group and a carboxylic anhydride group in the polymerization of PEIs.}
\label{fig:reaction_scheme}
\end{figure}
Four types of monomers are involved in the formation of branched PEIs, including 4,4'-bisphenol A dianhydride (BPADA), m-phenylenediamine (MPD), phthalic anhydride (PA), and tris[4-(4-aminophenoxy)phenyl] ethane (TAPE).\cite{Odle2018} The chemical structures of these monomers are shown in Fig.~\ref{fig:reaction_scheme}. The involved reaction is the condensation reaction between an amine group on MPD or TAPE and a carboxylic anhydride group on BPADA or PA. In the notation of the Flory-Stockmayer theory, PA is monomer $A_1$ with $f_1 = 1$, BPADA is monomer $A_2$ with $f_2 = 2$, MPD is monomer $B_1$ with $g_1 = 2$, and TAPE is monomer $B_2$ with $g_2 = 3$. Out of these monomers, PA is an end capper to terminate a chain and TAPE is a trifunctional branching agent. Fig.~\ref{fig:reaction_scheme} shows the representation of these monomers in our MC model. Each functional group containing one carboxylic anhydride is mapped to an $A$ bead and that containing one amine is mapped to a $B$ bead. Each $A$ bead can react with a $B$ bead to form a bond (i.e., $A+B\rightarrow AB$), which describes the condensation reaction between an amine group and a carboxylic anhydride group.
In the formation of branched PEIs consisting of the above 4 types of monomers, there are 4 possible reactions, as sketched in Fig.~\ref{fig:4_reactions}. Reaction 1 is between BPADA and MPD, which leads to the formation of a PEI backbone. Reaction 2 is between BPADA and TAPE that results in branching. Reaction 3 is between PA and MPD, which terminates a PEI chain. Reaction 4 is between PA and TAPE, which consumes one amine group on TAPE and effectively reduces its functionality by 1.
\begin{figure}[h]
\includegraphics[width = 0.48\textwidth]{{Figure2.four.reactions-eps-converted-to}.pdf}
\caption{The four reactions occurring in the polymerization of branched PEIs: (a) Reaction 1: BPADA + MPD, (b) Reaction 2: BPADA + TAPE, (c) Reaction 3: PA + MPD, and (d) Reaction 4: PA + TAPE.}
\label{fig:4_reactions}
\end{figure}
With the mapping in Fig.~\ref{fig:reaction_scheme} and the reaction scheme in Fig.~\ref{fig:4_reactions}, we perform MC simulations to study the polymerization of branched PEIs. We adopt the Gillespie algorithm to speed up MC simulations. Since only the final chain structures are concerned, we neglect the random process in the typical Gillespie algorithm that determines the time interval after which the next reaction occurs. We only keep the random process of picking a reaction at a time. At each MC step, all 4 reactions will have a probability to occur and the reaction rate of a particular reaction is determined by a rate constant and the concentration of the two types of monomers involved in that reaction. Mathematically, the probability of reaction $l$ is proportional to
\begin{align}\label{eq:reaction_rate}
P_l(L_l+R_l\rightarrow L_lR_l)=k_l n_{L_l}n_{R_l}~,
\end{align}
where $L_l$ ($R_l$) represents the reactant consisting of $A$ ($B$) beads, $k_l$ is a rate constant, $n_{L_l}$ ($n_{R_l}$) is a quantity that depends on the concentration of the reactant $L_l$ ($R_l$), and $l \in \{1, 2, 3, 4\}$ indexes the possible reactions sketched in Fig.~\ref{fig:4_reactions}. Specifically, $L_1$ and $L_2$ are BPADA, $L_3$ and $L_4$ are PA, $R_1$ and $R_3$ are MPD, and $R_2$ and $R_4$ are TAPE. Since all the 4 reactions can be reduced to the reaction between an $A$ bead and a $B$ bead (i.e., the reaction between a functional group containing one amine and another functional group containing one carboxylic anhydride) as shown in Fig.~\ref{fig:reaction_scheme}(e), $k_l$ will be set as a constant $k$ for all the 4 reactions and $n_{L_l}$ and $n_{R_l}$ can be expressed as
\begin{align}
\label{eq:concentration}
\begin{split}
& n_{L_1}=n_{L_2}=2n_\text{BPADA}~,\\
& n_{L_3}=n_{L_4}=n_\text{PA}~,\\
& n_{R_1}=n_{R_3}=2n_\text{MPD}~,\\
& n_{R_2}=n_{R_4}=3n_\text{TAPE}~,
\end{split}
\end{align}
where $n_\text{BPADA}$, $n_\text{PA}$, $n_\text{MPD}$, and $n_\text{TAPE}$ are the concentrations of monomers available for reactions (i.e., monomers with at least one unreacted functional group). In other words, $n_{L_l}$ ($n_{R_l}$) is the concentration in terms of the number of $A$ ($B$) beads on the reactant $L_l$ ($R_l$). The particular reason of writing $n_{L_l}$ and $n_{R_l}$ in this way will be discussed in Sec.~\ref{sec:rate_constant}.
At each MC step, the probability of Reaction $l$ to be chosen is equal to $P_l/\sum_{q=1}^4 P_q$. After a reaction is selected, a pair of $L_l$ and $R_l$ that have unreacted functional groups (i.e., with unreacted $A$ and $B$ beads, respectively) is randomly chosen to react. Then the system status is updated, including the bond information between the monomers and the identity of monomers with unreacted functional groups. The MC process is repeated for the updated system until no more reactions can occur or the system has reached a desired extent of reaction. The flow chart of the MC simulation model is shown in Fig.~\ref{fig:flow_chart}. Note that in this model, we made a simplification by not allowing backward reactions, which means that once formed, the bond between an $A$ bead and a $B$ bead cannot break. However, the model permits the formation of both rings and networks.
\begin{figure}
\center
\includegraphics[width = 0.45\textwidth]{{Figure3.flow.chart-eps-converted-to}.pdf}
\caption{The flow chart of the MC simulation model}
\label{fig:flow_chart}
\end{figure}
\section{Results and Discussion} \label{sec:results}
\subsection{Rate Constant $k$} \label{sec:rate_constant}
Equation (\ref{eq:concentration}) indicates that the reaction rate $P_l$ is based on the concentrations of the functional groups (i.e., $A$ beads or $B$ beads) on the reactants involved in that reaction. However, $P_l$ can also be computed from the concentrations of the available reactants themselves, i.e., the monomer concentrations. In this case, the reaction rate $P_l$ can be written in the same way as in Eq.~(\ref{eq:reaction_rate}) but with Eq.~(\ref{eq:concentration}) replaced by
\begin{align}
\label{eq:concentration_2}
\begin{split}
& n_{L_1}=n_{L_2}=n_\text{BPADA}~,\\
& n_{L_3}=n_{L_4}=n_\text{PA}~,\\
& n_{R_1}=n_{R_3}=n_\text{MPD}~,\\
& n_{R_2}=n_{R_4}=n_\text{TAPE}~.
\end{split}
\end{align}
To check which way of computing the reaction rates yields results that are more applicable to realistic systems, we performed a test with a simple system consisting of only PA and TAPE monomers, as shown in Table~\ref{table:test_reaction_rate}. For this system, there are only 4 possible final products, including single TAPEs and TAPEs connected with one, two, or three PAs, respectively.
\begin{table}[h]
\center
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Monomer & PA & BPADA & MPD & TAPE \\ \hline
Number & 2000 & 0 & 0 & 1000 \\ \hline
\end{tabular}
\caption{System used for checking the way to compute the reaction rates.}
\label{table:test_reaction_rate}
\end{table}
Figure~\ref{fig:check_reaction_rate} shows the results on the probability distribution of the 4 final products for the system in Table~\ref{table:test_reaction_rate}, for which gelation is not a concern. The comparison shows that the results from the MC simulations based on Eq.~(\ref{eq:concentration}) agree with the Flory-Stockmayer theory while those based on Eq.~(\ref{eq:concentration_2}) do not. Furthermore, for the molar ratio in Table~\ref{table:test_reaction_rate}, all the anhydride groups on the PA monomers are reacted and each amine group on a TAPE monomer has a 2/3 chance to be reacted in a fully reacted system. A simple statistical analysis shows that the probabilities for a TAPE monomer to react with 0, 1, 2, and 3 PAs are $\left(\frac{1}{3}\right)^3$, $3\times \frac{2}{3}\times \left(\frac{1}{3}\right)^2$, $3\times \left(\frac{2}{3}\right)^2\times \frac{1}{3}$, and $\left(\frac{2}{3}\right)^3$, respectively. These results are also plotted in Fig.~\ref{fig:check_reaction_rate} and are close to those from the Flory-Stockmayer theory and the MC simulations based on Eq.~(\ref{eq:concentration}). The small differences are due to the fact that the theory and simulations consider a finite system while the statistical model assumes an infinite system. We conclude that the reactions rates based on Eq.~(\ref{eq:concentration}) should be used in the MC simulations. From now on all the data presented in this paper are computed with Eq.~(\ref{eq:concentration}) for the reaction rates. In the next two sections, Sec.~\ref{sec:full_sys} and Sec.~\ref{sec:diff_size_sys}, we focus on fully reacted stoichiometric systems where $p_A=p_B=1$. We discuss partially reacted stoichiometric systems where $p_A=p_B<1$ in Sec.~\ref{sec:nfr_sys} and nonstoichiometric systems where $p_A \neq p_B$ in Sec.~\ref{sec:neq_sys}.
\begin{figure}
\center
\includegraphics[width = 0.45\textwidth]{{Figure4.test.reaction.rate-eps-converted-to}.pdf}
\caption{Probabilities of the 4 possible final products for the system in Table~\ref{table:test_reaction_rate}. Results are from the Flory-Stockmayer theory (red circles), the MC simulations based on Eq.~(\ref{eq:concentration}) (black crosses), the MC simulations based on Eq.~(\ref{eq:concentration_2}) (blue squares), and a simple statistical model discussed in the main text (green triangles). The MC results are averages of 10000 runs.}
\label{fig:check_reaction_rate}
\end{figure}
\subsection{Fully Reacted Stoichiometric Systems} \label{sec:full_sys}
For the branched PEIs considered in this paper, type $A$ monomers are BPADA and PA and type $B$ monomers are MPD and TAPE, with $f_1=1$, $f_2=2$, $g_1=2$ and $g_2=3$. From the Flory theory \cite{Flory1941}, the gel point is $\alpha_c=1/(g_2-1)=1/2$. However, for the systems at hand the expression of $\alpha$, which characterizes the level of cross-linking, has to be modified because each PA monomer as a chain terminator has only one functional group. The modified expression is
\begin{align}
\alpha&=\sum_{q=0}^\infty\left[p_A(1-\rho_1)p_B(1-\rho_2)\right]^q p_A(1-\rho_1)p_B\rho_2 \nonumber \\
&=p_Ap_B\frac{(1-\rho_1)\rho_2}{1-p_Ap_B(1-\rho_1)(1-\rho_2)}~,
\label{eq:alpha}
\end{align}
where $\rho_1$ is the fraction of functional groups on the terminators (i.e., PA monomers) with respect to all the functional groups on type $A$ monomers and $\rho_2$ is the fraction of functional groups on the branching agents (i.e., TAPE monomers) with respect to all the functional groups on type $B$ monomers. For a fully reacted stoichiometric system, $p_A=p_B=1$ and this expression can be simplified as
\begin{align}
\alpha=\frac{(1-\rho_1)\rho_2}{\rho_1+\rho_2-\rho_1\rho_2}~.
\label{eq:alpha_2}
\end{align}
\begin{table*}[h]
\resizebox{\textwidth}{!}{%
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
& PA & BPADA & MPD & TAPE & $\rho_1$ &$\rho_2$ & $p_A$ & $p_B$ & $\alpha$ & $M_n$ (Da) & $M_w$ (Da) & $M_z$ (Da) \\ \hline
$S_<$ & 50 & 670 & 680 & 10 &0.0360 & 0.0216 & 1 & 1 & 0.366 & $19120 \pm 33$ & $52126\pm 545$ & $78671\pm 2488$ \\ \hline
$S_\simeq$ & 50 & 670 & 671 & 16 &0.0360 & 0.0345 & 1 & 1 & 0.481 & $22000\pm 15$ & $77353\pm 307$ & $116227\pm 499$ \\ \hline
$S_>$ & 50 & 670 & 620 & 50 &0.0360 & 0.108 & 1 & 1 & 0.743 & $51055\pm 125$ & $330124\pm458$ & $369588\pm 348$ \\ \hline
\end{tabular}}
\caption{Three fully reacted, stoichiometric systems below, around, and beyond the gel point. The first column is the system label. The next 4 columns list the number of each type of monomers. The values of $\rho_1$ and $\rho_2$ are determined from the monomer numbers. The value of $\alpha$ is computed using Eq.~(\ref{eq:alpha}). The average molecular weights, $M_n$, $M_w$, and $M_z$, are from the MC simulations.}
\label{table:casestb1}
\end{table*}
We can vary the numbers of monomers to tune $\rho_1$ and $\rho_2$, thus putting the fully reacted system below, around, or beyond the gel point. Three such systems are listed in Table~\ref{table:casestb1}, where $\rho_2$ is changed by varying the numbers of MPD and TAPE monomers. In the MC simulations of these stoichiometric systems, we set $p_A = p_B = 1$, thus allowing the systems to be fully reacted.
\begin{figure}[h]
\center
\includegraphics[width = 0.45\textwidth]{{Figure5.three.systems-eps-converted-to}.pdf}
\caption{Molecular weight distribution for the three systems in Table~\ref{table:casestb1}: (a) $S_<$, (b) $S_\simeq$, and (c) $S_>$. The results are for the Flory-Stockmayer theory (red circles) and the MC simulations (blue squares). The MC results are averages of 1000 runs for $S_<$ and 10000 runs for $S_\simeq$ and $S_>$.}
\label{fig:three_systems}
\end{figure}
The results on the molecular weight distribution from the Flory-Stockmayer theory and the MC simulations are shown in Fig.~\ref{fig:three_systems}. The comparison shows that for a system below the gel point such as $S_<$ (Fig.~\ref{fig:three_systems}(a)), the MC results agree well with the Flory-Stockmayer theory. For $S_\simeq$ which is close to the gel point, the Flory-Stockmayer theory overestimates the fraction of low molecular weight polymers and underestimates the fraction of high molecular weight species when compared to the results from the MC simulations, as shown in Fig.~\ref{fig:three_systems}(b). The discrepancy between the Flory-Stockmayer theory and the MC results becomes more dramatic for systems above the gel point. For $S_>$, $\alpha = 0.74308$, way above the critical gel point $\alpha_c = 0.5$. The Flory-Stockmayer theory predicts a probability density that is about 8 times of the MC result in the region of low molecular weight from 0 to about $0.5\times 10^5$ Da, as shown in Fig.~\ref{fig:three_systems}(c). However, the MC simulations show a significant fraction of polymers in the region of molecular weight higher than about $1.5\times 10^5$ Da and these high molecular weight polymers are completely overlooked by the Flory-Stockmayer theory, as shown in the inset of Fig.~\ref{fig:three_systems}(c). This discrepancy is not surprising as beyond the gel point, polymers with a large network structure are expected and closed loops can frequently emerge in such polymers. The Flory-Stockmayer theory does not consider the formation of rings and thus cannot accurately predict the molecular weight distribution for systems above the gel point.
\subsection{Effect of System Size} \label{sec:diff_size_sys}
In experiments, the amount of monomers involved is at the order of moles, i.e., at the order of $10^{23}$. It is thus practically impossible to directly compute the molecular weight distribution from the Stockmayer formula (Eq.~(\ref{eq:stockmayer_dist})) for such macroscopic systems. These systems are also out of the reach of MC simulations that typically deals with systems of fewer than $10^6$ monomers. A natural question we can ask is: if we keep the molar ratios unchanged but reduce the numbers of participating monomers in proportion, can we use either the Flory-Stockmayer theory or the MC simulations to generate a molecular weight distribution that is applicable to a macroscopic system? To answer this question, we test 4 additional systems listed in Table~\ref{table:casestb2}. The smallest system has 10 PA, 134 BPADA, 146 MPD, and 2 TAPE and is denoted as $S_1$. Then the numbers of monomers are increased 10, 50, and 80 fold by keeping the ratios to generate systems $S_{10}$, $S_{50}$, and $S_{80}$. The subscript of the system label reflects the size ratio with respect to the smallest system, $S_1$. In this notation, the system $S_<$ in Table~\ref{table:casestb1} is equivalent to $S_5$. All these systems are still below the gel point when fully reacted.
\begin{table*}[h]
\resizebox{\textwidth}{!}{%
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
& PA & BPADA & MPD & TAPE & $\rho_1$ & $\rho_2$ & $p_A$ & $p_B$ & $\alpha$ & $M_n$ (Da) & $M_w$ (Da) & $M_z$ (Da) \\ \hline
$S_{1}$ & 10 & 134 & 136 & 2 &0.0360 & 0.0216 & 1 & 1 & 0.366 & $15742\pm 14$ & $30829\pm 46$ &$37334\pm 57$ \\ \hline
$S_{10}$ & 100 & 1340 & 1360 & 20 &0.0360 & 0.0216 & 1 & 1 & 0.366 & $19799\pm 18$ & $59940\pm 607$ & $101321\pm 1441$ \\ \hline
$S_{50}$ & 500 & 6700 & 6800 & 100 &0.0360 & 0.0216 & 1 & 1 & 0.366 & $20361\pm 4$ & $73582\pm 619$ & $161904\pm 2612$ \\ \hline
$S_{80}$ & 800 & 10720 & 10880 & 160 &0.0360 & 0.0216 & 1 & 1 & 0.366 & $20417\pm 3$ & $75980\pm 550$ & $177919\pm 2712$\\ \hline
\end{tabular}}
\caption{Four fully reacted, stoichiometric systems all below the gel point but with the size increased proportionally without changing the fraction of each type of monomers. The entries have the same format as in Table~\ref{table:casestb1}. The subscript of the system label in the first column indicates the size ratio with respect to the base system, $S_1$. The average molecular weights, $M_n$, $M_w$, and $M_z$, are from the MC simulations.}
\label{table:casestb2}
\end{table*}
\begin{figure}
\center
\includegraphics[width = 0.45\textwidth]{{Figure6.system.size.effect-eps-converted-to}.pdf}
\caption{Molecular weight distribution predicted by the Flory-Stockmayer theory for systems with different sizes: (a) Probability density and (b) cumulative probability. The main panels show the data in the low molecular weight region while the insets show the data in the high molecular weight region. Data are for $S_1$ (brown crosses), $S_<$ (red circles), $S_{10}$ (green squares), $S_{50}$ (blue triangles), and $S_{80}$ (black diamonds).}
\label{fig:system_size}
\end{figure}
The molecular weight distributions predicted by the Flory-Stockmayer theory for $S_1$, $S_<$, $S_{10}$, $S_{50}$, and $S_{80}$, including the probability density and the cumulative probability, are shown in Fig.~\ref{fig:system_size}. The main panels are for the region of low molecular weight and the insets show the data in the high molecular weight region. The data show that when the system size is increased, the curves of the molecular weight distribution converge quickly. There is a clear difference between the data for $S_1$ and those for $S_<$ (i.e., $S_5$). However, the difference between $S_<$ and $S_{80}$ is very small in the low molecular weight region and only discernible in the tail of the distribution in the region of high molecular weight (see the insets of Fig.~\ref{fig:system_size}). Furthermore, the results for $S_{50}$ and $S_{80}$ are almost indistinguishable in the entire region of molecular weight relevant to experiments, indicating that these systems are already large enough such that the molecular weight distribution is not affected by the finite system size any more.
\begin{figure}
\center
\includegraphics[width = 0.45\textwidth]{{Figure7.Stockmayer.vs.MC.S1.S80-eps-converted-to}.pdf}
\caption{Molecular weight distribution with data from for the Flory-Stockmayer theory for $S_1$ (brown crosses), the MC simulations for $S_1$ (blue circles), the Flory-Stockmayer theory for $S_{80}$ (black diamonds), and the MC simulations for $S_{80}$ (red squares). The MC results are averages of 50000 runs for $S_1$ and 1000 runs for $S_{80}$ (as well as $S_<$, $S_{10}$, and $S_{50}$).}
\label{fig:stockmayer_mc_S1_S80}
\end{figure}
Since $S_1$, $S_<$, $S_{10}$, $S_{50}$, and $S_{80}$ are all below the gel point, we expect the results from the Flory-Stockmayer theory and the MC simulations on the molecular weight distribution to agree. The comparison between the two is shown in Fig.~\ref{fig:stockmayer_mc_S1_S80} for $S_1$ and $S_{80}$. For $S_1$, some difference is observed between the prediction of the Flory-Stockmayer theory and the MC result because of the small size of this system. An excellent agreement is found between the theory and simulations for $S_{80}$. Similar agreements are also found for $S_{10}$ and $S_{50}$. A good agreement is already discussed earlier for $S_<$ as shown in Fig.~\ref{fig:three_systems}(a). These comparisons once again confirm that the Flory-Stockmayer theory provides a good description of the molecular weight distribution for systems well below the gel point, where ring formation is not a big concern. Below the gel point, both the Flory-Stockmayer theory and the MC simulations can be applied to a system containing only a few hundred to a few thousand monomers but having the same molar ratios of monomers as a macroscopic system to accurately predict the molecular weight distribution. As discussed earlier, the Flory-Stockmayer theory starts to fail when a system approaches or goes above the gel point. However, in these situations the MC simulations can still be used to quickly generate a molecular weight distribution that is applicable to an experimental system.
\subsection{Partially Reacted Stoichiometric Systems} \label{sec:nfr_sys}
Up to this point, we mainly focus on fully reacted stoichiometric systems as it is possible to compute the molecular weight distribution using the Stockmayer formula even for a system with a relatively large size such as $S_{80}$. In this and next section we show that the conclusions reached so far also apply to partially reacted and/or nonstoichiometric systems. However, because of the practical difficulty of using the Stockmayer formula to compute the molecular weight distribution when either $p_A$ or $p_B$, or both, are less than 1, we use small systems with sizes similar to $S_5$ to illustrate the main point.
In this section we discuss partially reacted stoichiometric systems where $\sum_{q=1}^i f_qA_q=\sum_{h=1}^j g_hB_h$ but $p_A = p_B < 1$. Five such systems with the same size as $S_>$ are listed in Table~\ref{table:casestb3} where the values of $p_A$ and $p_B$ are increased from 0.95 to 0.99. The corresponding values of $\alpha$ changes from about 0.42 to about 0.65, thus enclosing the gelation transition at $\alpha_c = 0.5$.
\begin{table*}[h]
\resizebox{\textwidth}{!}{%
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
& PA & BPADA & MPD & TAPE & $\rho_1$ &$\rho_2$ & $p_A$ & $p_B$ & $\alpha$ & $M_n$ (Da) & $M_w$ (Da) & $M_z$ (Da) \\ \hline
$S^{0.95}$ & 50 & 670 & 620 & 50 &0.0360 & 0.108 & 0.95 & 0.95 & 0.419 & $5965 \pm 3$ & $24779\pm 331$ & $47952\pm 824$ \\ \hline
$S^{0.96}$ & 50 & 670 & 620 & 50 &0.0360 & 0.108 & 0.96 & 0.96 & 0.462 & $7386\pm 5$ & $36488\pm 488$ & $69368\pm 1097$ \\ \hline
$S^{0.97}$ & 50 & 670 & 620 & 50 &0.0360 & 0.108 & 0.97 & 0.97 & 0.513 & $9655\pm 10$ & $58237\pm 807$ & $103512\pm 1504$\\ \hline
$S^{0.98}$ & 50 & 670 & 620 & 50 &0.0360 & 0.108 & 0.98 & 0.98 & 0.574 & $13780\pm 23$ & $105576\pm 1435$ & $165690\pm 2080$ \\ \hline
$S^{0.99}$ & 50 & 670 & 620 & 50 &0.0360 & 0.108 & 0.99 & 0.99 & 0.649 & $22710\pm 70$ & $200514\pm 1915$ & $266624\pm 2083$ \\ \hline
\end{tabular}}
\caption{Five partially reacted, stiochiometric systems (i.e., $p_A = p_B < 1$). The entries have the same format as in Table~\ref{table:casestb1}. The superscript of the system label indicates the values of $p_A$ and $p_B$. The first two are below and the rest three are beyond the gel point. The average molecular weights, $M_n$, $M_w$, and $M_z$, are from the MC simulations.}
\label{table:casestb3}
\end{table*}
The results on the molecular weight distribution from the Flory-Stockmayer theory and MC simulations at various values of $p_A$ and $p_B$ are shown in Figs.~\ref{fig:stoichiometric_pa95_pa99}(a) and (b), respectively. The molecular weight distribution predicted by the Flory-Stockmayer theory seems to be relatively insensitive to the values of $p_A$ and $p_B$. However, the MC results show that when the value of $p_A$ and $p_B$ is increased, the probability density in the low molecular weight region is reduced (see Fig.~\ref{fig:stoichiometric_pa95_pa99}(b)) while that in the high molecular weight region is enhanced (see the inset of Fig.~\ref{fig:stoichiometric_pa95_pa99}(b)). This systematic trend is expected as when the extent of reaction is larger, more polymers with higher molecular weights are anticipated to form.
To compare the predictions of the Flory-Stockmayer theory to the MC results on the molecular weight distribution, in Fig.~\ref{fig:stoichiometric_pa95_pa99}(c) their differences are shown for various $p_A$ and $p_B$. It is clear that when $p_A$ and $p_B$ are small, the systems are below the gel point and the results from the theory and simulations agree, as for $S^{0.95}$ and $S^{0.96}$. The difference becomes noticeable when the system approaches the gel point, such as $S^{0.97}$. For $S^{0.98}$ and $S^{0.99}$, they are above the gel point and clear differences in the probability density from the theory and simulations can be noted in both low (see Fig.~\ref{fig:stoichiometric_pa95_pa99}(c)) and high (see the inset of Fig.~\ref{fig:stoichiometric_pa95_pa99}(c)) molecular weight regions. The results for the partially reacted stoichiometric systems thus corroborate the conclusion that the Flory-Stockmayer theory only applies to systems well below the gel point. However, the MC simulations can be used to compute the molecular weight distribution for any systems no matter they are below, around, or above the gel point.
\begin{figure}[h]
\center
\includegraphics[width = 0.45\textwidth]{{Figure8.partially.reacted.stoi.pa.95.to.99-eps-converted-to}.pdf}
\caption{Molecular weight distribution (a) from the Flory-Stockmayer theory and (b) from the MC simulations. The inset of (b) shows the MC results in the high molecular weight region. (c) Difference between the results from the Flory-Stockmayer theory and the MC simulations on the probability density (PD). The inset of (c) shows the difference in the high molecular weight region. The data are for $S^{0.95}$ (brown crosses), $S^{0.96}$ (blue circles), $S^{0.97}$ (black diamonds), $S^{0.98}$ (red squares), and $S^{0.99}$ (green triangles). The MC results are averages of 1000 runs.}
\label{fig:stoichiometric_pa95_pa99}
\end{figure}
\subsection{Nonstoichiometric Systems} \label{sec:neq_sys}
We finally discuss nonstoichiometric systems where $\sum_{q=1}^i f_qA_q \neq \sum_{h=1}^j g_hB_h$ and $p_A \neq p_B$. Three systems with sizes similar to $S_>$ are shown in Table~\ref{table:casestb4}. We fix the value of $p_A$ at 0.99 but vary $p_B$ from 0.93 to 0.97. The numbers of monomers of PA, BPADA, and TAPE are all fixed. The number of MPD is varied according to Eq.~(\ref{eq:constraint}). Specifically, when the number of MPD is reduced, the values of $p_B$, $\rho_2$, and $\alpha$ are all increased. For the three systems in Table~\ref{table:casestb4}, $S_{<}^{n}$ is below, $S_{\simeq}^{n}$ is around, and $S_{>}^{n}$ is above the gel point. Here the superscript $n$ in the system labels indicates that these systems are nonstoichiometric.
\begin{table*}[h]
\resizebox{\textwidth}{!}{%
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
& PA & BPADA & MPD & TAPE & $\rho_1$ & $\rho_2$ & $p_A$ & $p_B$ & $\alpha$ & $M_n$ (Da) & $M_w$ (Da) & $M_z$ (Da) \\ \hline
$S_{<}^{n}$ & 50 & 670 & 664 & 50 & 0.0360 & 0.101 & 0.99 & 0.93 & 0.445 & $7225 \pm 2$ & $33130\pm 195$ & $62388\pm 448$ \\ \hline
$S_{\simeq}^{n}$ & 50 & 670 & 649 & 50 & 0.0360 & 0.104 & 0.99 & 0.95 & 0.502 & $9530\pm 4$ & $54269\pm 349$ & $96424\pm 656$ \\ \hline
$S_{>}^{n}$ & 50 & 670 & 634 & 50 & 0.0360 & 0.106 & 0.99 & 0.97 & 0.569 & $13824\pm 10$ & $103074\pm 624$ & $162837\pm 915$\\ \hline
\end{tabular}}
\caption{Three partially reacted, nonstiochiometric systems (i.e., $p_A \neq p_B$ and both are less than 1) below, around, and beyond the gel point. The entries have the same format as in Table~\ref{table:casestb1}. The average molecular weights, $M_n$, $M_w$, and $M_z$, are from the MC simulations.}
\label{table:casestb4}
\end{table*}
The results on the molecular weight distribution for the three nonstoichiometric systems are plotted in Fig.~\ref{fig:nonstoi_three_systems}. For $S_{<}^{n}$ which is below the gel point, the MC results agree with the prediction of the Flory-Stockmayer theory, as shown in Fig.~\ref{fig:nonstoi_three_systems}(a). The two start to differ when a system approaches the gel point. An example is shown in Fig.~\ref{fig:nonstoi_three_systems}(b) for $S_{\simeq}^{n}$ with $\alpha = 0.502$. For this system, the Flory-Stockmayer theory overestimates the probability of low molecular weight polymers while underestimates the probability in the region of molecular weight higher than about $0.5\times 10^5$ Da (see the inset of Fig.~\ref{fig:nonstoi_three_systems}(b)). For $S_{>}^{n}$ which is above the gel point, the MC results on the probability density are smaller than those calculated with the Flory-Stockmayer theory when the molecular weight is lower than about $1\times 10^5$ Da (Fig.~\ref{fig:nonstoi_three_systems}(c)) but higher at higher molecular weights (see the inset of Fig.~\ref{fig:nonstoi_three_systems}(c)). For $S_{>}^{n}$ the molecular weight distribution has a second peak around $2\times 10^5$ Da, while the Flory-Stockmayer theory predicts a monotonically decaying distribution in this region. The results on nonstoichiometric systems thus one more time indicate that the Flory-Stockmayer theory only applies to systems well below the gel point, for which the formation of cyclic polymers or closed loops is negligible.
\begin{figure}[h]
\center
\includegraphics[width = 0.4\textwidth]{{Figure9.nonstoi.pa99.pb93.pb95.pb97-eps-converted-to}.pdf}
\caption{Molecular weight distribution for the three systems in Table~\ref{table:casestb4}: (a) $S_<^{n}$, (b) $S_\simeq^{n}$, and (c) $S_>^{n}$. The results are for the Flory-Stockmayer theory (red circles) and the MC simulations (blue squares). The MC results are averages of 5000 runs.}
\label{fig:nonstoi_three_systems}
\end{figure}
\section{Conclusions}
\label{sec:conclusions}
We have used MC simulations to study the polymerization of branched PEIs from BPADA (backbone monomer), MPD (backbone monomer), PA (chain terminator), and TAPE (branching agent). All the reactions for this system can be reduced to a condensation reaction between an amine group and a carboxylic anhydride group and thus can be characterized by one reaction rate. Our work show that in the MC model, the reaction rate should be computed using the concentrations of the functional groups on the monomers involved in a specific reaction, not the concentrations of the monomers themselves. The MC results are compared to the predictions of the Flory-Stockmayer theory. A practical approach of using the Flory-Stockmayer theory to compute molecular weight distributions has been suggested. We find that both the Flory-Stockmayer theory and the MC simulations accurately predict the molecular weight distribution for systems well below the gel point that is set by the functionality of the branching agent, though ring formation is not considered by the Flory-Stockmayer theory but allowed in MC simulations. The agreement between the theory and simulations thus indicates that ring formation is negligible for systems well below the gel point. However, for systems close to or above the gel point, the Flory-Stockmayer theory is not applicable as many cyclic polymers can be produced and ring structures can form in highly branched networks. For these systems, the MC simulations can still be used to quickly compute the molecular weight distribution that can be used to describe experimental measurements including average molecular weights.
Our tests indicate that in the MC simulations, a system with only a few hundred to a few thousand monomers but the same molar ratios of participating monomers is large enough to yield converging results on the molecular weight distribution for the region of molecular weight relevant to typical experiments (from 0 to about $3\times 10^5$ Da in the case of PEIs). These conclusions have been thoroughly confirmed with simulations for fully reacted, partially reacted, stoichiometric, and nonstoichiometric systems. The MC model presented here is expected to be applicable to a wide range of step-growth polymers.
\section*{Acknowledgement}
This paper is based on the results from work supported by SABIC Innovative Plastics US LLC.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,365 |
_Nothing would be more tiresome than eating and drinking if God had not made them a pleasure as well as a necessity._
—VOLTAIRE
**foreword by Mario Batali**
# **Dad's own cookbook**
**by Bob Sloan**
**illustrated by Serge Bloch**
technical illustrations by Barbara Smullen
Workman Publishing, New York
## **Acknowledgments**
_This book is dedicated to my wife, my kids, my mom, and especially, my dad, Big Irv._
Cooking is ephemeral. You eat dinner—it's gone. Ruth Sullivan, my editor at Workman Publishing, has played a big part in helping me create something that, hopefully, will last a long time. I am very grateful to her. Special thanks go to Paul Hanson who brought me into this project and has created a handsomely designed book. Karen Watts played a crucial role throughout this process, and our friendship is the first positive result of the book. Though it's been many years since I've worked with them, I still consider Mary Cleaver of the Cleaver Company and the late Fred Rothberg to be my first and best teachers. And Carmine Cincotta is still my first and only produce man. I have also learned a great deal about food and cooking from David Sanfield of the Pitfire Pizza Restaurants. From Mario Batali I have learned not just about food, but about larger, more ontological concerns, like how to keep from slicing my drives. And listening to Jim Harrison describe a great meal is as sublime an experience as having actually eaten it.
Now that my catering business has taken a backseat to writing about food, I have to keep my skills sharp by cooking for friends. It seems curious to be thanking them for coming to dinner, but I do.
Phil and Sally Sanfield have continued to be incredibly supportive of all my ventures, as have Alice Jarcho and Tommy Gallagher, Pat and Ron Nicholson, and Paul and Karen Izenberg.
My brother Larry didn't help much with this project, but I love and miss him a lot. My kids, Nate and Leo, have eaten almost a decade's worth of meals, many of them cooked from this book. They haven't complained, so I guess the recipes still work.
Above all, I thank my wife, Randi. None of this would have happened without her.
## **Contents**
**Foreword**
**Introduction**
**Getting Started**
_Shopping_
_Shopping Through the Mail_
_Health Food_
_Labels_
_Ingredients_
**Herb & Spice Primer**
_Dad's Basic Kitchen Equipment_
**The Food Processor**
**The Microwave**
_Food Safety & Storage_
_Freezing_
_How Long Will It Last?_
_Real Men Do Measure_
_How to Read a Recipe_
**Demystifying the Sauté Pan**
_Cleanup_
**Breakfast**
**The Basic Egg**
_Boiled Eggs_
_Scrambled Eggs_
_Fried Eggs_
_Poached Eggs_
_Omelets_
_Pancakes_
_French Toast_
**Breakfast in Bed**
_Slow Scrambled Eggs with Smoked Salmon, Sour Cream & Caviar_
_Mimosa_
_Café au Lait_
_Hot Cereal_
_Puffed Pancake_
_Frittata_
_Home Fries Supremo_
_Muffins_
**A Good Cup of Coffee & a Nice Cup of Tea**
_The Yogurt & Fruit Breakfast_
**Lunch**
**_Six Sandwiches the Kids Will Eat_**
_Peanut Butter & Jelly_
_Tunafish Salad_
_BLT_
_Grilled Cheese_
_Turkey Club_
_Sloppy Joe_
**_Four All-American Lunches_**
_Hamburgers_
_Hot Dogs_
_Quick Macaroni & Cheese_
_Chef's Salad_
**The Lunchbox**
**_Instant No-Recipe Lunches_**
_English Muffin Pizza_
_Yogurt Buffet_
_Tuna Patties_
_Macaroni & Cheese_
_Instant Burritos_
**_Using Up Leftovers_**
_Quick Leftover Lo Mein_
_Chilaquiles with Chicken, Tomatoes & Cheese_
_Minestrone Deluxe_
**Dinner**
**Chicken Basics**
_Cuts, Servings, Storage_
_Roast Chicken_
_Broiled Chicken_
_Fried Chicken_
_Sautéed Chicken_
_Perfect Roast Chicken_
_Oven-Baked Middle Eastern "Fried" Chicken_
_Chicken Breast Piccata_
_Chicken with Tomato & Sausage_
**Beef Basics**
_Cuts, Servings, Storage_
_Broiled Beef_
_Stewed Beef_
_Braised Beef_
_Roast Beef_
_Panfried Beef & Burgers_
**How to Cut an Onion**
_Dad's Official Meat Loaf_
_Roast Beef_
_Pot Roast_
_Stuffed Flank Steak_
_London Broil_
_Stir-Fried Beef & Broccoli_
**Mexican Feast**
_Assembling the Feast_
_Steak Fajitas_
_Chicken Burritos_
_Vegetarian Tacos_
_Dirty Rice_
_Lemonade Ice-Cream Pie_
**Lamb Basics**
_Cuts, Servings_
_Panfried Lamb_
_Roast Lamb_
_Broiling Lamb_
_Loin Lamb Chops with Red Wine Sauce_
_Shoulder Lamb Chops with Garlic & Rosemary_
**Pork Basics**
_Cuts, Servings, Storage_
_Roast Pork_
_Panfried Pork_
_Baked Ham_
_Broiled Pork Chops_
_Hunan Orange-Ginger Roast Loin of Pork_
_Breaded Pork Chops_
_Pork Chop & Potato Casserole_
**Fish Basics**
_Buying, Servings, Storage_
_Broiled Fish_
_Panfried Fish_
_Baked Fish_
_Fish Baked in Foil_
_Poached Fish_
**Fish Primer**
_Red Snapper Baked in Foil_
_Fillet of Sole with Saffron & Tomato Cream Sauce_
_Cajun Baked Salmon_
_Baked Mackerel with Sun-Dried Tomatoes & Herbs_
_Panfried Flounder_
**Shellfish Primer**
_Cajun BBQ Shrimp_
_Stir-Fried Scallops with Red Pepper, Peas & Baby Corn_
**Rice & Potatoes**
_Boiled White Rice_
_Basic Rice Pilaf_
_Basic Brown Rice_
_Baked Wild Rice_
_Kasha_
**The Basic Potato**
_Boiled Potatoes_
_Baked Potatoes_
_Oven-Roasted Potatoes_
_Mashed Potatoes_
_French Fries_
_Oven-Roasted Fries_
**A Baked Potato as a Meal**
_Stuffed Potatoes with Bacon & Cheese_
_Pan-Roasted New Potatoes_
**Vegetables**
**Cooking the Basic Vegetable**
_Boiling_
_Steaming_
_Microwaving_
_Stir-Frying_
_Artichokes_
_Curry Dip_
_Asparagus_
_Orange Vinaigrette_
_Beets_
_Beet & Cucumber Salad_
_Broccoli_
_Sautéed Broccoli & Mushrooms_
_Carrots_
_Carrots with Orange & Mint_
_Microwaved Glazed Carrots_
_Cauliflower_
_Curried Cauliflower & Potato_
_Corn_
_Corn Pudding_
_Green Beans_
_Sautéed Green Beans with Garlic_
_Mushrooms_
_Peas_
_Peas with Cream & Almonds_
_Spinach_
_Spinach with Cheese_
_Zucchini_
_Zucchini & Tomatoes_
**Two Fancy Dinners**
**A Light Summery Supper**
_The Timetable_
**The Table Setting**
_Chicken Tortellini with Prosciutto & Tomato Cream Sauce_
_Baked Salmon with Herb Crust_
_Wild Rice with Grapes_
_Strawberry Mousse_
**Wine Primer**
**A Hearty Meal with a Mediterranean Flavor**
_The Timetable_
_Melon & Prosciutto_
_Mozzarella with Tomato & Fresh Basil_
_Fillet of Beef with Wild Mushrooms_
_Oven-Roasted Potatoes with Rosemary & Whole Garlic Cloves_
_Poached Pears with Vanilla Ice Cream & Orange Liqueur_
**Salads**
**The Basic Salad**
_Greens Primer Salad Vegetables_
**The Basic Dressing**
_Oil & Vinegar_
_Dad's Own Vinaigrette_
_Chicken Salad_
_White Bean & Basil Salad_
_Greek Salad_
_Caesar Salad_
_Spinach Salad_
_Waldorf Salad_
_Carrot & Black Bean Salad_
_Tuna, Chickpea & Smoked Cheddar Salad_
_Coleslaw_
_Red Potato Salad_
_Watercress, Snow Pea & Melon Salad_
**_Complete Meal Salads_**
_Salad Niçoise_
_Japanese Beef Salad_
_Chinese Chicken Salad_
**Pasta**
**Pasta Primer**
**Pasta Sauce Primer**
_Cream Sauces_
_Tomato-Based Sauces_
_Oil-Based Sauces_
_Basic Tomato Sauce_
_Meatballs_
_Dad's Own No-Boil Lasagna_
_Never-Fail Macaroni Casserole_
**Eight Steps to Pasta Heaven**
_Fettuccine with Tomato, Sausage & Basil_
_Seafood Linguine_
_Penne with Tuna, Tomatoes & Roasted Peppers_
_Spaghetti Carbonara_
_Empty Cupboard Pasta_
_Cold Tortellini Salad_
_Cold Peanut Noodles_
_Asian Noodles with Chicken & Ham_
**Soups & Stews**
**The Basic Soups**
_The Standard Soup_
_The Puréed Soup_
_The Hearty Soup_
_Minestrone_
_Split Pea Soup_
_Dad's Own Chicken Noodle Soup_
_New England Clam Chowder_
_Potato & Escarole Soup_
_Carrot & Orange Soup_
_Old-Fashioned Beef Stew_
_Broccoli & Apple Soup_
**Homemade Stock**
_Beef Stock_
_Chicken Stock_
_Mexican Chicken Stew_
_Mediterranean Fish & Seafood Stew_
**Desserts**
_Dad's Own Oatmeal-Raisin Cookies_
_Chocolate Pudding_
_Quick & Decadent Chocolate-Peanut Butter-Granola-Coconut Bars_
_Hermits_
_Dave's Key Lime Pie_
_Dad's Own Apple Pie_
_Dad's Own Pie Crust_
_Oatmeal Chocolate-Chip Cookies_
_Super-Fast Saucepan Brownies_
_Peach-Blueberry Brown Betty_
_Tiramisù_
**The Simplest & Healthiest Dessert**
_Baked Apples_
_Melon with Honey & Lime_
_Poached Pears_
_Sautéed Bananas with Strawberries_
_Crystallized Orange Sections_
**Making Bread & Pizza with the Kids**
**Bread Basics**
_Country White Bread_
_Whole Wheat Bread_
_Pumpernickel Raisin Bread_
_Corn Bread_
_Irish Soda Bread_
**Dad's Own Pizza**
_The Dough_
_The Pizza_
_Scones_
**Cooking in the Great Outdoors**
**The Basic Grill**
_Techniques_
_Maintenance_
_Marinades_
_Cooking Times_
_Basting_
_Dad's Own Barbecue Sauce_
_Wine- &-Herb Marinade_
_Asian Marinade_
_Barbecued Chicken_
_Barbecued Spareribs_
_Lamb Shish Kebab_
_Grilled Vegetables_
_Asian Grilled Swordfish_
_Pork or Chicken Saté_
_Peanut Dipping Sauce_
_Mary Cleaver's Boneless Chicken Breasts with Balsamic Vinegar & Rosemary_
**Cooking for a Crowd**
_Baked Smoked Ham_
_Dad's Own Chili_
_Red Snapper Vera Cruz_
_Chicken Breasts with Prosciutto & Mozzarella_
_Jambalaya with Shrimp & Chicken_
_Whole Roast Beef Tenderloin_
_Moroccan Veal, Sausage & Chicken with Couscous_
**Thanksgiving Dinner for Twelve**
_Roast Turkey_
_Dad's Own Apple Sausage Stuffing_
_Quick Cranberry Chutney_
_Candied Sweet Potatoes_
**How to Throw Your Own Cocktail Party**
**The Drinks**
**Simple Nibbles & Ethnic Edibles**
_Spring Rolls & Dim Sum_
_Guacamole_
_Miniature Quiches_
_Pâté_
_Dolmas & Spanakopita_
_Tapenade & Pesto_
_Pizza Rotolo_
_Salmon Caviar_
_Goat Cheese Pita Pizza_
_Barbecued Chicken Wings_
_Hummus or Baba Ghanoush with Pita Triangles_
_Shrimp & Cocktail Sauce_
_Cheese & Crackers_
**A Menu for a Fancy Cocktail Party for**
_The Timetable_
_The Shopping List_
_Crudités_
_Sun-Dried Tomato & Roasted Red Pepper Dip_
_Fresh Salsa & Chips_
_Jerk Chicken Wings_
_Salmon Hash in Endive_
_Melon & Prosciutto_
**Cheese Primer**
_Shrimp & Cocktail Sauce_
**Throwing a Birthday Party for Your Child**
**Party Themes**
_The Timetable_
**_Party Food_**
_Munchies_
_Pizza_
_Turkey Tacos_
_Sandwiches_
_Barbecued Hamburgers & Hot Dogs_
_Lasagna_
_Beverages_
**_The Birthday Cake_**
_Primo Birthday Cake_
_Luscious Chocolate Frosting_
_Quick Vanilla Frosting_
**Frosting & Decorating the Cake**
**Glossary**
**Index**
## **Foreword**
by Mario Batali
Bob Sloan is the quintessential dad/chef and this dual expertise is what makes this both a fun and a practical cookbook. My family and I have had many meals at the Sloan home and Bob's cooking is seemingly effortless, fun, kid friendly, and most importantly, delicious. That kind of cavalier approach to food is reflected in these recipes. They work. They're easy to prepare. They have abundant flavor. My kids like them. So will yours.
Like his cooking, his approach in the book is straightforward. But the information, though casually presented, is comprehensive and will sneak a lot of worthwhile knowledge into an unsuspecting dad's head while he thought he was just making a school-night dinner.
He challenges you to make some things you never thought you could, leading you through the recipe like the best kind of cooking coach, leaving nothing to the imagination but never making you feel dumb for not knowing it in the first place. The book is organized in a way that both dads with no confidence or no experience in the kitchen as well as dads who can cook will appreciate and, more importantly, use. (If Ronald Reagan had read some of the vegetable recipes, ketchup would never have been considered one of the major food groups on the school lunch lines.) The primer information, cooking techniques, and useful charts of this book could easily stretch into another tome altogether as they are filled with tons of useful and relevant info. But what is most important is the simplicity and ease that Bob brings to all kitchen tasks—everything from cutting an onion (for the kitchen stooge) to making stocks from scratch ("for the truly committed"). He demystifies the kitchen and yet makes cooking intuitive to the novice. His spirit of camaraderie and cooking skills serve to augment his obvious joy in and love for everything about preparing food, something all dads (and moms) can really catch on to.
Bob is intensely aware of his kids at all times. He is also intensely aware of everybody else's kids. And if I go to someone's house and they offer special hospitality not only to me, but to my kids, they are anointed as heroes. Bob is such a hero. As my kids always say after dinner at the Sloan house: "That Bob is a good cooker!" Use this book enough, and you will become a good cooker, too.
## Introduction
Are you, or is someone you know, culinarily challenged? Do you, or does someone you know, lose the use of major muscle groups when it's time to cook? Do you have a fear of frying? Imagine this scenario—for a whole week your wife or girlfriend is away, too busy, or just doesn't want to cook. She says, "You deal with feeding the kids." She says, "You make dinner." So, all right. The first night you order in—you and the kids sit by the TV, eat pizza, and watch _Jeopardy_. The second night it's Chinese. Then, something hits you—you should be able to _cook_ something. _Some_ thing. You've certainly eaten enough. You've watched enough people cook. There must be _some_ meal you could make, one dish you could serve for dinner besides tunafish salad or frozen entrées, something to keep your family from starving. But nothing comes to mind.
Sound familiar? Well, the reason you're stumped is that no one has ever taken the time to write a cookbook just for you. Other books intimidate you, or leave too much to your imagination. They figure you already _know_ how to grease a pan, preheat an oven, separate an egg. This is where _Dad's Own Cookbook_ comes in. It assumes that you know what you like to eat, but don't know how to make it. That you may have been brilliant at the operating table that morning, but are basically a dolt around the stove at dinnertime. _Dad's Own_ leaves nothing to your imagination. Steps are explained. Its primers, timetables, and tips are all designed to keep you on track. I may treat you like an idiot, but I don't make you feel like one.
Many recipes here are familiar. They are the favorite foods of your childhood, so they're bound to be hits with your kids. Some are slightly adventurous. A few are daring. There are meals for every occasion—Friday night pizza, an elegant dinner for two, a Thanksgiving feast. I'll tell what cans to stock in your cupboard, the pots that should fill your shelves, the necessary ingredients to keep in your fridge. I'll clue you in to cooking techniques, shortcuts, kitchen tips that have been kept from you (deliberately, I might add) for too long. I'll teach you how to shop, read a label, buy the prime cuts, the freshest produce. I'll be your friend on the inside; the guy in the know; your uncle with a hot tip on the first race. I'll hold your hand while you stir the soup. And _what_ soup! Dad's Own Chicken Soup. Dad's Apple Pie. Dad's Meat Loaf! The kids will hope _you've_ been busy in the kitchen when they come home from school.
This book will also wise you up to the latest health tips. While it's not necessarily a low-fat cookbook, I'm keen on helping Dad keep his cholesterol, salt, and fat intake in check. Options are given for low-fat variations, and salt, butter, and eggs are kept to a minimum throughout. There are even tips on how to get your kids to like vegetables.
Look, few of us want to rush into the kitchen after a hard day of work and start whipping up dinner. But more and more Dad is being called on to do his share of cooking. You've taken the right first step by starting with this book. Soon you'll be tearing up the kitchen, effortlessly throwing together simple, tasty, and healthful meals. And one night, when your kid has a friend over for dinner, after they've tasted the perfectly roasted chicken, savored the oven-roasted rosemary potatoes, crunched into steamed al dente green beans, the friend will say, "Hey, this is, like, really good." And your child will beam and respond, "Yeah, I know. My dad made it."
## Getting Started
Cooking is like changing your spark plugs. At first it seems a job for the experts. Then someone hands you the proper tools, points you in the right direction under the hood, and you soon realize it's easy to change your own plugs.
Having the proper tools is crucial to success in the kitchen. This is not to say that you can't cook well if you don't have expensive, shiny pots hanging over your stove. But you do need heavy-duty pots, sturdy pans, and good, sharp knives. Check the equipment you already have against the list in this chapter. Get acquainted with your food processor and microwave; they can be your third hand in the kitchen.
Though good, fresh ingredients alone don't assure a good meal, they increase your chances of success about 100 percent. Locate reliable sources for everything—meat, fish, produce, and staples—then follow the suggestions below about smart shopping.
#### **Shopping**
Becoming a smart shopper is easy if you follow one important rule: Buy food in the supermarket, but do your shopping at home. This means you make your shopping decisions at the kitchen table, where your primary tool is the shopping list.
To prepare the list, first plan what you are making for dinner in the upcoming days. Check the ingredients in the recipes against what you have in the cupboard and write down what you need. Be meticulous. Some recipes hinge on one simple ingredient. Next, check the staples in the house: milk, juice, eggs, butter or margarine, oil, peanut butter, and so on.
For fresh fruits and vegetables, wait until you get to the store to see what looks best and is plentiful, but make a few notes on what vegetables would be appropriate for the entrées you are planning.
Try to do your shopping during off-hours—early in the morning or late at night. Once in the store, buy only those items on your list. Let yourself drift through the aisles and you'll wind up with a wagonful of food but nothing to eat. Beware: Supermarkets are carefully organized to separate you from your money. For example, the meat and dairy sections are deviously situated in the back, forcing you to wend your way through much of the store before you find what you're looking for.
To combat this trickery, you must move quickly through the aisles, list in hand, checking off items as you place them in the wagon. Remember, life's too short to spend time ruminating over chunk light versus solid white tuna. If you're on line at the check out counter (thumbing through the _National Enquirer_ ) within 15 minutes or less, you know you've done some professional-quality shopping.
A final shopping tip: Make friends with your butcher, fishmonger, and produce manager so you won't feel reluctant to ask them questions. These people are great sources of information on choosing ingredients as well as cooking with them.
**Buying Fresh Food**
Using the freshest possible ingredients helps ensure that the food you cook will taste best and that it has the optimum number of nutrients.
Frequent markets where the meat and produce are really fresh and appealing, even if you have to go out of your way to get there. Here are some tips to help you choose the freshest ingredients:
• **Check dates.** Even canned and frozen foods don't last forever. Find dairy products with the latest date (they are often located in the back of the dairy case).
• **Buy meat, fish, and poultry from stores you trust.** Locate a good butcher and fishmonger whose fare is fresher and of higher quality than a supermarket's. For detailed information about choosing cuts and judging freshness, see individual entries in the Dinner chapter.
• **Don't be afraid to pick over piles of fruits and vegetables to find the choice one.** Examine your selections carefully for bumps, bruises, and other defects. For detailed information about choosing vegetables and fruits, see individual entries in the Vegetable and Dessert chapters. Wash all fruits and vegetables thoroughly before eating them as most have been sprayed with pesticides and other chemicals.
**The Cupboard**
Here's a list of pantry items you'll always want to have around for _Dad's Own_ recipes:
**Staples**
• Anchovies
• Beans: black and white
• Bread crumbs
• Bouillon cubes: chicken and beef
• Broth: chicken and beef
• Buckwheat: kasha
• Chickpeas
• Oil: extra-virgin olive oil, sesame, and corn
• Pasta: fettucine, lasagna, linguine, macaroni, penne, and spaghetti
• Peas: dried green
• Popcorn
• Pineapple
• Rice: converted and brown
• Salt
• Sugar: white, brown, and confectioners'
• Tomatoes: whole and crushed
• Tuna, canned
• Vinegar: white wine, red wine, and balsamic
**Condiments**
• Basil
• Bay leaves
• Garlic
• Ginger
• Horseradish
• Ketchup
• Mayonnaise
• Mustard: regular and Dijon
• Oregano
• Peppercorns
• Rosemary
• Sesame paste or tahini
• Soy sauce
• Tabasco
• Thyme
• Tomato purée
• Worcestershire sauce
**Baking Supplies**
• Baking powder
• Baking soda
• Cornmeal
• Flour: white and whole wheat
• Molasses
• Oats: rolled
• Wheat germ
• Yeast
#### **Shopping Through the Mail**
As a kid, I used to wait impatiently for the mailman to bring me the various premiums I had sent away for in exchange for box tops or proof-of-purchase seals. These days I wait, equally impatiently, for my latest order of specialty food items or equipment. The fact is, you can do a lot of shopping through the mail, especially for ethnic condiments and sauces, spices, and special flours. I order blocks of chocolate, oils, jams, vinegars, dried fruits, and dried peppers. Use the following sources when you need a special ingredient and don't have time to hunt it down. Either call or write for free catalogs.
**American Spoon Foods**
P.O. Box 566
Petosky, MI 49770
800-222-5886
FAX: 616-347-2512
www.spoon.com
_American-made products, such as preserves, dried fruit, mustards, maple sugar._
**G.B. Ratto & Co.**
821 Washington Street
Oakland, CA 94607
800-325-3483
FAX: 510-836-2250
_An excellent source for spices, chocolate, sauces, international specialty foods._
**Nodine's Smokehouse**
P.O. Box 1787
Torrington, CT 06790
800-222-2059
FAX: 203-496-9787
www.nodinesmokehouse.com
_Smoked meats, poultry, cheese, bacon._
**Penzey's Spices**
Brrokfield, WI
800-741-7787
FAX: 262-785-7678
www.penzeys.com
_High-quality international spices._
**Williams-Sonoma**
P.O. Box 7456
San Francisco, CA 94120-7456
800-541-2233
or 800-541-1262 (to request a catalog)
FAX: 415-421-5153
www.willliams-sonoma.com
_High-quality kitchenware and specialty foods._
**Zabar's**
2245 Broadway
New York, NY 100242
212-496-1234
FAX: 212-580-4477
www.zabars.com
_Competitively priced kitchen equipment and specialty food items._
**The Healthy Cupboard**
• **Organic fruits and vegetables**. If you are concerned about the pesticides and growth hormones sprayed on fruits and vegetables, then pay the extra money for organically grown products. You will be amazed at how much better a vine-ripened tomato or ungassed banana tastes. (Most supermarket bananas have been picked green and gassed to make them ripen in 3–4 days.)
• **Breakfast cereals** that are very tasty but generally have less sugar and more whole grains than the supermarket varieties.
• **Pasta** , in unusual shapes and colors to entice the kids.
• **Grains** , such as buckwheat groats (kasha), which are sometimes hard to find in standard supermarkets.
• **Salsas and tomato sauces** , made by small specialty companies, are often more flavorful than standard supermarket brands.
• **Vegetable broth powder** , which can be mixed into stews, stocks, and bread-crumb mixtures for added flavor.
• **Spices** , available in a wide variety and often sold in bulk.
• **Peanut butter** , unhydrogenated and often sold in large quantities.
• **Dried fruits** , including the unsulfured kind. (Sulfur dioxide gas is often sprayed on dried fruit to help to maintain the fruit's natural color and vitamins, but some people believe that this does more harm than good.)
• **Nuts** , available in a wide variety and usually sold in bulk.
• **Trail mix** , a more healthful alternative to sweet afternoon snacks.
#### **Health Food**
You can buy just about anything in the health food store these days. And with something like Whole Foods' success, more mainstream supermarkets are expanding their selections of health foods and organic products and produce. These foods are prepared with few additives, are minimally processed, and are, in some cases, organic (cultivated and processed without any chemicals or artificial ingredients).
Your health food shopping list should include macaroni and cheese, vegetarian chili, brown rice in various flavors, freeze-dried soups, tofu burger mix, and whole-wheat pancake and muffin mixes.
#### **Labels**
Labels and ingredient lists on prepared foods can be deceiving. Food companies cannot lie on their labels, so if a product says it's "nonfat" or "low-sodium," it has to live up to that claim. Often, however, companies will boast in big letters about some singularly healthful feature of their product merely as a distraction. For instance, a potato chip bag claims "no cholesterol." But a quick scan of the label reveals very high fat, calorie, and sodium counts, and reminds you of what _is_ there. "Lite" can have a variety of meanings, so read the small print carefully. Also check "serving size." For instance, a bottle of iced tea may not list a large amount of sugar, but when you multiply that by 3 (the number of servings in the bottle), it becomes excessive.
#### **Ingredients**
Everyone is much more health conscious these days, and as a result the information and ingredients list are much more comprehensive. The amounts of saturated fats and trans fats are clearly identified so you can keep the saturated fats to a minimum and avoid trans fats altogether. Also look for whole grains and organic whenever possible. Whole grains have much greater health benefits than white or processed flour. If organic products are available and the price is about the same, why not use them? Buying organic usually means you are getting something that is minimally processed, with a truer flavor, no antibiotics or hormones added, and with a better chance of being grown locally. The only downside is that in places where "organic" hasn't caught on, the produce may have sat around a little longer. So make sure it's really fresh.
**1. Ingredient list**
The product recipe lists ingredients _in order of quantity,_ so look carefully to see where such items as fats and sweeteners fall on the list. For example, on a pretzel package the largest single ingredient is flour (probably white, if not specified), there is more salt than sweetener, and maybe a few artificial ingredients.
**2. Special handling instructions and dating**
Follow directions and use dates for safe storing of products.
* * *
**Herb & Spice Primer**
All cooks should know the importance of seasoning—balancing sweet tastes with savory, bringing out the flavors of meats and fish with complementary herbs, and adding character to salads and vegetables. Your spice shelf does not need to be packed with exotic dried herbs and spices that are used only once a year. (In fact, herbs and spices lose their pungency in about six to nine months.) So stock up only a dozen or so essential herb and spices like the ones listed here.
Always use herbs and spices judiciously. Remember, you can add more seasonings, but you can't take them away.
**Dad's Handy Guide to Seasoning**
If a spice is listed in the ingredients in a recipe, that's easy. But what do you do when you want to enhance the flavor of a basic fish or simple dish, but are fearful of creating some volatile combination or culinary mutant? Here's a handy reference guide to what seasonings to use when, and on what. Do not mix seasonings indiscriminately. Consult the list below and the charts on page 27.
**Egg Dishes** Fresh dill; tarragon; fresh or dried basil; oregano; parsley
**Fatty Fish** Fresh dill; fresh or dried rosemary; thyme; garlic
**Lean White-Fleshed Fish** Fresh or dried ginger; basil or oregano; fresh tarragon
**Roast Chicken** Dried basil, oregano, and/or thyme; fresh or dried rosemary; paprika
**Sautéed Chicken** Dried basil, oregano, and/or thyme; fresh or dried rosemary; paprika
**Roast Beef** Dried basil, oregano, and/or thyme; garlic
**Roast Lamb or Lamb Chops** Fresh or dried rosemary and garlic; thyme
**Salad Dressings** Basil; thyme; garlic
**Tomato-Based Sauces and Stews** Fresh or dried basil; oregano, thyme, and/or rosemary; bay leaf; garlic for sauces
**Tuna Fish Salad** Fresh or dried dill; fresh or dried basil
**Fresh vs. Dried**
As fresh herbs have become more widely available, dried herbs have gotten a bad rap. The truth is that dried herbs are perfectly fine for dishes that cook for a long time, such as pasta sauces, stews, chili, and soups, as well as marinades and salad dressings. They can also be used when fresh herbs are unavailable; for each tablespoon of a fresh herb called for in a recipe, substitute 1 teaspoon dried.
Fresh herbs impart their flavor quickly and are best when added toward the end of cooking. Pinch or strip the leaves from the stem, then chop them coarsely (or as directed in your recipe) before combining with other ingredients. One exception to this rule is basil, which is very delicate and should be torn into pieces rather than chopped with a knife. Buy only as large a quantity of fresh herbs as you can use within 2 or 3 days as they do not last long. Fresh herbs are available in some specialty shops and better supermarkets throughout the year.
##### **A Well-Seasoned Trio**
_These three spices work well together, allowing their flavors to balance out. Use equal amounts of basil and oregano and half as much thyme._
##### **Solo Fliers**
_These herbs have strong, distinct flavors that will overwhelm other herbs or spices. As a rule, use them alone and sparingly._
##### **Finishing Touch**
_Add sparkle to your meal by sprinkling on one of these just before serving._
**Salt & Pepper**
Salt adds its own distinctive flavor to foods and also brings out the flavor of other ingredients. Too much salt, however, can easily overpower the flavor of a dish, so always add a little at a time, then stir and taste after each addition.
**Tips**
• The flavor of salt will develop and intensify during cooking. Salt should be added to any dish with a long cooking time such as stew, soup, or chili toward the end of the cooking.
• Stir the salt into whatever you are cooking and give it a few seconds for the flavor to develop before tasting.
• Salt can draw the juices from meat while it is roasting, so do not salt meat until after it is cooked.
Black pepper perks up everything from a garden salad to roast beef. Freshly ground peppercorns are always preferable to preground black pepper because their flavor is much fresher and more pungent.
**Tips**
• Pepper takes a minute or so for its flavor to be incorporated into the dish, so wait a bit before tasting.
• Peppercorns do vary from brand to brand. If you're feeling adventuresome, buy peppercorns in small quantities and experiment with them until you find the ones you like best.
• Keep a pepper grinder on the table so family and guests can pepper their food as they wish.
* * *
#### **Dad's Basic Kitchen Equipment**
High-quality pans and utensils make a big difference when you're cooking and will last a lifetime if cared for properly. The following equipment is all you'll need to prepare the recipes in this book.
**Caring for Your Knives**
• Knives should be washed by hand after each use and drained immediately. Water droplets left sitting too long on a knife can discolor even stainless steel. Never wash your knives in the dishwasher, even if the handles are dishwasher-safe. It will dull the edges.
• Store your knives on a magnetized bar or in a wooden knife block. Don't lay them loosely in a drawer. The banging together will dull and chip the edges.
• The sharpening steel does not actually sharpen your knife, it only restores a fine edge to an already sharpened knife. But if you use the steel regularly, your knives should need professional sharpening only once a year.
• Don't use your kitchen knives for anything but food-related activities. Never pry anything open with the tip of your knife. It will snap off.
**How to Use a Sharpening Steel**
• Hold the steel upright. Place the blade edge of the knife (nearest the handle) at a 20° angle to the steel, near its tip. Draw the blade down toward you and across the steel until the knife tip almost reaches the handle of the steel. Repeat five times on each side. For proper maintenance, use the steel every time you use the knife.
##### **Knives**
Your knives should be made from high-carbon stainless steel and should feel comfortable in your hand. Unlike free agents in baseball, usually the more money you pay for a knife, the better it is. You can count on the quality of German knives made by Wüsthof and Henckels as well as the French Sabatiers and the American Gerbers. The following knives will cover your basic needs:
**Chef's knife** ( _8 or 10 inches_ )
For most cutting and chopping. A cook's primary knife.
**Boning knife** _(5 inches_ )
For boning chicken and fish, trimming fat, and cutting meat into chunks.
**Paring knife** _(3 to 4 inches_ )
For peeling fruits and vegetables.
**Serrated bread knife** _(9 inches_ )
For cutting breads and cakes or very ripe tomatoes.
**Carving knife** _(8 or 10 inches_ )
For carving roasted meats and fowl.
**Sharpening steel** _(10 inches_ )
For maintaining a sharp edge on your knives. Sharp knives are safer than dull knives and are essential for efficient "prep" work.
**Kitchen shears**
For a variety of kitchen uses, especially cutting up cooked chicken
**Cutting board** _(11 x 17 inches_ )
A high-density plastic cutting board at least ¼ inch thick is best. Wooden boards look better, but don't last as long and harbor bacteria more easily. Thin plastic boards, which warp easily, and glass boards, which are fine for slicing but useless for chopping, should be avoided. _Always_ wash your cutting board after each use with ample soap and extremely hot water. Be especially diligent after cutting raw chicken and meats.
##### **Pots & Pans**
When choosing pots and pans, look for heavy-grade stainless steel, unless you're buying a pasta pot, which doesn't have to be made of such a heavy material, or a frying pan, which can be cast-iron.
**Heavy-grade sauté pan** _(10–12 inches_ )
with lid and heatproof handle. Since this will be the pan you use the most, shell out a couple of bucks and get yourself a good brand, such as Cuisinart or All-Clad.
**Nonstick sauté pan** _(8 inches_ )
with heatproof handle. Essential for cooking eggs and omelets. Use only wooden or plastic utensils with this pan to guard against scratching the surface. For cleaning, use a plastic scrubbing pad. Eggs can be wiped off with a paper towel. Don't be tempted to use this pan for heavy frying or for browning meats. It's really meant for lighter work.
**2½-quart saucepan**
with lid. For cooking vegetables and grains, and for reheating.
**4½-quart saucepan**
with lid. For making soups and tomato sauce. Make sure it has a nonreactive surface, either enamel or stainless steel, and a heavy bottom for sautéing vegetables.
**6-quart Dutch oven or casserole**
with lid. Great for chili, stews, soups, and casseroles. Can be used in the oven as well as on top of the stove. Le Creuset probably makes the best pot in this size.
**8-quart stockpot**
with lid. For boiling pasta and making stock.
**Roasting pan** _(11½ x 16 x 5 inches_ )
with rack. For roasting chicken or baking whole fish. It should be made of heavy-grade aluminum, stainless steel, glass, or enamel.
**Shallow roasting pan** _(10 x 15 x 2 inches)_
For baking such dishes as chicken breasts, fish steaks, and small casseroles.
**Microwave-safe casserole** _(9 x 9 inches)_
This is the most versatile pan for cooking and reheating. As you experiment with the microwave, you will want to acquire more microwave-safe pans.
**Assorted microwave-safe plastic containers**
Make it easy to transfer food directly from the refrigerator or freezer into the microwave.
**Note**
All pots and pans should be cleaned with minimal soap and low-abrasion scrubbers, and should be dried thoroughly after each use.
**Seasoning a Pan**
When you first buy a cast-iron pan it must be pretreated or "seasoned" with oil to keep food from sticking while you cook. Preheat the oven to 200°F. Scour the pan, dry it very well, then rub the inside with vegetable oil. Add enough oil to fill the pan to about ½ inch, then set the pan inside the hot oven for 3 hours. Remove the pan from the oven and let the oil cool before pouring it out. Finish seasoning the pan by wiping the inside with a paper towel.
##### **Bowls**
You can't have too many of these. A set of four nested stainless-steel mixing bowls will get you started; they are durable, store easily, and won't react with acidic foods. You're likely to want an extra medium-size bowl also.
##### **Baking Pans**
**2 heavy-grade stainless-steel or aluminum baking sheets** _(11 x 17 inches)_
Lightweight pans warp easily in a hot oven.
**2 loaf pans** _(5 x 9 inches)_
You never make one loaf of bread at a time.
**2 or 3 round cake pans** _(9 inches)_
For making layer cakes.
**Springform pan** _(9 inches)_
Lets you remove your cake easily after baking.
**2 heavy aluminum or glass pie pans** _(9 inches)_
**Muffin tin**
For muffins, of course.
**A Word About Tongs**
Tongs are the utensil most often used by restaurant chefs and most underused by home cooks. They are incredibly handy for moving and turning food as it cooks in the pan, especially when browning meat or chicken. They also make transferring cooked food from a hot pan to the dinner plate quite easy. Once you get the hang of using your tongs, you'll start feeling like a real pro.
##### **Utensils**
Stainless-steel utensils are best, as they are both durable and heatproof; plastic melts and loses its shape easily. The following list details the utensils you will use most.
• **Bulb baster**
• **Can opener**
• **Carving fork**
• **Colander** _(8 inches with legs)_
• **Corkscrew/bottle opener**
• **Dry measuring cups** _(including_ ¼, ⅓, ½, _and 1 cup)_
• **Grater**
• **Liquid measuring cup** _(2 cup)_
• **Pastry brush**
• **Pot holders** _(flame resistant)_
• **Rolling pin** _(wooden)_
• **Soup ladle**
• **Spatulas**
1 plastic _(for nonstick pans_ )
1 short stainless steel
1 small flexible rubber
1 large flexible rubber
• **Spoons**
1 long-handled slotted
1 set of measuring
3 wooden
• **Tongs** _(8 inches)_
• **Vegetable peeler**
• **Vegetable steamer** _(collapsible)_
• **Wire racks** _(for cooling baked goods)_
• **Whisk** _(wire)_
##### **Pot Holders**
Flame-resistant pot holders should be large and thick enough to keep you from burning your hand. If they don't go with the color scheme in the kitchen, too bad. Oven mitts are clumsier than potholders, and the space between the thumb and the rest of the hand often wears out, resulting in burns and dropped pots.
##### **Blender**
Great for puréeing soup and making shakes. Its principal function, of course, is to make margaritas, which are de rigueur on those long, hot summer weekends when the kids are away at camp.
