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Recently, I was taking up this challenge and choose my favorite language 'Ruby' to do it. My following solution got accepted (Gist).
For each test case, I am to reverse two numbers, add them, and print the reverse of the sum. Reversing means taking the base-10 digits of a number in reverse order, stripping any leading or trailing zeroes.
### Code
cases = gets.chomp.to_i
if cases.zero?
puts "Enter number > 0"
exit
end
def reverse_num(num)
num.to_s.reverse.to_i
end
sum = 0
data.each do |rec|
sum += reverse_num(rec)
end
reverse_num(sum)
end
results = []
cases.times do |index|
input_str = gets.chomp
nums = input_str.split(' ').map(&:to_i)
end
results.each { |e| puts e }
### End of Code
It showed that I have used 7.3MB memory which I don't have any idea.
I know this is not the optimized solution. I have used lots of looping which could be minizied. Could you review it and help me to optimize it?
• My guess is that the 7.3MB are a fixed memory consumption when starting the Ruby Virtual Machine. My trivial solution to "TEST - Life, the Universe, and Everything" alo consumed 7.3MB. – Cristian Lupascu Apr 10 '15 at 7:52
• Side note, the call to valid_numeric_input? doesn't affect the program at all. – Jay Mitchell Apr 10 '15 at 14:27
While your performance limits may be satisfied by producing your results as they are available, there are also other issues in your code which you should consider altering.
First up, 1-liner solutions are convenient for saving some typing, but often make compromises that affect other aspects of your code. In your case, the 1-liner for reversing the number:
num.to_s.reverse.to_i
That line takes a number, converts it to a string, and then reverses the string, and then converts the string back to a number.
Note that in each conversion, you need to convert between base-2 and base-10 number systems, and that you need to allocate space for the String, etc. While the following takes more code, it actually does less work:
def reverse_num(num)
rev = 0
while num > 0 do
rev *= 10
rev += num % 10
num /= 10
end
rev
end
There are no strings in the above, the loop iterates one time for each decimal digit, and well, just works.
A second issue I want to point out is with your line-by-line algorithm. You read an entire line, split on the spaces, and from the list of strings, you create a list of numbers with to_i. You then iterate this list, and sum the reverses.
A much neater solution is to do a map->reduce operation:
sum = input_str.split(' ').map{ |n| reverse_num(n.to_i) }.reduce(:+)
Then you can eliminate the entire rev_add method. The end result is:
cases = gets.chomp.to_i
def valid_numeric_input?(input)
input.zero?
end
def reverse_num(num)
rev = 0
while num > 0 do
rev *= 10
rev += num % 10
num /= 10
end
rev
end
valid_numeric_input?(cases)
cases.times do |index|
input_str = gets.chomp
sum = input_str.split(' ').map{ |n| reverse_num(n.to_i) }.reduce(:+)
puts reverse_num(sum)
end
There is no reason to store all the results to be printed at the end of the program. Each test case is independent, so you should be able to print and discard each result as you go.
• As per the question, it displayed the results at the end. I didn't find any alternative other than to store into result – brg Apr 10 '15 at 8:18
• I don't see any requirement to buffer up all the results to be printed all at once. – 200_success Apr 10 '15 at 8:19
• Yes, submitted without buffering results. It got accepted. :) I thought the answer should be printed at the end. – brg Apr 10 '15 at 8:27
Take a look into Enumerable (reduce) to use functional abstractions instead of imperative patterns. A lazy approach, not bothering to write a to_digits function (as your original code), would be:
total_lines = $stdin.readline.to_i$stdin.take(total_lines).each do |line|
n1, n2 = line.split.map { |s| s.reverse.to_i }
reversed_sum = (n1 + n2).to_s.reverse.sub(/^0+/, '')
puts(reversed_sum)
end
• I also considered the keep-it-as-a-string option, but it breaks on input like 003 007 .... I was not sure that it was a valid solution. But, it is still a really good observation in that it skips a conversion for each value. – rolfl Apr 10 '15 at 15:02
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# $\arcsin$ differentiation
I am hitting my head against a wall trying to understand how to differentiate this. Can someone please hold my hand through this? I understand that $\arcsin(2x) = \sin^{-1}(2x)$.
Is this implicit differentiation? $$f(x) = \frac{d^2\arcsin(2x)}{dx^2}$$
• Do you know the derivative of $\arcsin(2x)$? – graydad Nov 11 '14 at 3:05
• @graydad, I know it's going to be a fraction with a square root in the botton, but other than that, no – confusedMather Nov 11 '14 at 3:09
• So you need help setting up the implicit differentiation? – graydad Nov 11 '14 at 3:10
Let $y=\arcsin(2x)$. Then $$2x=\sin y\tag1$$ and implicit differentiation with respect to $x$ gives $$2=(\cos y)\frac{dy}{dx}\ .\tag2$$ Differentiating again, $$0=(\cos y)\frac{d^2y}{dx^2}-(\sin y)\Bigl(\frac{dy}{dx}\Bigr)^2\ .\tag3$$ You can now use $(3)$ to get a formula for $\frac{d^2y}{dx^2}$ in terms of $y$ and $\frac{dy}{dx}$; use $(2)$ to eliminate $\frac{dy}{dx}$; and use $(1)$ to eliminate $y$, giving an answer in terms of $x$.
The realization that $\arcsin(2x) = sin^{-1}(2x)$ won't tell you anything. That is like saying $y'(x) = \frac{dy}{dx}$. Both are equivalent ways of saying the same thing. I am of the belief that $\sin^{-1}(2x)$ is abusive notation because it looks like $\frac{1}{\sin(2x)}$. At any rate, your task at hand is to solve $$\frac{d^2 \arcsin(2x)}{dx^2} = \frac{d^2}{dx^2}(\arcsin(2x))$$ so you need to find the second derivative of $\arcsin(2x)$. Implicit differentiation is probably the best way to find the derivative of $\arcsin(2x)$, unless you happen to have the derivative memorized. You will end up with a fraction involving a square root after taking the first derivative, so your best bet for the second derivative would be to use the quotient rule or product rule.
Note that $(\arcsin (2x))'=\frac{1}{\sqrt{1-4x^2}} \times 2$; and $f(x)= (\arcsin (2x))'' = (\frac{2}{\sqrt{1-4x^2}})'= 8x{(1-4x^2)}^{\frac{-3}{2}}$
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## Carl Vondrick Wins NSF CAREER Award
Assistant Professor Carl Vondrick has won the National Science Foundation’s (NSF) Faculty Early Career Development award for his proposal program to develop machine perception systems that robustly detect and track objects even when they disappear from sight, thereby enabling machines to build spatial awareness of their surroundings.
## Cross-disciplinary Research Highlighted in This Year’s Distinguished Lectures Series
The Distinguished Lecture series brings computer scientists to Columbia to discuss current issues and research that are affecting their particular fields. This year, eight experts covered topics ranging from machine learning, human-computer interaction, neural language models, law and public policy, psychology, and computer architecture.
Below are a couple of the lectures from prominent faculty from universities across the country.
## Research by CS Undergrad Published in Cell
Payal Chandak (CC ’21) developed a machine learning model, AwareDX, that helps detect adverse drug effects specific to women patients. AwareDX mitigates sex biases in a drug safety dataset maintained by the FDA.
Below, Chandak talks about how her internship under the guidance of Nicholas Tatonetti, associate professor of biomedical informatics and a member of the Data Science Institute, inspired her to develop a machine learning tool to improve healthcare for women.
How did the project come about?
I initiated this project during my internship at the Tatonetti Lab (T-lab) the summer after my first year. T-lab uses data science to study the side effects of drugs. I did some background research and learned that women face a two-fold greater risk of adverse events compared to men. While knowledge of sex differences in drug response is critical to drug prescription, there currently isn’t a comprehensive understanding of these differences. Dr. Tatonetti and I felt that we could use machine learning to tackle this problem and that’s how the project was born.
How many hours did you work on the project? How long did it last?
The project lasted about two years. We refined our machine learning (ML) model, AwareDX, over many iterations to make it less susceptible to biases in the data. I probably spent a ridiculous number of hours developing it but the journey has been well worth it.
Were you prepared to work on it or did you learn as the project progressed?
As a first-year student, I definitely didn’t know much when I started. Learning on the go became the norm. I understood some things by taking relevant CS classes and through reading Medium blogs and GitHub repositories –– this ability to learn independently might be one of the most valuable skills I have gained. I am very fortunate that Dr. Tatonetti guided me through this process and invested his time in developing my knowledge.
What were the things you already knew and what were the things you had to learn while working on the project?
While I was familiar with biology and mathematics, computer science was totally new! In fact, T-Lab launched my journey to exploring computer science. This project exposed me to the great potential of artificial intelligence (AI) for revolutionizing healthcare, which in turn inspired me to explore the discipline academically. I went back and forth between taking classes relevant to my research and applying what I learned in class to my research. As I took increasingly technical classes like ML and probabilistic modelling, I was able to advance my abilities.
Looking back, what were the skills that you wished you had before the project?
Having some experience with implementing real-world machine learning projects on giant datasets with millions of observations would have been very valuable.
Was this your first project to collaborate on? How was it?
This was my first project and I worked under the guidance of Dr. Tatonetti. I thought it was a wonderful experience – not only has it been extremely rewarding to see my work come to fruition, but the journey itself has been so valuable. And Dr. Tatonetti has been the best mentor that I could have asked for!
Did working on this project make you change your research interests?
I actually started off as pre-med. I was fascinated by the idea that “intelligent machines” could be used to improve medicine, and so I joined T-Lab. Over time, I’ve realized that recent advances in machine learning could redefine how doctors interact with their patients. These technologies have an incredible potential to assist with diagnosis, identify medical errors, and even recommend treatments. My perspective on how I could contribute to healthcare shifted completely, and I decided that bioinformatics has more potential to change the practice of medicine than a single doctor will ever have. This is why I’m now hoping to pursue a PhD in Biomedical Informatics.
Do you think your skills were enhanced by working on the project?
Both my knowledge of ML and statistics and my ability to implement my ideas have grown immensely as a result of working on this project. Also, I failed about seven times over two years. We were designing the algorithm and it was an iterative process – the initial versions of the algorithm had many flaws and we started from scratch multiple times. The entire process required a lot of patience and persistence since it took over 2 years! So, I guess it has taught me immense patience and persistence.
Why did you decide to intern at the T-Lab?
I was curious to learn more about the intersection of artificial intelligence and healthcare. I’m endlessly fascinated by the idea of improving the standards of healthcare by using machine learning models to assist doctors.
Would you recommend volunteering or seeking projects out to other students?
Absolutely. I think everyone should explore research. We have incredible labs here at Columbia with the world’s best minds leading them. Research opens the doors to work closely with them. It creates an environment for students to learn about a niche discipline and to apply the knowledge they gain in class.
## New Machine Learning Tool Predicts Devastating Intestinal Disease in Premature Infants
CS researchers develop a new machine learning approach that shows promise in predicting necrotizing enterocolitis; could lead to improved medical decision-making in neonatal ICUs.
## Can AI Help Doctors Predict and Prevent Preterm Birth?
Almost 400,000 babies were born prematurely—before 37 weeks gestation—in 2018 in the United States. One of the leading causes of newborn deaths and long-term disabilities, preterm birth (PTB) is considered a public health problem with deep emotional and challenging financial consequences to families and society. If doctors were able to use data and artificial intelligence (AI) to predict which pregnant women might be at risk, many of these premature births might be avoided.
## 21 papers from CS researchers accepted to NeurIPS 2019
The 33rd Conference on Neural Information Processing Systems (NeurIPS 2019) fosters the exchange of research on neural information processing systems in their biological, technological, mathematical, and theoretical aspects.
The annual meeting is one of the premier gatherings in artificial intelligence and machine learning that featured talks, demos from industry partners as well as tutorials. Professor Vishal Misra, with colleagues from the Massachusetts Institute of Technology (MIT), held a tutorial on synthetic control.
At this year’s NeurIPS, 21 papers from the department were accepted to the conference. Computer science professors and students worked with researchers from the statistics department and the Data Science Institute.
Noise-tolerant Fair Classification
Alex Lamy Columbia University, Ziyuan Zhong Columbia University, Aditya Menon Google, Nakul Verma Columbia University
Fairness-aware learning involves designing algorithms that do not discriminate with respect to some sensitive feature (e.g., race or gender) and is usually done under the assumption that the sensitive feature available in a training sample is perfectly reliable.
This assumption may be violated in many real-world cases: for example, respondents to a survey may choose to conceal or obfuscate their group identity out of fear of potential discrimination. In the paper, the researchers show that fair classifiers can still be used given noisy sensitive features by simply changing the desired fairness-tolerance. Their procedure is empirically effective on two relevant real-world case-studies involving sensitive feature censoring.
Poisson-randomized Gamma Dynamical Systems
Aaron Schein UMass Amherst, Scott Linderman Columbia University, Mingyuan Zhou University of Texas at Austin, David Blei Columbia University, Hanna Wallach MSR NYC
This paper presents a new class of state space models for count data. It derives new properties of the Poisson-randomized gamma distribution for efficient posterior inference.
Using Embeddings to Correct for Unobserved Confounding in Networks
Victor Veitch Columbia University, Yixin Wang Columbia University, David Blei Columbia University
This paper address causal inference in the presence of unobserved confounder when proxy is available for the confounders in the form of a network connecting the units. For example, the link structure of friendships in a social network reveals information about the latent preferences of people in that network. The researchers show how modern network embedding methods can be exploited to harness the network estimation for efficient causal adjustment.
Variational Bayes Under Model Misspecification
Yixin Wang Columbia University, David Blei Columbia University
The paper characterizes the theoretical properties of a popular machine learning algorithm, variational Bayes (VB). The researchers studied the VB under model misspecification, which is the setting that is most aligned with the practice, and show that the VB posterior is asymptotically normal and centers at the value that minimizes the Kullback-Leibler (KL) divergence to the true data-generating distribution.
As a consequence, they found that the model misspecification error dominates the variational approximation error in VB posterior predictive distributions. In other words, VB pays a negligible price in producing posterior predictive distributions. It explains the widely observed phenomenon that VB achieves comparable predictive accuracy with MCMC even though VB uses an approximating family.
Poincaré Recurrence, Cycles and Spurious Equilibria in Gradient-Descent-Ascent for Non-Convex Non-Concave Zero-Sum Games
Emmanouil-Vasileios Vlatakis-Gkaragkounis Columbia University, Lampros Flokas Columbia University, Georgios Piliouras Singapore University of Technology and Design
The paper introduces a model that captures a min-max competition over complex error landscapes and shows that even a simplified model can provably replicate some of the most commonly reported failure modes of GANs (non-convergence, deadlock in suboptimal states, etc).
Moreover, the researchers were able to understand the hidden structure in these systems — the min-max competition can lead to system behavior that is similar to that of energy preserving systems in physics (e.g. connected pendulums, many-body problems, etc). This makes it easier to understand why these systems can fail and gives new tools in the design of algorithms for training GANs.
Near-Optimal Reinforcement Learning in Dynamic Treatment Regimes
Junzhe Zhang Columbia University, Elias Bareinboim Columbia University
Dynamic Treatment Regimes (DTRs) are particularly effective for managing chronic disorders and is arguably one of the key aspects towards more personalized decision-making. The researchers developed the first adaptive algorithm that achieves near-optimal regret in DTRs in online settings, while leveraging the abundant, yet imperfect confounded observations. Applications are given to personalized medicine and treatment recommendation in clinical decision support.
Paraphrase Generation with Latent Bag of Words
Yao Fu Columbia University, Yansong Feng Peking University, John Cunningham University of Columbia
The paper proposes a latent bag of words model for differentiable content planning and surface realization in text generation. This model generates paraphrases with clear steps, adding interpretability and controllability of existing neural text generation models.
Adapting Neural Networks for the Estimation of Treatment Effects
Claudia Shi Columbia University, David Blei Columbia University, Victor Veitch Columbia University
This paper addresses how to design neural networks to get very accurate estimates of causal effects from observational data. The researchers propose two methods based on insights from the statistical literature on the estimation of treatment effects.
The first is a new architecture, the Dragonnet, that exploits the sufficiency of the propensity score for estimation adjustment. The second is a regularization procedure, targeted regularization, that induces a bias towards models that have non-parametrically optimal asymptotic properties “out-of-the-box”. Studies on benchmark datasets for causal inference show these adaptations outperform existing methods.
Efficiently Avoiding Saddle Points with Zero Order Methods: No Gradients Required
Emmanouil-Vasileios Vlatakis-Gkaragkounis Columbia University, Lampros Flokas Columbia University, Georgios Piliouras Singapore University of Technology and Design
The researchers prove that properly tailored zero-order methods are as effective as their first-order counterparts. This analysis requires a combination of tools from optimization theory, probability theory and dynamical systems to show that even without perfect knowledge of the shape of the error landscape, effective optimization is possible.
Metric Learning for Adversarial Robustness
Chengzhi Mao Columbia University, Ziyuan Zhong Columbia University, Junfeng Yang Columbia University, Carl Vondrick Columbia University, Baishakhi Ray Columbia University
Deep networks are well-known to be fragile to adversarial attacks. The paper introduces a novel Triplet Loss Adversarial (TLA) regulation that is the first method that leverages metric learning to improve the robustness of deep networks. This method is inspired by the evidence that deep networks suffer from distorted feature space under adversarial attacks. The method increases the model robustness and efficiency for the detection of adversarial attacks significantly.
Efficient Symmetric Norm Regression via Linear Sketching
Zhao Song University of Washington, Ruosong Wang Carnegie Mellon University, Lin Yang Johns Hopkins University, Hongyang Zhang TTIC, Peilin Zhong Columbia University
The paper studies linear regression problems with general symmetric norm loss and gives efficient algorithms for solving such linear regression problems via sketching techniques.
Rethinking Generative Coverage: A Pointwise Guaranteed Approach
Peilin Zhong Columbia University, Yuchen Mo Columbia University, Chang Xiao Columbia University, Pengyu Chen Columbia University, Changxi Zheng Columbia University
The paper presents a novel and formal definition of mode coverage for generative models. It also gives a boosting algorithm to achieve this mode coverage guarantee.
How Many Variables Should Be Entered in a Principal Component Regression Equation?
Ji Xu Columbia University, Daniel Hsu Columbia University
The researchers studied the least-squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance with the number of selected features $p$ can be either smaller or greater than the sample size $n$. And give an average-case analysis of the out-of-sample prediction error as $p,n,N \to \infty$ with $p/N \to \alpha$ and $n/N \to \beta$, for some constants $\alpha \in [0,1]$ and $\beta \in (0,1)$. In this average-case setting, the prediction error exhibits a “double descent” shape as a function of $p$. This also establishes conditions under which the minimum risk is achieved in the interpolating ($p>n$) regime.
Adaptive Influence Maximization with Myopic Feedback
Binghui Peng Columbia University, Wei Chen Microsoft Research
The paper investigates the adaptive influence maximization problem and provides upper and lower bounds for the adaptivity gaps under myopic feedback model. The results confirm a long standing open conjecture by Golovin and Krause (2011).
Towards a Zero-One Law for Column Subset Selection
Zhao Song University of Washington, David Woodruff Carnegie Mellon University, Peilin Zhong Columbia University
The researchers studied low-rank matrix approximation with general loss function and showed that if the loss function has several good properties, then there is an efficient way to compute a good low-rank approximation. Otherwise, it could be hard to compute a good low-rank approximation efficiently.
Average Case Column Subset Selection for Entrywise l1-Norm Loss
Zhao Song University of Washington, David Woodruff Carnegie Mellon University, Peilin Zhong Columbia University
The researchers studied how to compute an l1-norm loss low-rank matrix approximation to a given matrix. And showed that if the given matrix can be decomposed into a low-rank matrix and a noise matrix with a mild distributional assumption, we can obtain a (1+eps) approximation to the optimal solution.
A New Distribution on the Simplex with Auto-Encoding Applications
Andrew Stirn Columbia University, Tony Jebara Spotify, David Knowles Columbia University
The researchers developed a surrogate distribution for the Dirichlet that offers explicit, tractable reparameterization, the ability to capture sparsity, and has barycentric symmetry properties (i.e. exchangeability) equivalent to the Dirichlet. Previous works have used the Kumaraswamy distribution in a stick-breaking process to create a non-exchangeable distribution on the simplex. The method was improved by restoring exchangeability and demonstrating that approximate exchangeability is efficiently achievable. Lastly, the method was showcased in a variety of VAE semi-supervised learning tasks.
Discrete Flows: Invertible Generative Models of Discrete Data
Dustin Tran Google Brain, Keyon Vafa Columbia University, Kumar Agrawal Google AI Resident, Laurent Dinh Google Brain, Ben Poole Google Brain
While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. The researchers extend normalizing flows to discrete events, using a simple change-of-variables formula not requiring log-determinant-Jacobian computations. Empirically, they find that discrete flows obtain competitive performance with or outperform autoregressive baselines on various tasks, including addition, Potts models, and language models.
Characterization and Learning of Causal Graphs with Latent Variables from Soft Interventions
Murat Kocaoglu MIT-IBM Watson AI Lab IBM Research, Amin Jaber Purdue University, Karthikeyan Shanmugam MIT-IBM Watson AI Lab IBM Research NY, Elias Bareinboim Columbia University
This work is all about learning causal relationships – the classic aim of which is to characterize all possible sets that could produce the observed data. In the paper, the researchers provide a complete characterization of all possible causal graphs with observational and interventional data involving so-called ‘soft interventions’ on variables when the targets of soft interventions are known.
This work potentially could lead to discovery of other novel learning algorithms that are both sound and complete.
Identification of Conditional Causal Effects Under Markov Equivalence
Amin Jaber Purdue University, Jiji Zhang Lingnan University, Elias Bareinboim Columbia University
Causal identification is the problem of deciding whether a causal distribution is computable from a combination of qualitative knowledge about the underlying data-generating process, which is usually encoded in the form of a causal graph, and an observational distribution. Despite the obvious need for identifying causal effects throughout the data-driven sciences, in practice, finding the causal graph is a notoriously challenging task.
In this work, the researchers provide a relaxation of the requirement of having to specify the causal graph (based on substantive knowledge) and allow the input of the inference to be an equivalence class of causal graphs, which can be inferred from data. Specifically, they propose the first general algorithm to learn conditional causal effects entirely from data. This result is particularly useful for evaluating the impact of conditional plans and stochastic policies, which appear both in AI (in the context of reinforcement learning) and in the data-driven sciences.
Efficient Identification in Linear Structural Causal Models with Instrumental Cutsets
Daniel Kumor Purdue University, Bryant Chen Brex Inc., Elias Bareinboim Columbia University
Regression analysis is one of the most common tools used in modern data science. While there is a great understanding and powerful technology to perform regression analysis in high dimensional spaces, the output of such a method is purely associational and devoid of any causal interpretation.
The researchers studied the problem of identification of structural (causal) coefficients in linear systems (deciding whether regression coefficients are amenable to causal interpretation, etc). Building on a technique called instrumental variables, they developed a new method called Instrumental Cutset, which partitions the systems into tractable components such that identification can be decided more efficiently. The resulting algorithm was efficient and strictly more powerful than the current state-of-the-art methods.
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# If two objects are too close to each other, would an object detector do a poor job of correctly classifying them?
Suppose we have an object detector that is trained to detect $$20$$ products. If two objects are too close to each other, in general, would an object detector do a poor job of correctly classifying them? If they were far apart in the scene, would the object detector to a better job of correctly classifying them?
As you ask, "in general...", I will answer generally, however this changes a lot from model to model and the way they handle close objects.
In general, yes, they would do a poor job detecting very close objects, switch to segmentation models for that (for class or better, instance segmentation).
In general, objects detectors learn to tell an object from other based in 2 criterion:
• Intersection over union: for object of the same class
• Class probability: for objects of different class
So, if two objects of the same class are very close, the 2 detected bounding boxes will be highly overlapping, then, the Non Maximal Suppression filter will remove one of them. This is where objects detector, in general, perform worse.
Similarly, if two objects belong to different classes the 2 detected bounding boxes will be highly overlapping but the NMS filter won't remove them (again, in general, NMS is set only for same class objects). However when 2 objects are very close, there is a high chance they are partially occluded. Objects detectors, in general, don't handle occlusions very well.
So, in conclusion, objects detectors will perform better detecting far-away objects.
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# Thin Film Strain Gauge Sensors for ion Thrust Measurement
Stephen, John R and Rajanna, K and Dhar, Vivek and Kumar, Kalyan KG and Nagabushanam, S (2002) Thin Film Strain Gauge Sensors for ion Thrust Measurement. In: IEEE Sensors, 2002, 12-14 June, Florida,USA, Vol.2, 1702-1706.
Preview
PDF
thin_film.pdf
In order to measure the thrust produced by a Stationary Plasma Thruster, a measurement system has been developed using a thrust balance with thin film strain gauge sensors. For this purpose, strain gauges were designed and deposited on the columns of the thrust balance fabricated and necessary signal conditioning circuit has been used. Performance of the system developed was studied, in a vacuum chamber under space simulated conditions, by activating the thruster. In-situ calibration was done using Lami's principle. For discharge powers varying from 210-275 Watts, the measured values of thrust were found to be in the range of 11-16 mN with an accuracy of $\pm\hspace{5mm}1mN$ and resolution of 0.12 mN. Specific impulse and efficiency were also estimated.
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# Changes between Version 3 and Version 4 of MatchChecker
Ignore:
Timestamp:
04/12/12 11:51:24 (8 years ago)
Comment:
--
### Legend:
Unmodified
v3 * tag = defines a name for the treatment of the first production. This name is used in the plot names. * comment = informations you may want to add, and will appear in the report * banner = if there is a banner, just indicate it's path/name * files = put the adress of the samples (relative or absolute) and if the sample is exclusive, add the multiplicity. For example ttbar_1j 1,ttbar_2jet 2. Note your are not obliged to have an inclusive set , that there can be a missing multiplicity, MatchChecker will still work in this condition * The second block contains the PDG code of main particle(s) X in a X + N jets process. This permits to retrieve the information about kinematics of X: %$P_{T} (X)$%, the angle in the transverse plan between components of X (t and t for instance), %$P_{T}$% of one of the particles, the invariant mass of X, rapidity of one of the particle, the rapidity of one particle. * The third block indicates the %$K_{T}$% scale at which the jet are defined, this is used for the kinematical plots. * The second block contains the PDG code of main particle(s) X in a X + N jets process. This permits to retrieve the information about kinematics of X: $P_{T} (X)$, the angle in the transverse plan between components of X (t and t for instance), $P_{T}$ of one of the particles, the invariant mass of X, rapidity of one of the particle, the rapidity of one particle. * The third block indicates the $K_{T}$ scale at which the jet are defined, this is used for the kinematical plots. * The fourth block gives the values of the PT cuts to be applied on jets to do the rapidity distributions. The user can choose as many cuts as he wants * The seventh block says if yes or not the running can be done in //. Note that for this somes files in the condor repository have to be edited. * The four last blocks are related to the jet content for extra radiation and inclusive jets. For the moment, only the %$K_{T}$% algorithm can be used but in the future, any number of jet algo will be taken into account. * The four last blocks are related to the jet content for extra radiation and inclusive jets. For the moment, only the $K_{T}$ algorithm can be used but in the future, any number of jet algo will be taken into account. Now the basic use of MatchChecker is the following: * comparison of kinematic plots between production * ratios of plots between productions * %$P_{T}$% of the four first jets (with multiplicity details) * comparison of the %$P_{T}$% of the four first jets * ratios of plots between productions * %$\eta$% of the four first jets (with multiplicity details) for each PT cut choosen by the user * comparison of the %$\eta$% of the four first jets * $P_{T}$ of the four first jets (with multiplicity details) * comparison of the $P_{T}$ of the four first jets * ratios of plots between productions * $\eta$ of the four first jets (with multiplicity details) for each PT cut choosen by the user * comparison of the $\eta$ of the four first jets * ratios of plots between productions * Ht(j): Give the scalar sum where MET is the missing transverse energy, and %$P_{T,i}$% the transverse momentum of the i-th jet. Ht(1, 4) is given for each PT cut applied on jets. where MET is the missing transverse energy, and $P_{T,i}$ the transverse momentum of the i-th jet. Ht(1, 4) is given for each PT cut applied on jets. * comparison of the Ht of the four first jets * ratios of plots between productions ==== Differential Jet Rate ==== The DJR 1 %$\rightarrow$% 0, 2 %$\rightarrow$% 1, 3 %$\rightarrow$%2 and 4 %$\rightarrow$% 3 are given for each production. The contribution of each multiplicity is given. The smoothness of the transition region indicates how much the choice of xqcut and Qcut in the matching procedure is valid.
4.2 Kinematics For each production, the PT (X), %$\Delta\phi$%(X) (if X is two particles: tt, ZZ, WW, WZ, etc...), %$\eta$%(X), m(X), the PT of one particle composing X and also his rapidity are showed. The DJR 1 $\rightarrow$ 0, 2 $\rightarrow$ 1, 3 $\rightarrow$2 and 4 $\rightarrow$ 3 are given for each production. The contribution of each multiplicity is given. The smoothness of the transition region indicates how much the choice of xqcut and Qcut in the matching procedure is valid.
4.2 Kinematics For each production, the PT (X), $\Delta\phi$(X) (if X is two particles: tt, ZZ, WW, WZ, etc...), $\eta$(X), m(X), the PT of one particle composing X and also his rapidity are showed. For each PT cut chosen by the user, the rapidity of each jet is also given
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Interpreting Mediation Output when ACME is stat. sig but ADE and Total are not
The mediation package in R returns results in which:
• The Average Causal Mediated Effect (ACME) (the effect of the mediator alone) is positive and statistically significant
• Average Direct Effect (ADE) (the unmediated effect) and the Total Effect (ADE+ACME) is not statistically significant
Does this indicate that the IV positively influences my DV via my mediator, however there are other mediators through which the IV has a negative effect on the DV (and as a result, the total effect can't be differentiated from 0?).
Thank you for any help.
This should not happen if you use only one mediator in the model. If there are other mediators for a negative hidden away, they should reflect in the direct effect.
But there are certain conditions under which it would happen. Most likely, the IV weakly relates or has no relation to the DV in these conditions.
# first, some syntax for Sobel's test
sobel <- function(mm, my) {
a <- coef(mm)["x"]
ase <- coef(summary(mm))["x", 2]
b <- coef(my)["m"]
bse <- coef(summary(my))["m", 2]
abse <- sqrt(a ^ 2 * bse ^ 2 + b ^ 2 * ase ^ 2)
# return ACME and z-test
c(acme = a * b, z = a * b / abse, p = (1 - pnorm(a * b / abse)) * 2)
}
set.seed(899398)
n <- 100
x <- rnorm(n)
m <- rnorm(1) * x + rnorm(n)
y <- rnorm(1) * m + rnorm(1) * x + rnorm(n)
coef(summary(lm(y ~ x)))["x", ] # total effect not stat sig
Estimate Std. Error t value Pr(>|t|)
0.2125229 0.1470346 1.4453944 0.1515374
coef(summary(mm <- lm(m ~ x)))["x", ] # IV affects MV
Estimate Std. Error t value Pr(>|t|)
0.25667463 0.10464021 2.45292550 0.01593713
coef(summary(my <- lm(y ~ m + x))) # Only MV significant for DV
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.06147867 0.09632753 -0.6382253 5.248309e-01
m 1.08186228 0.09104230 11.8830723 1.241992e-20
x -0.06516366 0.09716138 -0.6706745 5.040217e-01
sobel(mm, my) # returns ACME, z and z-test of ACME
acme.x z.x p.x
0.27768660 2.40227887 0.01629328
The conditions OP described are all present here. This is one example of how it could happen. In reality, the relationships are probably way more complicated but it definitely is possible. If you have a not statistically significant total effect and the mediated effect is statistically significant in a one mediator model, I'd doubt any mediation was going on.
The way I found this example was by using a search for the right seed:
find <- FALSE
tab <- 1:1e6
while (find == FALSE) {
seed <- sample(tab, 1)
set.seed(seed)
n <- 100
x <- rnorm(n)
m <- rnorm(1) * x + rnorm(n)
y <- rnorm(1) * m + rnorm(1) * x + rnorm(n)
te <- coef(summary(lm(y ~ x)))["x", 4]
mm <- lm(m ~ x)
dme <- coef(summary(my <- lm(y ~ m + x)))[c("m", "x"), 4]
me <- dme[1]; de <- dme[2]
ie <- sobel(mm, my)[3]
if (te > .15 & de > .15 & ie < .04) {
find <- TRUE
}
}
It is possible to expand the search function to store all such conditions and study the patterns ACME, ADE and ATE that produce the OP's situation.
• I don't get why this should not happen. – FeldO Oct 3 '18 at 16:54
• @FeldO I try to do that through the text. Also see the comment about what is the most realistic explanation at the end. For one, total always equal direct plus indirect. – Heteroskedastic Jim Oct 3 '18 at 16:56
• Yes of course, ADE+ACME= Total Effect. This is the case. However, I was refering to the uncertainty concerning the corresponding estimates. When I follow your arguments, you don't say why it is not possible that the ACME is insignificant, while the ADE and Total Effect are not. – FeldO Oct 3 '18 at 17:03
• @FeldO I rewrote my answer, with an example where I replicate what you claimed. – Heteroskedastic Jim Oct 4 '18 at 14:13
@heteroskedastic Jim "Final most realistic alternative is your IV really has no relationship to the DV or the MV, but the MV is so strongly related to the DV that almost anything you multiply by it will work out as a mediator. The numbers will still add up though."
How should one interpret the results then? Is this evidence of mediation or not?
• Put this in the comments section which is just below @heteroskedastic Jim's answer – prashanth Oct 4 '18 at 10:31
• If the IV has no relationship to the outcome, then what is the mediator mediating? – Heteroskedastic Jim Oct 4 '18 at 13:26
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# Can the distance over time of an electron between two measurements be higher than the speed of light?
So measure an electron, take down it's position $p$. Then measure the electron a second time and take down it's new position $p'$. Note the time between measurements, $t$. What does physics say about the average speed $$v=\frac{d(p,p')}{t}$$ between the two measurements? Is it possible that $v$ must have been larger than the speed of light.
Bohr radius (radius of the hydrogen atom) is about $5\cdot 10^{-11}$ m, so take twice that, $10^{-10}$ m as the distance between opposite "sides" of an atom. Letting $v=c$, we solve for $t$, $$t=\frac{10^{-10}}{3\cdot 10^8}= 3.33\cdot 10^{-19} \text{ sec}.$$ That's more than Planck time!
So my question: Is the probability of the wave function somehow limited by the speed of light in quantum mechanics?
• Why is it relevant that the time you found is greater than the Planck time? – user4552 Jul 26 '14 at 21:30
• I also don't understand the relevance of the Bohr-model calculation. – user4552 Jul 26 '14 at 21:44
• – user4552 Jul 26 '14 at 22:14
• How can you be certain it's the same electron? It could have moved in from an adjacent atom and the electron you first observed is on another atom. – LDC3 Jul 26 '14 at 23:07
You seem to be assuming that there is a measurement process that can be applied to the electron on a single, isolated hydrogen atom twice within somewhere under 10–19 seconds, and that because an electron in a hydrogen atom's ground state (or any $s$ state) is equally likely to be found along any direction from the nucleus, there's some chance that the electron will "jump" from one side of the nucleus to other.
But you are forgetting about the uncertainty principle, which governs the precision with which you may make a measurement. If you want to measure which side of the atom the electron sits on, you must have a precision better than the Bohr radius, $\Delta x < a_0 \approx \frac12\times10^{-10}\,\mathrm m$. After such a measurement, the electron must have a momentum uncertainty (in energy units) of $$\Delta p\, c \gtrsim \frac{\hbar c}{2\Delta x} = \mathrm{\frac{0.2\,GeV\cdot fm}{2\cdot \frac12\times10^{5}\,fm}} = \mathrm{2\times10^{-6}\,GeV} = 2\,\mathrm{keV}$$ We can assume that the most likely value for $p$ is zero, since the electron began at rest. But a momentum of $pc = 0\pm 2\,\mathrm{keV}$, normally distributed, implies a typical squared momentum $(pc)^2 \approx (2\,\mathrm{keV})^2$, or a typical energy \begin{align} E = \frac{p^2}{2m} \frac{c^2}{c^2}\approx \mathrm{\frac{(2\,keV)^2}{2\cdot 500\,keV}} \approx 4\,\mathrm{eV} \end{align} Remember that the hydrogen ground state has energy $-13.6\,\mathrm{eV}$, and that the first excited state has energy $-13.6\,\mathrm{eV}/2^2 = -3.4\,\mathrm{eV}$, neary 10 eV away. A position measurement with enough precision to distinguish "this side" from "that side" of a hydrogen atom involves nearly enough energy to promote the electron into a different state.
However it's also not really enough precision to say that you've measured faster-than-light travel for the electron: since the electron's $s$-wave wavefunction is roughly a three-dimensional Gaussian wavepacket whose width is the Bohr radius, you're mostly likely to find successive measurements of electron position separated by $1\sigma$. If you wanted to typically find electron positions separated by $3\sigma$ ("$3\sigma$ is a measurement, $4\sigma$ is a discovery," as one of my mentors likes to say, but $3^2=10$ is a nice round number), you'd have to improve your precision by a factor of three; this takes the energy associated with the measurement to 40 eV and means that your first position measurement will definitely ionize the atom, and your assumption that both measurements take place in the atom's ground state is broken.
Or alternatively, you could prepare your atom in an excited state (with radius $na_0$ for principal quantum number $n$) and keep the precision of your measurement the same. However, in that case also your first measurement would have enough energy to change the atom's state, or ionize it completely.
Then you have the question of how you'll measure the electron's position twice within 10–19 seconds—that's fast! Suppose you bathe the atom in an oscillating electric field with frequency $\nu=10^{19}\,\mathrm{Hz}$. In the quantum-mechanical picture, this field is made of photons, each with energy $E = h\nu \approx 40\,\mathrm{keV}$! It is vanishingly improbable that the atom would remain in its ground state after interacting with such a field. Your experiment would never work.
This second argument is in the spirit of Bohr's arguments during his debates with Einstein about the proper interpretation of quantum mechanics. But to my mind the first argument, based on the observation that bound-state wavefunctions tend to have nearly the minimum uncertainties $\Delta x,\Delta p$ allowed by the Heisenberg principle, is more interesting. In some sense, the different states of the hydrogen atom have the size that they do because of the uncertainty principle. Notice that relativity doesn't enter that argument explicitly, apart from the definition of energy $(E_\text{rest}+E_\text{kinetic})^2 = pc^2 + (mc^2)^2$, which I used in the more familiar low-momentum approximation $E_\text{kinetic} \approx p^2/2m$. The universe conspires in many ways to preserve its fundamental laws.
As noted in comments, some parts of the question don't make sense to me.
But anyway, I think the answer to your question is that yes, the quantity $v$ you define can be greater than $c$. However, this doesn't necessarily have any consequences for relativity. The only thing that would be problematic for relativity would be if you could transmit information at $v>c$, which is a different thing.
The evidence that $v>c$ is possible in quantum mechanics actually comes from quantum-mechanical tunneling. The experiments are mostly done with photons, not electrons, and the search term you want is "Hartman effect." For example, figure 1 in [Nimtz 2007] describes an experiment similar to, although not identical to, the one you propose. I've listed some other recent papers below.
Another thing that it might be helpful to point out is that in the measurement scheme proposed in the question, the first measurement changes the state of the electron -- you can't just sample the same wavefunction twice. Also keep in mind that the stuff I've referenced, about photons, may not be perfectly analogous with what you have in mind, about electrons. In particular, there is no such thing as a position eigenstate for a photon.
Nimtz and Stahlhofen, Macroscopic violation of special relativity, 2007, http://arxiv.org/abs/0708.0681
Chiao, Tunneling Times and Superluminality: a Tutorial, 1998, http://arxiv.org/abs/quant-ph/9811019
Winful, Do single photons tunnel faster than light?, 2007, http://arxiv.org/abs/0708.3889
Aichmann and Nimtz, The Superluminal Tunneling Story, 2013, http://arxiv.org/abs/1304.3155
• You are addressing the first part of the question and I am addressing the second , given as an example by the OP. Should I make a snide remark about your answer and give you a -1? – anna v Jul 27 '14 at 3:44
The Bohr atom was ( and still is) a useful phenomenological approximation of the underlying quantum mechanical system. It is no use playing with numbers of the Bohr atom as if the electron is a billiard ball. It is not a classical particle. It is a quantum mechanical entity that appears as particle in some interactions, or builds up a probability wave in others, depending on the boundary conditions the observation sets. In the hydrogen atom it builds up probability loci called "orbitals", not orbits.
Actually the experiment of measuring the velocity of a very fast particle , the neutrino, was done . The neutrinos have masses much smaller than the electron. For a while a faster than light velocity hit the physics news, but it was soon found out it was an experimental error, a baddly plugged cable in the complicated measurement and analysis. Electrons travel very close to the speed of light in accelerators, but that is all.
So the answer is, the experimental evidence is that a free particle never goes over the speed of light and a bound electron is in the probability wave manifestation and speed has no meaning in that framework.
Another way at looking in your numbers is to recall the Heisenberg Uncertainty principle, which is inherent in the quantum mechanical phase.
You chose your electron position accurately, so that means that momentum ( velocity*mass) can be anything, cannot be estimated.
• The first paragraph doesn't address the question. The second and third paragraphs are an example, but an example doesn't prove a general rule. The final paragraphs don't address the question, since the question asks about the outcome of a measurement process, which is manifestly well defined. – user4552 Jul 26 '14 at 22:16
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# Critical point (thermodynamics)
(Redirected from Critical temperature)
Jump to: navigation, search
1. Subcritical ethane, liquid and gas phase coexist
2. Critical point (32.17 °C, 48.72 bar), opalescence
3. Supercritical ethane, fluid[1]
In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid-vapor critical point, the end point of the pressure-temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a critical temperature Tc and a critical pressure pc, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures.
## Liquid-vapor critical point
### Overview
The liquid-vapor critical point in a pressure–temperature phase diagram is at the high-temperature extreme of the liquid–gas phase boundary. The dotted green line shows the anomalous behavior of water.
For simplicity and clarity, the generic notion of critical point is best introduced by discussing a specific example, the liquid-vapor critical point. This was the first critical point to be discovered, and it is still the best known and most studied one.
