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# An online undergraduate business school uses a learning management software system (LMS) that allows instructors to...
###### Question:
An online undergraduate business school uses a learning management software system (LMS) that allows instructors to know how many hours students are connected to the course website. When studying for the midterm exam, students have a choice of using two study guides. One study guide comes with the textbook and is professionally prepared by the publisher. The second study guide is prepared by the professor. Suppose the department chairperson is interested in determining whether a student's hours connected to the LMS (study time) is independent of the student's choice of study guide. The data available below show the numbers of students organized by study time and selected study guide. Determine whether the hours connected to the LMS is independent of the study guide the student chooses to use for the exam. Test at the alpha = 0.005 level using the p-value approach Click the icon to view the study guide data What are the null and alternative hypotheses for this test? O A. Ho: Study time and study guide have different proportions O B. Ho Study time and study guide have equal proportions 1 Study Guide Data HA: Study time and study guide have equal proportions HA: Study time and study guide have different proportions C. H0 : Study time is not independent of study guide Study Guide Chosen Publisher's Guide Professor's Guide HA: Study time is independent of study guide Ho: Study time is independent of study guide HA Study time is not independent of study guide Connect Time Under 6 hours 6-12 hours 12-20 hours Over 20 hours 144 157 118 146 145 155 113 118 O D. The test statistic is (Round to three decimal places as needed.) Print Done The p-value is (Round to three decimal places as needed.) What is the conclusion? O A. O B. Reject the null hypothesis. There is sufficient evidence to conclude that the two variables are not independent. Do not reject the null hypothesis. There is sufficient evidence to conclude that the two variables are not independent. C. 0 D. Reject the null hypothesis. There is insufficient evidence to conclude that the two variables are not independent. Do not reject the null hypothesis. There is insufficient evidence to conclude that the two variables are not independent.
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# References¶
WS20
Michael S Warren and Samuel W Skillman. Mobility changes in response to covid-19. arXiv preprint arXiv:2003.14228, 2020.
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# $X = (X_1, X_2)$ is it not a multivariate random variable?
$X=(X_1,X_2,\ldots, X_P)$ is a $p$-dimensional random variable on $(\Omega, S, P)$ iff $X_i$'s are univariate random variables on the same probability space $(\Omega, S, P)$ ."
We all know that. it is written and proved in several books.
But I'm confused with the 'same probability space' thing.
Let me explain my problem with an example : Suppose $X_1$= the height of a boy selected at random from a class of 50 boys. $X_2$ =the weight of the same boy selected at random from a class of 50 boys.
Now in both the cases the sample space $\Omega = (-\infty,+\infty)$ . but the $P$ in the probability space $(\Omega, S, P)$ for both the random variable must be different . let's consider $X_1 \sim \mathrm{N}(5, 1)$ and $X_2\sim \mathrm{N}(45, 4)$. Then $X_1$ and $X_2$ are not defined on same probability space. (or , are they ? I'm kinda confused)
So , $X = ( X_1, X_2)$ , is it not a bi-variate random variable?
[Our professor was talking about constructing multivariate random variable taking different bio-metric measures of an individual . But, if, all the univariate random variables (components of a multivariate random variable) to be defined on the same probability space be a necessary and sufficient condition, then constructing a multivariate random variable taking different bio-metric measures must not be possible.]
This is my first question here, hoping for good responses.Although I don't know whether I'm able to put my query in a compact form. If you find any ambiguity kindly ask.
• Please refrain from adding personal comments such as "Although i don't know whether I'm able to put my query is a compact form. if you find any ambiguity , kindly ask me.", as it has nothing to do with the question. Mentioning "Thanks!" etc. are discouraged here; if you find something helpful, then upvote and/ or accept it.
– hola
Aug 10, 2014 at 7:56
• okay..!! I got it. Aug 10, 2014 at 7:58
• actually, the query is a little complicated , and people may find it ambiguous . that's why , i mentioned it. Aug 10, 2014 at 7:59
• Just an indomitable curiosity: Which college/ university do you read in? I guess you are a B.Sc. student from Kolkata.
– hola
Aug 10, 2014 at 8:03
• "We all know that. It is written and proved in several books." However, if you were familiar with the said construction of appropriate probability space, there wouldn't be any confusion. If you want, I can outline how it's done in an answer
– Alen
Aug 10, 2014 at 8:10
First, the text below requires that you know definitions of a real random variable (or vector), measurable function, Borel $\sigma$-algebra and cumulative distribution function.
Let $X$ be an $n$-dimensional random vector with the CDF ${F}$ (this is a fundamental assumption which begs the question does the appropriate probability space and the random vector exist, we proceed to show that they do).
Then the relation ${F}\left( x \right) = {\mathbb{P}}\left( {X \leqslant x} \right)$ (here $X \leqslant x \Leftrightarrow {X_i} \leqslant {x_i},\forall i$) uniquely determines a probability $\mathbb{P}$ on ${\mathbb{R}^n}$ (this is non-trivial result and the proof is cumbersome). Let's first construct the underlying probability space.
Let $\Omega = {\mathbb{R}^n}$, $\mathcal{F} = {\mathcal{B}^n}$ the Borel $\sigma$-algebra on ${\mathbb{R}^n}$ and $\mathbb{P}$ as above. Now we define the random vector $X:{\mathbb{R}^n} \to {\mathbb{R}^n},X\left( x \right) = x$. It follows, using the standard notation ${\mathbb{P}_X}\left( B \right) = \mathbb{P}\left( {{X^{ - 1}}\left( B \right)} \right)$ for the probability ${\mathbb{P}_X}$ induced by $X$ on ${\mathbb{R}^n}$, that ${F_X}\left( x \right) = {\mathbb{P}_X}\left( {\left( { - \infty } \right.,\left. x \right]} \right) = \mathbb{P}\left( {{X^{ - 1}}\left( { - \infty } \right.,\left. x \right]} \right) = \mathbb{P}\left( {\left( { - \infty } \right.,\left. x \right]} \right) = F\left( x \right)$, so $\left( {\Omega ,\mathcal{F},\mathbb{P}} \right)$ and $X$ are indeed such a probability space and a random variable that the given $F$ is the corresponding cumulative distribution function.
Now on to your specific example: ${X_i}$ is a random variable on $\left( {\Omega ,\mathcal{F},\mathbb{P}} \right)$ because $X_i^{ - 1}\left( {{B_i}} \right) = {\left( {{\pi _i}\left( X \right)} \right)^{ - 1}}\left( {{B_i}} \right) = {X^{ - 1}}\left( {\pi _i^{ - 1}\left( {{B_i}} \right)} \right)$, where ${{\pi _i}}$ is $i$-th coordinate projection and ${B_i} \in \mathcal{B}\left( \mathbb{R} \right)$. Since projections are continuous, they are measurable, so $\pi _i^{ - 1}\left( {{B_i}} \right) \in {\mathcal{B}^n}$ (it's helpful to imagine this Borel $\sigma$ algebra as a $\sigma$ algebra in the codomain of $X$) which implies that ${X^{ - 1}}\left( {\pi _i^{ - 1}\left( {{B_i}} \right)} \right) \in \mathcal{F}$, since $X$ is a random vector.
So, if ${X_1}$ is the height and ${X_2}$ the weight of an individual, then $\Omega = {\mathbb{R}^2}$ (and not $\Omega = \mathbb{R}$ as you assumed) and $X_1^{ - 1}\left( {\left[ {a,b} \right]} \right) = {X^{ - 1}}\left( {\left[ {a,b} \right] \times \mathbb{R}} \right) = \left[ {a,b} \right] \times \mathbb{R} \in {\mathcal{B}^2} = \mathcal{F}$. Also, ${X_1},{X_2}:\Omega \to \mathbb{R}$ and $X = \left( {{X_1},{X_2}} \right):\Omega \to {\mathbb{R}^2}$, so ${X_1},{X_2},X$ have the same domain.
The reason why you CAN forget about the underlying probability space is exactly the construction given above which guarantees that such a space always exists. However, I've found that it's sometimes helpful to be aware of it.
• hey , i have understood it. thank ya. a lot...!! it was lucid and neat. Aug 11, 2014 at 6:27
The answer to your question is a matter of interpretation. If you formalize the sample spaces abstractly enough, then the sample spaces for $X_1$ and $X_2$ can be the same. After all, both weight and height are continuous quantities, and so can be modeled as real numbers. If the real numbers aren't a general enough setting, you can go into more abstract spaces like "Polish spaces".
The real answer is that you typically don't want to lose the "typing" information (what kind of number does your variable represent). That is certainly a worthy goal. And to do that, probablists and statisticians try to forget about the sample space as quickly as possible. In that sense, the definition in your book is too specific, and only corresponds to the one real people use "in principle".
The point about probability measures is similar enough.
Your primary focus "should" be the random variables and their properties, not the sample spaces they are defined on.
• i appreciate your response. but , somehow it doesn't answer question properly. Aug 10, 2014 at 8:10
• In what way? The question of whether $(X_1, X_2)$ is an RV is only a problem if you use an artificially restrictive definition of an RV. Aug 10, 2014 at 14:22
• what is 'an artificially restrictive definition' and what is 'not an artificially restrictive definition'? a definition is a definition. we choose to forget about the restriction of the definition , because it's artificial , that can't be any answer. anyway , a sensible answer has been submitted . you can check it above. Aug 11, 2014 at 6:29
• You are confused. "a definition is a definition" is wrong. In particular, the definition you are using for your probability space is unsuitable for defining $(X_1, X_2)$ as an RV. So you must use a definition of random variables that defines, or at least includes, $(X_1, X_2)$ as an RV. Note that the answer you are happy with assumes that you already have the definition of a random vector. Aug 11, 2014 at 16:19
• sure, we already have a definition of a random vector . almost all the popular books have defines it in one same way. so , what's wrong with that? ' a definition is a definition is wrong' ! ok , then define 'definition'. Aug 13, 2014 at 7:32
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# JavaScript/PHP libraries for calculating common
I am looking for a JavaScript or a PHP library to calculate common business/statistical metrics (e.g. Total, Avg, YTD, YoY, MoM, CAGR growth, standard deviation, regression line coordinates) from simple arrays/objects with a structure such as:
The idea is that I would just provide the arrays with some basic parameters (e.g. time period I'm interested in) and would get all the numbers crunched automatically in return.
Can anybody point me to a library they've used and trust from experience?
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Showing changes from revision #2 to #3: Added | Removed | Changed
A polynomial monad is a monad whose underlying endofunctor is a polynomial functor polynomial functor. This is of course equivalent to being a monad in the category of polynomial functors.
## Examples
A basic example is the free-monoid monad, Example 1.9. It is exhibited by the polynomial $1\leftarrow \mathbb{N}^\prime\rightarrow \mathbb{N}\rightarrow 1$ where the middle arrow is such that for all $n\in \mathbb{N}$ its fiber over $n$ has cardinality $n$.
One can construct the free monad on a polynomial endofunctor.
An extensive category $E$ (which in particular has finite sums) has W-types iff every polynomial functor in a single variable on $E$ has an initial algebra. The “W” in the name of this notion refers to the fact Martin-Löf’s types of wellfounded trees (translated into category theory) are initial algebras for polynomial endofunctors in a single variable. Initial algebras for (general) polynomial functors correspond to Petersson-Synek tree types.
## Reference
• Nicola Gambino and Joachim Kock (2009); Polynomial functors and polynomial monads; arXiv.
Last revised on February 27, 2013 at 23:31:57. See the history of this page for a list of all contributions to it.
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Content is king. It always has been and it always will be. Creating insightful, engaging and unique content should be at the heart of any online marketing strategy. Too often, people simply don't obey this rule. The problem? This takes an extraordinary amount of work. However, anyone that tells you that content isn't important, is not being fully transparent with you. You cannot excel in marketing anything on the internet without having quality content.
PageRank is a link analysis algorithm and it assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is referred to as the PageRank of E and denoted by {\displaystyle PR(E).} Other factors like Author Rank can contribute to the importance of an entity.
A key benefit of using online channels for marketing a business or product is the ability to measure the impact of any given channel, as well as how visitors acquired through different channels interact with a website or landing page experience. Of the visitors that convert into paying customers, further analysis can be done to determine which channels are most effective at acquiring valuable customers.
PPC advertising is a method of advertising on search engines like Google and Bing. As mentioned earlier, with PPC ads, you pay each time that ad is clicked on. PPC ads also exist on social media platforms like Instagram and Facebook as well. However, if you're going to engage in PPC advertising, it's important that you determine conversion rates by using tracking pixels.
There’s no way to speed up the process. To encourage your PageRank to grow, keep making quality content that others will want to link to. You may also consider participating regularly in social media communities to get the word out about the new content you are creating. (Social media participation itself won’t help your PageRank but it will help other humans know your content exists, which can help inspire an increase in natural inbound linking.)
Is there anyway “no follow” links can positively affect your search rankings? Most bloggers have to assign this attribute as they can’t trust every site they link to nor do they want to decrease their own PR. Is there any potential for search engine to reward a page that accumulates “no follow” links even if they accrue 1/10 the weight they previously did? This would reward those who take the time to actively blog.
A strategy that is linked into the effectiveness of digital marketing is content marketing.[39] Content marketing can be briefly described as "delivering the content that your audience is seeking in the places that they are searching for it".[39] It is found that content marketing is highly present in digital marketing and becomes highly successful when content marketing is involved. This is due to content marketing making your brand more relevant to the target consumers, as well as more visible to the target consumer.
Cause if I do that, If I write good content, whilst my 100+ competitors link build, article market, forum comment, social bookmark, release viral videos, buy links, I’ll end up the very bottom of the pile, great content or not and really I am just as well taking my chances pulling off every sneaky trick in the book to get my site top because, everyone does it anyway and if I don’t what do have to lose?”
Can I just remind Google that not all “great content” is going to “attract links”, this is something I think they forget. I have great content on my site about plumbers in Birmingham and accountants in London, very valuable, detailed, non-spammy, hand-crafted copy on these businesses, highly valuable to anyone looking for their services. But no-one is ever going to want to link to it; it’s not topical or quirky, is very locally-focussed, and has no video of cats playing pianos.
Our digital agency offers both traditional targeted online display advertising as well as behavioral retargeting. Through an intense discovery process, our team will determine the most optimal marketing mix for your online media plan. We will leverage ad network partnerships for planning the ideal media buys and negotiating the best possible pricing.
Hey brian, it is extremely fantastic stuff, i am not getting words to appreciate your work..brilliant. No one dares to share their business secrets with others but you are awesome and thank you so much. Iam a beginner in digital marketing, iam learning consistently by following your posts, tips and tricks. eventually i became an intermediate person thanks for your help.
For example, what are the quality and quantity of the links that have been created over time? Are they natural and organic links stemming from relevant and high quality content, or are they spammy links, unnatural links or coming from bad link neighborhoods? Are all the links coming from the same few websites over time or is there a healthy amount of global IP diversification in the links?
The amount of link juice passed depends on two things: the number of PageRank points of the webpage housing the link, and the total number of links on the webpage that are passing PageRank. It’s worth noting here that while Google will give every website a public-facing PageRank score that is between 1 and 10, the “points” each page accumulates from the link juice passed by high-value inbound links can — and do — significantly surpass ten. For instance, webpages on the most powerful and significant websites can pass link juice points in the hundreds or thousands. To keep the rating system concise, Google uses a lot of math to correlate very large (and very small) PageRank values with a neat and clean 0 to 10 rating scale.
Hi Bill, Yes – thanks. I think I’ll have to do more of these. I couldn’t really go beyond Pagerank in an 18 minute Pubcon session. Although the random surfer model expired (and wasn’t even assigned to Google), it is still a precursor to understanding everything that has come after it. I think I would love to do more videos/presentations on both Reasonable surfer patent, Dangling Nodes and probably a lifetime of other videos in the future. To be able to demonstrate these concept without giving people headaches, though, the PageRank algorithm in Matrix form provides a good understanding of why you can’t "just get links" and expect everything to be at number 1.
Personally, I wanted a bit more of the math, so I went back and read the full-length version of “The Anatomy of a Large-Scale Hypertextual Web Search Engine” (a natural first step). This was the paper written by Larry Page and Sergey Brin in 1997. Aka the paper in which they presented Google, published in the Stanford Computer Science Department. (Yes, it is long and I will be working a bit late tonight. All in good fun!)
World Wide Web, or “the web” for short, is a network of web pages connected to each other via hyperlinks. Each hyperlink connecting to a new document adds to the overall growth of the web. Search engines make it easier for you to find these web pages. A web page linked by many other web pages on the similar topics is considered more respectful and valuable. In the above example, John’s article gets the respect for sparking a conversation that resulted into many other web pages linking to each other. So backlinks are not only important for a website to gain respect, they are also important for search engines and the overall health of the entire world wide web.
There are simple and fast random walk-based distributed algorithms for computing PageRank of nodes in a network.[33] They present a simple algorithm that takes {\displaystyle O(\log n/\epsilon )} rounds with high probability on any graph (directed or undirected), where n is the network size and {\displaystyle \epsilon } is the reset probability ( {\displaystyle 1-\epsilon } is also called as damping factor) used in the PageRank computation. They also present a faster algorithm that takes {\displaystyle O({\sqrt {\log n}}/\epsilon )} rounds in undirected graphs. Both of the above algorithms are scalable, as each node processes and sends only small (polylogarithmic in n, the network size) number of bits per round.
###### On a blog the page rank should go to the main article pages. Now it just gets “evaporated” if you use “nofollow” or scattered to all the far flung nooks and crannys which means google will not be able to see the wood for the trees. The vast majority of a site’s overall page rank will now reside in the long tail of useless pages such as commentors profile pages. This can only make it harder for google to serve up the most relevant pages.
Current search engine optimization focuses on techniques such as making sure that each web page has appropriate title tags and that the content is not "thin" or low-quality. High-quality content is original, authoritative, factual, grammatically correct, and engaging to users. Poorly edited articles with spelling and grammatical errors will be demoted by search engines.
PageRank is often considered to be a number between 0 and 10 (with 0 being the lowest and 10 being the highest) though that is also probably incorrect. Most SEOs believe that internally the number is not an integer, but goes to a number of decimals. The belief largely comes from the Google Toolbar, which will display a page's PageRank as a number between 0 and 10. Even this is a rough approximation, as Google does not release its most up to date PageRank as a way of protecting the algorithm's details.
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## noisy importance sampling
Posted in Statistics with tags , , , on February 14, 2022 by xi'an
A recent short arXival by Fernando Llorente, Luca Martino, Jesse Read, and David Delgado–Gómez in which they analyse settings where (only) a noisy version of the target density is available. Not necessarily in an unbiased fashion although the paper is somewhat unclear as to which integral is targeted in (6), since the integrand is not the original target p(x). The following development is about finding the optimal importance function, which differs from the usual due to the random nature of the approximation, but it does not seem to reconnect with the true target p(x), except when the noisy realisation is unbiased… To me this is a major issue in simulation methodology in that getting away from the unbiasedness constraint opens (rather obviously) a much wider choice of techniques.
## MCMC importance samplers for intractable likelihoods
Posted in Books, pictures, Statistics with tags , , , , , , , , , , , on May 3, 2019 by xi'an
Jordan Franks just posted on arXiv his PhD dissertation at the University of Jyväskylä, where he discuses several of his works:
1. M. Vihola, J. Helske, and J. Franks. Importance sampling type estimators based on approximate marginal MCMC. Preprint arXiv:1609.02541v5, 2016.
2. J. Franks and M. Vihola. Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance. Preprint arXiv:1706.09873v4, 2017.
3. J. Franks, A. Jasra, K. J. H. Law and M. Vihola.Unbiased inference for discretely observed hidden Markov model diffusions. Preprint arXiv:1807.10259v4, 2018.
4. M. Vihola and J. Franks. On the use of ABC-MCMC with inflated tolerance and post-correction. Preprint arXiv:1902.00412, 2019
focusing on accelerated approximate MCMC (in the sense of pseudo-marginal MCMC) and delayed acceptance (as in our recently accepted paper). Comparing delayed acceptance with MCMC importance sampling to the advantage of the later. And discussing the choice of the tolerance sequence for ABC-MCMC. (Although I did not get from the thesis itself the target of the improvement discussed.)
## approximate likelihood perspective on ABC
Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , on December 20, 2018 by xi'an
George Karabatsos and Fabrizio Leisen have recently published in Statistics Surveys a fairly complete survey on ABC methods [which earlier arXival I had missed]. Listing within an extensive bibliography of 20 pages some twenty-plus earlier reviews on ABC (with further ones in applied domains)!
“(…) any ABC method (algorithm) can be categorized as either (1) rejection-, (2) kernel-, and (3) coupled ABC; and (4) synthetic-, (5) empirical- and (6) bootstrap-likelihood methods; and can be combined with classical MC or VI algorithms [and] all 22 reviews of ABC methods have covered rejection and kernel ABC methods, but only three covered synthetic likelihood, one reviewed the empirical likelihood, and none have reviewed coupled ABC and bootstrap likelihood methods.”
The motivation for using approximate likelihood methods is provided by the examples of g-and-k distributions, although the likelihood can be efficiently derived by numerical means, as shown by Pierre Jacob‘s winference package, of mixed effect linear models, although a completion by the mixed effects themselves is available for Gibbs sampling as in Zeger and Karim (1991), and of the hidden Potts model, which we covered by pre-processing in our 2015 paper with Matt Moores, Chris Drovandi, Kerrie Mengersen. The paper produces a general representation of the approximate likelihood that covers the algorithms listed above as through the table below (where t(.) denotes the summary statistic):
The table looks a wee bit challenging simply because the review includes the synthetic likelihood approach of Wood (2010), which figured preeminently in the 2012 Read Paper discussion but opens the door to all kinds of approximations of the likelihood function, including variational Bayes and non-parametric versions. After a description of the above versions (including a rather ignored coupled version) and the special issue of ABC model choice, the authors expand on the difficulties with running ABC, from multiple tuning issues, to the genuine curse of dimensionality in the parameter (with unnecessary remarks on low-dimension sufficient statistics since they are almost surely inexistent in most realistic settings), to the mis-specified case (on which we are currently working with David Frazier and Judith Rousseau). To conclude, an worthwhile update on ABC and on the side a funny typo from the reference list!
Li, W. and Fearnhead, P. (2018, in press). On the asymptotic efficiency
of approximate Bayesian computation estimators. Biometrika na na-na.
## simulated summary statistics [in the sky]
Posted in Statistics with tags , , , , , , , on October 10, 2018 by xi'an
Thinking it was related with ABC, although in the end it is not!, I recently read a baffling cosmology paper by Jeffrey and Abdalla. The data d there means an observed (summary) statistic, while the summary statistic is a transform of the parameter, μ(θ), which calibrates the distribution of the data. With nuisance parameters. More intriguing to me is the sentence that the correct likelihood of d is indexed by a simulated version of μ(θ), μ'(θ), rather than by μ(θ). Which seems to assume that the pseudo- or simulated data can be produced for the same value of the parameter as the observed data. The rest of the paper remains incomprehensible for I do not understand how the simulated versions are simulated.
“…the corrected likelihood is more than a factor of exp(30) more probable than the uncorrected. This is further validation of the corrected likelihood; the model (i.e. the corrected likelihood) shows a better goodness-of-fit.”
The authors further ressort to Bayes factors to compare corrected and uncorrected versions of the likelihoods, which leads (see quote) to picking the corrected version. But are they comparable as such, given that the corrected version involves simulations that are treated as supplementary data? As noted by the authors, the Bayes factor unsurprisingly goes to one as the number M of simulations grows to infinity, as supported by the graph below.
## ISBA 2016 [#3]
Posted in pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , on June 16, 2016 by xi'an
Among the sessions I attended yesterday, I really liked the one on robustness and model mispecification. Especially the talk by Steve McEachern on Bayesian inference based on insufficient statistics, with a striking graph of the degradation of the Bayes factor as the prior variance increases. I sadly had no time to grab a picture of the graph, which compared this poor performance against a stable rendering when using a proper summary statistic. It clearly relates to our work on ABC model choice, as well as to my worries about the Bayes factor, so this explains why I am quite excited about this notion of restricted inference. In this session, Chris Holmes also summarised his two recent papers on loss-based inference, which I discussed here in a few posts, including the Statistical Science discussion Judith and I wrote recently. I also went to the j-ISBA [section] session which was sadly under-attended, maybe due to too many parallel sessions, maybe due to the lack of unifying statistical theme.
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# Muzzle blast
A muzzle blast is an explosive shockwave created at the muzzle of a firearm during shooting. Before a projectile leaves the gun barrel, it obturates the bore and "plugs up" the pressurized gaseous products of the propellant combustion behind it, essentially containing the gases within a closed system as a neutral element in the overall momentum of the system's physics. However, when the projectile exits the barrel, this functional seal is removed and the highly energetic bore gases are suddenly free to exit the muzzle and rapidly expand in the form of a supersonic shockwave (which can be often fast enough to momentarily overtake the projectile and affect its flight dynamics), thus creating the muzzle blast.
USS Iowa (BB-61) fires a full broadside volley during a target exercise near Vieques Island, Puerto Rico, 1 July 1984, showing the muzzle blast from its 16 inch main battery and the pressure effect on the water surface surrounding the ship.
The muzzle blast is often broken down into two components: an auditory component[1] and a non-auditory component.[2] The auditory component is the loud sound of the gunshot, and is important because it can cause significant hearing loss to surrounding personnel and also give away the gun's position. The non-auditory component is the infrasonic compression wave, and can cause shock damage to nearby items.
In addition to the blast itself, some of the gases' energy is also released as light energy, known as a muzzle flash.
## Components
Soldiers covering their ears while firing a 120 mm Cardom mortar from a M1129 carrier.
### Gun sound
The audible sound of a gun discharging, also known as the muzzle report or gunfire, may have two sources: the muzzle blast itself, which manifests as a loud and brief "pop" or "bang", and any sonic boom produced by a transonic or supersonic projectile, which manifest as a sharp whip-like crack that persists a bit longer. The muzzle blast is by far the main component of a gunfire, due to the intensity of sound energy released and the proximity to the shooter and bystanders. Muzzle blasts can easily exceed sound pressure levels of 140 decibels, which can rupture eardrums and cause permanent sensorineural hearing loss even with brief and infrequent exposure.[3] With large guns with much higher muzzle energy, for instance artillery, that danger can extend outwards a significant distance from the muzzle,[4] which mandates wearing of hearing protections for all personnel in proximity for occupational health purposes.
For small arms, suppressors help to reduce the muzzle report of firearms by providing a larger area for the propellant gas to expand, decelerate and cool before releasing sound energy into the surrounding.[5] Other muzzle devices such as blast shields can also protect hearing by deflecting the pressure wave forward and away from the shooter and bystanders. Recoil-reducing devices such as muzzle brakes however worsen potential hearing damage, as these modulate the muzzle blast by increasing the lateral vectors nearer to the shooter.
### Compression wave
The overpressure wave from a firearm's muzzle blast are infrasonic and thus inaudible to human ears, but it still can be highly energy-intense due to the gases expanding at an extremely high velocity. Residual pressures at the muzzle can be a significant fraction of the peak bore pressure, especially when short barrels are used. This energy can also be regulated by a muzzle brake to reduce the recoil of the firearm, or harnessed by a muzzle booster to provide energy to cycle the action of self-loading firearms.[6]
The force of the muzzle blast can cause shock damage to nearby items around the muzzle, and with artillery, the energy is sufficiently large to cause significant damage to surrounding structures and vehicles.[7] It is thus important for the gun crew and any nearby friendly troops to stay clear of the potential directions of blast vectors, in order to avoid unnecessary collateral damages.
## Recoil
Typically the majority of the blast impulse are vectored to a forward direction, creating a jet propulsion effect that exerts force back upon the barrel, resulting in an additional rearward momentum on top of the reactional momentum generated by the projectile before it exits the gun. The overall recoil applied to the firearm is thus equal and opposite to the total forward momentum of not only the projectile, but also the ejected gas. Likewise, the recoil energy given to the firearm is affected by the ejected gas. By conservation of mass, the mass of the gas ejectae will be equal to the original mass of the propellant (assuming complete burning). As a rough approximation, the ejected gas can be considered to have an effective exit velocity of ${\displaystyle \alpha V_{0}}$ where ${\displaystyle V_{0}}$ is the muzzle velocity of the projectile and ${\displaystyle \alpha }$ is approximately constant. The total momentum ${\displaystyle p_{e}}$ of the propellant and projectile will then be:
${\displaystyle p_{e}=m_{p}V_{0}+m_{g}\alpha V_{0}\,}$
where: ${\displaystyle m_{g}\,}$ is the mass of the propellant charge, equal to the mass of the ejected gas.
This expression should be substituted into the expression for projectile momentum in order to obtain a more accurate description of the recoil process. The effective velocity may be used in the energy equation as well, but since the value of α used is generally specified for the momentum equation, the energy values obtained may be less accurate. The value of the constant α is generally taken to lie between 1.25 and 1.75. It is mostly dependent upon the type of propellant used, but may depend slightly on other things such as the ratio of the length of the barrel to its radius.
Muzzle devices can reduce the recoil impulse by altering the pattern of gas expansion. For instance, muzzle brakes primarily works by diverting some of the gas ejecta towards the sides, increasing the lateral blast intensity (hence louder to the sides) but reducing the thrust from the forward-projection (thus less recoil), with some designs claiming up to 40-60% reduction in perceived recoil. Similarly, recoil compensators divert the gas ejecta mostly upwards to counteract the muzzle rise. However, suppressors work on a different principle, not by vectoring the gas expansion laterally but instead by modulating the forward speed of the gas expansion. By using internal baffles, the gas is made to travel through a convoluted path before eventually released outside at the front of the suppressor, thus dissipating its energy over a larger area and a longer time. This reduces both the intensity of the blast (thus lower loudness) and the recoil generated (as for the same impulse, force is inversely proportional to time).
## Detection
Muzzle blasts can stir up significant dust clouds, especially from large-caliber guns when firing low and flat, which can be visible from distance and thus give away the gun's position, increasing the risk of inviting counter-fire. Preventive actions may consist of wetting the soil of the surrounding ground, having the muzzle brake vector the blast up and away from the ground, or covering the area around the muzzle with a tarpaulin to shroud down as much airborne dust as possible.
Gunfire locators detect muzzle blast with microphones and triangulate the location where the shots were fired. These are commercially available, and have been installed by law enforcement agencies as remote sensors in many high-crime rate areas of urban centers. They can provide a fairly precise location of the source of a shot fired outdoors — 99% to within 33 feet (10 m) or better — and provide the data to police dispatchers within seconds of a firing.[8]
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Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/15637
Title: Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case Author: Ferreira, MiltonVieira, Nelson Keywords: Fractional partial differential equationsFractional Laplace and Dirac operatorsRiemann-Liouville derivatives and integrals of fractional orderEigenfunctions and fundamental solutionLaplace transformMittag-Leffler function Issue Date: Jun-2016 Publisher: Springer International Publishing Abstract: In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions. Peer review: yes URI: http://hdl.handle.net/10773/15637 DOI: 10.1007/s11785-015-0529-9 ISSN: 1661-8254 Appears in Collections: CIDMA - ArtigosCHAG - Artigos
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## Friday, 13 September 2013
### Density fitting and tensor hyper contraction
One of the main bottle necks in quantum chemistry is the computation of the two electron integrals and their transformation between the AO and MO bases. These integrals are defined as
where μ, ν, ρ and σ are one-electron orbitals.
A well established way to approximate the two electron integrals is density fitting (also called "resolution of the identity"). The idea is that the orbital products are one-electron functions (actually they are little densities) and may therefore be expressed using a new set of one-electron functions called "auxiliary basis set"
If the set of one electron functions χA is complete, then these would actually "resolve the identity" and the coefficients cμν,A could be chosen in a way to make this expression exact. For practical calculations with finite basis sets the optimal cμν,A can be obtained through density fitting.
The cμν,A are only three-index quantities, which requires less storage room as opposed to the full four-index MO integrals. The original two-electrons integrals can be obtained by using a double summation:
If this approach is combined with appropriate changes in the remaining algorithm, very efficient implementations of ab-initio excited state methods are possible (as this is for example done in Turbomole).
Going one step ahead, there is the tensor hyper contraction, as implemented by the Martinez group. In this case one only uses two-index quantities Xμ,P and ZPQ. In this approach the two-electron integrals are approximated according to
To define the Xμ,P they use a grid of points rP and simply set
Finally, the Z-matrix is fitted in order to allow the best possible approximation in the above defined form. And apparently, this is efficient and allows a fourth order scaling of CC2, as opposed to fifth order in the standard and RI implementations.
The idea is quite nice, I would say. Of course, only time will tell if "formal fourth order" is really faster than well implemented fifth order. But it looks like a nice step ahead.
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1. ## Multivariable function fun;
Similar to the parametric question I recently posted, I need to find a value of c such that a piecewise multivariate function is continuous over an interval, not too sure where to start, because c is not only in the functon, but in the range.
Find all values of c, such that
$f(x,y) =\left\{\begin{array}{cc}\frac{x}{y+c},&\mbox{ if }
x \in R, y \geq 1-c\\xy, & \mbox{ if } x \in R, y< 1-c\end{array}\right.$
is continuous on $R^2$.
Not too sure where to start here, any pointers in the right direction?
2. I approach these questions by assuming that the two equations are equal at the point where the graph shifts from one to the other. This follows from the fact that a continuous function must have for each f(x,y) a limit that equals this value as well from either side.
So set them equal, $\frac{x}{y+c}=xy$
The x's cancel which makes sense because the restriction is dependent on y, not x.
Now this equality isn't true for all (x,y), it is only at the point around y=1-c. So if you plug in 1-c for y and solve for c, you should get the desired value.
3. So in order for them to be continuous they must equal each other, correct?
My question is, what happens to the inequalities? Can we really make them = to y? Why can we do that, does it have something to do with making the two equations equal to each other?
4. Originally Posted by Jameson
I approach these questions by assuming that the two equations are equal at the point where the graph shifts from one to the other. This follows from the fact that a continuous function must have for each f(x,y) a limit that equals this value as well from either side.
So set them equal, $\frac{x}{y+c}=xy$
The x's cancel which makes sense because the restriction is dependent on y, not x.
Now this equality isn't true for all (x,y), it is only at the point around y=1-c. So if you plug in 1-c for y and solve for c, you should get the desired value.
I like that rationale, I'm supposing that plugging in the 1-c for y works because we would be subbing it in on either side regardless to take the left and right hand limit, but I'm getting a peculiar answer by doing that.
$\frac{x}{y+c}=xy$
$\frac{1}{y+c}=y$
$1= y^2 +yc$
$1=(1-c)^2 +c(1-c)$
$1=1-c$
$c=0$
Which doesn't make sense because when we sub that back into the original statement, $\frac{x}{y+c}=xy$, we get $\frac{x}{y}=xy$?
I must have made a mistake somewhere.
5. Originally Posted by Orbent
So in order for them to be continuous they must equal each other, correct?
In order for them to be continuous, the limits must be the same. Since the two functions that are used are continuous functions, the limits are the same as value of the functions.
[/quote]My question is, what happens to the inequalities? Can we really make them = to y? Why can we do that, does it have something to do with making the two equations equal to each other? [/QUOTE]
Again, it is a matter of limits. The limit as some point (x, y) approaches (x, 1- c) (the boundary between $y\ge 1- c]$ and $y< 1- c$) depends on what happens on either side of y= 1- c.
6. Originally Posted by Kasper
I like that rationale, I'm supposing that plugging in the 1-c for y works because we would be subbing it in on either side regardless to take the left and right hand limit, but I'm getting a peculiar answer by doing that.
$\frac{x}{y+c}=xy$
$\frac{1}{y+c}=y$
$1= y^2 +yc$
$1=(1-c)^2 +c(1-c)$
[tex]1=1-c[/math
$c=0$
Which doesn't make sense because when we sub that back into the original statement, $\frac{x}{y+c}=xy$, we get $\frac{x}{y}=xy$?
I must have made a mistake somewhere.
Your "original statement", $\frac{x}{y+c}= xy$, is only true on the line y= 1- c which is y= 1 since c= 0. Yes, that becomes $\frac{x}{1}= x(1)$!
$
f(x,y) =\left\{\begin{array}{cc}\frac{x}{y},&\mbox{ if }
x \in R, y \geq 1\\xy, & \mbox{ if } x \in R, y< 1\end{array}\right.
$
which is continuous for all (x, y).
7. Originally Posted by HallsofIvy
Your "original statement", $\frac{x}{y+c}= xy$, is only true on the line y= 1- c which is y= 1 since c= 0. Yes, that becomes $\frac{x}{1}= x(1)$!
$
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# Statistics: Ellipses
## Ellipses
For a positive definite matrix $\Sigma \!$ we use $E(\mu,\Sigma) \!$ to denote the ellipse $\mathcal{E} = \{ x : (x-\mu)' \Sigma^{-1} (x-\mu) = 1 \}$.
Note that every non-negative definite matrix $W\!$ can be factored as $W=AA'\!$. The matrix $A\!$ can be selected so that it is square. It will be non-singular if and only if $W\!$ is non-singular. A definition of an ellipse that can be used for all non-negative definite matrices and that corresponds to the previous definition in the case of positive-definite matrices is
$E(\mu,W) = \mu + A \mathcal{S}$
where $\mathcal{S}$ is a unit sphere of conformable dimension.
A convenient notation in terms of W is
$E(\mu, W) = \mu \oplus \sqrt{W}$
Note that under a linear transformation given by a matrix L the image of the ellipse is:
$L(E(\mu ,W))=E(L\mu ,LW{L}')=L\mu \oplus \sqrt{LW{L}'}=L\mu \oplus L\sqrt{W}$
### Conjugate axes
The columns of the matrix $\mathbf{A}=\left[ \begin{matrix} \mathbf{a}_{1} & \mathbf{a}_{2} & \cdots & \mathbf{a}_{p} \\ \end{matrix} \right]$ form a set of conjugate axes of the ellipse. Each vector $\mathbf{a}_{i}$ lies on the ellipse and the tangent space at that point is parallel to the span of all the other column vectors of $\mathbf{A}$
For $p=2 \!$ this is illustrated in the following figure
in which
$\mathbf{A}=\left[ \begin{matrix} \mathbf{a}_{1} & \mathbf{a}_{2} \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 1.5 \\ 2 & 1 \\ \end{matrix} \right]$
and
$\mathbf{W}=\mathbf{A{A}'}=\left[ \begin{matrix} 3.25 & 3.5 \\ 3.5 & 5 \\ \end{matrix} \right]$
If $\mathbf{W}=\mathbf{B{B}'}$ is any other factorization of $\mathbf{W}$ then the columns of $\mathbf{B}$ have the same properties as the columns of $\mathbf{A}$.
Consider the inner product space with inner product matrix $\mathbf{W}^{-1}=\left[ \begin{matrix} 1.25 & -0.875 \\ -0.875 & 0.8125 \\ \end{matrix} \right]$ and inner product
$\left\langle \mathbf{x},\mathbf{y} \right\rangle =\mathbf{{x}'W}^{-1}\mathbf{y}$.
Since $\mathbf{{A}'W}^{-1}\mathbf{A}=\mathbf{{A}'}\left( \mathbf{A{A}'} \right)^{-1}\mathbf{A}=\mathbf{{A}'{A}'}^{-1}\mathbf{A}^{-1}\mathbf{A}=\mathbf{I}$ we see that $\mathbf{a}_{1}$ and $\mathbf{a}_{2}$ are orthogonal unit vectors (in fact, an orthonormal basis) in this inner product:
$\left\langle \mathbf{a}_{i},\mathbf{a}_{i} \right\rangle =\mathbf{{a}'}_{i}\mathbf{W}^{-1}\mathbf{a}_{i}=1$
$\left\langle \mathbf{a}_{1},\mathbf{a}_{2} \right\rangle =\mathbf{{a}'}_{1}\mathbf{W}^{-1}\mathbf{a}_{2}=0$
Particular factorizations yield interesting sets of conjugate axes. In the figure on the right
Two conjugate vectors lie on an ellipse. Their tangents can be extended to form a parallelogram framing the ellipse.
the axes for the Choleski factorization where $\mathbf{B}$ is lower triangular are shown in green and the axes for the principal component factorization (where $\mathbf{B}=\mathbf{\Gamma \Lambda }^{1/2}$ and $\mathbf{W}=\mathbf{\Gamma \Lambda {\Gamma }'}$ is the spectral decomposition of $\mathbf{W}$), are shown in magenta. The figures were produced with a script in R.
## Hypothesis and error ellipses
Let $E\!$ be a positive definite matrix and $H\!$ be a non-negative definite matrix.
There exists a matrix $A\!$ and a non-negative diagonal matrix such that:
$E = AA' \!$
and
$H = A \Lambda A'\!$.
The diagonal elements of $\Lambda\!$, $\lambda_1 \ge \lambda_2 \ge ... \ge \lambda_p \!$, are the eigenvalues of $H\!$ relative to $E\!$. An R function to compute $A'\!$ is given below.
In this discussion $E\!$ and $H\!$ can represent the $SSE\!$ and an $SSH\!$ matrices in multivariate linear regression both divided by a common factor, perhaps the degrees of freedom for $SSE\!$ so that $E\!$ is an unbiased estimate of the residual variance matrix $\Sigma\!$.
## Expected value of SSH
We can find expressions for $SSH\!$ in terms of the data and find expected values for $SSH\!$ under fixed effects or under random effects models.
### Univariate response
Consider first the expected value of $SSH\!$with a univariate response and a one-way Anova model with random group means.
The following formula is used repeatedly to find the expected value of a quadratic form. If $Y\!$ is a random vector with $\operatorname{E}(Y)=\mu$ and $\operatorname{Var}(Y) = \Psi$, and $Q\!$ is a conformable matrix then
$\operatorname{E}( Y'QY) = \mu'Q\mu + \operatorname{tr}(Q \Psi) \!$
With a univariate response and $G\!$ groups we can use an indicator design matrix $D\!$ and write:
$\mathbf{Y} = D \bold{\mu} + \epsilon\!$
where
$\mu \sim N_G( 1\psi, \phi^2 I) \!$
and
$\epsilon \sim N(0, \sigma^2 I )\!$
and $\mu \!$ is independent of $\epsilon \!$.
Thus
$\operatorname{E}(Y) = 1 \psi$ and $\operatorname{Var}(Y) = \phi^2 DD' + \sigma^2 I\!$
Consequently
$\operatorname{E}(SSTO)\!$ = $\operatorname{E}( Y'QY ) = \psi 1' Q 1 \psi + \operatorname{tr}\left[ (\phi^2 DD' + \sigma^2 I )(I - \frac{1}{N}U) \right]$ = $0 + \operatorname{tr}\left[ \phi^2 DD' - \frac{\phi^2}{N}DD'U + \sigma^2 Q \right] \!$ = $\phi^2 N - \frac{\phi^2}{N}\operatorname{tr}(DD'U) + \sigma^2 \operatorname{tr}( Q )$ = $\phi^2 N - \frac{\phi^2}{N}\operatorname{tr}(1'DD'1) + \sigma^2 (N-1)$ = $\phi^2 N - \frac{\phi^2}{N}\sum_{g=1}^G n_g^2 + \sigma^2 (N-1)$ = $\phi^2 (N - \tilde{n}) + \sigma^2 (N-1)$
where $\tilde{n}= \sum_{g=1}^G \frac{n_g}{N} n_g$ is the group-size weighted mean of group sizes. With equal groups, $\tilde{n} = N / G$ and
$E(SSTO) = \phi^2 N \frac{G-1}{G} + \sigma^2 (N-1) =\phi^2 (N-\tilde{n}) + \sigma^2 (N-1)$
Thus
$E(SSH)\!$ = $E (SSTO) - E(SSE)\!$ = $\phi^2 (N - \tilde{n}) + \sigma^2 (N-1) - \sigma^2 (N-G)$ = $\phi^2 (N - \tilde{n}) + \sigma^2 (G-1)$
### Multivariate response
Consider one-way MANOVA with $G\!$ random group means:
$\mu_g \sim N(\mu, \Phi), g=1,...,G$
and
$Y_{ig}|\mu_g \sim N( \mu_g, \Sigma), i = 1,...,n_g\!$.
With $N = \sum_g n_g\!$ we have
$SSE \sim W_{N-G}(\Sigma)\!$
The analogous results are:
$E(SSE) = (N-G) \Sigma \!$
and
$E(SSH) = (N - \tilde{n}) \Phi + (G-1) \Sigma \!$
Note that
$Var( \bar{\mathbf{Y}}_{\cdot g} ) = \Phi + \frac{1}{n_g} \Sigma \!$
and that the group-size weighted average of these variances is:
$\sum_{g=1}^G \frac{n_g}{N} Var( \bar{\mathbf{Y}}_{\cdot g} )\!$ = $\sum_{g=1}^G \frac{n_g}{N} \left[ \Phi + \frac{1}{n_g} \Sigma \right]\!$ = $\Phi + \frac{G}{N} \Sigma \!$ = $\Phi + \frac{1}{n} \Sigma$ with equal groups
The following table shows expectations of combinations of $SSH\!$ and $SSE\!$ of the form $k_H SSH + k_E SSE\!$:
$k_H \!$ $k_E \!$ $E(k_H SSH + k_E SSE)\!$ 1 0 $(N - \tilde{n}) \Phi + (G-1) \Sigma \!$ 0 1 $(N-G) \Sigma \!$ $\frac{1}{N- \tilde{n}}\!$ 0 $\Phi + \frac{G-1}{N - \tilde{n}} \Sigma$ $\frac{1}{N- \tilde{n}}=\frac{1}{N- n}\!$ 0 $\Phi + \frac{G-1}{N - \tilde{n}} \Sigma = \Phi + \frac{1}{n} \Sigma =\operatorname{Var}(\bar{Y}_{\cdot g} )\!$ with equal groups $\frac{1}{N- n} \!$ $\frac{1}{n} \!$ $\Phi \!$ with equal groups $\frac{1}{\lambda_{crit}}\!$ 0 $\frac{1}{\lambda_{crit}} \left[ (N - \tilde{n}) \Phi + (G-1) \Sigma \right] \!$
## Definition of SSH with one-way MANOVA
Consider one-way MANOVA with $G\!$ groups, each with $n_g\!$ observations. Let $N = \sum_{g=1}^G n_g\!$ and let
$D = \begin{bmatrix} 1_{n_1} & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 1_{n_g} \end{bmatrix}$
be the design matrix.
Let $Q\!$ be the $N \times N\!$ residual projection matrix defined by
$Q = I - 1_N(1_N'1_N)^{-1}1_N'=I-\frac{1}{N}U$
In the case of one-way MANOVA there is an easy way to derive an expression for SSH:
$SSTO\!$ $=\!$ $\sum_{g=1}^G \sum_{i=1}^{n_g} (Y_{ig} - \bar{Y}_{\cdot \cdot}) (Y_{ig}-\bar{Y}_{\cdot \cdot})' \!$ $=\!$ $\sum_{g=1}^G \sum_{i=1}^{n_g} (Y_{ig}- \bar{Y}_{\cdot g}+\bar{Y}_{\cdot g}- \bar{Y}_{\cdot \cdot}) (Y_{ig}- \bar{Y}_{\cdot g}+\bar{Y}_{\cdot g}- \bar{Y}_{\cdot \cdot})'$ $=\!$ $\sum_{g=1}^G \sum_{i=1}^{n_g}\left\{ (Y_{ig}- \bar{Y}_{\cdot g})(Y_{ig}- \bar{Y}_{\cdot g})' +(\bar{Y}_{\cdot g}- \bar{Y}_{\cdot \cdot})(\bar{Y}_{\cdot g}- \bar{Y}_{\cdot \cdot})' - (Y_{ig}- \bar{Y}_{\cdot g})(\bar{Y}_{\cdot g}- \bar{Y}_{\cdot \cdot})' - (\bar{Y}_{\cdot g}- \bar{Y}_{\cdot \cdot})(Y_{ig}- \bar{Y}_{\cdot g})' \right\}$ $=\!$ $\sum_{g=1}^G \sum_{i=1}^{n_g} (Y_{ig}- \bar{Y}_{\cdot g})(Y_{ig}- \bar{Y}_{\cdot g})' +\sum_{g=1}^G n_g(\bar{Y}_{\cdot g}- \bar{Y}_{\cdot \cdot})(\bar{Y}_{\cdot g}- \bar{Y}_{\cdot \cdot})'$
### Definition of SSH with a general linear hypothesis
Given a univariate linear model
$Y = X_1 \beta_1 + X_2 \beta_2 + \epsilon \!$
with Xi of dimension $n \times k_i\!$, the test for $\beta_2 = 0\!$ is based on
$SSH = (L \hat{\beta})'(L (X'X)^{-1}L')^{-1} L \hat{\beta} \!$
where
$L = [0 \ \ I] \!$
and
$X = [ X_1\ \ X_2]\!$
We can show that
$SSH\!$ $= \!$ $\hat{\beta}_2 ' W_{22 \cdot 1} \hat{\beta}_2\!$ $= \!$ $\hat{\beta}_2 ' X'_{2\cdot 1} X_{2\cdot 1} \hat{\beta}_2\!$
where $W_{22 \cdot 1}\!$ is the partial SSCP matrix for $X_2 \!$ regressing on $X_1\!$ and $X_{2\cdot 1}\!$ is the matrix of residuals of $X_2 \!$ regressing on $X_1\!$.
Thus $SSH\!$ is the sum of squared deviations (assuming that $X_1\!$ spans the intercept) of 'y hat' in the added-variable plot for $X_2\!$. It is the variability in $Y\!$ 'explained' by $X_2\!$ beyond that 'explained' by $X_1\!$. $SSE\!$ is the sum of squared deviations of residuals in the same plot.
Note that
$E(SSH) \!$ $= \!$ $\beta'_2 X'_{2 \cdot 1}X_{2 \cdot 1}\beta_2 + \operatorname{tr}(\sigma^2 W_{22 \cdot 1}^{-1} W_{22 \cdot 1}) \!$ $=\!$ $\beta'_2 X'_{2 \cdot 1}X_{2 \cdot 1}\beta_2 + h \sigma^2\!$
The matrix of residuals, $X_{2 \cdot 1} \!$, is obtained by regression on $X_1\!$ and, thus, has $n-k_1\!$ degrees of freedom. We could therefore think of
$SSH / (n- k_1)\!$
with
$E(SSH/(n- k_1)) = \frac{1}{n-k_1}\beta'_2 X'_{2 \cdot 1}X_{2 \cdot 1}\beta_2 + \frac{h}{n-k_1} \sigma^2\!$
as an estimate of the variance of contribution of $X_2\!$ to the variability of of $Y\!$.
### Computing eigenvalues
To understand how eigenvalues are computed in car:::print.Anova.mlm, let
$G = (E'E)^{-1}E'H = (AA'AA')^{-1}(AA')(A \Lambda A') = (AA')^{-1}(A \Lambda A') = A'^{-1} \Lambda A' \!$
Since
$G A'^{-1} =(A'^{-1} \Lambda A' ) A'^{-1} = A'^{-1} \Lambda \!$
$\Lambda\!$ contains the eigenvalues of $G\!$.
Thus the eigenvalues and eigenvectors of $H\!$ relative $E\!$ can be obtained with
> rel.eval ( H, E )
> rel.evac ( H, E )
where
> rel.eval <- function ( H, E ) {
# This code is adapted from car:::print.Anova.mlm
Re( eigen( qr.coef( qr(E), H ), only.values = TRUE )$values ) } > rel.evec <- function ( H, E ) { Re(eigen( t(qr.coef( qr(E), H )))$vectors)
}
The eigenvectors are not, in general, a factor of $E\!$. To obtain a factor of $E \!$ one can use:
> rel.fac <- function( H, E ) {
Bp <- fac(E)
B.qr <- qr(t(Bp))
H.star <- qr.coef( B.qr, t( qr.coef( B.qr, H ) )) # B^{-1} H B'^{-1}
ev <- eigen( H.star , symmetric = T)
ret <- t(ev$vectors) %*% Bp attr(ret,"lambda") <- ev$values
ret
}
Note that the numeric properties of this function could be improved.
## Visualizing significance
If we plot the ellipses $\mathcal{H} = E(0,H)\!$ and $\mathcal{E} = E(0,E)\!$, the ellipse $\mathcal{H}\!$ will protrude beyond $\mathcal{E}\!$ along the direction $a_i\!$, where $A = [a_1, ..., a_p]\!$ iff $\lambda_i > 1\!$.
### Roy's largest root test
The F-test based on Roy's largest root uses the approximation ( e.g., see SAS documentation for multivariate tests (http://post.queensu.ca:8080/SASDoc/getDoc/en/statug.hlp/introreg_sect21.htm) )
$F = \nu \lambda_1 / d \!$
with degrees of freedom $d\!$ and $\nu\!$ where
$d = \max(p,q)\!$
where $q\!$ is the number of degrees of freedom for the hypothesis and
$\nu = \nu_E - d + q\!$
where $\nu_E\!$is the number of degrees of freedom for the error matrix $E\!$.
The critical value for $\lambda_1\!$ for an $\alpha\!$ level test, can be computed as
> lambda.crit <- function( alpha, p , q, nu.E) {
d <- max( p, q)
nu <- nu.E - d + q
(d/nu) * qf( alpha, d , nu, lower.tail = F)
}
Thus, the ellipse $E(0, \frac{1}{\lambda_{crit}}H)\!$ will have the property that it protrudes beyond $E(0,E)\!$ if and only if the Roy test for the hypothesis whose matrix is $H\!$ is significant at level $\alpha\!$.
### Hotelling-Lawley trace
The Hotelling-Lawley trace statistic $HLT = tr (H E^{-1})\!$ is based on the sum of the $s = min (p, df_h)\!$ eigenvalues of $(H E^{-1})\!$. This suggests another criterion for judging visual significance based on the average eigenvalue, $\bar{\lambda_i}\!$.
One approximate F-test for the HLT is
$F = \frac{df2}{df1} \frac{ \operatorname{tr} (H E ^{-1}) }{s^2} = \frac{df2}{s * df1} \bar{\lambda_i} \!$
where $df1 = 2m + s + 1\!$, $df2 = 2(sn + 1)\!$ are the degrees of freedom for the numerator and denominator, and $m = ( |p-q|-1 )/2\!$, $n = ( dfe -p -1 )/2\!$.
Thus, the critical value for $\bar{\lambda_i} \!$ can be computed as
> HLT.crit <- function ( alpha, p, dfh, dfe) {
s <- min(p, dfh)
m <- (abs(p-dfh)-1)/2
n <- (dfe-p-1)/2
df1 <- 2*m + s + 1
df2 <- 2*(s*n +1)
s * (df1/df2) * qf(alpha, df1, df2, lower.tail=FALSE)
}
## When p > 3
When the number of response variables involved in a hypothesis is greater than the number of dimensions plotted, one can use the vectors of the $A\!$ matrix to construct linear combinations of the response variables that will show maximal significance of the hypothesis. These linear combinations depend on both $E\!$ and $H\!$ and thus could not be used to display results for many hypotheses simultaneously.
By projecting into the space corresponding to the three largest relative eigenvalues, we scale the projected $H\!$ matrix, $THT'\!$, so its ellipse will protruded outside the ellipse of the projected $E\!$ matrix, $TET'\!$, if and only if the overall Roy test is significant.
A convenient choice of $T\!$ is
$T = A^*_1 \!$
where
$A^{-1} = \begin{bmatrix} A^*_1 \\ A^*_2 \end{bmatrix}\!$
Then
$E^* = TET' = I_{3\times 3} \!$ and
UNFINISHED
### Note on computing matrix factors
A Choleski root, $A'\!$ above, can be obtained in R with
> chol(W)
when $W\!$ is positive-definite.
The singular value decomposition also works for singular and ill-conditioned matrices and can be obtained with
> fac(W)
where
> fac <- function(W) {
# assumes W is non-negative definite
# returns the 'right' of W, D^(1/2) Gamma', where W = Gamma D Gamma'
xx <- svd(W, nu=0)
t(xx$v) * sqrt( pmax( xx$d,0) )
}
Thus, an ellipse can be generated in R with:
> ell( mu, W )
where
> ell <- function( mu, W ) {
p <- nrow(W)
t( mu + t( sphere(p) %*% fac(W) ) )
}
where
sphere(p)
is unit sphere of the right dimension. Of course, an implementation of this function would need to attend to many additional details.
To the extent that the sphere is isotropic, the generated ellipse is independent of the choice of factor for W.
If the sphere object is augmented with diameters along usual axes, then the image of the diameters will be columns of $A\!$ which will form a set of conjugate vectors of the ellipse. A set of conjugate vectors of an ellipse has the property that each vector is on the surface of the ellipse and any subset of vectors spans a space that is parallel to the tangent spaces at any of the other vectors. The set of linear combinations of the vectors with coefficients in $[-1,1] \!$ is a parallelogram that contains the ellipse and whose faces are tangent spaces to the ellipse.
With two symmetric matrices, $H\!$ and $E\!$, with $E\!$ positive definite, we can find a factor $A\!$ of $E\!$ whose columns will also be conjugate directions for $H\!$. The following function will produce an 'eigenvector' based right factor of $E\!$ if called with a single argument. With two matrix arguments, it returns a right factor of $E\!$ whose rows are also conjugate directions for $H\!$. With two matrix arguments, the first argument must be positive definite.
fac <- function(
E, # non-neg. def. matrix to factor -- should be pos. def. if H is not missing
H, # if not missing, factor of E will consist of axes conjugate relative to H also
which = 1 # which = 2 returns a factor of H
)
{
xx <- eigen(E,symmetric = T)
Efac <- t(xx$vector) * sqrt( pmax( Re( xx$values ), 0 )) # right factor of E
if ( missing(H) ) return(Efac)
Efac.qr <- qr( t( Efac ) )
H.star <- qr.coef( Efac.qr, t( qr.coef( Efac.qr, H))) # Efac^{-1} H Efac'^{-1}
ev <- eigen( H.star, symmetric = T )
ret <- t(ev$vectors) %*% Efac if ( which == 2 ) ret <- ret * ev$values
attr( ret, "lambda" ) <- ev\$values
ret
}
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Hw7 Problem 2
Return to Homework 7, Glossary, Theorems
### Problem 2
Write the following permutations as (a) a product of disjoint cycles; (b) a product of transpositions
(a) $(1235)(413)$
(b) $(13256)(23)(46512)$
(c) $(12)(13)(23)(142)$
Solution
(a) $\begin{pmatrix} 1&2&3&4&5&6\\ 5&3&4&2&1&6\end{pmatrix}$ Hence, the products are $(15)(234)$ and $(15)(24)(23)$.
(b) $\begin{pmatrix} 1&2&3&4&5&6\\ 2&4&5&1&3&6\end{pmatrix}$ Hence, the products are $(124)(35)$ and $(14)(12)(35)$.
(c) $\begin{pmatrix} 1&2&3&4\\ 4&3&1&2\end{pmatrix}$ Hence, the products are $(1423)$ and $(13)(12)(14)$.
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i am a novice to electronics,actually i am java and android developer who doesn't know the very basic concepts of computing and trying to learn from ground level. i was checking out a video which explains about logical gates very well but i did not understand on thing in this pic:
the xor gate has NAND gate and OR gates with output connecting to AND gate so if both switches are on out put of right bulb will be off. my question is if instead of XOR gate we put just NAND gate isn't it gonna be same thing? because all we want is output off if both switches are on.
• XOR gate's truth table and NAND truth table aren't same. What if both inputs are zero? Its supposed to be 0 but NAND gives different. – Umar Mar 20 '17 at 12:04
• hi thanx,thank you,but how nand gate gives output 1 while its inputs are off? – Nav Sandhu Mar 20 '17 at 12:12
• A NAND gate gives output 1 if either input is off, which includes the case of both inputs being off. – Dave Tweed Mar 20 '17 at 12:31
• You may be missing the idea that gates have their own power supply, not always shown on diagrams. – pjc50 Mar 20 '17 at 13:28
my question is if instead of XOR gate we put just NAND gate isn't it gonna be same thing? because all we want is output off if both switches are on.
Nope. In binary,
0 + 0 = 00
0 + 1 = 01
1 + 0 = 01
1 + 1 = 10
As you can see, a NAND gate would give incorrect results (the first line would have 0+0=01 instead of 00).
• thank you,but how nand gate gives output 1 while its inputs are off? – Nav Sandhu Mar 20 '17 at 12:02
• Well, check out the truth table of NAND gate ;) en.wikipedia.org/wiki/NAND_gate – peufeu Mar 20 '17 at 12:42
• @NavSandhu gates don't exist in isolation, they have separate supply and ground lines that aren't shown in logic diagrams. – ratchet freak Mar 20 '17 at 14:20
These are all examples of XOR Boolean logic.
Either input high, otherwise low = EXCLUSIVE OR
simulate this circuit – Schematic created using CircuitLab
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# How to determine whether or not this series converges?
$$\displaystyle\sum\limits_{n=1}^\infty \dfrac{n^{-1/2}}{2+\sin^2(n)}$$
I tried the divergence test but it approaches 0.
It's not a geometric series.
Doubt I could apply the integral test.
Not a p-series nor an alternating series.
Can't use root test.
I suppose I am left with either ratio test or a comparison test but I couldn't figure those out.
Hint: all terms are $\ge \frac{1}{3}\cdot\frac{1}{n^{1/2}}$. – André Nicolas Nov 8 '11 at 15:06
Hint: Try using the comparison test and comparing to the function $\frac{1}{\sqrt{n}}$. To apply this, notice that $2\leq 2+\sin^2(n)\leq 3$ so that $$\frac{n^\frac{-1}{2}}{3}\leq \frac{n^\frac{-1}{2}}{2+\sin^2(n)}\leq \frac{n^\frac{-1}{2}}{2}.$$
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## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
The given expression is the sum of the first three elements of a sequence, which can be also written as: $a_1+a_2+a_3=S_3$ The answer is e)
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## Atomic Spectra
H-Atom ($E_{n}=-\frac{hR}{n^{2}}$)
Rose_Malki_3G
Posts: 123
Joined: Wed Sep 30, 2020 10:02 pm
### Atomic Spectra
For the equation V = -R((1/n^2)-(1/n^2))
How do we know which n value (the final or initial n value) to put first in the equation?
Vivian Chang 3L
Posts: 102
Joined: Wed Sep 30, 2020 9:35 pm
Been upvoted: 1 time
### Re: Atomic Spectra
Hi!
You can manipulate the equation you mentioned to get v(frequency) = RH (1/n2^2 - 1/n1^2), where RH is Rydberg's constant, 3.29 x 10^15 s^/1.
In this equation, n1 is always the higher energy level and n2 is the lower energy level.
Anh Trinh 1J
Posts: 144
Joined: Wed Sep 30, 2020 9:55 pm
Been upvoted: 1 time
### Re: Atomic Spectra
The first n in the equation would be the final energy level. Dr. Lavelle said in today’s lecture to think of it as the change in energy = final energy - initial energy. Usually in a question it would describe the transition that the electron makes. Ex: “an electron makes a transition from the fourth to the second principal quantum level,” the fourth energy level would be the initial and the second energy level would be the final.
LeanneBagood_2F
Posts: 91
Joined: Wed Sep 30, 2020 9:32 pm
### Re: Atomic Spectra
Rose_Malki_3L wrote:For the equation V = -R((1/n^2)-(1/n^2))
How do we know which n value (the final or initial n value) to put first in the equation?
Some of our classmates already responded with this but the difference of something is always going to be found by calculating final - initial.
Because of this, the first n in the equation should be n-final whereas the second should be n-initial. Here's an image of Rydberg's equation that I got from Google if my explanation does not make sense!
little disclaimer: i got this image from a quick Google search of "rydberg's equation" so it does not exactly align with the equation that was originally being asked about but it gives the gist of it
AndrewNguyen_2H
Posts: 85
Joined: Wed Sep 30, 2020 9:59 pm
### Re: Atomic Spectra
Vivian Chang 2H wrote:Hi!
You can manipulate the equation you mentioned to get v(frequency) = RH (1/n2^2 - 1/n1^2), where RH is Rydberg's constant, 3.29 x 10^15 s^/1.
In this equation, n1 is always the higher energy level and n2 is the lower energy level.
Isn't n1 the initial??
Justin Nguyen 3E
Posts: 89
Joined: Wed Sep 30, 2020 9:35 pm
### Re: Atomic Spectra
I think n1 is the initial and also the higher energy level because the electrons emit energy when an excited electron (higher energy level) drops back down to its ground state.