##### **Hand-Held Electric Mixer**
Essential for beating egg whites and for whipping cream. Also useful for mixing cookie and cake batters.
##### **Microwave & Food Processor**
These two technological wizards are great time-savers once you master the techniques (following four pages). Dads seem to take to these machines.
* * *
**The Food Processor**
A food processor can be your best friend in the kitchen. Depending on the blade you use, it can chop, grate, shred, slice, grind, and purée and knead bread dough in a fraction of the time it takes to complete these tasks by hand. It can also break your heart. The blade moves so fast that processing even a few seconds longer than you should can ruin your ingredients.
##### **Pulsing**
Because the blades move so quickly on a food processor, it takes only a matter of seconds to chop, slice, or otherwise process an ingredient to the desired consistency. To give you greater control over this process, food processors are equipped with a pulse lever, which you press and release in order to start and stop the processor. Hold the pulse lever down for 1- to 2-second intervals and check the size of the pieces between each pulse. The processor is also equipped with an on/off switch that can be used when you are preparing foods that need to be processed for more than a few seconds at a time, for example, when you are puréeing soups or making peanut butter.
##### **Chopping & Puréeing**
The metal blade is used to chop raw and cooked fruits, vegetables, meat, fish, cheese, and nuts. This blade is also used for puréeing and mixing batters that contain less than 3½ cups flour. To chop, insert the blade, then place the food that you are processing in the work bowl, lock the cover, and pulse until it reaches the desired consistency. Fill your work bowl no more than halfway to assure uniform results.
##### **Slicing & Shredding**
To slice or shred an ingredient (for example, carrots, zucchini, or cheese), use the slicing or shredding discs, respectively. Attach the disc and follow the manufacturer's instructions for slicing and shredding. Use gentle pressure on the pusher for cheeses and delicate foods (for example, strawberries); use medium pressure for harder foods (for example, raw potatoes, carrots, and pepperoni).
##### **To Process or Not to Process**
It always takes a few minutes to disassemble and clean the machine once you've used it, though most parts of a food processor are dishwasher-safe. For larger jobs, such as shredding a pound of cheese, chopping a pound of meat, or grating a few pounds of carrots, you'll definitely want to use the processor. But for smaller jobs, you may find that it's not worth the effort to set up and clean the processor, and that it's more efficient to do the work by hand.
**Food Processor Tips**
• To assure that foods processed at the same time are of uniform size, cut the foods into equal size pieces (about 1 inch) before you start, don't overload the processor (fill it half-way), and use the pulse lever for greater control when processing.
• If you are working with large quantities of ingredients, process them in batches, transferring each batch to a bowl as you finish it.
• To avoid leakage when combining liquids or puréeing, never add more than 2 cups of very thin liquid; thicker liquids can be added in larger quantities.
• Do not use the food processor to grind coffee beans or small spices as they fly to the sides of the bowl where the blade cannot reach them.
* * *
**The Microwave**
The microwave can act as a third hand in the kitchen. While the main courses cook on the stove and in the oven, the vegetables can be delegated exclusively to the microwave's domain. If the timer is set correctly, there is no chance of overcooking them.
If you have a microwave, you should definitely use it for cooking vegetables, as well as for reheating and defrosting. To use your microwave effectively, start with the manual that comes with your oven. If you want to be more adventurous with a microwave, get a specialized cookbook like Barbara Kafka's _Microwave Cooking. Dad's Own_ uses the microwave for time-saving steps in a recipe or in preparing a meal.
##### **Reheating**
The advantage of reheating food in the microwave is that it is often faster than reheating on the stove or in the oven, and there is less chance of the food drying out.
**To reheat refrigerated foods**
**1.** Place cold food in a microwavable container and cover loosely with plastic wrap.
**2.** Heat on _high_ setting for 2–5 minutes, depending on the quantity (1 cup of food needs 2 minutes, 4 cups need 5 minutes).
**3.** Stir well. Continue cooking on _high_ , stirring at 1-minute intervals, until the food is thoroughly reheated.
**Note**
Food in a sauce reheats with better results than dry food. If you wish to reheat a plain cooked chicken breast, for example, first cover it with a bit of sauce or gravy, or even some broth.
##### **Defrosting Cooked Food**
**1.** Transfer the microwavable container directly from the freezer to the microwave. Loosen the lid so the steam can escape.
**2.** Heat on _high_ setting for 5–7 minutes.
**3.** Change the power to _medium_ and continue heating for 5–8 minutes or until the food softens and can be broken up, if necessary.
**4.** The food may now be reheated as for refrigerated food.
**Note**
Some foods, such as vegetables and soup can be defrosted and reheated in one step on high setting. Eight ounces of frozen soup, for instance, can be defrosted and reheated on high for 4–6 minutes. Stir the soup three or four times during the process.
##### **Defrosting Uncooked Food**
**1.** Place the frozen food in the microwave.
**2.** Microwave on the _defrost_ setting for 6–10 minutes. Let the food sit for 7–10 minutes before continuing with cooking. For example, defrost two 8-ounce frozen steaks for 6–8 minutes, turning two or three times. They should then sit for 10 minutes before you continue with the cooking.
##### **Stirring & Standing**
Stirring is very important in microwave cooking. Since microwaves do not evenly heat all areas of the food in a container, stirring during the course of cooking or reheating helps ensure an all-over doneness.
After the prescribed cooking time in the microwave, there will usually be a short standing time. This allows the heat to be fully absorbed into the food. Most often the food should remain covered and can "stand" in the oven or on a heatproof counter.
##### **Warnings**
• Never heat a baby's milk bottle in the microwave, as it will heat unevenly. Some of the milk might be very hot without your being able to detect it and could burn the baby's mouth.
• Don't use a microwave when the food you are making is meant to have a crispy exterior.
• Microwave dishes and bowls can be deceptively hot. Always use pot holders and be careful of steam as you lift up the plastic wrap or cover.
• Chicken defrosted in the microwave should be cooked immediately after defrosting—whether you continue cooking it in the microwave or cook it conventionally.
**Equipment**
• If you have the space for it, get a full-power oven that uses 650 to 700 watts of energy. It is more efficient than the smaller, low-power ovens and can accommodate large dishes for heavy-duty cooking. A small low-power model that uses 400 to 650 watts is fine for reheating, defrosting, and cooking vegetables.
• 2 microwave-safe glass or ceramic casseroles, 1-quart and 2-quart, with covers, for things like rice, stews, soups, casseroles, and vegetables.
• 1 microwave-safe glass or ceramic rectangular baking dish, 8 x 12 inches, for cooking chicken parts, fish, or pasta.
• Several heavy microwave-safe plastic containers with lids, for freezing and reheating.
• 4–6 glass or ceramic cereal bowls, for small portions.
• Paper towels and paper plates. These can be used with foods that cook quickly, such as bacon.
* * *
#### **Food Safety & Storage**
In addition to the labor involved in shopping, cooking, and getting the kids to eat their food, there is another area of kitchen management that requires Dad's attention—food safety. Food must be bought, handled, and stored properly in order to prevent contamination. To avoid problems, follow these basic food-safety tips:
• Wash your hands before and during cooking.
• Defrost frozen food in the refrigerator, or in the microwave when appropriate.
• Keep cold foods cold and hot foods hot. Bacteria thrive between 40°F and 140°F.
• Never leave cooked food sitting at room temperature for more than two hours.
• Keep raw meat and poultry well wrapped in the refrigerator. Meat and poultry drippings can transfer bacteria to other foods.
• Always rinse your meat and poultry well in cold water before cutting and cooking, as this helps reduce bacteria, though it by no means eliminates them.
• Wash cutting boards and knives with soap and hot water immediately after cutting any raw poultry or meat.
• Always cook poultry to 170°F and pork to 160°F to kill bacteria.
• Cook meat, poultry, and fish within 24 hours of defrosting and never refreeze it once it has been defrosted. Freezing slows the growth of bacteria, but it doesn't kill them. Ice crystals formed during freezing break down cell walls, making defrosted food very susceptible to contamination.
#### **Freezing**
Freezing is the best way to manage leftovers and to avoid wasting food. If properly wrapped, labeled, and frozen, many foods will last 6–9 months, some even longer. Freezing also enables you to have an arsenal of ingredients or prepared foods at your fingertips.
##### **Rules for Freezing**
**Wrap tightly**
Air affects food. Choose a container that you can fill almost to the top, leaving ½ inch of open space to accommodate expansion during freezing. With meat and poultry, wrap each piece individually, first in plastic, then in aluminum foil, pressing out as much air as possible. This way all you need to do is remove the foil to defrost the meat or poultry in the microwave.
**Freeze quickly**
The fresher something is, the better it will survive its stay in the freezer. Set your freezer at or below 0°F, then use a standard weather thermometer to check its temperature. Frozen casseroles, stews, and vegetables can be moved directly from the freezer to the microwave, stovetop, or oven. Keep the flame low when reheating to avoid scorching and changing consistency.
**Label correctly**
There's no point in freezing food if you don't label it. Frozen foods wrapped in aluminum foil become indistinguishable lumps of something cold. Write the name of the food and the date on freezer tape or masking tape.
##### How Long Will It Last?
The print edition of this book includes a chart called **How Long Will It Last?**.
Please download a PDF of this chart here: workman.com/ebookdownloads
#### **Real Men Do Measure**
You've probably heard descriptions of your grandmother cooking without measuring, instead throwing in a fistful of this and a pinch of that, and the whole family sitting down for a delicious meal. But grandmothers usually have years of experience and a limited repertoire. No beginning cook should ever be cavalier about measuring.
Proper measuring is most crucial when you are baking. There, the balance of flour, leaveners, shortening, and liquids must be precise. Recipes are designed to have the proper balance of flavors, so follow the prescribed amounts of seasonings exactly. Improvising with the spices can make the final product overbearing or inedible.
As you begin to absorb the fundamentals of cooking, you'll feel freer about measuring some ingredients. You'll throw in those extra mushrooms, omit the cilantro, or splash a little more wine into the stew. But give it time. You're never too cool to measure.
#### **How to Read a Recipe**
This book, like most cookbooks, is filled with recipes. In general, _Dad's Own_ tries to explain all unfamiliar terms as we go. But learning how to decipher a recipe takes practice. Here are some decoding tips.
**1. Read the whole recipe first.**
This way you'll know in advance what ingredients you'll need, how much preparation and cooking time is required, and what the cooking methods will be (baking, sautéing, broiling, etc.). While reading, walk through the steps in your head, estimating how long each one will take. Note words like "beaten," "chopped," and "sliced" in the ingredient list and allow enough time for this "prep" work. Your ability to predict how long a recipe will take will get better and better.
**2. Make a shopping list.**
Go over the list of ingredients and see what you have in stock in the pantry and refrigerator. Make a shopping list of the ingredients you need.
**3. Get your equipment ready.**
_Dad's Own_ recipes include a list of the equipment you'll need to prepare each dish. Get the bowls, pots, pans, gadgets, and machinery ready and assembled before you start work so that you won't be interrupted while you're cooking.
**4. Preheat the oven and prepare the pans.**
There's nothing more annoying than charging through a recipe only to be stalled by a cold oven. And when you're baking, remember to butter and flour the pans before making the batter. It's easy to forget at the last minute when the batter is ready to be poured into the pans.
**5. Do all the prep work.**
Cooking _anything_ is a snap once your ingredients are ready. Look at the ingredient list and the recipe instructions to see how things need to be measured and sliced or chopped. Assemble the prepared ingredients in bowls and arrange them neatly on the counter before you actually start to cook.
**6. Once you start, don't stop.**
Cooking demands attention. Prop some books in front of the kids and let the answering machine take care of the phone. Dad's in the kitchen! Keep the recipe near your work area so you can refer to it easily, but not so close to the action that it will get splattered with food.
* * *
**Demystifying the Sauté Pan**
More happens in your sauté (or frying) pan than in any other place in the kitchen. It's where many sauces are made, where meat, chicken, and vegetables are sautéed, fish can be poached, and pancakes and French toast are grilled to golden perfection. I like to use a heavy cast-iron skillet (shown here). Or invest in a 10– or 12– inch, high-grade stainless-steel pan with a long handle and cover. (Cuisinart and All-Clad are both good brands.)
##### **The Right Heat**
Always heat the pan (about 45 seconds) before you start to cook. The hot pan will keep the food from sticking and will help seal in the juices of meats by searing the outside quickly. You know the pan has reached the right heat to start cooking when the butter stops sizzling or the oil moves easily over the surface. Flick a drop of water in the pan; if it sizzles, the pan is ready for action.
##### **Poaching**
To poach fish or chicken, add about ½ inch of water or stock to the sauté pan and bring it to a simmer over _high_ heat. As soon as the liquid is bubbling, add the food to be poached. When the liquid returns to a boil, reduce the heat immediately and cover the pan. The liquid should be barely simmering. If you don't have a tight-fitting cover for your pan, lay a piece of lightly greased foil on top of the food.
##### **Sautéing**
To sauté is to cook something quickly—often in a matter of minutes—over relatively _high_ heat in a minimal amount of oil or butter. Pat dry whatever you are sautéing before adding it to the pan, as excess liquid lowers the temperature and impedes browning. Pieces of food to be sautéed should be relatively thin or small. Otherwise, the outside will burn before the inside is fully cooked.
##### **Reducing Sauces**
Pasta sauces, simple sauces made with stock, complex sauces made with cream—all originate in your sauté pan. Because of its large cooking surface, a sauté pan is the best place to reduce a sauce. Reducing is the process of cooking a sauce so that some of the liquid evaporates, allowing the sauce to thicken and the flavors to intensify. Most cream sauces require reducing. Use _medium-high_ heat and stir the sauce regularly so it reduces evenly. A cream sauce is ready when it coats the back of a spoon. Simpler sauces (called "short sauces"), are made by deglazing the pan with wine or stock after the food has been cooked (see box).
**Butter & Oil**
SautéIng requires just enough butter or oil to cover the bottom of the pan; usually 1 to 2 tablespoons is enough. Sautéing differs in this way from frying, where a greater amount of oil is used. Using a combination of butter and oil prevents the butter from getting brown (butter that has turned brown will wreak havoc on the flavors of the food in your pan). Make a small pool of oil (a scant tablespoon) in the center of the pan and place a teaspoon of butter in the center of the oil, then swirl to coat the entire surface.
**About Deglazing**
Deglazing is the process of scraping up the flavorful bits of meat left on the bottom of the sauté pan after browning or frying. After removing the large pieces of meat, add the deglazing liquid (usually wine or chicken stock) to the hot pan. It will steam and sizzle. Working quickly, use a spatula or wooden spoon to scrape the bottom of the pan, incorporating the bits of meat into the liquid. Remove this liquid from the pan just as soon as it has reduced a bit and use as a sauce.
* * *
Cleanup
The cardinal rule is _clean as you go._ Here are a few tips to help you along the way:
• Wash and put away your pots, pans, bowls, food processor, measuring cups, and other cooking equipment as soon as you are done using them. Getting them out of the way will keep the sink and counters free, and you won't have to spend two hours cleaning up after everyone has finished eating. The only exception to this rule is pans and food stuck to them; fill them with warm water and a little bit of dishwashing liquid and let them soak overnight.
• Re-use bowls and pans rather than taking out every piece of cooking equipment in the house. A quick rinse and a wipe will ready a cup or bowl for another use. The exception to this is bowls, boards, or utensils that have come into contact with raw eggs, poultry, or meat. These should be washed carefully before re-using them.
• Keep the counters cleaned and wiped, so ingredients won't contaminate each other and the dessert won't taste of onion. Keep a garbage can or bag close by so you can sweep scraps directly off the counter and into it. Put away ingredients and equipment as soon as you have finished using them; clear surfaces give you room to maneuver.
• Wash your hands often. Besides being sanitary, it keeps food from being smudged on your clothes, the refrigerator door, and every pot handle you touch.
## Breakfast
Breakfast has traditionally been Dad's domain. When I was growing up, my dad would get up early on Sunday mornings and whip up a batch of pancakes, French toast, or a monster omelet. He did this partly to give Mom some extra time to sleep and partly to show her that cooking ain't so tough after all.
But preparing breakfast on a daily basis is another matter. It's wonderful to start the day with a bowl of hot cereal or a warm muffin or scone with jam, but most of us don't have time to eat breakfast, never mind make it. Nevertheless, breakfast is considered the most important meal of the day, capable of boosting energy and productivity in a big way.
Getting a healthful breakfast on the table every morning requires a combination of the microwave, a high flame under the omelet pan, some savvy shopping, and, sometimes, a few simple preparations the night before.
* * *
**The Basic Egg**
The egg you eat is one of about 250 that a poultry-farm chicken lays in a year, one of about 390 billion produced annually in the world. It weighs about 2 ounces and provides 6.5 grams of protein, which is about 13% of the recommended daily intake. It has 80 calories and healthy amounts of iron, phosphorus, and thiamine. The problem with the egg is that it is very high in cholesterol, all of which is contained in the yolk. To reduce cholesterol, try making your omelets with a combination of whole eggs and egg whites. Or serve your eggs "over easy," but accompany them with a few slices of orange or melon instead of bacon or sausage, and spread the toast with "fruit-only" jam, not butter.
**How to Cook The Perfect Hard-Boiled Egg**
Place cold eggs in a saucepan or pot and cover with cold water. Bring the water to a boil, then reduce the heat to a simmer. Simmer for 12 minutes. Plunge the eggs immediately into cold water to stop the cooking and to make them easy to peel right away.
##### **Boiled Eggs**
You could serve soft-boiled eggs in the shell, as the English prefer, but then you would need egg cups. A more down-home approach is to break the egg into a bowl with some bite-sized pieces of toast. This is especially good to serve the kids if they're laid up with a sore throat and are having trouble swallowing.
**Ingredients** _(serves two)_
_4 very fresh extra-large eggs_
**Equipment**
_Medium saucepan_
_Slotted spoon_
**1.** Fill a medium saucepan ⅔ full with water and bring to a boil on _high_ heat.
**2.** Reduce the heat to _medium_ and gently lower the eggs into the water with a slotted spoon.
**3.** Simmer for 3 minutes for regular soft-boiled eggs, or for 4 minutes if you like the yolks a bit harder.
**4.** Remove the eggs with a slotted spoon. Hold the hot eggs in a cloth or a doubled paper towel and gently crack the shell at the top with the back of a spoon. Peel away enough shell so you can ease the spoon into the egg. Scoop out the yolk and carefully scrape the white from the inside of the shell. Serve immediately with toast, as soft-boiled eggs cool quickly.
##### **Scrambled Eggs**
The secret is to get the pan nice and hot and to work quickly with the spatula.
**Ingredients** _(serves four)_
_8 large eggs_
_1½ tablespoons butter or margarine_
**Equipment**
_Large nonstick sauté pan_
_Medium bowl_
_Whisk_
_Short spatula_
**1.** Break the eggs into a medium bowl and beat with a whisk.
**2.** Put a large nonstick sauté pan on _high_ heat and let it get hot, about 30 seconds.
**3.** Spread the butter or margarine around the pan. When it stops sizzling, pour in the eggs. Let the bottom set for about 10 seconds. Then, with the spatula, scrape the cooked eggs up from the bottom and stir them.
**4.** When the eggs are the consistency that you like, remove them from the pan (or they'll keep cooking) and serve immediately.
**Variations**
If you want to add some pizzazz to your eggs but don't want to make omelets, add any combination of the following to the beaten eggs and cook as above:
• Small pieces of ham or cooked bacon
• Grated cheese (cheddar, Swiss, Gruyère, feta, or any hard cheese)
• Bits of smoked salmon
• Any one of these fresh or dried herbs: oregano, basil, thyme, or chives
• Thin slices of salami, pastrami, or corned beef
• Sautéed chopped onion, mushrooms, bell pepper, or zucchini
##### **Fried Eggs**
To get eggs "over easy" without breaking the yolks, do what an experienced short-order cook does: Brush your spatula with a bit of oil, slip it under the frying eggs, and ease them over gently.
**Ingredients** _(serves two)_
_1 tablespoon butter or margarine_
_4 large eggs_
**Equipment**
_Large frying pan_
_Spatula_
**1.** Put a frying pan on _high_ heat and let it get hot, about 30 seconds.
**2.** Spread the butter or margarine around the pan. When it stops sizzling, crack the eggs and open them just above the pan, easing the yolks onto the surface so they won't break when they land.
**3.** Fry the eggs until the whites are set, about 2 minutes. If you want "sunny-side up" eggs, lower the heat to _medium_ and cook for 1 minute more. For "over easy," flip as described above and cook them for 30 seconds longer.
**4.** Use the spatula to carefully lift the eggs from the pan, as the yolks can still break. (If necessary, use the edge of the spatula to separate eggs that have run into each other while cooking.)
**Tip**
Put the bread in the toaster just after you begin to cook the eggs so the toast will be ready at the same time as the eggs.
##### **Poached Eggs**
Poaching is a cooking technique in which a food such as eggs, fruit, or poultry is cooked in liquid at or below the boiling point. Properly poached eggs on toast make an especially comforting breakfast. Serve these to Mom when she's spending the morning in bed.
**Ingredients** _(serves two)_
_1 tablespoon white or cider vinegar_
_4 very fresh large eggs_
**Equipment**
_Large, deep-sided frying pan_
_4 small bowls_
_Slotted spoon_
**1.** Fill a large, deep-sided frying pan ⅔ full with cold water. Add the vinegar and bring to a boil on _high_ heat.
**2.** While the water comes to a boil, break 1 egg into each of the 4 bowls, being careful not to break the yolks. If a yolk breaks, save the egg for something else and try another.
**3.** When the water boils, reduce the heat to _medium_ so it is barely simmering. With a bowl tipped so that it's touching the water, let the egg slide gently into the water. Repeat with the remaining eggs, working quickly so that all of the eggs will be done at the same time.
**4.** Let the eggs simmer for 3 minutes, until the whites begin to get firm. Gently spoon some of the water over the yolks so they warm through. If the water begins to boil rapidly, reduce the heat a bit. When done, carefully remove the eggs with a slotted spoon and serve over toast or an English muffin.
##### **Omelets**
Great omelets depend as much on the proper proportion of eggs to the size of the pan as they do on the skill of the chef.
**3 large eggs = 8-inch pan _(for 1 person)_**
**5 large eggs = 10-inch pan _(for 2 people)_**
**8 large eggs = 12-inch pan _(for 3 people)_**
The omelet will not set correctly with too many eggs in the pan, too few and it will cook too quickly. It is always better to make more omelets than to try to overload the pan with too many eggs. And since the cooking time for omelets is only about a minute, once you get in the groove, you can start cranking them out.
**Ingredients** _(makes one)_
_About ½ cup filling (see below)_
_3 large eggs_
_1 teaspoon butter or margarine_
**Equipment**
_8-inch frying pan, preferably nonstick_
_Medium bowl_
_Whisk_
_Spatula_
**1.** Prepare the filling (if desired) and set aside.
**2.** Gently beat the eggs with a whisk in a medium bowl.
**3.** Put a small, preferably nonstick, frying pan on _high_ heat and let it get hot, about 30 seconds. Spread the butter or margarine around the pan. When it stops sizzling, pour the eggs in all at once. Let the bottom set, about 15 seconds.
**4.** Slip a spatula about a third of the way under one side of the omelet. Lift up that edge and tilt the pan toward it so the loose, uncooked egg on top runs toward the area of open pan. Continue until there is no more loose egg on top.
**5.** Quickly spread your filling down the middle of the eggs. Fold the thicker side of the omelet over the filling.
**6.** Take the pan to the serving plate and use the spatula to nudge the omelet onto the plate.
**7.** Wipe the pan clean with a cloth or paper towel and start again, if desired.
**Fillings**
• Grated cheddar, Monterey Jack, mozzarella, Swiss, Gruyère, Edam, or Parmesan or softer cheeses, such as Gorgonzola or feta, cut into small pieces
• Ham, salami, or cooked bacon, cut into bite-sized pieces
• Chopped onion, bell pepper, mushrooms, tomato, scallions (all can or should be sautéed briefly first)
• Reheated leftover chili, or reheated refried beans, or tomato salsa (at room temperature)
• A sprinkling of any combination of fresh or dried herbs, such as oregano, parsley, basil, rosemary, or, separately, tarragon (about 1 teaspoon per 4 eggs)
**About Eggs**
When considering eggs, freshness is key. The best eggs are bought from a local farmer—they have the most flavor. Organic and free range are also now widely available. There is no difference in taste or nutritional value between white and brown eggs. (The color of the shell is determined by the breed of hen that laid it.) For measurement purposes, especially in baking, it is important to have the right size eggs. Large or extra-large eggs are used in all of _Dad's_ recipes. When buying eggs, check the date on the side of the carton and buy the freshest ones you can. Eggs are best used within 1 week of purchase, but will last up to 3 weeks in the refrigerator. Always store them in their carton. Here's a neat test to tell whether an egg is still fresh: Place an egg in a small bowl of water. If it is a fresh egg it will stay on its side; if it is an older egg it will stand straight up and float. Air always passes through the porous shell of an egg, but if so much air has permeated the shell as to make the egg buoyant, the egg has been sitting around too long and should be thrown away.
* * *
#### **Pancakes**
Pancakes can range from the ridiculous to the sublime depending on who mixed the batter and who flipped the cakes. These are light and nutritious.
**Ingredients** _(serves four)_
_1 cup unbleached all-purpose flour_
_½ cup whole wheat flour_
_3 tablespoons sugar_
_2 tablespoons wheat germ (optional)_
_1½ teaspoons baking powder_
_½ teaspoon baking soda_
_½ teaspoon salt_
_1 large egg_
_1 cup milk_
_2 tablespoons butter or margarine, melted and cooled, or vegetable oil_
_1 teaspoon vanilla extract (optional)_
_Additional butter, margarine, or vegetable oil for cooking the pancakes_
_Pancake syrup, for serving_
**Equipment**
_Large frying pan or griddle_
_Medium bowl_
_Small bowl_
_Small pitcher (optional)_
_Whisk_
_Wooden spoon_
_Spatula_
**1.** Using a whisk, mix together all the dry ingredients in a medium bowl.
**2.** Gently whisk together the egg, milk, melted butter or margarine (or vegetable oil), and vanilla in a small bowl.
**3.** Pour the wet stuff into the dry and stir with a wooden spoon until it is just combined. Do not overmix. At this point you may want to transfer the batter to a small pitcher so it will be easier to pour into the frying pan.
**4.** Put a large frying pan (or set your griddle) on _high_ and let it get hot, about 30 seconds. Then reduce the heat to _medium_.
**5.** Spread about ½ tablespoon of butter or margarine around the pan. When it stops sizzling, pour the batter into the frying pan to the desired pancake size, as many as will fit without the edges touching.
**6.** Cook until craters _just begin_ to form on top of the pancakes. Turn and cook for 1–2 minutes more for thin cakes, slightly longer for thicker ones. Serve immediately with butter or margarine and your favorite syrup.
**Variations**
Mix into the batter a cup of blueberries (fresh or frozen), thinly sliced strawberries, or diced peaches. Apples need to be thinly sliced and briefly sautéed before being added to the batter.
Slice a banana and, in a sauté pan set over _medium_ heat, combine the slices with ⅓ cup real maple syrup. Cook just until warmed. Serve over the pancakes.
**Tips**
• Commercial pancake mixes found in supermarkets aren't always great, but there are many mixes sold in country stores, at roadside stands, in health food stores (this is where you'll find whole grain mixes), or through food catalogs that are quite wonderful. If you discover one you like, save time by keeping it on hand for a quick and easy pancake breakfast.
• If you have a crowd to feed and don't want to start serving until you've made enough to go around, keep the cooked pancakes warm for a few minutes on a baking sheet in a 200°F oven.
• The first batch of pancakes may not turn out exactly right as the pan needs to reach the proper temperature. If your first pancakes took a lot longer to cook than the recipe indicated, raise the heat under the pan. Lower the heat if your first batch overcooked.
• You may not need to add any butter to the pan after cooking the first batch.
#### **French Toast**
French toast was one of the few things my dad taught me to cook. With slight adjustments (he wasn't hip to the vanilla), this is his recipe.
**Ingredients** _(serves four)_
_6 large eggs_
_½ teaspoon vanilla extract_
_Splash of milk_
_Dash of cinnamon (optional)_
_8 slices of bread_
_1 teaspoon butter or margarine_
**Equipment**
_Large frying pan or griddle_
_Pie pan or wide bowl_
_Whisk_
_Spatula_
**1.** In a wide bowl or pie pan, whisk together the eggs, vanilla, milk, and cinnamon (if using).
**2.** Dip each slice of bread into the egg mixture, turning a few times so the eggs soak into both sides of the bread.
**3.** Put a large frying pan (or set your griddle) on _high_ heat for about 20 seconds, then reduce the heat to _medium_. (Unlike omelets, French toast needs to cook slowly.)
**4.** Add and swirl the butter or margarine around the pan. When it stops sizzling, add the bread. Cook for 3–4 minutes, until lightly browned. Turn and cook for 3–4 minutes more.
**Time-Saver**
Uncooked French toast freezes very well. Soak the bread in the egg mixture, then lay the slices in a single layer on a baking sheet in the freezer for a few hours until the bread is frozen through, then transfer the frozen slices to a plastic freezer bag.
To serve: Put the frozen bread on a lightly greased baking sheet and bake in a preheated 400°F oven for 15 minutes. This technique works especially well with English muffins.
**Tips**
• Whole wheat bread works just as well as white bread and is more nutritious.
• For a variation, try French bread, cut diagonally into 1-inch-thick slices.
• For a real Ukrainian effect, try thickly sliced challah bread.
• If you're not using presliced bread, cut it into 1-inch-thick slices for French toast.
• English muffins also make interesting French toast.
* * *
**Breakfast in Bed**
Some people think there is no better way to show their affection for a loved one than to appear at the bedroom door in the morning carrying a tray with freshly squeezed juice, hot coffee, and a sumptuous breakfast. Mother's Day, birthday, anniversary—any morning you want to make that special someone feel like a million bucks.
**MENU**
Slow scrambled eggs with smoked salmon, sour cream & caviar
* * *
Croissants
* * *
Mimosas
* * *
Café au lait
* * *
Fresh fruit
##### **Slow Scrambled Eggs with Smoked Salmon, Sour Cream & Caviar**
With its elegant presentation and delectable flavors, this breakfast begs for Champagne.
**Ingredients** _(serves two)_
_4 slices homestyle white bread_
_4 eggs_
_¼ pound smoked salmon, finely chopped_
_2 tablespoons butter_
_2 tablespoons sour cream, at room temperature_
_2 ounces black caviar_
_Fresh fruit slices or whole berries_
**Equipment**
_Double boiler_
_Medium bowl_
_4-inch heart-shaped cookie cutter (optional)_
_Whisk_
**1.** With a cookie cutter or a paring knife, cut and remove a heart shape from the center of each slice of bread. Discard the hearts or reserve for another purpose. Place the remaining bread in the center of two plates.
**2.** Whisk the eggs in a medium bowl. Stir in the smoked salmon.
**3.** Put 2 inches of water in the bottom of a double boiler. Put the butter in the top, and set the double boiler on _medium_ heat. When the butter is melted, swirl it around to coat the pan, then add the eggs. Stir continuously with the whisk until the eggs are just about congealed, about 2½ minutes.
**4.** Remove the eggs from the heat and stir in the sour cream. Spoon a quarter of the eggs into each of the hearts. Top with the caviar and garnish the edge of the plates with alternating slices of fresh fruit or whole berries. Serve immediately.
##### **Mimosa**
For two mimosas, squeeze three fresh oranges. Fill half each Champagne flute with the orange juice, then add an equal amount of chilled Champagne.
##### **Café au Lait**
With this special breakfast, serve a cup of café au lait. Brew the coffee as usual, only slightly stronger, and add a pinch of cinnamon to the grounds. At the same time, warm some milk in a small saucepan. Pour equal amounts of coffee and milk into each cup just before serving.
**Caviar Emptor**
Fresh black caviar, such as osetra or sevruga, is usually available at specialty food shops. If you can't find fresh caviar, you may substitute the pasteurized or pressed caviar that is sold in supermarkets, although it is not comparable in taste. Beware that the distinctive fishy taste of caviar is not to everyone's liking. If desired, substitute a pinch of chopped fresh chives or parsley.
* * *
#### **Hot Cereal**
When I was a desultory lad of 22 and my grandfather was a vigorous codger of 91, I decided the best thing I could do was eat what he did. And one thing he ate every morning without fail was hot cereal.
**Ingredients** _(makes one bowl)_
_⅓ cup old-fashioned rolled oats_
_¼ cup water_
_A bit of milk and brown sugar, maple syrup, or honey (optional)_
**Equipment**
_Microwave oven_
_Small microwave-safe bowl_
**1.** Put the oatmeal and water in a microwave-safe bowl and cover loosely with plastic wrap.
**2.** Put the bowl in the microwave and cook on _medium_ setting for 5–6 minutes. Mix well.
**3.** Add the milk and toppings of choice.
**Variation**
Mix in some fresh berries, banana slices, chopped apples, raisins, or flavored yogurt for the last 30 seconds of cooking.
**Old-Fashioned Oatmeal**
For stovetop oatmeal, bring the water to a brisk boil in a 1-quart saucepan. Use more water for thinner oatmeal; less water for thicker. Stir in the old-fashioned rolled oats and reduce the heat to _low_. Cook uncovered for 5 minutes, stirring frequently. Remove the oatmeal from the heat, cover, and let stand until it reaches the desired consistency. Mix well, then stir in the milk, sugar, maple syrup, or honey, if desired.
#### **Puffed Pancake**
This puffed pancake was one of the few foods my Dad made that we considered gourmet. It's a foolproof, impressive recipe.
**Ingredients** _(serves four)_
_6 large eggs_
_1½ cups milk_
_1 cup unbleached all-purpose flour_
_3 tablespoons granulated sugar_
_1 teaspoon vanilla_
_¼ teaspoon cinnamon_
_6 tablespoons_ ( _¾ stick) butter or margarine_
_Jam, syrup, or honey, for serving_
**Equipment**
_12-inch cast-iron or ovenproof skillet_
_Blender_
**1.** Preheat the oven to 425°F.
**2.** In a blender on medium speed, mix together the eggs, milk, flour, granulated sugar, vanilla, and cinnamon, until just combined, about 15 seconds. The batter should be a bit lumpy.
**3.** Melt the butter or margarine in a 12-inch cast-iron skillet by putting it in the hot oven for about 30 seconds.
**4.** Remove the skillet from the oven, spread the butter to coat the bottom and sides of the skillet, and pour in the batter. Return the skillet to the center oven rack and bake for about 20 minutes, or until the pancake is puffed and lightly browned. (Do not check before 17 minutes have passed, and close the oven door slowly and carefully after checking.)
**5.** Cut into wedges and serve immediately with jam, syrup, or honey.
**Variations**
The puffed pancake is nice accompanied by fresh slices of fruit, such as apples, bananas, berries, or peaches. If you serve apples, sauté them in a tablespoon of butter over _medium_ heat for a few minutes while the pancake is cooking.
**Tips**
• If the butter turns brown, it has burned and is unusable. Pour it out, wipe out your pan, and start again.
• The pan must be exactly 12 inches across or the pancake will not puff.
• If you don't have a blender, use a hand mixer or whisk, or pulse briefly in a food processor.
#### **Frittata**
Seen on antipasto tables in many trattorias, this classic Italian dish is like a quiche without the crust and cream—and it couldn't be easier to make.
**Ingredients** _(serves four)_
_8 large eggs_
_4 slices ham, prosciutto, Italian salami, or pepperoni_
_1 teaspoon dried oregano_
_1 medium zucchini_
_1 red bell pepper_
_6 button or wild mushrooms_
_2 shallots or 1 small onion_
_3 tablespoons olive oil_
_½ cup grated cheddar cheese_
**Equipment**
_Large, nonstick frying pan with heatproof handle_
_Medium bowl_
_2 spatulas_
_12-inch serving plate (optional)_
**1.** Preheat the broiler and arrange the rack in the lower third of the oven.
**2.** Lightly beat the eggs in a medium bowl. Cut up the meat into 1-inch pieces and add to the eggs with the oregano. Set aside.
**3.** Wash and dry the zucchini and bell pepper. Trim the ends of the zucchini, then cut it in half lengthwise, and cut the halves into ½-inch-thick slices. Core and seed the pepper and slice into ½-inch-wide strips. Cut these into 1-inch-long pieces. Slice the mushrooms thinly. Peel and cut the shallots or onion into thin slices.
**4.** Put a large nonstick frying pan with a heatproof handle on _medium_ heat and let it get hot, about 30 seconds. Add 2 tablespoons of the oil and the zucchini, bell pepper, mushrooms, and shallots. Sauté for 6 minutes, stirring often, until the vegetables are soft.
**5.** Add the remaining tablespoon of oil to the pan and spread it to coat the bottom. Pour the egg mixture into the pan. Mix in the grated cheese and cook, stirring often, until the bottom half of the frittata is firm. (The top should be loose.)
**6.** Remove the pan from the stove and place it on the lower rack in your hot oven. Broil for 3–5 minutes or until the frittata puffs and browns.
**7.** Remove the pan from the oven and let it cool for a minute to set.
**8.** Transfer the frittata from the pan to the serving plate with 2 spatulas or serve directly from the pan. (Use a hot pad to hold the skillet handle; it will remain hot for a long time.)
**9.** Cut the frittata into wedges and serve.
#### **Home Fries Supremo**
I've often ordered eggs or even a sirloin steak, just to have something to eat with my home fries.
**Ingredients** _(serves four)_
_4 or 5 large potatoes (russet, red, or new potatoes)_
_1 medium onion, peeled and cut into thin matchlike strips_
_1 green bell pepper, seeded and cut into thin matchlike strips_
_1 clove garlic, minced_
_2 tablespoons corn oil_
_1 teaspoon paprika_
_Salt and pepper_
**Equipment**
_Medium saucepan_
_Large nonstick frying pan_
_Colander_
**1.** Cut the potatoes lengthwise into quarters. Cut the quarters into 1-inch-thick chunks, put them in a medium saucepan with just enough cold water to cover them. If using new potatoes, just cut them into quarters. Bring to a boil over _high_ heat, then reduce the heat to _medium_ and simmer for 10 minutes. The potatoes should be slightly undercooked. Drain in a colander and set aside.
**2.** When the potatoes are cooked and drained, put a large nonstick frying pan on _high_ heat and let it get hot, about 30 seconds. Reduce the heat to _medium high_ , add the oil, onion, and bell pepper, and cook until the onion is soft, about 6 minutes. Add the garlic and cook for 1 minute more.
**3.** Add the potatoes. Cook for about 15 minutes, turning the potatoes frequently so that all sides get browned. Add the paprika and salt and pepper to taste.
**4.** Cook for 5 minutes more, until the potatoes are crisply browned.
**Time-Saver**
The potatoes can be boiled the night before. Just cover them tightly and refrigerate.
**Tip**
For crispier potatoes, omit the paprika and stir in another tablespoon of oil 10 minutes before they are finished cooking and then place a heavy, heatproof dinner plate or another frying pan directly on the potatoes.
#### **Muffins**
**Ingredients** _(makes 12 muffins)_
_2 cups unbleached all-purpose flour_
_3 teaspoons baking powder_
_¼ cup sugar_
_3 tablespoons wheat germ (optional)_
_½ teaspoon salt_
_1 large egg_
_1 cup milk_
_6 tablespoons melted butter or vegetable oil, plus extra for greasing muffin tin._
**Equipment**
_12-cup muffin tin_
_Small bowl_
_Medium bowl_
_Wooden spoon_
_Whisk_
**1.** Preheat the oven to 375°F.
**2.** Lightly grease a 12-cup muffin tin.
**Greasing a Pan**
Fold a paper towel into quarters and use it to rub a very light coating of butter, margarine, shortening, or vegetable oil on the baking surface (both sides and bottom) of a pan, muffin tin, or baking dish. It is best _not_ to use butter, as its burning point is too low. Vegetable oil sprays work well also and they save time as well as calories.
**3.** Mix the dry ingredients together in a medium bowl.
**4.** Gently whisk together the wet ingredients in a small bowl.
**5.** Pour the wet stuff into the dry. Stir with a wooden spoon until the ingredients are just combined. Do not overmix—the batter should be lumpy.
**6.** Spoon the batter into the muffin cups until each is ⅔ full.
**7.** Bake on the center oven rack for 20 minutes, or until the muffins are lightly browned and a cake tester inserted in the center of a muffin comes out clean.
**8.** Let the muffins cool in the tin for at least 10 minutes before removing them.
**Variations**
• Add 1 cup fresh or frozen blueberries, fresh cranberries, or chopped apple to the wet ingredients before mixing with the dry. Use muffin tin liners instead of greasing the tin when making muffins with fruit.
• Substitute 1 cup cornmeal for 1 cup of the unbleached flour. This is especially tasty with blueberries added to the batter as well, but be sure to use muffin tin liners.
• Substitute 1 cup rolled oats for 1 cup of the flour. In a small bowl, pour the milk over the oats and let them soak for 1 minute. Then add the oats and ½ cup raisins to the rest of the wet ingredients. Proceed as directed in Step 5.
**Time-Saver**
The easiest, fastest way to have freshly baked muffins in the morning is to assemble the ingredients the night before. Just mix together the dry ingredients in one bowl, and the wet in another. Cover both bowls tightly with plastic wrap; refrigerate the liquids. Combine the wet and dry ingredients first thing in the morning and bake as directed.
* * *
**A Good Cup of Coffee & a Nice Cup of Tea**
##### **Coffee**
Coffee beans are brown in warm climates and high altitudes, in places like Africa, Jamaica, Brazil, and, of course, Juan Valdez's home, Colombia. Different climates and soils produce beans with subtly different flavors and aromas. The beans are picked green, shipped to their destination, and then roasted, which turns them brown. The longer they are roasted, the darker and stronger the beans. French and Italian roasts, almost black in color, are two of the strongest-flavored beans and make rich, slightly harsh, but intensely flavored coffee. Viennese roast is light brown and produces milder, softer coffee with little aftertaste. There are many flavors in between. Often coffee emporiums sell what they call "house blends," mixtures of strong and mild beans that produce coffee with richer, more complex flavor than coffee made from one kind of bean. You can have your beans ground at the store, but your coffee will taste best if you grind the beans as you need them in your own home coffee grinder. For simpler, everyday coffee, a can of already ground, dark-roasted coffee, such as El Pico or Bustelo, will do just fine.
But whatever kind you buy, the amount of coffee is the same: 1 coffee measure (2 tablespoons) for each 6-ounce cup of water. Brew coffee, using any of the three methods on the following page and you're assured great results. Of course, the easiest way to make coffee is in an automatic drip machine. Simply follow instructions in the manual.
**Manual Drip Method**
_(Beans should be ground medium fine.)_
**1.** Bring a kettle of water just to the boiling point.
**2.** Fit a paper filter into the filter holder and measure the ground coffee into the filter.
**3.** Pour only a small amount of water into the filter to wet the sides of the paper and to just cover the grounds; let the water settle. Pour in the rest of the water very slowly, pausing to let it drip through.
**4.** Continue pouring water until the coffee has reached the desired level in the pot.
**Plunger Method**
_(Beans should be ground medium.)_
**1.** Bring a kettle of water to a boil.
**2.** While the water is heating, remove the plunger from the glass pot and measure the ground coffee into the bottom.
**3.** Fill the pot with as much water as you need. Insert the plunger so that it rests just at the water level, and the lid fits on the top, creating a vacuum.
**4.** Wait 5 minutes, then push the plunger down slowly. The coffee is now ready to pour.
**Freshness**
The freshest beans obviously make the best coffee. Aficionados store their beans in the freezer and grind them immediately before brewing. Ground beans also stay fresher if refrigerated or frozen. Once the container is opened, ground beans lose their intensity after about a month and will produce only bland coffee after 2 months. Lots of supermarkets and delis offer "gourmet coffee beans." But if the beans have been sitting around for a while, they've probably lost their edge, and you're better off buying canned or vacuum-packed ground beans.
**Espresso–Stovetop Method**
_(Beans should be ground extra-fine.)_
**1.** Fill the bottom section of the espresso maker with cold water up to the level of the little escape valve on the side.
**2.** Fit the filter section into the bottom section and fill the filter to the top with coffee. (Do not pack the coffee in.)
**3.** Screw the top on tightly and set the espresso maker on _medium_ heat. When the top section is filled with coffee and it starts sputtering, the espresso is done.
##### **Teas**
Devout coffee drinkers may find this hard to believe, but tea is actually the world's most popular beverage. There are three main types of tea: black (the strongest flavored), green (an unfermented tea, with a mild, slightly bitter taste), and oolong (a subtle, delicate tasting tea). Herb teas are not made from tea leaves at all but are infusions of herbs, flowers, and spices.
To brew the perfect pot of tea, bring a kettle of cold water to a rolling boil. Warm a teapot by rinsing it out with hot water. Add 1 teaspoon of tea or 1 teabag per cup of water and "one for the pot." Pour the boiling water over the tea and leave it to brew for 3 to 6 minutes. If using loose tea, pour through a strainer (to catch the tea leaves) into cups.
* * *
#### **The Yogurt & Fruit Breakfast**
A simple bowl of yogurt and fruit or cereal is another quick and healthy way to start the day. And deciding what ingredients to mix in each morning's bowl can be fun for the kids.
**Ingredients**
_Granola or wheat germ_
_Nuts, raisins, sunflower seeds_
_Assorted fruits, such as bananas, strawberries, blueberries, raspberries, pineapple, apples, or grapes_
_Plain or vanilla yogurt_
**1.** Assemble the toppings in small bowls.
**2.** Spoon a cup of yogurt into a bowl for each person.
**3.** Let each person add the toppings of his or her choice.
**About Yogurt**
Yogurt comes in many styles—low-fat, lite, plain, flavored, creamy—you name it. You don't need to buy a national brand, but read the label carefully. Many of the fruit yogurts have a great deal of added sugar. As an easy alternative, buy plain yogurt and mix in "fruit-only" jam at home. The kids will like it just as much and won't be consuming unnecessary sugar. For Dad, any kind of lowfat or no-fat yogurt is the best bet, as it is lower in cholesterol than the nonreduced-fat yogurts.
## Lunch
When I was a kid, lunch was definitely my Main Meal. Breakfast was hurried, dinner dragged on and required manners. But lunch was the meal to relish; you could get your hands dirty and lick your fingers. Even the language of lunch was fun; there were Dagwoods, Reubens, grinders, knockwursts, BLTs, malteds, and egg creams.
Lunch I liked.
For Dads, lunch can be a time for some culinary improvising with last night's leftovers, turning baked potatoes into stuffed skins, slicing London broil for steak sandwiches, using the remains of a roasted chicken for tacos or chilaquiles. Once you get the hang of it, you'll feel like the King of Lunch.
Six Sandwiches the Kids Will Eat
#### **Peanut Butter & Jelly**
Perhaps no other food more closely taps into the American zeitgeist. Transcending regional boundaries, ethnic backgrounds, and socioeconomic status, a peanut butter and jelly sandwich is part of every American childhood. I won't presume to tell you how to make one, but I do think you can tell a lot about someone by the proportion of jelly to peanut butter they prefer and whether they like smooth or chunky.
**Variations**
For a different taste sensation, omit the jelly and add one of the following to a peanut butter sandwich: sliced banana, sliced apples, or apple butter.
#### **Tunafish Salad**
Somewhere in America there is a luncheonette with a little sign behind the counter reading "Home of the First Tunafish Salad Sandwich" and we should all be beholden to that spot. Whoever invented this sandwich made feeding kids a whole lot easier. Basic tunafish salad is essentially canned tuna and some mayonnaise. After that, it's anybody's ball game. Here's mine.
**About Tuna**
Solid white tuna packed in water is your best bet for sandwiches. It has the most distinct taste, the fewest calories, and holds up the best in tunafish salad. While solid white is a bit more expensive than chunk, flaked, or grated tuna, the meat is denser, so you wind up getting more for your money. Buy only tuna that has the "dolphin-safe" label, which means the fish from which it was made was caught without using nets that trap and kill many dolphins.
**Ingredients** _(makes four sandwiches)_
_One 13-ounce can solid white tuna in water_
_2 ribs celery, finely chopped_
_1 carrot, peeled and grated_
_2 tablespoons mayonnaise_
_2 tablespoons plain yogurt_
_1 tablespoon Italian dressing or vinaigrette_
_Salt and pepper_
_8 slices bread_
_Chips and pickles, for serving_
**Equipment**
_Medium bowl_
_Fork_
_Spoon_
**1.** Drain the liquid from the can of tuna. Empty the tuna into a medium bowl and flake it with a fork.
**2.** Add the celery and carrot.
**3.** Spoon in the mayonnaise, yogurt, and dressing. Add the salt and pepper to taste.
**4.** Mix well and spread on the bread for sandwiches. Serve with chips and a pickle.
**Variations**
The following can be mixed into the tuna salad to give it more zip:
• lemon juice
• curry powder
• grated red onion
• chopped dill
• chopped hard-boiled egg
• raisins
• chopped almonds or walnuts
**Bread Box**
No matter how you slice it, whole grain bread is better for you than white bread. When a grain of wheat is milled to make flour, the main ingredient in bread, its three parts—the bran (high in fiber), the germ (high in nutrients), and the endosperm (the nutritional weakling of the three)—are separated. All three are recombined to make whole grain flour, but only the endosperm is used to make white flour. Often white bread is enriched with vitamins but it is still no match for whole grain.
If your kids absolutely blanch at whole grain bread, look for "country white" or oatmeal bread. These have the smooth, mellow taste of white, but are often made without additives and are less airy, meaning there's more bread in the bread.
Some of the larger bakeries have tried to bake breads that combine the benefits of whole grain with the texture of white, but beware. Some airy "whole grain" breads are made with lots of additives and do not include enough whole wheat to make them nutritious. So look for "whole grain" on the package.
#### **BLT**
Besides my own, the first initials I learned were BLT, for bacon, lettuce, and tomato sandwich. To a kid, it was an exotic concoction. Its double layers opened my eyes to a whole new dimension of sandwichdom. The BLT was another entry on the short list of foods my dad liked to cook. He would cut it into triangles, arrange the triangles around the edge of the plate, points facing out, and fill the center with potato chips, just like they did at the local diner. There were even some frilly toothpicks set aside just for this enterprise.
An official BLT is made up of two layers: lettuce and tomato along with a little mayo or butter on the upper deck, three or four slices of bacon on the lower deck, separated by the third slice of bread in the middle. BLTs can be made with only two slices of bread, but I wouldn't recommend it. Turkey, roast beef, or tuna salad can be substituted for the bacon, but then it becomes a club sandwich. And that's an easy next step.
#### **Grilled Cheese**
The grilled cheese sandwich is an important institution. For many people, men especially, it was the first food they cooked on their own. A grilled cheese sandwich is very easy to make, if you remember one simple rule: Cook it slowly. Once the pan is hot, grill the sandwich over _medium-low_ heat. Placing a bowl or small plate on top to weight the sandwich down while it's cooking is also a good idea. Serve with chips, a bowl of tomato soup, and a glass of chocolate milk.
**Ingredients** _(makes one sandwich)_
_2 slices (about 2 ounces) cheddar, Monterey Jack, Swiss, or American cheese_
_2 slices bread_
_Pats of butter or margarine_
**Equipment**
_12-inch frying pan_
_Cereal bowl or heavy mug_
_Spatula_
**1.** Put the cheese between the slices of bread.
**2.** Spread a pat of butter or margarine on the outside of the top piece of bread.
**3.** Place a frying pan on _high_ heat and let it get hot, about 30 seconds. Then reduce the heat to _medium low._
**4.** Spread a teaspoon of butter or margarine in the pan. Arrange the sandwiches (you can make two at a time) in the pan, buttered side up, and set a weight on top of the sandwiches.
**5.** Cook on _medium-low_ heat until the bottom of the bread is golden brown, about 5 minutes. You can't rush a grilled cheese sandwich—if you do, the bread will burn before the cheese melts.
**6.** Turn over each sandwich, replace the weight, and cook for 4 minutes more or until the bottom is golden brown.
**7.** Serve immediately.
**Variations**
For added flavor, place one or more of the following between the slices of cheese:
• A slice or two of ham, prosciutto, or salami
• Several pieces of cooked bacon
• Thin slices of tomato, avocado, and/or red onion (that's for Dad, of course!)
#### **Turkey Club**
Now you can make this diner favorite right in your very own home. Serve with chips, pickles, and egg creams.
**Ingredients** _(makes four sandwiches)_
_½ pound bacon_
_12 slices bread_
_1 pound sliced turkey_
_Mayonnaise_
_2 tomatoes, sliced_
_Lettuce_
**Equipment**
_Baking sheet_
_Frilled toothpicks_
**1.** Preheat the oven to 350°F.
**2.** Arrange the bacon in a single layer on a baking sheet. Bake in the center of the oven for 10–12 minutes, until the bacon is crisp. Transfer the bacon to paper towels to absorb the grease.
**3.** Lightly toast the bread.
**4.** Arrange ¼ of the turkey on a slice of bread. Spread the mayonnaise on a second slice and place it over the turkey, mayonnaise side down. Arrange 3 slices of bacon, sliced tomato, and some lettuce on the second slice of bread. Spread some mayonnaise on the third slice of bread and place it, mayonnaise side down, on top.
**5.** Cut each sandwich twice diagonally to make 4 triangles and place a frilled toothpick in each triangle.
#### **Sloppy Joe**
Another American classic, Sloppy Joe sandwiches make a great lunch on a chilly weekend afternoon—as long as your child's school didn't serve them more than three times that week. You can make Sloppy Joes by following the simple directions on a Sloppy Joes spice packet. Or brown 1 pound lean ground beef, drain off the fat, then add to the pan ½ cup ketchup, ½ cup tomato sauce, 1 tablespoon each red wine vinegar, Worcestershire sauce, and brown sugar, and a pinch of salt. Simmer for 15 minutes and pour the mixture over an open roll. This recipe serves four. For a leaner lunch, substitute ground turkey.
**All-Star Sandwiches**
**Tuna Melt**
Place tunafish salad and a slice of cheddar or American cheese on half an English muffin and melt under the broiler.
**Salad in a Pita Sandwich**
Stuff a pita with lots of greens, shredded carrot, cucumber slices, sprouts, sliced red onion, and chopped tomato. Add your favorite salad dressing and, if you like, some shredded Jarlsberg or crumbled feta cheese.
**Deli Sandwich**
A classic sandwich overstuffed with roast beef, turkey, salami, bologna, tongue, corned beef, or pastrami. Russian dressing is a must with the roast beef.
**Egg Salad**
Chopped hard-boiled eggs mixed with mayonnaise—the only sandwich I recommend eating on white bread.
**Lox and Cream Cheese on a Bagel**
A must for Sunday mornings. Hopefully your kid won't develop too much of a fondness for this expensive delicacy.
**Chicken Salad Sandwich**
Cut leftover chicken or turkey into chunks, add chopped celery, parsley, and just enough mayonnaise to hold them together.
**Hero**
Cut open a long loaf of Italian bread, lay it on a counter surrounded by cold cuts, cheeses, and condiments, and let the kids create their own.
**Smoked Turkey with Cranberry Sauce**
Tasty and refreshing; the cranberry flavor is a nice change. Serve with a bit of crisp lettuce on whole-grain bread.
Four All-American Lunches
They may not be haute cuisine, but you can't go wrong serving one of these for lunch. The only downside is that you may establish a reputation among your kid's friends, and they'll be showing up on a regular basis for Dad's homemade lunches.
#### **Hamburgers**
A hamburger is simply ground meat (sirloin, round, or chuck) that is shaped into a thick, slightly bulging patty, and grilled, broiled, or pan-fried. Thin patties don't count. Neither does meat mixed with egg, onion, bread crumbs, or herbs. Get fresh meat and cook it over _high_ heat, and you'll turn out perfect burgers every time.
**Ingredients** _(serves four)_
_1 ⅓ pounds ground round, sirloin, or chuck_
_4 hamburger buns_
**Equipment**
_Broiler pan or frying pan_
**1.** For broiling, shape the meat into 4 equal patties that are about 4 inches across and bulging slightly in the middle. For pan-frying, make the patties flatter. See Note.
**2.** Preheat the broiler or put the frying pan on _high_ heat and let it get very hot, about 1 minute. If you have a well-seasoned pan, you won't need to add any oil when you're frying the burgers. The fat in the meat will be sufficient.
**3.** Broil the burgers 4 inches from the heat for 5–6 minutes, until they are brown and a crust has formed on the top. Turn them over and grill 5 minutes more for medium rare, 6 minutes for medium. Alternatively, panfry the burgers for 6 minutes, making sure they are not touching in the pan. Turn them over and cook about 5 minutes more for medium rare, 6 minutes for medium. Reduce the heat slightly during the last few minutes if the pan begins to smoke.
**Note**
Do not cover the pan while the burgers are panfrying. This will steam them and make them mushy. If you're worried about grease splattering, get a splatter screen and rest it on top of the pan.
**Toppings**
• Cheese—Add it during the last minute of cooking. It will melt very quickly under the broiler, so be attentive. If panfrying, add the cheese as soon as you flip the burgers so the cheese has time to melt.
Put in buns and serve with:
• Sautéed mushrooms and onion
• Bacon
• Lettuce and tomato
• Condiments of choice
**Coney Islands**
This is the "official" lunch in the greater Detroit area. Take a boiled hot dog and put it in a bun. Top it with yellow mustard, tons of chili (canned or homemade), and chopped white onion. Patrons of the legendary Lafayette Coney Island restaurant in downtown Detroit eat these with a knife and fork. But in the privacy of your own home, you can cheat a little.
#### **Hot Dogs**
Let's face it. Ball-park franks taste great only because you're at the game. Better franks—crispy on the outside and juicy inside—can actually be made in a frying pan at home.
**Ingredients** _(serves four)_
_1 scant tablespoon vegetable oil_
_6–8 hot dogs (see Note)_
_6–8 hot dog rolls_
**Equipment**
_Frying pan_
**1.** Place a frying pan on _medium-high_ heat and let it get hot, about 45 seconds.
**2.** Spread a scant tablespoon of oil over the bottom of the pan and arrange the hot dogs in the pan so they aren't touching.
**3.** Cook for about 4 minutes, until the bottoms are brown. Turn the hot dogs and cook about 3 minutes more. Continue turning, so the hot dogs are lightly brown on all sides.
**Note**
Hebrew National Light or chicken and turkey hot dogs have less fat than regular franks.
#### **Quick Macaroni & Cheese**
This easy recipe puts to shame the boxes of macaroni and cheese sold in the supermarket.
**Ingredients** _(serves four)_
_10 ounces small elbow macaroni_
_2 tablespoons butter_
_1½ tablespoons unbleached all-purpose flour_
_¾ cup whole or nonfat milk_
_1½ cups (about 6 ounces) grated cheddar cheese_
**Equipment**
_Large saucepan_
_Large frying pan_
_Colander_
_Whisk_
_Wooden spoon_
**1.** Bring a large saucepan of water to a boil for the macaroni. Add the macaroni and cook until al dente, about 5–7 minutes. Drain in a colander.
**2.** While the water is coming to a boil and the macaroni is cooking, place the frying pan on _medium-low_ heat and add the butter. When the butter is melted, sprinkle on the flour and stir continuously with the whisk until the butter and flour become a thick paste, about 2 minutes.
**3.** Increase the heat to _medium high_ and add the milk. Stir continuously until the mixture thickens, about 5 minutes. Add the grated cheddar and stir with a wooden spoon until the cheese melts, about 2 minutes. Turn off the heat.
**4.** Drain the cooked macaroni, then add it to the pan with the cheese mixture. Stir the macaroni into the cheese mixture and serve.
**Variations**
• Add 1 cup small ham cubes when you're mixing the cheese sauce and pasta.
• Boil a few chunks of Polish kielbasa and serve with the macaroni and cheese for a hearty late-afternoon lunch or early supper.
#### **Chef's Salad**
Here's a salad that's a complete and healthy lunch. Follow this recipe or use your imagination to create another tasty and colorful combination.
**Ingredients** _(serves four)_
_1 large head leaf lettuce_
_1 small head Romaine lettuce_
_1 cucumber, peeled and sliced_
_2 tomatoes, each cut into 6 wedges_
_1 red bell pepper, cut into strips_
_4 large hard-boiled eggs, cut in half_
_¼ pound ham, cut into thin strips_
_¼ pound Swiss cheese, cut into thick strips_
_¼ pound sliced turkey, cut into thick strips_
_½ cup black olives_
_One 4-ounce jar artichoke hearts, drained and quartered_
_1 cup Dad's Own Vinaigrette (page 165) or bottled dressing_
**Equipment**
_Large salad bowl_
**1.** Wash and dry the lettuces. Tear the leaves into 1½-inch pieces and place in a large salad bowl.
**2.** Add half the cucumber slices, tomato wedges, bell-pepper strips, egg halves, ham, cheese, and turkey to the lettuce, and toss together.
**3.** Alternate the remaining cucumber slices, tomato wedges, bell-pepper strips, and egg halves around the edge of the bowl in a decorative pattern.
**4.** Arrange the remaining ham, cheese, and turkey in the center of the bowl. Scatter the olives and artichoke hearts over the top.
**Lunch Treats**
**Yogurt Smoothie**
Here's a healthy alternative to a milkshake: In a blender, combine 1 cup lowfat plain yogurt with 1 banana, a few strawberries or blueberries, 2 ice cubes, and ½ cup orange or apple juice. Purée on high speed until everything is combined, about 1 minute.
**Dad's Own Egg Cream**
So named because the frothy white bubbles on top look like beaten eggs, or that's one of at least a dozen official theories. To make a real New York egg cream, pour about 2 tablespoons chocolate syrup into a tall glass, add about 2 inches milk, and stir well. Slowly fill the glass the rest of the way up with cold seltzer, stirring continuously. If necessary, let the foam subside and then add more seltzer. Insert a straw and think of Coney Island.
**Trail Mix**
Here's a fun-to-make, relatively healthy snack or dessert for kids. Mix together equal parts of any combination of the following: roasted almonds, shelled peanuts, sunflower seeds, raisins, chocolate or carob chips, coconut flakes, chopped dates, cashews, dried apples, dried peaches, and dried banana chips. Eat out of hand or swirl into yogurt.
**5.** Present the salad at the table. Pour on the dressing, toss, and serve.
**Variations**
Use any of the following instead of or in addition to the meats listed in the basic recipe: salami, cooked chicken breast, leftover London broil or steak, or bacon.
* * *
**The Lunchbox**
Kids mean school, and school means lunch, and lunch means a lunchbox. The lunchbox hasn't changed much over the years. Pictures of Red Ryder, The Lone Ranger, and Zorro have given way to Spongebob Squarepants and Superman. Zip-top bags have replaced wax paper. And juice packs show up more often than Thermoses. Otherwise, the basic components are the same:
**Lunchbox Tips**
• Remember, your children have to eat in front of other kids, so don't turn their lunchboxes into exotic culinary adventures or the latest in macrobiotic cuisine.
• Put lettuce between the tunafish and bread to keep the bread from getting soggy.
• If your child's lunchbox will be sitting at room temperature for a while, prepare a sandwich that won't spoil in the heat, such as salami or peanut butter and jelly.
• Use small, reusable plastic containers to save on plastic wrap and plastic bags.
* * *
Instant No-Recipe Lunches
#### **English Muffin Pizza**
Have the kids top toasted English muffins with a spoonful of tomato sauce, cheese, veggies, salami, or anything they can find in the fridge. Put them on aluminum foil and place in the toaster oven until the cheese melts. Cool slightly, then dig in.
#### **Yogurt Buffet**
For healthful do-it-yourself sundaes, set a large bowl of vanilla yogurt on the counter along with granola, peanuts, and raisins, as well as fresh fruit, such as grapes, apple, or banana slices, pineapple chunks, or orange sections. Let the kids help themselves.
#### **Tuna Patties**
In a bowl, mash together 2 cans white meat tuna, 2 eggs, ½ cup grated cheddar, and ⅓ cup seasoned bread crumbs. Let the mixture sit for 15 minutes in the refrigerator, then have the kids shape it into 8 patties. Fry the patties in a few tablespoons of oil in a large frying pan on _medium-high_ heat until brown, about 3 minutes. Turn gently and fry for about 3 minutes more.
#### **Macaroni & Cheese**
Stock up on boxes of macaroni and cheese mixes from the health food store. You'll find several brands without added preservatives or hydrogenated oils. These handy meals always make kids happy.
#### **Instant Burritos**
Fill flour tortillas with a few tablespoons of canned chili with beans, grated cheddar, and shredded lettuce. Roll up and place, seam side down, in a lightly greased glass baking dish. Spoon on your favorite jarred taco sauce, cover the pan with aluminum foil, and bake in a preheated 350°F oven for 15–20 minutes.
Using Up Leftovers
Lunch is a great meal for using up leftovers. Two obvious ways to do this are to make sandwiches with leftover meat loaf or salads from the remainder of a cooked chicken or turkey. Here are three recipes that use leftovers in a slightly more adventurous fashion. None requires much preparation or cooking, but all are quite tasty. And if you have more or less of a particular leftover, feel free to improvise a bit.
#### **Quick Leftover Lo Mein**
This is a great dish to make with leftover shrimp (if you are ever lucky enough to have any), chicken, turkey, pork, beef, or just vegetables. Adding a handful of bean sprouts or snow peas makes it even more authentic.
**Ingredients** _(serves four)_
_1–2 cups diced cooked chicken, meat, or shrimp_
_1 cup leftover cooked vegetables_
_¾ pound spaghetti_
_2 tablespoons corn oil, plus extra for tossing with the spaghetti_
_1 medium onion, cut in half and thinly sliced_
_¾ pound mung bean sprouts_
_¼ pound snow peas, strings removed_
_⅓ cup bottled Asian stir-fry sauce, such as ginger or teriyaki_
**Equipment**
_Pasta pot_
_Large, heavy frying pan or wok_
_Colander_
_Wok spatula, for stir-frying_
**1.** Bring a large pot of water to a boil for the pasta. Add the spaghetti and cook until al dente, about 5 minutes. Drain in a colander, toss lightly in oil, and set aside.
**2.** Place a large frying pan or wok on _high_ heat and let it get very hot, about 90 seconds. Add the oil and onion, and stir-fry until the onion is soft, about 1 minute.
**3.** Add the chicken, meat, or shrimp along with the sprouts and snow peas. Stir-fry for 2 minutes more.
**4.** Add the spaghetti and the Asian sauce to the pan. Cook, stirring continuously, until the sauce thickens and all the pasta is coated, about 3 minutes. Serve hot.
**Asian Noodle Soup with Leftovers**
Health food stores and most supermarkets sell ramen or other packages of Asian noodles with a variety of different-flavored powdered broths. They make a quick bowl of soup to which leftover meat, chicken, or vegetables can easily be added. Just cut the leftovers into small pieces and add them to the boiling water as you're stirring in the powdered broth.
#### **Chilaquiles with Chicken, Tomatoes & Cheese**
This "Mexican lasagna" is a tasty way to use leftover chicken, turkey, beef, or hamburger.
**Ingredients** _(serves four)_
_1 23-ounce can crushed tomatoes_
_1 8-ounce jar red taco sauce, mild or hot_
_½ cup canned chicken broth or ½ bouillon cube dissolved in ½ cup hot water_
_1½ ounces taco seasoning mix_
_1 12-ounce bag unsalted tortilla chips_
_2 cups cooked chicken, cut into ½-inch strips (from about ½ roasted chicken) or cooked hamburger, steak, or turkey_
_1¾ cups (about 10 ounces) grated Monterey Jack or cheddar cheese_
**Equipment**
_Grater_
_Large frying pan_
_11 x 17-inch glass baking dish_
**1.** Preheat the oven to 350°F.
**2.** Put the tomatoes, taco sauce, chicken broth (or water and bouillon), and seasoning mix in a large frying pan on _high_ heat and cook until the mixture begins simmering, about 4 minutes. (If using the bouillon, make sure it dissolves completely.) Reduce the heat to _medium low_ and cook the mixture for about 5 minutes more, stirring well to incorporate the spices. Turn off the heat and let the sauce sit until you are ready to use it.
**3.** Lightly oil an 11 x 17-inch glass baking dish. Break up the tortilla chips into large pieces and spread half of them over the bottom of the pan.
**4.** Spoon half the sauce over the tortillas. Arrange half the chicken pieces over the sauce. Sprinkle half the cheese over the chicken. Make another layer of chips, sauce, and chicken, and top it off with the remaining cheese.
**5.** Bake, uncovered, on the center rack of the oven for 25 minutes. Let sit for 5 minutes before serving.
**Tips**
If you're short on leftovers, poach 1½ pounds boneless chicken thighs (about 6) in an inch of water in a large covered frying pan for 8 minutes. Use _medium_ heat so the water barely simmers.
#### **Minestrone Deluxe**
Make this when you have lots of leftover meat or poultry, vegetables, and pasta or rice.
**Ingredients** _(serves four)_
_1 16-ounce can whole tomatoes, with liquid_
_1 23-ounce can minestrone soup_
_2 beef bouillon cubes_
_1–2 cups diced cooked meat, chicken, or turkey_
_1–2 cups cooked pasta or rice_
_1 cup leftover (or frozen) vegetables, cut into small pieces_
_¼ cup grated Parmesan cheese, for serving_
**Equipment**
_Medium saucepan_
**1.** Chop the tomatoes coarsely.
**2.** Put all the ingredients except for the Parmesan in a medium saucepan and bring to a boil over _medium-high_ heat.
**3.** Reduce the heat to _low_ and simmer for 10 minutes.
**4.** Serve with a sprinkling of Parmesan over each bowl.
## Dinner
The last thing most people want to do after a hard day's work is to come home and make dinner. But somebody has to do it and sometimes it has to be Dad. Whereas cooking for family or friends on the weekend is usually more a pleasure than a chore—you have the luxury of taking your time and stretching your culinary limbs by experimenting with a new dish—preparing dinner on a weeknight can be tricky. Let's say you don't even get started until 6:00 P.M. Factoring in your family's various schedules, the preparation time, cooking time, and cleanup, you could be drying the last dish at 9:30 and falling into bed five minutes later. But not if you plan, shop, and map out dinner in advance.
**Plan your menus in advance.** Dinner is probably the best meal to try to map out on a weekly basis. Then you can do your main course and staple shopping ahead of time, and you're free to do any preliminary preparations (marinating, defrosting, etc.) as required for each meal. All you'll need to pick up on your way home from work are some fresh items—like fish or vegetables.
To choose your main courses, think about your family's favorites and the ways you might alternate meat, chicken, fish, pasta, and soups in your menus. For instance, break up a series of heavy meals with a light pasta dish and a salad, or some fish. And though it seems impossible to determine whether red meat is the key to good health or the bane of our diets, it's probably best to serve it only a couple of nights a week at most. Once you've decided on a main course, the rest of the meal should fall neatly into place. Use the recipe serving suggestions featured in this chapter to help you fill out your menus with vegetables, a starch, and a salad.
**Shop ahead.** Nothing slows down a cook more than not having the necessary ingredients on hand. While you're planning your menus, create your shopping list. Also take a moment to check the cupboard to see what staples may need replenishing (see "The Cupboard" on page 23). A well-stocked pantry will not only make your cooking easier, but will also allow you to throw together a last-minute meal when necessary.
**Prepare part of the meal beforehand.** Starting from scratch when you walk in the door can make cooking dinner seem an insurmountable task, even for the most enthusiastic cook. Taking just ten minutes the night before to ready the ingredients is time well spent. Another reliable time-saver is to wash and dry your salad greens in the morning, or even the night before, and pack them in well-sealed plastic bags, along with some paper towels to absorb moisture.
**Prepare ahead and freeze.** As you get used to shouldering the responsibility of making dinner, you may find it easier to give up a little time on a free night or the weekend to make a large batch of meatballs or a couple of pans of lasagna for freezing. It's nice to know that sometimes preparing dinner is merely a matter of remembering to defrost the entrée.