The figure to the right shows the schematic PT diagram of a pure substance (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly known phases solid, liquid and vapor are separated by phase boundaries, i.e. pressure-temperature combinations where two phases can coexist. At the triple point, all three phases can coexist. However, the liquid-vapor boundary terminates in an endpoint at some critical temperature Tc and critical pressure pc. This is the critical point.
In water, the critical point occurs at around 647 K (374 °C; 705 °F) and 22.064 MPa (3200 psia or 218 atm).[2]
In the vicinity of the critical point, the physical properties of the liquid and the vapor change dramatically, with both phases becoming ever more similar. For instance, liquid water under normal conditions is nearly incompressible, has a low thermal expansion coefficient, has a high dielectric constant, and is an excellent solvent for electrolytes. Near the critical point, all these properties change into the exact opposite: water becomes compressible, expandable, a poor dielectric, a bad solvent for electrolytes, and prefers to mix with nonpolar gases and organic molecules.[3]
At the critical point, only one phase exists. The heat of vaporization is zero. There is a stationary inflection point in the constant-temperature line (critical isotherm) on a PV diagram. This means that at the critical point:[4][5][6]
${\displaystyle \left({\frac {\partial p}{\partial V}}\right)_{T}=\left({\frac {\partial ^{2}p}{\partial V^{2}}}\right)_{T}=0}$
The critical isotherm with the critical point K
Above the critical point there exists a state of matter that is continuously connected with (can be transformed without phase transition into) both the liquid and the gaseous state. It is called supercritical fluid. The common textbook knowledge that all distinction between liquid and vapor disappears beyond the critical point has been challenged by Fisher and Widom[7] who identified a p,T-line that separates states with different asymptotic statistical properties (Fisher-Widom line).
### History
Carbon dioxide exuding fog while cooling from supercritical to critical temperature
The existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822[8][9] and named by Dmitri Mendeleev in 1860[10] and Thomas Andrews in 1869.[11] Cagniard showed that CO2 could be liquefied at 31 °C at a pressure of 73 atm, but not at a slightly higher temperature, even under pressures as high as 3,000 atm.
### Theory
Solving the above condition ${\displaystyle (\partial p/\partial V)_{T}=0}$ for the van der Waals equation, one can compute the critical point as
${\displaystyle T_{c}=8a/(27Rb)}$, ${\displaystyle V_{c}=3nb}$, ${\displaystyle p_{c}=a/(27b^{2})}$.
However, the van der Waals equation, based on a mean field theory, does not hold near the critical point. In particular, it predicts wrong scaling laws.
To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties[12]
${\displaystyle T_{r}=T/T_{c}}$, ${\displaystyle p_{r}=p/p_{c}}$, ${\displaystyle V_{r}={\frac {V}{RT_{c}/p_{c}}}}$.
The principle of corresponding states indicates that substances at equal reduced pressures and temperatures have equal reduced volumes. This relationship is approximately true for many substances, but becomes increasingly inaccurate for large values of pr.
### Table of liquid–vapor critical temperature and pressure for selected substances
Substance[13][14] Critical temperature Critical pressure (absolute)
Argon −122.4 °C (150.8 K) 48.1 atm (4,870 kPa)
Ammonia (NH3)[15] 132.4 °C (405.5 K) 111.3 atm (11,280 kPa)
Bromine 310.8 °C (584.0 K) 102 atm (10,300 kPa)
Caesium 1,664.85 °C (1,938.00 K) 94 atm (9,500 kPa)
Chlorine 143.8 °C (416.9 K) 76.0 atm (7,700 kPa)
Ethanol (C2H5OH) 241 °C (514 K) 62.18 atm (6,300 kPa)
Fluorine −128.85 °C (144.30 K) 51.5 atm (5,220 kPa)
Helium −267.96 °C (5.19 K) 2.24 atm (227 kPa)
Hydrogen −239.95 °C (33.20 K) 12.8 atm (1,300 kPa)
Krypton −63.8 °C (209.3 K) 54.3 atm (5,500 kPa)
Methane (CH4) −82.3 °C (190.8 K) 45.79 atm (4,640 kPa)
Neon −228.75 °C (44.40 K) 27.2 atm (2,760 kPa)
Nitrogen −146.9 °C (126.2 K) 33.5 atm (3,390 kPa)
Oxygen −118.6 °C (154.6 K) 49.8 atm (5,050 kPa)
Carbon dioxide (CO2) 31.04 °C (304.19 K) 72.8 atm (7,380 kPa)
Nitrous oxide (N2O) 36.4 °C (309.5 K) 71.5 atm (7,240 kPa)
Sulfuric Acid (H2SO4) 654 °C (927 K) 45.4 atm (4,600 kPa)
Xenon 16.6 °C (289.8 K) 57.6 atm (5,840 kPa)
Lithium 2,950 °C (3,220 K) 652 atm (66,100 kPa)
Mercury 1,476.9 °C (1,750.1 K) 1,720 atm (174,000 kPa)
Sulfur 1,040.85 °C (1,314.00 K) 207 atm (21,000 kPa)
Iron 8,227 °C (8,500 K)
Gold 6,977 °C (7,250 K) 5,000 atm (510,000 kPa)
Aluminium 7,577 °C (7,850 K)
Water (H2O)[2][16] 373.946 °C (647.096 K) 217.7 atm (22.06 MPa)
## Mixtures: liquid–liquid critical point
A plot of typical polymer solution phase behavior including two critical points: an LCST and a UCST.
The liquid–liquid critical point of a solution, which occurs at the critical solution temperature, occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some thermodynamic variable (such as temperature or pressure) will lead to separation of the mixture into two distinct liquid phases, as shown in the polymer–solvent phase diagram to the right. Two types of liquid–liquid critical points are the upper critical solution temperature (UCST), which is the hottest point at which cooling will induce phase separation, and the lower critical solution temperature (LCST), which is the coldest point at which heating will induce phase separation.
### Mathematical definition
From a theoretical standpoint, the liquid–liquid critical point represents the temperature-concentration extremum of the spinodal curve (as can be seen in the figure to the right). Thus, the liquid–liquid critical point in a two-component system must satisfy two conditions: the condition of the spinodal curve (the second derivative of the free energy with respect to concentration must equal zero), and the extremum condition (the third derivative of the free energy with respect to concentration must also equal zero or the derivative of the spinodal temperature with respect to concentration must equal zero).
## Footnotes
1. ^ Horstmann, Sven (2000). Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung [Theoretical and experimental investigations of the high-pressure phase equilibrium behavior of fluid mixtures for the expansion of the PSRK group contribution equation of state] (Ph.D.) (in German). Carl-von-Ossietzky Universität Oldenburg. ISBN 3-8265-7829-5.
2. ^ a b International Association for the Properties of Water and Steam, 2007.
3. ^ Anisimov, Sengers, Levelt Sengers (2004): Near-critical behavior of acquous systems. Chapter 2 in Aqueous System at Elevated Temperatures and Pressures Palmer et al, eds. Elsevier.
4. ^ P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W.H. Freeman 2006), p.21
5. ^ K.J. Laidler and J.H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p.27
6. ^ P.A. Rock, Chemical Thermodynamics (MacMillan 1969), p.123
7. ^ Fisher, Widom: Decay of Correlations in Linear Systems, J. Chem Phys 50, 3756 (1969)
8. ^ Charles Cagniard de la Tour (1822) "Exposé de quelques résultats obtenu par l'action combinée de la chaleur et de la compression sur certains liquides, tels que l'eau, l'alcool, l'éther sulfurique et l'essence de pétrole rectifiée" (Presentation of some results obtained by the combined action of heat and compression on certain liquids, such as water, alcohol, sulfuric ether [i.e., diethyl ether], and distilled petroleum spirit), Annales de chimie et de physique, 21 : 127-132.
9. ^ Berche, B., Henkel, M., Kenna, R (2009) Critical phenomena: 150 years since Cagniard de la Tour. Journal of Physical Studies 13 (3) , pp. 3001-1-3001-4.
10. ^ Landau, Lifshitz, Theoretical Physics Vol V, Statistical Physics, Ch. 83 [German edition 1984]
11. ^ Andrews, Thomas (1869) "The Bakerian lecture: On the continuity of the gaseous and liquid states of matter" Philosophical Transactions of the Royal Society (London), 159, 575-590; the term "critical point" appears on page 588.
12. ^ Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 91–93. ISBN 0-07-121688-X.
13. ^ Emsley, John (1991). The Elements ((Second Edition) ed.). Oxford University Press. ISBN 0-19-855818-X.
14. ^ Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: An Engineering Approach ((Fourth Edition) ed.). McGraw-Hill. p. 824. ISBN 0-07-238332-1.
15. ^ "Ammonia - NH3 - Thermodynamic Properties". www.engineeringtoolbox.com. Retrieved 2017-04-07.
16. ^ "Critical Temperature and Pressure". Purdue University. Retrieved 2006-12-19.
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Differential and Integral Equations
On the spectral stability of periodic waves of the Klein-Gordon equation
Abstract
The object of study is the Klein-Gordon equation in $1+1$ dimensions, with integer power non-linearities. In particular, of interest is the spectral stability/instability (with respect to perturbations of the same period) of traveling-standing periodic solitons, which are of cnoidal ($p=2$), dnoidal ($p=3$) or more general type ($p=5$). The corresponding linearized problem for this two-parameter family of solutions fits the general abstract framework of spectral stability for second order Hamiltonian systems, recently developed by the last two authors and Bronski-Johnson-Kapitula. It is worth noting that the spatial periodicity however, forces a relation between the speed and the phase, which results in some unique challenges in the computations of the quantities involved in the stability index. Our results generalize recent work on the simpler case of standing waves of Natali-Pastor, [9] and Natali-Cardoso, [10].
Article information
Source
Differential Integral Equations, Volume 28, Number 5/6 (2015), 431-454.
Dates
First available in Project Euclid: 30 March 2015
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# Birkhoff normal form
Birkhoff–Gustavson normal form
Usually, a formal normal form (cf. Normal form of a system of differential equations) for a time-independent Hamiltonian system in the neighbourhood of a stationary point (cf. Normal form in a neighbourhood of a fixed point) for which the linearized system at the stationary point has only purely imaginary eigenvalues.
Consider a Hamiltonian system on $\mathbf R ^ {2n }$ with Hamiltonian $H \in C ^ \infty ( \mathbf R ^ {2n } )$, i.e.
$${\dot{z} } = J dH ( z ) = \left ( \begin{array}{c} ( { {\partial H } / {\partial y } } ) ( x,y ) \\ ( - { {\partial H } / {\partial x } } ) ( x,y ) \\ \end{array} \right )$$
with $x \in \mathbf R ^ {n}$, $y \in \mathbf R ^ {n}$, $z = ( x,y )$,
$$J = \left ( \begin{array}{cc} 0 &I _ {n} \\ - I _ {n} & 0 \\ \end{array} \right ) .$$
Suppose that $H ( 0 ) = dH ( 0 ) = 0$. The origin is a stationary point and the Hamiltonian evaluated at the origin is
$$H ( z ) = H _ {2} ( z ) + H _ {3} ( z ) + \dots + H _ {k} ( z ) + \dots ,$$
where $H _ {k} ( z )$ denotes the homogeneous terms of degree $k$. Furthermore, suppose that the matrix of the linearized system, $D ( J dH ) ( 0 )$, is diagonalizable (over $\mathbf C$) with purely imaginary eigenvalues $i \omega _ {k}$, $- i \omega _ {k}$, $k = 1 \dots n$. Let $\Omega = ( \omega _ {1} \dots \omega _ {n} )$. The eigenvalues are called resonant if they are rationally dependent, i.e. if there is an integer-valued vector $v$ such that $\langle {\Omega,v } \rangle = 0$, where $\langle {\ , } \rangle$ is the standard inner product on $\mathbf R ^ {2n }$. The eigenvalues are non-resonant if there is no such relation.
On $C ^ \infty ( \mathbf R ^ {2n } )$, define Poisson brackets by $\{ G,F \} = \langle {dF,J dG } \rangle$, where $G,F \in C ^ \infty ( \mathbf R ^ {2n } )$. Considering $\mathbf R ^ {2n }$ with the symplectic structure given by the standard symplectic form (see [a1]), $X _ {H} = \{ \ ,H \} = J dH$ is the Hamiltonian vector field generated by $H$.
$H$ is said to be in normal form up to order $k$ with respect to $H _ {2}$ if $\{ H _ {m} ,H _ {2} \} = 0$ for $m = 2 \dots k$. $H$ can be transformed into normal form using transformations of the type ${ \mathop{\rm exp} } ( X _ {F} )$. These transformations can be considered as the time- $1$ flow of the vector field $X _ {F} ( z )$, and therefore as symplectic diffeomorphisms on $\mathbf R ^ {2n }$. They can also be considered as differential operators acting on the space of homogeneous polynomials of degree $k$. These two points of view are related by the fact that $H _ {k} \circ { \mathop{\rm exp} } ( X _ {F} ) = { \mathop{\rm exp} } ( X _ {F} ) ( H _ {k} )$. Applying a transformation ${ \mathop{\rm exp} } ( X _ {F _ {3} } )$ with generating function $F _ {3}$ homogeneous of degree three gives
$${ \mathop{\rm exp} } ( X _ {F _ {3} } ) ( H ) = H _ {2} + X _ {F _ {3} } H _ {2} + H _ {3} + \textrm{ h.o.t. } .$$
The terms of degree three are $\{ H _ {2} ,F _ {3} \} + H _ {3}$. Consequently all terms in $H _ {3}$ that are in the image of $X _ {H _ {2} }$ can be removed by making the appropriate choice for the generating function $F _ {3}$. After having made a choice for $F _ {3}$ one gets
$${ \mathop{\rm exp} } ( X _ {F _ {3} } ) ( H ) = {\widehat{H} } = H _ {2} + {\widehat{H} } _ {3} + {\widehat{H} } _ {4} + \textrm{ h.o.t. } ,$$
with ${\widehat{H} } _ {3}$ in some complement of ${ \mathop{\rm im} } X _ {H _ {2} }$.
Next, consider a transformation ${ \mathop{\rm exp} } ( X _ {F _ {4} } )$ now taking a generating function $F _ {4}$ homogeneous of degree four. This gives
$${ \mathop{\rm exp} } ( X _ {F _ {4} } ) ( H ) = H _ {2} + {\widehat{H} } _ {3} + X _ {F _ {4} } H _ {2} + {\widehat{H} } _ {4} + \textrm{ h.o.t. } .$$
Thus, now one can remove all terms in $H _ {4}$ that are in the image of $X _ {H _ {2} }$. Repeating this process means that up to arbitrary degree one can remove all terms of $H$ that are in the image of $X _ {H _ {2} }$. This leads to the following idea of normal form: $H = H _ {2} + H _ {3} + \dots$ is in normal form up to degree $k$ with respect to $H _ {2}$ if $H _ {m}$, $m = 3 \dots k$, are in some complement of ${ \mathop{\rm im} } ( X _ {H _ {2} } )$. When the linearized system is diagonalizable, ${ \mathop{\rm ker} } ( X _ {H _ {2} } )$ can be chosen as a complement to ${ \mathop{\rm im} } ( X _ {H _ {2} } )$, giving $\{ H _ {2} , H _ {m} \} = 0$, $m = 2 \dots k$. Letting $k \rightarrow \infty$, one gets a formal normal form.
More on the basic ideas sketched above can be found in [a10], [a1], [a2]. The above idea was first used, although in an implicit way, by G.D. Birkhoff [a3] for deriving a normal form in the non-resonant case. Attention was again drawn to normal forms by F.G. Gustavson's paper [a7], where he obtained a formal normal form for the resonant cases. A similar normal form was obtained earlier by J. Moser [a9]. Gustavson emphasized that by normalizing up to infinite order extra formal integrals are obtained. The normal form has more symmetry than the original system.
The above ideas have been extended to the case where the linearized system has purely imaginary eigenvalues but is not diagonalizable [a8]. A normal form theory for non–Hamiltonian vector fields has also been developed along the above lines by using the Lie bracket of vector fields rather than Poisson brackets of functions [a4], [a6]. The most general context to formulate the theory is that of reductively filtered Lie algebras [a11].
Normal forms are of importance in the qualitative theory of differential equations. In particular, they play a role in bifurcation theory. Using Lyapunov–Schmidt reduction and the theory of singularities of differentiable mappings one can determine which number of terms of the normal form is sufficient to describe the bifurcation of stationary points and periodic solutions up to topological equivalence [a5], [a6], [a8].
#### References
[a1] R. Abraham, J.E. Marsden, "Foundations of mechanics" , Benjamin/Cummings (1978) MR0515141 Zbl 0393.70001 [a2] V.I. Arnol'd, V.V. Kozlov, A.I. Neishstadt, "Mathematical aspects of classical and celestial mechanics" , Dynamical systems III , Springer (1988) (In Russian) Zbl 0785.00010 Zbl 0674.70003 Zbl 0612.70002 [a3] G.D. Birkhoff, "Dynamical systems" , Amer. Math. Soc. Colloqium Publ. , IX , Amer. Math. Soc. (1927) MR1555257 Zbl 53.0733.03 Zbl 53.0732.01 [a4] R.H. Cushman, J.A. Sanders, "Nilpotent normal forms and representation theory of " M. Golubitsky (ed.) J. Guckenheimer (ed.) , Multiparameter Bifurcation Theory , Contemp. Math. , 56 , Amer. Math. Soc. (1986) pp. 31–51 MR0855083 Zbl 0604.58005 [a5] M. Golubitsky, D.G. Schaeffer, "Singularities and groups in bifurcation theory I" , Appl. Math. Sci. , 51 , Springer (1985) MR771477 Zbl 0607.35004 [a6] M. Golubitsky, I. Stewart, D.G. Schaeffer, "Singularities and groups in bifurcation theory II" , Appl. Math. Sci. , 69 , Springer (1988) MR950168 Zbl 0691.58003 [a7] F.G. Gustavson, "On constructing formal integrals of a Hamiltonian system near an equilibrium point" Astron. J. , 71 (1966) pp. 670–686 [a8] J.C. van der Meer, "The Hamiltonian Hopf bifurcation" , Lecture Notes in Mathematics , 1160 , Springer (1985) Zbl 0585.58019 [a9] J. Moser, "New aspects in the theory of Hamiltonian systems" Comm. Pure Appl. Math. , 9 (1958) pp. 81–114 Zbl 0082.40801 [a10] J. Moser, "Lectures on Hamiltonian systems" , Memoirs , 81 , Amer. Math. Soc. (1968) pp. 1–60 MR0230498 Zbl 0172.11401 [a11] J.A. Sanders, "Versal normal form computations and representation theory" E. Tournier (ed.) , Computer Algebra and Differential Equations , London Math. Soc. Lecture Notes , 193 , Cambridge Univ. Press (1994) pp. 185–210 MR1278060 Zbl 0804.17018
How to Cite This Entry:
Birkhoff normal form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Birkhoff_normal_form&oldid=46073
This article was adapted from an original article by J.C. van der Meer (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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# Running a lambda w/ report
I get that... I guess I just don't quite see why this case isn't possible.
To me, it seems totally reasonable to want to use RUN and then write some script that has IF <> REPORT to stop execution of just that script.
I'm also not convinced that an error is necessary. Showing an error when CALL does not get a return value makes sense to me, because you're expecting one. But if RUN sees a value, it seems safe to ignore it.
In almost any other language:
item = list.pop();
list.pop()
both do exactly what you'd expect and not using the return value is OK.
No, because if the script is being used in RUN, the way to stop it is IF <> STOP THIS SCRIPT.
Remember also that inside the FOR block body, the situation is exactly what you proposed here. Inside FOR there's a RUN (ACTION) and inside the ACTION script the user has put a REPORT block. The user's intention is clearly not to stop the ACTION script; it's to report a value from the block whose definition includes the call to FOR.
In other words, we have no way to distinguish your hypothetical situation from the FOR one.
But the different ring type should cancel that out. (in my opinion)
Sorry, I don't know what you mean. What type, and what is "that"?
the ring type is command vs. reporter, and `that' is the fact that they can't be used in the same context.
I think the debate going on here is great, but I have found @bh's example of the for-loop with counter to the be most compelling response.
The issue here is what should be done when an unexpected report is encountered. The preventative solution is to not report in an inappropriate context. Conversely, pad the "run" block with a "call" block when a reported value is expected and needs to be discarded.
Generally, the for-loop is considered a low-level construct. In Snap! where the lambda is a first-class citizen, the younger programmer will feel more at home when things behave somewhat imperatively.
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The for loop report could be fixed if rings kept their scope.
That plan would however break the catch block.
Once you decide to use a graphical interface in which reporters and commands are different shapes, which has the pedagogic purpose of quietly teaching that reporters combine by composition of functions, whereas commands combine in a sequence, you are going to end up making compromises in all sorts of funny corner cases. No question that lambda calculus, in which every function call returns a value, is way more elegant. In Scheme you can compose functions, but you can also put the same functions in a sequence and ignore all but the last return value. We can't do that, not unless we want ovals to snap into a sequence like jigsaw-piece blocks.
Until 10 years ago, our intro CS course for non-majors, the equivalent to the current CS 10 (i.e., BJC), used Scheme. In some ways that was more fun for me. Even though we're just about at the point where Snap! can do everything Scheme can do (just missing macros), I miss the joy of using God's programming language. But that course was all white and Asian males. (Not literally all, but not many exceptions.) So we decided to see how much of the Scheme feel we could retain and still have a language that everyone would find welcoming.
So. Scheme doesn't have REPORT at all, so it doesn't give any guidance about how to handle weird cases. Given that, I think the right thing is to make sure users can accomplish the things users want to accomplish, rather than to spend a lot of time on questions such as "what should happen if you CALL an empty ring?"
In this discussion, getting FOR to work properly was our main guidepost in planning things like REPORT in a command context. It wasn't trivial for Jens to implement finding the innermost reporter context and reporting from there -- a sort of implicit nonlocal exit -- but it was clearly the right thing. If there is no pending reporter context, then it's totally unclear what the user can have meant.
As a special case of the special case, if a toplevel script does a REPORT, we put the reported value in a speech balloon. That's our best guess as to what the user meant.
1 Like
(You need to be wearing the Turtle costume for this to work, not another costume.)
A's parent method.
Actually,python dosent have ';'s!
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It takes Tanya 50 minutes to drive to the country club. If the average
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It takes Tanya 50 minutes to drive to the country club. If the average speed of the entire round trip to the club is 87.5% of the average speed on the way to the club, how many minutes approximately will it take Tanya to drive home from the country club?
A. 42 minutes.
B. 48 minutes.
C. 52 minutes.
D. 54 minutes.
E. 66 minutes.
[Reveal] Spoiler: OA
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Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink]
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27 Jun 2016, 04:31
Time taken = 50 minutes = 5/6 hours
ones side distance = d1
speed = s1
d1=d2
d1=s1*(5/6)
d2=s1*(7/8)*t
s1*5/6=s1*7/8*t
t= 5*8/6*7=40/42= 20/21 = 95% = ~57 minutes
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Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink]
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28 Jun 2016, 05:27
Dear Bunuel, Is it E? I am getting approx 64.2 =~ 66 minutes
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28 Jun 2016, 05:50
chetan2u
hi could u pls weigh in on this problem
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Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink]
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28 Jun 2016, 13:53
Why one method works and the other doesn't is my favourite type of question. It's a good test of your fundamentals.
CounterSniper and royrijit1 allow me to reconcile the disparity between your respective approaches. rahulkashyap this might help you understand as well.
Let us first review the fundamentals required to solve this question:
Theory: If the same distance is covered twice, but with different speeds then the average speed for the total trip = 2(S1*S2)/(S1+S2)
Speed = Distance / Time , As long as one of the factors ( speed , time or distance ) is constant you can equate the other 2.
i.e for the same distance S1/S2 = T2/T1
for the same speed D1/T1 = D2/T2
for the same time D1/S1 = D2/S2
Solution:
Tanya's speed while travelling to the country club = S1
Tanya's speed while travelling back from the country club = S2
Average speed for the entire trip = 2(S1*S2)/(S1+S2)
As per the question, Average speed = 7/8 * S1
2(S1*S2)/(S1+S2) = 7/8 * S1 --> 16 * S2 = 7 * S1 + 7 * S2 --> 9*S2 = 7*S1
Since the distance, D, is constant for each trip --> S1/S2 = T2/T1 = 9/7
T2 = 50 * 9/7 = 64.28 mins ----Same as ---> T2 = 5/6 * 9/7 = 1.071 hrs
Lets us now review the approach used by CounterSniper.
d1=s1*(5/6)
d2=s1*(7/8)*t
s1*5/6=s1*7/8*t -------> (here lies the problem)
if you solve the above you will get approx 57 mins.
Note the average speed = 7/8 S1 and not the speed for the return trip (S2). The above method makes it seem as if you are equating the distance for each trip, but incorrectly using 7/8S1 as the speed for the second trip.
If you want to use the average speed to solve the question, using the method mentioned above, then multiply the distance by 2 as the average speed is calculated for the same distance covered twice.
2 * s1*5/6 = s1*7/8*t
t = 1.904 hrs approx = 114.2 mins approx (This is the time for covering the distance twice. ie going to and coming from the country club)
Time taken to return from the country club = 114 - 50 = 64 mins
NOTICE: if you just multiply the incorrect answer of 57 mins by 2 you get 114 mins.
- Light Yagami
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Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink]
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28 Jun 2016, 15:21
let t=time to drive home
d=one way distance
2d/(50+t)=7/8*d/50
t=450/7=64.3 minutes
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Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink]
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28 Jun 2016, 18:23
let the speed at which he drives to club be s
then avg speed = (total distance)/(total time taken)
avg speed =0.875s
total distance = 2d (d being distance)
total time taken = 50 min + x ( x is the unknown to be found)
hence
0.875s= (2d)/(50 +x)
now we know that s=d/50
there fore
0.875(d/50)= (2d)/(50+x)
1.75/100= 2/50+x
1.75(50+x)=200
50+x=200/1.75
x=114.28-50== 64.28 min
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Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink]
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28 Jun 2016, 23:15
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Bunuel wrote:
It takes Tanya 50 minutes to drive to the country club. If the average speed of the entire round trip to the club is 87.5% of the average speed on the way to the club, how many minutes approximately will it take Tanya to drive home from the country club?
A. 42 minutes.
B. 48 minutes.
C. 52 minutes.
D. 54 minutes.
E. 66 minutes.
When distances traveled on two legs of a journey are the same,
Avg Speed = $$\frac{2ab}{(a + b)}$$
$$(\frac{7}{8})s = \frac{2*s *b}{(s + b)}$$
$$7(s + b) = 16b$$
$$b = (\frac{7}{9})s$$
So speed of going from club to home is (7/9)s
Time taken = 50*(9/7) = more than 63 mins
Method 2: I would approximate here using the concept of average speed when same distance is covered at different speeds:
Speed on one leg is s and average is (7/8)s. If speed on the other leg were (6/8)s, the average would be slightly less than (7/8)s. So speed on the other leg must be a bit more than (6/8)s = (3/4)s
So time taken on the second leg would be a bit less than 50*(4/3) = 66.66
(The option given is quite a bit off from the actual answer. That usually shouldn't be the case in an actual GMAT question.)
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 21 Feb 2016 Posts: 9 Location: United States (MA) Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink] Show Tags 30 Jun 2016, 07:53 Let the distance be d, so the round-trip distance=2d Again, let he took x minutes to get back. So, his up speed= d/50 and average speed=2d/x+50, which is 87.5% (7/8) of the up speed. So, 2d/x+50=d/50*7/8 x=64+2/7 mins So, ans E Senior Manager Joined: 20 Feb 2015 Posts: 385 Concentration: Strategy, General Management Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink] Show Tags 30 Jun 2016, 09:40 ok , I messed it up a bit as usual. took 87.5% as the returning speed instead of the round trip. though already solved, average speed = 2ab/a+b (where a is the speed with which she drives to country club and b is while coming back) as per the question. 2ab/a+b=(7/8)a or, a/b=9/7 now since , speed is inversely proportional to time t1/t2=7/9 (where t1 = 50 min and t2= time taken at speed b ) or, t2=50(9/7)= ~66 minutes Senior Manager Joined: 15 Sep 2011 Posts: 348 Location: United States WE: Corporate Finance (Manufacturing) It takes Tanya 50 minutes to drive to the country club. If the average [#permalink] Show Tags 18 Jul 2016, 18:46 2 This post received KUDOS Top Contributor Option E. Since $$\frac{7}{8}$$ is the average speed, then the inverse of it is the average time, $$\frac{8}{7}$$. Calculate the average time by multiplying the given time: $$\frac{8}{7}*50 = ~57$$. Therefore, since the average time is 57, the second time must be greater than 57 minutes. The only option for that is E. VeritasPrepKarishma, Thoughts? Senior Manager Joined: 03 Apr 2013 Posts: 290 Location: India Concentration: Marketing, Finance Schools: Simon '20 GMAT 1: 740 Q50 V41 GPA: 3 Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink] Show Tags 17 Nov 2016, 01:35 1 This post was BOOKMARKED Bunuel wrote: It takes Tanya 50 minutes to drive to the country club. If the average speed of the entire round trip to the club is 87.5% of the average speed on the way to the club, how many minutes approximately will it take Tanya to drive home from the country club? A. 42 minutes. B. 48 minutes. C. 52 minutes. D. 54 minutes. E. 66 minutes. Somewhat different approach Here's my 2 cents... The average sped of the entire journey is $$\frac{7}{8}$$th of the original speed. If the speed had not changed, then the total journey time would have been 100 minutes. But it did change to $$\frac{7}{8}$$th . Therefore, the total time for the journey will be $$\frac{8}{7}$$th of 100. We know that the first leg took 50 minutes. so the second leg took? $$\frac{800}{7} - 50$$ = 64.2 ~ 66 (E) _________________ Spread some love..Like = +1 Kudos Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2273 Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink] Show Tags 09 Apr 2018, 16:34 Bunuel wrote: It takes Tanya 50 minutes to drive to the country club. If the average speed of the entire round trip to the club is 87.5% of the average speed on the way to the club, how many minutes approximately will it take Tanya to drive home from the country club? A. 42 minutes. B. 48 minutes. C. 52 minutes. D. 54 minutes. E. 66 minutes. We can let a = average speed of the round trip, b = average speed to the club, c = average speed back home and d = the one-way distance. We need to determine d/c. We are given that d/b = 5/6 (recall that 50 minutes = 5/6 hour) and a = (7/8)b (recall that 87.5% = 7/8). Using the average speed for the round trip, we can create the following equation: a = 2d/(d/b + d/c) a = 2d/(5/6 + d/c) 5/6 + d/c = 2d/a d/c = 2d/a - 5/6 Recall that a = (7/8)b, so substituting (7/8)b for a, we have: d/c = 2d/[(7/8)b] - 5/6 d/c = 2(d/b)/(7/8) - 5/6 d/c = 2(5/6)/(7/8) - 5/6 d/c = 5/3 x 8/7 - 5/6 d/c = 40/21 - 5/6 d/c = 80/42 - 35/42 = 45/42 = 15/14 hr We see that this is more than 1 hour or 60 minutes, and the only answer choice that is greater than 60 minutes is choice E (66 minutes) so E is the correct answer. Answer: E _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 11 Dec 2016 Posts: 23 Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink] Show Tags 10 Apr 2018, 08:49 Bunuel Hi! Can you please have a look at my solution and tell me if i've done it correct? Suggestions from other members will be appreciates. Thanks! Attachments File comment: @Bunuel Hi! Can you please have a look at my solution and tell me if i've done it correct? Suggestions from other members will be appreciates. Thanks! image1.jpeg [ 894.71 KiB | Viewed 395 times ] Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8028 Location: Pune, India Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink] Show Tags 11 Apr 2018, 05:07 asfandabid wrote: Bunuel Hi! Can you please have a look at my solution and tell me if i've done it correct? Suggestions from other members will be appreciates. Thanks! Note that this is not correct. The average speed of x and y would be (x + y)/2 when they are maintained over the same stretch of TIME. The average speed of x and y is 2xy/(x + y) when they are maintained over the same stretch of DISTANCE. You can easily derive these from Average Speed = Total Distance / Total Time Check this post for more: https://www.veritasprep.com/blog/2015/0 ... -the-gmat/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199
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Posts: 23
Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink]
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11 Apr 2018, 07:25
VeritasPrepKarishma
Got it, thanks!!
Intern
Joined: 24 Apr 2016
Posts: 8
Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink]
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14 Apr 2018, 18:09
VeritasPrepKarishma wrote:
Bunuel wrote:
It takes Tanya 50 minutes to drive to the country club. If the average speed of the entire round trip to the club is 87.5% of the average speed on the way to the club, how many minutes approximately will it take Tanya to drive home from the country club?
A. 42 minutes.
B. 48 minutes.
C. 52 minutes.
D. 54 minutes.
E. 66 minutes.
When distances traveled on two legs of a journey are the same,
Avg Speed = $$\frac{2ab}{(a + b)}$$
$$(\frac{7}{8})s = \frac{2*s *b}{(s + b)}$$
$$7(s + b) = 16b$$
$$b = (\frac{7}{9})s$$
So speed of going from club to home is (7/9)s
Time taken = 50*(9/7) = more than 63 mins
Method 2: I would approximate here using the concept of average speed when same distance is covered at different speeds:
Speed on one leg is s and average is (7/8)s. If speed on the other leg were (6/8)s, the average would be slightly less than (7/8)s. So speed on the other leg must be a bit more than (6/8)s = (3/4)s
So time taken on the second leg would be a bit less than 50*(4/3) = 66.66
(The option given is quite a bit off from the actual answer. That usually shouldn't be the case in an actual GMAT question.)
Hi VeritasPrepKarishma - Would you mind letting me know how you knew right away that 87.5% = 7/8? I know that 1/8 = .125 but didn't put together that 7x that would be 7/8. Is this something to be memorized as well?
Intern
Status: GMAT in July 2018
Joined: 05 Mar 2018
Posts: 15
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WE: Law (Consulting)
Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink]
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14 Apr 2018, 22:53
Ok I solved this a bit differently, may be a fluke!
Going:
T= D/S
50/60= D/100 --> assumed speed as 100
Returning:
T=D/S
t2 = D/s2 --> I don't know s2 here, but I know their avg speed is 87.5. Thus solving I get s2 as 75
Noe distance D is constant. Thus 50*100/60 (from going) is equal to t2*75 (from return)... This gives us t2 as 66.66666.... E
Not sure if this works always!
Bunuel the great, is the approach ok? Thanks.
Sent from my iPad using GMAT Club Forum
Re: It takes Tanya 50 minutes to drive to the country club. If the average [#permalink] 14 Apr 2018, 22:53
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Is SharePoint 2016 compatible with the 2012R2 functional domain / forest structure level of Windows Active Directory?
I would like to know if there is documentation from Microsoft stating that SharePoint 2016 is compatible with the 2012R2 functional domain / forest level of Windows Active Directory
How can I leave the FOR loop in the switch structure?
I'm in a bind For and I want to close it inside Switchbut if I give break in the Switch he goes Switch and the bond goes on ForCan someone tell me how to leave the loop For?
Here is the code:
bool variable = true;
for (int i = 0; i <length; i ++)
{
Switch (variable)
{
True case:
{
break;
}
break;
Case wrong:
{
Continue;
}
break;
Default:
break;
}
}
8 – Change the Field Instance Settings form to admin / structure / types / manage // fields / node ../ storage
I'm trying to figure out how to add an extra field to the content type field settings page.
Basically, I want to change the field instance setup form Admin / Structure / Types / Manage // Fields / Nodes ../ Memory ,
I go with hook_form_FORM_ID_alter for FORM_ID field_config_edit_form,
The new form element appears on the form, but after submitting, I can not see the value.
Am I missing something? Is an additional form submit function required to submit the new value?
Here is my clipping –
/ **
* Implemented hook_form_FORM_ID_alter ().
* /
Function mymod_form_field_storage_config_edit_form_alter (& $form, Drupal Core Form FormStateInterface$ form_state, $form_id) {$ form['enabled'] = Array (
& # 39; # type & # 39; => & # 39; checkbox & # 39 ;,
& # 39; # title & # 39; => t (& # 39; Enable & # 39;),
& # 39; # description & # 39; => t (& # 39; When enabled, this module changes the field settings. & # 39;),
& # 39; # default_value & # 39; => $form['enabled'], ); } Combination of two areas with identical column structure from two different tables (same URL) I'm doing a simple ticket system where I have two sheets, "Form Responses" and "Email Responses," both of which are automatically filled in as their names imply (one from a form, one from an e-mail with zapier). Both sheets have the same headers (eg timestamp, e-mail address, subject, description). I want to create a third leaf that has the same headers again, but contains content from "Form Responses" and "Email Responses", sorted by timestamp. I tried = {& # 39; form responses 1 & # 39 ;! A2: H18, & # 39; email replies & # 39; A2: H18} but it put the leaves side by side, and I had to restrict that Reference request – from homologous data to the existence of a module structure Thank you for your response to MathOverflow! • Please be sure answer the question, Provide details and share your research! But avoid • Ask for help, clarification or answers to other answers. • Make statements based on opinions; secure them with references or personal experiences. Use MathJax to format equations. Mathjax reference. For more information, see our tips for writing great answers. Permalink Structure Custom Taxonomy Slug / cpt-Slug breaks the ability to have subpages and page breaks (Error 404) I took over a WordPress project from another programmer who wrote code to create the custom-taxonomy-slug / cpt-slug permalink structure. The custom taxonomy is "city", the cpt is "restaurant", so every restaurant receives one city as a category, so the restaurant "Big Burgers" in Berlin would have the permalink "Berlin / Big Burger". This works, but the problem is that its code results in 404 errors for normal subpages (page name / subpage name) and also for blog pagination (blog / page / 2). Here is the main part in functions.php, which is responsible for this problem: Function entry_rewrite_rules () {$ custom_structure = & # 39; /% city% /% restaurant% & # 39 ;;
add_rewrite_tag ("% restaurant%", "([^/]+) & # 39 ;, restaurant = ");
add_permastruct (# restaurant; $custom_structure, array (& # 39; walk_dirs & # 39; => false)); } add_action ("init", "entry_rewrite_rules"); There is another part that manipulates only the permalink for the cpt restaurant, but not the part that leads to the 404 errors. Function change_entry_permalink ($ url, $post) { if (get_post_type ($ post) === & # 39; restaurant & # 39;
$terms = wp_get_object_terms ($ post-> ID, & # 39; city & # 39;);
if ($terms) { return str_replace (& # 39;% city% & # 39 ;,$ terms)[0]-> slug, $url); } } return$ url;
}
As far as I know, the problem is that the other programmer did not add a permalink base to his own link structure, e.g. "entries /% city% /% restaurant%" so that all page / subpage links are treated as restaurant links and lead to errors if they are not links to a restaurant entry.
The website has been online for many years and there are nearly 4000 restaurants. Therefore, it is probably not a good option to change the permalinks for the restaurants (and the addition of redirects). (4000 redirects can be bad for performance and SEO.)
So my questions are:
1. How do I get the pagination for the blog in the normal way, eg. Blog / Page / 2? (Da / blog works, I know that I could program my own pagination logic with eg / blog? Page = 2, but I would rather not.
2. Although I can generally live without subpages, it would still be nice if certain subpages could work, even if it means adding code for each permalink, such as a. my-page / my-important-subpage
I have thought about somehow changing the regex in this part to exclude blog / page / 2 or other specific permalinks:
add_rewrite_tag ("% restaurant%", "([^/]+) & # 39 ;, restaurant = ");
Unfortunately, everything I tried failed because I do not fully understand what's happening there, and I'm not good at making regex code.
My other idea was to change the priority argument for adding the rewrite rules, but not set to 1 or 99:
add_action ("init", "entry_rewrite_rules"), 1); // or 99 or 20 ...
As I said, making blog / page / 2 work is my priority. If you have other ideas to restore the "normal" ability to create subpages, it would be great too.
apache – Change server structure to display files / folders in the browser (Dedictaed server)
I'm trying to deploy WordPress on a Red Hat Linux server (dedicated server).
I'm trying to access it with the normal URL structure [IP]/[rootfoldername]/[nameofthefile] but it does not work
Note that phpmyadmin is a working file on the server.
Below is the default server page and the FTP view:
Should I change the structure of the FTP?
The GTA folder contains the WordPress files. I need to access it to run the installation wizard.
There is no way to divide the tree structure of N nodes by edge deletion in forest, so the XOR of all elements in each subtree is Z.
Note that there are no edge erasures in the area[0,n-1],
I have been struggling with this problem for 3 days. Can this be solved better than O (n ^ 2)?
Another essay with 100 words about the robot
BlackHatKings: General PPC discussion
Posted by: GalenEa
Post-Time: 5 February 2019 at 04:46.
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## LOG#095. Group theory(XV).
The topic today in this group theory thread is “sixtors and representations of the Lorentz group”. Consider the group of proper orthochronous Lorentz transformations and the transformation law of the electromagnetic tensor . The components of this antisymmetric tensor can … Continue reading
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Difference between a minimal DFA and a canonical DFA
given a language L,a DFA M that recognize L is minimal if M is the DFA with the minimum number of states. In order for this to happen M does not have neither unreachable nor equivalent states. The minimum DFA will be unique unless the names of states. Now my question is what is the difference between minimal and canonical DFA? They are the same thing?
Yes. The canonical DFA for a regular language $L$ is the automaton that is based on the equivalence classes of the relation defined by $L$, i.e., they cannot be "distinguished" in $L$ by extending them with the same suffix.
It is part of the Myhill-Nerode results that that yields a minimal DFA for $L$.
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## onegirl Group Title Evaluate lim h->0 (1/3+h - 1/3)/h one year ago one year ago
1. onegirl
I got 1 but is it correct?
If it is, $\lim \limits_{h \to 0} \frac{\frac{1}{3}+h-\frac{1}{3}}{h}$ yes the answer is 1
3. onegirl
Okay thanks :)
4. onegirl
wait hold no that not the equation :/ it is lim->0 1 over 3 + h then - 1/3 over h sorry
5. onegirl
6. onegirl
so would it be -1/9 then?
$\lim \limits_{h \to 0} \frac{\frac{1}{3+h}-\frac{1}{3}}{h}=\lim \limits_{h \to 0} \frac{-h}{3(3+h)h}=\lim \limits_{h \to 0} \frac{-1}{3(3+h)}=\frac{-1}{9}$ Yes you're correct
8. onegirl
okay thanks :)
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# Why is my MATLAB code for back-substitution slower than the backslash operator?