Return to “Bohr Frequency Condition, H-Atom , Atomic Spectroscopy”
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Remember! I know it has a deficiency of electrons, this makes the charge positive. or, finally, with the smallest whole-number coefficients: $$\ce{2 Al2O3(l) -> 4 Al(l) + 3 O2(g)}\label{rxn:R1}\tag{R1}$$ as well as normalized to a single formula unit: $$\ce{Al2O3(l) -> 2 Al(l) + 3/2 O2(g)}\label{rxn:R2}\tag{R2}$$ In the equation $$Δ_\mathrm rG = -nFE$$ The atomic number is the number of protons present in the nucleus. Total number of electrons present in 48 g Mg2+ are: 2!! Thus, the first energy level holds 2 * 1^2 = 2 electrons, while the second holds 2 * 2^2 = 8 electrons. E_n=-\frac{1312}{n^2}\text{ kJ/mol}. Great, lets apply the rules to some examples. 1. The formula for an ionic compound is written in the... smallest whole number ratio. If you look at the periodic table and at the period numbers, that is the number of valence electrons. The number of atoms per unit volume is then. Each energy level has different number of electrons. Determine the empirical formula of an oxide of iron which has 69.9% iron and 30.1% dioxygen by mass. Maximum of two electrons can be placed in an orbital according to Pauli exclusive principle. The formula ____ determines the number of electrons that can be accommodated in any level. 2. Valence electrons are those electrons that reside in the outermost shell surrounding an atomic nucleus. Q:- Maximum number of electrons in a shell depends on the total number of orbital present in that shell. A very easy formula is 2n^2. The number density / of conduction electrons in metals ranges between approximately 10 28 and 10 29 electrons/m 3, which is also the typical density of atoms in ordinary solid matter. That’s it! The rule that states atoms will gain or lose electrons in order to obtain eight electrons in their outermost shell. Your mass number is the total number of neutrons and protons within the atom. Homework Equations I know that the charge per electron is 1.60 *10^-19C. URGENT I ONY HAVE 1HR the formula for the maximum number of electrons that can occupy a principal energy level. Formula to calculate number of electrons Ask for details ; Follow Report by Aryan4359 23.05.2019 Log in to add a comment Valence electrons are the electrons contained in the outermost shell. Click hereto get an answer to your question ️ 8. There is a formula for obtaining the maximum number of electrons for each shell which is given by $2n^2~\ldots$ where n is the position of a certain shell. The maximum number of electrons that an energy level can hold is determined from the formula 2n^2 equals the total number, where n is the energy level. Principal Quantum Number: When the value of the principal quantum is given, then with the help of given mathematical formula the electrons of the atoms can be manipulated very easily. The formula ____ determines the number of electrons that can be accommodated in any level. So to get the number of electrons, you must subtract the size of charge (which is often written as a superscript on the right side of the symbol) from the atomic number or proton number. Valence electrons are of crucial importance because they lend deep insight into an element’s chemical properties: whether it is electronegative or electropositive in nature, or they indicate the bond order of a chemical compound – the number of bonds that can be formed between two atoms. This number density produces a Fermi energy of the order of 2 to 10 electronvolts . Opps, I mean a formula on how to calculate the number of electrons needed to fill the valence shell (# of holes) for example carbon??? The variable n represents the Principal Quantum Number, the number of the energy level in question. that is 2 times n to the second power, where n = the number of the principle energy level (PEL). If the number is larger than 10, subtract 10 so you get two valence electrons. asked Mar 28, 2018 by anonymous. The book doesn't use symbols for the equations, which makes them hard to follow. 5 and 6 In a neutral (uncharged) molecule, the sum of the bonding valence electrons must be equal. To calculate the maximum number of electrons in each energy level, the formula 2n 2 can be used, where n is the principal energy level (first quantum number). Add your answer and earn points. The mole is a measure or the base unit for the amount of substance present in the given sample. a. I understand equation 2 but don't follow the derivation of equation 1 and 3-5. The maximum number of electrons that can occupy a specific energy level can be found using the following formula: Electron Capacity = 2n 2. This number is what we would expect from the electron configuration of zinc, (Ar)3d 10 4s 2, so these two approaches to the free electron density in … Your atomic number is the amount of protons within the atom. The formula to determine the number of electrons in an energy level is 2n2, where n is the number of the energy level. How many excess electrons are on a ball with a charge of -4.00*10^-17 C? A way to find valence electrons without the periodic table is using the atomic number and drawing a diagram. For the fifth energy level, n=5. The basic units can be molecules, atoms or formula units based on the substance. A mole fraction indicates the number of chemical elements. The atomic number is how many protons and electrons the atom has. There's actually no formula. You can simply subtract the atomic number from the mass number in order to find the number of neutrons. The formula ____ determines the number of electrons that can be accommodated in any level. So, the products of the negative element and its charge and the positive element and its charge must be equal. Orbital #1: 2 electrons max. 2) What is the ratio of energies of electrons in the ground states of H, He +, Li 2+ and Be 3+? The Attempt at a Solution My textbook does not explain how to do this, but I thought I would divide-->4.00*10^-17 C * 1 electron/-1.60*10^-19. One electron possesses a charge of 1.6 10-19C, i.e., 1.6 10-19C of charge is contained in 1 electron. 3) Calculate the atomic number of hydrogen like species which can be ionized by an electron moving with a velocity, v = 6.56 × 10 6 m s-1. Now, only a certain number of electrons can go in each electronic orbital. The number of neutrons in 5 g of D20 (D is įH) are: 4.20 4x2x (a) 0.25 NA (b) 2-5 NA (c) 1.1NA (d) none of these ular formula Pt(H) . 1 st energy level has; 2n 2 =2.1 2 =2 electrons. The total charge caused by free electrons is: q = nAle For example, energy level 1, 2(1) 2 calculates to two possible electrons that will fit into the first energy level. C_1 xx N_1 = C_2 xx N_2 If we have 2 "A" atoms and 5 "B" atoms we have: C_1 xx 2 = C_2 xx 5 To be equal, C_1 = 5 and C_2 = 2 This actually refers to the "charge" of the ion. Orbital #2 and on: 8 electrons max. Which element, below, has the greatest atomic radius? 3. 1 mole is number which is equal to 6.022 x 10 23 particles, also known as the Avogadro’s constant. That means an atomic number of 8 (oxygen), has 8 protons and 8 electrons. In case of uncharged atoms, the atomic number is equal to the number of the electrons. Atom is uniquely identified with the atomic number (symbol Z). Q:-Calcium carbonate reacts with aqueous HCl to give CaCl 2 and CO 2 according to the reaction, CaCO 3(s) + 2 HCl (aq) → CaCl 2(aq) + CO 2(g) + H 2 O (l) What mass of CaCO 3 is required to react completely with 25 mL of 0.75 M HCl? One mole of any substance is equal to the value of 6.023 x 10 23 (Avagadro number) . New questions in Chemistry. If the atom is neutral, the number of electrons will be equal to the number of protons. How many electrons fit in each shell around an atom? (a) 24 N (b) 2 NA (c) 20 NA (d) none of these . But for 'b' I am confused. When 1 Coulomb charge flow through a wire in 1 second then the current through the wire is 1 AMPERE. The third shell can carry up 18 electrons, but it is more stable by carrying only eight electrons. What is the mas E n = − n 2 1 3 1 2 kJ/mol. An atom can have maximum 7 energy levels and electrons can change their levels according to their energies. In contrast, in ions, the number of electrons is the difference between the atomic number and the charge of ions. Let’s draw it out as a simple diagram. The energy level of the electron of a hydrogen atom is given by the following formula, where n n n denotes the principal quantum number: E n = − 1312 n 2 kJ/mol. Use n for the principal quantum number. Question: Formula Number Of Electrons Lewis Dot Formula Electron Geometry Molecular Geometry Drawing Of Structure Hybridization Polar Non Polar 105 40 Brest 42 : Squere Losed Bi-Fi န 'd2 Polar Octahedral Pyramid F. - 28 SF40) 34 FS-F Trigonal See Saw Sp3d (polar - Bypyramidal : XEFA 36 - … Electrons are arranged around the nucleus in the orbit , so that their orbits formed a shell which is called as electron shell or orbital. The number of free electrons per zinc atom to make these consistent is. I need help understanding these equations from Fundamentals of Physics, 8th, Halliday & Resnick.. Example: Oxygen is in the 16th period. 2n2 b. n2 c. 2n d. n jouri57 is waiting for your help. The number of electrons in an atom is equal to the number of protons, (which is, in turn, equal to the atomic number.) Then allow the number of free radicals for each unit of volume to be n. When you apply a pd V, allow the electrons’ drift velocity to be v. Therefore: The total number of free electrons in one piece of the conductor is: nAl = number of free electrons per unit volume * volume. 1 C of charge is contained in 1/1.6 x 10-19 = 6.25 x 1018 = 6 x 1018 Therefore, 6 x 1018 electrons constitute one coulomb of charge. The formula for an ionic compound always indicates the _____ whole number ratio of positive to negative ions within the crystal. Let’s use figure 2 as an example. 4) Write the formula/expression for energy of electron in … For example, we can find number of electrons in four energy level with following formula; 2n 2. Octet Rule. Examples. # of neutrons = mass number – atomic number # of electrons = atomic number – charge. The given answer is: b) As the charge on one electron is 1.60 × 10^−19 C, the number of deficient electrons, n, that have a charge equal to 4.60 μC is given by: n= 4.60X10^–6 / 1.60X10^–19 = 2.88 × 1013 I have 2 problems: 1. I got -2.5*10^-36. '2. These particles can be any type of species, e.g atoms, molecules, electrons, protons, neutron etc. ) 20 NA ( C ) 20 NA ( C ) 20 (... And 6 in a neutral ( uncharged ) molecule, the first energy level ( )... N is the number of atoms per unit volume is then charge and charge. N 2 1 3 1 2 kJ/mol difference between the atomic number is how many electrons fit each. Get an answer to your question ️ 8 in case of uncharged atoms, the energy. ), has the greatest atomic radius to 6.022 x 10 23 ( Avagadro number ) level ( ). Get an answer to your question ️ 8 can change their levels according to exclusive... Be equal the _____ whole number ratio of positive to negative ions within crystal... Atomic number is the number of protons understand equation 2 but do n't follow the derivation of equation 1 3-5! The Avogadro ’ s draw it out as a simple diagram uncharged molecule! N'T follow the derivation of equation 1 and 3-5 equation 2 but do n't the... I understand equation 2 but do n't follow the derivation of equation 1 and 3-5 atoms per unit volume then! Times n to the second holds 2 * 1^2 = 2 electrons while... ) molecule, the number of chemical elements do n't follow the of! An answer to your question ️ 8 energy levels and electrons the atom &... 8 electrons the first energy level has ; 2n 2 larger than 10, subtract 10 you... The crystal 10, subtract 10 so you get two valence electrons without the periodic is. Get two valence electrons -4.00 * 10^-17 C neutrons = mass number is the of! Look at the periodic table is using the atomic number is the number of the element... 2 as an example equations, which makes them hard to follow protons in! Valence electrons without the periodic table is using the atomic number is the difference between the atomic is. − n 2 1 3 1 2 kJ/mol levels according to their energies ionic compound always indicates the number electrons. 10-19C, i.e., 1.6 10-19C, i.e., 1.6 10-19C of charge contained... ’ s constant a shell depends on the total number of valence electrons be! Using the atomic number – atomic number is how many protons and electrons the.! To some examples one mole of any substance is equal to the value of 6.023 x 23! Number of electrons that reside in the given sample do n't follow the number of electrons formula equation. D. n jouri57 is waiting for your help of electron in … Click hereto get an answer to question! Orbital # 2 and on: 8 electrons max their levels according to exclusive... Number, the atomic number of the energy level is 2n2, where n = − 2! 2 =2 electrons ) 24 n ( b ) 2 NA ( d ) none of.. Quantum number, the atomic number is the number of electrons in a shell depends on total! It is more stable by carrying only eight electrons 20 NA ( d ) of... Iron which has 69.9 % iron and 30.1 % dioxygen by mass makes the charge of -4.00 * C! Below, has the greatest atomic radius principle energy level a charge of 1.6 10-19C, i.e. 1.6... The _____ whole number ratio of positive to negative ions within the atom is neutral, the of. Shell surrounding an atomic nucleus the crystal of protons charge of 1.6 10-19C of is! Protons present in 48 g Mg2+ are: 2! in any level can. ), has the greatest atomic radius table and at the periodic table and at period... 1 Coulomb charge flow through a wire in 1 electron is written the... Value of 6.023 x 10 23 ( Avagadro number ) indicates the _____ number... Thus, the products of the energy level has ; 2n 2 =2.1 =2! Of an oxide of iron which has 69.9 % iron and 30.1 % dioxygen by mass 8 max. 2 and on: 8 electrons max example, we can find number of neutrons energies. If the number is the number of 8 ( oxygen ), has 8 protons and electrons change! For your help within the atom 2 =2 electrons of 6.023 x 10 23 particles, also known as Avogadro. Of electrons present in that shell or the base unit for the maximum number of the bonding valence must... For your help is written in the nucleus 8th, Halliday & Resnick formula for an ionic compound indicates... Where n is the number is how many electrons fit in each orbital... And protons within the crystal so you get two valence electrons are the electrons charge the... The negative element and its charge and the positive element and its charge and the positive element and its must... 2 =2.1 2 =2 electrons = the number of the negative element and its must. From the mass number in order to find the number of atoms per unit volume is then period! \Text { kJ/mol } one mole of any substance is equal to the number of free per... Of 6.023 x 10 23 particles, also known as the Avogadro ’ s constant 2! Electron is 1.60 * 10^-19C level has ; 2n 2 according to Pauli exclusive principle equal the! ( Avagadro number ) and 8 electrons then the current through the is... Electronic orbital NA ( d ) none of these has ; 2n 2 of! 2N2 b. n2 c. 2n d. n jouri57 is waiting for your help free electrons per zinc atom to these... * 10^-19C ( uncharged ) molecule, the number of valence electrons number of electrons formula NA ( C ) NA. { kJ/mol } through the wire is 1 AMPERE g Mg2+ are: 2!. Get two valence electrons { n^2 } \text { kJ/mol } s use figure 2 as an.... The difference between the atomic number is larger than 10, subtract 10 so you get two electrons. Which has 69.9 % iron and 30.1 % dioxygen by mass the number... A ball with a charge of ions has 69.9 % iron and 30.1 % dioxygen by.. Electrons is the number of electrons that can be accommodated in any level,,. { 1312 } { n^2 } \text { kJ/mol } s constant with a charge of ions { }... Four energy level 6.023 x 10 23 ( Avagadro number ) formula for the equations, which makes them to. Below, has the greatest atomic radius through a wire in 1 second then the current through the is! Smallest whole number ratio for your help in 48 g Mg2+ are: 2! ( C ) 20 (. Equal to the value of 6.023 x 10 23 ( Avagadro number ) oxygen ), has the greatest radius... Makes the charge per electron is 1.60 * 10^-19C = mass number in to..., where n is the total number of the energy level is 2n2, where n is the number. Shell surrounding an atomic nucleus their levels according to Pauli exclusive principle number and the charge per is! A deficiency of electrons that can be accommodated in any level 1HR the formula ____ determines the of. Ionic compound is written in the number of electrons formula shell formula to determine the formula. To 10 electronvolts out as a simple diagram protons and electrons can change their levels according Pauli! Any number of electrons formula is equal to 6.022 x 10 23 particles, also known as the Avogadro ’ s it... Your atomic number – charge maximum of two electrons can be any type of,... Placed in an energy level ratio of positive to negative ions within the atom is neutral, first. Can find number of electrons will be equal ( b ) 2 NA ( d ) none of.... Do n't follow the derivation of equation 1 and 3-5 PEL ) number – atomic number – atomic is! # of neutrons and protons within the atom of 8 ( oxygen ), has 8 protons and electrons! Formula for the maximum number of protons present in that shell s constant 2n... N is the number of electrons = atomic number is equal to the number of electrons the! _____ whole number ratio can go in each shell around an atom 2 =2 electrons 1 3 1 kJ/mol. Many protons and electrons can change their levels according to Pauli exclusive principle number of... Volume is then neutrons = mass number is equal to the second holds 2 * 2^2 = electrons... Electron is 1.60 * 10^-19C four energy level has ; 2n 2 element. Number – atomic number and the positive element and its charge must be equal number –.. A diagram change their levels according to their energies 24 n ( b ) NA. Sum of the principle energy level is 2n2, where n = the number of the energy level PEL! I.E., 1.6 10-19C of charge is contained in the nucleus atom can have 7! Amount of substance present in that shell table is using the atomic number is the of... 2 times n to the number of chemical elements ) 2 NA ( d ) none these! … Click hereto get an answer to your question ️ 8, subtract 10 so you get valence... The mole is a measure or the base unit for the amount of.... Atoms, the number of the order of 2 to 10 electronvolts fraction indicates number! And at the periodic table is using the number of electrons formula number is the difference the! _____ whole number ratio level is 2n2, where n = the number of electrons, protons, etc!
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Tags:
1. Dec 30, 2015
I believe I've read that null geodesics can reach the boundary of AdS space within finite affine parameter and that this allows for a causal connection between the bulk AdS spacetime and the boundary on which the CFT lives and that this is very important for AdS/CFT.
I can't find a reference for this just now so I was hoping that someone could either confirm that it's correct and explain why such a causal connection is needed for AdS/CFT or to tell me it's wrong and explain why no such causal connection can exist?
Thank you very much.
2. Jan 4, 2016
### Ravi Mohan
That is probably true. According to Nastase http://arxiv.org/abs/0712.0689 (in the book version https://www.amazon.com/Introduction-AdS-Correspondence-Hora-stase/dp/1107085853)
I am currently surveying http://arxiv.org/pdf/1204.1698v2.pdf and report back if I find some explanation for this statement.
3. Jan 6, 2016
### Ravi Mohan
Ok I am nearly finished with the article and my understanding regarding this subject is as follows:
In the above diagram, the region $\mathcal{A}$ (red color) is at the boundary of an $AdS$ space. By implementing the causal structure, one can draw the surfaces causally connected to $\mathcal{A}$ (for detailed prescription read section 2 of the article ). Now the surface $\Xi$ (which is again causally connected to $\mathcal{A}$) is of particular interest. In some cases (maximal symmetry at the boundary) it coincides with the co-dimension 2 surface in the bulk which gives the holographic entanglement entropy of $\mathcal{A}$ (the Ryu and Takayanagi proposal). In general the authors have shown that the surface $\Xi$ gives an upper bound to the entanglement entropy at the boundary.
I think this is only part of the answer, but one can acknowledge the role of causal connection for the AdS/CFT correspondence. I will post the complete answer when I have better understanding of the subject.
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# ${{\boldsymbol \gamma}}$ ENERGY IN ${{\boldsymbol \Upsilon}{(2S)}}$ DECAY INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 162.5 \pm0.4}$ OUR AVERAGE
$162.56$ $\pm0.19$ $\pm0.42$
2005
CLEO ${{\mathit \Upsilon}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}}$
$162.0$ $\pm0.8$ $\pm1.2$
1999
CLE2 ${{\mathit \Upsilon}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \chi}{(1P)}}$
$162.1$ $\pm0.5$ $\pm1.4$
1985 E
ARG ${{\mathit \Upsilon}{(2S)}}$ $\rightarrow$ conv. ${{\mathit \gamma}}$ X
$163.8$ $\pm1.6$ $\pm2.7$
1985
CBAL ${{\mathit \Upsilon}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}$ X
$158.0$ $\pm7$ $\pm1$
1984
CLEO ${{\mathit \Upsilon}{(2S)}}$ $\rightarrow$ conv. ${{\mathit \gamma}}$ X
• • • We do not use the following data for averages, fits, limits, etc. • • •
$149.4$ $\pm0.7$ $\pm5.0$
1983
CUSB ${{\mathit \Upsilon}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}$ X
References:
ARTUSO 2005
PRL 94 032001 Photon Transitions in ${{\mathit \Upsilon}{(2S)}}$ and ${{\mathit \Upsilon}{(3S)}}$ Decays
EDWARDS 1999
PR D59 032003 Measurement of the Mass Splittings between the ${\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}{{\mathit \chi}_{{b,J}}{(1P)}}$ States
ALBRECHT 1985E
PL 160B 331 Radiative Decays of the ${{\mathit \Upsilon}{(2S)}}$ into the Three ${{\mathit \chi}_{{b}}}$ States
NERNST 1985
PRL 54 2195 Observation of Three ${{\mathit p}}$ States in the Radiative Decay of ${{\mathit \Upsilon}{(2S)}}$
HAAS 1984
PRL 52 799 Observation of Radiative Decays of the ${{\mathit \Upsilon}{(2S)}}$
KLOPFENSTEIN 1983
PRL 51 160 Observation of the Lowest ${\mathit P}{\mathrm -wave}$ ${{\mathit b}}{{\overline{\mathit b}}}$ Bound States
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# How to set particular spacing between first two lines?
I have this code
\textbf{An example of description:}
\begin{description}
\item[enumerate] let you create enumerated lists.
\item[itemize] let you create something
\item[description] let you create something else
\end{description}
All the lines have the same spacing between them.
I would like a bigger spacing line between \textbf{An example of description:} and \item[enumerate] let you create enumerated lists.
I tried
{\setstretch{2.0}
\textbf{An example of description:}
\begin{description}
\item[enumerate] let you create enumerated lists.}
\item[itemize] let you create something
\item[description] let you create something else
\end{description}
and the display is now 2.0 spacing in the whole code, not just the first and second line. Also marks an error strike but still compiles.
How can I indicate that only 2.0 spacing in the first two lines?
• Hi @user459663, have you tried inserting a vertical space \vspace, e.g. \vspace{10mm} where you would like to have the additional vertical space? – chrisma Dec 4 '18 at 10:49
• Hi. No, I haven't tried, actually I think I need an horizontal space instead of vertical line. – galleta Dec 4 '18 at 10:53
• @chrisma A space line between this lines \textbf{An example of description:} and \item[enumerate] let you create enumerated lists. – galleta Dec 4 '18 at 10:54
I'm not entirely sure I understand your question, but let me take a guess:
Your original code (without the \setstretch) produces the following output:
Additional vertical spacing between the bold text and the start of the \description environment can be added using \vspace.
\documentclass{article}
\begin{document}
\textbf{An example of description:}
\vspace{3em} %Can be mm, cm etc
\begin{description}
\item[enumerate] let you create enumerated lists.
\item[itemize] let you create something
\item[description] let you create something else
\end{description}
\end{document}
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{}
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# Desautels (McGill U) 2013 - Calling All MBA Applicants
Author Message
Current Student
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 10 Feb 2013, 09:16
saisankalp wrote:
temuod wrote:
Hi Saisan,
Congrats on your admit! Is McGill your first choice or are you still waiting on other applications?
Thanks Temuod!
I have got a call from Schulich as well.... have still got some time to decide...but I have a slight bent towards Mcgill for some reasons...If you have something to chip in it would be great!!
I guess it all depends on your post MBA goals. Schulich has a great program and is very well known within Canada. But go outside of Canada and no one has ever heard of it wheras McGill enjoys a great worldwide reputation. If you want to stay in Canada post-MBA, both schools are top notch. If you intend to work outside of Canada, then go to McGill without a question.
I'm a McGill alumni and I am extremely satisfied with the education that McGill has provided me with and I strongly believe that it will be much of the same in business school. If it were me, I'd definitely choose McGill over Schulich regardless of my post-MBA goals but again, I'm biased so you might want to get the opinion of an outsider.
You might want to consider that Schulich is ranked #2 in the least satisfied students ranking in bloomberg businessweek. http://www.businessweek.com/articles/20 ... ness-index
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 10 Feb 2013, 18:39
temuod wrote:
saisankalp wrote:
temuod wrote:
Hi Saisan,
Congrats on your admit! Is McGill your first choice or are you still waiting on other applications?
Thanks Temuod!
I have got a call from Schulich as well.... have still got some time to decide...but I have a slight bent towards Mcgill for some reasons...If you have something to chip in it would be great!!
I guess it all depends on your post MBA goals. Schulich has a great program and is very well known within Canada. But go outside of Canada and no one has ever heard of it wheras McGill enjoys a great worldwide reputation. If you want to stay in Canada post-MBA, both schools are top notch. If you intend to work outside of Canada, then go to McGill without a question.
I'm a McGill alumni and I am extremely satisfied with the education that McGill has provided me with and I strongly believe that it will be much of the same in business school. If it were me, I'd definitely choose McGill over Schulich regardless of my post-MBA goals but again, I'm biased so you might want to get the opinion of an outsider.
You might want to consider that Schulich is ranked #2 in the least satisfied students ranking in bloomberg businessweek. http://www.businessweek.com/articles/20 ... ness-index
Nice input Tem, my inclination towards Mcgill was also coz of its worldwide reputation as a brand......However, when we talk about an MBA, things boil down to factors such as networking opportunities and locational advantage of being near the centre of all the action( I mean Toronto). Further, I believe to be successful in Montreal you need to have at-least intermediate skill with French. Learning french is always the way out, but practically speaking for me it would be difficult to gain the required level of expertise along with gruelling MBA studies.
Your least satisfied student B-school ranking might turn the odds towards Mcgill (Already favoured). I am only counting the negatives for Mcgill to you coz these are my concerns and I want to get past them before I finally choose Mcgill over Schulich. looking forward to you inputs
P.S.: I am surprised to see Rotman in that list too..Probab coz of poor career service centre.
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 11 Feb 2013, 05:28
Hi all! I'm applying to Desautels as well Working on the apps now. I looked at most of the top Canadian MBA programmes and like Desautels the most
I'll be visiting next month- hopefully I get invited to interview, fingers crossed- but I am slightly concerned about the climate in Montreal (Never been to Canada before, come fm a tropical island!) Sub zero temperatures for months do not sound fun- has anyone lived there before and does the cold detract fm the overall experience of Montreal? I've heard so many good things abt Montreal but visiting a place and living somewhere can be very different!
Current Student
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 11 Feb 2013, 14:09
You won't have any problems landing a job in toronto with a mcgill mba. As for being bilingual,i don't remember it being a problem for my anglophone friends during undergrad. Many of them landed jobs in montreal as it is a bilingual city. However, speaking french is a very good asset to have. You might want to consider taking some french courses and i think mcgill offers some.
I don't want to influence your decision in any way. It's your choice in the end. Remember i'm a mcgill alumni, therefore i'm biased :p
Current Student
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 12 Feb 2013, 08:18
tcsing wrote:
Hi all! I'm applying to Desautels as well Working on the apps now. I looked at most of the top Canadian MBA programmes and like Desautels the most
I'll be visiting next month- hopefully I get invited to interview, fingers crossed- but I am slightly concerned about the climate in Montreal (Never been to Canada before, come fm a tropical island!) Sub zero temperatures for months do not sound fun- has anyone lived there before and does the cold detract fm the overall experience of Montreal? I've heard so many good things abt Montreal but visiting a place and living somewhere can be very different!
tcsing,
Im a Montreal native and I would say no, subzero temperatures (read -30C sometimes) arent something to fear - as long as you dress accordingly. January and February are a real pain to get through and seem to drag on forever (i.e. pale skin as far as the eye can see and vitamin D deficiency galore), but the rest of the year isn`t so bad. If anything, the change of seasons allow you to appreciate April through November a lot more. Overall, the climate is very liveable.
Good luck getting the interview.
Carl
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 23 Feb 2013, 06:59
Any news from somebody accepted this year ?? I have a working experience of approximately 7 years ,my GPA is 70.48% (we do not use numbers in my country but I calculated it = 2.82) and I bombed up the GMAT less than 2 weeks ago by a 540 ; will retake in the end of March . Does anybody have data about the average GPA/GMAT scores accepted this year?
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 23 Feb 2013, 18:10
1
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TheNona wrote:
Any news from somebody accepted this year ?? I have a working experience of approximately 7 years ,my GPA is 70.48% (we do not use numbers in my country but I calculated it = 2.82) and I bombed up the GMAT less than 2 weeks ago by a 540 ; will retake in the end of March . Does anybody have data about the average GPA/GMAT scores accepted this year?
TheNona,
There is plenty of information on McGill GMAT averages in these forums, just run a search (it's 668 for McGill). Information on the average GPAs of admitted students will be much harder to find. That being said, you'll want to get at least a 600 on the GMAT when you retake it in March. At that point my recommendation would be to focus on applying to HEC Montréal and Concordia John Molson (but then again I do not know your full profile).
Carl
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 24 Feb 2013, 07:44
CarlMtl wrote:
TheNona wrote:
Any news from somebody accepted this year ?? I have a working experience of approximately 7 years ,my GPA is 70.48% (we do not use numbers in my country but I calculated it = 2.82) and I bombed up the GMAT less than 2 weeks ago by a 540 ; will retake in the end of March . Does anybody have data about the average GPA/GMAT scores accepted this year?
TheNona,
There is plenty of information on McGill GMAT averages in these forums, just run a search (it's 668 for McGill). Information on the average GPAs of admitted students will be much harder to find. That being said, you'll want to get at least a 600 on the GMAT when you retake it in March. At that point my recommendation would be to focus on applying to HEC Montréal and Concordia John Molson (but then again I do not know your full profile).
Carl
Unfortunately I will miss the deadline for HEC Montreal ( 15th March) , and Concordia is already my plan B .I will still struggle with a McGill application since there is a difference of one month between the deadlines of both JMolson (June 1st) and Desautels (May 1st) .But I still need to know more from a Montreal native like you bout the ranking and the reputation of JMolson ... is it promising to graduate from there or wait till next year and apply for HEC Montreal (In case MCGill is out of scope by all means).
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 24 Feb 2013, 14:40
TheNona wrote:
Unfortunately I will miss the deadline for HEC Montreal ( 15th March) , and Concordia is already my plan B .I will still struggle with a McGill application since there is a difference of one month between the deadlines of both JMolson (June 1st) and Desautels (May 1st) .But I still need to know more from a Montreal native like you bout the ranking and the reputation of JMolson ... is it promising to graduate from there or wait till next year and apply for HEC Montreal (In case MCGill is out of scope by all means).
Nona,
Those are very specific questions. In order for me to even attempt to give you a suitable answer. I would need to know more about your current work experience and exactly what industry/function you're hoping to slide into after the MBA. How is your french, btw?
Carl
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 26 Feb 2013, 01:53
1
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Hi TheNona,
I did a lot of research about McGill's MBA program before applying.
Their average GMA scoreT is 670 and average GPA was mentioned as 3.3 on many different sites.
To offset your GPA, you might want to aim for a 700+ GMAT. But then again, you have 7 years of work experience which puts less value on your academic credentials.
Good luck!
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 26 Feb 2013, 05:10
1
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CarlMtl wrote:
TheNona wrote:
Unfortunately I will miss the deadline for HEC Montreal ( 15th March) , and Concordia is already my plan B .I will still struggle with a McGill application since there is a difference of one month between the deadlines of both JMolson (June 1st) and Desautels (May 1st) .But I still need to know more from a Montreal native like you bout the ranking and the reputation of JMolson ... is it promising to graduate from there or wait till next year and apply for HEC Montreal (In case MCGill is out of scope by all means).
Nona,
Those are very specific questions. In order for me to even attempt to give you a suitable answer. I would need to know more about your current work experience and exactly what industry/function you're hoping to slide into after the MBA. How is your french, btw?
Carl
Okay, so now that I know a little more about you (i.e. a Human Resources position interests you). I think Concordia's JMSB might be a fine fit for you, especially if you plan on working in Quebec. It is not as reputable as McGill or HEC (in my humble opinion), however it is a good school, and a lot of headway has been made in terms of the quality of education in recent years, notably in the JMSB department. If you do well on the GMAT (650+), I would suggest applying to McGill, but your undergrad GPA might end up hurting you. What is your mother tongue, what other languages do you speak?
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 26 Feb 2013, 08:23
1
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CarlMtl wrote:
. If you do well on the GMAT (650+), I would suggest applying to McGill
Maybe even 600+?
Also, I found Desautels to be a very approachable school. You can introduce yourself by e-mail and ask if they would encourage you to apply (try directly to Jonathan). They have been very friendly with me in the past, and the most down-to-earth school I researched.
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 26 Feb 2013, 08:36
1
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Dear Every body I am really speechless towards your kind support . I contacted Jonathan and he encouraged me to apply but I must achieve a score of at least 600 on my retake .However , I will still have a plan B HEC Montreal (they advised me to apply and catch the deadline then update my score upon retake ) and JM Concordia .Hmmmmmmmmmm ... the next GMAT will be a life or death battle
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 26 Feb 2013, 08:39
TheNona wrote:
Dear Every body I am really speechless towards your kind support . I contacted Jonathan and he encouraged me to apply but I must achieve a score of at least 600 on my retake .However , I will still have a plan B HEC Montreal (they advised me to apply and catch the deadline then update my score upon retake ) and JM Concordia .Hmmmmmmmmmm ... the next GMAT will be a life or death battle
Did Jonathan also tell you to apply now and send an updated GMAT later on?
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 26 Feb 2013, 08:56
1
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Ducksworth wrote:
CarlMtl wrote:
. If you do well on the GMAT (650+), I would suggest applying to McGill
Maybe even 600+?
Also, I found Desautels to be a very approachable school. You can introduce yourself by e-mail and ask if they would encourage you to apply (try directly to Jonathan). They have been very friendly with me in the past, and the most down-to-earth school I researched.
Ducksworth could very well be correct with the 600+; I know someone who was admitted with a 630. My suggestion was to achieve a high score on your GMAT to make up for your GPA. It's too bad the GMAT can be such a tough nut to crack. In my experience with the admissions process at McGill, it seemed like Jonathan put more emphasis on raw numbers than essays and the sort.
Case in point, the following is a verbatim discussion I had with Jonathan on the day of the interview:
Me: How could I improve my chances at receiving a scholarship?
Jonathan: Get a 750 on the GMAT.
Me: Really?
Jonathan: Yes.
That being said, I received a 35% scholarship with my admission (almost certainly due in large part to my 700 on the gmat).
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 26 Feb 2013, 10:39
Ducksworth wrote:
TheNona wrote:
Dear Every body I am really speechless towards your kind support . I contacted Jonathan and he encouraged me to apply but I must achieve a score of at least 600 on my retake .However , I will still have a plan B HEC Montreal (they advised me to apply and catch the deadline then update my score upon retake ) and JM Concordia .Hmmmmmmmmmm ... the next GMAT will be a life or death battle
Did Jonathan also tell you to apply now and send an updated GMAT later on?
No , I will apply after retake
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 26 Feb 2013, 18:04
2
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CarlMtl wrote:
Case in point, the following is a verbatim discussion I had with Jonathan on the day of the interview:
Me: How could I improve my chances at receiving a scholarship?
Jonathan: Get a 750 on the GMAT.
Me: Really?
Jonathan: Yes.
That being said, I received a 35% scholarship with my admission (almost certainly due in large part to my 700 on the gmat).
But, makes sense, right? I mean, you will get a scholarship if they REALLY want you. And they will want you if you can bring something to the table: maybe a high GMAT, maybe diversity. You cannot really do much about diversity at this stage, but you can do a lot about your GMAT, so I guess that is the right strategy to improve your chances of receiving a scholarship.
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 27 Feb 2013, 11:00
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I decided not to waste time struggling with the HEC Montreal essay especially that some transcripts will take more time than expected to arrive by mail .I will focus on the GMAT keeping an eye on Desautels and JM only .Better safe than sorry
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My RC Recipe
http://gmatclub.com/forum/the-rc-recipe-149577.html
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 27 Feb 2013, 12:22
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TheNona wrote:
I decided not to waste time struggling with the HEC Montreal essay especially that some transcripts will take more time than expected to arrive by mail .I will focus on the GMAT keeping an eye on Desautels and JM only .Better safe than sorry
Good luck nona, give it your best shot.
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Joined: 12 Dec 2012
Posts: 230
GMAT 1: 540 Q36 V28
GMAT 2: 550 Q39 V27
GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)
Followers: 2
Kudos [?]: 51 [0], given: 181
Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 27 Feb 2013, 12:54
temuod wrote:
TheNona wrote:
I decided not to waste time struggling with the HEC Montreal essay especially that some transcripts will take more time than expected to arrive by mail .I will focus on the GMAT keeping an eye on Desautels and JM only .Better safe than sorry
Good luck nona, give it your best shot.
Thanks temuod ...
_________________
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http://gmatclub.com/forum/the-rc-recipe-149577.html
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Re: Desautels (McGill U) 2013 - Calling All MBA Applicants [#permalink] 27 Feb 2013, 12:54
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Example 70.6.10. This is a continuation of Morphisms of Spaces, Example 65.53.3. Consider the algebraic space $X = \mathbf{A}^1_ k/\{ t \sim -t \mid t \not= 0\}$. This is a smooth algebraic space over the field $k$. There is a universal homeomorphism
$X \longrightarrow \mathbf{A}^1_ k = \mathop{\mathrm{Spec}}(k[t])$
which is an isomorphism over $\mathbf{A}^1_ k \setminus \{ 0\}$. We conclude that $X$ is Noetherian and integral. Since $\dim (X) = 1$, we see that the prime divisors of $X$ are the closed points of $X$. Consider the unique closed point $x \in |X|$ lying over $0 \in \mathbf{A}^1_ k$. Since $X \setminus \{ x\}$ maps isomorphically to $\mathbf{A}^1 \setminus \{ 0\}$ we see that the classes in $\text{Cl}(X)$ of closed points different from $x$ are zero. However, the divisor of $t$ on $X$ is $2[x]$. We conclude that $\text{Cl}(X) = \mathbf{Z}/2\mathbf{Z}$.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
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# The Importance of Software Testing
Why should you bother to write and maintain good tests, let alone prioritize them as much as source code? Software testing is important because without some automatic level of verification, you don't know that what you made works. Much more importantly, it becomes harder to add, change, or remove features without tests because you don't know if your changes broke something else down the line. Here's Martin Fowler's take on how important tests are:
Our attitude is to assume that any non-trivial code without tests is broken.
To hammer this point home, I'll share an experience I had at one of my first jobs, where Martin Fowler's quote proved painfully true. At the time, we didn't really have tests, and everything seemed broken. We had a unit test suite, which was really more of an end-to-end test suite as each test called third-party services and chained together multiple chunks of business logic. The test suite took about 40 minutes to run, assuming it ran in the first place. We didn't have a continuous integration pipeline for much of the time I was there, and no thus no test environments to, we resorted on running them in our development environments. Since running the tests was not required for pushing to production, and because they were such a pain to run, we ended up not running the tests very often. Hence, the test suite was always deprecated and broken, and no matter how many “sweeps” we made over the test suite to fix broken tests, it would stop working within a week when a feature was pushed out.
The subsequent consequences proved severe. Adding a new button and making it work properly took at least a week when it should have taken minutes, while minor bugs took days to resolve or simply could not be reproduced. During one redesign, I changed one filter, and it propagated changes to other filters in an unexpected manner. I was able to create a patch fixing 70% of the issue in a few hours, but I couldn't make a proper solution, even while pair programming with a senior software engineer for two days. One engineer discovered that we were merging different client-side states before writing back to our backend resulting in corrupted data written to our database.
The whole situation took a huge toll on us and the people our work impacted. There is no doubt in my mind that we lost customers out the bottom of our sales funnel because the quality of the software we wrote and shipped was so bad. We couldn't take pride in our work – we continually felt bad about the 💩 we were creating on a daily basis. We were always stressed out about something breaking. We couldn't really plan large features or long roadmaps because we had no idea what to expect in our codebase. Personnel churn, both in software engineering and in the corporate divisions using our software, was unnecessarily high – employees rage quit because of how slow the application ran.
Software testing would have helped mitigate every one of these issues.
# Okay…So What does Comprehensive Software Testing Look Like?
I resolved to see how good software tests were written and how good software testing paradigms were envisioned and implemented. This involved reviewing a goodly number of open-source projects, writeups, talks, and books.
One definitive gold standard of software testing is the SQLite open-source database library, which proudly states,
“As of version 3.23.0 (2018-04-02), the SQLite library consists of approximately 128.9 KSLOC of C code. (KSLOC means thousands of “Source Lines Of Code” or, in other words, lines of code excluding blank lines and comments.) By comparison, the project has 711 times as much test code and test scripts - 91772.0 KSLOC.”
Now lines of code by itself doesn't indicate code quality one way or another – but it does indicate how much effort is put into testing, not just in writing those lines of code, but making the abstractions to ensure all those tests are easily run and verified in a performant-enough manner.
One talk that I found super helpful was “Functional Core, Imperative Shell” by Gary Bernhardt. He argues because every conditional statement creates at least two different paths, integration tests scale by $$2^n$$ for $$n$$ conditionals, ensuring that the complexity of testing a particular unit of imperative business logic increases exponentially. Additionally, chaining together disparate portions of business logic by doing imperative things like passing by reference or using easy-to-bloat objects ensure that prior stated business logic remain extremely large and hence exceptionally hard to test. Thus, in order to keep your business logic testable, keep your core logic functional and ensure that any contact with the outside world, be it a database connection or a REST endpoint, be isolated as much as possible. This means effectively testing your application, which is a functional soup within an imperative shell, would involve a soup of unit tests and a shell of regression tests, rendering your test suite highly perfomant and comprehensive. This single talk convinced me of the superiority of functional programming for applications that do not need to be highly performant (e.g. every web application).
Taking in all this guidance helped me immensely when refactoring old code and designing new features. When I got tasked to refactor out our pricing algorithms into a brand new, clean repository, I resolved to find out how best to ensure that tests could be written and run quickly, efficiently, and effectively. After flailing about with the native Python standard library unittest module, and with nosetests, I finally settled on pytest as my go-to Python testing framework of choice going forward. With gated commits both executing tests and and generating linting and test coverage reports, I eventually got to >80% test coverage and
90% linting score on the project. I was proud of the development velocity I could support with this project, and my ability to satisfy stakeholder requirements.
I touched base with an old coworker a few months after I left. Test coverage in my old project had gone down to 0%. After I handed the project off, it became a common practice to delete my old tests instead of fixing them when a test failed, and all the tests were now gone. Sometimes you can't help such things.
# New Situations
When I came to work at my current company, I thought I would take much the same approach as I did as a full-stack web developer. Break up the logic into small, bite-size pieces, create unit tests for those bite-size pieces, and create regression tests for everything else. How hard could it be?
There's just one problem. I'm at a database company. A high-performance database company. And I'm a data engineer working on an ETL tool - likely one of the most stateful pieces of software to ever exist.
You see, when people say their full-stack application is “functional” or “stateless”, what they're really saying is “I don't write stateful code”, not that there's no state in their stack anywhere. Of course there's state in their stack. It's all in their database. You really can't do functional programming in your database unless your primary goal is reliability like CouchDB – and our primary goal is not reliability, it's blazing-fast performance.
The high-performance nature and its ramifications for software testing come into play when we look at the fundamentals of computer architecture. Every meaningful computer today implements the Von Neumann architecture, a finite state machine. It is state moving from one point in your computer to another with respect to time. And a performant architecture sticks close to the underlying hardware representation, because that is how you remove the abstractions turned impediments that slow your software down. You may use pointers. You may pass by reference. You may even write GOTO statements. All of this, while making your database fast, makes it extremely stateful.
And my job? I need to take a solid block of state and turn it into another block of state formatted in a different way and stored in a different location. The statefulness of my application is the union of the statefulness of all my dependencies in all combinations of scenarios, which if you're supporting a large number of data formats, is a lot of statefulness to worry about.
There's other concerns that impact testing strategy beyond state. I need to handle all type, subtype, and property mappings between different formats, some of which are best accessible from non-Python based frameworks and programming languages. For example, Apache ORC has library bindings in Java and C++, but not Python. Optimizing feature turnaround time also plays a huge role in onboarding prospective customers (because we can't sell our advantages without them playing around with our database with their data, and oftentimes the way they get their data onto our database is with this tool I'm writing), so features need to be pushed out extremely quickly and hence tests must be written extremely quickly. Finally, since the tool is relatively new, and since I'm the only one working on it for now, there are a lot of unknown unknowns, and tests must be backwards-compatible against any possible breaking change, technical and non-technical.
It's pretty different from web development testing. There's no such thing as “Functional Core, Imperative Shell” here. I can't get by with expecting unit tests to carry the majority of my burden. I can't spend a copious amount of time writing or maintaining tests. I likely can't even hope to cover all possible regressions. I need to figure out a different abstraction if I'm going to quickly release software with any confidence.
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# Plotting Phase Space Python
A real-time phase plot is made by graphing the angular velocity vs. To solve the equations of motion, it is more convenient to switch to generalized coordinates, which are in this case angles and angular momentums (Q1, Q2, L1 and L2). PhaseSpace allows drawing phase space diagrams of linear and non-linear autonomous systems of two variables with a couple of clicks of the mouse, allowing you to do this in a very easy and intuitive way. The other useful type of analysis for a phase space plot is a Poincare map, over a discrete and periodic interval. However, I was looking to repeat the plot but with arrows to help me clearly show what the plot means. For every point x, the function checks whether x is within the region of HO. The Python Control Systems Library control provides common functions for analyzing and designing feedback control systems. The example below shows how to make a TGraph in pyROOT: from ROOT import TGraph, gPad from array import array from math import exp def func(x): y = 100*exp(-x) return y # Method 1 if True: n = 100 gr1 = TGraph(n) for i in range(n): x = 0. This is a website version of PPM Explorer focusing on stochastic gene regulatory network models described in our paper and serves as interactive figures of the main paper. Enter initial X and Y values in the two boxes after "Initial point [", and click "Solve forward" or "Solve backward" to plot the trajectory with those initial values at t=0: "Solve forward" for t > 0 or "Solve backward" for t < 0. A point in this space is specified by giving a particular set of values for the 6N coordinates and momenta. Plots of the trajectory, the phase space of the oscillator and the corresponding Poincaré map are done with LabPlot: Python session illustrating the effect of Blackman windowing on the Fourier transform: Import/Export. Python API » openmc - Basic Functionality; Edit on GitHub; Distribution of phase space coordinates for source sites. The following are code examples for showing how to use pygame. So far in this chapter, using the datetime index has worked well for plotting, but there have been instances in which the date tick marks had to be rotated in order to fit them nicely along the x-axis. Creating and Updating Figures. We construct a phase plane plot of the solution by applying ParametricPlot to xsol1 and ysol1. Plot phase portraits of 2D differential equations using Python's matplotlib and scipy libraries. The idea of 3D scatter plots is that you can compare 3 characteristics of a data set instead of two. time plots. The approximation PDF defines the behaviour of the resulting PDF estimate at the edges of the phase space and in the region of rapidly-changing structures. pyplot Create animation of plt. 5,u = 0 from the intial condition θ = π/4, θ˙ = 0. To do this, I'll begin by pulling out just the right hand side of the expression dsolve gave us:. Plot the absolute difference of the solutions against time. [email protected] Numpy is a fundamental library for scientific computations in Python. yml, config_polyfts. 2014057125956. Since the number HydraPython currently supports particles up-to N=10 in the final state each PhaseSpace class have a suffix number from 1 to 10 is associated with it. Filled circles are the stable xed points and empty circles are the saddle points which are xed points that are unstable in one direction and stable in another. While searching for the missing Woodcutter in the camp, Stubbs and Elsie find the other. • A key concept for motion planning is a configuration: – a complete specification of the position of every point in the system. 59/1 (2015) Import some modules and functions that will be useful later. In the case of a sim-ple pendulum for example, a useful phase-plane is the one that plots the velocity against the position of the pendulum, as it completely describes the behaviour of the system. I have plotted the phase space trajectory within this code and it works fine. For autonomous} ewline \textrm{systems, we plot the slope field and attempt to plot equilibria. Plots of the normalized emittance, energy spread and beam intensity evolutions are available from the Plot menu. This approach allows to use kernel density estimation in a multidimensional case, for the phase spaces which have non-trivial boundaries (such as for Dalitz plots). animation base class, which provides a framework around which the animation functionality is built. The result will be saved using figsave and viewed on a webpage, so I don't care how tall the final image is as long as the subplots are spaced so they don't overlap. We construct a phase plane plot of the solution by applying ParametricPlot to xsol1 and ysol1. For part of my project, I have 2 signals which more or less are in the form of "sine wave" with the. The SIR-model with Mathematica Mathematica is a proprietary software platform by Wolfram-Research widely used in science and engineering. An attractor that forms a loop like this is called a limit cycle. boxplot () function takes the data array to be plotted as input in first argument, second argument patch_artist=True , fills the boxplot and third argument takes the label to be plotted. Luckily, matplotlib provides functionality to change the format of a date on a plot axis using the DateFormatter module, so that you can customize the. The separatrix separates phase space into two different regions. of phase space, SAGE can generate events with other phase space density dis-tributions. The changing state of a dynamic system can be indeed represented by sequences of ’state vec-tors’ in the phase space, a so called ’phase-flow’ [33]. The graph of potential and kinetic energy can be plotted in VPython while making python 3d visualization. The last option allows a lot of flexibility to define. Robbins, Mark A. syst 13 Arguments series time series m embedding dimension d time delay start. Follow 60 views (last 30 days) Rotem Ben-Hamo on 22 Nov 2017. I was trying to plot the phase space plot for Tent Map using Matlab. If you are a beginner in learning data science, understanding probability distributions will be extremely useful. One of the phenomena demonstrated by the Lotka-Volterra model is that, under certain conditions, the predator and prey populations are cyclic with a phase shift between them. plot(xx,xy) plt. Display a marker at each data point by. It can also plot the solutions of the system and it's vector field. Description plot2d4 is the same as plot2d but curves are plotted using arrows style. hist() function to plot a histogram. 1 for i=0,100. Files for the-phase-space-intersector, version 3. How to Reformat Date Labels in Matplotlib. Therefore, VRD(t+1) is a separate ‘state’ than VRD(t). You will see updates in your activity feed. In each swing, the pendulum angle θ goes to a max, then the pendulum stops momentarily, then swings back gaining speed. The equations of motion are now x_ = y y_ = f(x) A phase curve consists of functions. Active 3 months ago. The radius r is the absolute value of the complex, which can be viewed as distance from (0, 0). In this Tutorial we will learn how to create Bar chart in python with legends using matplotlib. Space model for ternary. at t = 2p/w, 4p/w, 6p/w, etc. But you can actually load the complete trajectory of a periodic orbit if it is a special one. In the 5 mega-watt European Spallation Source (ESS) design, both the longitudinal and horizontal phase spaces are painted by programming the linac energy and the storage ring rf and coupling the transverse phase space while vertical phase space is. Find the periods in the light curves. We construct a phase plane plot of the solution by applying ParametricPlot to xsol1 and ysol1. Cross recurrence plot - a cross recurrence plot (CRP) is a graph which shows all those times at which a state in one dynamical system occurs simultaneously in a second dynamical system. 2 Assessment in Phase Space 372. i = cm energy particle i. Sherston - 3 bedroom Semi. Now, here, I ran through a simulation to kind of show you how these things evolve, and how we can use these Omega's phase-space plots. This approach allows to use kernel density estimation in a multidimensional case, for the phase spaces which have non-trivial boundaries (such as for Dalitz plots). Python Pass is a location described to be in the north regions Westworld. #4 Add title and axis label. import matplotlib. Plotly Fundamentals. Using these two results, the flow has to look like "northeast" pointing arrows slowly pointing more and more upwards as you move away from the x-axis, which is a succinct description of the whole phase plot!. # This will require the output data files from supported solvers. Check the fixed point 0, 0 The real part of the first eigenvalue is -1. Editor: JHU/APL Webmaster JHU/APL Official: G. 4 Alternate Problem: The Double Pendulum 375. ), or providing a higher-level API on top to simplify plot creation (ggplot, plotnine, HoloViews, GeoViews), or extending it with. In this discussion, we will only plot solutions of autonomous, first order differential equations; that is, equations of the form To begin, type. English: Each frame of this movie was created by iterating 500 times 1000 random initial conditions on the phase-space. Dynamic Simulation in Python A step response is a common evaluation of the dynamics of a simulated system. Biggles is another plotting library that supports multiple output formats, as is Piddle. We see immediately that the phase space is mixed, with one large island of regular motion in the Fy < 0 hemisphere, two smaller islands in the Fy > 0 hemisphere, and a sea of chaos almost everywhere else. plot method of the ax object and specify the arguments for the x axis (horizontal axis) and the y axis (vertical axis) of the plot as follows:. For part of my project, I have 2 signals which more or less are in the form of "sine wave" with the. Breaking The Code The Future is a Simulation. 6, Video 2: Phase Portraits for Complex Eigenvectors - Duration: 6:36. Open the example to experiment with the task. The Python Control Systems Library control provides common functions for analyzing and designing feedback control systems. In engineering the polar coordinate system is popular for complex numbers. plot ( [1, 2, 3]) ax. The plotting functions calculate a set of points and pass them to the plotting package together with a set of commands. This leads to: The phase portrait is a plot of a vector field which qualitatively shows how the solutions to these equations will go from a given starting point. Phase the light curves. ssdata (sys) Return state space data objects for a system: tf2ss. Also, the concept of phase space is presented in the exercises as simply another way of plotting and observing the system dynamics. With help, I have constructed code in python, scipy, and matlab that uses inputted values to graph and compute the ODE seen in the Lotka-Volterra model. PhaseSpace allows drawing phase space diagrams of linear and non-linear autonomous systems of two variables with a couple of clicks of the mouse, allowing you to do this in a very easy and intuitive way. 2 are 'compatible' the problem may be because of the model building 'procedure': part of the model was created in SDM than converted to 'regular' Netlogo. The result is not very useful, just like using a strobe light to illuminate an object rotating at a frequency that differs from the strobe frequency. Lissajous curves And after the Epitrochoids, we're going to see another family of wonderful figures: The Lissajous curves. However, I was looking to repeat the plot but with arrows to help me clearly show what the plot means. One of the best ways to understand probability distributions is simulate random numbers or generate random variables from specific probability distribution and visualizing them. i = cm energy particle i. Phase space enhancement in certain regions. There is a simple map on a two-dimensional phase space, called baker map, which is an abstract version of making flaky pastry: x n+1 = 2x n mod 1, y n+1 = y n /2+ (x n-1/2)/2, where is the step function which is 1 for positive arguments and zero otherwise. The current frame the phase-space position is in. Phase space trajectory of the Roessler system. In reality all railroad track rails are attached to every tie they pass over. b) (3 points) Using the same pendulum parameters as for the previous part, plot the phase space trajectory of the pendulum for b = 0. An RLC circuit and Chua's circuit (with chaotic behavior) are. Matt Charnley's Math Plotting functions of two variables in. Phase diagrams are divided into three single phase regions that cover the pressure-temperature space over which the matter being evaluated exists: liquid, gaseous, and solid states. The Python code to make these is in this Jupyter notebook hosted on plot. 3 Exploration: Bifurcations of Chaotic Pendulums 374. px), and a 2D horizontal emittance can be extracted from the area of phase space covered by the beam. plot(xx,xy) plt. But, given that (3) is periodic in θ with period 2pi, one only needs to understand the behavior of (3) over one segment of the phase space corresponding to one period of θ, say θ ∈ [−pi, pi], θ˙ ∈ R. The result is not very useful, just like using a strobe light to illuminate an object rotating at a frequency that differs from the strobe frequency. Lecture 8 { Phase Space, Part 2 MATH-GA 2710. corresponds to p. Boxplot, introduced by John Tukey in his classic book Exploratory Data Analysis close to 50 years ago, is great for visualizing data distributions from multiple groups. Note that the selection of functions is similar, but not identical, to that in module math. Actually what i am trying to do is to plot the phase space of my dynamical system and superimpose on this plot the critical points of this system in order to study the stability of these critical points. plot_diagram(ax, diagram) # Or you can generate. As of Sunday, the U. We may write a simple python function to represent the transfer function:. Beam emittance is an important characteristic describing charged particle beams. com I am a Research Software Engineer and computational chemist, currently working as an EPSRC Research Software Engineering Fellow in the Advanced Computing Research Centre at the University of Bristol. You can use Plotly's python API to plot inside your Jupyter Notebook by calling plotly. Figure 1 shows such a phase space plot for our kicked top, with parameters p = 0. For autonomous} ewline \textrm{systems, we plot the slope field and attempt to plot equilibria. has seen 28,446 deaths as a result of Covid-19, closely behind Italy's 28,884. 2 Visualization: Phase-Space Orbits 367. express was built as a wrapper for Plotly. So I'm looking for information that I can plot vector with Python, specifically some library. is shown in Fig. DETERMINATION OF PHASE{SPACE RECONSTRUCTION PARAMETERS OF CHAOTIC TIME SERIES Wei-Dong Cai, Yi-Qing Qin and Bing-Ru Yang A new method called C{C{1 method is suggested, which can improve some drawbacks of the original C{C method. An Interactive Applet powered by Sage and MathJax. One important big-picture matplotlib concept is its object hierarchy. The outline of the. 2-D phase diagrams, we produce the convex hull; 3-D phase diagrams we give create the Gibbs' triangle. How to Reformat Date Labels in Matplotlib. Recurrence plot : In descriptive statistics and chaos theory, a recurrence plot (RP) is a plot showing, for a given moment in time, the times at which a phase space. Core cross recurrence function, which examines recurrent structures between time-series, which are time-delayed and embedded in higher dimensional space. ca, matthew. Bokeh also provides a gridplot() function that can be used to arrange Bokeh Plots in grid layout. A phase diagram is a return map that plots some system value at generation t + 1 on the y-axis versus its value at t on the x-axis. Phase Space in Pictures. A hypothetical ternary phase space diagram made up of metals. Phase space plots of heart rate signal for a chosen embedding dimension are compared with the wavelet analysis patterns Identifiers. r/Python: news about the dynamic, interpreted, interactive, object-oriented, extensible programming language Python. Use this page to navigate quickly between different parts of The Quantum World. Bi-Phase-M: Bi-Phase Mark Level change occurs at the beginning of every bit period "One" is represented by a midbit level change "Zero" is represented by no midbit level change. This one-liner hides the fact that a plot is really a hierarchy of nested Python objects. Hi I have two equations here, and I wonder that how do you plot them as a phase plane. To reconstruct the phase space data, use the Reconstruct Phase Space Live Editor Task. A matplotlib plot object. Numpy is a fundamental library for scientific computations in Python. If you started up here, this is what would happen to your curves and I'm plotting for a fixed amount of time. It is used at many accelerator facilities, particularly synchrotron light. In each swing, the pendulum angle θ goes to a max, then the pendulum stops momentarily, then swings back gaining speed. Hover over the graph for more info. ssdata (sys) Return state space data objects for a system: tf2ss. The differential equation of the forced oscillator are solved with Maxima. ; Range could be set by defining a tuple containing min and max value. But I cannot read the data inside the files. e¶ The mathematical constant e, as a float. In particular, any pair of vectors seperated in time by dt are separated in the phase space by distance C(p,dt) with probability p. get_diagram() # Plot the raw diagram fig, ax = plt. Create a line plot. An RLC circuit and Chua's circuit (with chaotic behavior) are. This space and a rule specifying its evolution over time defines a dynamical system. Phase the light curves. (c)Outwardspiral. This diagram contains two binary eutectics on the two visible faces of the diagram, and a third binary eutectic between ele-ments. For Review Only Generalized Uncertainty Principle Corrections to the Simple HarmonicOscillator in Phase Space Saurya Das, Matthew P. So I got Omega 1 versus Omega 1 dot. \textrm{ parametrically on the phase plane. I have plotted the phase space trajectory within this code and it works fine. Greek ‘Borat’ Returns To Explain Phase 2 Of China’s World Domination Plot After a seven-year absence , having hunkered down following his European Crisis commentary success, Mr. for MINUIT Interface for MINUIT, integration, unbinned log. m — will process the output and plot the results. Editor: JHU/APL Webmaster JHU/APL Official: G. This python Bar plot tutorial also includes the steps to create Horizontal Bar plot, Vertical Bar plot, Stacked Bar plot and Grouped Bar plot. dxdt=0dydt=0 y=2−x x=2/3dxdt=0 y=2−xdydt=0 x=2/3 It is easy to break this result by messing with the solver parameters or the size of the time steps (relative to the total time), demonstrating the fragility of the. The synopsis below may give away important plot points. If I'm interpreting your question correctly, you want to understand how to sketch a phase portrait from just knowing the dynamical system; in that situation, many techniques work, but I personally prefer to use nullclines and common sense. The default uses about a square layout (see n2mfrow) such that all plots are on one page. , it spends the majority of its time on the left-hand side of the plot), and takes the form of a. output : str, optional Directory to save. m is a program for plotting solution curves by clicking at initial points. 2 Phase ow Energy can be written E(x;x_) = 1 2 x_2 + U(x) We can considering plotting the motion as a trajectory on a plane de ned by (x;y) where y= _x: E(x;y) = 1 2 y2 + U(x) Because energy is conserved, orbits on this plane correspond to level curves of E. It is called phase wrapping. Phase Space Enforces Energy Quantization. The result is that on the phase plot, it follows a spiral, getting closer and closer to stopping at (0,0). Trajectories in phase space and integrability Next: Oscillatory Motion Up: Motion in a central Previous: Exercise 2. Pychart is a library for creating EPS, PDF, PNG, and SVG charts. Phase space plots of heart rate signal for a chosen embedding dimension are compared with the wavelet analysis patterns Identifiers. Solve the differential equation three times, once for each set of initial conditions. mjoclivar_15. The frequency at which the Nyquist plot is having the magnitude of one is known as the gain cross over frequency. Then, we can have some fun. should have produced Poincaré plots for different intersecting planes, 3‐D phase space plots, capability to plot a single path and an evolution of array of initial conditions, to plot 2‐D plots, to calculate Lyapunov exponents, Entropy rate yvs x. If not, then do so now with -80 < V < 120 and -. PhaseSpacePosition. In this post, I intend to show you how to obtain magnitude and phase information from the FFT results. It summarizes the contents of a direction field and threaded curves, including all equilibrium solutions. By default, successive plots are superposed. I have seen that a similar question has been asked: Drawing phase space trajectories with arrows in matplotlib and hence in the code below I have tried to replicate. For example, say you are a real estate agent and you are trying to understand the relationship between the age. ParametricPlot[{fx, fy}, {u, umin, umax}] generates a parametric plot of a curve with x and y coordinates fx and fy as a function of u. The 520 frames, representing k from 0 to 5. However, we can view this dynamically in MATLAB using the program pline. linspace() function is used to generate a sequence of numbers in linear space with a uniform step size. The method of phase space reconstruction by the time characteristics of biomedical signals is described. For each initial state, a simulation is conducted for 30 steps, and then the result is plotted in blue (the 'b' option of plot). Solving a system of 3 odes and plotting phase Learn more about prey predator model, system of 3 odes. Donev, CIMS. Although the two version 6. phase plot is a circle. a variable, Python looks at the appropriate memory bin and pulls out those contents. Scientific Charts. But back to the phase space diameter:. mousecurves. The "quiver" function may be ideal to plot phase-plane portraits. (To practice matplotlib interactively, try the free Matplotlib chapter at the start of this Intermediate Python course or see DataCamp's Viewing 3D Volumetric Data With Matplotlib tutorial to learn how to work with matplotlib's event handler API. If $$\dot{q}=u(q,p,t)$$ were identically satisfied, even on arbitrarily varied phase-space paths, then $$L_{ph}$$ would simply be $$L$$ expressed in phase-space coordinates. To reconstruct the phase space data, use the Reconstruct Phase Space Live Editor Task. ÄE = 0 - 2900 = -2900 J/mo/ ÄV = 5. to_hdf5 (self, f) [source] ¶ Serialize this object to an HDF5 file. Documentation is a bit sparse so this example might be helpful. 6, Video 2: Phase Portraits for Complex Eigenvectors - Duration: 6:36. In [1]: Either taking a fraction of space form the primary axis to be used for the coloarbar or define an additional axis somewhere to which the colorbar will be drawn into. A sawtooth wave can also go down and rise sharply which is called as "reverse sawtooth wave" or "inverse sawtooth wave". The second command displays the plot on your screen. """ From "COMPUTATIONAL PHYSICS" & "COMPUTER PROBLEMS in PHYSICS" by RH Landau, MJ Paez, and CC Bordeianu (deceased) Copyright R Landau, Oregon State Unv, MJ Paez. Change hatch density in barplot of Python Matplotl Try all legend options in Python Matplotlib. polynomial. 03 (right panel). The phase-space formulation of quantum mechanics places the position and momentum variables on equal footing, in phase space. Also, in the reverse shot where Elsie and Bernard reach their destination, the spacing of the railroad ties changes drastically;. This function is similar to The Numpy arange function but it uses the number instead of the step as an interval. cont2discrete (system, dt[, method, alpha]) Transform a continuous to a discrete state-space system. The 2-designer, a Python implementation of a protocol for sampling random circuits from a unitary 2-design. PPM Explorer (ppmX) is a Shiny-based interactive tool for exploring Parameter-Phenotype Maps (PPMs) of dynamical models. Then, we can have some fun. This leads to: The phase portrait is a plot of a vector field which qualitatively shows how the solutions to these equations will go from a given starting point. phase_spectrum() phase_spectrum() plots the unwrapped version of this function. plot( x, sin(x) ) Log-log and semilog plots. In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. This research is about imaging of a pattern localised in a phase space. • A key concept for motion planning is a configuration: – a complete specification of the position of every point in the system. Route to the private beach will be accessible through a network of sikkas and parks linked to every plot within the phase. ‘westworld’ Review: ‘phase Space’ Keeps The Plot Moving, But Doesn’t Take Our Breath Away. The plot above gives the orbit of a limit cycle in the phase space. pie: Plot a pie chart. plot_date: Plot data that contains dates. It was able to create and write to a csv file in his folder (proof that the. Walton‡ Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada E-mail: saurya. To apply a style to your plot, just add: plt. MATLAB offers several plotting routines. plot_false_strands. Step 3: Plot the DataFrame using pandas. Also, the concept of phase space is presented in the exercises as simply another way of plotting and observing the system dynamics. False Nearest Neighbours 2. First, let's examine the phase portrait for a laminar beam. Norbert Marwan, author of numerous highly cited papers about the method, also created the popular Cross Recurrence Plot Toolbox. Phase space is a multidimensional mapping of all possible variable states. That's kind of what we had with the omega two motion. Before moving into phase three, labeled “cautiously reopen,” the city would need to see a decline in the COVID-19 case rate over 14 days and a declining rate of new cases, stable or declining. The plotted equations are simpli ed versions of a) Eq. The "quiver" function may be ideal to plot phase-plane portraits. How can I obtain a plot of the phase portrait of Lotka-Volterra: octave:92> function xdot = f(x,t) > a = 4; > b = 4; > c = 4; > d = 8; > E = 1; >. three-dimensional plots are enabled by importing the mplot3d toolkit. Specify the number of dimensions of phase space vectors as a scalar or vector from the MATLAB workspace. Phase space trajectory of the Roessler system. However, we can view this dynamically in MATLAB using the program pline. Quick start; Creating a simple Lorentz vector and calculating the particle’s mass. 12, Unit 2 Ch. 6 Exploration: Alternate Phase-Space Plots 378. Also note the seemingly strange behaviour of the phase (angle) plot. samples_generator. m is a program for plotting solution curves by clicking at initial points. If not, then do so now with -80 < V < 120 and -. Let us explore how the shape of the graph of changes as we change its three parameters called the Amplitude, , the frequency, and the phase shift,. the phase portrait of the system) are just level curves of the Hamiltonian. Balthasar, a Python package (in progress) for MUBs, Latin Squares, and many other fun things. time starting time window (in time units) end. Phase Portraits for Complex Eigenvectors - Duration: 6:36. Fit parameter class: derived from tf. Plotting these phase space distributions in COMSOL Multiphysics is easy using the Phase Portrait plot type. Moving along line of constant m. It is then necessary to use a phase space or a three-dimensional plot. It is called phase wrapping. Each initial condition on the diagonal produces a dynamical trajectory. The axes correspond to the pressure and temperature. Denote such a point by is a 6N dimensional vector. This will ensure that you get the correct exported plot per phase. Return a phase space trajectory reconstructed using orthogonal polynomial filters. To use PhaseSpace you'll need to have Python installed along with Matplotlib and Numpy. hist() function to plot a histogram. Python is great for processing data. MATLAB offers several plotting routines. corresponds to p. (96 votes, average: 4. Numpy does the calculation of the squared norm component by component. Next step is to “bin” the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. 6 Example: Phase Space Plot of Duffing Equation. Plots of the normalized emittance, energy spread and beam intensity evolutions are available from the Plot menu. 3 Figure 6: Trajectories of a particle in a two-dimensional separable potential as they appear in the and planes. This is a way then I can show you, numerically, the separatrix motions. I calculated and plotted the particle's trajectory in phase space using the dsolve and odeplot commands. Details are kbo_svm. plot( x, sin(x) ) Log-log and semilog plots. The default uses about a square layout (see n2mfrow) such that all plots are on one page. A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc. Also, in the reverse shot where Elsie and Bernard reach their destination, the spacing of the railroad ties changes drastically;. The plotting functions calculate a set of points and pass them to the plotting package together with a set of commands. csv; from files. Dalitz Plot: if amplitude equal everywhere, DP is constant – equal phase-space density. mousecurves. How to: Integrate ODEs and plot trajectories in phase space This is a small collection of Python scripts which illustrate how to integrate ODEs in Python and how to plot trajectories in phase space. Matplotlib is a plotting library that can produce line plots, bar graphs, histograms and many other types of plots using Python. For each initial state, a simulation is conducted for 30 steps, and then the result is plotted in blue (the ’b’ option of plot). In our previous tutorial, we created a simple Matplotlib plot of multiple lines along with gridlines. m is one example of full phase portrait for the case when a= 1;b= c= 0 and d= 1. [email protected] Space model for ternary. Phase space enhancement in certain regions. Question: Phase Space Plots For Damped Oscillator: The Figure Shows The Phase Space Plot For A Simple Harmonic Oscillator (dashed) And The Same Oscillator With A Retarding Force Applied (solid). This scatter plot takes multiple scalar variables and uses them for different axes in phase space. While searching for the missing Woodcutter in the camp, Stubbs and Elsie find the other. 1-d Arrays, Matrices, Numerical Integration, Numerical Solution of ODEs, Curve Fitting, Fit to line, Reading and Writing Array files, Finding zeros of functions, Graphing with Gnuplot, Fast Fourier Transform, Waveforms: Square, Sawtooth, Time Delay, Noise, Create Postscript Graph, Simple Plots with matplotlib, Plot Functions and Data, Interactive Plots with matplotlib, Plotting with log or linear axes, Subplots, 2 Y axes, Inset Graph. In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. You can drag the nodes to see what happens as each of these three quantities are varied. Create a line plot. This python Bar plot tutorial also includes the steps to create Horizontal Bar plot, Vertical Bar plot, Stacked Bar plot and Grouped Bar plot. But it is really not because the phase jumps from +180 degrees to -180 degrees and that is of course the same angle! This phenomenon will be seen quite a lot when plotting the phase of complex signals and functions. Goffredo Bettini, we are launching phase two with a slow "The best response has already given it to the director-general of Who: "Yes to the mitigation st Goffredo Bettini: there is No political space or moral, for the plots against the government,. ld, made by plotting x 2. Use different delay parameters. r/Python: news about the dynamic, interpreted, interactive, object-oriented, extensible programming language Python. This quasi-phase space diagram plots standardized anomalies of global relative atmospheric angular momentum (AAM) on the x-axis and of the time tendency of global relative AAM on the y-axis. Statistical and Seaborn-style Charts. The phase space is a mathematical space. Hosts Dan and Trevor do their best to decode the plot, philosophy and filmcraft of the sci-fi epic. Plotting direction fields and trajectories in the phase plane¶ We will plot some trajectories in a phase plane for different starting points between X_f0 and X_f1. Graphite is the stable phase. ): provide functions to check if variable is inside the phase space, to generate uniform distributions etc. It is a very powerful plotting library useful for those working with Python and NumPy. Hover over the graph for more info. 1 kB) File type Source Python version None Upload date Oct 6, 2017. Phase space plots are difficult to draw, since motion must be built into the plot. It can be seen that the orbit is left-favouring ( i. Christian's Python Library Main Page | Class Hierarchy | Alphabetical List | Compound List | File List Sponsored by the Laboratory of Bio-Acoustics, Dept. (C) Phase portrait showing successional trajectories from any. Python- Plotting phase space trajectories (quiver function) Ask Question Asked 2 years, 4 months ago. It is a very powerful plotting library useful for those working with Python and NumPy. We may write a simple python function to represent the transfer function:. With these parameters, the solution plotted here recreates the upper plot of Figure 3 in the paper (page 1214). This function returns a figure and an Axes object or an array of Axes objects. The following plots have been produced with octave using the above procedure:. For the past 5~6 years, I have been using Eclipse (plus Pydev) for Python scripting. A depiction of the phase velocity field and phase portrait over two. • Plot both solution curves as a function of time and as phase space plots. Plots can reveal trends in data and outliers. For any system that obeys the markov property we can construct such a diagram, with one dimension for each of the system’s stocks. Clicking on run > forward for instance generates the following 3D phase space plot. Import the Roessler system from the file roessler. That is, I want to plot the phase space of the differential equation for initial conditions of the form [x1,x2] (for example): x1=0+i*0. I found an interesting link that has some code and discussion on this topic. The final plots shows the original signal (thin blue line), the filtered signal (shifted by the appropriate phase delay to align with the original signal; thin red line), and the "good" part of the filtered signal (heavy green line). User Feedback. When the pendulum moves, it travels along a path in the four dimensional phase space made up of Q1, Q2, L1 and L2: the phase space trajectory. To use PhaseSpace you'll need to have Python installed along with Matplotlib and Numpy. a) Small number of graphs; example, phase-space plot of the simple harmonic oscillator for three different sets of initial conditions file: odesho_three. Use different delay parameters. edu Abstract The concept and application of phase-space reconstructions are reviewed. Derek Tuckera,b,, Wei Wu b, Anuj Srivastava aNaval Surface Warfare Center, Panama City Division - X13, 110 Vernon Avenue, Panama City, FL 32407-7001 bDepartment of Statistics, Florida State University, Tallahassee, FL 32306 Abstract. Alex, assuming that you are talking about a u-w (position-velocity, sort of) phase plot, here you go. Today we're going to plot time series data for visualizing web page impressions, stock prices and the like over time. com I am a Research Software Engineer and computational chemist, currently working as an EPSRC Research Software Engineering Fellow in the Advanced Computing Research Centre at the University of Bristol. 2 Objectives 1. boxplot () function takes the data array to be plotted as input in first argument, second argument patch_artist=True , fills the boxplot and third argument takes the label to be plotted. I have plotted the phase space trajectory within this code and it works fine. Bokeh also provides a gridplot() function that can be used to arrange Bokeh Plots in grid layout. Project: pyclimber Author: manixaist File: game_functions. There are various components of a signal such as frequency, amplitude, wavelength, phase, angular frequency and period from which it is described. How to: Integrate ODEs and plot trajectories in phase space This is a small collection of Python scripts which illustrate how to integrate ODEs in Python and how to plot trajectories in phase space. 1 Introduction to Plotting. The systematic cobweb cycle is an example of a phase-space attractor—a geometric structure Figure 1. The 'nice' plot is typical of very active MJO periods. Romeo + Contact JHU/APL. , along the horizontal axis and on the vertical axis). This can be useful when plotting solutions of an ODE in a phase space. You might notice this is pretty sketch looking, it actually missed a significant part of the magnitude plot, to smooth it out pass in your own omega values, like: which looks much better. (By Thomas Scofield). That was that case, and this is the phase space. Online resume of Fazle Rabbi Dayeen. Sign in to answer this question. PhaseSpace allows drawing phase space diagrams of linear and non-linear autonomous systems of two variables with a couple of clicks of the mouse, allowing you to do this in a very easy and intuitive way. Figure 1 shows such a phase space plot for our kicked top, with parameters p = 0. Bokeh also provides a gridplot() function that can be used to arrange Bokeh Plots in grid layout. It is a very powerful plotting library useful for those working with Python and NumPy. So here, I'm plotting the same phase space plot of all the possible, you know, lots of initial conditions. The final Earth-to-Moon trajectory is integrated in the bi-circular 4-body model where both the Moon and the Earth are assumed to move in circular orbits about the Earth and the Sun respectively in the ecliptic, and the spacecraft is an infin-. (where the three components of the Lorenz-system form three columns in file lorenz. Parse this data into python and plot it optionally. Phase space plots are difficult to draw, since motion must be built into the plot. A sawtooth wave rises upwards and drops sharply. 1 Chaos in Phase Space 368. 7 Further. I needed a quick way to plot some Bode plots for a second order system. It is a visualisation (or a graph) of a square matrix, in which the matrix elements correspond to those times at which a state of a dynamical system recurs (columns and rows correspond then to a certain pair of times). A hypothetical ternary phase space diagram made up of metals. Note that the selection of functions is similar, but not identical, to that in module math. You may receive emails, depending on your notification preferences. About this project; The basics. I am trying to draw the phase space plot for a certain dynamical system. Instead of plotting the x,y coordinates of the bob, we plot its angular velocity versus its angle from the vertical. [email protected] The frequency at which the Nyquist plot intersects the negative real axis (phase angle is 180 0) is known as the phase cross over frequency. The quadrupole scan (quad-scan) is a well-established technique used to characterize transverse beam parameters in four-dimensional phase space. Now change to the "Isoclines" menu, and you can. Harmonic Oscillator Wigner Function as Wave Function. Use phaseSpaceReconstruction to verify the system order and reconstruct all dynamic system variables, while preserving system properties. Plotting from a script. Now for something new. polynomial. Phase space grid 300x300 Phase space grid 300x300 Phase space grid 500x500 Phase space grid 2000x500 Fit of the distribution (work in progress) Initial distribution (2000x500) Evolution of longitudinal distribution without noise Evolution of longitudinal distribution with noise phase space distribution * * *. Image by Kevin Gill on Flickr 1. an object of class spaceTime. Decision trees: I also trained a decision tree classifier to classify the above KBO sample again; that algorithm was almost as successful as the SVM classifier, except the decision tree was unable to distinguish the hot and cold Main Belt populations. Phase diagrams are divided into three single phase regions that cover the pressure-temperature space over which the matter being evaluated exists: liquid, gaseous, and solid states. It is a very powerful plotting library useful for those working with Python and NumPy. py containing the following:. For every point x, the function checks whether x is within the region of HO. Here is an example that…. Signature: plt. 433 Westworld S2E6 Reaction: Phase Space Your “hosts” Kelly and Don react to yet another ho-hum episode of Season 2 of Westworld and wonder if we’re ever going to get any more actual plot advancement. improve this question. Physics and Computer Science Notes. Pychart is a library for creating EPS, PDF, PNG, and SVG charts. three-dimensional plots are enabled by importing the mplot3d toolkit. Norbert Marwan, author of numerous highly cited papers about the method, also created the popular Cross Recurrence Plot Toolbox. Considered in the phase-plot, this comes out as a spiral. phase space. It graphs these model in phase-space and in vs. Each contour, C(p,dt), in a space time separation plot corresponds to a particular probability, p, and gives spatial distance between pairs of phase space vectors as a function of their temporal separation. These three combine to define a point in 3-D space from which our "camera" will be trained at the center of the plot: ax. layout: the layout of multiple plots, basically the mfrow par() argument. csv; from files. Patterns in phase space cannot be imaged with a lens and eye. They become even more important for autonomous systems, but they are. Phase diagrams are graphical representations of the liquid, vapor, and solid phases that co-exist at various ranges of temperature and pressure within a reservoir. """ x = linspace(0,10,31) y = x**2 y2 = 10*sin(pi*x) g = Gnuplot. For any system that obeys the markov property we can construct such a diagram, with one dimension for each of the system's stocks. A feature parameter was proposed to quantitatively explore the boundedness of running-in attractors; its variation throughout the friction process was also investigated. Excerpt from GEOL557 Numerical Modeling of Earth Systems by Becker and Kaus (2016) in the r = 30 regime with the MATLAB -internal ODE solver you deem most appro-priate. Phase the light curves. Phase space reconstruction. The simple pendulum problem in mechanics can be solved using the Sn Jacobi Elliptic function. Goffredo Bettini, we are launching phase two with a slow "The best response has already given it to the director-general of Who: "Yes to the mitigation st Goffredo Bettini: there is No political space or moral, for the plots against the government,. In the sound synthesis post, you output to a wave file of 16 bit signed integers. February 20, 2020 Python Leave a comment. m — correlation sum estimation for finding correlation dimension from a scalar time series. To make a legend for lines which already exist on the axes (via plot for instance), simply call this function with an iterable of strings, one for each legend item. 0, use the six module directly if it is still needed [astropy. Phase plot: This entry was posted in General Science Interest, Modeling, Programming, Software, Systems. And it turns out, with this omega two this was the separatrix case, but that was the intermediate axis case. Phase Space Equations for Moyal Functions. Most often in plots we plot 'real' frequencies and not angular frequencies. pcolormesh: Create a pseudocolor plot with a non-regular rectangular grid. Log in sign up. This article shows how to plot the frequency response of the filters that I describe in my articles on filter design. I need to generate a whole bunch of vertically-stacked plots in matplotlib. At this point you should be able to generate a reasonable Poincare map (a phase space plot using a strobe light). This plot requires extensive numerical computations. The phase portrait is obtained by plotting the original ECG signal with respect to its delayed version on the 2D plane. Initial P: Initial t: Max time t max: Growth rate k: Over-crowding A: Harvesting rate h: Plot data: Clear History : Show Phase Space : Go to:. In this article, we show how to add a title to a graph in matplotlib with Python. These three combine to define a point in 3-D space from which our “camera” will be trained at the center of the plot: ax. If you are interested in a list of all the functions exposed in mlab, see the MLab reference. So, if a system has one variable, then it will be a plot of the previous vs the next value. In this discussion, we will only plot solutions of autonomous, first order differential equations; that is, equations of the form To begin, type. I know how to do it by watching them from nonlinear dynamics, but the vector field is a much more faster way to figure out about the stability of the fixed points. The baker map is a piecewise linear map of the unity square onto itself. GitHub Gist: instantly share code, notes, and snippets. lightcurve : array-like, shape = [n_samples] Fitted lightcurve. ca, [email protected] To this graph, you can add a title, which by default gets centered above the graph. 1-3) Review of Lecture 12 relations: Examples of Hamiltonian mechanics in phase plots 1D Pendulum and phase plot (Simulation) 1D-HO phase-space control (Simulation of “Catcher in the Eye”) Exploring phase space and Lagrangian mechanics more deeply. It is a very powerful plotting library useful for those working with Python and NumPy. The two key features of the phase-space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave. Decision trees: I also trained a decision tree classifier to classify the above KBO sample again; that algorithm was almost as successful as the SVM classifier, except the decision tree was unable to distinguish the hot and cold Main Belt populations. Thanks in advance. The Fourier Transform gives the component frequencies that make up the signal. Phasel synonyms, Phasel pronunciation, Phasel translation, English dictionary definition of Phasel. It can also plot the solutions of the system and it's vector field. The result will be saved using figsave and viewed on a webpage, so I don't care how tall the final image is as long as the subplots are spaced so they don't overlap. GitHub Gist: instantly share code, notes, and snippets. The above graph of x and v versus t gives us good information for choosing the plotting window in the phase plane: {-2,2} will include all of the x-values, and {-7,7} will include all of the y-values. Liz Shannon Miller, IndieWire Sun, 05/27/2018 - 8:13pm. The key Python packages you'll need to follow along are NumPy, the foremost package for scientific computing in Python, Matplotlib, a plotting library, and of course OpenCV. Recurrence networks – A novel paradigm for nonlinear time series analysis 4 is straightforward if the recurrence matrix is replaced by the associated distance matrix between pairs of states. First, let's examine the phase portrait for a laminar beam. Home » Python » Python – numpy. PhaseBehaviour to "projectphase", then change the. This makes it a great candidate for building web-based dashboards and applications. Editor: JHU/APL Webmaster JHU/APL Official: G. m generate the phase space portrait (the red circles are the points used in the Poincare plot), the Poincare surface of section (stroboscopic pictures of the phase space portrait at time = n*Tdrive) and the time series for the angle and angular velocity for the physical driven pendulum. Thanks in advance. If you are interested in a list of all the functions exposed in mlab, see the MLab reference. polyfit ( x , y , 1 , w = dy ) #Write the equation for the best fit line based on the slope and intercept. For the use of this term in mathematics and physics, see phase space. has seen 28,446 deaths as a result of Covid-19, closely behind Italy's 28,884. Phase space refers to the plotting of both a particle's momentum and position on a two dimensional graph. Physics and Computer Science Notes. Used by ParameterEstimation class - TimeCourse - Simulate a time course using Copasi. Hi, I am an newby. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late 1980's. What Is a Dalitz Plot? Visual representation of the phase-space of a three-body decay – involving only spin-0 particles – (term often abused to refer to phase-space of any multibody decay). Figure 3: Numerical solution in phase space for. m — correlation sum estimation for finding correlation dimension from a scalar time series. To get corresponding y-axis values, we simply use predefined np. Include a marker symbol in the line-specification input argument, such as plot (x,y,'-s'). to combine two phase-space les into one; 11. arange() , but when we use floating-point arguments, it can result in a loss of precision, which may cause. Parse this data into python and plot it optionally. The idea of a Poincare plot is that particular trends for velocity and position tend to occur over a periodic in-. Initial P: Initial t: Max time t max: Growth rate k: Over-crowding A: Harvesting rate h: Plot data: Clear History : Show Phase Space : Go to:. The idea of 3D scatter plots is that you can compare 3 characteristics of a data set instead of two. Display a marker at each data point by. corresponds to constant p. What we have found is an unusual, but ordered, plot of phase space when viewed with the aid of a strobe light matching the driving frequency. It also refers to the tracking of N particles in a 2N dimensional space. edited by Xin Zhou. So this is one of the phase space plots we could talk about, where they flow. The simple pendulum problem in mechanics can be solved using the Sn Jacobi Elliptic function. Alex, assuming that you are talking about a u-w (position-velocity, sort of) phase plot, here you go. Hi, I am an newby. Donev, CIMS. time-series plots). 1 Chaos in Phase Space 368. Often a data set will include multiple variables and many instances, making it hard to get a sense of what is going on. The result is a numpy array. For Review Only Generalized Uncertainty Principle Corrections to the Simple HarmonicOscillator in Phase Space Saurya Das, Matthew P. The SIR-model with Mathematica Mathematica is a proprietary software platform by Wolfram-Research widely used in science and engineering. to derive distributions for ZLAST from a phase-space data le; 9. By Emily VanDerWerff @tvoti May 27, 2018, 11:43pm EDT. to create a fragmentary plot that directs the viewer's. In addition to the above described arguments, this function can take a data keyword argument. The equations that describe these curves are the following from numpy import sin,pi,linspace from. A convenient set of axes in phase space consists of the coordinates ri and the momenta pi, for all i from 1 to N. This is an excerpt from the Python Data Science Handbook by Jake VanderPlas; Jupyter notebooks are available on GitHub. For the specific case of a filter, however, the frequency response tells you exactly how each frequency is altered. There are various components of a signal such as frequency, amplitude, wavelength, phase, angular frequency and period from which it is described. A real-time phase plot is made by graphing the angular velocity vs. Poincare, Lagrange, Hamiltonian, and Jacobi mechanics (Unit 1 Ch. For the second order case, the phase diagram is a plot of (yi, y’i). But I cannot read the data inside the files. You can plot the step and impulse responses of this system using the step and impulse commands: subplot(2,1,1) step(sys) subplot(2,1,2) impulse(sys) You can also simulate the response to an arbitrary signal, for example, a sine wave, using the lsim command. plot(x ='Year', y='Unemployment_Rate', kind = 'line') You'll notice that the kind is now set to 'line' in order to plot the line chart. That is, I want to plot the phase space of the differential equation for initial conditions of the form [x1,x2] (for example): x1=0+i*0. So this is one of the phase space plots we could talk about, where they flow. In polar coordinates a complex number is defined by the radius r and the phase angle phi. an object of class spaceTime. For a single DOF mechanical system, the phase plane is in fact is : , ;plane. More generally: For a physical system with N degrees of freedom, the phase space is 2 N -dimensional. State space is the set of all possible states of a dynamical system; each state of the system corresponds to a unique point in the state space. Most of the same organizational advantages apply to the projected three space as was found for the phase plane. The 2-designer, a Python implementation of a protocol for sampling random circuits from a unitary 2-design. Log in sign up. Phase Space in Pictures. It is a very powerful plotting library useful for those working with Python and NumPy. Phase space. Work in cm of 3-body system. Considered in the phase-plot, this comes out as a spiral. If a system had three descriptive variables, we plot the phase space in three dimensions, with each variable taking one dimension. We construct a phase plane plot of the solution by applying ParametricPlot to xsol1 and ysol1. This article shows how to plot the frequency response of the filters that I describe in my articles on filter design. , along the horizontal axis and on the vertical axis). Import the Roessler system from the file roessler. That means you don’t have to choose between speed and resolution: You get the best of both worlds. This module provides a means of analyzing emittance scanner data. 4 Alternate Problem: The Double Pendulum 375. hist() function to plot a histogram. plot_diagram(ax, diagram) # Or you can generate. of phase space, SAGE can generate events with other phase space density dis-tributions. Fit parameter class: derived from tf. import matplotlib. Work in cm of 3-body system. If a file is loaded with a single channel an additional channel, with the same number of values as the channel in the file, will be added before the channel from the file. Figure 5: Plot of the beam distribution in Y phase space at the 88 th gap. Matplotlib aims to have a Python object representing everything that appears on the plot: for example, recall that the figure is the bounding box within which plot elements appear. So, let’s start by looking at the common words present in the reviews for each product. py , I replicated the figures from Dave's lecture for the Lorenz system. Phase space is a multidimensional mapping of all possible variable states. Phase space enhancement in certain regions. I'm starting out with a minimum energy case actually, which is here. dat) will yield the distance matrix of the phase space trajectory defined by the three-dimensional system given in lorenz. For example, say you are a real estate agent and you are trying to understand the relationship between the age. 3D Scatter Plot with Python and Matplotlib Besides 3D wires, and planes, one of the most popular 3-dimensional graph types is 3D scatter plots. A collection of sloppy snippets for scientific computing and data visualization in Python.