**Mapping Out Dinner**
Chicken, beef, fish, lamb, and pork are the traditional centerpieces of most American dinners. And while there are innumerable ways to prepare these foods as entrées, for the purposes of planning dinner, think about them in three groups: dishes that require little attention but long cooking times, dishes that require a lot of attention but take very little time to cook, and dishes that can be made in advance and reheated.
Plan dinner around what you have time to do. A roast chicken may take an hour and a half to cook, but once you've done your ten minutes of prep work, you have nothing to think about until it comes out of the oven. Serving this kind of entrée will give you a chance to get the rest of the meal together, open the mail, and talk with the kids. Sautéed fillet of sole takes only a few minutes to cook, but requires your full attention. This means making the side dishes and setting the table ahead of time. If you make a stew or meat loaf in advance, all you need to do is reheat it and prepare your side dishes.
Coordinating the meal so that all of the different elements are done at the same time is probably the trickiest part of making dinner and will take some practice. Start with the food that takes longest to cook, jot down the cooking times of your other courses, and map it out from there.
Avoid planning a meal in which too many dishes require last-minute preparation. You can't fuss over a main course that needs sautéing, a sauce that needs stirring, and a broiled item that requires your watchful eye all at once. For example, if you are broiling swordfish steaks for the main course, make rice or microwave baked potatoes as a side dish. That way you'll be free to focus on the swordfish while the side dishes pretty much tend to themselves.
* * *
**Chicken Basics**
Chicken is an ever-fashionable main course that lends itself to an infinite variety of dishes. You can buy it whole or in parts, with or without bones. No matter the form, chicken will give you lots of protein with less fat and cholesterol and fewer calories than red meat. You can reduce the calories and fat even further by removing the skin before cooking or eating.
##### **Cuts & Parts**
**Broilers/fryers** weigh 2½ to 3½ pounds and are suitable for roasting, broiling, or frying, or for stew and soup. Most chicken parts are cut from this size chicken.
**Roasters** are larger, more mature birds, weighing between 5 and 7 pounds. These should be used exclusively for roasting, as they are too large for frying or broiling. They can also be stuffed if you desire. You'll find that roaster parts are generally available at your market; the breasts make for especially delicious eating.
**Stewing chickens** (aka hens) are 1 year or older and weigh between 4 and 7 pounds. They are tougher than younger chickens but are full of flavor and make excellent soup or stew chickens.
**Chicken parts** can come in very handy if your kids have strong preferences for white or dark meat. Additionally, since white and dark meats have different cooking times, it's wise to cook one or the other. Boneless breasts make for quick and easy entrées, and are perfect for stir-fries. Your butcher can debone them.
##### **Servings**
The basic rule of thumb for chicken and turkey is ¾ pound of meat (with bone) per person. But it's just as easy to roast two chickens as one, or to add a couple of extra chicken breasts to the pan. You'll have great leftovers for the next day's lunch or dinner. Count on 4–6 ounces per person of boneless chicken.
##### **Storage**
When purchasing poultry, always check the expiration date on the packaging. The chicken should be cooked or properly frozen before that date. If you are not using the chicken right away, remove it from the packaging, rinse under cold water, and pat dry. Then wrap the chicken loosely in foil or plastic wrap and store in the refrigerator for up to 3 days.
To freeze chicken, wrap it in a freezer bag, seal well, label it, and store in the freezer for up to 3 months. Defrost all poultry in the refrigerator, not on the kitchen counter where risk of contamination from the salmonella bacteria is greater. Chicken parts will defrost overnight, a whole chicken in 24 hours. Chicken should be cooked soon after it is defrosted and should not be refrozen.
##### **Roast Chicken**
Roasting is the simplest way to cook a whole chicken. First remove the giblets (they're usually wrapped in paper inside the cavity) and rinse the chicken well, inside and out, with cold water. Pat it dry and pull off any globs of fat around the cavity. Next, squeeze half an orange or lemon over the skin and rub it inside the cavity. Sprinkle the bird with salt, pepper, and a dash of paprika. Lay a few dots of butter on the back and legs and place the chicken in a roasting pan just large enough to hold it (use a rack if you've got one). Roast the chicken on the center rack of a preheated 350°F oven. Cook for 20 minutes per pound (about 1 hour 10 minutes for an average-size broiler/fryer), or until the juices run clear when a thigh joint is pricked with a knife.
##### **Broiled Chicken**
Broiling requires more attention than roasting. The chicken should be cut in half or in parts, rubbed with vegetable oil, seasoned with salt and pepper, and arranged in the broiler pan skin side down. Place the broiler pan 6 inches from the heat and broil for 20 minutes. Turn and broil for 20 minutes more. During the last 10 minutes brush the skin with a bit of butter or lime juice to keep it from drying out and turn if it starts to char. Marinating the chicken for several hours before broiling also keeps the meat from drying out.
##### **Fried Chicken**
Frying is the most difficult way to cook chicken. It requires careful monitoring of the temperature of the oil, otherwise the chicken turns into a soggy, greasy mess. There are as many authentic recipes for fried chicken as there are church suppers. The basic procedure calls for dredging (lightly coating) the chicken parts in flour, cornmeal, or seasoned bread crumbs, then frying a few pieces at a time in about ½ inch of hot oil. Have a seasoned cook walk you through it the first time.
##### **Sautéed Chicken**
Sautéing boneless chicken breasts is quick and easy. Simply flatten the breasts a bit (see box, page 80) and dredge (lightly coat) them in flour or bread crumbs, if desired. Heat the sauté pan over _medium_ heat, add a few tablespoons of oil, and sauté for 3–4 minutes until the underside is a nice medium brown. Turn and sauté for 3 minutes more.
* * *
#### **Perfect Roast Chicken**
You _can_ shove a chicken in the oven and forget about it for an hour or so and it will come out cooked. But with just a few simple touches, you can truly "roast" a chicken to golden-brown perfection.
**Ingredients** _(serves four)_
_1 4- to 5-pound chicken_
_1 lemon_
_1 small onion, peeled and cut in half_
_4 tablespoons (½ stick) butter or margarine_
_1 teaspoon salt_
_Freshly ground black pepper_
_1 sprig fresh rosemary or ½ teaspoon dried_
_Additional salt and pepper_
**Equipment**
_11 x 17-inch roasting pan_
_Roasting rack_
_4-inch metal skewer_
_Carving fork_
_Basting brush_
**1.** Preheat the oven to 400°F.
**2.** Rinse the chicken inside and out under cold water, and pat dry.
**3.** Cut the lemon in half. Squeeze one half over the outside of the chicken. Rub the other half inside the cavity of the chicken, squeezing the juice against the bones. Leave that lemon half in the cavity along with the onion halves, 2 tablespoons of the butter, the salt, pepper, and rosemary. Close the cavity by folding the flaps of skin over the opening. Secure them further by threading a 4-inch metal skewer through the skin.
**4.** Rub the breast side of the chicken with 1 tablespoon butter and place it on the roasting rack in the roasting pan, breast side up. Place the pan on the center rack of your oven.
**5.** After 30 minutes, turn the bird over to the other side with a carving fork. Rub on the remaining butter and continue roasting for 30 minutes more.
**6.** Turn the chicken breast side up and brush it with some of the pan juices. Roast it for 10–15 minutes more, until the leg and thigh move freely when jiggled or the juices run clear when the thigh joint is pricked with a knife.
**Cutting a Cooked Chicken**
The key to easy cutting is a good pair of kitchen shears. After you've let the chicken cool for a few minutes, place it on a cutting board and, using the shears, cut through the breast to the back. Open the chicken up and you will see the ridge of the backbone. Use the shears to cut along each side of the backbone. Place the chicken halves, skin side up, on the cutting board and use the shears or a chef's knife to cut through the cartilage between the leg and the breast. If you meet with distinct resistance (bone), adjust the knife or shears slightly until you find the cartilage. If you want to separate the drumstick as well, bend it back away from the thigh and then cut the joint with shears.
**Note**
For a smaller (3–4 pound) chicken, roast for 25 minutes on each side and 10 minutes more breast side up.
**Serving Suggestions**
• Serve with gravy and mashed potatoes, sweet potatoes, or rice.
• Serve steamed or boiled broccoli, glazed carrots, or sautéed zucchini.
#### **Oven-Baked Middle Eastern "Fried" Chicken**
Here is an easy way to get crispy chicken without the mess and calories of frying.
**Ingredients** _(serves four)_
_6 chicken legs_
_6 chicken thighs_
_1 cup plain bread crumbs_
_2 tablespoons coriander_
_1 tablespoon dried cumin_
_1 teaspoon onion powder_
_1 teaspoon garlic powder_
_1 teaspoon cinnamon_
_Dash of cayenne pepper_
_2 large eggs_
**Equipment**
_Large roasting pan_
_Roasting rack_
_Pie plate_
_Medium bowl_
_Aluminum foil_
**1.** Preheat the oven to 375°F. Rinse the chicken pieces under cold water and pat dry with paper towels.
**2.** Combine the bread crumbs and all the spices in a pie plate and set aside. Beat the eggs in a medium bowl and set aside.
**3.** Dip each piece of chicken in the egg and let the excess drip off. One by one, lay the chicken pieces in the bread crumbs. Turn each one so the entire outside skin is coated with bread crumbs. Shake gently to remove excess.
**4.** Line a large roasting pan with aluminum foil and set the rack in the pan. Lay the breaded chicken on the rack and bake for 35–40 minutes, until the chicken is cooked through.
**Variation**
For chicken breasts, prepare in exactly the same way but bake for only 30–35 minutes.
**Serving Suggestions**
• Serve with rice pilaf or home fries.
• Serve with steamed spinach or steamed, boiled, or sautéed green beans.
**Simple Pan Gravy**
Remove the roasted chicken, then, using a pot holder, tilt the roasting pan so the juice runs into one corner. Use a baster or serving spoon to skim off and discard the fat floating on the surface. Place the pan on top of the stove over _medium_ heat. Add about ½ cup water or white wine to the pan (large pans will require more liquid) and 1 tablespoon flour or cornstarch. Use a spatula to scrape up the bits of meat sticking to the bottom and stir regularly. When the liquid has reduced by half, transfer it to a bowl, along with any bits of meat stuck to the bottom of the pan. Add salt and pepper and serve with the chicken.
#### **Chicken Breast Piccata**
This is a simplified version of a classic Italian dish.
**Ingredients** _(serves four)_
_2 whole skinless, boneless chicken breasts, split and flattened_
_2 large eggs_
_1 cup Italian-style bread crumbs_
_2 tablespoons olive oil_
_¼ cup white wine_
_¼ cup canned chicken broth_
_Juice of 1 lemon_
_2 teaspoons capers (optional)_
_Salt and pepper_
**Equipment**
_Large frying pan_
_Small bowl_
_Pie plate_
_Dinner plate_
_Serving platter_
_Spatula_
**1.** Rinse the chicken breasts under cold water and pat them dry with paper towels. Beat the eggs lightly in a small bowl.
**2.** Put the bread crumbs in a pie plate.
**3.** Dip each chicken breast in the egg and let the excess drip off.
**4.** Dredge both sides of the breast in the bread crumbs and shake gently to remove the excess. Place the breasts on a plate.
**5.** Put a large frying pan on _high_ heat and let it get hot, about 30 seconds. Add the oil and chicken breasts. Sauté the chicken for 3–4 minutes, until the bottom is golden brown. Turn and cook for 3 minutes more. Reduce the heat to _medium_ and sauté for 2–3 minutes more, until the chicken is cooked through. Transfer the chicken to a serving platter.
**6.** Add the wine to the pan and let it simmer and reduce, using a spatula to scrape up any bits of chicken stuck to the pan. Add the broth, lemon juice, and capers, if using. Cook and stir for another 45 seconds, until the liquid thickens slightly. Season with salt and pepper. Pour the sauce over the chicken breasts and serve immediately.
**Variation**
For Chicken Parmesan, preheat the oven to 350°F. Flatten the chicken breasts only slightly and follow Steps 1–5. When the breasts are brown on both sides, transfer them to a baking sheet. Spoon on a bit of tomato sauce, sprinkle on about a tablespoon of Parmesan, and top with a slice of mozzarella cheese. Bake until the cheese melts and the chicken is cooked, about 10 minutes. Serve over a bed of spaghetti.
**Serving Suggestions**
• Serve with pasta or wild rice.
• Serve boiled or steamed broccoli.
**Flattening Breasts**
A whole chicken breast has two parts, one of which is usually considered a single portion. Most boneless breasts are sold already split. To flatten, lay 1 breast between 2 sheets of wax paper. Using the flat side of a meat mallet, pound the breast several times until it is about half its original thickness.
#### **Chicken with Tomato & Sausage**
This is a simple, hearty dish that the kids will love to eat with spaghetti.
**Ingredients** _(serves four)_
_1 3- to 4-pound chicken, cut into 8 pieces_
_3 tablespoons olive oil, plus extra for tossing with the spaghetti_
_1 medium onion, thinly sliced_
_1 green or red bell pepper, thinly sliced_
_2 cloves garlic, minced_
_½ pound sweet Italian sausage, cut into ½-inch pieces_
_¼ cup dry white wine_
_1 28-ounce can whole tomatoes, drained and chopped_
_3 tablespoons tomato paste_
_1 teaspoon dried basil_
_1 chicken bouillon cube_
_1 teaspoon salt_
_Freshly ground black pepper_
_¾ pound spaghetti_
**Equipment**
_Large frying pan_
_Large pasta pot_
_Medium bowl_
_Large plate_
_Large platter_
_Slotted spoon_
_Spatula_
_Tongs_
**1.** Rinse the chicken pieces under cold water and pat them dry with paper towels.
**2.** Place a large frying pan on _medium-high_ heat and let it get hot, about 45 seconds. Add the oil, onion, and bell pepper, and sauté, stirring often, until soft, about 5 minutes. Add the garlic and sauté for 1 minute more. Transfer the vegetables to a medium bowl.
**3.** Raise the heat to _high_ and add the sausage pieces to the pan. Sauté, stirring often, until the meat is cooked through, about 4 minutes. Use a slotted spoon to transfer the sausage to the bowl with the vegetables and discard the fat in the pan.
**4.** Return the pan to the burner and when it is very hot, after about 15 seconds, add the chicken pieces and cook until they are brown on all sides, using tongs to turn them. This should take about 5 minutes. Transfer the chicken to a large plate.
**5.** Add the wine to the pan and use a spatula to scrape up any bits of chicken stuck to the bottom.
**6.** Return the chicken, sausage, and vegetables to the pan. Add the tomatoes, tomato paste, basil, bouillon cube, salt and pepper. Bring the sauce to a boil, then reduce the heat to _low_ and simmer, partially covered, for 30 minutes, until the chicken is thoroughly cooked. Stir occasionally.
**7.** While the chicken is simmering, boil the water for the spaghetti. Cook the spaghetti until al dente, then drain it and toss lightly with olive oil.
**8.** To serve, arrange the spaghetti on a large platter and use a slotted spoon to place the chicken and sausage over the pasta. Pour on enough sauce to flavor the spaghetti well.
**Serving Suggestion**
Serve with garlic bread and a tossed green salad or a Caesar salad.
* * *
**Beef Basics**
Thanks to its high fat and calorie contents, red meat has borne its share of criticism during the past few years. But that doesn't mean you should give up meat altogether. Instead, try to get in the habit of choosing the leanest cuts, such as eye of round, round tip, top round, tenderloin, and sirloin. Trim excess fat, and prepare small portions. And don't try to fight the fact that hamburgers are a major feature in most kids' childhoods.
_A 1,000 pound steer = 475 pounds of retail cuts, including 75 lbs. of steaks_
##### **Cuts**
Hitching up with a good butcher is the first step toward understanding (and obtaining) good cuts of meat. The second step is understanding that beef is cut from two types of muscle. Meat from muscles that are used infrequently, such as the loin and rib, will be tender. Cuts from more active muscles, such as the leg and shoulder, will be tougher. Tender cuts should be cooked quickly: broiled, roasted, or pan-fried; tougher cuts should be cooked slowly usually stewed or braised.
**Whole fillet** (or tenderloin) is the most tender and expensive cut of beef. It should be roasted whole in a very hot oven and can be sliced thin for an appetizer or slightly thicker for a main course.
**Filet mignons** are 1- to 2-inch slices cut from the center part of the whole fillet and are best pan-fried in butter and oil. They can then be topped with herbs or different sauces.
**Sirloin steaks** are excellent and extremely flavorful cuts taken from the rump end of the loin. They should be broiled or panfried (as long as they are no thicker than 2 inches) and served simply.
**Porterhouse steaks** are taken from the shoulder end of the loin. They are usually cut thicker than sirloin steaks and are a little more tender as well. These should also be broiled and served simply.
**Chuck steaks** come from the shoulder and are tougher and fattier than the loin cuts. They can be broiled, but are more commonly used for stews and roasts or ground for hamburgers.
**Brisket** is taken from under the shoulder. Look for the "first cut" of brisket, sometimes called the "plate," which is leaner and more flavorful than the second cut. Brisket is ideal for pot roast as it needs long, slow cooking.
**Flank steaks** are thin, flavorful cuts taken from under the loin. These should be broiled and can be served with any number of sauces, or can be rolled and stuffed with flavorful fillings. Leftover flank steak is also great in sandwiches and salads.
**Chopped meat** is usually made from chuck, round, or sirloin. Chuck and round make for somewhat juicier—but fattier and more caloric—burgers. Leaner burgers are also very tasty. Hamburgers should be broiled, grilled, or panfried.
**Roasts** are larger cuts of meat, usually weighing between 3 and 6 pounds. The most succulent are the rib roasts (with bone in), which will yield hefty portions. Other roasts come from the round or rump, which are both in the general vicinity of the tail. The top round and eye round are the most tender of these cuts. Chuck, bottom round, and rump roasts are flavorful but not as tender.
**Ribs** are fatty and fun and will keep the kids busy at the table. They are easy to cook and can be prepared in a variety of ways.
##### **Servings**
For boneless steaks, figure on ¼ pound per person. For bone-in cuts and roasts, figure closer to ½ pound per person. For chopped meat, figure on ¼ pound per burger. For ribs, figure 1 pound per person. Leftover steak or roast beef will never go to waste, so don't hesitate to buy a little more than you need.
##### **Storage**
A roast will keep in the refrigerator for about 4 or 5 days. Whether storing in the refrigerator or the freezer, always rewrap beef in plastic and foil. Shape hamburger into patties before freezing and wrap individually so you can take out only what you need. Defrost meat in the refrigerator overnight, or in the microwave, removing the foil but leaving the meat in its plastic wrapping. Large roasts can take 2 to 3 days to defrost in the refrigerator. Meat should be cooked soon after it is defrosted and should not be refrozen.
**The Meat Thermometer**
An all-purpose thermometer can take much of the anxiety out of cooking a roast. Avoid the old-fashioned meat thermometer that is placed in the meat before cooking, and get a good-quality instant-read thermometer to use at the end of cooking. Shortly before you think the meat will be done, open the oven and maneuver your meat or poultry so you have access to the thickest part of the roast or the thigh of a chicken or turkey. Insert the point to the center of the roast or thigh, making sure the tip is not touching a bone. Take a reading when the needle stops. Keep in mind that roasts continue cooking for about 10–15 minutes after they're removed from the oven.
**Cooking Times**
Different roasts have different cooking times depending on tenderness. The time guidelines below are minutes per pound for medium rare. Remember to preheat the oven and let the meat come to room temperature before cooking.
##### **Broiled Beef**
Broiling is the most common way of cooking steaks, chops, and burgers. Thin cuts (1–1½ inches thick) should be cooked 3 inches from the heat. For thicker cuts (1½–2 inches thick), lower the meat to 4–5 inches from the heat, otherwise the outside will burn before the inside is done. Remember, this distance is not how far the rack is from the heat, but how far the actual surface of the meat is from the heat.
##### **Stewed Beef**
Stewing is the cooking of small pieces of meat in a covered pot in enough liquid to cover them. Vegetables and herbs are cooked with the meat to enhance the flavor. Stew meat on top of the stove over _low_ heat or in a 325°F oven for several hours.
##### **Braised Beef**
Braising is the process of cooking meat slowly in a small amount of liquid, either on top of the stove or in the oven. Cook over _low_ heat on the stove or in a 325°F oven. Cuts such as chuck roast, brisket, and short ribs can all be braised. It's best to brown the meat first before adding the hot liquid. After adding the liquid and spices, cover the pot tightly. Onions, potatoes, carrots, and celery can also be added to the pot.
##### **Roast Beef**
Roasting is the proper method for cooking larger (over 2 pounds) pieces of meat. The meat should be arranged, fat side up, on a rack in a roasting pan just large enough to hold it. Using a rack keeps the bottom of the roast from steaming. If there is no fat on the roast, brush it lightly with oil or spread on a thin layer of mustard. Let the meat come to room temperature before putting it in the oven or it will take longer to cook.
##### **Panfried Beef & Burgers**
Panfrying is another method for cooking thinly cut steaks and burgers. They should be cooked in a small amount of margarine or oil in a preheated pan over _medium-high_ heat. Fry until the bottom is brown, then turn the meat. Choose a pan that holds the meat comfortably. If the pan is too large, the drippings will start smoking before the meat is done. If the pan is too crowded, the meat will steam instead of fry.
* * *
**How to Cut an Onion**
Onions are the most frequently listed ingredient in recipes. They are common to all cuisines and are used in both rustic and elegant dishes. For variation, instead of the common yellow onion, try the sweet Vidalia, or substitute another member of the onion family such as shallots, scallions, or leeks. Use red onion for salads or in sandwiches.
**Peeling**
**1.** Trim ½ inch from both the stem and root ends of the onion.
**2.** Cut through the skin lengthwise and peel it off, taking with it as little of the onion as possible.
**Slicing**
Using a chef's knife, cut crosswise in ¼-inch-thick slices.
**Chopping & Dicing**
**1.** Using a chef's knife, cut the peeled onion in half lengthwise.
**2.** Place the flat side down and cut the onion crosswise in ¼-inch-thick slices.
**3.** Hold the onion firmly together and give a quarter turn; cut in ¼-inch pieces. (It will look like cross-hatching.) For even smaller pieces, continue to chop through.
* * *
#### **Dad's Official Meat Loaf**
The many ingredients here all get thrown into one big bowl and are mixed by hand—gooey but efficient.
**Ingredients** _(serves six)_
_½ cup milk_
_3 slices whole wheat bread, crusts removed_
_1 onion, finely chopped_
_1 red or green bell pepper, minced_
_½ cup (about 4) scallions, finely chopped_
_½ pound ground beef_
_½ pound ground veal_
_½ pound ground pork_
_2 large eggs, beaten_
_½ cup ketchup_
_½ cup chopped parsley_
_½ teaspoon nutmeg_
_¼ cup grated Parmesan_
**Equipment**
_Medium bowl_
_Large bowl_
_4 x 10-inch loaf pan_
_Large spatula_
**1.** Preheat the oven to 350°F.
**2.** Measure the milk into a medium bowl, then add the bread slices and let them soak until you need them.
**3.** In a large bowl, mix the onion, bell pepper, scallion, the meats, bread and milk, eggs, ketchup, parsley, nutmeg, and cheese, until they are completely combined. You'll need to use your hands.
**4.** Transfer the mixture to a 4 x 10-inch loaf pan and pat it down gently.
**5.** Bake for 50 minutes on the center rack of your oven until the top is a deep brown and the loaf has pulled away from the sides of the pan. Let the meat loaf cool for 5 minutes before removing from the pan and slicing. Use a large spatula to ease the meat loaf out of the pan.
**Slicing and Carving**
**Steak** —Hold the steak in place with a carving fork and cut the meat across the grain and on a slight angle into thin slices. You can also serve steaks in larger pieces to be sliced by each person.
**Boneless Roast** —Let the roast rest for 10 minutes, then trim off any fat. Lay the roast on its side and hold it in place with a carving fork a few inches from the end you are slicing. Cut across the grain into thin slices.
**Rib Roast** —Let the roast rest for 15 minutes, then trim away the large piece of fat on top. Place the roast on its end and use a small knife to cut straight down along the inside of the bone. Turn the roast on its side. Hold the roast in place with the flat side of a fork as you cut across the meat, making thin slices.
**Brisket** —Let the meat rest for 10 minutes, then trim off any fat. Hold the brisket in place with a carving fork and cut the meat across the grain and at a slight angle into thin slices.
**Time-Saver**
Assemble the meat loaf a night ahead. Cover the loaf pan tightly with plastic wrap and refrigerate. Add 5 minutes to the baking time if you are putting a cold meat loaf in the oven.
**Serving Suggestions**
• Serve the classic Blue Plate Special: meat loaf, mashed potatoes, and green beans.
• Or try it with spaghetti tossed with a simple tomato sauce.
• For vegetable accompaniments, consider spinach, carrots, or corn.
• For sandwiches, cut a ¾-inch slice of cold meat loaf, put it between rye or pumpernickel bread, and top with lettuce and mustard, ketchup, barbecue sauce, or mayonnaise.
#### **Roast Beef**
Still one of the classic American dinners, it's also one of the simplest to prepare. Roast beef usually needs at least an hour and a half in the oven, so don't plan on this as a last-minute meal.
**Ingredients** _(serves six)_
_3–4 pound tied roast beef (see Note)_
_2 cloves garlic_
**Equipment**
_Roasting pan with rack_
**1.** Preheat the oven to 325°F.
**2.** Set the roasting rack in the roasting pan.
**3.** Rinse the roast under very cold water and pat it dry with paper towels. Set the roast on the roasting rack.
**4.** Peel the garlic cloves and cut them into thin slices. Make slits in the top of the meat and insert a slice of garlic in each one.
**5.** Place the roast on the center rack of your oven and cook for 30 minutes per pound. Let the beef rest for 10 minutes before cutting off the strings and slicing.
**Tip**
Eye of the round roasts are the juiciest and most tender. Other roasts to look for are top round, bottom round, and rump roast.
**Serving Suggestions**
• Serve with baked or mashed potatoes.
• Serve steamed asparagus, peas, or glazed carrots.
**Note**
The roasts in the supermarket should already be tied, which helps them to keep their shape when they are cooked. If not, the butcher will gladly do it for you.
#### **Pot Roast**
You can assemble a pot roast very quickly, but it must cook for several hours. Since its flavor improves with a day in the refrigerator, you may want to cook the pot roast the night before you plan to serve it. Preparing dinner is then limited to boiling some wide noodles and heating up the meat.
**Ingredients** _(serves six)_
_3-pound chuck or rump roast or brisket_
_½ cup unbleached, all-purpose flour_
_1 tablespoon vegetable oil_
_3 large onions, sliced_
_2 cloves garlic, minced_
_¼ cup white wine_
_¼ cup ketchup_
_1 envelope onion soup mix_
_2 large carrots, cut into 1-inch rounds_
_1 large potato, cut into eighths_
**Equipment**
_Large frying pan or Dutch oven with cover_
**1.** Rinse the roast under very cold water and pat it dry with paper towels.
**2.** Sprinkle the meat with the flour, then shake off any excess.
**3.** Place a large frying pan on _high_ heat and let it get very hot, about 45 seconds. Add the vegetable oil and the meat and brown the meat on both sides.
**4.** Add the onions and garlic to the frying pan, arranging them around the meat. Add ½ cup water and the wine and ketchup to the pan and stir to incorporate. Sprinkle the onion soup mix on top of the meat.
**5.** When the liquid starts boiling, cover the pan and reduce the heat to _low_. Simmer the roast for 2½ hours, until the meat is very tender. Periodically spoon some of the sauce over the meat. If the sauce cooks away, add more water, ½ cup at a time.
**6.** Add the sliced carrots and potato pieces to the pan for the last hour of cooking.
**7.** To serve, let the roast cool for 10 minutes, then remove it from the pan juices. Slice the meat thinly and on an angle. Serve with the vegetables and pan juices.
**Serving Suggestions**
• Serve over wide noodles.
• Serve a mixed green salad or corn.
**Variation**
If you don't have a large enough frying pan or Dutch oven to cook the pot roast on the stove, you can also cook it in a preheated 325°F oven. After browning the meat in the frying pan (step 3), transfer it to a casserole. Add ½ cup water to the frying pan and, over _low_ heat, scrape up any bits of meat that are stuck to the bottom. Then add the wine, ketchup, and onion soup mix and stir together. Transfer the liquid to the casserole and add the onions, garlic, carrots, and potato. Cover the casserole with foil and bake for 2½ hours, until the meat is tender.
#### **Stuffed Flank Steak**
This dish requires a lot of ingredients but not a lot of work. It not only tastes great, but looks very impressive on a platter, with the red tomato sauce complementing the green spinach stuffing. Hearty and rich, this dish will satisfy even the seemingly insatiable appetites of growing teenagers.
**Ingredients** _(serves four)_
_Olive oil, for greasing the pan_
_1 10-ounce package frozen chopped spinach_
_¼ cup grated Parmesan_
_¼ cup bread crumbs_
_3 cloves garlic, minced_
_1 large egg_
_1 4-ounce jar roasted red bell peppers_
_1 medium flank steak (1½–2 pounds), butterflied by the butcher_
_2 ounces sliced prosciutto or Black Forest ham_
_2 cups Basic Tomato Sauce (page 182) or your favorite store-bought sauce_
**Equipment**
_9 x 16-inch roasting pan_
_Butcher's twine or heavy-duty uncoated all-cotton string_
_Small saucepan_
_Medium saucepan_
_Colander_
_Medium bowl_
**1.** Preheat the oven to 350°F. Lightly grease a 9 x 16-inch roasting pan with olive oil. Cut five 8-inch pieces of butcher's twine. Set all aside.
**2.** In a small saucepan, boil the spinach in 2 inches of water until cooked through. Transfer to a colander and rinse with cold water. Take a small clump of spinach and squeeze out the water. Transfer to a bowl and repeat with the rest of the spinach.
**3.** Add the Parmesan, bread crumbs, garlic, and egg to the spinach, and mix together.
**4.** Drain the roasted peppers and cut them into ½-inch strips.
**5.** Lay the flank steak on the work surface and open it up. Arrange a row of prosciutto or ham slices lengthwise down the center. Spread the spinach mixture in an even layer over the prosciutto or ham. Arrange the red pepper strips down the center of the spinach.
**6.** Roll the meat lengthwise into a long log (like a jelly roll). Slip a piece of string under the center of the meat and tie it relatively tightly in a knot. Repeat down the length of the roll, tying the remaining 4 pieces of string at equal intervals.
**7.** Place the rolled meat in the roasting pan and roast on the center rack of the oven for 40 minutes, until the top is browned and the meat is cooked but still pink in the center.
**8.** Remove the pan from the oven and let the meat sit for 5 minutes before slicing.
**9.** While the meat is resting, heat the tomato sauce in a medium saucepan on _medium_ heat until hot.
**10.** Cut the meat into 1½-inch slices, arrange them on a platter, and spoon a stream of tomato sauce down the center of the slices. Serve with the remaining sauce on the side.
**Serving Suggestions**
Serve with pasta or home fries, and snow peas or green beans.
#### **London Broil**
London broil is a good dish to make for a hearty last-minute dinner. It comes from a lean cut of beef, such as the top round, flank, or shoulder. It's best cooked to medium rare because it dries out if left in the oven much longer.
**Ingredients** _(serves four)_
_2-pound London broil or flank steak, ¾- to 1-inch thick_
_1 clove garlic, peeled and cut in half_
_1 tablespoon vegetable oil_
**Equipment**
_Broiler pan_
_Basting brush_
**1.** Preheat the broiler.
**2.** Rinse the meat under very cold water and pat it dry with paper towels.
**3.** Rub both sides of the meat with the cut side of the garlic clove, then lightly brush each side of the meat with the oil.
**4.** Lay the meat on the broiler pan and broil 2 inches from the flame for 6 minutes. Turn and broil for 5 minutes more.
**5.** Remove the meat from the oven and let it rest for 5 minutes before slicing.
**Tip**
London broil is best thinly sliced across the grain and on a slight angle.
**Serving Suggestions**
• Serve with pasta dressed with a simple herb-and-butter sauce.
• Serve a mixed green salad and steamed or boiled green beans.
#### **Stir-Fried Beef & Broccoli**
By taking advantage of the variety of Asian stir-fry sauces that are now widely available, you can whip up this meal in a flash. To make it even easier for Dad, many supermarkets sell beef that is already sliced.
**Ingredients** _(serves four)_
_2 cups broccoli florets_
_2 tablespoons vegetable oil_
_1 pound sirloin or flank steak, thinly sliced into ½-inch wide strips_
_1 medium onion, thinly sliced_
_1 red bell pepper, seeded and cut into strips_
_¼ cup bottled Asian stir-fry sauce, such as teriyaki or ginger_
**Equipment**
_Medium saucepan with lid_
_Strainer_
_Paper towels_
_Large, heavy frying pan or wok_
_Medium bowl_
**1.** Steam or boil the broccoli in the saucepan in ½ inch of water until it is cooked but still crunchy (about 3 minutes). Drain well and transfer to a double layer of paper towel so the florets will dry a little before stir-frying.
**2.** Place a large frying pan or wok on _high_ heat and let it get very hot, about 90 seconds. Add the oil and swirl it around so it coats the bottom of the pan. Add the beef and cook, turning and stirring, until the meat loses its pinkness, about 3 minutes. Remove the beef and transfer to a medium bowl.
**3.** Add the sliced onion and pepper to the pan and cook, stirring continuously until the vegetables soften slightly, about 2 minutes.
**4.** Add the beef and broccoli to the pan, and stir to heat it through. Add the sauce and stir to lightly coat all the ingredients. Serve immediately.
**Serving Suggestion**
Serve with white or brown rice, Chinese noodles, or thin pasta.
* * *
**Mexican Feast**
Mexican food seems to appeal to kids and adults alike. You can get this fun meal ready and on the table in just 2 hours, using a combination of fresh and packaged or canned ingredients. Make all three entrées to serve twelve, or prepare a single entrée for four.
**MENU**
Tortilla chips
* * *
Salsa
* * *
Chicken burritos
* * *
Steak fajitas
* * *
Vegetarian tacos
* * *
Lemonade ice-cream pie
* * *
Mexican beer
* * *
* * *
**Assembling the Feast**
In order to get everything on the table at the same time, enlist the help of a couple of youngsters to assist you during the last 20 minutes or so, when you are sautéing all the meat, assembling the burritos and tacos, and setting the accompaniments on the table.
**The Day Before**
• Make the ice-cream pie and freeze
**Two Hours Before**
• Broil the flank steak and cut into slices
• Cut the chicken into strips
• Make the chili for the tacos
• Shred the lettuce, put in a plastic bag, and refrigerate
**One Hour Before**
• Chop all the plum tomatoes, place in a bowl, and refrigerate
• Chop all the red onion, place in a bowl, and refrigerate
• Slice the yellow onion and refrigerate
• Grate all the cheese, place in a bowl, and refrigerate
• Make the rice
• Remove 16 tortillas from the refrigerator and wrap 8 of them in aluminum foil
• Preheat the oven to 275°F
**Just Before Serving**
• Sauté the steak, seasonings, and sauce
• Sauté the chicken, seasonings, and sauce
• Put the wrapped tortillas in the preheated oven
• Assemble the burritos and tacos
• Set the steak mixture, grated cheese, and flour tortillas on the table
• Set the rice on the table
**The Shopping List**
• 2 whole chicken breasts
• ¾ pound boneless sirloin steak
• 1½ pounds shredded Monterey Jack or cheddar cheese
• 1½ pounds (about 10) plum tomatoes
• 1 head Romaine or iceberg lettuce
• 1 green bell pepper
• 1 red bell pepper
• 2 medium red onions
• 1 medium yellow onion
• 3 cloves garlic
• 2 28-ounce cans crushed tomatoes
• 1 12-ounce can red beans
• 1 8-ounce can corn, without sugar
• 2 chicken bouillon cubes
• 16 ounces mild or medium red taco sauce
• 1 4-ounce jar green taco sauce
• 1–3 cups converted rice
• 1 packet taco seasoning mix
• 1 packet chili seasoning mix
• 16 flour tortillas
• 8 taco shells
• vegetable oil
• 1–2 quarts high-quality vanilla ice cream
• 1–2 6-ounce cans frozen lemonade or limeade
• 1–2 store-bought graham cracker pie crusts
* * *
#### **Steak Fajitas**
To make fajitas, sauté sliced flank steak with sliced onion, bell pepper, and garlic, add sauce and spices, and serve at the table with flour tortillas and grated cheese.
**Ingredients** _(serves four)_
_8 flour tortillas_
_¾ pound boneless sirloin steak_
_2 tablespoons vegetable oil_
_1 medium yellow onion, thinly sliced_
_1 red bell pepper, seeded and thinly sliced_
_3 cloves garlic, minced_
_¼ cup red taco sauce_
_¼ cup green taco sauce_
_½ packet taco seasoning mix_
_½ pound grated Monterey Jack or cheddar cheese_
**Equipment**
_Broiler pan_
_Large frying pan_
_Serving bowl_
**1.** Preheat the broiler. Remove the tortillas from the refrigerator and let them come to room temperature while you are preparing the fajitas.
**2.** Place the steak on a broiler pan. Broil about 3 inches from the heat for 5 minutes. Turn the steak over and broil 4 minutes more until nicely browned. Transfer the steak to a platter and let it cool for about 10 minutes before slicing.
**3.** Cut the steak into thin slices and set aside on a plate.
**4.** Put a large frying pan on _high_ heat and let it get very hot, about 1 minute. Add the oil and the sliced onion and bell pepper and sauté, stirring constantly, until soft, about 5 minutes.
**5.** Add the steak slices and garlic and cook 1 minute more. Stir in the taco sauces and taco seasoning and cook until the mixture is heated through, about 2 minutes. Turn off the heat. Transfer the steak mixture to a serving bowl.
**6.** Place the tortillas on a dinner plate, and bring them to the table along with the steak mixture and grated cheese. Guests and family can assemble their own fajitas by placing a few tablespoons of steak across the middle of their tortilla, topping with grated cheese, then rolling the whole thing up.
#### **Chicken Burritos**
To make this burrito, you sauté sliced chicken, add sauce and spices, then place the filling in a flour tortilla with chopped tomato, onion, shredded lettuce, and grated cheese, and wrap it all up.
**Ingredients** _(serves four)_
_8 flour tortillas_
_2 tablespoons vegetable oil_
_2 whole boneless chicken breasts, cut in half and sliced into ½-inch strips_
_½ cup canned crushed tomatoes_
_1 chicken bouillon cube_
_½ packet taco seasoning mix_
_¾ pound (about 5) fresh plum tomatoes_
_1 medium red onion_
_4 leaves Romaine lettuce or ¼ head iceberg_
_½ pound Monterey Jack or cheddar cheese, grated_
_1 6-ounce jar taco sauce_
**Equipment**
_Large frying pan_
_Medium bowl_
_4 small bowls_
**1.** Preheat the oven to 275°F. Wrap the tortillas well in aluminum foil and place them in the oven.
**2.** Put a large frying pan on _high_ heat and let it get very hot, about 1 minute. Add the oil and chicken strips and sauté until the chicken is opaque and just cooked through, about 5 minutes.
**3.** Add the crushed tomatoes, bouillon cube, and taco seasoning. Cook 2 minutes more, stirring often, until the sauce thickens. Be sure to break up the bouillon cube so it dissolves completely. Turn off the heat and cover the pan.
**4.** Cut the tomatoes lengthwise into quarters. Cut each quarter into ¼-inch slices and chop the slices roughly. Coarsely chop the onion.
**5.** Cut the lettuce into ¼-inch slices. Stack these and then cut them in half. Put the chopped tomato, shredded lettuce, chopped onion, and grated cheese in separate bowls.
**6.** Remove the tortillas from the oven. Open the package and place 2 tortillas on each dinner plate. Spoon 3 tablespoons of the chicken mixture down the center of each tortilla. Top the chicken with about 2 tablespoons each of grated cheese, chopped tomato and onion, and shredded lettuce.
**7.** Fold the bottom third of each tortilla over the filling. Fold the top third down so it overlaps slightly. Turn each burrito so the folded side faces down on the plate. Top each with taco sauce, if desired, just before serving.
#### **Vegetarian Tacos**
A Mexican feast is never complete without tacos.
**Ingredients** _(serves four)_
_1 tablespoon corn oil_
_1 green bell pepper, seeded and coarsely chopped_
_1 28-ounce can crushed tomatoes_
_1 packet chili seasoning mix_
_1 12-ounce can red beans, drained_
_1 8-ounce can corn, without sugar, drained_
_¾ pound (about 5) plum tomatoes_
_4 leaves Romaine lettuce or ¼ head iceberg lettuce_
_½ pound grated Monterey Jack or cheddar cheese_
_1 medium red onion_
_8 store-bought taco shells, warmed, if desired_
**Equipment**
_Large frying pan with cover_
_4 small bowls_
**1.** Put a large frying pan on _high_ heat and let it get hot, about 45 seconds. Add the oil and the bell pepper and sauté, stirring often, until cooked through but still crunchy, about 5 minutes.
**2.** Add the tomatoes, chili seasoning, and red beans. When the mixture starts boiling, reduce the heat to _low,_ partially cover, and simmer for 20 minutes. Stir the chili occasionally to keep it from sticking to the bottom of the pan.
**3.** Stir in the corn and cook until heated through. Turn off the heat.
**4.** Cut the tomatoes lengthwise into quarters, Cut each quarter into ¼-inch slices. Chop these roughly and set aside in a small bowl. Coarsely chop the onion. Put each topping in a bowl.
**5.** Cut the lettuce into ¼-inch slices. Stack these and then cut them in half. Put the lettuce in a bowl.
**6.** Place the taco shells on a platter. Fill each with about ¼ cup of the chili mixture. Top with the tomato, lettuce, cheese, and onion.
#### **Dirty Rice**
Dad's variation on the Cajun recipe, which is made with giblets, this "not so dirty rice" is a perfect accompaniment to a Mexican dinner.
**Ingredients** _(serves four)_
_1½ cups water_
_1 cup canned crushed tomatoes_
_1 chicken bouillon cube_
_1 cup converted white rice_
**Equipment**
_Medium saucepan_
**1.** Bring the water, crushed tomatoes, and bouillon cube to a boil in a medium saucepan. Add the rice. When the liquid returns to a boil, stir once, immediately cover the pan, and reduce the heat to _low_.
**2.** Cook the rice for 18 minutes or until the liquid is completely absorbed.
**Note**
If you are making the entire meal for 12, triple this recipe and use a large saucepan.
#### **Lemonade Ice-Cream Pie**
A perfect way to cool the palate after a spicy Mexican feast. Make your life easier by preparing this pie in advance, up to 4 days before the dinner.
**Ingredients** _(serves six generously)_
_1 quart high-quality vanilla ice cream_
_1 6-ounce can frozen lemonade or limeade (do not dilute)_
_1 store-bought graham cracker pie crust_
**Equipment**
_Food processor or blender_
_Large bowl_
_Rubber spatula_
**1.** Let the ice cream soften until it just begins to get runny. In 4 batches purée the ice cream in a food processor until light and creamy, about 15 seconds for each batch. If using a blender, purée the ice cream in 6 batches. Transfer the puréed ice cream to a large bowl.
**2.** Stir the frozen lemonade or limeade into the puréed ice cream until completely incorporated.
**3.** Transfer the mixture to the graham cracker crust, smoothing out the top with a rubber spatula. Place the pie in the freezer until ready to use.
**4.** Remove the pie from the freezer about 5 minutes before you want to serve it to let it soften.
**Note**
If you are serving the Mexican Feast for 12, make 2 pies.
* * *
**Lamb Basics**
Lamb chops are my personal favorite food. Thick chops simply grilled to a luscious pink medium rare with a glass of Italian Barolo is the way I like to celebrate special occasions. Other cuts, such as roast leg of lamb and shoulder chops, are both flavorful and easy to prepare.
##### **Cuts**
**Whole leg** is one of the most popular cuts of lamb and is the basis for many classic dishes. The whole leg comes either bone in and weighs 7–8 pounds, or boneless and weighs 5–6 pounds. Both should be roasted.
**Butterflied leg of lamb** is a boneless leg that has been trimmed and then opened up and slightly pounded out. Have your butcher do it.
**Boneless loin roast,** lean, flavorful, and succulent, is one of the premier cuts of meat. The whole loin actually comes in 2 pieces and each should be rolled and tied before roasting.
**Loin chops** are cut from the loin and include the bone. Chops should be cut thick, about 1½ inches.
**Shoulder chops** are also very flavorful but are not nearly as lean as loin chops. They are cut thinner and can be either broiled or panfried.
**Lamb chunks,** which are great for stews or curries, are usually cut from the shoulder, although a friendly butcher might give you some from the leg, which are a bit leaner.
**Rack of lamb** is cut from the ribs, and while there is not a lot of meat, what there is is divine and expensive!
##### **Servings**
A whole leg of lamb (bone in or boneless) will serve 8 to 10 people. A rack of lamb serves 2 and a loin roast serves 6 people. Allow 2 lamb chops and 2 shoulder chops per person.
##### **Panfried Lamb**
**Loin chops** To fry, chops should be only 1-inch thick (thinner than those cut for broiling). Measure a scant 2 tablespoons olive oil (for 4 chops) into a large frying pan, place it on _high_ heat, and let it get very hot, about 1 minute. Just when the oil starts smoking, place the chops in the pan so that they aren't touching. Panfry for 4–5 minutes. Then turn the chops and cook 3–4 minutes more. Don't let them go too long on the second side as loin chops overcook easily.
**Shoulder chops** Season with salt, pepper, and garlic powder and prepare as above. Because shoulder chops are streaked with fat, you need very little oil to cook them.
##### **Roast Lamb**
**Leg of lamb, bone in** Preheat the oven to 400°F. Lightly oil a large roasting pan and rack. On the bottom of the pan, arrange 2 thinly sliced onions, 6 coarsely chopped cloves garlic, and 1 28-ounce can plum tomatoes, drained and coarsely chopped. Set a roasting rack over the vegetables and place the lamb on the rack. Rub the lamb with olive oil, salt, pepper, garlic powder, and rosemary. Roast for about 1 hour 15 minutes. Remove the lamb from the oven and let sit for 10 minutes before slicing. Skim the grease off the surface of the sauce in the roasting pan. Serve the lamb topped with the vegetables and sauce.
**Boneless loin roast** Preheat the oven to 400°F. Lightly oil a roasting rack and place it in a roasting pan. Place the lamb on the rack and rub the roast with olive oil, salt, pepper, garlic powder, and rosemary. Roast for about 1 hour 10 minutes. Let the meat sit for 10 minutes before carving.
##### **Broiling Lamb**
**Butterflied leg of lamb** Preheat the broiler. Open up the leg and arrange it on a broiler tray with the smooth side down. You can marinate up to 6 hours before cooking. If you haven't marinated the lamb, rub the top lightly with olive oil and sprinkle on some rosemary. Broil 4 inches from the heat for 6 minutes, then turn the meat and broil 6 minutes more. Lower the rack and broil 6 inches from the heat for 8–10 minutes, then turn and broil 6–8 minutes more. Cut into the meat at its thickest point. If it is pink, it is cooked to medium. The meat will continue cooking for about 10 minutes after it leaves the oven.
**Shish kebab** Preheat the broiler. Thread 1½- to 2-inch cubes of lamb through metal skewers and arrange the skewers on a broiler tray. If you haven't marinated the lamb, brush the cubes lightly with olive oil and sprinkle on some rosemary. Broil 4 inches from the heat for 5–6 minutes. Turn them over and broil 5–6 minutes more. The cubes should be browned all over.
**Loin chops** Preheat the broiler. Arrange the chops on a broiler tray. Broil 1¼-to 1½-inch chops 4 inches from the heat for 7 minutes. Then turn them over and broil 5–6 minutes more. For thicker 2-inch chops, broil 4 inches from the heat for 7 minutes, turn, and broil 4 minutes more. Then lower the chops to 6 inches from the heat and broil for 5 more minutes. The chops should be slightly springy to the touch.
**Shoulder chops** Broil 4 inches from the heat for 7 minutes. Turn and broil about 5 minutes more.
* * *
#### **Loin Lamb Chops with Red Wine Sauce**
Loin lamb chops fall into that elite category of foods, like lobster or Porterhouse steaks, that taste best when prepared as simply as possible. Thick chops, broiled medium rare, make for a perfect dinner. This classic red wine sauce, however, is a subtle enhancement and makes them absolutely sublime. The sauce is quite easy to assemble but does take about ½ hour to reduce.
**Ingredients** _(serves four)_
_2 cups dry red wine_
_4 shallots, peeled and sliced_
_1 carrot, cut into 1-inch pieces_
_1 clove garlic, peeled and crushed_
_2 sprigs parsley_
_1 bay leaf_
_½ teaspoon dried thyme_
_1 cup homemade or canned chicken or beef stock (see Note)_
_3 tablespoons butter, cut into ¼-inch pieces_
_1 teaspoon cornstarch_
_Salt and pepper_
_8 loin lamb chops, cut 1¼–1½ inches thick_
_Sprigs of mint or parsley, for garnish_
**Equipment**
_Medium saucepan_
_Fine-mesh strainer_
_Small saucepan with cover_
_Small bowl_
_Broiler pan_
**1.** Place the wine, shallots, carrot, garlic, parsley, bay leaf, and thyme in a medium saucepan and bring to a boil over _high_ heat. Reduce the heat to _medium_ and simmer, uncovered, until the liquid is reduced to about ⅔ cup, about 15 minutes. Add ¾ cup chicken or beef stock, increase the heat to _high,_ and bring to a boil. Again reduce the heat to _medium_ and simmer, uncovered, until the liquid is reduced to 1 cup, about 10 minutes.
**2.** Set a fine-mesh strainer in a small saucepan and pour the liquid through it. Set the small saucepan over _low_ heat and stir in the butter, piece by piece. Mix the cornstarch with the remaining ¼ cup stock in a small bowl. Slowly drizzle this into the sauce, stirring continuously. Season with salt and pepper and simmer another 5 minutes, then turn off the heat.
**3.** Preheat the broiler.
**4.** Arrange the lamb chops on a broiler pan. Broil the chops 3 inches from the heat for 7 minutes on 1 side. Then turn the chops and broil for 5–6 minutes on the other side, depending on the thickness, for medium rare. For medium, broil 1 minute more on each side.
**5.** When the chops are done, remove them from the oven and let them sit for 3 minutes. Meanwhile, reheat the sauce over _low_ heat for a few minutes, until it is hot. Spoon a thin layer of sauce over the bottom of each dinner plate and arrange 2 chops on each plate. Garnish with a sprig of mint or parsley.
**Serving Suggestions**
• Serve with baked potatoes or spaghetti squash.
• Serve asparagus and a mixed green salad.
**Note**
Do not replace the chicken or beef stock with bouillon cubes for this sauce. The seasonings in the bouillon will become too concentrated and will overpower the sauce.
**Time-Saver**
The sauce can be made a night ahead. Let it cool before transferring to a plastic container or a small bowl. Lay a piece of plastic wrap directly on the surface of the sauce to keep a crust from forming on the top. Tightly cover the container or bowl before storing in the refrigerator. Add another tablespoon or so of wine or stock when reheating.
#### **Shoulder Lamb Chops with Garlic & Rosemary**
Here is an easy and tasty way to prepare the "other" lamb chop. The aroma of the garlic sautéing will probably draw a crowd to the kitchen.
**Ingredients** _(serves four)_
_1 tablespoon olive oil_
_8 shoulder lamb chops, trimmed of fat_
_10 cloves garlic, minced_
_8 shallots, peeled and finely chopped_
_1 cup chicken stock or 1 bouillon cube dissolved in 1 cup boiling water_
_½ cup canned crushed tomatoes_
_2 tablespoons tomato paste_
_1 teaspoon dried rosemary_
_Salt and pepper_
**Equipment**
_Large frying pan_
_Medium baking dish_
_Aluminum foil_
**1.** Preheat the oven to 350°F.
**2.** Place a large frying pan on _medium-high_ heat and let it get hot, about 45 seconds. Add the oil and 4 of the chops, and sauté them until they are brown, about 2 minutes. Turn the chops and cook them for 2 minutes more. Transfer the chops to a medium baking dish and brown the remaining 4 chops.
**3.** Pour out all but a bit of the oil from the frying pan. Return the pan to the stove and lower the heat to _medium_. Add the garlic and shallots, and sauté, stirring often, until soft, about 3 minutes.
**4.** Add the chicken stock or bouillon to the pan and simmer until it is reduced by half, about 2 minutes. Add the crushed tomatoes, tomato paste, rosemary, and salt and pepper, and cook until the sauce thickens, about 2 minutes.
**5.** Pour the sauce over the chops. Cover the baking dish with aluminum foil and place it on the center rack of your oven for 20–25 minutes, until the chops are cooked through.
**Serving Suggestions**
• Serve with orzo or boiled new potatoes.
• Serve beets, sautéed escarole, or zucchini.
* * *
**Pork Basics**
In recent years, farmers have been working to raise pigs that yield leaner pork, and Americans have been rethinking their attitudes toward "the other white meat." Still, only the loin should be thought of as lean—although who can resist a slab of baby back ribs dripping with barbecue sauce or a succulent slice of glazed smoked ham? Just don't indulge too often. Instead, expand your repertoire of recipes that call for pork loin.
##### **Cuts**
**Uncured pork cuts** come from several different parts of the pig, including the shoulder, leg, and loin. But concern yourself primarily with meat from the loin, which is the most lean and comes whole or cut into chops.
**Whole boneless loin of pork** weighs 2 to 4 pounds and is a great dish to serve to a small crowd of 6 to 8 people.
**Loin chops** are simply bone-in cuts taken from the loin. These can be pan-fried, broiled, or baked. Because the meat is so lean, loin chops should be cooked quickly over _high_ heat.
**Crown roast** is a circular arrangement of chops that have been scored, not separated. It is a majestic dish that can easily become the centerpiece at a dinner party for 6 to 8 people. Your butcher can prepare a crown roast for you.
**Ribs** come in 2 different sizes—country- style and baby back. Country-style have more meat on them. Baby backs are smaller but more succulent.
**Cured pork** comes in many shapes and sizes, from a small hock to an 8- to 18-pound ham. There are two processes for curing pork: It can be soaked in brine or dry-cured with a mixture of salt, sugar, and spices. After curing, the pork is usually smoked.
**Smoked hams** come from the hind leg of the hog, and have been both cured and smoked. They usually weigh between 11 and 14 pounds and are very simply cooked.
##### **Servings**
When buying boneless loin, figure on 6–8 ounces per person. Figure on 1 thickly cut (1½-inch) loin chop per person. A 5-pound crown roast, stuffed, will feed 6 to 8 people. Because there is so much bone on them, buy at least 1 pound of ribs per person.
##### **Storage**
Store pork the same way you would chicken. Remember to cook refrigerated meat within 2 days of purchase.
##### **Roast Pork**
Roasting is the proper method for cooking a whole boneless loin or a crown roast. A loin roast can be marinated in many kinds of sauces, including Japanese and barbecue, and then simply roasted in the oven. The loin should be basted frequently with the sauce to help keep it from drying out. Cook either a crown or loin roast in a preheated 350°F oven for 20–22 minutes per pound or until the roast reaches an internal temperature of 150°–160°F on a meat thermometer. Thick chops can also be baked, but brown them first in a frying pan, to make them crispy.
##### **Panfried Pork**
Panfrying is a great way to cook chops, with or without the bone. The chops can be breaded or not, depending on your preference. Thinner chops should be fried over _medium-high_ heat. Thicker chops should be browned quickly in the pan over _high_ heat to get them crispy and seal in the juices. Then add ½ cup apple juice, salt and pepper, reduce heat to _low_ , cover, and simmer for 40 minutes. Thick chops can also be finished in a 350°F oven after browning. Cook for 20–25 minutes.
##### **Baked Ham**
Arrange the smoked ham, fat side up, in a roasting pan and place it on a low rack of a preheated 350°F oven. Add about an inch of apple juice or cider to the pan and cook for 15–18 minutes per pound. Then take the ham out of the oven and use a serrated knife to trim away the fat and rind. Cover the top of the ham with a sweet glaze, such as one made from 1 cup crushed pineapple mixed with 1 cup orange marmalade, and return it to the oven for 20 minutes or so, until the glaze is set.
##### **Broiled Pork Chops**
Broiling is an excellent method for cooking pork chops. For thin chops, broil 3–4 inches from the heat. For thicker chops (1¼ inches and up), lower the meat to 5 inches from the heat to keep it from drying out. Figure on 3–5 minutes per side, depending on the thickness. You must keep a close eye on the meat or it's likely to dry out.
**Cooking Pork**
Even though modern breeding practices have decreased the likelihood of contamination, it is still important to make sure your pork is cooked through and there is no pink in the center. At the same time, you need to watch that your pork doesn't get overdone as it tends to dry out quickly. It may be necessary to cut into a chop or the center of a loin to check whether it is done. Use a meat thermometer for roast pork.
* * *
#### **Hunan Orange-Ginger Roast Loin of Pork**
Using orange when roasting meats is traditional in the Hunan region of China. Here, the sweetness of the orange mixes with the pungent ginger and sesame to make for a lively sauce.
**Ingredients** _(serves six)_
_¼ cup orange juice_
_½ cup white wine_
_¼ cup honey_
_¼ cup soy sauce_
_2 tablespoons sesame oil_
_1 tablespoon minced fresh ginger or 1 teaspoon dried_
_½ cup apricot jam_
_2½- to 3-pound boneless pork loin_
**Equipment**
_Medium bowl_
_Small bowl_
_Large plastic container_
_Roasting pan_
_Meat thermometer_
**1.** Mix together the orange juice, wine, honey, soy sauce, sesame oil, and ginger in a medium bowl. Place the apricot jam in a small bowl.
**2.** Place the pork loin in a plastic container just large enough to hold it. Pour the marinade over the pork, cover, and refrigerate for 6–12 hours.
**3.** Preheat the oven to 350°F.
**4.** Arrange the pork loin in a roasting pan and pour the sauce over it. Place the pan on the center rack of your oven and roast the loin for 1 hour 15 minutes.
**5.** After 1 hour 15 minutes, remove the roast from the oven. Take 3 tablespoons of pan drippings from the roasting pan and mix it with the jam in the bowl. Spoon the jam mixture over the loin and return it to the oven. Roast for 20–25 minutes more or until the meat reaches a temperature of 150°–160°F on a meat thermometer. Let the roast sit for 10 minutes before cutting into 1-inch slices.
**Serving Suggestions**
• Serve with white, brown, or wild rice.
• Serve sautéed green beans or broccoli.
#### **Breaded Pork Chops**
Start marinating the chops in the morning, and they'll be ready to be transformed into a quick and delicious entrée by dinnertime.
**Ingredients** _(serves four)_
**Marinade**
_⅓ cup olive oil_
_Juice of 1 lemon_
_1 clove garlic, mashed_
_½ teaspoon dried thyme_
_½ teaspoon salt_
_Freshly ground black pepper_
**Chops**
_4 center-cut loin pork chops, about 1½ inches thick_
_2 large eggs, lightly beaten_
_1 cup Italian-style bread crumbs_
_¼ cup grated Parmesan_
_2 tablespoons chopped fresh parsley or 1 tablespoon dried_
_½ teaspoon dried thyme_
_Salt and pepper_
_1 tablespoon vegetable oil_
**Equipment**
_Large plastic container_
_Medium shallow bowl_
_Pie plate_
_Dinner plate_
_Large, ovenproof frying pan with cover_
**1.** To marinate the chops, first trim away any excess fat and arrange them in a large plastic container in a single layer. Pour the olive oil and lemon juice over them, then add the garlic and sprinkle on the thyme, salt, and pepper. Turn the chops once so they are completely coated, cover the container, and refrigerate for 2–12 hours.
**2.** Preheat the oven to 325°F.
**3.** Remove the chops from the marinade and pat them dry with paper towels.
**4.** Beat the eggs in a medium bowl. Mix together the bread crumbs, Parmesan, parsley, thyme, and salt and pepper in a pie plate.
**5.** Dip the pork chops in the eggs and let the excess drip off. Dredge both sides of the chops in the bread crumbs and shake them gently to allow the excess crumbs to fall off. Lay the breaded chops on a dinner plate. (Wash the plate before reusing.)
**6.** Place a large ovenproof frying pan on _medium-high_ heat and let it get hot, about 45 seconds. Add the vegetable oil and the chops and sauté them until golden brown, about 2 minutes. Turn the chops and cook for 2 minutes more.
**7.** Cover the pan and move it to the center rack of your oven for 20–25 minutes, until the chops are springy to the touch.
**Serving Suggestions**
• Serve with bow-tie noodles tossed with olive oil and fresh parsley.
• Serve tomato slices topped with chopped onion, lots of freshly ground black pepper, and a simple vinaigrette.
#### **Pork Chop & Potato Casserole**
This classic American casserole, held together with condensed mushroom soup, is guaranteed to warm your cockles on a cold winter night.
**Ingredients** _(serves four)_
_1 tablespoon butter_
_1 can condensed mushroom soup_
_6 medium potatoes, peeled and thinly sliced_
_6 loin pork chops, about 1-inch thick_
_1 teaspoon garlic powder_
_Salt and pepper_
_½ teaspoon dried thyme_
**Equipment**
_8 x 12-inch baking dish_
_Small bowl_
**1.** Preheat the oven to 350°F and use the butter to lightly grease a 8 x 12-inch baking dish.
**2.** In a small bowl, combine the mushroom soup with ½ can of warm water, stirring well. Set aside.
**3.** Arrange half the sliced potatoes in an even layer over the bottom of the prepared baking dish and season with salt and pepper.
**4.** Arrange the pork chops in a single layer over the potatoes. Season with the garlic powder and salt and pepper. Sprinkle on the thyme. Arrange the remaining potato slices over the chops.
**5.** Pour the mushroom soup over the top of the casserole so it almost reaches the level of the second layer of potatoes. If there isn't enough soup, add a little more water.
**6.** Bake the casserole, uncovered, on the center rack of the oven for 1 hour or until the potatoes are cooked and the liquid is almost completely absorbed.
**Serving Suggestion**
Serve with glazed carrots and a simple green salad.
* * *
**Fish Basics**
The sublime taste of fresh fish is best shown off in the simplest of preparations. In a hot pan with a little oil or butter, you can sauté a few fillets of sole in 5 minutes. Bay scallops take even less time to sauté. Salmon steaks can be baked in a lightly greased pan, and then need only a dash of salt and pepper and a spritz of lemon to finish them off. More complex sauces can be made for fish as well, but they are by no means a requirement.
##### **How to Buy Fish**
The easiest way to ensure that you are buying fresh, high-quality fish is to get it at a busy fish market with lots of turnover. When buying whole fish, look for plump, bright ones with good muscle tone. The eyes should be bright and slightly bulging. Saggy or sunken eyes are a sign of old fish.
**Fillets** are cut lengthwise from the backbone, so they are boneless. They are skinned and ready to cook.
**A steak** is a crosscut section of a cleaned, scaled fish cut at least ¾ inch thick from the thickest part of the fish. Fillets and steaks should be moist and firm, and the flesh should be well toned. If it is soft or at all mushy, or if it has a film on the surface, look for something else.
**Cooking Times**
The standard rule for cooking fish is 10 minutes per inch of thickness, as measured at the thickest point. However, if you are cooking the fish in foil, figure on 15 minutes per inch of thickness.
##### **Servings**
The rule of thumb for serving sizes is 6 ounces of fillet, steak, or whole fish per person. For brook trout, figure one trout per person. For shrimp, get ⅓ pound of medium or large shrimp per person. For jumbo shrimp, judge by number (4 or 5 per person). For lobster, you'll need at least one 1¼-pounder per person. When buying fillets, check to make sure that they are all of equal thickness. If they are not, oine piece will cook faster than the other and with fish, even 1 minute can mean the difference between succulent and dried out.
##### **Storage**
With fish, freshness is critical because its flavor and texture break down quickly. It's important to cook fish the day you buy it.
If you must keep your fish until the next day, follow this procedure: Remove the wrapping and dip the fish in a bowl of ice water with some freshly squeezed lemon juice which helps to slow down aging. Then pat the fish dry, wrap it in plastic, and place it on the bottom (the coldest part) of the refrigerator. If fish develops a mild fishy smell, use it in chowder. If the smell is pronounced and the fish feels filmy, discard it.
##### **Broiled Fish**
Broiling is a good method for cooking fattier fish, such as tuna, swordfish, and salmon, as they are sturdier and can withstand the intense heat. Broiling leaves the fish slightly crusty on the outside, which seals in the juices. Place the fish on a lightly oiled baking sheet. Sprinkle with a few teaspoons of water, lemon juice, or wine to keep it from drying out. Broil 4 inches from the heat. Thick steaks (1–1¾ inches) will need to be turned once after 6–7 minutes. Thinner steaks or fillets needn't be turned at all. Thin fillets (¾ inch or less), such as flounder or sole, should not be broiled as they will dry out.
##### **Panfried Fish**
Like broiling, panfrying allows the fish to develop a crust on the outside while keeping the inside moist. Panfrying is also suitable for fillets too thin to broil. Before frying, lean fillets can be dipped in milk or a well-beaten egg, and dredged in flour, bread crumbs, or cornmeal to seal in moisture. Steaks cut from fatty fish, such as tuna, salmon, or swordfish, do not need to be coated before cooking. Small whole fish, such as brook trout, can also be panfried and do not need to be coated.
Heat the pan over _medium-high_ heat until it is hot, about 30 seconds. Then add a few tablespoons of olive oil or a combination of olive oil and butter. Gently lay the pieces of fish in the pan, being sure not to crowd them together. Cook half the prescribed time and then turn the fish over. It's important to use a large spatula to turn a large fillet to keep it from falling apart.
##### **Baked Fish**
Baking is perhaps the easiest way to cook fish and it gives you the most room for error. Fillets, steaks, and whole fish can all be baked with very good results. Simply arrange the fish in a lightly oiled baking pan and bake in a preheated 400°F oven for 10 minutes per inch of thickness. Whole fish which have been scaled and gutted by the fishmonger can be stuffed with a combination of herbs, sautéed vegetables, nuts, and bread crumbs. Another way to enhance the flavor is to place the fish on a bed of thinly sliced, lightly sautéed vegetables, such as onions, celery, or carrots. Chopped garlic and/or fresh ginger are two of the best herbs for fish. A bit of wine or soy sauce added to the bottom of the pan makes a delicate sauce that can be served over the fish.
##### **Fish Baked in Foil**
Baking in foil is an almost foolproof way of cooking moist fish. Place a 9-inch square of foil on the work surface and lightly oil or butter it. Lay the fish in the center and sprinkle it with salt and pepper and a dot of butter. You can also add a marinade of 1 tablespoon soy sauce, white wine, or broth, and a pinch of chopped scallions, fresh ginger, or garlic. Pull the top and bottom sides of the foil together and fold them down to make a loose package. Then fold the ends securely. Place the foil in a baking pan and bake in the middle of a preheated 400°F oven for 15 minutes per inch of thickness.
##### **Poached Fish**
Poaching is simply cooking the fish in a small amount of water and lends itself to cooking thin fillets and smaller whole fish. Keep the water just barely simmering. If it boils too rapidly the fish will be tough. Fillets and small whole fish can be poached in a covered sauté pan on top of the stove. Bring ½ inch water to a simmer, add the fillets (in 1 layer) or the whole fish and cover the pan. Increase the heat until the liquid is simmering again, then quickly lower the heat. Start timing now, following the 10-minute-per-inch rule.
A fish poacher enables you to cook large fish because it has an insert that allows you to raise and lower the fish into the hot liquid. Bring a few inches of water to a boil in the bottom of the poacher. Lower the fish into the pan and let the liquid return to a boil. Proceed as above.
* * *
**Fish Primer**
The print edition of this book includes charts for **Fish Primer**.
Please download a PDF of the charts here: workman.com/ebookdownloads
These fatty fish are best for broiling, baking, and grilling. Meatier than flatfish, they can be cut into steaks or thick fillets. Use these fish in chowders and pasta sauces, as they won't flake and dissolve into the liquid.
These fish are lean and delicate and yield thin fillets that are best poached, cooked in foil, baked whole, or gently sautéed. They cook up quickly and their mild flavor makes them family favorites.
* * *
#### **Red Snapper Baked in Foil**
Baking in foil is one of the easiest ways to cook fish. This technique also helps to keep fish moist and flavorful.
**Ingredients** _(serves four)_
_1 tablespoon butter_
_4 red snapper fillets, 4–6 ounces each_
_1 tablespoon lemon juice_
_1 teaspoon chopped parsley_
_Salt and pepper_
**Equipment**
_Four 9-inch squares of aluminum foil_
_11 x 17-inch baking sheet_
**1.** Preheat the oven to 375°F.
**2.** Place four 9-inch squares of aluminum foil on the counter and butter them lightly.
**3.** Lay 1 fillet in the center of each piece of foil. Sprinkle each fillet with lemon juice, parsley, and salt and pepper.
**4.** Bring together the top and bottom ends of the foil and fold together, without pressing on the fillets, until you have a neat package. Now fold over the sides, being careful not to press too close to the fish.
**5.** Arrange the foil packets on the baking sheet and bake for 10 minutes.
**6.** Slit open the packets with a knife and ease the fish and its juices onto a plate.
**Serving Suggestions**
• Serve with herbed baked new potatoes.
• Serve steamed snow peas, sugar snap peas, or asparagus.
**Three Foil Sauces**
These pungent sauces can be used to spice up seafood baked in foil.
• Spoon 1 tablespoon crushed tomatoes in the center of each lightly buttered square of foil, and sprinkle with a pinch of parsley and oregano. Lay the fish fillets on top of the tomato and season them lightly with salt and pepper. Fold and bake as described in recipe for Red Snapper Baked in Foil.
• Lay 6 large, peeled and deveined shrimp on the center of each lightly buttered piece of foil. In a small bowl, mix together 4 teaspoons vermouth or white wine, 4 tablespoons finely chopped prosciutto, and 4 teaspoons chopped scallions. Spoon ¼ of the mixture over each group of shrimp. Season the shrimp lightly with salt and pepper and a spritz of lemon. Fold and bake about 8–10 minutes in a preheated 350°F oven.
• Lay a 6-ounce sea bass fillet on the buttered foil. In a small bowl, mix together 4 teaspoons soy sauce, 4 teaspoons lemon juice, 2 teaspoons chopped fresh ginger, and 2 teaspoons chopped scallions. Spoon ¼ of the mixture over each sea bass fillet. Fold and bake 10 minutes in a preheated 350°F oven.
#### **Fillet of Sole with Saffron & Tomato Cream Sauce**
This is an elegant dish for when Dad wants to show off. The saffron has a sublime flavor and turns the sauce bright yellow, which always intrigues the kids.
**Ingredients** _(serves four)_
_½ teaspoon dried saffron threads_
_1 16-ounce can whole tomatoes, well drained_
_1 tablespoon butter, plus extra for greasing the aluminum foil_
_3 shallots, minced_
_¾ cup white wine_
_¾ cup heavy cream_
_4 sole or flounder fillets (about 6 ounces each)_
_Salt and pepper_
_4 cups cooked rice, for serving_
_¼ cup chopped fresh parsley, for garnish_
**Equipment**
_9 x 12-inch baking dish_
_Aluminum foil_
_Small bowl_
_Large frying pan_
**1.** Preheat the oven to 350°F. Lightly butter a 9 x 12-inch baking dish as well as a piece of aluminum foil large enough to cover it.
**2.** Put the saffron threads in a small bowl. Add a few tablespoons warm water and let the threads soften.
**3.** Chop the tomatoes lengthwise into quarters and then into 1-inch chunks. Set aside.
**4.** Place a large frying pan on _medium_ heat and add 1 tablespoon butter. When the butter stops sizzling, add the shallots and sauté until soft, about 3 minutes, stirring often. Increase the heat to _high_. Add the wine and cook until the liquid is reduced by half.