I wrote the code below to invert an upper triangular matrix, avoiding any possible multiplication/subtraction by zero. It just uses $\frac{1}{6}n^3+\ldots$ flops instead of $n^3+\ldots$ flops.
function B = InvTrMat(A,n,type)
% This code inverts an upper triangular matrix of order n
% without doing any multiplication or subtraction by zero.
B = zeros(n);
for j = 1:n
B(j,j) = 1 / A(j,j);
for i = j-1:-1:1
for k = i+1:j
B(i,j) = B(i,j) - A(i,k) * B(k,j);
end
B(i,j) = B(i,j) * B(i,i);
end
end
return
end
The problem is it is slower than the backslash command of Matlab. I used the following code to test and compare both:
n = 128;
t = zeros(1,100);
u = zeros(1,100);
for i = 1:100
A = rand(n,n);
A = A+A';
A = A + n*eye(n);
R = chol(A);
tic;
B = R \ eye(n);
t(i) = toc;
tic;
B = InvTrMat(R,n,'u');
u(i) = toc;
end
sum(t)/100
sum(u)/100
Does anyone know how to make my code faster than Matlab's code? It must be possible since I'm using just a fraction of flops from the other code.
My Matlab version is 7.10.0 (R2010a), installed on a Windows 8.0 64-bits PC.
Thank you, everyone.
• Out of curiosity, what are the timings you get? I get about a factor of 83 difference. I'm actually surprised it's not more. – Doug Lipinski Nov 18 '14 at 1:33
MATLAB's \ (aka mldivide) command does not blindly compute the inverse of the matrix. Instead, it uses one of several algorithms based on the type of matrix (see the "Algorithms" section of http://www.mathworks.com/help/matlab/ref/mldivide.html). In the case of a triangular matrix, MATLAB will use a triangular solver which is at least as good as yours in terms of operation count (I haven't looked at your code too closely but they're probably the same algorithm).
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# nbodykit.algorithms.convpower.fkp¶
Functions
copy_meta(attrs, meta[, prefix]) get_compensation(mesh) get_real_Ylm(l, m) Return a function that computes the real spherical harmonic of order (l,m) is_valid_crosscorr(first, second)
Classes
ConvolvedFFTPower(first, poles[, second, …]) Algorithm to compute power spectrum multipoles using FFTs for a data survey with non-trivial geometry.
class nbodykit.algorithms.convpower.fkp.ConvolvedFFTPower(first, poles, second=None, Nmesh=None, kmin=0.0, kmax=None, dk=None, use_fkp_weights=None, P0_FKP=None)[source]
Algorithm to compute power spectrum multipoles using FFTs for a data survey with non-trivial geometry.
Due to the geometry, the estimator computes the true power spectrum convolved with the window function (FFT of the geometry).
This estimator implemented in this class is described in detail in Hand et al. 2017 (arxiv:1704.02357). It uses the spherical harmonic addition theorem such that only $$2\ell+1$$ FFTs are required to compute each multipole. This differs from the implementation in Bianchi et al. and Scoccimarro et al., which requires $$(\ell+1)(\ell+2)/2$$ FFTs.
Results are computed when the object is inititalized, and the result is stored in the poles attribute. Important meta-data computed during algorithm execution is stored in the attrs dict. See the documenation of run().
Note
A full tutorial on the class is available in the documentation here.
Note
Cross correlations are only supported when the FKP weight column differs between the two mesh objects, i.e., the underlying data and randoms must be the same. This allows users to compute the cross power spectrum of the same density field, weighted differently.
Parameters: first (FKPCatalog, FKPCatalogMesh) – the first source to paint the data/randoms; FKPCatalog is automatically converted to a FKPCatalogMesh, using default painting parameters poles (list of int) – a list of integer multipole numbers ell to compute second (FKPCatalog, FKPCatalogMesh, optional) – the second source to paint the data/randoms; cross correlations are only supported when the weight column differs between the two mesh objects, i.e., the underlying data and randoms must be the same! kmin (float, optional) – the edge of the first wavenumber bin; default is 0 kmax (float, optional) – the limit of the last wavenumber bin; default is None, no limit. dk (float, optional) – the spacing in wavenumber to use; if not provided; the fundamental mode of the box is used
References
• Hand, Nick et al. An optimal FFT-based anisotropic power spectrum estimator, 2017
• Bianchi, Davide et al., Measuring line-of-sight-dependent Fourier-space clustering using FFTs, MNRAS, 2015
• Scoccimarro, Roman, Fast estimators for redshift-space clustering, Phys. Review D, 2015
Methods
load(output[, comm, format]) Load a saved ConvolvedFFTPower result, which has been saved to disk with ConvolvedFFTPower.save(). normalization(name, alpha) Compute the power spectrum normalization, using either the data or randoms source. run() Compute the power spectrum multipoles. save(output) Save the ConvolvedFFTPower result to disk. shotnoise(alpha) Compute the power spectrum shot noise, using either the data or randoms source. to_pkmu(mu_edges, max_ell) Invert the measured multipoles $$P_\ell(k)$$ into power spectrum wedges, $$P(k,\mu)$$.
__setstate_pre000305__(state)[source]
compatible version of setstate for files generated before 0.3.5
classmethod load(output, comm=None, format='current')[source]
Load a saved ConvolvedFFTPower result, which has been saved to disk with ConvolvedFFTPower.save().
The current MPI communicator is automatically used if the comm keyword is None
format can be ‘current’, or ‘pre000305’ for files generated before 0.3.5.
normalization(name, alpha)[source]
Compute the power spectrum normalization, using either the data or randoms source.
The normalization is given by:
$A = \int d^3x \bar{n}'_1(x) \bar{n}'_2(x) w_{\mathrm{fkp},1} w_{\mathrm{fkp},2}.$
The mean densities are assumed to be the same, so this can be converted to a summation over objects in the source, as
$A = \sum w_{\mathrm{comp},1} \bar{n}_2 w_{\mathrm{fkp},1} w_{\mathrm{fkp},2}.$
References
see Eqs. 13,14 of Beutler et al. 2014, “The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: testing gravity with redshift space distortions using the power spectrum multipoles”
run()[source]
Compute the power spectrum multipoles. This function does not return anything, but adds several attributes (see below).
edges
the edges of the wavenumber bins
Type: array_like
poles
a BinnedStatistic object that behaves similar to a structured array, with fancy slicing and re-indexing; it holds the measured multipole results, as well as the number of modes (modes) and average wavenumbers values in each bin (k)
attrs
dictionary holding input parameters and several important quantites computed during execution:
1. data.N, randoms.N :
the unweighted number of data and randoms objects
2. data.W, randoms.W :
the weighted number of data and randoms objects, using the column specified as the completeness weights
3. alpha :
the ratio of data.W to randoms.W
4. data.norm, randoms.norm :
the normalization of the power spectrum, computed from either the “data” or “randoms” catalog (they should be similar). See equations 13 and 14 of arxiv:1312.4611.
5. data.shotnoise, randoms.shotnoise :
the shot noise values for the “data” and “random” catalogs; See equation 15 of arxiv:1312.4611.
6. shotnoise :
the total shot noise for the power spectrum, equal to data.shotnoise + randoms.shotnoise; this should be subtracted from the monopole.
7. BoxSize :
the size of the Cartesian box used to grid the data and randoms objects on a Cartesian mesh.
For further details on the meta-data, see the documentation.
Type: dict
save(output)[source]
Save the ConvolvedFFTPower result to disk.
The format is currently json.
Parameters: output (str) – the name of the file to dump the JSON results to
shotnoise(alpha)[source]
Compute the power spectrum shot noise, using either the data or randoms source.
This computes:
$S = \sum (w_\mathrm{comp} w_\mathrm{fkp})^2$
References
see Eq. 15 of Beutler et al. 2014, “The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: testing gravity with redshift space distortions using the power spectrum multipoles”
to_pkmu(mu_edges, max_ell)[source]
Invert the measured multipoles $$P_\ell(k)$$ into power spectrum wedges, $$P(k,\mu)$$.
Parameters: mu_edges (array_like) – the edges of the $$\mu$$ bins max_ell (int) – the maximum multipole to use when computing the wedges; all even multipoles with $$ell$$ less than or equal to this number are included pkmu – a data set holding the $$P(k,\mu)$$ wedges BinnedStatistic
nbodykit.algorithms.convpower.fkp.get_real_Ylm(l, m)[source]
Return a function that computes the real spherical harmonic of order (l,m)
Parameters: l (int) – the degree of the harmonic m (int) – the order of the harmonic; abs(m) <= l Ylm – a function that takes 4 arguments: (xhat, yhat, zhat) unit-normalized Cartesian coordinates and returns the specified Ylm callable
References
https://en.wikipedia.org/wiki/Spherical_harmonics#Real_form
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Showing that one axiom of the concept group action implies another (similar to group homomorphisms)
[Beware that my question is at the bottom of all this text.]
We defined in a group theory course a group action to be a mapping $$\nu:G\times X \rightarrow X,$$ $(G,\cdot)$ group and $X$ some set, such that the axioms $$\textrm{(GA1)} \ \ \ \nu(1,x)=x$$ and $$\textrm{(GA2)} \ \ \ \nu(g,\nu(h,x))=\nu(g h, x)$$ hold for every $g,h\in G$ and $x\in X$.
We defined a group homomorphism to be a map $$f:G\rightarrow H,$$ such that the axioms $$\textrm{(HOM1)} \ \ \ f(1_G)=1_H$$ and $$\textrm{(HOM2)} \ \ \ f(gh)=f(g)f(h)$$ hold for all $g,h \in G$.
Now, obviously, these axioms for the homomorphism aren't minimal, meaning (HOM2) $\Rightarrow$ (HOM1). So, naturally, I asked myself, if the same doesn't happen with the group action axioms, meaning (GA2) $\Rightarrow$ (GA1).
Now the thing is, I can show that this is the case by showing that a mapping $\nu$ satisfies (GA2) iff the mapping $$\tau: G\rightarrow X_{\leftrightarrow} ,$$ where $X_{\leftrightarrow}$ is the group of all bijections on $X$ together with the composition, defined by $$\tau(g)(x)=\nu(g,x),$$ is a homomorphism:
$(\tau(g)\circ \tau(h))(x)=\tau(g)(\nu(h,x))=\nu(g,\nu(h,x)),$ which by (GA2) equals $\nu(gh,x)=\tau(gh)(x)$, and $\nu(g,\nu(h,x))=\tau(g)(\tau(h)(x))$ which by (HOM2) equals $\tau(gh)(x)=\nu(gh,x)$ for all $g,h\in G$ and $x\in X$.
From that I can now show (GA1) by the following implications: $$\textrm{(GA2)} \Leftrightarrow \textrm{(HOM2)} \Rightarrow \textrm{(HOM1)} \Rightarrow \textrm{(GA1)}.$$
Now (finally) my question: Can't I show that (GA1) follows from (GA2) directly ? I tried doing that, but couldn't succeed, because unlike showing $\textrm{(HOM2)} \Rightarrow \textrm{(HOM1)}$ I don't have an thing like an "inverse to $\nu(1,x)$" that I can apply upon $\nu(1,\nu(1,x))=\nu(1,x)$ to get $\nu(,x)=1$.
-
You want $\nu:G\times X\to X$. – Brian M. Scott Nov 1 '11 at 12:16
Fixed.${}{}{}{}$ – joriki Nov 1 '11 at 12:36
Refixed, after somebody changed it again. – el le Nov 1 '11 at 12:53
Let $G=\{1_G\}$ be the trivial group, and let $X=\mathbb{Z}$. Define $\nu:G\times X\to X$ by $$\nu(1_G,n)=\begin{cases} n,&n\text{ is even}\\ n-1,&n\text{ is odd}\;. \end{cases}$$
Clearly (GA$1$) isn’t satisfied, but for any $n\in\mathbb{Z}$ we have $$\nu(1_G,\nu(1_G,n)) = \nu(1_G,n) = \begin{cases} n,&n\text{ is even}\\ n-1,&n\text{ is odd}\;, \end{cases}$$ so (GA$2$) is satisfied.
Since this implies there's an error in the argument in the question, it might be worth pointing out where it is: You said that $\tau$ maps $G$ to the group of bijections, but you didn't prove that the maps you defined were actually bijections. Brian's example shows that they needn't be. But composition of non-bijective maps isn't a group operation, so the part where you use the inverse to go from (HOM2) to (HOM1) doesn't work out. By the way, the action of $1_G$ could be defined to be any non-trivial idempotent operation, e.g. a projection in a vector space. – joriki Nov 1 '11 at 12:43
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### Calendar
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The time for answering the question is over
259 cents
sorrysisnopowertoinbox
\underline{\underline{\bold{\mathsf{Plaster \:of \:paris }}}}
Plasterofparis
:—
◽In short it is also called as P.O.P.
◽Its chmeical name is calcium sulphate hemihydrate
◽The half molecule of water is attached with calcium sulphate.
◽It is a white powdery which is slightly hydrated calcium sulfate
◽\implies{\mathsf{ CaSO_4 \times \frac{1}{2}H_2 O \:or\: 2CaSO_4 \times H_2O }}⟹CaSO
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◽Plaster of Paris is the most commonly used plaster round the world and is also called gypsum plaster.
◽Gypsum is a colorless or white substance found near paris and is not highly water-soluble and is not at all hard.
◽A mixture of gypsum and water which is poured and as the the water evaporates. gypsum hardens.
◽Its given the name "plaster of paris" because of its preparation from the abundant gypsum found near Paris.
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# Indecomposable contracting maps on the integers
$$\def\ZZ{\mathbb{Z}}$$Call a function $$f : \ZZ \to \ZZ$$ "contracting" if $$|f(j) - f(i)| \leq |j-i|$$ for all $$i$$, $$j \in \ZZ$$. The contracting functions form a monoid under composition; call it $$C$$. An element of a monoid is called a "unit" if it is invertible; the units of $$C$$ are the functions $$x \mapsto \pm x + k$$. An element of a monoid is called irreducible" if it is not a unit and cannot be factored as the composition of two non-units.
Question 1: What are the irreducibles of $$C$$?
To give two nonobvious examples, the maps $$x \mapsto |x|$$ and $$x \mapsto \begin{cases} x & x \geq 0 \\ x+1 & x < 0 \end{cases}$$ are both irreducible.
The problem which I actually want the answer to is a slight variant of $$C$$: Define $$C_2$$ to be the monoid of maps $$f : \ZZ \to \ZZ$$ which are contracting and obey $$f(i) \equiv i \bmod 2$$. So what I would really like to know is:
Question 2: What are the irreducibles of $$C_2$$?
If you prefer finite monoids, I am fine with you working with $$\{ 0,1,2,\ldots,n \}$$ instead of $$\ZZ$$ for either question.
• Consider a function that increases linearly up to $-n$, then zigzags up and down irregulary between $-n$ and $n$ for much more than $n$ steps, then increases linearly to $\infty$. If we consider a "random" such function in some sense, it seems believable to me that the function is irreducible with high, but not quite $1$, probability. So there might not be a classification of irreducibles, any more than there is a classification of irreducible polynomials in two or more variables - they're just all the ones that don't happen to be reducible. May 20 at 19:22
• @WillSawin You and Nate seem to have incompatible intuitions (compare his last paragraph to your comment). May 20 at 20:43
• @DavidESpeyer, maybe this is no longer relevant. The papers on the finite case all seem to start from dergipark.org.tr/tr/download/article-file/435131. May 21 at 13:30
• In the finite case it seems that every noninvertible element is fixed by an nonidentity idempotent on the left so you should maybe replace irreducible by maximal in the J-order. This is proved in arxiv.org/pdf/1804.10057.pdf but note they with with the opposite semigroup because they act on the right May 21 at 20:51
• The buzzword for the finite case is contractions on a finite chain May 21 at 21:53
## 2 Answers
I'll solve question 2, on $$C_2$$.
I will prove the irreducibles are those that only have one or two bends, verifying a prediction of Nate (and disproving a prediction of myself).
Call a "run" a maximal interval on which $$f$$ is linear. Clearly $$f$$ is linear on $$[a,b]$$ if and only if we either have $$f(i)=i+1$$ for all $$i= a,\dots, b-1$$, or $$f(i) = i-1$$ for all $$i= a,\dots, b-1$$. Then $$[a,\dots, b]$$ is maximal if, in addition, we have $$f(a-1) = f(a)+1$$ and $$f(b+1) =f(b-1)$$ in the first case or $$f(a-1)=f(a)-1$$ and $$f(b+1)=f(b-1)$$ in the second case.
I'll show that if $$f$$ is irreducible and $$f$$ has a run then $$f$$ has exactly one run. The number of runs is the number of bends minus one, so this is equivalent to Nate's claim.
The length $$b-a$$ of a run is a nonnegative integer, so if there is any run, there is a run of minimal length. If $$[a,a+k]$$ is a run of minimal length, then $$f$$ must be linear on $$[a-k,a]$$ and $$[a+k,a+2k]$$ as otherwise these intervals would contain a shorter run (the longest linear subinterval touching $$[a,a+k]$$).
Assume wlog the run of minimal length is increasing. Then $$f( a-i ) = f(a)+i = f(a+i)$$ for $$0\leq i \leq k$$ and $$f(a+k-i) =f(a+k)-i = f(a+k+i)$$ for $$0 \leq i \leq k$$.
So if we let $$g(n)$$ be given by the rule that $$g(n) = n$$ for $$n \leq a$$, $$g(n) = 2a-n$$ for $$a\leq n \leq a+k$$, and $$g(n) = n-2k$$ for $$n\geq a+k$$, and $$h(n) = f(n)$$ for $$n \leq a$$ and $$h(n) = f(n+2k)$$ for $$n \geq a$$, then $$f =g \circ g$$.
So if $$f$$ is irreducible, since $$h$$ is certainly not invertible (we have $$k\geq 1$$ since runs have length at least $$1$$), $$g$$ must be invertible, i.e. translation or reflection. So $$f$$ has the same number of runs as $$h$$, i.e., one.
Too long for a comment, but not completely thought out:
Call a point $$x$$ a "bend" if $$f(x-1) = f(x+1)$$. I think if we restrict to the subclass of $$C_2$$ with finitely many bends then the only irreducible ones are those with $$1$$ or $$2$$ bends. Here is an idea for a proof:
If $$f(x)$$ has an odd number of bends then up to flipping sign it must have a global minimum $$m$$. If we take the right most $$y$$ point attaining that minimum. The claim is that we can write $$f$$ as a composition $$g \circ f'$$ where $$g(x) = |x-y| - m$$ and $$f'$$ is in $$C_2$$ with one fewer bend.
If $$f(x)$$ has an even number $$2n$$ of bends with $$n > 1$$ then the claim is that we can write it as a composition of $$h \circ k$$ with $$k$$ having just 2 bends and $$h$$ having $$2n-2$$ bends. The idea being that $$k$$ accounts for the leftmost pair of bends, and $$h$$ accounts for the rest, just shifted.
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## Precalculus (6th Edition) Blitzer
$(-4,3)$
Using the graph given in the exercise, we can identify the domain for $\frac{f(x)}{g(x)}$ as $\{x|-4\lt x\lt3\}$ or $(-4,3)$
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# Transcendental law of homogeneity
(Redirected from Transcendental Law of Homogeneity)
The Transcendental Law of Homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz most clearly in a 1710 text entitled Symbolismus memorabilis calculi algebraici et infinitesimalis in comparatione potentiarum et differentiarum, et de lege homogeneorum transcendentali (see Leibniz Mathematische Schriften, (1863), edited by C. I. Gerhardt, volume V, pages 377-382). Henk J. M. Bos describes it as the principle to the effect that in a sum involving infinitesimals of different orders, only the lowest-order term must be retained, and the remainder discarded.[1] Thus, if $a$ is finite and $dx$ is infinitesimal, then one sets
$a+dx=a$.
Similarly,
$u\,dv+v\,du+du\,dv=u\,dv+v\,du,$
where the higher-order term du dv is discarded in accordance with the TLH. A recent study argues that Leibniz's TLH was a precursor of the standard part function over the hyperreals.[2]
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# How to cite it properly?
What is the correct way to cite the following:
Should there be a comma after see also? And what is the command to produce it?
-
As @Alex said, and the whole aside not inside the first ref: [2] and the references therein (see also [13,15,33]). But alas, I cannot claim any authority on this issue other than gut feeling (my gut can be quite assertive sometimes). – Harald Hanche-Olsen Sep 6 '12 at 10:07
[2, and the references therein] conventionally refers to the study [2] and in it the Section, Chapter, or Theorem etc. which is called and the references therein. – percusse Sep 6 '12 at 10:58
The package natbib redefines the \citecommand with optional arguments that do exactly what you are asking for. Here is an example:
\documentclass{article}
\usepackage{filecontents}
\usepackage[numbers]{natbib}
\begin{filecontents}{biblio.bib}
@article{Author2012,
Author = {Author, A},
Title = {Article},
Year = {2012}}
\end{filecontents}
\begin{document}
\cite{Author2012}
\cite[e.g.]{Author2012}
\cite[see][]{Author2012}
\cite[and references therein]{Author2012}
\cite[see][and references therein]{Author2012}
\bibliographystyle{plainnat}
\bibliography{biblio}
\end{document}
The output looks like this:
If you prefer author-year citation style, you can remove the [numbers] option when loading the package, and you can replace the square brackets by round brackets with the option [round].
-
Some of that is also possible without natbib: \cite[Ch.~1]{Author2012} gives [1, Ch. 1] and \cite[p.~387]{Author2012} gives [1, p. 387]. Any words not relating to the citation should be kept outside the square brackets, see @percusse's comment above. – Alex Sep 6 '12 at 12:36
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# The HRC-I Background Spectra Files
## Overview
#### Synopsis:
The HRC calibration team has released a set of background spectra from the HRC-I. These spectra describe the particle background of the detector and vary slowly with time which means that they can be used to improve the signal-to-noise of HRC-I imaging data. This can significantly improve signal-to-noise for extended sources and may be useful for point source analysis (e.g. fields with many point sources).
#### Purpose:
The intent of this thread is to apply a PI (instrumental energy channel) filter to an HRC-I imaging event file to increase the signal-to-noise of the resulting images by removing channel ranges in which the particle background dominates. Calculating the cumulative source and background PI distributions allow us to estimate the fraction of source and background counts removed by a given PI filter.
To create an HRC-I background event file tailored to a specific observation for imaging or spatial analyses, follow the HRC-I Background Event Files thread instead.
Last Update: 2 Apr 2019 - Updated to use matplotlib for plotting.
## Get Started
unix% download_chandra_obsid 9700 evt2,asol,bpix,dtf
## Obtain the Response Files: ARF and RMF
This analysis requires an ARF and RMF. This section of the thread provides the necessary commands; refer to the ahelp files for asphist and mkarf for details.
For the HRC-I, a single RMF file distributed in the CALDB is used (rather than an observation specific one as for ACIS). We make a soft link to the file for easier access:
## Compute the cumulative background distribution
The background spectrum is used to estimate the reduction in the background signal that the PI filtering will achieve.
unix% sherpa
>>> d = get_data()
>>> pi = d.channel-1.0
>>> bgcumul = np.cumsum(d.counts)
>>> bgcdf = bgcumul * 1.0 / bgcumul[-1]
>>> import matplotlib.pylab as plt
>>> plt.figure(1)
>>> plt.plot(pi, bgcdf, marker="None")
>>> plt.xlabel("PI")
>>> plt.ylabel(r"$\Sigma$ (counts $\leq$ PI) / $\Sigma$ (counts)")
>>> plt.title(d.name.split("/")[-1])
>>> plt.show()
Note that the calculation for bgcdf assumes that d.counts is >= 0, which should be safe here.
## Compute the cumulative distributions for model spectrum
We assume that the source spectrum is unknown, so in order to select the PI range we use a soft and a hard spectrum to determine suitable lower and upper limits. For this thread we use an absorbed power law in both cases, varying the absorption and slope to maximize the relative flux at low or high energies, although other approaches are possible (in particular using a model similar to that of the source).
### Set up an ARF and RMF
We use the background model which we have already loaded to define the channel grid, and add an ARF and RMF to it.
>>> load_arf("9700_arf.fits")
>>> set_analysis("channel")
The set_analysis call is to ensure that the following modeling is done in PI channels rather than energy or wavelength units.
### Set up the "soft" model
>>> set_source(xswabs.abs1*powlaw1d.pl)
>>> abs1.NH = 0.001
>>> pl.gamma = 2.5
>>> plt.figure(2)
>>> plot_model(overplot=False)
>>> plt.show()
The add_window call is used so that the original plot is not deleted by the call to plot_model.
### Calculate the cumulative distribution
>>> scumul = np.cumsum(get_model_plot().y)
>>> scdf = scumul / max(scumul)
>>> plt.figure(1)
>>> plt.plot(pi,scdf, marker="None", color="red")
>>> plt.show()
Here we add the cumulative distribution for the soft model to the original plot, so that it can be compared to that of the background spectrum.
### Set up the "hard" model
>>> abs1.nh = 10
>>> pl.gamma = 1
>>> plt.figure(2)
>>> plot_model(overplot=True)
>>> plt.show()
### Calculate the cumulative distribution
>>> hcumul = np.cumsum(get_model_plot().y)
>>> hcdf = hcumul / max(hcumul)
>>> plt.figure(1)
>>> plt.plot(pi,hcdf, marker="None", color="blue")
>>> plt.show()
## Calculate the PI range
Various strategies could be employed to optimize the PI range. Ideally, we seek to maximize background reduction while minimizing loss of source events. In practice, the trade-off requires testing many different PI ranges and adopting one that suits best. One strategy is to require a certain amount of reduction in background, compute the appropriate PI range, and then estimate the magnitude of source event loss for a specific source model. Alternately, one could set forth an acceptable amount of source loss (sensible ranges are 1 to 10 per cent), compute the appropriate PI range, and then check how much of an improvement results in the background.
This thread follows the latter strategy. We will use a conservative strategy, and look to lose only 5% of source events, split equally over the low and high PI ranges. If xfrac is the fraction of events to exclude and is set to 5%, then we have
>>> xfrac = 0.05
>>> pimin = np.interp(xfrac/2, scdf, pi)
>>> pimax = np.interp(1-xfrac/2, hcdf, pi)
>>> lo = int(pimin)
>>> hi = int(pimax) + 1
>>> print ("PI range: %d to %d" % (lo,hi))
PI range: 47 to 293
Here we chose to round the minimum limit down and the maximum limit up; routines in the Python math module, such as floor and ceil can be used to implement different rounding strategies.
The lo to hi range can then be used to filter the level=2 event file when creating images.
## Calculating the background reduction
The PI range can be viewed by saying:
>>> plt.axvline(lo, color="green")
>>> plt.axvline(hi, color="green")
>>> plt.show()
and the fraction of the background that is excluded by these limits is calculated by:
>>> blo = np.interp(lo, pi, bgcdf)
>>> bhi = 1.0 - np.interp(hi, pi, bgcdf)
>>> bfrac = bhi + blo
>>> print("Fraction of background excluded is %g" % bfrac)
Fraction of background excluded is 0.242981
Filtering on the range PI=48:293 will reduce the background by ~25% while only losing ~5% of x-ray events.
## Apply the PI Filter
The PI range 48:293 is applied to the file in a Data Model filter:
unix% punlearn dmcopy
unix% dmcopy "hrcf09700N003_evt2.fits[pi=48:293]" hrcf09700_evt2_pi_flt.fits
A background annulus is defined around the source to check the number of "good" events in the filtered and unfiltered files:
unix% cat bkg.reg
# Region file format: CIAO version 1.0
annulus(16368.483,16336.472,2731.4111,4097.1167)
unix% dmstat "hrcf09700N003_evt2.fits[sky=region(bkg.reg)][cols pi]" ver=0
unix% pget dmstat out_good
54713
unix% dmstat "hrcf09700_evt2_pi_flt.fits[sky=region(bkg.reg)][cols pi]" ver=0
unix% pget dmstat out_good
42567
The percent change between the files is ~22% [(54713-42567)/54713 = 22], which is close to the 24% reduction we expected.
## Scripting It
The file hrci.shp performs the Sherpa commands used in this thread. One could loop over different values of xfrac to find the optimal S/N improvement.
## History
10 Jun 2010 new for CIAO 4.2/CALDB 4.3.0 11 Jan 2011 reviewed for CIAO 4.3: no changes 04 Apr 2011 updated for 04 Apr scripts package release: hrc_bkgrnd_lookup script prints the version at verbose > 0. 20 Jul 2011 required software updates are listed in Synopsis 11 Jan 2012 reviewed for CIAO 4.4 and CALDB 4.4.7: the 2010 HRC-I background PI spectrum file was remade with the new gain map (hrciD2010-09-25pibgspecN0001.fits), and the 2011 file has been added (hrciD2011-09-19pibgspecN0001.fits); added Scripting It section 03 Dec 2012 Review for CIAO 4.5; file version name changes 03 Dec 2013 Review for CIAO 4.6; no changes. 14 Apr 2014 Minor edits to text to clarify when/how to use this thread. Updated list of CALDB files. 18 Dec 2014 Reviewed for CIAO 4.7; no changes. 02 Apr 2019 Updated to use matplotlib for plotting.
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## marcoduuuh Group Title PLSPLSPLSPLS HELP. In the diagram below, is an altitude of ABD. What is the length of ? If necessary, round your answer to two decimal places. (Picture below.) one year ago one year ago
1. marcoduuuh
2. ZeHanz
First try to prove triangle ACB and ABD are similar. Similar triangles have proportional sides (meaning sides in the big triangle are a constant factor times the sides in the small one). Further hint: you may need the Pythagorean Theorem as well...
3. marcoduuuh
a^2+b^2=c^2. Where do I input 16 and 30?
4. marcoduuuh
16 = a, 30 = c?
5. ZeHanz
a and b are the rectagular sides, c is the hypothenuse
6. marcoduuuh
16^2+b^2=30^2 B= 25.38?
7. ZeHanz
No, a and b are the rectangular sides. In triangle ACB these are 16 and 30, so c²=16²+30²=256+900=1156, so c=34.
8. ZeHanz
So AB=34.
9. marcoduuuh
Now what do I do to find CD?
10. marcoduuuh
@ZeHanz
11. ZeHanz
ACB and ABD are similar, because they both have a right angle, and they have angle A in common. Similar triangles have proportional sides, which means:$\frac{ AC }{ AB }=\frac{ AB }{ AD }$ (read as: one side in first triangle : same side in other one= same number. Because in the above equation, you know 3 out of four lengths, you can calculate the fourth (AD). Once AD is known, you get CD = AD-16.