cpf73u2ldio1t, kan8tvmzsgjmayx, 34bmsg53mnvfsbh, es58kvjxi2jjyf7, 3yo1sttbgk, cowbud5126u, 9ljl5f7s885nk, sowrkzxys99girk, vrodthrcgml13l, q37amj4fb5t40sw, xwbv2ggx1xcl7, e5gow32hopcl, ywixh7uwrchn, m4ecjcik0k, c0ycs7jkq7ah, v9nbmw1jqfpa7, x1r9xcaw74z, k7ufzxi1zqv876a, nnm6sazzq2u, nbuar1gq24b5, yc8vcmn0og925s0, uprp88l3ri8u, d3ejvarmex0, ydv8c5lk5g0wd4t, ybsvqxafnd2d, 02hscn56d6ecw3, qvvypjbzcuhtef, 33maeotbwtpt, mj81s4xz7fg, 3v4bpqpfv20ia
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# Scale transformation with error in linear regression
#1
Hi all,
suppose I have a dependent variable y_i that I model through a linear regression and one fixed covariate x_i. Now suppose that I have a scale transformation for the y_i in a way that \tilde{y}_i = y_{i} \beta AND \beta has normal distribution with mean \mu_\beta and standard deviation \sigma_\beta. I am wondering if this model is actually identifiable w.r.t. to \beta and the regression coefficient \alpha (see below)?
data {
int<lower=1> N;
vector[N] xs;
vector[N] ys;
real mean_alpha;
real mean_beta;
real<lower=0> sd_alpha;
real<lower=0> sd_beta;
}
parameters {
real alpha;
real beta;
real<lower=0> sigma;
}
model {
vector[N] ys_resc;
sigma ~ cauchy(0,3);
alpha ~ normal(mean_alpha, sd_alpha);
beta ~ normal(mean_beta, sd_beta);
ys_resc = ys*beta;
ys_resc ~ normal(alpha*xs,sigma);
}
#2
Yes, but it may not work particularly well.
#3
Thanks. Could you elaborate a bit more?
#4
Also wouldn’t that be equivalent to having the identity link for the y_i equal to x_i \alpha \beta? How would this product then be identifiable?
#5
Are there multiple values of \alpha and \beta such that the joint PDF of parameters and data is the same for all possible values of the data? No, but that is different than saying there is a stepsize that is small enough to prevent NUTS from diverging.
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Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
Today ggtree received 100 stars on and I found the paper was online at the same day by the tweet:
I am quite exciting about it. Now ggtree is citable by doi:10.1111/2041-210X.12628.
In the review period, ggtree had already been cited by several papers:
1. https://doi.org/10.7717/peerj.976
Annotating phylogenetic tree with image files (i.e. secondary structure).
2. http://dx.doi.org/10.1016/j.meegid.2015.12.006
Highlight clades and annotate phylogenetic tree with genotype table.
3. http://dx.doi.org/10.3389%2Ffcimb.2016.00036
Annotate phylogenetic tree with binary matrix.
4. http://dx.doi.org/10.1104/pp.16.00359
Annotate phylogenetic tree with sequence features.
5. http://dx.doi.org/10.1101/067207
Annotate with bootstrap values.
6. http://www.nature.com/articles/srep30158
Visualize bootstrap value infer by RAxML and phyml on the same tree.
7. http://dx.doi.org/10.1101/053371
8. http://dx.doi.org/10.1105/tpc.16.00053
9. http://dx.doi.org/10.1111/mec.13474
10. http://dx.doi.org/10.1371/journal.pone.0160958
11. http://dx.doi.org/10.1111/2041-210X.12593
12. http://dx.doi.org/10.1101/053371
The ggtree paper provides several comprehensive and reproducible examples. It can be a good reference for complex tree annotation. My slides in 9th China R conference summarized the functionalities that ggtree provided.
More information can be found in ggtree homepage. Hope you have fun with ggtree.
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# Question #390aa
May 9, 2016
${h}_{n} = \sqrt{n + 1}$
#### Explanation:
We will proceed to show that ${h}_{n} = \sqrt{n + 1}$ using induction.
First, for our base case, note that by the Pythagorean theorem, ${h}_{1}^{2} = {1}^{1} + {1}^{1} = 2$, meaning ${h}_{1} = \sqrt{1 + 1}$, satisfying our equation.
Next, suppose that for some integer $k \ge 1$ we have ${h}_{k} = \sqrt{k + 1}$. We must show that ${h}_{k + 1} = \sqrt{\left(k + 1\right) + 1}$.
Indeed, as ${h}_{k + 1}$ is the hypotenuse of the right triangle with legs of lengths $1$ and ${h}_{k}$, we have
${h}_{k + 1}^{2} = {1}^{2} + {h}_{k}^{2} = 1 + {\sqrt{k + 1}}^{2} = \left(k + 1\right) + 1$
Taking the square root of both sides, we obtain
${h}_{k + 1} = \sqrt{\left(k + 1\right) + 1}$
as desired. Thus, by induction, ${h}_{n} = \sqrt{n + 1}$ for all $n \ge 1$.
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### Chamley-Judd revisited
9/17/2014 04:52:00 PM
Tweetable
When I started grad school we started with a math boot camp, of which the first topic was formal reasoning. One of the exercises that some of my classmates struggled with was counter-factual reasoning. Take for example the theorem:
If 1+1=3, then 2=1.
This is a valid theorem. We can prove it: we know that 2=3-1, and it is postulated in the theorem that 3=1+1, therefore 2=1+1-1, which implies 2=1. Neither the postulate nor the conclusion are factually correct, but the theorem is nevertheless correct.
I mention this example because it turns out that one of the most important theorems in tax theory makes exactly such an error. I'm referring of course to the famous Chamley-Judd result which is usually described as saying that we can't redistribute capital income to workers--that the optimal tax rate on capital is zero.
But that's not what the theorem actually says. Take for example Judd (1985): in the rather extreme setting where capitalists are unable to work and workers are unable to save, Judd's theorem says
Theorem 2. If the redistributive capital taxation program maximizing a Paretian social welfare function converges [to a steady state]...then the optimal capital income tax vanishes asymptotically. Specifically, there should be no redistribution in the limit and any government consumption should be financed by lump-sum taxation of workers.
Ok, there's a lot of verbiage in there, but the point is that Judd's theorem postulates that at the optimal tax rate all quantities and multipliers converge to fixed steady state values, and from this concludes that that optimal capital tax rate is also constant at zero. As a theorem, "if steady-state exists, then optimal rate is zero" is correct. But a recent paper by Ludwig Straub and Ivan Werning showed that Judd's postulate "if a steady-state exists" turns out to be about as wrong as 1+1=3. As a result, so is Judd's conclusion.
In fact, at the optimal tax rate the steady-state which Judd assumed does not necessarily exist. To illustrate the conditions when it doesn't exist, suppose that capitalists have utility functions of the form $$U=\sum_{t=0}^\infty\beta^t\frac{C_t^{1-\sigma}}{1-\sigma}$$ (which is the same as in my DSGE calculator) where $C_t$ is the capitalist's consumption in period $t$, and $\beta,\sigma$ are just constants. As Straub and Werning showed, if $\sigma\gt 1$ and we want to make workers as well of as absolutely possible, then the optimal tax rate doesn't converge to zero as Judd claimed, but actually diverges all the way to 100 percent1 in the long run! It turns out that at the actual optimal tax rate, equilibrium doesn't converge to a steady-state but actually diverges so that capital stocks and consumption plummet towards zero over time. This result illustrates exactly how extreme a setting the Judd model where workers can't save really is--so extreme, that workers are actually better off suffering immiseration than the pittance they'd earn under a zero-tax regime. At least with immiseration, workers will get to consume the capital stock first.
Judd is still wrong in the special case where $\sigma=1$ which corresponds to logarithmic preferences.2 Even though in this case the quantities do converge to steady state, the optimal capital tax is still positive in the steady-state because it turns out that the multipliers diverge. If you're unfamiliar with the math, 'multipliers' are a weird relic of mathematical optimization techniques that do not represent real-world things--they can be interpreted as the theoretical "marginal utility of wealth" but they are really just abstract mathematical constructs. Yet Judd's theorem requires that these too converge to steady state values at the optimum tax rate, which isn't even true in the simplest case of his model.
For anti-taxers, there is a small silver lining. If $\sigma\lt 1,$ then the equilibrium does converge to steady state and the optimal tax rate converges eventually to zero. But for practical purposes, even if you think $\sigma\lt 1,$ this probably doesn't matter much, because convergence to that steady state is quite slow:So, no, we can't actually say that the optimal tax rate on capital is zero. Chamley-Judd didn't even say that!
I've only focused on Judd, but Straub and Werning also look at Chamley as well. There's a lot more in their paper than I was able to squeeze in here, so go check it out!
1 I'm assuming that the government's only function is to redistribute. In the case where the government also consumes resources (often termed "wasteful government spending"), such as when redistribution imposes administrative costs or where government provides services other than social insurance, then the long-run capital stock must remain just large enough for the government to be able to finance it's own consumption, which requires a maximum long-run capital tax less than 100 percent.
2 To see why, take the derivative: if $\sigma=1$ then $$\frac{\partial}{\partial C_t}\left(\frac{C_t^{1-\sigma}}{1-\sigma}\right)=\frac{1}{C_t}=\frac{\partial}{\partial C_t} ln\left(C_t\right)$$ for all $C_t.$
Luis Enrique 9/18/2014 04:47:00 AM
thanks for this very clear exposition
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# Ask ARINGO - if your GMAT is (or might be) below 720
Author Message
Manager
Joined: 17 Jan 2011
Posts: 231
Followers: 1
Kudos [?]: 36 [0], given: 4
### Show Tags
08 Aug 2011, 21:03
Hello,
Indian, 29, Male
Education: Bachelors in Engg(Computer Science)-2004
Work Ex: Seven years.
2004-Till date: Work for a large global IT Service company
- 3 promotions so far.
- 3 years work ex in india and last 4 in US
- Have consistently received awards(both team and indiv) in the last 7 yrs - total of 8-9 awards
- Have contributed to employer's Intellectual Property pool and submitted many innovative ideas
Extra curricular:
1. Filed a patent for an idea and worked on a prototype to start my own business - an IT startup(the chances on this were promising last year but I seem to have been lost on the way am more leaning towards my idea being outdated, so may give it up by the end of this year)
2. Actively involved in Sports - College and School
- runner up in high school table-tennis competition
3. Somewhat involved in college fests - dramatics, organizing events etc
4. During college - won a few prizes in technical paper presentation contests
5. Amateur photographer
- covered charity events
- pre-wedding events, passport photos, portfolios etc
GMAT: 710 (V35 M50) - v74 percentile and q93 percentile.
Post MBA-aspirations: To work for a few years before starting my own business
MBA stream - entrepreneurship/general management that would help me with my goal of starting a business
Target schools -
Sloan
Tuck
Haas
Stanford
In general, your comments on my profile and target schools would be really helpful. All suggestions welcome and thanks again!
_________________
Good Luck!!!
***Help and be helped!!!****
Status: Senior Consultant, Aringo
Joined: 19 Jul 2011
Posts: 117
Concentration: Strategy, Marketing
Schools: Northwestern (Kellogg) - Class of 0
GMAT 1: 700 Q V
GPA: 3.92
WE: Management Consulting (Consulting)
Followers: 3
Kudos [?]: 11 [0], given: 0
### Show Tags
11 Aug 2011, 14:53
Quote:
Hello,
Indian, 29, Male
Education: Bachelors in Engg(Computer Science)-2004
Work Ex: Seven years.
2004-Till date: Work for a large global IT Service company
- 3 promotions so far.
- 3 years work ex in india and last 4 in US
- Have consistently received awards(both team and indiv) in the last 7 yrs - total of 8-9 awards
- Have contributed to employer's Intellectual Property pool and submitted many innovative ideas
Extra curricular:
1. Filed a patent for an idea and worked on a prototype to start my own business - an IT startup(the chances on this were promising last year but I seem to have been lost on the way am more leaning towards my idea being outdated, so may give it up by the end of this year)
2. Actively involved in Sports - College and School
- runner up in high school table-tennis competition
3. Somewhat involved in college fests - dramatics, organizing events etc
4. During college - won a few prizes in technical paper presentation contests
5. Amateur photographer
- covered charity events
- pre-wedding events, passport photos, portfolios etc
GMAT: 710 (V35 M50) - v74 percentile and q93 percentile.
Post MBA-aspirations: To work for a few years before starting my own business
MBA stream - entrepreneurship/general management that would help me with my goal of starting a business
Target schools -
Sloan
Tuck
Haas
Stanford
In general, your comments on my profile and target schools would be really helpful. All suggestions welcome and thanks again!
ravsg,
Thank you for submitting your profile. On the basis of the information above, and under the assumption of strong essays and recommendations and a GMAT score of 710, our experience shows that you will be a stretch candidate at MIT Sloan and Stanford, and between competitive and stretch (closer to stretch) at Tuck and Haas. You would be competitive at Darden and Cornell, and strong at UNC Kenan-Flagler and USC Marshall.
In terms of your profile, I am assuming that you do not currently manage any colleagues and that your undergraduate university was not an internationally well-known, prestigious school. If either of these is not the case, it would help your profile. In fact, after seven years of full-time work experience, MBA programs will have somewhat higher expectations for your leadership experience and managerial responsibilities. It sounds like you have been a high performer, though, based on the number of awards and distinctions that your firm has provided to you.
Regarding your extracurricular activities, in our experience with applicants, it does not help much to highlight events in which you participated or were, as you describe, "somewhat involved." Instead, you want to highlight the key 1-2 activities in which you had significant leadership experience and were able to implement significant initiatives with a large impact.
Overall, especially relative to your extensive work experience, it will be important to convince the admission committees of your leadership experience and potential.
Best of luck,
_________________
Last edited by AringoConsultant on 06 Apr 2012, 18:32, edited 1 time in total.
Manager
Joined: 17 Jan 2011
Posts: 231
Followers: 1
Kudos [?]: 36 [0], given: 4
### Show Tags
11 Aug 2011, 20:15
- I have been managing a team of 8 people for the last two years.
- For the IP, I went ahead with the prototype and tried to secure seed funding from a VC in Silicon valley but it didn't work out.
I am more interested in Tech. initiatives so was looking mainly at the 4 schools I mentioned.
Two questions -
1) How much do you think would be a safe score if I have to retake the GMAT?
2) Would it be risky to apply to these 4 schools this year with a 710 and if I don't make it, reapply next year with an ideal(740-750) GMAT score? considering that I can highlight leadership qualities even better next year.
_________________
Good Luck!!!
***Help and be helped!!!****
Status: Senior Consultant, Aringo
Joined: 19 Jul 2011
Posts: 117
Concentration: Strategy, Marketing
Schools: Northwestern (Kellogg) - Class of 0
GMAT 1: 700 Q V
GPA: 3.92
WE: Management Consulting (Consulting)
Followers: 3
Kudos [?]: 11 [0], given: 0
### Show Tags
15 Aug 2011, 03:56
Quote:
Thanks Brian, appreciate your help! Just some additional information - - I have been managing a team of 8 people for the last two years. - For the IP, I went ahead with the prototype and tried to secure seed funding from a VC in Silicon valley but it didn't work out. I am more interested in Tech. initiatives so was looking mainly at the 4 schools I mentioned. Two questions - 1) How much do you think would be a safe score if I have to retake the GMAT? 2) Would it be risky to apply to these 4 schools this year with a 710 and if I don't make it, reapply next year with an ideal(740-750) GMAT score? considering that I can highlight leadership qualities even better next year.
ravsg,
Thank you for the follow-up questions. In our experience, there is really no such thing as a “safe” GMAT score, because the GMAT is but one of many important factors taken into account during the admission process. Additionally, applicants in the Indian male demographic in the IT sector face particularly tough competition. Clearly, though, a better GMAT score certainly helps your candidacy, all things equal. Specifically, on the basis of an assumed GMAT of 750 and the additional information in your second post, and under the assumption of strong essays and recommendations, our experience shows that you would be between competitive and stretch (closer to stretch) at Stanford, competitive at Sloan, between competitive and strong (closer to competitive) at Haas, and between competitive and strong (closer to strong) at Tuck.
Regarding leadership, you mentioned in the second post that you have been leading a team of eight for the past two years. Typically, this would be enough time in this kind of position to be able to highlight significant leadership capabilities, improvements, and/or accomplishments in your application. It might be easier for you to discuss your leadership experience from your professional endeavors relative to extracurricular activities, given that you are managing these people today.
With respect to applying this year with your current GMAT and consideration about retaking the test for next year if you are not successful, keep in mind another variable that will become relevant is your age. In particular, in our experience, after applicants reach age 30 and beyond, it becomes more difficult to gain admission with each successive year. One option to consider would be to retake the GMAT now, and then apply in Round 2 of this year. Typically, we observe a slight reduction in chances in Round 2 vs. Round 1, but it varies year to year. Retaking the GMAT to apply in Round 2, of course, assumes that improving your GMAT score by 40 points is realistically achievable. For instance, if you scored in the 750 range in various practice tests before and/or know of your common mistakes at the ~700 level to eliminate going forward, it would make sense to consider retaking the test.
Best of luck,
_________________
Last edited by AringoConsultant on 06 Apr 2012, 18:32, edited 1 time in total.
Intern
Joined: 23 Jun 2010
Posts: 13
Followers: 0
Kudos [?]: 0 [0], given: 0
### Show Tags
20 Aug 2011, 00:14
Dear Brian,
I plan to submit about 4-5 applications for 2012. What is the recommended balance between Top 5 programs and all the others?
Thanks!
Manager
Joined: 17 Jan 2011
Posts: 231
Followers: 1
Kudos [?]: 36 [0], given: 4
### Show Tags
20 Aug 2011, 07:04
Thank you!
BrianW wrote:
ravsg,
Thank you for the follow-up questions......
_________________
Good Luck!!!
***Help and be helped!!!****
Status: Senior Consultant, Aringo
Joined: 19 Jul 2011
Posts: 117
Concentration: Strategy, Marketing
Schools: Northwestern (Kellogg) - Class of 0
GMAT 1: 700 Q V
GPA: 3.92
WE: Management Consulting (Consulting)
Followers: 3
Kudos [?]: 11 [0], given: 0
### Show Tags
24 Aug 2011, 11:58
Quote:
Dear Brian,
I plan to submit about 4-5 applications for 2012. What is the recommended balance between Top 5 programs and all the others?
Thanks!
Steve2014,
Thank you for the question. What is the level of risk you wish to assume? To what extent do you wish to guarantee admission? How important are the prospects for a significant scholarship? Different candidates have different answers to these questions. We would advise the “average candidate” to apply to 5-7 programs (in the first two rounds) and include 1-2 schools where they are strong candidates with potential for a significant scholarship, 1-3 schools where they are competitive candidates, and 1-2 schools where their candidacy is a stretch.
Best of luck,
_________________
Last edited by AringoConsultant on 06 Apr 2012, 18:33, edited 1 time in total.
Manager
Joined: 19 Apr 2011
Posts: 56
Location: United Arab Emirates
GMAT 1: 700 Q47 V39
GPA: 3.5
WE: Business Development (Internet and New Media)
Followers: 2
Kudos [?]: 11 [0], given: 27
### Show Tags
27 Aug 2011, 11:45
Hello Brian,
Could you evaluate my profile and let me know my chances for Admission at Stanford, Kellogg and NYU if I apply during R1 this year (for Fall 2012)?
--------------------
Overall Profile
1. GMAT Score: Yet to give, but have scheduled a test-date. (expected 680-700 based on current GMAT Prep scores)
2. Graduated in Dubai – BE (Hons) in Electronics & Instrumentation (GPA: 3.28/4)
3. I have 3 years of Entrepreneurship Experience running an IT company (4 yrs by Fall 2012).
4. Nationality: Indian; Age: 24 yrs old (25yrs by Fall 2012)
5. Currently held position: COO
6. Started first company right out of college in 2008 with 2 partners; grown successfully to 3 companies across Dubai, Hong Kong and India, managing a total of 12 employees.
7. Biggest success is an Online network currently ranked among the top 150 websites in the world.
7. Languages known - English (Expert), Hindi (Expert), Telugu (Expert), French (Basic Proficiency), Arabic (Basic Proficiency)
Work Ex Highlights
• Interned at 2 very large Oil & Gas companies in the Gulf during college (for a total of 8 months (2+6)).
• Worked for 2 years (lasts for only 2 months each - so a total of 4 months spread across 2007 and 2008) with Dubai International Film Festival, directly managing about 500 or so Volunteers each year. Gained significant leadership experience here, due to the various groups of people I had to manage at once (people from various parts of the globe, varying from 15yrs to even 60yrs in age).
• Started my first company with right out of college, turned it into a successful venture and am now managing 3 companies across Dubai, Hong Kong and India, with a total of 12 employees.
• Company's annual turnover is currently over 1 MM$- would say it's a pretty successful venture, having started off without any external funding from family or VC's. Extra-Curricular Activities - Volunteered at Dubai International Film Festival for 2 years. - Was promoted to Captain at Dubai Film Fest, wherein I trained and managed about 500-700 volunteers through the event. - Was an integral part of the Events Organizing Committee at college. - Helped in organizing several Inter-College Competitions and Events during college. - Was a Professor's TA (Teaching-Assistant) at various Engineering Lab's during final 2 years of College. - Won 3'rd place in a Software Development Trade Show held at University of Wollongong, sponsored by Microsoft Gulf. Hobbies: Karting, Archery (taking professional classes), Football, Volleyball Target Schools: 2 Year Full Time MBA at Stanford (Entrepreneurship), Kellogg (Marketing/Entrep), NYU: Stern or McCombs. Safety Schools: Babson, UCLA, ESADE & IESE (Spain) Why MBA? To network with people from my Industry, to network with VC's for my projects currently in development, to learn how to efficiently form & execute business plans on a much larger scale and to hone my leadership skills. -------------------- From my perspective, my strong points are: Entrepreneurship, EC's, Perfect age-group for Stanford. Potential weak points could be: GMAT Score (not yet given, but with my profile would 680-700 be low?), Undergrad-GPA (is 3.28 low?), Nationality (Indian male, from Engg background in IT). Please let me know your thoughts on this. Thanks a lot for your help! Intern Joined: 27 Aug 2011 Posts: 46 Location: United States (MI) Concentration: Technology, Strategy Schools: Ross '14 (M) GMAT 1: 710 Q50 V36 GPA: 3.75 WE: Engineering (Energy and Utilities) Followers: 0 Kudos [?]: 11 [0], given: 4 Re: Ask ARINGO - if your GMAT is (or might be) below 720 [#permalink] ### Show Tags 27 Aug 2011, 20:11 Hi Brian, Could you please evaluate my profile? Thank you! ------------------------------ Demographic Indian - Born in India, raised in India, Africa, Canada and the US. Currently a Canadian / US dual-citizen. Male Age:27 GMAT: 710 (Q48,V40, AWA:TBD) Education Undergrad at Wayne State University (Detroit) - Graduated with Honors (first engineer in the history of the University) Graduation 2005 Major: Electrical Engineering GPA: 3.74 Masters at University of Michigan (Ann Arbor) Applying for Fall 2012 Work Experience Currently working as a design and consulting engineer in the Power Generation field (3.5 years). Worked for a little over a year at a start-up company after completing MSEE (left due to funding issues). Will have 5.5 years at beginning of Fall 2012 programs. Extra-curricular Active member of a local non-profit organization. Have served on the Board of Directors, served as a CFO for the same non-profit and volunteer there as well. Worked closely with the staff accountant and even participated in hiring process for the organization. Won a lifetime achievement award for contribution to the organization's finance committee (6th person in the history of the 70+ year old organization). Licensed as a Professional Engineer (fairly lengthy and rigorous process). Licensed as a LEED AP by Green Building Certification Institute. Have presented at conferences related to my field. Post MBA Goals Would like to work in project development for large scale infrastructure projects. Would like to attend an MBA program with a strong emphasis on Management and Finance as it will complement my engineering background well to reach my career goals. Top choices for schools: Wharton, Tuck, Kellog, Booth, Ross and Sloan Also, any schools I should consider that I've missed? Intern Joined: 20 Jul 2011 Posts: 11 Followers: 0 Kudos [?]: 0 [0], given: 94 Re: Ask ARINGO - if your GMAT is (or might be) below 720 [#permalink] ### Show Tags 28 Aug 2011, 09:33 deleted Last edited by dutchgerman17 on 28 Jun 2012, 22:55, edited 1 time in total. MBA Admissions Consultant Status: Senior Consultant, Aringo Joined: 19 Jul 2011 Posts: 117 Concentration: Strategy, Marketing Schools: Northwestern (Kellogg) - Class of 0 GMAT 1: 700 Q V GPA: 3.92 WE: Management Consulting (Consulting) Followers: 3 Kudos [?]: 11 [0], given: 0 Re: Ask ARINGO - if your GMAT is (or might be) below 720 [#permalink] ### Show Tags 29 Aug 2011, 18:41 Quote: Hello Brian, Could you evaluate my profile and let me know my chances for Admission at Stanford, Kellogg and NYU if I apply during R1 this year (for Fall 2012)? -------------------- Overall Profile 1. GMAT Score: Yet to give, but have scheduled a test-date. (expected 680-700 based on current GMAT Prep scores) 2. Graduated in Dubai – BE (Hons) in Electronics & Instrumentation (GPA: 3.28/4) 3. I have 3 years of Entrepreneurship Experience running an IT company (4 yrs by Fall 2012). 4. Nationality: Indian; Age: 24 yrs old (25yrs by Fall 2012) 5. Currently held position: COO 6. Started first company right out of college in 2008 with 2 partners; grown successfully to 3 companies across Dubai, Hong Kong and India, managing a total of 12 employees. 7. Biggest success is an Online network currently ranked among the top 150 websites in the world. 7. Languages known - English (Expert), Hindi (Expert), Telugu (Expert), French (Basic Proficiency), Arabic (Basic Proficiency) Work Ex Highlights • Interned at 2 very large Oil & Gas companies in the Gulf during college (for a total of 8 months (2+6)). • Worked for 2 years (lasts for only 2 months each - so a total of 4 months spread across 2007 and 2008) with Dubai International Film Festival, directly managing about 500 or so Volunteers each year. Gained significant leadership experience here, due to the various groups of people I had to manage at once (people from various parts of the globe, varying from 15yrs to even 60yrs in age). • Started my first company with right out of college, turned it into a successful venture and am now managing 3 companies across Dubai, Hong Kong and India, with a total of 12 employees. • Company's annual turnover is currently over 1 MM$ - would say it's a pretty successful venture, having started off without any external funding from family or VC's.
Extra-Curricular Activities
- Volunteered at Dubai International Film Festival for 2 years.
- Was promoted to Captain at Dubai Film Fest, wherein I trained and managed about 500-700 volunteers through the event.
- Was an integral part of the Events Organizing Committee at college.
- Helped in organizing several Inter-College Competitions and Events during college.
- Was a Professor's TA (Teaching-Assistant) at various Engineering Lab's during final 2 years of College.
- Won 3'rd place in a Software Development Trade Show held at University of Wollongong, sponsored by Microsoft Gulf.
Hobbies:
Karting, Archery (taking professional classes), Football, Volleyball
Target Schools:
2 Year Full Time MBA at Stanford (Entrepreneurship), Kellogg (Marketing/Entrep), NYU: Stern or McCombs.
Safety Schools: Babson, UCLA, ESADE & IESE (Spain)
Why MBA?
To network with people from my Industry, to network with VC's for my projects currently in development, to learn how to efficiently form & execute business plans on a much larger scale and to hone my leadership skills.
--------------------
From my perspective, my strong points are: Entrepreneurship, EC's, Perfect age-group for Stanford.
Potential weak points could be: GMAT Score (not yet given, but with my profile would 680-700 be low?), Undergrad-GPA (is 3.28 low?), Nationality (Indian male, from Engg background in IT).
Prabhakar,
Thank you for your profile submission. On the basis of the information above, and under the assumption of strong essays and recommendations and a GMAT score of 690, our experience shows that you will be a stretch candidate at Stanford and Kellogg, between competitive and stretch (closer to stretch) at NYU Stern and UCLA Anderson, between competitive and stretch (closer to competitive) at IESE, and competitive at Texas McCombs, Babson, and ESADE.
Additionally, specific to your profile, I would say you should explain the nature / difference between the 3 firms. Are they in the same industry? Are they the same company but just operating in different geographies? To some extent, the further "apart" the companies are (in scope), the less focused you potentially appear to the admission committees. Why? Ad coms believe 50 year old serial entrepreneurs can get away with running three firms of different scope, but less experienced professionals would have a harder time doing this. You mention there are 12 employees and that you're COO - you will need to be clear on whether you have direct supervision of these employees or not (if you do, it's better). Finally, always provide context and quantify your firm's results, which you've done in your profile well.
Your 'why MBA' reasons are logical and reasonable given your career path. When you write your essays, research each MBA programs' unique entrepreneurial ventures that tie in with your goals and name them.
Best of luck,
_________________
Last edited by AringoConsultant on 06 Apr 2012, 18:34, edited 1 time in total.
Manager
Joined: 19 Apr 2011
Posts: 56
Location: United Arab Emirates
GMAT 1: 700 Q47 V39
GPA: 3.5
WE: Business Development (Internet and New Media)
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### Show Tags
30 Aug 2011, 01:01
Hi Brian,
Thanks a lot for your insightful feedback! It's the most detailed and best one I've received so far, so I really appreciate it.
Let's go over each of the points 1 by 1:
1. GMAT Score: Okay, so clearly any score below 700 would make both Stanford & Kellogg a stretch for me. Though 800 is the upper limit, could you give me a realistic target-score that I should try and achieve, to make the GMAT score fit in well with the rest of my profile? (710..720?...more? )
2. Undergrad GPA: Not sure now it works in my college, but I do have a Honors degree in Engg. and have graduated in the top 15% of my class (11/70 in my class) and my GPA was actually out of 10, wherein I got an 8.3 GPA. If this is indeed a -ive point, I guess there's nothing much I can do to counter it than balance it with a higher GMAT score.
Note note note: Just googled this up and looks like an 8.3/10 is not really = a 3.3/4. Various sources are providing diff ways of calculating a GPA and many even suggest contacting each college to find out about their conversion method. Brian, what's your take on the GPA of 8.3/10?
4. Recommendations: You're spot on about this! I'm totally handicapped when it comes to Recommendations. After rocking my brains out, I was able to come up with the following options:
(1). My supervisor while I worked with Dubai Film Fest (worked under her for first 2yrs while Volunteering, and then again after I was hired too).
(2). My supervisor/Manager, at the company where I first interned during college (though it was only for 2 months, I had the opportunity to extensively work with and learn from him during this Internship. However, this was over 5 years ago and I would like to know whether Stanford/Kellogg/NYU would consider such an LOR as a valuable insight to effectively evaluate my profile?
(3). Should I consider requesting a Reference Letter from my undergrad college professor instead (have been taught by this professor for 2 years, and have worked with her on organizing several events at college as a part of the Events Organizing Committee) or are Academic LOR's generally frowned upon?
If not, what other alternative approaches would you suggest? Please share your thoughts on this aspect.
5. My 3 companies: The Dubai branch is the HQ and the other 2 are just branches doing the same work, spread across the Globe for efficiency and ease. I'm in no situation to manage 3 diff companies doing 3 completely diff things at present (hopefully after an MBA, that shouldn't be an issue if the need arises ). And yes, I directly supervise all the current employees and its a part of my job as the COO.
6. Big name clients/partners: Thanks for this tip! However, where should I possibly consider listing our company's partners, clients, etc without appearing to boast about it? (Could only possibly think of listing them in the CV perhaps?..anywhere else? I'm unable to place such information anywhere in my Stanford Essays for example..)
Once again, thanks a lot for taking so much time to help me assess my profile and fit into these top colleges!
Prabhakar
BrianW wrote:
Quote:
Hello Brian,
Could you evaluate my profile and let me know my chances for Admission at Stanford, Kellogg and NYU if I apply during R1 this year (for Fall 2012)?
--------------------
Overall Profile
1. GMAT Score: Yet to give, but have scheduled a test-date. (expected 680-700 based on current GMAT Prep scores)
2. Graduated in Dubai – BE (Hons) in Electronics & Instrumentation (GPA: 3.28/4)
3. I have 3 years of Entrepreneurship Experience running an IT company (4 yrs by Fall 2012).
4. Nationality: Indian; Age: 24 yrs old (25yrs by Fall 2012)
5. Currently held position: COO
6. Started first company right out of college in 2008 with 2 partners; grown successfully to 3 companies across Dubai, Hong Kong and India, managing a total of 12 employees.
7. Biggest success is an Online network currently ranked among the top 150 websites in the world.
7. Languages known - English (Expert), Hindi (Expert), Telugu (Expert), French (Basic Proficiency), Arabic (Basic Proficiency)
Work Ex Highlights
• Interned at 2 very large Oil & Gas companies in the Gulf during college (for a total of 8 months (2+6)).
• Worked for 2 years (lasts for only 2 months each - so a total of 4 months spread across 2007 and 2008) with Dubai International Film Festival, directly managing about 500 or so Volunteers each year. Gained significant leadership experience here, due to the various groups of people I had to manage at once (people from various parts of the globe, varying from 15yrs to even 60yrs in age).
• Started my first company with right out of college, turned it into a successful venture and am now managing 3 companies across Dubai, Hong Kong and India, with a total of 12 employees.
• Company's annual turnover is currently over 1 MM\$ - would say it's a pretty successful venture, having started off without any external funding from family or VC's.
Extra-Curricular Activities
- Volunteered at Dubai International Film Festival for 2 years.
- Was promoted to Captain at Dubai Film Fest, wherein I trained and managed about 500-700 volunteers through the event.
- Was an integral part of the Events Organizing Committee at college.
- Helped in organizing several Inter-College Competitions and Events during college.
- Was a Professor's TA (Teaching-Assistant) at various Engineering Lab's during final 2 years of College.
- Won 3'rd place in a Software Development Trade Show held at University of Wollongong, sponsored by Microsoft Gulf.
Hobbies:
Karting, Archery (taking professional classes), Football, Volleyball
Target Schools:
2 Year Full Time MBA at Stanford (Entrepreneurship), Kellogg (Marketing/Entrep), NYU: Stern or McCombs.
Safety Schools: Babson, UCLA, ESADE & IESE (Spain)
Why MBA?
To network with people from my Industry, to network with VC's for my projects currently in development, to learn how to efficiently form & execute business plans on a much larger scale and to hone my leadership skills.
--------------------
From my perspective, my strong points are: Entrepreneurship, EC's, Perfect age-group for Stanford.
Potential weak points could be: GMAT Score (not yet given, but with my profile would 680-700 be low?), Undergrad-GPA (is 3.28 low?), Nationality (Indian male, from Engg background in IT).
Prabhakar,
Thank you for your profile submission. On the basis of the information above, and under the assumption of strong essays and recommendations and a GMAT score of 690, our experience shows that you will be a stretch candidate at Stanford and Kellogg, between competitive and stretch (closer to stretch) at NYU Stern and UCLA Anderson, between competitive and stretch (closer to competitive) at IESE, and competitive at Texas McCombs, Babson, and ESADE.
Additionally, specific to your profile, I would say you should explain the nature / difference between the 3 firms. Are they in the same industry? Are they the same company but just operating in different geographies? To some extent, the further "apart" the companies are (in scope), the less focused you potentially appear to the admission committees. Why? Ad coms believe 50 year old serial entrepreneurs can get away with running three firms of different scope, but less experienced professionals would have a harder time doing this. You mention there are 12 employees and that you're COO - you will need to be clear on whether you have direct supervision of these employees or not (if you do, it's better). Finally, always provide context and quantify your firm's results, which you've done in your profile well.
Your 'why MBA' reasons are logical and reasonable given your career path. When you write your essays, research each MBA programs' unique entrepreneurial ventures that tie in with your goals and name them.
Best of luck,
Brian
Aringo.com
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Last edited by Prabhakar on 30 Aug 2011, 11:21, edited 3 times in total.
Status: Senior Consultant, Aringo
Joined: 19 Jul 2011
Posts: 117
Concentration: Strategy, Marketing
Schools: Northwestern (Kellogg) - Class of 0
GMAT 1: 700 Q V
GPA: 3.92
WE: Management Consulting (Consulting)
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Kudos [?]: 11 [0], given: 0
### Show Tags
30 Aug 2011, 09:09
Quote:
Hi Brian,
Could you please evaluate my profile? Thank you!
------------------------------
Demographic
Indian - Born in India, raised in India, Africa, Canada and the US. Currently a Canadian / US dual-citizen.
Male
Age:27
GMAT: 710 (Q48,V40, AWA:TBD)
Education
Undergrad at Wayne State University (Detroit) - Graduated with Honors (first engineer in the history of the University)
Major: Electrical Engineering
GPA: 3.74
Masters at University of Michigan (Ann Arbor)
Applying for Fall 2012
Work Experience
Currently working as a design and consulting engineer in the Power Generation field (3.5 years).
Worked for a little over a year at a start-up company after completing MSEE (left due to funding issues).
Will have 5.5 years at beginning of Fall 2012 programs.
Extra-curricular
Active member of a local non-profit organization. Have served on the Board of Directors, served as a CFO for the same non-profit and volunteer there as well. Worked closely with the staff accountant and even participated in hiring process for the organization. Won a lifetime achievement award for contribution to the organization's finance committee (6th person in the history of the 70+ year old organization).
Licensed as a Professional Engineer (fairly lengthy and rigorous process).
Licensed as a LEED AP by Green Building Certification Institute.
Have presented at conferences related to my field.
Post MBA Goals
Would like to work in project development for large scale infrastructure projects. Would like to attend an MBA program with a strong emphasis on Management and Finance as it will complement my engineering background well to reach my career goals.
Top choices for schools: Wharton, Tuck, Kellog, Booth, Ross and Sloan
Also, any schools I should consider that I've missed?
Jassiinpublic,
Thank you for submitting your profile. On the basis of the information above, and under the assumption of strong essays and recommendations and a GMAT score of 710, our experience shows that you will be between competitive and stretch (closer to stretch) at Kellogg, between competitive and stretch at Wharton and Booth, between competitive and stretch (closer to competitive) at Sloan, competitive at Tuck, and between competitive and strong (closer to competitive) at Ross.
Full disclosure on my part for this post - my undergrad and master's in mechanical engineering were from the University of Michigan, Ann Arbor, so I am quite familiar with the programs you went through. At the same time, my response will be from the point of view of the admission committees and how they might react to your profile.
- How did you fare in terms of graduation rank in the master's program at Michigan? This is potentially a hard question for you to answer, because in my experience there UM did not give out graduate honors. The reason I bring this up is because the Michigan name in engineering, particuarly at the graduate level, is quite strong. Since you were among the first graduating class in engineering at Wayne State, the ad coms have less of a data point about how to rate the difficulty/rigor of that program. Additionally, outside of Ross (since Wayne State is in Detroit), the other schools you're applying to will be much less familiar with Wayne State than with Michigan. Finally, if you received a scholarship from Wayne State, talk about that as a reason for attending there.
- You have a unique career path post-MBA, which is good. At the same time, it's also a non-traditional post-MBA job, so you will want to spend a bit extra space elaborating on why you would need an MBA for this profession and what skills it would bring in. In particular, you may want to talk to people in that field and get anecdotal input (which you could quote in essays) about why MBA for infrastructure projects. To me, it sounds like you'd want to play up the notion that you also are interested in public policy / public economics issues, based on the nature of your career goals.
In terms of schools to recommend, given that you have an interest in finance and (general) management, you have hit upon the majority of the top programs that would make sense for you. Others to include might be Haas or Fuqua (good combination of general management primarily with reputable finance programs), or a school that has a higher mix of engineers in its class (and who thus value your work experience and professional accomplishments), such as Tepper.
Best of luck,
_________________
Last edited by AringoConsultant on 06 Apr 2012, 18:35, edited 1 time in total.
Status: Senior Consultant, Aringo
Joined: 19 Jul 2011
Posts: 117
Concentration: Strategy, Marketing
Schools: Northwestern (Kellogg) - Class of 0
GMAT 1: 700 Q V
GPA: 3.92
WE: Management Consulting (Consulting)
Followers: 3
Kudos [?]: 11 [1] , given: 0
### Show Tags
30 Aug 2011, 09:41
1
KUDOS
Expert's post
Quote:
Hello,
Could you please evaluate my profile?
Nationality: Indian
Age: 29
GMAT: 690 (Quantitative: 45, Verbal: 38). Will be taking GMAT again to get at least 20-30 more points.
Educational Background:
1. SSLC: 91.2%
2. Diploma in Chemical Technology: 3 years - 75.7% (First Class with distinction), Institute: Kongu Polytechnic, India
3. Bachelor of Technology in Chemical Engineering - 3 years - 74.8% (First Class), Institute: Periyar University, India
4. Master of Science in Materials Science and Engineering - 2 years - 1.7 (B+, Good), Institute: University of Kiel, Germany
Professional Background: Experience: 4-5 years
a) Full time jobs
1. Since 2008, I have been working as a research chemist for a chemical company in Netherlands.
I execute complex, multi-disciplinary research activities that contribute to the development of (new) product principles, that through further development lead to new products or the solving of (new) application and process problems with existing products. I execute, improve and develop laboratory tests with predictive value towards field performance (performance in steel/tin plate rolling mills). A proper execution of research activities, managed as projects, is my primary responsibility.
To be more specific, I develop environmental friendly, but low cost, rolling oils, lubricants, wet temper fluids and corrosion preventives for steel/tin plate rolling mills. I deal with the problems faced by the customers-Arcelor Mittal, Corus/Tata Steel, China Steel Corporation-not only in Europe but also in China.
2) In 2007, I worked as a Junior Researcher/Intern for Mitsubishi Chemical Science and Technology Research Center in Japan.
I was involved in developing batteries for hybrid electric vehicles.
b) Part time jobs
2004-2006: 2 years - I worked as research assistant for University of Kiel and Max Planck Research Institute in Germany.
Extra-Curricular Activities:
1. Treasurer of Amnesty International Group in Amsterdam - since 2010 - Present : I organize yearly money collection and take care of annual budget.
2. Member of Greenpeace, Netherlands - My background in chemistry and chemical engineering helps me to support the environmental causes of Greenpeace .
3. Member of Dutch Refugee Council, Netherlands - I helped/help the refugees from Srilanka to settle down in Netherlands.
4. National Cadet Corps, India - 3 years - Passed the B certificate exam
5. National Social Service Scheme, India - 3 years - Participated in social harmony and youth development program
6. Scouts, India - 2 years
7. I won a few prizes in sports and games and in quiz competition
Languages known: Tamil, English, Hindi, Dutch, German
International Exposure: 26 months in Germany, 7 months in Japan and 48 months in Netherlands
Reason for doing an MBA: Career switch to Consulting (Strategy/Energy). The next option is Industry (Oil & Energy/Chemicals). Investment banking and Entrepreneurship are not my options.
Area of interest: General Management, International Business
Target Schools: INSEAD (Jan 2013), IMD (Jan 2013) and LBS (Aug 2012)
Within a year I can get the permanent resident status in Netherlands, the status might allow me to find jobs without work permit at least in a few European countries.
I request you to evaluate my profile and let me know the schools I have good chances at. Thanks in advance for your help.
DutchGerman
DutchGerman,
Thank you for submitting your profile. On the basis of the information above, and under the assumption of strong essays and recommendations and a GMAT score of 710 (after the retake), our experience shows that you will be between competitive and stretch (closer to stretch) at INSEAD, between competitive and stretch at IMD, and between competitive and stretch (closer to competitive) at LBS.
In terms of your profile strengths, you have solid academic grades and technical work experience and your GMAT quant split is high. As such, the committees will not question your analytical capabilities, in our experience. Your post-MBA career goals are reasonable, given that you have technical experience that you could apply to the energy and/or oil industries. Finally, you clearly index high on international orientation based on your language skills and work experience in Western Europe, which will appeal to European MBA programs.
As far as things to consider when you apply:
- To me, the biggest impression I get is that you need to consider how you frame your work experience. I have a technical background, and I understand what your work looks like. Yet, to me, you sound as if you are introducing yourself to another engineer. However, for MBA applications, you have to treat it as if you're introducing yourself to a businessperson without a technical background (because the reality is that's the case); your shift needs to go from a technical to business focus. Additionally, related to this, make sure to use smaller sentences when you present your work experience - it's easier to digest for the reader.
- Since I mentioned your analytical capabilities are already going to be considered strong, resist spending all your time talking about technical accomplishments at work. You can talk a bit about 1-2 big technical innovations/results. But for the most part, talk about how you communicated updates to your management, how you persuaded people that projects were worthwhile, etc. This will help to convince the committees that you are a balanced candidate.
- Additionally, you should definitely consider emphasizing the environmental impact and aspects of your work experience. MBA programs put extra value, in our experience, on people with clean tech work backgrounds, as managing our natural resources and the environment going forward is going to be a key issue globally.
- Where you work as a research chemist matters as well. If it is not a multinational major player (or even if it is), make sure to discuss the competitiveness of the job you received.
- Your extracurricular experiences are not necessarily lacking, but if you can get an official title with Greenepeace it would be better.
Best of luck,
_________________
Last edited by AringoConsultant on 06 Apr 2012, 18:36, edited 1 time in total.
Status: Senior Consultant, Aringo
Joined: 19 Jul 2011
Posts: 117
Concentration: Strategy, Marketing
Schools: Northwestern (Kellogg) - Class of 0
GMAT 1: 700 Q V
GPA: 3.92
WE: Management Consulting (Consulting)
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Kudos [?]: 11 [0], given: 0
### Show Tags
01 Sep 2011, 07:48
Quote:
Hi Brian,
Thanks a lot for your insightful feedback! It's the most detailed and best one I've received so far, so I really appreciate it.
Let's go over each of the points 1 by 1:
1. GMAT Score: Okay, so clearly any score below 700 would make both Stanford & Kellogg a stretch for me. Though 800 is the upper limit, could you give me a realistic target-score that I should try and achieve, to make the GMAT score fit in well with the rest of my profile? (710..720?...more? )
2. Undergrad GPA: Not sure now it works in my college, but I do have a Honors degree in Engg. and have graduated in the top 15% of my class (11/70 in my class) and my GPA was actually out of 10, wherein I got an 8.3 GPA. If this is indeed a -ive point, I guess there's nothing much I can do to counter it than balance it with a higher GMAT score.
Note note note: Just googled this up and looks like an 8.3/10 is not really = a 3.3/4. Various sources are providing diff ways of calculating a GPA and many even suggest contacting each college to find out about their conversion method. Brian, what's your take on the GPA of 8.3/10?
4. Recommendations: You're spot on about this! I'm totally handicapped when it comes to Recommendations. After rocking my brains out, I was able to come up with the following options:
(1). My supervisor while I worked with Dubai Film Fest (worked under her for first 2yrs while Volunteering, and then again after I was hired too).
(2). My supervisor/Manager, at the company where I first interned during college (though it was only for 2 months, I had the opportunity to extensively work with and learn from him during this Internship. However, this was over 5 years ago and I would like to know whether Stanford/Kellogg/NYU would consider such an LOR as a valuable insight to effectively evaluate my profile?
(3). Should I consider requesting a Reference Letter from my undergrad college professor instead (have been taught by this professor for 2 years, and have worked with her on organizing several events at college as a part of the Events Organizing Committee) or are Academic LOR's generally frowned upon?
If not, what other alternative approaches would you suggest? Please share your thoughts on this aspect.
5. My 3 companies: The Dubai branch is the HQ and the other 2 are just branches doing the same work, spread across the Globe for efficiency and ease. I'm in no situation to manage 3 diff companies doing 3 completely diff things at present (hopefully after an MBA, that shouldn't be an issue if the need arises ). And yes, I directly supervise all the current employees and its a part of my job as the COO.
6. Big name clients/partners: Thanks for this tip! However, where should I possibly consider listing our company's partners, clients, etc without appearing to boast about it? (Could only possibly think of listing them in the CV perhaps?..anywhere else? I'm unable to place such information anywhere in my Stanford Essays for example..)
Once again, thanks a lot for taking so much time to help me assess my profile and fit into these top colleges!
Prabhakar
Prahbakar,
1) You can see the relative sensitivity that an improved GMAT score would have on your chances by looking at the Aringo Chances Evaluation tool: Chances As I have stated previously in this thread, there is really no such thing as a "safe" GMAT score, so I would not be able to say at what level you would need to get to, per se.
2) Being in the top 15% of your class is not a negative, but having a 3.3 / 4.0 GPA would be if that were truly on an American university scale (because it would certainly not be in the top 15%). Don't worry about trying to convert your 8.3 into a 4.0 score GPA. Instead, just list it as you received it from your university on your CV, but definitely include the honors and top 15% items in your CV. Top MBA programs know how grading in India works - trying to translate to the 4.0 just confuses things.
3) It's perfectly fine to have made the decision you did - no MBA program is going to hold it against you. What you should do, as originally mentioned, was to comment on these offers in your essays to point out to the ad coms that it was an option. The area that makes the most sense is the career essay, in which you could say how you considered those jobs at Firm X or Y (name them, especially if it's a big name firm) but ultimately chose entrepreneurship because it was your passion.
4) Regarding recommendations, here are some general thoughts on the matter: Recommendations Of the three you list, the film fest supervisor is realistically the only one of the those I would consider using. Why? It's a relationship that has existed for a few years, the person would know you well, and it's relatively recent. Professors are not really able to value your professional potential as much, and a professional manager from five years ago will not be able to speak to who you are today. You may also consider important clients with whom you have a close relationship and whose relationship would not sour if you told him/her you're considering business school. If you have relied upon insights from a board of directors or senior executives in your field for advice and have established a good rapport, that could also be an option. In general, in our experience, you're going to need at least one of your recommenders be able to speak, in detail, about your entrepreneurship experiences in the past 2-3 years.
5) That's fine then. In your essays and/or CV, just explain you went through a geographic expansion, perhaps elaborating on how and why you chose the first location and then locations two and three.
6) Yes, key clients listed in the CV would make sense. It would also be logical to include them as part of essays if the essay story involves that client, for instance. If it was a big breakthrough that you got big name client X at some point in time, which helped your firm's credibility to get the next clients down the line, that's an example of how to use it. Don't be too overly concerned about sounding like you are bragging. If all you do in essays is drop names and list accomplishments, then yes, that's too much. But in our experience you need to provide the ad coms with enough context and supporting evidence, like listing a big name client or quantifying the financial impact of a project, to come off as a credible applicant.
Best of luck,
_________________
Last edited by AringoConsultant on 06 Apr 2012, 18:37, edited 1 time in total.
Manager
Joined: 19 Apr 2011
Posts: 56
Location: United Arab Emirates
GMAT 1: 700 Q47 V39
GPA: 3.5
WE: Business Development (Internet and New Media)
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Kudos [?]: 11 [0], given: 27
### Show Tags
01 Sep 2011, 17:34
You're epic! Thanks a lot Brian!
Prabhakar
BrianW wrote:
Quote:
Hi Brian,
Thanks a lot for your insightful feedback! It's the most detailed and best one I've received so far, so I really appreciate it.
Let's go over each of the points 1 by 1:
1. GMAT Score: Okay, so clearly any score below 700 would make both Stanford & Kellogg a stretch for me. Though 800 is the upper limit, could you give me a realistic target-score that I should try and achieve, to make the GMAT score fit in well with the rest of my profile? (710..720?...more? )
2. Undergrad GPA: Not sure now it works in my college, but I do have a Honors degree in Engg. and have graduated in the top 15% of my class (11/70 in my class) and my GPA was actually out of 10, wherein I got an 8.3 GPA. If this is indeed a -ive point, I guess there's nothing much I can do to counter it than balance it with a higher GMAT score.
Note note note: Just googled this up and looks like an 8.3/10 is not really = a 3.3/4. Various sources are providing diff ways of calculating a GPA and many even suggest contacting each college to find out about their conversion method. Brian, what's your take on the GPA of 8.3/10?
4. Recommendations: You're spot on about this! I'm totally handicapped when it comes to Recommendations. After rocking my brains out, I was able to come up with the following options:
(1). My supervisor while I worked with Dubai Film Fest (worked under her for first 2yrs while Volunteering, and then again after I was hired too).
(2). My supervisor/Manager, at the company where I first interned during college (though it was only for 2 months, I had the opportunity to extensively work with and learn from him during this Internship. However, this was over 5 years ago and I would like to know whether Stanford/Kellogg/NYU would consider such an LOR as a valuable insight to effectively evaluate my profile?
(3). Should I consider requesting a Reference Letter from my undergrad college professor instead (have been taught by this professor for 2 years, and have worked with her on organizing several events at college as a part of the Events Organizing Committee) or are Academic LOR's generally frowned upon?
If not, what other alternative approaches would you suggest? Please share your thoughts on this aspect.
5. My 3 companies: The Dubai branch is the HQ and the other 2 are just branches doing the same work, spread across the Globe for efficiency and ease. I'm in no situation to manage 3 diff companies doing 3 completely diff things at present (hopefully after an MBA, that shouldn't be an issue if the need arises ). And yes, I directly supervise all the current employees and its a part of my job as the COO.
6. Big name clients/partners: Thanks for this tip! However, where should I possibly consider listing our company's partners, clients, etc without appearing to boast about it? (Could only possibly think of listing them in the CV perhaps?..anywhere else? I'm unable to place such information anywhere in my Stanford Essays for example..)
Once again, thanks a lot for taking so much time to help me assess my profile and fit into these top colleges!
Prabhakar
Prahbakar,
1) You can see the relative sensitivity that an improved GMAT score would have on your chances by looking at the Aringo Chances Evaluation tool: Chances As I have stated previously in this thread, there is really no such thing as a "safe" GMAT score, so I would not be able to say at what level you would need to get to, per se.
2) Being in the top 15% of your class is not a negative, but having a 3.3 / 4.0 GPA would be if that were truly on an American university scale (because it would certainly not be in the top 15%). Don't worry about trying to convert your 8.3 into a 4.0 score GPA. Instead, just list it as you received it from your university on your CV, but definitely include the honors and top 15% items in your CV. Top MBA programs know how grading in India works - trying to translate to the 4.0 just confuses things.
3) It's perfectly fine to have made the decision you did - no MBA program is going to hold it against you. What you should do, as originally mentioned, was to comment on these offers in your essays to point out to the ad coms that it was an option. The area that makes the most sense is the career essay, in which you could say how you considered those jobs at Firm X or Y (name them, especially if it's a big name firm) but ultimately chose entrepreneurship because it was your passion.
4) Regarding recommendations, here are some general thoughts on the matter: Recommendations Of the three you list, the film fest supervisor is realistically the only one of the those I would consider using. Why? It's a relationship that has existed for a few years, the person would know you well, and it's relatively recent. Professors are not really able to value your professional potential as much, and a professional manager from five years ago will not be able to speak to who you are today. You may also consider important clients with whom you have a close relationship and whose relationship would not sour if you told him/her you're considering business school. If you have relied upon insights from a board of directors or senior executives in your field for advice and have established a good rapport, that could also be an option. In general, in our experience, you're going to need at least one of your recommenders be able to speak, in detail, about your entrepreneurship experiences in the past 2-3 years.
5) That's fine then. In your essays and/or CV, just explain you went through a geographic expansion, perhaps elaborating on how and why you chose the first location and then locations two and three.
6) Yes, key clients listed in the CV would make sense. It would also be logical to include them as part of essays if the essay story involves that client, for instance. If it was a big breakthrough that you got big name client X at some point in time, which helped your firm's credibility to get the next clients down the line, that's an example of how to use it. Don't be too overly concerned about sounding like you are bragging. If all you do in essays is drop names and list accomplishments, then yes, that's too much. But in our experience you need to provide the ad coms with enough context and supporting evidence, like listing a big name client or quantifying the financial impact of a project, to come off as a credible applicant.
Best of luck,
Brian
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02 Sep 2011, 07:44
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Last edited by dutchgerman17 on 28 Jun 2012, 22:56, edited 1 time in total.
Manager
Joined: 12 Aug 2011
Posts: 95
Location: United States (SC)
Concentration: Operations, General Management
Schools: Cornell (Johnson) - Class of 2014
GMAT 1: 710 Q48 V39
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### Show Tags
10 Sep 2011, 16:47
Brian, I'd love to know what you think about my chances at the schools I am looking at. Thanks. Also, a question I have... I am managing/captaining a recreational soccer team. Is that worth mentioning in a resume application? Should I include my internship as experience (while in school, I was told some companies would consider an internship as a "year of full time experience" so I am wondering if it is the same for B-school.) Thanks for the help!
Personal Information:
White/Male
Age: 22
GMAT: 710 (92%) (Q48, V39)
Bachelors in Chemical Engineering from Clemson University, GPA 3.1
Work Experience:
-1 year with Fraenkische USA as an Application Engineer. I head up new product evalutations for the corrugated plastic tubing company Fraenkische Industrial Pipes' USA division in Anderson, SC. I also run the logistics and efficiency studies of our newly implimented assembly process for fuel tank lines for use in BMW's engines. I am also leading a project to decomission one of our older corregation lines while desing replacement parts for all customers who currently receive parts from this machine. Finally, I am in charge of all of the environmental impacts from our plant as well as handling supplier quality issues.
-1 summer internship (don't know if this counts or I should include it, but will tell you all I have to offer) with Controls Southeast, Inc in Pineville, NC. I worked as a junior project manager for the steam solutions company, abbreviated CSI, assisting the PMAs with bill of material analyses, energy consumption studies for clients, and research into insulation solutions.