**5.** Add the cream and the saffron with the water and cook, stirring constantly, until the liquid is reduced by half, about 2 minutes. Add the chopped tomatoes and turn off the heat. Let the sauce sit while you cook the sole.
**6.** Arrange the sole fillets on the prepared baking dish in a single layer and lightly salt and pepper them. Cover the fish with the prepared aluminum foil, buttered side down. Bake on the center rack of the oven for 7 minutes.
**7.** A few minutes before the fish is done cooking, reheat the sauce over low heat.
**8.** Spoon enough cream sauce onto each dinner plate to cover the bottom. Using a spatula, gently place the fish on top of the sauce. Arrange rice around the fish, and garnish with a bit more sauce and the chopped parsley.
#### **Cajun Baked Salmon**
This awe-inspiring dish couldn't be easier to prepare: It's simply a matter of sprinkling the spices on the salmon steaks and throwing them in the oven. The Cajun flavor enhances the natural taste of the salmon.
**Ingredients** _(serves four)_
_1 tablespoon onion powder_
_1 tablespoon garlic powder_
_1 tablespoon paprika_
_1 tablespoon chili powder_
_1 teaspoon dried oregano_
_½ teaspoon dried rosemary_
_½ teaspoon salt_
_Pinch of cayenne pepper_
_Vegetable oil, for greasing the baking pan_
_4 salmon steaks, cut 1 inch thick_
_2 cups salsa, if serving fish at room temperature_
_1 lime, cut into quarters_
**Equipment**
_Small bowl_
_9 x 12-inch baking pan_
_Aluminum foil_
**1.** Preheat the oven to 325°F.
**2.** Combine all the spices through the cayenne pepper in a small bowl and set aside.
**3.** Line a 9 x 12-inch baking pan with aluminum foil, then lightly grease the foil with vegetable oil.
**4.** Sprinkle half the prepared spice mixture over the top of the salmon steaks. Place the steaks, spiced side down, on the aluminum foil-lined baking pan and sprinkle on the remaining spice mixture.
**5.** Bake the salmon, uncovered, on the center rack of the oven for 12–14 minutes, until the fish flakes when tested with a fork.
**6.** Serve the fish immediately with wedges of lime, or let it cool about 1 hour and serve at room temperature topped with salsa and garnished with lime wedges.
#### **Baked Mackerel with Sun-Dried Tomatoes & Herbs**
The sauce of tomatoes and herbs gives this fish a distinctive flavor. Fresh herbs are best with this dish, but if they're not available, soak the dried herbs overnight in the oil and sun-dried tomatoes.
**Ingredients** _(serves four)_
_Vegetable oil, for greasing the casserole_
_4 ounces sun-dried tomatoes in oil_
_1 clove garlic, mashed_
_¼ cup parsley leaves_
_1 teaspoon fresh oregano or ½ teaspoon dried_
_½ teaspoon fresh or dried rosemary_
_½ teaspoon salt_
_2 fillets (1½ pounds) mackerel_
**Equipment**
_9 x 14-inch casserole_
_Blender or food processor_
**1.** Preheat the oven to 375°F. Lightly grease a 9 x 14-inch casserole.
**2.** Remove the sun-dried tomatoes from the oil and finely chop them. Save the remaining oil.
**3.** Put the garlic, herbs, salt, and 3 tablespoons of the oil from the tomatoes in a blender or food processor. Blend until just puréed.
**4.** Lay the fish in the prepared pan. Spread the herb mixture over the fish. Sprinkle on the chopped sun-dried tomatoes.
**5.** Bake for 12–15 minutes on the middle rack of the oven, until the fish begins to flake.
**Serving Suggestions**
• Serve with fusilli or radiatore in a light herb sauce.
• Serve mixed greens sprinkled with diced red, yellow, and green bell peppers.
#### **Panfried Flounder**
This is a very quick way to cook any fillet of white-meat fish. The Parmesan and garlic add extra zip.
**Ingredients** _(serves four)_
_½ cup bread crumbs_
_3 tablespoons Parmesan_
_1 clove garlic, minced_
_3 tablespoons finely chopped fresh parsley_
_Salt and pepper_
_2 large eggs_
_4 flounder fillets (4–6 ounces each)_
_2 tablespoons vegetable oil_
_1 lemon, cut into wedges_
**Equipment**
_Large frying pan_
_Pie plate_
_Medium shallow bowl_
_Dinner plate_
_Spatula_
**1.** Mix the bread crumbs, Parmesan, garlic, parsley, and salt and pepper in a pie plate. Beat the eggs in a medium shallow bowl.
**2.** Dip each fillet in the egg and let the excess drain off. Lay both sides of the fillets in the bread crumb mixture and shake gently to release excess crumbs. Lay the breaded fillets on a dinner plate.
**3.** Place a large frying pan on _medium-high_ heat and let it get hot, about 45 seconds. Add the oil and the fish fillets and cook until they are lightly browned, about 3 minutes. Turn the fillets with a spatula (being careful not to break the fish) and cook the other side for 2 minutes.
**4.** Lower the heat to _medium_ and cook until the fish flakes, 1–2 minutes more. Lightly season with salt and pepper and a spritz of lemon and serve hot.
**Variations**
This dish also works with sole, trout, or snapper fillet. For thicker pieces of fish, like mackerel, cod, or scrod, preheat the oven to 350°F. Sauté the fish in an ovenproof frying pan for 2 minutes on each side until lightly browned, then put the pan in the oven and bake until the fish flakes, about 4–6 minutes.
**Serving Suggestions**
• Serve with garlic bread.
• Serve with endive salad or steamed broccoli.
* * *
**Shellfish Primer**
Shrimp, scallops, lobster, clams, and mussels are the most popular shellfish. Shrimp and scallops have usually been frozen and are defrosted by the fishmonger before selling. They will last a day in your refrigerator, after which they should definitely be cooked. Lobsters, clams, and mussels are sold live. It is best to cook and eat lobster the day it is purchased. Clams and mussels in their shells can be stored in the refrigerator covered with a damp towel for several days.
The print edition of this book includes a chart for **Shellfish Primer**.
Please download a PDF of this chart here: workman.com/ebookdownloads
* * *
#### **Cajun BBQ Shrimp**
Once the shrimp are prepared this dish is easy to make and it will give your kids a little taste of New Orleans.
**Ingredients** _(serves four)_
_1½ pounds large shrimp_
_4 tablespoons (½ stick) butter or margarine_
_2 tablespoons Worcestershire sauce_
_3 tablespoons ketchup_
_1 tablespoon Cajun or Creole seasoning_
_¼ teaspoon cayenne pepper_
_Juice of 2 lemons_
_3 cloves garlic, minced_
_1 bay leaf_
**Equipment**
_9 x 11-inch casserole_
_Medium saucepan_
_Whisk_
**1.** Preheat the oven to 450°F.
**2.** Peel and devein the shrimp. Keep refrigerated until ready to use.
**3.** Melt the butter or margarine in a medium saucepan. Remove from the heat. Whisk in the Worcestershire sauce, ketchup, Cajun seasoning, cayenne pepper, lemon juice, garlic, and bay leaf.
**4.** Arrange the shrimp in a single layer in a 9 x 11-inch casserole, then pour the butter mixture over the shrimp.
**5.** Bake on the center rack of your oven for 3 minutes. Turn the shrimp and bake for 2 minutes more.
**6.** Transfer the shrimp to a serving platter and pour on any remaining sauce.
**Serving Suggestions**
• Serve with rice or crusty bread to soak up any leftover sauce.
• Serve diced tomato and onion, and corn-on-the-cob.
**Peeling and Deveining Shrimp**
The good news about shrimp is that it's easy to cook. The bad news is that it's a pain in the neck to prepare. Allow yourself about 20 minutes per pound.
**Removing the Shell**
**1.** Hold the shrimp firmly just above the tail between your thumb and first two fingers.
**2.** With your other hand, pull away the body. The tail should now come loose easily.
**3.** Strip away the rest of the shell by peeling from the underside. It should come away in one or 2 sections. Remove the shells from all the shrimp before starting to devein.
**Deveining**
Lay the shrimp on its side and with a sharp paring knife make a shallow slit along the back from the head almost to the tail (about ⅛ inch into the shrimp). This will expose the "vein," which can be lifted out with the point of the knife. Scrape away any residual dirt.
• Lay ice cubes on top of the shrimp to keep them cold during cleaning.
• Cover the shrimp well in the refrigerator, as they tend to share their shrimpy aroma with other foods.
#### **Stir-Fried Scallops with Red Pepper Peas & Baby Corn**
I like to make this colorful and lively dish on hot summer evenings when I'm tired of barbecuing. It's light and festive and needs only some rice or thin noodles to accompany it.
**Ingredients** _(serves four)_
_1 cup chicken broth, plus 1 tablespoon_
_2 tablespoons soy sauce_
_1 tablespoon white wine or dry sherry_
_1 teaspoon sugar_
_2 teaspoons cornstarch_
_1 tablespoon oil_
_1 small red bell pepper, cored, seeded, and cut into ¼-inch strips_
_1 small red onion, thinly sliced_
_8–10 ears canned baby corn, patted dry_
_1 pound scallops (if using sea scallops, cut them in half)_
_2 cloves garlic, minced_
_1 tablespoon fresh ginger, minced, or 1 teaspoon ground ginger_
_½ cup frozen peas, thawed_
**Equipment**
_Small bowl_
_Large, heavy frying pan or wok_
**1.** To make the sauce, in a small bowl stir together the chicken broth, soy sauce, white wine or sherry, and sugar. If using the ground ginger, add it now and stir it into the sauce.
**2.** In a small bowl, dissolve the cornstarch in the 1 tablespoon broth and set aside.
**3.** Place a large, heavy frying pan or wok on _high_ heat and let it get very hot, about 90 seconds. Add the oil, bell pepper, onion, and baby corn, and stir-fry until the pepper softens, about 3 minutes. Add the scallops and stir-fry until they begin to get opaque, 3–4 minutes depending on their size. Add the garlic and fresh ginger (if using) and stir-fry 1 minute more.
**4.** Add the sauce and the frozen peas. As soon as the sauce starts simmering, add the cornstarch mixture and stir to combine. Continue cooking another minute or so until the sauce begins to thicken and a nice glaze begins to form on the vegetables and scallops. Serve immediately.
## Rice & Potatoes
Packed with complex carbohydrates, rice and potatoes are two of the best foods you can eat. Either can be served as a side dish or spruced up and turned into a main course. A baked potato with lots of nutritious toppings can be a meal in itself—one that both the kids and Dad sometimes prefer to fancier dishes—and rice served with beans provides as much protein as a meat-based entrée. Rice comes in several varieties, white and brown being the most common. Brown rice, with its outside bran layer intact, is more nutritious than white rice, although "converted" white rice is more nutritious than plain white rice.
Although rice and potatoes are two of the easiest dishes to cook, both can become disastrous blobs if you don't know the few basic rules in this chapter.
#### **Boiled White Rice**
Though any long-grain white rice will do, converted (aka parboiled) rice, which is soaked and steamed under pressure before it is milled, has greater nutritional value than regular white rice and tends to be less sticky.
**Ingredients** _(serves four)_
_4 cups water_
_2 cups long-grain white rice_
_1 teaspoon salt (optional)_
_1 tablespoon butter or margarine (optional)_
**Equipment**
_Medium saucepan with lid_
**1.** Bring the water to a boil in a medium saucepan over _high_ heat.
**2.** Add the rice, salt, and butter (if using).
**3.** When the liquid returns to a boil, immediately cover the pan and reduce the heat to _low_.
**4.** Cook for 17–20 minutes, depending on the nature of your stove's _low_ setting. Turn off the heat and let the rice sit, covered, for 5 minutes.
**5.** Fluff with a fork before serving.
**Variation**
For more flavorful rice, cook it in chicken or beef broth instead of water, or add 1 bouillon cube per cup of boiling water.
#### **Basic Rice Pilaf**
With just a few simple touches, plain rice can become an exciting side dish. For pilaf, rice is sautéed in butter or oil before cooking in stock. Pilafs are variously seasoned and often contain other ingredients such as chopped vegetables, poultry, or nuts and raisins.
**Ingredients** _(serves four)_
_2 tablespoons butter, margarine, or vegetable oil_
_2 small onions, finely chopped_
_1½ cups white rice_
_3 cups canned chicken broth or 3 bouillon cubes dissolved in 3 cups boiling water_
_½ teaspoon dried basil_
_½ teaspoon salt_
_Freshly ground black pepper_
**Equipment**
_Large frying pan with cover_
**1.** Place a large frying pan on _medium-high_ heat until hot, about 45 seconds. Add the butter, margarine, or oil and the onions and sauté them for 3 minutes.
**2.** Add the rice and sauté, stirring continuously, until it starts to become transparent, about 2 minutes.
**3.** Add the broth, basil, salt, and pepper, and bring to a boil.
**4.** When the liquid boils, immediately cover the pan and reduce the heat to _low_.
**5.** After 20 minutes, turn off the heat and let the rice sit, covered, for 5 minutes. Fluff with a fork before serving.
**Variations**
• **For curried rice:** Omit the basil and add 1½ tablespoons curry powder to the onions after cooking them for 3 minutes, then cook for 1 minute more. After 15 minutes of cooking, add ¼ cup raisins or currants and ¼ cup chopped walnuts or slivered almonds to the rice, and cook for 5 more minutes.
• **For Mexican rice:** Omit the basil. After the rice is cooked, stir in 3 tablespoons room-temperature sour cream, ¼ cup grated Fontina, Monterey Jack, or white cheddar cheese, and ¼ cup chopped green bell pepper or pimiento. Let the rice mixture sit covered for 5 minutes before fluffing and serving.
**How to Cook Rice**
**1.** Carefully measure your rice and water.
**2.** Turn the heat down to _low, immediately_ after the water with the rice in it returns to a boil (for white rice) or begins boiling (for brown rice).
**3.** Set the timer and don't lift the lid until the timer goes off.
#### **Basic Brown Rice**
It is no myth that brown rice is more nutritious than white rice. It has considerably more protein, vitamins, potassium, and dietary fiber. Unlike white rice, brown rice is added to cold water that is then brought to a boil rather than being added to boiling water.
**Ingredients** _(serves four)_
_3 cups water_
_1½ cups short- or long-grain brown rice_
_½ teaspoon salt_
**Equipment**
_Medium saucepan with cover_
**1.** Measure the water into a medium saucepan. Add the rice and salt.
**2.** Bring to a boil, uncovered, over _medium-high_ heat. This should take 5–7 minutes.
**3.** When the water begins boiling, immediately cover the saucepan and reduce the heat to _low_.
**4.** Cook for 50 minutes. (Do _not_ lift the lid.) Remove the saucepan from the heat and let the rice sit, covered, for 5 minutes.
**5.** Fluff with a fork before serving.
**Variation**
You can enhance the flavor of brown rice by using chicken or beef broth instead of water, or by adding a bouillon cube or a tablespoon of miso soup powder to the water.
**Tip**
If the kids can't quite get used to the taste of brown rice, mix it in with some white rice. It's easy to cook in the same pot. Bring 1 cup brown rice and 3 cups water to a boil in a medium saucepan. Cover and reduce the heat to _low_. After 30 minutes, stir in ½ cup white rice. Raise the heat momentarily to _high_ to return the water to a boil, then reduce the heat to _low,_ cover, and simmer for another 20 minutes. Remove the saucepan from the heat and let sit, covered, for 5 minutes. Fluff with a fork before serving.
#### **Baked Wild Rice**
The sweetness of grapes complements the strong, nutty flavor of the rice (and is a big draw for the kids). This dish goes well with meat, chicken, or salad and is perfect for a small dinner party.
**Ingredients** _(serves six)_
_1½ tablespoons oil_
_1 medium onion, finely chopped_
_1 carrot, grated_
_¼ pound shiitake or button mushrooms, sliced_
_1 scallion, chopped_
_1 clove garlic, minced_
_1½ cups wild rice_
_3 cups canned chicken broth or 3 bouillon cubes dissolved in 3 cups boiling water_
_½ pound seedless green grapes (optional)_
**Equipment**
_Large, ovenproof frying pan with cover_
**1.** Preheat the oven to 375°F.
**2.** Place a large ovenproof frying pan on _medium-high_ heat and let it get hot, about 45 seconds. Add the oil, onion, carrot, mushrooms, and scallion, and sauté, stirring frequently, until the onion is soft, about 6 minutes. Add the garlic and cook for 1 minute more.
**3.** Add the rice to the pan and sauté, stirring continuously, until the rice is hot, about 2 minutes.
**4.** Increase the heat to _high,_ pour in the broth, and let it come to a boil. When it does, immediately cover the pan and place it in the hot oven. Be careful not to tilt the pan or the hot liquid will spill. Bake for 45–55 minutes or until the rice if fluffy and the dark brown shell opens a bit to reveal the whitish inside.
**5.** While the rice is baking, slice the grapes in half and set aside. Scatter them over the rice for the last 10 minutes of cooking.
**6.** Remove the pan from the oven and let it sit, covered, for 5 minutes before serving.
**Wild Rice**
Wild rice is not technically a rice at all, but the seed of a wild grass native to the Great Lakes region. Originally it was harvested by Indians who would paddle their canoes next to the plants and shake the seeds onto the bottom of their boats. It is now cultivated commercially and is available in most markets.
Wild rice is very high in fiber, protein, and vitamin B. And while it is the most expensive kind of rice, it cooks to four times its original size, so a little goes a long way. Because wild rice and brown rice have the same cooking times, you can easily mix them together and cook them in the same pot. Cook wild rice exactly as you would plain brown rice and prepare the baked variation at left.
#### **Kasha**
Kasha, or buckwheat groats, are the gently roasted kernels of the buckwheat plant. A staple food of the Russian steppes, kasha is packed with protein and vitamins. When combined with bow-tie noodles, it becomes the classic Jewish dish, "kasha varnishkas."
**Ingredients** _(serves four)_
_2 cups canned chicken broth or 2 bouillon cubes dissolved in 2 cups boiling water_
_1 large egg_
_1 cup buckwheat groats_
_1 tablespoon margarine or vegetable oil_
_Salt and pepper_
**Equipment**
_Small saucepan_
_Medium bowl_
_Large frying pan with cover_
**Canned Broth and Bouillon**
Chicken or beef broth can be used in place of water to add extra flavor when making rice, casseroles, and sauces. Or instead of canned broth, bouillon cubes or powder can be mixed with boiling water. Bouillon is more highly seasoned than canned broth, and is usually a bit saltier. Part or all of a bouillon cube can be added directly to a soup, stew, or sauce to enhance the flavor. Just be sure to stir well to dissolve the cube completely.
**1.** Heat the broth in a small saucepan until hot.
**2.** As the broth is heating, beat the egg in a medium bowl. Add the buckwheat groats and stir well to combine.
**3.** Place a large frying pan on _high_ heat and let it get very hot, about 45 seconds. Add the margarine or vegetable oil and the egg-coated buckwheat groats. Cook, stirring constantly to break up the lumps, until the mixture dries and the buckwheat groats are mostly separate, about 2 minutes.
**4.** Add the hot broth to the frying pan, cover, and immediately reduce the heat to _low_. Simmer for 12 minutes. Remove the cover and check the kasha. If the kernels are still hard, replace the cover and continue cooking for 3–5 minutes longer, adding a bit of water if necessary. When the kernels are soft, turn off the heat. Let the kasha sit covered for 5 minutes. Season with salt and pepper and fluff with a fork before serving.
**Variations**
• **Kasha varnishkas:** While the kasha is simmering (Step 4), add ¼ pound medium bow-tie noodles to a pot of boiling water and cook for about 8 minutes or according to the package instructions. Drain the noodles in a colander and transfer them to a large bowl. Add the kasha and mix together.
• **Kasha pilaf:** In a large frying pan over _medium_ heat, sauté 1 chopped onion, a few sliced mushrooms, and a chopped red bell pepper or carrot in a tablespoon of oil or butter. When the vegetables are soft (about 5 minutes), turn up the heat to _high_ and add the uncooked kasha and egg mixture. Continue cooking as instructed in Step 3 of the basic kasha recipe.
* * *
**The Basic Potato**
Potatoes are the classic American side dish, expertly filling up that section of the plate between the meat loaf and the green beans. The potato is rich in protein and vitamin C and has only a modest number of calories, 100 for a five-ounce baked potato. There are several types of potato available; the most popular are:
• **Maine or all-purpose potatoes** Roundish, about the size of a racquetball, these are best when boiled.
• **Sweet potatoes** Long and orange or slightly larger and rounder, these are suitable for baking, roasting alongside meats, frying, or for use in casseroles.
• **Idaho or russet potatoes** Large and oblong, these are the sturdiest and best for baking.
• **New potatoes** These small red or white taters are sweeter and more moist than other varieties. They stand on their own with just some butter or herbs or can be cast as the blushing star of potato salad.
##### **Boiled Potatoes**
For boiling, use new potatoes or all-purpose potatoes. Peel the potatoes or scrub them well. If they are very large, cut them into quarters. For good results, the trick is to start boiling potatoes in _cold_ water and to keep the water barely simmering as they cook. This will keep the potatoes from becoming mealy or from turning into overcooked mush.
Bring the water and potatoes to a boil over _high_ heat. As soon as the water boils, reduce the heat to _medium-low_ and let the potatoes simmer. Rapidly boiling water will cause the potatoes to fall apart. Cook the potatoes until they begin to soften, 12–15 minutes. Test by pricking them with a skewer or the tip of a paring knife. If it goes in easily but with some resistance, the potatoes are done. They will continue cooking a bit longer after you remove them from the water. Drain the potatoes in a colander.
Serve boiled potatoes with a bit of butter or margarine, salt and pepper, and a sprinkling of fresh parsley.
##### **Baked Potatoes**
Look for potatoes of uniform hardness with no dark spots, cracks, or sprouting "eyes." Serve baked potatoes accompanied with a pat of butter or margarine, or a tablespoon of sour cream or yogurt with chives.
**Oven Method**
Preheat the oven to 350°F. Select potatoes that are about the same size and scrub them well. Prick the potatoes with a skewer or a fork in about 10 places. Place the potatoes directly on the center rack of the oven and bake for 1 hour or until soft when pricked with a fork. Let rest a few minutes before slicing them lengthwise.
**Variation**
It might take ten extra minutes, but it will turn plain old baked potatoes into a real taste treat. Slit the cooked baked potato in half and scoop the insides into a bowl. Add 2 tablespoons milk, 1 teaspoon butter, and salt and pepper, then mash the ingredients together. Put the mixture back into the skins, sprinkle grated cheddar or Parmesan cheese on top, and put under the broiler for about 5 minutes or until the top is brown.
**Microwave Method**
The skin will not be as crusty, but this way you can have a baked potato on the spur of the moment rather than waiting an hour. Scrub, then prick the potatoes as directed for the oven method. Arrange the potatoes at least 1 inch apart around the edge of a microwave turntable or on the bottom of the microwave. This positioning will allow the energy to hit them from all sides. Bake on the _high_ setting for the specified amount of time:
**1 potato 4–5 minutes**
**2 potatoes 7–9 minutes**
**3 potatoes 9–11 minutes**
**4 potatoes 11–14 minutes**
Cook for half the allotted time, then turn the potatoes over. Finish cooking and remove the potatoes when they are still slightly firm. Wrap the potatoes individually in aluminum foil and let them rest for 5 minutes before serving.
**Note**
For microwave ovens with less than 650 watts of power, add 1–2 minutes to the cooking times.
##### **Oven-Roasted Potatoes**
For roasting, use new potatoes or any baking potato. Count on about ½ pound per person. Cut the larger potatoes into 1½-inch pieces. Preheat the oven to 375°F. Using vegetable oil, grease a 9 x 14-inch casserole and arrange the potatoes in an even layer. Melt 3 tablespoons butter in a small saucepan and use a pastry brush to coat the potatoes with it. Sprinkle the potatoes with salt and pepper and place them on the center rack of your oven. Roast the potatoes for 30 minutes, then turn them over and roast for 20 minutes more. Use a skewer or the tip of a paring knife to see if the potatoes are done. They should be soft on the inside with a deep golden brown crust outside.
**To Roast with Meat**
Peel; then parboil the potatoes for about 12 minutes. Add them to the roasting pan about ½ hour before the meat is done, turning them so that the meat juices cover all sides.
##### **Mashed Potatoes**
Every dad can be an expert at making mashed potatoes. My Dad would have Mom cook the potatoes for him. Then he'd enter the kitchen with the debonair manner of a master safe-cracker and coolly practice his art with the potato masher.
**Ingredients** _(serves four)_
_2 pounds all-purpose potatoes, or new potatoes_
_¼ cup milk_
_2 tablespoons butter or margarine_
_Salt and pepper_
**Equipment**
_Vegetable peeler_
_Medium saucepan_
_Small saucepan_
_Colander_
_Medium bowl_
_Potato masher or hand-held electric mixer_
**1.** Peel the potatoes, then cut them into ½-inch slices or in half if using new potatoes. Follow the instructions for boiled potatoes, cooking the slices in a medium saucepan until you can pierce them easily with the tip of a paring knife, about 15 minutes.
**2.** As the potatoes cook, heat the milk in a small saucepan over _medium-low_ heat until hot. Do not boil.
**3.** Drain the cooked potatoes in a colander and immediately transfer them to a medium bowl. Add the hot milk and the butter or margarine, and mash with a potato masher or hand-held electric mixer set at medium speed until smooth. Season lightly with salt and pepper. Serve immediately (mashed potatoes cool quickly).
**Tips**
• To keep mashed potatoes hot for up to 15 minutes, cover the bowl and set it in a large pan of hot water. Set the pan over _low_ heat but don't let the water boil.
• Don't use a food processor to mash potatoes as it turns them into wallpaper paste.
* * *
#### **French Fries**
French fries are a cinch; the hardest part is cutting them into thin sticks.
**Ingredients** _(serves four)_
_4 medium baking potatoes_
_Approximately 3½ cups vegetable oil_
**Equipment**
_Vegetable peeler_
_Large saucepan_
_Slotted spoon_
_Paper towels_
_Baking pan_
**1.** Preheat the oven to 200°F.
**2.** Peel the potatoes and slice about ½ inch off each end. Cut the potatoes into ½-inch slices. Stack 3 slices together and cut them lengthwise into ¼-inch sticks. Wrap the cut potatoes in a dish towel to keep them from browning.
**3.** Pour the oil into a large saucepan to a depth of about 1 inch. Heat the oil over _high_ heat, 2–3 minutes. As a test, place 1 potato stick in the oil; if it sizzles immediately and starts cooking rapidly, the oil is ready.
**4.** Using a slotted spoon, gently lower half of the potato sticks into the oil and stir. Fry the potatoes until golden brown, about 8–10 minutes.
**5.** Using a slotted spoon, transfer the French fries from the hot oil to several layers of paper towels to drain. Transfer the drained potatoes to a baking pan and place in the oven to keep warm.
**6.** Let the oil get hot again (about 30 seconds) before making your next batch.
#### **Oven-Roasted Fries**
An easy substitute for French fries, these potatoes are just as tasty and have considerably less fat.
**Ingredients** _(serves four)_
_1 tablespoon oil, for greasing the baking sheet_
_4 large baking potatoes or 2 pounds (about 16) new potatoes_
_1 teaspoon garlic powder_
_1 teaspoon salt_
_Freshly ground black pepper_
_1 tablespoon butter or margarine, melted_
**Equipment**
_11 x 17-inch baking sheet_
_Small saucepan_
_Basting brush or spoon_
_Spatula_
**1.** Preheat the oven to 375°F. Grease an 11 x 17-inch baking sheet with the oil.
**2.** Scrub the potatoes well. Cut them into ½-inch rounds. Arrange the rounds in rows on the baking sheet, overlapping slightly. Sprinkle with the garlic powder, salt, and pepper.
**3.** Put the baking sheet in the center of the hot oven. After 30 minutes, brush or drizzle the tops of the potatoes with the melted butter using a basting brush or spoon. Continue baking for another 12 minutes or until the potatoes are golden brown. Serve immediately, removing the potatoes from the pan with a spatula.
* * *
**A Baked Potato as a Meal**
_What's for dinner, Dad?_ Next time you hear that question and haven't had a second to think about food, try one of the easiest meals ever. Bake a potato (it will take only ten minutes in the microwave), split it open on a plate, and let your kids heap on any of the toppings suggested below. Heated-up leftovers are great for this. But just about anything goes!
**Toppings**
• Broccoli
• Baked beans
• Chopped onion
• Sweet corn
• Bacon bits
• Grated cheese
• Yogurt, sour cream or cottage cheese
* * *
#### **Stuffed Potatoes with Bacon & Cheese**
Serve these with a bowl of soup or chili for dinner and you'll knock the kids' socks off. This is a great way to use up leftover baked potatoes.
**Ingredients** _(serves four)_
_4 large russet or Idaho potatoes, baked (seepage 125 for instructions)_
_½ cup milk_
_2 large eggs_
_1 cup (about 4 ounces) grated cheddar, Gruyère, or Swiss cheese_
_½ teaspoon salt_
_Freshly ground black pepper_
_Pinch of nutmeg_
_2 links sweet Italian sausage, cooked, or 4 slices bacon, cooked_
_¼ cup grated Parmesan (optional)_
**Equipment**
_Medium bowl_
_Small saucepan_
_11 x 17-inch baking sheet_
_Potato masher or hand-held mixer_
**1.** Preheat the oven to 350°F.
**2.** Slice the baked potatoes in half lengthwise. Scoop out the center, leaving ¼ inch of shell. Mash the pulp in a medium bowl and set aside.
**3.** Heat the milk in a small saucepan until it's just hot. Do _not_ let it boil.
**4.** Add the hot milk to the potato pulp and mix well with a potato masher until the potatoes are smooth. Beat in the eggs, one at a time, then stir in the grated cheese, salt, pepper, and nutmeg.
**5.** Crumble the cooked sausage or bacon into small pieces and stir into the potato mixture.
**6.** Spoon the mixture into the shells, heaping it in the center. Sprinkle with the Parmesan (if using).
**7.** Arrange the filled shells on an 11 x 17-inch baking sheet. Bake on the center rack of the oven until the filling puffs and bubbles, about 20 minutes. Serve immediately.
**Tips**
• Chopped ham, salami, or prosciutto, or finely chopped scallion can be used if there's no leftover bacon or sausage or if you don't feel like cooking any.
• Unbaked filled potatoes can be tightly wrapped in plastic and stored overnight in the refrigerator. Add 8 minutes to the baking time if you're putting cold potatoes in the oven.
#### **Pan-Roasted New Potatoes**
You may find yourself roasting a chicken just because you have a hankering for these potatoes and want something to go with them.
**Ingredients** _(serves four)_
_2 pounds (about 12–14) small new potatoes_
_1½ cups canned chicken broth or 1½ bouillon cubes dissolved in 1½ cups boiling water_
_2 tablespoons butter or margarine_
_1 tablespoon fresh thyme or 1 teaspoon dried_
_1 teaspoon chopped fresh rosemary or ½ teaspoon dried_
_2 tablespoons chopped fresh parsley_
_Salt and freshly ground black pepper_
**Equipment**
_Large frying pan with cover_
**1.** Scrub the potatoes well. Cut them in half and fit as many as possible in one layer in a large frying pan.
**2.** Pour the broth over the potatoes. Bring the liquid to a boil over _medium_ heat, cover the pan, and cook until the broth is almost gone, about 20 minutes.
**3.** Just before the liquid is boiled away, reduce the heat to _medium low_ and add the butter or margarine. Add the thyme and rosemary (if using dried herbs), and salt and pepper. Continue cooking, uncovered, shaking the pan often, for another 10 minutes. The potatoes should be soft but not mushy, with a deep golden brown crust. Add a bit of water to the pan if the potatoes start to burn.
**4.** Sprinkle on the thyme and rosemary (if using fresh herbs), and the parsley, and season with salt and pepper. Serve immediately, or cover and keep warm in a 250°F oven for up to 15 minutes.
## Vegetables
The great thing about vegetables is that the less you do to them, the more nutritious and flavorful they are. Unfortunately, many people have gotten into the habit of using canned veggies or smothering fresh ones with cheese or sauce to entice their kids to eat them. But the best way to retain the distinct flavor and texture of vegetables is to steam or stir-fry them.
Fresh vegetables are always preferable, but frozen peas, spinach, corn kernels, and cauliflower taste okay if cooked for slightly less time than instructed on the package. Avoid canned vegetables with these few exceptions: artichokes, corn packed in water, and stewed tomatoes.
Getting your kids to eat vegetables (let alone the 3–5 servings a day recommended by the USDA) can be a battle. Be resourceful: put carrot sticks or cucumber slices on your child's lunch plate instead of potato chips. Add a cup of frozen peas or cut green beans to your tomato sauce. It also helps to give your children a choice: "Okay, kids, what do you want tonight? Broccoli or cauliflower?" Then hold them to their decision.
* * *
**Cooking the Basic Vegetable**
When cooking vegetables, less is more. To preserve color, flavor, and nutrition, we recommend the following methods. Cooking times are for crunchy (al dente) vegetables. For vegetables without any crunch, cook a bit longer but not so long that they become mushy and dull.
##### **Boiling**
Bring 1–2 inches of water to a boil in a saucepan on _high_ heat. Add the vegetables. (Do not fill more than halfway with vegetables.) When the water returns to a boil, reduce the heat to _low,_ cover the pan tightly, and simmer for the prescribed amount of time. To blanch vegetables, boil a full pot of water, plunge the vegetables in, and remove after 30 seconds to 1 minute. Rinse vegetables under cold water.
##### **Steaming**
Fill a medium-sized pot with 1–2 inches of cold water. Set the vegetable steamer in the pot. (The water level should not reach the bottom of the steamer.) Place the vegetables in the steamer and cover the pot tightly.
Bring the water to a boil on _high_ heat. When the water boils, reduce the heat to _low_ and steam for the prescribed amount of time.
##### **Microwaving**
Unless a recipe states otherwise, put the vegetables in a microwave-safe bowl just large enough to hold them comfortably. Add 2 tablespoons water and cover tightly with microwavable plastic wrap. Cook on _high_ heat for the prescribed amount of time. (Times given in this chapter are for large, high-wattage microwave ovens. Small, low-wattage oven owners should add 30% more time.) Remove the vegetables from the microwave, let them sit, covered, for a few finished cooking, then lift the plastic carefully.
**Steam for Health**
Steaming is the most healthful way to cook vegetables. It also intensifies the color, so vegetables look vibrant on the plate. When you boil vegetables, many of the nutrients get lost in the water, but steaming prevents this because the water doesn't come in contact with the vegetables. Steaming takes a few minutes longer than boiling or cooking in the microwave, but it also leaves you more margin for error. Vegetables mistakenly left steaming for a few extra minutes will probably stay crunchy. When steaming, just remember to turn the heat down once the water boils; otherwise you'll wind up with a scorched pot.
##### **Stir-Frying**
Heat 2 tablespoons vegetable oil in a heavy frying pan or wok on _high_ heat and let it get very hot, about 1 minute. Add the cut-up vegetables all at once and fry, stirring continuously, until they are cooked but still slightly crunchy, usually about 4 minutes. Add 1 minced clove of garlic and/or 2 tablespoons soy sauce, and stir-fry for 1 minute more before serving. There are a number of interesting Asian sauces available in supermarkets that you can add instead of plain soy sauce.
**Photo Finish: Timing**
To be sure your vegetables are done at the same time as the rest of the meal, follow these steps:
**1.** Clean and cut the vegetables and prepare them for cooking, whether conventionally or by microwave. This can be done early on in the dinner preparation or even in the morning (just keep the veggies covered and refrigerated).
**2.** If the main course is a roast meat or fowl, start the vegetables just before you take the roast from the oven. Remember, both roast meat and fowl need to sit for 10 minutes before they are sliced, which is enough time for vegetables to cook.
**3.** If your main course takes a short time to cook, such as sautéed fish fillets or boneless chicken breasts, start cooking the vegetables just before you begin sautéing.
* * *
#### **Artichokes**
Artichokes are surprisingly easy to prepare and the involved process of eating them makes them especially appealing.
**Freshness**
Fresh artichokes are distinguished by their bright-green color, tightly packed leaves, and absence of brown spots.
**Preparation**
Pull off tough outside leaves. Cut off the entire stem and trim about ½ inch from the top. Trim the tip of each leaf with scissors. Rinse well.
**Portion Size**
1 artichoke per person.
**Cooking**
**To steam:** Place the artichokes, stem side down, in a pot just large enough to accommodate them. Add 2 inches water, 2 teaspoons salt, and 2 lemon slices. Bring the water to a boil on _high_ heat. When the water boils, immediately turn the heat to _low,_ cover, and steam for 35–45 minutes, depending on the size of the artichokes. They are done when a middle leaf can be pulled out with ease. Remove the artichokes from the pot with tongs and turn them over in a colander to drain.
**To microwave:** Loosely wrap each artichoke individually in plastic wrap. Cook 1 artichoke for 7 minutes; 2 artichokes for 10 minutes; 4 artichokes for 12–15 minutes.
**Curry Dip**
With its subtle curry flavor, this quick dip is a great accompaniment for artichokes.
**Ingredients**
_3 tablespoons sour cream_
_3 tablespoons mayonnaise_
_1 teaspoon curry powder_
_½ teaspoon garlic powder_
_½ teaspoon salt_
_Dash cayenne pepper_
**Equipment**
_Medium bowl_
_Wooden spoon_
Mix all the ingredients together and refrigerate until ready to serve.
**Note**
2 tablespoons plain yogurt can be substituted for 2 tablespoons of the sour cream.
**Eating**
Place the artichoke in the center of a plate. To eat, gently tug on a leaf to remove it, then scrape off the meaty bottom portion of the leaf with your teeth. The rest of the leaf is inedible. After all the leaves have been eaten, you'll have worked your way down to the choke, which is covered with fuzz and very small leaves. Cut off the fuzz and discard. Underneath is the meaty bottom, called the heart, which is a delicacy. The leaves and heart can be sprinkled with lemon juice or dipped in different sauces, such as melted butter, a vinaigrette, or hollandaise sauce.
#### **Asparagus**
Asparagus is a curious vegetable in that it has no real leaves, only small nibs that run along the stalk. No longer the expensive delicacy it once was, asparagus is now generally available year-round.
**Freshness**
Look for firm, green stalks. The cluster at the top should be tightly closed and firm.
**Preparation**
Stalks can be thin, medium, or wide. All need about 1 inch trimmed off the end. If you bend the stalk, it will break at the right point. Thicker stalks, those that are 10–12 to a pound, need to be trimmed and peeled. Use a vegetable peeler to gently scrape off the tough outer skin, working from the middle of the stalk down to the end.
**Portion Size**
6 stalks per person.
**Cooking**
**To steam:** Place asparagus in an asparagus steamer with the water boiling—4 minutes for thin stalks, 6 minutes for medium stalks, and 8 minutes for thick stalks. Asparagus should be cooked through but still slightly crunchy.
**To boil:** Use a wide pot or deep frying pan to accommodate the asparagus. Fill halfway with water, add 2 teaspoons salt, and bring the water to a boil. Add the asparagus all at once. Cook 4 minutes for thin stalks, 6–7 minutes for medium stalks, and 8–9 minutes for thick stalks.
**To microwave:** Because of their delicacy and quick cooking time, it is not advisable to cook asparagus in the microwave.
**Serving**
Asparagus is traditionally served with hollandaise or béarnaise sauce. Just as satisfying is a bit of butter, salt, and pepper. It can also be served chilled with a tangy vinaigrette (see box).
**Orange Vinaigrette**
In a small mixing bowl, whisk together ¼ cup orange juice, 2 tablespoons red wine vinegar, 2 tablespoons lemon juice, 2 teaspoons Dijon mustard, ½ teaspoon salt, and freshly ground black pepper to taste. Drizzle in 1 cup olive oil and continue whisking until completely combined. Spoon lightly over chilled asparagus. _Makes about 1½ cups._
#### **Beets**
Like great actors in bad plays, beets have been cast poorly, canned in water or in jars of sweet syrup. But fresh medium-sized beets, simply cooked, can be a surprisingly wonderful addition to a meal.
**Freshness**
Beets should be hard with no wrinkles, bruises, or soft spots. Choose beets that are slightly larger than a golf ball.
**Preparation**
Trim the stems, leaving about an inch. Rinse gently. (Do not scrub or you could puncture the skin, which will cause the juice to run during cooking and cause a considerable loss of flavor.)
**Portion Size**
2 medium-sized beets per person.
**Cooking**
**To boil:** Put the beets in a pot and add water to cover them halfway. Cover the pot and bring the water to a boil. Reduce the heat to _low_ and simmer for 35–45 minutes. When soft, transfer the beets to a large bowl of cold water. Slip off the skins with your fingers as soon as the beets are cool enough to handle.
**To bake:** Trim the stems and place the unwashed beets in an aluminum foil-lined casserole. Bake in a 325°F oven for about 1½ hours. Peel the skin with a paring knife when the beets are cool enough to handle.
**To microwave:** Trim the stems and wrap each beet loosely in plastic wrap. On _high_ setting, cook ½ pound of medium beets for 12–13 minutes. Cook 1 pound for 16–17 minutes. Peel the skin with your fingers or a paring knife when the beets are cool enough to handle.
**Serving**
Slice the beets and serve dotted with butter and a sprinkling of dill, salt, and pepper; or sprinkle with white vinegar.
**Beet & Cucumber Salad**
Peel 4 cooked beets and 1 hothouse cucumber, slice thinly, and place in a medium bowl. In a small bowl, mix together ¼ cup plain yogurt, 2 tablespoons mayonnaise, 2 teaspoons chopped fresh dill or 1 teaspoon dried, and ¼ teaspoon salt. Pour the dressing on the vegetables and toss them gently. _Serves four._
#### **Broccoli**
Broccoli is always available and is highly nutritious, boasting large amounts of vitamins A and C. It also scores high in iron, calcium, and potassium content. Like other members of the cabbage family, it has been shown to be helpful in the prevention of some kinds of cancer.
**Freshness**
Look for bunches that have abundant florets with tightly packed buds. Also look for the thinnest stalks. Avoid any bunches with yellowing areas or buds that have begun to flower.
**Preparation**
Rinse the broccoli. Trim 1 inch or more off the stem, depending on how thick and tough it is. Snap off the florets and then slice the stalks into ½-inch medallions.
**Portion Size**
1 bunch (3 stalks) serves 4–5.
**Cooking**
**To steam:** Steam for 8–10 minutes. Stems will be slightly crunchy.
**To boil:** Boil for 6–8 minutes.
**To microwave:** Microwave 3 cups florets for 4–5 minutes, stirring once.
**Serving**
Broccoli is great plain, seasoned with salt and pepper or topped with a sprinkling of freshly grated Parmesan cheese. Or serve with a simple sauce, heated until warm, of equal proportions fresh lemon juice and butter with a dollop of Dijon mustard.
**Sautéed Broccoli & Mushrooms**
Pat dry 1 bunch boiled or steamed broccoli florets and set aside. Trim the stems of ¼ pound mushrooms and cut them into thin slices. Mince 1 clove garlic. Place a frying pan on _high_ heat and let it get hot, about 30 seconds. Add 1 tablespoon olive oil, then the mushrooms and the broccoli. Sauté for 3 minutes, stirring often. Add the garlic and a pinch of salt, and sauté for 1 minute more. Season with freshly ground black pepper. _Serves four._
#### **Carrots**
Carrots are inexpensive and are always available. Lightly seasoned and not overcooked, they make a tasty and highly nutritious side dish.
**Freshness**
Carrots are usually packed in plastic bags that are deceptively tinted orange, making it difficult to tell the color of the carrots inside. Try to find firm, bright orange carrots that have no sprouts at their tops. Carrots sold with green tops taste fresher and do not need to be peeled.
**Preparation**
Cut carrots into ½-inch circles or slice lengthwise in quarters and cut into 3-inch sticks.
**Portion Size**
1 medium-sized carrot per person.
**Cooking**
**To steam:** For firm carrots, steam for 8–10 minutes.
**To boil:** Boil for 6–8 minutes.
**To microwave:** For 5 carrots, microwave for 5 minutes, stirring once.
**Serving**
Serve carrots seasoned with a pinch of salt and pepper, and if you like, a bit of chopped fresh dill or mint.
**Carrots with Orange & Mint**
Bring 1 cup orange juice, 1 tablespoon butter, 1 tablespoon sugar, and a coin-sized slice of peeled ginger to a boil on _high_ heat in a heavy saucepan. Add ½ pound sliced carrots and reduce the heat to _medium low_. Cook, uncovered, for 10–12 minutes, until the carrots are soft and the juice begins to thicken. Remove the carrots with a slotted spoon, discard the ginger, and sprinkle with chopped fresh mint. _Serves four._
**Microwaved Glazed Carrots**
Mix together ½ pound sliced carrots with 1 tablespoon each brown sugar and butter in a microwave-safe casserole. Cover and microwave for 8 minutes, stirring once. _Serves four._
#### **Cauliflower**
Perhaps because of its nonthreatening color and somewhat mild flavor, cauliflower is often popular with kids.
**Freshness**
Look for heads that are firm and white with no brown spots. The florets should be tightly packed. If the head develops a few brown spots in the fridge, simply trim them away. The rest is perfectly fine.
**Preparation**
Cut the head in half lengthwise. Using a paring knife, cut the florets from the main stalk. Cut any extra-large florets in half lengthwise.
**Portion Size**
1 medium-sized head serves 6.
**Cooking**
**To steam:** Steam for 8–10 minutes.
**To boil:** Boil for 6–8 minutes.
**To microwave:** For 1 medium size head, cut into florets, microwave for 4 minutes.
**Serving**
Serve with salt and pepper and an optional dot of butter or a sprinkling of freshly grated Parmesan, if desired.
**Curried Cauliflower & Potato**
In a large frying pan on _high_ heat, sauté 2 peeled and diced medium-sized potatoes in 2 tablespoons vegetable oil for 3 minutes. Add 2 cups cauliflower florets, 1 minced garlic clove, 1 tablespoon curry powder, and 1 teaspoon salt, and sauté, stirring continuously, for 3 minutes more. Add ½ cup chicken stock (or ½ bouillon cube dissolved in ½ cup boiling water) to the pan and bring the liquid to a boil. Immediately reduce the heat to _medium low,_ cover the pan, and simmer for 12 minutes, until the potatoes are soft. Garnish with chopped fresh coriander or parsley. _Serves four._
#### **Corn**
The taste of the first locally grown ears of corn is bittersweet, for as delicious as they are, they mean that summer is nearing its end.
**Freshness**
Try to find a market or stand that sells fresh local corn. Peel back the husk a bit and check inside to see if the kernels are small, packed tightly, full and shiny, and that there are no shriveled areas or worm holes. Florida farmers now grow excellent hybrids, giving us sweet-tasting corn starting in late spring.
**Preparation**
Keep corn refrigerated and shuck as close to cooking time as possible.
**Portion Size**
1½ ears per person.
**Cooking**
**To boil:** Place corn in a large pan with enough water to just cover the ears. Boil for 3–5 minutes.
**To microwave:** Wrap 4 ears of corn in microwavable plastic, microwave for 8 minutes (2 minutes each), turning once.
**Serving**
Serve with butter and salt and pepper. Extremely fresh corn, however, needs no enhancement. Give the kids corn holders or just run an ear under cold water for a few seconds until it is cool enough for them to hold.
**Corn Pudding**
This is a great way to use up leftover cooked corn. With a sharp knife, scrape the kernels from 5 ears of cooked corn and transfer to a medium bowl. In a separate bowl, beat 3 large eggs with 1 cup cream, 1 cup milk, 2 tablespoons melted butter, 1 tablespoon sugar, and ½ teaspoon salt. Stir in the corn and transfer the mixture to a 9 x 9-inch buttered casserole. Bake in a preheated 350°F oven until the pudding is set, about 1 hour. _Serves four._
#### **Green Beans**
Fresh green beans are a far cry from the tasteless, waxy canned beans served in school cafeterias. They can be prepared in a variety of ways, none of which will remind you of the soggy green horrors of your youth.
**Freshness**
Look for firm beans of a rich green color without any shriveling at the ends. If you can get away with it, snap one and eat it. It should be crisp and slightly sweet.
**Preparation**
Rinse the beans and cut ¼ inch from each end. Cut in half or thirds if desired. This is about a 5–10 minute job that the kids can help you with.
**Portion Size**
¾ pound serves 4.
**Cooking**
**To steam:** For crunchy beans, steam for 6–8 minutes.
**To boil:** Boil for 5–7 minutes.
**To microwave:** For 1 pound of beans, microwave for 6–8 minutes.
**Stir-fry:** Green beans lend themselves very well to stir-frying. Just before they are finished cooking, add 1 clove minced garlic and 2 tablespoons soy sauce to the pan.
**Serving**
Serve plain beans with a dot of butter, and salt and pepper.
**Sautéed Green Beans with Garlic**
Pat dry ¾ pound of cooked al dente beans with paper towels. Heat 1 tablespoon olive oil in a heavy frying pan on _high_ heat and let it get very hot, about 45 seconds. Add the beans and sauté, stirring often, for 2 minutes. Add 1 clove minced garlic and sauté for 1 minute more. Season with salt, pepper, and some dried basil or oregano. _Serves four._
#### **Mushrooms**
America is finally waking up to the world of mushrooms. Wild mushrooms, such as shiitake, porcini, oyster, and even morel, are becoming popular in home kitchens. And with good reason, for their earthy taste can earn them a starring role in many intriguing recipes. Or they can be served as a side dish. Even the common button mushroom can enhance a recipe significantly.
**Freshness**
Mushrooms shouldn't have any slimy spots or other signs of decay. The membrane under the cap should be attached to the stem. Button mushrooms that are just slightly brown are fine for sauces, but only the freshest should be eaten raw in salads. _All_ wild mushrooms should be cooked through before eating.
**Preparation**
Trim the stems of the mushrooms. Unless the tops have bits of dirt on them, they should not be cleaned. If there is dirt, brush it off or wipe the caps with a slightly damp cloth or paper towel. Never immerse the mushrooms in water. For most recipes, mushrooms are cut lengthwise into thin slices.
**Portion Size**
¼ pound per person.
**Cooking**
Do not boil or steam mushrooms.
**To sauté:** Heat 3 tablespoons butter, margarine, or oil in a large (non-iron) frying pan over _medium-high_ heat until hot, about 45 seconds. Add 1 pound sliced mushrooms and cook, stirring occasionally, until they are soft and lose their moisture, about 8 minutes. Mushrooms shrink considerably during cooking.
**About Dried Mushrooms**
Italian porcini, French morel, and several different kinds of Chinese mushroom are available dried. To use these intensely flavorful fungi, simply let them soak in a small bowl of lukewarm water for an hour or so, until they are soft. Remove the mushrooms. Strain the liquid through a layer of cheesecloth or a fine-mesh strainer, then let the mushrooms sit for a minute on some paper towels before using. For extra flavor, add some of the strained soaking liquid to the recipe you are preparing.
#### **Peas**
Besides being a real delicacy, fresh peas can also keep the kids busy. Have them shell the peas while you prepare the rest of the meal.
**Freshness**
The pods should be a deep green color. Before purchasing, snap one open and make sure the peas inside are glossy and full, and taste fresh and sweet.
**Preparation**
Shell the peas. Do not rinse before cooking.
**Portion Size**
About ¾ pound per person (weighed before shelling).
**Cooking**
**To boil:** For peas with a bite to them, boil for 6 minutes. Boil 8 minutes for softer peas.
**To microwave:** For ½ pound of shelled peas, microwave for 3 minutes, stirring once.
**Serving**
Serve peas with a pinch of salt and pepper, or an optional dot of butter.
**In the Pod**
Sugar snaps and snow peas are very popular with the kids. In both cases the whole pod is eaten. Before cooking, snap off the stem and peel away the string that runs along the length of the pod. Snow peas are available all year. Sugar snaps are one of the first vegetables harvested and show up for a short time in the beginning of the summer. Both need only a quick cooking, either blanched, steamed, or sautéed for 2–3 minutes.
**Peas with Cream & Almonds**
In a medium frying pan, melt 2 tablespoons butter on _medium_ heat. Add ¾ pound fresh peas and ¾ cup heavy cream. Cook until the peas are soft and the cream thickens, about 10 minutes. Stir in 1½ tablespoons sugar and ¼ cup slivered almonds. _Serves four._
#### **Spinach**
Popeye notwithstanding, kids don't often take to spinach. Nevertheless, it's extremely nutritious, a cinch to prepare, and tastes good to most adults.
**Freshness**
Spinach is most often sold prewashed in 1-pound plastic bags or not very well washed in tied bundles. Avoid bags or bundles with leaves that are dark and moist or yellowed.
**Preparation**
Pinch off the stems and put the leaves in a large bowl filled with cold water. Swish the leaves around and lift them from the water into a colander set in the sink. Pour out the water from the bowl, rinse out any grit that has collected on the bottom, and fill the bowl again with cold water. Return the spinach to the bowl and swish it around again. Then lift out the leaves and shake off the excess water. It is now ready for cooking. Packaged "prewashed" spinach needs to be rinsed only once.
**Portion size**
A generous ¼ pound uncooked spinach per person.
**Cooking**
**To boil:** Put the spinach in a large, heavy-bottomed pot with a tight-fitting lid. Do _not_ add water. The water remaining on the leaves from washing will be enough to cook the spinach. Cover the pot and turn the heat to _medium low_. Cook for about 6 minutes, until all the leaves are wilted. Turn the spinach a couple of times with tongs while it is cooking to keep the bottom leaves from burning.
**To microwave:** For 1 pound of spinach, microwave for 6–8 minutes, stirring twice.
**Serving**
Transfer the spinach to a colander to drain. Serve immediately with a light seasoning of salt and pepper.
**Spinach with Cheese**
Cook 2 pounds spinach, drain it well, and chop finely. Put the spinach in a medium bowl and stir in ¼ cup heavy cream, ¼ cup milk, 1 beaten egg, 1 teaspoon salt, and a pinch of nutmeg. Transfer to a buttered pie plate. Top the mixture with ¼ pound grated cheddar or mozzarella. Bake in a preheated 350°F oven for 20 minutes, until the cheese melts and the spinach is warm. _Serves four._
#### **Zucchini**
The thinnest zucchini are best. Kids may not eat them plain, but mixed with tomato sauce and sprinkled with Parmesan, they become a popular side dish.
**Freshness**
Zucchini should be very firm with no scrapes or bruises.
**Preparation**
Zucchini need to be rinsed well. Rub them with your hand to get rid of stubborn fuzz and grit. Trim both ends and cut into ½-inch rounds. Or slice lengthwise into quarters and cut into 3-inch sticks.
**Portion Size**
1 small zucchini per person.
**Cooking**
Do not boil zucchini.
**To steam:** Steam for 6–8 minutes.
**To microwave:** For 3 small zucchini, in ¼-inch slices, microwave for 2½ minutes, stirring once.
**To sauté:** Heat 2 tablespoons olive oil in a heavy frying pan on _high_ heat until it gets hot, about 30 seconds. Add the zucchini and sauté, stirring and turning often, until soft but still crunchy, about 5 minutes. Add 1 minced garlic clove and sauté for 1 minute more.
**Serving**
Sprinkle zucchini with a pinch of salt and pepper and some grated Parmesan cheese, if desired.
**Zucchini & Tomatoes**
Preheat the broiler. Heat 2 tablespoons olive oil over _high_ heat in a heavy ovenproof frying pan large enough to accommodate all of the zucchini (it all needs to touch the surface of the pan) for about 45 seconds. Add 1 finely chopped medium onion and sauté for 2 minutes, stirring often. Add ¾ pound zucchini cut into ½-inch rounds and sauté for 5 minutes. Add 1 minced garlic clove and cook for 1 minute. Add a 14-ounce can of drained whole tomatoes, roughly chopped. Cook for an additional 5 minutes. Turn on the broiler. Stir 1 teaspoon each of dried oregano, basil, and salt into the vegetable mixture. Sprinkle with ¼ cup grated Parmesan cheese. Cook under the hot broiler for 2 minutes. _Serves four._
## Two Fancy Dinners
After just a bit of culinary cross-training, when your knives and sauté pan seem more like friends than strangers, you're ready to prepare a really special meal. Whether it's Mom's birthday, your wedding anniversary, or a promising first date, either of these elegant meals is sure to create a dramatic impression. First, some timely advice for smooth moves in the kitchen.
• Do as much as you can the night before so you can have a few minutes to enjoy the pre-dinner wine and conversation. Lists of what can be prepared and stored ahead of time are noted for each menu.
• Photocopy the recipes and tape them to the refrigerator or a cabinet where they're easy to see.
• Go over the list of tasks that must be done just before serving so you don't forget any of them. Stay cool. The last thing you want to do during a romantic evening is to be jumping up and down like a jack-in-the-box.
* * *
**A Light Summery Supper**
These are foods you wouldn't want to share with just anyone. The tortellini is a light, festive starter. The fresh herbs add character to the salmon. Start your meal at sunset and you'll be savoring the airy strawberry mousse by the light of the midsummer moon. A glass of _eau de poire_ would be a perfect ending to this meal.
##### **The Timetable**
**The Night Before**
• Make the strawberry mousse.
• Refrigerate the wine.
**2 Hours Before**
• Chop the carrot, celery, and onion for the wild rice.
• Make the prosciutto and tomato cream sauce.
• Purée the herbs, shallot, garlic, olive oil, and mustard; mix together with the bread crumbs, salt, and pepper for the salmon, and set aside.
• Arrange the salmon fillets on a baking sheet and coat thickly with the herb mixture. Cover the pan loosely with plastic wrap and refrigerate.
• Make the salad dressing (see page 164).
• Wash and dry the mixed greens for the salad and refrigerate in a plastic bag.
• Halve grapes for the wild rice.
• Set the table.
**1 Hour Before**
• Cook the wild rice.
• Bring a pot of water to a boil for the pasta.
• Preheat the oven to 325°F.
• Prepare the broccoli for steaming by cutting it into florets and placing them in the steamer. If microwaving the broccoli, place the florets in a bowl with a few tablespoons of water and cover with plastic wrap.
• Set up your coffeemaker so it is ready to go.
**To Start the Dinner**
• Check the wild rice. When it's done, turn off the heat, add the grapes, and leave the pot covered until you're ready to serve.
• Put the tortellini in the boiling water. Reheat the sauce over _low_ heat. When the tortellini is done, top with the sauce, sprinkle with parsley and Parmesan, and serve.
• Pour the wine.
• Before you sit down for the first course, take a moment to place the salmon in the oven and set the timer for 12 minutes.
• Start steaming or microwaving the broccoli.
• Finish the first course.
**To Serve the Main Course**
• When the timer rings, remove the salmon from the oven and place 1 fillet on each dinner plate.
• Spoon on the wild rice, arrange some broccoli florets alongside, and serve.
**For the Salad**
• After you've finished the main course, it's fine to take a few minutes to throw the salad together.
• Arrange the greens on salad plates and sprinkle on the dressing.
• Turn on coffeemaker or put on water for tea.
**For Dessert**
• Place a few whole strawberries on top of the mousse and serve.
• Finish making coffee or tea and serve.
**MENU**
**Appetizer**
Chicken tortellini with prosciutto & Tomato cream sauce
**Main Course**
Baked salmon with herb crust
* * *
Wild rice with grapes
* * *
Steamed broccoli
* * *
Mixed green salad
* * *
Sourdough bread
**Dessert**
Strawberry mousse
**Wine**
California Chardonnay, French Muscadet, or Beaujolais
* * *
* * *
The Table Setting
This is a fancy table setting for a formal dinner, but why not do it up royally? If you are not serving soup or salad, simply leave out those pieces of tableware.
#### **Chicken Tortellini with Prosciutto & Tomato Cream Sauce**
**Ingredients** _(serves two)_
_2 tablespoons olive oil_
_2 cloves garlic, minced_
_2 ounces prosciutto, chopped_
_⅔ cup canned crushed tomatoes_
_¼ cup frozen peas_
_½ cup heavy cream_
_Salt and pepper_
_8 ounces fresh chicken tortellini (see Note)_
_Chopped parsley, for garnish_
_Grated Parmesan_
**Equipment**
_Medium sauté pan_
_Pasta pot_
_Colander_
**1.** Place a medium sauté pan on _medium-high_ heat and let it get hot, about 30 seconds. Add the oil and garlic and sauté for 1 minute. Add the prosciutto and sauté 1 minute more.
**2.** Add the crushed tomatoes and peas, reduce the heat to _medium,_ and simmer for 10 minutes.
**3.** Increase the heat to _high_ and add the cream. Cook until the cream reduces, about 1–2 minutes. Season with salt and pepper and remove from the heat.
**4.** Bring a pot of water to a boil for the pasta. Add the tortellini, and stir to make sure none are stuck together. Boil for 3–5 minutes, until cooked through, then drain in a colander.
**5.** If necessary, reheat the sauce over _medium_ heat and pour it over the tortellini. Top with chopped parsley and grated Parmesan.
**Note**
If chicken tortellini isn't available, substitute another kind of tortellini.
#### **Baked Salmon with Herb Crust**
Because of the thick coating of herbs, this salmon doesn't need a sauce. Cooking it slowly at a low temperature keeps it moist.
**Ingredients** _(serves two)_
_1 cup fresh parsley leaves_
_4 scallions, green part only_
_¼ cup fresh basil leaves or 1 teaspoon dried_
_6 stalks fresh chives or ½ teaspoon dried_
_2 shallots, peeled_
_1 clove garlic, peeled_
_¼ cup olive oil, plus extra for oiling the baking sheet_
_3 tablespoons plain bread crumbs_
_1 teaspoon Dijon mustard_
_Salt and pepper_
_2 salmon fillets (about 8 ounces each)_
**Equipment**
_Food processor or blender_
_Medium bowl_
_Baking sheet_
_Aluminum foil_
_Rubber spatula_
**1.** Preheat the oven to 325°F.
**2.** Place the parsley, scallions, basil, chives, shallots, garlic, and ¼ cup olive oil in a food processor or blender and process until smooth.
**3.** Transfer the mixture to a medium bowl and stir in the bread crumbs, mustard, and season with salt and pepper.
**4.** Line a baking sheet with aluminum foil and oil the foil lightly. Arrange the salmon fillets on the foil. Using a rubber spatula, spread a thick coating of the herb mixture over the fish, making sure the fillets are covered right to the edge.
**5.** Bake the fish on the center rack of the oven until it flakes when pricked with a fork, 12–15 minutes. Serve immediately.
#### **Wild Rice with Grapes**
The simple addition of grapes turns wild rice into a special side dish.
**Ingredients** _(serves two)_
_2 tablespoons vegetable oil_
_1 carrot, diced_
_1 rib celery, diced_
_1 small onion, diced_
_½ cup wild rice_
_1 bouillon cube_
_½ cup green seedless grapes, cut in half lengthwise_
**Equipment**
_Medium saucepan with cover_
_Slotted spoon_
**1.** Place a medium saucepan on _medium-high_ heat and let it get hot, about 30 seconds. Add the oil and the diced carrot, celery, and onion, and sauté until soft, about 5 minutes.
**2.** Add the wild rice and cook, stirring constantly, until the rice is hot, about 1 minute.
**3.** Add 1½ cups water and the bouillon cube, and bring to a boil. Stir the rice, cover the pan, and reduce the heat to _low._ Simmer for 45–55 minutes, until the rice is cooked through.
**4.** Turn off the heat, add the grapes, stir, and cover until ready to serve. Serve with a slotted spoon in case there is any excess water.
#### **Strawberry Mousse**
Much easier than most mousse recipes, this one requires no cooking.
**Ingredients** _(serves four)_
_2 quarts fresh strawberries_
_1 cup sugar_
_¼ cup fresh lemon juice_
_1 cup heavy cream_
_½ cup amaretto liqueur_
_Whites of 4 large eggs_
**Equipment**
_2 large bowls_
_Food processor or blender_
_2 medium bowls_
_Hand-held electric mixer_
**1.** Set aside a few whole strawberries for garnish. Wash, hull, and cut up the remaining strawberries and put half of them into a food processor. Add the sugar and lemon juice and purée the mixture, transfer to a large bowl, then add the rest of the berries and purée the second half. Add that to the bowl of purée.
**2.** In a medium bowl, using a hand-held electric mixer set on medium-high speed, whip the cream until soft peaks form. Beat in the amaretto, then gently fold into the puréed strawberries.
**3.** In another medium bowl, beat the egg whites on medium-high speed until stiff. Gently fold the egg whites into the strawberry mixture.
**4.** Cover the mousse with plastic wrap and refrigerate for at least 2 hours or overnight. Garnish with the reserved strawberries.
**Variation**
Replace 1 quart of the strawberries with 1 quart raspberries.
**Special Touch**
One finishing touch for an elegant table setting is a specially folded napkin. It's fairly simply and will let your guest know that she's not getting the Blue Plate Special. Use square cloth napkins made of heavy cotton or linen.
The "Quick Snap" is a simple triangular fold that every busperson learns early in his or her career.
**1.** Fold the napkin in quarters.
**2.** Fold it into a triangle.
**3.** Grasp the napkin in the center of the long side, placing your thumb on the bottom. Place your index finger and middle fingers, which are on the top side of the napkin, on either side of your thumb (like a modified fastball grip).
**4.** With a quick snap of the wrist, shape the napkin into a triangular tent and place it on the dinner plate.
* * *
**Wine Primer**
Whether you're entertaining at home or dining at a four-star restaurant, you'll want to be able to choose an appropriate wine to drink with your meal. On the next pages you'll find information to help you make your choice. The best way to choose wine, however, is to find a local wine shop with a large stock, steady turnover, and a helpful salesperson. The days of snobby, effete wine merchants are over. They are, almost without exception, extremely enthusiastic about wine and anxious to share their knowledge. Tell the salesperson what you're serving, what you've liked and not liked about wines you've had before, and how much you want to spend. With a little help, you're sure to wind up with one or more special bottles of wine.
The simplest way to begin thinking about wine is to classify it into two groups: hearty, well-rounded, full-bodied wines and lighter, crisper wines. Wines in both groups differ subtly in taste and wildly in price. The labels chosen here are ones that are widely available and of consistent quality. Your local merchant may have access to certain smaller or more obscure labels or know of new labels that offer great taste and real value.
#### **California**
California vineyards name their wines not after the region or vineyard where they're grown (as is the custom in France), but after the predominant grape used in making the wine. These are the most popular varieties.
The print edition of this book includes wine charts for **Wine Primer**.
Please download a PDF of the charts here: workman.com/ebookdownloads
##### **White Wines**
##### **Red Wines**
##### **Rosé Wines**
#### **France**
Understanding the nuances of French wine is very complicated. There are many different vineyards in Bordeaux and Burgundy and each produces wines of varied tastes and finishes. However, you can count on certain wines to deliver distinctive tastes; full-bodied and light/crisp are the differentiating characteristics used here.
##### **White Wines**
##### **Red Wines**
**Wine Tip**
Much is made of the rule, "Red wine with meat, white with fish or chicken." And you certainly would not serve a _grand cru_ red Bordeaux with fillet of sole, nor a light Frascati with roast lamb. But some of the lighter and fruitier reds, such as Beaujolais, Barbera, or Valpolicella, are fine for roast chicken or grilled fish. And some of the heartier whites, such as a white Burgundy, will stand up to a veal chop.
#### **Italy**
Italy is known for its dry, crisp white wines and large, powerful reds. Of course there's also a lot of wine in between, like Barberas and Dolcettos, which are both light and fruity Italian reds. While the giant Italian wine labels that are distributed in grocery stores and less distinguished liquor stores may be unsatisfying, in a better wine shop you are bound to discover some wonderful Italian wines that rival the best of France and California.
##### **White Wines**
##### **Red Wines**
**Wine Bargains**
There are lots of very decent whites and reds in the $5 to $6 price range. Some are simply called "table wines" and can vary greatly in quality. Others are from some of the newer wine-producing countries such as chile, Australia, and New Zealand. Ask your local wine merchant for his recommendations. Then take home four or five different wines and try them out. You really will taste the differences. The one you like most may even be the cheapest. Once you've found your favorite, pick up a case.
* * *
**A Hearty Meal with a Mediterranean Flavor**
To be alone together is cause for celebration and would make almost any menu a success. But this one with its earthy Mediterranean flavors and its balance of sweet and savory tastes makes it a meal to linger over and remember.
##### **The Timetable**
**The Night Before**
• Prepare the poached pears. Remove them from the liquid after they are cool and refrigerate.
• Make sure you have the wine you need.
**2 Hours Before**
• Mince the shallots for the beef recipe and refrigerate in a bowl covered with plastic.
• Stem and slice the mushrooms and seed and slice the red pepper for the beef recipe.
• Make the salad dressing (page 164).
• Wash and dry the mixed greens for the salad and refrigerate them in a plastic bag.
• Assemble the prosciutto and melon or mozzarella and tomato on individual appetizer plates, wrap loosely in plastic, and refrigerate.
• Peel, cut, and blanch the potatoes and drain them in a colander. Arrange the potatoes in the baking dish along with the garlic cloves, rosemary, and butter. Season with salt and pepper.
• Set the table.
**1 Hour Before**
• Open the red wine.
• Preheat the oven to 450°F for the potatoes.
• Cook the beef tenderloin through Step 4.
• Remove the appetizer from the refrigerator and let it come to room temperature.
• Put the potatoes in the oven.
• Set up your coffeemaker so it's ready to go.
• Remove the pears from the refrigerator and let them come to room temperature.
**To Start the Dinner**
• Place the appetizer on the table.
• When the potatoes are done, turn off the heat and leave the oven door closed until you're ready to serve the main course.
• Finish the first course.
• Pour the wine.
**To Serve the Main Course**
• Return the vegetables and meat to the pan and reheat.
• Transfer the meat and vegetables to dinner plates and spoon on the sauce.
• Add the potatoes and serve.
**For the Salad**
• When you've finished the main course, arrange the greens on salad plates and sprinkle on the dressing.
• Turn on the coffeemaker or put on water for tea.
**For Dessert**
• Arrange the poached pears and ice cream on plates. Spoon on the berries and orange liqueur and serve.
• Finish making coffee or tea and serve.
**MENU**
**Appetizer**
Melon & prosciutto or mozzarella with tomato & fresh basil
**Main course**
Fillet of beef with wild mushrooms
* * *
Oven-roasted potatoes with rosemary & whole garlic cloves
* * *
Mixed green salad
* * *
Crusty French bread
**Dessert**
Poached pears with vanilla ice cream & orange liqueur
**Wine**
French Burgundy or Bordeaux, or California Merlot
* * *
* * *
#### **Melon & Prosciutto**
**Ingredients** _(serves two)_
_2 2-inch wedges cantaloupe, honeydew, or Crenshaw melon_
_⅓ pound prosciutto or Black Forest ham, thinly sliced by the butcher_
_2 lime wedges_
**1.** Cut the flesh from the rind of the melon and brush off any seeds.
**2.** Lay the 2 pieces of melon on a serving plate and drape with the slices of prosciutto.
**3.** Serve with a wedge of lime on each side of the plate.
#### **Mozzarella with Tomato & Fresh Basil**
**Ingredients** _(serves two)_
_½ pound fresh mozzarella_
_1 large vine-ripened tomato_
_6 fresh basil leaves_
_Extra-virgin olive oil_
_Salt and freshly ground black pepper_
**1.** Cut the mozzarella into 6 slices.
**2.** Cut the tomato into 6 slices.
**3.** Rinse the basil and pat dry with a paper towel.
**4.** Arrange 3 slices of tomato on each of 2 plates. Lean the slices of mozzarella on the tomato. Lay a basil leaf on each slice of mozzarella.