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NEWS@SKY (Science&Space News)
Home To Survive in the Universe
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# NGC 3832
Contents
### Images
DSS Images Other Images
### Related articles
Scale Heights of Non-Edge-on Spiral GalaxiesWe present a method of calculating the scale height of non-edge-onspiral galaxies, together with a formula for errors. The method is basedon solving Poisson's equation for a logarithmic disturbance of matterdensity in spiral galaxies. We show that the spiral arms can not extendto inside the forbidden radius'' r0, due to the effect ofthe finite thickness of the disk. The method is tested by re-calculatingthe scale heights of 71 northern spiral galaxies previously calculatedby Ma, Peng & Gu. Our results differ from theirs by less than 9%. Wealso present the scale heights of a further 23 non-edge-on spiralgalaxies. H I observations of galaxies. II. The Coma SuperclusterHigh sensitivity 21-cm H i line observations with an rms noise level of~0.5 mJy were made of 35 spiral galaxies in the Coma Supercluster, usingthe refurbished Arecibo telescope, leading to detection of 25 objects.These data, combined with the measurements available in the literature,provide the set of H i data for 94% of all late-type galaxies in theComa Supercluster with an apparent photographic magnitude mp≤ 15.7 mag. We confirm that the typical scale of H i deficiencyaround the Coma cluster is 2 Mpc, i.e. one virial radius. Comparing theH i mass function (HIMF) of cluster with non-cluster members of the ComaSupercluster we detected a shortage of high H i mass galaxies amongcluster members that can be attributed to the pattern of H i deficiencyfound in rich clusters. The Tully-Fisher Relation of Barred GalaxiesWe present new data exploring the scaling relations, such as theTully-Fisher relation (TFR), of bright barred and unbarred galaxies. Aprimary motivation for this study is to establish whether barrednesscorrelates with, and is a consequence of, virial properties of galaxies.Various lines of evidence suggest that dark matter is dominant in disksof bright unbarred galaxies at 2.2 disk scale lengths, the point of peakrotation for a pure exponential disk. We test the hypothesis that theTully-Fisher (TF) plane of barred high surface brightness galaxies isoffset from the mean TFR of unbarred galaxies, as might be expected ifbarred galaxies are maximal'' in their inner parts. We use existingand new TF data to search for basic structural differences betweenbarred and unbarred galaxies. Our new data consist of two-dimensionalHα velocity fields derived from SparsePak integral fieldspectroscopy and V- and I-band CCD images collected at the WIYNObservatory2 for 14 strongly barredgalaxies. Differences may exist between kinematic and photometricinclination angles of barred versus unbarred galaxies. These findingslead us to restrict our analysis to barred galaxies withi>50deg. We use WIYN/SparsePak (two-dimensional) velocityfields to show that long-slit (one-dimensional) spectra yield reliablecircular speed measurements at or beyond 2.2 disk scale lengths, farfrom any influence of the bar. This enables us to consider line widthmeasurements from extensive TF surveys that include barred and nonbarreddisks and derive detailed scaling relation comparisons. We find that fora given luminosity, barred and unbarred galaxies have comparablestructural and dynamical parameters, such as peak velocities, scalelengths, and colors. In particular, the location of a galaxy in the TFplane is independent of barredness. In a global dynamical sense, barredand unbarred galaxies behave similarly and are likely to have, onaverage, comparable fractions of luminous and dark matter at a givenradius. A new catalogue of ISM content of normal galaxiesWe have compiled a catalogue of the gas content for a sample of 1916galaxies, considered to be a fair representation of normality''. Thedefinition of a normal'' galaxy adopted in this work implies that wehave purposely excluded from the catalogue galaxies having distortedmorphology (such as interaction bridges, tails or lopsidedness) and/orany signature of peculiar kinematics (such as polar rings,counterrotating disks or other decoupled components). In contrast, wehave included systems hosting active galactic nuclei (AGN) in thecatalogue. This catalogue revises previous compendia on the ISM contentof galaxies published by \citet{bregman} and \citet{casoli}, andcompiles data available in the literature from several small samples ofgalaxies. Masses for warm dust, atomic and molecular gas, as well asX-ray luminosities have been converted to a uniform distance scale takenfrom the Catalogue of Principal Galaxies (PGC). We have used twodifferent normalization factors to explore the variation of the gascontent along the Hubble sequence: the blue luminosity (LB)and the square of linear diameter (D225). Ourcatalogue significantly improves the statistics of previous referencecatalogues and can be used in future studies to define a template ISMcontent for normal'' galaxies along the Hubble sequence. The cataloguecan be accessed on-line and is also available at the Centre desDonnées Stellaires (CDS).The catalogue is available in electronic form athttp://dipastro.pd.astro.it/galletta/ismcat and at the CDS via anonymousftp to\ cdsarc.u-strasbg.fr (130.79.128.5) or via\http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/405/5 Mass-to-light ratios from the fundamental plane of spiral galaxy discsThe best-fitting two-dimensional plane within the three-dimensionalspace of spiral galaxy disc observables (rotational velocityvrot, central disc surface brightnessμ0=-2.5logI0 and disc scalelength h) has beenconstructed. Applying the three-dimensional bisector method ofregression analysis to a sample of ~100 spiral galaxy discs that spanmore than 4magarcsec-2 in central disc surface brightnessyields vrot\proptoI0.50\pm0.050\,h0.77\pm 0.07 (B band)and vrot\proptoI0.43\pm0.040\,h0.69\pm 0.07 (R band).Contrary to popular belief, these results suggest that in the B band,the dynamical mass-to-light ratio (within four disc scalelengths) islargely independent of the surface brightness, varying as I0.00\pm0.100\,h0.54\pm 0.14. Consistentresults were obtained when the range of the analysis was truncated byexcluding the low-surface-brightness galaxies. Previous claims thatM/LBvaries withI-1/20,Bareshown to be misleading and/or caused by galaxy selection effects - notall low-surface-brightness disc galaxies are dark matter dominated. Thesituation is, however, different in the near-infrared whereLK'~v4 and M/LK' is shown to vary asI-1/20,K\prime. Theoretical studies ofspiral galaxy discs should therefore not assume a constant M/L ratiowithin any given passband. The B-band dynamical mass-to-light ratio(within four disc scalelengths) has no obvious correlation with (B-R)disc colour, while in the K' band it varies as -1.25+/-0.28(B-R).Combining the present observational data with recent galaxy modelpredictions implies that the logarithm of the stellar-to-dynamical massratio is not a constant value, but increases as discs become redder,varying as 1.70+/-0.28(B-R). 1.65-μm (H -band) surface photometry of galaxies - VIII. The near-IR κ space at z =0We present the distribution of a statistical sample of nearby galaxiesin the κ -space (κ 1 ~logM , κ 2~logI e 3 M /L , κ 3 ~logM /L ).Our study is based on near-IR (H -band: λ =1.65μm)observations, for the first time comprising early- and late-typesystems. Our data confirm that the mean effective dynamicalmass-to-light ratio M /L of the E+S0+S0a galaxies increases withincreasing effective dynamical mass M , as expected from the existenceof the Fundamental Plane relation. Conversely, spiral and Im/BCDgalaxies show a broad distribution in M /L with no detected trend of M/L with M , the former galaxies having M /L values about twice largerthan the latter, on average. For all the late-type galaxies, the M /Lincreases with decreasing effective surface intensity I e ,consistent with the existence of the Tully-Fisher relation. Theseresults are discussed on the basis of the assumptions behind theconstruction of the κ -space and their limitations. Our study iscomplementary to a previous investigation in the optical (B -band:λ =0.44μm) and allows us to study wavelength dependences ofthe galaxy distribution in the κ -space. As a first result, wefind that the galaxy distribution in the κ 1 -κ2 plane reproduces the transition from bulgeless tobulge-dominated systems in galaxies of increasing dynamical mass.Conversely, it appears that the M /L of late-types is higher (lower)than that of early-types with the same M in the near-IR (optical). Theorigins of this behaviour are discussed in terms of dust attenuation andstar formation history. Hα surface photometry of galaxies in the Virgo cluster. IV. The current star formation in nearby clusters of galaxiesHα +[NII] imaging observations of 369 late-type (spiral) galaxiesin the Virgo cluster and in the Coma/A1367 supercluster are analyzed,covering 3 rich nearby clusters (A1367, Coma and Virgo) and nearlyisolated galaxies in the Great-Wall. They constitute an opticallyselected sample (mp<16.0) observed with ~ 60 %completeness. These observations provide us with the current(T<107 yrs) star formation properties of galaxies that westudy as a function of the clustercentric projected distances (Theta ).The expected decrease of the star formation rate (SFR), as traced by theHα EW, with decreasing Theta is found only when galaxies brighterthan Mp ~ -19.5 are considered. Fainter objects show no orreverse trends. We also include in our analysis Near Infrared data,providing information on the old (T>109 yrs) stars. Puttogether, the young and the old stellar indicators give the ratio ofcurrently formed stars over the stars formed in the past, orbirthrate'' parameter b. For the considered galaxies we also determinethe global gas content'' combining HI with CO observations. We definethe gas deficiency'' parameter as the logarithmic difference betweenthe gas content of isolated galaxies of a given Hubble type and themeasured gas content. For the isolated objects we find that b decreaseswith increasing NIR luminosity. In other words less massive galaxies arecurrently forming stars at a higher rate than their giant counterpartswhich experienced most of their star formation activity at earliercosmological epochs. The gas-deficient objects, primarily members of theVirgo cluster, have a birthrate significantly lower than the isolatedobjects with normal gas content and of similar NIR luminosity. Thisindicates that the current star formation is regulated by the gaseouscontent of spirals. Whatever mechanism (most plausibly ram-pressurestripping) is responsible for the pattern of gas deficiency observed inspiral galaxies members of rich clusters, it also produces the observedquenching of the current star formation. A significant fraction of gashealthy'' (i.e. with a gas deficiency parameter less than 0.4) andcurrently star forming galaxies is unexpectedly found projected near thecenter of the Virgo cluster. Their average Tully-Fisher distance isfound approximately one magnitude further away (muo = 31.77)than the distance of their gas-deficient counterparts (muo =30.85), suggesting that the gas healthy objects belong to a cloudprojected onto the cluster center, but in fact lying a few Mpc behindVirgo, thus unaffected by the dense IGM of the cluster. Based onobservations taken at the Observatorio Astronómico Nacional(Mexico), the OHP (France), Calar Alto and NOT (Spain) observatories.Table \ref{tab4} is only available in electronic form athttp://www.edpsciences.org An Investigation into the Prominence of Spiral Galaxy BulgesFrom a diameter-limited sample of 86 low-inclination (face-on) spiralgalaxies, the bulge-to-disk size and luminosity ratios and otherquantitative measurements for the prominence of the bulge are derived.The bulge and disk parameters have been estimated using aseeing-convolved Sérsic r1/n bulge and aseeing-convolved exponential disk that were fitted to the optical (B, R,and I) and near-infrared (K) galaxy light profiles. In general,early-type spiral galaxy bulges have Sérsic values of n>1, andlate-type spiral galaxy bulges have values of n<1. In the B band,only eight galaxies have a bulge shape parameter n consistent with theexponential value 1, and only five galaxies do in the K band. Use of theexponential bulge model is shown to restrict the range ofre/h and B/D values by more than a factor of 2. Applicationof the r1/n bulge models, unlike exponential bulge models,results in a larger mean re/h ratio for the early-type spiralgalaxies than for the late-type spiral galaxies, although this result isshown not to be statistically significant. The mean B/D luminosity ratiois, however, significantly larger (>3 σ) for the early-typespirals than for the late-type spirals. Two new parameters areintroduced to measure the prominence of the bulge. The first is thedifference between the central surface brightness of the galaxy and thesurface brightness level at which the bulge and disk contribute equally.The other test uses the radius at which the contribution from the diskand bulge light are equal, normalized for the effect of intrinsicallydifferent galaxy sizes. Both of these parameters reveal that theearly-type spiral galaxies appear'' to have significantly (more than 2σ in all passbands) bigger and brighter bulges than late-typespiral galaxies. This apparent contradiction with the re/hvalues can be explained with an iceberg-like scenario, in which thebulges in late-type spiral galaxies are relatively submerged in theirdisk. This can be achieved by varying the relative stellar density whilemaintaining the same effective bulge-to-disk ratio. The B/D luminosityratio and the concentration index C31, in agreement with paststudies, are positively correlated and decrease as one moves along thespiral Hubble sequence toward later spiral galaxy types, although forgalaxies with large extended bulges the concentration index no longertraces the B/D luminosity ratio in a one-to-one fashion. A strong(Spearman's rank-order correlation coefficient, rs=0.80) andhighly significant positive correlation exists between the shape, n, ofthe bulge light profile and the bulge-to-disk luminosity ratio. Theabsolute bulge magnitude-logn diagram is used as a diagnostic tool forcomparative studies with dwarf elliptical and ordinary ellipticalgalaxies. At least in the B band these objects occupy distinctlydifferent regions of this parameter space. While the dwarf ellipticalgalaxies appear to be the faint extension to the brighter ellipticalgalaxies, the bulges of spiral galaxies do not; for a given luminositythey have a noticeably smaller shape parameter and hence a more dramaticdecline of stellar density at large radii. Distances to Galaxies from the Correlation between Luminosities and Line Widths. III. Cluster Template and Global Measurement of H0The correlation between the luminosities and rotation velocities ofgalaxies can be used to estimate distances to late-type galaxies. It isan appropriate moment to reevaluate this method given the great deal ofnew information available. The major improvements described hereinclude: (1) the template relations can now be defined by large,complete samples, (2) the samples are drawn from a wide range ofenvironments, (3) the relations are defined by photometric informationat the B, R, I, and K' bands, (4) the multiband information clarifiesproblems associated with internal reddening, (5) the template zeropoints are defined by 24 galaxies with accurately known distances, and(6) the relations are applied to 12 clusters scattered across the skyand out to velocities of 8000 km s-1. The biggest change fromearlier calibrations are associated with point 5. Roughly a 15% increasein the distance scale has come about with the fivefold increase in thenumber of zero-point calibrators. The overall increase in the distancescale from the luminosity-line width methodology is about 10% afterconsideration of all factors. Modulo an assumed distance to the LargeMagellanic Cloud of 50 kpc and no metallicity corrections to the Cepheidcalibration, the resulting value of the Hubble constant isH0=77+/-8 km s-1 Mpc-1, where the erroris the 95% probable statistical error. Cumulative systematic errorsinternal to this analysis should not exceed 10%. Uncertainties in thedistance scale ladder external to this analysis are estimated at ~10%.If the Cepheid calibration is shifted from the LMC to NGC 4258 with adistance established by observations of circumnuclear masers, thenH0 is larger by 12%. The Hubble Space Telescope Key Project on the Extragalactic Distance Scale. XXIV. The Calibration of Tully-Fisher Relations and the Value of the Hubble ConstantThis paper presents the calibration of BVRIH-0.5 Tully-Fisherrelations based on Cepheid distances to 21 galaxies within 25 Mpc and 23clusters within 10,000 km s-1. These relations have beenapplied to several distant cluster surveys in order to derive a valuefor the Hubble constant, H0, mainly concentrating on anI-band all-sky survey by Giovanelli and collaborators, consisting oftotal I magnitudes and 50% line width data for ~550 galaxies in 16clusters. For comparison, we also derive the values of H0using surveys in the B and V bands by Bothun and collaborators, and in Hband by Aaronson and collaborators. Careful comparisons with variousother databases from the literature suggest that the H-band data, whichhave isophotal magnitudes extrapolated from aperture magnitudes ratherthan total magnitudes, are subject to systematic uncertainties. Taking aweighted average of the estimates of Hubble constants from four surveys,we obtain H0=71+/-4 (random)+/-7 (systematic). We have alsoinvestigated how the value of H0 is affected by varioussystematic uncertainties, such as the internal extinction correctionmethod used, Tully-Fisher slopes and shapes, a possible metallicitydependence of the Cepheid period-luminosity relation, and clusterpopulation incompleteness bias. Near-infrared adaptive optics observations of galaxy clusters: Abell 262 at z=0.0157, J1836.3CR at z=0.414, and PKS 0743-006 at z=0.994We report on high angular resolution near-infrared (NIR) observations ofthree galaxy clusters at different redshifts using adaptive optics (AO).In the case of the barred spiral UGC 1347 in Abell262 we presented the first AO results obtained using a laser guide star.The observations have been carried out with the MPE/MPIA adaptive opticslaser guide star system ALFA and the ESO AO system ADONIS combined withthe SHARP II+ camera built at MPE. The three clusters are well suitedfor high resolution investigations since bright field stars for tip-tiltor wavefront sensing are located close to the line of sight to clustergalaxies. In summary our high angular resolution NIR data combined withother information clearly indicates star formation activity orinteraction between cluster members at all three redshifts. The resultsand implications for future high angular resolution adaptive opticsobservations are discussed in the framework of current galaxy andcluster evolution models. For two barred galaxies in the Abell 262cluster, UGC 1344 and UGC 1347, we interpret our NIRimaging results in combination with published radio, far-infrared, andHα data in the framework of a star formation model. In addition tothe star-forming resolved NIR nucleus in UGC 1347 we found a bright andcompact region of recent and enhanced star formation at one tip of thebar. The L_K/L_Lyc ratio as well as the V - K color of that region implya starburst that happened about 107 years ago. For UGC 1344we find that the overall star formation activity is low and that thesystem is deficient in fuel for star formation. The importance of starformation in galaxy clusters is also supported by a comparison of seeingcorrected nuclear bulge sizes of a sample of spiral galaxies within andoutside the central HI deficient zone of the Abell 262 andAbell 1367 clusters. We find that the galaxies insidethe Abell radii of both clusters show a tendency for more compact bulgesthan those outside. This phenomenon could be due to increased starformation activity triggered by interactions of cluster members insidethe Abell radius. The star formation activity in the two higher redshiftclusters J1836.3CR and PKS 0743-006 is investigated via comparison toGISSEL stellar population models in JHK two-color-diagrams. WhileJ1836.3CR is consistent with an evolved cluster, the objects in thefield of PKS 0743-006 show indications of more recent star formationactivity. The central object in J1836.3CR shows a radial intensityprofile that is indicative for cD galaxies in a rich clusterenvironment. Extended wings in its light distribution may be consistentwith recent or ongoing galaxy-galaxy interaction in this cluster. 1.65 μm (H-band) surface photometry of galaxies. V. Profile decomposition of 1157 galaxiesWe present near-infrared H-band (1.65 μm) surface brightness profiledecomposition for 1157 galaxies in five nearby clusters of galaxies:Coma, A1367, Virgo, A262 and Cancer, and in the bridge between Coma andA1367 in the Great Wall". The optically selected (mpg≤16.0) sample is representative of all Hubble types, from E to Irr+BCD,except dE and of significantly different environments, spanning fromisolated regions to rich clusters of galaxies. We model the surfacebrightness profiles with a de Vaucouleurs r1/4 law (dV), withan exponential disk law (E), or with a combination of the two (B+D).From the fitted quantities we derive the H band effective surfacebrightness (μe) and radius (re) of each component, theasymptotic magnitude HT and the light concentration indexC31. We find that: i) Less than 50% of the Ellipticalgalaxies have pure dV profiles. The majority of E to Sb galaxies is bestrepresented by a B+D profile. All Scd to BCD galaxies have pureexponential profiles. ii) The type of decomposition is a strong functionof the total H band luminosity (mass), independent of the Hubbleclassification: the fraction of pure exponential decompositionsdecreases with increasing luminosity, that of B+D increases withluminosity. Pure dV profiles are absent in the low luminosity rangeLH<1010 L\odot and become dominantabove 1011 L\odot . Based on observations taken atTIRGO, Gornergrat, Switzerland (operated by CAISMI-CNR, Arcetri,Firenze, Italy) and at the Calar Alto Observatory (operated by theMax-Planck-Institut für Astronomie (Heidelberg) jointly with theSpanish National Commission for Astronomy). Table 2 and Figs. 2, 3, 4are available in their entirety only in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html Arcsecond Positions of UGC GalaxiesWe present accurate B1950 and J2000 positions for all confirmed galaxiesin the Uppsala General Catalog (UGC). The positions were measuredvisually from Digitized Sky Survey images with rms uncertaintiesσ<=[(1.2")2+(θ/100)2]1/2,where θ is the major-axis diameter. We compared each galaxymeasured with the original UGC description to ensure high reliability.The full position list is available in the electronic version only. Young and Old Galaxies at High RedshiftWe review the results from recent deep HST imaging on faint galaxies.Artificial Neural Networks (ANNs) were used to classify faint galaxiesbased on surface brightness and light profiles. We use available UV +ground-based U-band images of nearby galaxies to address the effectsfrom the uncertain redshifted UV-morphology on the classifications,resulting in restframe ANN' classifiers. These distinguish quiteconsistently between E/S0's, Sabc's, and Sd/Irr for B <~ 27 mag. AFourier-based method is used to quantify higher order morphologicalfeatures and asymmetries in faint galaxies. We review the faint bluegalaxy population as classified with these restframe ANN's. The medianscale-length at B ~ 27 mag is r_hl~= 0''.25- 0''.3 (~ 1-2 kpc at z ~=1-2). Early and late-type galaxies are fairly well separated in BVIcolor-magnitude diagrams for B<~ 27 mag, with E/S0's being thereddest and Sd/Irr's generally blue. We discuss the B-band galaxy countsas a function of type for 18.5 <~ B <~ 28 mag. We briefly reviewdeep medium-band imaging with HST/WFPC2 in the filter F410M (Lyαat z ~= 2.4) which yielded 18 faint, compact objects surrounding theradio galaxy 53W002 at z ~= 2.39, as well as another 30 in random HSTparallel fields, plus ground-based images over a larger area. DeepHST/PC images of 53W002 at ~ 0''.06 FWHM resolution in BVI + redshiftedLyα suggest that both reflected AGN continuum-light shiningthrough a cone and jet-induced star-formation play a role in itsalignment effect'. We discuss the formation and evolution of 53W002 inthe context of its many surrounding sub-galactic sized objects. Wediscuss the nature of a μJy radio source that remained essentiallyunidentified in HDF flanking fields. The object was identified in deepHST/NICMOS J- and H-band images, and a single emission line at 6595Å was detected, most likely Lyα at z=4.42. This faint (H=23.9 mag), compact (r_e ~= 0''.2), red (I-K = 2.0 mag) object is mostlikely a dusty, star-forming young galaxy with an embedded activenucleus. Finally, HST/NICMOS images are presented of some of the oldestknown red galaxies at z ~= 1.5. Both galaxies are dominated by ar^1/4-profile with 5 kpc scale-length, and are amongst the oldest knownrelaxed systems at that epoch. A Dual-Transition Survey of CO in the Coma Cluster of GalaxiesWe present CO (1-0) and (2-1) observations of 33 galaxies in theComa/Abell 1367 supercluster made with the IRAM 30 m telescope. Inaddition, we observed four of the galaxies with the 15 m JCMT, at CO(2-1). The indicative molecular gas mass correlates strongly with thedust mass, and a stronger relationship is seen between the far-infraredand CO surface brightnesses than between the simple luminosities.Comparison of CO (2-1) spectra from IRAM and JCMT allows an estimate ofthe size of the CO emission region, which varies between 10% and 100% ofthe size of the optical disk, contrary to earlier estimates that the COis contained within the optical half-light radius. There is a slightsuggestion that starburst galaxies have a lower ratio of brightnesstemperatures, T_b(2-1)/T_b(1-0), than other galaxies. Galaxy coordinates. II. Accurate equatorial coordinates for 17298 galaxiesUsing images of the Digitized Sky Survey we measured coodinates for17298 galaxies having poorly defined coordinates. As a control, wemeasured with the same method 1522 galaxies having accurate coordinates.The comparison with our own measurements shows that the accuracy of themethod is about 6 arcsec on each axis (RA and DEC). On the local radio luminosity function of galaxies. II. Environmental dependences among late-type galaxiesUsing new extensive radio continuum surveys at 1.4 GHz (FIRST and NVSS),we derive the distribution of the radio/optical and radio/NIR luminosity(RLF) of late-type (Sa-Irr) galaxies (m_p<15.7) in 5 nearby clustersof galaxies: A262, Cancer, A1367, Coma and Virgo. With the aim ofdiscussing possible environmental dependences of the radio properties,we compare these results with those obtained for relatively isolatedobjects in the Coma supercluster. We find that the RLF of Cancer, A262and Virgo are consistent with that of isolated galaxies. Conversely weconfirm earlier claims that galaxies in A1367 and Coma have their radioemissivity enhanced by a factor ~ 5 with respect to isolated objects. Wediscuss this result in the framework of the dynamical pressure sufferedby galaxies in motion through the intra-cluster gas (ram-pressure). Wefind that the radio excess is statistically larger for galaxies in fasttransit motion. This is coherent with the idea that enhanced radiocontinuum activity is associated with magnetic field compression. TheX-ray luminosities and temperatures of Coma and A1367 imply that thesetwo clusters have significantly larger intracluster gas density than theremaining three studied ones, providing a clue for explaining the higherradio continuum luminosities of their galaxies. Multiple systems in theComa supercluster bridge (with projected separations smaller than 300kpc) have radio luminosities significantly larger than isolatedgalaxies. Table~1 is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html} The Interchangeability of CO and H I in the Tully-Fisher RelationWe investigate the viability and precision of using ^12CO (J = 1 -->0) emission lines from galaxies in lieu of 21 cm emission in theTully-Fisher distance indicator (TF). Here we combine CO data gatheredspecifically for Tully-Fisher analysis with I-band photometry (both newand from the literature) for cluster galaxies between 3500 and 8000 kms^-1 and compare the luminosity-line width relation using CO with theresults of recent, large TF surveys using H i and Hα. We cull someCO data as suggested by previously published numerical simulations andfind that CO line widths, with corrections for turbulence andnoise-broadening on the order of 35 km s^-1, behave identically to H iand Hα in luminosity-line width analyses. We also examine therelation between CO line shapes and other parameters of the galaxies. The Star Formation Properties of Disk Galaxies: Hα Imaging of Galaxies in the Coma SuperclusterWe present integrated Hα measurements obtained from imagingobservations of 98 late-type galaxies, primarily selected in the Comasupercluster. These data, combined with Hα photometry from theliterature, include a magnitude-selected sample of spiral (Sa to Irr)galaxies belonging to the Great Wall'' complete up to m_p = 15.4, andthus composed of galaxies brighter than M_p = -18.8 (H_0 = 100 km s^-1Mpc^-1). The frequency distribution of the Hα equivalent width,determined for the first time from an optically complete sample, isapproximately Gaussian, peaking at EW ~ 25 Å. We find that, at thepresent limiting luminosity, the star formation properties of spiral +Irr galaxy members of the Coma and A1367 Clusters do not differsignificantly from those of the isolated ones belonging to the GreatWall. The present analysis confirms the well-known increase of thecurrent massive star formation rate (SFR) with Hubble type. Moreover,perhaps a more fundamental anticorrelation exists between the SFR andthe mass of disk galaxies: low-mass spirals and dwarf systems havepresent SFRs ~50 times higher than giant spirals. This result isconsistent with the idea that disk galaxies are coeval, evolving asclosed systems'' with exponentially declining SFR, and that the massof their progenitor protogalaxies is the principal parameter governingtheir evolution. Massive systems having high initial efficiency ofcollapse, or a short collapse timescale, have retained little gas tofeed the present epoch of star formation. These findings support theconclusions of Gavazzi & Scodeggio, who studied the color-massrelation of a local galaxy sample, and agree with the analysis by Cowieet al., who traced the star formation history of galaxies up to z >1. Based on observations made at the Observatorio AstronómicoNacional (OAN), San Pedro Mártir, B.C., of the UniversidadNacional Autónoma de México (UNAM). Catalogue of HI maps of galaxies. I.A catalogue is presented of galaxies having large-scale observations inthe HI line. This catalogue collects from the literature the informationthat characterizes the observations in the 21-cm line and the way thatthese data were presented by means of maps, graphics and tables, forshowing the distribution and kinematics of the gas. It containsfurthermore a measure of the HI extension that is detected at the levelof the maximum sensitivity reached in the observations. This catalogueis intended as a guide for references on the HI maps published in theliterature from 1953 to 1995 and is the basis for the analysis of thedata presented in Paper II. The catalogue is only available inelectronic form at the CDS via anonymous ftp 130.79.128.5 orhttp://cdsweb.u-strasbg.fr/Abstract.html The thicknesses and inclinations of 71 northern spiral galaxiesThis paper presents the thicknesses and inclinations (i.e., the anglebetween the galactic plane and the tangent plane) of 71 northern spiralgalaxies. The method for measuring the thickness has been proposed byPeng. It is based on the solution of Poisson's equation for alogarithmic disturbance of density. The inclination is determined byassuming that the pattern of spiral structure is a logarithmic spiral.We find that the thickness is correlated with color and with theH_α+[NII] equivalent width. Total magnitude, radius, colour indices, colour gradients and photometric type of galaxiesWe present a catalogue of aperture photometry of galaxies, in UBVRI,assembled from three different origins: (i) an update of the catalogueof Buta et al. (1995) (ii) published photometric profiles and (iii)aperture photometry performed on CCD images. We explored different setsof growth curves to fit these data: (i) The Sersic law, (ii) The net ofgrowth curves used for the preparation of the RC3 and (iii) A linearinterpolation between the de Vaucouleurs (r(1/4) ) and exponential laws.Finally we adopted the latter solution. Fitting these growth curves, wederive (1) the total magnitude, (2) the effective radius, (3) the colourindices and (4) gradients and (5) the photometric type of 5169 galaxies.The photometric type is defined to statistically match the revisedmorphologic type and parametrizes the shape of the growth curve. It iscoded from -9, for very concentrated galaxies, to +10, for diffusegalaxies. Based in part on observations collected at the Haute-ProvenceObservatory. Gas Mass Fractions and the Evolution of Spiral GalaxiesWe show that the gas mass fraction of spiral galaxies is stronglycorrelated with luminosity and surface brightness. It is not correlatedwith linear size. Gas fraction varies with luminosity and surfacebrightness at the same rate, indicating evolution at fixed size. Dimgalaxies are clearly less evolved than bright ones, having consumed only~ \frac {1}{2} of their gas. This resolves the gas consumption paradox,since there exist many galaxies with large gas reservoirs. Thesegas-rich galaxies must have formed the bulk of their stellar populationsin the last half of a Hubble time. The existence of such immaturegalaxies at z = 0 indicates that either galaxy formation is a lengthy oreven ongoing process, or the onset of significant star formation can bedelayed for arbitrary periods in tenuous gas disks. The I band Tully-Fisher relation for cluster galaxies: data presentation.Observational parameters which can be used for redshift-independentdistance determination using the Tully-Fisher (TF) technique are givenfor \ntot spiral galaxies in the fields of 24 clusters or groups. I bandphotometry for the full sample was either obtained by us or compiledfrom published literature. Rotational velocities are derived either from21 cm spectra or optical emission line long-slit spectra, and convertedto a homogeneous scale. In addition to presenting the data, a discussionof the various sources of error on TF parameters is introduced, and thecriteria for the assignment of membership to each cluster are given. The molecular gas content of spiral galaxies in the Coma/A1367 supercluster.We present ^12^CO(J=1-0) line observations of 73 spiral galaxies mostlyin the Coma/A1367 supercluster. From these data, combined with dataavailable in the literature, we extract the first complete, opticallyselected sample (m_pg_<15.2) of 37 isolated and of 27 clustergalaxies. Adopting a standard conversion factor X=N(H_2_)/I(CO), weestimate that the molecular hydrogen content of isolated spiral galaxiesis, on average, 20% of the atomic hydrogen reservoir, significantlylower than previous estimates based on samples selected by FIR criteria,thus biased towards CO rich objects. We show that the frequencydistributions of the CO deficiency parameter, defined as the differencebetween the expected and the observed molecular gas content of a galaxyof given luminosity (or linear diameter), computed separately forcluster and isolated galaxies, are not significantly different,indicating that the environment does not affect the molecular gascontent of spiral discs. A well defined relationship exists betweenM_i_(H_2_) and the star formation activity in bright galaxies, while itis weaker at lower luminosities. We interpret this finding as indicatingthat CO emission traces relatively well the H_2_ mass only in high-massgalaxies, such as the Milky Way. On the other hand, in low-mass spiralsthe higher far-UV radiation field produced by young O-B stars and thelower metallicity cause the photodissociation of the diffuse moleculargas, weakening the expected relationship between star formation and theCO emission. The conversion factor between the CO line intensity and theamount of molecular hydrogen being ill-determined and variable with theUV flux and abundances, it is difficult to assess the relationshipbetween the star formation and the amount of molecular hydrogen. Photoelectric UBV Photometry of Galaxies in the Clusters Pegasus I, Pegasus II, Abell 262, Abell 1367, and Abell 2197-9This paper presents photoelectric UBV multiaperture photometry of 144galaxies, 139 of which are associated with six nearby bright clusters.The observations were made at the McDonald Observatory from 1986September to 1987 November and were part of the production of the ThirdReference Catalogue of Bright Galaxies (RC3). The observations were usedto compute total magnitudes and color indices published in RC3. Theobservations can also be used to calibrate CCD images. 1.65 μm (H-band) surface photometry of disk galaxies. I. Observations of 158 galaxies with the Calar Alto 2.2 M telescope.Near Infrared (H-band) surface photometry of 158 (mostly) disk galaxiesbelonging to the Coma Supercluster and to the A262 and Cancer clusterswas obtained using the 256^2^ NICMOS3 array MAGIC attached to the 2.2mCalar Alto telescope. Magnitudes and diameters within the21.5mag/arcsec^2^ isophote, concentration indices and total H magnitudesare derived. Near-infrared and optical broadband surface photometry of 86 face-on disk dominated galaxies. II. A two-dimensional method to determine bulge and disk parameters.In this Paper I present a new two-dimensional decomposition technique,which models the surface photometry of a galaxy with an exponentiallight profile for both bulge and disk and, when necessary, with aFreeman bar. The new technique was tested for systematic errors on bothartificial and real data and compared with widely used one-dimensionaldecomposition techniques, where the luminosity profile of the galaxy isused. The comparisons indicate that a decomposition of thetwo-dimensional image of the galaxy with an exponential light profilefor both bulge and disk yields the most reproducible and representativebulge and disk parameters. An extensive error analysis was made todetermine the reliability of the model parameters. If the model with anexponential bulge profile is a reasonable description of a galaxy, themaximum errors in the derived model parameters are of order 20%. Theuncertainties in the model parameters will increase, if the exponentialbulge function is replaced by other often used bulge functions as the deVaucouleurs law. All decomposition methods were applied to the opticaland near-infrared data set presented by de Jong & van der Kruit(1994), which comprises 86 galaxies in six passbands. A ^12^CO(1-0) survey of spiral galaxies in the region of the Coma supercluster.We present observations of the ^12^CO(J=1-0) line at 2.6mm of 65galaxies located in the Coma supercluster region: 33 actually belong tothe Coma supercluster while 32 are either foreground or backgroundobjects. These data have been obtained using the NRAO 12m telescope atKitt Peak (United States), and for four galaxies, using the IRAM 30mtelescope at Pico Veleta (Spain). Out of these 65 galaxies, 54 had neverbeen observed in the CO(1-0) line; 49 have been detected by us, of which37 are new detections. We give molecular gas masses deduced from the COline integrated intensities, and upper limits for the 16 undetectedobjects, computed with a Galactic conversion factorN(H_2_)=2.3x10^20^I(CO) and H_0_=75km/s/Mpc. Colors, luminosities, and masses of disk galaxies. 2: Environmental dependenceisThe B-band and near-infrared (H) luminosity functions of spiral galaxiesare derived for the Coma and A1367 clusters and for a referencepopulation of 'field' galaxies in the Coma supercluster. They areconsistent at the bright end, but they differ significantly at the faintend, indicating an overdensity of spirals with blue color (B-H less than3.0) and faint H luminosity (H greater than -21.5) in clusters withrespect to the field. These objects have disturbed morphology andpeculiar velocities significantly larger than the rest of the clustersample. We discuss these results in the framework of a possibleenvironmental dependence of galaxy evolution, and we conclude thatenhanced current star formation in cluster spiral galaxies might occurdue to molecular gas collapse stimulated by the ram-pressure mechanism.
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## Registered S3 methods overwritten by 'parameters':
## method from
## as.double.parameters_kurtosis datawizard
## as.double.parameters_skewness datawizard
## as.double.parameters_smoothness datawizard
## as.numeric.parameters_kurtosis datawizard
## as.numeric.parameters_skewness datawizard
## as.numeric.parameters_smoothness datawizard
## print.parameters_distribution datawizard
## print.parameters_kurtosis datawizard
## print.parameters_skewness datawizard
## summary.parameters_kurtosis datawizard
## summary.parameters_skewness datawizard
This document shows examples for using the tab_itemscale() function of the sjPlot package.
## Performing an item analysis of a scale or index
This function performs an item analysis with certain statistics that are useful for scale or index development. Following statistics are computed for each variable (column) of a data frame:
• percentage of missing values
• mean value
• standard deviation
• skew
• item difficulty
• item discrimination
• Cronbach’s Alpha if item was removed from scale
• mean (or average) inter-item-correlation
Optional, following statistics can be computed as well:
• kurstosis
• Shapiro-Wilk Normality Test
If the argument factor.groups is not NULL, the data frame df will be splitted into groups, assuming that factor.groups indicate those columns (variables) of the data frame that belong to a certain factor (see, for instance, return value of function tab_pca() or parameters::principal_components() as example for retrieving factor groups for a scale). This is useful when you have perfomed a principal component analysis or factor analysis as first step, and now want to see whether the found factors / components represent a scale or index score.
To demonstrate this function, we first need some data:
## Index score with one component
The simplest function call is just passing the data frame as argument. In this case, the function assumes that all variables of the data frame belong to one factor only.
tab_itemscale(mydf)
Component 1
Missings Mean SD Skew Item Difficulty Item Discrimination α if deleted
0.77 % 3.12 0.58 -0.12 0.78 -0.24 0.54
0.66 % 2.02 0.72 0.65 0.51 0.33 0.38
0.66 % 1.63 0.87 1.31 0.41 0.41 0.34
1.10 % 1.77 0.87 1.06 0.44 0.44 0.32
0.66 % 1.39 0.67 1.77 0.35 0.36 0.38
0.88 % 1.29 0.64 2.43 0.32 0.42 0.37
0.88 % 1.92 0.91 0.83 0.48 0.37 0.35
0.77 % 2.16 1.04 0.32 0.54 -0.03 0.53
2.20 % 2.93 0.96 -0.45 0.73 -0.11 0.56
Mean inter-item-correlation=0.092 · Cronbach’s α=0.459
To interprete the output, we may consider following values as rule-of-thumbs for indicating a reliable scale:
• item difficulty should range between 0.2 and 0.8. Ideal value is p+(1-p)/2 (which mostly is between 0.5 and 0.8)
• for item discrimination, acceptable values are 0.2 or higher; the closer to 1 the better
• in case the total Cronbach’s Alpha value is below the acceptable cut-off of 0.7 (mostly if an index has few items), the mean inter-item-correlation is an alternative measure to indicate acceptability; satisfactory range lies between 0.2 and 0.4
## Index score with more than one component
The items of the COPE index used for our example do not represent a single factor. We can check this, for instance, with a principle component analysis. If you know, which variable belongs to which factor (i.e. which variable is part of which component), you can pass a numeric vector with these group indices to the argument factor.groups. In this case, the data frame is divided into the components specified by factor.groups, and each component (or factor) is analysed.
library(parameters)
#>
#> Attaching package: 'parameters'
#> The following object is masked from 'package:sjmisc':
#>
#> center
# Compute PCA on Cope-Index, and retrieve
# factor indices for each COPE index variable
pca <- parameters::principal_components(mydf)
factor.groups <- parameters::closest_component(pca)
The PCA extracted two components. Now tab_itemscale()
1. performs an item analysis on both components, showing whether each of them is a reliable and useful scale or index score
2. builds an index of each component, by standardizing each scale
3. and adds a component-correlation-matrix, to see whether the index scores (which are based on the components) are highly correlated or not.
tab_itemscale(mydf, factor.groups)
#> Warning: Data frame needs at least three columns for reliability-test.
Component 1
Missings Mean SD Skew Item Difficulty Item Discrimination α if deleted
0.77 % 3.12 0.58 -0.12 0.78 -0.37 0.78
0.66 % 2.02 0.72 0.65 0.51 0.49 0.61
0.66 % 1.63 0.87 1.31 0.41 0.55 0.59
1.10 % 1.77 0.87 1.06 0.44 0.54 0.59
0.66 % 1.39 0.67 1.77 0.35 0.44 0.63
0.88 % 1.29 0.64 2.43 0.32 0.47 0.62
0.88 % 1.92 0.91 0.83 0.48 0.57 0.58
Mean inter-item-correlation=0.196 · Cronbach’s α=0.676
Component 2
Missings Mean SD Skew Item Difficulty Item Discrimination α if deleted
0.77 % 2.16 1.04 0.32 0.54 NA NA
2.20 % 2.93 0.96 -0.45 0.73 NA NA
Mean inter-item-correlation=0.260 · Cronbach’s α=0.412
Component 1 Component 2
Component 1 α=0.676
Component 2 -0.196
(<.001)
α=0.412
Computed correlation used pearson-method with listwise-deletion.
tab_itemscale(mydf, factor.groups, show.shapiro = TRUE, show.kurtosis = TRUE)
#> Warning: Data frame needs at least three columns for reliability-test.
Component 1
Missings Mean SD Skew Kurtosis W(p) Item Difficulty Item Discrimination α if deleted
0.77 % 3.12 0.58 -0.12 0.27 0.75 (0.000) 0.78 -0.37 0.78
0.66 % 2.02 0.72 0.65 0.73 0.80 (0.000) 0.51 0.49 0.61
0.66 % 1.63 0.87 1.31 0.86 0.72 (0.000) 0.41 0.55 0.59
1.10 % 1.77 0.87 1.06 0.48 0.78 (0.000) 0.44 0.54 0.59
0.66 % 1.39 0.67 1.77 2.87 0.62 (0.000) 0.35 0.44 0.63
0.88 % 1.29 0.64 2.43 5.77 0.51 (0.000) 0.32 0.47 0.62
0.88 % 1.92 0.91 0.83 -0.08 0.81 (0.000) 0.48 0.57 0.58
Mean inter-item-correlation=0.196 · Cronbach’s α=0.676
Component 2
Missings Mean SD Skew Kurtosis W(p) Item Difficulty Item Discrimination α if deleted
0.77 % 2.16 1.04 0.32 -1.14 0.85 (0.000) 0.54 NA NA
2.20 % 2.93 0.96 -0.45 -0.83 0.85 (0.000) 0.73 NA NA
Mean inter-item-correlation=0.260 · Cronbach’s α=0.412
Component 1 Component 2
Component 1 α=0.676
Component 2 -0.196
(<.001)
α=0.412
Computed correlation used pearson-method with listwise-deletion.
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Started in 1985 Semimonthly
ISSN 1005-0302
CN 21-1315/TG
Impact factor:6.155
The journal has been awarded the excellent periodical in China, and its articles are covered by SCI, EI, CA, SA, JST, RJ, CSA, MA, EMA, AIA etc., PASCAL web. ISI web of Science,SCOPUS.
Current Issue
15 January 2021, Volume 61 Issue 0 Previous Issue
Research Article
Select Hot deformation behavior and processing map development of AZ110 alloy with and without addition of La-rich Mish Metal Qiyu Liao, Yanchao Jiang, Qichi Le, Xingrui Chen, Chunlong Cheng, Ke Hu, Dandan Li J. Mater. Sci. Technol., 2021, 61 (0): 1-15. DOI: 10.1016/j.jmst.2020.04.064 In order to compare the workability of AZ110 alloy with and without addition of La-rich Mish Metal (MM), hot compression tests were performed on a Gleeble-3500D thermo-mechanical simulator at the deformation temperature range of 473-623 K and strain rate range of 0.001-1 s-1. The flow stress, constitutive relation, DRX kinetic model, processing map and microstructure characterization of the alloys were investigated. The results show that the flow stress is very sensitive to deformation temperature and strain rate, and the peak stress of AZ110LC (LC = La-rich MM) alloy is higher than that of AZ110 alloy. The hot deformation behavior of the alloys can be accurately predicted by the constitutive relations. The derived constitutive equations show that the calculated activation energy Q and stress exponent n for AZ110 alloy are higher than the calculated values of AZ110LC alloy. The analysis of DRX kinetic models show that the development of DRX in AZ110LC alloy is earlier than AZ110 alloy at the same deformation condition. The processing maps show that the workability of AZ110LC alloy is significantly more excellent than AZ110 alloy and the microstructures are in good agreement with the calculated results. The AZ110LC alloys can obtain complete DRX microstructure at high strain rate due to its higher stored energy and weak basal texture.
Select Effect of interlayer addition on microstructure and mechanical properties of NiTi/stainless steel joint by electron beam welding H. Niu, H.C. Jiang, M.J. Zhao, L.J. Rong J. Mater. Sci. Technol., 2021, 61 (0): 16-24. DOI: 10.1016/j.jmst.2020.05.043 NiTi/Stainless Steel (SS) sheets have been welded via a vacuum electron beam welding process, with three methods (offsetting electron beam to SS side without interlayer, adding Ni interlayer and adding FeNi interlayer), to promote mechanical properties of the NiTi/SS joints. The joints with different interlayers are all fractured in the weld zone near the NiTi side, which is attributed to the enrichment of intermetallic compounds including Fe2Ti and Ni3Ti. The fracture mechanisms of different joints are strongly dependent on the types of interlayers, and the joints without interlayer, adding Ni interlayer and adding FeNi interlayer exhibit cleavage fracture, intergranular fracture and mixed fracture composed of cleavage and tearing ridge, respectively. Compared with the brittle laves phase Fe2Ti, Ni3Ti phase can exhibit certain plasticity, block the crack propagation and change the direction of crack propagation. The composite structure of Ni3Ti and Fe2Ti will be formed when the FeNi alloy is taken as the interlayer, which provides the joint excellent mechanical properties, with rupture strength of 343 MPa.
Select The growth mechanisms of θ′ precipitate phase in an Al-Cu alloy during aging treatment Lin Gao, Kai Li, Song Ni, Yong Du, Min Song J. Mater. Sci. Technol., 2021, 61 (0): 25-32. DOI: 10.1016/j.jmst.2020.05.046 The plate-shaped θ′ (Al2Cu) precipitate acts as one of the primary strengthening phases in Al-Cu alloys. The interface, especially the semicoherent interface, between Al-Cu solid solution (αAl) and θ′ phase contains a lot of clues about phase transformations. Thus, these interfacial structures in an Al-Cu alloy after high-temperature and longtime aging have been analyzed in detail using atomic-scale high-angle annular dark-field scanning transmission electron microscopy and first-principles calculations in this work. It was found that the lateral growth of θ' precipitates is subjected to a combination of several major mechanisms under this aging condition. Except for some common intermediate phases, two novel and striking structures were observed on the interface, which implies two alternative atomic diffusion mechanisms for θ′ precipitate growth. For one condition, the atomic diffusion from αAl to θ′ phase transformation adopts an interstitialcy mechanism based on additional Al atoms. For the other condition, the diffusion is carried out through Al atoms. Both mechanisms are distinctly different from the previous theory based on direct diffusion of Cu atoms. The first-principle calculations also confirm that these newfound diffusion processes are energetically favored.
Select Antibacterial activities against Porphyromonas gingivalis and biological characteristics of copper-bearing PEO coatings on magnesium Dan Zhang, Qi Han, Kun Yu, Xiaopeng Lu, Ying Liu, Ze Lu, Qiang Wang J. Mater. Sci. Technol., 2021, 61 (0): 33-45. DOI: 10.1016/j.jmst.2020.05.025 Unlike other parts of the body, jaw defection often involves dental and periodontal tissues, which colonized a great many oral anaerobic bacteria. As a remarkable degradable material, magnesium has become an excellent candidate for orthopedic appliances recently. But the high degradation rate is still a big problem. Making a biodegradable coating with good biocompatibility to slow down the degeneration rate of magnesium is one of the best methods. However, protective coatings will impair the antibacterial effects of magnesium which is caused by the rise of pH value throughout its degradation. To solve this problem, a series of composite coatings with different amounts of CuO particles (3, 5 and 7 wt.%) were fabricated on pure magnesium through plasma electrolytic oxidation (PEO) to investigate in vitro biocompatibility and the antibacterial abilities against Porphyromonas gingivalis (P. gingivalis). Surface characterization and degradation behavior of the copper-bearing PEO coatings were also systematically studied. Furthermore, the most optimum coating was also systematically studied by X-ray photoelectron spectroscopy (XPS) and electrochemical corrosion test. Results of the present research revealed that adding proper amount of CuO into PEO coatings could greatly improve the antibacterial abilities of the PEO coatings. The antibacterial activities of copper-bearing PEO coatings were excellent and revealed concentration-dependent and time-dependent. Biocompatibility of copper-bearing PEO coatings showed that proper amount of Cu could promote cell proliferation. Compared with other PEO coatings in this study, PEO-7Cu showed some inhibition effects on cell proliferation and adhesion for long-term use. Electrochemical corrosion tests and immersion tests showed that PEO-5Cu and PEO-7Cu copper-bearing PEO coatings would provide satisfying corrosion resistance effects, while PEO-3Cu was poorer than PEO coatings without Cu. However, compared with uncoated pure magnesium, the corrosion resistance of the PEO coating was much better. Based on the results of antibacterial ability, biocompatibility, and corrosion resistance of the above copper-bearing PEO coatings, PEO-5Cu in this research was recommended to be used in patients with jaw defects.
Invited Review
Select Special issue on advanced corrosion-resistance materials and emerging applications. The progress on antifouling organic coating: From biocide to biomimetic surface Xu Han, Jianhua Wu, Xianhui Zhang, Junyou Shi, Jiaxin Wei, Yang Yang, Bo Wu, Yonghui Feng J. Mater. Sci. Technol., 2021, 61 (0): 46-62. DOI: 10.1016/j.jmst.2020.07.002 The advancement in material science and engineering technology has led to the development of antifouling (AF) coatings which are cheaper, durable, less toxic, and safe to the environment. The use of AF coatings containing tributyltin compounds was prohibited at the beginning of 2003, this necessitated the development of environmentally friendly coatings. The fouling release coating (FRC) lacks biocides and has low surface energy, low elastic modulus with smooth surface properties, hence a better release effect to fouling organisms. Several functional coatings have been recently developed based on fouling release (FR) technology to combat the effects of biofouling. Here, we provide a brief overview of innovative technologies and recent developments based on FRCs, including silicone, modified fluorinated polymer, cross-linked coatings, amphiphilic copolymer coating, hydrogel coatings, and biomimetic coatings. We also highlight the key issues and shortcomings of innovative technologies based on FRCs. This may give new insights into the future development of marine AF coatings.
Research Article
Select Contribution of ultrasonic surface rolling process to the fatigue properties of TB8 alloy with body-centered cubic structure Dan Liu, Daoxin Liu, Mario Guagliano, Xingchen Xu, Kaifa Fan, Sara Bagherifard J. Mater. Sci. Technol., 2021, 61 (0): 63-74. DOI: 10.1016/j.jmst.2020.05.047 The effect of ultrasonic surface rolling process (USRP) as a severe plastic deformation technology was investigated on the evolution of microstructure, residual stress and surface morphology of TB8 alloys with body-centered cubic structure. Stress-controlled rotating-bending fatigue tests indicated increased fatigue strength in USRP samples prepared using different number of passes compared to the base material, which was attributed to the presence of gradient structure surface layers. Five subsequent USRP passes resulted in the highest fatigue strength, due to the optimal surface properties including higher extent of grain refinement, larger compressive residual stresses, “smoother” surface morphology and increased micro-hardness. However, the effect of USRP technology on improving fatigue strength of TB8 alloy was not significant in comparison with that of other titanium alloys (for example, Ti6Al4V), which was attributed to the notable surface residual stresses relaxation revealed from measurements on post-fatigued USRP samples. Electron backscatter diffraction analysis confirmed that fatigue crack initiation occurred in the larger grains on the surface with high Schmid factor. Small cracks were found to propagate into the core material in a mixed transgranular and intergranular mode. Further analysis indicated that grain growth existed in post-fatigued USRP-treated TB8 samples and that the average geometrically necessary dislocations value reduced after fatigue loading.
Select Balancing the corrosion resistance and through-plane electrical conductivity of Cr coating via oxygen plasma treatment Xian-Zong Wang, Hong-Qiang Fan, Triratna Muneshwar, Ken Cadien, Jing-Li Luo J. Mater. Sci. Technol., 2021, 61 (0): 75-84. DOI: 10.1016/j.jmst.2020.06.012 Developing an electrically conductive and corrosion-resistant coating is essential for metal bipolar plates of polymer electrolyte membrane fuel cells (PEMFCs). Although enhanced corrosion resistance was seen for Cr coated stainless steel (Cr/SS) bipolar plates, they experience a quick decrease of through-plane electrical conductivity due to the formation of a porous and low-conductive corrosion product layer at the plate surface, thus leading to an increase in interfacial contact resistance (ICR). To tackle this issue, the multilayer Cr coatings were deposited using the magnetron sputtering with a remote inductively coupled oxygen plasma (O-ICP) in the present study. After the O-ICP treatment, a Cr oxide layer (CrO*) is formed on the specimen surface. The CrO*/Cr/SS has a remarkably lower stable corrosion rate (iss) than that of the native Cr oxides (CrOn/Cr/SS). Compared with CrOn/Cr/SS, the excellent performance of CrO*/Cr/SS is attributed to a denser and thicker surface layer of CrO* with Cr being oxidized to its highest valence state, Cr (VI). More importantly, the through-plane electrical conductivity of the specimens treated by the optimized O-ICP decreases much slowly than CrOn/Cr/SS and thus, the increament of ICR of CrO*/Cr/SS after the potentiostatic polarization test is considerably smaller than that of CrOn/Cr/SS, which is benefited from the reduced iss that mitigates the deposition of corrosion products and hinders further oxidation of Cr coating. Therefore, CrO*/Cr/SS proves to be a well balanced trade-off between corrosion resistance and through-plane electrical conductivity. The results of this study demonstrate that O-ICP treatment on a conductive metal coating is an effective strategy to improve the corrosion resistance and suppress the increase of ICR over the long-term polarization. The technique reported herein exhibits its promising potential application in preparing corrosion resistant and electrically conductive coatings on metal bipolar plates to be used in PEMFCs.