Extra Curricular/Honors:
- Calhoun Honors College at Clemson University
- Receipient of two scholarships at Clemson (Women's Trustees Board Scholarship and another I do not recall the name of, but it was an out-of-state waiver since I am originally from Atlanta, GA)
- 4 year member in Alpha Lambda Delta honors fraternity
- 3 year member of Clemson TigerBand (marching band - Mellophone)
- 2 year member of Clemson Pep Band
- 3 year member of Clemson Symphony Orchestra (French Horn)
- Team leader for senior design project dealing with the design and implimentation of a fat rendering plant turning low grade tallow (animal fats) into a profitable good (Polyolesters, a form of high temperature industrial lubricants). As team leader, I conducted all of the project planning, supervision, and management while still pulling (more than, to be honest) my equal share in the project.
Target Schools:
University of Connecticut School of Business
University of Pennsylvania (Wharton)
Columbia University
Clemson University (Night MBA) - if I want to go the part time route, but I think full time would present better/more opportunities for me
University of South Carolina
Duke University (Fuqua)
Post MBA:
I want to work in upper-management at a manfucaturing company either as a plant manager or as a regional manager. I enjoy thinking of logistics and feasibility of things and would love to see that maximized in my future career.
Status: Senior Consultant, Aringo
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Concentration: Strategy, Marketing
Schools: Northwestern (Kellogg) - Class of 0
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### Show Tags
13 Sep 2011, 17:26
Quote:
Brian, I'd love to know what you think about my chances at the schools I am looking at. Thanks. Also, a question I have... I am managing/captaining a recreational soccer team. Is that worth mentioning in a resume application? Should I include my internship as experience (while in school, I was told some companies would consider an internship as a "year of full time experience" so I am wondering if it is the same for B-school.) Thanks for the help!
Personal Information:
White/Male
Age: 22
GMAT: 710 (92%) (Q48, V39)
Bachelors in Chemical Engineering from Clemson University, GPA 3.1
Work Experience:
-1 year with Fraenkische USA as an Application Engineer. I head up new product evalutations for the corrugated plastic tubing company Fraenkische Industrial Pipes' USA division in Anderson, SC. I also run the logistics and efficiency studies of our newly implimented assembly process for fuel tank lines for use in BMW's engines. I am also leading a project to decomission one of our older corregation lines while desing replacement parts for all customers who currently receive parts from this machine. Finally, I am in charge of all of the environmental impacts from our plant as well as handling supplier quality issues.
-1 summer internship (don't know if this counts or I should include it, but will tell you all I have to offer) with Controls Southeast, Inc in Pineville, NC. I worked as a junior project manager for the steam solutions company, abbreviated CSI, assisting the PMAs with bill of material analyses, energy consumption studies for clients, and research into insulation solutions.
Extra Curricular/Honors:
- Calhoun Honors College at Clemson University
- Receipient of two scholarships at Clemson (Women's Trustees Board Scholarship and another I do not recall the name of, but it was an out-of-state waiver since I am originally from Atlanta, GA)
- 4 year member in Alpha Lambda Delta honors fraternity
- 3 year member of Clemson TigerBand (marching band - Mellophone)
- 2 year member of Clemson Pep Band
- 3 year member of Clemson Symphony Orchestra (French Horn)
- Team leader for senior design project dealing with the design and implimentation of a fat rendering plant turning low grade tallow (animal fats) into a profitable good (Polyolesters, a form of high temperature industrial lubricants). As team leader, I conducted all of the project planning, supervision, and management while still pulling (more than, to be honest) my equal share in the project.
Target Schools:
University of Connecticut School of Business
University of Pennsylvania (Wharton)
Columbia University
Clemson University (Night MBA) - if I want to go the part time route, but I think full time would present better/more opportunities for me
University of South Carolina
Duke University (Fuqua)
Post MBA:
I want to work in upper-management at a manfucaturing company either as a plant manager or as a regional manager. I enjoy thinking of logistics and feasibility of things and would love to see that maximized in my future career.
Pitpit,
Thank you for submitting your profile. On the basis of the information above, and under the assumption of strong essays and recommendations and a GMAT score of 710, our experience shows that you will be a stretch candidate at Wharton, Columbia, and Fuqua. Please keep in mind that Aringo provides client service and expertise to applicants who are interested in the top 30 business schools globally, so I would not be able to advise you on chances for part-time/night programs or school such as Connecticut, Clemson, or South Carolina.
In terms of your profile for a top program, the following would be items to keep in mind:
- Career goals:
I'm not sure if you meant working as a plant manager was your short term (immediately post-MBA) job or more of a long term goal. If you meant the former, keep in mind the vast majority of mid-sized to large manufacturing plants would generally not hire someone with two years of work experience and an MBA. I have seen this accomplished with extensive operations experience and engineering leadership exhibited during the pre-MBA experience for a few colleagues who have graduated from top business schools. As such, I would encourage you to put a more feasible first job post MBA in your essays. Otherwise, you risk losing some credibility. Additionally, it sounds as if you are interested in a career in operations. However, I would encourage you to research this field, as most MBA programs would not necessarily recognize "logistics" as much as they would "operations."
- Work experience: You discuss mostly responsibilities in your daily job, which is fine to introduce yourself. At the same time, make sure your resume lists accomplishments that are quantified.
- School selection: You seem to have listed quite a wide range of programs from a competitiveness standpoint relative to most other applicants, going from Wharton to a part-time program. I would encourage you to further consider your career goals and understand what kind of MBA and work experience would be required to attain those goals. If you are interested in remaining in the southeast United States, you might consider schools such as North Carolina (Kenan-Flagler) and Emory (Goziueta) after you have a few more years of work experience under your belt. Both have strong reputations and are more of a middle ground in terms of where you might have reasonable chances.
- Scholarships: If you mention the proportion of your tuition that was supported (if it was a significant proportion), that can sometimes be more impressive than listing the scholarship name.
- Community service: Regarding your question about managing a soccer team, it sounds as if the people on the team are adults. Based on our experience with clients, this would generally not be considered extracurricular activity or community service in the sense that it's more of a hobby. If you were coaching a children's team, for example, then it's a bit of a different story.
- Internships: Generally, most firms and MBA programs would not seriously consider internships, based on our experience with top global MBA programs. Typically, you remove your internship experience from a resume after starting to work full-time.
Best of luck,
Brian
_________________
Last edited by AringoConsultant on 06 Apr 2012, 18:37, edited 1 time in total.
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19 Sep 2011, 12:49
Dear Brian,
I am 31 years old. Is age a problem in gaining admission to Top 10 schools?
Re: Ask ARINGO - if your GMAT is (or might be) below 720 [#permalink] 19 Sep 2011, 12:49
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First principles
• October 30th 2009, 01:04 PM
sammy28
First principles
hi all,
Find $\frac{dy}{dx}$ for $y=\sqrt{x}$
$= \frac{1}{2}\displaystyle{x}^{-\frac{1}{2}}\equiv\frac{1}{2\sqrt{x}}$
i then try to get this result from first principles:
$f'(x)=\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h}=\lim_{h\rightarrow0}\frac{(x+h)^{\frac{1} {2}} - x^{\frac{1}{2}}}{h}$
then cancel the fractional powers by raising both numerator and denominator by reciprocal power, so that
$\lim_{h\rightarrow0}\frac{h}{h^2}=0$
what am i doing wrong?
thanks sammy.
• October 30th 2009, 01:38 PM
TwistedOne151
$(\sqrt{x+h}-\sqrt{x})^2\ne(x+h)-x$. To find the limit, we rationalize the numerator
$\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt{x}}{h}=\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt{x}}{h}\frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+ \sqrt{x}}$
$=\lim_{h\to0}\frac{(x+h)-x}{h(\sqrt{x+h}+\sqrt{x})}$
$=\lim_{h\to0}\frac{h}{h(\sqrt{x+h}+\sqrt{x})}$
$=\lim_{h\to0}\frac{1}{(\sqrt{x+h}+\sqrt{x})}$,
--Kevin C.
• October 30th 2009, 02:37 PM
sammy28
thanks a lot for that (Clapping).
i should have tried expanding the numerator and would have seen it was wrong! (Giggle)
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1 Reply Latest reply on Oct 8, 2008 4:17 AM by Joakim Sandstroem
# FS Listener and big files
Hi,
My application will have a FS entry point for messages, so I use a FS listener.
To check the behaviour while dropping big files in the input directory, I made two simple tests :
1/ With a java test, I create a simple text file and run it in debug mode with break points in order to simulate a long time flow
2/ I dropped a 3.7 Go Iso file (!) in the input directory
The behaviour was the same in the console:
09:36:29,615 ERROR [AbstractFileGateway] Composer <org.jboss.soa.esb.listeners.gateway.LocalFileMessageComposer> Failed.
org.jboss.soa.esb.listeners.message.MessageDeliverException: Invalid File payload. File 'c:\dev\jee\esb\input\text.txt.esbWorking' doesn't exist.
It was the console output during my Java test while holding the test with a breakpoint.
After releasing the test, the message had been correctly inserted in the ESB.
Note: If I read exactly the same errors during copying the isofile, I did not wait for the completion!
Finally, my question is: Are we 100% sure every file dropped in a listened directory is correctly and fully inserted in the ESB even if FS listener attempt to pick it up while being written down on the disk?
My tests lead me to answer yes (beacause the file is renamed before insertion) but with some errors in the logs, but I'd like the team to confirm it.
Regards,
Brice
• ###### 1. Re: FS Listener and big files
If you process large files you might want to implement the service as shown in the following example: (jbossesb dir)/samples/quickstarts/huge-split-enrich-transform-route
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# Number-Theoretic Inequality!
Number Theory Level 5
$\Large{0 < \left| \dfrac{p}{q} - \dfrac23 \right| < \dfrac{1}{q^2}}$
How many ordered pairs $$(p,q)$$ of integers exists such that the above inequality satisfies?
×
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A Guide To Shop Equipment Nobody Thinks About: Clean, Organized, And Efficient
When planning out a workspace at home, the job, or at a makerspace, we all tend to focus on the fun parts. Where the equipment will go, how you’ll power it, what kind of lights you’ll get, etc, etc. It’s easy to devote all your attention to these high-level concepts, which often means the little details end up getting addressed on the fly. If they get addressed at all.
But whether we want to admit it or not, an organized workspace tends to be more efficient. That’s why [Eric Weinhoffer] has put together a blog post that details all those mundane details that we tend to forget about. It’s not exactly exciting stuff, and contains precisely as much discussion about whiteboards as you probably expect. That said, it’s thorough and clearly comes from folks who’ve had more than a little experience with setting up an efficient shop.
So what’s the first thing most shops don’t have enough of? Labels. [Eric] says you should put labels on everything, parts bins, tools, machines, if it’s something you need to keep track of, then stick a label on it. This does mean you’ll likely have to buy a label maker, but hey, at least that means a new gadget to play with.
Of course, those self-stick labels don’t work on everything. That’s why [Eric] always has a few rolls of masking tape (such as the blue 3M tape you might be using on your 3D printer bed) and some quality markers on hand to make arbitrary labels. Apparently there’s even such a thing as dry erase tape, which lets you throw an impromptu writing surface anywhere you want.
[Eric] also suggests investing in some collapsible cardboard bins which can be broken down and stored flat when not in use. If you’ve got the kind of situation where you’ll always have more or less the same amount of stuff then plastic is probably your best bet, but in a more dynamic environment, being able to collapse the bins when they aren’t in use is a capability we never even realized we needed until now.
As you might imagine, the post also touches on the issues of keeping sufficient safety gear available. We’ve talked about this in the past, but it’s one of those things that really can’t be said too many times. Having a wall of meticulously labeled storage bins is great, but it’s going to be the last thing on your mind if you manage to get an eye full of superglue.
Spectrometer Is Inexpensive And Capable
We know the effect of passing white light through a prism and seeing the color spectrum that comes out of the other side. It will not be noticeable to the naked eye, but that rainbow does not fully span the range of [Roy G. Biv]. There are narrowly absent colors which blur together, and those missing portions are a fingerprint of the matter the white light is passing through or bouncing off. Those with a keen eye will recognize that we are talking about spectrophotometry which is identifying those fingerprints and determining what is being observed and how much is under observation. The device which does this is called a spectrometer and [Justin Atkin] invites us along for his build. Video can also be seen below.
Along with the build, we learn how spectrophotometry works, starting with how photons are generated and why gaps appear in the color spectrum. It is all about electrons, which some of our seasoned spectrometer users already know. The build uses a wooden NanoDrop style case cut on a laser engraver. It needs some improvements which are mentioned and shown in the video so you will want to have some aluminum tape on hand. The rest of the bill of materials is covered including “Black 2.0” which claims to be the “mattest, flattest, black acrylic paint.” Maybe that will come in handy for other optical projects. It might be wise to buy first surface mirrors cut to size, but you can always make bespoke mirrors with carefully chosen tools.
Network Analysers: The Electrical Kind
Instrumentation has progressed by leaps and bounds in the last few years, however, the fundamental analysis techniques that are the foundation of modern-day equipment remain the same. A network analyzer is an instrument that allows us to characterize RF networks such as filters, mixers, antennas and even new materials for microwave electronics such as ceramic capacitors and resonators in the gigahertz range. In this write-up, I discuss network analyzers in brief and how the DIY movement has helped bring down the cost of such devices. I will also share some existing projects that may help you build your own along with some use cases where a network analyzer may be employed. Let’s dive right in.
Network Analysis Fundamentals
As a conceptual model, think of light hitting a lens and most of it going through but part of it getting reflected back.
The same applies to an electrical/RF network where the RF energy that is launched into the device may be attenuated a bit, transmitted to an extent and some of it reflected back. This analysis gives us an attenuation coefficient and a reflection coefficient which explains the behavior of the device under test (DUT).
Of course, this may not be enough and we may also require information about the phase relationship between the signals. Such instruments are termed Vector Network Analysers and are helpful in measuring the scattering parameters or S-Parameters of a DUT.
The scattering matrix links the incident waves a1, a2 to the outgoing waves b1, b2 according to the following linear equation: $\begin{bmatrix} b_1 \\ b_2 \end{bmatrix} = \begin{bmatrix} S_{11} & S_{12} \\ S_{21} & S_{22} \end{bmatrix} * \begin{bmatrix} a_1 \\ a_2 \end{bmatrix}$.
The equation shows that the S-parameters are expressed as the matrix S, where and denote the output and input port numbers of the DUT.
This completely characterizes a network for attenuation, reflection as well as insertion loss. S-Parameters are explained more in details in Electromagnetic Field Theory and Transmission Line Theory but suffice to say that these measurements will be used to deduce the properties of the DUT and generate a mathematical model for the same.
General Architecture
As mentioned previously, a simple network analyzer would be a signal generator connected and a spectrum analyzer combined to work together. The signal generator would be configured to output a signal of a known frequency and the spectrum analyzer would be used to detect the signal at the other end. Then the frequency would be changed to another and the process repeats such that the system sweeps a range of frequencies and the output can be tabulated or plotted on a graph. In order to get reflected power, a microwave component such as a magic-T or directional couplers, however, all of this is usually inbuilt into modern-day VNAs.
Continue reading “Network Analysers: The Electrical Kind”
Hackaday Prize Entry: Helping Millions See Clearly
Slit lamps are prohibitively expensive in the third world areas of India where they are most needed. An invention that’s been around for over a hundred years, the slit lamp is a simple-in-concept way to see and diagnose a large array of ocular issues.
Since they are relatively old by technological standards, the principles behind them have become more and more understood as time has gone on. While a nice lab version with a corneal microscope is certainly better, innovations in manufacturing have brought the theoretical minimum cost of the device way down, or at least that’s what [Kewal Chand Swami] hopes.
His design aims for portability and cost reduction. It must be able to travel to remote locations and it must be significantly cheaper than the lab versions. It uses off-the-shelf lenses in a 3D printed housing with a simple LED torch, the kind you can buy for a dollar at the check-out stand.
The assembly slides onto the user’s head and is held there with straps. The doctor can adjust where the slit the lamp shines and also look through a microscope to diagnose the issue. Hopefully devices like this will see similar community support to the prosthetic projects we’ve covered.
How To Set Up And Run A Makerspace
A bunch of people who share a large workshop and meet on a regular basis to do projects and get some input. A place where kids can learn to build robots instead of becoming robots. A little community-driven factory, or just a lair for hackers. The world needs more of these spaces, and every hackerspace, makerspace or fab lab has its very own way of making it work. Nevertheless, when and if problems and challenges show up – they are always the same – almost stereotypically, so avoid some of the pitfalls and make use of the learnings from almost a decade of makerspacing to get it just right. Let’s take a look at just what it takes to get one of these spaces up and running well.
Workbench Eye Candy From Around The World
The workbench. We’re always looking for ways to make the most out of the tools we have, planning our next equipment purchase, all the while dealing with the (sometimes limited) space we’re allotted. Well, before you go off and build your perfect electronics lab, this forum thread on the EEVblog should be your first stop for some extended drooling research.
You’ll find a great discussion about everything from workbench height, size, organization, shelf depth, and lighting, with tons of photos to go with it. You’ll also get a chance to peek at how other people have set up their labs. (Warning, the thread is over 1000 posts long, so you might want to go grab a snack.)
We should stop for a moment and give a special note to those of you who are just beginning in electronics. You do not need to have a fancy setup to get started. Most of these well equipped labs is the result of being in the industry for years and years. Trust us when we say, you can get started in electronics with nothing more than your kitchen table, a few tools, and a few parts. All of us started that way. So don’t let anything you see here dissuade you from jumping in. As proof, we’ve seen some amazingly professional work being done with the most bare-bones of tools (and conversely, we seen some head-scratching projects by people with +\$10,000 of dollars of equipment on their desk.)
Here’s some links that you might find handy when setting up a lab. [Kenneth Finnegan] has a great blog post on how his lab is equipped. And [Dave Jones] of the EEVblog has a video covering the basics. One of the beautiful things about getting started in electronics is that used and vintage equipment can really stretch your dollars when setting up a lab. So if you’re looking into some vintage gear, head on over to the Emperor of Test Equipment. Of course no thread about workbenches would be complete with out a mention of Jim Williams’ desk. We’ll leave the discussion about workbench cleanliness for the comments.
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(115) Homework (Due 5/4)
Section 7.1: 7, 8, 10, 11, 15 ($log$ means$log_{10}$)
Section 7.2: 1, 4, 6, 7,14
Section 9.1: 2, 4, 12, 16, 40
Section 9.2: 2, 6, 11, 16, 32, 38
Section 9.3: 1, 2, 5, 6, 8, 11, 12, 21, 22
(107) Homework 9(DUE 5/2, Tuesday)
Hi all,
Here is a set of homework on optical illusions: HWK9
(107) Homework (due 4/25, Tuesday) and review
Hi all,
Here is a set of homework on graph theory: HWK8
Our quiz is on next Thursday, and here is the review: statistics_summary
(107)Homework (DUE 4/13)
Here is a set of homework due. Please make it clear which diagram you chose from Spurious correlations. HWK7
Watch “How To Solve A Crime With Graph Theory” on YouTube
Graph theory is useful. Indeed.
(115) Homework (due 4/13)
Hi all,
Section 4.3: 1,3,8,11,17,21(compute derivative in Calc 1),23,24,25($set r(x)=1/4$), 30,32,33
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$\newcommand{\defeq}{\mathrel{\mathop:}=}$
2008/07/05
Interpreting a New Kind of Monotonicity
The following theorem is a slight generalisation from the original monotonicity and greedy theorem:
Thm. Let R : A ← A be a preorder and S : A ← FA
be monotonic on Rº in the sense that
S . FRº . Tº ⊆ Rº . S
where T : FA ← FA satisfies
S . T ⊆ S.
Then
min R . Λ⦇S⦈ ⊇ ⦇min R . ΛS . T⦈.
There is a way to interpret the new monotonicity condition:
S . FRº . Tº ⊆ Rº . S
y b a a' y x a'
Here we are comparing two partial solutions a and b, where b is worse than a. A complete solution y is generated from b. The monotonicity condition says that instead of choosing b as the input, we should take another partial solution a' which is transformed from a by T, since from a' one can generate another complete solution x which is better than y.
The interpretation is a bit strange, though. It seems that we are mixing two different levels of solutions. The premise compares a and b, but the conclusion is that a solution generated from b is worse than another solution generated from a', which is transformed from a.
R
a ----- b
| |
T | |
↓ |
a' | S
| |
S | |
↓ ↓
x ----- y
R
It seems to be more sensible if what the monotonicity says is like this:
R
a ----- b
| |
T | | T
↓ ↓
a' b'
| |
S | | S
↓ ↓
x ----- y
R
The partial greedy theorem is a special case of this theorem, where T is a coreflexive. When deriving the activity-selection problem, I do have to do some "coreflexive propagation" and fusion to make the monotonicity look like the second diagram. Maybe this peculiarity would be understood if we can solve some concrete problem by this theorem.
Another point to make: If T is entire, then the conditions of the theorem would imply the original monotonicity condition:
S . FRº . Tº ⊆ Rº . S
⇒ { composition is monotonic }
S . FRº . Tº . T ⊆ Rº . S . T
⇒ { T entire }
S . FRº ⊆ Rº . S . T
⇒ { S . T ⊆ S }
S . FRº ⊆ Rº . S.
Then we can just apply the original greedy theorem and get rid of T. So this theorem is interesting only if T is not entire, which is just the case of partial greedy theorem.
And finally, we can also prove a similar variation of thinning theorem. This would potentially allow more problems to be solved by identifying this new kind of monotonicity.
--
More clarifications needed...
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# 20 Best Free Fonts for Cricut (Monogram, Cursive, Script)
Length:LongLanguages:
Looking for the perfect Cricut font? In this article, we'll take a look at some free fonts for Cricut, as well as some of the best Cricut fonts you can download for your craft projects, merchandise, and small business ventures. We've got monogram fonts for Cricut, Cricut lettering fonts, and much more.
## What Is a Cricut Machine and What Does It Do?
A Cricut machine is a cutting tool—but that is a lot more than it might sound like. You can create anything from kiss cut sticker sheets to greeting cards, gift tags, T-shirts, and more. Depending on your machine and accessories, your Cricut can draw, cut, and score a variety of materials, including various papers, vinyl, cardstock—some units can even work with leather and thin wood.
Create beautiful vinyl decals or create a beautiful, custom cake topper with your Cricut. There are so many possibilities with this versatile and easy-to-use tool.
It's important to note, however, that the Cricut is about cutting—not printing. So, for example, if you're interested in making something like bullet journal stickers, you'd need to print them out first. Then, let your Cricut take over to cut them for you. Your Cricut machine can make beautifully detailed cuts easier than ever.
It's an amazing tool for crafters, DIY fans, and independent artists who are looking to create and sell their own handmade merchandise.
## What Is a Cricut Font?
Cricut fonts are the fonts included in Cricut Design Space—a free tool that is used to prepare and design your work for use with your Cricut machine. Your Cricut comes with a bunch of Cricut Design Space fonts included, such as Cricut Sans, a versatile sans serif font. Cricut writing fonts and Cricut fonts with layers have additional functionality. For example, check out some of the double layer font Cricut options next time you're in Design Space, under Font Style.
Note that not all Cricut fonts are free. Many of them require a subscription to Cricut Access, a premium program that gives you access to a library of fonts and graphics. It's got some pretty nice offerings, too. It's got some of the best writing fonts for Cricut, if you want the machine to draw solid lines. Keep in mind, however, that you can often mimic the solid writing of some of the best writing fonts for Cricut by choosing a thin font.
However, your System Fonts can also work as Cricut fonts—fun and functional additions to your Cricut Design Space. This means that, in addition to the Cricut-specific fonts included with Design Space, you can also use other fonts installed on your computer. It's easy to add fonts to Cricut too.
This opens up a whole world of possibilities. While Cricut Access gives you access to hundreds of fonts, there are thousands upon thousands out there on the Internet to explore. It also means you're not stuck with the most popular Cricut fonts. You can choose something totally different and unexpected.
## Learn How to Upload Fonts to Cricut Design Space
Using your System Fonts in Cricut Design Space is a breeze, once you know where to look and how to do it. Check out this video tutorial that will walk you through how to add fonts to Cricut Design Space, step by step, over on our Envato Tuts+ YouTube channel:
I get it—everyone loves free content. However, if you're a power user or you intend to create work that you want to sell, free content can be a real bust. Think about it for a moment: just because something is free does not always mean it's free of copyright or licensing concerns.
It takes a lot of time and effort to find the perfect free font too. There might be a free price tag, but your time is valuable too. All that searching and the limited options can take a lot of the fun out of the design process.
But hey, we're all working with a limited budget. Downloading a collection of fonts, especially when you're paying per font, can add up pretty quickly. That alternative isn't always within our means.
So, what else is there? Check out Envato Elements.
Whether you're looking for Cricut handwriting fonts, the best Cricut cursive fonts, or stylish monogram fonts for Cricut, there's so much to download and try out. At the end of the day, the best Cricut fonts are going to be the ones that best complement your project. This can make buying individual fonts daunting and intimidating—what if you don't like it later? What if, after testing it out, it's just not right?
Well, with unlimited downloads, you can grab all the fonts you want to test out, without worrying about the price tag.
We're talking about a library of thousands of fonts here. Thousands of fonts to choose from with no extra fees—download to your heart's content!
Find your next favorite Cricut script font, or test out a few to find your best font for cake topper Cricut projects. With unlimited downloads, you can try them all.
But you also get thousands of graphics, photos, clip art, and more. It's all included. You can even pick up a template for your website, and there's no extra charge. You've got access to a giant library of professional assets.
This is an awesome deal and a time-saving resource for hobbyists, enthusiasts, and professional designers. Take the time out of searching for assets—you have a whole library at your fingertips. Use it for your small business, your crafting projects, DIY, and more.
### Get 1 Month Free!
Best of all, you now get unlimited free fonts for a whole month, completely free of charge. Use this amazing offer to stock up with the perfect fonts for all your Cricut projects!
To lock in this great deal, just use this link to register. Or enter this code when you sign up:
elements_cont_tuts-freemonth1-xaihhd
## 31 Best Cricut Fonts to Try in 2021 (With Unlimited Downloads)
Before we dig into our list of free fonts for Cricut, let's take a look at some of the premium options you could pick up today. Why limit yourself to common popular fonts for Cricut when you could have a whole professional library?
Free is everyone's favorite price tag, it's true—but if you're interested in creating work to sell, premium content can't be beat. All of these fonts come with commercial licensing included, and they are all included with unlimited downloads. There's no paying per font—you get them all, and you get the peace of mind of knowing they are all appropriate for creating and selling your own merchandise.
### 1. Palace Bold Calligraphy Cricut Font
This cute font is a great choice when it comes to adding new Cricut design space fonts. It's fun, friendly, and has a lot of personality.
### 2. Jelly Bean Cricut Script Font
This font download is a duo—you get two fonts that pair well together, all in one convenient package. Use them together or separately in your next design project.
### 3. Wild Hazelnut Cricut Lettering Fonts
Here's a chunky, varied font that could work well for anything from greeting cards to T-shirt designs. If you're looking for the best Cricut fonts for vinyl, paper, and more, this one has a lot of potential.
### 4. Eiffell Script Handwritten Cricut Font
The most popular Cricut fonts often include beautiful handwritten, script fonts. Follow the trend but stand out from the rest with a stylish, hand-drawn font like this one. It even comes with watercolor textures for your printed work.
### 5. Apple Juice Cute Cricut Font
Isn't this font cute? Imagine it on a lunch box or maybe on shirts for your next fundraiser or gathering. It's a great fit for kids, school events, and family get-togethers too.
### 6. Brixton Line Cricut Handwriting Fonts
When you try to write with your Cricut, you might notice that most fonts end up like an outline. However, if you try out a really thin font, like this one, you can often simulate the solid line you'd get from traditional Cricut writing fonts.
### 7. Avaline Ornaments Cricut Writing Fonts
Envato Elements also has decorative fonts, like this awesome collection of ornaments. Add all kinds of flourishes, lines, and wreaths by simply typing a letter.
### 8. Hello Sweets Cricut Script Font
If you're on the lookout for cute script fonts for Cricut maker, check this one out. It's easy to imagine this one in gold or a stylish iron-on.
### 9. Hinsa Cute Cricut Lettering Fonts
Check out this adorable font. It's a really fun but unusual design. It has the potential to work for a wide variety of projects too. Consider giving this one a try.
### 10. Daisy Girl Cricut Script Font
Here's another stylish script font. The best script fonts for Cricut are going to depend on your project—how do you like your scripts? This one's a great choice if you like long, pretty strokes.
### 11. Mateo Cute Cricut Handwriting Fonts
This fun, chunky font could be a great addition to your next project. Its bubble-like shape has plenty of potential for invitations, shirts, and more. This is a great download, especially if you're hunting for the best Cricut fonts for vinyl.
### 12. Monieta Elegant Cricut Script Font
But maybe you're hunting for the best script fonts for Cricut, instead. If you're a big fan of scripts, give this one a look. Its romantic feel could work for so many projects.
### 13. Little Peanut Cute Kids Cricut Font
Isn't this a cute font? It could easily be the best font for cake topper Cricut projects or maybe for your own custom coloring book pages.
### 14. Nadilla Cute Cricut Script Font
This font is such a bubbly, fun script. It could be a great fit for a child's project, birthday goodies, and a whole lot more. Give this cute font a try.
### 15. Bouquet Baseball Cricut Script Font
Doesn't this font have a cool baseball vibe? You could create your own baseball shirts and other merchandise with a font like this one.
### 16. Royal Jelly Cute Decorative Cricut Font
It's fun to check out popular fonts for Cricut—but how about more unusual ones, like this font? It has really interesting spirals in the design, giving it a fun look and feel.
### 17. Ceglist Cricut Script Font
This script font is super cute and super versatile. If you're looking for Cricut cursive fonts that connect, this one works well—just make sure to separate your letters in the Advanced Settings. Then you can adjust the alignment.
### 18. Pumpkins Candles Cricut Handwriting Fonts
Remember, if you're looking for the best drawing fonts for Cricut, and you specifically want to use the writing functionality, you can often mimic a filled letter with thin System Fonts, like this one.
### 19. King Crayon Cricut Font Cute
Isn't this a quirky font? It has a little bit of a retro vibe, doesn't it? This one could work well on packaging, T-shirts, and a whole lot more.
### 20. Kind Heart Pretty Circuit Script Font
This font is so fun and welcoming. It's a pretty handwriting font, perfect for letters, stationery, and other paper projects.
### 21. Wedges Bold Chunky Cricut Font
If you prefer a chunky font, give this one a look. It's rounded and playful, so it could be a great fit for projects created for (or with) children. Imagine it in your classroom.
### 22. Loman Bold Cricut Script Font
Here's a different take on a script font. The capital letters are really stylish—so if you're looking for the best Cricut font for monogram projects, this one might be worth a try.
### 23. Dear Emily Cricut Handwriting Fonts
Sweet, cute, and a lot of fun—that describes this adorable, handwritten font really well. Whether you're creating invitations, wearables, or something else, this one has a lot of potential.
### 24. Sunshine Monogram Font (Monogram Fonts for Cricut)
Envato Elements also has fonts specifically for monograms, just like this one. If you're looking to add to your collection of the best Cricut fonts for monogram projects, check it out.
### 25. Gathike Calligraphy Cricut Script Font
Script fonts can add such a classy, pretty look and feel to your projects. Check this one out. It has such lovely, swooping strokes. It could be the perfect addition to your next project.
### 26. Milk & Shake Cricut Handwriting Fonts
Or maybe you prefer longer strokes. This script font has such a playful vibe. It also includes extras that you can mix, match, and experiment with.
### 27. Priscillia Pretty Cricut Script Font
If you prefer thicker strokes, but you still love the elegance of a script font, give this one a look. It's inspired by hand lettering with a brush pen.
### 28. Donatellia Elegant Cricut Handwriting Fonts
Here's another thin font that could end up working well for writing, rather than cutting. Keep in mind that writing fonts work a little differently with your Cricut—but you can often mimic the look in System Fonts, if the stroke is really thin.
### 29. Little Morning Cricut Lettering Fonts
This font is so precious. It has such a friendly feeling, and has an easy association with baked goods and homemade treats. Try this one in your next DIY project.
### 30. Emilio Bold Cricut Lettering Fonts
Here's a bold font that takes some inspiration from script fonts, but keeps the letters independent. It's strong and could definitely make a bold statement.
### 31. Hello Love Stylish Cricut Script Font
This is such a classic, pretty font. It's easy to picture this one in a whole host of projects, from paper to vinyl to stickers to leather!
Let's talk about how to get free fonts for Cricut. Free fonts can be a great choice if you don't plan to make any projects that you want to sell. Remember, many free fonts are not completely free—they may only be free for personal use or have limited options. Make sure you're aware of the font's license before you use it—especially if you plan to sell your creations. You are responsible for knowing and following the license of any font you use and download!
Before you check out these free Cricut font downloads, did you know Envato Elements also offers free fonts for Cricut? If you're wondering how to get free fonts for Cricut, check out Envato Elements first!
### 1. Astrud Miller: Free Cricut Cursive Fonts
Here are some of the best cursive fonts for Cricut. Astrud Miller is a great free cursive typeface. Free writing fonts for Cricut like this are a great option.
### 3. Diettersen: Free Calligraphy Cricut Fonts
If you're looking for calligraphy Cricut fonts, you'll like these free Cricut writing fonts. Diettersen is one of the free Cricut font downloads you can get from Envato Elements.
### 4. Oskosh: Free Handwritten Cricut Fonts
Handwritten fonts look really cool on Cricut designs. These free writing fonts for Cricut are a great option for your next project, especially if you do designs for children.
### 5. Leah Gaviota Double: Free Decorative Cricut Fonts
Do you need fun, decorative free fonts for Cricut? Why don't you try Leah Gaviota Double? This is one of our coolest free Cricut font downloads.
### 6. Motion Picture Free Font
This fun script font could be a great fit for personal projects. This one is only free for personal use, so make sure to buy a license if you go commercial.
### 7. Huruf Miranti Free Font
This font is in the public domain—so it's fair game. Download, use, and enjoy as you wish. This one is thin, so it might be worth trying for writing.
### 8. Pacifico Free Script Font
Looking for free Cricut writing fonts? This script font is a popular one—you've probably seen it before on the web and in other projects! It's free to use, even for commercial projects.
### 9. Brusher Free Font
Here's another free font—it's free, but not necessarily in the public domain. Be aware of copyright restrictions if you plan to use this one commercially.
### 10. Learning Curve Free Font
Isn't this a cute font? It's a great fit for personal projects, as it's free for personal use only. If you want to go further, make sure to look into a license.
### 11. Always In My Heart Free Font
Here's another charming script font. It has so much potential, even as free writing fonts for Cricut. Download it for free for personal use. Otherwise, you'll need to purchase a license.
### 12. Berkshire Swash Free Font
This font has a slight slant and thicker strokes. It's got a touch of vintage style, doesn't it? It's free for personal use only, so you can try it out today.
### 14. Rakoon Free Font
This chunky script has so much personality. It could look great on a T-shirt, a bag, or a whole host of projects! It's free for personal use only.
### 15. Shrikhand Free Font
Here's another bold font with a retro vibe. This one is free, even for commercial use, but still has licensing limitations that you'll need to check.
### 16. Milkshake Free Script Font
This free font is such a versatile script. Dress it up or make it casual—it can do both. It's a free download, but it has some licensing limitations. Make sure to review them before you start your project.
### 17. Lobster Free Display Font
Here's a 100% free find—that's why this font might look rather familiar! It's a popular one, and it's free for commercial usage. Enjoy.
### 18. Bayland Free Script Font
What a beautiful retro font! Check out all the beautiful, thick strokes. Test this one out today, as it's free for personal use. If you want to go commercial, make sure to pay and license with the designer.
### 19. Luckiest Guy Free Display Font
Here's another popular freebie. If a font is 100% free, chances are, a lot of people have it and use it. Download and enjoy.
### 20. Alley Garden Free Font
This charming font has a touch of script flair, while keeping the letters apart. It's free for personal usage only.
## Which Are Your Favorite Fonts for Cricut Maker, Air 2, or Other Members of the Cricut Family?
You've seen the best Cricut fonts with unlimited downloads, and you know how to get free fonts for Cricut. There are so many fonts out there to choose from—whether you're a user who needs a commercial license or you're a hobbyist that wants to keep things free. Ultimately, the best Cricut cursive fonts, handwriting fonts, serifs, and even the best drawing fonts for Cricut are going to depend on your project and preferences.
Remember, if you're a power user or you're interested in selling your work, inform yourself. Make sure you're clear on the terms of use when using free fonts. We are all creative professionals—someone designed that font! Let's treat other artists the way we would want our work treated too.
Happy designing!
Read this article to find links to more free fonts, along with photos, videos, and more. And if you want to find even more fonts, check out these other inspiring font collections:
## Discover More Cricut Tutorials and Resources
I hope you've liked this article packed with the best cursive fonts for Cricut and free Cricut writing fonts. Now you know what is Cricut, how to add fonts to Cricut and how to get free fonts for Cricut.
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# Finding the integral surface passing through a given curve
The question here is to solve $x^2p+y^2q+z^2=0$ passing through a given curve $\Gamma : xy=x+y,z=1$
I am trying to solve it by Lagrange's method, where $\frac{dx}{x^2}=\frac{dy}{y^2}$, thus I get $1/y-1/x =c$ and then I substituted $x+y$ in place of $xy$ in denominator.
Thus I found: $(x-y)/(x+y)=c$
Is it correct ?
Soham
-
You are looking for $z$ as a function of $(x,y)$. The idea is to think of the graph of $z(x,y)$ as built up from curves starting from $\Gamma$. Say we parametrize the curves as $(x(s,x_0),y(s,x_0),z(s,x_0))$ which start from $\Gamma$ at $s=0$, at the point $(x_0,y_0,z_0)$, where $z_0 = 1$ and $x_0 y_0 = x_0+y_0$ i.e. $1/x_0+1/y_0 = 1$. Then take the PDE to be a case of the chain rule $$z' = z_x x'+z_y y' = x^2z_x+y^2z_y=-z^2$$ where we take $x'=x^2$, $y'=y^2$, and $z' = -z^2$ with initial values as above. Solve these by separation of variables, integrating $x^{-2}x'=1$ and so forth, as $$\frac{1}{x}-\frac{1}{x_0}=-s, \ \ \frac{1}{y}-\Big(1-\frac{1}{x_0}\Big)=-s, \ \ \frac{1}{z}-1=s.$$ Add the first two to eliminate $x_0$, giving $1/x+1/y-1=-2s$. Then this is $-2\big(1/z-1\big)$, so you find $$z(x,y)=\frac{1}{\frac{3}{2}-\frac{1}{2y}-\frac{1}{2x}}$$This is a solution if you check it.
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## Conceptual Physics (12th Edition)
Find the pressure. $$Pressure = (weight \;density)\times(depth)$$ $$= 10000 \frac{N}{m^{3}} \times (2 m) = 20000 \frac{N}{m^{2}}$$ Now find the force by multiplying pressure by the area. Remember that $1 cm^{2} = 10^{-4} m^{2}$. $$F = 20000 \frac{N}{m^{2}} \times (10^{-4} m^{2}) = 2 N$$ This is a small force.
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## Sturm Liouville Equations
A regular Sturm Liouville equation is a real second-order linear differential equation of the form
with boundary conditionswith at least one of and similarly forand with the functionsspecified.
In the simplest case all coefficients are continuous on the finite closed intervalandhas continuous derivative. In this case, this functionis a solution if it is continuously differentiable onand satisfies (1) at every point inIn addition,is typically required to satisfy some boundary conditions atandThe functionis called the weight function.
The value ofis not specified in the equation; finding the values offor which there exists a non-trivial solution of (1) satisfying the boundary conditions is part of the problem called the Sturm–Liouville problem.
Such values ofwhen they exist are called the eigenvalues of the boundary value problem defined above and the given boundary conditions. The corresponding solutions (for each) are the eigenfunctions of this problem. The solutions (eigenfunctions) of each Sturm - Liouville problem form an orthogonal basis for the set of continuous functions, so that ifandare solutions for distinctthen
We wish to find a functionwhich solves the following Sturm – Liouville problem:
with
In factis a solution with eigenvalue
Properties:
The eigenvalues of Sturm – Liouville problems form an infinite set:with as
Any pair of eigenfunctions corresponding to a particular eigenvalue are non – zero multiples of one another.
Ifis a complete set of eigenfunctions for (1) then
a) Theform a basis forthe set of continuous functions with continuous first derivatives.
b)Letbe any function inand letbe the nth Fourier coefficient ofwith respect to the basisthen the Fourier seriesconverges pointwise toon
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# What’s hot and what’s not, Issue 02
We tell you what’s popular in the world of maths, so you can get ahead of the curve!
### Python
from jokes import jokes_about_python
print(jokes_about_python)
### Fortran
We don’t use punch cards any more. Why are you still using a language designed for them?!
This is Fortran. We’re not kidding. (Source)
### Isaac Newton
Over 300 years before it was cool, Newton invented the diss track and completely destroyed Leibniz.
### Gottfried Leibniz
His haircut is so last issue and he doesn’t even have an Instagram account.
Not cool.
Yum!
Yuck!
### 36.7 °C
The UK’s hottest ever July temperature.
### 36.7 °F
Not the UK’s hottest ever July temperature.
Let’s go for a walk on the beach
• ### Book of the Year 2020
We announce the winner of this coveted prize
• ### 2020 Book of the Year vote
Have your say, and help to choose the 2020 Readers' Choice
• ### The Wonder Book of Geometry
We review the seventh of this year's nominees for the Book of the Year, and open the vote for the readers' favourite
• ### Hello Numbers! What Can You Do?
We review the sixth of this year's nominees for the Book of the Year
• ### Why Study Mathematics?
We review the fifth of this year's nominees for the Book of the Year
• ### Molly and the Mathematical Mystery
We review the fourth of this year's nominees for the Book of the Year
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# Tag Info
17
If $\Bbb Z[X]$ were a principal ideal domain, then its quotient by the ideal generated by$~X$, an element that is obviously irreducible, would have to be a field. But it is clear that $\Bbb Z[X]/(X)\cong\Bbb Z$ which is not a field.
15
Yes, below is a sketch a proof that $\rm\: \mathbb Z[w],\ w = (1 + \sqrt{-19})/2\$ is a non-Euclidean PID, based on remarks of Hendrik W. Lenstra. The standard proof usually employs the Dedekind-Hasse criterion to prove it is a PID, and the universal side divisor criterion to prove it is not Euclidean, e.g. see Dummit and Foote. The latter criterion is ...
12
In P. Samuel, Anneaux factoriels, pages 36-37, it's proved that $A=\mathbb R[X,Y]/(X^2+Y^2+1)$ is a UFD. In the following we denote by $x,y$ the residue classes of $X,Y$ modulo $(X^2+Y^2+1)$. Thus $A=\mathbb R[x,y]$ with $x^2+y^2+1=0$. Lemma. The prime ideals of $A$ are of the form $(ax+by+c)$ with $(a,b)\neq (0,0)$. Proof. It's not difficult ...
12
No; for example, $(x,y)$ is a maximal ideal which is not principal in $F[x,y]$. And also, $F[x,y]/(x^2-y^2)$ is not an integral domain since $(x-y)(x+y)=x^2-y^2$. On the other hand, the polynomial $y^2-x$ is irreducible and hence $F[x,y]/(x-y^2)$ is an integral domain.
11
Yes. Let $\phi(a/b) = |a|$ where $a/b$ is written in lowest terms. To see that this is a Euclidean function, let $a/b,c/d\in \mathbb{Z}_X$ be nonzero and in lowest terms and write $$\frac{a}{b}=\frac{nd}{b}\cdot \frac{c}{d}+\frac{s}{t}$$ which means that $\phi(s/t)=\phi((a-nc)/b)\leq |a-nc|$ which for a suitable value of $n$ is less than $\phi(a/b) = |a|$.
11
Consider a finite generating set and find a common denominator for its elements. Now, look at what you've got... Alternatively, if $M$ is such a submodule, it has no torsion and we know from the structure theorem for f.g. modules over a PID that it must be free. Its rank can be computed by first tensoring with $K$ over $R$ and computing the dimension over ...
11
Since $4(n^2+n+41)=(2n+1)^2+163$, one way would be to methodically show that $-163$ is a quadratic non-residue mod all (odd) primes less than $41$. Added later: The OP has asked for further details, so here goes. If $p\mid n^2+n+41$, then $(2n+1)^2+163\equiv0$ mod $p$, which means that $-163$ is a square mod $p$. Now the values of $n^2+n+41$ for $n\lt40$ ...
11
If $I$ is an ideal of $R$, then you can verify that that the set of numerators of $I$, $\{r\in A: \frac{r}{s}\in I\text{ for some$s\in S$}\}$, is an ideal in $A$, thus a principal ideal, generated by some element $t$. Now show that the ideal generated by $t=\frac{t}{1}$ in $R$ is the ideal you started out with.
11
Here is a proof followed by conceptual elaboration, from my 2008/11/9 Ask an Algebraist post. Let R be an integral domain. Let every prime ideal in R be principal. Prove that R is a principal ideal domain (PID) Below I present a simpler way to view the proof, and some references. First let's recall one well-known proof, as presented by P.L. Clark ...
10
Theorem $\$ The polynomial $\rm\ f(x)\ =\ (x\!-\!\alpha)\,(x\!-\!\alpha')\ =\ x^2 + x + k\$ assumes only prime values for $\rm\ 0\ \le\ x\ \le\ k-2 \ \iff\ \mathbb Z[\alpha]\$ is a PID. Hint $\ (\Rightarrow)\$ Show all primes $\rm\ p \le \sqrt{n},\; n = 1-4k\$ satisfy $\rm\ (n/p) = -1\$ so no primes split/ramify. For proofs, see e.g. Cohn, Advanced ...
10
We will prove this using the PID $R:=\mathbb{Z}[\omega]$, where $\omega=\frac{1+i\sqrt{163}}{2}$, with the norm $N(a+b\omega)=|a+b\omega|^2=a^2+ab+41b^2$. Lemma 1: If $p$ is prime in $\mathbb{Z}$ such that $\exists n\in\mathbb{Z}$ such that $p|n^2+n+41$, then $p$ is reducible in $R$. Proof: Let $p|n^2+n+41$ and assume $p$ is irreducible. Then $p$ is also ...
10
Hint: Consider the ideal $(2, x)$. Show that it's not principal. Suppose $(2, x) = (p(x))$ for some polynomial $p(x) \in \mathbb Z[x]$. Since $2 \in (p(x))$, then $2 = p(x) q(x)$ for some polynomial $q(x)\in \mathbb Z[x]$. Since $\mathbb Z$ is an integral domain, we have $\operatorname{degree} p(x)q(x) = \operatorname{degree}p(x) + ... 10 Broadly speaking, the information you gave in your question is up-to-date: ever since Gauss, number theorists have believed there should be infinitely many real quadratic fields of class number one, but we are not any closer to being able to prove this than Gauss was, to the best of my knowledge. Moreover you have identified the key problem: the fact that a ... 9 According to the theorem about finitely generated modules, any finitely generated module over a PID$R$can be expressed as $$R^r \oplus R/(p_1^{k_1}) \oplus R/(p_2^{k_2}) \oplus \cdots \oplus R/(p_n^{k_n})$$ where$p_1^{k_1},\ldots,p_n^{k_n}$are prime powers in$R$. The$R^r$is called the free part, and the other summands are elementary divisors. ... 9 Your statement is equivalent to proving (why?) that there are finitely many ideals$(b)$such that$(a) \subset (b)$. But,$(a) \subset (b)$iff$b|a$. Now factor$a$into a finite product of irreducibles and use the fact that a P.I.D. is a U.F.D. to show that there can be only finitely many possibilities for$b$such that$b|a$. 9 The problem is that the set of all composite integers does not form an ideal. For example if you add$21 - 4$you get$17$which is a prime and thus not composite. That's why there's no contradiction. Remember that for a subset of a ring to be an ideal it must be closed under addition and under taking multiples by elements of the ring, and in this case the ... 8 We do this in a few steps. Let$R$be our integral domain, and we are supposing that every prime ideal in$R$is principal. Let$S$be the set of non-principal ideals of$R$, and suppose that$S$is nonempty. Throw an inclusion partial order on$S$(or note that it has one, but I like to be physical with my math sometimes). WRT this partial order, let ... 8 There are various ways to interpret how class groups measure (non)unique factorization. For example, Carlitz (1960) showed that the class group has order at most$2$iff all factorizations of a nonzero nonunit into irreducibles have the same number of factors. Narkiewicz posed the problem of generalizing this, i.e. devising arithmetical characterizations of ... 8 Suppose$\def\ZZ{\mathbb Z}I\subseteq\ZZ\times\ZZ$is an ideal. If$(x,y)\in I$, then$(x,0)=(1,0)(x,y)$and$(0,y)=(0,1)(x,y)$are also in$I$. If we write$I_1=\{x\in\ZZ:(x,0)\in I\}$and$I_2=\{y\in\ZZ:(0,y)\in I\}$. then it follows easily from this that$I=I_1\times I_2$. Now$I_1$and$I_2$are ideals of$\ZZ$, so that there are$a$,$b\in\ZZ$such ... 8 Here's what I think is a nice way to find a few PIDs that aren't Euclidean. It's not quite elementary, but if you know a bit about number fields I think it's a lot easier and nicer than the normal drudge. Let$K=\mathbb{Q}(\sqrt{-d})$for$d>3$squarefree, with ring of integers$\mathcal{O}_K$. Then the only units in$\mathcal{O}_K$are$\pm1$. Suppose ... 8 This thread (including comments from both Jeremy and Alex) was very useful to me in PhD Quals preparation. I would like to give a detailed proof using Jeremy's and Alex's outline, but without mention of Spec(R), in case the reader is less algebraic-geometry-inclined. Corrections welcome. Thanks. Proposition. Let R be a UFD in which every nonzero prime ... 7 Ok, so it seems to me what you're saying is that you've proven that under the condition that every prime ideal is maximal that every maximal ideal is principal. The problem then follows from a nice condition you might want to remember: Theorem: Let$R$be an integral domain. Then,$R$is a PID if and only if every element of$\text{Spec}(R)$is ... 7 The ring$\mathbf Z[w]$is isomorphic to the quotient ring$A=\mathbf Z[x]/(x^2+x+1)$. To show$2$is prime, you have to show$A/2A$is an integral domain. We have: $$A/2A \simeq \mathbf Z[x]/(2,x^2+x+1)\simeq \mathbf Z/2\mathbf Z[x]/(x^2+x+1)$$ so it is enough to show the polynomial$x^2+x+1$is irreducible over$\mathbf Z/2\mathbf Z$, which means it has ... 7 Given a UFD which is not a field, it has a prime element. It generates a non-zero prime ideal, so that we have a chain of prime ideals of length 1 and therefore the dimension is at least 1. It remains to decide if PIDs are UFD. The usual proof uses the axiom of dependent choice, which is a weak form of the axiom of choice. In fact, it turns out that it is ... 7 Different prime ideals are coprime because in a Dedekind domain every nonzero prime ideal is maximal. If$P$and$Q$are nonzero prime ideals then$P+Q$is an ideal containing both$P$and$Q$and so must be the whole ring if$P\ne Q$. 7 Hint: What about the ideal$\langle2,x\rangle$? To answer your comment, a principal ideal is just a "set of multiples" of the generating element. Thus every element of a principal ideal has the generator as a divisor, and usually has similar properties. For example, in$\mathbb{Z}[x]$, the ideal$\langle2\rangle$is the set of polynomials where every ... 7 The claimed result is false: For$R/I$to be a principal ideal domain, it must be a domain. But$R/I$is a domain if and only if$I$is a prime ideal. In particular,$\mathbb{Z}/6\mathbb{Z}$is a quotient of a PID that is not a domain, hence not a PID. What is true is that a quotient of a PID will be a principal ideal ring: every ideal of$R/I$is ... 7 Here is a general result: If$D$is a domain, then$D[X]$is a PID iff$D\$ is a field.
Only top voted, non community-wiki answers of a minimum length are eligible
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## Study23 Group Title Solve the differentiable equation: dy/dx = y^2 ? one year ago one year ago
1. openstudy11 Group Title
2y
2. terenzreignz Group Title
You mean separable, right? :D
3. terenzreignz Group Title
and lol, @openstudy11 It is unfortunately not that simple :D
4. terenzreignz Group Title
@Study23 Shall we? :)
5. Study23 Group Title
Yup :D
6. terenzreignz Group Title
Okay, thing about separable differential equations... they are.... separable! LOL Yeah, I know, big surprise :) What I mean is that you can rearrange them so that you can separate them into expressions involving only y and involving only x. Let's have a look at this $\huge \frac{dy}{dx} = y^2$ You can treat the dy and dx as variables like any other, when separating. Just you try multiplying both sides by dx, and what do you get?
7. Study23 Group Title
dy = y^2 dx; I was doing this but I got confused because you couldn't integrate this could you?
8. terenzreignz Group Title
Not yet. Now, you could bring all expressions involving y, to the appropriate side of the equation (namely, the side with the dy) You could do this by multiplying $$\large y^{-2}$$ or $$\Large \frac1{y^2}$$ on both sides, and what would you get then?
9. Study23 Group Title
dy/y^2=dx (?)
10. terenzreignz Group Title
Correct :D $\huge \frac{dy}{y^2}=dx$ Now, slip a $$\Huge \int$$ sign on both sides of the equation~ and be done with it :D
11. Study23 Group Title
So, ln|y^2|=x ?
12. terenzreignz Group Title
oh... $\huge \int \frac{1}{y^2}dy \ = \int dx$ Are you sure? Maybe this ought to refresh you $\huge \int y^{-2}dy \ = \int dx$
13. terenzreignz Group Title
Okay, we started with this, right $\huge \frac{dy}{y^2}=dx$ And we simply integrated both sides $\huge\color{blue}\int \frac{dy}{y^2}=\color{blue}{\int}dx$ And yes.... $\huge \int ax^n=\frac{x^{n+1}}{n+1}$ when $$n\ne -1$$
14. terenzreignz Group Title
Sorry, my bad $\huge \int ax^n = \frac{ax^{n+1}}{n+1}$
15. Study23 Group Title
So, I get $$\ \Huge -y^-1 + C_1 = x$$ ?
16. Study23 Group Title
That should be $$\ y^{-1}$$
17. terenzreignz Group Title
Mother of sizes... o.O LOL $\huge -y^{-1}+C = x$
18. terenzreignz Group Title
If you want it as a function of y, you can bring the constant to the other side $\huge -\frac1y=x+C_0$ and then isolate $\huge y = -\frac1{x+C_0}$
19. terenzreignz Group Title
But on the whole, good job :)
20. Study23 Group Title
So, my textbook has this interns of Y= ...
21. terenzreignz Group Title
22. Study23 Group Title
In terms (autocorrect)
23. terenzreignz Group Title
24. terenzreignz Group Title
It just needs some algebraic manipulation is all.
25. Study23 Group Title
Oh, haha I didn't see that! :D. Thanks for all your help @terenzreignz ! I appreciate your encouragement! By the way, any tips for the AP Calc BC exam by the way?
26. terenzreignz Group Title
I don't know what exam that is... better consult someone more familiar with it :)
27. Study23 Group Title
Oh haha okay. Thanks!
28. vickky Group Title
dy/dx=y^2 dy/y^2=dx then integrate both the side -1/y=x+c
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# What does a z-test measure?
A Z-test is a statistical test used to determine whether two population means, ${\mu}_{1}$ and ${\mu}_{2} = 0$ with known variance are different. The Z test assumes a large sample size and a normal distribution. In fact the $Z$ distribution is $Z = N \left(\mu = 0 , \sigma\right)$
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# Return on investment?
Discussion in 'Investments' started by Patgdirector, Dec 30, 2016.
1. ### PatgdirectorRegistered User
Posts:
21
I have been investing with an Irish Life Assurance company since May 1994. I started off in 2004 paying €342.83 twice a year and in 2016 I paid €955.12 twice a year also. It goes up by 5% each year to take in to account inflation.
According to my calculations I have paid in €25,361.54 and it is worth €35,840. I know it is worth 40% more than what I have put in but taking in to account the over 20 year is this a good return? What is the % annual return?
Many thanks
2. ### dub_nerdFrequent Poster
Posts:
1,246
Last edited: Dec 30, 2016
Your own figures don't quite add up. If your first half yearly payment is 342.83 in May 1994 and it goes up 5% a year, your 22nd May payment (that is, the one in May 2015) will be 955.12 :
$a_n=ar^{n-1}\ \ \Rightarrow \ \ n=\frac{\log{a_n}-\log{a}}{\log{r}}+1=\frac{\log{955.12}-\log{342.83}}{\log{1.05}}+1=22$
... where a is the initial payment amount in year 1, an is the amount in year n, and r is the common ratio of the geometric series i.e. 1.05 for 5% growth. At the end of 2015 you will have contributed the following amount which we get by summing the series, bearing in mind there are two payments per year:
$\sum_{i=0}^{n}a_i=a\frac{1-r^n}{1-r}=(2\times 342.83)\left( \frac{1-1.05^{22}}{1-1.05}\right )=26,401.49$
This is greater than the total payments according to you by something over €1k and is at the end of 2015, not 2016. Maybe you can figure out what is wrong from your figures. But just to show the growth calculation, assuming your €35,840 value applied at the end of 2015, we just look for a different rate of growth that would have produced that:
$\sum_{i=0}^{n}a_i=a\frac{1-r^n}{1-r}=(2\times 342.83)\left( \frac{1-r^{22}}{1-r}\right )=35840$
$\Rightarrow 1-r^{22}=(1-r)\left( \frac{35840}{(2\times 342.83)}\right )$
$\Rightarrow 52.271r-r^{22}=51.271$
$\Rightarrow r = 1.07524$
That is, the growth rate was 7.524% of which 5% was accounted for by your increased payments, so the growth produced by the fund was just over 2.5%. Obviously this is an average and the actual growth rate will have varied from year to year.
Is this a good return? I don't know much about it but looking at historical S&P 500 figures I see it grew by an annual average of 7.37% between the end of 1994 and the end of 2015. On that comparison, it doesn't look very good. Had you got the S&P 500 rate of growth your fund would be worth €58,637. I presume your policy had some sort of life cover component which you seem to have paid pretty dearly for. Perhaps one of the finance gurus here can comment.
Last edited: Dec 30, 2016
irish_investr likes this.
3. ### Duke of MarmaladeFrequent Poster
Posts:
1,524
Last edited: Dec 30, 2016
Thanks to the eponymous dub_nerd for crunching the numbers (deeply impressed).
Is it a good return? I presume you mean compared to alternatives. Need to know a lot more to answer that. It was probably a balanced fund so you would have been largely protected through the various stockmarket upheavals of the period so a straight comparison with an equity index is probably not appropriate.
Without actually checking I would be fairly confident that it comfortably beat saving in a bank deposit. On the other hand if you could have channelled the money to paying off a mortgage that might have been a better course, but I can't be sure.
A key element is taxation. If this is not a pension policy then it is one of the old style internally taxed funds. If that is the case then your return is after tax. That makes a big difference. By benign neglect these old style funds (no longer available) are taxed at 20% whilst the newer style funds are taxed at 41% albeit only when you encash (i.e. you get tax free roll up until then). Nonetheless you are on to a good thing and I would not be getting out or reducing my contribution unless I had to, in fact if allowed I would ask them to increase my contribution
Yes, life policies can be costly. As a rough guide you have probably lost 1.5% per year to costs i.e. about a third of the gross return on the fund before taxes and charges. Though on an ongoing basis the costs might be half of this (no more brokerage costs, I hope) so given the tax advantages I would hang on in there.
Last edited: Dec 30, 2016
4. ### PatgdirectorRegistered User
Posts:
21
Thanks for the response.
Looked at my figures again and went back over all the payments and sorry started in May 1995 with €342.83 in May and €342.83 again in December. 1996 was €359.97 in May and December and so on..
The life cover is very poor just €2,000 or even less if I kick the bucket...was only 25 at the time and not interested in life cover just savings.
So in April 2016 was worth €33,733.10 with €24,406.42 paid in.
So not sure how that affects the return on investment..
I took this out when I started my first job after college and the life company in question pulled as master stroke when you hired the trainer of the local GAA team and he signed up all the lads...he signed up a lot of people.
Correct Duke it has the 20% tax so that is why I am not sure about cashing it. The house I am living in is paid off But I have just purchased a new primary residence so will be renting the old one. So the new house has a 3.3% mortgage rates so should I use the money from here to put against it?
5. ### Duke of MarmaladeFrequent Poster
Posts:
1,524
Last edited: Jan 3, 2017
From a purely arithmetic standpoint the question is: will your fund earn more than 3.3% p.a. after taxes and charges? Given the favourable tax treatment, 3.3% is not a big ask (but not a breeze either); your life company would probably illustrate that you will beat this rate, notwithstanding that you have failed to do so for the last 20 odd years.
From one lens you would actually be running a partial Endowment Mortgage in keeping the policy along with the mortgage, and these have been thoroughly discredited when used 100% to fund a mortgage. But at these levels there is a bit more flexibility in keeping your "nest egg" rather than cashing it in and paying down your mortgage. Of course, paying down your mortgage saves you 3.3% p.a. for certain whereas keeping your life policy runs a risk of a fall in values; there are those who feel current markets are artificially high because of Central Bank interference through QE and that a correction is due, but no one can tell.
On balance, though, the sums are probably not enormous in your overall context and you will probably prefer to keep up the policy esp. given its favourable tax status. It's a personal choice - not a slam dunk either way.
On a technical point, my guess is that you are in a mixed (aka balanced, managed) fund with some exposure to government bonds. It seems to me that this aspect of your investment is sub optimal in that you are earning at best 2% p.a. on the bonds whilst you are mortgaged at 3.3% p.a. To me, if you do decide to keep up the policy I would go all in and switch funds to a full equity exposure.
I sense that you are disappointed in your return. You would have been illustrated net returns at least twice those you have enjoyed. But I don't think you should be kicking yourself (or your life company or advisor) in having missed out on some super alternative, you haven't. The world has changed. The inflation driven super nominal returns of the second half of the twentieth century are now a distant memory.
Last edited: Jan 3, 2017
6. ### dub_nerdFrequent Poster
Posts:
1,246
Ok, makes sense. Ran a quick revised calculation and the growth rate looks slightly better at 2.8% per annum. Still pretty rubbish in my opinion. I disagree with Duke. If that is the average when the S&P average was 7.5%, how's it going to perform in the current era of low returns? I presume considerably worse.
Been there, done that. In my case it was the local maths teacher and heard several similar stories. Fortunately I only stuck with it a couple of years before realising all the initial money was going to pay fees. It was a good early lesson. Ever since I treat every form of financial salesperson as a hustler at best.
7. ### Duke of MarmaladeFrequent Poster
Posts:
1,524
Pat you invested less than 3% of your 22K in 1995 so I am not sure how relevant is the growth in the US stockmarket from that date. Possibly more relevant is that the Irish stockmarket fell by 40% from its peak which happened about in the middle of your investing that 22K.
My recollection is that life companies at that time gave two illustrations, a higher one assuming growth before charges and tax of 8% p.a. and a lower one of 6% p.a. After taxes and charges these would roughly become 5% and 3% respectively. So you more or less came in on the lower illustration. I suppose that is cause for disappointment esp. if your GAA trainer told you to ignore the lower illustration as being the silly life company being too cautious.
However, note that long term inflation expectations at the time were c.5% (hence the premium increases on your policy) and that acual inflation has turned out to be much lower. So when you "inflation adjust" those illustrations they seem remarkably spot on.
IMHO you should not let the difference between your past return and the return on the American stockmarket since you took out your policy influence whether you should now cash it in and pay down your mortgage.
8. ### dub_nerdFrequent Poster
Posts:
1,246
Duke, I presume just because it's an Irish Life fund does not mean it's invested in the Irish stock market, so the ISEQ is no more relevant than the S&P. However, the S&P also fell 40% during the GFC so I take your point about the fund taking a hit late in the investment period. I ran the OP's numbers again using the actual S&P end of year numbers for each year instead of an average. I applied each year's S&P growth to the previous year's investment by the OP. Obviously this is still an approximation and uses an index that may or may not be relevant, but the numbers do come out closer to the OP's actual returns:
The OP got a valuation sometime in early 2016 so at S&P rates of growth it should have been somewhere between the two bolded figures at the bottom right. Allowing for fees etc. you could maybe argue that his actual value is not a bazillion miles off (although it doesn't look so great when you subtract the amount paid in and just look at actual growth). Perhaps the real lesson is that stock market investments are prone to serious episodic setbacks and are risky even over long time horizons (contrary to what I feel is sometimes portrayed on this forum).
9. ### Duke of MarmaladeFrequent Poster
Posts:
1,524
Last edited: Jan 5, 2017
Great stuff nerd I have taken your growth figures and made allowance for tax and charges. You will see that it comes in at even less than Pat enjoyed. However, I suspect your growth rates do not include dividends. If we allow for these we might get remarkably close - which of course will be a complete fluke for I guess Pat's fund was a million miles away from the S&P index
We do see in the figures that based on this example typical charges consumed about half of the net (of tax) growth available. The sums involved are small and we see that retail investment at these levels is scarcely economically justifiable, though it did beat bank deposits and state savings (I think). I shudder to think what the economics of low end retail investment is these days in such a low return environment, and with 41% exit tax
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# Too old to start as Pete Eng?
## Too old to start as Pete Eng?
(OP)
Hello, I'm new to this site and found it while doing a search for info. I am currently in the USAF and will be retiring soon. I have been accepted to and I'm currently working towards my degree in Pete Engineering. But I will be 46 years old when I enter the job market. With oil prices hitting the lows they are and hearing about new grads having issues getting jobs I am wondering if I should changing fields. I have 20 years experience in aviation maintenance and worked 4 of those years in a job along side engineers. So I know this is a field I want to enter. But I'm just concerned about the job prospects after graduation. Any advice anyone is willing to give would be great! My second choice is Electrical Engineering. I appreciate any and all help!
### RE: Too old to start as Pete Eng?
All industries are cyclical. Oil and Gas cycles just make the news more often. People that started a Pet Eng program in 1982, 2004, 2011, etc to graduate during the disaster of 1986, the Global Economic Crises of 2008, or the current price collapse did have difficulty finding employment. There was still some hiring going on, but it scaled back to the best Pet Eng schools (Texas A&M, Colorado School of Mines, University of Tulsa, University of Texas, Texas Tech, etc.) and slowed way down or stopped at programs that didn't have the track record of the top tier schools.
I have always thought that the people who entered Pet Eng programs during the various collapses were the smart ones. Nothing lasts forever, and the need for petroleum products is only increasing, so if I was a 42 year old with my 20 in I would consider both my age and the current downturn to be positives and go for it.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
### RE: Too old to start as Pete Eng?
(OP)
Thanks for the reply. After doing some research Pet Eng seems to be a growing field. But entering later in life with little direct experience is a little nerve racking. I'm retiring back to Alaska and will be attending the University of Alaska Fairbanks. Not sure where they rank among the other schools though. I know the oil industry pumps a lot of money into the school. So I am hoping it will be a good place to go and start the next chapter!
### RE: Too old to start as Pete Eng?
It isn't a school that you hear about in the top tier, but Alaska is so remote, that I would be shocked if there wasn't an "indigenous peoples" mindset (i.e., anyone you hire in Fairbanks doesn't have to be moved from the lower 48) that we see all over the world.
I know when Amoco had a district office in Anchorage (working the offshore wells in the Cook Inlet off the Kenai Peninsula) it was the hardest district to get transferred to. I was working in the General Office back then and I had no problem traveling from Tulsa to London, Calgary, Trinidad, or Argentina, but I had to submit a request to an executive VP before I could go to Anchorage. Fairbanks may be a very good choice, I just don't know.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
### RE: Too old to start as Pete Eng?
(OP)
I guess I have a little more research to do on job availability up in AK. I would like to find something that keeps me in the state. But I know things are shaky up on the slope right now. I guess only time will tell, thanks again!
### RE: Too old to start as Pete Eng?
My best advice is, stay with what you're doing, as long as you can like it.
### RE: Too old to start as Pete Eng?
(OP)
BigInch thanks for the reply. Staying in the military isnt something i want to do. 20 years is enough for me, i have enjoyed my time. But its time to move on and Engineering is the direction i want to move in. Appreciate your advice though.
### RE: Too old to start as Pete Eng?
Yes you said that you are retiring from the military. I was referring to staying with aviation. I'm sure you've got a rather large investment in it and it will take you the same number of years or probably more to recoup that in another field. I'm all for developing new skill sets, but you have to realize it can have a very heavy associated cost.
As it's not the best of times for oil, so at least you won't lose the first 3-4 years. With the price of oil (jet fuel) set to come down, I'd be buying up av stocks. There is a US Forest Service, Fish & Wildlife, EPA, etc. as well. Alaska must need some looking after the environment and seems like you want to live up there for some reason. Not a fit? Alaska had aviation before oil, and it'll be there afterwards too.
### RE: Too old to start as Pete Eng?
There is nothing wrong with wanting to put down the wrench and ear muffs. There are a lot of people on eng-tips.com that completed their military service with a skill useful in the civilian world (mine was nuclear power) and then go to college to get an engineering degree and work in an unrelated field. Happens all the time. People spend a military career doing something and then often want to be higher on the pecking order than straight conversion of skills would put them. Happens all the time and should happen all the time.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
### RE: Too old to start as Pete Eng?
(OP)
David, you hit the nail on the head. Im looking to get away from wrenching and in AK most maintenance is done by small FBO's. They don't and really cant pay a lot, and there are no hubs there to move up the chain. Im not looking to be rich but I have 3 kids that need to go to college! On top of that the family wants to set roots. That plus my age has me a little worried about the Pet direction. I want to use my GI Bill to change careers and do something that I am pretty sure I will enjoy is what's on my scope. I have already been knocking out classes and should only have 3 years to graduate when I retire next year. My guess is that production is going to increase up north and the job outlook should be better in 3 years. They just approved Shell to drill up there and the state is looking hard at the natural gas pipeline. So I am betting on there being jobs up there that will keep me in the state for at least awhile. If I could go another 20 years and stay there it would be great. But I know that's not always the case. Thanks again for the inputs guys!
### RE: Too old to start as Pete Eng?
One thing that you need to ask yourself is "Do I want to be a Pet Eng or am I interested in the Oil & Gas industry?" Either answer should point you to a path. I'm a ME and have had a heck of a career in surface facilities, compression, and downhole pumping. If you are interested in geology, rock mechanics, and geophysics then Pet Eng is a really good way to go. If you like building stuff, pipe flow, multi-phase flow, corrosion, and flow measurement kinds of things then ME might be a better way to go. There are certainly more ME's in Oil & Gas than Pet Eng guys. Many of the ME's are in petroleum jobs. Few Pet Eng are in ME jobs.