**5.** Drizzle on the olive oil and sprinkle with salt and freshly ground black pepper.
**The Triple Fold**
This special napkin has a pocket where you can slip a little note, a rose, two tickets to the opera or a professional wrestling match, or whatever seems appropriate.
**1.** Fold the napkin in quarters.
**2.** Arrange the napkin so the free corners are in the upper right.
**3.** Roll down the first layer to just past the center of the napkin.
**4.** Fold down the second layer and tuck the point under the first fold.
**5.** Fold down the third layer and tuck the point under the second fold. Make sure the 3 bands are of equal size.
**6.** Fold under the right and left sides.
**7.** Place the napkin just to the left of the fork(s).
#### **Fillet of Beef with Wild Mushrooms**
The earthy flavor of the mushrooms complements the subtle flavor of the beef. Buy your fillet at a high-quality meat market.
**Ingredients** _(serves two)_
_3 tablespoons olive oil_
_⅓ pound shiitake mushrooms, stems discarded, caps cut into ¼-inch slices_
_1 red bell pepper, seeded and cut into strips_
_3 shallots, minced_
_2 tablespoons butter_
_½ pound beef fillet, cut into ⅔-inch-thick slices_
_⅓ cup white wine_
_⅓ cup Marsala_
_1 beef bouillon cube_
_Salt and pepper_
_Chopped parsley, for garnish_
**Equipment**
_Large sauté pan_
_Medium bowl_
**1.** Place a large sauté pan on _medium-high_ heat and let it get hot, about 45 seconds. Add the olive oil, mushrooms, and bell pepper, and sauté, stirring often, until they are almost tender, about 4 minutes. Add the shallots and sauté 3 minutes more, stirring frequently.
**2.** Transfer the vegetables to a medium bowl and return the pan to the stove. Increase the heat to _high_ and add the butter.
As soon as the butter stops foaming, add the slices of tenderloin.
**3.** Brown the meat quickly, about 2 minutes on each side, then transfer to a plate.
**4.** Add the white wine, Marsala, and bouillon cube to the pan and reduce until the liquid is almost entirely evaporated, about 3 minutes.
**5.** Return the vegetables and meat to the pan. Cook just long enough to reheat the meat and vegetables, 1–2 minutes, turning the meat a few times. Season with salt and pepper, if desired. Serve immediately, pouring the pan juices over the meat. Garnish with parsley.
#### **Oven-Roasted Potatoes with Rosemary & Whole Garlic Cloves**
**Ingredients** _(serves two)_
_Olive oil, for greasing the pan_
_2 medium-sized baking potatoes_
_8 cloves garlic, unpeeled_
_1 teaspoon chopped fresh rosemary or a pinch of dried_
_2 tablespoons butter, cut into small pieces_
_Salt and pepper_
**Equipment**
_Medium saucepan_
_9 x 9-inch baking pan_
_Colander_
**1.** Preheat the oven to 450°F.
**2.** Fill a medium saucepan halfway with water and bring to a boil over _high_ heat.
**3.** Lightly grease a 9-inch square baking pan with the olive oil.
**4.** Cut the potatoes in half lengthwise. Cut each half into 4 wedges.
**5.** When the water boils, add the potatoes and blanch for 3 minutes.
**6.** Drain the potatoes well in a colander and transfer to the prepared baking pan.
**7.** Trim the nibs off the top of the garlic cloves (but do not peel them), and add the cloves to the potatoes. Sprinkle on the rosemary and dot with butter. Season with salt and pepper.
**8.** Bake in the center of the oven for 15 minutes. Turn the potatoes and bake for 15 minutes more or until browned all over and cooked through.
#### **Poached Pears with Vanilla Ice Cream & Orange Liqueur**
A simple yet elegant dessert that makes a fitting ending to a special meal. This recipe makes 4 pears, so that you can choose the 2 best ones for this dinner and save the others.
**Ingredients** _(serves four)_
_4 Bosc pears_
_Approximately 1 bottle fruity red wine, such as Beaujolais or Zinfandel_
_1 cup sugar_
_Approximately 1 cup water_
_1 teaspoon vanilla extract_
_1 pint best-quality vanilla ice cream_
_½ pint whole raspberries, blueberries, or sliced strawberries_
_4 tablespoons orange liqueur_
**Equipment**
_Medium saucepan_
_Vegetable peeler_
_Ice cream scoop_
**1.** Gently peel the pears, leaving the stems intact.
**2.** Combine the remaining ingredients through the vanilla extract in a medium saucepan and bring to a boil over _high_ heat, stirring to dissolve the sugar. Reduce the heat to _medium_ and place the pears in the pan.
**3.** Cover the pan and poach the pears until they are slightly soft, about 20 minutes. Remove the pan from the heat and let the pears cool in the poaching liquid, about 20 minutes.
**4.** Arrange the two best-looking pears and the berries on individual dessert plates and accompany with a scoop of ice cream. Pour 2 tablespoons of orange liqueur over the berries and serve.
**Note**
Leftover pears should be removed from the poaching liquid and refrigerated in a plastic container. They should last for about 2 days.
## Salads
Salad can be as simple as a plate of leafy lettuce with balsamic vinegar and olive oil, or as complex as salad Niçoise with its eight-plus ingredients, or anything in between. There are really only two things that are essential to a successful salad: good fresh greens and a tasty dressing.
The versatile salad can be created out of almost any vegetable, raw or cooked, as well as poultry, fish, fruit, pasta, smoked meats, and a myriad of dressings. Served with a hunk of bread, some salads can be an entire meal.
Dad shouldn't overlook the benefits of getting the kids to eat even a small plate of leafy green lettuce with dinner. It's a great source of calcium and will get them started eating healthy foods.
* * *
**The Basic Salad**
Greens can be prepared several hours ahead of time. Wash and pack them in plastic bags with a few sheets of paper towel to absorb the excess water.
For a salad with interesting colors and flavors, mix lighter leaves with darker ones and bitter salad greens with milder leafy ones. There is no exact formula to the basic salad, but figure on mixing in about half as many bitter greens as milder. There is also a wide assortment of packaged, pre-washed salad greens. Arugula and watercress stand nicely alone as the sole green in a salad. A combination of complementary greens with a good vinaigrette dressing makes a sophisticated salad, or greens can form a base for any of the vegetables on pages 162–.
**The Salad Spinner**
The salad spinner is one of the greatest kitchen innovations of all time. It lets you rinse and dry greens with minimal work, which means a nutritious salad is never more than a few minutes away.
**1.** Discard any outside leaves that are tough or have brown spots.
**2.** To separate the leaves, cut across the base about 2 inches from the bottom.
**3.** Run each leaf briefly under cold water to wash off grit.
**4.** Tear the leaves into 1½- to 2-inch pieces and put the pieces in the spinner.
**5.** Fill the spinner with cold water and swish the leaves around. Remove the basket and let the water drain out. Pour out the water in the base of the spinner, reinsert the basket of lettuce and spin until dry. Transfer the greens to a salad bowl. If your spinner doesn't have a removable basket, rinse the greens first in a large bowl of cold water, then transfer to the spinner and spin dry.
The print edition of this book includes charts called **Leafy Lettuces** and **Bitter Salad Greens**.
Please download a PDF of the charts here: workman.com/ebookdownloads
##### **Leafy Lettuces**
##### **Bitter Salad Greens**
Once you've chosen your greens (see chart), you can build a salad with any number of vegetables, from the "garden variety" carrots and tomatoes to the more exotic fennel. Most vegetables can be prepared well in advance, but mushrooms, avocados, fennel, and endive should be sliced just before serving the salad, as they turn brown quickly. Dress the salad just before you serve it, tossing so that all the ingredients are coated.
##### **Avocados**
This vegetable-like fruit has smooth, mild flesh that complements the crunchy components of a salad and soaks up the flavors of the dressing. Choose avocados that yield to gentle pressure. Peel, then cut in half, twisting the halves around the pit to release them. Slice crosswise or cube.
##### **Bell Peppers**
Thin strips of bell pepper add crunch to a salad. The red, orange, and yellow varieties add vivid color.
##### **Broccoli**
Florets of broccoli complement any salad containing meat or poultry. Cut the florets into pieces small enough to eat in 1 bite. To tenderize broccoli slightly, blanch (boil for 1 minute), then drain and cool under cold water.
##### **Carrots**
Peel first, then either grate, slice into thin rounds, or continue peeling and let the slivers fall into the salad bowl. Carrots with green tops are apt to be less woody than the packaged variety.
##### **Celery**
Kids relish the familiar flavor of celery in salads. Use the mild inner stalks, if possible, and slice very thin. Cut through a stalk lengthwise, then cut into ⅛-inch pieces.
##### **Cucumbers**
Look for the thinnest, firmest ones, preferably unwaxed. Peel (if waxed) and slice thinly for salad. If they are very large, cut lengthwise and scrape out the seeds with a spoon before slicing.
##### **Fennel**
This is a bulb similar to celery, but it is rounder and has a slight licorice flavor that makes a piquant addition to a salad. Trim the bottom, then trim the stalks to within about ¾ inch of the bulb and cut the bulb in half lengthwise. Cut crosswise into thin slices for salad.
##### **Mushrooms**
For salad, use button mushrooms. They should be very white, and the membrane connecting the cap and stem should be intact. Trim the stem, and slice the cap thinly just before serving, as mushrooms brown quickly. Do not use wild mushrooms in a raw salad as they must be cooked before eating.
##### **Radishes**
With their deep red skin and refreshingly peppery flavor, radishes can perk up a common salad. Slice them as thin as possible they are almost transparent.
##### **Red Onion**
Essential for a Greek salad. Peel, cut in half, and slice thinly. Wrap the remainder tightly in plastic and refrigerate. Look for firm onions with dry skin and no sprouting green shoots.
##### **Scallions**
(aka green onions) Many people feel scallions are essential to a good salad because they cut the vinegar and add a sharpness to the very mild taste of lettuce.
Wash and remove the small roots from the end. Chop the white bulb and green stalks for salad.
##### **Snap & Snow Peas**
Either can be included raw in a salad. Peel away the strings and rinse well. Do not buy peas if they are limp or pale.
##### **Tomatoes**
Use only vine-ripened tomatoes in salads. Off-season, your best bets are ripe plum tomatoes, cherry tomatoes, or the Israeli or Latin American tomatoes. Avoid packaged tomatoes and the generic, pale red tomatoes, sold as "slicing tomatoes," as they are mealy and tasteless. Nothing matches the taste of local farm stand tomatoes allowed to ripen on the vine, so grab them whenever you can (they're usually around between July and September).
##### **Zucchini**
Use only small, thin zucchini for salad. Wash well, rubbing off any stubborn dirt or fuzz. Trim the ends and cut into paper-thin slices.
**What to Buy**
Supermarkets like to pretend that vegetables have no seasons. They feel it is better to have tasteless waxed cucumbers at exorbitant prices in the middle of winter than not to have them at all. Increasingly though, you can get some tasty fresh produce—tomatoes from Israel and avocados from California or Florida—year round. You still need to shop with discretion, however. As a general rule all greens should have crisp, deeply colored leaves with no brown or soft spots or other signs of decay. Cucumbers must be firm; tomatoes should be firm (but not hard) and richly colored; carrots should be sprout-free. The maxim that great ingredients make great cooks is most true when it comes to making salad.
* * *
**The Basic Dressing**
There are some decent bottled vinaigrettes that you should keep on hand for use in a pinch, such as Newman's Own and Blanchard & Blanchard. But once you learn how easy it is to make your own dressing, the bottled ones may not seem as appealing. Remember dressing is meant to enhance the flavor of the salad, not smother it. Create salads with interesting and diverse flavors and dress them sparingly.
##### **Olive Oil**
The recent surge of interest in olive oil in the United States elevated this rustic food to a lofty status, with connoisseurs touting the virtues of oil costing upwards of $20 a bottle. While there are subtle distinctions among oils, you need not spend exorbitant sums to get a flavorful one.
You should, however, buy only "extra-virgin" olive oil to use on your salads. "Extra-virgin" comes from the first pressing of the olives and is, therefore, the purest and most flavorful oil. Subsequent pressings, designated superfine, fine, virgin, pure, or simply olive oil, are perfectly suitable for use in cooking. In fact, the subtle flavor of finer olive oils is lost at high temperatures. Olive oil does eventually become rancid, so store it in a cool, dry place and buy only as much as you can use in 6 months. In hot weather olive oil should be stored in the refrigerator. It will get cloudy and thick, but returns to normal when brought to room temperature.
##### **Vinegar**
The two kinds of vinegar most commonly used to make vinaigrette are red wine vinegar and white wine vinegar. Though most brands of vinegar look alike, they do have distinct differences in taste due to subtle differences in acidity. Try a few brands until you find one you like. Other kinds of vinegar include:
• Balsamic vinegar, imported from Modena, Italy, is aged in barrels made of different kinds of wood. Its rich, pungent, slightly sweet flavor lends a distinctive taste to any salad.
• Champagne vinegar is made from Champagne and has a slightly milder and sweeter flavor than white wine vinegar.
• Herb-infused vinegars are made by steeping herbs, such as tarragon, chives, basil, or dill, in vinegar.
• Fruit vinegars, such as raspberry or strawberry, are slightly sweet. These are especially well suited for dressing fruit salads.
• Rice vinegar is made from fermented rice and is a frequent ingredient in a number of Eastern cuisines.
##### **Dad's Own Vinaigrette**
Because it is light, this basic vinaigrette enhances the salad. Heavier, gloppier dressings tend to swamp the delicate taste of interesting greens.
As a general rule, use one part vinegar to three parts oil.
**Ingredients** _(dresses a salad for eight)_
_¼ cup red or white wine vinegar (or balsamic vinegar)_
_1–2 cloves garlic, minced_
_1 teaspoon Dijon mustard_
_Salt and pepper to taste_
_¾ cup olive oil_
**Equipment**
_Medium bowl_
_Whisk_
**1.** Combine all the ingredients except the oil in a medium bowl, and whisk for 15 seconds.
**2.** Add the oil in a slow, steady stream, whisking continuously until it is incorporated into the dressing.
**3.** Whisk again before using to recombine the oil and vinegar.
**Variations**
• **Basil dressing** Gently whisk ¼ cup chopped fresh basil leaves into the dressing after the oil is incorporated. This dressing is excellent on a fresh tomato salad.
• **Poppy seed dressing** Add 2 tablespoons sugar, 1 large egg, and 3 tablespoons poppy seeds to the vinegar mixture and whisk until smooth; then add the oil. This dressing is particularly good on spinach salad.
• **Lemon and tarragon dressing** Substitute ¼ cup freshly squeezed lemon juice for the vinegar in the basic vinaigrette. Gently whisk in 1 teaspoon chopped fresh or dried tarragon after the oil has been incorporated.
• **Anchovy dressing** Substitute ¼ cup freshly squeezed lemon juice for the vinegar, then add 2 anchovy fillets to the basic vinaigrette and purée. Use this dressing to make a great salad Niçoise.
• **Parmesan dressing** Gently whisk ⅓ cup freshly grated Parmesan into the basic vinaigrette after the oil has been incorporated.
• **Bacon and scallion dressing** Add 2 finely chopped scallions, 4 slices cooked and crumbled bacon, and 1 teaspoon bottled white horseradish to the basic vinaigrette and whisk until smooth. This dressing adds sparkle to a simple green salad.
**Tip**
Equal parts lemon juice can be used in combination with the vinegar in any of the vinaigrette recipes.
* * *
#### **Chicken Salad**
This old standby always seems to put the kids in a good mood and it doesn't take long to throw together, especially if you have a lot of leftover chicken. If you don't have any cooked chicken, allow a few hours for cooking and cooling a raw one.
**Ingredients** _(serves four)_
_3 cups cooked chicken or 1 4–5 pound whole chicken or 2–3 whole breasts_
_2 stalks celery, cut into ½-inch slices_
_1 medium red onion, chopped_
_¼ cup chopped fresh parsley_
**Dressing**
_¾ cup mayonnaise_
_2 tablespoons sour cream_
_1 teaspoon mustard_
_1 teaspoon dried basil_
_1 teaspoon dried thyme_
_1 teaspoon salt_
**Equipment**
_Large pot with cover_
_Medium bowl_
_Large bowl_
_Small bowl_
**1.** If using cooked chicken, skip the first 4 steps and proceed with Step **5.** If not, bring a large pot of water to a boil. Add the chicken. When the water returns to a boil, lower the heat to _medium_ and let the chicken simmer, partially covered, until the dark meat is just cooked through, about 1¼–1½ hours.
**2.** Transfer the cooked chicken to a medium bowl and let it cool, about 1½ hours.
**3.** When the chicken is cool enough to handle, peel the skin from the meat and discard it. Pull the meat from the bones, chop it into bite-sized pieces, and transfer it to a large bowl. (Be careful that no bones make their way into the bowl.)
**4.** Combine the dressing ingredients in a small bowl.
**5.** Add the celery, onion, and parsley to the chicken. Pour the dressing over the chicken and vegetables and toss.
**Tips**
• This salad can be stored for several hours in a tightly-covered plastic container in the refrigerator. Let the salad sit at room temperature for ½ hour before serving.
• Once it is dressed, chicken salad cannot be frozen. Cooked chicken, however, freezes very well. Cut it into bite-size pieces and freeze in an airtight bag for up to a month. Let the chicken defrost overnight in the refrigerator before using it in the salad.
**Variation**
Curried Chicken Salad: Add ½ cup coarsely chopped walnuts and ½ cup raisins to the chicken. Eliminate the mustard, basil, and thyme from the dressing and substitute 1 tablespoon curry powder.
#### **White Bean & Basil Salad**
This salad plays the part of coleslaw in Northern Italy where it is sold in most _salumerie,_ or corner delis. A really fine extra-virgin olive oil will enhance its flavor.
**Ingredients** _(serves four)_
_2 10-ounce cans cannellini beans, drained_
_1 red bell pepper, cut into short, thin strips_
_½ cup fresh basil leaves or 3 teaspoons dried_
_4 tablespoons extra-virgin olive oil, or more if needed_
_1 teaspoon salt_
_Freshly ground black pepper_
**Equipment**
_Food processor or blender_
_Medium bowl_
_Colander_
**1.** Put the beans in a colander and rinse them with cold water. Drain well and transfer to a medium bowl. Add the red bell pepper.
**2.** In a food processor or blender, combine the fresh basil with the olive oil and purée, adding more oil, 1 teaspoon at a time, if needed.
**3.** Pour the basil purée over the beans and peppers. If you're using dried basil, sprinkle it over the beans and then drizzle on the oil. Season with salt and pepper, then toss lightly.
#### **Greek Salad**
The feta cheese and olives are of Greek origin, but the salad itself is an American innovation. Feel free to add or subtract ingredients according to your family's tastes.
**Ingredients** _(serves four)_
_1 head Romaine, iceberg, or leaf lettuce, or a combination_
_¼ pound feta cheese_
_2 tomatoes, quartered_
_1 cucumber, peeled and sliced_
_½ cup black olives_
_1 4-ounce jar marinated artichokes, drained and quartered_
_5 peperoncini (hot peppers; optional)_
_½ small red onion, thinly sliced_
_Dad's Own Vinaigrette (page 165), made with red wine vinegar_
**1.** Wash and dry the lettuce well and tear into 1½-inch pieces. Place in a salad bowl.
**2.** Crumble the feta over the center of the lettuce. Arrange the tomatoes and cucumber around the edge of the bowl. Scatter the olives, artichokes, and peperoncini, if using, on top. Lay the onions over the cheese.
**3.** Present the salad at the table before adding the dressing sparingly, tossing, and serving.
#### **Caesar Salad**
The pungent dressing livens up this simple salad of Romaine lettuce.
**Ingredients** _(serves four)_
_1 large head Romaine lettuce_
_1 large clove garlic, minced_
_3 anchovy fillets, plus additional fillets for garnish, if desired_
_¼ cup white wine vinegar_
_2 tablespoons fresh lemon juice (from about 1 small lemon)_
_½ teaspoon Dijon mustard_
_½ teaspoon bottled white horseradish_
_½ cup olive oil_
_¼ cup grated Parmesan_
_4 tablespoons croutons, for garnish_
**Equipment**
_Medium bowl_
_Food processor or whisk_
**1.** Wash and dry the lettuce well, tear into 1½-inch pieces, and place in a salad bowl.
**2.** Combine all the remaining ingredients except the oil, Parmesan, and croutons in a medium bowl or in a food processor. (If using a bowl and whisk, the anchovies must be finely chopped.) Whisk or process the mixture until it is smooth, about 30 seconds. Add the oil in a slow, steady stream until it's completely incorporated. Add the Parmesan and mix briefly.
**3.** Just before serving, pour ⅔ of the dressing on the lettuce and toss until it is lightly coated. Add more dressing if needed.
**4.** Garnish with croutons and additional anchovy fillets (if using).
**Croutons**
Boxed croutons are fine, but making your own is a snap and they taste much better. Any stale bread will do, though day-old French bread is preferable. Preheat the oven to 375°F. Cut the bread into ½-inch cubes. In a medium bowl, whisk together ¼ cup olive oil, 1 clove minced garlic, ½ teaspoon dried oregano, ½ teaspoon salt, and some freshly ground black pepper. Add the cubes of bread and toss them until they are lightly coated with the oil mixture. Spread the cubes of bread on a baking sheet and bake, shaking the pan occasionally, until crisp and golden brown, about 5–8 minutes.
#### **Spinach Salad**
The key to this simple salad is using the freshest spinach you can find. Look for spinach that isn't prepackaged. If that's unavailable, examine the packaged spinach well for mushy leaves.
**Ingredients** _(serves six)_
_1 pound fresh spinach_
_10 strips bacon, cooked and broken into small pieces_
_2 scallions, chopped into thin rings_
_¼ pound button mushrooms, thinly sliced_
**Dressing**
_2 tablespoons lemon juice_
_2 tablespoons olive oil_
_¾ teaspoon salt_
_¾ teaspoon pepper_
_¼ teaspoon garlic salt_
_⅛ teaspoon dry mustard_
_¼ teaspoon sugar_
_1 tablespoon buttermilk_
**Equipment**
_Salad spinner_
_Small glass jar with cover_
**1.** Pinch off the stems of the spinach and rinse the leaves well under cold water before drying in a salad spinner.
**2.** Transfer the spinach to a salad bowl. Arrange the bacon, scallions, and mushroom slices on top.
**3.** Combine the dressing ingredients in a glass jar, cover, and shake well.
**4.** Drizzle the dressing over the salad, toss, and serve.
**Variation**
Add walnuts or sliced avocado, or if you have an adventurous palate, try adding Roquefort or other blue cheese.
#### **Waldorf Salad**
Legend has it that Oscar Tschirky, the noted maître d' of the Waldorf-Astoria Hotel in New York City, created this famous salad in the 1890s. It's best to compose Waldorf salad on individual plates.
**Ingredients** _(serves four)_
_2 heads Boston lettuce or 1 bunch leaf lettuce_
_2 ribs celery_
_2 apples, such as Granny Smith, McIntosh, or Golden Delicious_
_1 tablespoon mayonnaise_
_1 tablespoon plain yogurt_
_½ cup walnuts, coarsely chopped_
**Equipment**
_Salad spinner_
_Medium bowl_
**1.** Wash and dry the lettuce leaves in a salad spinner, tear them into pieces approximately 4 inches square, and divide them among 4 salad plates.
**2.** Cut the celery ribs in half lengthwise, then cut them into approximately ½-inch pieces. Peel, then cut the apples lengthwise into quarters. Trim off the core and cut each quarter lengthwise into thirds. Cut each wedge into approximately ½-inch pieces.
**3.** Put the celery and apples in a medium bowl and add the mayonnaise and plain yogurt. Toss. Add the chopped walnuts.
**4.** Spoon helpings of the salad mixture over the lettuce leaves on the salad plates.
#### **Carrot & Black Bean Salad**
This refreshing, colorful main course salad takes time (about two hours). The effort might be lost on the kids, but this salad makes a distinguished luncheon for friends. You can make the dressing and cook the beans and rice a day ahead of time and refrigerate.
**Ingredients** _(serves four)_
_¾ cup dried black beans, soaked overnight or for one hour in boiling water before cooking (or 16 ounces of canned black beans, drained and rinsed well)_
_1 cup brown rice_
_6 carrots_
_1 tablespoon plus 1 teaspoon olive oil_
_1 small red bell pepper_
_1 small green bell pepper_
_½ medium red onion_
_1 jalapeño pepper (optional)_
_½ cup pineapple juice_
_¼ cup freshly squeezed lime juice_
_1 tablespoon sugar_
_2 teaspoons finely grated ginger_
_½ teaspoon salt_
_½ small honeydew melon_
_¼ cup raw cashews_
_¼ cup shredded unsweetened coconut (available at health food stores;see Tips)_
_¼ cup raisins_
**Equipment**
_2 medium saucepans_
_Colander_
_Food processor with small shredder blade_
_Large frying pan_
_Large bowl_
_Small bowl_
**1.** If you are using canned beans, proceed to Step 2. Otherwise, rinse the beans, then place them in a medium saucepan with 3 cups of water. Bring the water to a boil, reduce to a simmer, and cook the beans for about 1 hour, until tender. Drain in a colander, then cool to room temperature.
**2.** In another medium saucepan over _medium-high_ heat, combine the 1 cup rice with 2 cups water. Bring the mixture to a boil, then reduce to a simmer, cover, and cook for about 50 minutes, until all of the water is absorbed. Cool to room temperature.
**3.** While the beans and rice are cooking, cut the carrots into sticks, then grate in the food processor using the small shredder blade specifically designed for this purpose. (If a food processor is unavailable, you can use a knife to cut the carrots into thin matchsticks but it's a tedious chore.)
**4.** Measure the oil into a large skillet over _medium-high_ heat and let it get hot, about 45 seconds. Add the grated carrots and cook, stirring continuously, until the carrots are crisp-tender, about 5 minutes. Cool to room temperature.
**5.** Cut the bell peppers into ¼-inch dice. Coarsely chop the onion. Cut the jalapeño pepper in half, then remove the seeds and ribs and chop finely.
**6.** In a large bowl, combine the beans, rice, carrots, bell peppers, and onion. Cover and refrigerate until chilled, at least 1 hour.
**7.** In a small bowl, combine the jalapeño, pineapple juice, lime juice, sugar, ginger, and salt.
**8.** Scoop the seeds out of the honeydew, then cut the honeydew half into 2 pieces, cut the flesh from the rind, and cut the flesh into ¼-inch dice. Coarsely chop the cashews.
**9.** Toss together the rice-and-bean mixture and the dressing. Stir in the honeydew, nuts, coconut, and raisins. Serve.
**Tips**
• You'll probably have to go to the health food store to get the unsweetened coconut. If it's too far out of the way, skip the coconut altogether. But, if you are going to make the trip, pick up the cashews, black beans, brown rice, and raisins there as well.
• If you are in a rush to cool the carrots, beans, or rice to room temperature, transfer them from the pans in which they were cooked to bowls and place them in the refrigerator for a little while.
#### **Tuna, Chickpea & Smoked Cheddar Salad**
This quick and easy salad is especially tasty with fresh basil and is great for picnics.
**Ingredients** _(serves four)_
_2 6-ounce cans solid white tuna in water_
_2 ribs celery_
_1 15-ounce can chickpeas_
_1 6-ounce jar artichoke hearts in oil_
_1 4-ounce jar roasted red peppers_
_¼ pound smoked cheddar or any smoked cheese_
_¼ cup fresh basil leaves, or 1 tablespoon dried_
_¼ cup fresh parsley, chopped_
_¼ cup Dad's Own Vinaigrette (page 165)_
**Equipment**
_Medium bowl_
_Colander_
**1.** Drain the tuna, empty it into a medium bowl, and flake it with a fork.
**2.** Rinse and dry the celery, then cut it on an angle into ⅛-inch slices. Add to the tuna.
**3.** Drain the chickpeas in a colander. Rinse them and shake the colander vigorously to remove the excess water.
**4.** Drain the artichoke hearts and cut them into quarters. Add to the tuna.
**5.** Drain the red peppers and chop them coarsely. Add to the tuna.
**6.** Cut the cheese into ½-inch cubes. Add to the tuna.
**7.** Wash, dry, and tear the basil leaves into ½-inch pieces. Add the basil and parsley to the tuna.
**8.** Drizzle on the dressing, toss, and serve.
**Tip**
This salad can be stored, without dressing, for several hours in a tightly covered plastic container in the refrigerator. Let the salad sit at room temperature for ½ hour before adding the dressing and serving.
#### **Coleslaw**
This is not the sodden version found in diners and school cafeterias across the country. Instead, it is a crisp, fresh-tasting side dish just begging for freshly grilled burgers or chicken.
**Ingredients** _(serves four)_
_1 medium head cabbage_
_2 carrots_
_1 small red onion_
**Dressing**
_3 tablespoons mayonnaise_
_2 tablespoons sour cream_
_2 tablespoons corn oil_
_2 tablespoons white wine vinegar_
_1 tablespoon sugar_
_2 teaspoons celery seed_
_2 teaspoons salt_
**Equipment**
_Large bowl_
_Small bowl_
_Food processor_
_Whisk_
**1.** Cut the cabbage lengthwise into quarters. Trim the core section from the bottom of each quarter. Put each quarter through the food processor, using the shredder blade. Transfer to a large bowl.
**2.** Grate the carrots in the food processor, using the small shredder blade. Chop the onion. Add the vegetables to the cabbage.
**3.** In a small bowl, whisk together all of the dressing ingredients.
**4.** Pour the dressing over the vegetables and, using your hands (it's the only way), mix everything together. Refrigerate until ready to serve.
#### **Red Potato Salad**
This recipe doesn't swamp the potatoes with dressing, but instead coats them lightly. There's no need to peel the potatoes. Besides contributing nutritionally, the red skins make the salad more colorful.
**Ingredients** _(serves four to six)_
_2½ pounds small red potatoes_
_2 ribs celery_
_1 medium red onion_
_2 scallions_
_1 red or green bell pepper_
_½ cup chopped fresh parsley_
**Dressing**
_½ cup mayonnaise_
_2 tablespoons sour cream or additional mayonnaise_
_1 tablespoon Dijon mustard_
_1 tablespoon salt_
_Freshly ground black pepper_
**Equipment**
_Large pot_
_Large bowl_
_Small bowl_
_Colander_
_Rubber spatula (optional)_
**1.** Rinse the potatoes, scrubbing off any spots of dirt with a potato brush or dish towel.
**2.** Put the potatoes in a large pot. Cover with cold water to about 1 inch above the potatoes and bring to a boil, uncovered, on _high_ heat.
**3.** When the water reaches a boil, reduce the heat to _medium-low_ and simmer the potatoes until just tender (when a paring knife can pierce the potatoes easily), about 15 minutes. Drain and cool in a colander.
**4.** While the potatoes are cooking, rinse and dry the celery ribs and cut them on an angle into ⅛-inch slices. Cut the onion in half and then into thin slices. Chop the green parts of the scallions into ½-inch pieces. (Discard the white parts.) Seed the bell pepper and cut it into short thin strips.
**5.** To make the dressing, combine all of the ingredients in a small bowl.
**6.** When the potatoes are cool enough to handle, cut them into quarters and transfer them to a large bowl. Add the vegetables and chopped parsley.
**7.** Pour the dressing on the potato mixture and gently combine with your hands or a rubber spatula. Refrigerate, covered, for at least 2 hours. Remove from the refrigerator ½ hour before serving.
**Variation**
Substitute 2 tablespoons plain low-fat yogurt for the sour cream to help reduce calories.
#### **Watercress, Snow Pea & Melon Salad**
This is a wonderful way to start a summer meal. The kids will love the touch of sweetness the melon adds.
**Ingredients** _(serves four or five)_
_2 bunches of watercress_
_½ pound snow peas or sugar snap peas_
_½ honeydew or cantaloupe_
_¼ cup Dad's Own Vinaigrette (page 165), made with lemon juice instead of vinegar_
**1.** Wash and dry the watercress and divide it among salad plates.
**2.** Remove the strings from the snow peas or snap peas, rinse, and dry on paper towels. Arrange the peas over the watercress.
**3.** Cut the melon in half and remove the seeds, then cut each half into quarters. Cut the flesh from the rind and slice it into 1-inch pieces. Arrange 6–8 melon slices on top of the watercress.
**4.** Drizzle on the dressing just before serving.
**Variations**
• Three sectioned clementines can be used in place of the melon. Or try two 6-ounce cans mandarin orange slices, well-drained.
• Boston or green leaf lettuce can be used in place of the watercress.
• Green beans or jicama can replace the snow peas.
Complete Meal Salads
Many salads, like the three that follow, are meals in themselves. Oftentimes, especially in summer, a salad with a good loaf of bread sounds and tastes better than any hot entrée you can imagine. The salads that follow, classic salad Niçoise, exotic-tasting Japanese beef, and Chinese-style chicken salad, all provide a full complement of meat or fish, vegetables, and carbohydrates. Other salads in _Dad's Own Cookbook_ that can be served as complete meals are the Chef's Salad (page 67) and the Cold Tortellini Salad (page 192).
#### **Salad Niçoise**
This classic salad originated in the city of Nice on the French Rivera.
**Ingredients** _(serves four)_
_6–8 small red potatoes, cut in half_
_½ pound green beans or haricots verts (very thin French green beans)_
_1 head Romaine or leaf lettuce, torn into bite-sized pieces_
_1 red bell pepper, seeded and cut into ½-inch strips_
_2 6-ounce cans solid white tuna in water, drained_
_3 large hard-boiled eggs, shelled and cut lengthwise into quarters_
_1 medium red or yellow onion, sliced into thin rings_
_½ cup (about ¼ pound) pitted black olives (Niçoise or kalamata)_
_Freshly ground black pepper_
**Dressing**
_2 garlic cloves_
_5 tablespoons freshly squeezed lemon juice (from 1 large lemon)_
_½ cup plus 1 tablespoon extra-virgin olive oil_
_1¼ teaspoons dried basil_
_½ teaspoon salt_
**Equipment**
_2 medium saucepans_
_Colander_
_Salad spinner_
_Glass jar with cover_
**1.** Fill a medium saucepan with water and bring to a boil. Add the potatoes and boil for 10–15 minutes or until tender. Drain in a colander. Set aside to cool.
**2.** Bring another medium saucepan of water to a boil and blanch the green beans for 1 minute or the haricots verts for 30 seconds. Drain immediately in a colander and run under cold water to cool.
**3.** Wash and dry the lettuce in a salad spinner. Transfer to a salad bowl. Add the bell pepper, tuna, eggs, onion, olives, potatoes, and green beans, and stir gently to combine.
**4.** Combine the dressing ingredients in a glass jar. Cover and shake well.
**5.** Drizzle the dressing over the salad and toss well. Grind the pepper over the top and serve.
**Variations**
Artichoke hearts or sliced cucumbers can be substituted for the hard-boiled eggs.
#### **Japanese Beef Salad**
If your kids like meat, they'll love this salad. It can be made ahead of time for a no-fuss dinner.
**Ingredients** _(serves four)_
_1¾ pounds flank steak, about ½-inch thick_
_½ pound green beans or snow peas_
_2 cups broccoli florets_
_1 red bell pepper, cut into strips_
_1 medium onion, thinly sliced_
_2 scallions, cut into ½-inch pieces_
**Dressing**
_¼ cup soy sauce_
_¼ cup white wine (or clear apple juice)_
_1 tablespoon sesame oil_
_1 tablespoon sugar_
_1 teaspoon garlic powder_
_1 teaspoon ground ginger_
**Equipment**
_Broiler pan_
_Medium saucepan_
_Medium bowl_
_Colander_
_Large bowl_
_Whisk_
**1.** Preheat the broiler.
**2.** Place the flank steak on the broiler pan and broil 4 inches from the flame for 5–7 minutes on each side. Let the steak cool while you assemble the rest of the salad.
**3.** Fill a medium saucepan halfway with water and bring it to a boil. Fill a medium bowl with cold water. Trim the ends of the green beans or peel the strings from the snow peas. Blanch the beans or snow peas for 1 minute in the boiling water. Drain them in a colander and transfer them to a bowl of cold water. Repeat with the broccoli. Allow the vegetables to cool.
**4.** Slice the steak across the grain into very thin slices and transfer to a large bowl. Pat the broccoli and beans or snow peas dry with paper towels and add them to the beef along with the rest of the vegetables.
**5.** Whisk together the dressing ingredients in a small bowl. Pour the dressing over the salad and toss together.
**Tips**
• This salad can be stored for several hours, without dressing, in a tightly covered plastic container in the refrigerator. Let the salad sit at room temperature for ½ hour before adding the dressing and serving.
• To save time, the flank steak can be broiled that morning or the night before.
#### **Chinese Chicken Salad**
The slicing of the chicken, cucumber, and carrots takes a while; otherwise this salad is a cinch to make. If desired, prepare the dressing in advance.
**Ingredients** _(serves four)_
_1 pound plain cooked chicken, cut into 3-inch strips_
_½ pound bean sprouts_
_1 medium cucumber, peeled, seeded, and cut into 3-inch matchsticks_
_2 large carrots, cut into thin 3-inch matchsticks_
**Dressing**
_3 tablespoons peanut butter or sesame paste (tahini)_
_2 scallions, chopped_
_⅔ cup chicken broth_
_3 tablespoons soy sauce_
_2 tablespoons rice vinegar (see Tip)_
_1 tablespoon dry sherry or rice wine (see Tip)_
_2 teaspoons sesame oil_
_2–4 cloves garlic, minced_
_1 teaspoon sugar_
_1 teaspoon salt_
_Chopped fresh cilantro, for garnish (optional)_
**Equipment**
_Large bowl_
_Glass jar with cover_
**1.** Combine the chicken, bean sprouts, cucumber, and carrots in a large bowl.
**2.** Put the dressing ingredients in a glass jar, cover, and shake vigorously.
**3.** Drizzle the dressing over the salad and toss gently. Sprinkle the cilantro over the salad, if desired.
**Tip**
Cider vinegar can be substituted for the rice vinegar and dry white wine can be substituted for the dry sherry or rice wine.
**Note**
If you don't have any pre-cooked chicken in the refrigerator, place 1 pound boneless chicken breasts on a rimmed baking sheet, cover the pan securely with foil, and bake in a preheated 350°F oven for 20–25 minutes, until cooked through but still juicy.
## Pasta
Popular legend would have us believe that Marco Polo was responsible for carrying the idea of noodles back with him from China to Italy, but in actuality some form of pasta was being eaten in both places before Polo even set out on his voyage in 1271.
Whatever its history, pasta is loved today by children and adults alike and, fortunately, is very healthy, economical, and easy to prepare: You make the sauce or broth, cook the pasta, put the two together, and dinner (or lunch) falls neatly into place.
Some people still think of pasta as a plate of spaghetti with tomato sauce, a couple of meatballs, and a sprinkling of Parmesan cheese. But pasta possibilities are much more varied. This chapter covers the basics, like tomato sauce, lasagna, and macaroni casserole, and also explores more adventuresome dishes like penne with tuna, tomatoes, and roasted peppers; Asian noodles with chicken and ham; cold peanut noodles; and tortellini salad.
* * *
**Pasta Primer**
Pasta comes in many sizes, shapes, even colors; there are cords, tubes, ribbons, and special shapes like shells, wheels, and even butterflies. Two pastas, ravioli and tortellini, have fillings. When marrying sauce to pasta keep in mind a simple rule: the longer the pasta, the thinner the sauce. That means, use light sauces for delicate pastas like angel hair and chunky, heavier sauces for sturdy pastas like fusilli. One exception is fettuccine, which works best with thick cream sauces. Cooking times depend not on the size or length of the pasta, but on its thickness.
**Fresh vs. Dried**
Both fresh and dried pastas have their own virtues. Fresh pasta, which is usually made with all-purpose flour and eggs, is lighter and richer than dried pasta and shines when matched with light sauces. Fresh pasta is best when eaten the day it is made but can be stored in the refrigerator for about 4 days.
Dried pasta is made with a harder flour than fresh pasta and is, in most cases, suited to more robust sauces, for example, tomato and sausage, carbonara, or puttanesca sauces. Whenever possible, use imported Italian dried pasta, which is higher in quality than most domestic dried pastas. It doesn't absorb too much water and is pleasantly firm.
The print edition of this book includes a chart for **Pasta Primer**.
Please download a PDF of this chart here: workman.com/ebookdownloads
* * *
**Pasta Sauce Primer**
Don't be put off by the complexity of some pasta sauces. Quite simply all Italian sauces use either cream, tomatoes, or oil as their base. Cream sauces are cooked in a frying pan for a short amount of time. The cream is added last and reduced to the desired thickness. Tomato sauces are usually cooked in a large pot and allowed to simmer for at least an hour to thicken and enhance the flavor. Sauces using fresh tomatoes, however, are more often made quickly in a frying pan. The tomatoes are sautéed along with other fresh ingredients like basil and onions. Oil-based sauces are the fastest sauces, usually requiring only a quick sauté of the main ingredients in a frying pan with enough olive oil to coat the pasta.
Below is a quick reference guide for sauces. Those included in _Dad's Own Cookbook_ are noted with stars. Others can be found in any number of Italian or pasta cookbooks. Most recipes use sautéed onions and garlic as prime ingredients.
**Garlic**
Dealing with garlic quickly and efficiently will propel you through many recipes. Garlic burns easily (making it bitter) and should be sautéed for no more than a minute or so.
**Minced garlic**
**1.** Separate the clove from the head of garlic.
**2.** Using a paring knife, trim off the stem end. Peel off the shell from the garlic clove.
**3.** Place the flat side of a chef's knife over the clove and smack it hard enough to mash the clove.
**4.** Chop the mashed clove until it is finely minced.
To prepare garlic for cooking, chop it with a knife. But for salad dressing, peel the clove, then use a garlic press to crush it fine enough to dissolve into the liquid.
The print edition of this book includes charts for **Pasta Sauce Primer**.
Please download a PDF of the charts here: workman.com/ebookdownloads
##### **Cream Sauces**
##### **Tomato-Based Sauces**
##### **Oil-Based Sauces**
* * *
#### **Basic Tomato Sauce**
This tomato sauce can be used on its own or as the foundation for many different sauces.
**Ingredients** ( _makes 2½ quarts, enough for 5–6 pounds spaghetti)_
_1 tablespoon olive oil_
_1 large onion, finely chopped_
_2 ribs celery, finely chopped_
_2 large carrots, finely chopped_
_1 green bell pepper, seeded and diced_
_2 cloves garlic, minced_
_½ cup red or white wine_
_2 28-ounce cans crushed Italian plum tomatoes_
_1 6-ounce can tomato paste_
_3 tablespoons chopped fresh basil or 2 teaspoons dried_
_3 tablespoons chopped fresh parsley_
_2 teaspoons dried oregano_
_1 tablespoon salt_
_Freshly ground black pepper_
**Equipment**
_Large, heavy pot with cover_
**1.** Place a large pot on _medium-high_ heat and let it get hot, about 45 seconds. Add the olive oil and the onion, celery, carrots, and bell pepper. Sauté, stirring often, until the vegetables are soft, about 10 minutes.
**2.** Add the garlic. Stir and cook for 1 minute more.
**3.** Increase the heat to _high,_ add the wine, and cook until the liquid is reduced by half. Stir in the tomatoes, tomato paste, 2 cups water, and the basil, parsley, oregano, salt, and pepper to taste.
**4.** When the sauce begins to bubble, turn the heat down to _low,_ cover the pot halfway, and let the sauce simmer, stirring occasionally for at least 45 minutes, until it begins to thicken. Longer cooking time makes for a thicker, more intensely flavored sauce.
**Tip**
The flavor of tomato sauce will intensify if you let it sit for a day. If you have the time, make it a day ahead and refrigerate. Tomato sauce also freezes well. With this amount of sauce, you can freeze half of it. Let the sauce cool before either refrigerating or storing in well-sealed plastic containers in the freezer. Freeze the sauce in 2- or 3-cup containers so you can defrost only what you need for each meal.
**Variations**
• **With meat:** Brown 1 pound chopped beef, veal, or a combination of the two in a frying pan over _high_ heat for 5–6 minutes. Transfer the meat to a colander to let the fat drain off. Add the meat to the sauce when you add the crushed tomatoes.
• **With sausage:** Brown ½ pound sweet Italian sausage meat in a frying pan over _high_ heat for 5–6 minutes breaking it up into small chunks as it cooks. Transfer the meat to a colander to let the fat drain off. Add the sausage to the sauce when you add the crushed tomatoes. Sausage can also be used in combination with ground beef.
• **With mushrooms:** Thinly slice ¾ pound white or wild mushrooms or a combination of the two. Sauté these with the other vegetables.
• **Puttanesca:** Coarsely chop any 3 or more of the following: 4 anchovy fillets, 2 tablespoons capers, 1 can tuna in oil (drained), a dozen pitted black olives, 1 4-ounce jar roasted Italian red peppers (drained), and 1 4-ounce jar artichoke hearts (drained). Add to the sauce when you add the crushed tomatoes.
#### **Meatballs**
These are the Titleists of meatballs. You can freeze half the batch and still feed a foursome with what's left.
**Ingredients** _(makes 24 meatballs)_
_3 slices bread, crusts trimmed, broken into pieces_
_½ cup whole milk_
_2 pounds ground beef, or 1 pound ground beef and 1 pound ground veal_
_½ pound sweet Italian sausage meat, removed from casing_
_3½ cups Basic Tomato Sauce (opposite page) or your favorite store-bought sauce_
_2 large eggs_
_¼ cup grated Parmesan_
_1 teaspoon dried oregano_
_1 teaspoon dried basil_
_3 tablespoons olive oil_
**Equipment**
_12 x 16-inch casserole_
_Medium bowl_
_Large bowl_
_Large frying pan_
_Aluminum foil_
**1.** Preheat the oven to 375°F. Lightly grease a 12 x 16-inch casserole with vegetable oil.
**2.** Put the bread in a medium bowl, pour in the milk, and let sit for 1 minute.
**3.** In a large bowl, combine the meats, the bread mixture, ½ cup of the tomato sauce, the eggs, cheese, oregano, and basil, using your hands if necessary.
**4.** Shape the meat mixture into 1½-inch balls by rolling them between your palms. Arrange the balls on a large platter or baking sheet.
**5.** Measure 1½ tablespoons of the oil into a large frying pan and place over _medium-high_ heat for about 1 minute. Add half the meatballs and cook until brown on all sides, turning as needed, about 5 minutes.
**6.** Transfer the cooked meatballs to the prepared casserole and repeat with the remaining oil and meatballs. When all the meatballs are browned, pour the remaining 3 cups tomato sauce into the casserole and stir briefly so that all the meatballs are coated.
**7.** Cover the casserole dish with aluminum foil and bake for 30 minutes until the meatballs are firm and cooked through. Remove the foil and bake for 15 minutes more.
**Tips**
• Meatballs can be made a day in advance and refrigerated.
• To reheat, place the meatballs in a large saucepan with ½ cup tomato sauce and heat slowly on _medium low_ for 12–15 minutes.
• Cool the meatballs completely before freezing in a tightly sealed plastic container. Place a layer of plastic wrap directly on the meatballs to protect them against freezer burn. Defrost the meatballs in the refrigerator for 24 hours.
#### **Dad's Own No-Boil Lasagna**
Every time I make lasagna this way (without cooking the lasagna noodles first) I'm convinced it's not going to work. But it always comes out perfectly. Since it's both easy to make and a meal that nearly every kid loves, there's no reason not to double the ingredients and make two pans at once. Serve one for dinner and store the other in the freezer.
**Ingredients** _(serves six)_
_1 pound ground beef_
_½ pound sweet Italian sausage, removed from its casing and broken into small chunks_
_5 cups Basic Tomato Sauce (page 182) or your favorite store-bought sauce_
_2 6-ounce packages frozen chopped spinach_
_24 ounces ricotta cheese_
_2 extra-large eggs_
_½ cup grated Parmesan_
_1 tablespoon salt_
_Olive oil or butter, for greasing the pan_
_1 pound lasagna noodles_
_1 pound mozzarella, thinly sliced or grated_
**Equipment**
_9 x 13-inch baking pan (see Tips)_
_Large frying pan_
_Colander_
_Medium saucepan_
_2 large bowls_
_Aluminum foil_
**1.** Preheat the oven to 350°F.
**2.** Place a large frying pan on _high_ heat and let it get very hot, about 45 seconds. Add the ground beef and sausage and brown, stirring frequently, until all the meat is cooked through. Transfer the meat to a colander and let the fat drain. Then transfer the meat to a large bowl, add the tomato sauce, and stir to combine.
**3.** In a medium saucepan over _medium-high_ heat, cook the spinach in enough boiling water to cover, until cooked through, about 5 minutes. (The spinach can also be cooked in the microwave; see page 142). Transfer the spinach to a colander and rinse with cold water. Squeeze small clumps of spinach between your hands until the water is thoroughly extracted.
**4.** Transfer the spinach to a large bowl. Add the ricotta, eggs, ¼ cup of the Parmesan, and the salt, and mix well.
**5.** Lightly oil or butter a 9 x 13-inch baking pan. Spoon in just enough meat sauce to thickly cover the bottom. Cover the sauce with a layer of pasta, laying the strips lengthwise, side-by-side, and up to the edges of the pan.
**6.** Cover the pasta with ¼ of the remaining sauce and top with half the mozzarella. Cover the mozzarella with a second layer of pasta and spread the pasta with ⅓ of the remaining sauce.
**7.** Spread on _all_ of the spinach-ricotta mixture in an even layer and cover it with a third layer of pasta.
**8.** Spread on ½ of the remaining sauce and top with the remaining mozzarella. Arrange a fourth layer of pasta and cover with a final layer of sauce. Sprinkle on the remaining ¼ cup Parmesan.
**9.** Cover the pan securely with aluminum foil and bake about 50 minutes, until the cheese melts and the noodles are cooked through.
**10.** Remove the lasagna from the oven and let rest for 5 minutes before serving.
**Time-Saver**
The meat sauce and the spinach-ricotta mixture can be prepared a day in advance, sealed in plastic wrap, and refrigerated.
**Tips**
• To freeze lasagna, let it cool, then wrap tightly in plastic wrap and cover with aluminum foil. If you plan to freeze lasagna, bake it in a disposable aluminum pan so you won't tie up one of your best baking pans in the freezer.
• To reheat a whole pan of frozen lasagna, unwrap it and place in a preheated 325°F oven for 30 minutes. Raise the temperature to 350°F and cook until heated through, about 20 minutes more. Cover the top of the lasagna with aluminum foil for the last 10 minutes of cooking so it won't dry out.
• Refrigerated leftover lasagna is best reheated in the microwave, which keeps it moist. Place a portion of lasagna on a plate and cover with plastic wrap. Reheat on _medium high_ —4 minutes for 1 portion, 6 minutes for 2, 8 minutes for 4. Otherwise, spread a couple of tablespoons of tomato sauce on the bottom of a small casserole and lay the cold lasagna over the sauce. Cover the pan and heat in a 300°F oven until heated through, about 12–15 minutes.
#### **Never-Fail Macaroni Casserole**
While not the most elegant of meals, this easy casserole is high on the list of children's favorites.
**Ingredients** _(serves four)_
_1 package #7 macaroni_
_8- to 10-ounces extra-sharp cheddar cheese_
_1 28-ounce can crushed tomatoes_
_¼ cup seasoned bread crumbs_
_1 tablespoon butter, cut into small pieces_
_Freshly ground black pepper_
**Equipment**
_Pasta pot_
_2-quart casserole_
_Colander_
**1.** Preheat the oven to 350°F. Lightly grease the casserole with margarine or vegetable oil.
**2.** Bring a large pot of water to a boil for the pasta. Cook the macaroni until al dente, about 7–9 minutes, then drain it well in a colander.
**3.** While the pasta is cooking, cut the cheese into thin slices.
**4.** Layer ⅓ of the cooked macaroni in the bottom of the casserole dish. Add ⅓ of the cheese slices followed by ⅓ of the tomato sauce. Repeat the layering 2 more times. Add pepper to each layer. Sprinkle with the bread crumbs and dot with the butter.
**5.** Bake for 45 minutes, until lightly browned.
* * *
**Eight Steps To Pasta Heaven**
##### **1. The Big Pot**
Use at least a 6-quart pot when cooking pasta.
##### **2. The Water**
One pound of pasta needs to cook in at least 4 quarts of rapidly boiling water. Less water will not allow the individual pieces of pasta to float freely, causing them to stick together. Bring the water to a fast rolling boil before adding the pasta.
##### **3. The Oil**
Add 1 tablespoon oil to the water. This helps prevent the pasta from sticking together.
##### **4. The Salt**
Add 1 teaspoon salt to the boiling water. This helps bring out the flavor of the pasta.
##### **5. The Pasta**
Add the pasta to the pot in a slow, steady stream. This will help keep the pieces separate and the water boiling. Push down strands of spaghetti as they soften. Once all the pasta is in the pot, stir quickly to keep it from sticking. Stirring occasionally during cooking helps keep thicker pasta, like ziti or lasagna, from sticking to the bottom.
##### **6. The Timing**
• **Dried Pasta:** Begin timing the pasta when the water returns to a boil. Check the pasta about 1 minute before the time specified by the manufacturer by lifting a few strands or pieces from the pot, letting them cool a few seconds, then taking a bite. If the pasta is not yet done, continue cooking it and test every 30 seconds or so. Pasta should not be overcooked, it should be al dente ("to the tooth")—tender but firm.
• **Fresh:** Fresh pastas cook in a fraction of the time necessary for dried pastas. Begin timing as soon as the pasta is in the water. Check the pasta at the prescribed time. If it's not ready, check it again every 15 seconds or so.
##### **7. The Draining**
Drain the pasta in a large, stable colander set in the sink. Using pot holders, shake the colander vigorously to release any remaining water. Transfer to a bowl and toss with 1 tablespoon olive oil to keep the pasta separate. Some recipes recommend draining pasta in cold water, which stops the cooking process. I recommend doing this only when the pasta is going to be served cold.
##### **8. The Serving**
Pasta needs to get to the table fast as it cools quickly (even when it's not rinsed in cold water). Immediately after the pasta is drained, transfer it to the serving bowl or individual plates. Quickly pour on enough hot sauce to coat lightly, but not smother the pasta, then toss to combine. If serving on individual plates, you might want to put some sauce on the plate first, add pasta, then put more sauce on top.
##### **Reheating**
Place pasta in a heatproof bowl, add enough boiling water to cover pasta, let stand for 1 minute, and drain well.
**How Much to Cook**
**Timing**
Check individual recipes or instructions on packages for recommended timing. Cooking time varies according to manufacturer and whether fresh or dried (homemade pasta cooks more quickly). But here are some general guidelines.
* * *
#### **Fettuccine with Tomato, Sausage & Basil**
This dish is best when made with fresh pasta and fresh basil.
**Ingredients** _(serves four)_
_1 pound fresh fettuccine or ¾ pound dried_
_2 28-ounce cans Italian plum tomatoes, drained and coarsely chopped_
_½ cup fresh basil leaves, torn into pieces, or 2 tablespoons dried_
_1 tablespoon olive oil plus additional olive oil for tossing the pasta_
_½ pound sweet Italian sausage, cut into ½-inch pieces_
_2 cloves garlic, minced_
_Salt and pepper_
_Grated Parmesan, for serving_
**Equipment**
_Pasta pot_
_Large frying pan_
_Colander_
**1.** Bring a large pot of water to a boil for the pasta. Add the pasta and cook until al dente. Drain in a colander and toss with some olive oil.
**2.** While the pasta water is coming to a boil and the pasta is cooking, heat the 1 tablespoon olive oil in a large frying pan on _medium-high_ heat, about 1 minute. Add the sausage and cook thoroughly, about 4 minutes. Pour out any excess fat. Add the garlic and cook for 1 minute longer.
**3.** Add the tomatoes and the fresh or dried basil, and cook until the sauce begins to bubble. Reduce the heat to _medium low_ and cook, stirring often, until the sauce begins to thicken, about 5 minutes. Add salt and pepper to taste. Turn off the heat and let the sauce sit, covered, until the pasta is cooked.
**4.** Divide the pasta among 4 dinner plates and top with the sauce. Sprinkle with grated Parmesan before serving.
**Fresh Basil**
When purchasing basil (or any other herb), look for leaves that are green all over. Yellowing leaves indicate that the herb is past its prime. Moist black spots indicate bruising.
**Cleaning:** Basil has a tendency to be gritty and needs to be rinsed thoroughly before using. To do so, pinch the leaves from the stalks and swish them in a bowl of cold water. Then remove the leaves from the water, lay them between sheets of paper towel, and gently pat them dry. Handle fresh basil as little as possible, because it bruises easily.
Twenty medium basil leaves will yield about ¼ cup, tightly packed.
#### **Seafood Linguine**
The assortment of seafood makes this an especially tasty and enticing dish.
**Ingredients** _(serves four)_
_12 ounces linguine_
_2 tablespoons olive oil_
_½ pound medium shrimp, peeled and deveined (seepage 117)_
_½ pound bay scallops (see Notes)_
_½ pound bluefish, cut into 1-inch chunks (see Notes)_
_1 7-ounce can minced clams, drained_
_3 cups Basic Tomato Sauce (page 182) or your favorite store-bought sauce_
_1 6-ounce package frozen peas_
_Grated Parmesan, for serving_
**Equipment**
_Pasta pot_
_Large frying pan with cover_
_Colander_
**1.** Bring a large pot of water to a boil for the pasta. When the water boils, add the linguine and cook until al dente, about 7 minutes, then drain well in a colander.
**2.** While the pasta water is coming to a boil and the pasta is cooking, place a large frying pan on _high_ heat and let it get hot, about 45 seconds. Add the oil and all the shrimp, scallops, and bluefish. Sauté, stirring and turning often, until the shrimp turns pink, about 4 minutes.
**3.** Add the clams and tomato sauce, bring to a boil, then reduce the heat to _medium._ Add the peas, cover, and cook for another 3 minutes, until the peas are cooked through. Let the sauce sit, covered, until the pasta is done.
**4.** Divide the pasta among 4 dinner plates, spoon on the sauce, and sprinkle with Parmesan.
**Notes**
• If bluefish isn't available, use any fatty fish, such as swordfish, tuna, cod, or mackerel.
• If bay scallops are unavailable, the larger sea scallops can be used instead. If very large, cut sea scallops in half.
**Parmesan Cheese**
The crème de la crème of Parmesan cheeses is Parmigiano-Reggiano, which is produced exclusively around Parma, Reggio Emilia, and Modena in Northern Italy. It is more expensive than other Parmesan cheese but is well worth the price. Look for pale yellow wedges that are slightly grainy in texture, mellow, rich and both salty and fruity in flavor. To know you're getting the real thing, check the rind: The words Parmigiano-Reggiano are etched around the entire circumference of the 60- to 70-pound wheels, so each wedge should include at least a few letters. To protect your investment, wrap it in aluminum foil and refrigerate for up to several months. Some stores sell their own freshly grated Parmesan, but the truth is that Parmesan loses its flavor very quickly once it is grated. It is always preferable to grate your own just before serving or at the table with a rotary cheese grater.
#### **Penne with Tuna, Tomatoes & Roasted Peppers**
This is a hearty, rustic sauce that can be put together quickly.
**Ingredients** _(serves four)_
_¾ pound penne_
_1 7-ounce can solid white tuna in oil_
_1 4-ounce jar roasted red peppers, drained and thinly sliced_
_1 6-ounce jar artichoke hearts, drained and quartered_
_2 tablespoons olive oil, plus additional oil for tossing the pasta_
_2 shallots, finely chopped_
_2 cloves garlic, minced_
_1 28-ounce can whole Italian plum tomatoes, drained_
_1 cup frozen peas_
_3 tablespoons fresh parsley, chopped_
_1 teaspoon salt_
_Freshly ground pepper_
**Equipment**
_Pasta pot_
_Large frying pan_
_Small bowl_
_Serving bowl_
_Colander_
_Wooden spoon_
**1.** Bring a large pot of water to a boil for the pasta. When the water boils, add the penne and cook until al dente, about 7–9 minutes. Drain well in a colander and toss with olive oil.
**2.** While the pasta water is coming to a boil and the pasta is cooking, drain the tuna, transfer it to a small bowl, and coarsely flake with a fork. Add the roasted peppers and artichokes, mix together, and set aside.
**3.** Place a large frying pan on _medium_ heat and let it get hot, about 45 seconds. Add the 2 tablespoons olive oil and the shallots and sauté, stirring frequently, until the shallots are soft, about 3 minutes. Add the garlic and sauté for 1 minute more.
**4.** Raise the heat to _high_ and add the tomatoes, peas, and tuna mixture. Break up the tomatoes with a wooden spoon and cook the sauce until it begins to bubble.
**5.** Reduce the heat to _medium,_ add the parsley, and season with salt and pepper. Continue cooking for 3 more minutes, stirring frequently, until the sauce thickens slightly. Remove the pan from the heat and keep it covered until the pasta is cooked.
**6.** Transfer the pasta to a serving bowl. Pour the sauce over the pasta, toss, and serve.
#### **Spaghetti Carbonara**
Spaghetti carbonara is actually not a traditional Italian dish. It was improvised using the American food supplies—bacon, eggs, and cheese—flown into Italy after World War II.
**Ingredients** _(serves four)_
_12 ounces spaghetti_
_¼ pound pancetta (Italian bacon), slab bacon, or regular sliced bacon_
_¼ cup white wine (optional)_
_Yolks of 4 large eggs_
_⅔ cup grated Parmesan_
**Equipment**
_Pasta pot_
_Large frying pan_
_Medium bowl_
_Colander_
_Whisk_
_2 large mixing spoons_
**1.** Bring a large pot of water to a boil for the pasta. When the water comes to a boil, cook the pasta until al dente, about 7 minutes, then drain well in a colander.
**2.** While the pasta water is coming to a boil and the pasta is cooking, cut the pancetta or bacon slices into ½-inch pieces.
**3.** Place a large frying pan on _medium_ heat and let it get hot, about 45 seconds. Add the pancetta or bacon pieces and sauté until cooked through, about 5 minutes. If using wine, drain off the fat, add the wine to the meat, and heat 1 minute longer. If not using wine, turn off the heat, leaving the meat and fat in the pan.
**4.** Whisk the egg yolks well in a medium bowl. Then stir in half the Parmesan until well combined. Set aside.
**5.** When the spaghetti is ready, return the frying pan to _medium_ heat for 30 seconds, then add the drained spaghetti to the pan. Using 2 large mixing spoons, combine the pasta with the bacon slices.
**6.** Remove the frying pan from the heat. Immediately pour the egg mixture over the spaghetti and stir quickly until all the strands are coated. (The heat of the pasta will cook the egg and thicken the sauce.)
**7.** Serve the pasta immediately, topped with the remaining Parmesan.
#### **Empty Cupboard Pasta**
The first time you prepare this dish it may be out of desperation, but after that the kids may start requesting it regularly.
**Ingredients** _(serves four)_
_12 ounces spaghetti or macaroni_
_3 tablespoons butter, cut into small pieces_
_⅓ cup grated Parmesan_
_1 teaspoon dried basil, oregano, or parsley_
_Freshly ground black pepper_
**Equipment**
_Pasta pot_
_Colander_
**1.** Bring a large pot of water to a boil. When the water comes to a boil, cook the pasta until al dente, about 7 minutes for spaghetti, 9 minutes for macaroni. Drain well in a colander and transfer to a serving bowl.
**2.** Immediately add the butter and Parmesan to the pasta; toss until well coated.
**3.** Sprinkle on the herbs and freshly ground black pepper. Serve immediately.
#### **Cold Tortellini Salad**
Most pasta salads leave me cold, but this one, with its earthy flavors and colors, has a lot of punch. It requires a bit of chopping, but the time is well spent.
**Ingredients** _(serves six)_
_1 pint cherry tomatoes, cut in half_
_3 scallions, coarsely chopped, cut in half_
_½ cup (4 ounces) sun-dried tomatoes packed in oil, drained and coarsely chopped_
_1 6-ounce jar artichoke hearts packed in oil, quartered_
_1 4-ounce jar roasted peppers, drained and coarsely chopped_
_1 whole clove garlic_
_½ cup chopped fresh basil, or 1 tablespoon dried_
_1 teaspoon dried oregano_
_¼ cup olive oil_
_1 pound fresh tortellini (see Tip)_
_¼ pound sliced prosciutto, cut into 2-inch pieces_
_½ pound mozzarella, coarsely grated_
_Salt and pepper_
**Equipment**
_Pasta pot_
_Medium bowl_
_Large bowl_
_Colander_
**1.** Place the cherry tomatoes, scallions, sun-dried tomatoes, artichokes, roasted peppers, garlic, basil, and oregano in a medium bowl. Add the olive oil and mix gently to coat
everything with oil. Refrigerate the mixture for 2 hours.
**2.** Bring a large pot of water to a boil for the pasta. When the water starts to boil, add the tortellini and cook for about 4 minutes, until cooked through. Drain the pasta in a colander, rinse under cold water, then drain again, shaking the colander well to remove all the water. Transfer the pasta to a large bowl.
**3.** Remove the garlic clove from the tomato mixture, then add the mixture to the pasta along with the prosciutto and mozzarella. Season with salt and pepper, mix well, and serve, or cover the salad tightly and refrigerate. This salad will keep for up to 48 hours. Remove it from the refrigerator ½ hour before serving.
**Tip**
If you can't find fresh tortellini, use dried fusilli or penne for this dish.
**Sun-Dried Tomatoes**
In Southern italy, sun-dried tomatoes are still made in the traditional way by salting the tomatoes and leaving them to dry on the roof. After they are dried, they are soaked briefly in water and then covered with olive oil, oregano, and garlic. Gourmet shops and better supermarkets sell them both in olive oil and dried. If using dried tomatoes instead of tomatoes in oil for this pasta salad, first soak them for 15 minutes in warm water, drain, and cover with olive oil. Next add 1 clove garlic and 1 tablespoon oregano, cover, and refrigerate for at least 2 hours. Remove from the refrigerator ½ hour before using. Sun-dried tomatoes are rather expensive, but a few go a long way. Once they are soaked in oil, sun-dried tomatoes will last up to 2 weeks in the refrigerator.
#### **Cold Peanut Noodles**
This cool noodle dish makes a perfect warm-weather lunch or dinner.
**Ingredients** _(serves four)_
_6 ounces Chinese ramen noodles or 8 ounces vermicelli_
_2 tablespoons vegetable oil_
_1 cucumber_
_½ cup smooth, "natural" peanut butter_
_¼ cup soy sauce_
_¼ cup white wine_
_2 tablespoons fresh lemon juice_
_1 tablespoon honey_
_1 small clove garlic_
_1-inch piece fresh ginger or 1 teaspoon ground ginger_
_Chopped scallion, for garnish_
**Equipment**
_Pasta pot_
_Medium bowl_
_Colander_
_Blender or food processor_
**1.** Bring a large pot of water to a boil for the pasta. When the water starts to boil, add the pasta and cook the ramen noodles according to the package directions, or the vermicelli until al dente, about 5 minutes. Drain the noodles in a colander and rinse under cold water until cool. Shake the colander well to release as much water as possible, then add the vegetable oil to the noodles and toss gently.
**2.** While the water is coming to a boil and the pasta is cooking, peel the cucumber
and cut it in half lengthwise. Scrape out the seeds with the tip of a spoon and cut the cucumber into ½-inch slices. Put the slices in a medium bowl, cover, and refrigerate until ready to use.
**3.** Blend the peanut butter, soy sauce, white wine, lemon juice, honey, garlic, and ginger in a blender on _medium_ speed or in a food processor, until completely smooth. Set the mixture aside.
**4.** Transfer the noodles to a serving platter. Pour on the peanut sauce and toss gently. Garnish with the cucumber slices and chopped scallion. Serve immediately.
**Tip**
"Natural" or unhydrogenated peanut butter is available in most supermarkets and all health food stores. It has the proper texture and flavor for this dish. For a more subtle flavor, substitute sesame butter (also known as tahini).
**Stir-Frying with a Wok**
Stir-frying involves cooking at a very high temperature for a short time, stirring constantly so the ingredients don't burn. You can get good results with either a large, heavy frying pan or a Chinese wok. Do not be afraid to let the pan get very hot before adding the ingredients. Always have your vegetables, meat, and sauce lined up in small bowls ready to be added at the moment the recipe specifies. And don't forget to stir continuously—this is called a stir-fry for a reason.
#### **Asian Noodles with Chicken & Ham**
This dish requires some serious stir-frying, a technique that is a study in contrasts. First there is the chopping, methodical and neat. Then you heat up the frying pan or wok and start cooking like mad, tossing in ingredients, adding sauces, all the while stirring rapidly. You'll be done with the stir-frying in about 5 minutes, and the results will be better than most dishes you get in a Chinese restaurant.
**Ingredients** _(serves four)_
_¾ pound soba (buckwheat) noodles or thin spaghetti_
_1 tablespoon olive oil, for tossing the noodles_
_½ teaspoon curry powder_
_½ teaspoon Chinese five-spice powder_
_¼ cup soy sauce_
_¼ cup white wine or sherry_
_1 tablespoon honey_
_1 medium onion, thinly sliced_
_2 ribs celery, cut diagonally into ¼-inch slices_
_2 cloves garlic, minced_
_2 carrots, grated_
_1 cup frozen peas_
_2 boneless chicken breasts, cut into thin slices_
_4 slices cooked ham (about 4 ounces), cut into 2 x ½-inch strips_
_5 tablespoons corn oil_
**Equipment**
_Pasta pot_
_Colander_
_4 small bowls_
_Whisk_
_Large, heavy frying pan or wok_
_Large cooking spoon_
_Medium bowl_
**1.** Bring a large pot of water to boil for the noodles. When the water comes to a boil, cook the noodles until soft, about 4 minutes. Drain in a colander, toss with 1 tablespoon olive oil, and set aside.
**2.** While the water is coming to a boil and the noodles are cooking, in a small bowl, combine the curry powder, five-spice powder, soy sauce, wine or sherry, and honey. Whisk together and set aside.
**3.** In another small bowl, combine the sliced onion and celery. In another bowl, combine the garlic, carrots, and peas. Place the sliced chicken and ham in separate bowls.
**4.** Heat 2 tablespoons of the corn oil in a large frying pan or wok on _high_ heat until it just begins to smoke, about 90 seconds.
**5.** Add the onion and celery, and stir-fry for 2 minutes. Add the garlic, carrot, and peas, and cook 1 minute, continuing to stir constantly. Transfer the vegetables to a medium bowl. Wipe out the pan with paper towels and put it back on the heat.
**6.** Add the remaining 3 tablespoons oil to the pan and let it get hot, about 15 seconds. Add the chicken slices and stir-fry until opaque, about 2 minutes. Add the ham and cook for 1 minute more. Add the vegetables and noodles to the pan and gently toss them together. Add the sauce, toss again, and turn off the heat.
**7.** Transfer to a serving bowl and serve immediately.
## Soups & Stews
In an old-fashioned country kitchen, you will find a large soup pot simmering on the stove's back burner, ready to receive any of the day's leftover scraps of meat or vegetables. By evening, this potful of stuff has become dinner. Traditional soups in the Béarnaise region of France turn out so thick by day's end that the ladle is known to stand straight up in the pot.
Making a meal in one pot clearly has its advantages: Preparation is relatively simple and there's less to clean up. Soups are also a great way to improvise with the leftovers you have in the fridge.
These dishes generally take an hour or more to cook, so they are not your best bet for a last-minute supper (though a freezer stocked with soup favorites can be your best friend in a pinch). Soups store very well and their flavor actually intensifies after a day in the refrigerator. When freezing soups or stews, use containers that hold enough for one meal so you can defrost exactly what you need.