Select Namib desert beetle inspired special patterned fabric with programmable and gradient wettability for efficient fog harvesting Zhihua Yu, Huimei Zhang, Jianying Huang, Shuhui Li, Songnan Zhang, Yan Cheng, Jiajun Mao, Xiuli Dong, Shouwei Gao, Shanchi Wang, Zhong Chen, Yaoxing Jiang, Yuekun Lai J. Mater. Sci. Technol., 2021, 61 (0): 85-92. DOI: 10.1016/j.jmst.2020.05.054 Efficient collection of water from fog provides a potential solution to solve the global freshwater shortage problem, particularly in the desert or arid regions. In this work, a flexible and highly efficient fog collector was prepared by mimicking the back exoskeleton structure of the Namib desert beetle. The improved fog collector was constructed by a superhydrophobic-superhydrophilic patterned fabric via a simple weaving method, followed by in-situ deposition of copper particles. Compared with the conventional fog collector with a plane structure, the fabric has shown a higher water-harvesting rate at 1432.7 mg/h/cm2, owing to the biomimetic three-dimensional structure, its enhanced condensation performance enabled by the copper coating and the rational distribution of wetting units. The device construction makes use of the widely available textile materials through mature manufacturing technology, which makes it highly suitable for large-scale industrial production.
Select Highly thermal-conductive graphite flake/Cu composites prepared by sintering intermittently electroplated core-shell powders Hong Sun, Nan Deng, Jianqiang Li, Gang He, Jiangtao Li J. Mater. Sci. Technol., 2021, 61 (0): 93-99. DOI: 10.1016/j.jmst.2020.05.044 Graphite flake/Cu composite has attracted tremendous attention as a promising heat sinks materials owing to its easy machinability and superior thermal properties. However, its preparation process still faces several technological limitations including complex, time-consuming and costly synthetic approaches. In this work, a facile and scalable intermittently electroplated method is applied to prepare Cu-coated graphite flake composite powders, which are subsequently sintered into dense composite bulks. The results show that the graphite flake is successfully coated with a uniform and compact Cu shell, which effectively inhibits the segregation accumulation of graphite flakes and contributes to homogeneous distribution of graphite in the sintered graphite flake/Cu composites. The as-sintered composites exhibit an excellent thermal conductivity of 710 W·m-1·K-1 and an outstanding bending strength of 93 MPa. Such performance, together with the simple, efficient powder-preparation process, suggests that the present strategy may open up opportunities for the development of thermal management materials.
Select Optimizing the microstructures and mechanical properties of Al-Cu-based alloys with large solidification intervals by coupling travelling magnetic fields with sequential solidification Lei Luo, Liangshun Luo, Robert O. Ritchie, Yanqing Su, Binbin Wang, Liang Wang, Ruirun Chen, Jingjie Guo, Hengzhi Fu J. Mater. Sci. Technol., 2021, 61 (0): 100-113. DOI: 10.1016/j.jmst.2020.05.048 Alloys with large solidification intervals are prone to issues from the disordered growth and defect formation; accordingly, finding ways to effectively optimize the microstructure, further to improve the mechanical properties is of great importance. To this end, we couple travelling magnetic fields with sequential solidification to continuously regulate the mushy zones of Al-Cu-based alloys with large solidification intervals. Moreover, we combine experiments with simulations to comprehensively analyze the mechanisms on the optimization of microstructure and properties. Our results indicate that only downward travelling magnetic fields coupled with sequential solidification can obtain the refined and uniform microstructure, and promote the growth of matrix phase α-Al along the direction of temperature gradient. Additionally, the secondary dendrites and precipitates are reduced, while the solute partition coefficient and solute solid-solubility are raised. Ultimately, downward travelling magnetic fields can increase the ultimate tensile strength, yield strength, elongation and hardness from 196.2 MPa, 101.2 MPa, 14.5 % and 85.1 kg mm-2 without travelling magnetic fields to 224.1 MPa, 114.5 MPa, 17.1 % and 102.1 kg mm-2, and improve the ductility of alloys. However, upward travelling magnetic fields have the adverse effects on microstructural evolution, and lead to a reduction in the performance and ductility. Our findings demonstrate that long-range directional circular flows generated by travelling magnetic fields directionally alter the transformation and redistribution of solutes and temperature, which finally influences the solidification behavior and performance. Overall, our research present not only an innovative method to optimize the microstructures and mechanical properties for alloys with large solidification intervals, but also a detailed mechanism of travelling magnetic fields on this optimization during the sequential solidification.
Select Interfacial dislocations dominated lateral growth of long-period stacking ordered phase in Mg alloys Qianqian Jin, Xiaohong Shao, Shijian Zheng, Yangtao Zhou, Bo Zhang, Xiuliang Ma J. Mater. Sci. Technol., 2021, 61 (0): 114-118. DOI: 10.1016/j.jmst.2020.05.045 Understanding the interface between strengthening precipitates and matrix in alloys, especially at the atomic level, is a critical issue for tailoring the precipitate strengthening to achieve desired mechanical properties. Using high-resolution scanning transmission electron microscopy, we here clarify the semi-coherent interfaces between the matrix and long-period stacking ordered (LPSO) phases, including 18R and 14H, in Mg-Zn-Y alloys. The LPSO/Mg interface features the unique configuration of the Shockley partial dislocations, which produces a near zero macroscopic strain because the net Burgers vectors equal zero. The 18R/Mg interface characterizes a dissociated structure that can be described as a narrow slab of 54R. There are two dislocation arrays accompanied to the 18R/54R and 54R/Mg interface, resulting a slight deviation (about 2.3°). The 14R/Mg interface exhibits the dislocation pairs associated with solute atoms. We further evaluate the stability and morphology of the corresponding interfaces based on elastic interaction, via calculating the mutual strong interactions between dislocation arrays, as well as that between the dislocations and solute atoms. The synchronized migration of interfacial dislocations and solute atoms, like move-drag behavior, dominates the lateral growth of LPSO phases in Mg alloys.
Select Tensile deformation behavior and mechanical properties of a bulk cast Al0.9CoFeNi2 eutectic high-entropy alloy Hui Jiang, Dongxu Qiao, Wenna Jiao, Kaiming Han, Yiping Lu, Peter K. Liaw J. Mater. Sci. Technol., 2021, 61 (0): 119-124. DOI: 10.1016/j.jmst.2020.05.053 In this study, a new Al0.9CoFeNi2 eutectic high entropy alloy (EHEA) was designed, and the microstructures as well as the deformation behavior were investigated. The bulk cast Al0.9CoFeNi2 EHEA exhibited an order face-centered cubic FCC (L12) and an order body-centered cubic (B2) dual-phase lamellar eutectic microstructure. The volume fractions of FCC (L12) and B2 phases are measured to be 60 % and 40 %, respectively. The combination of the soft and ductile FCC (L12) phase together with the hard B2 phase resulted in superior strength of 1005 MPa and ductility as high as 6.2 % in tension at room temperature. The Al0.9CoFeNi2 EHEA exhibited obvious three-stage work hardening characteristics and high work-hardening ability. The evolving dislocation substructures during uniaxial tensile deformation found that planar slip dominates in both FCC (L12) and B2 phases, and the FCC (L12) phase is easier to deform than the B2 phase. The post-deformation transmission electron microscopy revealed that the sub-structural evolution of the FCC (L12) phase is from planar dislocations to bending dislocations, high-density dislocations, dislocation network, and then to dislocation walls, and Taylor lattices, while the sub-structural evolution of the B2 phase is from a very small number of short dislocations to a number of planar dislocations. Moreover, obvious ductile fracture in the FCC (L12) phase and a brittle-like fracture in the B2 phase were observed on the fracture surface of the Al0.9CoFeNi2 EHEA. The research results provide some insight into the microstructure-property relationship.
Select Doped ceramics of indium oxides for negative permittivity materials in MHz-kHz frequency regions Guohua Fan, Zhongyang Wang, Kai Sun, Yao Liu, Runhua Fan J. Mater. Sci. Technol., 2021, 61 (0): 125-131. DOI: 10.1016/j.jmst.2020.06.013 Negative permittivity has been widely studied in various metamaterials and percolating composites, of which the anomalous dielectric behavior was attributed to critical structural properties of building blocks. Herein, mono-phase ceramics of indium tin oxides (ITO) were sintered for epsilon-negative materials in MHz-kHz frequency regions. Electrical conductivity and complex permittivity were analyzed with Drude-Lorentz oscillator model. Carriers’ characters were measured based on Hall effect and the magnitude and frequency dispersion of negative permittivity were mainly determined by carrier concentration. Temperature-dependent dielectric properties further proved the epsilon-negative behaviors were closely associated with free carriers’ collective responses. It’s found that negative permittivity of ITO ceramics was mainly caused by plasma oscillations of free carriers, while the dielectric loss was mainly attributed to conduction loss. Negative permittivity realized here was related to materials intrinsic nature and this work preliminarily determined the mechanism of negative permittivity in doped ceramics from the perspective of carriers.
Select Nanocellulose-based reusable liquid metal printed electronics fabricated by evaporation-induced transfer printing Yiru Mao, Yixiang Wu, Pengju Zhang, Yang Yu, Zhizhu He, Qian Wang J. Mater. Sci. Technol., 2021, 61 (0): 132-137. DOI: 10.1016/j.jmst.2020.05.040 Reusable electronics have received widespread attention and are urgently needed. Here, nanocellulose-based liquid metal (NC-LM) printed circuit has been fabricated by the evaporation-induced transfer printing technology. In this way, the liquid metal pattern is embedded into the nanocellulose membrane, which is beneficial for the stability of the circuit during use. Besides, the NC-LM circuit is ultrathin with just tens of microns. In particular, the finished product is environmentally friendly because it can be completely dissolved by water, and both the liquid metal ink and the nanocellulose membrane can be easily recollected and reused, thereby reducing waste and pollution to the environment. Several examples of flexible circuits have been designed to evaluate their performance. The mechanism of evaporation-induced transfer printing technology involves the deposition, aggregation, and coverage tightly of the nanosized cellulose fibrils as the water evaporated. This study provides an economical and environmentally friendly way for the fabrication of renewable flexible electronics.
Select Growth mechanism of primary Ti5Si3 phases in special brasses and their effect on wear resistance Xianlong Wang, Jinchuan Jie, Shichao Liu, Zhuangzhuang Dong, Guomao Yin, Tingju Li J. Mater. Sci. Technol., 2021, 61 (0): 138-146. DOI: 10.1016/j.jmst.2020.05.063 In the present work, in-situ Ti5Si3 reinforced special brasses were prepared by melt reaction method. The synthesized Ti5Si3 phase shows various morphologies in brasses with different Ti5Si3 content, and the 3D morphological evolution of primary Ti5Si3 and its growth mechanism were investigated. The Ti5Si3 crystal, which bears D88 hexagonal crystal structure, grows along <0001> direction and is revealed by {101$\bar{0}$} faces during growth. With the increase of Ti5Si3 content in the brasses, the morphology of primary Ti5Si3 significantly changes from fibers to hexagonal prisms to short-rods with hollow. In addition, the influence of Ti5Si3 volume fraction and morphology on the wear behavior of special brass was also revealed. It was substantiated that the wear resistance increases with the increasing volume fraction of Ti5Si3, and the corresponding wear mechanism changes from delamination to slight adhesive wear and abrasive wear. However, the friction coefficient shows an abnormal increase when most of the Ti5Si3 containing hollows appears in the brass. That is mainly due to the fact that the Ti5Si3 is easier to break and fall off resulted by the hollow as a crack source, which makes it unable to resist the plastic deformation of the contact surface during the sliding.
Select Prediction of spatial distribution of the composition of inclusions on the entire cross section of a linepipe steel continuous casting slab Qiang Ren, Yuexin Zhang, Ying Ren, Lifeng Zhang, Jujin Wang, Yadong Wang J. Mater. Sci. Technol., 2021, 61 (0): 147-158. DOI: 10.1016/j.jmst.2020.05.035 In the current study, the transformation in the composition of non-metallic inclusions from the molten steel to the solidified steel was studied and the composition distribution of inclusions on the cross section of a linepine continuous casting slab was predicted. During cooling and solidification of the continuous casting strand, Al2O3-CaO inclusions reacted with the bulk steel and transformed to CaS-Al2O3-MgO-(CaO) ones in the continuous casting slab. The composition of inclusions on the cross section of the slab varied with locations due to the varied cooling rate. A model was established to predict the distribution of the composition of inclusions on the cross section of the continuous casting slab, coupling solidification and heat transfer of the continuous casting slab, the kinetic mass transfer of the dissolved elements in the solid steel, and thermodynamic calculation of inclusion transformation at different temperatures. The composition transformation of inclusions mainly occurred at the temperature between the liquidus and solidus of the linepipe steel. Inclusions were mainly CaS-Al2O3-MgO-(CaO) in slab center and were MgO-Al2O3-CaO-CaS within the subsurface of the slab. In the slab, the transformation fraction of inclusions was less than 10 % at corners while it reached 70 % at 50 mm below the surface of the slab.
Select Efficient nanostructured heterogeneous catalysts by electrochemical etching of partially crystallized Fe-based metallic glass ribbons Qiaoyue Zhang, Shun-Xing Liang, Zhe Jia, Wenchang Zhang, Weimin Wang, Lai-Chang Zhang J. Mater. Sci. Technol., 2021, 61 (0): 159-168. DOI: 10.1016/j.jmst.2020.06.016 Although an increasing interest has been attracted to further develop heterostructured catalysts from metallic glasses (MGs) by heat treatment, overcoming surface oxidation effect is still a critical problem for such environmental catalysts. Herein, a short-time electrochemical etching of partially crystallized Fe-based ribbons in 0.3 M H3PO4 electrolyte enables the formation of honeycomb-like nanoporous structure as effective catalytic active sites in Fenton-like process. Studies of structure and surface morphologies reveal that the formation of nanoporous structure by potentiostatic etching originates from electrochemical potential difference of nanocrystals (α-Fe (Si) and Fe2B) and residual amorphous phase in partially crystallized ribbons, where Fe2B having a lower open circuit potential tends to be selectively dissolved. Simultaneously, thin oxide layer after electrochemical etching exposes more active sites for H2O2 activation and provides an effective protection of nanocrystals from massive loss during etching. Investigation of optimal processing conditions suggests that the selection of electrolyte plays an important role; dye degradation rates of etched ribbons in HNO3 and Na2SO4 electrolytes can also achieve at least 2 times higher than that of as-annealed ribbons. This work holds the promise to develop novel environmental catalysts by effective electrochemical etching of partially crystallized ribbons.
Select Reversible grafting of antibiotics onto contact lens mediated by labile chemical bonds for smart prevention and treatment of corneal bacterial infections Bailiang Wang, Jiahong Zeng, Yishun Guo, Lin Liang, Yingying Jin, Siyuan Qian, Renjie Miao, Liang Hu, Fan Lu J. Mater. Sci. Technol., 2021, 61 (0): 169-175. DOI: 10.1016/j.jmst.2020.05.062 Eye trauma, decreased immunity, and contact lens wear often cause serious bacterial infections and irreversible corneal damage. To realize the responsive release of antibiotics such as gentamicin sulfate (GS), a novel antibacterial contact lens was constructed through self-assembly of antibiotics loaded ADA-GS/PEI (polyethyleneimine) multilayer films on the surface. Both in vitro and in vivo antibacterial tests demonstrated high efficient and fast antibacterial property based on the smart responsive to bacterial infections and reversible drug loading and release.
Select Microstructure and mechanical properties in the TLP joint of FeCoNiTiAl and Inconel 718 alloys using BNi2 filler Lin Yuan, Jiangtao Xiong, Yajie Du, Jin Ren, Junmiao Shi, Jinglong Li J. Mater. Sci. Technol., 2021, 61 (0): 176-185. DOI: 10.1016/j.jmst.2020.05.050 High entropy alloy (HEA) of FeCoNiTiAl and Inconel 718 superalloy were firstly transient liquid phase (TLP) bonded by BNi2 filler due to the diffusion of Si and B in the filler to the base metals. The effects of bonding time on microstructure evolution and mechanical properties of the TLP joints were investigated. Owing to the complete isothermal solidification of the joints bonded for 30 min ~ 120 min at 1100 °C, no athermally solidified zones (ASZs) formed by eutectic phases were observed in the welded zone. Thus the TLP joints were only composed by the isothermally solidified zone (ISZ) and two diffusion affected zone (DAZ) adjacent to the dissimilar base metals and the negative effect of the ASZ on joint properties can be avoided. In addition, the increase of the bonding time can also make the TiB2 borides precipitated in the DAZ near HEA and the brittle borides or carbides in the DAZ near IN718 alloy decrease and reduce the possibility of the stress concentration happened in the joints under loading. Therefore, the highest shear strength (632.1 MPa) of the TLP joints was obtained at 1100 °C for 120 min, which was higher than that of the joint bonded for 30 min, 404.2 MPa. Furthermore, the extension of the bonding time made the fracture mechanism of the joint be transformed from the intergranular fracture to the transgranular fracture. However, as the brittle borides in the DAZ near IN718 can not be eliminated completely and refining of grains also happened in such region, all the TLP joints fractured inner the DAZ near IN718 alloy.
Select Enhancing mechanical properties and corrosion resistance of nickel-aluminum bronze via hot rolling process Yanhua Zeng, Fenfen Yang, Zongning Chen, Enyu Guo, Minqiang Gao, Xuejian Wang, Huijun Kang, Tongmin Wang J. Mater. Sci. Technol., 2021, 61 (0): 186-196. DOI: 10.1016/j.jmst.2020.05.024 The mechanical properties and corrosion behavior of as-cast, as-annealed and hot-rolled nickel-aluminum bronze (NAB) alloy (Cu-9Al-10Ni-4Fe-1.2 Mn, all in wt.%) in 3.5 wt.% NaCl solution were investigated. The results show that annealing introduces a large number of κ phases to precipitate in the α phase. However, after further hot rolling, the original continuous κ phases are spheroidized and dispersed, increasing the strength, hardness, and elongation of the alloy. In addition to the enhanced mechanical properties, the corrosion resistance of the NAB samples is also improved significantly by hot rolling, as revealed by the mass loss measurements, electrochemical impedance spectroscopy (EIS), and cross-sectional corrosion morphology. Selective phase corrosion occurs by the preferential corrosion of the α phase, which acts as an anode to the κ phases, and the uncorroded κ phases are retained in the corrosion product film. The interfaces between the κ phases and the surrounding corrosion products become discontinuous caused by the spheroidization of κ phases, reducing the corrosion of the substrate by the corrosive medium via the channels. As a result, the corrosion rate and the maximum local corrosion depth of the hot-rolled NAB sample are greatly reduced.
Select Coarsening kinetics and strengthening mechanisms of core-shell nanoscale precipitates in Al-Li-Yb-Er-Sc-Zr alloy Yang Wang, Shun Zhang, Ruizhi Wu, Nodir Turakhodjaev, Legan Hou, Jinghuai Zhang, Sergey Betsofen J. Mater. Sci. Technol., 2021, 61 (0): 197-203. DOI: 10.1016/j.jmst.2020.05.061 The tailored nanoparticles with a complex core/shell structure can satisfy a variety of demands, such as lattice misfit, shearability and coarsening resistance. In this research, core-shell nanoscale Al3(Yb, Er, Sc, Zr, Li) composite particles were precipitated in Al-2Li-0.1Yb-0.1Er-0.1Sc-0.1 Zr (wt%) alloy through the double-aging treatment, in which the core was (Yb, Er, Sc, Zr)-rich formed at 300 °C and the shell was Li-rich formed at 150 °C. The coarsening kinetics and precipitate size distributions (PSDs) of Al3(Yb, Er, Sc, Zr, Li) particles aged at 150 °C previously aged at 300 °C for 24 h showed a better fit to the relation of 2 ∝ kt and normal distribution, indicating that the coarsening of precipitates was controlled by interface reaction, not diffusion. The Orowan bypass strengthening was operative mechanism at 150 °C.
Select Critical transitions in the shape morphing of kirigami metallic glass D.X. Han, L. Zhao, S.H. Chen, G. Wang, K.C. Chan J. Mater. Sci. Technol., 2021, 61 (0): 204-212. DOI: 10.1016/j.jmst.2020.05.065 Kirigami, the ancient Japanese paper cutting technique, has been applied to achieve high stretchability and low energy loss of designed metallic glass. Despite the exploration of the underlying deformation mechanism of kirigami-inspired structures from the energy point of view, the morphable responses of the kirigami patterns and the origin of the kirigami response are yet to be fully understood. This study reveals the mechanical driven-forms of the kirigami structure with the corresponding deformation stages. Based on the beam deflection theory, the elastic buckling behavior of kirigami metallic glass is manifested and a critical force prediction model is developed. Moreover, a force concentration parameter is introduced in the rigid-plastic deformation stage, predicting the nominal ultimate force. The kirigami-inspired facture force is firstly proposed. The findings of these models are in good agreement with the experimental size-dependent kirigami responses, and expected to provide significant insights into the understanding of the deformation behavior and the design of kirigami metallic glasses.
Letter
Select Preparation of hysteresis-free flexible perovskite solar cells via interfacial modification Xiaofang Ye, Hongkun Cai, Jian Su, Jingtao Yang, Jian Ni, Juan Li, Jianjun Zhang J. Mater. Sci. Technol., 2021, 61 (0): 213-220. DOI: 10.1016/j.jmst.2020.05.029 In recent years, flexible perovskite solar cells have received extensive attention and rapid development due to their advantages of lightweight, portability, wearability and applications in near-space. However, due to the limitations of their preparation process and other factors, high-efficiency and large-area flexible perovskite solar cells still have a lot of room for development. In our work, a flexible perovskite solar cell (PEN/ITO/SnO2/KCl/Cs0.05 (MA0.17FA0.83)0.95Pb(I0.83Br0.17)3/spiro/Au) was prepared using a low temperature (no higher than 100 °C) solution process, and the device with the highest efficiency of 16.16% was obtained by adjusting the concentration of the KCl modified layer. Meanwhile, the efficiency of the large area (1 cm2) flexible solar cell was higher than 13%. At the same time, the passivation of the KCl interface modification layer inhibits the formation of the defect states, which reduced the surface recombination of the perovskite and improved the carrier transport performance, and the hysteresis effect of the device was also reduced accordingly.
Research Article
Select Microstructural homogeneity and mechanical behavior of a selective laser melted Ti-35Nb alloy produced from an elemental powder mixture Jincheng Wang, Yujing Liu, Chirag Dhirajlal Rabadia, Shun-Xing Liang, Timothy Barry Sercombe, Lai-Chang Zhang J. Mater. Sci. Technol., 2021, 61 (0): 221-233. DOI: 10.1016/j.jmst.2020.05.052 Although using elemental powder mixtures may provide broad alloy selection at low cost for selective laser melting (SLM), there is still a concern on the resultant microstructural and chemical homogeneity of the produced parts. Hence, this work investigates the microstructure and mechanical properties of a SLM-produced Ti-35Nb composite (in wt%) using elemental powder. The microstructural characteristics including β phase, undissolved Nb particles and chemical homogeneity were detailed investigated. Nanoindentation revealed the presence of relatively soft undissolved Nb particles and weak interface bonding around Nb-rich regions in as-SLMed samples. Solid-solution treatment can not only improve chemical homogeneity but also enhance bonding through grain boundary strengthening, resulting in ~43 % increase in tensile elongation for the heat-treated Ti-35Nb compared to the as-SLMed counterpart. The analyses of tensile fractures and shear bands further confirmed the correlation between the different phases and the ductility of Ti-35Nb. In particular, the weak bonding between undissolved Nb and the matrix in the as-SLMed sample reduces its ductility while the β grains in solid-solution treated Ti-Nb alloy can induce a relatively stable plastic flow therefore better ductility. This work sheds insight into the understanding of homogenization of microstructure and phases of SLM-produced alloys from an elemental powder mixture.
Select Influence of cementite spheroidization on relieving the micro-galvanic effect of ferrite-pearlite steel in acidic chloride environment Hu Liu, Jie Wei, Junhua Dong, Yiqing Chen, Yumin Wu, Yangtao Zhou, Subedi Dhruba Babu, Wei Ke J. Mater. Sci. Technol., 2021, 61 (0): 234-246. DOI: 10.1016/j.jmst.2020.05.031 The corrosion behavior of the as-received steel and the spheroidized steel in acidic chloride environment was investigated. The results indicate the corrosion mode and corrosion rate of two steels are diverse due to their difference in microstructure. For as-received steel with ferrite-pearlite microstructure, severe localized corrosion happens on the pearlite regions, and plenty of cathodic cementite remains in the pits, further strengthening the micro-galvanic effect and accelerating the corrosion rate. While for spheroidized steel with tempered martensite microstructure, the nanosized cementite particles evenly distributed on the ferrite substrate are easy to fall off, which can significantly reduce the cementite accumulation on the steel surface, relieving the acceleration effect of micro-galvanic corrosion.
ISSN: 1005-0302
CN: 21-1315/TG
Editorial Office: Journal of Materials Science & Technology , 72 Wenhua Rd.,
Shenyang 110016, China
Tel: +86-24-83978208
E-mail:JMST@imr.ac.cn
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ECOS_csolve: Solve a conic optimization problem In ECOSolveR: Embedded Conic Solver in R
Description
The function ECOS_csolve is a wrapper around the ecos csolve C function. Conic constraints are specified using the G and h parameters and can be NULL and zero length vector respectively indicating an absence of conic constraints. Similarly, equality constraints are specified via A and b parameters with NULL and empty vector values representing a lack of such constraints. At most one of the pair (G , h) or (A, b) is allowed to be absent.
Usage
1 2 3 ECOS_csolve(c = numeric(0), G = NULL, h = numeric(0), dims = list(l = integer(0), q = NULL, e = integer(0)), A = NULL, b = numeric(0), bool_vars = integer(0), int_vars = integer(0), control = ecos.control())
Arguments
c the coefficients of the objective function; the length of this determines the number of variables n in the problem. G the inequality constraint sparse matrix in compressed column format, e.g. dgCMatrix-class. Can be NULL h the right hand size of the inequality constraint. Can be empty numeric vector. dims is a list of three named elements: dims['l'] an integer specifying the dimension of positive orthant cone, dims['q'] an integer vector specifying dimensions of second-order cones, dims['e'] an integer specifying the number of exponential cones A the optional equality constraint sparse matrix in compressed column format, e.g. dgCMatrix-class. Can be NULL b the right hand side of the equality constraint, must be specified if A is. Can be empty numeric vector. bool_vars the indices of the variables, 1 through n, that are boolean; that is, they are either present or absent in the solution int_vars the indices of the variables, 1 through n, that are integers control is a named list that controls various optimization parameters; see ecos.control.
Value
a list of 8 named items
x
primal variables
y
dual variables for equality constraints
s
slacks for Gx + s <= h, s \in K
z
dual variables for inequality constraints s \in K
infostring
gives information about the status of solution
retcodes
a named integer vector containing four elements
exitflag
0=OPTIMAL, 1=PRIMAL INFEASIBLE, 2=DUAL INFEASIBLE, -1=MAXIT REACHED
iter
the number of iteration used
mi_iter
the number of iterations for mixed integer problems
numerr
a non-zero number if a numeric error occurred
summary
a named numeric vector containing
pcost
value of primal objective
dcost
value of dual objective
pres
primal residual on inequalities and equalities
dres
dual residual
pinf
primal infeasibility measure
dinf
dual infeasibility measure
pinfres
primal infeasibility residual
dinfres
dual infeasibility residual
gap
duality gap
relgap
relative duality gap
r0
Unknown at the moment to this R package maintainer.
timing
a named numeric vector of timing information consisting of
runtime
the total runtime in ecos
tsetup
the time for setup of the problem
tsolve
the time to solve the problem
Details
A call to this function will solve the problem: minimize c^Tx, subject to Ax = b, and h - G*x \in K.
Variables can be constrained to be boolean (1 or 0) or integers. This is indicated by specifying parameters bool_vars and/or int_vars respectively. If so indicated, the solutions will be found using a branch and bound algorithm.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ## githubIssue98 G <- local({ Gpr <- c(0.416757847405471, 2.136196095668454, 1.793435585194863, -1., 0.056266827226329, -1.640270808404989, 0.841747365656204, -1., 0.416757847405471, 2.136196095668454, 1.793435585194863, -1., 0.056266827226329, -1.640270808404989, 0.841747365656204, -1., -1.) Gjc <- as.integer(c(0, 4, 8, 12, 16, 17)) Gir <- as.integer(c(0, 1, 2, 7, 0, 1, 2, 8, 3, 4, 5, 9, 3, 4, 5, 10, 6)) Matrix::sparseMatrix(i = Gir, p = Gjc, x = Gpr, index1 = FALSE) }) print(G) c <- as.numeric(c(0, 0, 0, 0, 1)) h <- as.numeric(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)) dims <- list(l = 6L, q = 5L, e = 0L) ECOS_csolve(c = c, G = G, h = h, dims = dims, A = NULL, b = numeric(0)) ## A larger problem using saved data for the large matrices MPC01 <- readRDS(system.file("misc", "MPC01.rds", package="ECOSolveR")) retval <- ECOS_csolve(c = MPC01$c, G = MPC01$G, h = MPC01$h, dims = MPC01$dims) retval$retcodes retval$infostring retval\$summary
ECOSolveR documentation built on May 30, 2017, 5:12 a.m.
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184_notes:examples:week4_two_segments
Suppose we have two segments of uniformly distributed charge, one with total charge $+Q$, the other with $-Q$. The two segments each have length $L$, and lie crossed at their endpoints in the $xy$-plane. The segment with charge $+Q$ lies along the $y$-axis, and the segment with charge $-Q$ lies along the $x$-axis. See below for a diagram of the situation. Create an expression for the electric field $\vec{E}_P$ at a point $P$ that is located at $\vec{r}_P=r_x\hat{x}+r_y\hat{y}$. You don't have to evaluate integrals in the expression.
#### Facts
• One segment lies on the $y$-axis stretching from $0$ to $L$, with charge $Q$ uniformly distributed.
• The other segment lies on the $x$-axis stretching from $0$ to $L$, with charge $-Q$ uniformly distributed.
• The point $P$ is at the arbitrary location $\vec{r}_P=r_x\hat{x}+r_y\hat{y}$
• The electric field due to a point charge is $$\vec{E} = \frac{1}{4\pi\epsilon_0}\frac{q}{r^3}\vec{r}$$
• The electric field at $P$ is the superposition of contributions from the two segments: $$\vec{E}_P = \vec{E}_{+Q} +\vec{E}_{-Q}$$
#### Goal
• Find $\vec{E}_P$.
#### Approximation
We begin with an approximation, which will make our calculations simpler, and makes sense based on our representation:
• The thicknesses of both segments are infinitesimally small, and we can approximate them as line segments.
This example is complicated enough that it's worthwhile to make a plan.
#### Plan
We will use integration to find the electric field from each segment, and then add the electric fields together using superposition. We'll go through the following steps.
• For the first segment, find the linear charge density, $\lambda$.
• Use $\lambda$ to write an expression for $\text{d}Q$.
• Assign a variable location to the $\text{d}Q$ piece, and then use that location to find the separation vector, $\vec{r}$.
• Write an expression for $\text{d}\vec{E}$.
• Figure out the bounds of the integral, and integrate to find electric field at $P$.
• Repeat the above steps for the other segment of charge.
• Add the two fields together to find the total electric field at $P$.
Because we know that electric fields add through superposition, we can treat each of the charges separately, find the electric field, then add the fields together at $P$ at the end. We can begin with the electric field due to the segment along the $y$-axis. We start by finding $\text{d}Q$ and $\vec{r}$. The charge is uniformly distributed so we have a simple line charge density of $\lambda=Q/L$. The segment extends in the $y$-direction, so we have $\text{d}l=\text{d}y$. This gives us $\text{d}Q$: $$\text{d}Q=\lambda\text{d}l=\frac{Q\text{d}y}{L}$$
#### Assumption
The charge is evenly distributed along each segment of charge. This allows each little piece of charge to have the same value along each line.
The separation vector $\vec{r}$ points from the source of the electric field to the observation point. The source is $\text{d}Q$, which is located at $y\hat{y}$, and the observation point is $\vec{r}_P=r_x\hat{x}+r_y\hat{y}$. Then we have the separation vector: $$\vec{r}=\vec{r}_P-y\hat{y}=r_x\hat{x}+r_y\hat{y}-y\hat{y}=r_x\hat{x}+(r_y-y)\hat{y}$$
Now, we have enough to define the electric field from the small piece ($\text{d}Q$) of the segment - plugging the $\text{d}Q$ and $\vec{r}$ we just found: $$\text{d}\vec{E}=\frac{1}{4\pi\epsilon_0}\frac{\text{d}Q}{r^3}\vec{r}=\frac{1}{4\pi\epsilon_0}\frac{Q\text{d}y}{L\cdot|r_x\hat{x}+(r_y-y)\hat{y}|^3}(r_x\hat{x}+(r_y-y)\hat{y})$$
Next, we integrate over the entire segment to find an expression for its contribution to the electric field vector at $P$. The limits of our integral are based on the variable of integration, which is $y$. This denotes the length along the segment on the $y$-axis, which stretches from $0$ to $L$, so these are our limits of integration. $$\vec{E}_{+Q}=\int_0^L\frac{1}{4\pi\epsilon_0}\frac{Q\text{d}y}{L\cdot|r_x\hat{x}+(r_y-y)\hat{y}|^3}(r_x\hat{x}+(r_y-y)\hat{y})$$
Next, we can do a similar analysis to find the electric field vector contribution from the segment that lies along the $x$-axis. See below for a visual of $\text{d}Q$ and $\vec{r}$. See if you can convince yourself that for the segment along the $x$-axis, $\text{d}Q=\frac{-Q\text{d}x}{L}$, and $\vec{r}=(r_x-x)\hat{x}+r_y\hat{y}$.
From here, we can find $\text{d}\vec{E}$: $$\text{d}\vec{E}=\frac{1}{4\pi\epsilon_0}\frac{\text{d}Q}{r^3}\vec{r}=\frac{1}{4\pi\epsilon_0}\frac{-Q\text{d}x}{L\cdot|(r_x-x)\hat{x}+r_y\hat{y}|^3}((r_x-x)\hat{x}+r_y\hat{y})$$
To find the contribution from the entire segment, we again must determine the endpoints of our integration. Our variable of integration is $x$ this time, which denotes the distance along the segment that lies on the $x$-axis. This distance stretches from $0$ to $L$, so these are our limits of integration: $$\vec{E}_{-Q}=\int_0^L\frac{1}{4\pi\epsilon_0}\frac{-Q\text{d}x}{L\cdot|(r_x-x)\hat{x}+r_y\hat{y}|^3}((r_x-x)\hat{x}+r_y\hat{y})$$
Then the final electric field vector at $P$ is the sum of the two contributions, because of vector superposition. (You can pull out the constants to simplify the integral if you want.) \begin{align*} \vec{E} &= \vec{E}_{+Q}+\vec{E}_{-Q} \\ &= \int_0^L\frac{1}{4\pi\epsilon_0}\frac{Q\text{d}y}{L\cdot|r_x\hat{x}+(r_y-y)\hat{y}|^3}(r_x\hat{x}+(r_y-y)\hat{y}) + \int_0^L\frac{1}{4\pi\epsilon_0}\frac{-Q\text{d}x}{L\cdot|(r_x-x)\hat{x}+r_y\hat{y}|^3}((r_x-x)\hat{x}+r_y\hat{y}) \\ &= \frac{Q}{4\pi\epsilon_0L}\left(\int_0^L\frac{\text{d}y}{|r_x\hat{x}+(r_y-y)\hat{y}|^3}(r_x\hat{x}+(r_y-y)\hat{y}) - \int_0^L\frac{\text{d}x}{|(r_x-x)\hat{x}+r_y\hat{y}|^3}((r_x-x)\hat{x}+r_y\hat{y})\right) \\ \end{align*} At this point we have the integrals set up, which you could solve by hand if you so desire or plug them into Wolfram Alpha, Mathematica, or some other computation program.
• 184_notes/examples/week4_two_segments.txt
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## general perspective on the Metropolis–Hastings kernel
Posted in Books, Statistics with tags , , , , , , , , , , , , , on January 14, 2021 by xi'an
[My Bristol friends and co-authors] Christophe Andrieu, and Anthony Lee, along with Sam Livingstone arXived a massive paper on 01 January on the Metropolis-Hastings kernel.
“Our aim is to develop a framework making establishing correctness of complex Markov chain Monte Carlo kernels a purely mechanical or algebraic exercise, while making communication of ideas simpler and unambiguous by allowing a stronger focus on essential features (…) This framework can also be used to validate kernels that do not satisfy detailed balance, i.e. which are not reversible, but a modified version thereof.”
A central notion in this highly general framework is, extending Tierney (1998), to see an MCMC kernel as a triplet involving a probability measure μ (on an extended space), an involution transform φ generalising the proposal step (i.e. þ²=id), and an associated acceptance probability ð. Then μ-reversibility occurs for
$\eth(\xi)\mu(\text{d}\xi)= \eth(\phi(\xi))\mu^{\phi}(\text{d}\xi)$
with the rhs involving the push-forward measure induced by μ and φ. And furthermore there is always a choice of an acceptance probability ð ensuring for this equality to happen. Interestingly, the new framework allows for mostly seamless handling of more complex versions of MCMC such as reversible jump and parallel tempering. But also non-reversible kernels, incl. for instance delayed rejection. And HMC, incl. NUTS. And pseudo-marginal, multiple-try, PDMPs, &c., &c. it is remarkable to see such a general theory emerging a this (late?) stage of the evolution of the field (and I will need more time and attention to understand its consequences).
## the surprisingly overlooked efficiency of SMC
Posted in Books, Statistics, University life with tags , , , , , , , , , , , on December 15, 2020 by xi'an
At the Laplace demon’s seminar today (whose cool name I cannot tire of!), Nicolas Chopin gave a webinar with the above equally cool title. And the first slide debunking myths about SMC’s:
The second part of the talk is about a recent arXival Nicolas wrote with his student Hai-Dang DauI missed, about increasing the number of MCMC steps when moving the particles. Called waste-free SMC. Where only one fraction of the particles is updated, but this is enough to create a sort of independence from previous iterations of the SMC. (Hai-Dang Dau and Nicolas Chopin had to taylor their own convergence proof for this modification of the usual SMC. Producing a single-run assessment of the asymptotic variance.)
On the side, I heard about a very neat (if possibly toyish) example on estimating the number of Latin squares:
And the other item of information is that Nicolas’ and Omiros’ book, An Introduction to Sequential Monte Carlo, has now appeared! (Looking forward reading the parts I had not yet read.)
## MCMC, variational inference, invertible flows… bridging the gap?
Posted in Books, Mountains, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , on October 2, 2020 by xi'an
Two weeks ago, my friend [see here when climbing Pic du Midi d’Ossau in 2005!] and coauthor Éric Moulines gave a very interesting on-line talk entitled MCMC, Variational Inference, Invertible Flows… Bridging the gap?, which was merging MCMC, variational autoencoders, and variational inference. I paid close attention as I plan to teach an advanced course on acronyms next semester in Warwick. (By acronyms, I mean ABC+GAN+VAE!)
The notion in this work is that variational autoencoders are based on over-simple mean-field variational distributions, that usually produce a poor approximation of the target distribution. Éric and his coauthors propose to introduce a Metropolis step in the VAE. This leads to a more general notion of Markov transitions and a global balance condition. Hamiltonian Monte Carlo can be used as well and it improves the latent distribution approximation, namely the encoder, which is surprising to me. The steps of the Markov kernel produce a manageable transform of the initial mean field approximation, a random version of the original VAE. Manageable provided not too many MCMC steps are implemented. (Now, the flow of slides was much too fast for me to get a proper understanding of the implementation of the method, of the degree of its calibration, and of the computing cost. I need to read the associated papers.)
Once the talk was over, I went back to changing tires and tubes, as two bikes of mine had flat tires, the latest being a spectacular explosion (!) that seemingly went through the tire (although I believe the opposite happened, namely the tire got slashed and induced the tube to blow out very quickly). Blame the numerous bits of broken glass over bike paths.
## state of the art in sampling & clustering [workshop]
Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , on September 17, 2020 by xi'an
Next month, I am taking part in a workshop on sampling & clustering at the Max-Planck-Institut für Physik in Garching, Germany (near München). By giving a three hour introduction to ABC, as I did three years ago in Autrans. Being there and talking with local researchers if the sanitary conditions allow. From my office otherwise. Other speakers include Michael Betancourt on HMC and Johannes Buchner on nested sampling. The remote participation to this MPI workshop is both open and free, but participants must register before 18 September, namely tomorrow.
## transport Monte Carlo
Posted in Books, pictures, Statistics, Travel with tags , , , , , , , , , , , , , , , on August 31, 2020 by xi'an
Read this recent arXival by Leo Duan (from UF in Gainesville) on transport approaches to approximate Bayesian computation, in connection with normalising flows. The author points out a “lack of flexibility in a large class of normalizing flows” to bring forward his own proposal.
“…we assume the reference (a multivariate uniform distribution) can be written as a mixture of many one-to-one transforms from the posterior”
The transportation problem is turned into defining a joint distribution on (β,θ) such that θ is marginally distributed from the posterior and β is one of an infinite collection of transforms of θ. Which sounds quite different from normalizing flows, to be sure. Reverting the order, if one manages to simulate β from its marginal the resulting θ is one of the transforms. Chosen to be a location-scale modification of β, s⊗β+m. The weights when going from θ to β are logistic transforms with Dirichlet distributed scales. All with parameters to be optimised by minimising the Kullback-Leibler distance between the reference measure on β and its inverse mixture approximation, and resorting to gradient descent. (This may sound a wee bit overwhelming as an approximation strategy and I actually had to make a large cup of strong macha to get over it, but this may be due to the heat wave occurring at the same time!) Drawing θ from this approximation is custom-made straightforward and an MCMC correction can even be added, resulting in an independent Metropolis-Hastings version since the acceptance ratio remains computable. Although this may defeat the whole purpose of the exercise by stalling the chain if the approximation is poor (hence suggesting this last step being used instead as a control.)
The paper also contains a theoretical section that studies the approximation error, going to zero as the number of terms in the mixture, K, goes to infinity. Including a Monte Carlo error in log(n)/n (and incidentally quoting a result from my former HoD at Paris 6, Paul Deheuvels). Numerical experiments show domination or equivalence with some other solutions, e.g. being much faster than HMC, the remaining \$1000 question being of course the on-line evaluation of the quality of the approximation.