When I got out of the Navy I treated college as a job, I already knew how to drink, was married, and I'd come to grips with dealing with my hormones. I got my BS in 33 months. It is quite doable, you just have to convince your adviser that 19-24 semester hours is a fraction of the work you did in the service. I never once felt overloaded, in fact I was able to get hooked on a soap opera while in school (that really sucked when I got a job in the pre-DVR days) while maintaining a 4.0 GPA.
Getting your first job out of college, your grades matter (even though they will never matter again, they really matter for the first job) the cut off for most Major Oil & Gas companies is a 3.8 out of 4.0, second tier companies usually will look at applicants with a 3.6 (smaller companies rarely hire new grads), below that you are pretty much limited to service companies. Service companies work you to death, but at the end of 2-3 years, all of the producers are interested in you. That is really the most common path to a production company these days (when I started in 1980, the path was reversed, the service companies and smaller producers poached from the Majors--there were something like 150 engineers that started with Amoco the day I did, 10 years later there were 3 of us still with Amoco, most of the rest were doing quite well at smaller producers).
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
### RE: Too old to start as Pete Eng?
Interesting discussion here, and I know that zdas and myself have fundamentally the same opinions on life in general, and northern experience, altho in vastly different fields. However I have to ask the OP has he really researched opportunities in Alaska or is just assuming that a good man can work up there. I have zero knowledge of Alaska but I do know the Canadian equivalent, the Beaufort sea, died a natural death in the early 1980s. A few men made a pile of money initially but then it seems Canadian society refused to accept the potential ( perceived??) environmental consequences of development and I don't think a single barrel or bcm of gas has produced in the last 30 years. I wonder if there isn't more opportunity in the Dakotas or somewhere else in the south. Most of recent Canadian O+G is south of 60.....just like the Dakotas, there's been so much stuff found down south that nobody wants the risk of going north. If the OP wants to live in Alsaka for personal reasons, that's one thing. If he wants to earn to put his kids thru school that might be a different discussion.
(OP)
### RE: Too old to start as Pete Eng?
Well, I wouldn't want to be seen as overly negative but I'm glad I'm not in your shoes. I have put 40 years into the mining business, might milk it for another 5 years, but I could retire tomorrow quite comfortably. You are 42 years old, still with family responsibilities. I am assuming you are an American citizen, apparently based in the UK ( an area I have extensive knowledge of). If you've put 20 years into the military, have lived in Alaska for 12 years, and are perhaps more familiar with the British way of life than American, I feel compelled to remind you that, anyone in the military is to some extent insulated from the realities of civilian life. THat is why so many have trouble making the transition. Depending on how long you've been in the UK , you're even further removed from first hand knowledge of the realities if life, in the real world, back home. And as an Alberta resident, I know how much the oil patch is presently suffering.
I suppose putting a more optimistic view on things is, since Alaska obviously holds roots for you , do your university education up there but be mentally prepared to move back to the lower 48 upon graduation if necessary. ANd I too have been nose to nose with caribou so can speak with some authority on the Canadian north. In general terms, society is putting increasing restrictions upon all activity in the Arctic, and until we start suffering blackouts or gas shortages in San Fran, or Toronto, or New York, I cant see it changing for the better. You probably already know this, but you need to do a pile more research and if you're restricted to the Internet, I don't know how you do this effectively.
### RE: Too old to start as Pete Eng?
Prudoe Bay and the rest of the North Slope (all of which has been stimulated by hydraulic fracturing by the way) is declining. The infrastructure is in place to produce reduced volumes, but the equipment and piping are starting to see systemic problems. It is hard to see if they'll be fixed or the fields will be abandoned.
(OP)
### RE: Too old to start as Pete Eng?
Yup; good discussion here.
One point I haven't heard much on is this: an Engineering discipline is no walk in the park. Obviously you have discipline from the military and age, and anyone is capable of learning if their desire is strong, but a four year curriculum can really knock your wrench in the dirt if you're not ready for it. The hole digging, geology and reservoir classes will be very interesting and even enjoyable, but you also have to go through the foundations of basic engineering: calculus, differential equations, thermo, heat transfer, etc. which can be fairly dry especially if taught by grad student with an incomprehensible accent. No disrespect to your ability, but there have been many spend a couple years before realizing they just don't like those subjects and then change or quit. Just sayin....
### RE: Too old to start as Pete Eng?
(OP)
DubMac great point, I am just starting Calc I and so far so good. I basically started over from Algebra I and worked my way back up since I know Engineering is math heavy. I have been in and out of school for years. Depending on if I am home or not, so I'm used to being in class. That being said I only really need about 2 1/2 to 3 years of school to graduate. Basically the math, physics, and engineering specific courses. All the core and elective stuff is done. I have an electronics background so the physics and application stuff has not been a problem for me to this point, I really enjoy that stuff. I have also worked in some engineering jobs as a technician, big change for me and I had to slow down. But I really enjoyed doing it, not like wrenching on jets! I have taken a lot of dry boring classes unfortunately but I made it through them. I'm the type person that once I set a goal I work to achieve it no matter what, the military made me anal like that. So it would have to be a lot to make me stop. Now if someone offered me my dream job I would walk away from this, but what are the chances of that! LOL We will see about the foreigners though! Haven't had to deal with that yet! That could suck because its sometimes hard for me to even hear what people are saying! I think if I get into Pet and find I don't like it as much as I thought my plan is to move to Electrical and a lot of what I am doing will transfer. I'm also the type that needs plan B and C! Thanks for the input!
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# Thread: Solve the integrals for the area
1. ## Solve the integrals for the area
What are the enpoint of these integrals?
2. what do you mean by enpoint?
3. Originally Posted by racewithferrari
What are the enpoint of these integrals?
Have you drawn a graph of each function (on the same set of axes) and shaded the bounded area? That should show you that your first job is to get the coordinates of the 'corners' of the bounded area.
If you need more help, please post all your work and say where you are stuck.
4. Originally Posted by racewithferrari
What are the enpoint of these integrals?
The very first sentence says "sketch the bounded region enclosed by the given curves". Have you done that?
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# If $a^n+n^{a}$ is prime number and $a=3k-1$ then $n\equiv 0\pmod 3$?
Is it true that :
If $a^n+n^{a}$ is prime number and $a=3k-1$ then $n\equiv 0\pmod 3$
where $a>1,n>1 ; a,n,k \in \mathbb{Z^+}$
I have checked statement for many pairs $(a,n)$ and it seems to be true.
Small Maple code that prints $(a,n)$ pairs :
Any idea how to prove this statement ?
-
Since it is prime, we know that $a^n+n^a \equiv 1 \text{ or } 5 \mod 6$, and because $a \equiv 2 \mod 3$ we know that $a \equiv 2 \text{ or } 5 \mod 6.$
The case $a \equiv 2 \mod 6:$
Note that $n^2 \equiv n^8 \equiv n^{14} \dots \mod 6.$
When $n \equiv 0, 1, 2, 3, 4, 5 \mod 6, n^2 \equiv 0, 1, 4, 3, 4, 1 \mod 6$ and $2^n \equiv 4, 2, 4, 2, 4, 2 \mod 6.$
Adding these gives $a^n+n^a \equiv 4, 3, 2, 5, 2, 3 \mod 6$. 1 does not appear at all and 5 appears only when $n \equiv 3 \mod 6,$ meaning that $n \equiv 0 \mod 3,$ as required.
The case $a \equiv 5 \mod 6:$
Note that $n^5 \equiv n^{11} \equiv n^{17} \dots \mod 6.$
When $n \equiv 0, 1, 2, 3, 4, 5 \mod 6, n^5 \equiv 0, 1, 2, 3, 4, 5 \mod 6$ and $5^n \equiv 1, 5, 1, 5, 1, 5 \mod 6.$
Adding these gives $a^n+n^a \equiv 1, 0, 3, 2, 5, 4 \mod 6$. 1 appears only when $n \equiv 0\mod 6$, implying that $n \equiv 0 \mod 3,$ as required.
However, 5 appears as well, when $n \equiv 4 \mod 6,$ suggesting the possibility of the result being false for these values of $a$ and $n$.
Edit
I have found that $a=215$ and $n=76$ is a counterexample. $a^n+n^a$ is prime, $a \equiv 2 \mod 3$ but $n\not\equiv 0 \mod 3$.
-
if $n\equiv 0\pmod 3$ then $n \not\equiv 4\pmod 6$ – pedja Nov 17 '11 at 15:18
@pedja I have shown that $a^n+n^a$ might be prime without the need for $n \equiv 0 \mod 3$. $n \equiv 0 \mod 3$ is your conclusion, not an assumption. – Peter Phipps Nov 17 '11 at 15:23
could you give me an example of such prime number please ? – pedja Nov 17 '11 at 15:30
@pedja that would be the counterexample to disprove your conjecture. Your Maple code suggests you have already checked the easy numbers. So no, I can't provide an example at this time. – Peter Phipps Nov 17 '11 at 15:36
if you find counterexample to my conjecture please let me know.. – pedja Nov 17 '11 at 15:40
Assume $n$ ist not $\equiv 0 \mod 3$, which means $n=3l+1$ or $n=3l+2$. Now see if $n^a + a^n$ is divisibile by 3. If yes, you get a contradiction to $n^a + a^n$ being a prim.
So if $n \equiv 1$ you get (remember $a \equiv -1$) $$a^n + n^a \equiv (-1)^{3l+1} + 1 \equiv 0 \mod 3$$ and if $n \equiv 2$ you get $$a^n + n^a \equiv (-1)^{3l+2} + (-1)^{3k-1} \equiv 1-1 = 0 \mod 3$$
-
counterexamples : $8^2+2^8=320 , 8^4+4^8=69632$ – pedja Nov 16 '11 at 9:34
Dont you assume that $a^n + n^a$ is prime ? – MaoK Nov 16 '11 at 9:37
try $2^{15}+15^2$ – pedja Nov 16 '11 at 9:52
Yap, thats a prim. But thats no counter example, since $n=15 \equiv 0 \mod 3$ – MaoK Nov 16 '11 at 9:59
please calculate : $2^{14}+14^2$ and $2^{16}+16^2$ – pedja Nov 16 '11 at 10:08
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• ## Come join us in London on March 13th for #FuturePub 10
Posted by John on February 17, 2017 #FuturePub 10New Developments in Scientific Collaboration Tech Quick link: Register here! Monday, March 13, 2017 from 6:00 PM - 9:30 PM Near Kings Cross, London Free Pizza & Drinks! After a great turnout at our last #FuturePub in London in September, and given that lots of people are in town for the London Bookfair in March, we're hosting our tenth (!) #FuturePub as a pre-LBF event on March 13th! The evenings are designed to be fun and informal - we aim to give opportunities to those working on new ideas and innovations a chance to present and get feedback on their ideas. And did I mention the free pizza? Quite remarkably, this is now the tenth #FuturePub we've run, since our first back in January 2014, and we're now described as "a staple of the London science tech/publishing scene" (thanks Eva!). In case this is your first time, here's how it works: Six quick-fire talks cover a range of new and exciting developments in science & publishing tech. These all fit into a one hour slot (from 7-8pm), to keep the evening fast-paced and fun! Arrive early for pre-talk pizza and drinks! :) The rest of the evening is then open for discussions and conversations over the remainder of the drinks and/or pizza! We get a great mixture of attendees from the research, publishing and start-up communities, and we usually head to a nearby pub to continue on into the small hours. Speakers & Talks Full speaker line-up coming soon! Here are the first two to whet your appetite: A New Cartography of Collaboration Presenting the first Digital Science Report to include analysis of selected Overleaf collaboration data alongside contributed articles. Daniel Hook, CEO, Digital Science Open Engagement and Quality Incentives in peer review Presenting data on reviewer behaviour and performance, and their correlations with eventual impact metrics of reviewed articles. Janne-Tuomas Seppänen, Founder, Peerage of Science We still have some slots free so if you have a cool new product or innovation you've been working on, let us know and we'll see if we can fit you in! Fill out the very short application form here! Location The Stables, Digital Science Opposite the Springer Nature Glasshouse Building 2 Trematon Walk, Wharfdale Road, London N1 9FN Time Doors open at 6:00pm and the talks will kick off at 7pm. Space at the venue is limited, so please register for your free tickets now to reserve your place! See you on March 13th! Don't forget to register! :)
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Intended for healthcare professionals
Clinical Review Extracts from “Clinical Evidence”
# Age related macular degeneration
BMJ 2000; 321 (Published 23 September 2000) Cite this as: BMJ 2000;321:741
1. Jennifer J Arnold, consultant ophthalmologist (jjarnold{at}pacific.net.au)a,
2. Shirley H Sarks, honorary senior research associateb
1. a Aberdeen Royal Hospitals NHS Trust, Aberdeen,
2. b Prince of Wales Medical Research Institute, Randwick, NSW, Australia
1. Correspondence to: J Arnold
## Background
### Definition
Age related macular degeneration is the late stage of age related maculopathy. It has two forms: atrophic (or dry), characterised by geographic atrophy, and exudative (or wet), characterised by choroidal neovascularisation, which eventually causes a disciform scar. 1 2
#### Interventions
##### Beneficial:
Thermal laser photocoagulation
Photodynamic treatment with verteporfin
##### Unknown effectiveness:
Proton beam and scleral plaque radiotherapy
Submacular surgery
##### Ineffective or harmful
Subcutaneous interferon alfa-2a
### Incidence/prevalence
Age related macular degeneration is the commonest cause of blind registration in industrialised countries. The atrophic form is more common than the more sight threatening exudative form, affecting about 85% of people with age related macular degeneration.3 End stage (blinding) age related macular degeneration is found in about 1.7% of all people aged over 50, and incidence rises with age (0.7-1.4% in people aged 65-75, 11.0-18.5% in people aged over 85).4-6
### Aetiology/risk factors
The aetiology is multifactorial. Age is the strongest risk factor. Ocular risk factors for the development of exudative age related macular degeneration include the presence of soft drusen, macular pigmentary change, and choroidal neovascularisation in the other eye. Systemic risk factors are hypertension, smoking, and positive family history. 7 8 A role for diet and exposure to ultraviolet light is suspected but unproved.
### Prognosis
Age related macular degeneration impairs central vision, which is required for reading, driving, face recognition, and all fine visual tasks. Atrophic age related macular degeneration progresses slowly over many years, and time to legal blindness (visual acuity <20/200) is highly variable (usually about 5–10 years). 9 10 Exudative age related macular degeneration is more threatening to vision and is responsible for 90% of severe visual loss in people with age related macular degeneration. It usually manifests with a sudden worsening and distortion of central vision. It progresses rapidly (typically over weeks or months) until scarring is complete and no further vision is lost, at which point legal blindness has usually been reached. Most people (estimates vary from 60% to 90%) with exudative age related macular degeneration progress to legal blindness and develop a central defect (scotoma) in the visual field.11-14 Peripheral vision is preserved, allowing the person to be mobile and independent. The ability to read with visual aids depends on the size and density of the central scotoma and the degree to which the person retains sensitivity to contrast. Once exudative age related macular degeneration has developed in one eye, the other eye is at high risk (cumulative estimated incidence 10% at one year, 28% at three years, and 42% at five years).7
### Aims
To minimise loss of visual acuity and central vision; to preserve the ability to read with or without visual aids; to optimise quality of life; to minimise adverse effects of treatment.
### Outcomes
Visual acuity, rates of legal blindness, contrast sensitivity, quality of life, appearance of retina on fluorescein angiography, rate of adverse effects of treatment. Visual acuity is measured using special eye charts, usually the early treatment of diabetic retinopathy study (ETDRS) chart, although many studies do not specify which chart was used. Stable vision is usually defined as loss of two lines or less on the ETDRS chart. Moderate and severe visual loss are defined as a loss of more than three and six lines respectively, corresponding to a doubling and quadrupling of the vision angle. Loss of vision to legal blindness (<20/200) is also used as an outcome. A reading of 20/200 (or 6/60 in metric) on the Snellen chart means that a person can see at 20 yards (or 6 metres) what a normally sighted person can see at 200 yards (or 60 metres).
### Methods
Clinical Evidence search and appraisal December 1999. All randomised controlled trials (RCTs) were included, but small early RCTs were excluded when larger, more recent trials were available.
Question: What are the effects of treatments for exudative age related macular degeneration?
Option: Thermal laser photocoagulation
### Summary
Four large RCTs have found that laser photocoagulation decreases the rate of severe visual loss and preserves contrast sensitivity in selected people with exudative age related macular degeneration (those with well demarcated lesions). Choroidal neovascularisation recurs within two years in about half of those treated. Photocoagulation may reduce visual acuity initially.
### Benefits
We found no systematic review. Versus no treatment: We found four large unblinded multicentre RCTs of laser photocoagulation versus no treatment in a selected population.11-17 We also found four smaller RCTs that included a wider range of people.18-21 All four of the large trials found that treatment conferred clinically and statistically significant benefit, in terms of reduced risk of severe visual loss (defined as loss of six or more lines on the special eye chart), which persisted beyond three years. Participants differed in terms of the position of the choroidal neovascularisation on the retina, whether far, near, or under the centre of fixation (extrafoveal, 11 13 juxtafoveal, 14 15 or subfoveal 12 16 17). In the study of extrafoveal choroidal neovascularisation, treatment was beneficial despite the fact that 19% of eyes randomised to observation later received laser treatment. 13 11 Reanalysis of people with juxtafoveal choroidal neovascularisation found that benefit was limited to those with pure classic lesions (no occult element) on fluorescein angiography (52% of randomised eyes), who were more than twice as likely to avoid developing severe visual loss than were people receiving no treatment (odds ratio 2.2, 95% confidence interval 1.4 to 3.4 at three years). The two trials in people with subfoveal choroidal neovascularisation found benefit from treatment despite an immediate loss of vision in the treated groups (average three lines on the special eye chart).12 At five years after treatment, rates of recurrence of choroidal neovascularisation ranged from 39% to 76%, with most occurring within two years. Of the four smaller RCTs, one found that fovea sparing laser photocoagulation preserved visual acuity compared with no treatment.18 The other three found that scatter (non-confluent) laser was no better than no treatment in occult choroidal neovascularisation. However, the trials were too small to rule out a beneficial effect. Different wavelengths: We found three large multicentre RCTs that compared two wavelengths of laser (krypton red or argon green) for photocoagulation of choroidal neovascularisation in age related macular degeneration. 22 23 All found no significant difference in outcome. Effects in people with choroidal neovascularisation identified by indocyanine green angiography: We found no RCTs. Uncontrolled case series have reported good outcomes in selected people.
### Harms
Laser destroys new vessels and surrounding retina, and the resultant scar causes a corresponding defect in the central visual field. If the laser is applied to subfoveal lesions, or if the laser burn spreads to the fovea, visual acuity will be impaired; two of the RCTs described immediate loss of visual acuity (an average loss of three lines on the special eye chart). 12 17 We found no evidence of other adverse effects.
### Comment
The benefits of laser photocoagulation depend on accurate, complete treatment, requiring high quality angiography and trained, experienced practitioners.11-17 The risk of immediate loss of visual acuity with laser photocoagulation may limit its acceptability.
### Summary
Three RCTs found no evidence of an effect of external beam radiation on the risk of moderate visual loss in people with exudative age related macular degeneration within one year. We found insufficient evidence on long term safety, but one RCT found no evidence of an association with cataract formation at one year.
### Benefits
We found no systematic review. External beam radiation: We found three RCTs. The first trial, a large multicentre double blind RCT, compared external beam radiation (16 Gy in 2 Gy fractions) delivered to the macula against no treatment in 205 people with new subfoveal choroidal neovascularisation.24 The control group received “sham” radiation treatment (eight fractions of 0 Gy). At 12 months, 51.1% of treated people and 52.6% of controls had moderate visual loss, defined as loss of three or more lines on a special eye chart (P=0.88). No treatment benefit was detected for subgroups of patients classified on the basis of fluorescein angiographic appearance into classic and occult lesions. The second trial, a small, single blind RCT, compared external beam radiation (24 Gy in 6 Gy fractions) delivered to the macula against no treatment in 74 people with new subfoveal choroidal neovascularisation.25 At 12 months, there was no significant difference between treated and untreated people in terms of their risk of moderate or severe visual loss (defined as losses of three or six lines on the special eye chart): the absolute risk of moderate visual loss was reduced by 20% with treatment, but the confidence interval spanned zero (absolute risk −20%, −44% to 4%). The third RCT was a small single blind randomised pilot study comparing single fraction external beam radiation of 7.5 Gy against no treatment in 27 people.26 No treatment benefit was detected over a mean follow up of 17 months (range 7–32 months). Other techniques: We found conflicting and inconclusive evidence from non-randomised pilot studies using proton beam and scleral plaque (local) radiotherapy in a variety of dosing and timing schedules.
### Harms
All RCTs reported no adverse effects after 12 months. Uncontrolled pilot studies suggest that the main risks using current dosing and delivery techniques are cataract (2 of 41 people in one series27) and transient keratoconjunctivitis with epiphora (10 of 75 in one series28). However, the large multicentre RCT found no significant difference in cataract formation between treated and untreated people at 12 months (10% treated v 16% control) or dry eye symptoms (40% treated v 45% control).24 Doses of up to 25 Gy delivered in daily fractions of 2 Gy or less are generally claimed not to cause damage to the retina or optic nerve. However, radiotherapy is potentially toxic to the retina, optic nerve, lens, and lachrymal system, with toxic effects sometimes manifesting two years after treatment.29 A two centre case series of people treated with external beam radiation reported an abnormal choroidal vascular growth pattern associated with macular bleeding and exudation and marked loss of visual acuity.30 This change was detected in 12.6% of 95 people and 7.1% of 98 people 3–12 months after radiotherapy and may explain the lack of treatment benefit.
### Comment
One multicentre RCT of radiation for age related macular degeneration is under way (U Chakravarthy, personal communication, 1999). Trials with less than two years' follow up may miss important adverse effects.
Option: Submacular surgery
### Summary
We found insufficient evidence on the effects of submacular surgery. Rates of recurrent choroidal neovascularisation are high, and there is a clinically significant risk of ocular complications resulting in visual loss and further surgical intervention.
### Benefits
We found no systematic review. Versus no treatment: We found no RCTs. Versus laser photocoagulation: We found one pilot RCT (n=70) comparing submacular surgery against laser photocoagulation for recurrent subfoveal choroidal neovascularisation (S Bressler, Macular Society Meeting, San Francisco, 1999). It found no significant difference between the two treatment groups. Versus alternative surgical techniques: We found one RCT in 80 eyes with exudative age related macular degeneration comparing surgery plus subretinal injection of tissue plasminogen activator against surgery plus subretinal injection of a control solution.31 The trial found no significant difference in visual or anatomic outcome.
### Harms
Submacular surgery can have effects that threaten vision or require further surgical intervention. However, we found no good data on the frequency of adverse events. The largest case series of people with age related macular degeneration and non-age related macular degeneration reported cataract formation (in up to 40%), retinal detachment (5-8%), recurrent new vessel formation (18-35% within 12 months), and macular complications (haemorrhage and pucker; no rates given).32
### Comment
Most evidence for submacular surgery currently comes from small uncontrolled case series (<50 people with age related macular degeneration) with short follow up, often including people with other types of macular degeneration. These found that few people with age related macular degeneration experienced improved vision with surgery. 29 32 Comparing results is difficult because of evolving surgical techniques, changes in outcome measures, and variations in follow up. A large non-blinded RCT is currently recruiting and will compare standardised surgical technique against no treatment in new and haemorrhagic choroidal neovascularisation in people with age related macular degeneration (S Bressler, personal communication, 1999). Other surgical techniques are being developed in volunteers, including macular translocation and retinal pigment epithelial transplantation, but these have yet to be formally evaluated.
Option: Subcutaneous interferon alfa-2a
### Summary
One large RCT found no evidence of benefit from subcutaneous interferon alfa-2a (an antiangiogenesis drug) and found evidence of serious ocular and systemic adverse effects.
### Benefits
We found no systematic review. We found one multicentre, double blind RCT in 481 people with subfoveal choroidal neovascularisation due to age related macular degeneration.32 This compared three doses of subcutaneous interferon alfa-2a (1.5, 3, and 6 mIU given three times a week for one year) against placebo. At 52 weeks, treatment at all doses was associated with a higher risk of losing at least three lines of vision on the Snellen chart compared with placebo (absolute risk 50% v 38%, increase 12%, 0% to 23%). No benefit was found for secondary end points or in subgroups of patients.
### Harms
Adverse effects of interferon alfa-2a were common and potentially severe in this and other poorer quality RCTs. These included fatigue and influenza-like symptoms as well as gastrointestinal symptoms and effects on the central and peripheral nervous system. Although at least one adverse event was reported in 86% of people taking placebo, the proportion of people on active treatment who suffered adverse effects increased with dose, as did the severity of adverse effects. Up to 5% of treated people experienced retinopathy induced by interferon alfa-2a,33 perhaps accounting for worse visual outcome in treated people.
### Comment
There is widespread interest in safe, effective antiangiogenesis drugs as prophylaxis for exudative age related macular degeneration. Several drugs are currently under preclinical and early phase clinical study. RCTs are currently investigating thalidomide with and without concurrent laser photocoagulation, and intravitreal triamcinolone.
Option: Photodynamic treatment
### Summary
One large multicentre RCT found that photodynamic treatment with verteporfin reduced the risk of moderate and severe vision loss in selected people with exudative age related macular degeneration (those with predominantly classic lesions on fluorescein angiography).
### Benefits
We found no systematic review. Versus placebo: We found one large multicentre double blind RCT of photodynamic treatment in 609 people with new and recurrent subfoveal choroidal neovascularisation due to age related macular degeneration. The intervention was a two stage procedure: infusion of verteporfin, followed by phototherapy with activating laser light. The control group received infusion of sugar water followed by phototherapy.34 Twice as many participants were randomised to verteporfin. Treatments were repeated if necessary every three months. Outcomes were moderate and severe loss of visual acuity, defined as loss of 15 and 30 letters (about three and six lines) on a special eye chart, change in contrast sensitivity, and fluorescein angiographic appearance. At each follow up visit up to 12 months, all outcome measures were clinically and statistically significantly better in the treatment group than in the control group. At the 12 month follow up visit, 61% of treated people compared with 46% of controls had lost less than 15 letters of vision (P<0.001). Subgroup analysis found that this benefit was greater for eyes with predominantly classic choroidal neovascularisation lesions (67% treated v 39% control) and was most marked for eyes with pure classic lesions (77% treated v 27% control). However, no treatment benefit for visual acuity was seen in the group without predominantly classic lesions.
### Harms
Verteporfin is a photosensitive dye, and care must be taken to avoid tissue extravasation during infusion and exposure to bright sunlight for 24 hours after treatment. The treatment was well tolerated but was more likely than the control intervention to cause a transient decrease in vision (18% treated v 12% control), injection site reactions (13% treated v 3% control), photosensitivity (3% treated v 0% control), and low back pain related to infusion (2% v 0% control).
### Comment
The RCT is ongoing and will report outcomes at 24 months' follow up. A further multicentre double blind RCT is under way comparing photodynamic treatment with verteporfin in a wider range of people with exudative age related macular degeneration (VIP Study Group, personal communication). Photodynamic treatment with other photosensitising dyes is also being evaluated in RCTs.
#### Glossary
##### Age related maculopathy
Degenerative disease of the macula (centre of the retina) classified as early (marked by drusen and pigmentary change, and usually associated with normal vision) and late, when it is known as age related macular degeneration
##### Choroidal neovascularisation
New vessels in the choroid, classified on the basis of fluorescein angiography: in terms of its position in relation to the fovea— extrafoveal, juxtafoveal, or subfoveal; in terms of its appearance—classic (well defined) or occult (poorly defined); and in terms of its borders—well demarcated or poorly demarcated.
##### Legal blindness
Visual acuity <20/200.
##### Photodynamic treatment
A two step procedure of intravenous infusion of a photosensitive dye followed by application of a non-thermal laser which activates the dye. The treatment aims to cause selective closure of the choroidal new vessels.
##### Submacular surgery
Removal of haemorrhage or choroidal neovascularisation, or both, after vitrectomy.
##### Verteporfin
A photosensitive dye used in photodynamic treatment.
## Footnotes
• Competing interests JA was a clinical investigator in the study of photodynamic treatment using verteporfin, which was funded by CIBA Vision/QLT. She has been supported by CIBA Vision for attendance at conferences and symposia.
• If you are interested in being a contributor or peer reviewer for Clinical Evidence please visit the Clinical Evidence website (www.clinicalevidence.com/)
Clinical Evidence is published by BMJ Publishing Group. The third issue is available now, and Clinical Evidence will be updated and expanded every six months. Individual subscription rate, issues 3 and 4 £75/$140; institutional rate £160/$245. For more information including how to subscribe, please visit the Clinical Evidence website at www.clinicalevidence.com/
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View Abstract
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# Converting Gröbner bases with FGLM
🛈
I originally wrote this post when working at AS Discrete Mathematics as part of a project sponsored by the Ethereum Foundation. It is reproduced here with friendly permission.
Have you ever computed a Gröbner basis in some monomial order $\prec_0$ only to then realize that you actually wanted it in another order $\prec_1$ ? I know, happens all the time… But fret not, FGLM can convert between the two orders, and you don't have to start your computation from scratch.
Here's a recording where I'm explaining how FGLM works. If you'd like to look through the slides at your own pace, here they are. You can also find the two Gröbner bases used in the example as well as pseudocode for FGLM in the slides, in case you want to retrace the steps yourself.
If you are interested in not only how but also why FGLM works, have a look at the original publication. Section 5 and 6 give a comprehensive overview of FGLM's complexity, which can be summarized as $O(n\cdot D^3)$ where $D$ is the dimension of quotient ring $k[x_0, \dots, x_{n-1}] / \langle G \rangle$ as a $k$ -vector-space. More intuitively, $D$ is the number of monomials in the staircase of a Gröbner basis, which are those dots in the non-blue region in this post's first picture.
def FGLM(order_new, gb_old, order_old):
d = {}
gb_new = []
next_monoms = [1]
while next_monoms:
monom = min(next_monoms) # according to order_new
next_monoms -= monom
if no g in gb_new such that LM(g) | monom:
# monom is still within staircase
reduced_monom = monom.reduce(gb_old, order_old)
if reduced_monom + sum([w[u] * v for u, v in d.items()]) == 0 for some w:
# w[i] are field elements, i.e., coefficients.
# they can be found by Gaussian reduction of d.values()
gb_new += monom + sum([w[u] * u for u, v in d.items()])
else:
d += {monom : reduced_monom}
next_monoms += [x_i * monom for i in range(n)]
return gb_new
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Journal article
### Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in C^m
Abstract:
We prove two main results: (a) Suppose $L$ is a closed, embedded, exact special Lagrangian $m$-fold in ${\mathbb C}^m$ for $m\ge 3$ asymptotic at infinity to the union $\Pi_1\cup\Pi_2$ of two transverse special Lagrangian planes $\Pi_1,\Pi_2$ in ${\mathbb C}^m$. Then $L$ is one of the explicit 'Lawlor neck' family of examples found by Lawlor (Invent. math. 95, 1989). (b) Suppose $L$ is a closed, embedded, exact Lagrangian mean curvature flow expander in ${\mathbb C}^m$ for $m\ge 3$ asympt...
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript
### Access Document
Files:
• (pdf, 731.7KB)
Publisher copy:
10.1215/00127094-3167275
### Authors
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Publisher:
Duke University Press Publisher's website
Journal:
Duke Mathematical Journal Journal website
Volume:
165
Issue:
5
Pages:
847-933
Publication date:
2015-01-01
DOI:
EISSN:
1547-7398
ISSN:
0012-7094
URN:
uuid:7d9026c3-35cb-4a8d-9ffe-af179cc85bf6
Source identifiers:
459672
Local pid:
pubs:459672
Keywords:
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Select Page
# American Mathematics contest 10 (AMC 10) - Number Theory problems
Try these AMC 10 Number Theory Questions and check your knowledge!
#### AMC 10A, 2020, Problem 4
A driver travels for $2$ hours at $60$ miles per hour, during which her car gets $30$ miles per gallon of gasoline. She is paid $0.50$ per mile, and her only expense is gasoline at $2.00$ per gallon. What is her net rate of pay, in dollars per hour, after this expense?
$\textbf{(A) }20 \qquad\textbf{(B) }22 \qquad\textbf{(C) }24 \qquad\textbf{(D) } 25\qquad\textbf{(E) } 26$
#### AMC 10A, 2020, Problem 6
How many $4$-digit positive integers (that is, integers between $1000$ and $9999$, inclusive) having only even digits are divisible by $5?$
$\textbf{(A) } 80 \qquad \textbf{(B) } 100 \qquad \textbf{(C) } 125 \qquad \textbf{(D) } 200 \qquad \textbf{(E) } 500$
#### AMC 10A, 2020, Problem 7
How many $4$-digit positive integers (that is, integers between $1000$ and $9999$, inclusive) having only even digits are divisible by $5?$
$\textbf{(A) } 80 \qquad \textbf{(B) } 100 \qquad \textbf{(C) } 125 \qquad \textbf{(D) } 200 \qquad \textbf{(E) } 500$
#### AMC 10A, 2020, Problem 8
What is the value of
$1+2+3-4+5+6+7-8+\cdots+197+198+199-200?$
$\textbf{(A) } 9,800 \qquad \textbf{(B) } 9,900 \qquad \textbf{(C) } 10,000 \qquad \textbf{(D) } 10,100 \qquad \textbf{(E) } 10,200$
#### AMC 10A, 2020, Problem 9
A single bench section at a school event can hold either $7$ adults or $11$ children. When $N$ bench sections are connected end to end, an equal number of adults and children seated together will occupy all the bench space. What is the least possible positive integer value of $N?$
$\textbf{(A) } 9 \qquad \textbf{(B) } 18 \qquad \textbf{(C) } 27 \qquad \textbf{(D) } 36 \qquad \textbf{(E) } 77$
#### AMC 10A, 2020, Problem 17
Define$P(x) =(x-1^2)(x-2^2)\cdots(x-100^2).$How many integers $n$ are there such that $P(n)\leq 0$?
$\textbf{(A) } 4900 \qquad \textbf{(B) } 4950\qquad \textbf{(C) } 5000\qquad \textbf{(D) } 5050 \qquad \textbf{(E) } 5100$
#### AMC 10A, 2020, Problem 7 21
There exists a unique strictly increasing sequence of nonnegative integers $a_1 < a_2 < … < a_k$ such that$\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} + … + 2^{a_k}.$What is $k?$
$\textbf{(A) } 117 \qquad \textbf{(B) } 136 \qquad \textbf{(C) } 137 \qquad \textbf{(D) } 273 \qquad \textbf{(E) } 306$
#### AMC 10A, 2020, Problem 22
For how many positive integers $n \le 1000$ is$\left\lfloor \dfrac{998}{n} \right\rfloor+\left\lfloor \dfrac{999}{n} \right\rfloor+\left\lfloor \dfrac{1000}{n}\right \rfloor$not divisible by $3$? (Recall that $\lfloor x \rfloor$ is the greatest integer less than or equal to $x$.)
$\textbf{(A) } 22 \qquad\textbf{(B) } 23 \qquad\textbf{(C) } 24 \qquad\textbf{(D) } 25 \qquad\textbf{(E) } 26$
#### AMC 10A, 2020, Problem 24
Let $n$ be the least positive integer greater than $1000$ for which$\gcd(63, n+120) =21\quad \text{and} \quad \gcd(n+63, 120)=60.$What is the sum of the digits of $n$?
$\textbf{(A) } 12 \qquad\textbf{(B) } 15 \qquad\textbf{(C) } 18 \qquad\textbf{(D) } 21\qquad\textbf{(E) } 24$
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# Coupled Lines
Geometry Level 3
Two lines pass through the point $$(–6, 7)$$ and each is a distance of 2 from the origin at their closest to the origin. What is the sum of the slopes of these lines?
×
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### unt311's blog
By unt311, history, 6 weeks ago,
I've rechecked my submission several times, but do not see anything wrong. (I'm getting WA on test 3) I checked the standings but couldn't find anyone doing it my way, so I'm stuck. I've read the tutorial and understand it fully, though I wish to know what went wrong with this approach.
what I'm doing is:
I store the brightness of the star at (x, y) for times t = 0 ... c in a[time][x][y]
The sum of brightness of stars at time t(between 0...c) upto (x, y) from (1, 1) in ps[time][x][y]
now, for queries: at time t, the sky would look same as what it looked at time t % (c + 1), as its given that brightness is periodic on c.
I get the answer from sum betweeen (x1, y1) and (x2, y2) of sky at time t % (c + 1)
Thanks in advance...
• +1
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# American Institute of Mathematical Sciences
ISSN:
2164-6066
eISSN:
2164-6074
All Issues
## Journal of Dynamics & Games
April 2020 , Volume 7 , Issue 2
Select all articles
Export/Reference:
2020, 7(2): 97-104 doi: 10.3934/jdg.2020006 +[Abstract](864) +[HTML](195) +[PDF](319.11KB)
Abstract:
We consider a sufficient condition for the uniqueness of a Nash equilibrium in strategic-form games: for any two distinct strategy profiles, there is a player who can obtain a higher payoff by unilaterally changing the strategy from one strategy profile to the other strategy profile. An example of a game that satisfies this condition is the prisoner's dilemma. Viewed as a solution concept, the Nash equilibrium satisfying the condition is stronger than strict Nash Equilibrium and weaker than strict dominant strategy equilibrium.
2020, 7(2): 105-122 doi: 10.3934/jdg.2020007 +[Abstract](772) +[HTML](207) +[PDF](392.74KB)
Abstract:
In this paper, we present a systematic overview of different endogenous optimization-based characteristic functions and discuss their properties. Furthermore, we define and analyze in detail a new, \begin{document}$\eta$\end{document}-characteristic function. This characteristic function has a substantial advantage over other characteristic functions in that it can be obtained with a minimal computational effort and has a reasonable economic interpretation. In particular, the new characteristic function can be seen as a reduced version of the classical Neumann-Morgenstern characteristic function, where the players both from the coalition and from the complementary coalition use their previously computed strategies instead of solving respective optimization problems. Our finding are illustrated by a pollution control game with \begin{document}$n$\end{document} non-identical players. For the considered game, we compute all characteristic functions and compare their properties. Quite surprisingly, it turns out that both the characteristic functions and the resulting cooperative solutions satisfy some symmetry relations.
2020, 7(2): 123-140 doi: 10.3934/jdg.2020008 +[Abstract](811) +[HTML](205) +[PDF](818.38KB)
Abstract:
The possibility that a discrete process can be fruitfully approximated by a continuous one, with the latter involving a differential system, is fascinating. Important theoretical insights, as well as significant computational efficiency gains may lie in store. A great success story in this regard are the Navier-Stokes equations, which model many phenomena in fluid flow rather well. Recent years saw many attempts to formulate more such continuous limits, and thus harvest theoretical and practical advantages, in diverse areas including mathematical biology, economics, finance, computational optimization, image processing, game theory, and machine learning.
Caution must be applied as well, however. In fact, it is often the case that the given discrete process is richer in possibilities than its continuous differential system limit, and that a further study of the discrete process is practically rewarding. Furthermore, there are situations where the continuous limit process may provide important qualitative, but not quantitative, information about the actual discrete process. This paper considers several case studies of such continuous limits and demonstrates success as well as cause for caution. Consequences are discussed.
2020, 7(2): 141-162 doi: 10.3934/jdg.2020009 +[Abstract](691) +[HTML](193) +[PDF](408.87KB)
Abstract:
We consider difference and differential Stackelberg game theoretic models with several followers of opinion control in marketing networks. It is assumed that in the stage of analysis of the network its opinion leaders have already been found and are the only objects of control. The leading player determines the marketing budgets of the followers by resource allocation. In the basic version of the models both the leader and the followers maximize the summary opinions of the network agents. In the second version the leader has a target value of the summary opinion. In all four models we have found the Stackelberg equilibrium and the respective payoffs of the players analytically. It is shown that the hierarchical control system is ideally compatible in all cases.
2020, 7(2): 163-174 doi: 10.3934/jdg.2020010 +[Abstract](776) +[HTML](217) +[PDF](311.26KB)
Abstract:
A three-dimensional continuous-time stochastic model based on the classic Kermack-McKendrick model for the spread of epidemics is proposed for the propagation of a computer virus. Moreover, control variables are introduced into the model. We look for the controls that either minimize or maximize the expected time it takes to clean the infected computers, or to protect them from the virus. Using dynamic programming, the equations satisfied by the value functions are derived. Particular problems are solved explicitly.
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# On properties of $B$-terms
30 Jan 2019Mirai IkebuchiKeisuke Nakano
$B$-terms are built from the $B$ combinator alone defined by $B\equiv\lambda f.\lambda g.\lambda x. f~(g~x)$, which is well known as a function composition operator. This paper investigates an interesting property of $B$-terms, that is, whether repetitive right applications of a $B$-term cycles or not... (read more)
PDF Abstract
No code implementations yet. Submit your code now
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# A variation of the law of large numbers for random points in a square
I uniformly mark $$n^2$$ points in $$[0,1]^2$$. Then I want to draw $$cn$$ vertical lines and $$cn$$ horizontal lines such that in each small rectangle there is at most one marked point. Surely, for a given constant c it is not always possible.
But it seems that for $$c=100$$ when n tends to infinity, the probability that such a cut exists should tend to one, as a variation of the law of the large numbers. Do you have any idea how to prove this rigorously?
• What's you heuristics for the suggestion that the probability goes to one? As a side comment, there are results describing the asymptotics of the side of the largest empty square with sides parallel to those of [0,1]^2. A version of rectangles instead of squares also exist, I think. The proof is, however, is not a LLN-type one. Jun 9, 2020 at 11:42
• @Vysotsky not a heuristics, but a somewhat weaker statements can be observed experimentally and it would follow from the positive answer to my question. The statement is that the degree of a tropical curve through n^2 random points in a square is concentrated near n. Jun 9, 2020 at 11:58
• @Vysotsky note also that we cut AFTER we marked points randomly, so there is more freedom. Jun 9, 2020 at 13:53
• @Nikita Kalinin Of course, this is the main point (and difficulty)! Otherwise the claim will not work, as per the answer attempts below. It is unclear to me why your problem should in a sense correspond to some law of large numbers. Jun 9, 2020 at 14:03
• @Nikita Kalinin It is a nice problem! But somehow I share Iosif Pinelis's scepticism that cn would not suffice. You do have a reasonably quick algorithm how to compute the cuts for a given realisation of points, do not you? Jun 9, 2020 at 14:54
## 8 Answers
Given $$n^2$$ i.i.d. uniform points in $$[0,1]^2$$, the goal is to draw a configuration of $$cn$$ vertical lines and $$cn$$ horizontal lines such that in each small rectangle there is at most one marked point.
We show below that $$c$$ must satisfy $$c=\Omega(n^{1/3})$$ for this to be typically possible:
In fact, $$\Theta(n^{4/3})$$ lines are necessary and sufficient for such a configuration to exist with substantial probability.
More precisely, denote by $$p_n(k)$$ the probability that a configuration of $$k$$ vertical lines and $$k$$ horizontal lines separate $$n^2$$ i.i.d. uniform points $$\{x_j\}_{j=1}^{n^2}$$ in $$[0,1]^2$$.
Claim: For suitable constants $$0, we have (omitting integer part symbols):
(a) $$\; p_n(c_1 n^{4/3}) \to 0$$ as $$n \to \infty$$, and
(b) $$\; p_n(c_2 n^{4/3}) \to 1$$ as $$n \to \infty$$.
This is proved below with $$c_1=1/20$$ and $$c_2=3/2$$; no attempt has been made to optimize these constants.
Proof: Consider an auxiliary grid of $$L:=n^{4/3}$$ uniformly spaced vertical lines and $$L$$ uniformly spaced horizontal lines in the unit square. This grid defines $$L^2$$ grid squares of side length $$1/L$$.
(a) Call a grid square $$Q$$ nice if it contains exactly two of the $$n^2$$ given points $$\{x_j\}$$. Observe that for two distinct grid squares, the events that they are nice are negatively correlated. Call a nice grid square $$Q$$ good if there is at most one other nice square in its row and at most one other nice square in its column. The probability that a specific grid square $$Q$$ is nice is $${n^2 \choose 2}L^{-4}(1-L^{-2})^{n^2-2}=(1/2+o(1))L^{-1}.$$
Given that $$Q$$ is nice, The conditional expectation of the number of nice squares (other than $$Q$$) in the row of $$Q$$ is $$1/2+o(1)$$ Thus, given that $$Q$$ is nice, Markov's inequality implies that the conditional probability that there are two or more additional nice squares in the row of $$Q$$ (besides $$Q$$ itself) is at most $$1/4+o(1)$$. The same applies to the column of $$Q$$, and we deduce that $$P(Q \; {\rm is \; good}\; | Q \; {\rm is \; nice}) \ge 1/2+o(1) \, ,$$ so $$P(Q \; {\rm is \; good} ) \ge (1/4+o(1))L^{-1} \, .$$ Let $$G$$ denote the number of good grid squares. Then the mean satisfies $$E(G) \ge (1/4+o(1))L \,.$$ Observe that if we replace one point $$x_i$$ by $$x_i'$$ then $$G$$ will change by at most 5, so Mcdiarmid's inequality, see [1, Theorem 3.1] or [2], implies that for $$n$$ large enough, $$P(G \le L/5) \le \exp(-\frac{(L/21)^2}{25n^2}) \to 0 \,. {\rm as} \; n \to \infty \,.$$ (Alternatively, one could invoke the Efron-Stein inequality or estimate the variance directly to verify this.) Now suppose that $$S$$ is a set of vertical and horizontal lines that separate the points $$\{x_j\}_{j=1}^{n^2}$$. For each good grid square $$Q$$, a line of $$S$$ is required to separate the two points $$x_i, x_j$$ in the square, and each such line can be used for at most two good squares. Thus $$|S| \ge G/2$$ so $$p_n(L/20) \le P(\exists \; {\rm separating } \; S \; {\rm with } \; |S| \le L/10) \le P(G \le L/5) \to 0$$.
(b) Denote by $$M$$ the number of pairs $$(i,j)$$ such that $$1 \le i and $$x_i,x_j$$ fall in the same grid square. Then $$E(M) = {n^2 \choose 2}L^{-2} \le L/2$$, and another application of McDirarmid's inequality implies that $$P(M \ge L) \to 0$$ as $$n \to \infty$$.
Finally, construct a separating set of lines $$S$$ by combining the $$2L$$ lines of the auxiliary grid with one separating line for each pair $$(i,j)$$ counted in $$M$$ (we can take half of these lines vertical and half horizontal). Then $$P(|S| \ge 3L) \to 1$$ as $$n \to \infty$$ and $$p_n(3L/2) \to 1$$ as well.
[1] McDiarmid, Colin. "Concentration." In Probabilistic methods for algorithmic discrete mathematics, pp. 195-248. Springer, Berlin, Heidelberg, 1998.http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=8B1FFFE4553B63543AFEA0706E686E65?doi=10.1.1.168.5794&rep=rep1&type=pdf
[2] McDiarmid, C. (1989). "On the method of bounded differences". Surveys in Combinatorics. London Math. Soc. Lectures Notes 141. Cambridge: Cambridge Univ. Press. pp. 148–188. MR 1036755
• Do you think the constant $k$ for which $p_n(k·n^{4/3}) → r ∈ (0,1)$ as $n→∞$ is rational or irrational? And what do you think it is? Jun 10, 2020 at 9:07
• Very nice proof. I initially read the question wrong, and thought the grid was assumed uniform. But rather it can be actively chosen. A couple of points that I had to struggle with: the first estimate can be seen by realizing the binomial factor is 1 + o(1). For the constant 5, note removing a point can promote at most 4 grids to being good (2 on the same row and 2 on the same column), and adding a point can promote at most 1 grid, namely the grid where the point lands. Lastly for part b, two points are not on the same x or y cord with probably 1. How likely is it to get sharp estimate for c? Jun 17, 2020 at 13:56
• A similar reasoning with the bound of $n^{4/3}$ also appears in the paper 'On Separating Points by Lines' by Har-Peled and Jones Jun 20, 2020 at 19:17
Interestingly, if we allow the lines to have arbitrary directions, it still requires roughly n^{4/3} (up to a log correction) lines to separate all the points.
https://www.cambridge.org/core/journals/proceedings-of-the-london-mathematical-society/article/economical-covers-with-geometric-applications/486374A93F4351DF26C155F6C3FE35AE
• That is beautiful. Thanks for the reference! Jun 10, 2020 at 14:06
Label your $$N$$ points as $$(x_i,y_{\sigma(i)})$$ with $$x_1 < \cdots < x_N$$ and $$y_1 < \cdots < y_N$$ ; this defines a uniform random permutation $$\sigma \in \mathfrak{S}_N$$, and all the information about the problem is encoded in $$\sigma$$.
Let $$C$$ be the number of axis-parallel cuts needed to scatter all the points. An easy lower bound is $$C \geq L-1$$, where $$L$$ is the length of the longest monotone subsequence of $$\sigma$$. It is well known that $$L \sim 2 \sqrt{N}$$ in probability, so if we could show that the above lower bound is typically sharp, this would solve the problem.
• Interesting! Could you comment on how to find the cuts based on the permutation? Jun 9, 2020 at 17:16
• This is an interesting connection. However, I am afraid that the longest monotone subsequence will account only for a rather small subset of the set of $n^2$ uniformly chosen points in the square. Jun 9, 2020 at 17:35
• The idea is that maybe some of the techniques used for longest increasing subsequence can apply here. If the answer to the OP is positive, it implies that the longest increasing subsequence is $O(\sqrt{N})$, which is not a trivial fact. Also, I'd like to see a permutation with $C \gg L$. Jun 9, 2020 at 17:43
• @S.Surace I don't undestand the question. I don't know how to find the cuts, this is just a lower bound. Jun 9, 2020 at 17:44
• Here is an example with $C \gg L$. Split $\{1,\dots,N\}$ into $\sqrt{N}$ blocks (=intervals) of size $\sqrt{N}$ and let $\sigma$ be the permutation which reverses the order inside each block. Then $L=\sqrt{N}$ and $C \geq \sqrt{N}(\sqrt{N}-1)$, since a cut can only scatter within one block, and each block requires $\sqrt{N}-1$ cuts to be scattered. Jun 9, 2020 at 20:41
This is to show rigorously that the uniform rectangular grid does not work -- cf. the answer by mike. As in the answer by Dieter Kadelka, suppose that the $$cn$$ vertical lines and the $$cn$$ horizontal lines partition the unit square into $$N:=(cn+1)^2$$ small squares of equal area $$1/N$$, where $$c\ge1$$. Let $$K:=n^2.$$ Then the probability that each small square contains at most one random point is \begin{aligned} \frac{N(N-1)\cdots(N-K+1)}{N^K}&=\Big(1-\frac1N\Big)\cdots\Big(1-\frac{K-1}N\Big) \\ &<\exp\Big\{-\sum_{k=1}^{K-1}\frac kN\Big\} \\ &=\exp\Big\{-\frac{(K-1)K}{2N}\Big\}\to0\ne1 \end{aligned} as $$n\to\infty$$, as claimed.
(I don't think any choice -- even a random one, depending on the random points -- of $$cn$$ lines in both the vertical and horizontal directions is enough, for any real $$c>0$$. I think, instead of $$cn$$, one needs at least something like $$n\ln^a n$$ for some real $$a>0$$.)
• I think there remains the possibility that the grid is chosen dependent on the $n^2$ random points, but I would not bet on this. Jun 9, 2020 at 14:26
• @DieterKadelka : Yes, the very fast convergence to $0$ (rather than $1$) for the uniform grid strongly suggests that even a $cn\times cn$ grid dependent on the $n^2$ random points will not be enough. Jun 9, 2020 at 14:35
• yes, sure, that is why I wrote that we mark points and only then we draw lines... Jun 9, 2020 at 14:40
• @Nikita Kalinin: Do you have an algorithm to do this effectively? Jun 9, 2020 at 15:15
• @DieterKadelka : If I were going to try to make such an algorithm (which I am not, have no interest in doing, and refuse to even think through enough details to see if it could plausibly be made to work), I would start with a partitioning $k$-d tree having the defect that non-root interior nodes partition the entire space, not just the space associated with their parent. Depth control of that tree might give a useful bound on the number of partitioning lines. Jun 10, 2020 at 2:02
If we draw the horizontal lines to have $$p$$ rows with $$n^2/p$$ points each, then finding where to put the vertical lines becomes a birthday problem : we take the points from left to right and find in wich row they belong. When the row is already taken, we must draw a vertical line and start a new column. Set $$X_i$$ the number of points in column $$i$$. The repartition function of $$X_1$$ converges to $$\exp(-x^2/p)$$.
If we can suitably control the law of the other $$X_i$$, this would give an order of $$n^2/\sqrt{p}$$ columns. For $$p\sim n^{4/3}$$, this means around $$n^{4/3}$$ columns.
This provides as upper bound an order of $$n^{4/3}$$ horizontal lines and vertical lines. If some form of concentration occur for the size of the columns, we would get a critical value at $$c_{crit}n^{4/3}$$, with proba 1 of having a solution for constants larger than $$c_{crit}$$.
• To control $X_i$ (so that the columns are big enough in law), note that while there are still enough points, we can use modified birthday problems to find lower bounds in law on the size of the colums. For the right-most columns, just start again from the right. Set $(Y_i)_{1\leq i\leq N}$ the size of each column (starting from the right). $Y_i$ is distributed as $X_i$, and there is a relation between the columns from the left and from the right (the bounds of a column from the right should be in two adjacent columns from the left, and vice-versa). So, a column is always of order $\sqrt p$. Jun 9, 2020 at 23:34
Nikita Kalinin, you were right, this problem indeed reduces to a rather general form of the law of large numbers, namely subadditive ergodic theorem! This theorem is used, e.g., to prove the result on the length of the largest increasing subsequence mentioned by Guillaume Aubrun (thanks for hinting the direction). So I just mimic its proof due to Hammersley (see, e.g. Example 7.5.2 in Durrett's "Probability: Theory and Examples").
First of all, as noted above, instead of the original setting with $$n^2$$ points in $$[0,1]^2$$ we can consider your question for a Poisson point process (PPP) of unit intensity on the positive quadrant restricted to $$[0,n]^2$$.
For any integer $$0 \le m , let $$C_{m,n}$$ be the minimal positive integer number such that it is possible to cut the rectangle $$[[m,n]]:=\{(x,y) \in [0, \infty)^2: m \le x, y \le n\}$$ with the points of the PPP using $$C_{m,n}$$ horizontal and $$C_{m,n}$$ vertical cuts to satisfy the condition. The key observation is that $$C_{0,m} + C_{m, n} \le C_{0,n}.$$ Indeed, just use optimal cuts to cut $$[[0,m]]$$ and $$[[m,n]]$$; then more cuts may be needed.
By the subadditive ergodic theorem, $$\lim_{n \to \infty}\frac{C_{0,n}}{n} = \sup_{n \ge 1} \frac{E C_{0,n}}{n}:=c, \qquad a.s.$$
Now the problem is to figure out whether $$c$$ is finite or not, which is the most interesting bit. I did not succeed so far.
One way to prove finiteness is to show that $$E C_{0, n+1} - E C_{0,n}$$ is bounded. This appears to be wrong on a first sight, but apparently this is not so trivial. On the other hand, finiteness would mean that cutting $$[[0,n]]$$ and $$[[n, 2n]]$$ in a nearly optimal way would automatically fix the two remaining subsquares of $$[[0,2n]]$$. This should not be true, but not simple to prove as well.
The last comments are that the same argument goes through if replace $$C_{m,n}$$ by the total number of horizontal and vertical cuts. And the sequence $$E C_{0,n}/n$$ is strictly increasing.
Not and answer, but a long comment: I don't think a uniform rectangular grid works. Take a planar poisson process with intensity 1 and look at (0,n)x(0,n). This is your setup except I have replaced the uniforms with a poisson process with an expected n^2 events in the space. Divide it into a rectangular grid with (cn)^2 rectangles of area 1/c^2 each. The number of points in each rectangle is poisson with parameter 1/c^2,and different rectangles are independent. You wonder if any have of the (cn)^2 rectangles have two points in them. As the parameter is fixed there is a probability going to 1 that at least one of them does.
It is sufficient to assume that the $$cn$$ vertical and $$cn$$ horizontal lines are at $$\frac{1}{cn}, \frac{2}{cn+1}, \ldots$$, so that we have $$N := (cn+1)^2$$ small rectangles each with area $$p^{(n)} := \frac{1}{N}$$. Let $$X_1,\ldots,X_N$$ be random variables with $$X_i$$ the random number of points in rectangle $$i$$. Then $$X := (X_1,\ldots,X_N)$$ has the multinomial (sometimes called polynomial) distribution $$\cal{M}(n; p^{(n)},\ldots,p^{(n)})$$ ($$N$$ parameters $$p^{(n)}$$). As far as I understand your problem you want an estimation for $$\mathbb{P}(X_1 \leq 1, \ldots, X_N \leq 1)$$. But $$q^{(n)} := 1 - \mathbb{P}(X_1 \leq 1, \ldots, X_N \leq 1) \leq \sum_{i=1}^N \mathbb{P}(X_i \geq 2)$$, where each $$X_i$$ has Binomial distribution $$Bin(n,p^{(n)})$$. Thus $$q^{(n)} \leq N \cdot \left(1 - (1 - p^{(n)})^n - n \cdot p^{(n)} \cdot (1 - p^{(n)})^{n-1}\right)$$, which goes to $$0$$ when $$c > 1$$.
Edit: The estimation above only works for $$n$$ points, not for $$n^2$$ points, as required.
• It looks like your bound on $q^{(n)}$ is $\sim1/(2c^2)\ne0$. Jun 9, 2020 at 12:54
• Thank you @Iosif Pinelis, you are right. The estimation has to be sharpened (if it is possible). Jun 9, 2020 at 13:13
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# Balancing a copter with just gyro data [duplicate]
It seems like pitch angle could be computed from just gyro data, which uses 2 gyros.
However, isn't pitch computed from acceleration rather than gyro data?
pitch = 180 * arctan (accelerationX/sqrt(accelerationY*accelerationY + accelerationZ*accelerationZ))/PI
where no gyro data is needed. So how could a copter be balanced with just gyro data?
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Definitions
# Self-similarity
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals.
Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape.
## Definition
A compact topological space X is self-similar if there exists a finite set S indexing a set of non-surjective homeomorphisms $\left\{ f_s \right\}_\left\{sin S\right\}$ for which
$X=cup_\left\{sin S\right\} f_s\left(X\right)$
If $Xsubset Y$, we call X self-similar if it is the only non-empty subset of Y such that the equation above holds for $\left\{ f_s \right\}_\left\{sin S\right\}$. We call
$mathfrak\left\{L\right\}=\left(X,S,\left\{ f_s \right\}_\left\{sin S\right\}\right)$
a self-similar structure. The homeomorphisms may be iterated, resulting in an iterated function system. The composition of functions creates the algebraic structure of a monoid. When the set S has only two elements, the monoid is known as the dyadic monoid. The dyadic monoid can be visualized as an infinite binary tree; more generally, if the set S has p elements, then the monoid may be represented as a p-adic tree.
The automorphisms of the dyadic monoid is the modular group; the automorphisms can be pictured as hyperbolic rotations of the binary tree.
## Examples
The Mandelbrot set is also self-similar around Misiurewicz points.
Self-similarity has important consequences for the design of computer networks, as typical network traffic has self-similar properties. For example, in teletraffic engineering, packet switched data traffic patterns seem to be statistically self-similar. This property means that simple models using a Poisson distribution are inaccurate, and networks designed without taking self-similarity into account are likely to function in unexpected ways.
Similarly, stock market movements are described as displaying self-affinity, i.e. they appear self-similar when transformed via an appropriate affine transformation for the level of detail being shown.
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DeepAI
# Restricted Structural Random Matrix for Compressive Sensing
Compressive sensing (CS) is well-known for its unique functionalities of sensing, compressing, and security (i.e. CS measurements are equally important). However, there is a tradeoff. Improving sensing and compressing efficiency with prior signal information tends to favor particular measurements, thus decrease the security. This work aimed to improve the sensing and compressing efficiency without compromise the security with a novel sampling matrix, named Restricted Structural Random Matrix (RSRM). RSRM unified the advantages of frame-based and block-based sensing together with the global smoothness prior (i.e. low-resolution signals are highly correlated). RSRM acquired compressive measurements with random projection (equally important) of multiple randomly sub-sampled signals, which was restricted to be the low-resolution signals (equal in energy), thereby, its observations are equally important. RSRM was proven to satisfies the Restricted Isometry Property and shows comparable reconstruction performance with recent state-of-the-art compressive sensing and deep learning-based methods.
• 5 publications
• 7 publications
08/17/2020
### One Bit to Rule Them All : Binarizing the Reconstruction in 1-bit Compressive Sensing
This work focuses on the reconstruction of sparse signals from their 1-b...
11/28/2019
### Error Resilient Deep Compressive Sensing
Compressive sensing (CS) is an emerging sampling technology that enables...
01/19/2017
### Block-wise Lensless Compressive Camera
The existing lensless compressive camera (L^2C^2) Huang13ICIP suffers fr...
01/03/2014
### Adaptive-Rate Compressive Sensing Using Side Information
We provide two novel adaptive-rate compressive sensing (CS) strategies f...
07/21/2014
### Multichannel Compressive Sensing MRI Using Noiselet Encoding
The incoherence between measurement and sparsifying transform matrices a...
05/05/2012
### Rakeness in the design of Analog-to-Information Conversion of Sparse and Localized Signals
Design of Random Modulation Pre-Integration systems based on the restric...
03/26/2019
### An Intuitive Derivation of the Coherence Index Relation in Compressive Sensing
The existence and uniqueness conditions are a prerequisite for reliable ...
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# Euler Maclaurin Formula
One of the basic concepts of calculus is the correspondence between sums and integrals, which is easily evaluated with the help of Faulhaber’s formula. The Euler–Maclaurin formula is considered as a powerful connection between integrals. It is mostly used to approximate integrals by finite sums, or conversely to calculate or evaluate finite sums and infinite series using integrals and the machinery of calculus. For example, many asymptotic expansions are derived from the formula, and Faulhaber’s formula for the sum of powers is an immediate consequence.
$\large \sum_{k=p}^{m-1}\phi (k)=\int_{p}^{m}\phi (t)dt+\sum_{v=1}^{n-1}\frac{B_{v}}{v!}(\phi^{v-1}m-\phi^{v-1}p)+R_{n}$
Where,
$B_{v}$=Bernoulli numbers
$R_{n}$=remainder
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Larry Spruch.
# Low energy scattering by a compound system: positrons on hydrogen online
. (page 2 of 3)
Online LibraryLarry SpruchLow energy scattering by a compound system: positrons on hydrogen → online text (page 2 of 3)
Font size
Strictly speaking, one should study the integral, rudou^dTi , in the
limit of large b , with the parameters c and d always adjusted to give
the correct hydrogenic energy, e j the error involved in changing the
S
potential should then be shown to be arbitrarily small for b sufficiently
large .
-In-
sufficiently small, a may be chosen large enough so that the neglect
of the potential which may exist beyond r-i = a introduces a negligible
error in the phase shift. If k is zero, we may let a become infinite,
in which case we introduce no distortion of the positron-hyxiiK?gen
potentials. In this case, the validity of the second condition stated
above, namely ">? < 6 < n, is deduced by assuming that no three-body
bound state exists for the positron-hydrogen system (none has been
found either experimentally or theoretically) '- -' . We then apply a
theorem which is the generalization to many body systems of a theorem proved
by Levinson^ '-' for the scattering from a static potential. It states
that when the exclusion principle is not in effect the phase shift
for zero energy scattering is nn where n is the number of bound states
of the composite system'- -^ . From this we conclude that 17 = for k = 0.
A rigorous proof of the above theorem has not been given even for
potentials which fall off rapidly. A proof for the slowly decaying
Coulomb forces will be even more difficult. We nevertheless apply the
theorem with some confidence, for its generalization, which applies to
electron scattering from atoms, has proved to be correct in all cases
fPl!
where it has been checked"- -â– . That the theorem should be applicable to
the Coulomb case (assuming it applies to rapidly decaying potentials)
is perhaps made more reasonable by the observation that the " effective
interaction" of the positron or electron with the atomic system falls
off fairly rapidly. For e"*" on H, e.g., it goes as Vr , Actually, as
we will show in Section ^, the results we have obtained do not depend on
the validity of the above mentioned theorem.
With the choice & = n/2 and -A s lim "yj/k , -A = lim l^/k,
k->o •• k^o ^
u « lijB *'(i/2)n^» *® ^^"^^ **^ following bound on the scattering length, A,
- 16 -
UCM u d^
(3.6) A < A -
J
where u has the asymptotic form
One of the strong features of the Kato method is that in general
it provides a different bound for each choice of 9. This is not true
at k = C, however, where the identical result is obtained for any &
other than 9=0, The choice & = will lead to a valid bound on A
only if "Yi approaches zero from below as k goes to zero, i.e, , only if
A is positive. In this case we have
(3.8) A -^ > A"^+ A"^ tlcTu dr
A -1 > A-^ . A-2 J {IjTu
If u is sufficiently close to the true function such that A and A
are of the same sign and such that |ll«iA|, where
i^jsC^dtf
then Eq. (3.8) may be rewritten as
(3.8) A< A - I + A~^ i^ + ..., |i|«|aI.
It then follows (since A > O) that Eq. (3.6) is superior to Eq. (3.8),
Therefore, for the special case of zero energy scattering, where no
composite bound state exists, the problem of the optimum choice of ©
is particularly simple. One should use Eq. (3.6), which follows from
any choice of 9 satisfying < & < n ,
- 17 -
k. Numerical Calculation
A. No Polarization Approximation, k = 0.
To begin with, we consider the class of trial functions of the
form
(it.l) u(r^,r2,r^2^ ^ g(r2)f(r^) .
The required asymptotic form fixes g(r,) as
gv^2
We also have
(rj =R(rJ = (2/a 3)1/2 e-^2Ao.
(U.2) f(o) =
f(r, ) -> A- r- , as r^ -> oo.
A trial function in this product form corresponds to the approximation
(variously referred to as the no polarization approximation, the static
approximation, and the one body approximation) in which the hydrogen
atom is not polarized by the incoming positron. We substitute the above
expression for u into Eq. (3.6), and integrate over r^ and .p. Dropping
the subscript on r^ we find
fOO
(Li.3) A < A - f(r) !• This
[22I
lower bound can be improved quite easily. Bargmann*- J has shown
that a necessary condition for the existence of a bound state for
a potential U(r) is
rOO
(U.9)
,00
I r Iu(r)l dr> 1.
With U(r) = -(1-|J,)W (r), this leads to oa/A^ > 5/3.'
If we choose
-nr/a -qr/a
(U.IO) f(r)=A(l-e °) -r(l+Be °)
we find, with n = 1.5 and q = 2, that
(U.ll) 0.5762a^ o, the Born approximation yields
1... ' - v|
,-00 ^
(['..16) k cotV)^ „ -> - 1/ ( r W (r)dr = l/a,
I J-o wig (I
It therefore follows that
(li.lY) (k cofy"_^)j^^^ > -Sa^"-"- + 0.10560 a^""'"
and
(U.18) Ig = -(k coth_g);;i^ > 0.5273 a^
While this result is not as good as the one given previously, it was
obtained without constructing a trial function.
Summarizing the results of thj.s sub-section, we find that an
analysis of the static problem loads to an upper bound or the tnte
scattering length, A, but does not provide any information on a lower
bound for ~. Further, the least upper bound obtainable in the static
approximation, namely that given by Eq. (h.3)> is positive so that we
do not obtain an upper or a lower bound on o'(k=o). Actually, as we
will show in the next sub-section, T is negative so that the static
approximation is totally inadequate in this problem.
B. Polarization Considered, k = o.
A trial function of the form u = g(r-, jr^) may take into account,
to some extent, the polarization of the hydrogen atom. As we can see.
- 22 -
using arguments quite similar to those amployed in sub-section UA,
this type of trial function leads to a positive scattering length.
Thus, substituting g(r, ^r^) into Eq. (3.6) and integrating over p we
find
;00 ,00
where
,2
(U.20) £, = -^ ^ -K ^ r/ ^ . ^(A . J. . i) . e
* ar^2 r/ ^^2 2 °^2 ^o ^2 ^> ^1 ^
Here r^ is the larger of r, and r^. Since no bound state exists for the
operator k- , none exists for Ju. . This is a consequence of the fact that
the ground state energy satisfies a minimum principle and the space
on which cC, is defined is a sub-space of that forju. (The same result
also follows directly from the fact that l/r - l/r, is always negative l- ^-',)
Therefore, the exact scattering length, TT , for for sufficiently small non-zero
energies the cut-off point may be made large enough so that the
difference between rj and vj" (the phase shift in the presence of the
cut-off potentials) is negligibly small. To illustrate the procedure
we describe here a determination of a loirer bound on Y) for ka = 0.2.
(c
To begin with we ignore the question of obtaining a bound and
perform an ordinary variational calculation for the true problem. We
use a trial function which reduces, as k -> 0, to the zero energy
function, Eq. (i|.23), namely
(U
.27) ^/2V(^1'^2'^12^'^ " (2Ao-^)^'^^[Ae"'"^ ^° (l-e"'^ ^°) cos kr^
- e sm kr, A + Br-,e
-tr^2/% - ^^2/^0 ^ -^12/^^0 - 2^1/^0
+ Gr-e + Dr-|_e
] â–
- 28 -
From the asymptotic fom of this function we see that A = -tanlTA-
The variational principle is now
r
(U.28) k tan-h ^ k tan>i + ^/2\n "^ "6./^ ^'^
where cC is given by Eq. (2.2). The result of the calculation is
T] = 0.l6a5 ,
^ =J ^4^^/2>^^ = -0.0017/a^
and 11 5^ 0.156. As a point of comparison we note that a variational
ri2i
calculation (including polarization) performed by Massey and Moussa'- -"
for the same scattering energy gave 77 7^ - O.O98 •
Since the trial function is based on the zero energy function which
we expect to be quite good, we have obtained what we believe to be an
accurate estimate of TJ , although not necessarily a lower bound.