* * *
**The Basic Soups**
Soups are best when made with homemade stock, so we've provided a couple of recipes. But finding the time to make your own isn't always easy. Fortunately, there are some good canned chicken and beef broths (like those made by College Inn) that can be used instead. Also, bouillon cubes and powders, which are evaporated seasoned meat extracts, can be used to replace stock or enhance the flavor of a soup. Health food stores sell vegetable bouillon cubes for a strictly vegetarian soup.
Once you get the hang of making soup, you'll want to start improvising. The soup pot can accommodate just about anything: almost any vegetable (raw or cooked), most cooked meat, pasta, sausage, and even pieces of cold cuts. If you start with a good stock, you'll find that even the scrappiest scraps can be turned into a hearty, nutritious, and very respectable soup.
##### **The Standard Soup**
These clear soups have a broth base to which vegetables and/or pieces of meat, chicken, or fish have been added. Chicken soup falls into this category as does minestrone. To make these soups, the broth is reduced slightly to concentrate its distinctive flavor and then vegetables and additional meat or chicken are added.
##### **The Puréed Soup**
Puréed soups are made by simmering stock and vegetables until the vegetables are just cooked, usually about 25 minutes. The vegetables and stock are then puréed until smooth and thickened in a blender or food processor. These are usually light soups, although the addition of potatoes can make them a bit thicker and heavier, and adding milk or cream can make them anything but light.
##### **The Hearty Soup**
Minestrone and fish chowder are prime examples of hearty soups, where lots of chopped vegetables and chunks or meat, chicken, or fish come together to produce a filling dish. Pasta, rice, and beans can also be added. These soups are made by first browning the vegetables and meat in the stockpot, then adding the stock and spices and simmering, usually for an hour or so. The soup can be served right from the pot.
A stew is a hearty soup that you can eat with a fork. For the most part, you prepare stew the same way you do soup, only you cut everything up into slightly larger pieces and add less broth. A stew can be a meal in itself or it can be served over rice or broad noodles. No matter how you serve it, you must have some thick slices of bread on the table to sop up what's left in the bottom of the bowl.
* * *
#### **Minestrone**
Minestrone can accommodate just about any kind of leftover vegetable or meat. Chop it up and throw it in.
**Ingredients** _(serves six)_
_3 slices bacon, cut into 1-inch pieces_
_1 large onion, coarsely chopped_
_2 ribs celery, coarsely chopped_
_2 carrots, coarsely chopped_
_2 small zucchini, cut into ½-inch pieces_
_2 cloves garlic, mashed and finely chopped_
_3 tablespoons tomato paste_
_2 teaspoons dried basil_
_1 teaspoon dried oregano_
_½ teaspoon dried rosemary_
_1 28-ounce can whole tomatoes, with their liquid_
_8 cups canned beef stock or 4 bouillon cubes dissolved in 8 cups boiling water_
_3 russet or large red potatoes, cut into ½-inch cubes_
_1 cup small elbow macaroni_
_1 10-ounce can red kidney beans, with their liquid_
_1 cup frozen peas_
_3 teaspoons chopped fresh parsley or 1 teaspoon dried_
_Salt and pepper_
_Grated Parmesan, for garnish_
**Equipment**
_Large stockpot_
_Medium saucepan_
_Wooden spoon_
_Colander_
**1.** Place a large stockpot on _medium-high_ heat and let it get hot, about 45 seconds. Add the bacon, onion, celery, carrots, and zucchini, and sauté until the vegetables are soft, about 6 minutes, stirring often. Add the garlic and sauté 1 minute more.
**2.** Stir in the tomato paste and 3 tablespoons water along with the basil, oregano, and rosemary.
**3.** Add the canned tomatoes with their liquid, breaking them up with a wooden spoon. Add the beef stock or bouillon and the potatoes. Bring the soup to a boil over _high_ heat, then reduce the heat to _low_ and simmer, partially covered, for 40 minutes.
**4.** While the soup is simmering, bring a medium saucepan of water to a boil for the pasta. Cook the macaroni until al dente according to package directions, then drain in a colander.
**5.** When the soup has simmered for 40 minutes, add the macaroni along with the beans and their liquid, the peas, and parsley. Season with salt and pepper. Simmer for 10 minutes more, until all of the ingredients are heated through. Serve hot in soup bowls and sprinkle with the grated Parmesan.
**Note**
The not-so-crucial ingredients in minestrone, such as the zucchini, celery, frozen peas, and carrots, can be replaced or combined with other vegetables. Don't be afraid to chop up and add what you have on hand, for example, broccoli, squash or sweet potato, a leek or two, a bit of fennel, baked potato, a piece of cabbage, or some leftover pasta. You can also throw in leftover meat or chicken.
#### **Split Pea Soup**
As a kid, my idea of the perfect winter lunch was a bowl of split pea soup and a tuna melt on an English muffin. Of course, I also had to have saltines to break into the soup. I often make this for my own kids and they agree that it's a pretty darn good lunch.
**Ingredients** _(serves six)_
_1 pound split peas_
_1 ham bone with meat on it, ham hock, or a 1-inch-thick slice baked deli ham_
_1 medium onion, coarsely chopped_
_1 rib celery, cut into 1-inch pieces_
_2 cloves garlic, mashed and coarsely chopped_
_8 cups canned or homemade chicken stock or 4 bouillon cubes dissolved in 8 cups boiling water_
_3 carrots, cut into ½-inch slices_
_½ teaspoon ground cloves_
_Milk (optional)_
_Pepper_
_Saltines, croutons, or thick slices of crusty peasant bread, to serve_
**Equipment**
_Medium bowl_
_Colander_
_Large stockpot with cover_
_Food processor or blender (optional)_
**1.** Put the peas in a medium bowl and cover with cold water. Swirl the peas around, pour them into a colander to drain, and return them to the bowl. Pick through the peas and discard any that are discolored.
**2.** Put the peas in a large stockpot along with the ham, onion, celery, garlic, and chicken stock or dissolved bouillon. Bring to a boil, cover, and simmer over _low_ heat for 1 hour, stirring occasionally. (When stirring, make sure you get right down to the bottom so the peas don't scorch.)
**3.** Add the carrots, cover and continue simmering and stirring occasionally for another hour.
**4.** Remove the ham bone from the soup and let it cool a bit; then cut the meat off and chop it into small pieces. If you're using a ham hock, break off any bits of meat you can find. If you're using a thick slice of ham, cut whatever is left into small pieces.
**5.** Return the bits of ham to the pot along with the ground cloves. Thin the soup, if necessary, with milk or water. Add pepper to taste. (Thanks to the ham you won't need salt.) Serve hot with saltines, croutons, or crusty bread.
**Tips**
• Pea soup can be puréed after Step 3. Remove the ham bone, hock, or slice, and run batches of soup through a food processor or blender. Add the bits of ham to the soup after it is puréed. If you decide to purée the soup you can add the carrots with the other vegetables at the very beginning.
• This soup can also be made without the ham. Just add some extra celery and the white parts of 2 leeks to enhance the flavor.
#### **Dad's Own Chicken Noodle Soup**
Years from now your daughter will sit down to a bowl of chicken soup that her new husband has made for her. She'll taste it, and as a tiny tear trickles down her cheek, she'll say "It's good, honey, but not as good as my Dad's."
**Ingredients** _(serves six)_
_1 large leek_
_1 4–5 pound chicken plus 4 additional chicken legs_
_1 large onion_
_1 whole turnip_
_2 whole carrots_
_1 turnip, cut into ½-inch slices_
_2 carrots, cut into ½-inch slices_
_2 tablespoons honey (optional; adds interesting flavor)_
_1½ tablespoons salt_
_1 teaspoon fresh or dried dill_
_6 ounces string-shaped egg noodles_
_1 cup frozen peas_
_Chopped fresh parsley, for garnish_
**Equipment**
_2 large stockpots, or 1 large stockpot and 1 very large bowl_
_Large slotted spoon_
_Medium bowl_
_Colander_
_Cheesecloth_
_Large spoon_
**1.** Trim the bottom of the leek at the roots and cut the leek in half lengthwise. Separate the layers and rinse them very well on both sides under cold water.
**2.** Put the leek in a large stockpot along with the whole chicken, chicken legs, onion, turnip, and carrots. Add at least 3 quarts water to cover the chicken and bring it all to a boil over _high_ heat. Reduce the heat to _medium low_ and simmer for 2 hours 15 minutes, skimming off any scummy foam that collects on the surface as it cooks.
**3.** Using a large slotted spoon, remove the chicken and chicken parts to a medium bowl and discard the vegetables. When the chicken has cooled, pick off the meat and chop it coarsely. Set it aside (see Tips).
**4.** Place a clean stockpot or very large bowl in the sink. Line a colander with a double layer of cheesecloth and set it over the stockpot or bowl in the sink. Slowly pour the soup through the cheesecloth so that all the solids are caught in the cheesecloth, being careful not to let it splatter. Discard the solids. If using a bowl, transfer the stock to the stockpot. Using a large spoon, skim and discard the fat floating on top of the stock.
**5.** Add the sliced turnip and carrots, the honey (if using), salt, and dill to the stock. Bring to a boil over _high_ heat, then reduce to _low_ and simmer for 30 minutes. Increase the heat to _medium_ and add the noodles, frozen peas, and chicken meat (if using). Simmer until the noodles are cooked through, about 8 minutes. Add more salt if necessary. Serve hot, garnished with chopped parsley.
**Tips**
• You may find you have more than enough chicken meat for the soup. What's left over makes great chicken salad. See the recipe on page 166.
• Make the broth (Steps 1–4) the day before you plan to serve the soup. Let the broth cool and refrigerate right in the covered pot. Once the soup is completely cold, skim off the congealed fat.
#### **New England Clam Chowder**
Once they taste Dad's homemade chowder, the kids may be asking for it all the time. Fortunately, it's an easy soup to throw together. Serve the chowder with hunks of fresh whole wheat bread to soak up the important stuff that's left in the bottom of the bowl.
**Ingredients** _(serves six)_
_3 slices bacon_
_1 large onion, coarsely chopped_
_4 russet or large red potatoes, peeled and dried_
_1 cup bottled clam juice_
_2 7-ounce cans minced clams_
_2 cups milk_
_2 cups half-and-half_
_1 tablespoon all-purpose flour_
_1 tablespoon butter, at room temperature_
_1 teaspoon salt_
_Pepper_
_Chopped fresh parsley, for garnish_
_Oyster crackers, for garnish_
**Equipment**
_Small frying pan_
_Large stockpot with cover_
_Small bowl_
**1.** Place a small frying pan on _medium_ heat and let it get hot, about 45 seconds. Add the bacon and cook, stirring occasionally, until crisp. Remove the bacon slices to paper towels and pat them dry. Break up the bacon into small pieces and set aside.
**2.** Pour 1 tablespoon of the bacon fat into a large stockpot. Put the pot on _medium-high_ heat and let it get hot, about 45 seconds. Add the chopped onion and sauté, stirring often, until soft, about 6 minutes. Add the potatoes, bacon pieces, clam juice, and 1 cup water, and bring to a boil. Reduce the heat to _low_ and simmer, partially covered, for 10 minutes.
**3.** Increase the heat to _medium high_. Add the clams in their juice, the milk, and half-and-half, and bring to a boil. Reduce the heat to _medium low_ and let the soup simmer for 5 minutes.
**4.** In a small bowl, mix together the flour and butter until completely combined. Break off small pieces of the mixture and add them to the soup one at a time, stirring well to incorporate. Add the salt and pepper to taste. Let the soup come to a boil one last time, then remove it from the heat. Serve the soup hot, topped with a bit of chopped parsley and oyster crackers.
**Variation**
This recipe can easily be adapted for fish chowder. Simply cut 1 pound skinless and boneless fillets of cod, scrod, red snapper, or any firm fish into 1½-inch pieces. Add these to the pot along with the can of clams and simmer until the fish begins to flake, about 10 minutes. Add the milk and half-and-half and continue as for clam chowder. Alternatively, add 2 pounds of fish and eliminate the clams completely.
#### **Potato & Escarole Soup**
This is a thick, hearty soup that can be thrown together in minutes.
**Ingredients** _(serves six)_
_4 russet or large red potatoes_
_1 large head escarole_
_1 tablespoon butter or margarine_
_1 onion, sliced_
_2 cloves garlic, minced_
_6 cups chicken stock or 3 bouillon cubes dissolved in 6 cups boiling water_
_Salt and pepper_
**Equipment**
_Large bowl_
_Large stockpot with cover_
_Colander_
_Ladle_
_Blender or food processor (see Tip if using the food processor)_
_Large saucepan_
**1.** Peel the potatoes. Cut them into ½-inch slices and place them in a large bowl of cold water. Set aside.
**2.** Discard any brown leaves of escarole. Trim the stems and cut the leaves into 2-inch pieces. Thoroughly wash and dry the escarole.
**3.** Place a large stockpot on _medium-high_ heat and let it get hot, about 45 seconds. Add the butter or margarine; when it stops sizzling, add the onion and sauté until soft, about 6 minutes. Add the garlic and sauté for 1 minute more.
**4.** Add the chicken stock or bouillon and bring to a boil on _high_ heat. Drain the potatoes in a colander and add them to the pot. When the soup begins to boil, reduce the heat to _low,_ cover, and simmer for 20 minutes, or until the potatoes are soft.
**5.** Add the escarole to the pot and stir. Cover and simmer for 8 minutes more. Remove from the heat.
**6.** Using a ladle, fill a blender halfway with soup and purée. Transfer the puréed soup to a large saucepan. Continue blending until all the soup is puréed.
**7.** Season the puréed soup with salt and pepper. Serve hot, or let it cool, refrigerate for several hours, and serve cold.
**Tip**
If you want to use a food processor instead of a blender to purée the soup, you will need to strain the soup and separate the solids from the liquid first. Set a colander over a large saucepan and pour the soup through the colander. Then transfer the solids to the bowl of the processor. Add 1 cup of the hot broth to the solids and process until the mixture is smooth. Stir the puréed mixture back into the soup and stir until combined. If you try to purée the soup in the food processor with too much liquid, the vegetables will remain in little chunks and the liquid may leak.
#### **Carrot & Orange Soup**
Here's a simple gem of a recipe that my wife prepares when it's her turn to cook.
**Ingredients** _(serves six)_
_2 tablespoons butter or margarine_
_1 large onion, coarsely chopped_
_½-inch piece ginger, peeled and finely chopped_
_8 carrots (about 1½ pounds), sliced into 1-inch pieces_
_4 cups chicken stock or 2 bouillon cubes dissolved in 4 cups boiling water_
_1 cup orange juice, preferably freshly squeezed_
_Salt and pepper_
_Chopped fresh mint or parsley_
**Equipment**
_Large stockpot with cover_
_Ladle_
_Blender or food processor (if using the food processor,see Tip at end of Potato and Escarole Soup)_
_Large saucepan_
**1.** Place a large stockpot on _medium-high_ heat and let it get hot, about 45 seconds. Add the butter or margarine; when it stops sizzling, add the onion and sauté until soft, about 6 minutes. Add the ginger and sauté for 2 minutes more.
**2.** Add the carrots and the chicken stock or bouillon to the stockpot and bring to a boil over _high_ heat. Reduce the heat to _low_ and simmer, covered, until the carrots are tender, about 35 minutes.
**3.** Remove from the heat. Using a ladle, fill the blender halfway with the soup and purée. Transfer the puréed soup to a large saucepan and continue blending until all the soup is puréed.
**4.** Return the large saucepan with the soup to _medium high_. Add the orange juice and bring to a boil one more time, then remove from the heat and season with salt and pepper. Serve the soup hot, garnished with chopped mint or parsley. Be sure to let it cool before refrigerating or freezing.
**Serving Suggestion**
This soup can also be served chilled as part of a refreshing summer meal.
**Adjusting the Seasoning**
People have different tastes when it comes to salt and pepper. Most of _Dad's Own_ recipes call for a minimal amount of salt. You may find you and your family like more or less salt, so go ahead and adjust the seasoning accordingly. Always add salt or pepper in small amounts, because once a dish is overseasoned, there is little you can do to correct it.
#### **Old-Fashioned Beef Stew**
Adapted from a recipe by James Beard, the late dean of American cooking, this recipe scores high on the "hearty" scale. Don't worry about making it look pretty. Just get everything into the pot and let it cook. You can serve this over wide noodles or with a thick slice of brown bread.
**Ingredients** _(serves six)_
_2 cups unbleached all-purpose flour_
_3 pounds beef brisket or chuck, cut into 2-inch cubes (your butcher will cut it for you)_
_4 tablespoons oil_
_¼ cup red wine_
_1 whole medium onion_
_1 whole carrot_
_1 turnip_
_1 teaspoon dried thyme_
_1 bay leaf_
_2 cups canned or homemade beef stock or 2 bouillon cubes dissolved in 2 cups boiling water_
_3 carrots, cut into 1-inch rounds_
_3 russet or large red potatoes, cut into eighths_
_2 russet or large red potatoes, peeled and grated_
_1 large onion, coarsely chopped_
_3 ribs celery, cut into 1-inch slices_
_3 cloves garlic, minced_
_Salt and pepper_
_½ pound green beans, trimmed and cut in half_
_10-ounce package frozen peas_
**Equipment**
_Large bowl_
_Large platter or baking sheet_
_Large frying pan_
_Large stockpot with cover_
**1.** Measure the flour into a large bowl. Add the cubed meat and toss it in the flour with your hands. Shake off the excess flour and place the meat on a large platter or baking sheet.
**2.** Place a large frying pan on _high_ heat and let it get very hot, about 1 minute. Add 2 tablespoons of the oil and as many pieces of the meat as will fit in a single layer. Brown the meat, turning so the pieces cook on all sides, about 6 minutes.
**3.** Transfer the browned meat to a large stockpot and finish cooking the rest of beef in the remaining 2 tablespoons oil. Deglaze the frying pan with the red wine and add the liquid and bits of meat to the stockpot along with the whole onion and carrot, turnip, thyme, bay leaf, and beef stock or bouillon. Bring to a boil on _high_ heat, then reduce the heat to _low_ and simmer, covered, for 1½ hours.
**4.** Add the sliced carrot, all the potatoes, chopped onion, celery, garlic, and season with salt and pepper. Simmer, covered, until the meat is very tender, about 50 minutes more. Stir the soup occasionally.
**5.** Adjust the seasoning and add the green beans and frozen peas. Cook for 10 minutes more. Serve hot or let the stew cool a bit before refrigerating or freezing.
**Tips**
• The flavor of the stew is enhanced if it's refrigerated overnight. Reheat the stew in a stockpot over _low_ heat, adding a bit more water or beef stock if needed.
• An easy way to flour the meat is to use a large plastic container with a tight-fitting lid. Put the flour into the container, add the meat, close the container and shake vigorously, keeping a tight hold on the lid. Lift the meat out with a slotted spoon and shake off the excess flour.
#### **Broccoli & Apple Soup**
The subtle sweetness of apples offsets the slight bitterness of the broccoli and gives this soup a refreshing flavor.
**Ingredients** _(serves six)_
_1 large head broccoli_
_2 large McIntosh or Golden Delicious apples_
_1 tablespoon butter or margarine_
_1 medium onion, sliced_
_6 cups chicken stock or 6 bouillon cubes dissolved in 6 cups boiling water_
_Salt and pepper_
_Plain yogurt or sour cream, for garnish_
**Equipment**
_Large stockpot with cover_
_Ladle_
_Blender or food processor (if using the food processor, see Tip at end of Potato and Escarole Soup,page 202)_
_Large saucepan_
**1.** Trim and discard about 1 inch from the bottom of the broccoli stalks. Cut the broccoli just below the florets. Set the florets aside and cut the stalks into 1-inch pieces.
**2.** Peel the apples and cut them into quarters. Trim the core from each quarter and cut into thirds.
**3.** Place a large stockpot on _medium-high_ heat and let it get hot, about 45 seconds. Add the butter or margarine and when it stops sizzling, add the onion and apple slices. Sauté until the onions are soft, about 6 minutes.
**4.** Add the chicken stock or bouillon and the broccoli stalks. Bring the soup to a boil on _high_ heat. Reduce the heat to _low,_ cover, and simmer for 20 minutes.
**5.** Add the broccoli florets to the pot and simmer for 5 minutes more, until the broccoli is heated through. Remove from the heat.
**6.** Using a ladle, fill the blender halfway with soup and purée. Transfer the puréed soup to a large saucepan and continue blending until all the soup is puréed.
**7.** Season the puréed soup with salt and pepper and serve hot, garnished with a small dollop of plain yogurt or sour cream, if desired.
**Tips**
• To make handling the soup easier, let it cool a bit before you begin to purée it.
• When blending the soup, start on a slow speed and work up to the purée speed in 2 or 3 steps.
* * *
**Homemade stock: for the truly committed**
##### **Beef Stock**
Making beef stock is a long process, though once the stock is on the stove it doesn't require much attention. The bones and vegetables need to roast in the oven for an hour, and then simmer for 4–5 hours more. It winds up being a whole day affair, so leave it for a weekend when you're planning to stick around the house. A large pot will yield 4 quarts of stock, allowing you to freeze enough to make a few batches of soup. Roasting the bones and vegetables in a hot oven before simmering helps to intensify their flavor and enhance the color of the stock.
**Ingredients** _(makes 4 quarts)_
_2 large onions, unpeeled and cut into quarters_
_4 cloves garlic_
_2 ribs celery_
_2 carrots, unpeeled and cut in half lengthwise_
_3 pounds beef bones_
_3 pounds veal bones_
_1 pound oxtail_
_1 bay leaf_
_10 peppercorns_
**Equipment**
_Large roasting pan_
_2 large stockpots with covers, or 1 large stockpot and 1 very large bowl_
_Colander_
_Cheesecloth_
**1.** Preheat the oven to 500°F.
**2.** Arrange the onions, garlic, celery, and carrots in a large roasting pan, then layer the bones and oxtail on top of them. Roast in the oven for 1 hour.
**3.** Transfer the bones and vegetables to a large stockpot. Add 1 quart cold water to the roasting pan and use a large spoon to scrape up any bits of meat or vegetable that have stuck to the bottom. Transfer this to the stockpot along with 5 quarts cold water.
**4.** Add the bay leaf and peppercorns and bring the liquid to a boil over _high_ heat. Once the liquid is boiling, reduce the heat to _low,_ cover the pot, and simmer for 5 hours. Remove the pot from the heat and let it cool for ½ hour.
**5.** Line a colander with cheesecloth and place the colander over another large stockpot or a very large bowl. Very carefully pour the stock through the lined colander so that all of the solids are caught in the cheesecloth. Discard the solids.
**6.** Let the stock sit for at least 20 minutes to allow the fat to rise to the top. Then use a large serving spoon to degrease the stock. The stock is now ready for use.
**7.** If you are freezing the stock, let it cool completely before transferring it to well-sealed pint or quart containers.
##### **Chicken Stock**
Having a few pints of chicken stock in the freezer can make it a cinch to throw together a tasty soup or to enhance the flavor of a sauce or stew.
**Ingredients** _makes 3 quarts)_
_1 2–3 pound whole chicken_
_1 pound chicken legs_
_5 peppercorns_
_Any or all of the following:_
_1 large onion, 1 carrot,_
_1 rib celery, 1 leek,_
_5 sprigs parsley,_
_4 unpeeled cloves garlic_
**Equipment**
_2 large stockpots, or 1 large stockpot and 1 very large bowl_
_Colander_
_Cheesecloth_
_Large bowl_
**1.** Rinse the chicken and the chicken legs. Place them in a large stockpot with enough water to cover them by at least 2 inches. Bring the water to a boil over _high_ heat, then skim any scum that has risen to the surface.
**2.** Add the peppercorns and any or all of the vegetables and herbs to the stock. Return to a boil over _high_ heat, then reduce the heat to _medium low_ and simmer, uncovered, for 2 hours, skimming occasionally.
**3.** Remove the chicken to a bowl. (The meat can be removed from the bones and frozen for another use.) Line a colander with cheesecloth and place the colander over another large stockpot or very large bowl. Pour the stock through the lined colander so that all of the solids are caught in the cheesecloth, being careful not to let the stock splatter. Discard the solids. If using a bowl, transfer the stock back into the stockpot.
**4.** Return the stock to the stovetop and bring to a boil over _high_ heat. When it comes to a boil, reduce the heat to _medium low_ and simmer, uncovered, for another hour. The stock is now ready for use. When it cools, skim any fat from the surface.
**5.** If you are freezing the stock, let it cool before transferring to well-sealed pint or quart containers.
**Tip**
Any bones, skin, or bits of meat you get from boning or trimming chicken for other recipes can be used to enhance the flavor of your stock. Simply freeze the scraps in a plastic bag, then when you are making a stock, add them to the pot along with the rest of the chicken and vegetables.
**Degreasing**
Degreasing is the process of removing fat from stock or gravy. A large mixing spoon works best for stocks; a soup spoon is best for gravies. There are also special "gravy degreasers" that work well for smaller amounts of liquid. Once a stock or gravy has settled, the fat rises to the surface, forming an even layer across the top or beading up into puddles. The areas of fat glisten slightly. To remove the fat, lower your spoon very slowly into the surface of the liquid, so the edge is dipped just under the fat. This allows the fat to flow into the spoon. Dispose of the fat and repeat the process until all of the fat is gone. Don't worry if some of the broth or gravy mixes into the fat—it can't be helped. Letting the stock cool in the refrigerator will cause the fat to congeal on the surface, making it easy to scrape off. If you have the time, this is the most efficient way to degrease.
* * *
#### **Mexican Chicken Stew**
This dish is great whenever you have a hankering for chili but know you should fix something a little lighter. Serve it over brown rice with corn bread for a healthful and tasty dinner.
**Ingredients** _(serves four)_
_1 cup cornmeal_
_1¼ pounds boneless chicken thighs, cut into 2-inch pieces_
_2 tablespoons corn oil_
_¼ pound chorizo or hot Italian sausage, cut into ½-inch slices_
_1 green bell pepper, seeded and sliced into ½-inch strips_
_1 red bell pepper, seeded and sliced into ½-inch strips_
_1 large onion, thinly sliced_
_3 cloves garlic, minced_
_¼ cup red wine_
_1 cup canned or homemade chicken stock or 1 bouillon cube dissolved in 1 cup boiling water_
_1 28-ounce can whole tomatoes, drained and coarsely chopped_
_1 package chili seasoning mix_
_2 tablespoons chopped fresh cilantro or 1 teaspoon dried_
_Cooked brown rice, for serving_
**Equipment**
_2 medium bowls_
_Large platter or baking sheet_
_Large frying pan with cover_
**1.** Measure the cornmeal into a medium bowl. Add the chicken pieces and toss them in the cornmeal with your hands. Shake off the excess cornmeal and place the chicken pieces on a large platter or baking sheet.
**2.** Place a frying pan on _high_ heat and let it get very hot, about 1 minute. Add 1 tablespoon of the oil, the sausage, bell peppers, and onion, and sauté for 1 minute more. Transfer the vegetables and sausage to a medium bowl.
**3.** Add the remaining 1 tablespoon oil to the frying pan and let it get hot, about 30 seconds. Add the chicken pieces and brown, turning so they cook on all sides, about 6 minutes.
**4.** Return the sausage and pepper mixture to the frying pan. Add the wine and cook until the liquid is reduced by half. Add the chicken stock or bouillon, tomatoes, chili seasoning, and cilantro, and bring to a boil. Reduce the heat to _low,_ cover, and simmer for 45 minutes. Serve hot over brown rice.
**Variation**
If your family's taste will allow it, the flavor of this stew can be enhanced by adding 2 dried ancho peppers. Ancho peppers are mild with a somewhat smoky flavor and are available in many specialty food shops or through one of the mail-order catalogs listed on pages –24. To use the peppers, place them in a small bowl and cover with boiling water. Weigh the peppers down with a small bowl or cup and let them soak for 2 hours. When they are soft, cut them open and rinse away the seeds. Chop the ancho peppers coarsely and sauté them with the fresh bell peppers in Step 2. While the ancho peppers are not very hot to the taste, you may want to wear rubber gloves when working with them. And wash your hands well after working with them. The insides of many peppers, and especially the seeds, can sting the skin.
#### **Mediterranean Fish & Seafood Stew**
This stew is a variation on the traditional bouillabaisse. Though considered a delicacy in fancy American restaurants, in Southern France, where the dish originated, bouillabaisse is standard fare and is often made with whatever wound up in the fisherman's net that morning. Black or French bread, cheese, and a garden salad will turn this into a wonderfully satisfying meal.
**Ingredients** _(serves six)_
_2 leeks, white part only_
_2 tablespoons olive oil_
_1 large onion, finely chopped_
_2 cloves garlic, minced_
_¼ cup white wine_
_1 28-ounce can crushed tomatoes_
_2 tablespoons tomato paste_
_2 cups bottled clam juice_
_1 cup canned or homemade chicken stock or 1 bouillon cube dissolved in 1 cup boiling water_
_¼ cup chopped fresh parsley_
_1 bay leaf_
_1 teaspoon dried thyme_
_1 teaspoon salt_
_2 pounds skinless, boneless firm white fish fillets, such as bass, snapper, scrod, cod, or haddock, cut into 1½-inch pieces_
_¾ pound shrimp, shelled and deveined_
_¾ pound scallops_
_1 7-ounce can whole or minced clams, with juice_
**Equipment**
_Large stockpot with cover_
**About Cleaning Leeks**
For this recipe, cut off and discard (or reserve for another recipe) the green part of the leeks. Trim the roots from the bottoms and cut the white parts in half lengthwise. Separate the layers and rinse them well on both sides under cold water. Grit tends to hide between the layers of the leeks, so they really must be cleaned attentively. Shake the leeks over the sink to release excess water
**1.** Clean and thinly slice the leeks crosswise (see box).
**2.** Place a large stockpot on _medium_ heat and let it get hot, about 45 seconds. Add the olive oil, onion, and leeks, and sauté until soft, about 6 minutes. Add the garlic and sauté for 1 minute more.
**3.** Increase the heat to _high_. Add the white wine and cook until the liquid is reduced by half. Add the crushed tomatoes and tomato paste and bring to a boil. Add 2 cups water, the clam juice, chicken broth or bouillon, parsley, bay leaf, thyme, and salt, and bring to a boil. Reduce the heat to _low_ and simmer, partially covered, for 15 minutes.
**4.** Increase the heat to _medium_. Add the fish and simmer for 8 minutes. Add the shrimp, scallops, and clams, and simmer for 8 minutes more, until all the seafood is cooked through. Serve hot.
**Time-Saver**
The tomato broth (Steps 1–3) can be prepared a day ahead. Let it cool before refrigerating in a tightly sealed container. Slowly bring the broth to a boil on _medium low_ heat before continuing with Step 4.
## Desserts
Let's face it. For most kids (and plenty of grown-ups), dinner is just something to climb over to get to dessert. And to the dismay of child psychologists, desperate parents still use dessert as a bargaining tool: "No dessert unless you finish your vegetables!"
The recipes in this chapter range from brownies and chocolate pudding (sure to inspire your children to finish their broccoli), to American classics like peach cobbler and Key lime pie. By the end of this chapter, Dad's skills will have developed enough for him to attempt a sophisticated tiramisù.
#### **Dad's Own Oatmeal-Raisin Cookies**
Most oatmeal-raisin cookies pale next to these extra-special ones made with walnuts and optional butterscotch chips.
**Ingredients** _(makes two dozen cookies)_
_Margarine or cooking spray, for greasing the baking sheets_
_½ cup (1 stick) butter, at room temperature_
_6 tablespoons granulated sugar_
_6 tablespoons light brown sugar_
_1 large egg, well beaten_
_¾ cup unbleached all-purpose flour_
_½ teaspoon baking soda_
_½ teaspoon salt_
_3 tablespoons maple syrup_
_1 cup rolled oats_
_1 cup raisins or butterscotch chips, or a combination of the two_
_½ cup chopped walnuts_
_1 teaspoon vanilla extract_
**Equipment**
_2 baking sheets_
_2 medium bowls_
_Whisk or hand-held electric mixer_
_Wire rack_
**1.** Preheat the oven to 375°F. Lightly grease 2 baking sheets with margarine or nonstick cooking spray.
**2.** In a medium bowl, use the whisk or mixer to cream together the butter and sugars until fluffy. Add the beaten egg and incorporate well.
**3.** In another medium bowl, whisk together the flour, baking soda, and salt.
**4.** Add the flour mixture to the butter mixture and stir until well combined. Stir in the maple syrup, oats, raisins and/or butterscotch chips, and walnuts. Stir in the vanilla.
**5.** One teaspoon at a time, drop the dough onto prepared baking sheets, leaving 1 inch between each cookie. Bake for 8–10 minutes, until the cookies are brown. They should be soft to the bite, so do not overbake.
**6.** Cool the cookies for 10 minutes, then, using a spatula, transfer the cookies to the wire rack and cool completely.
**Chipwiches**
Place a dollop of vanilla ice cream between 2 completely cooled cookies. Press together, wrap tightly with plastic wrap, and freeze. You'll be a hero doling out these treats in the summer.
#### **Chocolate Pudding**
This is major league chocolate pudding and takes only a few more minutes to prepare than the packaged kind.
**Ingredients** _(serves four)_
_½ cup sugar_
_2 tablespoons cornstarch_
_¼ teaspoon salt_
_2 cups whole milk_
_4 ounces bittersweet chocolate pieces or ⅔ cup chocolate chips_
_1½ teaspoons vanilla extract_
**Equipment**
_2 medium saucepans_
_Whisk_
**1.** Combine the sugar, cornstarch, and salt in a medium saucepan.
**2.** Measure the milk into a second saucepan and scald over _medium_ heat (see box).
**3.** Remove the milk from the heat and pour it slowly into the dry ingredients, stirring the mixture gently with the whisk so as not to make too many bubbles. Whisk in the chocolate pieces and vanilla.
**4.** Return the saucepan to _medium-low_ heat and bring to a gentle boil, whisking continuously until the pudding thickens. This will take about 90 seconds once the mixture begins simmering.
**5.** Pour the pudding into a serving bowl or 4 dessert cups. Cool at room temperature, then refrigerate until ready to serve.
**Tip**
If you don't like skin on the top of your pudding, lay a piece of plastic wrap directly on the pudding as it is cooling.
**Variation**
To make chocolate pudding pie, pour the hot pudding mixture into a graham cracker crust. Cool as directed for chocolate pudding. If desired, before serving, cover the pudding or the pie with whipped cream and chocolate sprinkles.
**About Scalding Milk**
Measure the milk into a saucepan and bring it to a boil over _medium_ heat, stirring occasionally to keep the milk from burning around the edge of the pan. As soon as the surface of the milk begins bubbling, remove the pan from the heat. If the milk boils, it will form a thick scum on top. Remove before using.
#### **Quick & Decadent Chocolate-Peanut Butter-Granola-Coconut Bars**
Every once in a while we all deserve the chance to unashamedly indulge in something gooey, chocolatey, and decadent. These bars are just for that occasion and, fortunately (or unfortunately—you may be tempted to indulge more often than your waistline can withstand), they are incredibly simple to make.
**Ingredients** _(makes two dozen bars)_
_½ cup (1 stick) unsalted butter or margarine_
_12 4¾ x 2½-inch graham crackers, coarsely crumbled, or 2 cups graham cracker crumbs_
_1 14-ounce can sweetened condensed milk_
_½ cup peanut butter_
_¾ cup granola_
_½ cup raisins_
_2 cups (12 ounces) semisweet chocolate chips_
_1½ cups sweetened flaked coconut_
**Equipment**
_9 x 13-inch baking pan_
_Medium bowl_
_Metal spatula_
**1.** Preheat the oven to 350°F.
**2.** Place the butter in a 13 x 9-inch baking pan and place the pan in the oven until the butter melts.
**3.** Spread the crumbled graham crackers in the baking pan with the melted butter.
**4.** In a medium bowl, combine the sweetened condensed milk and the peanut butter. Drizzle the peanut butter mixture evenly over the graham cracker crumbs, then sprinkle on the granola, raisins, and chocolate chips. Cover with the coconut and, using the palms of your hands, press down firmly on the mixture.
**5.** Bake for 25–30 minutes, until light golden brown. Cool completely, then cut into 24 bars and remove from the pan with a metal spatula. Store in the refrigerator in a well-sealed container.
#### **Hermits**
This old-fashioned favorite never ceases to please young and old alike.
**Ingredients** _(makes eighteen hermits)_
_½ cup (1 stick) margarine, at room temperature_
_¾ cup granulated sugar_
_½ cup light brown sugar_
_1 large egg_
_¼ cup molasses_
_Scant 6 tablespoons water_
_3 cups unbleached all-purpose flour_
_1½ teaspoons baking soda_
_1 teaspoon cinnamon_
_½ teaspoon cloves_
_1 teaspoon ginger_
_½ teaspoon salt_
_1½ cups raisins_
_Margarine or cooking spray, for greasing the baking sheets_
**Equipment**
_2 baking sheets_
_2 medium bowls_
_Whisk or hand-held electric mixer_
_Wire rack_
**1.** In a medium bowl, use the whisk or mixer to cream together the margarine and sugar until fluffy. Blend in the egg, molasses, and water.
**2.** In another medium bowl, combine the flour, baking soda, cinnamon, cloves, ginger, and salt. Add to the butter mixture and stir or combine. Stir in the raisins.
**3.** Chill the dough, covered in plastic, for 2 hours or overnight.
**4.** Divide the dough into 4 pieces and roll each into a sausage shape.
**5.** Preheat the oven to 350°F. Grease 2 baking sheets with margarine or cooking spray.
**6.** Place 2 "sausages" lengthwise on each baking sheet. Bake for 15 minutes. They will come out in 2 flat sheets. Cut into pieces while still warm and remove to the wire rack to cool.
**Note**
Hermits should be moist and chewy, so don't overcook.
#### **Dave's Key Lime Pie**
My brother-in-law makes a dozen of these every morning in his restaurant.
**Ingredients** _(makes one pie)_
_Yolks from 4 extra-large eggs_
_1 14-ounce can sweetened condensed milk_
_¾ cup Key lime juice (about 6 Key limes;see Note)_
_1 store-bought graham cracker crust_
_1 cup whipping cream_
_¾ cup sugar_
**Equipment**
_2 medium bowls_
_Hand-held electric mixer_
**1.** Preheat the oven to 325°F.
**2.** Combine the egg yolks and the condensed milk in a medium bowl. Using a hand-held electric mixer, beat on medium speed until light and fluffy, about 5 minutes.
**3.** With the beaters on, drizzle in the lime juice and continue beating for 2 minutes more. Quickly pour the filling into the graham cracker crust.
**4.** Bake on the center rack for 22 minutes or until firm. Do not open the oven door while the pie is baking. If the pie is still a bit loose in the center, bake for 3–5 minutes more.
**5.** While the pie is baking, thoroughly wash and dry the beaters, then, using a hand-held mixer set at a medium speed, beat the cream in a medium bowl until light and frothy.
**6.** Add the sugar to the cream 2 tablespoons at a time and beat until the sugar is incorporated and the mixture is stiff, about 5 minutes. Refrigerate until ready to use.
**7.** When the pie is finished baking, cool for at least 1 hour. Then, using a rubber spatula, very gently spread the whipped cream over the top of the pie.
**8.** Refrigerate the pie until ready to serve.
**Note**
If Key limes aren't available, any fresh limes will do. Or use bottled Key lime juice, which is sold in most supermarkets. Check in the produce section or in the frozen foods aisle. The bottle will tell you how much to substitute for fresh juice.
#### **Dad's Own Apple Pie**
Baking apple pies is an American pastime and a sure way to earn accolades from your kids. Thanks to ready-made frozen crusts—look for them in the frozen food aisle at the supermarket—making apple pie is a speedy affair. Should you choose to make your own crust, a recipe follows.
Among the best apples for baking are the mild Rome Beauty, the mildly tart McIntosh, and the moderately tart Pippin and Granny Smith apples. Don't hesitate to combine more than one kind in a pie or to experiment with other varieties, but note that the popular Red Delicious apple completely loses its shape when baked. Save it for eating out of hand.
**Ingredients** _(makes one double-crusted pie)_
_4 pounds baking apples (see above for suggestions)_
_⅓ cup sugar_
_2 tablespoons unbleached all-purpose flour_
_2 tablespoons fresh lemon juice_
_½ teaspoon cinnamon_
_¼ teaspoon ground nutmeg (optional)_
_2 homemade or store-bought pie crusts_
**Equipment**
_Large bowl_
_Wire rack_
_Rubber spatula (optional)_
**1.** Preheat the oven to 425°F. Position a rack in the lower third of the oven.
**2.** Peel the apples with a paring knife or vegetable peeler. Cut the apples into quarters, trim off the core, and slice each quarter into thirds lengthwise.
**3.** Put the apples in a large bowl. Sprinkle on the sugar, flour, lemon juice, cinnamon, and nutmeg, if using. Toss with your hands or a rubber spatula until all the slices are coated with the mixture.
**4.** Fill the bottom pie crust with the apple mixture, heaping the apples about an inch above the edge of the pie crust.
**5.** Cover with the top crust and crimp the top and bottom crusts together. Make 3 1-inch slits in the center of the top crust as steam vents.
**6.** Place the pie in the oven and bake for 10 minutes. Lower the heat to 350°F and bake for 40 minutes longer, until the top crust is golden brown.
**7.** Let the pie cool for 30 minutes before slicing.
**Tips**
• Use unpeeled apples to make this a more rustic pie.
• Serve with vanilla ice cream or a small wedge of sharp cheddar cheese.
#### **Dad's Own Pie Crust**
The trick to making a perfect crust is understanding the process and then moving fast. You may stumble through your first attempt, but after that you'll find it's, well, as easy as pie.
**Ingredients** _(makes one double crust)_
_1½ cups unbleached all-purpose flour_
_2 tablespoons sugar_
_½ teaspoon salt_
_7 tablespoons cold butter_
_¼ cup vegetable shortening or 3 more tablespoons butter_
_¼ cup ice water_
**Equipment**
_Large bowl_
_Dinner fork_
_Rolling pin_
_9-inch pie plate_
**1.** Measure the flour, sugar, and salt into a large bowl.
**2.** Cut the butter in half lengthwise, then crosswise into thin slices. Add the butter and shortening to the flour. Working quickly, using just your fingertips, break up the butter and shortening into tiny pieces, about the size of dried split peas. These bits of butter are what make the dough flaky.
**3.** Add the ice water in a steady stream, stirring with a fork until the water is incorporated into the flour.
**4.** When all the flour is moist, use your fingertips to form the dough into a ball. Do not handle any more than is necessary. If the dough seems dry or flaky, add more cold water, a tablespoon at a time.
**5.** Place an 18-inch length of wax paper on your work table. Cut the ball of dough in half and place one half in the center of the wax paper. Cover with another sheet of wax paper.
**6.** Tap the dough with a rolling pin so it begins to flatten out. Working firmly and quickly with the rolling pin, roll the dough outward from the center in all directions. Continue to roll out the dough until you have a circle that is about 4 inches larger than your pie pan. This will be the bottom crust.
**7.** Leave the dough between the pieces of wax paper and transfer it to a baking sheet for support. Store in the refrigerator until you're ready to use, up to 12 hours. You must keep the dough cold so the bits of butter don't get mushy.
**8.** Repeat the rolling process with the second half of the dough, rolling it out into a circle only 1 inch larger than the pie plate. This will be the top crust. Refrigerate until ready to use.
**9.** When ready to assemble your pie, remove the dough for the pie bottom from the refrigerator. Peel away the top piece of wax paper, carefully flip the crust over into the pie plate, and remove the other piece of wax paper. Gently push the crust into the bottom and around the sides of the pie pan. Trim the crust so it hangs 1 inch over the edge of the pie plate.
**10.** After the pie is filled, remove the top crust from the refrigerator, and peel away the top piece of wax paper. Carefully flip the crust over the filling and remove the other piece. Crimp the top and bottom crusts together and make 3 1-inch slits in the center of the top crust or as directed in the specific pie recipe.
#### **Oatmeal Chocolate Chip Cookies**
These are quite simply the best chocolate chip cookies you can find.
**Ingredients** _(makes four dozen cookies)_
_Margarine or cooking spray, for greasing the baking sheets_
_1 cup (2 sticks) butter or margarine, at room temperature_
_¾ cup granulated sugar_
_¾ cup dark brown sugar_
_2 extra-large eggs_
_1 teaspoon vanilla extract_
_1½ cups unbleached all-purpose flour_
_1 teaspoon baking soda_
_½ teaspoon salt_
_2½ cups old-fashioned rolled oats_
_2 cups (12 ounces) chocolate chips_
**Equipment**
_2 11 x 17-inch baking sheets_
_Large bowl_
_Wooden spoon_
_Medium bowl_
_Spatula_
_Wire rack_
**1.** Preheat the oven to 375°F. Lightly grease 2 11 x 17-inch baking sheets with margarine or cooking spray.
**2.** In a large bowl, using a wooden spoon, cream together the butter and sugars until light and fluffy. Stir in the eggs, 1 at a time, until completely incorporated. Stir in the vanilla and set the mixture aside.
**3.** In a medium bowl, stir together the flour, baking soda, and salt.
**4.** Stir the flour mixture into the butter mixture and mix until completely incorporated. Stir in the oats. (The batter should be stiff but not sticky.) Add the chocolate chips.
**5.** Using a tablespoon, drop 2-inch rounds of dough onto a cookie sheet, leaving about 2 inches between each cookie.
**6.** Bake on the center rack of your oven for 10–12 minutes, until the cookies are light brown on top.
**Tip**
If you like your cookies chewy, let them cool for a minute on the baking sheet, then remove them with a spatula to a wire rack. If you like crunchy cookies, set the baking sheet on the wire rack and let the cookies cool (and harden). While the first sheet of cookies is baking, prepare the second sheet.
#### **Super-Fast Saucepan Brownies**
When you want fudgy brownies in a hurry, these will most certainly do.
**Everything Fudge Brownie Sundae**
Place a generous brownie square in a dessert plate. Top with an ample scoop of vanilla ice cream. Spoon some chocolate syrup or hot fudge over the ice cream. Finish it off with a dollop of whipped cream and a cherry.
**Ingredients** _(makes sixteen brownies)_
_Margarine or cooking spray, for greasing the baking dish_
_2 extra-large eggs_
_⅔ cup unbleached all-purpose flour_
_¼ teaspoon baking soda_
_¼ teaspoon salt_
_½ cup sugar_
_2 tablespoons (¼ stick) butter or margarine_
_2 tablespoons water_
_2 cups (12 ounces) chocolate chips_
_1 teaspoon vanilla extract_
_½ cup chopped walnuts (optional)_
**Equipment**
_9 x 9-inch baking dish_
_Small bowl_
_Medium bowl_
_Medium saucepan_
_Wooden spoon_
_Rubber spatula_
_Wire rack_
**1.** Preheat the oven to 350°F. Line a 9-inch square baking dish with aluminum foil so that the foil extends about 2 inches beyond all 4 sides of the pan, then lightly grease the foil with margarine or cooking spray.
**2.** Beat the eggs in a small bowl until thoroughly mixed and set aside. Stir together the flour, baking soda, and salt in a medium bowl and set aside.
**3.** Combine the sugar, butter, and water in a medium saucepan and bring to a boil over _low_ heat, stirring constantly. Remove it from the heat and add 1 cup of the chocolate chips. Stir until the chocolate is melted, then stir in the beaten eggs and the vanilla.
**4.** Add the flour mixture to the chocolate mixture and mix well with a wooden spoon. Stir in the remaining chocolate chips and the walnuts (if using).
**5.** Scrape the batter into the baking dish with a rubber spatula and spread it evenly in the pan.
**6.** Bake on the center rack of your oven for 20–25 minutes, until a toothpick inserted in the center comes out with only a few moist crumbs clinging to it.
**7.** Transfer the pan to a wire rack and cool completely. Using 2 opposite ends of the foil as handles, life the brownies out of the pan and invert onto a cutting board. Peel away the foil and cut into 16 squares.
#### **Peach-Blueberry Brown Betty**
This dessert is a takeoff on the traditional American dessert, apple brown betty. It is simple and delicious, especially when served with vanilla ice cream. It's a foolproof recipe, even for the most inexperienced cook. This dessert can be prepared a day ahead of time and then reheated in the microwave or in a 300°F oven.
**Ingredients** _(serves four)_
_Margarine or cooking spray, for greasing the casserole_
_4 cups sliced fresh peaches_
_1 pint fresh or frozen blueberries_
_½ cup granulated sugar_
_1¼ cups unbleached all-purpose flour_
_½ cup dark brown sugar_
_½ cup (1 stick) butter or margarine, cut into ½-inch slices_
**Equipment**
_9 x 14-inch casserole_
_Large bowl_
_Medium bowl_
**1.** Preheat the oven to 350°F. Lightly grease a 9 x 14-inch casserole with margarine or cooking spray.
**2.** Put the peaches and berries in a large bowl, add the granulated sugar and ¼ cup of the flour, and toss gently to coat each piece. Arrange the fruit mixture evenly in the prepared casserole.
**3.** Combine the remaining flour and the brown sugar in a medium bowl. Add the butter and use the tips of your fingers to incorporate the ingredients and to crumble the mixture into small pieces about the size of dried peas.
**4.** Spoon the flour mixture on top of the fruit and pat down gently.
**5.** Bake, uncovered, on the center rack of your oven for 45 minutes, until the top is lightly browned. Let sit for 30 minutes before serving.
**Variations**
• To make a traditional apple brown betty, substitute 3 pounds baking apples, cored and cut into slices, for the peaches and blueberries, and replace the ¼ cup flour tossed with the blueberries and sugar with the juice of 1 lemon.
• To make a pear brown betty, follow the tip above for the apple brown betty but use hard Bosc or Bartlett pears instead of apples. Or make a brown betty with a combination of apples and pears.
#### **Tiramisù**
Tiramisù is a swanky Venetian dessert that features alternating layers of coffee-soaked cake, rich, sweet cream, and chocolate. This is a simplified, Americanized version. It will keep for 2 days, but it is best when made in the morning and served that evening.
**Ingredients** _(serves six)_
_1 store-bought yellow pound cake or 1 box ladyfingers_
_1 16-ounce container ricotta cheese_
_½ cup plus 2 tablespoons sugar_
_½ cup heavy cream_
_8 ounces semisweet chocolate chips_
_1½ cups strong coffee (I use decaffeinated for the kids)_
_Unsweetened cocoa powder_
**Equipment**
_2 medium bowls_
_Hand-held electric mixer_
_Rubber spatula_
_Pastry brush_
**1.** Put a medium bowl in the freezer.
**2.** Cut the pound cake into ½-inch slices.
**3.** In a second medium bowl, combine the ricotta with the ½ cup sugar.
**4.** Remove the bowl from the freezer, add the cream, and beat with a mixer on high speed until it holds stiff peaks.
**5.** With a rubber spatula, fold the whipped cream into the ricotta mixture. Then fold in the chocolate chips.
**6.** Line the bottom of a deep glass serving bowl with slices of pound cake, cutting the cake as needed to cover the bottom.
**7.** Stir the remaining 2 tablespoons sugar into the coffee. Dip a pastry brush in the coffee and dab it on the cake until it is soaked through.
**8.** Using a rubber spatula, spread ¼ of the ricotta mixture gently over the cake.
**9.** Arrange another layer of cake on the ricotta mixture and use the pastry brush to soak it with coffee. Cover the cake with another layer of ¼ of the ricotta mixture. Repeat until you have 4 layers of each, ending with a ricotta layer.
**10.** Cover and refrigerate for at least 4 hours. Sprinkle the cocoa powder on top before serving.
**Tip**
When serving, scoop all the way down to the bottom of the bowl with your serving spoon so you get to all of the layers. The portions will not be neat, but you'll find that no one will complain once they start eating.
* * *
**The Simplest & Healthiest Dessert**
In the face of more sumptuous desserts, we often forget about the wonderful flavor of a crisp apple or a ripe, juicy peach. Fruit is always best when it is in season locally—that's when you should buy plentifully. But even though more fruits are available year-round in supermarkets, few of us know what to look for when purchasing fruit or what to do when we take them home. You'll need to enlist your senses—eyes, nose, and fingers—when selecting the best fruit.
##### **Apples**
Fall apples bought at local stands, with names you don't recognize, are always better than the mass produced varieties available year-round. Flavors vary from sweet (Red Delicious and Golden Delicious) to tart (Granny Smith, Macoun, and Stayman). Choose apples that are smooth, firm, and blemish free. Store them in a plastic bag in the refrigerator.
##### **Bananas**
Bananas are fully ripe and sweet when the skins have a few brown speckles. Make sure the skin is unbroken and there are no brown patches. Greenish-yellow bananas will ripen on the countertop away from direct sunlight.
##### **Berries**
Buy strawberries and raspberries locally during the months of June and July. Strawberries from California and raspberries from Chile are available at other times of the year. Berries should be firm, plump, and intensely colored (not pale or browned). Store berries covered with plastic wrap in your refrigerator's fruit bin.
##### **Cherries**
Cherries are around only for a month or so in early summer, so eat them while you can. Choose plump, bright cherries (with stems) that are slightly tender, but not at all mushy. Store them in a plastic bag in the refrigerator.
##### **Grapefruit**
Look for grapefruits that are flat at both ends and heavy for their size and have thin, smooth skin. Store at cool room temperature for up to a week, or longer in the refrigerator.
##### **Grapes**
Slightly tart red and green seedless grapes are available year-round. Ripe grapes should be plump and remain firmly attached to their stems when the bunch is gently shaken. Store in a plastic bag in the refrigerator.
##### **Melons**
Melons smell fragrant when ripe and their stem ends should yield to gentle pressure. The rind of a cantaloupe should be more beige than green and a honeydew should be cream-colored and waxy. Most melons can do with a day or two at room temperature to increase their sweetness.
##### **Oranges**
Since most oranges are dyed a bright orange, do not judge them by color. Look for oranges that are firm and heavy for their size. Florida oranges have thin, smooth skins whereas naval oranges from California have thicker, bumpier skins. Store oranges for a week or more in a plastic bag in the refrigerator.
##### **Peaches**
Look for tender peaches with a yellow or cream tinge beneath the blush. Avoid rock-hard peaches as well as soft peaches which are apt to taste woolly. Peaches in supermarkets are often sold before fully ripened and need a day or two on the countertop. Store ripe peaches in a plastic bag in the refrigerator.
##### **Pears**
Bosc pears have rough brown skin and are a bit crunchy when ripe. Barletts have smooth green skin, are plump, and have a silken texture. Buy pears when they are still slightly firm and allow them to ripen at home. You'll know a pear is ready to eat when it 'gives' a little at the neck.
##### **Pineapples**
The best pineapples come from Hawaii. Look for a plump, bright, sweet-smelling pineapple that yields to slight pressure and has flat, shiny "eyes." A leaf from the center should pull out easily. Store at room temperature away from direct sunlight.
* * *
#### **Baked Apples**
**Ingredients** _(serves four)_
_2 tablespoons butter or margarine, plus extra for greasing the baking dish_
_4 large cooking apples, such as Winesap or Pippin_
_¼ cup currants and/or chopped walnuts_
_¼ cup apricot, strawberry, or peach jam_
_¼ cup real maple syrup or honey_
**Equipment**
_9-inch square glass baking dish_
_Small bowl_
_Paring knife_
**1.** Preheat the oven to 375°F and lightly grease a 9-inch square glass baking dish with butter or margarine.
**2.** Use a paring knife to core the apples ¾ of the way down. Arrange the apples in the baking dish without letting them touch each other. Fill the cores with the currants and/or nuts.
**3.** Mix the jam and maple syrup or honey in a small bowl and spoon the mixture over the apples. Dot with the 2 tablespoons butter.
**4.** Bake the apples, uncovered, on the center rack of your oven for 30 minutes. Baste the apples with the pan juice and bake for another 20 minutes.
**5.** Transfer the baking dish to a wire rack to cool. Serve lukewarm.
**Tip**
When buying maple syrup, read the labels carefully. Neither maple-flavored syrup (usually a combination of corn syrup and just a tad of real maple syrup) nor pancake syrup (often corn syrup combined with artificial maple flavor) will do for this recipe.
#### **Melon with Honey & Lime**
**Ingredients** _(serves four)_
_1 large honeydew or cantaloupe (or a combination of the two)_
_¼ cup honey_
_2 limes_
**Equipment**
_Melon baller_
_Rubber spatula_
**1.** Cut the melon in half and scoop out the seeds with a spoon.
**2.** Use a melon baller to scoop out rounds and put the rounds in a serving bowl.
**3.** Drizzle the honey and squeeze the limes over the melon balls. Toss gently with a rubber spatula. Let the melon sit at room temperature for 30 minutes to intensify the flavor before serving.
**Serving Suggestion**
Serve on chilled plates as an appetizer or for dessert.
#### **Poached Pears**
These are wonderful served with whipped cream or vanilla ice cream.
**Ingredients** _(serves four)_
_5 hard Bosc or Bartlett pears_
_1½ cups dry red wine (or grape juice)_
_½ cup sugar_
_1 cinnamon stick or ½ teaspoon ground cinnamon_
**Equipment**
_Paring knife or peeler_
_Medium saucepan with cover_
_Slotted spoon_
**1.** Using a paring knife or vegetable peeler, peel the skin off the bottom ⅔ of each pear, leaving the upper ⅓ and stem intact. If necessary, trim a bit off the bottom of the pears, so they will sit without falling over.
**2.** Combine the wine or grape juice, sugar, and cinnamon in a medium saucepan over _medium_ heat, stirring to dissolve the sugar. Set the pears in the pan so they're not touching and bring the liquid to a boil.
**3.** Reduce the heat to _medium low,_ cover the pan, and simmer until the pears are soft. Hard pears may take 30 minutes to soften, ripe pears as little as 15 minutes.
**4.** When the pears are soft, carefully remove them to serving plates with a slotted spoon. Discard the cinnamon stick.
**5.** Continue simmering the liquid over _medium_ heat, uncovered, until thick and syrupy, about 12 minutes.
**6.** Serve the pears topped with the reduced and thickened syrup.
#### **Sautéed Bananas with Strawberries**
**Ingredients** _(serves three)_
_Juice of 1 large orange_
_2 teaspoons honey_
_1 teaspoon vanilla extract_
_Pinch of cinnamon_
_3 medium bananas, peeled and halved lengthwise_
_12 strawberries, hulled and sliced_
_Grated orange zest, to taste (see Note)_
**Equipment**
_Large frying pan_
_Grater_
**1.** Place the frying pan over _medium-high_ heat until hot. Add the orange juice, honey, vanilla, and cinnamon, and stir to combine. Add the banana halves and sauté about 2 minutes on each side. Remove the bananas from the skillet and put 2 on each dessert plate.
**2.** Add the strawberry slices to the pan and sauté about 1 minute. Spoon the strawberries over the bananas and drizzle the pan juices on top. Garnish with orange zest and serve.
**Note**
Orange zest is the orange part of the peel of an orange. When grating, do not include the white part of the peel which is unpleasantly bitter.
#### **Crystallized Orange Sections**
When you eat the sliced orange you are served at the end of a meal in a Chinese restaurant, you are participating in a custom that is at least a thousand years old. And there is no reason why you shouldn't adopt this custom in your home. But for those meals when you want the effect to be just a touch more elegant, try this recipe.
**Ingredients** _(serves four)_
_4 oranges, tangerines, or clementines_
_Whites of 2 large eggs_
_2 cups sugar_
_Fresh mint, for garnish_
**Equipment**
_11 x 17-inch baking sheet_
_Pie plate_
_Medium bowl_
_Whisk_
**1.** Line an 11 x 17-inch baking sheet with wax paper.
**2.** Peel and carefully separate the oranges, tangerines, or clementines into sections without breaking the membranes. Remove any of the bitter white pith clinging to the fruit.
**3.** Beat the egg whites in a medium bowl with a whisk until just frothy. Measure the sugar into the pie plate and shake the plate so that the sugar spreads out and covers the surface.
**4.** Rest a fruit section on a fork (do not pierce) and dip it into the egg whites, just enough to coat it, then transfer to the pie plate. Repeat. Place about 8 egg-coated pieces of fruit at a time in the sugar and shake the plate so that the sugar coats the fruit.
**5.** Use a fork to lift the fruit sections from the sugar (do not pierce the fruit), tapping the fork gently on the edge of the pan to release any excess sugar. Transfer the fruit to the wax paper to dry, about 12 minutes.
**6.** When the fruit sections are completely dry, place a second piece of wax paper on top of them and store in the refrigerator until serving time. Carefully arrange the orange sections on a decorative serving platter and garnish with fresh mint.
**Variation**
The same process can be used with seedless grapes. Orange sections and grapes together make a colorful presentation.
## Making Bread & Pizza with the Kids
Never having tasted homemade bread still warm from the oven is like having watched only black-and-white television—without cable. Baking your own bread is uniquely satisfying: First, there's the tactile sensation of kneading and shaping the loaves; then, as the house fills with the fragrant and comforting aroma, your taste buds begin to anticipate the first bites of warm, sweet, yeasty goodness.
We try to bake bread every Sunday in our house; one loaf goes in the bread drawer, one in the freezer, and we're set for the week. The great thing about baking bread with the kids is that all hands can be involved in the measuring and mixing, and there's always enough kneading and punching to go around. You can incorporate the process into other Sunday afternoon activities. We often assemble the dough before kickoff, let it rise during the first half, punch it down and make the loaves during halftime, and put it in the oven after the third quarter. By the time the teams are heading for the locker room, we're tearing off our first chunks.
Included here are recipes for three basic breads as well as a couple of special breads and a quick pizza primer. Once you master these recipes, you can begin to improvise, and then the sky's the limit. First, though, a few of the ABCs of bread-making.
* * *
**Bread Basics**
To novice breadmakers, the directions for making bread—"punch down," "knead," "double in bulk"—sound more like a physical workout than a recipe. And is yeast really _that_ fussy? Dissolve in "warm but not hot liquid." In time you'll learn that yeast, though high spirited, is actually quite resilient. It's the magic that determines all the motions and rhythms of baking bread.
##### **About Yeast**
Yeast is a fungus that eats sugar, which results in fermentation. The fermentation creates gas, causing the dough to rise. The yeast feeds first off the sugar added to the dough, and then on the sugar contained in the starch granules of the flour.
Yeast is activated by contact with warm liquid. All recipes specify "lukewarm" liquid (105°–115°F). If it's too hot, it will kill the yeast; if it's too cold, it will slow its action. A good test is to put a few drops on your wrist. If it feels a tad warmer than your body temperature, you'll know, like Goldilocks, it's just right.
##### **Proofing**
Proofing enables you to judge if the yeast is active and the liquid is the right temperature (sort of like a pre-game warmup). Combine the yeast, warm liquid, and sugar in a large bowl. After about 5 minutes a distinct odor will develop and a foam of active yeast will appear on the surface of the water. The foam is the proof that the yeast is ready to work.
##### **The Work Surface**
A large wooden board is ideal, as the rough surface of the wood helps in the kneading. If necessary, you can use a section of countertop, as long as it is completely dry and there are no appliances around to impede kneading. Keep the surface very lightly floured to prevent the bread from sticking, being careful not to add too much flour. Once the dough stops sticking to your hands and the work surface, do not add any more flour.
##### **Kneading**
Kneading helps develop the gluten and the minuscule air pockets in the dough. The process is one of turning, folding, and pressing the dough. First, lightly flour the work surface. Grip the lump of dough in the center with both hands, as if you are gripping the handlebars of a bicycle. Then dig your palms into the dough as you press down and slightly out, making sure the dough is rubbing hard against the board. Fold the dough over itself and repeat, making sure the new section has contact with the board. This is repeated steadily for 6 to 8 minutes (though it may take up to 10 or 12) until the dough is smooth and satiny.
Lightly pushing the dough against the board is not kneading. You really must put your weight into it. Work on a low table if that gives you better leverage, and provide a stool for the kids if they need it. Above all, kneading requires patience and stamina.
##### **Rising**
As the yeast cells multiply, they continue to produce carbon dioxide, which causes the dough to expand and rise. The dough should be in a warm place (though not in the oven or near a heater) to keep the yeast active. Cover the bowl with a damp dish towel to protect the dough from drafts and contamination. Bread dough usually takes 1½–2 hours to rise until doubled in bulk. Denser doughs, such as pumpernickel, will take a bit longer. Do not let the dough more than double in size. It will lose its chewiness and taste too yeasty.
##### **Shaping Loaves**
Divide the dough in half. Shape each piece into a rectangle slightly shorter than the length of the loaf pan, then fold up the dough in thirds, the way you would a letter. Gently pinch the seam together and lay the dough in the pan, seam side down.
##### **Testing**
When tapped gently on the bottom, a fully baked loaf will sound hollow. Do not judge by the crust, which gets hard before the bread is fully baked and softens as the bread cools. If you don't trust the hollow tapping method, insert a wooden skewer into the middle of the bread. If it comes out clean, the bread is done.
##### **Removing & Slicing**
Most breads pull away from the sides of the pan as they bake. Before removing a loaf from its pan, run a butter knife around the edge of the pan to loosen it. Then turn the loaf pan upside down to release the bread. Transfer the loaf to a cooling rack.
You can work all afternoon making some fine bread and then ruin it by slicing it too soon. Be patient and let the loaf cool properly, for at least 20 minutes, before trying to slice it. Still, cutting those first few slices can be tricky. Lay the warm loaf on its side and cut with a serrated bread knife. Use only the lightest possible pressure and cut slowly. If you press down hard you'll wind up crushing the loaf.
##### **Storing & Freezing Bread**
Hard-crusted breads should be stored in a paper bag on the countertop or, ideally, in a traditional bread box or drawer. Soft-crusted bread should be stored in a plastic bag on the countertop or, again, in a bread box or drawer. If you plan on keeping a loaf of homemade bread for more than 2 or 3 days (commercial bread will last longer), wrap it in plastic and put it in the freezer. I don't recommend storing homemade bread in the refrigerator as it gets stale more quickly than if left at room temperature. You can freshen stale bread by warming it in a hot oven or toaster for a minute or two.
To freeze loaves of bread, let them cool completely, for at least 2 hours on a cooling rack, before storing in well-sealed plastic bags. If desired, slice the bread before freezing it so that you can take out only what you need.
**Flour**
You're at the grocery store ready to buy the all-purpose flour that your recipe calls for and, all of a sudden, you realize that you are being confronted by a myriad of choices. How can this be? All you were looking for was plain old flour. To help you avoid confusion, here is a brief lexicon of the terms you may find on the bags of all-purpose flour in your market.
• **All-Purpose Flour** _(aka family, plain, white, or general-purpose flour)_ This is the most popular kind of flour for home-baking. It is used to make all sorts of breads, cakes, and cookies. I prefer unbleached.
• **Presifted Flour** Sometimes flour is sifted before it is packaged, ostensibly to save the cook time in the kitchen. Unfortunately, flour settles and becomes more compact in storage, making it advisable to sift flour (if instructed to do so in a recipe) even if the manufacturer claims that the flour was presifted.
• **Enriched Flour** Because many vitamins as well as valuable dietary fiber are lost in the process used to make white flour, many states require that it be "enriched" with B-complex vitamins (thiamin, riboflavin, and niacin), in addition to iron and sometimes calcium and vitamin D. The "enrichment" does not affect the flour's baking properties.
• **Bleached Flour** After flour is milled it is either aged naturally—during which time the color of the flour changes from pale yellow to white and the flour's gluten-producing potential develops (gluten is a protein that gives dough its strength and elasticity)—or it is bleached, which speeds up the aging process. If a recipe calls for unbleached flour and all you have in the house is bleached flour, go ahead and use what you have.
• **Self-Rising Flour** This kind of flour contains salt and a leavening agent, supposedly to save the cook the time it takes to measure and combine these ingredients for an individual recipe. Because the strength of the leavener deteriorates within months, it is not advisable to buy this kind of flour.
* * *
#### **Country White Bread**
This is white bread the way it's supposed to be, thick, chewy, and full flavored. Have some butter and jam ready when it's time for slicing. This bread also makes sublime French toast.
**Ingredients** _(makes two loaves)_
_¼ cup butter or margarine, melted_
_2 cups milk_
_2 tablespoons sugar_
_1 package (1 scant tablespoon) active dry yeast_
_2 teaspoons salt_
_5–6 cups unbleached all-purpose flour, plus extra for dusting the work surface_
_Vegetable oil, for oiling bowl and loaf pans_
_1 large egg white beaten with 1 tablespoon water (optional)_
**Equipment**
_Small saucepan_
_2 large bowls_
_Wooden spoon_
_2 5 x 9-inch loaf pans_
_Serrated knife_
_Pastry brush (optional)_
_Cooling rack_
**1.** Add the milk to the saucepan and heat until just lukewarm. Remove the milk from the heat and let cool slightly.
**2.** Pour the lukewarm milk into a large bowl. Add the sugar. Sprinkle the yeast evenly on top of the milk. Let the mixture sit in a warm place for 5 minutes until the yeast begins to bubble and foam.
**3.** Add the melted butter or margarine and the salt to the yeast mixture and stir with a wooden spoon. Add the 5 cups flour, 1 cup at a time, blending well after each addition. Add only enough flour to make a firm but pliable dough that is just slightly sticky.
**4.** Sprinkle a work surface with a scant ¼ cup flour. Transfer the dough to the work surface and knead the dough for about 7 minutes, until it is smooth and supple. Add more flour, ¼ cup at a time, if the dough is still sticky.
**5.** Wipe the inside of another large bowl with vegetable oil. Place the dough in the bowl and then turn it over so the top of the dough is coated with a thin layer of oil. Place a slightly damp dish towel over the bowl and put it in a warm, draft-free place until it has doubled in bulk, about 1½–2 hours.
**6.** Punch down the dough with your fist until all the air pockets burst. Knead the dough a few more times on a lightly floured work surface, then divide the dough in half and shape it into loaves.
**7.** Wipe the inside of the loaf pans well with oil. Place the dough in the pans, cover with the damp dish towel, and set aside to double in bulk, about 45 minutes.
**8.** Preheat the oven to 375°F.
**9.** When the dough has fully risen, use a serrated knife or single-edge razor to make 3 shallow slashes in the top of each loaf. If you want a soft, shiny crust, brush the top of the loaves with the egg white–water mixture. (The crust will be crisp if you don't brush with egg white mixture.) Place the loaf pans on the center rack of the oven and bake about 40–45 minutes, until the loaves sound hollow when tapped in the center.
**10.** Run a butter knife around the edge of the pan and tip out the loaves. Place them on a cooling rack for at least 20 minutes before slicing.
#### **Whole Wheat Bread**
This hearty bread, made slightly sweet with the addition of molasses, could easily become the loaf of preference around your house.
**Ingredients** _(makes two loaves)_
_1 cup milk_
_¼ cup molasses_
_2 tablespoons vegetable oil, plus extra for oiling the bowl and loaf pans_
_2 teaspoons salt_
_1 teaspoon honey_
_1 package (1 scant tablespoon) active dry yeast_
_1–1½ cups unbleached all-purpose flour, plus extra for dusting the work surface_
_4 cups whole wheat flour_
_1 large egg white beaten with 1 tablespoon water (optional)_
**Equipment**
_Small saucepan_
_2 large bowls_
_Small bowl_
_Wooden spoon_
_2 5 x 9-inch loaf pans_
_Cooling rack_
**1.** Heat the milk in a small saucepan over _low_ heat until tiny bubbles appear around the edges (this is called scalding). Pour the scalded milk into a large bowl and stir in the molasses, oil, and salt. Cool to lukewarm.
**2.** Measure 1 cup lukewarm water into a small bowl. Stir in the honey and evenly sprinkle on the yeast. Let sit for 3 minutes, then add this mixture to the cooled milk mixture, stirring with a wooden spoon. Stir in 1 cup all-purpose flour, then add the whole wheat flour, 1 cup at a time, blending well after each addition. Add only enough flour to make a firm but pliable dough that is just slightly sticky.