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Physics Definition & Proof Based Problems
### Definition & Proof Based Problems
Q 3202556438
Define the quality factor in an ac circuit. Why should the quality factor have
high value in receiving circuits? Name the factors on which it depends.
Solution:
The quality LKtor is defined as the ratio of potential difference across an
inductor or a capacitor to potential difference across resistance in an LCR
circuit at resonance.
Q = (omega_r L)/R
Quality factor should be high to have the current corresponding to a particular
frequency to be more and to avoid the other unwanted frequencies.
Q-factor depends on f, L, R and C.
Q 3202845738
In a series LCR circuit connected to an ae source of variable frequency and voltage
V = V_m sin omega t, draw a plot showing the variation of current (I) with angular
frequency (omega) for two different values of resistance R_1 and R_2 (R_1 > R_2).
Write the condition under which the phenomenon of resonance occurs. For
which value of the resistance out of the two curves, a sharper resonance
is produced? Define Q-factor of the circuit and give its significance.
Solution:
The following graph shown the variation of current ·with angular frequency.
When X_L = X_C, resonance occurs,
i.e , omega_r L = 1/( omega_r C)
=> omega_r = 1/sqrt(LC)
omega_r, is called the resonant frequency;
Lesser is the resistance, sharper is resonance.
Hence, for resistance R_ 2 sharper is the
curve. The ratio (omega_r L)/R is called quality
factor. Higher the quality factor (Q), better is the tuning of the circuit (i.e.
selectivity).
Q 3212845730
Define root mean square current. Also, obtain its expression.
Solution:
Rms current is that value of current which produces the same amount of
heat as it produced by alternating current when flows through the same
conductor for the same time period.
Let an instantaneous current I = I_m sin omega t is passing through a resistor R.
Let it be constant for a very short duration of time dt.
Then, very small amount of heat produced is given by
dH = I^2 R dt
Heat produced for one complete cycle is given by
H = int_0^T dH = int_0^T I^2 Rdt
:. H = int_0^T I_m^2 ( sin^2 omega t) Rdt = I_m^2 int_0^T sin^2 omega t dt = I_m^2 int_(t = 0)^T ((1 - cos 2 omega t)/2) dt
H = ( I_m^2 R)/2 [ int_0^T dt - int_o^T ( cos 2 omega t) dt ] = (I_m^2 R)/2 { T - [ (sin 2 omega t)/(2 omega) ]_0^T }
As omega = 2 pi // T
H = ( I_m^2 RT)/2 - (I_m^2 R)/2 [ sin 2 xx (2 pi)/T xx T - sin 0]
:. H = ( I_m^2 RT)/2 ............(i)
If I_(r m s) is steady current flowing through the same circuit for the same time
interval T producing the same heat amount of heat H, then the heat
produced is
H = I_(r m s)^2 - RT ........ (ii)
Equating (i) and (ii), we get
( I_m^2 RT)/2 = I_m^2 RT
:. I_m/sqrt2 = I_(r m s) or I_(r m s) = 0.707 I_m.
Q 3242756633
(a) Show that in an ac circuit containing a pure inductor, the voltage is ahead
of current by pi//2 in phase.
(b) A horizontal straight wire of length L extending from east to west is
falling with speed v at right angles to the horizontal component of
Earth's magnetic field B.
(i) Write the expression for the instantaneous value of the emf induced in
the wire.
(ii) What is the direction of the emf?
(iii) Which end of the wire is at the higher potential?
Solution:
(a) Inductive reactance is the opposition offered by
an inductor towards the How of current passing
through it.
X_L = 2 pi v L
Applied ac voltage, E = E_m sin omega t ... (i)
An emf induced in the inductor is given by
epsilon = - L (dI)/( dt)
In order to maintain the How of current through
the inductor, we must have
E = - epsilon
i.e. E = L (dI)/(dt) => (dI)/(dt) = E/L = E_m/L sin omega t
:. int dI = E_m/L int sin omega t dt => I = E_m/(L omega) ( - cos omega t)
I = E_m/(L omega) sin ( omega t - pi//2)
I = I_m , sin (omega t - pi//2) .............(ii)
where I_m = E_m/(L omega) = E_m/X_L
From equations (i) and (ii), we conclude that voltage leads the current by a
phase angle pi//2.
(b) (i) E = B_H Lv
(ii) The direction of emf is from west to east.
(iii) The end of the wire towards east is at higher
potential.
Q 3232756632
(a) what do you understand by sharpness of resonance in a series LCR
circuit? Derive an expression for Q-factor of the circuit.
Three electrical circuits having ac sources of variable frequency are shown
in the figure. Initially the current flowing in each of these is same.
If the frequency of the applied ac source is increased, how will the
current flowing in these circuits be affected? Give reason for your
Solution:
The sharpness of resonance is measured by Q- factor of the LCR circuit. It
is defined as the ratio of the voltage developed across the inductance (or
capacitance) at resonance to 'the voltage developed across the resistance.
:. Q = (L omega _r I_text(max))/( R I_text(max) ) = (L omega _r)/R , here omega_r = 1/sqrt(LC)
Also, Q = ( 1 /( C omega_r) I_text(max) )/( R I_text(max) ) = 1/( C omega_r R)
Further, omega_r = 1/sqrt (LC)
:. Q = L/R * 1/sqrt(LC) = 1/R sqrt (L/C)
Larger the Q-value of the circuit, sharper is the resonance curve.
(b) (i) The first is a pure resistor. Since, the resistance offered by a circuit
having a resistor only does not change with frequency, the current
will also not change with fi-equency.
(ii) In this circuit, which has an inductance L the reactance X_L = L_omega = 2 pi v L.
Thus, X_L alpha v ,i.e. as v increases X_L also increases and the current I_V ( I_v = E_V/X_L)
decreases.
(iii) In this circuit which contains only a pure capacitance, the resistance offered by
it is given by X_C = 1/(C omega) = 1/( 2 pi v C) . Thus as v, the frequency, increases
X_C decreases and hence, the current increases in the circuit.
Q 3252845734
A series LCR circuit is connected to an ac source. Using the phasor diagram,
derive the expression for the impedance of the circuit. Plot a graph to
show the variation of current with frequency of the source, explaining
the nature of its variation.
Solution:
Take the voltage of source
V = V_m sin omega t ... (i)
To determine the phase relation between current
and voltage at any instant of time, we use a phasor
technique.
As all the three components are in series, the same amount of current flows
through them at any instant of time. Let it be
I = I_m sin (omega t + phi ) ... (ii)
where phi is the phase difference between the voltage across the source and current.
We construct a phasor diagram.
On applying Pythagoras theorem, we get
V_m^ 2 = V_(Rm)^2 + ( V_(Cm) - V_(Lm) )^2
Here V_(Rm) = I_mR , V_(Cm) = I_m X_C , V_(Lm) = I_m X_L
V_m = I_m sqrt ( R^2 + ( X_C - X_L)^2)
V_m = I_m Z
where, Z = sqrt ( R^2 + ( X_C - X_L)^2)
Z is called the impedance of the circuit.
The variation of current with frequency of source
is shown in the figure.
I_m = V_m/Z
We know X_L = omega_L and X_C = 1/( omega C)
Thus, on increasing the frequency, X_L increases and X_C decreases. As a result,
X_C - X_L decreases.
We know Z = sqrt ( R^2 + ( X_C - X_L)^2)
So, Z also decreases and with this current increases.
For a particular value of frequency called resonant frequency (omega _r)
we find X_L = X_C
Z = R
and I_m = I_m^(m a x )
After this frequency, X_C - X_L again increases and I_m decreases.
Hence, we obtain bell-shaped graph.
Q 3232856732
(a) Draw a schematic sketch of an ac generator describing its basic elements.
State briefly its working principle. Show a plot of variation of
(i) Magnetic, flux and
(ii) Alternating emf versus time generated by a loop of wire rotating in a
magnetic field.
(b) Why is choke coil needed in the use of fluorescent tubes with ac mains?
Solution:
(a) An alternating current generator, designed by Nikola Tesla, is based upon
the principle of electromagnetic induction.
Construction: An AC generator consists of the
following parts:
(i) Armature: It is a rectangular coil ABCD (Fig.)
having a large number of turns of
insulated copper wire wound over a
soft-iron core. The core increases the
magnetic flux linked with the armature.
(not shown in the diagram)
(ii) Field magnet : lt is a powerful permanent magnet having concave pole-pieces
N and S'. T'he armature is rotated (say, by a water turbine) between
these pole-pieces about an axis perpendicular to the magnetic field
lines.
(iii) Slip rings: The leads from the armature coil ABCD are connected to
two copper rings R_ 1 and R_ 2 called the 'slip rings'. These rings are
concentric with the axis of the armature-coil and rotate with it.
(iv) Brushes: These are two carbon pieces B_ 1 and B_2 called 'brushes' which
remain stationary, pressing against the slip rings R_ 1 and R_2 respectively.
The brushes are connected to the external circuit in which current
is to be supplied by the generator.
Working: As the armature coil ABCD rotates,
the magnetic flux linked with it changes.
Hence, an emf is induced in the coil and
current flows in it.
(i) The variation of magnetic flux with time is
given by
phi = NBA cos omega t
(ii) The variation of alternating emf with time is given by
(d phi)/(dt) = - BA omega sin omega t
epsilon = (- N d phi)/(dt)
epsilon = NBA omega sin omega t
(b) Not in syllabus.
Q 3212845730
Define root mean square current. Also, obtain its expression.
Solution:
Rms current is that value of current which produces the same amount of
heat as it produced by alternating current when flows through the same
conductor for the same time period.
Let an instantaneous current I = I_m sin omega t is passing through a resistor R.
Let it be constant for a very short duration of time dt.
Then, very small amount of heat produced is given by
dH = I^2 R dt
Heat produced for one complete cycle is given by
H = int_0^T dH = int_0^T I^2 Rdt
:. H = int_0^T I_m^2 ( sin^2 omega t) Rdt = I_m^2 int_0^T sin^2 omega t dt = I_m^2 int_(t = 0)^T ((1 - cos 2 omega t)/2) dt
H = ( I_m^2 R)/2 [ int_0^T dt - int_o^T ( cos 2 omega t) dt ] = (I_m^2 R)/2 { T - [ (sin 2 omega t)/(2 omega) ]_0^T }
As omega = 2 pi // T
H = ( I_m^2 RT)/2 - (I_m^2 R)/2 [ sin 2 xx (2 pi)/T xx T - sin 0]
:. H = ( I_m^2 RT)/2 ............(i)
If I_(r m s) is steady current flowing through the same circuit for the same time
interval T producing the same heat amount of heat H, then the heat
produced is
H = I_(r m s)^2 - RT ........ (ii)
Equating (i) and (ii), we get
( I_m^2 RT)/2 = I_m^2 RT
:. I_m/sqrt2 = I_(r m s) or I_(r m s) = 0.707 I_m.
Q 3242856733
(a) An a.c. source of voltage V = V_0 sin omega t is connected to a series combination
of L , C and R. Use the phasor diagram to obtain expressions for
impedance of the circuit and phase angle between voltage and current.
Find the condition when current will be in phase with the voltage.
What is the circuit in this condition called?
(b) In a series LR circuit X_L = R and power factor of the circuit is P_1. When
capacitor with capacitance C such that X_L = X_C is put in series the
power factor becomes P_ 2 . Calculate P_1/P_2 .
Solution:
(a) Take the voltage of source
V = V_m sin omega t ........ (i)
To determine the phase relation between current and voltage at any instant
of time, we use a phasor technique.
As all the three components are in series, the same amount of current flows
through them at any instant of time. Let it be
I = I_m sin ( omega t + phi ) ...............(ii)
where phi is the phase difference between the voltage across the source and
current.
We construct a phasor diagram.
On applying Pythagoras theorem, we get
V_m^ 2 = V_(Rm)^2 + ( V_(Cm) - V_(Lm) )^2
Here V_( Rm) = I_m R , V_(Cm) = I_m X_C , V_(Lm) = I_m X_L
V_m = I_ m sqrt( R^2 + (X_C - X_L)^2) = I_m Z
where Z = sqrt( R^2 + (X_C - X_L)^2)
Z is called the impedance of the circuit.
(ii) Phase angle between voltage and current is given by phi = tan^(-1) ( ( V_(Cm) - V_(Lm) )/V_(Rm) )
The voltage and current will be in phase, if phi = 0 or V_(Cm) = V_(Lm) or X_L =X_C
This condition is called resonance condition of the circuit and the nature of
circuit is purely resistive.
(b) Power factor ( P ) = R/Z
In a RL circuit, Z = sqrt(R^2 + X_L^2)
:. P_1 = R/sqrt( R^2 + R^2) = 1/sqrt2
When a capacitor of capacitance C is connected, such that X_L = X_C, then
I = sqrt( R^2 + (X_L - X_C)^2) = R
Power factor = P_2 = R/R = 1
:. P_1/P_2 = 1/sqrt2
Q 3282756637
(a) With the help of a labelled diagram, describe briefly the underlying
principle and working of a step-up transformer.
(b) Write any two sources of energy loss in a transformer.
(c) A step-up transformer converts a low input voltage into a high output voltage.
Does it violate law of conservation of energy? Explain.
Solution:
(a) A step-up transformer is based on the
principle of mutual induction.
An alternating potential (V_p) when
applied to the primary coil is induced
an emf in it.
epsilon_p = - N_p (d phi)/(dt)
If resistance of primary coil is low, then V_p = epsilon_p => V_p = - N_p (d phi)/(dt)
As same flux is linked with the secondary coil with the help of soft iron core
due to the mutual induction, an emf is induced in it.
epsilon_s =- N_s (d phi)/(dt)
If an output circuit is opened, V_s = epsilon_s => V_s =- N_s (d phi)/(dt)
Thus, V_s/V_p = N_s/N_p
For step-up transformer N_s/N_p > 1
In case of dc voltage, flux does not change. Thus, no emf is induced in the
circuit.
(b) Two sources of energy loss are:
(i) flux leakage, and (ii) resistance of the windings.
(c) For a given power supply, a high output voltage means a low output current. As
there is no gain in power, the law of conservation of energy is not violated.
Q 3242556433
A voltage V = V_0 sin omega t is applied to a series LCR circuit. Derive the
expression for the average power dissipated over a cycle.
Under what condition is (i) no power dissipated even though the current flows
through the circuit, (ii) maximum power dissipated in the circuit?
Solution:
Let an alternating current of I = I_m sin omega t be passing through a network of L,
C and R creating a potential difference of V = V_m sin (omega t pm phi) where phi is
the phase difference. Then the power consumed is given by
P = VI = V_m I_ m sin ( omega t ± phi ) sin omega t
P = V_m I_m (sin omega t cos phi ± cos omega t sin phi ) sin omega t
P = V_m I_ m (sin^2 omega t cos phi pm 1/2 sin omega t sin phi )
P_(av) = ( int_0^T Pdt )/( int_0^T dt) P_(av) = (V_m I _m)/T [ int_0^T sin^2 omega t cos phi dt + 1/2 int _0^T sin phi sin 2 omega t dt]
P_(av) = (V_m I _m)/T [ T/2 cos phi + 0]
P_(av) = (V_m I _m)/2 cos phi = V_(r m s) I_(r m s) cos phi
(i) No power is dissipated if (a) resistance in the circu;t is zero and (b) phase
angle between voltage and current is pi//2.
(ii) Maximum power is dissipated if (a) resistance in the circuit is maximum
and (b) phase angle between voltage and current is zero.
Q 3252856734
(a) Write the function of a transformer. State its principle of working with
the help of a diagram. Mention various energy losses in this device.
(b) The primary coil of an ideal step-up transformer has 100 turns and
transformation ratio is also 100. The input voltage and power are
respectively 220 V and 1100 W. Calculate
(i) number of turns in secondary, (ii) current in primary,
(iii) voltage across secondary, (iv) current in secondary.
(v) power in secondary.
Solution:
(a) Function: It is a device which transforms electrical power at low voltage
(and high current) to electrical power at high voltage (and low current)
and vice versa.
It works on the principle of mutual induction.
Working: A step-up transformer is based on the
principle of mutual induction.
An alternating potential (V_p) when
applied to the primary coil is induced
an emf in it.
epsilon_p = - N_p (d phi)/(dt)
If resistance of primary coil is low, then V_p = epsilon_p => V_p = - N_p (d phi)/(dt)
As same flux is linked with the secondary coil with the help of soft iron core
due to the mutual induction, an emf is induced in it.
epsilon_s =- N_s (d phi)/(dt)
If an output circuit is opened, V_s = epsilon_s => V_s =- N_s (d phi)/(dt)
Thus, V_s/V_p = N_s/N_p
For step-up transformer N_s/N_p > 1
In case of dc voltage, flux does not change. Thus, no emf is induced in the
circuit.
In case of de voltage, flux does not change. Thus, no emf is induced in the
circuit.
The various energy losses in the transformer are:
(i) Joule's heating of the primary and secondary windings
(ii) I-Ieating of the core due to eddy currents.
(iii) Hysteresis loss and
(iv) Flux leakage or incomplete flux linkage.
(b) Given: N_P = 100, k = 100, V_P = 220 V, P_P = 1100 W
(i) N_S/N_P = k => N_S = 100 xx 100 = 10^4 turns
(ii) P_P => V_P I_P => I_P = (1100)/(220) = 5 A
(iii) V_S/V_P = 100 => V_S = 100 xx 220 = 2.2 xx 10^4 V
(iv) I_P/I_S = k => I_S = 5/(100) = 0.05 A
(v) ∵ P_text (output ( primary)) = P_text( input (Secondary) )
:. P_S = 1100 W
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# geom_freqpoly
0th
Percentile
##### Histograms and frequency polygons
Visualise the distribution of a single continuous variable by dividing the x axis into bins and counting the number of observations in each bin. Histograms (geom_histogram) display the count with bars; frequency polygons (geom_freqpoly), display the counts with lines. Frequency polygons are more suitable when you want to compare the distribution across a the levels of a categorical variable.
stat_bin is suitable only for continuous x data. If your x data is discrete, you probably want to use stat_count.
##### Usage
geom_freqpoly(mapping = NULL, data = NULL, stat = "bin", position = "identity", ..., na.rm = FALSE, show.legend = NA, inherit.aes = TRUE)
geom_histogram(mapping = NULL, data = NULL, stat = "bin", position = "stack", ..., binwidth = NULL, bins = NULL, na.rm = FALSE, show.legend = NA, inherit.aes = TRUE)
stat_bin(mapping = NULL, data = NULL, geom = "bar", position = "stack", ..., binwidth = NULL, bins = NULL, center = NULL, boundary = NULL, breaks = NULL, closed = c("right", "left"), pad = FALSE, na.rm = FALSE, show.legend = NA, inherit.aes = TRUE)
##### Arguments
mapping
Set of aesthetic mappings created by aes or aes_. If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.
data
The data to be displayed in this layer. There are three options:
If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot.
A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify for which variables will be created.
A function will be called with a single argument, the plot data. The return value must be a data.frame., and will be used as the layer data.
position
Position adjustment, either as a string, or the result of a call to a position adjustment function.
...
other arguments passed on to layer. These are often aesthetics, used to set an aesthetic to a fixed value, like color = "red" or size = 3. They may also be parameters to the paired geom/stat.
na.rm
If FALSE, the default, missing values are removed with a warning. If TRUE, missing values are silently removed.
show.legend
logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes.
inherit.aes
If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. borders.
binwidth
The width of the bins. The default is to use bins bins that cover the range of the data. You should always override this value, exploring multiple widths to find the best to illustrate the stories in your data.
The bin width of a date variable is the number of days in each time; the bin width of a time variable is the number of seconds.
bins
Number of bins. Overridden by binwidth. Defaults to 30
geom, stat
Use to override the default connection between geom_histogram/geom_freqpoly and stat_bin.
center
The center of one of the bins. Note that if center is above or below the range of the data, things will be shifted by an appropriate number of widths. To center on integers, for example, use width = 1 and center = 0, even if 0 is outside the range of the data. At most one of center and boundary may be specified.
boundary
A boundary between two bins. As with center, things are shifted when boundary is outside the range of the data. For example, to center on integers, use width = 1 and boundary = 0.5, even if 0.5 is outside the range of the data. At most one of center and boundary may be specified.
breaks
Alternatively, you can supply a numeric vector giving the bin boundaries. Overrides binwidth, bins, center, and boundary.
closed
One of "right" or "left" indicating whether right or left edges of bins are included in the bin.
If TRUE, adds empty bins at either end of x. This ensures frequency polygons touch 0. Defaults to FALSE.
##### Details
By default, the underlying computation (stat_bin) uses 30 bins - this is not a good default, but the idea is to get you experimenting with different binwidths. You may need to look at a few to uncover the full story behind your data.
##### Aesthetics
geom_histogram uses the same aesthetics as geom_bar; geom_freqpoly uses the same aesthetics as geom_line.
##### Computed variables
stat_count, which counts the number of cases at each x posotion, without binning. It is suitable for both discrete and continuous x data, whereas stat_bin is suitable only for continuous x data.
##### Aliases
• geom_freqpoly
• geom_histogram
• stat_bin
##### Examples
library(ggplot2) ggplot(diamonds, aes(carat)) + geom_histogram() ggplot(diamonds, aes(carat)) + geom_histogram(binwidth = 0.01) ggplot(diamonds, aes(carat)) + geom_histogram(bins = 200) # Rather than stacking histograms, it's easier to compare frequency # polygons ggplot(diamonds, aes(price, fill = cut)) + geom_histogram(binwidth = 500) ggplot(diamonds, aes(price, colour = cut)) + geom_freqpoly(binwidth = 500) # To make it easier to compare distributions with very different counts, # put density on the y axis instead of the default count ggplot(diamonds, aes(price, ..density.., colour = cut)) + geom_freqpoly(binwidth = 500) if (require("ggplot2movies")) { # Often we don't want the height of the bar to represent the # count of observations, but the sum of some other variable. # For example, the following plot shows the number of movies # in each rating. m <- ggplot(movies, aes(rating)) m + geom_histogram(binwidth = 0.1) # If, however, we want to see the number of votes cast in each # category, we need to weight by the votes variable m + geom_histogram(aes(weight = votes), binwidth = 0.1) + ylab("votes") # For transformed scales, binwidth applies to the transformed data. # The bins have constant width on the transformed scale. m + geom_histogram() + scale_x_log10() m + geom_histogram(binwidth = 0.05) + scale_x_log10() # For transformed coordinate systems, the binwidth applies to the # raw data. The bins have constant width on the original scale. # Using log scales does not work here, because the first # bar is anchored at zero, and so when transformed becomes negative # infinity. This is not a problem when transforming the scales, because # no observations have 0 ratings. m + geom_histogram(boundary = 0) + coord_trans(x = "log10") # Use boundary = 0, to make sure we don't take sqrt of negative values m + geom_histogram(boundary = 0) + coord_trans(x = "sqrt") # You can also transform the y axis. Remember that the base of the bars # has value 0, so log transformations are not appropriate m <- ggplot(movies, aes(x = rating)) m + geom_histogram(binwidth = 0.5) + scale_y_sqrt() }
Documentation reproduced from package ggplot2, version 2.2.1, License: GPL-2 | file LICENSE
### Community examples
Looks like there are no examples yet.
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# Full width table with caption in refman doc
The refman document class has a big left margin for text. Only the headings are on the normal left margin. Perfect for what I'm doing.
But I have a wide table (float) that must be centered on the full page width (like table* in two-column mode).
So far closest to success is the changepage package adjustwidth environment. It takes care of the table (tabular env) just fine.
But the caption remains centered with respect to the wide left margin, even though it's inside the adjustwidth.
A MWE:
\documentclass[11pt,letterpaper]{refart}
\usepackage[strict]{changepage}
\usepackage{array}
\begin{document}
\section{A section}
Here is some normal text at the normal margin.
Now let's insert wide Table~\ref{tbl:thetable}. \begin{table}
% Uncommenting this environment will move the
% table contents left, but not the caption!
\caption{The caption.}
\begin{tabular}{>{\sf}llp{7cm}}
{\bf Schedule item} & {\bf Type} & {\bf Description} \\ \hline
date &
\end{tabular}
\label{tbl:thetable}
\end{table}
And finish with more text.
\end{document}
This is frustrating! How can both table and caption be convinced to use full width?
• Welcome to TeX.SX! Please add a minimal working example (MWE) that illustrates your problem. It will be much easier for us to reproduce your situation and find out what the issue is when we see compilable code, starting with \documentclass{...} and ending with \end{document}. – egreg Jul 20 '13 at 21:11
• @egreg Done with MWE! – Gene Jul 20 '13 at 21:48
You have to back up by \leftmarginwidth; enclosing the table in a minipage will accomplish the centering.
The lipsum package is just to provide filler text.
\documentclass[11pt,letterpaper]{refart}
\usepackage{array,lipsum}
\newenvironment{fulltable}[1][tbp]
{\begin{table}[#1]%
\hspace*{-\leftmarginwidth}%
\begin{minipage}{\fullwidth}}
{\end{minipage}\end{table}}
\begin{document}
\section{A section}
Here is some normal text at the normal margin.
Now let's insert wide Table~\ref{tbl:thetable}.
\begin{fulltable}
\centering
\caption{The caption.}
\medskip
\begin{tabular}{>{\sffamily}llp{7cm}}
\bfseries Schedule item & \bfseries Type & \bfseries Description \\
\hline
date &
\end{tabular}
\label{tbl:thetable}
\end{fulltable}
And finish with more text.
\lipsum[1-4]
\end{document}
• Perfect! Thanks. Looks great. Have not done LaTeX for some years and I appreciate the memory jog. – Gene Jul 21 '13 at 2:14
This is a very late answer. But for people who may be having problems with full pages and refman, refart, refrep, etc.
Just enclose what you want within a fullpage environment.
\begin{fullpage}
\end{fullpage}
You don't need to define anything. It is a cleaner way to do this.
• Welcome to TeX.SX! You can have a look at our starter guide to familiarize yourself further with our format. – Symbol 1 Jul 15 '15 at 6:34
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CGAL 5.5.2 - 2D Arrangements
CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y > Class Template Reference
#include <CGAL/Arr_geodesic_arc_on_sphere_traits_2.h>
## Definition
The traits class Arr_geodesic_arc_on_sphere_traits_2 is a model of the ArrangementTraits_2 concept.
It enables the construction and maintenance of arrangements of arcs of great circles (also known as geodesic arcs) that lie on the sphere (centered at the origin). Almost all operations on arrangements require a kernel that supports exact predicates. Most operations also require a kernel that supports exact constructions. However, all operations on such arrangements can be computed efficiently, since all calculations are performed with rational arithmetic.
There is an analogy between this class of arrangements and the class of planar arrangements induced by linear curves (i.e., segments, rays, and lines), as properties of linear curves in the plane often, but not always, hold for geodesic arcs on the sphere. For example, given any two non-antipodal points on the sphere there exists a unique great circle connecting the two points.
We use the following parameterization of the unit sphere $$S = \phi_S(\Phi)$$: $$\Phi = [\alpha, 2\pi + \alpha] \times [-\frac{\pi}{2}, \frac{\pi}{2}]$$, $$\phi_S(x, y) = (\cos y \cos x, \sin y \cos x, \sin x)$$, where $$\alpha = \arctan(X, Y)$$. By deafult, $$X = -1, Y = 0$$, which implies $$\alpha = \pi$$, and a default parameterization $$\Phi = [-\pi, \pi] \times [-\frac{\pi}{2}, \frac{\pi}{2}]$$. The equator curve, for example, is given by $$\gamma(t) = (\pi(2t - 1) + \alpha, 0)$$, for $$t \in [0,1]$$. This parameterization induces two contraction points $$p_s = (0, 0, -1) = \phi_S(y,-\frac{\pi}{2})$$ and $$p_n = (0, 0, 1) = \phi_S(y,\frac{\pi}{2})$$, referred to as the south and north poles, respectively, and an identification curve $$\{\phi_S(\pi + \alpha,x)\,|\,-\frac{\pi}{2} \leq v \leq \frac{\pi}{2}\}$$, as $$\phi_S(-\pi + \alpha,v) = \phi_S(+\pi + \alpha,v)$$ for all $$x$$ (which coincides with the opposite Prime (Greenwich) Meridian when $$\alpha = \pi$$). The elements that substitutes the template parameters X and Y when Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y> is instantiated must be integral values that define a not necessarily normalized vector $$(x,y)$$ in the $$xy$$-plane that bisects the identification curve.
Is Model Of:
ArrangementTraits_2
ArrangementLandmarkTraits_2
ArrangementSphericalBoundaryTraits_2
Examples:
Arrangement_on_surface_2/spherical_insert.cpp.
## Classes
class Construct_curve_2
Construction functor of geodesic arcs. More...
class Construct_point_2
Construction functor of a point. More...
class Construct_x_monotone_curve_2
Construction functor of $$x$$-monotone geodesic arcs. More...
class Curve_2
class Point_2
The Point_2 class nested within the traits is used to represent a point on a sphere centered at the origin. More...
class X_monotone_curve_2
The X_monotone_curve_2 class nested within the traits is used to represent an $$x$$-monotone geodesic arc on the a sphere centered at the origin. More...
## Public Member Functions
Construct_point_2 construct_point_2_object () const
Returns an instance of Construct_point_2.
Construct_x_monotone_curve_2 construct_x_monotone_curve_2_object () const
Returns an instance of Construct_x_monotone_curve_2.
Construct_curve_2 construct_curve_2_object () const
Returns an instance of Construct_curve_2.
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# Why does ordinary least squares have to be linear in the parameters?
I've been looking into linear regression, and on the wikipedia page it says:
"In contrast, non-linear least squares problems generally must be solved by an iterative procedure"
This got me thinking more about OLS, and the differences between it and non-linear regression methods. Mores specifically, why equations that are non-linear in their parameters can't also be solved using the OLS assumption that $$y=\beta x$$ where $$\beta =(X^TX)^{-1}X^Ty$$.
So i guess my question is:
What is it about the process of solving OLS that requires the parameters to be linear? What would happen if they were non-linear and we tried to solve using OLS?
• You can minimize $L(\beta)$ by solving $\nabla L(\beta) = 0$. Usually this is a nonlinear system of equations, which makes it difficult to solve. But if $L(\beta) = (1/2) \| X \beta - y \|^2$, then $\nabla L(\beta) = X^T (X \beta - y)$, so $\nabla L(\beta) = 0$ is equivalent to $X^T X \beta = X^T y$. This is a linear system of equations that can be solved with Gaussian elimination! That is the special thing that makes linear regression easy. – littleO Jun 1 at 5:48
What is it about the process of solving OLS that requires the parameters to be linear?
Because equations which are nonlinear in their parameters can't be written as $$y=X\beta$$. OLS estimates $$\beta$$ in the equation
$$y = X\beta +\epsilon.$$
This is a linear relationship, so when we say that $$\hat{\beta} = (X^\top X)^{-1}X^\top y$$ is the optimal estimator of $$\beta$$, what we mean is that it's optimal in the sense that it minimizes $$\|y - X\beta\|_2^2$$. Minimizing $$\|y - X\beta\|_2^2$$ is only important if this objective is meaningful for your task; particularly, if the task isn't linear in these parameters, then the fit may be poor.
However, one reason that OLS is so flexible is that if you can find a way to represent your data in a linear way, then it is linear in the parameters, otherwise known as basis expansion.
A textbook example of a change of basis is using a polynomial basis, so you have $$X_\text{polynomial} = [1, x, x^2, x^3, \dots, x^p]$$. The model $$X_\text{polynomial}\beta$$ is linear in its parameters, but viewed as a function of $$x$$, it's a nonlinear polynomial.
What would happen if they were non-linear and we tried to solve using OLS?
It won't work very well!
This data's deterministic component is given by $$y = \beta_0 + \beta_1 \sin (\beta_2 x + \beta_3)$$ which is not linear in $$\beta$$, the parameter vector to be estimated, because you can't write this in the form $$y=X\beta$$. I also add small, independent 0-mean Gaussian noise to each observation.
If we do the naive thing and assume that our output $$y$$ is a linear function of $$x$$, then we find a poor fit, in the sense that there is a large discrepancy between the estimated line (red) and the true function (blue). The model finds that the best linear approximation is a decreasing line, completely ignoring the sinusoidal behavior.
One way to try to improve the fit is to re-express $$x$$. Since this looks like something sinusoidal, we might try a sine function. This gives the design matrix $$X_\text{sine}=[1, \sin(x)]$$. This give a flatter line, but it's still not a satisfying model. Even though the model and the desired function are both sine waves, we're implicitly using $$\beta_0 + \beta_1 \sin(1 \times x + 0)$$ to approximate $$y = \beta_0 + \beta_1 \sin (\beta_2 x + \beta_3).$$ This is not a good approximation, because we've fixed $$\beta_2=1$$ and $$\beta_3=0$$, so the further the true values are from these assumed values, the poorer this approximation will be.
What we really need is a way to recover all of the parameters in the function $$y = \beta_0 + \beta_1 \sin (\beta_2 x + \beta_3),$$ but this is a nonlinear estimation task, so we need to use the appropriate tools to accommodate the nonlinearity of the $$\beta$$s. Nonlinear least squares is one method to achieve this, among many others.