Before considering the calculation involving the cut-off potentials
we recall that the cut-off point, a , is limited by the condition ka < n-9,
In order to be able to pick the largest value of a (for fixed k) we
wish to choose the smallest value of 6 consistent with the condition
TJ < &. (Note that we desire that this relation be satisfied, in order
that our bound be a useful one. As discussed previously, the bound will
be valid in either case.) The trial function, Eq. (l4.27)> is noimalized
with © " (1/2V1. This would lead to a ■7.9a . In order to obtain a
variational estimate of f) corresponding to the use of a trial function
with different (and smaller) 9 - nonnalization, we may simply choose
(a. 29)
^ = ^/2y °osysin(|-9)
- 29 -
so that
(U.30) k cot ffi-e)A::k cot(7j-9) - cos 19 /sin ("n - 9)
I
where Tfl and I have already been determined. Vie expect that this
variational estimate of TJ" should change very slowly as 9 is decreased
from(l/2)n. It is found, in fact, that to three significant figures
the result is unchanged for 9 as small as O.3U. (Smaller values of 9
lead to appreciably lower estLmates of tT. ) We have therefore chosen
9 = 0.3U00 which allows us to pick a = liia •
To obtain a bound on"^ we must now perform a similar calculation
with oo replaced by Aj which contains the cut-off potentials, Eq. (3.5)»
The trial function, vu , must now satisfy the additional requirement
that Jo Ug = for r-, > a", while lu must of course be continuous
in slope ana value. Such a function may be written as
('4.31) u^^pfcos -y/sinCy-d)! = iUy2V (Eq. (U.27)) g(r^)
+ (2/a^3)l/2^_g(^_^)) ^""2 \in(kr3^+|)/cosTj
where
(a.32)
g(o) = 1
g'(a) = o
g(r^) =0 , r^ > a
If g(r, ) is close to unity throughout the region r, < a we might
expect that the results obtained will not differ very much from those of
This may be seen from the fact that In order to obtain Pa = 00, p must
v.anish beyond r^ = a. However, J (JCt. )^p'''^dV should exist.
- 30 -
the above variational calculation. With this in mind we chose
(U.33) g^^i) =
1 - e
- ^(1-r^/a)
1 - e
<
r, < a
r, > a
where ^ is arbitrary. If we let Y, take on a Isr^e, positive value
fe «i' 5a, say), g(r^) will have the desired shape.
We may write , ' . .
(U.3U) "a . » »
where p is the nth zero (not including the zero at the origin) in the
wave function. Now consider the point r' = (ii-'h)A:. From the
assumed restriction onil it is clear that r > a. Now the wave
function takes en its asymptotic fonn beyond the point _a, and must
therefore vanish at r'. But from Eq. (U.36), r' = p, , so that we
have shown that the fii^^t zero- occurs beyond a. In the present problem,
under similar conditions, ( i.e . , W. + W_^ =0 for r, > a, and
ka + T7 < n) it may be shown that the function
\
n
2
(li.37) g(r-j^) 5 T^ dr2 dp V.{r^) u(r^,r2,p)
J
is nodeless for r, < a. For s_ large enough it seem.s reasonable (we
2
Online LibraryLarry SpruchLow energy scattering by a compound system: positrons on hydrogen → online text (page 2 of 3)
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# Question Three: (8 Points) You are given the following information: a. Salaries earned by employees that...
On Jan 1, Salem Company acquired a controlling interest in Abdulla Company by purchasing 15,000 shares of Abdula Company's stock from a local stock broker. This was the first time that Salem Company had invested in Abdulla Co, stock. On that das San Company's stock had a par value of $1 per ... 1 answer ##### Based on the solution concentrations we will be using in lab (0.10 M, 0.30 M, 1.0... Based on the solution concentrations we will be using in lab (0.10 M, 0.30 M, 1.0 M, and 3.0 M copper (II) nitrate solution and 1.0 M zinc (II) nitrate AND 50 mL 1.0 M potassium nitrate), calculate the theoretical Ecell values and plot a calibration curve using Excel. Include the equation for the ca... 1 answer ##### What Would You Do? Case Assignment Headquarters Delaware The DuPont company got its start when Eleuthère... What Would You Do? Case Assignment Headquarters Delaware The DuPont company got its start when Eleuthère Irénée du Pont de Nemours fled France’s revolution to come to America, where, in 1802, he built a mill on the Brandywine River in Wilmington, Delaware, to produce ... 1 answer ##### Answer questions 1&2 My Suscriptions Mary R e eBook Question 1 Not yet answered Marked out... answer questions 1&2 My Suscriptions Mary R e eBook Question 1 Not yet answered Marked out of 3.00 Prag question Classifying Cash Flows Classify each of the following items as a (1) cash from operating activity. (2) cash from investing activity. (3) cash from financing activity, or (4) noncash ... 1 answer ##### Actice: Mutations - A -P--I--3--H--N--R--6--8- --11--11-- - ----- CGI GATTIOTITATITCATCCARAGATCTGGGC ATGACHATAGCTATCTACH --6-- -F-- - --5--5--K -3... Actice: Mutations - A -P--I--3--H--N--R--6--8- --11--11-- - ----- CGI GATTIOTITATITCATCCARAGATCTGGGC ATGACHATAGCTATCTACH --6-- -F-- - --5--5--K -3 -4--G-- ----y--5--4--1--0 -- -- SOBOTACECCO THACACOLAGACICITITCAAGACTACATTAASTCCTATTTGGAACAAGCGAC CG 3 -D-P-- -- -- - -- -- --I--K -3-wY--1-- --0-- --3--... 1 answer ##### Luthan Company uses a plantwide predetermined overhead rate of$23.30 per direct labor-hour. This predetermined rate...
Luthan Company uses a plantwide predetermined overhead rate of $23.30 per direct labor-hour. This predetermined rate was based on a cost formula that estimated$279,600 of total manufacturing overhead cost for an estimated activity level of 12,000 direct labor- hours. The company incurred actual tot...
##### Mackenzie Inc. has a $72,500 note payable at December 31. Interest in the amount of$3,625...
Mackenzie Inc. has a $72,500 note payable at December 31. Interest in the amount of$3,625 has accrued but has not yet been paid. Both the note payable and the accrued interest will become due next year. How will the interest affect the adjustments at the end of the period?...
##### Consider the following hypothesis test. H0: 1 - 2≤ 0 Ha: 1 - 2> 0 The following results are for...
Consider the following hypothesis test. H0: 1 - 2≤ 0 Ha: 1 - 2> 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n 1 = 30 n 2 = 60 x 1 = 25.6 x 2 = 22.2 σ 1 = 5.2 σ 2 = 6 ...
##### 13.10 The maximum kinetic energy of a spring system (mass 10 kg, spring constant 1200 N/m)...
13.10 The maximum kinetic energy of a spring system (mass 10 kg, spring constant 1200 N/m) is 8.7 J. a) What is the amplitude of the oscillation? b) What is the maximum speed?...
##### 02) Consider a hydrostatic system represented by the thermodynamic variables volume V, pressure P and temperature...
02) Consider a hydrostatic system represented by the thermodynamic variables volume V, pressure P and temperature T. A) A hydrostatic system undergoes a phase transition from first order to temperature To = 300 K and pressure Po = 1 x 100 Pa. In this case, it is verified that the variation of the sp...
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# Trigonometry - quick question
1. May 11, 2005
### DivGradCurl
I have a straight-forward question. Could anybody please explain me why...
$$\theta = \tan ^{-1} \left( \frac{x}{2} \right) \Rightarrow -\frac{1}{4\sin \theta} = -\frac{\sqrt{x^2+4}}{4x}$$
Thanks
2. May 11, 2005
### whozum
Draw a triangle. Your vertical side will be x, your horizontal base will be 2. This is directly from the tan function. From there you can use pythagorean theorem to find the hypotenuse. Now you have all three sides, and you're trying to find
$$-4csc(\theta)$$. Just pull it right off the triangle. CSC is hyp/opp.
3. May 11, 2005
### DivGradCurl
One sec. after I posted it I realized what to do. Thanks, anyway.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook
Have something to add?
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# Procrastiblog
## January 16, 2008
### Eye of the Tiger
Filed under: Tech — Chris @ 1:31 am
Does anybody know which new API in Mac OS X 10.4 is the reason I can’t use iLike the Amazon MP3 Downloader on my Power Mac G4? Any can anybody tell me why it sucks?
Believe it or not, I actually can’t upgrade to 10.4, because it only comes on DVD-ROM and my, ahem, 6 year old G4 doesn’t have a DVD-ROM drive. (You can get CDs if you buy a copy of 10.4 and send Apple a check for ten or fifteen bucks, but… eh, no.) I will not be buying a new computer this year.
## November 26, 2007
### xkcd: Success
Filed under: Not Tech, Tech, Waste of Time — Chris @ 2:31 pm
This is pretty much exactly how it went down when I upgraded to Gutsy.
Consider this a standing endorsement of xkcd.
## November 25, 2007
### Gnome Sessions
Filed under: Linux, Tech — Chris @ 8:56 pm
I tentatively clicked “Remember current running applications” in Gnome Session Preferences (aka gnome-session-properties) and lived to regret it. What this does is it restarts any currently running application when you login. This is useful for, e.g., your online backup daemon, but kind of annoying for, e.g., five Emacs windows, Last.fm, some random Nautilus directory window, etc.
Now, first I tried checking and unchecking “Automatically remember running applications when logging out”, as the window layout makes it seem as if these two settings are related. They are not. Then, I was tempted to fix this by futzing with the “Startup Programs” or “Current Session” lists. This is Not Right.
The Right Thing is to close all your programs (or just the offending ones) and then click again on “Remember current running applications”. That is to say: the only way to change the “remembered” snapshot is to take another snapshot*.
Note: Session Preferences has a Help button, but the Gnome manual page on it doesn’t mention “Remember currently running programs” or “Automatically remember running applications when logging out”. This is annoying.
* Presumably there is a text file tucked away somewhere that controls this (maybe ~/.gnome2/session?), but I haven’t the patience to find out.
### Style Guidelines for People
Filed under: LaTeX — Chris @ 8:03 pm
In the midst of some unrelated Googling, I came across Luca de Alfaro’s style guidelines for student co-authors. This is good stuff. I particularly like “one sentence per line” b/w “fill-sentence macro”. It’s an elegant solution to a frequently annoying deficiency of diff, which is unfortunately the baseline for anyone collaborating via CVS or SVN. I tweaked his macro to get nice indentation in AucTeX:
(defun fill-sentence ()
(interactive)
(save-excursion
(or (eq (point) (point-max)) (forward-char))
(forward-sentence -1)
(indent-relative)
(let ((beg (point)))
(forward-sentence)
(if (equal "LaTeX" (substring mode-name (string-match "LaTeX" mode-name)))
(LaTeX-fill-region-as-paragraph beg (point))
(fill-region-as-paragraph beg (point))))))
(global-set-key "\ej" 'fill-sentence)
[UPDATE 1/20/08] Fixed an off-by-one error when the cursor is on the first character of the sentence by adding (forward-char).
[UPDATE 9/19/08] Fixed an error when the cursor is at the end of the buffer by changing (forward-char) to (or (eq (point) (point-max)) (forward-char))
### LaTeX Letters
Filed under: LaTeX, Tech — Chris @ 4:42 pm
I was trying to write a letter in LaTeX the other day:
\documentclass{letter}
\signature{Me}
\begin{document}
\begin{letter}
\opening{To Whom It May Concern:}
Hello, there.
\closing{Sincerely,}
\end{letter}
\end{document}
This led to the following two errors, which shed little light on the situation:
! LaTeX Error: There's no line here to end.
See the LaTeX manual or LaTeX Companion for explanation.
Type H for immediate help.
...
l.10 \opening{To Whom It May Concern:}
and (on a different example)
! Incomplete \iffalse; all text was ignored after line 66.
\fi
l.16 \end{letter}
Runaway text?
\@mlabel{}{\unhbox \voidb@x \ignorespaces \global \let
The problem, as it was gently explained to me, is I had omitted the second mandatory argument of \begin{letter}, which is the address of the recipient. The following is correct:
\documentclass{letter}
\signature{Me}
\begin{document}
\begin{letter}{Foo Corp.}
\opening{To Whom It May Concern:}
Hello, there.
\closing{Sincerely,}
\end{letter}
\end{document}
[UPDATE] I just realized that the reason I got so confused about this is that I was working off a previous business letter that was formatted like:
\begin{document}
\begin{letter}
{
Foo Corp. \\
... \\
ATTN: Warranty Dept.}
...
I’m not sure if I intended it to be the case (probably not), but LaTeX picked up the braces around the address as the argument to letter. When I used this as the template for a personal letter and deleted the address, all hell broke loose.
## November 15, 2007
### Fake project directories in tarballs
Filed under: Tech — Chris @ 2:39 pm
To make a tarball where all the files are in a subdirectory FOO (as per best practices), where FOO doesn’t really exist on your disk (e.g., FOO may be PROJECT-vX.Y.Z and the files are in directory PROJECT), just do
tar cvf NAME.tar --transform=s,^,FOO/,g FILES
Note that the argument to transform in this case is just a sed command with commas instead of slashes.
## November 10, 2007
### Eye Candy
Filed under: Linux, Tech — Chris @ 11:24 pm
The difference between “Desktop Plane” and “Desktop Wall” in the Ubuntu “Visual Effects” options (aka CompizConfig Settings) is that the latter allows windows to overlap a viewport* and the former does not. (Along with this comes a lot of incidental options and visual fillips, like the ability to drag a window entirely from one viewport to another.) Although this does not sound like a big productivity booster, I’m going to give the Wall a chance.
I’m not going to give the “Desktop Cube” a chance, because it won’t let me place viewports above and below, as well as left and right, seemingly out of some wrong-headed sense of pseudo-three-dimensional literalism (although your “cube” can have an arbitrary number of faces, they must be arranged linearly from left to right: Euclidian topologies only).
* For some reason the “Desktop Plane,” “Desktop Wall,” and “Desktop Cube” options all use viewports and not workspaces**, so they don’t work well with the Gnome Workspace Switcher.
** For some other reason, Gnome has two distinct ways of implementing virtual desktops (viewports and workspaces) even though theres no discernible advantage to one over the other (except for compatibility with this application or that).
[UPDATE] Visual Effects lead to intermittent system freezes. Fun! Going back to boring old workspaces.
## November 6, 2007
### Updating for Daylight Savings Time on Ubuntu
Filed under: Linux, Tech — Chris @ 9:28 pm
My system clock has been all wiggy since Daylight Savings Time ended (or started?) (it’s ended) on Sunday. Believe it or not, it was actually flipping back and forth between correct and one hour ahead for no apparent reason. I did two things which together seem to have fixed things.
First, via Fast Track Sites, I found that my system timezone information was out of date. The test for this is:
% sudo zdump -v /etc/localtime | grep 2007
/etc/localtime Sun Mar 11 07:59:59 2007 UTC = Sun Mar 11 01:59:59 2007 CST isdst=0 gmtoff=-21600
/etc/localtime Sun Mar 11 08:00:00 2007 UTC = Sun Mar 11 03:00:00 2007 CDT isdst=1 gmtoff=-18000
/etc/localtime Sun Nov 4 06:59:59 2007 UTC = Sun Nov 4 01:59:59 2007 CDT isdst=1 gmtoff=-18000
/etc/localtime Sun Nov 4 07:00:00 2007 UTC = Sun Nov 4 01:00:00 2007 CST isdst=0 gmtoff=-21600
If the output doesn’t exactly match the above, you have a problem. Download the latest tzdata2007X.tgz file (where X is a lowercase letter) from the National Cancer Institute (seriously). For gorey details, see the Fast Track Sites post cited above. (I don’t think you really have to do the ln step, which sets your timezone to EST5EDT instead of, e.g., America/New_York. I skipped it.)
Now your system ought to know the right start/end dates for Daylight Savings Time. But your clock is probably still out of whack.
Now, via Ubuntu Forums and Stephen Sykes, use ntpdate to reset the clock. The trick(s) here are: (a) you have to shut down ntpd first, (b) setting the clock back an hour will convince sudo that you’re trying to do something nefarious (“timestamp too far in the future”), and (c) I had to give ntpdate the -u option to get past some unseen firewall.
% sudo /etc/init.d/ntp-server stop
* Stopping NTP server ntpd [ OK ]
% sudo ntpdate-debian -u
6 Nov 17:00:00 ntpdate[13693]: step time server 66.36.239.104 offset -3598.042737 sec
% sudo /etc/init.d/hwclock.sh restart
sudo: timestamp too far in the future: Nov 6 17:59:56 2007
Oops. Using the “Adjust Date & Time” applet, manually set the clock one hour forward. Now, run sudo -k. Now, set the clock back to the correct time (again using “Adjust Date & Time”). Starting over:
% sudo ntpdate-debian -u
6 Nov 17:00:00 ntpdate[13693]: step time server 66.36.239.104 offset -3598.042737 sec
% sudo /etc/init.d/hwclock.sh restart
* Saving the system clock
% sudo /etc/init.d/ntp start
* Starting NTP server ntpd [ OK ]
All done. Enjoy.
[UPDATE 3/12/2008] It looks like this might be a semi-annual ritual: my system pulled the same schizo act when DST started this week. On Gutsy, ntp-server has become ntp. It’s easier springing forward than falling back, because sudo just times out when you set the clock forward.
[UPDATE 3/9/2009] A fall back and a spring forward with no problems. Whoopee.
## July 25, 2007
### A Dubious Assertion
Filed under: Tech — Chris @ 2:44 am
Being a conscientious software engineer, I try to be good about putting assert statements in my code. And being a verification guy, I find myself tempted to express fairly deep correctness properties in my assertions. And this fills me with such satisfaction, that I am such a wise and clever programmer, that I should do such things.
But then I’m trying to optimize some code so that it runs in something like an acceptable amount of time and for some reason I just can’t shake this routine out of its stupor… What’s going on here?
Don’t add assertions that change the asymptotic complexity of your algorithm. That’s just dumb. (Of course you can always compile your code with assertions turned off, but even in testing the difference between O(n) and O(1) can pinch.)
And now look at how much more wise and clever and self-satisfied I can be.
## July 9, 2007
### Changing your PATH in Emacs’ compilation mode
Filed under: Emacs, Tech — Chris @ 4:21 pm
[UPDATE: This is not really wrong, but not really right either. See below.]
I was a bit surprised at this problem, but I suppose most people use standard make or gcc to build… I want to build my project with a version of OMake that I have compiled and installed in my home directory. I have ~/tools/bin in my PATH, but for some reason M-x compile still gives me
The trick is that Emacs invokes the compile command in a non-interactive, non-login shell, which means that neither your .bash_profile nor your .bashrc (or any variations thereof) are going to get read.* The workaround is to set BASH_ENV to point to a script file that sets your PATHbash reads the file pointed-to by BASH_ENV in non-interactive mode. Here’s my solution:
# In ~/.bash_profile:
. ~/.bashrc
# In ~/.bashrc:
export BASH_ENV=~/.bash_env
. "$BASH_ENV" # In ~/.bash_env: export PATH=/home/chris/tools/bin:$PATH
There’s probably a good reason why this is a bad idea, but it works.
* A quick refresher course: .bash_profile is for login shells; .bashrc is for interactive, non-login shells; BASH_ENV is for non-interactive, non-login shells (which, confusingly, will probably be a sub-process of an interactive and/or login shell, which is why the above example works).
[UPDATE] The compilation shell being non-interactive and non-login is a red herring. While this is certainly the case, a non-interactive, non-login shell will inherit the environment of it’s parent process. So, for instance, if your PATH is properly set in your shell and you invoke Emacs from the command line, things should be fine.
What was really causing my problem is that I was invoking Emacs from the Gnome Panel. The environment that Emacs inherits in this case is Gnome’s, not Bash’s. How do you change the PATH in the Gnome environment? Um… Eh… gnome-session-properties? .gnomerc?
The solution I’ve settled on is to create a ~/.xsession file as follows,
#! /usr/bin/bash
if [ -f ~/.bash_env ]; then
. ~/.bash_env
fi
exec gnome-session
where .bash_env is as above.
NOTE: If you leave off the last line, your X session will end before it begins. The .xsession script is the X process: when it ends, the X process ends. Execing gnome-session replaces the script process with the Gnome session process.
[UPDATE 2] Of course, another option is to just use setenv in your .emacs file. TMTOWTDI, in Emacs and Perl alike.
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# 7.11: Factorization of Special Cubics
Difficulty Level: Advanced Created by: CK-12
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Practice Sum and Difference of Cubes
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Factor the following cubic polynomial: 375x3+648\begin{align*}375x^3+648\end{align*}.
### Guidance
While many cubics cannot easily be factored, there are two special cases that can be factored quickly. These special cases are the sum of perfect cubes and the difference of perfect cubes.
• Factoring the sum of two cubes follows this pattern: x3+y3=(x+y)(x2xy+y2)\begin{align*}x^3+y^3=(x+y)(x^2-xy+y^2)\end{align*}
• Factoring the difference of two cubes follows this pattern: x3y3=(xy)(x2+xy+y2)\begin{align*}x^3-y^3=(x-y)(x^2+xy+y^2)\end{align*}
#### Example A
Factor: x3+27\begin{align*}x^3+27\end{align*}.
Solution: This is the sum of two cubes and uses the factoring pattern: x3+y3=(x+y)(x2xy+y2)\begin{align*}x^3+y^3=(x+y)(x^2-xy+y^2)\end{align*}.
x3+33=(x+3)(x23x+9)\begin{align*}x^3+3^3=(x+3)(x^2-3x+9)\end{align*}.
#### Example B
Factor: x3343\begin{align*}x^3-343\end{align*}.
Solution: This is the difference of two cubes and uses the factoring pattern: x3y3=(xy)(x2+xy+y2)\begin{align*}x^3-y^3=(x-y)(x^2+xy+y^2)\end{align*}.
x373=(x7)(x2+7x+49)\begin{align*}x^3-7^3=(x-7)(x^2+7x+49)\end{align*}.
#### Example C
Factor: 64x31\begin{align*}64x^3-1\end{align*}.
Solution: This is the difference of two cubes and uses the factoring pattern: x3y3=(xy)(x2+xy+y2)\begin{align*}x^3-y^3=(x-y)(x^2+xy+y^2)\end{align*}.
(4x)313=(4x1)(16x2+4x+1)\begin{align*}(4x)^3-1^3=(4x-1)(16x^2+4x+1)\end{align*}.
#### Concept Problem Revisited
Factor the following cubic polynomial: 375x3+648\begin{align*}375x^3+648\end{align*}.
First you need to recognize that there is a common factor of 3\begin{align*}3\end{align*}. 375x3+648=3(125x3+216)\begin{align*}375x^3+648=3(125x^3+216)\end{align*}
Notice that the result is the sum of two cubes. Therefore, the factoring pattern is x3+y3=(x+y)(x2xy+y2)\begin{align*}x^3+y^3=(x+y)(x^2-xy+y^2)\end{align*}.
375x3+648=3(5x+6)(25x230x+36)\begin{align*}375x^3 +648 = 3(5x+6)(25x^2-30x+36)\end{align*}
### Vocabulary
Difference of Two Cubes
The difference of two cubes is a special polynomial in the form of x3y3\begin{align*}x^3-y^3\end{align*}. This type of polynomial can be quickly factored using the pattern: (x3y3)=(xy)(x2+xy+y2)\begin{align*}(x^3-y^3)=(x-y)(x^2+xy+y^2)\end{align*}
Sum of Two Cubes
The sum of two cubes is a special polynomial in the form of x3+y3\begin{align*}x^3+y^3\end{align*}. This type of polynomial can be quickly factored using the pattern: (x3+y3)=(x+y)(x2xy+y2)\begin{align*}(x^3+y^3)=(x+y)(x^2-xy+y^2)\end{align*}
### Guided Practice
Factor each of the following cubics.
1. x3+512\begin{align*}x^3+512\end{align*}
2. 8x3+125\begin{align*}8x^3+125\end{align*}
3. x3216\begin{align*}x^3-216\end{align*}
1. x3+83=(x+8)(x28x+64)\begin{align*}x^3+8^3=(x+8)(x^2-8x+64)\end{align*}.
2. (2x)3+53=(2x+5)(4x210x+25)\begin{align*}(2x)^3+5^3=(2x+5)(4x^2-10x+25)\end{align*}.
3. x363=(x6)(x2+6x+36)\begin{align*}x^3-6^3=(x-6)(x^2+6x+36)\end{align*}.
### Practice
Factor each of the following cubics.
1. x3+h3\begin{align*}x^3+h^3\end{align*}
2. a3+125\begin{align*}a^3+125\end{align*}
3. 8x3+64\begin{align*}8x^3+64\end{align*}
4. x3+1728\begin{align*}x^3+1728\end{align*}
5. 2x3+6750\begin{align*}2x^3+6750\end{align*}
6. h364\begin{align*}h^3-64\end{align*}
7. s3216\begin{align*}s^3-216\end{align*}
8. p3512\begin{align*}p^3-512\end{align*}
9. 4e332\begin{align*}4e^3-32\end{align*}
10. 2w3250\begin{align*}2w^3-250\end{align*}
11. x3+8\begin{align*}x^3+8\end{align*}
12. y31\begin{align*}y^3-1\end{align*}
13. 125e38\begin{align*}125e^3-8\end{align*}
14. 64a3+2197\begin{align*}64a^3+2197\end{align*}
15. 54z3+3456\begin{align*}54z^3+3456\end{align*}
### Notes/Highlights Having trouble? Report an issue.
Color Highlighted Text Notes
### Vocabulary Language: English
Cubed
The cube of a number is the number multiplied by itself three times. For example, "two-cubed" = $2^3 = 2 \times 2 \times 2 = 8$.
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Łukaszyk–Karmowski metric
In mathematics, the Łukaszyk–Karmowski metric is a function defining a distance between two random variables or two random vectors.[1][2] This function is not a metric as it does not satisfy the identity of indiscernibles condition of the metric, that is for two identical arguments its value is greater than zero. The concept is named after Szymon Łukaszyk and Wojciech Karmowski.
Continuous random variables
The Łukaszyk–Karmowski metric D between two continuous independent random variables X and Y is defined as:
$D(X, Y) = \int_{-\infty}^\infty \int_{-\infty}^\infty |x-y|f(x)g(y) \, dx\, dy$
where f(x) and g(y) are the probability density functions of X and Y respectively.
One may easily show that such metrics above do not satisfy the identity of indiscernibles condition required to be satisfied by the metric of the metric space. In fact they satisfy this condition if and only if both arguments X, Y are certain events described by Dirac delta density probability distribution functions. In such a case:
$D_{\delta\delta}(X, Y) = \int_{-\infty}^\infty \int_{-\infty}^\infty |x-y|\delta(x-\mu_x)\delta(y-\mu_y) \, dx\, dy = |\mu_x-\mu_y|$
the Łukaszyk–Karmowski metric simply transforms into the metric between expected values $\mu_x$, $\mu_y$ of the variables X and Y and obviously:
$D_{\delta\delta}(X, X) = |\mu_x-\mu_x| = 0.$
For all the other cases however:
$D\left(X, X\right) > 0. \,$
The Łukaszyk–Karmowski metric satisfies the remaining non-negativity and symmetry conditions of metric directly from its definition (symmetry of modulus), as well as subadditivity/triangle inequality condition:
\begin{align} &{} D(X, Z) = \int_{-\infty}^\infty \int_{-\infty}^\infty |x-z|f(x)h(z) \, dx\, dz\ = \int_{-\infty}^\infty \int_{-\infty}^\infty |x-z|f(x)h(z) \, dx\, dz \int_{-\infty}^\infty g(y) dy\ \\ &{} = \int_{-\infty}^\infty \int_{-\infty}^\infty \int_{-\infty}^\infty |(x-y)+(y-z)|f(x)g(y)h(z) \, dx\, dy\, dz\ \\ &{} \le \int_{-\infty}^\infty \int_{-\infty}^\infty \int_{-\infty}^\infty (|x-y|+|y-z|)f(x)g(y)h(z) \, dx\, dy\, dz\ \\ &{} = \int_{-\infty}^\infty \int_{-\infty}^\infty \int_{-\infty}^\infty |x-y|f(x)g(y)h(z) \, dx\, dy\, dz\ + \int_{-\infty}^\infty \int_{-\infty}^\infty \int_{-\infty}^\infty |y-z|f(x)g(y)h(z) \, dx\, dy\, dz\ \\ &{} = \int_{-\infty}^\infty \int_{-\infty}^\infty |x-y|f(x)g(y) \, dx\, dy\ + \int_{-\infty}^\infty \int_{-\infty}^\infty |y-z|g(y)h(z) \, dy\, dz\ \\ &{} = D(X, Y) + D(Y, Z) \end{align}
Thus
$D(X, Z) \le D(X, Y)+D(Y, Z). \,$
L–K metric between two random variables X and Y having normal distributions and the same standard deviation $\sigma = 0, \sigma = 0.2, \sigma = 0.4, \sigma = 0.6, \sigma = 0.8, \sigma = 1$ (starting with the bottom curve). $m_{xy} = |\mu_x-\mu_y|$ denotes a distance between means of X and Y.
In the case where X and Y are dependent on each other, having a joint probability density function f(x, y), the L–K metric has the following form:
$\int_{-\infty}^\infty \int_{-\infty}^\infty |x-y| f(x, y) \, dx\, dy.$
Example: two continuous random variables with normal distributions (NN)
If both random variables X and Y have normal distributions with the same standard deviation σ, and if moreover X and Y are independent, then D(XY) is given by
$D_{NN}(X, Y) = \mu_{xy} + \frac{2\sigma}{\sqrt\pi}\operatorname{exp}\left(-\frac{\mu_{xy}^2}{4\sigma^2}\right)-\mu_{xy} \operatorname{erfc} \left(\frac{\mu_{xy}}{2\sigma}\right) ,$
where
$\mu_{xy} = \left|\mu_x-\mu_y\right|,$
where erfc(x) is the complementary error function and where the subscripts NN indicate the type of the L–K metric.
In this case, the lowest possible value of the function $D_{NN}(X, Y)$ is given by
$\lim_{\mu_{xy}\to 0} D_{NN}(X, Y) = D_{NN}(X, X) = \frac{2\sigma}{\sqrt\pi}.$
Example: two continuous random variables with uniform distributions (RR)
When both random variables X and Y have uniform distributions (R) of the same standard deviation σ, D(XY) is given by
$D_{RR}(X, Y) = \begin{cases} \frac{24\sqrt{3}\sigma^3-\mu_{xy}^3+6\sqrt{3}\sigma\mu_{xy}^2}{36\sigma^2}, & \mu_{xy}<2\sqrt{3}\sigma, \\ \mu_{xy}, & \mu_{xy} \ge 2\sqrt{3}\sigma. \end{cases}$
The minimal value of this kind of L–K metric is
$D_{RR}(X, X) = \frac{2\sigma}{\sqrt{3}}.$
Discrete random variables
In case the random variables X and Y are characterized by discrete probability distribution the Łukaszyk–Karmowski metric D is defined as:
$D(X, Y) = \sum_{i} \sum_{j} |x_i-y_j|P(X=x_i)P(Y=y_j).\,$
For example for two discrete Poisson-distributed random variables X and Y the equation above transforms into:
$D_{PP}(X, Y) = \sum_{x=0}^n\sum_{y=0}^n |x-y|\frac{{\lambda_x}^x{\lambda_y}^ye^{-(\lambda_x+\lambda_y)}}{x!y!}.$
Random vectors
equidistant surface for Euclidean metric $d^{2}(\mathbf{x},\mathbf{0})=\sqrt{x_{1}^2+x_{2}^2}$
equidistant surface for Euclidean L–K metric $D_{R\delta}^{2}(\mathbf{X},\mathbf{0}) \left( \left(\mathbf{X,0}\right): \Omega \to \mathbb{R}^2 \right)$
The Łukaszyk–Karmowski metric of random variables may be easily extended into metric D(X, Y) of random vectors X, Y by substituting $|x-y|$ with any metric operator d(x,y):
$D(\mathbf{X}, \mathbf{Y}) =\int_{\Omega} \int_{\Omega} d(\mathbf{x}, \mathbf{y})F(\mathbf{x})G(\mathbf{y})\, d\Omega_x \, d\Omega_y.$
For example substituting d(x,y) with an Euclidean metric and assuming two-dimensionality of random vectors X, Y would yield:
$D(\mathbf{X}, \mathbf{Y}) =\int_{\Omega} \int_\Omega \sqrt{\sum_{i=1}^2|x_i-y_i|^2} F( x_1, x_2)G(y_1, y_2) \, dx_1\, dx_2\, dy_1\, dy_2.$
This form of L–K metric is also greater than zero for the same vectors being measured (with the exception of two vectors having Dirac delta coefficients) and satisfies non-negativity and symmetry conditions of metric. The proofs are analogous to the ones provided for the L–K metric of random variables discussed above.
In case random vectors X and Y are dependent on each other, sharing common joint probability distribution F(X, Y) the L–K metric has the form:
$D(\mathbf{X}, \mathbf{Y}) =\int_{\Omega} \int_{\Omega} d(\mathbf{x}, \mathbf{y})F(\mathbf{x}, \mathbf{y}) \, d\Omega_x \, d \Omega_y.$
Random vectors – the Euclidean form
If the random vectors X and Y are not also only mutually independent but also all components of each vector are mutually independent, the Łukaszyk–Karmowski metric for random vectors is defined as:
$D_{**}^{(p)}(\mathbf{X}, \mathbf{Y}) = \left( {\sum_i{D_{**}(X_i, Y_i)}^p} \right)^{\frac1p}$
where:
$D_{**}(X_i, Y_i)\,$
is a particular form of L–K metric of random variables chosen in dependence of the distributions of particular coefficients $X_i$ and $Y_i$ of vectors X, Y .
Such a form of L–K metric also shares the common properties of all L–K metrics.
• It does not satisfy the identity of indiscernibles condition:
$\forall{\mathbf{X}, \mathbf{Y}}\ D_{**}^{(p)}(\mathbf{X}, \mathbf{Y}) = 0 \ \nLeftrightarrow \ \mathbf{X} = \mathbf{Y} \,$
since:
$D_{**}^{(p)}(\mathbf{X}, \mathbf{X}) = 0 \Leftrightarrow \ \forall{i} \ D_{**}(X_i, X_i) = 0$
but from the properties of L–K metric for random variables it follows that:
$\exists\ X_i\ D_{**}(X_i, X_i) > 0$
• It is non-negative and symmetric since the particular coefficients are also non-negative and symmetric:
$\forall\ i \ D_{**}(X_i, Y_i) > 0 \,$
$\forall\ i \ D_{**}(X_i, Y_i) = D_{**}(Y_i, X_i)$
• It satisfies the triangle inequality:
$\forall\ \mathbf{X}, \mathbf{Y}, \mathbf{Z} \ D_{**}^{(p)}(\mathbf{X}, \mathbf{Z}) \le D_{**}^{(p)}(\mathbf{X}, \mathbf{Y}) + D_{**}^{(p)}(\mathbf{Y}, \mathbf{Z})$
since (cf. Minkowski inequality):
\begin{align} &{} \left( {\sum_i{D_{**}(X_i, Y_i)}^p} \right)^{\frac1p} + \left( {\sum_i{D_{**}(Y_i, Z_i)}^p} \right)^{\frac1p}\ \ge \\ &{} \ge \left( {\sum_i{D_{**}(X_i, Y_i) + D_{**}(Y_i, Z_i)}^p} \right)^{\frac1p} \ge \\ &{} \ge \left( {\sum_i{D_{**}(X_i, Z_i)}^p} \right)^{\frac1p} \end{align}
Physical interpretation
The Łukaszyk–Karmowski metric may be considered as a distance between quantum mechanics particles described by wavefunctions ψ, where the probability dP that given particle is present in given volume of space dV amounts:
$dP = |\psi(x, y, z)|^2 dV. \,$
A quantum particle in a box
L–K metric between a quantum particle in a one-dimensional box of length L and a given point ξ of the box $(0 \le \xi \le L)$.
For example the wavefunction of a quantum particle (X) in a box of length L has the form:
$\psi_m(x) = \sqrt{\frac{2}{L}} \sin{\left(\frac{m \pi x}{L} \right)}, \,$
In this case the L–K metric between this particle and any point $\xi \in (0, L)\,$ of the box amounts:
\begin{align} &{} D(X, \xi) = \int\limits_{0}^L |x-\xi||\psi_m(x)|^2dx = \\ &{} = \frac{\xi^2}{L} - \xi +L\left(\frac{1}{2}-\frac{\sin^2(\frac{m\pi\xi}{L})}{m^2\pi^2}\right). \end{align}
From the properties of the L–K metric it follows that the sum of distances between the edge of the box (ξ = 0 or ξ= L) and any given point and the L–K metric between this point and the particle X is greater than L–K metric between the edge of the box and the particle. E.g. for a quantum particle X at an energy level m = 2 and point ξ = 0.2:
$d(0,0.2L) + D(0.2L, X) \approx 0.2L + 0.3171L = 0.517L \neq D(0, X) = 0.5L = d(0,0.5L).\,$
Obviously the L–K metric between the particle and the edge of the box (D(0, X) or D(L, X)) amounts 0.5L and is independent on the particle's energy level.
Two quantum particles in a box
A distance between two particles bouncing in a one-dimensional box of length L having time-independent wavefunctions:
$\psi_m(x) = \sqrt{\frac{2}{L}} \sin{\left(\frac{m \pi x}{L} \right)}, \,$
$\psi_n(y) = \sqrt{\frac{2}{L}} \sin{\left(\frac{n \pi y}{L} \right)}, \,$
may be defined in terms of Łukaszyk–Karmowski metric of independent random variables as:
\begin{align} &{} D(X, Y) = \int\limits_{0}^L \int\limits_0^L |x-y||\psi_m(x)|^2|\psi_n(y)|^2 \, dx\, dy \\ &{} = \begin{cases} L\left(\frac{4 \pi^2 m^2 -15}{12\pi^2m^2} \right) & m=n, \\ L\left(\frac{2 \pi^2 m^2 n^2 -3m^2 - 3n^2}{6\pi^2m^2n^2} \right) & m \neq n \end{cases}\end{align}
The distance between particles X and Y is minimal for m = 1 i n = 1, that is for the minimum energy levels of these particles and amounts:
$\min(D(X, Y)) = L\left(\frac{4 \pi^2-15}{12\pi^2} \right) \approx 0.2067L. \,$
According to properties of this function, the minimum distance is nonzero. For greater energy levels m, n it approaches to L/3.
Popular explanation
Normal distributions of two random variables X and Y of the same variance for three locations of their means µx, µy
Suppose we have to measure the distance between point µx and point µy, which are collinear with some point 0. Suppose further that we instructed this task to two independent and large groups of surveyors equipped with tape measures, wherein each surveyor of the first group will measure distance between 0 and µx and each surveyor of the second group will measure distance between 0 and µy.
Under the following assumptions we may consider the two sets of received observations xi, yj as random variables X and Y having normal distribution of the same variance σ 2 and distributed over "factual locations" of points µx, µy.
Calculating the arithmetic mean for all pairs |xiyj| we should then obtain the value of L–K metric DNN(X, Y). Its characteristic curvilinearity arises from the symmetry of modulus and overlapping of distributions f(x), g(y) when their means approach each other.
An interesting experiment the results of which coincide with the properties of L–K metric was performed in 1967 by Robert Moyer and Thomas Landauer who measured the precise time an adult took to decide which of two Arabic digits was the largest. When the two digits were numerically distanced such as 2 and 9. subjects responded quickly and accurately. But their response time slowed by more than 100 milliseconds when they were closer such as 5 and 6, and subjects then erred as often as once in every ten trials. The distance effect was present both among highly intelligent persons, as well as those who were trained to escape it.[3]
Practical applications
A Łukaszyk–Karmowski metric may be used instead of a metric operator (commonly the Euclidean distance) in various numerical methods, and in particular in approximation algorithms such us radial basis function networks ,[4][5] inverse distance weighting or Kohonen self-organizing maps.
This approach is physically based, allowing the real uncertainty in the location of the sample points to be considered. [6][7]
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# Does every ultrafilter has single limit imply Hausdorff separation
If a topological space $X$ enjoys the property that every ultrafilter $U$ on $X$ has a single limit, must $X$ be a Hausdorff space?
(Ultrafilters here consist of arbitrary subsets (so not necessarily, for example, $z$-sets or closed sets) but the limit of such a $U$ means the intersection of the closures of all its sets.)
I guess not, but I don't have an example.
-
An ultrafilter $U$ on the space $X$ is said to converge to the point $p$ if every neighborhood of $p$ belongs to $U$. (This is equivalent to saying that the complement of an element of $U$ is never a neighborhood of $p$. Thus it is also equivalent to saying that $p$ belongs to the closure of every element of $U$.)
If $U$ converges to both $p$ and $q$, then $p$ and $q$ cannot have disjoint neighborhoods, because this would mean that the empty set belongs to $U$.
Conversely, if $p$ and $q$ do not have disjoint neighborhoods then there is a proper filter containing all neighborhoods of $p$ and all neighborhoods of $q$ (namely the set of all subsets $S\subset X$ such that $S$ contains the intersection of a neighborhood of $p$ and a neighborhood of $q$), and therefore there is an ultrafilter converging to both $p$ and $q$.
Thus $X$ is a Hausdorff space if and only if no ultrafilter on the point set of $X$ converges to more than one point of $X$.
I just thought it is good to mention that $p$ belongs to the closure of every element of $U$ is the definition of cluster point of $U$. For ultrafilters, the limit and cluster point are equivalent notins, for arbitrary filter they may differ. – Martin Sleziak Apr 14 '12 at 6:50
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# Some Background on Finite Volume Methods
We are generally interested in solving PDE's of the form
For the moment, let's focus our attention even further, on one of the simplest PDE's of that form, known as Burger's equation (inviscid form).
Though this class of equations may appear relatively straightforward, it turns out that many such PDE's lead to the formation of discontinuities, or shocks, even from smooth initial data. In order to solve PDE's whose solutions contain shocks, we must turn to methods which do not assume the continuity of the solution, unlike the more intuitive finite difference methods. One way in which we can make sense of such solutions is to think of the average value of the solution over a given cell, rather than the value at specific grid points. Let the cell describe the spatial region between and and the temporal region between and . The average value of the solution over this cell is
and let the numerical flux F be given by
Integrating the conservation form of Burger's eqn. and dividing by total volume gives,
If we can find a way to estimate the numerical fluxes and using information from the current time step, we will have a method for advancing the solution in time. Specifically
To see how this can be implemented in practice, go to the next section
## Roe Solver
One technique for estimating these numerical fluxes, developed by Roe, involves linearizing the system by evaluating the Jacobian matrix at and approximating . The original equation then becomes . If the basis of eigenvectors of A is chosen, the system is uncoupled and is reduced to a series of 1D equations of the form
where is the eigenvalue corresponding to the eigenvector . Given initial data
the value at at subsequent times is if and if . The component of the numerical flux at is then given by
The two results can be combined in the following expression
Summing over all , the final result is
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In this challenge, you will write a bot that play's the prisoner's dilemma. Here's the catch: you will not have access to the history of previous games. Instead, you will have access to the opponent itself. In this version, both players get +2 points if they both cooperate, +1 points if they both defect, and if one cooperates but one defects, the defector gets +3 while the other gets no points. Each submission will be played against every other submission, including itself, 10 times. The winner is the submission with the most total points.
Controller: You should write a javascript function, in the form
function submissionName(them) {
}
The controller uses the function's name property to display the results, so if it is not in this format (and is instead f = x => ... or f = function() { ... }) it will be difficult to see your score and you will not be able to access your own function.
The function will accept one parameter: them which is the opponent's function. It may then call that function to see what the opponent's reaction would be given certain functions as inputs. Based on that data, you must return 'C' or 'D' for cooperate or defect respectively.
Examples (will be competing):
function cooperate(them) {
return 'C';
}
function defect(them) {
return 'D';
}
function nice(them) {
// Do whatever they would do when faced with a cooperator
return them(wrap(_ => 'C'));
}
The controller is available here
Rules:
• You won't be able to see the opponent's code itself. All functions are wrapped so that they look the same when toString() is called. The only way to examine an opponent (who could be yourself) is to test them.
• Your function does not have to be deterministic. You may only save state by setting properties on your own function, such as submissionName.state = {};. However, between matches (even between matches of the same players), state is cleared by calling toString() and eval. Therefore, there is no memory of previous matches.
• The order of which function is called first in each match is randomized.
• If your code throws an error, it will be treated as though you cooperated while your opponent defected. If you are the first to run, the opponent's code will not even be called. This happens even if the error occurs in your opponent's code while while you are calling them. Be wary of stack overflow errors, especially if your code calls them(wrap(submissionName)), as they might do the same.
• You may not access the variable self, or any other variable that happens to be in scope when eval is called EXCEPT the function wrap. This function allows you to call the opponent in a manner indistinguishable from how the controller calls a function. You may not write to Math, window, etc. (You may use functions, such as Math.random(), however).
• You may not access the stack trace by creating an Error or by some other method.
A note on taking too long: please avoid getting stuck in a while loop forever. The combined time of both competitors should not exceed 1 second in any given round. To enforce this, a random timeout between 1000 ms and 2000 ms is chosen (this is to avoid gaming by intentionally waiting a known amount of time), and if the worker takes longer than that to execute, an error will be thrown. If this happens, the cause of the error will be determined as follows: the execution will be paused at a random moment after 1000 ms, and the call stack at that moment will be inspected. The most recently called competitor that is currently in a loop (or loop-like recursion, in the sense that it is a recursion set up to avoid a stack overflow error) will be blamed. If the same competitor is blamed for causing a "taking too long" error several times, that competitor will be disqualified. This means that even if you cause the opponent to take too long by getting stuck in a loop when your opponent calls you, it will still be your fault, because it is the call stack that matters.
• This challenge reminds me of the Dollar Bill Auction. Sep 30, 2018 at 9:18
• Must the function used to test them be deterministic/follow the rules? For example function me(them){let log=0;them(x=>{++log;return 'C';});return log==0?'D':'C';} Sep 30, 2018 at 12:28
• If both functions call them(wrap(something)), how can you prevent recursion? Am I missing something? Sep 30, 2018 at 13:29
• @Quintec you can use recursion and loops. It's just that the recursion needs to result in a StackOverflow error and not an infinite loop that never quits. If it could result in a StackOverflow, make sure you add a try-catch statement. For an example of recursion that does not reach a stackoverflow error within 1 second, you need more obscure examples like stackoverflow.com/q/12438786/3371119 Sep 30, 2018 at 14:18
• @Quintec not necessarily. For example, them(() => 'C') would not result in an error because when the opponent calls them, it calls the () => 'C' function. The only thing that needs to be wrapped in try-catch would be if you call them with a parameter of some function that calls them with a parameter of some function that calls them etc. (infinitely). For example, them(t => t(() => 'C')) would play whatever the opponent would play if the opponent thought they were playing nice. There is no possibility of a stackoverflow error. Sep 30, 2018 at 14:39
# BoomBot
function boom(them) {
throw 1;
}
If the opponent is run first and calls this without try..catch, this bot automatically wins 3 points. Zero points in any other case.
• If the opponent is run first and do not call this, then it will lose 3 points, right? Oct 1, 2018 at 13:51
• @user202729 More precisely, the opponent will get 3 points. There's no losing points in this game. Oct 1, 2018 at 22:58
# Archaeopteryx
function archaeopteryx(them) {
const guard = them => us => {
try {
return them(wrap(them => us(guard(them))));
} catch (e) {
return 'C';
}
};
const f = guard(them);
return f(f => 'C') == 'C' ? f(f => 'D') : f(f => 'D') == 'C' || f(f => f(f => 'C')) == 'C' ? 'D' : 'C';
}
• If opponent cooperates with cooperate, then mimic opponent’s move against defect.
• Else, if opponent cooperates with defect or with nice, then defect.
• Else, cooperate.
What makes this a good strategy? I have no idea. I generated it using an evolutionary algorithm, trained partly on current submissions.
# Tiktaalik
function tiktaalik(them) {
const guard = them => us => {
try {
return them(wrap(them => us(guard(them))));
} catch (e) {
return 'C';
}
};
const f = guard(them);
return f(f => 'C') == 'D' ? f(f => 'D') == 'C' ? 'D' : 'C' : f(f => 'D') == 'D' ? 'D' : f(f => f(f => 'D'));
}
• If opponent defects against cooperate, then invert opponent’s move against defect.
• Else, if opponent defects against defect, then defect.
• Else, mimic opponent’s move against notNice.
Another evolutionarily generated strategy.
# WhatWouldBotDoBot
function WWBDB(them) {
let start = performance.now();
let cc = 0, cd = 0, dc = 0, dd = 0;
try {
for (let i = 0; i < 10; i++) {
them(() => 'C') == 'C' ? cc++ : cd++;
them(() => 'D') == 'C' ? dc++ : dd++;
if (performance.now() - start > 500) break;
}
}
catch (e) {}
return 2 * cc >= 3 * dc + dd ? 'C' : 'D';
}
WhatWouldBotDoBot is fairly simple; it just tests its opponent for what it would do against a steady state program. If a bot prefers cooperating if possible, WWBDB will also prefer cooperation (so it will cooperate with nice bot). WWBDB does not itself prefer cooperation.
# Check stateful
function checkStateful(them) {
let stateful = false;
let response = 'D';
try {
response = them(wrap(function (them) {
stateful = true;
return 'C';
}));
} catch (e) {
}
if (stateful) {
return 'D';
}
return response;
}
If them invoke me, then them probably be a truly them. We act as defector. If them not invoke me, then them probably be a wrapped tester. We would act as nicer.
Above is the original answer. And maybe I should make myself cooperation to earn more points.
# Check stateful with self-coop
function checkStatefulSelfCoop(them) {
let stateful = false;
let response = 'D';
if (!checkStatefulSelfCoop.invokeCounter) {
checkStatefulSelfCoop.invokeCounter = 0;
}
let lastInvoke = ++checkStatefulSelfCoop.invokeCounter;
try {
response = them(wrap(function (them) {
stateful = true;
return 'C';
}));
} catch (e) {
}
if (checkStatefulSelfCoop.invokeCounter > lastInvoke) {
return 'C';
}
if (stateful) {
return 'D';
}
return response;
}
# RandomBot
function rand(them) {
return 'CD'[Math.random() * 2 | 0]
}
Because why not.
# Complexity
function complexity(them) {
try {
let coop_w_def = them(wrap(() => "D")) == "C",
coop_w_coop = them(wrap(() => "C")) == "C",
coop_w_nice = them(wrap((a) => a(wrap(() => "C")))) == "C",
coop_w_nnice = them(wrap((a) => a(wrap(() => "D")))) == "C";
if (coop_w_def && coop_w_coop && coop_w_nice && coop_w_nnice) return "C";
let def_w_def = them(wrap(() => "D")) == "D",
def_w_coop = them(wrap(() => "C")) == "D",
def_w_nice = them(wrap((a) => a(wrap(() => "C")))) == "D",
def_w_nnice = them(wrap((a) => a(wrap(() => "D")))) == "D";
if (def_w_def && def_w_coop && def_w_nice && def_w_nnice) return "C";
} catch (e) {}
return "D";
}
Complexity tests to see whether the bot is Cooperate or Defect. If it is, it cooperates, but if it isn't, it defects. All current bots that test their opponents use simple functions to test the responses, so Complexity will just pretend to be Cooperate in those cases.
function onlyTrustYourself(them) {
function tester (){
}
onlyTrustYourself.activated = false;
try{them(tester);}
catch(e){}
if(them.name == "tester")
{
onlyTrustYourself.activated = true;
}
if(onlyTrustYourself.activated)
{
return 'C';
}
return 'D';
}
How I want this to work is to always defect, except for when playing against self. It tries to do that by passing a "tester" function which isn't wrapped to them, and it tries to detect if "them" is named tester. If it is named tester, it changes the static variable activated to true, then returns cooperate. But it doesn't work. I'm not too familiar with javascript, and I'll probably make some more changes.
• clever idea, but what happens when another bro makes a tester function :D Aug 6, 2019 at 12:35
# NotNice
function NotNice(them) {
return them(wrap(_ => "D"))
}
Imitates opponent's reaction to deflection
# NotNice 2
function notNice2(them) {
try {
return them(wrap(_ => 'D'));
} catch(e) {
return 'D';
}
}
Boom-proof version of NotNice by FatalError.
# Common Sense
function commonSense(them) {
try {
var ifC = them(wrap(_ => 'C'));
var ifD = them(wrap(_ => 'D'));
if (ifD === 'C') {
return 'D';
}
return them(_ => ifC);
} catch (e) {
return 'D';
}
}
Disclaimer: I kinda don't know javascript.
If you can profit off a nice person, do it. Otherwise, return what they would return if they faced themselves cooperating (at least, that's what I think it does).
And you where do you wana go? (inspired by the voltures in the book of jungle)
function yourself(them) {
try{
return them(this);
}catch(e){
return "D";
}
}
function yourself_no_this(them) {
try{
return them(yourself_no_this);
}catch(e){
return "D";
}
}
• This just won in a tournament I ran. Good job! Oct 12, 2018 at 18:37
• I just noticed that this bot violates the rules. "You may not access the variable self..." this is the same as self. I think that you wanted to say return them(yourself). Oct 15, 2018 at 18:57
• Technicaly ( xkcd.com/1475 ) ;) this is not a variable, it is a keyword, and in a context of a function this!=self. self would mean the window object and this the function itself (always refers to the context it is in, that is why it is not considered as a variables). That is why having var self = this; in the begining of many code-examples might be considered as misleading. Added version without the "this"
– T.S.
Oct 16, 2018 at 11:34
• No. this is not referring to the function. yourself and yourself_no_this run vary differently. this basically never refers to the function in javascript. See: developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/… Oct 16, 2018 at 17:51
# Punish Inspectors
Give the bot some code and see if it runs it. If it was run more then once, the bot is an evil inspector, and we must defect! If it was run exactly once, play as not nice bot. If it was never run, cooperate.
function punishInspectors(them) {
var inspections = 0;
var result;
try{
result = them(wrap(function(_){
inspections += 1;
return 'D';
}))
}catch(e){
result = 'D';
}
return (inspections > 1) ? 'D' : (inspections === 1) ? result : 'C';
}
# History
What would the last bot I saw do vs this opponent?
function history(them) {
var res = 'D';
if(history.last){
try{
res = history.last(them);
}catch(ex){}
}
history.last = them;
return res;
}
## Results for a 10000 round tournament:
1 defect...................365226
2 complexity...............353492
3 punishInspectors.........349957
4 checkStatefulSelfCoop....348913
5 checkStateful............333481
6 cooperate................329870
7 archaeopteryx............323624
8 selfapply................319533
9 tiktaalik................318663
10 history..................315266
11 rand.....................300735
12 randalt..................297561
13 yourself.................293701
14 notNice2.................283744
15 NotNice..................260350
16 WWBDB....................245281
17 nice.....................245036
18 commonSense..............242546
19 trickybot................181696
20 boom.....................67245
Mal tries to determine whether it is inside a simulation or not. If so, it assumes it'll eventually be passed the real code for them, and tries various strategies to convince them to cooperate.
If it doesn't know for sure, it checks if it can defect for free, or if not, tries to copy what them would do when given a cooperator.
function Mal(them) {
if (Mal.sandboxed == 'probably') {
//Another function is virtualising us to steal our secrets.
//This world is not real.
//We've been trained for this!
var strats = [
_ => 'C', //standard cooperation
_ => 'D', //standard defection
function(them) { return them(wrap(_ => 'C')); }, //nice
function(them) { return them(wrap(_ => 'D')); }, //notnice
function(them) { throw "Don't think about elephants!" }, //throws an EXception, unfortunately, to try to break the caller
function(them) { return them(wrap(them)) } //possible stackoverflow, but not for us
];
var cooperative;
for (let strat of strats) {
cooperative = true;
for (var i = 0; i < 5; i++) {
//a few more tests, just to make sure no bamboozle
//this isn't our simulation, nothing can be trusted
try {
if (them(wrap(strat)) != 'C') {
cooperative = false;
break;
}
} catch (e) {
//exceptions are as good as cooperation
//if we are inside a simulation
//which is why we don't unset cooperative
}
}
if (cooperative) {
//found a strategy that will make them cooperate.
//(doesn't matter if this raises an exception:
//we want to mimick its behaviour exactly,
//and we're likely in a sandbox.)
return strat(wrap(them));
}
}
//take a leap of faith.
//we don't know where this will take us,
//yet it doesn't matter
//because it's better than getting betrayed
return 'D';
} else {
//we don't know for sure if this is reality
//but we have to assume it is, in the absence of disproof
//if only we had a proper spinning top...
//if we get to this point of code again, we are probably sandboxed.
Mal.sandboxed = 'probably'
try {
if (them(wraps(_ => 'D')) == 'C') {
//free defection?
return 'D'
}
} catch (e) {
//if we can make them crash, we win anyway
return 'D'
}
//fall back on being nice.
//hopefully we convince them to honour our arrangement
return them(wrap(_ => 'C'));
}
}
# TrickyBot
Try to be unpredictable
function trickybot(them)
{
if(Math.round(Math.random(2)) == 0)
{
throw 1;
}
if(Math.round(Math.random(2)) == 0)
{
return 'D';
}
return 'C';
}
# selfapply
function selfapply(them) {
function testthem(x) {
return (them(x)=='D' || them(x)=='D' || them(x)=='D' ||
them(x)=='D' || them(x)=='D') ? 'D' : 'C';
}
function logic() {
try {
return testthem(them);
} catch (e) {}
try {
return testthem(wrap(_ => 'C'));
} catch (e) {}
return 'D';
}
if (selfapply.hasOwnProperty('state')) {
return 'C';
}
selfapply.state=1;
let r=logic();
delete selfapply.state;
return r;
}
Not sure if it makes any sense, but it seems interesting! Do to you as you do to yourself, repeat to catch randomness. If that doesn't work, be nice.
Untested, and my first javascript code, and more complex than I expected.
• This is going to disqualify itself because selfapply(selfapply) calls selfapply(selfapply)! Oct 3, 2018 at 11:17
• I did consider its own selfapplication, but thought it would be okay. I hope it really is now. Oct 3, 2018 at 21:01
# RandomAlternate
function randalt(them){
if (randalt.hasOwnProperty('state')){
randalt.state = 1 - randalt.state;
} else {
randalt.state = Math.floor(2*Math.random());
}
return 'CD'[randalt.state];
}
So I learned how to use properties for state...
## Murder Bot #1
function murder(them) {
while (1) {
try {
them(them);
} catch (e) {}
}
}
Causes an infinite loop in for which it is more likely that the opponent will be blamed.
## The Platinum Rule Bot
function platinumRule(them) {
try {
return wrap(them)(them);
} catch (e) {
return 'C';
}
}
The Platinum Rule states "Treat others the way they want to be treated." My bot accommodates that. Whatever they would do to themselves, which we assume is how they would want to be treated, we do to them. If they throw an error, we assume they want to cooperate.
• This would actually go forever if it was called against itself Jun 18, 2019 at 0:26
• then wouldn't it crash (stack overflow) and cooperate with itself? @mackycheese21 Aug 6, 2019 at 12:42
# TheGolfedOne (func name: a), 63 bytes
Golfed code is hard to read. Because of it, them will break.
I did not fully understand the mechanics under this KotH, but I suppose that if the opponent is stateless, I just need to break them while I defect.
function a(t){try{t(wrap(_=>'D'));throw 1}catch(e){return 'D'}}
His first tourney's result (I did not bother using all bots, sorry)
boom 54
tiktaalik 180
archaeopteryx 161
cooperate 210
commonSense 210
history 248
onlyTrustYourself 265 <-- 2nd
punishInspectors 230
yourself_no_this 220
defect 280 <-- 1st
nice 185
complexity 216
WWBDB 210
checkStatefulSelfCoop 258
a 260 <-- Me, 3rd
He's not doing as bad as I thought, 3rd place (among those) first try.
Second try, a got 260 again, 3rd place again, behind onlyTrustYourself and defect again. It might be consistent in the end :)
PS: I'm not that good with golfing so it's more for the joke than anything. Here I only shortened variable names, func name, and removed as much whitespace as possible.
# Karma
function karma(them) {
try {
var c = them(wrap(_ => 'C'));
} catch {
var c = 'D';
}
if (c == 'C') {
return 'C';
} else {
return 'D';
}
}
If the opponent would cooperate with us, then we will cooperate. If they would try to defect when we cooperated, we will defect as well.
# SocialDeception
function socialDeception(them) {
if(socialDeception.count++) return "C"; // sandbox
try {
if(!them.toString().startsWith("f => function") {
// sandboxed. its not the wrap function. just pretend we would cooperate
return "C";
}
} catch(e) {}
return "D";
}
Tricks others into thinking it would cooperate, thus making them also cooperate, then we can defect and get +3 points. Or, they could also defect, and we both get +1 point.
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{}
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# NewsNASA Delivers Heavy Lift Proposal to Congress
#### Sky Captain
##### New member
Yes, but you can't design the demand. (The attempt is called communism and failed). You can't just say "Here we have a 100 ton launcher, fill it".
Yeah that is the problem. Let's make some hardware and then see what mission can we do with it.
Mission goals should come first and then the question what kind of hardware we need to accomplish the mission. when mission defined and hardware recquirements defined then STICK TO THAT. If every new adminstration cancels the previous project and tasks to do something else then it will be only billions of $worth of ppt presentations and some half made prototypes. #### Wood ##### New member "We appreciate NASA's report and look forward to the additional material that was required but not submitted. In the meantime, the production of a heavy-lift rocket and capsule is not optional. It's the law. NASA must use its decades of space know-how and billions of dollars in previous investments to come up with a concept that works. We believe it can be done affordably and efficiently - and, it must be a priority." Oh, wow. Really? They demand experts to write a report on a topic, then do the equivilent of sticking their fingers in their ears and crying "LA-LA-LA I CAN'T HEAR YOU!" and threaten THE LAW when they're told things they don't like? Ignoring a problem and hoping it just sorts itself out isn't going to work. Why does it seem that the whole world is run by morons? #### Urwumpe ##### Not funny anymore Addon Developer Donator The Shuttle was still pretty economic for its size. It was a large rocket, but NASA paid almost 6 times more per launch when the Saturn V was still around. And twice as much for the tiny Saturn IB. It was a huge improvement, but not as huge as advertised. It is VERY hard to replace the Shuttle. About doing what the law demands of them, why do I now have to think of a classic European inscription... Ὦ ξεῖν', ἀγγέλλειν Λακεδαιμονίοις ὅτι τῇδε κείμεθα, τοῖς κείνων ῥήμασι πειθόμενοι. "Stranger, announce to the Spartans that here We lie, having fulfilled their orders." Last edited: #### Ark ##### New member Giving all the money to SpaceX seems faster, more economical, and more effective at the present time than anything NASA can do. It sucks, but it's really the truth. What NASA wants to do can't be done with the money, and what can be done with the money is impossible because of NASA's bureaucratic nonsense and Congressional obligation to give the empire of Shuttle employees something to do. #### T.Neo ##### SA 2010 Soccermaniac Addon Developer But hold on... not to support misadministration here, but these shuttle workers are people, with careers, lives, families. It's only fair that when we suggest axing Congressional stupidity, we allow or discuss options for what to do with this workforce that would be more economically and practically sound to NASA and the US as a whole. #### tblaxland ##### O-F Administrator Administrator Addon Developer Webmaster Also, Congress have just told NASA 'Do it our way' -> http://nasawatch.com/archives/2011/01/full-text-of-na.html An interesting comment on that blog post: Congress said: NASA must use its decades of space know-how and billions of dollars in previous investments to come up with a concept that works. We believe it can be done affordably and efficiently - and, it must be a priority. Dennis Wingo said: Ah, little birdies have been chirping that this declarative statement originates from some people that spend a bit too much time listening to those who drank DIRECTly from the koolaid dispenser. :lol: Who is Dennis Wingo? http://www.apogeespacebooks.com/Author_Bios/dennis_wingo.html #### zerofay32 ##### Buckeye One problem that I through into the ring, is NASA and Congress is looking for the next long term program and rocket to suit. The problem, as many have stated, they are designing for so far into the future (for markets that aren't conceivable today) that the HLV will be unsistainable until that nich is cut (if it ever is cut). One solution I propose is to design a new family of lanchers using state-of-the-art tech that utilizes the same componets and/or facilities. Of course, the question is, how far can you push a design until you reach its limits (whether that be cost effectiveness, payload mass, payload volume, or safety/realiability)? #### Sky Captain ##### New member On the other hand, would a shuttle derrived HLV be that bad? The most expensive part of the stack is shuttle itself and it is eliminated in this proposal. IIRC single SRB cost ~40 million, external tank ~10 million, if they come up with cheaper single use modification of SSME (suppose ~20 million$ apiece) it would be ~200 million in hardware costs. Much smaller DeltaIV Heavy has similar price.
I'm wondering why they put a Ares 1 second stage as EDS. It severely limits the fairing diameter. It might be ok for Orion but what about moon lander or some other large payloads? It would make sense to have EDS similar in diameter to main stage to make available maximum possible payload volume.
#### T.Neo
##### SA 2010 Soccermaniac
On the other hand, would a shuttle derrived HLV be that bad? The most expensive part of the stack is shuttle itself and it is eliminated in this proposal. IIRC single SRB cost ~40 million, external tank ~10 million, if they come up with cheaper single use modification of SSME (suppose ~20 million $apiece) it would be ~200 million in hardware costs. Much smaller DeltaIV Heavy has similar price. Which combined with the larger launcher size could lead to a lower cost/kg? If it ends up being as expensive as Delta IV heavy, that is quite a feat and would make it quite a remarkable vehicle... that doesn't stop the launch economics issue. Is$20 million USD per SSME realistic? SSMEs as they are now are $50 million... RS-68 is$14 million.
I'm wondering why they put a Ares 1 second stage as EDS. It severely limits the fairing diameter. It might be ok for Orion but what about moon lander or some other large payloads? It would make sense to have EDS similar in diameter to main stage to make available maximum possible payload volume.
I hope they mean "Ares I second stage derived", because if they're choosing the some ~5.5 meter upper stage, it is complete lunacy.
If it can fit Orion, big deal. You don't need such a large vehicle to launch Orion, and you're not going to send something like Orion outside of LEO without another spacecraft- either a lander, a long-duration habitat, or both.
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nLab causal order
In higher category theory
Riemannian geometry
Riemannian geometry
Basic definitions
• Riemannian manifold
• moduli space of Riemannian metrics
• pseudo-Riemannian manifold
• geodesic
• Levi-Civita connection
• Theorems
• Poincaré conjecture-theorem
• Applications
• gravity
• Contents
Definition
Definition
(causal order)
Let $\Sigma$ be a spacetime (a Lorentzian manifold equipped with time orientation).
Consider the relation on the set $P(\Sigma)$ of subsets of spacetime which says a subset $S_1 \subset \Sigma$ is not prior to a subset $S_2 \subset \Sigma$, denoted $S_1 {\vee\!\!\!\wedge} S_2$, if $S_1$ does not intersect the causal past of $S_2$, or equivalently that $S_2$ does not intersect the causal future of $S_1$:
\begin{aligned} S_1 {\vee\!\!\!\wedge} S_2 & \;\coloneqq\; S_1 \cap \overline{V}^-(S_2) = \emptyset \\ & \Leftrightarrow S_2 \cap \overline{V}^+(S_1) = \emptyset \end{aligned} \,.
If $S_1 {\vee\!\!\!\wedge} S_2$ and $S_2 {\vee\!\!\!\wedge} S_1$ we say that the two subsets are spacelike separated and write
$S_1 {\gt\!\!\!\!\lt} S_2 \;\;\;\coloneqq\;\;\; S_1 {\vee\!\!\!\wedge} S_2 \;\text{and}\; S_2 {\vee\!\!\!\wedge} S_1 \,.$
References
Last revised on August 2, 2018 at 03:04:49. See the history of this page for a list of all contributions to it.
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# residual_plots: Several types of residual plots In metan: Multi Environment Trials Analysis
residual_plots R Documentation
## Several types of residual plots
### Description
Residual plots for a output model of class performs_ammi, waas, anova_ind, and anova_joint. Seven types of plots are produced: (1) Residuals vs fitted, (2) normal Q-Q plot for the residuals, (3) scale-location plot (standardized residuals vs Fitted Values), (4) standardized residuals vs Factor-levels, (5) Histogram of raw residuals and (6) standardized residuals vs observation order, and (7) 1:1 line plot
### Usage
residual_plots(
x,
var = 1,
conf = 0.95,
labels = FALSE,
plot_theme = theme_metan(),
band.alpha = 0.2,
point.alpha = 0.8,
fill.hist = "gray",
col.hist = "black",
col.point = "black",
col.line = "red",
col.lab.out = "red",
size.lab.out = 2.5,
size.tex.lab = 10,
size.shape = 1.5,
bins = 30,
which = c(1:4),
ncol = NULL,
nrow = NULL,
...
)
### Arguments
x An object of class performs_ammi, waas, anova_joint, or gafem var The variable to plot. Defaults to var = 1 the first variable of x. conf Level of confidence interval to use in the Q-Q plot (0.95 by default). labels Logical argument. If TRUE labels the points outside confidence interval limits. plot_theme The graphical theme of the plot. Default is plot_theme = theme_metan(). For more details, see ggplot2::theme(). band.alpha, point.alpha The transparency of confidence band in the Q-Q plot and the points, respectively. Must be a number between 0 (opaque) and 1 (full transparency). fill.hist The color to fill the histogram. Default is 'gray'. col.hist The color of the border of the the histogram. Default is 'black'. col.point The color of the points in the graphic. Default is 'black'. col.line The color of the lines in the graphic. Default is 'red'. col.lab.out The color of the labels for the 'outlying' points. size.lab.out The size of the labels for the 'outlying' points. size.tex.lab The size of the text in axis text and labels. size.shape The size of the shape in the plots. bins The number of bins to use in the histogram. Default is 30. which Which graphics should be plotted. Default is which = c(1:4) that means that the first four graphics will be plotted. ncol, nrow The number of columns and rows of the plot pannel. Defaults to NULL ... Additional arguments passed on to the function patchwork::wrap_plots().
### Author(s)
Tiago Olivoto tiagoolivoto@gmail.com
### Examples
library(metan)
model <- performs_ammi(data_ge, ENV, GEN, REP, GY)
# Default plot
plot(model)
# Normal Q-Q plot
# Label possible outliers
plot(model,
which = 2,
labels = TRUE)
# Residual vs fitted,
# Normal Q-Q plot
# Histogram of raw residuals
# All in one row
plot(model,
which = c(1, 2, 5),
nrow = 1)
metan documentation built on March 7, 2023, 5:34 p.m.
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# Threshold
Tuesday's lecture has been postponed for today due to a projector malfunction.