**3.** Sprinkle the work surface with a scant ¼ cup all-purpose flour. Transfer the dough to your work surface.
**4.** Knead the dough for about 9 minutes, until it is smooth and supple, adding more all-purpose flour, ¼ cup at a time, if it is still sticky.
**5.** Wipe the inside of a large bowl with vegetable oil. Place the dough in the bowl, then turn it over so the top of the dough is coated with a thin layer of oil. Place a slightly damp dish towel over the bowl and set aside in a warm, draft-free place until doubled in bulk, about 1½–2 hours.
**6.** Punch down the dough with your fist until there are no air bubbles left. Knead the dough a few more times on a lightly floured work surface, then divide the dough in half and shape it into 2 loaves.
**7.** Wipe the inside of 2 loaf pans well with oil. Place the dough in the pans, cover with the dish towel, and set aside until doubled in bulk, about 45 minutes.
**8.** Preheat the oven to 425°F.
**9.** After the dough has risen a second time, use a pastry brush to gently brush the top of the loaves with some water to make a crisper crust. Brush with the egg white– water mixture for a softer, shinier crust.
**10.** Place the pans on the center rack of the oven and bake for 10 minutes, then lower the heat to 350°F and bake about 45 minutes more, until the loaves sound hollow when tapped and have shrunk slightly from the sides of the pan.
**11.** Run a butter knife around the edges of the pans and tip out the loaves. Place on a cooling rack for at least another 20 minutes before slicing.
#### **Pumpernickel Raisin Bread**
Pumpernickel dough is denser than other dough, so it takes more strength to knead and more time to rise—about 4 hours total as opposed to approximately 2¾ hours for the Country White Bread.
**Ingredients** _(makes one loaf)_
_1¼ cups lukewarm water (105°–115°F)_
_1 tablespoon sugar_
_1 package (1 scant tablespoon) active dry yeast_
_2 tablespoons molasses_
_2 tablespoons vegetable oil, plus extra for greasing the baking pan_
_1 tablespoon salt_
_1½ cups whole wheat flour_
_1½ cups rye flour_
_1 cup unbleached all-purpose flour, plus extra for dusting the work surface_
_¼ cup cornmeal_
_¾ cup raisins_
**Equipment**
_2 large bowls_
_Medium bowl_
_Wooden spoon_
_Whisk_
_11 x 17-inch baking sheet_
_Cooling rack_
**1.** Measure ¼ cup of the warm water into a large bowl. Stir in the sugar and evenly sprinkle on the yeast. Let the mixture sit for 5 minutes.
**2.** Stir in the molasses, oil, salt, and the remaining 1 cup warm water. Set aside.
**3.** In a medium bowl, use a whisk to combine the whole wheat, rye, and all-purpose flours and the cornmeal. Add the flour mixture to the yeast mixture 1 cup at a time, mixing well with a wooden spoon after each addition. The last 2 cups will take a bit more effort to incorporate. Add only enough flour to make a pliable and somewhat sticky dough.
**4.** Sprinkle a work surface with a scant ¼ cup all-purpose flour. Transfer the dough to the work surface.
**5.** Knead the dough for at least 10 minutes. It should still be slightly sticky. _Do not try to make the dough completely smooth._ Toward the end of the kneading, spread the raisins, a handful at a time, on the work surface and knead them into the dough.
**6.** Wipe the inside of another large bowl with vegetable oil. Place the dough in the bowl and then turn it over so the top of the dough is coated with a thin layer of oil. Cover the bowl with a slightly damp dish towel and put it in a warm, draft-free place until doubled in bulk, about 2–2½ hours.
**7.** Punch down the dough with your fist until there are no air bubbles left. Knead the dough a few more times on a floured work surface, then shape it into a round loaf.
**8.** Lightly grease an 11 x 17-inch baking sheet. Place the loaf on the baking sheet and cover it with the damp dish towel. Set aside in a warm, draft-free place until doubled in bulk, about 1½–2 hours.
**9.** Preheat the oven to 375°F.
**10.** When the dough has fully risen, place the baking pan on the center rack of the oven and bake about 35–40 minutes, until the loaf sounds hollow when tapped.
**11.** Place the loaf on a rack and cool for at least 20 minutes before slicing.
**Using Stale Bread**
While fresh homemade bread tastes so good it's nearly magical, stale bread is sad and unsatisfying. Fortunately, there are ways of salvaging stale bread as long as it is not so old that mold has developed. The easiest thing to do is make toast but there is only so much toast one can eat. Other alternatives including making bread crumbs and croutons.
To make dried bread crumbs, break the bread into manageable pieces and pulverize in a food processor or blender. Alternatively, place the bread in a plastic or paper bag and run over it with a rolling pin. If the bread that you are using is not quite dry, place it in a 250°F oven for a few minutes before turning it into crumbs. If not using immediately, freeze the bread crumbs in an airtight container.
To make your own croutons, see recipe page 168.
#### **Corn Bread**
This sweet bread can be served with all sorts of meals, most happily with chili. This recipe makes a lot of corn bread, but the kids always seem to gobble it down fast.
**Ingredients** _(makes twenty pieces)_
_10 tablespoons (1¼ sticks) butter, plus extra for greasing the pan_
_3 cups unbleached all-purpose flour_
_2 cups yellow cornmeal_
_1 cup sugar_
_1 tablespoon baking powder_
_1 teaspoon salt_
_2 ⅔ cups milk_
_2 large eggs_
**Equipment**
_9½ x 13½-inch baking pan_
_Small saucepan_
_Large bowl_
_Whisk_
_Medium bowl_
_Wooden spoon_
_Rubber spatula_
_Cooling rack_
**1.** Preheat the oven to 350°F. Grease a 9½ x 13½-inch baking pan with butter.
**2.** Melt the butter in a small saucepan.
**3.** Use a whisk to combine the flour, cornmeal, sugar, baking powder, and salt in a large bowl.
**4.** Whisk together the milk, eggs, and the melted butter in a medium bowl. Pour the liquid mixture into the flour mixture and blend well with a wooden spoon until all the flour mixture is incorporated. The batter should be very moist but not runny.
**5.** Use a rubber spatula to transfer the batter to the prepared baking pan and spread the batter evenly over the whole pan.
**6.** Bake the bread on the center rack of the oven about 12 minutes, until it is set (i.e., doesn't wiggle in the middle) and a toothpick inserted in the center comes out clean.
**7.** Let the bread cool on a rack in the pan for 20 minutes before cutting into squares.
#### **Irish Soda Bread**
This bread doesn't use yeast and requires no rising time, so you can throw it together in a jiffy. Keep it in mind when you want to take a gift of food along to a dinner party.
**Ingredients** _(makes two loaves)_
_4 cups unbleached all-purpose flour_
_¼ cup plus 2 tablespoons sugar_
_3 teaspoons baking powder_
_1 teaspoon baking soda_
_1 teaspoon salt_
_1¾ cups buttermilk_
_1 large egg_
_½ cup raisins or currants_
_¼ cup vegetable oil, plus extra for greasing the baking sheet_
**Equipment**
_11 x 17-inch baking sheet_
_Large bowl_
_Whisk_
_Medium bowl_
_Wooden spoon_
_Serrated knife_
_Cooling rack_
**1.** Preheat the oven to 375°F. Lightly grease an 11 x 17-inch baking sheet with vegetable oil.
**2.** Use a whisk to combine the flour, sugar, baking powder, baking soda, and salt in a large bowl.
**3.** Whisk together the buttermilk, egg, raisins or currants, and ¼ cup vegetable oil in a medium bowl.
**4.** Pour the wet ingredients into the flour mixture and mix well with a wooden spoon.
**5.** Transfer the dough to a lightly floured work surface and knead until smooth, about 2 minutes.
**6.** Divide the dough in half and shape each half into a round loaf. Place each loaf on the prepared baking sheet, leaving a few inches between them to allow for expansion. Use a serrated knife or a single-edge razor blade to make an "X" in the center of each loaf.
**7.** Bake the bread on the center rack of the oven about 35–40 minutes, until the top is light brown and a toothpick inserted in the center comes out clean.
**8.** Let the loaves cool on the baking sheet for 20 minutes. Transfer the loaves to a rack and let them cool for another 20 minutes before slicing.
**Cake Tester**
A cake tester is nothing more than a toothpick or a thin metal skewer. If you have neither of these on hand, use the clean end of a broom bristle. To test breads, cakes, and other baked goods for doneness, simply insert the tester into the thickest part of what you are testing and pull it out. If it comes out clean, or with tiny dry crumbs clinging to it, what you are baking is done. If it is at all damp, then more baking is required.
* * *
**Dad's Own Pizza**
Making pizza at home is a simple operation. It requires few ingredients, little work, and no special equipment. And your pizza will be as good as, if not better than, the pies made in most local pizza shops.
##### **The Dough**
**Ingredients** _(makes two 16-inch pizza crusts)_
_2 cups lukewarm water (105°–115°F)_
_1 teaspoon sugar_
_2 packages active dry yeast_
_4½ cups unbleached all-purpose flour_
_1½ cups whole wheat flour_
_¼ cup olive oil, plus extra for greasing the baking sheet_
_1 tablespoon salt_
**Equipment**
_11 x 17-inch baking sheet_
_2 large bowls_
_Whisk_
_Wooden spoon_
**1.** Lightly grease an 11 x 17-inch baking sheet with vegetable oil.
**2.** Measure the lukewarm water into a large bowl. Add the sugar and sprinkle on the yeast in an even layer. Let the mixture sit for 7 minutes.
**3.** Combine the flours in a large bowl using the whisk.
**4.** Add the olive oil and salt to the yeast mixture, then the flours, 1 cup at a time, and stir with a wooden spoon until the flour is incorporated. The dough should be slightly sticky.
**5.** Lightly flour a work surface and knead the dough for 8–10 minutes, until smooth.
**6.** Divide the dough in half and shape each half into a ball. Place each ball on the prepared baking sheet, leaving about 4 inches between to accommodate expansion.
**7.** Cover the dough with a damp dish towel and let it rise in a warm, draft-free place for 1 hour.
**Freezing Pizza Dough**
Pizza dough freezes very well. Follow the recipe for making the dough, but let the dough rise for only 30 minutes (instead of 1 hour). Wrap each half of the dough loosely in 2 layers of plastic wrap and place immediately in the freezer. To use the frozen dough, either transfer it to the refrigerator the night before or leave it on the counter until it thaws, about 4–5 hours, depending on the temperature of the room. If you've thawed the dough in the refrigerator, remove it 1 hour before you bake so it can come to room temperature.
##### **The Pizza**
Although pizza can be made on ordinary baking sheets, for a crisper crust it is best to use a round pizza stone or screen. (Both are found in most kitchenware stores.) You can count on using it again and again to make this Friday-night special that kids just scarf up.
**Ingredients** _(makes two 16-inch pizzas)_
_Olive oil, if using baking sheets_
_Flour, for dusting the work surface_
_1 recipe Pizza Dough or your favorite store-bought dough_
_2 cups Basic Tomato Sauce (page 182) or your favorite store-bought sauce_
_1 pound mozzarella cheese, grated_
_Assorted toppings (seeopposite page)_
**Equipment**
_Pizza stone, pizza screen, or 2 11 x 17-inch baking sheets_
_Rolling pin (optional)_
_Ladle_
_Large spatula_
_Pizza cutter_
_Cutting board_
**1.** Position a rack as low as possible in the oven and preheat to 450°F. If using baking sheets, lightly grease them with the olive oil.
**2.** Lightly dust a work surface with flour. Punch down 1 ball of dough and use your fingers (or rolling pin) to push it out to half the desired size, roughly 8 inches across.
**3.** Lightly flour both sides of your hands. Drape the edge of the dough over your fists and use your knuckles to turn and stretch the dough until it is approximately 16 inches across. It should be slightly thicker around the edges.
**4.** Lay the dough on the pizza stone or screen or fit the dough into the baking sheets.
**5.** Assemble and bake one pizza at a time, as follows: Ladle 1 cup tomato sauce in the center of the dough and spread evenly to cover.
**6.** Sprinkle on half the grated mozzarella in an even layer.
**7.** Arrange your choice of toppings over the cheese.
**8.** Bake the pizzas, one at a time, on the lowest rack of the oven for about 10 minutes, until the cheese bubbles and the bottom of the crust is crispy.
**9.** Use a large spatula to slide the pizza from the stone or baking sheet onto a cutting board. Let the pizza cool for 1 minute before slicing with a pizza cutter or large knife.
**10.** Assemble the second pizza while the first one is in the oven, then put the second one in the oven as you sit down to eat the first.
**Tips**
• Make sure there are no holes in the dough. If any holes appear while you are stretching the dough, patch them up by folding the dough over the hole and stretching again.
• Stretching the dough over the backs of your hands assures that the crust will be light and crispy, but it takes a little practice. After three or four pizzas, you should get the hang of it. If necessary, roll the dough out fully with a rolling pin.
• To make a lip around the pizza, fold the dough over itself around the edge.
**Topping Suggestions**
• Extra cheese
• Capers
• Chile peppers
• Sun-dried tomatoes
• Thinly sliced red onion
• Italian sausage
• Pine nuts
• Sautéed spinach
• Artichoke hearts
• Anchovies
• Shrimp
• Thinly sliced pepperoni
• Sliced mushrooms
• Gorgonzola
• Strips of red, yellow, and green bell peppers
• Hamburger
• Sliced olives
* * *
#### **Scones**
These old-fashioned biscuits are quick and easy to make. Serve with butter, jam, or marmalade.
**Ingredients** _(makes twelve scones)_
_2 cups unbleached all-purpose flour_
_6 tablespoons sugar_
_3 teaspoons baking powder_
_½ teaspoon salt_
_6 tablespoons (¾ stick) cold butter, plus extra for greasing the baking sheet_
_1 large egg_
_1 cup heavy cream or whole milk_
_½ cup currants, dried cranberries, raisins, or chocolate chips (optional)_
**Equipment**
_11 x 17-inch baking sheet_
_Large bowl_
_Medium bowl_
_Whisk_
_Wooden spoon_
_Pastry brush_
_Cake tester_
**1.** Preheat the oven to 375°F. Lightly grease the baking sheet with butter.
**2.** Using a wooden spoon, mix together the dry ingredients in a large bowl.
**3.** Cut the cold butter (margarine is not suitable as it changes the consistency of the dough) into small pieces and scatter them into the dry mixture. Working quickly with the tips of your fingers, break the butter into pieces the size of peas.
**4.** Beat the egg with a whisk in a medium bowl, then add the cream or milk. Set aside 2 tablespoons of the egg mixture to use later for brushing on top of the scones. Add the currants, cranberries, raisins, or chocolate chips to the egg mixture.
**5.** Pour the wet ingredients into the flour mixture. Stir with the wooden spoon until the liquid is just incorporated. The dough should be soft and slightly sticky. If the dough sticks to your fingers, add more flour 1 tablespoon at a time. If the dough is stiff and doesn't hold together, add more cream or milk 1 tablespoon at a time.
**6.** Divide the dough in half and shape into 2 balls. Place each ball on either end of the prepared baking sheet and press down to form 2 circles, each about 6 inches across and 1 inch thick.
**7.** Cut each circle of dough into 6 wedges, then pull the wedges away from each other slightly so they are barely touching. Lightly brush the tops of the wedges with the reserved egg mixture.
**8.** Bake on the center oven rack for 12 minutes, or until the tops are lightly browned and a cake tester inserted in the thickest part comes out clean.
**Time-Saver**
Steps 2, 3, and 4 can be done in advance. Just cover the separate bowls with plastic wrap and refrigerate the liquids.
## Cooking in the Great Outdoors
In other times and other cultures women tended to the fire, but today in suburban America, Dad is often in charge of the charcoal. This chapter will expand your repertoire beyond hamburgers, hot dogs, and steak—to impressive fare like chicken saté and Asian swordfish.
* * *
**The Basic Grill**
You don't need to spend a lot of money on a deluxe grill with fancy gadgets. A good, sturdy grill with a cover and rack that can be adjusted toward or away from the flame will do. It should be made of heat-resistant material that won't rust if left in the rain (such as enameled steel, stainless steel, or treated cast-iron). Brands to look for are Weber, Sunbeam, and Kingsbord.
Consider your needs and the size of a grill: A small hibachi is fine for grilling a couple of pieces of chicken or a single steak. But if you've got a family of four or more, or plan on hosting outdoor functions, think about investing in a medium-sized or large grill.
Grill aficionados regularly debate the merits of charcoal vs. gas. The advantage of a gas grill that runs on bottled propane: it has an instant flame (though you have to wait for coals to heat), and you can control the strength of the flame during cooking. Though more convenient, a gas grill is a greater initial expense. Charcoal grills, on the other hand, have tradition as well as taste on their side, the charcoal imparting a slightly smoky flavor to the food. And with charcoal, there's more hands-on connection to the process.
##### **Getting the Coals Ready**
Though convenient, chemical starters are damaging to the environment and not recommended. Instead, use either an electric starter or a chimney. This cylinder of perforated metal makes lighting charcoal simple and fast. Place a loosely-crumpled sheet of newspaper in the bottom of the chimney and pile the coals into the top. Light the paper. In about ten minutes the coals on top will be gray. Dump them into the grill.
If you really must use charcoal starter, first cover the bottom of the grill with a dense single layer of coals. Then arrange the briquets in a tight pyramid in the center of the grill. Squirt about ⅓ cup of fluid on the coals and let them soak for 2 minutes. Give one more quick squirt, then light the coals—from both sides so they'll burn evenly.
Whichever method you use, you'll know that the charcoals are lit when the edges of the individual briquets start turning gray. Let them heat in the pyramid for 30 minutes, then spread them out over the grill floor with a grilling fork or spatula. After spreading the coals, set the grilling rack in place and wait about 5 more minutes until the coals are about half gray. A single layer of briquets will give you 40–50 minutes of optimum heat.
##### **Grilling Technique**
Grilling is an inexact science, requiring ingenuity and improvisation. Fires invariably reach different temperatures, altering cooking times. In other words, you don't just leave the chicken or burgers alone while you sip mint juleps with the guests. You have to be a "nudge" at the grill, regularly checking, turning, rotating, monitoring flareups, and basting. Because the heat is not uniform and certain areas of the grill are hotter than others, grilling requires constant adjustment. Even short distraction can mean the difference between succulent medium rare and dried out. Here are some tips to help with your grilling technique:
• Trim excess fat from all cuts of meat to reduce flareups.
• Have a table nearby to hold your spray bottle, platters, utensils, and a cold beer, so you'll never have to leave the grill for any period of time.
• Make sure the coals are hot enough before you begin to barbecue. You shouldn't be able to hold your hand 5 inches over the grill for more than 3 seconds.
• Determine your grill's hot spots—for example, the center is usually hotter than the edges. Rotate the food around the grill so that the pieces cook evenly, which may mean moving each piece of food every few minutes.
• When you grill chicken, keep the dark meat around the hottest part of the grill and the white meat where it is less hot. This will help all of the chicken cook at the same rate.
• Always begin cooking bone-in chicken with the bone side down to keep the skin from burning.
• Designate one of the kids as chief assistant, responsible for all emergency runs into the house.
##### **Grill Maintenance**
Always keep your grill in good working order. For gas grills, refer to the manufacturer's instructions for cleaning and maintenance. For charcoal grills, refer to the following tips:
• Clean out the ashes after every use. Make sure ashes have cooled completely, then tip the grill and pour the ashes into a garbage bag.
• Scrape the grill rack with a wire brush before and after each use to keep the grease from building up. If desired, clean the outside with warm, sudsy water. If you need to clean the inside, brush it down with the same brush you used to clean the grill.
• Always cover your grill when you're finished using it. Top-grade grills won't be bothered by a little rain, but it's best to store your grill in the garage, or under a protected awning or grill tarp.
• Store the grill in the garage for the winter. If you must leave it outside, cover it with plastic. A painter's plastic drop cloth does the trick nicely.
##### **About Marinades**
The flavor and tenderness of some cuts of beef, lamb, and poultry can be enhanced by letting them sit in a marinade for several hours in the refrigerator. Turn the meat 3 to 4 times so that all sides can absorb the marinade. If you are pressed for time, you can marinate at room temperature, which speeds up the process, but do not leave meat or fish out for more than 1 hour before you begin cooking it. Better cuts of meat, such as porterhouse and sirloin don't need marinating. Chicken and pork can always do with a marinade to keep them from drying out. Fish or seafood should not be marinated for more than 2 hours as the flesh begins to break down. Thin fillets, such as sole and flounder, should not be marinated at all. Do not reuse the marinade the raw meat or fish was in—if you want to baste while grilling, set aside some marinade before you marinate the meat or fish.
##### **Marinating Technique**
**1.** Place the meat, chicken, or fish in a large plastic container or sealable plastic bag.
**2.** If you want to baste while cooking, set aside about ½ cup of the marinade. Pour the rest over the meat, chicken, or fish, turn it once so both sides are covered, cover the container, and refrigerate, turning occasionally.
**3.** After marinating, remove the meat, chicken, or fish from the marinade and place on the hot grill. Discard the marinade. About 5 minutes before the end of the cooking, brush the top of the meat, chicken, or fish with the reserved marinade and turn over. Cook for 1 minute, brush the other side, and turn over again. Continue cooking and turning every minute or so until the meat, chicken or fish is nicely glazed.
##### **Cooking Times**
It would be nice if there were exact cooking times for the barbecue, but unfortunately, too many variables are involved in grilling. Besides, one person's medium rare is another person's "on the hoof." Only you can cook your idea of the perfect steak. Nevertheless, keep these general hints in mind when you're tending the grill:
• Keep a close eye on the food for doneness. An extra-hot fire can turn a medium-rare steak into a medium-well steak in an instant. It is best to use the professional chef's method—pressing a finger into the meat—to gauge doneness. Remember that meat begins to get more taut as it cooks. Uncooked meat is soft and flabby while overdone meat is stiff and tough. In between, it has a kind of tight springiness. Poke a steak you've cooked to your liking to get a sense of how it feels for future reference. If absolutely necessary you can cut into a piece of meat to see if it is cooked, but remember that you will release some of the meat's flavorful juices.
• When you're figuring your cooking times, remember that meat and poultry continue to cook after they're removed from the grill. A medium-rare steak will become almost medium by the time it reaches the table, so remove it from the grill accordingly.
• Do not judge whether your meat is cooked by how it looks on the outside. Meat and poultry can quickly char on the outside and remain uncooked on the inside. If necessary, douse the coals slightly to cool them down.
• The cooking times on the following page are educated ballpark figures. Your best gauge of doneness is an attentive eye and experience. If you like your meat more well-done than "medium," just leave it on the grill a few minutes longer. Unless otherwise noted, times are given according to the thickness of the cut. The fire should be at its peak heat with the grill rack set 4–5 inches from the coals. If your rack is not adjustable, partially or fully cover the grill to slow cooking down.
The print edition of this book includes charts for **Cooking Times**.
Please download a PDF of the charts here: workman.com/ebookdownloads
**Steaks**
**Hamburgers**
**Lamb Chops (Loin)**
**Pork Chops (Loin)** _Cook with the grill partially covered._
**Chicken** _Cook 5–6 inches from coals (medium-high setting)._
**Fish** _Use a hinged wire grill basket for best results_.
**Equipping the Grill**
• **Long Spatula** for flipping burgers and fish.
• **Long Tongs** for turning and rearranging food on the grill. Never use a fork, as piercing the meat will cause it to lose flavorful juices.
• **Spray Bottle or Squirt Gun** filled with water to spritz coals flaming from dripping grease.
• **Basting Brush** for spreading on sauce or marinade during the last moments of grilling.
• **Flame-Resistant Cooking Gloves,** preferably the longer variety, to protect your hands and arms.
• **Wire Brush** for scraping the grill before and after each use.
• **Hinged Wire Grill Basket** for grilling fish fillets and vegetables.
• **Skewers** for all kinds of kebabs. Use thick metal skewers for meat and thin skewers for vegetables. Bamboo skewers are excellent for foods that have short cooking times. Soak the bamboo skewers in warm water for 1 hour before using in order to keep them from burning. Bamboo skewers won't get hot like the metal ones, so you can transfer them directly from the grill to the dinner plates. Food cooked on metal skewers should be removed from the skewers before serving.
• **Charcoal** Regular charcoal briquets work very well, but "natural" untreated charcoal further enhances the flavor of whatever you're grilling. You should, however, avoid the presoaked briquets as they have a tendency to impart a vaguely chemical taste to the food.
##### **Basting**
Basting sauces should be applied only during the last stages of grilling. The sauce does not actually add flavor to the meat itself, but forms a tasty coating over the meat. Sauces, especially those that contain sugar or honey, will burn if applied too early, diminishing the flavor of both the sauce and the meat.
* * *
#### **Dad's Own Barbecue Sauce**
This sauce is best for chicken, flank steak, ribs, or pork chops.
**Ingredients** _(makes enough for 1 cut-up chicken or 2 pounds meat)_
_1 tablespoon vegetable oil_
_1 medium onion, finely chopped_
_3 cloves garlic, minced_
_1 cup ketchup_
_2 tablespoons Dijon mustard_
_2 tablespoons honey_
_2 tablespoons Worcestershire sauce_
_1 tablespoon malt or cider vinegar_
_1 tablespoon molasses (or honey)_
_¼ teaspoon ground cinnamon_
_1 teaspoon salt_
_Dash of cayenne pepper_
**Equipment**
_Medium saucepan_
_Medium bowl_
**1.** Place a saucepan on _medium high_ until it gets hot, about 45 seconds. Add the oil and the onion and sauté until soft, about 5 minutes. Add the garlic and sauté for a minute more.
**2.** Transfer the onion and garlic to a medium bowl. Add the ketchup, mustard, honey, Worcestershire sauce, vinegar, molasses, cinnamon, salt, and cayenne pepper, and mix well.
**3.** Pour over the meat.
#### **Wine- &-Herb Marinade**
This marinade is best for chicken and fish.
**Ingredients** _(makes enough for 1 cut-up chicken or 2 pounds chicken or fish)_
_2 cups white wine_
_1 medium onion, thinly sliced_
_3 whole cloves garlic_
_2 tablespoons chopped fresh parsley_
_2 tablespoons chopped fresh oregano or 2 teaspoons dried oregano_
_2 tablespoons chopped fresh basil or 2 teaspoons dried basil_
_½ teaspoon chopped fresh or dried rosemary_
**Equipment**
_Medium bowl_
In a medium bowl, combine all the ingredients. Pour over the meat.
#### **Asian Marinade**
This marinade is suitable for chicken, fatty fish, flank steak, ribs, or pork chops.
**Ingredients** _(makes enough for 1 cut-up chicken or 2 pounds meat or fish)_
_¾ cup soy sauce_
_¾ cup white wine_
_¼ cup lemon juice_
_3 scallions, chopped_
_3 tablespoons dark brown sugar_
_1 teaspoon garlic powder_
_½ teaspoon ground ginger_
**Equipment**
_Medium bowl_
Combine all the ingredients in a medium bowl. Pour over the meat.
#### **Barbecued Chicken**
As far as I'm concerned, grills were made for barbecuing chicken. This recipe will probably leave you with some leftovers to serve for lunch the next day.
**Ingredients** _(serves four)_
_Dad's Own Barbecue Sauce (page 247), for basting the chicken_
_2¾-pound chicken, cut into quarters_
**Equipment**
_Tongs_
_Barbecue brush_
**1.** Light the charcoal. When the briquets are hot, place the chicken pieces on the grill, skin side up. Grill the chicken for 25 minutes, then turn and grill for 15 minutes more.
**2.** Baste the chicken with the barbecue sauce, turn, and grill for 3 minutes more, until the chicken begins to get dark brown. Baste again, turn, and grill for 3 minutes more. The skin should start getting very dark, but don't let it burn.
**Serving Suggestion**
Serve with corn, coleslaw, thick crusty bread, and lots of extra sauce on the side (see Tips).
**Tips**
• Because the dark meat legs take longer to cook than the white meat breasts, arrange the legs in the center of the grill, where it is hotter, and place the breasts around them. If the breasts still finish cooking sooner than the legs, move them to the outer edge of the grill or transfer them to a platter and cover with foil.
• Larger chickens may need longer cooking times. To check for doneness, press down on the breast. If it is firm but springy, it is done. If it is very firm, it is overdone. If you're not sure, cut into 1 of the breasts to see if the meat is white. To check the legs for doneness, prick the thigh area. If the juices run clear (not pink), they are done.
• After you have finished basting the chicken with the barbecue sauce, transfer the sauce to a small saucepan and simmer for several minutes. This is to kill any bacteria that may have been transferred while basting from the not-yet-fully-cooked chicken. Alternatively, make extra barbecue sauce for serving and discard the sauce used for basting.
#### **Barbecued Spareribs**
Ribs are surprisingly easy to make; just remember to get them started early in the day so they have time to marinate. They take up a lot of room on the grill, so if you don't have a large grill, be prepared to cook them in shifts.
**Ingredients** _(serves four)_
_4 pounds country-style or baby-back pork ribs_
_1 large onion_
_3 whole cloves garlic_
_2 bay leaves_
_Double batch (about 3½ cups) Dad's Own Barbecue Sauce (page 247) or favorite store-bought sauce_
**Equipment**
_Large pot_
_Colander_
_1 or more large plastic containers or stainless-steel bowls_
_Spray bottle or squirt gun_
_Barbecue brush_
**1.** Trim away any excess fat from the ribs.
**2.** Because the ribs would burn and dry out if cooked solely on the grill, you want to parboil them first. Put the ribs in a large pot and add enough water to cover. Add the onion, whole cloves of garlic, and bay leaves, and bring to a boil over _high_ heat. Reduce the heat to _medium low_ and simmer, uncovered, for 1 hour.
**3.** When the ribs are done simmering, drain them in a colander and place them in a large plastic container or stainless steel bowl. You may have to use more than 1 bowl or pan. Set aside ¾ cup of the barbecue sauce for basting. Pour the rest over the ribs, cover, and refrigerate for at least 2 hours.
**4.** Light the charcoal. When the briquets are hot, place the ribs on the grill. Cook for 20 minutes, turning frequently. Keep your spray bottle or squirt gun handy as fat dripping from the ribs can cause small flareups. To control larger flareups, cover the grill for about 30 seconds.
**5.** Baste the ribs and continue cooking for 10 more minutes, turning and basting every couple of minutes.
**Serving Suggestion**
Serve hot with coleslaw, potato salad, corn bread, and lots of napkins.
**Variation**
Instead of parboiling the ribs before grilling them, you can bake them. Preheat the oven to 350°F. Arrange the ribs on a lightly oiled baking pan, cover the pan with foil, and bake them on the center rack of the oven—1 hour for country-style ribs, 45 minutes for baby backs.
#### **Lamb Shish Kebab**
Grilling on skewers is one of the oldest ways to cook and still one of the best. Here is a basic recipe, but feel free to improvise. Just about any meat or vegetable that fits on a skewer can be grilled.
**Ingredients** _(serves four)_
_½ cup olive oil_
_¼ cup red wine or dry sherry_
_¼ cup fresh lemon juice_
_2 tablespoons soy sauce_
_1 medium onion, thinly sliced_
_2 cloves garlic, minced_
_1 teaspoon dried cumin_
_1 teaspoon dried rosemary_
_Freshly ground black pepper_
_1½ pounds lamb for shoulder or leg, cut into 1½-inch cubes_
_2 medium onions, cut into eighths_
_2 red or green bell peppers, seeded and cut into 1½-inch squares_
**Equipment**
_Large plastic container, stainless-steel bowl, or glass or enamel baking dish_
_Medium bowl_
_4 metal skewers_
**1.** In a medium bowl, combine the olive oil, red wine or sherry, lemon juice, soy sauce, onion, garlic, cumin, rosemary, and pepper.
**2.** Arrange the cubed lamb in a large plastic container, stainless-steel bowl, or glass or enamel baking dish.
**3.** Set aside ½ cup of the marinade for basting. Pour the rest over the lamb, mix well, cover, and refrigerate for at least 4 hours. Do not marinate the vegetables.
**4.** When the meat is ready, light the charcoal. While the coals are heating, assemble the skewers, alternating pieces of lamb with the onion and bell pepper.
**5.** When the coals are hot, cook the shish kebabs for 12–18 minutes, turning once after 7 minutes, until the meat is cooked through. During the last 5 minutes of cooking, baste the shish kebabs with the reserved marinade and turn the skewers frequently.
**Serving Suggestion**
Serve with rice pilaf and green salad.
**Kebab-O-Rama**
In addition to lamb, many other kinds of meat, poultry, and fish can be used to make great kebabs. Here are a couple of ideas to get you started.
• 1½-inch pieces of boneless chicken thighs marinated in either the Asian or Wine-&-Herb marinade. Look for "roaster" thighs, which are bigger and meatier and hold up better on the grill. Grill for 7–8 minutes on each side.
• 1½-inch chunks of swordfish or tuna, marinated in the Asian marinade. Grill for 6–7 minutes on each side.
• 1½-inch pieces of sirloin or round steak, marinated in the Asian marinade. Grill for 7–8 minutes on each side.
#### **Grilled Vegetables**
Grilled vegetables make a colorful centerpiece when served on a platter or over rice. Many vegetables can be cooked on the grill right along with the main course. Others need to be skewered or cooked in a hinged grill. Vegetables must be cut specially to fit the skewers. The grill basket accommodates various sizes of vegetables, conveniently rests right on the barbecue grill, and can be turned easily for even cooking.
• **Carrots** Cut into 2-inch pieces for skewers, in half lengthwise for the grill basket. Blanch in a large pot of boiling water for 5 minutes and then refresh with cold water. Brush lightly with oil before grilling for 6–8 minutes, turning once.
• **Cherry Tomatoes** Marinate whole in vegetable oil along with ½ teaspoon each dried basil and dried rosemary. Place on a thin skewer and grill for 5 minutes, turning often.
• **Corn** To roast with foil, husk the ears and wrap them in foil. Place on the grill for 12 minutes, turning 3 or 4 times. To roast without foil, husk the ears and rub lightly with butter. Grill for 8–10 minutes, turning often until they begin to brown.
• **Mushrooms** Leave them whole, trimming only the bottom of the stem. Skewer through the stem with a thin metal or bamboo skewer, working slowly to keep the mushrooms from splitting, or place them in a hinged grill. Brush lightly with oil before grilling for 6–8 minutes, turning 3 or 4 times.
• **Onions** Peel a medium onion and cut it into quarters, then cut each quarter in half crosswise. Skewer across the grain or place in a grill basket. Brush lightly with oil before grilling for 10–12 minutes, turning 2 or 3 times.
• **Bell Peppers** Seed and cut into 2-inch squares for skewers, quarters for the grill basket. Brush lightly with oil before grilling for 8–10 minutes, turning 2 or 3 times.
• **Potatoes** Use small new potatoes whole or cut large potatoes into 1½-inch cubes. Put the potatoes in a pot and cover them with cold water. Bring to a boil, reduce the heat, and let simmer until just barely cooked through, about 12 minutes. Immediately drain the potatoes and when they are cool enough to handle, place them on thin skewers or in a grill basket. Brush them lightly with oil before grilling for 10–12 minutes, turning 3 or 4 times.
• **Summer Squash and Zucchini** Cut into 1-inch rounds for skewers, halve lengthwise for a grill basket. Brush lightly with oil or Italian salad dressing before grilling for 6–8 minutes, turning 3 or 4 times. (Skewer the rounds through the skin and grill them with the cut sides on the rack.)
**Tip**
Vegetables that take approximately the same amount of time to cook can be skewered or arranged in a grill basket together.
#### **Asian Grilled Swordfish**
Swordfish holds up well on the grill and is a nice change of pace from the usual barbecue fare. Marinate the steaks for no more than 2 hours and remove them from the grill when they are just cooked through and begin to flake.
**Ingredients** _(serves four)_
_¼ cup soy sauce_
_2 tablespoons lemon juice_
_2 tablespoons sherry or sake_
_1 teaspoon sesame oil_
_1 clove garlic, mashed and chopped_
_1 teaspoon sugar_
_4 8-ounce swordfish steaks, 1–1½ inches thick_
_Vegetable oil, for brushing on the grill rack_
**Equipment**
_Large plastic container or glass baking dish_
_Medium bowl_
_Barbecue brush_
_Large spatula_
**1.** In a medium bowl, combine the soy sauce, lemon juice, sherry or sake, sesame oil, garlic, and sugar, then pour it over the fish. Cover the fish with plastic wrap and marinate for at least 30 minutes and no more than 2 hours, turning once.
**2.** Lay the fish in a large plastic container or glass baking dish.
**3.** Brush the grill rack with vegetable oil, and light the coals. When the fire is very hot, lay the fish on the grill. Cook for about 5 minutes for 1-inch steaks, 6 minutes for 1½-inch steaks. Turn the fish carefully with a large spatula and grill until it begins to flake, about 5 minutes more.
**Serving Suggestion**
Serve with corn on the cob and rice.
#### **Pork or Chicken Saté**
An Indonesian specialty, these skewers of meat can be served as appetizers or a main course. The meat is cut into small pieces so it grills very quickly.
**Ingredients** _(serves six as an appetizer, four as a main course)_
_½ medium onion, quartered_
_3 cloves garlic_
_1-inch piece lemon zest (yellow part of skin), finely chopped_
_1 tablespoon brown sugar_
_2 tablespoons fresh lemon juice_
_¼ cup soy sauce_
_1 tablespoon curry powder_
_1 pound boneless pork, cut into 1-inch cubes_
_OR_
_¾ pound skinless, boneless chicken breasts, cut into 2 x ½-inch strips_
_Peanut Dipping Sauce (recipe follows), for serving_
**Equipment**
_Medium bowl_
_Blender or food processor_
_Approximately 24 bamboo or thin metal skewers_
**1.** Put all the ingredients (through curry powder) in a blender or food processor and purée. Transfer to a medium bowl.
**2.** Add the pieces of pork or chicken to the marinade and stir to coat the meat uniformly. Marinate at room temperature for 1 hour or in the refrigerator for at least 2 hours.
**3.** If using bamboo skewers, soak them in warm water for 1 hour before grilling.
**4.** Light the charcoal. While the coals are heating, place 1 chicken strip or 2 pork cubes on each skewer (the skewer should be inserted through the chicken lengthwise).
**5.** When the coals are ready, place the meat on the grill for 6–8 minutes for chicken, 10–12 minutes for pork, turning once. Serve hot with peanut dipping sauce.
**Note**
To make beef saté, cut a ½-inch-thick piece of sirloin into 4- or 5-inch strips. Marinate and place on skewers. Grill for 8–10 minutes, turning once.
**Serving Suggestion**
Accompany with rice pilaf and a few skewers of grilled vegetables.
#### **Peanut Dipping Sauce**
**Ingredients**
_½ cup smooth "natural" peanut butter_
_¼ cup fresh lime juice_
_¼ cup water_
_2 tablespoons soy sauce_
_1 tablespoon honey_
_½ teaspoon sesame oil_
_1 whole clove garlic_
_½ teaspoon ground coriander_
**Equipment**
_Food processor or blender_
Place all the ingredients in a food processor or blender and process until smooth. Serve at room temperature in individual dipping bowls.
#### **Mary Cleaver's Boneless Chicken Breasts with Balsamic Vinegar & Rosemary**
The New York caterer Mary Cleaver is a wonderful chef who makes light and intensely flavored food. Here is one of her favorite dishes for marinated, grilled chicken. The marriage of a few simple yet bold flavors is typical of Mary's food. I prepared this dish many times working in the Cleaver Co. kitchen and now make it for my family on our patio grill.
**Ingredients** _(serves four)_
_¼ cup extra-virgin olive oil_
_¼ cup balsamic vinegar_
_4 cloves garlic, peeled and mashed_
_2 sprigs fresh rosemary or 1 teaspoon dried_
_Freshly ground black pepper_
_2 whole boneless, skinless chicken breasts, cut in half_
**Equipment**
_Small bowl_
_Plastic container or stainless steel or ceramic bowl_
_Grill_
**1.** Combine the oil, vinegar, garlic, rosemary, and pepper in a small bowl.
**2.** Rinse the chicken breasts in cold water and pat them dry. Place the chicken in a plastic container or stainless steel or ceramic bowl just large enough to hold them and pour on the marinade. Turn the chicken breasts to coat both sides with marinade. Cover and refrigerate for at least 6 hours and up to 24 hours.
**3.** Light the coals in the grill. When they are hot, place the chicken breasts on the rack and grill for 4–5 minutes. Turn the chicken, basting it with the marinade, and grill for 4–5 minutes more, until cooked through.
**Serving Suggestion**
Boneless breasts don't take up much room on the grill, so plan on grilling an assortment of skewered vegetables, such as bell peppers, tomatoes, and onions right alongside.
## Cooking for a Crowd
Making dinner for 12 people is not much more work than making dinner for four. It's simply a matter of roasting an 18-pound turkey instead of a 4-pound chicken, or putting 12 potatoes in the oven instead of four. Coming up with the extra seating might be more of a problem than preparing the extra food.
Cooking for a crowd does, however, require extra planning. It means leaving more time for preparation, choosing dishes that lend themselves to feeding larger numbers, and making sure you have large enough pans and serving platters for the quantity of food you're cooking and serving. The recipes included in this section will allow you to cook for eight to twelve guests without too much fuss. These entrées were chosen so that Dad can enjoy the company and not spend the whole night in the kitchen.
#### **Baked Smoked Ham**
There are a lot of advantages to serving a baked ham at a dinner party: It's easy to prepare, it goes a long way, and you can serve it either hot or at room temperature. And when you're done, you'll have the bone to make a great soup. Smoked hams are available in most supermarkets or at your local butcher. Even though these hams are smoked, they still need to be cooked through.
**Ingredients** _(serves twelve to sixteen)_
_1 smoked ham, bone in, about 10 pounds_
_About 8 cups apple cider_
_1 cup brown sugar_
_2 tablespoons Dijon mustard_
_1½ cups bread crumbs_
**Equipment**
_Large roasting pan_
_Medium bowl_
**1.** Preheat the oven to 350°F and position a rack in the lower third of the oven.
**2.** Place the ham, fat side down, in a large roasting pan and fill the pan halfway with apple cider. Place the pan on the lower rack of the oven and bake for 18 minutes per pound (3 hours for a 10-pound ham).
**3.** Meanwhile, combine the brown sugar, mustard, and bread crumbs in a medium bowl. Set aside.
**4.** When the ham is cooked, remove it from the oven (leave the oven on) and use a knife to trim off the skin and fat. Spread the bread crumb mixture on the surface of the ham and bake for 30 minutes more, until the glaze is crusty. Let the ham sit for 10 minutes before slicing.
**5.** Slice the ham across the grain and straight down toward the bone. Serve topped with some of the pan juices.
**Serving Suggestions**
Serve the ham with mashed potatoes, baked sweet potatoes, or hash browns. (If you have a double oven you can make oven-fried potatoes.) Irish soda bread is also a great companion for ham. For vegetable accompaniments, consider corn on the cob, string beans, or carrots.
**Country Hams**
Dry-cured country hams, like Smithfield hams, are available through the mail and come with specific cooking instructions. These hams have a somewhat sharper and more distinct flavor than smoked hams. Dry-cured hams need to be soaked in water for 12–24 hours to remove the curing salt, so be sure to leave yourself enough time.
#### **Dad's Own Chili**
A great pot of chili with hot corn bread is always a crowd pleaser. Save yourself a bit of trouble and make it a day in advance. The extra time in the refrigerator will enhance its flavor.
**Ingredients** _(serves twelve)_
_3 tablespoons corn or vegetable oil_
_1 large onion, diced_
_1 green bell pepper, diced_
_2 cloves garlic, chopped_
_2 pounds ground beef_
_2 cups beef broth or 2 bouillon cubes dissolved in 2 cups water_
_1 35-ounce can crushed tomatoes_
_3 tablespoons tomato paste_
_¼ cup chili powder (see Note)_
_2 teaspoons ground cumin_
_1 teaspoon dried oregano_
_1 teaspoon salt_
_¼ teaspoon cayenne pepper_
_1 16-ounce can red kidney beans, drained_
**Equipment**
_Large frying pan_
_Large soup pot_
_Colander_
**1.** Place a large frying pan on _medium-high_ heat and let it get hot, about 45 seconds. Add 1 tablespoon of the oil, then the onion and peppers, and sauté until soft, about 6 minutes. Add the garlic and sauté for 2 minutes more. Transfer the mixture to a large soup pot.
**2.** Increase the heat under the frying pan to _high_ and let the pan get very hot, about 90 seconds. Add 1 tablespoon of the remaining oil and 1 pound of the ground beef. Brown the meat for about 6 minutes, then transfer it to a colander to let the fat drip off. Repeat with the remaining oil and beef. Transfer the meat to the soup pot.
**3.** Add the beef broth, crushed tomatoes, tomato paste, and all of the spices to the soup pot. Bring the mixture to a boil over _medium-high_ heat, then reduce the heat to _low_ and simmer for 45 minutes, stirring occasionally.
**4.** Add the beans and simmer for 15 minutes more, until the beans are heated through.
**Note**
The flavor and spiciness of standard supermarket-brand chili powders are usually much less robust than the flavor and spiciness of specialty chili powders, such as those from New Mexico.
**Serving Suggestions**
• Prepare bowls of sour cream, grated Monterey Jack or cheddar, chopped bell pepper, crumbled cooked bacon, and chopped red onion, and let people add their own toppings.
• Serve with corn bread (recipe on page 235) and a mixed green salad, or with fresh corn and French bread.
**Variations**
• You can substitute ground turkey for any or all of the ground beef and end up with a tasty pot of reduced-fat chili.
• Some chili aficionados assert that real chili features small chunks of beef instead of ground meat. If you're so inclined, cut 2 pounds chuck steak or round steak into small cubes and use in place of the ground beef.
#### **Red Snapper Vera Cruz**
The slightly sweet taste of red snapper combines wonderfully with the piquant tomato sauce in this effortless dish. Buy the freshest fillets you can lay your hands on.
**Ingredients** _(serves eight)_
_2½ pounds red snapper fillets_
_2½ tablespoons butter, melted, plus extra butter for greasing the baking dish_
_Salt and pepper_
_2½ tablespoons olive oil_
_1¼ cups chopped onion_
_1 ⅓ cans (28 ounces) of solid pack tomatoes, with water_
_6-ounce can tomato paste_
_1¼ tablespoons hot green chiles, chopped_
_1 tablespoon capers_
_1 teaspoon salt_
_⅛ teaspoon black pepper_
_½ cup Spanish green olives, for garnish_
_Sprigs of watercress, for garnish_
**Equipment**
_Shallow 10 x 13-inch baking pan_
_Basting brush_
_Large sauté pan_
**1.** Preheat the oven to 350°F. Butter a shallow 10 x 13-inch baking pan.
**2.** Place the snapper fillets in a single layer in the pan, brush the fillets with the melted butter, and season with salt and pepper.
**3.** Bake for about 18–20 minutes or until the fish flakes easily when tested with a fork.
**4.** While the fish is baking, add the olive oil to a large sauté pan. Place the pan on _high_ about 45 seconds. Add the chopped onion and sauté over _medium-high_ heat until tender, about 5 minutes. Add the canned tomatoes, tomato paste, chiles, capers, salt and pepper. Simmer uncovered over _medium_ heat for about 15 minutes.
**5.** When the fish is done, transfer it to a large serving dish. Pour the tomato sauce over the snapper, then garnish with olives and watercress.
**Serving Suggestions**
To complement this robust dish, serve mildly flavored side dishes, such as green beans, rice, or boiled new potatoes. Serve with salad.
#### **Chicken Breasts with Prosciutto & Mozzarella**
These luscious chicken bundles are first sautéed and then quickly finished in the oven. This recipe calls for a little too much cheese in the stuffing, which means it usually leaks out when it's baking—but I wouldn't have it any other way.
**Ingredients** _(serves eight)_
_4 large whole, skinless, boneless chicken breasts, cut in half_
_Salt and pepper_
_2 tablespoons dried basil_
_8 ounces mozzarella, grated_
_8 slices prosciutto or smoked ham_
_2 large eggs_
_2 cups Italian-style bread crumbs_
_2 tablespoons olive oil_
_1 tablespoon butter_
_1 cup Basic Tomato Sauce (page 182) or your favorite store-bought sauce_
_2 tablespoons chopped fresh parsley_
**Equipment**
_Meat pounder_
_Platter_
_Medium bowl_
_Pie plate_
_Large frying pan_
_11 x 17-inch baking pan_
_Small saucepan_
**1.** Preheat the oven to 350°F.
**2.** Using a meat pounder, flatten each chicken breast to a thickness of ¼ inch and arrange them on your worktable with the smooth outer side down. Season each breast lightly with salt and pepper and a pinch of the basil.
**3.** Place about 2 tablespoons of the grated mozzarella in the center of each breast, leaving a ½-inch margin all around. Lay a slice of prosciutto over the cheese.
**4.** Fold the breasts lengthwise, place on a platter, and set aside.
**5.** Beat the eggs in a medium bowl. Put the bread crumbs in a pie plate.
**6.** Dip each chicken bundle in the egg and then dredge it in the bread crumbs, holding it carefully to keep it from unfolding. Gently shake the bundle to release excess bread crumbs, then place it back on the platter, seam side down.
**7.** Place a large frying pan on _medium-high_ heat and let it get hot, about 45 seconds. Add 1 tablespoon of the olive oil to the center of the pan and place ½ tablespoon of the butter in the pool of oil. When the butter stops sizzling, spread it around the pan and add 4 of the breasts, seam side down. Cook until the bottoms are lightly browned, about 2 minutes. Turn and cook 2 minutes more.
**8.** Transfer these bundles to the baking pan. Wipe out the frying pan with a paper towel and repeat with the remaining oil, butter, and breasts.
**9.** Place the chicken in the oven and bake until firm and springy to the touch, about 8 minutes.
**10.** While the chicken is baking, heat the tomato sauce in a small saucepan. Wash and dry the platter and arrange the cooked breasts on it. Top each one with a bit of tomato sauce and a sprinkling of parsley. Serve immediately.
**Tip**
The chicken breasts can be prepared through Step 4 up to a day ahead of time. Refrigerate, tightly covered, until ready to use.
**Serving Suggestion**
Serve with a simple pasta or rice pilaf and a vegetable, such as green beans, zucchini and tomatoes, or broccoli.
#### **Jambalaya with Shrimp & Chicken**
There are as many ways to make jambalaya as there are cooks in New Orleans. Start with this version and then create your own. There are lots of ingredients here, but there's not a lot of work.
**Ingredients** _(serves eight)_
_1½ pounds boneless chicken thighs_
_½ pound andouille or chorizo sausage (see Note) or smoked ham_
_2 teaspoons salt_
_2 teaspoons chili powder_
_1 tablespoon dried oregano_
_1 teaspoon garlic powder_
_1 teaspoon dried thyme_
_1 teaspoon paprika_
_1 teaspoon onion powder_
_½ teaspoon cayenne pepper_
_3 bay leaves_
_2 tablespoons corn oil_
_1 large onion, chopped_
_4 ribs celery, finely chopped_
_2 large green bell peppers, chopped_
_4 cloves garlic, minced_
_2 cups canned crushed tomatoes_
_1 cup Basic Tomato Sauce (page 182) or your favorite store-bought sauce_
_4 scallions, chopped_
_3 cups chicken broth or 3 bouillon cubes dissolved in 3 cups boiling water_
_3 cups white rice, uncooked_
_1 pound shrimp, peeled and deveined (seepage 117)_
**Equipment**
_Small bowl_
_Large frying pan, preferably cast-iron_
_11 x 17-inch baking pan_
**1.** Preheat the oven to 350°F.
**2.** Cut the chicken into ½-inch pieces. Cut the sausage or ham into ½-inch slices. Set aside.
**3.** Mix together all the spices through the cayenne pepper in a small bowl, add the bay leaves, and set aside.
**4.** Place a large frying pan, preferably cast-iron, over _high_ heat and let it get very hot, about 1 minute. Add 1 tablespoon of the oil and the sausage pieces, and brown on all sides, about 3 minutes. Add the chicken pieces and cook until the chicken is brown, about 4 minutes. Transfer the chicken and sausage, including any crunchy bits stuck to the bottom, to an 11 x 17-inch baking pan.
**5.** Put the frying pan back on _high_ heat, add the remaining tablespoon of oil, and let it get hot, about 15 seconds. Add the onion, celery, and bell pepper, and cook, stirring often, until the vegetables just begin to brown, about 6 minutes. Add the garlic and cook for 1 minute more.
**6.** Reduce the heat to _medium_ and add all the spices and the bay leaves. Cook for 3 minutes more, stirring continuously to keep the spices from sticking to the pan.
**7.** Add the tomatoes, tomato sauce, and scallions, and simmer for 8 minutes.
**8.** Add the broth or bouillon and increase the heat to _high_. Bring the liquid to a boil, then turn off the heat. Carefully transfer the contents of the frying pan to the baking pan.
**9.** Stir the rice and shrimp into the mixture in the baking pan. Cover the pan well with aluminum foil and bake until the rice is cooked through, about 25 minutes.
**Note**
Andouille and chorizo are both highly seasoned pork sausages. Andouille, French in origin, is a Cajun specialty. Chorizo is a specialty of Spain and Latin America. Both are usually sold at specialty food shops.
**Tips**
• Jambalaya can be prepared through Step 8 the night before you plan to serve it. Let it cool. Cover and refrigerate. When you're ready to resume cooking, add an extra ½ cup broth to the mixture, bring to a boil, and continue with the recipe at Step 9.
• If you don't feel like peeling and deveining the shrimp, buy them precleaned or substitute ½ pound smoked ham cut into chunks.
**Serving Suggestion**
Serve the jambalaya with a mixed green salad, lots of corn bread, cold lemonade, and beer.
#### **Whole Roast Beef Tenderloin**
Beef tenderloin is a pricey but easy entrée to cook for a crowd. Roasted to medium-rare perfection, it will instantly turn any gathering into a special occasion.
**Ingredients** _(serves twelve)_
_1 beef tenderloin (3½–5 pounds), trimmed of fat and tied by the butcher_
_¼ cup Dijon mustard_
_3 cloves garlic, minced_
_1 2-inch piece fresh ginger, finely chopped_
_2 tablespoons soy sauce_
_Vegetable oil, for oiling the roasting rack_
_1 bunch watercress, for garnish_
_Chopped parsley, for garnish_
**Equipment**
_Small bowl_
_Roasting pan with rack_
**1.** Preheat the oven to 500°F for ½ hour. Remove the meat from the refrigerator while the oven is preheating.
**2.** In a small bowl, combine the mustard, garlic, ginger, and soy sauce and set aside.
**3.** Line a roasting pan with a double layer of aluminum foil. Lightly oil a roasting rack and set it inside the roasting pan.
**4.** Place the meat on the rack and cover it with a thick coating of the mustard mixture.
**5.** Transfer the meat to the oven and roast to medium rare: 35 minutes for a 4-pound piece of meat; 42 minutes for a 5-pound piece of meat. Do not open the oven door while the meat is roasting.
**6.** Remove the meat from the oven and let it rest for 10 minutes before slicing. To serve, remove the strings and cut the meat across the grain into ¾-inch slices. Arrange the slices on a serving platter and top with some of the pan juices. Garnish with the watercress on the sides and a sprinkling of chopped parsley down the center of the meat.
#### **Moroccan Veal, Sausage & Chicken with Couscous**
This mild and delicious curry, sweetened with raisins, spooned over a bed of couscous, is an excellent introduction to Middle Eastern cuisine. A staple of North Africa, couscous is gaining popularity in the States. These grains of pasta take just a few minutes to prepare. Do not be intimidated by the list of ingredients. They all wind up in one big pot.
**Ingredients** _(serves twelve)_
_5 tablespoons vegetable oil_
_¾ pound Merguez sausages, cut into 1-inch pieces_
_1½ pounds veal shoulder or leg, cut into 1½-inch cubes_
_1½ pounds boneless, skinless chicken thighs, cut into 1-inch pieces_
_1 large onion, halved and thinly sliced_
_4 cloves garlic, coarsely chopped_
_2 28-ounce cans crushed tomatoes_
_9 cups canned chicken broth or 9 bouillon cubes dissolved in 9 cups of water_
_2 tablespoons mild curry powder_
_1 teaspoon ground cumin_
_1 teaspoon ground cinnamon_
_1 teaspoon salt_
_2 9-ounce packages frozen artichoke hearts_
_1 cup raisins_
_4 cups couscous_
**Equipment**
_Large frying pan_
_Slotted spoon_
_2 large casseroles with covers_
**1.** Place a large frying pan on _high_ heat and let it get very hot, about 90 seconds. Add 1 tablespoon of the oil and the sausage pieces and cook, stirring often, until they are browned on all sides, about 4 minutes. Using a slotted spoon, transfer the sausage to a large casserole.
**2.** Return the frying pan to _high_ heat and add 1 tablespoon of the remaining oil and the veal. Cook, stirring often, until browned on all sides, about 4 minutes. Use the slotted spoon to transfer the veal to the casserole with the sausage.
**3.** Return the frying pan to _high_ heat and add another tablespoon of the oil. Add the chicken and onion and cook, stirring often, until the chicken is browned on all sides, about 4 minutes. Add the garlic and cook 1 minute more.
**4.** Transfer the chicken mixture to the casserole and add the crushed tomatoes, 4 cups of the chicken broth or bouillon, the curry powder, cumin, cinnamon, and salt and stir well. Bring the mixture to a boil over _high_ heat, then reduce the heat to _medium_ and simmer, uncovered, for 20 minutes, stirring occasionally. Add the artichoke hearts and raisins and cook 10 minutes more. Turn off the heat and cover the casserole.
**5.** Make the couscous in another large casserole. Bring the remaining 5 cups chicken broth or bouillon and the remaining 2 tablespoons oil to a boil. Stir in the couscous, turn off the heat, cover the pot, and let the couscous sit for 5 minutes. Immediately fluff the couscous with a fork to help separate the grains.
**6.** To serve, transfer the couscous to a large platter and spoon on the curry, being sure that the sauce covers all the couscous.
**Time-Saver**
The veal, sausage, and chicken curry can be made up to 2 days in advance. Let the mixture cool before refrigerating. Reheat the casserole over _medium_ heat for 10 minutes before making the couscous.
**Note**
Merguez is the traditional sausage of Morocco and gives this dish its distinctive flavor. You can find it at many specialty food stores.
* * *
**Thanksgiving Dinner for Twelve**
Holidays are an excuse for bringing this traditional fare to table. But the obligatory Thanksgiving bird can make a lot of people thankful any time of year. A turkey dinner requires advance planning, but your oven actually does most of the work. Make the stuffing and Dad's Own Apple Pie (page 216) the night before.
**MENU**
Roast turkey with Dad's own apple sausage stuffing
* * *
Quick cranberry chutney
* * *
Candid sweet potatoes
* * *
Breads
* * *
Dad's own apple pie
* * *
* * *
#### **Roast Turkey**
A bird this large is as simple to prepare as a small one, but it does take a long time to cook—about 4½ to 6 hours—so plan ahead. If you buy a frozen bird, you also need to allow time for it to defrost: about 3 to 4 hours per pound. Leave the turkey in its original wrapping and defrost on a tray in the refrigerator.
**Ingredients** _(serves sixteen)_
_1 16–20 pound turkey_
_½ cup (1 stick) butter or margarine_
_2 oranges_
_Dad's Own Apple Sausage Stuffing (recipe follows), optional_
_1 large onion, peeled (if not stuffing turkey)_
_Rosemary sprigs (if not stuffing turkey)_
_Salt and pepper_
**Equipment**
_Small saucepan_
_Thin metal skewer or toothpicks_
_Large roasting pan_
_Cheesecloth_
_Bulb baster_
**1.** Preheat the oven to 325°F.
**2.** Remove the giblets from the front and back cavities of the turkey. Rinse the inside and outside of the turkey thoroughly with cold water and pat dry with paper towels.
**3.** Melt the butter or margarine in a small saucepan and set aside.
**4.** Cut the oranges in half. Squeeze the juice of 1 orange into the large cavity and rub it around. Squeeze the juice of the second orange over the outside of the bird.
**5.** Fill the cavity loosely with the stuffing, if using and secure the opening with a thin metal skewer or toothpicks. If you're not stuffing the bird, leave the orange halves inside the cavity, along with a peeled onion and a couple of sprigs of rosemary. Salt and pepper the outside of the turkey.
**6.** Place the turkey, breast side up, in a large roasting pan. Cut a double layer of cheesecloth to cover the top and sides of the turkey. Dip the cheesecloth in the melted butter, and then drape it over the turkey. Drizzle on the remaining butter.
**7.** Roast the turkey for about 18 minutes per pound—basting with pan juices every 30 minutes after the first hour of cooking. The bird is done when a meat thermometer inserted in the thickest part of the thigh registers 180°F and the stuffing, if used, registers 165°F (A stuffed turkey may take longer to cook.) Remove the cheesecloth for the last ½ hour of cooking to allow the skin to crisp.
**8.** Remove the turkey from the oven and let it sit for 20 minutes before slicing. Remove all of the stuffing from the bird and serve it in a separate dish.
**Note**
To determine when the turkey is done without a meat thermometer, try moving the leg. If it feels loose and moves easily in the joint, the turkey is ready. Another way to tell is to prick the skin at the thigh. If the juices run clear, not pink, the turkey is done. Begin checking the turkey for doneness about 20 minutes before its allotted time.
**Serving Suggestion**
For a vegetable accompaniment, try cooked hubbard squash, string beans, cauliflower, or peas with cream and almonds.
#### **Dad's Own Apple Sausage Stuffing**
To save time on the day you are cooking the turkey, prepare the stuffing a day ahead and store it in an airtight container in the refrigerator. Do not stuff the bird until you are ready to put it in the oven.
**Ingredients** _(enough to stuff a 16- to 20-pound turkey)_
_3 large, tart apples, such as McIntosh or Macoun_
_1 pound sweet Italian sausage meat, crumbled_
_¼ cup (½ stick) butter_
_1 large onion, diced_
_1 small fennel bulb, diced (optional)_
_½ cup marsala or sherry_
_1 chicken bouillon cube_
_3 cups (about 5 slices) diced whole wheat bread_
_3 cups (about 5 slices) diced white bread_
_¼ cup chopped fresh parsley_
_1 teaspoon dried thyme_
_Salt and pepper_
**Equipment**
_Large frying pan_
_Colander_
_Large bowl_
**1.** Core and coarsely chop the apples and set aside.
**2.** Place a large frying pan on _medium-high_ heat and let it get hot, about 45 seconds. Add the sausage meat and cook, stirring constantly, until browned, about 4–5 minutes. Transfer the meat to a colander, let the fat drain off, then transfer it to a large bowl.
**3.** Wipe out the frying pan with a paper towel, return it to _high_ heat, and add the butter. When the butter has melted, add the diced onions, chopped apples, and fennel, if using. Cook, stirring frequently, until soft, about 12 minutes. Add the marsala or sherry and the bouillon cube and cook until the bouillon is dissolved and the liquid is reduced by half, about 3 minutes. Transfer to the bowl with the sausage.
**4.** Add the diced bread, parsley, thyme, and salt and pepper to the bowl, and stir gently to combine. Let the mixture cool before stuffing the bird, or cover and refrigerate until ready to use.
**Variations**
• Substitute 3 cups cooked white, brown, or wild rice for 3 cups of the diced bread.
• Substitute 3 cups crumbled corn bread for 3 cups of the diced bread.
• Substitute 1 cup chopped walnuts or pecans and ½ cup raisins for the sausage.
**Time-Saver**
If you don't have time to make your own stuffing from scratch, you can purchase bags of preseasoned bread crumbs, intended for stuffing making, in the grocery store. Follow the instructions on the bag but feel free to improvise a bit with your favorite ingredients. For example, if you like chestnuts or raisins in your stuffing, go ahead and add some.
#### **Quick Cranberry Chutney**
Fresh oranges and strawberry vinegar help to refine a Thanksgiving classic.
**Ingredients** _(serves twelve)_
_1 seedless orange, cut into eighths_
_1 12-ounce package fresh cranberries_
_1 16-ounce can whole berry cranberry sauce_
_¼ cup dried currants_
_1 tablespoon strawberry or red wine vinegar_
**Equipment**
_Food processor_
_Baking pan_
_Medium bowl_
**1.** Put the orange sections (with the skin) in the food processor fitted with the steel blade. Pulse a few times until the orange sections are very coarsely chopped.
**2.** Wash and drain the fresh cranberries, then dump them in the baking pan and sort through them, discarding any that are mushy.
**3.** Transfer the cranberries to the processor bowl along with the orange. Pulse until the cranberries are very coarsely chopped (roughly cut into thirds). Transfer the chopped cranberries and orange to a medium bowl.
**4.** Add the can of cranberry sauce, the currants, and vinegar, and mix together well. Refrigerate until ready to serve.
#### **Candied Sweet Potatoes**
Kids especially like this Thanksgiving treat topped with tiny marshmallows.
**Ingredients** _(serves twelve)_
_3 tablespoons butter_
_10 medium-large sweet potatoes_
_1 cup brown sugar or 1 ⅓ cups real maple syrup_
_24 tiny marshmallows (optional)_
**Equipment**
_12 x 18-inch baking dish_
_Large bowl_
_Vegetable peeler_
**1.** Preheat the oven to 375°F. Grease a 12 x 18-inch baking dish with 1 tablespoon of the butter.
**2.** Peel the sweet potatoes and cut them in half lengthwise. Cut each half into 1-inch pieces. Put the cut pieces in a bowl of cold water to keep them from turning brown as you finish cutting the rest.
**3.** Arrange the sweet potatoes in the prepared baking dish and top with the brown sugar or syrup. Cut the remaining 2 tablespoons butter into little pieces and dot the top of the potatoes with them.
**4.** Bake the sweet potatoes on the center rack of the oven for 1¼ hours or until the top is nicely browned and glazed. If using marshmallows, add them during the last 10 minutes of cooking.
## How to Throw Your Own Cocktail Party
Cocktail parties are best attended, not hosted. But if you're feeling adventurous, filling your living room with friends can be a lot of fun. The food at a cocktail party should be simple, flavorful, and not too messy. Your memories of the party should be in your heart, not smeared into your upholstery.
Start the party early, about 6:30 or 7:00 PM, and figure it will last about two hours. Make it clear on the invitation that the guests are joining you for cocktails. This way they won't be expecting dinner. Plan to serve about six or seven appetizers, some to be passed, others to be set out in baskets or on platters.
You will need to set aside a couple of hours the day before to plan what you're serving, shop, and do some preliminary set up.
Here are some party tips from a pro:
**Pace the food.** The first 10 guests can wolf down all the shrimp, leaving none for those arriving fashionably late. Set the food out slowly, but be prepared for a rush around 30 minutes after the party starts. Hold one dish back until the second half of the party. This will keep the surprises coming.
**Keep the bar simple.** It's better to invest in a few high-quality wines and liquors than in lots of cheaper stuff.
**Don't feel you have to serve your guests mountains of food.** They'll probably be going out for dinner afterward. Rather, present them with a few distinct and interesting dishes. For a rough idea of the amount of food you will need, figure 1½ portions of each appetizer per person.
* * *
**The Drinks**
The caterer's rule of thumb for the bar is one drink per person per hour. What you stock the bar with depends on who's coming. A younger crowd will favor vodka, wine, beer, and sparkling water. Old groups savor their Scotch and martinis. If your guests are mostly friends, then you probably know what they like most.
##### **The Basic Bar for 25 Guests**
_5 bottles white wine (chilled)_
_5 bottles red wine_
_1 fifth Scotch_
_1 fifth vodka_
_1 fifth gin_
_8 ounces vermouth_
_2 liters tonic water_
_5 liters sparkling water_
_2 quarts orange juice_
_2 quarts grapefruit juice_
_2 quarts cranberry juice_
##### **Equipment for the Bar**
_Corkscrew_
_Pitchers for water and juice_
_Ice bucket and tongs_
_3 limes, cut into wedges_
_2 lemons, half cut into wedges, half cut into twists_
_10 pounds ice_
_Beer opener_
_Bucket for slop (remnants of drinks)_
_Tub to keep back-up ice and wine in_
_Stirrer_
_Cocktail napkins_
_50 glasses_
**Tips**
You'll need a 4-foot table for the bar.
• Most guests leave their glasses somewhere and then go back to the bar for a new one. For this reason, stock the bar with at least 2 glasses per person.
• Open 2 bottles of white wine to start and the rest as you need it. Don't open any red wine until someone asks. There is a chance no one will. Here are a few wine suggestions:
• **White wines** Robert Mondavi "Woodbridge" Sauvignon Blanc, Georges Duboeuf Chardonnay, and Fontana Candida Frascati
• **Red wines** Sebastiani Zinfandel, Georges Duboeuf Beaujolais, and Lindemans "Bin 99" Pinot Noir
* * *
Simple Nibbles & Ethnic Edibles
Here's the easy way to lay out a great cocktail party spread with little fuss and only about an hour of shopping. Investigate your local gourmet shops, bakeries, restaurants, and ethnic food stores to see what they have in the way of dips and finger foods. Then assemble an assortment of international taste treats along with some American standbys. You will have little more to do than assemble what you bought on platters, and your guests will appreciate the variety of flavors. Quantities given assume you will be serving at least six appetizers.
#### **Spring Rolls & Dim Sum**
Order a variety of spring rolls and dim sum (Chinese appetizers) from your favorite Chinese restaurant. Reheat them in a 300°F oven and serve them with duck sauce and Chinese mustard. Also look for small steamed or baked buns, dumplings, or chunks of beef or chicken steeped in various spicy sauces (these can be served with toothpicks). Order 30 spring rolls for a party with 25 guests.
#### **Guacamole**
A good local Mexican restaurant might sell you some great guacamole. But it's also a cinch to make yourself. Cut open 3 very ripe California avocados, scoop out the flesh into a medium (preferably wooden) bowl, and mash it with a potato masher or large fork. Stir in 1 cup chopped tomatoes, ½ cup chopped red onion, 3 tablespoons chopped fresh cilantro, the juice of 2 limes, and salt and pepper to taste. Serve with 2 pounds of corn tortilla chips.
#### **Miniature Quiches**
Many gourmet shops, pastry shops, and local caterers sell a variety of mini quiches, such as onion, ham, broccoli, and mushroom, that are perfect for parties.
Just heat them on a baking sheet according to the shop's instructions and let them cool before serving, so they can be handled comfortably. Buy 30 mini quiches for 25 guests.
#### **Pâté**
Vegetable, liver, and other pâtés are readily available, both in supermarkets and gourmet shops, but the quality and taste vary widely. Be sure to sample before you buy. One and a half pounds will serve 25 guests. Serve the pâté on a small wooden cutting board with a sharp paring knife. Guests will cut what they want. Accompany with a basket of sliced French bread and/or pita triangles and a bowl of grainy Dijon mustard.
#### **Dolmas & Spanakopita**
Dolmas are savory stuffed foods and among the most common are little grape leaf packets stuffed with rice, spices, and sometimes ground lamb. They are available in better supermarkets and at shops featuring Middle Eastern specialties. Spanakopita (spinach pies) are available in Greek bakeries. Cut them in half or quarters, depending on the size. Buy 40 dolmas and 12 spanakopita.
#### **Tapenade & Pesto**
Tapenade is a dip made from puréed olives, capers, anchovies, olive oil, and fresh basil and other seasonings. Pesto is a mixture of fresh basil, Parmesan, olive oil, and pine nuts. Both dips go well with crudités and small rounds of French bread. One and a half pounds will be enough for 25.
#### **Pizza Rotolo**
Available in some pizza shops and Italian specialty stores, this is a hearty and filling appetizer. It's basically pizza crust rolled around spicy ham, salami, provolone, and roasted peppers. Cut into ¼-inch slices and arrange on a platter. About two pounds will serve 25 guests.