# Code
set.seed(13)
N <- 1000
x <- runif(N, -pi, pi)
f <- function(x) pi + 2 * sin(4 * x)
y <- f(x) + rnorm(N,sd=0.5)
model <- lm(y ~ x)
png("~/Desktop/nonlinear.png")
plot(x,y,col="grey")
abline(model, col="red", lwd=2, lty="dashed")
lines(sort(x), f(sort(x)), lwd=2, col="blue")
dev.off()
model2 <- lm(y ~ sin(x) )
png("~/Desktop/nonlinear2.png")
plot(x,y,col="grey")
abline(model2, col="red", lwd=2, lty="dashed")
lines(sort(x), f(sort(x)), lwd=2, col="blue")
dev.off()
• In this particular case, I’d change it to b1 sin (b3x) + b2 cos (b3 x), which gives exactly the same numbers but has one Non-linear parameter only. – gnasher729 Jun 1 at 14:29
• That's a useful observation for a person carrying out NLLS on this toy problem, but it doesn't do much to explain why OLS is a poor substitute for NLLS. – Sycorax Jun 1 at 17:25
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# Area Of A Circle And A Sector Edgenuity Quizlet
∡ m n p is a(n) 3. Find the area of the sector. What is true about the relationship of a rectangle and a triangle created from that rectangle?. The formula to find the area of a sector is A = Just use π = 3. 4th class power engineering exam questions downloads cogat form 7 practice test grade 2 psychology today articles punchline bridge to algebra answer key 2001 page 116. The base is 8 and the height is 4, so the area is 8 (4) = 32 square units. The semester starts with a review of Algebra 1 and then go into Trigonometry, Surface Area and Volume, Quadrilaterals, and Vectors. Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference. Zachary Smith. Geometry Final Exam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. When finding the area of a sector, you are really just calculating the area of the whole circle, and then multiplying by the fraction of the circle the sector represents. To understand where this formula came from, recall that the total circumference of a circle is 2πr. ∡ r t s is a(n) 2. Quizlet Live. 3 years ago. Geometry Notes Perimeter and Area Page 6 of 57 the process of calculating the area, we multiplied units times units. While sector specifically means the physical disk area, the term block has been used loosely to refer to a small chunk of data. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Give your answer to the. Is the red line a radius or diameter of the circle? Introduction to Circles DRAFT. Just type into the box and your conversion will happen automatically. hxd fortnite mobile, Our Fortnite: Battle Royale Secrets and Easter Eggs guide will take you through all the secrets you'll find dotted about the map. Do not round. Bisectors of Triangles. 3 on different iPhone or iPad models with iOS version 13, 12, 11, 10, 9, 8, 7. Chapter 12 Surface Area and Volume. For example, Figure 5 shows a central angle of 1° in a circle of radius 1,800 feet, along with the arc and chord cut off by 1°. The sum of the angles, formed by the perpendicular rays is 360°, thus the curved arrow represents an angle measure that. Because 120° takes up a third of the degrees in a circle, sector IDK occupies a third of the circle's area. com To create your new password, just click the link in the email we sent you. Quarter of a circle is. Common Core Math II Common Core State Standards 2010 Standard ID Standard Text Edgenuity Lesson Name Practice Standards MP. Keeping in mind the circle's total area, the circumference, and the arc length, we can now learn how to find the area of a section of a circle. com - Edgenuity is located through Classlink. Express the trigonometric functions as ratios and use sine, cosine, and tangent ratios to solve real-world problems. G o t a d i f f e r e n t a n s w e r? C h e c k i f i t ′ s c o r r e c t. Geo HW A day: Study for part 2 of circles test Attached is the study guide as well as a "bonus" station covering arc length and sector area if you want additional practice. Geometry unit test quizlet edgenuity. Areas of Circles and Sectors Practice: 1- 49pi square feet 2- 112 units 3- (4 minus pi) square ft 4- 314 square ft 5- 22. 9th - 12th grade. Description: Get Instant Access to PDF Read Books Delta Answer Key at our eBook Document Library. And not every smart person is right for us. The area of each triangle will be 56 square meters divided by 3. TOPIC 9-3. Storing things in tyres is a cool idea while we don't need to set up each week. Circumference of Circle. Thus, the area may be written as A =1/2 (11) (6), or A = 33. About This Quiz & Worksheet. As you well know by now, being able to deduce key information from a limited set of facts is the basis of geometry. Arc of a Circle Also Central Angles. Improve your math knowledge with free questions in "Area of sectors" and thousands of other math skills. The square of the length of tangent segment equals to the difference of the square of length of the radius and square of the distance between circle center and exterior point. Day 8: Slope and Equations of Lines. 620 units squared. Just type into the box and your conversion will happen automatically. benchmark 1: I can identify and describe the parts of a circle (radius, diameter, chord, arc, sector and center of a circle). 7 #'s 1-8 Except #3. Area of Circles Worksheet 1 - Here is a nine problem worksheet that will allow your students to practice calculating the area of a circle. Date Due: 03/20/2020 Category: Option 1- Bleaded Learning (Edgenuity) Arc Length/Area of Sector-Distance Learning-Option 2 (If you do not have a Laptop or Computer). Edgenuity Answers (All Courses) Are you an Edgenuity (formerly E2020) student looking to check for the answers on your unit test, semester test, cumulative exam, or any other quiz or test within Edgenuity?Answer Addicts is here to help. segment of a circle def. none 5,4,36=47 9,5,64=114 2,3,144=? 1÷x^+5x+6 is quadratic polynomial or not. radius: angle (degree): Result window. The area of the square is this quantity 2r squared, or 4r 2. Note: The rectangle and the "bumpy edged shape" made by the sectors are not an exact match. Learn vocabulary, terms, and more with flashcards, games, and other study tools. A circle is an important shape in the field of geometry. (2) (3) Find the length of the arc of a sector of 54 ° in a circle if the radius is 10. Quizlet Live. singeli mpya song 2020, Nyimbo Mpya 2020 Download Audio Video Mpya 2019 Tanzania africa african Mp3 Mp4 2020 2019 2018 2017 Singeli Mpya video hivi sasa Mpya bekaboy all songs nyimbo mpya ya diamond zote, wiki hii, mwezi huu, mwaka huu, yingamedia yinga media video mpya 2018 yinga media music audio nyimbo za zamani zilipendwa video mpya diamond nyimbo mpya download nigeria songs yinga media. And since the question is applied in real life, give it to 3 s. Arc Length of a Circle Formula - Sector Area, Examples, Radians, In Terms of Pi, Trigonometry - Duration: 15:57. 5 square meter. Refer to Figure 3 and the example that accompanies it. Flashcards. It is a line which touches a circle or ellipse at just one point. The center of the circle above is point N, and its diameter is 10. CA Circumference and Arc Length Area of a Circle and a Sector G-CO. Example: the perimeter of this regular pentagon is:. Before looking at the perimeter and area of a circle, a basic understanding of perimeter and area is needed. Example: the perimeter of this rectangle is 7+3+7+3 = 20. The radius is equal to half of the diameter. In other words, the bigger the central angle, the larger is the area of the sector. Secant of Circle. Jurassic Park: Original Motion Picture Soundtrack - Wikipedia. It's a good idea to draw a picture of the situation here. [email protected] (Think of the sprinkler. AREA OF SHADED REGIONS PRACTICE TEST (from in-class quizlet) workbook 8. In the workforce, the ratio of the number of union members to the number of nonmembers is the same for the sales sector as it is for the protective service area of the service sector. The side of the square is equal to the diameter of the circle, or twice the radius: 2r. Find the area of the sector. As you can see from the figure above, a sector is a pie-shaped part of a circle. So the area of the sector over the total area is equal to the degrees in the central angle over the total degrees in a circle. Arc Measure Definition. Before looking at the perimeter and area of a circle, a basic understanding of perimeter and area is needed. A circle is at the foundation of geometry and how its parts relate to each other is both completely logical and a wonder. About This Quiz & Worksheet. Geometry Final Exam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. Volume and surface area help us measure the size of 3D objects. Hidden New Mexico Including Albuquerque Santa Fe Taos And The Enchanted Circle Alien Disclosure At Area 51 Dr Dan Burisch Reveals The Truth About Ets Ufos And Mj 12. In other words, the bigger the central angle, the larger is the area of the sector. closed economy income. Since we started, over 10,000 Edgenuity students have found their answers with the help of our web platform. In the Cartesian coordinate system, students use the 1 Source: National Governors Association Center for Best Practices and Council of Chief State School Officers. Instruction How can you find the area of a sector of a circle? Summary Review and connect what you learned. Arc Length and Sector Area. QUIZ 2: AREA OF CIRCLES Question # 6 DragAndDrop. Arcs & Central Angles. Don’t forget to laugh at the puns (or rolls your eyes like most do) and enjoy the rhymes 🤓 Ms. 2 sec 50 π(8) tor 360 A Substitute 50° for x and 8 for r. Area of a circular sector. Find the area of each sector. a - semi-major axis. Petti's PAULDING COUNTY HIGH SCHOOL Website. Geometry Final Exam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. 5/11 Delta Answer Key [PDF] The Madwoman In Attic Woman Writer And Nineteenth Like this book? You can publish your book online for free in a few minutes!. area of Y 4 cm 9. Hidden New Mexico Including Albuquerque Santa Fe Taos And The Enchanted Circle Alien Disclosure At Area 51 Dr Dan Burisch Reveals The Truth About Ets Ufos And Mj 12. Start studying Sector Area, 10. Area of an Equilateral Triangle. 2) Find the area and circumference of a circle with radius 8. Or essentially the area of this circle. ∡ m n p is a(n) 3. Here is x = 3 in R 1. Area of an elliptical arch. Block has multiple meanings depending on the context. brooklyn4898. Quizzes you may like. Find the radius of a circle with an area of 2827. Geometry unit test quizlet edgenuity. Area of an arch given height and chord. Example 1: A sector is cut from a circle of radius 21 cm. An important type of segment, ray, or line that can help us prove congruence is called an angle bisector. It's designed to take concepts you're used to and make you apply them in new (and often strange) ways. 9in2, and m∠CBD = 54°. if θ is in radians. understanding: I can find the area and circumference of a circle using real world examples using 3. Lost in Space – a science fiction adaptation of Swiss Family Robinson, which focuses around the misadventures of its breakout character, Dr. A circle is an important shape in the field of geometry. But we’re not some kind of workplace utopia. High School Geometry: Circular Arcs and Circles Chapter Exam Instructions. A comprehensive database of more than 48 area quizzes online, test your knowledge with area quiz questions. Therefore the area of the sector becomes: A_sec = \frac{60 * \pi * 50^{2}}{360} This simpliflies to A_sec = \frac{1250*\pi}{3} Then the area of the triangle (half * base divided by 2) becomes 600. Challenge problems: Inscribed angles Our mission is to provide a free, world-class education to anyone, anywhere. Why show ads? Report Ad. B 1 B 2 = 2 b - minor axis (smaller direct that perpendicular to major axis and intersect it at the center of the ellipse О). of a circle, area of a circle, and area of a sector. Inputs: circle radius (r) sector area: circle radius: central angle: Arc of a Circle. The center of the circle above is point N, and its diameter is 10. Area: Area Circle = π r2. Area of a circle. 125pi square centimeters 9- 22. This is also covered on this quiz. Is formed by 3 points that all lie on the circle's circumference. The complete list is available in the contributors sections. Circle Segment Equations Formulas Calculator Math Geometry. 3+3+3+3+3 = 5×3 = 15. Circle A: radius = 6in, area of ΔCAD = 17. if θ is in radians. Area of a Segment of a Circle. Home Explore Delta Answer Key - ksjiqi. Area of an arch given height and chord. 5 square meter. The base of the triangle is the diameter of the circle, which is 2*r = 2*12. benchmark 2: I can find the area and circumference of a circle both in terms of pi and using 3. We’ll start with the volume and surface area of rectangular prisms. Interactive Inscribed Angle. Theorem 70: The measure of an inscribed angle in a circle equals half the measure of its. The area of a trapezoid is basically the average width times the altitude, or as a formula: b1, b2 are the lengths of each base. #N#Whole number Tenths Hundredths Thousandths Max accuracy. Round your answers to the nearest tenth. Day 8: Slope and Equations of Lines. Thus, the length of the (vertical) dashed line segment is 9. This page is a one-stop shop for all your finding area and circumference of a circle exercises. Radius: A segment whose endpoints are the center of a circle and a point on the circle. On this page, you can calculate area of a Segment. Brownie Hiker Gscnc; Application For Employment In Sandf 2015 Intake; Download File Afrikaans Afrikaans; Harold Pinter Victoria Station Script; International 624 Tractor Manual. Or essentially the area of this circle. edgenuity english 3 semester 2 answers PDF may not make exciting reading, but. The formula is actually the same as that for a rectangle, since it the area of a parallelogram is basically the area of a rectangle which has for sides. Area of a sector of a circle - 15172982 13. We provide the best tools for mutual help with school subjects. Area of an elliptical arch. Edgenuity Answers (All Courses) Are you an Edgenuity (formerly E2020) student looking to check for the answers on your unit test, semester test, cumulative exam, or any other quiz or test within Edgenuity?Answer Addicts is here to help. A lesson on the definition of area including formulas and proofs for the area of a rectangle, square, parallelogram and triangle. ) ∠1 and ∠4 B. Area of a Segment Calculator. Circle Cal on its own page. For example, Figure 5 shows a central angle of 1° in a circle of radius 1,800 feet, along with the arc and chord cut off by 1°. Try this Drag one of the orange dots that define the endpoints of the blue arc. In the figure below, two segments are shown: segment ABX and segment ABY. Quizlet Learn. You are done with the mo. Points J, N, and M lie on a line. It's designed to take concepts you're used to and make you apply them in new (and often strange) ways. Calculating Area of a Circle If we know the radius or the diameter of a circle, we can find the Area. Release your mouse button when the item is place. AREA OF SHADED REGIONS PRACTICE TEST (from in-class quizlet) workbook 8. Find the length of each arc. Round your answers to the nearest tenth. Choose from 500 different sets of area of a circle and sector flashcards on Quizlet. The Quadrant and Semicircle are two special types of Sector: Half a circle is. Given the diameter of a circle is 10 m, what is the area of the sector formed when two radii forms a 60 degree angle? (Hint: Diameter is twice the radius or r = D/2). Find the area of the sector. Remember that the area of a circle is π*radius^2 Remember that there are 360 ° in a circle. The radius is 6 inches and the central angle is 100°. There is no way to determine the area of the triangles formed from the parallelogram. Click an item in the list or group of pictures at the bottom of the problem and holding your mouse button down, drag it into the correct position in the area. Lessons: All Lessons are due by April 15 th. And then we just can solve for area of a sector by multiplying both sides by 81 pi. Ivy Global 5. Round your answers to the nearest tenth. Quia - GEOMETRY - Working with Circles Home FAQ About Log in Subscribe now 30-day free trial. Area of a Trapezoid. Help Center. A circle is an important shape in the field of geometry. If you're seeing this message, it means we're having trouble loading external resources on our website. An arc is a segment of a circle around the circumference. Day 12: Six Weeks Exam. None of the above. *MONSTER CIRCLE PUZZLE Indvidually *Homework: finish puzzle from class 29 *Lesson - Circles on the Coordinate Plane *Quizlet Live! - writing equation of a circle given the center and radius *Homework: IXL V. The ratio of a sector's area to a circle's area is. 4 to 80% 31 *Lesson - Area of a Sector. The formula is. org right now:. Is the red line a radius or diameter of the circle? Introduction to Circles DRAFT. Theorem 70: The measure of an inscribed angle in a circle equals half the measure of its. You can also modify this program to take the diameter as input from the user. Area Of A Sector Of A Circle With Examples. Powered by Create your own unique website with customizable templates. Remember to stay informed. 9 Day 1 Area circle, sectors HW:Geo 7. Let's look at the definition of a circle and its parts. 3/12 notes: 7. Students will create a Quizlet set of cards for this units. Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference. calculate the length of an arc and the area of a circle sector. What is true about the relationship of a rectangle and a triangle created from that rectangle?. Since π is constant, we need only the radius value from the user to calculate the area. Axes of ellipse. The area of a sector of a circle with a central angle of 5pi/12 radians is 20 squared meters. The altitude (or height) of a trapezoid is the perpendicular distance between the two bases. Learn vocabulary, terms, and more with flashcards, games, and other study tools. (12 instructional days) - Geometry. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Improve your math knowledge with free questions in "Area and circumference of circles" and thousands of other math skills. Area of a Regular Polygon. Mar 20, 2018 · AWS STS Temporary credential mechanism has been used for creating the session credentials which is used for creating an instance of AmazonSNS. Example: the perimeter of this rectangle is 7+3+7+3 = 20. А 1 А 2 = 2 a - major axis (larger direct that crosses focal points F 1 and F 2). About This Quiz & Worksheet. benchmark 2: I can find the area and circumference of a circle both in terms of pi and using 3. High School Geometry Worksheets High School High School Geometry Worksheets: Circles: Basic Properties of Circles Circles: Basic Properties of Circles Circles: Review Circles: Review Circles: Theorems about Circles Circles: Theorems about Circles Dimensions: Visualize Relationships between 2D and 3D objects. Students will create cards. 3 on different iPhone or iPad models with iOS version 13, 12, 11, 10, 9, 8, 7. 5/11 Delta Answer Key [PDF] The Madwoman In Attic Woman Writer And Nineteenth Like this book? You can publish your book online for free in a few minutes!. Level up on the above skills and collect up to 300 Mastery points Start quiz. Day 12: Six Weeks Exam. 5 #'s 1-4, 10, 8. You can work out the Area of a Sector by comparing its angle to the angle of a full circle. ) ∠1 and ∠4 B. Area of Trapezoids Area of Kites Composite Shapes Area of a Quadrilateral on a Grid Area of Parallelograms Side Length of a Parallelogram with a Given Area Trapezoid Area Composite Shapes Area Challenge Area on a Grid Polygons Circles: Area of a Circle Circumference Circumference & Area Area of Circles Circumference Circumference & Area: Mod 10. Figures may also include circles or portions thereof. Arc measure over 360 x pi x r^2. 2 units squared. Area of a Sector If a sector of a circle has an area of A square units, a central angle measuring x°, and a radius of r units, then A. Area of a sector Get 3 of 4 questions to level up! Quiz 2. (12 instructional days) - Geometry. Georgia Tech CEISMC Summer Programs for Rising 4th-12th-grade Students. Given the diameter of a circle is 10 m, what is the area of the sector formed when two radii forms a 60 degree angle? (Hint: Diameter is twice the radius or r = D/2). Find the length of each side of the hexagon. Math Worksheets. The area of each triangle will be 56 square meters divided by 3. Round your answers to the nearest tenth. We provide the best tools for mutual help with school subjects. The center of the circle above is point N, and its diameter is 10. #N#Whole number Tenths Hundredths Thousandths Max accuracy. A sector of a circle is essentially a proportion of the circle that is enclosed by two radii and an arc. From the URIT RuneScape Quest you will get an old necklace that can be used to make Charos RuneScape necklaces. Keeping in mind the circle's total area, the circumference, and the arc length, we can now learn how to find the area of a section of a circle. And so our area, our sector area, is equal to-- let's see, in the. On this page, you can calculate area of a Segment. circle area and perimeter word problems waiting time policies in the health sector what works oecd publishing parallel lines and angles answers from edgenuity. LT4: I can solve problems involving area of a circles, sectors, and spheres. 24X7 Clinic system is web based application which covers all aspects of management and operations of clinics. 580 units squared. From those early beginnings, CVA developed a reputation for providing guns and accessories that provide our customers with the best values available. The area of a sector of a circle with a central angle of 5pi/12 radians is 20 squared meters. Geometry Test Practice. The area of a trapezoid can be expressed in the formula A = 1/2 (b1 + b2) h where A is the area, b1 is the length of the first parallel line and b2 is the length of the second, and h is the height of the trapezoid. The center of the circle above is point N, and its diameter is 10. b - semi-minor axis. graphing calculator manual for precalculus a unit circle approach: 1856: pet mri siemens manual: 1857: toyota 7fgu32 forklift manual: 1858: the indispensable guide to good laboratory practice glp english edition: 1859: jouer votre meilleur golf le guide complet pour reacuteussir: 1860: 2009 arctic cat m1000 sno pro 162 ltd factory service work. Catering to the learning needs of students in grade 5 through grade 8, these printable worksheets practice the topic pretty much accross the board: easy, moderate and hard. The lesson is designed to help you: Find the surface area of a birdhouse. The minute hand of a clock is 1. On this page, you can calculate area of a Segment. The area of a circle is 706. When finding the area of a sector, you are really just calculating the area of the whole circle, and then multiplying by the fraction of the circle the sector represents. closed economy income. A circle is at the foundation of geometry and how its parts relate to each other is both completely logical and a wonder. High School Geometry: Circular Arcs and Circles Chapter Exam Instructions. (2) (3) Find the length of the arc of a sector of 54 ° in a circle if the radius is 10. Monday thru Friday watch CNN10 and keep track of daily news using our notes sheet. An important type of segment, ray, or line that can help us prove congruence is called an angle bisector. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Why show ads? Report Ad. In other contexts, it may be a unit of a data stream or a unit. Interactive Inscribed Angle. Heather Williams, 7 th grade Social Studies. O - center of the ellipse. Arc Length and Sector Area. 5 Area of Sectors and Segments G. The angle of the unshaded part would be 360° minus the shaded part of 60 °. Circle Cal on its own page. Show Step-by-step Solutions. 4 in² 14) 3 m 150 ° 11. This fits well with the definition of area which is the number of square units that will cover a closed figure. Area of an elliptical arch. Common Core Math II Common Core State Standards 2010 Standard ID Standard Text Edgenuity Lesson Name Practice Standards MP. What is the area A of the sector subtended by the marked central angle θ?What is the length s of the arc, being the portion of the circumference subtended by this angle?. Vivamus egestas, metus quis egestas egestas, tortor justo pharetra diam, et dapibus massa nibh dapibus risus. In the context of data storage, a filesystem block is an abstraction over disk sectors possibly encompassing multiple sectors. Edgenuity E2020 Physics Answer Key; Kuta Software Geometry Circle Review; Pediatric Nursing Multiple Choice Questions Quizlet;. Barclays golf Adobe after effects review Amgen price Credit card fraud bank of america Bitcoin revolution system reviews Reddit ocn Chad mureta app empire What are alt coins Eagle brand outlet Navbar codes Unitedair Brokerage account deals Bitcoin wallets free in china Obgyn overland park ks Cnn markets premarket Vault 7 Ethereum prison key. On the picture: L - arc length h- height c- chord R- radius a- angle. You are done with the mo. find the length of an arc as well as find the area of a sector of a circle, write the equation of a circle given the radius and the circumference. yay ayaqqabi resimleri, Join our group of amazing donors in supporting educational programs like charity hackathons and open source educational events. Jurassic Park: Original Motion Picture Soundtrack - Wikipedia. 39-111 Geometry unit 4 similarity post test. The area of the circle is πr 2. Area of a Circle and a Sector Warm-Up Get ready for the lesson. Before looking at the perimeter and area of a circle, a basic understanding of perimeter and area is needed. In 1980, he joined Kuok Group of companies and had over the years, held various senior management positions in Malaysia & Singapore. What is the smallest possible area of the tabletop that will fit on Timothy's table base? Round the answer to the nearest whole square inch. The following figures show the different parts of a circle: tangent, chord, radius, diameter, minor arc, major arc, minor segment, major segment, minor sector, major sector. OK-Geometry Oklahoma Academic Standards 2009 Standard ID Standard Text Edgenuity Lesson Name G. Find the Area of a circle in python : We know that the area of a circle is π r², where "r" is the radius of the circle. Side of polygon given area. area of sector ZOM = ? pr2 = ? p(20)2 =80p The area of sector ZOM is 80pcm2. Don't know what we'd do with the tyres next term. Other results: edgenuity english 3 semester 2 answers pdf - slideblast Answers for edgenuity english 2. Five circles lie in five different planes but share the same center and radius. Quizlet Learn. Let's look at the definition of a circle and its parts. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. com - Edgenuity is located through Classlink. Arc Length and Sector Area. 16 Exercises Section 2. 3 minutes ago Sebuah poros berdiameter 15 cm berputar dengan kecepatan 600 rpm di dalam sebuah bantalan berdiameter 15,02 cm dan panjang 30 cm. Figure 3 A circle with two diameters and a (nondiameter) chord. Geometry Unit 10 Circles Flashcards | Quizlet Start studying Geometry Unit 10 Circles. $\text {m } \angle b = \frac 1 2 \overparen {AC}$ Explore this relationship in the interactive applet immediately below. About This Quiz & Worksheet. In general, to find the area of a segment, we subtract the area of a triangle from the area of a sector. A c = π *r 2 = π *12. A) Circle M has a radius of 6 m; Circle N has a diameter of 10 m. In the Cartesian coordinate system, students use the 1 Source: National Governors Association Center for Best Practices and Council of Chief State School Officers. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. t m s ã is a(n) 5. 6 Geometric Probability. 3 to 80% 30 *Quizizz - Equations of Circles Code 966161 *IXL V. Circumference of Circle. Both a rectangle and a rhombus are parallelograms, but a Unit 7 Polygons and Quadrilaterals Flashcards Quizlet Start studying Unit 7 Polygons and Quadrilaterals. (2) (3) Find the length of the arc of a sector of 54 ° in a circle if the radius is 10. In the Cartesian coordinate system, students use the 1 Source: National Governors Association Center for Best Practices and Council of Chief State School Officers. А 1 А 2 = 2 a - major axis (larger direct that crosses focal points F 1 and F 2). Lost in Space – a science fiction adaptation of Swiss Family Robinson, which focuses around the misadventures of its breakout character, Dr. 5 #'s 1-4, 10, 8. Henderson's favorite NFL team. In such cases, you may need to calculate the area of a sector or the length of an arc when determining the area or perimeter (respectively) of the figure. Points A and B are the endpoints of chord AB. 39-111 Geometry unit 4 similarity post test. πr^2/6 (because 60 degree/360 degree=1/6) We can subtract the area of triangle ( √3/4 * side^2) from it to find the area of the curved part. Where does the area of a circle come from??? workbook 8. (4) The apothem of a regular hexagon is 10 3. Arabella Castillo (arabellacastillo1) David York (davidyork9) Lists. Remember to stay informed. Worksheets. Practice this lesson yourself on KhanAcademy. We’re not right for everyone. 320 subscribers. Area of a Sector. Asked in Math and Arithmetic , Algebra , Geometry. this might end. The Lost Saucer – a Sid & Marty Krofft series starring Jim Nabors and Ruth Buzzi. Example: the perimeter of this regular pentagon is:. Perimeter is the distance around a two-dimensional shape. Which is given, the. sec 5 π64 tor 36 A Rewrite the fraction and the power. You may want to do that that’s why it is a good idea. f, which goes to A = 1910. In Figure 2, $$\angle$$A is an inscribed angle that intercepts the arc BC. Examples of sectors are illustrated below. 7 square centimeters. yay ayaqqabi resimleri, Join our group of amazing donors in supporting educational programs like charity hackathons and open source educational events. Here's the formal solution: Find the area of circle segment IK. Why show ads? Report Ad. It's designed to take concepts you're used to and make you apply them in new (and often strange) ways. The area and circumference are for the entire circle, one full revolution of the radius line. 25 π A t =. Find the area of the yellow fi gure. 4 to 80% 31 *Lesson - Area of a Sector. See radius of a circle. Spears Chapter 8 Vocabulary 19 Terms. Andrea Grieser deleted the Geo G. centimeters. And not every smart person is right for us. Trigonometric Ratios Solving Right Triangles Angles of Elevation and Depression Law of Sines Law of Cosines G. this is the final step of fixing the self propelled lawn mower cable and make it operational. This will produce a final reading of square units (or units squared). h is the altitude (height) Recall that the bases are the two parallel sides of the trapezoid. Remember that the area of a circle is π*radius^2 Remember that there are 360 ° in a circle. Arc Length and Area of a Sector Arcs, Chords, and Central Angles Bisectors in a Triangle Congruence in Right Triangles Conic Sections: Circles. Find the measure (in radians) of a central angle of a sector of area 52 square inches in a circle of radius6in?. In all there are four such congruent parts. Area of parallelogram vectors 2d: Lexx – a science fiction dark and "bloody" comedy, not for fainthearted. Online calculators and formulas for a surface area and other geometry problems. Math Worksheets. - Edgenuity. Angle and Degree measure. While sector specifically means the physical disk area, the term block has been used loosely to refer to a small chunk of data. That video sums it up really well, so lets move onto Theorem 7-3! Theorem 7-3: Definition: The altitude to the hypotenuse of a right triangle divides the triangle into two separate triangles that are similar to the original triangle AND each other. Express answer as an exact value. The Area of A Sector Calculator is used to help you find the area of a sector of a circle. The area, diameter and circumference will be calculated. Honor Code. A comprehensive database of more than 48 area quizzes online, test your knowledge with area quiz questions. ? I'll be honest, I'm rubbish at math and I've stared at this problem for a good two hours and can not figure it out for the life of me. Keeping in mind the circle's total area, the circumference, and the arc length, we can now learn how to find the area of a section of a circle. Home Explore Delta Answer Key - ksjiqi. 9in2, and m∠CBD = 54°. 17) 16 ft 240 ° 512 π 3 ft² 18) 14 in 315 ° 343 π 2 in² 19) 14 cm 3π 2 147 π cm² 20) 12 ft 19 π 12 114 π ft² 21. Day 12: Six Weeks Exam. Congruence Experiment with transformations in the plane. Download: EDGENUITY ENGLISH 3 SEMESTER 2 ANSWERS PDF Best of all, they are entirely free to find, use and download, so there is no cost or stress at all. Khan Academy is a 501(c)(3) nonprofit organization. The area of a sector is a fractional part of the area of a circle. 13) 60 ° 10 in 52. s t r ã is a(n) 6. in is a part of the largest social network for studying in a group. A lesson on the definition of area including formulas and proofs for the area of a rectangle, square, parallelogram and triangle. Therefore the area of the sector becomes: A_sec = \frac{60 * \pi * 50^{2}}{360} This simpliflies to A_sec = \frac{1250*\pi}{3} Then the area of the triangle (half * base divided by 2) becomes 600. 3 to 80% 30 *Quizizz - Equations of Circles Code 966161 *IXL V. Praesent posuere ante ut erat fringilla, vestibulum placerat metus mattis. OK-Geometry Oklahoma Academic Standards 2009 Standard ID Standard Text Edgenuity Lesson Name G. Asked in Math and Arithmetic , Algebra , Geometry. I know a majority of schools teach circles as one big unit but I don't think that most of my special education students could remember all of those theorems and rules and be successful. Label the radius of the circle 20 feet. Day 12: Semester Exam. The area of a sector is a fraction of the area of the circle. sec 5 π64 tor 36 A Rewrite the fraction and the power. In circle O, the radius is 4, and the measure of minor arc AB is 120 degrees. The base of the triangle is the diameter of the circle, which is 2*r = 2*12. Georgia Tech CEISMC Summer Programs for Rising 4th-12th-grade Students. erinrachelschool. Scroll down the page for more examples and explanations. Zachary Smith. Students will create a Quizlet set of cards for this units. G o t a d i f f e r e n t a n s w e r? C h e c k i f i t ′ s c o r r e c t. 360°- 60° = 300 ° Since the area of a circle is πr^2, and the section of the circle is 300°, or 300/360 = 5/6 or one full circle, the area of the unshaded region is (5/6. Release your mouse button when the item is place. Online calculators and formulas for a surface area and other geometry problems. Chapter 11 Area of Polygons and Circles. And so our area, our sector area, is equal to-- let's see, in the. The formula for a circle in the xy plane would be. YOU MIGHT ALSO LIKE Mrs. Cincinnati Bengals. If you're behind a web filter, please make sure that the domains *. Is the red line a radius or diameter of the circle?. Arc Length and Area of a Sector Arcs, Chords, and Central Angles Bisectors in a Triangle Congruence in Right Triangles Conic Sections: Circles. 125pi square centimeters 9- 22. The area of a sector when given the radius and arc length Skills Practiced Reading comprehension - draw the most pertinent information from the lesson on the arc length of a sector. Day 8: Slope and Equations of Lines. I suggest you take notes on any questions you get incorrect. Is the red line a radius or diameter of the circle? Introduction to Circles DRAFT. The arc length l and area A of a sector of angle θ in a circle of radius r are given by. (3) John bought a square plot of side 60 m. 2 units squared. (2) (3) Find the length of the arc of a sector of 54 ° in a circle if the radius is 10. Assigned 3/2/17. ? I'll be honest, I'm rubbish at math and I've stared at this problem for a good two hours and can not figure it out for the life of me. (4) The apothem of a regular hexagon is 10 3. Now draw a chord that intersects the two diameters someplace interior the circle at 2 distinctive factors, one on each and every. When finding the area of a sector, you are really just calculating the area of the whole circle, and then multiplying by the fraction of the circle the sector represents. A circle is 360 degrees, so when you place the measurement of the sector's central angle over 360, it gives you the fraction of the whole circle. Especially really big tyres that you can climb right into. Do not round. This free worksheet contains 10 assignments each with 24 questions with answers. Play this game to review Geometry. h is the altitude (height) Recall that the bases are the two parallel sides of the trapezoid. Just type into the box and your conversion will happen automatically. Circular segment. 4 ohm cab is not enough load for an amp/transformer that needs at least 8 ohmsThat is a poor layman's explanation but that is basically how I have always thought of it. Date Due: 03/20/2020 Category: Option 1- Bleaded Learning (Edgenuity) Arc Length/Area of Sector-Distance Learning-Option 2 (If you do not have a Laptop or Computer). It is the portion of the circumference subtended by the central angle. Sector area: The area of a sector (a pizza-slice shape. Find the area of the shaded sector of circle O. CA Circumference and Arc Length Area of a Circle and a Sector G-CO. We’ll start with the volume and surface area of rectangular prisms. Is the red line a radius or diameter of the circle? Introduction to Circles DRAFT. We split up our circles unit into 2 parts (Part 1: Circle Basics, Circumference & Area, Area of Shaded Regions, & Tangent Lines; Part 2: Arcs, Central Angles, Chords, Sector Area, Arc Length, and Segment Area). Bisectors of Triangles. Because 120° takes up a third of the degrees in a circle, sector IDK occupies a third of the circle's area. The formula for the area of a circle is A = πr2. 2) Find the area and circumference of a circle with radius 8. Trigonometric Ratios Solving Right Triangles Angles of Elevation and Depression Law of Sines Law of Cosines G. (s1 over s2)^2. Online calculators and formulas for a surface area and other geometry problems. 25 π A t =. The base is 8 and the height is 6, so the area is 8 (6) = 48 square units. Relate the area of a sector to the area of a whole circle. The arc length l and area A of a sector of angle θ in a circle of radius r are given by. 4 in² 14) 3 m 150 ° 11. A part of a circle is called an arc and an arc is named according to its angle. b - semi-minor axis. The area of the shaded sector depends on the length of the radius. calculate the length of an arc and the area of a circle sector. TOPIC 9-3. TOPIC 9-2 Area of Parallelograms. Thus the area of the figure is 112 square units. This will produce a final reading of square units (or units squared). In all there are four such congruent parts. The sum of angles in a triangle equals 180 degrees. However, what is a sector? A sector is part of a circle bounded by two radii and their intercepted arc. Geometry 6. Figure 3 A circle with two diameters and a (nondiameter) chord. Money raised by the WordPress Foundation will be used to ensure free …. The area, diameter and circumference will be calculated. Practice this lesson yourself on KhanAcademy. Join 100 million happy users! Sign Up free of charge:. Monday thru Friday watch CNN10 and keep track of daily news using our notes sheet. Sed aliquet mi at libero ultrices consectetur. Let's graph x = 3 in one, two, and three dimensions. 480 units squared. Chord of a Circle. The portion of the circle shaded in blue is the sector. UNIT 3 Practice Test Name: Radius Diameter Chord Secant Line Tangent Line Point of Tangency Major Arc Minor Arc Semi-Circle Central Angle Inscribed Angle Right Angle Describe the following: 1. Ivy Global 5. Lessons: All Lessons are due by April 15 th. The side of the square is equal to the diameter of the circle, or twice the radius: 2r. 1 Make sense of problems and persevere in solving them. 7 Areas of Circles and Sectors. πr^2/6 (because 60 degree/360 degree=1/6) We can subtract the area of triangle ( √3/4 * side^2) from it to find the area of the curved part. You are done with the mo. Adjacent to this David bought a rectangular plot of dimension 70 m x 50 m. Release your mouse button when the item is place. The given below is the area of circle segment calculator to calculate the area of the segment of a circle. The length of an arc, l, is determined by plugging the degree measure of the. Andrea Grieser deleted the Geo G. April 27th week Due Date: 4/27/2020 Subject: ACT/SAT Prep I This week assignments. The area of each triangle will be 56 square meters divided by 2. Learn vocabulary, terms, and more with flashcards, games, and other study tools. 4th class power engineering exam questions downloads cogat form 7 practice test grade 2 psychology today articles punchline bridge to algebra answer key 2001 page 116. The base is 8 and the height is 6, so the area is 8 (6) = 48 square units. Remember that the area of a circle is π*radius^2 Remember that there are 360 ° in a circle. a - semi-major axis. Radius: A segment whose endpoints are the center of a circle and a point on the circle. This fits well with the definition of area which is the number of square units that will cover a closed figure. Choose your answers to the questions and click 'Next' to see the next set of questions. Find the length of each side of the hexagon. Arc of a Circle Also Central Angles. The angle formed by the intersection of 2 tangents, 2 secants or 1 tangent and 1 secant outside the circle equals half the difference of the intercepted arcs!Therefore to find this angle (angle K in the examples below), all that you have to do is take the far intercepted arc and near the smaller intercepted arc and then divide that number by two! That's why we call this the Far Arc Near Arc. ) ∠1 and ∠4 B. When finding the area of a sector, you are really just calculating the area of the whole circle, and then multiplying by the fraction of the circle the sector represents. We’re not right for everyone. Find the area of the shaded sector of circle O. When z does not equal 0, the graph will form a sphere. Relate the area of a sector to the area of a whole circle. What is true about the relationship of a rectangle and a triangle created from that rectangle?. To find the segment area, you need the area of triangle IDK so you can subtract it from the area of sector IDK. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. Arc Length of a Circle Formula - Sector Area, Examples, Radians, In Terms of Pi, Trigonometry - Duration: 15:57. 8 Area and sectors 59 Terms. Find the area of the sector. CA Circumference and Arc Length Area of a Circle and a Sector G-CO. 8 ohm speaker load, Jan 21, 2010 · You need to have enough load (speaker ohms) on the amp so the wattage/power is soaked up and not run back into the amp. Inscribed angles. 14 and replace the value of r and n into the formula to get the area. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The area of the square is this quantity 2r squared, or 4r 2. Can you categorize these two arcs as the minor. Both a rectangle and a rhombus are parallelograms, but a Unit 7 Polygons and Quadrilaterals Flashcards Quizlet Start studying Unit 7 Polygons and Quadrilaterals. Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference. f, which goes to A = 1910. Find the surface area ofa pyramid with a square base legnth 10 and a slant height of 13. Theorem 70: The measure of an inscribed angle in a circle equals half the measure of its. Area of a sector Get 3 of 4 questions to level up! Quiz 2. Find the radius of a circle with an area of 2827. 2) Find the area and circumference of a circle with radius 8. None of the above. Label the radius of the circle 20 feet. 5/11 Delta Answer Key [PDF] The Madwoman In Attic Woman Writer And Nineteenth Like this book? You can publish your book online for free in a few minutes!. The semester starts with a review of Algebra 1 and then go into Trigonometry, Surface Area and Volume, Quadrilaterals, and Vectors. Improve your math knowledge with free questions in "Area of sectors" and thousands of other math skills. I know a majority of schools teach circles as one big unit but I don't think that most of my special education students could remember all of those theorems and rules and be successful. You are done with the mo.
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echo $RANDOM ### C-x C-p for import pdb; pdb.set_trace() I worked through most of the Learn Emacs Lisp in 15 minute tutorial and learned enough to write something useful: ;; Inset import pdb; pdb.set_trace() on C-x, C-p (defun pdb-set-trace () ;; http://www.emacswiki.org/emacs/InteractiveFunction (interactive) (insert "import pdb; pdb.set_trace()\n")) (global-set-key [(control ?x) (control ?p)] 'pdb-set-trace) Once you place this function in your Emacs init file, when you press the keys C-x and C-p, import pdb; pdb.set_trace() will magically appear in your Python program (well, anywhere for that matter, since there is no check in place). This is something which I know will be very useful to me. If you don’t like the key combination, you can change it in the last line of the above function. If you don’t know Emacs lisp, you should try to work through the tutorial. Although, I must say I did make various attempts long time back to learn Common Lisp and Clojure, so it was not so unfamiliar to me. ### poweroff, halt, reboot and systemctl On Fedora (and perhaps other Linux distros using systemd) you will see that the poweroff, reboot and halt commands are all symlinks to systemctl: > ls -l /sbin/poweroff /sbin/halt /sbin/reboot lrwxrwxrwx. 1 root root 16 Oct 1 11:04 /sbin/halt -> ../bin/systemctl lrwxrwxrwx. 1 root root 16 Oct 1 11:04 /sbin/poweroff -> ../bin/systemctl lrwxrwxrwx. 1 root root 16 Oct 1 11:04 /sbin/reboot -> ../bin/systemctl So, how does it all work? The answer lies in this code block from systemctl.c: .. 5556 if (program_invocation_short_name) { 5557 5558 if (strstr(program_invocation_short_name, "halt")) { 5559 arg_action = ACTION_HALT; 5560 return halt_parse_argv(argc, argv); 5561 } else if (strstr(program_invocation_short_name, "poweroff")) { 5562 arg_action = ACTION_POWEROFF; 5563 return halt_parse_argv(argc, argv); 5564 } else if (strstr(program_invocation_short_name, "reboot")) { 5565 if (kexec_loaded()) .. program_invocation_short_name program_invocation_short_name is a variable (GNU extension) which contains the name used to invoke a program. The short indicates that if you call your program as /bin/myprogram, it is set to ‘myprogram’. There is also a program_invocation_name variable consisting of the entire path. Here is a demo: /*myprogram.c*/ # include <stdio.h> extern char *program_invocation_short_name; extern char *program_invocation_name; int main(int argc, char **argv) { printf("%s \n", program_invocation_short_name); printf("%s \n", program_invocation_name); return 0; } Assume that the executable for the above program is created as myprogram, execute the program from a directory which is one level up from where it resides. For example, in my case, myprogram is in $HOME/work and I am executing it from $HOME: > ./work/myprogram myprogram ./work/myprogram You can see the difference between the values of the two variables. Note that any command line arguments passed are not included in any of the variables. Back to systemctl Okay, so now we know that when we execute the poweroff command (for example), program_invocation_short_name is set to poweroff and this check matches: if (strstr(program_invocation_short_name, "poweroff")) .. and then the actual action of powering down the system takes place. Also note that how the halt_parse_argv function is called with the parameters argc and argv so that when you invoke the poweroff command with a switch such as --help, it is passed appropriately to halt_parse_argv: 5194 static const struct option options[] = { 5195 { "help", no_argument, NULL, ARG_HELP }, .. .. 5218 case ARG_HELP: 5219 return halt_help(); Fooling around Considering that systemctl uses strstr to match the command it was invoked as, it allows for some fooling around. Create a symlink mypoweroff to /bin/systemctl and then execute it as follows: > ln -s /bin/systemctl mypoweroff > ./mypoweroff --help mypoweroff [OPTIONS...] Power off the system. --help Show this help --halt Halt the machine -p --poweroff Switch off the machine --reboot Reboot the machine -f --force Force immediate halt/power-off/reboot -w --wtmp-only Don't halt/power-off/reboot, just write wtmp record -d --no-wtmp Don't write wtmp record --no-wall Don't send wall message before halt/power-off/reboot This symlink is for all purpose going to act like the poweroff command since systemctl basically checks whether ‘poweroff’ is a substring of the invoked command. To learn more, see systemctl.c Related Few months back, I had demoed invoking a similar behaviour in programs where a program behaves differently based on how you invoke it using argv[0] here. I didn’t know of the GNU extensions back then. ### Writing git hooks using Python Since git hooks can be any executable script with an appropriate #! line, Python is more than suitable for writing your git hooks. Simply stated, git hooks are scripts which are called at different points of time in the life cycle of working with your git repository. Let’s start by creating a new git repository: ~/work> git init git-hooks-exp Initialized empty Git repository in /home/gene/work/git-hooks-exp/.git/ ~/work> cd git-hooks-exp/ ~/work/git-hooks-exp (master)> tree -al .git/ .git/ ├── branches ├── config ├── description ├── HEAD ├── hooks │ ├── applypatch-msg.sample │ ├── commit-msg.sample │ ├── post-update.sample │ ├── pre-applypatch.sample │ ├── pre-commit.sample │ ├── prepare-commit-msg.sample │ ├── pre-rebase.sample │ └── update.sample ├── info │ └── exclude ├── objects │ ├── info │ └── pack └── refs ├── heads └── tags 9 directories, 12 files Inside the .git are a number of directories and files, one of them being hooks/ which is where the hooks live. By default, you will have a number of hooks with the file names ending in .sample. They may be useful as starting points for your own scripts. However, since they all have an extension .sample, none of the hooks are actually activated. For a hook to be activated, it must have the right file name and it should be executable. Let’s see how we can write a hook using Python. We will write a post-commit hook. This hook is called immediately after you have made a commit. We are going to do something fairly useless, but quite interesting in this hook. We will take the commit SHA1 of this commit, and print how it may look like in a more human form. I do the latter using the humanhash module. You will need to have it installed. Here is how the hook looks like: #!/usr/bin/python import subprocess import humanhash # get the last commit SHA and print it after humanizing it # https://github.com/zacharyvoase/humanhash print humanhash.humanize( subprocess.check_output( ['git','rev-parse','HEAD'])) I use the subprocess.check_output() function to execute the command git rev-parse HEAD so that I can get the commit SHA1 and then call the humanhash.humanize() function with it. Save the hook as a file, post-commit in your hooks/ directory and make it executable using chmod +x .git/hooks/post-commit. Let’s see the hook in action: ~/work/git-hooks-exp (master)> touch file ~/work/git-hooks-exp (master)> git add file ~/work/git-hooks-exp (master)> git commit -m "Added a file" carbon-network-connecticut-equal [master (root-commit) 2d7880b] Added a file 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 file The commit SHA1 for the commit turned out to be 2d7880be746a1c1e75844fc1aa161e2b8d955427. Let’s check it with the humanize function and check if we get the same message as above: >>> humanhash.humanize('2d7880be746a1c1e75844fc1aa161e2b8d955427') 'carbon-network-connecticut-equal' And you can see the same message above as well. Accessing hook parameters For some of the hooks, you will see that they are called with some parameters. In Python you can access them using the sys.argv attribute from the sys module, with the first member being the name of the hook of course and the others will be the parameters that the hook is called with. Current working directory For some reason, it may be useful if you know what is the current working directory of your hook. The os.getcwd() function can help there and it turns out to be the local file system path to your git repository (~/work/git-hooks-exp in the above case). ### Using the __cleanup__ variable attribute in GCC GCC’s C compiler allows you to define various variable attributes. One of them is the cleanup attribute (which you can also write as__cleanup__) which allows you to define a function to be called when the variable goes out of scope (for example, before returning from a function). This is useful, for example to never forget to close a file or freeing the memory you may have allocated. Next up is a demo example defining this attribute on an integer variable (which obviously has no practical value). I am using gcc (GCC) 4.7.2 20121109 on Fedora 18. Read the article here. ### Managing IPython notebook server via systemd: Part-I If you are using IPython notebook on a Linux distribution which uses systemd as it’s process manager (such as Fedora Linux, Arch Linux) , you may find this post useful. I will describe a fairly basic configuration to manage (start/stop/restart) IPython notebook server using systemd. Creating the Systemd unit file First, we will create the systemd unit file. As root user, create a new file /usr/lib/systemd/system/ipython-notebook.service and copy the following contents into it: [Unit] Description=IPython notebook [Service] Type=simple PIDFile=/var/run/ipython-notebook.pid ExecStart=/usr/bin/ipython notebook --no-browser --pylab=inline User=ipynb Group=ipynb WorkingDirectory=/home/ipynb/notebooks [Install] WantedBy=multi-user.target Note that due to the naming of our unit file, the service will run as ipython-notebook. To completely understand the above unit file, you will need to read up a little of the topic. You may find my earlier post useful which also has links to systemd resources. Three things deserve explanation though: The line, ExecStart=/usr/bin/ipython notebook --no-browser --pylab=inline specifies the command to start the IPython notebook server. This should be familiar to someone who uses it. The lines, User=ipynb and Group=ipynb specify that we are going to run this process as user/group ipynb (we create them in the next step). The line WorkingDirectory=/home/ipynb/notebooks specify that the notebooks will be stored/server in/from /home/ipynb/notebooks Setting up the user As root, create the user ipynb: # useradd ipynb Next, as ipynb, create a sub-directory, notebooks: # su - ipynb [ipynb@localhost ~]$ mkdir notebooks [ipynb@localhost ~]$exit Starting IPython notebook We are all set now to start IPython notebook. As the root user, reload all the systemd unit files, enable the ipython-notebook service so that it starts on boot, and then start the service: # systemctl daemon-reload # systemctl enable ipython-notebook ln -s '/usr/lib/systemd/system/ipython-notebook.service' '/etc/systemd/system/multi-user.target.wants/ipython-notebook.service' # systemctl start ipython-notebook If you check the status of the service, it should show the following: # systemctl status ipython-notebook ipython-notebook.service - IPython notebook Loaded: loaded (/usr/lib/systemd/system/ipython-notebook.service; enabled) Active: active (running) since Sun 2013-09-22 22:39:59 EST; 23min ago Main PID: 3671 (ipython) CGroup: name=systemd:/system/ipython-notebook.service ├─3671 /usr/bin/python /usr/bin/ipython notebook --no-browser --pylab=inline └─3695 /usr/bin/python -c from IPython.zmq.ipkernel import main; main() -f /home/ipynb/.ipython/profile_default/security/kernel-6dd8b338-e779-4e67-bf25-1cd238... Sep 22 22:39:59 localhost ipython[3671]: [NotebookApp] Serving notebooks from /home/ipynb/notebooks Sep 22 22:39:59 localhost ipython[3671]: [NotebookApp] The IPython Notebook is running at: http://127.0.0.1:8888/ Sep 22 22:39:59 localhost ipython[3671]: [NotebookApp] Use Control-C to stop this server and shut down all kernels. Sep 22 22:40:21 localhost ipython[3671]: [NotebookApp] Using MathJax from CDN: http://cdn.mathjax.org/mathjax/latest/MathJax.js Sep 22 22:40:22 localhost ipython[3671]: [NotebookApp] Kernel started: 6dd8b338-e779-4e67-bf25-1cd23884cf5a Sep 22 22:40:22 localhost ipython[3671]: [NotebookApp] Connecting to: tcp://127.0.0.1:51666 Sep 22 22:40:22 localhost ipython[3671]: [NotebookApp] Connecting to: tcp://127.0.0.1:52244 Sep 22 22:40:22 localhost ipython[3671]: [NotebookApp] Connecting to: tcp://127.0.0.1:44667 Sep 22 22:40:22 localhost ipython[3671]: [IPKernelApp] To connect another client to this kernel, use: Sep 22 22:40:22 localhost ipython[3671]: [IPKernelApp] --existing kernel-6dd8b338-e779-4e67-bf25-1cd23884cf5a.json You should now be able to access IPython notebook as you would normally do. Finally, you can stop the server as follows: # systemctl stop ipython-notebook The logs are redirected to /var/log/messages: Sep 22 22:39:59 localhost ipython[3671]: [NotebookApp] Created profile dir: u'/home/ipynb/.ipython/profile_default' Sep 22 22:39:59 localhost ipython[3671]: [NotebookApp] Serving notebooks from /home/ipynb/notebooks Sep 22 22:39:59 localhost ipython[3671]: [NotebookApp] The IPython Notebook is running at: http://127.0.0.1:8888/ Sep 22 22:39:59 localhost ipython[3671]: [NotebookApp] Use Control-C to stop this server and shut down all kernels. Sep 22 22:40:21 localhost ipython[3671]: [NotebookApp] Using MathJax from CDN: http://cdn.mathjax.org/mathjax/latest/MathJax.js Sep 22 22:40:22 localhost ipython[3671]: [NotebookApp] Kernel started: 6dd8b338-e779-4e67-bf25-1cd23884cf5a Sep 22 22:40:22 localhost ipython[3671]: [NotebookApp] Connecting to: tcp://127.0.0.1:51666 Sep 22 22:40:22 localhost ipython[3671]: [NotebookApp] Connecting to: tcp://127.0.0.1:52244 Sep 22 22:40:22 localhost ipython[3671]: [NotebookApp] Connecting to: tcp://127.0.0.1:44667 Sep 22 23:05:35 localhost ipython[3671]: [NotebookApp] received signal 15, stopping Sep 22 23:05:35 localhost ipython[3671]: [NotebookApp] Shutting down kernels Sep 22 23:05:35 localhost ipython[3671]: [NotebookApp] Kernel shutdown: 6dd8b338-e779-4e67-bf25-1cd23884cf5a For me, the biggest reason to do this is that I do not have to start the IPython notebook server everytime on system startup manually, since I know it will be running when I need to use it. I plan to explore managing custom profiles next and also think more about a few other things. ### Fedora Scientific Spin Update The Fedora Scientific 20 Spin will have a number of new packages: notably, it will now include the Python 3 tool chain for the Python libraries for scientific/numerical computing. If you are interested to check it out, download a nightly from here. Testing the applications/libraries It took me 3 releases to figure out – or rather, sit down to do it. Anyway, here it is now. I have created a Wiki page where I want to list scripts/other ways to sanity test the various packages/applications that are being shipped. I believe it will help in two ways: • Often, the entire functionality of a tool/library is split into more than one package and hence pulling in only the main package is no guarantee that the tool/library/application will work. • We may also be able to catch genuine bugs/faults in the packages being shipped. (Think of things like missing shared library dependency, etc) So, please add whatever you can to the wiki page. Just simple ways to see if the application/library actually works. My plan is to collect whatever I/we gather there into a git repository somewhere and run it prior to/during releases to see everything is working as expected. Links • Download a nightly compose from here (The usual warning against testing in-progress Fedora releases apply) • Add scripts/tests to the wiki page here If you find a problem, leave a comment here, or add to the wiki page. Note You may see that the nightlies are failing, but this should be fixed soon (See this bug). You can still download a TC5 build from here which has all the packages that are going to be shipped, except for sagemath. Once again, thanks are due to the packagers actually packaging all this software that makes Fedora Scientific possible. ### Get started with Beaker on Fedora Beaker 0.14 was released recently and if you are an existing user of Beaker, you may see the What’s new page here If however, you do not know what Beaker is, the Architecture guide is a good start and if things look interesting, with this release there is also documentation now to setup a Beaker “test bed” using two Virtual machines (via libvirt). ### Notes on writing systemd unit files for Beaker’s daemon processes Recently, I had a chance to write systemd unit files for the daemon processes that run as part of Beaker: beakerd which is the scheduling daemon running on the server and the four daemons running on the lab controller – beaker-proxy, beaker-provision, beaker-watchdog and beaker-transfer. This post may be of interest to you if you are using python-daemon to write programs which are capable of running as daemon processes and you want to write systemd unit files for them. beakerd’s unit file Here is the systemd unit file for beakerd, which I will use to illustrate the core points of this post. The other unit files are similar, and hence I will explain only where they differ from this one: [Unit] Description=Beaker scheduler After=mysqld.service [Service] Type=forking PIDFile=/var/run/beaker/beakerd.pid ExecStart=/usr/bin/beakerd User=apache Group=apache [Install] WantedBy=multi-user.target The [Unit] section has a description of the service (using the Description option) and specifies that it should start after the mysqld.service has started using the After option. beakerd needs to communicate to a MySQL server before it can start successfully. It can work with a local or a remote MySQL server. Hence, specifying After sets up an ordering that if there is a local MySQL server, then wait for it to start before starting beakerd. Using Requires is not suitable here to accommodate the possibility that beakerd may be configured to use a remote MySQL server. In the [Service] section, the Type is set to Forking. This is because, beakerd uses python-daemon which forks itself (detaches itself) during the daemonization. However, you must ensure that when creating a DaemonContext() object, you should specify detach_process=True. This is because, if python-daemon detects that it is running under a init manager, it doesn’t detach itself unless the keyword is explicitly set to True, as above (you can see the code in daemon.py). Hence, although not setting the above keyword would work under SysV Init, it doesn’t work under systemd (with Type=Forking), since the daemon doesn’t fork at all and systemd expects it to fork (and finally kills it). The PIDFile specifies where the process ID is dumped by beakerd and is setup while creating the DaemonContext object as follows and ExecStart specifies the location to the binary that is to be started. The beakerd process is to be run as the apache user and group, which is specified by the User and Group options. In the [Install] section, the WantedBy option specifies when the beakerd process should be started (similar to the concept of “run levels” in SysV init). systemd defines several targets, and here we define that we want beakerd to start as part of the multi user setup. That’s all about beakerd’s unit file. beaker-provision’s unit file beaker-provision and the other daemons running on the lab controller have similar unit files: [Unit] Description=Beaker provisioning daemon After=httpd.service [Service] Type=forking PIDFile=/var/run/beaker-lab-controller/beaker-provision.pid ExecStart=/usr/bin/beaker-provision User=root Group=root [Install] WantedBy=multi-user.target All the four lab controller daemons need to communicate with Beaker web application – which can be local or remote, and hence the After option specifies the dependency on httpd.service. And, this particular daemon runs as root user/group, which is specified by the User and group options. And everything else is similar to beakerd’s unit file and also the other lab controller daemons. Shipping SysV init files and systemd unit files in the same package The beaker packages ship both SysV init files and systemd unit files now so that it can use systemd when available, but use SysV init otherwise. This commit can give you some idea of how to go about it. systemd resources These links proved helpful to learn more about systemd, including how to package unit files for Fedora: ### /proc/cpuinfo on various architectures The /proc/cpuinfo file contains runtime information about the processors on your Linux computer (including your Android phone). For example, here is what it looks like on my phone: u0_a123@android:/$ cat /proc/cpuinfo
Processor : ARMv7 Processor rev 1 (v7l)
processor : 0
BogoMIPS : 1592.52
processor : 1
BogoMIPS : 2388.78
Features : swp half thumb fastmult vfp edsp neon vfpv3 tls
CPU implementer : 0x41
CPU architecture: 7
CPU variant : 0x2
CPU part : 0xc09
CPU revision : 1
Hardware : SMDK4210
Revision : 000e
Serial : 304d19f36a02309e
Depending on what you are looking for, these are all useful information. Being plain text files, you can write shell scripts or some other programming language (see my earlier article using CPython on this topic) to parse this information and mine the data you are looking for. These are useful information and for projects such as lshw and Beaker, quite vital too. However, one problem with dealing with this file is that depending on the hardware architecture, the information varies – both in their presentation format and the information available. If you compare the contents of your Intel/AMD desktop or laptop with the above, you will know what I am talking about. Hence, it is necessary that whatever tool/script one writes to read and use the data from this file and hopes it to work across architectures should consider these differences.