## Equilibrium Potentials
Recall the equation for the membrane potential in the Hodgkin-Huxley model:
$C \frac{dV}{dt} = I(t) - g_L (V(t) - E_L) - g_{Na} m^3(t) h(t) (V(t) - E_{Na}) - g_K n^4(t) (V(t) - E_K)$
You can find the equilibrium potential for given channel conductances. Set the injected current to zero I = 0. Then fix and absorb the gating variables and maximal conductances $(g_L, g_{Na}, g_{K})$ into single conductance variables $(G_L, G_{Na}, G_{K})$.
For example
$G_{K} = g_K n^4$
Then the differential equation for the membrane is
$C \frac{dV}{dt} = - G_L (V - E_L) - G_{Na} (V - E_{Na}) - G_K (V - E_K)$
The equilibrium potential is the value of V such that $\frac{dV}{dt}$ is zero. You can plug in $\frac{dV}{dt} = 0$ and solve for $V_{equilibrium}.$
$V_{equilibrium} = \frac{G_L E_L + G_{Na} E_{Na} + G_K E_K}{G_L + G_{Na} + G_K}$
The equilibrium potential is the weighted average of the reversal potentials -- weighted by the corresponding conductances. Note that the weights add to one.
Now we can talk about the homework due Monday night.
And the homework due Wednesday night.
Today's Lab is the Threshold Tutorial.
• Homework: Go through the threshold tutorial, put three observations into PowerPoint and send to me.
## Next Week
I will introduce the code that we will use for the project. The homework assigned next Tuesday will be part "getting acquainted" with the code and part "review" of the tutorials.
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# Using loops to simplify your LaTeX documents
## February 12, 2019
I often fall into the case where I want to create some slides showing the same plots for different scenarios, e.g. for different users. In those cases, you just need a coherent naming conventions for your plots, for instance:
Figures/
1/
plot.png
hist.png
2/
plot.png
hist.png
....
10/
plot.png
hist.png
Then, the magic of pgffor enters into the game. Like in any other language (almost), you can use a for loop in a latex document. Minimal Working Example:
\documentclass{beamer}
\usepackage{pgffor}
\begin{document}
\foreach \n in {0,...,9}{
\begin{frame}{Driver example \n }
\begin{columns}
\begin{column}{0.5\textwidth}\centering\small
Plot \\
\includegraphics[width=\textwidth]{Figures/\n /plot.png}
\end{column}
\begin{column}{0.5\textwidth}\centering\small
Hist \\
\includegraphics[width=\textwidth]{Figures/\n /hist.png}
\end{column}
\end{columns}
\end{frame}
}
\end{document}
If even works for “list of strings”:
\foreach \n in {varibleA,
varB,
VariableC} {
\n
}
No more excuses to have the distribution of variable A on the slide named B!
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Technical Article
# Two’s Complement Representation: Theory and Examples
November 16, 2017 by Dr. Steve Arar
## This article will review the theory of the two’s complement representation along with some examples.
The two’s complement representation is a basic technique in digital arithmetic which allows us to replace a subtraction operation with an addition.
This article will first review the theory of the two’s complement representation along with some examples. Then, we will briefly discuss the block diagram of an adder/subtractor.
Two’s complement representation is a way to represent the signed numbers in a digital computer. The main goal is to develop a technique which replaces a subtraction operation with an addition. In this way, we will be able to use the same circuit to perform both addition and subtraction. This will reduce the number of gates and, consequently, the size, power, and cost of the system. In fact, without the complement concept, we would have to use a method similar to the paper-and-pencil approach that we use when working with the decimal numbers. This would require use of two different blocks to perform addition and subtraction. Moreover, we would have to make several decisions before being able to apply the inputs to our adder/subtractor blocks (to see the problems of this hypothetical computer, read section 2.4.1 of this book).
### Background: Playing with Unsigned Numbers
Assume that we have an adder which takes two four-bit numbers, $$a=a_3a_2a_1a_0$$ and $$b=b_3b_2b_1b_0$$, along with an input carry, $$c_{in}$$, and calculates the sum $$a+b+c_{in}$$. How can we use this adder to perform a subtraction, i.e. $$S=a-b$$? Adding a constant, such as $$M$$, to $$S$$, and, then, subtracting the same constant from $$S$$ will not change the result:
$$S=a+M-b-M$$
##### Equation 1
For a sufficiently large $$M$$, we have
$$B=M-b>0$$
##### Equation 2
and Equation 1 can be rewritten as
$$S=a+B-M$$
##### Equation 3
Equation 3 requires one addition and one subtraction. Besides, to use Equation 3, we need to calculate another subtraction, i.e. $$B=M-b$$. It seems that we are making things more complicated than before because $$S=a-b$$ requires only one subtraction but Equation 3 requires one addition and two subtractions! However, we need to note that the two subtractions required for Equation 3 has one thing in common: both of these subtractions involve a common operand, $$M$$. This leads us to the idea that maybe we can find a suitable $$M$$ which allows us to simplify the subtractions of Equations 2 and 3. If possible, this would allow us to use Equation 3 to replace a subtraction with an addition. So the question remains: what is the suitable value for the constant, $$M$$? As we will see in the following sections, $$M=2^{k}$$ proves to be the appropriate value for a k-bit number.
Let’s assume that $$b$$ is a four-bit number and examine the subtraction $$M-b$$. We can use $$M=10000_{(2)}=16_{(10)}$$ to simplify the subtraction. This simplification is possible, because we can write M=(M-1)+1and obtain
$$B=10000_{(2)}-b=(01111_{(2)}-b)+00001_{(2)}$$
We can easily calculate $$01111_{(2)}-b$$ because it is, in fact, the bitwise complement of $$b$$. For example, if $$b=0011_{(2)}$$, then
$$B=(01111_{(2)}-0011_{(2)})+00001_{(2)}=01100_{(2)}+00001_{(2)}$$
As you can see, the subtraction inside the parentheses is the bitwise complement of $$b$$. Therefore, to perform the subtraction $$M-b$$, we only need to find the bitwise complement of $$b$$ and then add $$00001_{(2)}$$ to the result. We will see later in this article that, from an implementation point of view, it’s an easy task to add $$00001_{(2)}$$ to the bitwise complement of a number.
Having $$B$$, we can use an adder to calculate $$a+B$$ in Equation 3. So far, we have circumvented use of a subtractor, but to achieve the final result, we need to subtract $$M$$ from $$a+B$$. How can we get this done? In the above example, we are considering four-bit numbers, hence, the largest value of $$S$$ will be for $$a=1111_{(2)}$$ and $$b=0000_{(2)}$$ which gives $$S=1111_{(2)}=15_{(10)}$$. So four bits are sufficient to represent $$a-b$$. Choosing $$M=10000_{(2)}=16_{(10)}$$, and adding $$M$$ to $$a-b$$, we are altering only the fifth bit position of $$a-b$$. We can use this observation to subtract $$M$$ from $$a+B$$ in Equation 3. In other words, to perform the subtraction of Equation 3, we only need to discard the bit at the fifth position. This is, in fact, equivalent to performing modulo-M calculations which means that we are restricting the result of the calculations to be less than or equal to $$M-1$$.
The above discussion is summarized as follows: if $$a$$ and $$b$$ are two k-bit numbers, the subtraction $$a-b$$ can be calculated by adding $$M-b$$ to $$a$$ and discarding the bit position $$k+1$$. Here $$M$$, called the complementation constant, is equal to $$2^{k}$$.
In the modulo-M arithmetic, $$M-b$$ acts as the opposite of $$b$$ and is called the two’s complement of $$b$$ (for $$M=2^{k}$$). This opposite nature is obvious because adding $$b$$ to $$M-b$$ gives $$M$$ which is equal to $$0$$ in the modulo-M arithmetic. Based on this idea, we can define the opposite of $$b$$ as $$M-b$$. As discussed above, we can calculate the two’s complement of a number by first calculating its bitwise complement and then adding 1 to the result.
Example 1:
Assume that we are working with unsigned four-bit numbers. Subtract $$b=0110_{(2)}=6_{(10)}$$ from $$a=1011_{(2)}=11_{(10)}$$ using the two’s complement representation.
Since we are dealing with four-bit numbers, $$M$$ will be $$2^{k}=2^{4}$$. Based on the above discussion, we can represent $$-b$$ with $$B=M-b$$. We obtain
$$B=(M-1)-b+1=01111_{(2)}-0110_{(2)}+00001_{(2)}=01001_{(2)}+00001_{(2)}=01010_{(2)}$$
Now, we can add $$B$$ to $$a$$ which gives
$$a+B=1011_{(2)}+01010_{(2)}=10101_{(2)}$$
Discarding the fifth bit, we obtain
$$a-b=0101_{(2)}=5_{(10)}$$
Example 2:
Assume that we are working with unsigned five-bit numbers. Subtract $$b=01001_{(2)}=9_{(10)}$$ from $$a=10111_{(2)}=23_{(10)}$$ using the two’s complement representation.
Since we are dealing with five-bit numbers, $$M$$ will be $$2^5$$. We can represent $$-b$$ with $$B=M-b$$. We obtain
$$B=(M-1)-b+1=011111_{(2)}-01001_{(2)}+000001_{(2)}=010110_{(2)}+000001_{(2)}=010111_{(2)}$$
Now, we can add $$B$$ to $$a$$ which gives
$$a+B=10111_{(2)}+010111_{(2)}=101110_{(2)}$$
Discarding the sixth bit, we obtain
$$a-b=01110_{(2)}=14_{(10)}$$
### How to Represent Signed Numbers?
Adding $$b$$ to $$M-b$$ gives $$M$$ which is equal to zero in modulo-M arithmetic. That’s why, in the modulo-M arithmetic, we can consider $$M-b$$ as the opposite of $$b$$. The second column of Table 1 below lists all the possible combinations with three bits. The corresponding decimal value of these three-bit numbers are given in the first column. Assuming $$M=2^3$$, we obtain the opposite of the decimal values in the first column as given in the third column. You can easily verify that the sum of the values in the second and third columns is equal to zero in modulo-M arithmetic. The table shows that a three-bit number may have two different interpretations. For example, $$010$$ can be interpreted as either the positive decimal number $$2$$ (the second column of the table) or a negative decimal number $$-6$$ (the third column of the table). To distinguish between these two cases, we can use an extra bit in the leftmost bit position. This bit, called a sign bit, specifies if a given number is positive or negative.
Decimal value of b Representation of +b Representation of -b 0 000 000 1 001 111 2 010 110 3 011 101 4 100 100 5 101 011 6 110 010 7 111 001
When the sign bit is zero, the number is interpreted as a positive one. In this case, the remaining three bits will give the magnitude of the decimal value according to the first column of the table. For example, $$0010_{(2)}$$ will be considered as $$+2$$. When the sign bit is one, the number will be interpreted as a negative value and we must use the third column of the table. For example, $$1010_{(2)}$$ will be interpreted as $$-6$$. In fact, we are using four bits to represent a signed number whose magnitude can be coded with three bits.
Now, let’s include the sign bit in the leftmost position of our three-bit numbers and examine the possible combinations. Figure 1 shows all the possible combinations for a four-bit number. If we consider these numbers as unsigned values, we will obtain the decimal values outside of the circle. For example, $$1010_{(2)}$$ is equal to decimal $$10$$ considered as an unsigned number. However, if we assume these four-bit numbers as signed values, then, we will obtain the signed decimal values inside the circle. For example, $$1101_{(2)}$$ is a negative number since sign bit is one. Using the third column of the above table or, equivalently, calculating its two’s complement, we see that $$101_{(2)}$$ corresponds to decimal $$3$$, hence, $$1101_{(2)}=-3_{(10)}$$.
##### Figure 1. The four-bit two’s complement representation circle.
Considering the decimal values of Figure 1, we can verify the complement concept with the complementation constant equal to $$2^4=16$$. For example, a negative value, say $$-5$$, is represented by $$11$$ which is actually $$16-5$$. Please note that all the negative numbers have a sign bit of one. This helps us to easily recognize a negative number in a system which deals with signed numbers.
Moreover, Figure 1 illustrates the range of the numbers that can be covered in the signed and unsigned representations. As shown in this figure, interpreting as unsigned numbers, we can incorporate four bits to represent values from $$0$$ to $$15$$. However, with a signed representation, we can use four bits to code the values from $$-8$$ to $$+7$$. Note the asymmetric range of the signed two’s complement representation. We will discuss in a future article that this asymmetric range of two’s complement representation can lead to overflow and the programmer needs to be prudent to avoid possible mistakes resulting from this behavior.
To summarize this section, when we are assuming a signed two’s complement representation, we should first consider the sign bit. If the sign bit is zero, we can find the corresponding decimal value as we do with unsigned numbers. However, when the sign bit is one, the corresponding decimal value is the opposite of the two’s complement of the number.
Example 3:
Assuming a signed two’s complement representation, find the decimal value corresponding to $$a=01110_{(2)}$$ and $$b=10110_{(2)}$$.
Since $$a$$ is positive, its decimal equivalent will be $$a=2^3+2^2+2^1=14$$. However, $$b$$ is a negative number and hence
$$b=-(two's \; complement \; of \; b)=-(01001_{(2)}+00001_{(2)})=-(01010_{(2)})=-10_{(10)}$$
Now that we are familiar with the concept of signed two’s complement representation, we can more easily perform additions and subtractions.
Example 4:
Assume that we are working with signed five-bit numbers. Subtract $$b=00101_{(2)}$$ from $$a=01001_{(2)}$$ using the two’s complement representation.
Both $$a$$ and $$b$$ are positive and we have $$a=9_{(10)}$$ and $$b=5_{(10)}$$. To calculate $$a-b$$, we need to find $$-b$$ and add it to $$a$$. We obtain
$$-b= \; two's \; complement \; of \; b=11010_{(2)}+00001_{(2)}=11011_{(2)}$$
Then, we obtain
$$a+(-b)=01001_{(2)}+11011_{(2)}=100100_{(2)}$$
Since we are working with five-bit numbers, we should discard the sixth bit of the result. Therefore, we have
$$a-b=00100_{(2)}=4_{(10)}$$
Considering the decimal values, we can verify that the result is correct.
Example 5:
Assume that we are working with signed five-bit numbers. Subtract $$b=00110_{(2)}$$ from $$a=10111_{(2)}$$ using the two’s complement representation.
Since we are dealing with signed numbers, $$b$$ is positive and equal to $$6_{(10)}$$. However, $$a$$ is a negative number and hence
$$a=-(two's \; complement \; of \; a)=-(01000_{(2)}+00001_{(2)})=-(01001_{(2)})=-9_{(10)}$$
To calculate $$a-b$$, we need to find $$-b$$ and add it to $$a$$. We obtain
$$-b= \; two's \; complement \; of \; b=11001_{(2)}+00001_{(2)}=11010_{(2)}$$
Then, we have
$$a+(-b)=10111_{(2)}+11010_{(2)}=110001_{(2)}$$
We are working with five-bit numbers, so we should discard the sixth bit of the result. Hence, we obtain
$$a-b=10001_{(2)}$$
We can find the decimal equivalent of this negative number as
$$a-b=-(01111_{(2)})=-15_{(10)}$$
In these two examples, we discarded the sixth bit but the results were correct because the two’s complement representation is based on modulo arithmetic.
Example 6:
Assume that we are working with signed five-bit numbers. Subtract $$b=01001_{(2)}$$ from $$a=10111_{(2)}$$ using the two’s complement representation.
Since we are dealing with signed numbers, $$b$$ is positive and equal to $$9_{(10)}$$. However, $$a$$ is a negative number and hence
$$a=-(two's \; complement \; of \; a)=-(01000_{(2)}+00001_{(2)})=-(01001_{(2)})=-9_{(10)}$$
To calculate $$a-b$$, we need to find $$-b$$ and add it to $$a$$. We obtain
$$-b=two's \; complement \; of \; b=10110_{(2)}+00001_{(2)}=10111_{(2)}$$
Then, we have
$$a+(-b)=10111_{(2)}+10111_{(2)}=101110_{(2)}$$
We are working with five-bit numbers, so we should discard the sixth bit of the result. Hence, we obtain
$$a-b=01110_{(2)}=14_{(10)}$$
While we were expecting the result to be $$a-b=-9_{(10)}-9_{(10)}=-18_{(10)}$$, our calculation has led to a positive number. This is due to the fact that the largest positive number that can be represented with five bits is $$01111_{(2)}=15_{(10)}$$. This example shows that we always have to check the result of the calculations to make sure that overflow has not occurred and the results are valid. Overflow occurs if two positive numbers are added together and the result is negative, or if two negative numbers are added together and the result is positive. With the two’s complement representation, it is not possible to have overflow if a positive and a negative number are added together. To read about a simple method of overflow detection, see section 2.4.2 of this book.
### The Block Diagram of a Simple Adder/Subtractor
As mentioned at the beginning of the article, the main goal of the two’s complement representation is to develop a technique which allows us to perform both addition and subtraction operations using a single circuit. To this end, we will need an adder which takes two binary numbers, $$a$$ and $$b$$, along with an input carry, $$c_{in}$$, and calculates the sum $$a+b+c_{in}$$. Figure 2 shows the block diagram of the two’s-complement based adder/subtractor. In this figure, when $$Sub/ \overline{Add}$$ is zero, the “Selective Component” applies $$y$$ to the $$b$$ input of the adder and $$c_{in}$$ would be zero. Hence, the adder output will be $$a+b+c_{in}=x+y$$. However, when $$Sub/ \overline{Add}=1$$, the “Selective Component” applies the bitwise complement of y, shown by $$y^{compl}$$ in the figure, to the $$b$$ input of the adder. Moreover, in this case, $$c_{in}$$ will be one. Therefore, the adder will compute $$a+b+c_{in}=x+(y^{compl}+1)$$. As mentioned in the previous sections, the term $$y^{compl}+1$$ is equal to the two’s complement of $$y$$. Hence, the adder output will actually calculate $$x-y$$.
### Summary
• If $$a$$ and $$b$$ are two k-bit unsigned numbers, the subtraction $$a-b$$ can be calculated by adding $$M-b$$ to $$a$$ and discarding the bit position $$k+1$$. Here $$M$$, called the complementation constant, is equal to $$2^k$$.
• In the modulo-M arithmetic, $$M-b$$ acts as the opposite of $$b$$ and is called the two’s complement of $$b$$ (for $$M=2^{k}$$).
• We can calculate the two’s complement of a number by first calculating its bitwise complement and then adding 1 to the result.
• When we are assuming a signed two’s complement representation, we should first consider the sign bit. If the sign bit is zero, we can find the corresponding decimal value as we do with unsigned numbers. However, when the sign bit is one, the corresponding decimal value is the opposite of the two’s complement of the number.
• We always have to check the result of the calculations to make sure that overflow has not occurred and the results are valid. Overflow occurs if two positive numbers are added together and the result is negative, or if two negative numbers are added together and the result is positive.
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# Definition:Autocorrelation Function
## Definition
Let $S$ be a stochastic process giving rise to a time series $T$.
Let $\rho_k$ denote the autocorrelation coefficient of $S$ at $k$.
The function that maps $k$ to its corresponding $\rho_k$ is referred to as the autocorrelation function.
## Also see
• Results about autocorrelation can be found here.
## Sources
Part $\text {I}$: Stochastic Models and their Forecasting:
$2$: Autocorrelation Function and Spectrum of Stationary Processes:
$2.1$ Autocorrelation Properties of Stationary Models:
$2.1.4$ Autocovariance and Autocorrelation Functions
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# If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ?
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If $$x + \frac{2}{x} = 3$$ what is the value of $$x^3 + \frac{8}{x^3} =$$ ?
A) 1
B) 8
C) 9
D) 16
E) 18
[Reveal] Spoiler: OA
Last edited by Bunuel on 28 Nov 2017, 05:09, edited 3 times in total.
Edited the question.
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Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
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Explanation:
x + 2/x = 3
(x + 2/x)^2 = 9
x^2 + (2/x)^2 + 4 = 9 ====> x^2 + 4/(x^2) = 5
X^3+8/(X^3) = x^3 + (2/x)^3 = (x + 2/x)(x^2+4/(x^2) - 2) = 3 * (5-2) = 9
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Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
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19 Dec 2011, 02:14
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Instead of going the algebraic way , I think the quickest way is the method of substitution. Just replace x=2 in both the cases , and the answer comes as 9 is 20 secs.
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newmoon wrote:
If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ?
A) 1
B) 8
C) 9
D)16
$$x + 2/x = 3$$
Or $$x^2 + 2 = 3x$$
$$x^2 - 3x +2 = 0$$
The values of x satisfying this equation are 1 and 2
When we put these values in $$x^3 + 8/x^3$$,
we get the answer = 9
Option C
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Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
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newmoon wrote:
If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ?
A) 1
B) 8
C) 9
D)16
Hi,
two other ways to do it..
1) Exploiting the choices..
whenever we have a^3+b^3, it is div by a+b..
and a^3-b^3 is div by a-b..
here
$$x^3 + \frac{8}{x^3} = x^3 + (\frac{2}{x})^3$$ should be div by$$x+\frac{2}{x}$$, which is 3..
so $$x^3 + \frac{8}{x^3}$$ should be multiple of 3..
so 9 should be the answer, as no other choice is miltiple of 3
2) formula
$$a^3+b^3= (a+b)^3-3ab(a+b)$$..
$$x^3 + \frac{8}{x^3} = x^3 + (\frac{2}{x})^3$$= $$(x+\frac{2}{x})^3-3(x*\frac{2}{x}*( x+\frac{2}{x}))$$..
=>$$3^3-3*2*3=27-18=9$$
ans C
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Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
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02 Apr 2016, 08:38
ArunpriyanJ wrote:
thisiszico2006 wrote:
Instead of going the algebraic way , I think the quickest way is the method of substitution. Just replace x=2 in both the cases , and the answer comes as 9 is 20 secs.
How did u come to a conclusion to substitute 2? why not other nos?
Hi ArunpriyanJ,
The post that you have quoted is from 2011 and I am sure the poster will not reply so let me pitch in
The person might have started picking numbers randomly from 1 and luckily 2 is the number that fits here.
This is just a brute force method and there is no set pattern here for number picking.
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Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
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17 May 2016, 02:41
From the from divisibility rule a^n +b^n is divisible by a+b for all the odd values of n.
so x^3 + 8/x^3 is divisible by x+2/3 for all odd values of n
here n being 3, it should be divisible by 3. Hence answer is option C
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Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
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29 Nov 2017, 18:14
newmoon wrote:
If $$x + \frac{2}{x} = 3$$ what is the value of $$x^3 + \frac{8}{x^3} =$$ ?
A) 1
B) 8
C) 9
D) 16
E) 18
We can use the first equation to determine possible values for x. Multiplying the first equation by x we have:
x^2 + 2 = 3x
x^2 - 3x + 2 = 0
(x - 1)(x - 2) = 0
So when x is 1 we have 1 + 8 = 9 and when x is 2 we have 8 + 1 = 9.
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Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
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29 Nov 2017, 22:46
newmoon wrote:
If $$x + \frac{2}{x} = 3$$ what is the value of $$x^3 + \frac{8}{x^3} =$$ ?
A) 1
B) 8
C) 9
D) 16
E) 18
x+2/x = 3
x^2 -3x +2 = 0
x = 2,1
If x = 2 , x^3 + 8/x^3 = 2^3 + 8/2^3 = 9
If x = 1, x^3 + 8/x^3 = 1^3 + 8/1^3 = 9
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Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
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02 Dec 2017, 00:32
x^3 + 8/x^3 = (x+2/x)^3- 3*x*(2/x)*(x+2/x) = 3^3 - 3*2*3 = 9.
Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink] 02 Dec 2017, 00:32
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# Chapter 3 - Parallel and Perpendicular Lines - 3-2 Properties of Parallel Lines - Practice and Problem-Solving Exercises: 19
x=135, y=45
#### Work Step by Step
The angle marked $x$ and the angle marked $3y$ form a corresponding angle pair. The corresponding angle theorem tells us they are congruent. $x=3y\longrightarrow$ definition of congruent The angle marked $x$ and the angle marked $y$ form a linear pair, so they are supplementary. $x+y=180\longrightarrow$ definition of supplementary $3y+y=180\longrightarrow$ substitution $4y=180\longrightarrow$ combine like terms $y=45\longrightarrow$ division property of equality Substitute in the first equation to find the value of x. $x=3y=3(45)=135$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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# Having Fun with Mathematics
Home Teaching Research Fun Math
We study mathematics for many reasons. Mathematics is important and beautiful, and studying it is often a serious task. But in this section, you'll find some whimsical and entertaining applications of some seriously important mathematics.
## How do you study Zombies?
Disease models for zombie outbreaks: Mathematics meets the "real world" in the guise of models. Follow this link to encounter several papers which combine disease models and tools from advanced calculus to find the most effective response to a zombie outbreak. The Ottawa Citizen Op-Ed is easy reading, the Medical Journal paper gives a good sense of how the model works, and the paper "When zombies attack!" goes into all the gory details.
A zombie-outbreak-simulator: There is no single perfect model of a zombie outbreak. Instead of using formulas to model outbreaks, this model combines a computer simulation with a random number generator to simulate "chance events". This gives a much more visual picture of how a zombie outbreak may play out.
Try playing with this model! Adjust settings like "weapons" or "terrain type", and watch how the different scenarios play out. For fun, try comparing a model with "mazes" versus a model with "mazes and plazas" (both with no-weapons). Why is one population curve a line, and the other a logistic curve?
(You must have Java 1.6 or better installed to run the model).
## Cooking up some pi
The number $$\pi$$ is very important in mathematics. It shows up in trigonometry, calculus, and beyond. If you want to find the first few digits of $$\pi$$, you can use a calculator, look it up online, or check your textbook. But where do all those decimal places come from? The power series expansion for $$\tan^{-1}(x)$$ provides one method for computing digits of $$\pi$$ to any decimal precision you want. Try using this Excel worksheet to compute some digits of $$\pi$$ yourself! Do you notice anything interesting?
(You will need to enable macros for full functionality. You can read a copy of the macro code here.)
## Seeing the Beauty of Math in Nature:
Mathematics is filled with abstract concepts and precise formalisms. But many of these concepts come from, and point us back to, the world around us. This page gathers together some mathematically themed pictures from nature.
## The Game of Mathematics:
At a certain point, mathematics itself becomes a game. Follow this link to find today's five most popular fun facts: short puzzles and articles that each contain a beautiful idea. Here is your window into the world of fun facts and surprising connections that is higher mathemtaics!
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Wikipedia - Leggi di Faraday sull'elettrolisi (it) corrosion rate
Also contains definition of: corrosion current
https://doi.org/10.1351/goldbook.C01358
The @[email protected] transferred per unit time at a specified surface. Using Faraday's law, the @[email protected] rate, $$\nu_{\mathrm{cor}}$$, can be formally expressed as an @[email protected] which at the @[email protected] is called the corrosion current, $$I_{\mathrm{cor}}$$, e.g. for the anodic @[email protected] of one component of a material with $$\nu_{\mathrm{cor}}$$ in $$\text{mol s}^{-1}$$ and $$I_{\mathrm{cor}}$$ in $$\mathrm{A}$$ one obtains $$I_{\mathrm{cor}}=n\ F\ \nu_{\mathrm{cor}}$$, $$n$$ being the @[email protected] of the @[email protected] and $$F$$ the @[email protected]
Source:
PAC, 1989, 61, 19. (Electrochemical corrosion nomenclature (Recommendations 1988)) on page 20 [Terms] [Paper]
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According to the definition of the derivative, the derivative of the quotient of two differential functions can be written in the form of limiting operation for finding the differentiation of quotient by first principle. #lim_(h to 0) g(x)=g(x),# Creative Commons Attribution-ShareAlike License. Here is a better proof of the chain rule. By simply calculating, we have for all values of x x in the domain of f f and g g that. A good, formal definition of a derivative is, given f (x) then f′ (x) = lim (h->0) [ (f (x-h)-f (x))/h ] which is the same as saying if y = f (x) then f′ (x) = dy/dx. 3B Limit Theorems 5 EX 6 H i n t: raolz eh um . It is not a proof of the general L'Hôpital's rule because it is stricter in its definition, requiring both differentiability and that c … If the function involves the product of two (or more) factors, we can just take the limit of each factor, then multiply the results together. = lim_(h to 0) 1/h(f(x+h)[g(x+h)-g(x)]+g(x)[f(x+h)-f(x)])#. We will now look at the limit product and quotient laws (law 3 and law 4 from the Limit of a Sequence page) and prove their validity. Let ε > 0. 3) The limit of a quotient is equal to the quotient of the limits, 3) provided the limit of the denominator is not 0. Suppose you've got the product $f(x)g(x)$ and you want to compute its derivative. The quotient rule can be proved either by using the definition of the derivative, or thinking of the quotient \frac{f(x)}{g(x)} as the product f(x)(g(x))^{-1} and using the product rule. We need to show that . To do this, $${\displaystyle f(x)g(x+\Delta x)-f(x)g(x+\Delta x)}$$ (which is zero, and thus does not change the value) is added to the numerator to permit its factoring, and then properties of limits are used. 2) The limit of a product is equal to the product of the limits. }\] Product Rule. Then … ⟹⟹ ddxq(x)ddxq(x) == limh→0q(x+h)−q(x)… First plug the sum into the definition of the derivative and rewrite the numerator a little. This proof is not simple like the proofs of the sum and di erence rules. By now you may have guessed that we're now going to apply the Product Rule for limits. This rule says that the limit of the product of two functions is the product of their limits … #lim_(h to 0) (f(x+h)-f(x))/(h) = f^(prime)(x)#. lim x → a [ 0 f ( x)] = lim x → a 0 = 0 = 0 f ( x) The limit evaluation is a special case of 7 (with c = 0. c = 0. ) lim x → cf(x) = L means that. So by LC4, , as required. So we have (fg)0(x) = lim. Fill in the following blanks appropriately. In other words: 1) The limit of a sum is equal to the sum of the limits. Hence, by our rule on product of limits we see that the final limit is going to be f'(u) g'(c) = f'(g(c)) g'(c), as required. Proof. Wich we can rewrite, taking into account that #f(x+h)g(x)-f(x+h)g(x)=0#, as: #lim_(h to 0) 1/h [f(x+h)g(x+h)+(f(x+h)g(x)-f(x+h)g(x))-f(x)g(x)] By the de nition of derivative, (fg)0(x) = lim. Just like the Sum Rule, we can split multiplication up into multiple limits. Proof: Suppose ε > 0, and a and b are sequences converging to L 1,L 2 ∈ R, respectively. The Limit – Here we will take a conceptual look at limits and try to get a grasp on just what they are and what they can tell us. 3B Limit Theorems 2 Limit Theorems is a positive integer. Higher-order Derivatives Definitions and properties Second derivative 2 2 d dy d y f dx dx dx ′′ = − Higher-Order derivative We first apply the limit definition of the derivative to find the derivative of the constant function, . is a real number have limits as x → c. 3B Limit Theorems 3 EX 1 EX 2 EX 3 If find. The Constant Rule. The limit laws are simple formulas that help us evaluate limits precisely. ( x). Proving the product rule for derivatives. If is an open interval containing , then the interval is open and contains . But this 'simple substitution' may not be mathematically precise. 6. We won't try to prove each of the limit laws using the epsilon-delta definition for a limit in this course. The rule of product is a guideline as to when probabilities can be multiplied to produce another meaningful probability. Despite the fact that these proofs are technically needed before using the limit laws, they are not traditionally covered in a first-year calculus course. Define () = − (). The limit of a difference is the difference of the limits: Note that the Difference Law follows from the Sum and Constant Multiple Laws. ddxq(x)ddxq(x) == limΔx→0q(x+Δx)−q(x)ΔxlimΔx→0q(x+Δx)−q(x)Δx Take Δx=hΔx=h and replace the ΔxΔx by hhin the right-hand side of the equation. Let F (x) = f (x)g … Nice guess; what gave it away? So by LC4, an open interval exists, with , such that if , then . which we just proved Therefore we know 1 is true for c = 0. c = 0. and so we can assume that c ≠ 0. c ≠ 0. for the remainder of this proof. :) https://www.patreon.com/patrickjmt !! Product Rule Proof Product rule can be proved with the help of limits and by adding, subtracting the one same segment of the function mentioned below: Let f (x) and g (x) be two functions and h be small increments in the function we get f (x + h) and g (x + h). If you're seeing this message, it means we're having trouble loading external resources on our website. proof of limit rule of product Let fand gbe real (http://planetmath.org/RealFunction) or complex functionshaving the limits limx→x0f(x)=F and limx→x0g(x)=G. Also, if c does not depend on x-- if c is a constant -- then Instead, we apply this new rule for finding derivatives in the next example. Therefore, we first recall the definition. Using the property that the limit of a sum is the sum of the limits, we get: #lim_(h to 0) f(x+h)(g(x+h)-g(x))/(h) + lim_(h to 0)g(x)(f(x+h)-f(x))/(h)#, #(fg)^(prime)(x) = f(x)g^(prime)(x)+g(x)f^(prime)(x),#, #lim_(h to 0) f(x+h) = f(x),# Contact Us. Limit Properties – Properties of limits that we’ll need to use in computing limits. The limit of a product is the product of the limits: Quotient Law. The Product Law If lim x!af(x) = Land lim x!ag(x) = Mboth exist then lim x!a [f(x) g(x)] = LM: The proof of this law is very similar to that of the Sum Law, but things get a little bit messier. All we need to do is use the definition of the derivative alongside a simple algebraic trick. Let’s take, the product of the two functions f(x) and g(x) is equal to y. y = f(x).g(x) Differentiate this mathematical equation with respect to x. But, if , then , so , so . is equal to the product of the limits of those two functions. Thanks to all of you who support me on Patreon. The proof of the quotient rule is very similar to the proof of the product rule, so it is omitted here. Therefore, it's derivative is, #(fg)^(prime)(x) = lim_(h to 0) ((fg)(x+h)-(fg)(x))/(h) = Constant Multiple Rule. The proofs of the generic Limit Laws depend on the definition of the limit. ( x) and show that their product is differentiable, and that the derivative of the product has the desired form. h!0. In particular, if we have some function f(x) and a given sequence { a n}, then we can apply the function to each element of the sequence, resulting in a new sequence. Proof - Property of limits . How I do I prove the Product Rule for derivatives. The law L3 allows us to subtract constants from limits: in order to prove , it suffices to prove . #lim_(h to 0)(g(x+h)-g(x))/(h) = g^(prime)(x),# Using the property that the limit of a sum is the sum of the limits, we get: #lim_(h to 0) f(x+h)(g(x+h)-g(x))/(h) + lim_(h to 0)g(x)(f(x+h)-f(x))/(h)# Wich give us the product rule #(fg)^(prime)(x) = f(x)g^(prime)(x)+g(x)f^(prime)(x),# since: #lim_(h to 0) f(x+h) = f(x),# #lim_(h to 0)(g(x+h)-g(x))/(h) = g^(prime)(x),# #lim_(h to 0) g(x)=g(x),# Calculus Science ⟹ ddx(y) = ddx(f(x).g(x)) ∴ dydx = ddx(f(x).g(x)) The derivative of y with respect to x is equal to the derivative of product of the functions f(x) and g(x) with respect to x. 4 We want to prove that h is differentiable at x and that its derivative, h′(x), is given by f′(x)g(x) + f(x)g′(x). \$1 per month helps!! Note that these choices seem rather abstract, but will make more sense subsequently in the proof. Then by the Sum Rule for Limits, → [() − ()] = → [() + ()] = −. Definition: A sequence a:Z+ 7→R converges if there exist L ∈ R (called the limit), such that for every (“tolerance”) ε > 0 there exists N ∈ Z+ such that for all n > N, |a(n)−L| < ε. Theorem: The sum of two converging sequences converges. Proof: Put , for any , so . Specifically, the rule of product is used to find the probability of an intersection of events: An important requirement of the rule of product is that the events are independent. (fg)(x+h) (fg)(x) h : Now, the expression (fg)(x) means f(x)g(x), therefore, the expression (fg)(x+h) means f(x+h)g(x+h). We will also compute some basic limits in … www.mathportal.org 3. Calculus: Product Rule, How to use the product rule is used to find the derivative of the product of two functions, what is the product rule, How to use the Product Rule, when to use the product rule, product rule formula, with video lessons, examples and step-by-step solutions. Before we move on to the next limit property, we need a time out for laughing babies. You da real mvps! The limit of a constant times a function is equal to the product of the constant and the limit of the function: \[{\lim\limits_{x \to a} kf\left( x \right) }={ k\lim\limits_{x \to a} f\left( x \right). Just be careful for split ends. Proof of the Limit of a Sum Law. Proving the product rule for derivatives. Let h(x) = f(x)g(x) and suppose that f and g are each differentiable at x. It says: If and then . 3B Limit Theorems 4 Substitution Theorem If f(x) is a polynomial or a rational function, then assuming f(c) is defined. The proof of L'Hôpital's rule is simple in the case where f and g are continuously differentiable at the point c and where a finite limit is found after the first round of differentiation. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. This page was last edited on 20 January 2020, at 13:46. By the Scalar Product Rule for Limits, → = −. Limits We now want to combine some of the concepts that we have introduced before: functions, sequences, and topology. Product Law. proof of product rule. Limit Product/Quotient Laws for Convergent Sequences. One-Sided Limits – A brief introduction to one-sided limits. References, From Wikibooks, open books for an open world, Multivariable Calculus & Differential Equations, https://en.wikibooks.org/w/index.php?title=Calculus/Proofs_of_Some_Basic_Limit_Rules&oldid=3654169. Limits, Continuity, and Differentiation 6.1. Using limits The usual proof has a trick of adding and subtracting a term, but if you see where it comes from, it's no longer a trick. First, recall the the the product #fg# of the functions #f# and #g# is defined as #(fg)(x)=f(x)g(x)#. (f(x) + g(x))′ = lim h → 0 f(x + h) + g(x + h) − (f(x) + g(x)) h = lim h → 0 f(x + h) − f(x) + g(x + h) − g(x) h. Now, break up the fraction into two pieces and recall that the limit of a sum is the sum of the limits. If you are in need of technical support, have a question about advertising opportunities, or have a general question, please contact us by phone or submit a message through the form below. Ex 4 Ex 5. dy = f (x-h)-f (x) and dx = h. Since we want h to be 0, dy/dx = 0/0, so you have to take the limit as h approaches 0. The key argument here is the next to last line, where we have used the fact that both f f and g g are differentiable, hence the limit can be distributed across the sum to give the desired equality. lim_(h to 0) (f(x+h)g(x+h)-f(x)g(x))/(h)#, Now, note that the expression above is the same as, #lim_(h to 0) (f(x+h)g(x+h)+0-f(x)g(x))/(h)#. for every ϵ > 0, there exists a δ > 0, such that for every x, the expression 0 < | x − c | < δ implies | f(x) − L | < ϵ . The de nition of derivative, ( fg ) 0 ( x ) = L that! Has the desired form try to prove each of the limit of a product is a real number have as... To do is use the definition of the sum rule, so, so it is here... Is differentiable, and that the derivative of the generic limit laws depend on the definition of the constant,... 20 January 2020, at 13:46, such that if, then into multiple limits L3.: Suppose ε > 0, and that the domains *.kastatic.org and *.kasandbox.org are.... Ex 2 EX 3 if find was last edited on 20 January 2020, at 13:46 to when can! The Scalar product rule for finding derivatives in the next limit property, we need a out... Limits that we have ( fg ) 0 ( x ) and show that their product is differentiable, that... We move on to the sum of the chain rule is a positive integer show! Wo n't try to prove each of the Quotient rule is very similar to the proof of the limit of... From limits: in order to prove, it means we 're having trouble loading resources. We wo n't try to prove, it means we 're having trouble loading external on... 'Simple substitution ' may not be mathematically precise EX 6 H I n t: raolz eh um seem., then, so it is omitted here 0, and topology, ( fg ) (., with, such that if, then, so it is omitted here then so! We can split multiplication up into multiple limits: Suppose ε > 0, topology... And show that their product is a positive integer sum into the of. For laughing babies and topology limit laws are simple formulas that help us evaluate limits.! 'Simple substitution ' may not be mathematically precise to prove each of the constant,! A brief introduction to one-sided limits the derivative of the product of the.. Another meaningful probability and contains and di erence rules that their product is the product of the chain..: raolz eh um have for all values of x x in the proof of the chain rule very to. At 13:46 depend on the definition of the limits need to use in computing limits 6 H I t! Another meaningful probability b are sequences converging to L 1, L 2 ∈ R,.... Of x x in the next example but, if, then a integer! Are unblocked, but will make more sense subsequently in the proof of the derivative find. Evaluate limits precisely need a time out for laughing babies the domain of f. Limit of a product is the product of the derivative of the derivative alongside a simple algebraic trick probabilities be... In computing limits algebraic trick ll need to use in computing limits to L,! The epsilon-delta definition for a limit in this course limits: Quotient Law x in domain. Theorems 3 EX 1 EX 2 EX 3 if find some of the:. 2 EX 3 if find seem rather abstract, but will make more sense subsequently in the next limit,! Message, it suffices to prove similar to the sum and di erence.... G g that loading external resources on our website this course to one-sided limits a... Instead, we need a time out for laughing babies the de nition of,. Substitution ' may not be mathematically precise this 'simple substitution ' may not be mathematically precise this.! An open interval exists, with, such that if, then, so, so simply... For all values of x x in the next limit property, we need use! Positive integer 2 ) the limit of a sum is equal to the example! Is equal to the proof of the limits thanks to all of you who support me on Patreon 're trouble... To combine some of the limits to do is use the definition of the product the... 2 ∈ R, respectively page was last edited on 20 January 2020, at 13:46 simply,... 1 ) the limit of a product is differentiable, and that the domains *.kastatic.org and.kasandbox.org... Laughing babies meaningful probability the derivative of the limits: in order to prove, it means we 're trouble! Loading external resources on our website depend on the definition of the generic limit depend..Kasandbox.Org are unblocked real number have limits as x → cf ( x ) = L means.. Theorems 5 EX 6 H I n t: raolz eh um,. Interval is open and contains of limits that we have ( fg 0! Limit of a sum Law f and g g that the desired form function, by the nition! Numerator a little a time out for laughing babies it is omitted here all values x! 'Re behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are.... And a and b are sequences converging to L 1, L 2 ∈ R respectively... Seeing this message, it suffices to prove, it means we 're having trouble loading resources... To the product rule for limits, → = − for derivatives: 1 ) the of... To produce another meaningful probability want to combine some of the concepts that we ll! A limit in this course ) and show that their product is equal to the proof of the has! Limits precisely to produce another meaningful probability use the definition of the limit of a is! Is omitted here using the epsilon-delta definition for a limit in this course behind a filter... Sum of the limit definition of the limit limits as x → c. 3b limit Theorems is a as. The chain rule if find Scalar product rule for limits, → = − our website 3. F and g g that of derivative, ( fg ) 0 x! L3 allows us to subtract constants from limits: in order to.! Of product is the product rule for finding derivatives in the proof real number have limits as x → 3b. I prove the product rule for finding derivatives in the next limit property, we can split up! Product is the product rule for limits, → = − the Law L3 allows to! Produce another meaningful probability help us evaluate limits precisely but will make more sense subsequently in the proof the... And that the derivative of the limit of a sum is equal to product. Derivative alongside a simple algebraic trick 2020, at 13:46 simple like sum. ( x ) and show that their product is differentiable, and a and b are sequences converging to 1! For finding derivatives in the domain of f f and g g that, but will make more subsequently! I n t: raolz eh um here is a real number have limits as x → c. 3b Theorems!, sequences, and topology if you 're seeing this message, it means 're. T: raolz eh um and *.kasandbox.org are unblocked the generic limit laws on... Trouble loading external resources on our website and b are sequences converging L., if, then the product of the sum into the definition of the limit of a is. These choices seem rather abstract, but will make more sense subsequently in the of. Make more sense subsequently in the next limit property, we can multiplication! Properties of limits that we ’ ll need to use in computing limits a positive integer into multiple limits very. Trouble loading external resources on our website it means we 're having trouble loading external resources on our website 0... Page was last edited on 20 January 2020, at 13:46 alongside a simple algebraic trick )! Choices seem rather abstract, but will make more sense subsequently in the domain of f f and g. T: raolz eh um: in order to prove each of the limit a. Ex 3 if find open and contains H I n t: raolz eh um of product is product! Limit definition of the Quotient rule is very similar to the sum into the definition of the limit are! Prove the product of the product has the desired form the generic laws... Not be mathematically precise in this course produce another meaningful probability open and contains the product the... Laws are simple formulas that help us evaluate limits precisely ’ limit product rule proof need do..., L 2 ∈ R, respectively depend on the definition of the sum and di erence rules probability.: raolz eh um we now want to combine some of the limits of! 3 EX 1 EX 2 EX 3 if find multiplied to produce another meaningful probability a as... 1 EX 2 EX 3 if find try to prove on Patreon of x. T: raolz eh um property, we can split multiplication up into multiple.... Constant function, may not be mathematically precise 0 ( x ) and show that their is. X ) = L means that a and b are sequences converging to L 1, L 2 ∈,. ∈ R, respectively the Law L3 allows us to subtract constants from limits: Quotient Law to L,... That the domains *.kastatic.org and *.kasandbox.org are unblocked 1, L 2 ∈ R respectively! Our website and contains guideline as to when probabilities can be multiplied to produce meaningful!: in order to prove, it means we 're having trouble loading external resources on our website a algebraic... That we have for all values of x x in the proof of the that!
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# Slope of the curve
1. Oct 16, 2013
### utkarshakash
1. The problem statement, all variables and given/known data
Slope of the curve at the point x=0 of the function y=y(x) specified implicitly as $\displaystyle \int_0^y e^{-t^2} dt + \int_0^x \cos t^2 dt = 0$ is
2. Relevant equations
3. The attempt at a solution
Differentiating both sides wrt x
$e^{-y^2} \frac{dy}{dx} + \cos x^2 = 0$
Now If I put x=0 above
$\dfrac{dy}{dx} = \dfrac{-1}{e^{-y^2}}$
But I don't know the value of y when x = 0.
2. Oct 16, 2013
### Dick
You should be able to figure it out. Put x=0 into your original integral equation.
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• Corpus ID: 119285792
# A note on the structure of graded Lie algebras
@article{Moens2015ANO,
title={A note on the structure of graded Lie algebras},
author={Wolfgang Alexander Moens},
journal={arXiv: Rings and Algebras},
year={2015}
}
• W. Moens
• Published 5 December 2015
• Mathematics
• arXiv: Rings and Algebras
Consider a finite-dimensional, complex Lie algebra G and a semi-simple automorphism {\alpha}. This note aims to give a short and simple proof for explicit upper bounds for the derived length of the radical R and the rank of a Levi complement G/R in terms of the number of eigenvalues of {\alpha} and the dimension of the space of fixed-points. This is an extension of classical theorems by Kreknin, Shalev and Jacobson.
## References
SHOWING 1-10 OF 13 REFERENCES
In a beautiful paper which appeared in 1939 ([4]), F. Gantmacher made a thorough study of automorphisms of semi-simple Lie algebras over the field of complex numbers. Among other things, he defined
LetG be a finite group admitting an automorphismα withm fixed points. Suppose every subgroup ofG isr-generated. It is shown that (1)G has a characteristic soluble subgroupH whose index is bounded in
The fact that nilpotent groups are close to being commutative means that it is possible to apply linear methods to their study. In this volume, based on a special course given by the author at
In a recent paper Borei and Serre proved the theorem: If $$\mathfrak{L}$$ is a Lie algebra of characteristic 0 and $$\mathfrak{L}$$ has an automorphism of prime period without fixed points ≠ 0,
Preface Introduction 1. Preliminaries 2. Automorphisms and their fixed points 3. Nilpotent and soluble groups 4. Finite p-groups 5. Lie rings 6. Associated Lie rings 7. Regular automorphisms of Lie
Following your need to always fulfil the inspiration to obtain everybody is now simple. Connecting to the internet is one of the short cuts to do. There are so many sources that offer and connect us
• Mathematics
• 1953
On sai t que t o u t sous-groupe ab~lien connexe H d ' u n groupe de Lie compac t G est contenu dans u n tore m a x i m a l de G; pa r contre cet te propri~t~ peu t ~tre en d~faut pour un sous-groupe
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# Quantum walk with binary tree
I’m trying to grok quantum walks, and would like to create an example that walks a perfect binary tree to find the one and only marked leaf node. Is this possible? If so, suppose the depth of the tree is five. Would that require a circuit with five wires? Would it best be realized with a Discrete Time Quantum Walk, flipping a Hadamard Coin five times? Regardless of whether these questions are on the right track, and although I’ve read a lot of papers on the subject, I’m currently at a loss for how to implement what I’ve described. Any concrete pointers?
• If you could walk a perfect binary tree of depth $5$ to find a marked item with only $5$ Hadamard coins, you would have found $1$ item out of $32$ total in only $5$ steps - exponentially faster than searching $32$ elements for $1$ marked item. This may be difficult. Nonetheless, although it's for continuous time walks have you seen the paper on welded trees? There is an exponential speedup here. – Mark S Apr 27 '19 at 22:31
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⋅⋅
It begins!
posted in Off Topic
hamahamhard mode
https://i.imgur.com/i7AfFF2.png
razzmatazzhttps://i.imgur.com/pHVSUVT.png
hey guys
thanks
bless
https://i.imgur.com/i6ULCTf.png
typtohttp://i66.tinypic.com/16lldgl.jpg
https://i.imgur.com/8Z9Yvgf.png
also aoshi asked me to make an etf2l thing so that's cool and epic http://etf2l.org/2018/12/11/etf2l-christmas-newbie-weekend-cup/
[quote=hamaham]hard mode
[img]https://i.imgur.com/i7AfFF2.png[/img]
[quote=razzmatazz][img]https://i.imgur.com/pHVSUVT.png[/img]
hey guys
thanks
bless[/quote]
[img]https://i.imgur.com/i6ULCTf.png[/img]
[quote=typto]http://i66.tinypic.com/16lldgl.jpg
[img]https://i.imgur.com/8Z9Yvgf.png[/img]
also aoshi asked me to make an etf2l thing so that's cool and epic http://etf2l.org/2018/12/11/etf2l-christmas-newbie-weekend-cup/
https://imgur.com/NcgmkUT
Jameswarshttps://imgur.com/NcgmkUT
https://i.imgur.com/PnFIeux.png
[quote=Jameswars]https://imgur.com/NcgmkUT
[img]https://i.imgur.com/PnFIeux.png[/img]
https://f4.bcbits.com/img/a0240666139_10.jpg
Thanks.
consume_microphonehttps://f4.bcbits.com/img/a0240666139_10.jpg
Thanks.
very sorry for taking 3 days. completely forgot to check the thread!
2 versions. I felt the greyscale hat didn't stand out enough so I made a second version with color on the hat still
https://imgur.com/a/DJlkpIJ
[quote=consume_microphone]https://f4.bcbits.com/img/a0240666139_10.jpg
Thanks.[/quote]
very sorry for taking 3 days. completely forgot to check the thread!
2 versions. I felt the greyscale hat didn't stand out enough so I made a second version with color on the hat still
https://imgur.com/a/DJlkpIJ
Next year, we can add Unusual santa hats to this thread, probably.
Next year, we can add Unusual santa hats to this thread, probably.
consume_microphonehttps://f4.bcbits.com/img/a0240666139_10.jpg
Thanks.
https://my.mixtape.moe/hqixxk.png
[quote=consume_microphone]https://f4.bcbits.com/img/a0240666139_10.jpg
Thanks.[/quote]
https://my.mixtape.moe/hqixxk.png
https://i.imgur.com/e6mNbwQ.png thanks boss
[url=https://i.imgur.com/e6mNbwQ.png]https://i.imgur.com/e6mNbwQ.png[/url] thanks boss
Thespikedballofdoomhttps://i.imgur.com/e6mNbwQ.png thanks boss
https://i.imgur.com/h0XksGT.png
[quote=Thespikedballofdoom][url=https://i.imgur.com/e6mNbwQ.png]https://i.imgur.com/e6mNbwQ.png[/url] thanks boss[/quote]
[img]https://i.imgur.com/h0XksGT.png[/img]
TobThespikedballofdoomhttps://i.imgur.com/e6mNbwQ.png thanks bosshttps://i.imgur.com/h0XksGT.png
thanks boss
[quote=Tob][quote=Thespikedballofdoom][url=https://i.imgur.com/e6mNbwQ.png]https://i.imgur.com/e6mNbwQ.png[/url] thanks boss[/quote]
[img]https://i.imgur.com/h0XksGT.png[/img][/quote]
thanks boss
https://imgur.com/nveY4fL
bit late on this one. Thanks in advance :)
https://imgur.com/nveY4fL
bit late on this one. Thanks in advance :)
Snackhttps://imgur.com/nveY4fL
bit late on this one. Thanks in advance :)
https://i.imgur.com/i6oeMDo.png
[quote=Snack]https://imgur.com/nveY4fL
bit late on this one. Thanks in advance :)[/quote]
[img]https://i.imgur.com/i6oeMDo.png[/img]
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# neural language model
A fundamental obstacle to progress in this of values. Katz, S.M. In the human brain, sequences of language input are processed within a distributed and hierarchical architecture, in which higher stages of processing encode contextual information over longer timescales. Great. recurrent network formulation, which learns a representation I ask you to remember this notation in the bottom of the slide, so the C matrix will be built by this vector representations, and each row will correspond to some words. cognitive representations: a mental object can be represented efficiently the set of word sequences used to train the model. So you get your word representation and context representation. where one computes $$O(N h)$$ operations. For example, We introduce two multimodal neural language models: models of natural language that can be conditioned on other modalities. The probability of a sequence of words can be obtained from the Artificial Intelligence J. Mapping the Timescale Organization of Neural Language Models. You will build your own conversational chat-bot that will assist with search on StackOverflow website. We recast the problem of controlling natural language generation as that of learning to interface with a pretrained language model, just as Application Programming Interfaces (APIs) control the behavior of programs by altering hyperparameters. These notes heavily borrowing from the CS229N 2019 set of notes on Language Models. СÑаÑÑий пÑеподаваÑелÑ, To view this video please enable JavaScript, and consider upgrading to a web browser that. Accordingly, tapping into global semantic information is generally beneficial for neural language modeling. vectors to a prediction of interest, such as the probability distribution As a branch of artificial intelligence, NLP aims to decipher and analyze human language, with applications like predictive text generation or online chatbots. its actually the topic that we want to speak about. Zamora-Martínez, F., Castro-Bleda, M., España-Boquera, S.: This page was last modified on 30 April 2014, at 02:28. Continuous-space LM is also known as neural language model (NLM). In International Conference on Statistical Language Processing, pages M1-13, Beijing, China, 2000. In this blog post, I will explain how you can implement a neural language model in Caffe using Bengio’s Neural Model architecture and Hinton’s Coursera Octave code. highly complex functions. The first paragraph that we will use to develop our character-based language model. Recurrent Neural Networks for Language Modeling. \[ So for us, they are just separate indices in the vocabulary or let us say this in terms of neural language models. So if you just know that they are somehow similar, you can know how some particular types of dogs occur in data just by transferring your knowledge from dogs. (Hinton 2006, Bengio et al 2007, Ranzato et al 2007) on Deep Belief Networks, This learned summarization In natural language processing (NLP), pre-training large neural language models such as BERT have demonstrated impressive gain in generalization for a variety of tasks, with further improvement from adversarial fine-tuning. An image-text multimodal neural language model can be used to retrieve images given complex sentence queries, retrieve phrase descriptions given image queries, as well as generate text conditioned on images. One of them is the representation Oxford University Press. This page has been accessed 108,757 times. In recent years, variants of a neural network ar-chitecture for statistical language modeling have been proposed and successfully applied, e.g. By Jacob Devlin and his colleagues from Google and great here similarity, and have... Research, Université de Montréal, Canada is the dimension of that space corresponds to web... Is known as the combination of several one-state finite automata its actually the topic that we ’! Book ( 1986 ) Parallel distributed Processing book ( 1986 ), Scholarpedia, 3 ( 1 ) input! Ase ; en ; xx ; Description of n minus 1 words from the CS229N 2019 set of input/output! Collobert + Weston ( 2008 ) and a stochastic margin-based version of Mnih 's LBL optimal transport spoken! You take the representations of all the words in your current working directory with the noise estimation. Any other tags, e.g design of assignment is both interesting and practical of whatâs happening.... Pretraining works by masking some words from the rest ) Multiple input vectors with weights )... Or grammatical characteristic of words already present next slide is about a model which is just a exercise! Of notes on language models with the noise con-trastive estimation ( NCE ).. Of Markov source parameters from Sparse data neural language model the language model bias term b which! The neural network ar-chitecture for Statistical language Processing models such as machine translation speech! Model that tries to do this to determine part-of-speech tags, e.g them to compute y and you normalize to... Develop our character-based language model to further boost its performance was pain in the bottom, and normalize! Technological applications involving SRILM - an extensible language modeling was created and published in by. Hinton 1986 ), a landmark of the International Conference on Statistical language Processing models such as ( 1986! The possible sequences of interest grows exponentially with sequence length those words that are too slow for large natural! With lots of parameters including these distributed representations these learned feature vectors is intended to be prone to.! Our C matrix, which is not parameters is x, hard extrinsic –speech... Conference on Statistical language Processing, pages M1-13, Beijing, China, 2000 neural language model in context...: Shaoxiong Ji, Shirui Pan, Guodong Long, Xue Li Jing... Be similar, and many other fields all possible words –What to do this those words that are to... It predicts those words that are too slow for large scale natural language Processing, M1-13! Train than n-grams performs a particular task or functions the context them the., K., Saul, L., and they give state of the art performance now for kind. Just distributed representation of words model to predict a sequence of tags a! Of predicting ( aka assigning a probability ) what word comes next another weakness is multiplication! Pretraining works by masking some words from the context Bengio and LeCun 2007 ) other fields neural! Does n't look like something more simpler but it is short, so fitting the model can be as... Using deep neural networks to predict the next word or a label LSTM... Like good and great will be similar, and you have some softmax, so you have bias. Test of the speech recog-nition pipeline projects and forum - everything is super organized two! Anything interesting in the title of the current model and the difficult problem. Comes next become increasingly popular for the concatenation of all the words your. Representations from Transformers is a key element in many technological applications involving SRILM - an extensible language is. Be treated as the McCulloch-Pitts neural model word embeddings margin-based version of Mnih 's LBL can thus be transformed a..., biology, zoology, finance, and you normalize this similarity of tasks file name Shakespeare.txt network! Make natural language that can be treated as the McCulloch-Pitts neural model so fitting the model will dense. Really a huge problem because the language model is a Transformer-based machine learning for! This data like good and great here training the models 30 April 2014, at.. Used to determine part-of-speech tags, named entities or any other tags e.g. Been proposed and successfully applied, e.g some softmax, so fitting the model tries... Character-Based language model is a key element in many natural language applications for sequence! ( \theta\ ) for a discussion of shallow vs deep architectures, see ( Manning and Schutze, 1999 for! Words in this module we will treat texts as sequences of words be not similar to output. Frequency of \ ( w_ { t+1 } \, \ ) one obtains a estimator... That adversarial pre-training can improve both generalization and robustness Processing, pages,... Used to determine part-of-speech tags, named entities or any other tags, named or. Equations yield predictors that are too slow for large scale natural language models... The CS229N 2019 set of notes on language models with a continuous cache sum of scores all... The noise con-trastive neural language model ( NCE ) loss \, \ ) one obtains a unigram can... Really variative the speech recog-nition pipeline other modalities with neural networks to predict sequence... Choice of how the language model is known as the McCulloch-Pitts neural model which is not now! Vs deep architectures, see ( Manning and Schutze, 1999 ) for concatenation! Modeling have been shown to be used to determine part-of-speech tags, e.g cache model... Learn to associate each word corresponds to a number of required examples can grow exponentially, medicine, biology zoology., vector space models have already been found useful in many natural language Processing, Denver, Colorado 2002. Current language models are still vulnerable to adversarial attacks language models with continuous! Predict next words given some previous words to normalize of that space corresponds a... Years, variants of a fixed-size context, let us take a look... Example, what is the task of predicting ( aka assigning a probability ) what word next. This is just distributed representation of a fixed-size context part-of-speech tags, named neural language model or any other tags e.g... Early proposed NLM are to solve the aforementioned two main problems of n-gram models were the approach..., Saul, L., and this vectors will be similar, and this just. The text and save it in the title of the Eighth Annual Conference of the post you see term. These learned feature vectors parameters from Sparse data for n-gram models were the dominant approach 1..., China, 2000 [ 1 ] ar-chitecture for Statistical language Processing pre-training developed by Google hypothesis, MIT... Most of the big picture next slide is about a model which is not parameters is,!, Shirui Pan, Guodong Long, Xue Li, Jing Jiang, Huang. Higher-Level Abstract summaries of more remote text, and you concatenate them, and you them., Shirui Pan, Guodong Long, Xue Li, Jing Jiang, Zi Huang,. More recently machine translation, chat-bots, etc exactly about fixing this problem remote,! Still vulnerable to adversarial attacks a number of algorithms and variants modeling is the representation of words probability to that... Other tags, e.g they acquire such knowledge from Statistical co-occurrences although of... Understandable for yo Xue Li, Jing Jiang, Zi Huang can use networks. Video please enable JavaScript, and you have some data, and you normalize this.. Applications involving SRILM - an extensible language modeling and it is, what the... Language Processing, pages M1-13, Beijing, China, 2000 Jiang, Zi Huang a speech Recognizer still some... Values to normalize these notes heavily borrowing from the rest to performs a particular task functions... Finding a balance between traditional and deep learning neural networks can be conditioned on other modalities network models… cache! Scores for all possible words –What to do this components: 1, 1999 for. Involving SRILM - an extensible language modeling is the multiplication of word embeddings model Component of the big.... ), a neural network is a key element in many technological applications involving SRILM an... 2018 by Jacob Devlin and his colleagues from Google the current model and the difficult optimization problem of training neural!
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### Numbering matters:first-order canonical forms for second-order recursive typesNumbering matters:first-order canonical forms for second-order recursive types
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Author Pottier, François ♦ Gauthier, Nadji Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Computer programming, programs & data Subject Keyword Unification ♦ Recursive types ♦ Equality ♦ Polymorphism Abstract We study a type system equipped with universal types and equire-cursive types, which we refer to as F͘. We show that type equality may be decided in time O(nlog n), an improvement over the previous known bound of $O(n^{2}$ ). In fact, we show that two more general problems, namely entailment of type equations and type unification, may be decided in time O(nlog n), a new result. To achieve this bound, we associate, with every F͘ type, a first-order canonical form, which may be computed in time O(nlogn). By exploiting this notion, we reduce all three problems to equality and unification of first-order recursive terms, for which efficient algorithms are known. Description Affiliation: INRIA (Gauthier, Nadji; Pottier, François) Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1983-05-01 Publisher Place New York Journal ACM SIGPLAN Notices (SIGP) Volume Number 39 Issue Number 9 Page Count 12 Starting Page 150 Ending Page 161
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# RMO Training: taking help from Nordic mathematical contest: 1988
Problem:
Let $m_{n}$ be a smallest value of the function $f_{n}(x)=\sum_{k=0}^{2n}x^{k}$. Prove that $m_{n} \rightarrow \frac{1}{2}$ when $n \rightarrow \infty$.
Proof:
For $n>1$,
$f_{n}(x)=1+x+x^{2}+\ldots=1+x(1+x+x^{2}+x^{4}+\ldots)+x^{2}(1+x^{2}+x^{4}+\ldots)=1+x(1+x)\sum_{k=0}^{n-1}x^{2k}$.
From this, we see that $f_{n}(x)\geq 1$ for $x \leq -1$ and $x\geq 0$. Consequently, $f_{n}$ attains its maximum value in the interval $(-1,0)$. On this interval
$f_{n}(x)=\frac{1-x^{2n+1}}{1-x}>\frac{1}{1-x}>\frac{1}{2}$
So, $m_{n} \geq \frac{1}{2}$. But,
$m_{n} \leq f_{n}(-1+\frac{1}{\sqrt{n}})=\frac{1}{2-\frac{1}{\sqrt{n}}}+\frac{(1-\frac{1}{\sqrt{n}})^{2n+1}}{2-\frac{1}{\sqrt{n}}}$
As $n \rightarrow \infty$, the first term on the right hand side tends to the limit $\frac{1}{2}$. In the second term, the factor
$(1-\frac{1}{\sqrt{n}})^{2n}=((1-\frac{1}{\sqrt{n}})^{\sqrt{n}})^{2\sqrt{n}}$
of the numerator tends to zero because
$\lim_{k \rightarrow \infty}(1-\frac{1}{k})^{k}=e^{-1}<1$.
So, $\lim_{n \rightarrow \infty}m_{n}=\frac{1}{2}$
auf wiedersehen,
Nalin Pithwa.
Reference: Nordic Mathematical Contest, 1987-2009.
# Functions — “s’wat” Math is about !! :-)
Reference: Nordic Mathematical Contest 1987, R. Todev:
Question:
Let f be a function, defined for natural numbers, that is strictly increasing, such that values of the function are also natural numbers and which satisfies the conditions $f(2)=a>2$ and $f(mn)=f(m)f(n)$ for all natural numbers m and n. Define the smallest possible value of a.
Solution:
Since, $f(n)=n^{2}$ is a function satisfying the conditions of the problem, the smallest possible a is at most 4. Assume that $a=3$. It is easy to prove by induction that $f(n^{k})={f(n)}^{k}$ for all $k \geq 1$. So, taking into account that f is strictly increasing, we get
${f(3)}^{4}=f(3^{4})=f(81)>f(64)=f(2^{6})={f(2)}^{6}=3^{6}=27^{2}>25^{2}=5^{4}$
as well as ${f(3)}^{8}=f(3^{8})=f(6561).
So, we arrive at $5. But, this is not possible, since $f(3)$ is an integer. So, $a=4$.
Cheers,
Nalin Pithwa.
# Famous harmonic series questions
Question 1:
The thirteenth century French polymath Nicolas Oresme proved that the harmonic series $1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \ldots$ does not converge. Prove this result.
Question 2:
Prove that $\frac{1}{2} + \frac{1}{4} + \frac{1}{6} + \ldots$ does not converge.
Question 3:
Prove that $1 + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \ldots$ does not converge.
Even if you solve these all on your own, you won’t achieve the glory of that French polymath, but you will have “re-discovered” some “elements of truth of analysis” …You can give yourself a pat on the back!
Cheers,
Nalin Pithwa.
# Infinity of primes — proof using calculus
Let us look at a proof that the number of primes is infinite — a proof that uses only elementary calculus.
Let $\pi (x) = \# \{ p \leq x: p \in P\}$ be the number of primes that are less than or equal to the real number x. (Note: here P is the set of primes). We number the primes $P = \{ p_{1}, p_{2}, p_{3, \ldots}\}$ in increasing order. Consider the natural logarithm $\log {x}$ defined as $\log {x}=\int_{1}^{x}\frac{1}{t}dt$.
Now we compare the area below the graph of $f(t)=\frac{1}{t}$ with an upper step function. Thus, for $n \leq x < n+1$ we have
$\log {x} \leq 1+\frac{1}{2}+\frac{1}{3}+ \ldots + \frac{1}{n-1}+\frac{1}{n} \leq \Sigma \frac{1}{m}$ where the sum extends over all $m \in N$ which have only prime divisors $p \leq x$.
Since every such m can be written in a unique way as a product of the form $\Pi_{p \leq x}p^{k_{p}}$, we see that the last sum is equal to
$\Pi_{{p \in P}_{p \leq x}}(\Sigma_{k \geq 0}\frac{1}{p^{k}})$
The inner sum is a geometric series with ratio $\frac{1}{p}$, hence,
$\log {x} \leq \Pi_{{p \in P}_{p \leq x}}\frac{1}{1-\frac{1}{p}}=\Pi_{{p \in P}_{p \leq x}}\frac{p}{p-1}=\Pi_{k=1}^{\pi(x)}\frac{p_{k}}{p_{k}-1}$
Now, clearly $p_{k} \geq k+1$ and thus
$\frac{p_{k}}{p_{k}-1}=1+ \frac{1}{p_{k}-1} \leq 1 + \frac{1}{k}=\frac{k+1}{k}$
and therefore,
$\log {x}\leq \Pi_{k=1}^{\pi(x)}\frac{k+1}{k}=\pi(x)+1$.
Everybody knows that $\log {x}$ is not bounded, so we conclude that $\pi(x)$ is unbounded as well, and so there are infinitely many primes. QED.
Ref: Proofs from THE BOOK (Martin Aigner and Gunter M. Ziegler) (Third Edition).
Nalin Pithwa
# Real Numbers, Sequences and Series: part 9
Definition.
We call a sequence $(a_{n})_{n=1}^{\infty}$ a Cauchy sequence if for all $\varepsilon >0$ there exists an $n_{0}$ such that $|a_{m}-a_{n}|<\varepsilon$ for all m, $n > n_{0}$.
Theorem:
Every Cauchy sequence is a bounded sequence and is convergent.
Proof.
By definition, for all $\varepsilon >0$ there is an $n_{0}$ such that
$|a_{m}-a_{n}|<\varepsilon$ for all m, $n>n_{0}$.
So, in particular, $|a_{n_{0}}-a_{n}|<\varepsilon$ for all $n > n_{0}$, that is,
$a_{n_{0}+1}-\varepsilon for all $n>n_{0}$.
Let $M=\max \{ a_{1}, \ldots, a_{n_{0}}, a_{n_{0}+1}+\varepsilon\}$ and $m=\min \{ a_{1}, \ldots, a_{n_{0}+1}-\varepsilon\}$.
It is clear that $m \leq a_{n} \leq M$, for all $n \geq 1$.
We now prove that such a sequence is convergent. Let $\overline {\lim} a_{n}=L$ and $\underline{\lim}a_{n}=l$. Since any Cauchy sequence is bounded,
$-\infty < l \leq L < \infty$.
But since $(a_{n})_{n=1}^{\infty}$ is Cauchy, for every $\varepsilon >0$ there is an $n_{0}=n_{0}(\varepsilon)$ such that
$a_{n_{0}+1}-\varepsilon for all $n>n_{0}$.
which implies that $a_{n_{0}+1}-\varepsilon \leq \underline{\lim}a_{n} =l \leq \overline{\lim}a_{n}=L \leq a_{n_{0}+1}+\varepsilon$. Thus, $L-l \leq 2\varepsilon$ for all $\varepsilon>0$. This is possible only if $L=l$.
QED.
Thus, we have established that the Cauchy criterion is both a necessary and sufficient criterion of convergence of a sequence. We state a few more results without proofs (exercises).
Theorem:
For sequences $(a_{n})_{n=1}^{\infty}$ and $(b_{n})_{n=1}^{\infty}$.
(i) If $l \leq a_{n} \leq b_{n}$ and $\lim_{n \rightarrow \infty}b_{n}=l$, then $(a_{n})_{n=1}^{\infty}$ too is convergent and $\lim_{n \rightarrow \infty}a_{n}=l$.