#### **Salmon Caviar**
Cheap caviar _tastes_ like cheap caviar. But fresh salmon roe is very palatable and not too pricey. Look for bright, glistening orange eggs that are round and full with no shriveling. Serve in a small ceramic bowl set in a larger bowl of ice. Accompany with melba toast and a small bowl of sour cream. Three-quarters of a pound will suffice.
#### **Goat Cheese Pita Pizza**
Crumble goat cheese on pita rounds and heat them in a 325°F oven just until the cheese melts, about 10 minutes. Let them cool slightly before serving. Goat cheese works well because it doesn't run and it tastes good warm.
#### **Barbecued Chicken Wings**
Buy the best quality barbecue sauce you can find and marinate the wings for 4 hours in the refrigerator. Cook as described in the recipe for Jerk Chicken Wings on page 277. Serve at room temperature.
#### **Hummus or Baba Ghanoush with Pita Triangles**
Find a local gourmet shop that makes really great dips. Buy about 2 pounds of hummus or baba ghanoush and set it in a bowl next to a basket of pita bread cut into cracker-size triangles.
#### **Shrimp & Cocktail Sauce**
Spring for 2 pounds of cleaned and cooked shrimp from your local fish store. It'll save a lot of time. Accompany with homemade cocktail sauce (page 282).
#### **Cheese & Crackers**
Set out a selection of 1-pound chunks of 3 or 4 different cheeses and a basket of assorted crackers. Remember that some guests will go for the soft and semisoft cheeses while others will stick to hard cheese. For many suggestions on what cheese to serve consult the Cheese primer on page 280.
* * *
**A Menu for a Fancy Cocktail Party for 25**
If you're up for it, you may want to prepare some of these more elegant appetizers, which are sure to impress even the most jaded party goer. Be forewarned: This fancy party menu takes time. You'll need a few hours the day before to do the shopping, and plan to spend most of the day of the party preparing the food. You'll also need some help in the kitchen and one waiter to replenish the hors d'oeuvres. Usually kids love to be part of the action, so enlist their help in passing the trays of hors d'oeuvres. The shopping list and the timetable are to help keep you on track.
**MENU**
Fresh salsa & chips
* * *
Sopressata or dried salami with French bread
* * *
Crudités with sun-dried tomato & roasted red pepper dip
* * *
Jerk chicken wings
* * *
Shrimp & cocktail sauce
* * *
Melon & prosciutto
* * *
Salmon hash in endive
* * *
* * *
**The Timetable**
**A Few Days Before the Party**
• Purchase the liquor, wine, mixers, juices, lemons, limes, plastic glasses, and cocktail napkins for the bar.
• Make sure you have the necessary platters on hand. If not, borrow some.
• If you're not using plastic cups, make sure you have enough glasses for the bar.
**The Day Before the Party**
• Do all your shopping.
• Marinate the chicken wings.
**The Morning of the Party**
• Make the crudité dip and refrigerate.
• Make the salmon hash and refrigerate.
• Shell and devein the shrimp. This takes a lot of time; try to find someone to help you.
• Cook the shrimp and refresh them under cold water. Drain well, cover tightly, and refrigerate.
• Make the cocktail sauce.
• Blanch, then refrigerate any crudité vegetables that require it.
• Make the salsa and refrigerate.
**3 Hours Before the Party**
• Slice the sopressata or salami and the French bread. Arrange the salami on one side of the basket and the bread on the other. Cover everything with a lightly damp paper towel.
• Bake the chicken wings.
• Cut the melon into chunks.
• Set up the bar.
**2 Hours Before the Party**
• Arrange the crudités on a platter, cover it with a damp paper towel, and leave it at room temperature.
• Put toothpicks in about 15 shrimp and arrange them on a lettuce-lined platter with a bowl of cocktail sauce. Cover the shrimp with a slightly damp paper towel.
• Fill a small bowl with dip and set the crudité platter on the serving table.
• Fill a serving bowl with salsa and a basket with chips and set them both out on the serving table.
• Finish cooking the chicken wings under the broiler. Arrange a dozen or so on a platter lined with lettuce. Set the rest aside at room temperature, uncovered.
• Assemble the melon and prosciutto.
• Assemble the salmon hash and endive.
**During the Party**
Replenish the trays as needed.
* * *
**The Shopping List**
**Dairy**
• 4 ounces cream cheese
**Produce**
• 3 small red onions
• 1 large red onion
• 2 pounds plum tomatoes
• 2 green bell peppers
• 1 bunch scallions
• 1 bunch cilantro
• 1 garlic head
• 3 limes (includes 2 for bar)
• 3 lemons (includes 2 for bar)
• 2 large cantaloupes or 1 large honeydew
• 1 pound Belgian endive
• 1 pound Kirby cucumbers or 3 English (seedless) cucumbers
• 2 pints cherry tomatoes
• 1 head broccoli
• 1 pound carrots
• 1 pound red bell peppers
• 2 heads green leaf or Boston lettuce
**Condiments**
• Red horseradish
• Ketchup
• Tabasco sauce
• Malt vinegar
• White wine vinegar
• Vegetable oil
• Pickapeppa or Worcestershire sauce
• 1 jar salsa
**Bakery**
• 3 long French breads
• Bread sticks
**Cupboard Items**
• 4-ounce jar roasted red peppers
• 3 ounces sun-dried tomatoes (not packed in oil)
• 6-ounce can tomato paste
• 5 ounces high-quality canned Sockeye or red salmon
• 3 1-pound bags tortilla chips
**Spices**
• Chili powder
• Curry powder
• Garlic powder
• Paprika
• Onion powder
• Ground allspice
• Cinnamon
• Cayenne pepper
**Meat and Fish**
• 4 pounds chicken wings
• ½ pound prosciutto or Black Forest ham
• 2½ pounds large shrimp
• 2 pounds dried salami or sopressata
* * *
#### **Crudités**
A basket or platter of crudités is always a welcome sight at a cocktail party. It lets the guests nibble on something that is not rich or fattening and it adds color to the table.
The simplest way to arrange crudités is on a round platter. Set a small bowl for the dip in the center. Arrange the vegetables in wedges (like pieces of a pie) around the bowl, putting contrasting colors next to each other. You can set this up 45 minutes or so before the party. Cover the vegetables with slightly damp paper towels. Fill the bowl with dip just before serving.
For extra color, use a small head of red cabbage as a bowl for the dip. Trim the base so it sits flat. Then use a chef's knife to cut a crater out of the top of the cabbage. Hollow it out further with a paring knife, if necessary.
**Crudité Suggestions**
• **Kirby cucumbers** —Cut these lengthwise into quarters.
• **English (seedless) cucumbers** —Wash well and cut into ½-inch rounds. These do not need peeling.
• **Carrots** —Peel, cut them lengthwise into quarters, and slice into 3-inch sticks.
• **Broccoli** —Trim the stalk and separate the florets. Blanch the florets in a large pot of salted water for 1 minute. Transfer them to a large bowl of cold water to refresh. Drain, then refrigerate in plastic bags between layers of paper towels to absorb excess water. Puncture the bags in several places, or a strong odor will develop.
• **Cauliflower** —Prepare and store the same way as for broccoli.
• **Cherry tomatoes** —Wash and remove stems.
• **Celery** —Cut stalks lengthwise into thirds, then cut these into 3-inch sticks.
• **Red and yellow bell peppers** —Seed, then cut into ½-inch strips.
• **Endive** —Trim ½ inch off the bottom and separate the leaves.
• **Bread sticks**
#### **Sun-Dried Tomato & Roasted Red Pepper Dip**
**Ingredients** _(serves twenty-five)_
_3 ounces (about 1 cup) sun-dried tomatoes (not packed in oil)_
_1 4-ounce jar roasted red peppers, drained_
_4 ounces cream cheese_
_1 small red onion, sliced_
_1 teaspoon chili powder_
_½ teaspoon curry powder_
_½ teaspoon garlic powder_
_Salt and pepper_
_Crudités, for serving_
**Equipment**
_Small bowl_
_Blender or food processor_
**1.** Soak the sun-dried tomatoes in hot water in a small bowl for 2 hours or until soft.
**2.** Remove the tomatoes from the liquid, reserving the liquid, and place them in a blender or the bowl of a food processor fitted with the steel blade. (The processor works best for this.)
**3.** Add the rest of the ingredients and process until the mixture is smooth, 1–2 minutes. Add a bit of the liquid from the tomatoes if the dip seems too thick.
**4.** Transfer the dip to a decorative serving bowl and serve with crudités.
#### **Fresh Salsa & Chips**
**Ingredients** _(serves twenty-five)_
_2 pounds plum tomatoes, quartered_
_1 large red onion, quartered_
_1 green bell pepper, seeded and quartered_
_2 cloves garlic, mashed_
_Juice of 2 limes_
_4 tablespoons finely chopped fresh cilantro, or 1 tablespoon dried_
_1 tablespoon chili powder_
_1 teaspoon salt_
_½ teaspoon cayenne pepper_
_2 pounds tortilla chips_
**Equipment**
_Food processor or blender_
_Medium bowl_
**1.** Put the tomatoes, onion, bell pepper, and garlic in the bowl of your food processor fitted with the steel blade. (The vegetables will process evenly if they are all cut into approximately the same size pieces.) Pulse about 4 times until the vegetables are coarsely chopped.
**2.** Transfer the vegetables to a medium bowl. Stir in the lime juice, cilantro, chili powder, salt, and cayenne pepper.
**3.** Transfer the salsa to a decorative serving bowl. Serve with a large bowl of tortilla chips.
#### **Jerk Chicken Wings**
These wings have a real Jamaican flavor. The list of ingredients is long, but the cooking is easy.
**Ingredients** _(serves twenty-five)_
_1 cup water_
_½ cup ketchup_
_½ cup malt vinegar_
_¼ cup white wine vinegar_
_¼ cup vegetable oil_
_4 tablespoons Pickapeppa or Worcestershire sauce_
_¼ cup tomato paste_
_¼ cup sugar_
_3 tablespoons salt_
_1 tablespoon garlic powder_
_1 tablespoon onion powder_
_2 teaspoons ground allspice_
_1 teaspoon cinnamon_
_1 teaspoon freshly ground black pepper_
_½ teaspoon Tabasco sauce_
_Dash of cayenne pepper_
_4 pounds chicken wings_
_Margarine or cooking spray, for greasing the pan_
_Lettuce leaves, for lining the serving platter_
**Equipment**
_Medium bowl_
_Large plastic container_
_11 x 17-inch baking pan_
**1.** Mix together all the ingredients (except the chicken wings and lettuce) in a medium bowl.
**2.** Put the chicken wings in a large plastic container and cover with the marinade. Stir so that all the wings are coated. Refrigerate, well covered, for 24 hours.
**3.** Preheat the oven to 375°F. Line an 11 x 17-inch baking pan with aluminum foil and lightly grease the foil with margarine or cooking spray.
**4.** Arrange as many wings as will fit in the pan in 1 layer. Bake for 20 minutes.
**5.** Remove the wings from the oven and turn on the broiler.
**6.** Broil the wings 5 inches from the flame until they brown, about 5 minutes. Turn and broil for 3 minutes more. Repeat with the remaining wings.
**7.** To serve, line a platter with lettuce and arrange the wings on top.
**Note**
Have plenty of cocktail napkins on hand.
#### **Salmon Hash in Endive**
A variation of the exquisite snapper hash served at Zarela, my favorite Mexican restaurant in New York.
**Ingredients** _(serves twenty-five)_
_15 ounces high-quality canned Sockeye or red salmon_
_1 small red onion, finely chopped_
_½ green bell pepper, finely chopped_
_2 scallion greens, finely chopped_
_¼ cup of your favorite bottled salsa_
_1 clove garlic, minced_
_1 teaspoon chili powder_
_Salt_
_Dash of cayenne pepper_
_1 lime, halved_
_6 medium Belgian endive_
**Equipment**
_2 medium bowls_
**1.** Drain the salmon and place it in a medium bowl. Carefully pull the meat apart to expose the backbone. Remove this, along with any other bones or pieces of skin. Working with a little at a time, flake the salmon into a second medium bowl, removing any remaining bits of bone or skin.
**2.** Add the onion, bell pepper, scallion greens, salsa, garlic, chili powder, salt to taste, and cayenne pepper, and mix together. Squeeze on the lime juice and mix well. Refrigerate the mixture until ready to fill the endive spears.
**3.** Trim about ½ inch off the base of each head of endive and separate the spears. Use only the first few layers, those that are about 4 inches long. The smaller, inner leaves should be saved for salad.
**4.** Place a scant teaspoon of salmon hash in each endive spear, about a third of the way up from the bottom. Arrange the spears on a platter and serve. If desired, place a fresh flower, such as a lily or rose, in the center of the platter for decoration.
#### **Melon & Prosciutto**
This version of the traditional Italian appetizer, which appears on page 156, is easy to adapt for a crowd. Serving it on bamboo skewers makes an attractive hors d'oeuvre that doesn't require a plate.
**Ingredients** _(serves twenty-five)_
_2 large cantaloupes or 1 large honeydew_
_½ pound prosciutto or Black Forest ham, thinly sliced_
_2 limes, halved_
**Equipment**
_6-inch bamboo skewers or frilled toothpicks_
_Large plastic container_
**1.** Cut the melons in half, scoop out the seeds, and cut each half lengthwise into 3 sections.
**2.** With a paring knife, cut the flesh from the rinds and slice each section into 1-inch pieces.
**3.** Wrap each piece of melon with ½ slice of prosciutto. Pin the prosciutto in place with a skewer or toothpick.
**4.** Refrigerate the melon and prosciutto in a large covered plastic container until ready to serve. Squeeze lime juice over the melon before arranging on a platter.
* * *
**Cheese Primer**
Most cheese is made by heating milk to separate the curd from the whey. Enzymes or acids are added to the curd, which is then shaped and allowed to harden. This can take a couple of hours, a few months, or a year or more, depending on the type of cheese. The flavor of cheese depends on the kind of milk used (cow, goat, or sheep), the different cultures that are added, and how it is aged. At right is a chart showing some of the more common cheeses. A store with a large cheese department will surely let you taste a number of different kinds so you can widen your appreciation.
**Cheese Wisdom**
• **Storing:** Cheese should be stored well wrapped in plastic in the refrigerator. The exception is feta cheese, which should be stored covered in water. Softer cheeses generally last 3–5 days if they are properly stored. Harder cheeses can be stored much longer. Discard any moldy sections of a piece of cheese about ½ inch beyond the point where the mold ends. Discard the entire piece of cheese if it tastes distinctly bitter.
• **Freezing:** Cheese can be frozen, but it loses some of its flavor and texture so once frozen it is best used for cooking or melting. Cut it into pieces of one pound or less and wrap each piece in aluminum foil.
• **Buying:** Look for cheese with a smooth, even texture. There should be no evidence of hard, dry spots or cracking or green mold. Packaged cheese in the supermarket should have no liquid inside. Check the expiration date.
• **Grating:** Hard cheeses grate easily. If you need to grate a soft cheese, put it in the freezer for a few hours before grating. It is best to grate cheese or slice it thinly before melting.
The print edition of this book includes a chart for **Cheese Primer**.
Please download a PDF of this chart here: workman.com/ebookdownloads
* * *
#### **Shrimp & Cocktail Sauce**
Cocktail parties and shrimp seem to be synonymous. Upon arrival, after hitting the bar, most guests start scoping out the shrimp. Why disappoint them? Buy large or jumbo shrimp. To save time, buy shrimp shelled and deveined at your local fishmonger.
**Ingredients** _(serves twenty-five)_
_2½ pounds large shrimp (31–35 per pound)_
_1½ cups ketchup_
_2 tablespoons bottled red horseradish, or more to taste_
_1 small red onion, grated_
_Juice of 1 lemon_
_Dash of Tabasco sauce, or more to taste_
_1 teaspoon garlic powder_
_½ teaspoon paprika_
_Lettuce leaves, for lining the serving platter_
**Equipment**
_Paring knife_
_1 or 2 plastic containers_
_Large pot_
_Colander_
**1.** Clean and devein the shrimp as described on page 117, making sure to keep the shrimp cold while you're cleaning them. After they're cleaned, refrigerate immediately in a well-sealed plastic bag or container.
**2.** Mix together the ketchup, horseradish, onion, lemon juice, Tabasco, garlic powder, and paprika in a small serving bowl. Refrigerate until ready to serve.
**3.** Bring 6 quarts water to a boil in a large pot.
**4.** Add the shrimp all at once to the boiling water and stir briefly to separate. Cook for 3 minutes, then remove one shrimp from the water and cut it in half. If it is opaque in the center it is done. If it's not cooked through, check the shrimp again in 20 seconds.
**5.** When the shrimp are done, drain immediately in a colander, then rinse briefly under cold water to stop the cooking process. Transfer the shrimp to a clean plastic container, cover, and refrigerate until ready to serve.
**6.** To serve, line a serving platter with large leaves of clean lettuce. Put the serving bowl of sauce in the center of the platter. Put toothpicks in the shrimp and arrange them on the platter.
## Throwing a Birthday Party for Your Child
This year _you_ are going to throw your child a birthday party—cake, decorations, games—the works. And as your child throws her arms around you at the news, for a moment, you are truly tops.
From planning the theme and games together to decorating the house and cake, you and your birthday girl (or boy) share the anticipation and excitement. Even the big day goes smoothly because you planned out everything in advance ( _Dad's timetable_) and kept the party short ( _Party tips_). And the smile on her face when you bring out the "cake that Dad made" makes it all worthwhile.
* * *
**Party Themes**
A theme for a party can be just about anything, including favorite superheroes, characters from a well-loved book, animals, or a favorite sport. Let the theme influence all aspects of the party. If it's a dinosaur party, for example, play Pin the Tail on the Dinosaur and get some dinosaur cookie cutters and cut cookies or sandwiches into dinosaur shapes. You can even put little dinosaurs on the birthday cake. If it's an alphabet party (a good idea for very young kids), make letter-shaped cookies and let each child try to spell his or her name. Have extra cookies on hand so kids with short names don't feel cheated.
##### **Activity Ideas**
**Create a large mural**
Get some plain brown wrapping paper and tape a long sheet of it to the floor. Give each kid an assigned space on the paper and some colored pencils, crayons, stickers, or stencils.
**Musical chairs**
You need space for this. Make a circle of chairs with the seats facing out, one for each kid, less one. Play the piano or put some fun music on the stereo and have the kids walk around the chairs until you stop the music suddenly. The child who's left without a chair is out. The rounds continue until only one child is left sitting. Have a prize ready for the winner.
**Make a large collage**
Buy a roll of transparent contact paper. Remove the backing, lay the paper, sticky side up on the floor, and tape it down at the edges. Get out the big bag of stuff you've collected over the past few weeks—bits of yarn, bottle caps, string, small pieces of colored paper, foreign coins, and pictures from magazines. Have the kids sit along the length of the contact paper and stick on their items of choice.
**For Older Children**
If your child is older (6–10) you might consider taking her or him with invited friends to a roller-skating rink, a bowling alley, an ice skating rink, or a local museum or sports event. Then return home for cake, ice cream, and presents. Be sure to have at least one other adult with you to help drive and to keep the high spirits from getting out of control.
**Party Bags**
However you do it, all the kids who come to the party should go home with a little present. It's called a "party bag." It can be filled with lots of little trinkets and candy, a small toy, or a book. Hand these to the kids as they are on their way out the door.
**Make your own music videos**
(You'll need a video camera for this one.) On the invitation, ask each child to bring a cassette of a favorite song (s)he knows very well. Provide a box full of costume pieces—old clothes, hats, and accessories—for the kids to put on, and find a neutral background. Set up the camera and cassette player and let the kids sing along or lip-sync the songs as they move to the music.
**Hold backyard races**
If you have a backyard, set up lots of relay races, two-legged races, potato sack races, and obstacle courses.
**Set up a treasure hunt**
Kids love treasure hunts with lots of clues—enlist a few neighbors to have clues hidden on their porches or in their yards.
**Pass the parcel**
Get a small gift for each child, for example, a box of decorated Band-Aids, a Matchbox car, magnets, crayons, flip books, or playing cards. Wrap 1 item, then wrap the second item with the first, then the third with the first 2, and continue until all presents are wrapped in 1 large package. The kids sit in a circle and unwrap the parcel 1 layer at a time and keep the toy they unwrap. The last toy should be special as the last kid has to wait the longest.
**Make body puzzles**
Get a few rolls of brown wrapping paper and spread out kid-sized sheets of it on the floor. Have the kids lie on the paper on their backs and ask an adult to trace their outlines with a crayon. Have the kids color their own figures. Then have the adults cut out the figures and then cut the figures into 6 or 7 large sections. The kids now have puzzles of their bodies. Mix up the pieces and have a race to see who can reassemble themselves the fastest.
**Birthday Party Tips**
• Keep the food simple. The kids are usually too excited to eat much and the majority of molecules in their bodies are focused on the cake and ice cream anyway.
• Keep the party short: 2½ hours maximum. After that the kids start getting cranky.
• Come up with a theme for the party; it makes decorating easier and allows you to be inventive about coordinating the games and food with the décor.
If you are serving ice cream (and what birthday party would be complete without it?), save a lot of aggravation by preparing it ahead of time in the following manner. Put a scoop of ice cream in a muffin tin liner (one per child) and lay the muffin liners on a cookie sheet. Refreeze quickly, then cover the entire sheet with plastic wrap. When it's dessert time, empty 1 scoop on each plate with the cake or in a bowl for sundaes.
* * *
**Timetable for a One O'Clock Party**
**4–5 Weeks Before the Party**
Decide on the location and theme for the party. Send out invitations.
**2 Weeks Before the Party**
Get all the paper plates, tablecloths, candles, and plasticware you need. Decide on what activities and games you want to play and buy any supplies you need. This is also a good time to enlist a neighborhood teenager or favorite babysitter to help out at the party.
**2 Days Before the Party**
Prepare your shopping list and shop for the food and party favors. Remember all of the ingredients necessary for cake, frosting, and toppings.
**1 Day Before**
Bake the cake and frost.
**The Day of the Party**
**9:00** Make the food. Do all the chopping and crumbling, and make the ice cream scoops. Be sure anything that needs defrosting has been attended to.
**11:00** Decorate the space, setting new trends in your work with balloons and rolls of crepe paper. Set the lunch table. Make sure your table is well protected with a tablecloth.
**1:00** The guests start arriving. Collect the gifts, making sure cards are firmly attached so you can help your child write thank-yous. Put the gifts out of the way until later.
**1:15** Get the activities started. If you are having entertainment of any kind—a clown, a pony, a video—this is when it should happen.
**2:00** Serve lunch.
**2:30** Serve dessert and the birthday cake. The party photographer (maybe Mom will volunteer for this job) should get in position for the blowing-out of the candles.
**3:00** Open gifts and hand out the party bags.
**3:30** Make sure each of your child's friends leaves with his or her parent or other responsible adult.
**3:45** Pop a video in the VCR for your child to watch. Give yourself a pat on the back and collapse.
* * *
Party Food
The highlight of a birthday party is always the cake. However, if you want to feed the kids a little something before dessert, here are ideas for the munchies and the main course.
#### **Munchies**
Try to keep the chips to a minimum; instead, serve bowls of air-popped popcorn and low-salt pretzels as well as fun-to-eat fruits like grapes, bananas, and berries.
#### **Pizza**
The most popular party food to serve both the kids and their parents. You can make the pies yourself (see page 237) or order in. Be sure you have plenty of plain slices for the kids who don't like extra toppings. Figure on 1½ slices per child.
#### **Turkey Tacos**
Follow the directions on the back of the taco seasoning packet but use ground turkey instead of ground beef. Put out bowls of shredded lettuce, chopped tomato, shredded cheese, and mild salsa, and let the kids build their own tacos. This can get messy, but it's also a lot of fun.
**Design Your Own Cupcakes**
Make a batch of cupcakes using the birthday cake batter as explained on pages –90 and vanilla frosting, page 291. Set out bowls of toppings—chocolate chips, M&Ms, nuts, and sprinkles—and let the kids decorate their own cakes.
#### **Sandwiches**
Get some brown lunch bags and write the kids' names on them. Fill each bag with a peanut butter-and-jelly, tuna salad, turkey, or cheese sandwich (preferably on whole wheat bread), a small bag of trail mix, and an apple. Put a little toy in the bag, like they do at the fast-food chains, and the kids will be thrilled.
#### **Barbecued Hamburgers & Hot Dogs**
An outdoor barbecue is a great idea provided, of course, your child was born in the spring of summer. If your grill station isn't protected from the rain, have a back-up plan ready (for instance, the telephone number of the nearest pizza parlor).
**Make Your Own Sundaes**
The sundae bar is always a favorite at parties. Put a paper cloth down on the table and set up little bowls full of sundae toppings: sprinkles, chocolate syrup, broken-up Oreos, chopped Reese's peanut butter cups, M&Ms, nuts, raisins, sliced strawberries, whipped cream, cherries, etc. Drop a scoop of ice cream into each bowl and let the kids proceed down the table concocting their own monstrosities. Plan to do this right before the end of the party so the kids are already heading home when the sugar starts pulsing through their veins.
#### **Lasagna**
This is a great party food because it can be made weeks ahead of time and frozen until the day of the party. See page 184 for the recipe.
#### **Beverages**
If you can get away with it, skip the soda; instead, have plenty of milk (regular and chocolate) and all-natural fruit juice on hand. And don't forget the straws!
The Birthday Cake
You don't have to make a cake from scratch to make your child's birthday party terrific (with all the excitement, the kids won't know the difference). Buy a cake mix (one box will yield two layers), and take the extra five minutes to make your own frosting (recipe follows). But there is a certain pride in making your _own_ cake. Bake it the night before the party so you have energy for the sugar highs of the next day.
#### **Primo Birthday Cake**
This is the perfect birthday cake because it's foolproof and can be decorated just about any way imaginable. With the same batter you can also make cupcakes or a sheet cake. Directions for the variations are given at the end of the recipe.
**Ingredients** _(makes one 3-layer cake)_
_4 large eggs_
_1¼ cups (2½ sticks) butter or margarine, at room temperature, plus extra for greasing the cake pans_
_2 cups sugar_
_2 teaspoons vanilla extract_
_3 cups cake flour_
_3 teaspoons baking powder_
_1 teaspoon salt_
_1 cup milk_
**Equipment**
_3 9-inch round cake pans (disposable aluminum pans are fine)_
_2 medium bowls_
_Small bowl_
_Large bowl_
_Hand-held electric mixer_
_Whisk_
_Large rubber spatula_
_Cake tester or toothpick_
_Cooling racks_
**1.** Preheat the oven to 350°F.
**2.** Place a 9-inch round cake pan on a piece of wax paper and trace around the bottom with a pencil. Cut out the circle, then repeat 2 more times for a total of 3 circles. Butter 3 9-inch round cake pans. Lay the wax paper circles in the cake pans, and lightly butter them.
**3.** Separate the eggs, putting the whites in a medium bowl and the yolks in a small bowl.
**About Separating Eggs**
Have two bowls, one for the whites and one for the yolks. Crack the egg neatly in the center and hold it over a bowl to receive the whites. The yolk should rest in the bottom half of the shell. Gently roll the yolk from the bottom shell to the empty top half, letting the white spill off into the bowl. Pass the yolk from shell to shell, until all the white has dropped off. Put the yolk in another bowl. Be careful not to break the yolk. Even a drop of egg yolk mixed with the whites will keep the whites from beating up properly.
**4.** In a large bowl, using a hand-held electric mixer on medium-low speed, cream the butter, 1½ cups of the sugar, and the vanilla until light and fluffy, about 4 minutes. Add the egg yolks in 2 additions, beating well after each addition. Rinse and dry the beaters.
**5.** In a second medium bowl, whisk together the cake flour, baking powder, and salt.
**6.** Using a hand-held electric mixer on low speed, beat the egg whites until foamy and opaque, about 30 seconds. Raise the speed to medium and continue beating until very soft peaks begin to form. In a slow, steady stream, add the remaining ½ cup sugar and continue beating until firm (but not stiff) peaks form.
**7.** Using a large rubber spatula, alternately fold the flour mixture and the milk into the butter mixture in 3 additions each. Do not mix the batter vigorously.
**8.** When the flour and milk have been incorporated, use a rubber spatula to gently fold in the beaten egg whites in 3 additions (see Note).
**9.** Divide the batter among the 3 prepared cake pans and bake on the center rack of the oven for about 25 minutes, until a toothpick or cake tester inserted in the center comes out clean. If the cakes don't all fit on one oven rack, the cake on the top rack may take a bit longer.
**10.** Let the cakes cool on racks for 1 hour before removing them from the pans. Let the cakes cool another 30 minutes before frosting.
**Variations**
• To make cupcakes, lightly grease a cupcake tin and insert paper liners. Fill the liners ⅔ of the way to the top with batter and bake for 21 minutes. Let the cupcakes cool completely before frosting. This recipe makes 24 cupcakes.
• To feed a larger group, this batter can easily be turned into a sheet cake. _First, increase all the ingredients 1½ times._ Instead of using 3 round cake pans, use an 11 x 17-inch baking pan. Prepare the baking pan in the same way, by greasing the pan with butter or margarine, laying on a sheet of wax paper cut to fit inside, and lightly greasing the wax paper. Bake for the same amount of time, 25 minutes. Test for doneness with a toothpick or cake tester. Let the cake cool completely, at least 1 hour. Then run a butter knife around the edge of the cake, loosening it from the pan. Lay the bottom of a second baking pan of equal size over the cake and then invert. Cut a piece of cardboard the same size as the cake and place it over the cake. Invert the cake onto the cardboard. It's now ready for frosting. This rectangular cake can be easily decorated to look like a football field, basketball or volleyball court, or dinosaur play area.
**Note**
After you whip the egg whites, it is important to incorporate them into the batter without causing them to lose all the air you have beaten into them. You must add them slowly, or "fold" them in, using a large rubber spatula. As you add the egg whites to the batter, move the spatula continuously in a slow, steady motion down the edge of the bowl and up through the center, until the egg whites are completely incorporated.
#### **Luscious Chocolate Frosting**
**Ingredients** _(enough for a 3-layer cake)_
_5 ounces semisweet chocolate_
_½ cup (1 stick) butter, at room temperature_
_4 cups confectioners' sugar, sifted_
_½ teaspoon salt_
_6 tablespoons heavy cream_
_2 teaspoons vanilla extract_
**Equipment**
_Double boiler or saucepan and stainless-steel bowl to fit on top_
_Medium bowl_
_Hand-held electric mixer_
_Sifter_
**1.** Melt the chocolate in the top of a double boiler or in a stainless-steel bowl set in a saucepan filled with 3 inches of very gently simmering water, stirring the chocolate frequently as it melts. Remove the chocolate from the heat and set aside.
**2.** In a medium bowl, using a hand-held electric mixer on medium speed, beat the butter until light and fluffy. Add the melted chocolate. Gradually beat the sifted sugar into the butter mixture until fully incorporated. Beat in the salt, heavy cream, and vanilla.
**3.** Gradually beat in the remaining 1 cup sugar until the frosting is smooth and spreadable.
#### **Quick Vanilla Frosting**
Young kids tend to like their frosting in different colors, for example, lime green and pale pink. All it takes is a few drops of food coloring, so go ahead and indulge your child's fancy.
**Ingredients** _(enough for a 3-layer cake)_
_14 tablespoons (1¾ sticks) butter, at room temperature_
_5 cups confectioners' sugar, sifted_
_½ teaspoon salt_
_5 tablespoons heavy cream or whole milk_
_1 tablespoon vanilla extract_
**Equipment**
_Medium bowl_
_Sifter_
_Hand-held electric mixer_
**1.** In a medium bowl, using a hand-held electric mixer set at high speed, beat the butter until light and fluffy, about 2 to 3 minutes. With the mixer running, gradually add 4 cups of the sifted sugar, ½ cup at a time, until it is fully incorporated. Add the salt, cream or milk, and vanilla, and continue beating until well combined.
**2.** Gradually beat in the remaining 1 cup sugar a few tablespoons at a time, until the frosting is smooth and spreadable. (You may not need to use all the sugar.)
* * *
**Frosting the Cake Decorating the Cake**
**1.** Cut a circle slightly smaller than the cake out of heavy cardboard. Place the circle on a cake stand or a flat surface.
**2.** If your cake layers are rounded on top, cut off the rounded portion by holding a serrated knife parallel to the work surface and gently sawing through the cake to make it flat.
**3.** Place 1 of the cake layers on the cardboard. Spread the frosting over the top of the first layer with a rubber spatula or a long-bladed metal spatula.
**4.** Place the second layer on top of the frosting and press down very gently so that the cakes are as even as possible. Frost the top of the second cake.
**5.** Place the third layer neatly on top of the second layer, then frost the top. Once the top is frosted, begin working around the sides, applying the frosting in short, circular strokes. Always be gentle with the cake, especially around the sides.
**6.** After the cake is frosted, it should be refrigerated. Use a cake box from your local bakery or a plastic cake saver. Or make a tent out of aluminum foil using toothpicks; insert them into the cake to keep the foil from touching the top or sides of the cake. You may have to touch up the frosting in some places before serving.
Here are four easy and fun ways to decorate your child's birthday cake. If you have the patience—and time—invite your child to help. Most important of all, don't forget the candles.
• Buy tubes of colored decorating icing (available in most grocery stores) and a couple of small plastic figures (available at toy stores as well as party and card shops). Any kind of figure or small toy will do, as long as it is light—and you remember to remove it before serving the cake. Think about what your little Ninja Turtle-fan, Batman-fan, Sesame Street-fan, or troll-lover might like to see on top of his or her cake. Then use the tubes of colored icing to embellish the figures and to write a birthday message to your child.
• Buy a selection of brightly-colored candies, such as candied fruit slices, lollipops, gum drops, and jelly beans, and arrange them on the top and sides of the cake in a decorative fashion.
• For a more sophisticated effect, use a decorating comb (available at specialty food stores) to decorate the cake. Place the cake on a cake stand and frost as usual. Immediately after the whole cake is frosted, dip the comb in hot water and shake off the excess, then place the edge of the comb at a slight angle on the side of the cake and gently draw the comb around the sides (by turning the cake stand) so that decorative lines are imprinted in the frosting. To decorate the top of the cake, place the edge of the comb at a slight angle on the top of the cake and turn the cake stand, holding the comb still.
• If you are trying to keep the party food at least marginally healthy, decorate the cake with fresh berries, such as blueberries, raspberries, blackberries, and strawberries. For a particularly decorative effect, place two contrasting colors of berries (such as blackberries and raspberries) in concentric circles on the top of the cake and place a ring of berries around the bottom edge of the cake. This looks best with white frosting.
* * *
## Glossary
**Baste** To coat with sauce, marinade, or pan juices during the process of cooking to add flavor and color, and to keep food from drying out. A bulb baster works best when you're cooking in a large roasting pan. Use a brush for broiling or barbecuing.
**Blanch** To cook a food (such as fruit or vegetables) very briefly in a large amount of boiling water; often the food is plunged into cold water after it is blanched in order to keep it from cooking longer.
**Brown** To sear meat or poultry in a very hot pan to give it color and seal in juices. Usually this is done before adding the meat to the stew or casserole.
**Clarify** To remove impurities, usually from butter or stock. When you clarify butter you remove the milk solids. Slowly melt butter in a small pan. When it's completely melted, carefully pour off the clear butter on top for use in cooking.
**Cream** To mix a softened ingredient, like butter, alone or with other ingredients until well blended.
**Deep-Fry** To cook completely submerged in fat.
**Deglaze** To add liquid to a hot roasting or frying pan to loosen particles and glaze that adhere to the bottom of the pan during cooking. Frequently a frying pan is deglazed with a bit of wine. This liquid is tasty and is added to or becomes the base for a sauce or gravy.
**Dice** To cut into small cubes.
**Dredge** To coat a food lightly, usually with flour, bread crumbs, or cornmeal before cooking. With a boneless chicken breast, for example, lay both sides of the breast in a plate of flour, then shake off the excess.
**Fillet** ( _v_.) To cut meat, chicken, or fish from the bones. ( _n_.) A piece of boneless fish; the whole tenderloin of beef, trimmed; the little flap of boneless meat on a chicken or turkey breast.
**Flake** To break something apart in ragged pieces with your fingers or a fork. Often you will flake chicken for a chicken salad. Also used to determine when fish is finished cooking, as when the meat flakes apart.
**Fold** To incorporate one ingredient into another without beating, but gently lifting from underneath with a rubber spatula.
**Grease** To lightly coat a pan with fat, such as vegetable oil, to keep foods from sticking and to encourage browning.
**Julienne** To cut into thin matchstick-size strips.
**Marinate** To soak fish, fowl, or vegetables in a flavored liquid before cooking to impart flavor and, often, to tenderize.
**Mince** To chop into extremely fine pieces.
**Nap** To dab with sauce, usually before serving or putting under the broiler.
**Poach** To cook food gently in simmering liquid that does not boil.
**Pound** To flatten meat, often between sheets of wax paper, using a mallet or heavy saucepan.
**Parboil** To boil briefly before cooking further in another manner.
**Pinch** A very small amount, usually as much as you can pick up between your thumb and forefinger.
**Preheat** To heat the oven to the proper temperature before baking.
**Purée** To blend or process into a smooth paste or liquid.
**Reduce** To cook a liquid uncovered over a high heat to let it partially evaporate and thicken, thus concentrating the flavor.
**Refresh** After boiling, to immediately transfer to cold water. This stops the cooking process and preserves the color of the vegetables.
**Roux** A mixture of flour and a fat, such as butter or pork or beef fat, used to thicken sauces and soups, usually in Cajun cooking.
**Sauté** To cook quickly in a pan over high heat in a small amount of oil or butter.
**Scald** To bring a liquid, usually milk, to the point just before it starts to boil and then remove it from the heat.
**Sear** To brown the surface of meat very quickly in a pan over high heat, either on top of the stove or in the oven.
**Sift** To press one or more dry ingredients (such as flour or confectioners' sugar) through a fine screen (or filter) to remove large particles and lighten texture.
**Simmer** To keep a liquid at a very gentle boil over low heat. Once a liquid is boiling, it takes surprisingly little heat to keep it simmering, especially with the pot covered.
**Skim** To remove the top layer from a liquid, such as a layer of fat or scum, from a soup or broth.
**Steam** To cook a food on a rack or in a specially designed basket over simmering or boiling water in a covered pan.
**Strain** To remove solids from liquids by pouring through a colander or sieve.
**Toss** To quickly mix ingredients together, usually salad or pasta, using a large spoon and fork.
**Zest** The colored part of a citrus fruit peel or the action of removing it.
## Index
**A | B | C | D | E
F | G | H | I | J
K | L | M | N | O
P | R | S | T | V
W | Y | Z**
**A**
Anchovy dressing,
Appetizers:
barbecued chicken wings,
cheese and crackers,
crudités,
dolmas and spanakopita,
fresh salsa and chips,
goat cheese pita pizza,
guacamole,
hummus or baba ghanoush with pita triangles,
jerk chicken wings, –78
melon and prosciutto, ,
miniature quiches, –71
mozzarella with tomato and fresh basil,
pâté,
pizza rotolo,
salmon caviar,
salmon hash in endive, –79
shrimp and cocktail sauce,
spring rolls and dim sum,
sun-dried tomato and roasted red pepper dip, –77
tapenade and pesto,
Apple(s),
baked,
and broccoli soup,
pie, Dad's own,
sausage stuffing, Dad's own,
Artichokes,
curry dip for,
Asian grilled swordfish,
Asian noodle soup with leftovers,
Asian noodles with chicken and ham,
Asparagus,
orange vinaigrette for,
Avocados,
for guacamole,
**B**
Bacon:
lettuce, and tomato sandwich,
and scallion dressing,
stuffed potatoes with cheese and,
Bananas,
with strawberries, sautéed, –26
Basil,
dressing,
fettuccine with tomato, sausage and,
fresh, mozzarella with tomato and,
and white bean salad,
Beef, –91
braising,
and broccoli, stir-fried,
broiling,
and burgers, panfried,
cuts, –83
in Dad's official meat loaf, –88
fillet of, with wild mushrooms,
grilling times for, –46
for hamburgers, –65, –88
London broil, –91
pot roast, –89
roast,
roasting (about),
salad, Japanese,
serving size,
slicing and carving of,
in Sloppy Joe sandwiches,
steak fajitas,
stew, old-fashioned, –5
stewing,
stock,
storage,
stuffed flank steak, –90
tenderloin, whole roast,
Beet(s), –36
and cucumber salad,
Bell peppers,
grilled,
roasted red, and sun-dried tomato dip, –77
roasted red, penne with tuna, tomatoes and,
stir-fried scallops with peas, baby corn and,
Beverages:
café au lait,
at cocktail parties,
coffee, –57
Dad's own egg cream,
mimosas,
teas,
yogurt smoothie,
Birthday parties, –93
food and beverages for, –88
make your own sundaes at,
planning and preparing for, –86
primo birthday cake for, –93
Black bean and carrot salad, –71
BLT sandwich,
Breads, , –40
basics, –31
corn, –36
country white, –33
flour types for,
Irish soda,
muffins,
pumpernickel raisin, –35
scones,
stale, for crumbs,
whole wheat, –34
Breakfast, –58
boiled eggs, –45
coffee and tea, –57
French toast,
fried eggs, –46
frittata, –54
home fries supremo,
hot cereal,
muffins,
omelets, –47
pancakes, –49
poached eggs,
puffed pancake, –53
scrambled eggs,
yogurt and fruit,
Breakfast in bed, –51
café au lait,
mimosa,
slow scrambled eggs with smoked salmon, sour cream and caviar, –51
Broccoli, –37,
and apple soup,
sautéed mushrooms and, –37
stir-fried beef and,
Brown Betty, peach-blueberry,
Brownies, super-fast saucepan, –20
Buckwheat groats, _see_ Kasha
Burritos:
chicken, –96
instant,
**C**
Caesar salad,
Cajun baked salmon, –14
Cajun BBQ shrimp,
Cakes:
decorating,
designing cupcakes,
primo birthday, –93
testers,
Carbonara, spaghetti, –91
Carrots, ,
and black bean salad, –71
grilled,
microwaved glazed,
with orange and mint,
and orange soup,
Cauliflower,
curried potato and,
Caviar,
salmon,
slow scrambled eggs with smoked salmon, sour cream and, –51
Celery,
Cereal, hot,
Cheese, –81
chilaquiles with chicken, tomatoes and,
and crackers,
goat, pita pizza,
macaroni and, quick, ,
mozzarella, chicken breasts with prosciutto and, –59
mozzarella with tomato and fresh basil,
Parmesan, for pasta,
Parmesan dressing,
sandwich, grilled,
smoked cheddar, tuna, and chickpea salad,
spinach with,
stuffed potatoes with bacon and,
types and uses of, –81
Chicken, –81
Asian noodles with ham and,
barbecued, –49
breast piccata,
breasts with balsamic vinegar and rosemary, Mary Cleaver's boneless,
breasts with prosciutto and mozzarella, –59
broiling,
burritos, –96
chilaquiles with tomatoes, cheese and,
cutting cooked,
flattening breasts of,
frying,
grilling times for, –46
jambalaya with shrimp and, –61
noodle soup, Dad's own, –201
oven-baked Middle Eastern "fried,"
Parmesan,
perfect roast, –79
roasting,
saté, –53
sautéing,
serving size,
simple pan gravy for,
stew, Mexican, –9
stock,
storage, –77
with tomato and sausage,
tortellini with prosciutto and tomato cream sauce,
types of,
veal, and sausage with couscous, Moroccan, –62
wings, barbecued,
wings, jerk, –78
chicken salad,
Chinese,
curried,
sandwich,
Chickpea, tuna, and smoked cheddar salad,
Chilaquiles with chicken, tomatoes, and cheese,
Chili, Dad's own, –57
Chinese chicken salad,
Chocolate:
chip oatmeal cookies, –19
chips, in super-fast saucepan brownies, –20
frosting, luscious,
-peanut butter-granola-coconut bars, quick and decadent, –14
pudding, –13
Chutney, quick cranberry,
Clam chowder, New England, –2
Cleanup tips,
Cocktail parties, –82
drinks at,
fancy menu for, , –82
food for, –72, –82
Coffee, –57
café au lait,
Coleslaw,
Corn, –39
baby, stir-fried scallops with red pepper, peas and,
bread, –36
grilled,
pudding,
Couscous, Moroccan veal, sausage, and chicken with, –62
Cranberry chutney, quick,
Croutons, homemade,
Crowd, cooking for, –66
baked smoked ham,
candied sweet potatoes,
chicken breasts with prosciutto and mozzarella, –59
Dad's own apple sausage stuffing,
Dad's own chili, –57
jambalaya with shrimp and chicken, –61
Moroccan veal, sausage, and chicken with couscous, –62
quick cranberry chutney,
red snapper Vera Cruz, –58
roast turkey,
whole roast beef tenderloin,
Cucumber(s),
and beet salad,
**D**
Desserts, –26
baked apples,
chipwiches,
chocolate pudding, –13
crystallized orange sections,
Dad's own apple pie,
Dad's own oatmeal-raisin cookies,
Dad's own pie crust, –18
Dave's Key lime pie,
everything fudge brownie sundae,
fresh fruit as, –23
hermits,
lemonade ice-cream pie,
melon with honey and lime,
oatmeal chocolate chip cookies, –19
peach-blueberry brown Betty,
poached pears,
poached pears with vanillaice cream and orange liqueur,
primo birthday cake, –93
quick and decadent chocolate-peanut butter-granola-coconut bars, –14
sautéed bananas with strawberries, –26
scalding milk for,
strawberry mousse,
super-fast saucepan brownies, –20
tiramisù,
Dinner, –118
Asian grilled swordfish,
baked mackerel with sun-dried tomatoes and herbs, –15
baked salmon with herb crust, –48
baked smoked ham,
barbecued chicken, –49
barbecued spareribs,
breaded pork chops, –5
broiled chicken,
Cajun baked salmon, –14
Cajun BBQ shrimp,
chicken breast piccata,
chicken breasts with prosciutto and mozzarella, –59
chicken burritos, –96
chicken tortellini with prosciutto and tomato cream sauce,
chicken with tomato and sausage,
Chinese chicken salad,
Dad's official meat loaf, –88
Dad's own chili, –57
Dad's own no-boil lasagna, –85,
fettuccine with tomato, sausage, and basil,
fillet of beef with wild mushrooms,
fillet of sole with saffron and tomato cream sauce, –13
fried chicken,
Hunan orange-ginger roast loin of pork,
jambalaya with shrimp and chicken, –61
Japanese beef salad,
lamb shish kebab,
loin lamb chops with red wine sauce, –101
London broil, –91
Mary Cleaver's boneless chicken breasts with balsamic vinegar and rosemary,
Mediterranean fish and seafood stew, –10
Mexican chicken stew, –9
Mexican feast, –97
Moroccan veal, sausage, and chicken with couscous, –62
old-fashioned beef stew, –5
oven-baked Middle Eastern "fried" chicken,
panfried flounder,
pan gravy, simple,
perfect roast chicken, –79
planning for, –75
pork chop and potato casserole, –6
pork or chicken saté, –53
pot roast, –89
red snapper baked in foil,
red snapper Vera Cruz, –58
roast beef,
roast turkey,
salad Niçoise, –75
sautéed chicken,
seafood linguine,
shoulder lamb chops with garlic and rosemary,
steak fajitas,
stir-fried beef and broccoli,
stir-fried scallops with red pepper, peas, and baby corn,
stuffed flank steak, –90
whole roast beef tenderloin, _see also_ Fancy dinners
Dips:
curry,
fresh salsa and chips,
hummus or baba ghanoush,
sun-dried tomato and roasted red pepper, –77
**E**
Egg(s), –47
boiled, –45
freshness and storage of,
fried, –46
in frittata, –54
omelets, –47
perfect hard-boiled,
poached,
salad sandwich,
scrambled,
separating of,
slow scrambled, with smoked salmon, sour cream, and caviar, –51
Egg cream, Dad's own,
Escarole and potato soup, –3
**F**
Fajitas, steak,
Fancy dinners, –58
hearty Mediterranean menu and recipes, –58
light summer supper menu and recipes, –49
Fennel,
Fish, –15
baked in foil,
baking,
broiling,
buying,
flounder, panfried,
grilling times for, –46
mackerel, baked, with sun-dried tomatoes and herbs, –15
panfried,
poached,
red snapper baked in foil,
red snapper Vera Cruz, –58
salmon, baked, with herb crust, –48
salmon, Cajun baked, –14
salmon hash in endive, –79
and seafood stew, Mediterranean, –10
serving size,
sole, fillet of, with saffron and tomato cream sauce, –13
storage,
swordfish, Asian grilled,
types of, and their uses, –11 _see also_ Tuna, canned
Flounder, panfried,
Food processors, –33
Food safety and storage, –37
French fries,
French toast,
Frittata, –54
Frostings:
luscious chocolate,
quick vanilla,
spreading on cake,
Fruit:
as dessert, –23
and yogurt breakfast,
**G**
Garlic,
oven-roasted potatoes with rosemary and whole cloves of, –58
sautéed green beans with,
shoulder lamb chops with rosemary and,
Glossary of terms, –95
Grapes,
wild rice with,
Greek salad,
Green beans,
sautéed, with garlic,
Grilled dishes, –54
barbecued chicken, –49
barbecued spareribs,
chicken saté, –53
kebab-o-rama,
lamb shish kebab,
Mary Cleaver's boneless chicken breasts with balsamic vinegar and rosemary,
peanut dipping sauce for,
pork saté, –53
swordfish, Asian,
vegetables,
Grilling, –48
Asian marinade for,
cooking times for, –46
Dad's own barbecue sauce for,
equipment and techniques for, –46
wine-and-herb marinade for,
Guacamole,
**H**
Ham,
Asian noodles with chicken and,
baked smoked,
baking,
Hamburgers, –65, –88
Health foods, –25
Herb(s):
baked mackerel with sun-dried tomatoes and, –15
crust, baked salmon with, –48
seasoning with spices and, –27
-and-wine marinade,
Hermits, –15
Hot dogs, –66, –88
Hunan orange-ginger roast loin of pork,
**I**
Irish soda bread,
**J**
Jambalaya with shrimp and chicken, –61
Japanese beef salad,
**K**
Kasha:
basic,
pilaf,
varnishkas,
Kitchen equipment, –31, –35
Knives, caring for, –29
**L**
Lamb, –101
broiling,
cuts,
grilling times for, –46
loin chops with red wine sauce, –101
panfrying, –99
roasting,
shish kebab,
shoulder chops with garlic and rosemary,
Lasagna, Dad's own no-boil, –85,
Leftovers:
Asian noodle soup with,
in chilaquiles with chicken, tomatoes, and cheese,
lo mein, quick,
in minestrone deluxe,
Lemonade ice-cream pie,
Lemon and tarragon dressing,
Lo mein, quick leftover,
Lox and cream cheese on a bagel,
Lunch, –72
all-star sandwiches,
Asian noodle soup with leftovers,
BLT sandwich,
chef's salad,
chilaquiles with chicken, tomatoes, and cheese,
Dad's own egg cream,
English muffin pizza,
grilled cheese sandwich,
hamburgers, –65, –88
hot dogs, –66, –88
instant burritos,
macaroni and cheese,
minestrone deluxe,
peanut butter and jelly sandwich,
quick leftover lo mein,
quick macaroni and cheese, ,
school lunchbox tips,
Sloppy Joe sandwich,
trail mix,
tunafish salad sandwich, –61
tuna patties,
turkey club sandwich, –63
yogurt buffet,
yogurt smoothie,
**M**
Macaroni:
casserole, never-fail,
and cheese, quick,
Mackerel, baked, with sun-dried tomatoes and herbs, –15
Main dishes, _see_ Dinner
Marinades:
Asian,
wine-and-herb,
Measuring ingredients,
Meatballs,
Meat loaf, Dad's official, –88
Meats, _see_ specific meats
Meat thermometers,
Mediterranean fish and seafood stew, –10
Melon(s),
with honey and lime,
and prosciutto, ,
watercress, and snow pea salad,
Mexican chicken stew, –9
Mexican feast, –97
Microwave ovens, –35
baking potatoes in,
cooking vegetables in,
glazed carrots in,
Minestrone,
deluxe,
Moroccan veal, sausage, and chicken with couscous, –62
Muffins,
Mushrooms,
dried,
grilled,
in salad, –63
sautéed broccoli and, –37
wild, fillet of beef with,
**N**
Napkins, special folding techniques for, ,
New England clam chowder, –2
Niçoise, salad, –75
**O**
Oatmeal:
chocolate chip cookies, –19
old-fashioned,
-raisin cookies, Dad's own,
Onions:
grilled,
how to cut,
red, in salad,
Orange(s),
and carrot soup,
carrots with mint and,
crystallized, sections,
-ginger roast loin of pork, Hunan,
vinaigrette,
**P**
Pancakes:
basic, –49
puffed, –53
Pantry necessities,
Pasta, –94
empty cupboard,
fettuccine with tomato, sausage, and basil,
fresh basil for,
fresh vs. dried,
how to cook, –87
lasagna, Dad's own no-boil, –85,
linguine, seafood,
macaroni and cheese, quick, ,
macaroni casserole, never-fail,
meatballs for,
noodles, cold peanut,
noodles with chicken and ham, Asian,
Parmesan cheese for,
penne with tuna, tomatoes, and roasted peppers,
spaghetti carbonara, –91
sun-dried tomatoes for,
tortellini, chicken, with prosciutto and tomato cream sauce,
tortellini salad, cold,
types of, and cooking times, –79,
Pasta sauces, –81
basic tomato,
puttanesca,
tomato with meat,
tomato with mushrooms,
tomato with sausage,
Peach(es),
-blueberry brown Betty,
Peanut butter:
-chocolate-granola-coconut bars, quick and decadent, –14
in cold peanut noodles,
dipping sauce,
and jelly sandwiches,
Pears,
poached,
poached, with vanilla ice cream and orange liqueur,
Peas, –41
with cream and almonds,
in the pod, ,
snow pea, watercress, and melon salad,
stir-fried scallops with red pepper, baby corn and,
Pie crust, Dad's own, –18
Pies:
Dad's own apple,
Dave's Key lime,
lemonade ice-cream,
Pita bread:
pizza, goat cheese,
sandwich, salad in,
triangles, hummus or baba ghanoush with,
Pizza:
at birthday parties,
Dad's own, –39
dough, freezing of,
English muffin,
goat cheese pita,
rotolo,
Poppy seed dressing,
Pork, –6
barbecued spareribs,
chop and potato casserole, –6
chops, breaded, –5
chops, broiling,
cuts,
grilling times for, –46
panfrying,
roasting,
roast loin of, Hunan orange-ginger,
saté, –53
serving size,
storage, _see also_ Ham
Potato(es), –30
baked,
baked, as a meal,
boiled,
candied sweet,
curried cauliflower and,
and escarole soup, –3
French fries,
grilled,
home fries supremo,
mashed,
microwave method for,
oven-roasted,
oven-roasted, with rosemary and whole garlic cloves, –58
oven-roasted fries,
pan roasted new,
and pork chop casserole, –6
red, salad, –73
stuffed, with bacon and cheese,
types of,
Prosciutto:
chicken breasts with mozzarella and, –59
chicken tortellini with tomato cream sauce and,
and melon, ,
**R**
Radishes,
Recipes, how to read,
Red snapper:
baked in foil,
Vera Cruz, –58
Rice, –22
baked wild,
basic, pilaf,
basic brown,
boiled white,
curried,
dirty,
how to cook,
Mexican,
using canned broth or bouillon in,
about wild,
wild, with grapes,
Rosemary:
Mary Cleaver's boneless chicken breast with balsamic vinegar and,
oven-roasted potatoes with whole garlic cloves and, –58
shoulder lamb chops with garlic and,
**S**
Salad dressings, –65
anchovy,
bacon and scallion,
basil,
Dad's own vinaigrette,
lemon and tarragon,
olive oil and vinegar in, –65
orange vinaigrette, for asparagus,
Parmesan,
poppy seed,
Salads, –76
beet and cucumber,
Caesar,
carrot and black bean, –71
chef's,
chicken,
Chinese chicken,
cold tortellini,
coleslaw,
curried chicken,
Greek,
greens for, types of,
homemade croutons for,
Japanese beef,
Niçoise, –75
red potato, –73
spinach, –69
spinners,
tuna, chickpea, and smoked cheddar,
vegetables for, –63
Waldorf,
watercress, snow pea, and melon,
white bean and basil,
Salad spinners,
Salmon:
baked, with herb crust, –48
Cajun baked, –14
hash in endive, –79
smoked, slow scrambled eggs with sour cream, caviar and, –51
Sandwiches, –63
at birthday parties,
BLT,
chicken salad,
deli,
egg salad,
grilled cheese,
hero,
lox and cream cheese on a bagel,
peanut butter and jelly,
salad in a pita,
Sloppy Joe,
smoked turkey with cranberry sauce,
tunafish salad, –61
tuna melt,
turkey club, –63
Sauces,
cocktail, shrimp and,
curry dip, for artichokes,
Dad's own barbecue,
peanut dipping,
red wine, loin lamb chops with, –101
saffron and tomato cream, fillet of sole with, –13
salsa, fresh, and chips,
three, for foil-baked seafood,
tomato cream, chicken tortellini with prosciutto and,
using canned broth and bouillon in, _see also_ Pasta sauces
Sausage(s):
apple stuffing, Dad's own,
chicken with tomato and,
fettuccine with tomato, basil and,
Moroccan veal, chicken, and couscous with, –62
tomato sauce with,
Sauté pan techniques, –41
Scallions,
and bacon dressing,
Scallops, stir-fried, with red pepper, peas, and baby corn,
Scones,
Seafood linguine,
Seasoning:
with herbs and spices, –27
with salt and pepper, ,
Shellfish, –18
stir-fried scallops with red pepper, peas, and baby corn,
types of, and their uses, _see also_ shrimp
Shopping tips and sources, –24
Shrimp:
Cajun BBQ,
and cocktail sauce,
jambalaya with chicken and, –61
peeling and deveining of,
Smoked salmon, slow scrambled eggs with sour cream, caviar and, –51
Sole, fillet of, with saffron and tomato cream sauce, –13
Soups, –207
Asian noodle, with leftovers,
basic, –97
beef stock,
broccoli and apple,
carrot and orange,
chicken stock,
cleaning leeks for,
Dad's own chicken noodle, –201
degreasing stocks,
hearty,
minestrone,
minestrone deluxe,
New England clam chowder, –2
potato and escarole, –3
puréed,
seasoning,
split pea,
standard,
Spinach, –42
with cheese,
salad, –69
Split pea soup,
Steaming vegetables, –33
Stews:
Mediterranean fish and seafood, –10
Mexican chicken, –9
old-fashioned beef, –5
Strawberry(ies),
mousse,
sautéed bananas with, –26
Sweet potatoes, candied,
**T**
Table setting,
Tacos:
turkey,
vegetarian, –97
Teas,
Thanksgiving dinner, –66
Tiramisù,
Tomato(es):
chicken with sausage and,
chilaquiles with chicken, cheese and,
cream sauce, fillet of sole with saffron and, –13
fettuccine with sausage, basil and,
grilled cherry,
and mozzarella with fresh basil,
penne with tuna, roasted peppers and,
in salads,
sauce, basic, –83
sun-dried, baked mackerel with herbs and, –15
sun-dried, for pasta,
zucchini and,
Trail mix,
Tuna, canned,
chickpea, and smoked cheddar salad,
melt sandwich,
patties,
penne with tomatoes, roasted peppers and,
salad sandwich, –61
Turkey:
club sandwich, –63
roast,
smoked, sandwich with cranberry sauce,
tacos,
**V**
Vanilla frosting, quick,
Veal, sausage, and chicken with couscous, Moroccan, –62
Vegetables, –42
artichokes,
artichokes, curry dip for,
asparagus,
asparagus, orange vinaigrette for,
basic cooking techniques for, –33
beet and cucumber salad,
beets, –36
broccoli, –37
broccoli and mushrooms, sautéed, –37
buying and using in salads, –63
carrots,
carrots, microwaved glazed,
carrots with orange and mint,
cauliflower,
cauliflower and potato, curried,
corn, –39
corn pudding,
green beans,
green beans with garlic, sautéed,
grilled,
peas, –41
peas in the pod, ,
peas with cream and almonds,
spinach, –42
spinach with cheese,
steaming, –33
stir-frying,
zucchini,
zucchini and tomatoes, _see also_ Potato(es)
Vegetarian tacos, –97
**W**
Waldorf salad,
Watercress, snow pea, and melon salad,
White bean and basil salad,
wild rice,
baked,
with grapes,
Wine:
classifications and choices, –53
at cocktail parties,
-and-herb marinade,
**Y**
Yogurt,
buffet,
and fruit breakfast,
smoothie,
**Z**
Zucchini, ,
grilled,
and tomatoes,
Copyright © 1993, 2007 by Bob Sloan and Paul Hanson
Illustrations © Serge Bloch
Technical illustrations © Barbara Smullen
All rights reserved. No portion of this book may be reproduced—mechanically, electronically, or by any other means, including photocopying—without written permission of the publisher. Published simultaneously in Canada by Thomas Allen & Son Limited.
Library of Congress Cataloguing-in-Publication Data is available.
eISBN: 9780761172635
Designed by Paul Hanson and Beverly McClain
Workman Books are available at special discounts when purchased in bulk for premiums and sales promotions as well as for fund-raising or educational use. Special editions or book excerpts also can be created to specification. For details, contact the Special Sales Director at the address below.
Workman Publishing Company, Inc.
225 Varick Street
New York, NY 10014-4381
www.workman.com
## About the Author
Bob Sloan is a professional chef, teacher, and author who runs his own catering business. He lives in New York City with his wife and two sons, both of whom love to cook.
| {
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Q: Is there any way to make some words (only some words not whole editor) in Rad editor for Ajax read only? I am using Telerik Rad Editor for Ajax in my project,I want to make some fields/words read only. I tried couple of things and it's working for whole editor.. meaning whole editor becomes read only. I just want some words and rest of the editor as it is to edit for users. Is it possible ? which property to set ?
Thanks in advance.
A: In order to define editable and non-editable regions in RadEditor, you should place several DIV or SPAN element containers in the editor content area. After that, set the unselectable="on" attribute to their tags in order to prohibit selection of these elements. You should also set the contentEditable attribute to "false" to put these elements in non-editable mode.
Example: Adding editable and non-editable areas in RadEditor.
<div style="border: red 1px solid;" contenteditable="false" unselectable="on">
Non Editable AREA
<div style="border: green 1px solid;" contenteditable="true" unselectable="off">
<!--Content name="info" -->
Editable REGION...
<!--/Content -->
</div>
Non Editable AREA
</div>
| {
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} | 9,381 |
Civic Ed>
Asked why they don't vote, here is what people say
Andrew Joseph Pegoda
"Some people might be indifferent or simply not care, but many who forgo voting have legitimate reasons," argues Andrew Joseph Pegoda.
Pegoda is a lecturer in women's, gender and sexuality studies, as well as religious studies, at the University of Houston.
At least 40 percent to 90 percent of American voters stay home during elections, evidence that low voter turnout for both national and local elections is a serious problem throughout the United States.
Now that the 2020 campaign is in something close to a state of suspended animation — the novel coronavirus pandemic having taken almost all attention away from the presidential race and forced delays in a dozen states' primaries — directives for people to "get out and vote" have some time to get fired up again.
But if and when outbreak subsides, some people might remain indifferent or simply not care. And many who forgo voting have legitimate reasons.
Over the past decade, through my extensiveresearch on civil rights and oppression, through my observations of social media comments and through my conversations with hundreds of college students, I have concluded that such reasons are both important and, generally, unnoticed.
First, Republican-led efforts to diminish participation in voting and voter registration have greatly contributed to the number of nonvoters.
Since 2010, 25 states have adopted measures specifically aimed at making voting more difficult. Such measures include additional voter identification requirements.
Sometimes lawmakers said these were necessary to curb illegal voting, which research shows is an all-but-nonexistentproblem.
Some counties and states have also created confusion and uncertainty about how to initially register or re-register after a voter has moved.
In other cases, people might not know where to vote, due to the distribution of deliberately false information.
Since the Supreme Court ruled in Shelby County v. Holder in 2013 that key aspects of the Voting Rights Act of 1965 were unconstitutional, states have closed more than 1,000 polling locations, half of them in Texas.
Second, some people decide to forgo voting. I hear again and again that sometimes people make such choices after they were intimidated by friends, by family members or by people at polling places.
When facing the complexities of races with dozens of candidates and complicated issues, others say they don't feel they know enough to make informed decisions.
People have also told me they worry about feeling personally responsible if they vote for a candidate or position and there are unforeseen consequences, such as cuts to important aid programs. Members of any group, but especially those of underrepresentedgroups, may long to vote for desirable candidates but not feel that current candidates offer the possibility that anything will really change.
Individuals have shared with me that they have not voted because they do not trust a nation that they feel has lied and perpetuated systemic abuse against minorities, aggravated further by widespreadgerrymandering and for presidential elections, by an Electoral College system that doesn't weigh each vote the same.
In France and India, for example, people who dislike all of the candidates can formally "vote" without endorsing any candidate by selecting "none of the above." Not having this option in the U.S. might affect turnout, too.
Third, voting may simply be too difficult for some people.
I often hear of people who – even with early voting or absentee options – cannot vote because they lack transportation. They are homeless. They lack child care. They are disabled. They work, go to school and live in different cities.
This is even more applicable for the 7 to 8 million in the U.S. who hold multiple jobs. Laws guaranteetime offfor voting but aren't enforceable and aren't always workable.
Such people are effectively disenfranchised.
Finally and importantly, only nonincarcerated, mentally competent and registered citizens of age may vote.
Based on 2015 data, the right to vote was not extended to more than 13 million people with green cards, work visas or refugee status. Given the total population of people 18 and older exceeded 248 million in 2015, that means one out of every 20 adults living, working and spending money in the United States was not eligible to vote.
Using vague and inconsistent language, states have also worked to denydisabled or mentallyill people a political voice. This affects potentially over a million people nationwide.
As discussed in the books "The New Jim Crow" and in "Race, Incarceration and American Values," an additional 6 million Americans cannot vote because of felony convictions, an issue that disproportionately affects black people. In some states, this disenfranchisement remains in effect for life.
Given the legitimacy of reasons why they don't participate, nonvoters certainly shouldn't be scolded with, "If you don'tvote, you can'tcomplain." Or with even harsher words, as one friend on Facebook put it: "If you don't vote, everything wrong in the world is your fault."
People long to be heard and deserve fair representation. Instead of bashing nonvoters, I recommend taking some deep breaths and initiating friendly conversations. Listen and learn. At a time when public trust in government is at historic lows, such conversations might even encourage someone to demand a voice.
This article is republished from The Conversation under a Creative Commons license. Click here to read the original article.
Why registered voters say they didn't vote in 2016 | Pew Research ... › | {
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Q: Regex com lookbehind não funciona no Firefox Criei um projeto em Angular e estou usando a seguinte expressão regular:
export const INTERFACE_REGEX = new RegExp(/(?<=.*\/)(.*?)(?=@|-.+)/gi);
Acontece que ao usar o Goggle Chrome o projeto funciona normal, mas se eu tentar abrir pelo Firefox dá erro:
Erro: syntax invalid regex group
Eu fiz vários testes e descobri que se eu tirar o ?<= da expressão deixa assim eu consigo compilar usando o firefox.
Qual seria o equivalente desse trecho da expressão (?<=.*\/)?
A:
Nota: quando a pergunta foi feita, o Firefox não tinha suporte a lookbehind (por isso o erro), mas atualmente suporta e o erro não ocorre mais.
Primeiramente, um detalhe: não precisa construir a regex desta forma. Ao usar as barras (que é a notação literal para expressões regulares), você já está criando um RegExp, então passá-lo para o construtor é redundante. Ou seja, as 4 formas abaixo são equivalentes:
regex = /expressão/gi;
regex = new RegExp('expressão', 'gi');
regex = new RegExp(/expressão/gi);
regex = new RegExp(/expressão/, 'gi');
Mas eu só usaria as 2 primeiras (a primeira se a expressão for "fixa", e a segunda se você tiver uma string que represente a expressão - desde que se tome os devidos cuidados). As 2 últimas são redundantes (a última talvez seja útil em casos nos quais as flags são dinâmicas, mas vale lembrar que ela só é válida a partir do ECMAScript 6).
Dito isso, vamos ao problema em si:
O erro ocorre porque o trecho (?<=.*\/) é um lookbehind, e na data em que esta resposta foi escrita, o Firefox não tinha suporte (mas atualmente tem, portanto não precisaria usar mais a solução abaixo, a menos que você precise dar suporte a algum dos browsers que ainda não suportam - por isso, de qualquer forma, fica documentada aqui a alternativa).
Enfim, existe uma forma de simular isso em qualquer outro ambiente que não suporte lookbehind. A ideia do lookbehind é verificar se algo existe antes do match atual. Sendo assim, basta quebrar a regex em duas (a parte que vem antes e o restante). Se eu encontrar um match, eu vejo se o que vem antes dele corresponde ao lookbehind. Mais ou menos assim:
let r_match = /(.?)(?=@|-.+)/gi;
let lookbehind = /.*\/$/; // simula o lookbehind
let match;
let results = [];
while (match = r_match.exec('./a@ ./x-fd')) { // testando com uma string qualquer
if (match.index == r_match.lastIndex) r_match.lastIndex++;
// obtém a substring de zero até o índice em que o match ocorre
let leftContext = match.input.substring(0, match.index);
if (lookbehind.test(leftContext)) { // simular lookbehind
results.push(match[1]);
}
}
console.log(results); // [ 'a', 'x' ]
Então a ideia é primeiro verificar se tem um match. Depois eu pego a substring, do início da string até o ponto em que o match foi encontrado, e vejo se ele termina com o trecho correspondente ao lookbehind. Para isso adicionei o marcador $, que significa o final da string. E nesse caso específico, a regex poderia ser apenas /\/$/- termina com / - pois .* significa "zero ou mais caracteres" e nesse caso não faz diferença ("terminar com zero ou mais caracteres seguidos de /" é a mesma coisa que "terminar com /").
Se quiser, você pode fazer push de todo o match (pois o objeto contém mais informações, como por exemplo o índice em que ocorre o match, etc). No caso, eu optei por apenas pegar o caractere correspondente a (.?).
O if (match.index == r_match.lastIndex) é para corrigir um bug no caso de zero width matches (explicado em detalhes aqui).
Outra alternativa é não usar lookbehind e obter somente o grupo de captura correspondente à informação que você quer:
let regex = /([^\/]*\/)(.?)(?=@|-.+)/gi;
let s = './a@ ./x-fd';
console.log([...s.matchAll(regex)].map(m => m[2])); // [ 'a', 'x' ]
Como agora o trecho (.?) é o segundo par de parênteses da expressão, ele está no grupo 2, por isso usei m[2] (mas você poderia eliminar o map caso queira um array com os matches).
E mudei o ponto para [^\/] (qualquer caractere que não seja /), pois senão a regex pode acabar pegando mais caracteres do que deve (inclusive a própria barra), dando resultados incorretos (como pegar somente o x, por exemplo).
Se bem que neste caso, não precisa do primeiro parênteses (assim, a informação que eu quero estará no grupo 1):
let regex = /[^\/]*\/(.?)(?=@|-.+)/gi;
let s = './a@ ./x-fd';
console.log([...s.matchAll(regex)].map(m => m[1])); // [ 'a', 'x' ]
Por fim, a flag i serve para deixar a regex case insensitive (não diferencia letras maiúsculas e minúsculas). Mas como sua regex não tem letras, esta flag é desnecessária (pode deixar somente o g, que no seu caso não fará diferença).
Veja mais detalhes em "Negative lookbehind só funciona no Google Chrome, existe uma alternativa para os outros browsers?".
A: Suporta a partir da versão 78, que foi lançada em junho de 2020.
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/RegExp#browser_compatibility
| {
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