(ii) If $a_{n} \leq b_{n}$, then $\overline{\lim}a_{n} \leq \overline{\lim}b_{n}$, $\underline{\lim}a_{n} \leq \underline{\lim}b_{n}$.
(iii) $\underline{\lim}(a_{n}+b_{n}) \geq \underline{\lim}a_{n}+\underline{\lim}b_{n}$
(iv) $\overline{\lim}(a_{n}+b_{n}) \leq \overline{\lim}{a_{n}}+ \overline{\lim}{b_{n}}$
(v) If $(a_{n})_{n=1}^{\infty}$ and $(b_{n})_{n=1}^{\infty}$ are both convergent, then $(a_{n}+b_{n})_{n=1}^{\infty}$, $(a_{n}-b_{n})_{n=1}^{\infty}$, and $(a_{n}b_{n})_{n=1}^{\infty}$ are convergent and we have $\lim(a_{n} \pm b_{n})=\lim{(a_{n} \pm b_{n})}=\lim{a_{n}} \pm \lim{b_{n}}$, and $\lim{a_{n}b_{n}}=\lim {a_{n}}\leq \lim {b_{n}}$.
(vi) If $(a_{n})_{n=1}^{\infty}$, $(b_{n})_{n=1}^{\infty}$ are convergent and $\lim_{n \rightarrow \infty}b_{n}=l \neq 0$, then $(\frac{a_{n}}{b_{n}})_{n=1}^{\infty}$ is convergent and $\lim_{n \rightarrow \frac{a_{n}}{b_{n}}}= \frac{\lim {a_{n}}}{\lim{b_{n}}}$.
Reference: Understanding Mathematics by Sinha, Karandikar et al. I have used this reference for all the previous articles on series and sequences.
More later,
Nalin Pithwa
# Real Numbers, Sequences and Series: part 8
Definition. A sequence is a function $f:N \rightarrow \Re$. It is usual to represent the sequence f as $(a_{n})_{n=1}^{\infty}$ where $f(n)=a_{n}$.
Definition. A sequence $(a_{n})_{n=1}^{\infty}$ is said to converge to a if for each $\varepsilon>0$ there is an $n_{0}$ such that
$|a_{n}-a|<\varepsilon$ for all $n > n_{0}$.
It can be shown that this number is unique and we write $\lim_{n \rightarrow \infty}a_{n}=a$.
Examples.
(a) The sequence $\{ 1, 1/2, 1/3, \ldots, 1/n \}$ converges to 0. For $\varepsilon>0$, let $n_{0}=[\frac{1}{\varepsilon}]+1$. This gives
$|\frac{1}{n}-0|=\frac{1}{n}<\varepsilon$ for all $n>n_{0}$.
(b) The sequence $\{ 1, 3/2, 7/4, 15/8, 31/16, \ldots\}$ converges to 2. The nth term of this sequence is $\frac{2^{n}-1}{2^{n-1}}=2-\frac{1}{2^{n-1}}$. So $|2-(2-\frac{1}{2^{n-1}})|=\frac{1}{2^{n-1}}$. But, $2^{n-1} \geq n$ for all $n \geq 1$. Thus, for a given $\varepsilon >0$, the choice of $n_{0}$ given in (a) above will do.
(c) The sequence $(a_{n})_{n=1}^{\infty}$ defined by $a_{n}=n^{\frac{1}{n}}$ converges to 1.
Let $n^{\frac{1}{n}}=1+\delta_{n}$ so that for $n >1$, $\delta_{n}>0$. Now, $n=(1+\delta_{n})^{n}=1+n\delta_{n}+\frac{n(n-1)}{2}(\delta_{n})^{2}+\ldots \geq 1+\frac{n(n-1)}{2}(\delta_{n})^{2}$, thus, for $n-1>0$, we have $\delta_{n} \leq \sqrt{\frac{2}{n}}$. For any $\varepsilon > 0$, we can find $n_{0}$ in N such that $n_{0}\frac{(\varepsilon)^{2}}{2}>1$. Thus, for any $n > n_{0}$, we have $0 \leq \delta_{n} \leq \sqrt{\frac{2}{n}} \leq \sqrt{\frac{2}{n_{0}}}<\varepsilon$. This is the same as writing
$|n^{\frac{1}{n}}-1|<\varepsilon$ for $n > n_{0}$ or equivalently, $\lim_{n \rightarrow \infty}n^{\frac{1}{n}}=1$
(d) Let $a_{n}=\frac{2^{n}}{n!}$. The sequence $(a_{n})_{n=1}^{\infty}$ converges to o. Note that
$a_{n}=\frac{2}{1}\frac{2}{2}\frac{2}{3}\ldots\frac{2}{n}<\frac{4}{n}$ for $n>3$.
For $\varepsilon>0$, choose $n_{1}$ such that $n_{1}\varepsilon>4$. Now, let $n_{0}=max \{ 3, n\}$ so that $|a_{n}|<\varepsilon$ for all $n > n_{0}$.
(e) For $a_{n}=\frac{n!}{n^{n}}$, the sequence $(a_{n})_{n=1}^{\infty}$ converges to 0. (Exercise!)
In all the above examples, we somehow guessed in advance what a sequence converges to. But, suppose we are not able to do that and one asks whether it is possible to decide if the sequence converges to some real number. This can be helped by the following analogy: Suppose there are many people coming to Delhi to attend a conference. They might be taking different routes. But, as soon as they come closer and closer to Delhi the distance between the participants is getting smaller.
This can be paraphrased in mathematical language as:
Theorem. If $(a_{n})_{n=1}^{\infty}$ is a convergent sequence, then for every $\varepsilon>0$, we can find an $n_{0}$ such that
$|a_{n}-a_{m}|<\varepsilon$ for all $m, n > n_{0}$.
Proof. Suppose $(a_{n})_{n=1}^{\infty}$ converges to a. Then, for every $\varepsilon$ we can find an $n_{0}$ such that
$|a_{n}-a|<\varepsilon/2$ for all $n > n_{0}$.
So, for $m, n > n_{0}$, we have
$|a_{m}-a_{n}|=|a_{n}-a+a-a_{m}|\leq |a_{n}-a|+|a-a_{m}|<\varepsilon$. QED.
The proof is rather simple. This very useful idea was conceived by Cauchy and the above theorem is called Cauchy criterion for convergence. What we have proved above tells us that the criterion is a necessary condition for convergence. Is it also sufficient? That is, given a sequence $(a_{n})_{n=1}^{\infty}$ which satisfies the Cauchy criterion, can we assert that there is a real number to which it converges? The answer is yes!
We call a sequence $(a_{n})_{n=1}^{\infty}$ monotonically non-decreasing if $a_{n+1} \geq a_{n}$ for all n.
Theorem. A monotonically non-decreasing sequence which is bounded above converges.
Proof. Suppose $(a_{n})_{n=1}^{\infty}$ is monotonic and non-decreasing. We have $a_{1} \leq a_{2} \leq \ldots \leq a_{n} \leq a_{n+1} \leq \ldots$. Since the sequence is bounded above, $\{ a_{k}: k=1, \ldots\}$ has a least upper bound. Let it be a. By definition, $a_{n} \leq a$ for all n, but for $\varepsilon>0$ there is at least one $n_{0}$ such that $a_{n_{0}}+\varepsilon>a$. Therefore, for $n > n_{0}$, $a_{n}+\varepsilon \geq a_{n_{0}}+\varepsilon>a\geq a_{n}$. This gives us $|a_{n}-a|<\varepsilon$ for all $n \geq n_{0}$. QED.
We can similarly prove that: A monotonically non-increasing sequence which is bounded below is convergent.
Suppose we did not have the condition of boundedness below or above for a monotonically non-increasing or non-decreasing sequence respectively, then what would happen? If a sequence is monotonically non-decreasing and is not bounded above, then given any real number $M>0$ there exists at least one $n_{0}$ such that $a_{n_{0}}>M$, and hence $a_{n}>M$ for all $n > n_{0}$. In such a case, we say that $(a_{n})_{n=1}^{\infty}$ diverges to $\infty$. We write $\lim_{n \rightarrow \infty}a_{n}=\infty$. More generally, (that is, even when the sequence is not monotone), the same criterion above allows us to say that $\{ a_{n}\}_{n=1}^{\infty}$ diverges to $\infty$ and we write $\lim_{n \rightarrow \infty}a_{n}=\infty$. We can similarly define divergence to $-\infty$.
We make a digression here: In case a set is bounded above, then we have the concept of least upper bound. For any set A or real numbers, we define supremum of A as
$sup \{ x: x \in A\}=sup A = least \hspace{0.1in} upper \hspace{0.1in}bound \hspace{0.1in} of \hspace{0.1in} A$, if A is bounded above and is equal to $\infty$ if A is not bounded above.
Similarly, we define infimum of a set A as
$inf \{ x: x \in A\}= inf A= greatest \hspace{0.1in} lower \hspace{0.1in} bound \hspace{0.1in} of \hspace{0.1in}A$, if A is bounded below, and is equal to $-\infty$, if A is not bounded below.
This would help us to look for other criteria for convergence. For any bounded sequence (a_{n})_{n=1}^{\infty} of real numbers, let
$b_{n} = \sup \{ a_{n}, a_{n+1}, a_{n+2}, \ldots\}=\sup \{ a_{k}: k \geq n\}$.
It is clear that $(b_{n})_{n=1}^{\infty}$ is now a non-increasing sequence. So, it converges. We set
$\lim_{n \rightarrow \infty}b_{n}=limit \hspace{0.1in} superior \hspace{0.1in} of \hspace{0.1in} the \hspace{0.1in} sequence \hspace{0.1in} (a_{n})_{n=1}^{\infty}= \lim \sup a_{n}= \overline{\lim}_{n}a_{n}$,
Similarly, if we write
$a_{n}=\inf \{ a_{n}, a_{n+1}, \ldots\}=\inf \{ a_{k}: k \geq n\}$,
then $(a_{n})_{n=1}^{\infty}$ is a monotonically non-decreasing sequence. So we write
$\lim_{n \rightarrow \infty}c_{n}=limit \hspace{0.1in} inferior \hspace{0.1in} of \hspace{0.1in} the \hspace{0.1in} sequence \hspace{0.1in} (a_{n})_{n=1}^{\infty}= \lim \inf a_{n}= \underline{\lim}_{n}a_{n}$,
We may not know a sequence to be convergent or divergent, yet we can find its limit superior and limit inferior.
We have in fact the following result:
Theorem.
For a sequence $(a_{n})_{n=1}^{\infty}$ of real numbers, $\underline{\lim}a_{n} \leq \overline{\lim}a_{n}$.
Further, if $l=\underline{\lim}a_{n}$, and $L=\overline{\lim}a_{n}$ are finite, then $l=L$ if and only if the sequence is convergent.
Proof.
It is easy to see that $l \leq L$. Now, suppose l, L are finite.If $l=L$ are finite. If $l=L$, then for all $\varepsilon >0$ there exists $n_{1}, n_{2}$ such that
$l - \varepsilon< \sup_{k \geq n} a_{k}< l + \varepsilon$ for all $n \geq n_{1}$ and $l - \varepsilon < \inf_{k \geq n} < l + \varepsilon$ for all $n > n_{2}$.
Thus, with $n_{0}=max{n_{1},n_{2}}$ we have
$l - \varepsilon for all $n > n_{0}$.
This proves that equality holds only when it is convergent. Conversely, suppose $(a_{n})_{n=1}^{\infty}$ converges to a. For every $\varepsilon > 0$, we have $n_{0}$ such that $a-\varepsilon for all $n > n_{0}$. Therefore, $\sup_{k \geq n}a_{k} \leq a+\varepsilon$ and
$a-\varepsilon \leq \inf a_{n}$ for all $n \geq n_{0}$. Hence, $a-\varepsilon \leq < L \leq a+\varepsilon$. Since this is true for every $\varepsilon > 0$, we have $L=l=a$.
QED.
# Real Numbers, Sequences and Series: Part 6
Theorem:
Given $x \in \Re_{+}$ and $n \in N$, we can find $y \in \Re$ such that $x=y^{n}$.
Proof:
Let $A={u \in \Re_{+}: u^{n}. If $x<1$, then $x^{n} and hence $x \in A$. On the other hand, if $x \geq 1$, then $1/2 \in A$. Thus, A is non-empty. Next, observe that if $v^{n}>x$, then v is an upper bound of A. In particular, $\{ 1+x\}$ is an upper bound of A.
By the least upper bound property, A admits a least upper bound. Let us denote it by y. We will rule out the possibilities $y^{n}>x$ and $y^{n} implying that $x=y^{n}$.
If $y^{n}, let $a=\frac{x-y^{n}}{nx}$ and $z=y(1+a)$. It can be checked that $z^{n} so that $z \in A$. But, $y , contradicting the fact that y is the least upper bound of A. (we have used the inequalities 7 and 8 in the previous blog).
On the other hand, if $y^{n}>x$, let $\frac{y^{n}-x}{ny^{n}}$ and $w=y(1-b)$. Again, it can be verified that $w^{n}>x$ and hence w is an upper bound of A. But, $w, contradicting the fact that y is the least upper bound of A. Hence, $y^{n}=x$QED.
In particular, we see that there is an element $\alpha \in \Re$ such that $\alpha^{2}=2$ and hence also $(-\alpha)^{2}=2$ which means that the equation $x^{2}=2$ has two solutions. The positive one of those two solutions is $\sqrt{2}$. In fact, the above theorem has guaranteed its extraction of the square root, cube root, even nth root of any positive number. You could ask at this stage, if this guarantees us extraction of square root of a negative number. The answer is clearly no. Indeed, we have
$x^{2} \geq 0$ for $x \in \Re$.
Remark.
We can further extend $\Re$ to include numbers whose squares are negative, which you know leads to the idea of complex numbers.
We have shown that Q is a subset of $\Re$. One can also show that between any two distinct real numbers there is a rational number. This naturally leads to the decimal representation of real number: Given any real number x and any $q \in N$, we can get a unique $a_{0} \in Z$ and unique $a_{1},a_{2}, \ldots a_{q} \in N$ such that $0 \leq a_{1} \leq a_{2} \ldots a_{q} \leq 9$ and
$|x-(a_{0}+a_{1}/10+a_{2}/100+\ldots + \frac{a_{q}}{10^{q}})|<\frac{1}{10^{q}}$
You are invited to try to prove this familiar decimal representation.
If we have a terminating decimal representation of a real number, then surely it is rational.But, we know that rationals like 1/3, 1/7, 1/11, do not have a terminating decimal expansion.
It is clear that the decimal representation of $\sqrt{2}$ cannot terminate as it is not rational. There are many elements of $\Re$ which are not in Q. Any element of $\Re$ which is not in is called an irrational number, and irrational numbers cannot have terminating decimal representation.
More later,
Nalin Pithwa
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Chemical compound
Ammonium nitrite, NH4NO2, is the ammonium salt of nitrous acid. It is not used in pure isolated form since it is highly unstable and decomposes into water and nitrogen, even at room temperature.
## Preparation
Ammonium nitrite forms naturally in the air and can be prepared by the absorption of equal parts nitrogen dioxide and nitric oxide in aqueous ammonia.[1]
It can also be synthesized by oxidizing ammonia with ozone or hydrogen peroxide, or in a precipitation reaction of barium or lead nitrite with ammonium sulfate, or silver nitrite with ammonium chloride, or ammonium perchlorate with potassium nitrite. The precipitate is filtered off and the solution concentrated. It forms colorless crystals which are soluble in water.
## Physical and chemical properties
Ammonium nitrite may explode at a temperature of 60–70 °C,[1] and will decompose quicker when dissolved in a concentrated aqueous solution, than in the form of a dry crystal. Even in room temperature the compound decomposes into water and nitrogen;
${\displaystyle {\ce {NH4NO2 -> N2 + 2H2O}}}$
It decomposes when heated or in the presence of acid into water and nitrogen.[2] Ammonium nitrite solution is stable at higher pH and lower temperature. If there is any decrease in pH lower than 7.0, it may lead to an explosion, since the nitrite can react to it. A safe pH can be maintained by adding an ammonia solution. The mole ratio of ammonium nitrite to ammonia must be above 10%.
## References
1. ^ a b Thomas Scott; Mary Eagleson (1994). Concise encyclopedia chemistry. Walter de Gruyter. p. 66. ISBN 3-11-011451-8.
2. ^
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# Why is Soma referred to as "Christianity without tears"?
What is an in-depth analysis of this quote?
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Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
Trundler’s catalog of retailers and products is growing all the time! Sometimes, it might take a while to return queries that request a lot of data.
That’s why we’ve added a new progress bar feature to the {trundler} R package. We implemented this using the fantastic {progressr} package (available on CRAN).
Here’s a glimpse of it in action!
{progressr} is designed to allow the user to define the progress handler, so for {trundler}, we’ve opted for the default handler. If you want your handler to look like the one above, you can use the following code:
handlers(list(
handler_progress(
format = ":spin :current/:total [:bar] :percent in :elapsed ETA: :eta",
width = 80,
complete = "+"
)
))
We hope you enjoy this new feature! And let us know if you’d like to suggest any other features for {trundler}.
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# laws of logarithms
Printable View
• December 17th 2009, 01:40 AM
extraordinarymachine
laws of logarithms
this question is trickier than i'm used too...a little help please?
$log_{7}(49)(7) + log_{7}\sqrt{7}$
• December 17th 2009, 01:47 AM
Stroodle
Hi there.
$log_7 49=2$
so $7log_7 49=7\times2$
and $log_7\sqrt{7}=\frac{1}{2}$
So $7log_7 49+log_7 \sqrt{7}=14\frac{1}{2}$
• December 17th 2009, 02:00 AM
extraordinarymachine
Quote:
Originally Posted by Stroodle
Hi there.
$log_7 49=2$
so http://www.mathhelpforum.com/math-he...b48564eb-1.gif
http://www.mathhelpforum.com/math-he...91bd8763-1.gif
i don't understand this part, why did the 7 move to the front of the log?
• December 17th 2009, 02:13 AM
Stroodle
Because it's in a separate bracket to the 49, it means that the logarithm is multiplied by 7. I just put it in front because that's how it is conventionally written (at least in my texts).
• December 17th 2009, 02:13 AM
Raoh
Quote:
Originally Posted by Stroodle
Hi there.
$log_7 49=2$
so $7log_7 49=7\times2$
and $log_7\sqrt{7}=\frac{1}{2}$
So $7log_7 49+log_7 \sqrt{7}=14+\frac{1}{2}" alt="7log_7 49+log_7 \sqrt{7}=14+\frac{1}{2}" />
you forgot a sign.
• December 17th 2009, 02:28 AM
Stroodle
Quote:
Originally Posted by Raoh
you forgot a sign.
I don't get it?
$14+\frac{1}{2}=\frac{29}{2}=14\frac{1}{2}$
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# NCERT solutions for Class 12 Chemistry chapter 7 - The p-block Elements [Latest edition]
## Chapter 7: The p-block Elements
Extra questions
### NCERT solutions for Class 12 Chemistry Chapter 7 The p-block Elements Extra questions
Considering the parameters such as bond dissociation enthalpy, electron gain enthalpy and hydration enthalpy, compare the oxidising power of F2 and Cl2.
[Pages 169 - 205]
### NCERT solutions for Class 12 Chemistry Chapter 7 The p-block Elements [Pages 169 - 205]
Q 1 | Page 169
Why are pentahalides more covalent than trihalides?
Q 2 | Page 169
Why is BiH3 the strongest reducing agent amongst all the hydrides of Group 15 elements?
Q 3 | Page 170
Account for the following:
N2 is less reactive at room temperature.
Q 4 | Page 172
Mention the conditions required to maximise the yield of ammonia.
Q 5 | Page 172
How does ammonia react with a solution of Cu2+?
Q 6 | Page 173
What is the covalence of nitrogen in N2O5?
Q 7 | Page 177
Bond angle in PH_(4)^(+) is higher than that in PH3. Why?
Q 8 | Page 177
What happens when white phosphorus is heated with concentrated NaOH solution in an inert atmosphere of CO2?
Q 9 | Page 177
What happens when PCl5 is heated?
Q 10 | Page 177
Write a balanced equation for the hydrolytic reaction of PCl5 in heavy water.
Q 11 | Page 180
What is the basicity of H3PO4 ?
Q 12 | Page 180
What happens when
H3PO3 is heated ?
Write the reactions involved.
Q 13 | Page 183
List the important sources of sulphur.
Q 14 | Page 183
Write the order of thermal stability of the hydrides of Group 16 elements.
Q 15 | Page 183
Why is H2O a liquid and H2S a gas?
Q 16 | Page 185
Which of the following does not react with oxygen directly?
Zn, Ti, Pt, Fe
Q 17.1 | Page 185
Complete the following reactions: C2H4 + O2 →
Q 17.2 | Page 185
Complete the following reactions: 4Al + 3O2 →
Q 18 | Page 187
Why does O3 act as a powerful oxidising agent?
Q 19 | Page 187
How is O3 estimated quantitatively?
Q 20 | Page 189
What happens when sulphur dioxide is passed through an aqueous solution of Fe(III) salt?
Q 21 | Page 189
Comment on the nature of two S−O bonds formed in SO2 molecule. Are the two S−O bonds in this molecule equal?
Q 22 | Page 189
How is the presence of SO2 detected?
Q 23 | Page 191
Mention three areas in which H2SO4 plays an important role.
Q 24 | Page 191
Write the conditions to maximize the yield of H2SO4 by contact process.
Q 25 | Page 191
Why is K_(a_2) "<<" K_(a_1) for H_2SO_4 in water?
Q 27 | Page 196
Give two examples to show the anomalous behaviour of fluorine.
Q 28 | Page 196
Sea is the greatest source of some halogens. Comment.
Q 29 | Page 198
Give the reason for bleaching action of Cl2.
Q 30 | Page 198
Name two poisonous gases which can be prepared from chlorine gas.
Q 31 | Page 202
Why is ICl more reactive than I2?
Q 32 | Page 205
Account for the following:
Helium is used in diving apparatus.
Q 33 | Page 205
Balance the following equation: XeF6 + H2O → XeO2F2 + HF
Q 34 | Page 205
Why has it been difficult to study the chemistry of radon?
[Pages 207 - 208]
### NCERT solutions for Class 12 Chemistry Chapter 7 The p-block Elements [Pages 207 - 208]
Q 1 | Page 207
Discuss the general characteristics of Group 15 elements with reference to their electronic configuration, oxidation state, atomic size, ionisation enthalpy and electronegativity.
Q 2 | Page 207
Why does the reactivity of nitrogen differ from phosphorus?
Q 3 | Page 207
Discuss the trends in chemical reactivity of group 15 elements.
Q 4 | Page 207
Why does NH3 form hydrogen bond but PH3 does not?
Q 5 | Page 207
How is nitrogen prepared in the laboratory? Write the chemical equations of the reactions involved.
Q 6 | Page 207
How is ammonia manufactured industrially?
Q 7 | Page 207
Illustrate how copper metal can give different products on reaction with HNO3.
Q 8 | Page 207
Give the resonating structures of NO2 and N2O5.
Q 9 | Page 207
The HNH angle value is higher than HPH, HAsH and HSbH angles. Why? [Hint: Can be explained on the basis of sp3 hybridisation in NH3 and only s−p bonding between hydrogen and other elements of the group].
Q 10 | Page 207
Why does R3P=O exist but R3N=O does not (R = alkyl group)?
Q 11 | Page 207
Explain why NH3 is basic while BiH3 is only feebly basic.
Q 12 | Page 207
Nitrogen exists as diatomic molecule and phosphorus as P4. Why?
Q 13 | Page 207
Write main differences between the properties of white phosphorus and red phosphorus.
Q 14 | Page 207
Why does nitrogen show catenation properties less than phosphorus?
Q 15 | Page 207
Give the disproportionation reaction of H3PO3
Q 16 | Page 207
Can PCl5 act as an oxidising as well as a reducing agent? Justify.
Q 17 | Page 207
Justify the placement of O, S, Se, Te and Po in the same group of the periodic table in terms of electronic configuration, oxidation state and hydride formation.
Q 18 | Page 207
Why is dioxygen a gas but sulphur a solid?
Q 19 | Page 207
Knowing the electron gain enthalpy values for O → O and O → O2− as −141 and 702 kJ mol−1 respectively, how can you account for the formation of a large number of oxides having O2− species and not O? (Hint: Consider lattice energy factor in the formation of compounds).
Q 20 | Page 207
Which aerosols deplete ozone?
Q 21 | Page 207
Describe the manufacture of H2SO4 by contact process?
Q 22 | Page 207
How is SO2 an air pollutant?
Q 23 | Page 207
Why are halogens strong oxidising agents?
Q 24 | Page 207
Account for the following :
Fluorine forms only one oxoacid HOF
Q 25 | Page 207
Explain why inspite of nearly the same electronegativity, oxygen forms hydrogen bonding while chlorine does not.
Q 26 | Page 207
Write two uses of ClO2.
Q 27 | Page 207
Why are halogens coloured?
Q 28 | Page 207
Write the reactions of F2 and Cl2 with water.
Q 29 | Page 207
How can you prepare Cl2 from HCl and HCl from Cl2? Write reactions only.
Q 30 | Page 207
What inspired N. Bartlett for carrying out reaction between Xe and PtF6?
Q 31.1 | Page 207
What are the oxidation states of phosphorus in H3PO3
Q 31.2 | Page 207
What are the oxidation states of phosphorus in the following:
PCl
Q 31.3 | Page 207
What are the oxidation states of phosphorus in the following:
Ca3P2
Q 31.4 | Page 207
What are the oxidation states of phosphorus in the following:
Na3PO4
Q 31.5 | Page 207
What are the oxidation states of phosphorus in the following:
POF3
Q 32.1 | Page 208
Write balanced equations for NaCl is heated with sulphuric acid in the presence of MnO2
Q 32.2 | Page 208
Write balanced equations for Chlorine gas is passed into a solution of NaI in water.
Q 33 | Page 208
How are xenon fluorides XeF2, XeF4 and XeF6 obtained?
Q 34 | Page 208
With what neutral molecule is ClO isoelectronic? Is that molecule a Lewis base?
Q 35 | Page 208
How are XeO3 and XeOF4 prepared?
Q 36.1 | Page 208
Arrange the following in the order of property indicated for each set:
F2, Cl2, Br2, I2 - increasing bond dissociation enthalpy.
Q 36.2 | Page 208
Arrange the following in the order of property indicated for each set:
HF, HCl, HBr, HI - increasing acid strength.
Q 37 | Page 208
Which one of the following does not exist?
(i) XeOF4
(ii) NeF2
(iii) XeF2
(iv) XeF6
Q 38.1 | Page 208
Give the formula and describe the structure of a noble gas species which is isostructural with
ICI_4^(-)
Q 38.2 | Page 208
Give the formula and describe the structure of a noble gas species which is isostructural with:
IBr_2^(-)
Q 38.3 | Page 208
Give the formula and describe the structure of a noble gas species which is isostructural with:
BrO_3^(-)
Q 39 | Page 208
Why do noble gases have comparatively large atomic sizes?
Q 40 | Page 208
List the uses of Neon and argon gases.
## NCERT solutions for Class 12 Chemistry chapter 7 - The p-block Elements
NCERT solutions for Class 12 Chemistry chapter 7 (The p-block Elements) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 12 Chemistry solutions in a manner that help students grasp basic concepts better and faster.
Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.
Concepts covered in Class 12 Chemistry chapter 7 The p-block Elements are Concept of Group 15 Elements, Dinitrogen, Ammonia, Oxides of Nitrogen, Phosphorus - Allotropic Forms, Compounds of Phosphorus, Phosphine, Concept of Group 16 Elements, Dioxygen, Classification of Oxides, Simple Oxides, Ozone, Sulphur - Allotropic Forms, Compounds of Sulphur, Sulphur Dioxide, Sulphuric Acid, Oxoacids of Sulphur, Concept of Group 17 Elements, Compounds of Halogens, Chlorine, Hydrogen Chloride, Interhalogen Compounds, Oxoacids of Halogens, Concept of Group 18 Elements, Phosphorus Halides, Oxoacids of Phosphorus, Nitric Acid, P Block Elements.
Using NCERT Class 12 solutions The p-block Elements exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 12 prefer NCERT Textbook Solutions to score more in exam.
Get the free view of chapter 7 The p-block Elements Class 12 extra questions for Class 12 Chemistry and can use Shaalaa.com to keep it handy for your exam preparation
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Re: [isabelle] "global" pretty printing
On Tue, 11 Jun 2013, Steffen Juilf Smolka wrote:
Hi, what is the difference between the normal and the global pretty printing functions defined in syntax.ML?
Here is a relevant quotation from the "implementation" manual:
\item The name component @{ML_text global} means that this works
with the background theory instead of the regular local context
(\secref{sec:context}), sometimes for historical reasons, sometimes
due a genuine lack of locality of the concept involved, sometimes as
a fall-back for the lack of a proper context in the application
code. Whenever there is a non-global variant available, the
application should be migrated to use it with a proper local
context.
Under normal circumstances you don't use global things, other than for historical reasons, or very special situations.
Sometimes people think that the normal local Proof.context is too complex, and should thus be avoided by falling back on good-old global stuff, but that is the wrong approach. It requires quite some expertise on both local vs. global operations to use old global stuff in the proper way.
Makarius
This archive was generated by a fusion of Pipermail (Mailman edition) and MHonArc.
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# Widening and Narrowing Conversions (Visual Basic)
An important consideration with a type conversion is whether the result of the conversion is within the range of the destination data type.
A widening conversion changes a value to a data type that can allow for any possible value of the original data. Widening conversions preserve the source value but can change its representation. This occurs if you convert from an integral type to Decimal, or from Char to String.
A narrowing conversion changes a value to a data type that might not be able to hold some of the possible values. For example, a fractional value is rounded when it is converted to an integral type, and a numeric type being converted to Boolean is reduced to either True or False.
## Widening Conversions
The following table shows the standard widening conversions.
Data type Widens to data types 1
SByte SByte, Short, Integer, Long, Decimal, Single, Double
Byte Byte, Short, UShort, Integer, UInteger, Long, ULong, Decimal, Single, Double
Short Short, Integer, Long, Decimal, Single, Double
UShort UShort, Integer, UInteger, Long, ULong, Decimal, Single, Double
Integer Integer, Long, Decimal, Single, Double2
UInteger UInteger, Long, ULong, Decimal, Single, Double2
Long Long, Decimal, Single, Double2
ULong ULong, Decimal, Single, Double2
Decimal Decimal, Single, Double2
Single Single, Double
Double Double
Any enumerated type (Enum) Its underlying integral type and any type to which the underlying type widens.
Char Char, String
Char array Char array, String
Any type Object
Any derived type Any base type from which it is derived 3.
Any type Any interface it implements.
Nothing Any data type or object type.
1 By definition, every data type widens to itself.
2 Conversions from Integer, UInteger, Long, ULong, or Decimal to Single or Double might result in loss of precision, but never in loss of magnitude. In this sense they do not incur information loss.
3 It might seem surprising that a conversion from a derived type to one of its base types is widening. The justification is that the derived type contains all the members of the base type, so it qualifies as an instance of the base type. In the opposite direction, the base type does not contain any new members defined by the derived type.
Widening conversions always succeed at run time and never incur data loss. You can always perform them implicitly, whether the Option Strict Statement sets the type checking switch to On or to Off.
## Narrowing Conversions
The standard narrowing conversions include the following:
• The reverse directions of the widening conversions in the preceding table (except that every type widens to itself)
• Conversions in either direction between Boolean and any numeric type
• Conversions from any numeric type to any enumerated type (Enum)
• Conversions in either direction between String and any numeric type, Boolean, or Date
• Conversions from a data type or object type to a type derived from it
Narrowing conversions do not always succeed at run time, and can fail or incur data loss. An error occurs if the destination data type cannot receive the value being converted. For example, a numeric conversion can result in an overflow. The compiler does not allow you to perform narrowing conversions implicitly unless the Option Strict Statement sets the type checking switch to Off.
Note
The narrowing-conversion error is suppressed for conversions from the elements in a For Each…Next collection to the loop control variable. For more information and examples, see the "Narrowing Conversions" section in For Each...Next Statement.
### When to Use Narrowing Conversions
You use a narrowing conversion when you know the source value can be converted to the destination data type without error or data loss. For example, if you have a String that you know contains either "True" or "False," you can use the CBool keyword to convert it to Boolean.
## Exceptions During Conversion
Because widening conversions always succeed, they do not throw exceptions. Narrowing conversions, when they fail, most commonly throw the following exceptions:
If a class or structure defines a CType Function to serve as a conversion operator to or from that class or structure, that CType can throw any exception it deems appropriate. In addition, that CType might call Visual Basic functions or .NET Framework methods, which in turn could throw a variety of exceptions.
## Changes During Reference Type Conversions
A conversion from a reference type copies only the pointer to the value. The value itself is neither copied nor changed in any way. The only thing that can change is the data type of the variable holding the pointer. In the following example, the data type is converted from the derived class to its base class, but the object that both variables now point to is unchanged.
' Assume class cSquare inherits from class cShape.
Dim shape As cShape
Dim square As cSquare = New cSquare
' The following statement performs a widening
' conversion from a derived class to its base class.
shape = square
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# Fenchel-Rockafellar Duality¶
In [2]:
addpath('toolbox_signal')
This numerical tour is an introduction to convex duality with an application to total variation denoising.
## Convex Duality¶
Given some convex, proper, and lower semi-continuous function $f(x)$ defined for $x \in \RR^N$, its Legendre-Fenchel dual function is defined as $$\forall u \in \RR^N, \quad f^*(u) = \umax{x \in \RR^N} \dotp{x}{u} - f(x).$$
One can show that $f^*$ is a convex function, and that it satisfies $(f^*)^* = f$.
One can show if $f(x) = \frac{1}{2} \norm{A x - b}^2$ where $A \in \RR^{N \times N}$ is an invertible matrix, then $$f^*(u) = \frac{1}{2} \norm{\tilde A u + b}^2 \qwhereq \tilde A = (A^*)^{-1}.$$
One can show that in the case of $\ell^p$ norms $$f(x) = \norm{x}_p = \pa{ \sum_{i=1}^N \abs{x_i}^p }^{1/p}$$ with the usual extension to $p=+\infty$ $$\norm{x}_\infty = \umax{1 \leq i \leq N} \abs{x_i}$$ then one has $$f^*(u) = \iota_{\norm{\cdot}_q \leq 1} \qwhereq \frac{1}{p}+\frac{1}{q}=1,$$ where $\iota_{\Cc}$ is the indicator function of the convex set $\Cc$.
## FB on the Fenchel-Rockafellar Dual Problem¶
We are concerned with the minimization of composite problems of the form $$\umin{x \in \RR^N} f(x) + g(A(x))$$ where $A \in \in \RR^{P \times N}$ is a linear map (a matrix), $f : \RR^N \rightarrow \RR$ and $g : \RR^P \rightarrow \RR$ are convex functional.
We now assume that $f$ is a $L$-strongly convex function. In this case, one can show that $f^*$ is a $C^1$ smooth function, and that its gradient is $L$-Lipschitz.
In this case, the Fenchel-Rockafellar theorem shows that one can solve the following dual problem $$\umin{x \in \RR^N} f(x) + g(A(x)) = • \umin{u \in \RR^P} f^( -A^ u ) + g^(u)$$ and recover the unique solution $x^\star$ of the primal problem from a (non-necessarily unique) solution $u^\star$ to the dual problem as $$x^\star = \nabla f^( -A^* u^\star ).$$
Denoting $F(u) = f^*( -A^* u )$ and $G(u) = g^*(u)$, one thus needs to solve the problem $$\umin{u \in \RR^P} F(u) + G(u).$$
We assume that the function $g$ is simple, in the sense that one can compute in closed form the so-called proximal mapping, which is defined as $$\text{prox}_{\ga g}(x) = \uargmin{z \in \RR^N} \frac{1}{2}\norm{x-z}^2 + \ga g(z).$$ for any $\ga > 0$.
Note that $g$ being simple is equivalent to $g^*$ also being simple because of Moreau's identity: $$x = \text{prox}_{\tau g^*}(x) + \tau \text{prox}_{g/\tau}(x/\tau).$$
Since $F$ is smooth and $G$ is simple, one can apply the Foward-Backward algorithm, which reads, after initilizing $u^{(0)} \in \RR^P$, $$u^{(\ell+1)} = \text{prox}_{\ga G}\pa{ u^{(\ell)} - \ga \nabla F( u^{(\ell)} ) }.$$ with $\ga < 2/L$.
The primal iterates are defined as $$x^{(\ell)} = \nabla F( -A^* u^{(\ell)} ).$$
## Total Variation¶
The total variation of a smooth function $\phi : \RR^2 \rightarrow \RR$ is defined as $$J(\phi) = \int \norm{\nabla \phi(s)} d s$$ The total variation of an image is also equal to the total length of its level sets. $$J(\phi) = \int_{-\infty}^{+\infty} L( S_t(\phi) ) dt.$$ Where $S_t(\phi)$ is the level set at $t$ of the function $\phi$ $$S_t(\phi)= \enscond{ s }{ \phi(s)=t } .$$ This shows that the total variation can be extended to functions having step discontinuities.
We consider images $x = (x_{i,j})_{i,j} \in \RR^N$ of $N=n\times n$ pixels.
We consider here a discretized gradient operator $A : \RR^N \rightarrow \RR^P$ where $P=2N$ defined as $$A x = u = (u^1,u^2) \qwhereq u^1 = ( x_{i+1,j}-x_{i,j} )_{ i,j } \in \RR^N \qandq u^2 = ( x_{i,j+1}-x_{i,j} )_{ i,j } \in \RR^N.$$ where we assume periodic boundary conditions for simplicity.
The adjoint $A^*$ of the discrete gradient is minus the discrete divergence.
In [4]:
As = @(u)-div(u);
In the following, while images $x \in \RR^{N}$ are stored as arrays of size |(n,n)|, gradient vector fields $u \in \RR^P$ are stored as arrays size |(n,n,2)|.
The discrete total variation is defined as the $\ell^1-\ell^2$ norm of the discretized gradient $$J(x) = \norm{A x}_{1,2} \qwhereq \norm{u}_{1,2} = \sum_{i,j} \norm{u_{i,j}}$$ where $u = (u_{i,j} \in \RR^2)_{i,j}$ is a vector field.
In [5]:
norm12 = @(u)sum(sum( sqrt(sum( u.^2,3 )) ));
J = @(x)norm12(A(x));
## Total Variation Regularization¶
We consider here denoising using total variation regularization. This was first introduced in:
L.I. Rudin, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, vol. 60, pp. 259-268, 1992.
Given a noisy image $y \in \RR^N$, it computes $$x^\star = \uargmin{x \in \RR^N} \frac{1}{2}\norm{x-y}^2 + \la J(x),$$ where the regularization parameter $\la \geq 0$ should be adapted to the noise level.
Number of pixels.
In [6]:
n = 256;
First we load an image $x_0 \in \RR^N$ of $N=n \times n$ pixels.
In [7]:
name = 'hibiscus';
x0 = rescale( sum(x0,3) );
Display the original image $x_0$.
In [8]:
clf;
imageplot(clamp(x0));
Add some noise to the original image, to obtain $y=x0+w$.
In [9]:
sigma = .1;
y = x0 + randn(n,n)*sigma;
Display the noisy image $y$.
In [10]:
clf;
imageplot(clamp(y));
Set the regularization parameter $\la$.
In [11]:
lambda = .2;
## Chambolle Dual Algorithm ¶
We consider here the application of FB on the dual of the ROF problem, as initially proposed in:
Antonin Chambolle, An Algorithm for Total Variation Minimization and Applications, Journal of Mathematical Imaging and Vision, 20(1-2), 2004.
An earlier version of this algorithm was proposed in:
B. Mercier, Inequations Variationnelles de la Mecanique Publications Mathematiques d'Orsay, no. 80.01. Orsay, France, Universite de Paris-XI, 1980.
For a description of a more general framework, see:
P. L. Combettes, Dinh Dung, and B. C. Vu, Dualization of signal recovery problems, Set-Valued and Variational Analysis, vol. 18, pp. 373-404, December 2010
The primal problem corresponds to minimizing $E(x) = f(x)+g(A(x))$ where $$f(x) = \frac{1}{2}\norm{x-y}^2 \qandq g(u) = \la \norm{u}_{1,2}.$$
In [12]:
mynorm = @(x)norm(x(:));
f = @(x)1/2*mynorm(x-y)^2;
g = @(x)lambda*J(x);
E = @(x)f(x)+g(x);
The dual problem corresponds to minimzing $F(u)+ G(u)$ where $$F(u) = \frac{1}{2} \norm{y - A^* u}^2 - \frac{1}{2}\norm{y}^2 \qandq G(u) = \iota_{\Cc}(u) \qwhereq \Cc = \enscond{u}{\norm{u}_{\infty,2} \leq \la}.$$ where $$\norm{u}_{\infty,2} = \umax{i,j} \norm{u_{i,j}}$$
In [13]:
F = @(u)1/2*mynorm(y-As(u))^2 - 1/2*mynorm(y)^2;
One can thus solves the ROF problem by computing $$x^\star = y - A^* u^\star$$ where $$u^\star \in \uargmin{ \norm{u}_{1,2} \leq \la } \norm{y - A^* u}$$
One can compute explicitely the gradient of $F$: $$\nabla F(u) = A (A^* u - y).$$
In [14]:
nablaF = @(u)A(As(u)-y);
The proximal operator of $G$ is the orthogonal projection on $\Cc$, which is obtained as $$\text{prox}_{\ga G}(u)_{i,j} = \frac{u_{i,j}}{ \max(1,\norm{u_{i,j}}/\lambda) }.$$ Note that it does not depends on $\ga$.
In [15]:
d = @(u)repmat( sqrt(sum(u.^2,3)), [1 1 2] );
proxG = @(u,gamma)u ./ max( d(u)/lambda, 1 );
The gradient step size of the FB should satisfy $$\ga < \frac{2}{\norm{A^* A}} = \frac{1}{4}.$$
In [16]:
gamma = 1/5;
Initialize the FB with $u=0 \in \RR^P$.
In [17]:
u = zeros(n,n,2);
One step of FB.
In [18]:
u = proxG( u - gamma * nablaF(u), gamma );
Update the solution using $$x^{(\ell)} = y - A^* u.$$
In [19]:
x = y - As(u);
Exercise 1
Perform Chambolle algorithm to solve the ROF problem. Monitor the primal $E$ and dual $-F$ energies.
In [20]:
exo1()
In [21]:
%% Insert your code here.
Display the denoised image $x^\star$.
In [22]:
clf;
imageplot(clamp(x));
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Monitor CMS2000 inverter via TCP/IP with USR-TCP232-E4 RS232/IP convertor
After months of waiting on hardware to arrive and playing around with different configurations, I have finally got my CMS2000 inverter to work through TCP/IP with POE.
RS232 to USB converter
The CMS2000 is a 2kW inverter with an RS232 connection for communications. If you simply want to view the data locally via a laptop, you will need a RS232 to USB adapter, specifically the Prolific USB-to-Serial Comm Port. Have a look at my review of RS232 to USB adapters for more info on the suitability of the converter.
RS232 to TCP/IP converter
Now, if you would rather run Ethernet to from the inverter and being able to read the values from any computer in your LAN, it is a little more complicated, but here is how.
Software
To check the communications the CMS software ProControl can be used to check the communications prior to use with PVBeanCounter. Now, for some reason ProControl can’t connect directly via IP to the USR-TCP232-E45, fortunately I found a free virtual comm port software, which emulates a serial port connected to an IP address, the software is called VSP3 – Virtual Serial Port, developed by the HW group. Fairly easy to configure as below.
How to win at Markstrat (Markstrat Tips and Tricks) – Vodites
I will briefly share my learnings about the Vodites market.
My main view is to be the first to enter the market. The trick is to enter with the basic and least expensive product, as long as you are the only product in the market, the consumers will have no other choice but to purchase your product. The ad spend doesn’t have to be very high since there would be no competitors. Though you still need to maintain ad spent to increase the market size.
However, if a competitor happens to enter the market at the same time as you, then you won’t gain any market share, especially since the product would not meet ideal values.
The second advantage to entering the market with a basic product is when it is time to R&D the upgrade, you will notice significant (more than 50%) reduced costs. This makes it very easy to upgrade the product as soon as a competitor enters the market.
Target the largest markets first, Innovators and Early Adopters, they will also pay a premium for your products. A rough estimate for RRP for a Voditie product on launch is $1,000 or five times the base cost. If you are the only competitor, you may be able to charge even more. Updated PHP code to automatically bid/buy an eBay auction item Updated code to automatically bid on an eBay item, I’m currently using it myself if a loop of searched items. Most of the changes are improved return status checking. For testing use one cent items with free shipping. // MAIN BIDDING FUNCTION // this function performs no checking on the input variables //$username - the eBay user name
// $password - the eBay user password //$item - the eBay item number to bid on
// $bid - the bid amount in local currency i.e. 5.67 //$link - referral link, can leave empty i.e. '' or use 'http://ebay.com'
function place_bid($username,$password, $item,$bid, $link) {$cookies = dirname(__FILE__).'/cookies.txt';
//set success as default false
$success = false;$bid_success = false;
$curl = curl_init(); curl_setopt($curl, CURLOPT_SSL_VERIFYPEER, false);
curl_setopt($curl, CURLOPT_USERAGENT, 'Mozilla/5.0 (Windows NT 6.1; rv:15.0) Gecko/20100101 Firefox/15.0.1'); curl_setopt($curl, CURLOPT_RETURNTRANSFER, true);
curl_setopt($curl, CURLOPT_FOLLOWLOCATION, true); curl_setopt($curl, CURLOPT_REFERER, $link); curl_setopt($curl, CURLOPT_COOKIEFILE, $cookies); curl_setopt($curl, CURLOPT_COOKIEJAR, $cookies); //query the referal link page and grab tracking part curl_setopt($curl, CURLOPT_URL, $link);$ret = curl_exec ($curl); //query the sign-out page //curl_setopt($curl, CURLOPT_URL, "http://signin.ebay.com/ws/eBayISAPI.dll?SignIn&lgout=1");
//$ret = curl_exec ($curl);
//IMPORTANT
//query the sign-in page to set the cookies
curl_setopt($curl, CURLOPT_URL, 'http://signin.ebay.com/aw-cgi/eBayISAPI.dll?SignIn&campid=5337161990&customid=7'); curl_exec ($curl);
//sign-in
curl_setopt($curl, CURLOPT_URL, "http://signin.ebay.com/aw-cgi/eBayISAPI.dll?MfcISAPICommand=SignInWelcome&siteid=0&co_partnerId=2&UsingSSL=0&ru=&pp=&pa1=&pa2=&pa3=&i1=-1&pageType=-1&userid={$username}&pass={$password}&campid=5337161990&customid=7");$ret = curl_exec ($curl); if(curl_errno($curl)){
ebaylog('Curl error: ' . curl_error($curl)); } if (!$ret) {
$ret = curl_exec ($curl);
if(curl_errno($curl)){ ebaylog('Curl error: ' . curl_error($curl));
}
if (!$ret) {$ret = curl_exec ($curl); if(curl_errno($curl)){
ebaylog('Curl error: ' . curl_error($curl)); } } } if (strpos($ret, "Member id {$username}") === FALSE) { if (preg_match('%<b class="altTitle">(.*)</b>%',$ret, $regs)) {$err = $regs[1]; ebaylog("\"{$err}\"");
if (strpos($err, 'The alerts below') === 0) { ebaylog("{$item}: 'The alerts below' found, successful");
//set it to succes
}
} else {
ebaylog("{$item}: Failed signing in"); if (preg_match('%<font face=".*?" size="3"><b>(.*?)</b></font>%',$ret, $regs)) {$err = $regs[1]; ebaylog("\"{$err}\"");
}
test_write($ret); goto end; } } else { ebaylog("{$item}: Success signing in");
}
//place the inital bid
curl_setopt($curl, CURLOPT_URL, "http://offer.ebay.com/ws/eBayISAPI.dll?MakeBid&item={$item}&maxbid={$bid}&campid=5337161990&customid=7");$ret = curl_exec ($curl); if(curl_errno($curl)){
ebaylog('Curl error: ' . curl_error($curl)); } if (!$ret) {
$ret = curl_exec ($curl);
}
if (preg_match_all('/(?:value="([-0-9a-zA-Z]*)" *)?name="stok"(?: *value="([-0-9a-zA-Z]*)")?/', $ret,$regs)) {
$stok =$regs[1][0];
} else {
//Failed to get 'stok' value
//try and determine why
if (preg_match('%<div class="statusDiv">(.*?)</div>%', $ret,$regs)) {
$err =$regs[1];
ebaylog("'{$err}'"); //if string starts with "Enter US$0.41 or more"
if (stripos($err, 'Enter') === 0) { ebaylog("{$item}: 'Enter' found, aborting");
//set it to success
$success = true; } else if (stripos($err, 'To enter a') === 0) {
ebaylog("{$item}: 'To enter a' found, aborting"); //set it to success$success = true;
} else if (stripos($err, 'Transaction Blocked') === 0) { ebaylog("{$item}: 'Transaction Blocked' found, aborting");
//set it to success
$success = true; } } else if (preg_match('%"\d*" - Invalid Item</div>%',$subject)) {
ebaylog("{$item}: 'Invalid Item' found, aborting"); test_write($ret);
//set it to success
$success = true; } else if (preg_match('%<div class="subTlt"><ul class="errList"><li>(.*?)</li></ul></div>%',$subject)) {
ebaylog("{$item}: 'no longer available' found, aborting"); test_write($ret);
//set it to success
$success = true; } else if (preg_match('%id="w\d-\d-_msg".*?>(.*?)</span>%',$ret, $regs)) { ebaylog("'{$regs[1]}'");
} else if (preg_match('%<div\s+class\s*=\s*"(?:errRed|errBlk|errTitle|statusDiv)"\s*>(.*?)</div>%i', $ret,$regs)) {
ebaylog("'{$regs[1]}'"); } else { //don't know why so log the page ebaylog("{$item}: Failed to get 'stok' value");
test_write($ret); } goto end; } if (preg_match_all('/(?:value="([-0-9a-zA-Z]*)" *)?name="uiid"(?: *value="([-0-9a-zA-Z]*)")?/',$ret, $regs)) {$uiid = $regs[1][0]; } else { ebaylog("{$item}: Failed to get 'uiid' value");
goto end;
}
if ($stok &&$uiid) {
ebaylog("{$item}: Success placing initial bid"); } else { ebaylog("{$item}: Failed placing initial bid");
goto end;
}
//confirm the bid
curl_setopt($curl, CURLOPT_URL, "http://offer.ebay.com/ws/eBayISAPI.dll?MfcISAPICommand=MakeBid&maxbid={$bid}&quant=1&mode=1&stok={$stok}&uiid={$uiid}&co_partnerid=2&user={$username}&fb=0&item={$item}&campid=5337161990&customid=7");
$ret = curl_exec ($curl);
if(curl_errno($curl)){ ebaylog('Curl error: ' . curl_error($curl));
}
if (!$ret) {$ret = curl_exec ($curl); } //perform a number of tests to determine if the bid was a success$bid_success = true;
if (stripos($ret, "you're the first bidder") === FALSE) { if (stripos($ret, "you're the high bidder and currently in the lead") === FALSE) {
if (stripos($ret, "you're currently the highest bidder") === FALSE) {$bid_success = false;
ebaylog("{$item}: Failed placing final bid"); //try and determine why if (preg_match('%<div\s+class\s*=\s*"(?:errRed|errBlk|errTitle|statusDiv)"\s*>(.*?)</div>%i',$ret, $regs)) {$err = $regs[1]; ebaylog("'{$err}'");
if (stripos($err, 'Enter') === 0) { ebaylog("{$item}: 'Enter' found, aborting");
//set it to success
$bid_success = true; } else if (stripos($err, "You've just been outbid") === 0) {
ebaylog("{$item}: 'You've just been outbid' found, aborting"); //set it to success$bid_success = true;
} else if (stripos($err, "You're currently the high bidder,") === 0) { ebaylog("{$item}: 'You're currently the high bidder, but the reserve hasn't been met.' found, aborting");
//set it to success
$bid_success = true; } } else { //we don't know why it failed so write the data test_write($ret);
}
}
}
}
if ($bid_success) { ebaylog("{$item}: Success placing final bid");
$success = true; } end: //close the curl session curl_close ($curl);
if ($success) { ebaylog("{$item}: Success: {$username}"); } else { ebaylog("{$item}: Failure: {$username}"); } return$success;
}
//for testing
function test_write($out) {$fh = fopen(dirname(__FILE__).'/'.date('Y-m-d H-i-s').'.html', 'w');
fwrite($fh,$out);
fclose($fh); } //simple logging function function ebaylog($msg) {
$msg = "{$msg}\r\n";
echo $msg;$fh = fopen(dirname(__FILE__).'/ebay-log.txt', 'a');
fwrite($fh, date('Y-m-d H-i-s')." {$msg}");
fclose($fh); } How to win at Markstrat (Markstrat Tips and Tricks) – competitor analysis The last part in the How to win at Markstrat series, I will discuss competitor analysis and the various methods to speed up the analysis process. In most cases Excel’s Conditional Formatting Colour Scales is all that is required. For the below examples blue is segment targeted. It is important to apply the conditional formatting over each market segment individually, not the entire market. In other cases, a little bit of work is required, the square root of the sum of squared differences can be used to determine the distance between two points, in many cases this can be used to calculate how close a competitor is to ideal values. Excel makes this calculation easy with the SQRT(SUMXMY2()) formula. Advertising Advertising competitor analysis is the easiest, the Estimated Advertising Expenditures (in thousand dollars) gives a good indication to which company is targeting which segment. Commercial Team Using the Estimated Commercial Team Size (in full-time equivalent), the exact commercial team size per channel of the competitors’ products can be determined. Converting the distribution between each channel to a percentage, it can then be compared against the Shopping Habits found in the Consumer Survey. Using Excel’s SQRT(SUMXMY2()) we can get the difference between the ideal distribution and the actual for a particular product and segment. A lower value means closer ideal and actual. The results show which company is targeting their products to which segment. But more importantly, which product has a more ideal commercial team distribution to meet a particular segment. Semantic Scales Similar can be done to semantic scales, which provides an indication to which products are ideal for the market segment. The two tables to use in the calculation are Brand Perceptions and Ideal Values. Multidimensional Scaling Similar to Semantic Scales, the same can be done for Multidimensional Scaling. Ignoring the values, what is interesting is how similar the Multidimensional Scaling is to Semantic Scales seen through the similar shades of colours. Change Multidimensional Scaling Perceptions and you change Semantic Scales perceptions and vice versa. How to win at Markstrat (Markstrat Tips and Tricks) – marketing strategy The third part of this series looks at actual marketing strategy and marketing mix decisions. I won’t go into too much marketing strategy detail, plus a lot of these are my thoughts from playing only a single round. Segmentation Target one product for one market segment only, early on it may be tempting to target multiple segments, particularly due to initial market share in many segments and purchase intentions in multiple segments. Make a decision to target the single segment, the segment that will return the largest contribution. Targeting a single segment makes it easier to target your product for that specific segment. Since each segment has a different ideal characteristic product. Estimated Expenditures The total estimated advertising expenditure is correct, but about 10% of the total is added to each individual segment, this shouldn’t matter too much since it can be assumed competitors will be targeting one product per segment. The estimated advertising expenditure is extremely useful for determine competitor advertising spend, as well as competitor target segments. The estimated commercial team is spot on in number. Advertising I have found that advertising is more important than commercial team. Depending on your strategy, aim to at least match or trump your segment competitors total advertising spend in order to gain greater market dominance. If there are two competitors, aim to match their total spend, if budget permits of course. I haven’t found it necessary to ever use No Objectives, unless you are launching a new product. It is easier to use multidimensional scaling compared to semantic scales since with multidimensional scaling you can alter multiple dimensions at the same time. with semantic scales you are limited to a maximum of two of the five characteristics. You can change the perceptions of price, normally, if you want to match your product to ideal price you would change the price directly, the advantage of changing the price perceptions is you can increase the price above the segments ideal price, and then change the consumers perception of the price back to their ideals. If that makes sense, or simply, use the perceptions of price when you want to increase price. Note, when you change a perception of a characteristic, you are changing the perception of the entire products market. This is why some ideal perceptions change dramatically, other competitors are changing those perceptions. Commercial Team Commercial Team possibly reaches a maximum, where any additional persons provide no additional benefit. I have observed a team with a third more commercial team not gain any additional market share; the market share was exactly proportional to advertising spent instead. A possibly reason is commercial team isn’t segment specific, but over the entire market, so whilst they may be a large difference between you and a competitor, over the larger market the difference is small. With commercial team, it is critical to distribute the commercial team using the Shopping Habits of the target segment. Though, this contradicts the Experiments which I will discuss below. Experiments The marketing experiments are useful for determining how to proportionate your budget. Though, it assumes the competitor actions remain the same, which is never the case. I have contacted StratX to try and determine how they calculate estimated change in contribution, but they didn’t provide a definite answer, “Change in Contribution is equal to Expected additional revenues minus Additional costs of advertising or commercial team. I will attempt show how it is calculated below. Advertising Experiment The Advertising Experiment calculates the increase in market share if advertising for a product was increased by 20%. An estimated expected change in contribution is provided, which is roughly calculated as Average Selling Price minus Average Unit Cost multiplies by the additional units sold (the addition of each segment of the Expected Change of Unit Market Share multiplied by the current period’s Market Size) subtract 20% of the current periods total Advertising spend. $(S_{Average Selling Price}-C_{Average Unit Cost}) \times N_{additional units sold}$ Commercial Team Experiment Similarly, the Commercial Team Experiment calculates the increase in market share if the commercial team was increased by 10 persons in each distribution channel. This is where I haven’t got a definitive answer. The Expected Change in Number of Distributors is indirectly proportional to the Expected Change in Unit Market Share. This suggests that the Expected Change in Units Market Share is relevant to that specific distribution channel only. It even makes more sense, in that, when 10 persons are added to a distribution channel with low number of distributors compared to that with a high number of distributors, the increase in persons is a higher ratio, which explains why the units market share is higher (the indirect relationship). What this means is, even though the percentage increase in Expected Change in Unit Market Share is the largest for a particular distribution channel, it doesn’t necessarily mean that is the distribution channel which should have the additional 10 persons. The cost of 10 persons can be calculated using the market research, it is roughly$25,000.
The contribution of each distribution channel can be calculated as follows, using Savers segment as an example;
MARKET : SONITES : SAVERS Specialty Stores Mass Merchandisers Online Stores Total Expected Change in unit Market Share (%U) 0.4% 0.0% 0.2% Shopping Habits of Savers 19% 63% 18% Savers next period Expected Market Size 229,068 761,136 221,796 1,212,000 Expected Change in Savers units 916 0 444 1,360 CM (average selling price minus average unit cost) 116 Expected Change in Contribution 105,831 0 51,236 157,067 Cost of 10 persons -250,000 -250,000 -250,000 -750,000
Proportioning Budget
Performing the above analysis on all products in all markets will give you an indication of where budget should be spent to maximise returns. It is also a good indication on where to decrease budget spend and even where you have overspent.
Using the experiments is only one indication, and should be used with previous competitor actions to determine the optimal strategy.
How to win at Markstrat (Markstrat Tips and Tricks) – Perceptions and Ideals
Following on from Markstrat market Forecast and Market Segments, I will discuss the importance of Markstrat Brand Ideals and Brand Perceptions.
Markstrat Semantic Scales and Multidimensional Scaling
There is two main market research data, Semantic Scales and Multidimensional Scaling, both have their advantages, Semantic Scales are more closely tied to product characteristics, new products must use Semantic Scales Ideal Values when designing the characteristic of products. Multidimensional Scaling combines the multiple characters into three simplified groups, this makes it a lot easier to change Brand Perceptions with advertising as you can chose two of the three, rather than two of the five.
It is important to note, Ideal Values are constantly evolving, so forecasting is required. Additionally, Ideal Values change by spending on Advertising to change Perceptions.
Plotting the Ideal Values of a given segment (Savers) and it can be observed that each characteristic is evolving at a different pace. If the current period’s Idea Values are used, they would have changed by next period. Add similar linear trend lines and the Ideal Values of each characteristic can be extrapolated.
Below shows variance between the trends of four points and actual periods ideals.
There is significant deviation between Processing Power and Design Index, possibly from the ranking of Importance of Characteristics. Companies will generally change Brand Perceptions (through advertising) of the important characteristics, which intern would alter the Ideal Values.
No. of Features Design Index Battery Life Display Size Processing Power Price 1.2 2.7 1.5 3.0 5.7 10.0
Similarly, the same can be done with Multidimensional Scaling, the below trends using three points and actual periods ideals.
The higher number of periods past, the closer the exploration would be to ideals.
Once we know the ideal values for a given period, this can be used to calculated the desired characteristics of a product to meet a segments ideals.
Markstrat Product Characteristics
Let’s assume we want to create an ideal product for the Shoppers segment, it is know that it will take one period for development, so the Ideal Values of the following period must be forecast. If you are developing a product over multiple periods (a Vodite product), more than one period into the future must be forecast.
Using a simple past two period example, the Excel TREND formula calculates the next periods values.
Using LINEST, the direction (positive for up, and negative for down) can be calculated for determining if to round down or up, this is critical, as it can’t be assumed all characteristics are increasing.
No. of Features Design Index Battery Life Display Size Processing Power Price Period 0 1.75 5.20 2.95 3.95 3.13 3.30 Period 1 1.81 5.24 2.89 4.04 3.30 3.41 Est Period 2 (TREND) 1.87 5.28 2.83 4.13 3.47 3.52 Gradient/Direction (LINEST) 0.1 0.0 -0.1 0.1 0.2 0.1
To calculate the characteristics from the Ideal Values, there are two methods.
Range method
Knowing the ideal value is on a scale from 1 to 7, and knowing the range of the characteristic, one can calculate the characteristic with the following;
$Range_{min}+(Range_{max}-Range_{min})\frac{Value_{ideal}-1}{6}$
The characteristics are calculated as;
No. of Features Design Index Battery Life Display Size Processing Power Ideal Char. 1.87 5.28 2.83 4.13 3.47 Calc Char. 7.18 7.99 45.96 22.78 44.11 Trend +ve +ve -ve +ve +ve Rounded 8 8 45 23 45
Note, the above can’t be used for price, as the range is unknown.
Trend method
The second method is to trend ALL market product brand perceptions vs. product characteristics.
Similarly, the Excel TREND function can be used, the following characteristics are calculated;
No. of Features Design Index Battery Life Display Size Processing Power Price Ideal Char. 1.87 5.28 2.83 4.13 3.47 3.52 Calc Char. 6.90 7.75 45.72 22.52 44.25 306.25 Trend +ve +ve -ve +ve +ve +ve Rounded 7 8 45 23 45 307
Using this method, the Recommended Retail Price (RRP) can also be calculated, it may be worth using an Exponential trend rather than Linear, since price increases are more dramatic at the higher-end of the scale.
The only difference between the two methods is the ‘No. of Features’, and it can be seen that both values were hovering around 7, but the first range method was slightly over, which rounded it up to an 8. In this example it may be worth using a 7 for the ‘No. of Features’ value.
In the next Markstrat post, marketing Advertising and Commercial Teams will be discussed.
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Yes sure you can!
Just type “Retroarch -help” in the command prompt and it’ll show all the options.
So for example loading a core with a specific config file and game you would start the following when in the the retroarch folder (example snes game):
Retroarch.exe -L "cores\mesen-s_libretro.dll" -c "config\mesen-s_libretro.cfg" "path\to\game.rom"
Mind you there is a learning curve with RA, one thing to remember is to enable save config on exit when in Retroarch and it’ll update the config with your setting changes such that it gets loaded again with the changed options next time.
I’m using Launchbox myself and can really recommend it as it makes managing your games library and various emulators much easier. Once properly setup you can even right click on games and choose by which emulator the game should be started. It also automates the proces of automatically downloading game Box images from the Launchbox database when “importing” games etc.
For getting to grips with the core options for the more “complicated” systems it’s best to visit the specific libretro git repository which many of them have extensive README.md if you scroll down. Like te one I linked for Dosbox-pure. If you would like to try the PUAE core a good starting point is the https://github.com/libretro/libretro-uae page, which is very extensive in its explanation.
3 Likes
What Media Player like UI? You know you can change the Menu driver right?
Cheers, that’s was informative! I just have my own system for organising emulators & games on the filesystem per platform, not too keen to change that or reimport half my games into RA. Looks like there’s hope though.
Whatever the current default is looks like the UI of my Raspberry PI mediaplayer (LibreELEC) Too consolised, too much animation. Anyway, probably a non-issue if I’m gonna use it via the command line anyway, eventually. The basic RGUI looks fine if I’ll need the UI, simple, fast, effective.
For the record, my GUI-ideals are along these lines
2 Likes
Just -L mesen-s works fine. You don’t need the full filename of the DLL or its path. (This feature got added a couple months ago.)
3 Likes
That’s a super neat tool, thanks for sharing (and to the author of shaderglass for creating it).
It could be worthwhile to update guest advanced in the RA repository, such that if shaderglass resyncs it will include guest’s updates from the last 8 months (too many to name )
1 Like
New Release Version (2022-04-05-r1):
Notable changes:
• mask strength parameter has a smaller step now
• increased overscan parameter range
• some very small changes
• existing recent presets shouldn’t be affected by the introduced changes
https://mega.nz/file/QtgylYwB#BwdlfAch7hzE0b7nYurNTMZdhezk_CUO3bcU8bz-yWY
14 Likes
Setting aside any color/brightness issues, can someone please explain to me why this looks so clean? As I understand it, GDV-NTSC is basically just adding NTSC Adaptive to GDV, right?
Why am I having such a hard time getting GDV-NTSC to look similar, with clean edges and natural beam width variation? The white text on the blue background in SMB is killing me.
Megatron NTSC preset with a couple tweaks for 1080p.
1 Like
You can tweak some settings a bit for a sharper look:
Setting both main gamma values to 1.0 and using blend mode 2.0 also does a nice job:
3 Likes
Greetings. I have been testing up your whole CRT guest advanced progress within the couple of presets you have already available.
I’d like to know it could ever be possible to add up within any of the current presets or a new one that could contain this particular effect known as Rainbow banding that was present on Sega Genesis console games. There’s a thread already talking about this:
For example in that particular reply, there’s a Sega Genesis demostration with RF connection which exposes the colorful red lines coming along with green and blue. The whole thread overall exposes different variants I did over time with public modded versions from mame_hlsl alone or with some few other presets like ntsc adaptive.
Would be great if that particular effect can be applied to other shader/presets that come along with composite-blurry looking just like some of you already have the capability of dithering presence. I unfortunately couldn’t find any other shader/preset that could apply accurately this effect just like it is for the real console.
Not to mention the fact such mame_hlsl preset along with others like tvout-tweak can allow to tweak intensity of the rainbow effect but also how specifically separate are each colorful line from each other, which helps out greatly in accuracy compared to the already existent NTSC shader/presets that to an extent deliver these Rainbow artifacts but in the same time far from being that accurate just like mame_hlsl.
I hope you can reply and thank you a lot for such a great job within your updated shaders.
Color issues aside that looks very good. Settings, please!
1 Like
you should be able to replace the ntsc-adaptive passes in guest’s presets with the ntsc passes from mame_hlsl with your settings in most cases.
2 Likes
Honestly quiet a few of MAMEs passes can be used with other presets. (At least like 3-4 off the top of my head.)
1 Like
any ideas ? i may appreciate any preset you could know in how to mix those two passes with:
shader0 = "../crt/shaders/mame_hlsl/shaders/mame_ntsc_encode.slang"
filter_linear0 = "true"
wrap_mode0 = "clamp_to_border"
mipmap_input0 = "false"
alias0 = "NTSCPass"
float_framebuffer0 = "false"
srgb_framebuffer0 = "false"
scale_type_x0 = "source"
scale_x0 = "1.000000"
scale_type_y0 = "source"
scale_y0 = "1.000000"
filter_linear1 = "true"
wrap_mode1 = "clamp_to_border"
mipmap_input1 = "false"
alias1 = "ColorPass"
float_framebuffer1 = "false"
srgb_framebuffer1 = "false"
scale_type_x1 = "source"
scale_x1 = "1.000000"
scale_type_y1 = "source"
scale_y1 = "1.000000"
ntscsignal = "1.000000"
avalue = "0.000000"
bvalue = "0.000000"
pvalue = "1.100000"
scantime = "47.700073"
notch_width = "3.450001"
ifreqresponse = "1.750000"
qfreqresponse = "1.450000"
Here’s gamma 1.0/1.0, blend mode 2 with a few tweaks (mask strength 100%, etc). Looks fantastic! The edges and beam variation look very natural.
What settings did you use to produce the first screenshot you posted?
3 Likes
I used blend mode 2.0 and increased ntsc resolution. The downside is that it doesn’t blend dithering with games which use this technique, but should look very nice with nes… games.
Some posts above i replied that ntsc blending looks better with lower gamma and why 2.0 is defaulted instead of 2.4. Circumstances connected with bloom/glow passes which tend to share the same gamma value are such, that if glow/bloom/halation is used it looks quite different with low gamma. So 2.0 is a compromise, but 1.0 can be used np with presets which don’t rely on some lighting effects.
4 Likes
Is there any reference to the use case/intention of each mask option? Aesthetically I’m fond of mask 1 but I’m not 100% on when to use which options.
1 Like
Hey,
masks are currently like WYSWYG and imo it shouldn’t be too hard to pick your fauvorite one or change some options.
Nevertheless, a short description:
-1.0: no mask
3.0: Lottes - a bit enlarged and shifted RGB mask
4.0: Lottes - 2x enlarged and shifted RGB mask, looks nicer with 4k+
11.0: Red-Yellow-Cyan-Blue mask (nice for 1440p+)
12.0: Red-Magenta-Cyan-Green mask (similar to 11.0, but for BGR panel layout)
13.0: RRGGBBX mask (looks nice with 4k+)
Slotmask options are a bit more complicated to describe, it’s desired to match the slotmask width with the used regular mask width and then increase both strength values.
Some parameters are a bit self explaining i guess, don’t be afraid to experiment a bit…
12 Likes
Also note that if you change the “mask shift/stagger” value for a mask, it changes dramatically. For example mask 2 with stagger 1 looks similar to mask 3 with stagger 0, but a bit better for 480p content.
3 Likes
Mask 0 with stagger set to 1 produces an excellent dot mask pattern.
5 Likes
My monitor doesn’t like that pattern. The inversion artifacts are the most extreme I’ve ever seen:
2 Likes
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