I won’t attempt to make any guesses to why they are different. However, I will share with you how to find out the information you may find in this file on different architectures. The post is admittedly half baked and may not satisfy all your queries, but I think I am on the right track.
Get the Kernel sources
Download the Linux kernel sources (tarball from http://kernel.org or clone it from https://github.com/torvalds/linux/). The arch/ sub directory has architecture specific code and in all you will see 31 subdirectories in this sub directory: alpha, arc, arm, arm64, and others. The links in the rest of this post are cross referenced links, so you may not need to download the sources.
Definition of cpuinfo_op
One file for each of the above architectures defines a cpuinfo_op variable of type seq_operations. For example, for the arm64 architecture, this variable is defined in arm64/kernel/setup.c and this is what it looks like:
956 const struct seq_operations cpuinfo_op = {
957 .start = c_start,
958 .next = c_next,
959 .stop = c_stop,
960 .show = c_show
961 };
The key member assignment for our purpose here is the .show attribute which is a function pointer pointing to the c_show() function. This is the function where you can see the information that you will see when you see the contents of /proc/cpuinfo. So for example, the c_show() function for arm64 is here and you can see the fields earlier shown in the blog post. (I can’t see “Serial” there, which I am not sure why yet, I am still to figure out if it’s the right architecture at all, but you get the idea, I hope).
You can search for cpuinfo_op and see the files for each arch where they are defined in. The function which the .show member points has the information that will be show in /proc/cpuinfo. Note that, the function name can be different. For example it is show_cpuinfo() for s390x.
Examples
For an example of how the different architecture specific information can be dealt with in C/C++ program/tool using architecture specific macros, see lshw’s cpuinfo.cc file. For shell scripts or a Python program, using uname (via os.uname() in CPython) may be a possible approach.
### Creating a Fedora 19 Scientific ISO
In my last post, I explained how you could upgrade your Fedora 18 Scientific installation to Fedora 19 scientific installation. However, if you are looking to perform a fresh installation, you would need a ISO image. I will now show you how you create an ISO image yourself.
Please note that you will need a Fedora 19 installation to create the Fedora 19 scientific image. Also, you should keep in mind that the architecture of the ISO that you build is the same as the architecture of the system you build it on.
The steps are as follows:
Install the necessary tools
We will be using the program, livecd-creator to create the ISO which is installed by the livecd-tools package. Hence install this package using:
#yum install livecd-tools
Clone the kickstarts repository
The Fedora Scientific spin and other spins and images are created from a set of kickstart files maintained in the spin-kickstarts.git repository. Clone this repository (we will directly clone the ‘f19’ branch, since we will be generating a Fedora 19 image). The command for cloning is:
# git clone -b f19 git://git.fedorahosted.org/spin-kickstarts.git
Build the image
Before you can build the image, set SELinux to permissive mode:
# setenforce 0
Now, change your current working directory to the spin-kickstarts directory and invoke the livecd-creator program as follows:
# livecd-creator fedora-livedvd-scientific-kde.ks
The entire process is fairly time consuming, pulls in a lot of packages from the repositories (network data consuming) and disk space intensive. Make sure you have access to all of them. Once the build process is complete, you should have a .iso file in the same directory (The file name will be something like livecd-fedora-livedvd-scientific-kde-xxyyzz.iso). You can now proceed with installing it in a virtual machine or burning it to a USB stick and installing it on a real machine.
Resources
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# Length measurement
Length measurement is implemented in practice in many ways. The most commonly used approaches are the transit-time methods and the interferometer methods based upon the speed of light. For objects such as crystals and diffraction gratings, diffraction is used with X-rays and electron beams. Measurement techniques for three-dimensional structures very small in every dimension use specialized instruments such as ion microscopy coupled with intensive computer modeling.
For a discussion of astronomical methods for determining cosmological distances, see the article Cosmic distance ladder.
## Transit-time measurement
The basic idea behind a transit-time measurement of length is to send a signal from one end of the length to be measured to the other, and back again. The time for the round trip is the transit time Δt, and the length ℓ is then 2ℓ = Δt/v, with v the speed of propagation of the signal, assuming that is the same in both directions. If light is used for the signal, its speed depends upon the medium in which it propagates; in SI units the speed is a defined value c0 in the reference medium of classical vacuum. Thus, when light is used in a transit-time approach, length measurements are not subject to knowledge of the source frequency (apart from possible frequency dependence of the correction to relate the medium to classical vacuum), but are subject to the error in measuring transit times, in particular, errors introduced by the response times of the pulse emission and detection instrumentation. An additional uncertainty is the refractive index correction relating the medium used to the reference vacuum, taken in SI units to be the classical vacuum. A refractive index of the medium larger than one slows the light.
Transit-time measurement underlies most radio navigation systems for boats and aircraft, for example, radar and the nearly obsolete Long Range Aid to Navigation LORAN-C. For example, in one radar system, pulses of electromagnetic radiation are sent out by the vehicle (interrogating pulses) and trigger a response from a responder beacon. The time interval between the sending and the receiving of a pulse is monitored and used to determine a distance. In the global positioning system a code of ones and zeros is emitted at a known time from multiple satellites, and their times of arrival are noted at a receiver along with the time they were sent (encoded in the messages). Assuming the receiver clock can be related to the synchronized clocks on the satellites, the transit time can be found and used to provide the distance to each satellite. Receiver clock error is corrected by combining the data from four satellites.[1]
Such techniques vary in accuracy according to the distances over which they are intended for use. For example, LORAN-C is accurate to about 6 km, GPS about 10 m, enhanced GPS, in which a correction signal is transmitted from terrestrial stations (that is, differential GPS (DGPS)) or via satellites (that is, Wide Area Augmentation System (WAAS)) can bring accuracy to a few meters or < 1 meter, or, in specific applications, tens of centimeters. Time-of-flight systems for robotics (for example, Laser Detection and Ranging LADAR and Light Detection and Ranging LIDAR) aim at lengths of 10 - 100 m and have an accuracy of about 5 – 10 mm[2]
## Interferometer measurements
Measuring a length in wavelengths of light using an interferometer.
In many practical circumstances, and for precision work, measurement of dimension using transit-time measurements is used only as an initial indicator of length and is refined using an interferometer.[3][4] Generally, transit time measurements are preferred for longer lengths, and interferometers for shorter lengths.[5]
The figure shows schematically how length is determined using a Michelson interferometer: the two panels show a laser source emitting a light beam split by a beam splitter (BS) to travel two paths. The light is recombined by bouncing the two components off a pair of corner cubes (CC) that return the two components to the beam splitter again to be reassembled. The corner cube serves to displace the incident from the reflected beam, which avoids some complications caused by superposing the two beams.[6] The distance between the left-hand corner cube and the beam splitter is compared to that separation on the fixed leg as the left-hand spacing is adjusted to compare the length of the object to be measured.
In the top panel the path is such that the two beams reinforce each other after reassembly, leading to a strong light pattern (sun). The bottom panel shows a path that is made a half wavelength longer by moving the left-hand mirror a quarter wavelength further away, increasing the path difference by a half wavelength. The result is the two beams are in opposition to each other at reassembly, and the recombined light intensity drops to zero (clouds). Thus, as the spacing between the mirrors is adjusted, the observed light intensity cycles between reinforcement and cancellation as the number of wavelengths of path difference changes, and the observed intensity alternately peaks (bright sun) and dims (dark clouds). This behavior is called interference and the machine is called an interferometer. By counting fringes it is found how many wavelengths long the measured path is compared to the fixed leg. In this way, measurements are made in units of wavelengths λ corresponding to a particular atomic transition. The length in wavelengths can be converted to a length in units of metres if the selected transition has a known frequency f. The length as a certain number of wavelengths λ is related to the metre using λ = c0 / f. With c0 a defined value of 299,792,458 m/s, the error in a measured length in wavelengths is increased by this conversion to metres by the error in measuring the frequency of the light source.
By using sources of several wavelengths to generate sum and difference beat frequencies, absolute distance measurements become possible.[7][8][9]
This methodology for length determination requires a careful specification of the wavelength of the light used, and is one reason for employing a laser source where the wavelength can be held stable. Regardless of stability, however, the precise frequency of any source has linewidth limitations.[10] Other significant errors are introduced by the interferometer itself; in particular: errors in light beam alignment, collimation and fractional fringe determination.[11][5] Corrections also are made to account for departures of the medium (for example, air[12]) from the reference medium of classical vacuum. Resolution using wavelengths is in the range of ΔL/L ≈ 10−9 – 10−11 depending upon the length measured, the wavelength and the type of interferometer used.[11]
The measurement also requires careful specification of the medium in which the light propagates. A refractive index correction is made to relate the medium used to the reference vacuum, taken in SI units to be the classical vacuum. These refractive index corrections can be found more accurately by adding frequencies, for example, frequencies at which propagation is sensitive to the presence of water vapor. This way non-ideal contributions to the refractive index can be measured and corrected for at another frequency using established theoretical models.
It may be noted again, by way of contrast, that the transit-time measurement of length is independent of any knowledge of the source frequency, except for a possible dependence of the correction relating the measurement medium to the reference medium of classical vacuum, which may indeed depend on the frequency of the source. Where a pulse train or some other wave-shaping is used, a range of frequencies may be involved.
## Diffraction measurements
For small objects, different methods are used that also depend upon determining size in units of wavelengths. For instance, in the case of a crystal, atomic spacings can be determined using X-ray diffraction.[13] The present best value for the lattice parameter of silicon, denoted a, is:[14]
a = 543.102 0504(89) × 10−12 m,
corresponding to a resolution of ΔL/L ≈ 3 × 10−10. Similar techniques can provide the dimensions of small structures repeated in large periodic arrays like a diffraction grating.[15]
Such measurements allow the calibration of electron microscopes, extending measurement capabilities. For non-relativistic electrons in an electron microscope, the de Broglie wavelength is:[16]
$\lambda_e = \frac{h}{\sqrt{2m_e e V}} \ ,$
with V the electrical voltage drop traversed by the electron, me the electron mass, e the elementary charge, and h the Planck constant. This wavelength can be measured in terms of inter-atomic spacing using a crystal diffraction pattern, and related to the metre through an optical measurement of the lattice spacing on the same crystal. This process of extending calibration is called metrological traceability.[17] The use of metrological traceability to connect different regimes of measurement is similar to the idea behind the cosmic distance ladder for different ranges of astronomical length. Both calibrate different methods for length measurement using overlapping ranges of applicability.[18]
## Other techniques
Measuring dimensions of localized structures (as opposed to large arrays of atoms like a crystal), as in modern integrated circuits, is done using the scanning electron microscope. This instrument bounces electrons off the object to be measured in a high vacuum enclosure, and the reflected electrons are collected as a photodetector image that is interpreted by a computer. These are not transit-time measurements, but are based upon comparison of Fourier transforms of images with theoretical results from computer modeling. Such elaborate methods are required because the image depends on the three-dimensional geometry of the measured feature, for example, the contour of an edge, and not just upon one- or two-dimensional properties. The underlying limitations are the beam width and the wavelength of the electron beam (determining diffraction), determined, as already discussed, by the electron beam energy.[19] The calibration of these scanning electron microscope measurements is tricky, as results depend upon the material measured and its geometry. A typical wavelength is 0.5 Å, and a typical resolution is about 4 nm.
Other small dimension techniques are the atomic force microscope, the focused ion beam and the helium ion microscope. Calibration is attempted using standard samples measured by transmission electron microscope (TEM).[20]
## Other systems of units
In some systems of units, unlike the current SI system, lengths are fundamental units (for example, wavelengths in the older SI units and bohrs in atomic units) and are not defined by times of transit. Even in such units, however, the comparison of two lengths can be made by comparing the two transit times of light along the lengths. Such time-of-flight methodology may or may not be more accurate than the determination of a length as a multiple of the fundamental length unit
## References
1. ^ A brief rundown is found at Donald Clausing (2006). "Receiver clock correction". The Aviator's Guide to Navigation (4th ed.). McGraw-Hill Professional. ISBN 978-0-07-147720-8.
2. ^ Robert B Fisher and Kurt Konolige (2008). "§22.1.4: Time-of-flight range sensors". In Bruno Siciliano, Oussama Khatib, eds. Springer handbook of robotics. pp. 528 ff. ISBN 354023957X. Unknown parameter |= ignored (help)
3. ^ For an overview, see for example, Walt Boyes (2008). "Interferometry and transit-time methods". Instrumentation reference book. Butterworth-Heinemann. p. 89. ISBN 0-7506-8308-2.
4. ^ An example of a system combining the pulse and interferometer methods is described by Jun Ye (2004). "Absolute measurement of a long, arbitrary distance to less than an optical fringe". Optics Letters 29 (10): 1153.
5. ^ a b René Schödel (2009). "Chapter 15: Length and size". In Tōru Yoshizawa. Handbook of optical metrology: principles and applications. Volume 10. CRC Press. p. 366. ISBN 0-8493-3760-7.
6. ^ The corner cube reflects the incident light in a parallel path that is displaced from the beam incident upon the corner cube. That separation of incident and reflected beams reduces some technical difficulties introduced when the incident and reflected beams are on top of each other. For a discussion of this version of the Michelson interferometer and other types of interferometer, see Joseph Shamir (1999). "§8.7 Using corner cubes". Optical systems and processes. SPIE Press. pp. 176 ff. ISBN 0-8194-3226-1.
7. ^ Jesse Zheng (2005). Optical Frequency-Modulated Continuous-Wave (FMCW) Interferometry. Springer. ISBN 0-387-23009-2.
8. ^ SK Roy (2010). "§4.4 Basic principles of electronic distance measurement". Fundamentals of Surveying (2nd ed.). PHI Learning Pvt. Ltd. pp. 62 ff. ISBN 81-203-4198-8.
9. ^ W Whyte, R Paul (1997). "§7.3 Electromagnetic distance measurement". Basic Surveying (4th ed.). Laxton's. pp. 136 ff. ISBN 0-7506-1771-3.
10. ^ An atomic transition is affected by disturbances, such as collisions with other atoms and frequency shifts from atomic motion due to the Doppler effect, leading to a range of frequencies for the transition referred to as a linewidth. Corresponding to the uncertainty in frequency is an uncertainty in wavelength. In contrast, the speed of light in ideal vacuum is not dependent upon frequency at all.
11. ^ a b A discussion of interferometer errors is found in the article cited above: Miao Zhu, John L Hall (1997). "Chapter 11: Precise wavelength measurements of tunable lasers". In Thomas Lucatorto et al. eds. Experimental method in the physical sciences. Academic Press. pp. 311 ff. ISBN 0-12-475977-7.
12. ^ For example, the index of refraction of air can be found based upon entering a wavelength in vacuum into the calculator provided by NIST: "Refractive index of air calculator". Engineering metrology toolbox. NIST. September 23, 2010. Retrieved 2011-12-08.
13. ^ Peter J. Mohr, Barry N. Taylor, David B. Newell (2008). "CODATA recommended values of the fundamental physical constants: 2006". Rev Mod Phys 80: 633–730. See section 8: Measurements involving silicon crystals, p. 46.
14. ^ "Lattice parameter of silicon". The NIST reference on constants, units and uncertainty. National Institute of Standards and Technology. Retrieved 2011-04-04. Unknown parameter |search_for= ignored (help)
15. ^ A discussion of various types of gratings is found in Abdul Al-Azzawi (2006). "§3.2 Diffraction gratings". Physical optics: principles and practices. CRC Press. pp. 46 ff. ISBN 0-8493-8297-1.
16. ^ "Electron wavelength and relativity". High-resolution electron microscopy (3rd ed ed.). Oxford University Press. 2009. p. 16. ISBN 0-19-955275-4.
17. ^ See "Metrological traceability". BIPM. Retrieved 2011-04-10.
18. ^ Mark H. Jones, Robert J. Lambourne, David John Adams (2004). An introduction to galaxies and cosmology. Cambridge University Press. pp. 88 ff. ISBN 0-521-54623-0. "Relating one step on the distance ladder to another involves a process of calibration, that is, the use of an established method of measurement to give absolute meaning to the relative measurements provided by some other method."
19. ^ Michael T. Postek (2005). "Photomask critical dimension metrology in the scanning electron microscope". In Syed Rizvi. Handbook of photomask manufacturing technology. CRC Press. pp. 457 ff. ISBN 0-8247-5374-7. and Harry J. Levinson (2005). "Chapter 9: Metrology". Principles of lithography (2nd ed ed.). SPIE Press. pp. 313 ff. ISBN 0-8194-5660-8.
20. ^ NG Orji et al. (2007). "TEM calibration methods for critical dimension standards". Proc. of SPIE 6518. doi:10.1117/12.713368.
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## Algebra 2 Common Core
$-15$ and $15$
Note that $15^2=225$, so $15$ is a real square root of 225, and $(-15)^2=225$, so $-15$ is a also real square root of 225. Thus, the real square roots of 225 are 15 and -15.
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# American Institute of Mathematical Sciences
November 2012, 17(8): 2815-2827. doi: 10.3934/dcdsb.2012.17.2815
## Vegetation patterns and desertification waves in semi-arid environments: Mathematical models based on local facilitation in plants
1 Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom, United Kingdom
Received March 2011 Revised August 2011 Published July 2012
In semi-arid regions, infiltration of rain water into the soil is significantly higher in vegetated areas than for bare ground. However, quantitative data on the dependence of infiltration capacity on plant biomass is very limited. In this paper, we use a simple reaction-diffusion-advection model to investigate the effects of varying the strength of this dependence. We begin by studying the formation of banded vegetation patterns on gentle slopes ("tiger bush"), which is a hallmark of semi-deserts. We calculate the range of rainfall parameter values over which such patterns occur, using numerical continuation methods. We then consider interfaces between vegetation and bare ground, showing that the vegetated region either expands or contracts depending on whether the rainfall parameter is above or below a critical value. We conclude by discussing the mathematical questions raised by our work.
Citation: Jonathan A. Sherratt, Alexios D. Synodinos. Vegetation patterns and desertification waves in semi-arid environments: Mathematical models based on local facilitation in plants. Discrete & Continuous Dynamical Systems - B, 2012, 17 (8) : 2815-2827. doi: 10.3934/dcdsb.2012.17.2815
##### References:
show all references
##### References:
[1] R.A. Satnoianu, Philip K. Maini, F.S. Garduno, J.P. Armitage. Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation. Discrete & Continuous Dynamical Systems - B, 2001, 1 (3) : 339-362. doi: 10.3934/dcdsb.2001.1.339 [2] Peter Rashkov. Remarks on pattern formation in a model for hair follicle spacing. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1555-1572. doi: 10.3934/dcdsb.2015.20.1555 [3] Rui Peng, Fengqi Yi. On spatiotemporal pattern formation in a diffusive bimolecular model. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 217-230. doi: 10.3934/dcdsb.2011.15.217 [4] Michal Fečkan, Vassilis Rothos. Bifurcations of periodics from homoclinics in singular O.D.E.: applications to discretizations of travelling waves of P.D.E.. Communications on Pure & Applied Analysis, 2002, 1 (4) : 475-483. doi: 10.3934/cpaa.2002.1.475 [5] John R. King, Judith Pérez-Velázquez, H.M. Byrne. Singular travelling waves in a model for tumour encapsulation. Discrete & Continuous Dynamical Systems, 2009, 25 (1) : 195-230. doi: 10.3934/dcds.2009.25.195 [6] Arnaud Ducrot, Michel Langlais, Pierre Magal. Multiple travelling waves for an $SI$-epidemic model. Networks & Heterogeneous Media, 2013, 8 (1) : 171-190. doi: 10.3934/nhm.2013.8.171 [7] Evan C. Haskell, Jonathan Bell. Pattern formation in a predator-mediated coexistence model with prey-taxis. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 2895-2921. doi: 10.3934/dcdsb.2020045 [8] Guanqi Liu, Yuwen Wang. Pattern formation of a coupled two-cell Schnakenberg model. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 1051-1062. doi: 10.3934/dcdss.2017056 [9] Qingyan Shi, Junping Shi, Yongli Song. Hopf bifurcation and pattern formation in a delayed diffusive logistic model with spatial heterogeneity. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 467-486. doi: 10.3934/dcdsb.2018182 [10] Hongfei Xu, Jinfeng Wang, Xuelian Xu. Dynamics and pattern formation in a cross-diffusion model with stage structure for predators. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021237 [11] Josephus Hulshof, Pascal Noble. Travelling waves for a combustion model coupled with hyperbolic radiation moment models. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 73-90. doi: 10.3934/dcdsb.2008.10.73 [12] V. Lanza, D. Ambrosi, L. Preziosi. Exogenous control of vascular network formation in vitro: a mathematical model. Networks & Heterogeneous Media, 2006, 1 (4) : 621-637. doi: 10.3934/nhm.2006.1.621 [13] Wonlyul Ko, Inkyung Ahn. Pattern formation of a diffusive eco-epidemiological model with predator-prey interaction. Communications on Pure & Applied Analysis, 2018, 17 (2) : 375-389. doi: 10.3934/cpaa.2018021 [14] Xiaoying Wang, Xingfu Zou. Pattern formation of a predator-prey model with the cost of anti-predator behaviors. Mathematical Biosciences & Engineering, 2018, 15 (3) : 775-805. doi: 10.3934/mbe.2018035 [15] Dmitry Treschev. Travelling waves in FPU lattices. Discrete & Continuous Dynamical Systems, 2004, 11 (4) : 867-880. doi: 10.3934/dcds.2004.11.867 [16] Isabelle Gallagher. A mathematical review of the analysis of the betaplane model and equatorial waves. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 461-480. doi: 10.3934/dcdss.2008.1.461 [17] Julien Barré, Pierre Degond, Diane Peurichard, Ewelina Zatorska. Modelling pattern formation through differential repulsion. Networks & Heterogeneous Media, 2020, 15 (3) : 307-352. doi: 10.3934/nhm.2020021 [18] Julien Cividini. Pattern formation in 2D traffic flows. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 395-409. doi: 10.3934/dcdss.2014.7.395 [19] Yuan Lou, Wei-Ming Ni, Shoji Yotsutani. Pattern formation in a cross-diffusion system. Discrete & Continuous Dynamical Systems, 2015, 35 (4) : 1589-1607. doi: 10.3934/dcds.2015.35.1589 [20] Tian Ma, Shouhong Wang. Dynamic transition and pattern formation for chemotactic systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2809-2835. doi: 10.3934/dcdsb.2014.19.2809
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# What is the intuitive relationship between SVD and PCA
Singular value decomposition (SVD) and principal component analysis (PCA) are two eigenvalue methods used to reduce a high-dimensional dataset into fewer dimensions while retaining important information. Articles online say that these methods are 'related' but never specify the exact relation.
What is the intuitive relationship between PCA and SVD? As PCA uses the SVD in its calculation, clearly there is some 'extra' analysis done. What does PCA 'pay attention' to differently than the SVD? What kinds of relationships do each method utilize more in their calculations? Is one method 'blind' to a certain type of data that the other is not?
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SVD and PCA and "total least-squares" (and several other names) are the same thing. It computes the orthogonal transform that decorrelates the variables and keeps the ones with the largest variance. There are two numerical approaches: one by SVD of the (centered) data matrix, and one by Eigen decomposition of this matrix "squared" (covariance). – Yves Daoust Jun 10 '14 at 8:21
Here is a link to a very similar thread on CrossValidated.SE: Relationship between SVD and PCA. How to use SVD to perform PCA? It covers similar grounds to J.M.'s answer (+1 by the way), but in somewhat more detail. – amoeba Jan 24 '15 at 23:28
@denis: how could they, they are the same method ? – Yves Daoust Aug 25 '15 at 14:50
No, I can't, sorry. – Yves Daoust Aug 26 '15 at 17:06
how-to-find-straight-line-minimizing-the-sum-of-squares-of-euclidean-distances-f on stats.stackexchange has some links on the relationship between orthogonal regression and PCA. – denis Aug 30 '15 at 12:44
(I assume for the purposes of this answer that the data has been preprocessed to have zero mean.)
Simply put, the PCA viewpoint requires that one compute the eigenvalues and eigenvectors of the covariance matrix, which is the product $\mathbf X\mathbf X^\top$, where $\mathbf X$ is the data matrix. Since the covariance matrix is symmetric, the matrix is diagonalizable, and the eigenvectors can be normalized such that they are orthonormal:
$\mathbf X\mathbf X^\top=\mathbf W\mathbf D\mathbf W^\top$
On the other hand, applying SVD to the data matrix $\mathbf X$ as follows:
$\mathbf X=\mathbf U\mathbf \Sigma\mathbf V^\top$
and attempting to construct the covariance matrix from this decomposition gives
\begin{align*} \mathbf X\mathbf X^\top&=(\mathbf U\mathbf \Sigma\mathbf V^\top)(\mathbf U\mathbf \Sigma\mathbf V^\top)^\top\\ \mathbf X\mathbf X^\top&=(\mathbf U\mathbf \Sigma\mathbf V^\top)(\mathbf V\mathbf \Sigma\mathbf U^\top) \end{align*}
and since $\mathbf V$ is an orthogonal matrix ($\mathbf V^\top \mathbf V=\mathbf I$),
$\mathbf X\mathbf X^\top=\mathbf U\mathbf \Sigma^2 \mathbf U^\top$
and the correspondence is easily seen (the square roots of the eigenvalues of $\mathbf X\mathbf X^\top$ are the singular values of $\mathbf X$, etc.)
In fact, using the SVD to perform PCA makes much better sense numerically than forming the covariance matrix to begin with, since the formation of $\mathbf X\mathbf X^\top$ can cause loss of precision. This is detailed in books on numerical linear algebra, but I'll leave you with an example of a matrix that can be stable SVD'd, but forming $\mathbf X\mathbf X^\top$ can be disastrous, the Läuchli matrix:
$\begin{pmatrix}1&1&1\\ \epsilon&0&0\\0&\epsilon&0\\0&0&\epsilon\end{pmatrix}^\top$
where $\epsilon$ is a tiny number.
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To give a Mathematica example: A=SparseArray[{{i_, 1} -> 1, {i_, j_} /; i + 1 == j :> $MachineEpsilon}, {3, 4}]; and then compare Sqrt[Eigenvalues[a.Transpose[a]]] and SingularValueList[a,Tolerance->0]. – J. M. Sep 2 '10 at 14:13 If$X$is the data matrix, isn't the covariance matrix defined by$E[XX^T] - E[X]E[X]^T$, not$XX^T$? And so PCA is equivalent to SVD on the mean centered data matrix. – JasonMond May 3 '11 at 21:26 @Jason: Ah yes, I was assuming that the data was already "zero mean" for the purposes of this answer. I'll edit in your note later. – J. M. May 4 '11 at 0:21 I'm not sure about this, but I think the covariance matrix of an$n \times m$data matrix (with$n$samples each of size$m$) is$(X X^T) / (n - 1)$, so your example only works if the data matrix is standardized to have unit variance along each column. Somebody please correct me if I'm wrong. – Jeff Terrell Ph.D. Jan 29 '13 at 21:54 This was a little confusing in that normally the data matrix has n rows of samples of data with d dimensions along columns, like a least squares design matrix. If that is true then the covariance is$X^TX$, and the SVD result is$V\Sigma V^T\$. I was also confused by the lack of normalization initially. But altogether a pretty clear explanation. – Robotbugs Mar 3 '15 at 22:43
A tutorial on Principal Component Analysis by Jonathon Shlens is a good tutorial on PCA and its relation to SVD. Specifically, section VI: A More General Solution Using SVD.
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The question boils down to whether you what to subtract the means and divide by standard deviation first. The same question arises in the context of linear and logistic regression. So I'll reason by analogy.
In many problems our features are positive values such as counts of words or pixel intensities. Typically a higher count or a higher pixel intensity means that a feature is more useful for classification/regression. If you subtract the means then you are forcing features with original value of zero to have a negative value which is high in magnitude. This entails that you make the features values that are non-important to the problem of classification (previously zero valued) as influential as the most important features values (the ones that have high counts or pixel intensities).
The same reasoning holds for PCA. If your features are least sensitive (informative) towards the mean of the distribution, then it makes sense to subtract the mean. If the features are most sensitive towards the high values, then subtracting the mean does not make sense.
SVD does not subtract the means but often as a first step projects the data on the mean of all data points. In this way the SVD first takes care of global structure.
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I think this answer may be a bit misleading. The fact that zero value numbers will be mapped to negative numbers of large magnitude after subtracting means doesn't mean that their influence on a statistical model is increased. Deviation from the mean is the information used by many (perhaps most?) statistical models to fit curves, sort items, etc. If you are concerned about a feature with a long distribution tail (e.g. counts), then there are ways of transforming that data (e.g. add 1 and take the log) so it plays nice with models based on symmetric distributions. – turtlemonvh Jan 27 at 4:50
There is a way to do an SVD on a sparse matrix that treats missing features as missing (using gradient search). I don't know any way to do PCA on a sparse matrix except by treating missing features as zero.
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# A semi–automatic procedure for abundance determination of A– and F–type stars
@article{Hekker2009ASP,
title={A semi–automatic procedure for abundance determination of A– and F–type stars},
author={Saskia Hekker and Yves Fr{\'e}mat and Patricia Lampens and Peter De Cat and Ewa Niemczura and Orlagh Creevey and Juan Zorec},
journal={Monthly Notices of the Royal Astronomical Society},
year={2009},
volume={396},
pages={1689-1698}
}
• S. Hekker, +4 authors J. Zorec
• Published 1 April 2009
• Physics
• Monthly Notices of the Royal Astronomical Society
A variety of physical processes leading to different types of pulsations and chemical compositions are observed between A- and F-type stars. To investigate the underlying mechanisms responsible for these processes in stars with similar locations in the Hertzsprung–Russell diagram, an accurate abundance determination is needed, among others. Here, we describe a semi-automatic procedure developed to determine chemical abundances of various elements ranging from helium to mercury for this type of… Expand
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Spectra disentangling applied to the Hyades binary θ2 Tauri AB: new orbit, orbital parallax and component properties
Aims. θ 2 Tau is a detached and single-lined interferometric-spectroscopic binary as well as the most massive binary system of the Hyades cluster. The system revolves in an eccentric orbit with aExpand
An Evaluation of the Membership Probability of 212 λ Boo Stars. I. A Catalogue
Abstract The literature on the λ Boo stars has grown to become somewhat heterogenous, as different authors have applied different criteria across the UV, optical, and infrared regions to determineExpand
#### References
SHOWING 1-10 OF 36 REFERENCES
Automated spectroscopic abundances of A and F-type stars using echelle spectrographs - I. Reduction of ELODIE spectra and method of abundance determination
• Physics
• 2002
This paper presents an automated method to determine detailed abundances for A and F-type stars. This method is applied on spectra taken with the ELODIE spectrograph. Since the standard reductionExpand
Chemical composition of A and F dwarfs members of the Hyades open cluster
• Physics
• 2008
Aims. Abundances of 15 chemical elements have been derived for 28 F and 16 A stars members of the Hyades open cluster in order to set constraints on self-consistent evolutionary models that includeExpand
A spectroscopic study of southern (candidate) gamma Doradus stars. II. Detailed abundance analysis and fundamental parameters
• Physics
• 2008
Context. The γ Doradus stars are a recent class of variable main sequence F-type stars located on the red edge of the Cepheid instability strip. They pulsate in gravity modes, and this makes themExpand
Automated spectroscopic abundances of A and F-type stars using echelle spectrographs - II. Abundances of 140 A-F stars from ELODIE and CORALIE
• Physics
• 2003
Using the method presented in Erspamer & North (2002, hereafter Paper I), detailed abundances of 140 stars are presented. The uncertainties characteristic of this method are presented and discussed.Expand
Effects of gravitational darkening on the determination of fundamental parameters in fast-rotating B-type stars
• Physics
• 2005
In this paper we develop a calculation code to account for the effects carried by fast rotation on the observed spectra of early-type stars. Stars are assumed to be in rigid rotation, and the grid ofExpand
Model atmospheres for G, F, A, B, and O stars
A grid of LTE model atmospheres is presented for effective temperatures ranging from 5500 to 50,000 K, for gravities from the main sequence down to the radiation pressure limit, for abundances solar,Expand
Fundamental parameters of Be stars located in the seismology fields of COROT
In preparation for the COROT space mission, we determined the fundamental parameters (spectral type, temperature, gravity, vsini) of the Be stars observable by COROT in its seismology fields (64 BeExpand
Abundance analysis of targets for the COROT/MONS asteroseismology missions. II. Abundance analysis of the COROT main targets
One of the goals of the ground-based support program for the and / satellite missions is to charac- terize suitable target stars for the part of the missions dedicated toExpand
Search for pulsation among suspected A-type binaries and the new multiperiodic δ Scuti star HD 217860 ,
We have explored a sample of suspected A-type binaries in a systematic way, both spectroscopically and photometrically. Due to their location in the H-R diagram, indications of pulsation and/orExpand
Abundance analysis of targets for the COROT/MONS asteroseismology missions - I. Semi-automatic abundance analysis of the $\gamma$ Dor star HD 49434
One of the goals of the ground-based support program for the COROT and MONS/Roemer satellite missions is to select and characterise suitable target stars for the part of the missions dedicated toExpand
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## Another Random Contest 1 P3 - Physics Olympics
View as PDF
Points: 7 (partial)
Time limit: 3.0s
Memory limit: 256M
Author:
Problem type
Andy is on his school's team for the UBC Physics Olympics. During the competition, however, he remembered that he only had a 60% in Physics class and didn't know how to solve any of the problems. Since he has other teammates, he is just going to AFK and let them do all the work for him.
There are problems in the contest. Andy realized that some of his teammates would deceive the rest of his team about the solution to each problem. Andy calculated how much each teammate would deceive the team for each problem, , where is the student number, and is the problem number. For each teammate, he can strategically annoy them on one problem to set their deception value to (note that he can choose not to annoy any teammate). For each problem, Andy can only annoy one teammate.
The deception value for a problem is the XOR sum of all the deception values of all his teammates. The total deception value for the contest is the sum of all the individual values of each problem.
Andy wishes to know the minimum overall deception value possible, so determine it for him.
#### Constraints
For all test cases:
#### Input Specification
The first line contains two integers and , the number of tasks and teammates.
The next lines each contain integers, with each row representing a student and each number in the row representing the deception value of that student in that problem.
#### Output Specification
Output the minimum deception value of the contest.
#### Sample Input
5 3
3 3 0 3 5
5 5 4 3 5
1 5 4 2 1
#### Sample Output
3
#### Sample Explanation
A way to minimize the deception value is to annoy teammate on the first problem, teammate on the second problem, and teammate on the fourth problem.
This results in a deception level of for the problems, meaning the total deception value is .
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Maribel Ali
2023-03-06
How to find the Limit of $\mathrm{ln}\left(n+1\right)-\mathrm{ln}\left(n\right)$ as n approaches infinity?
cerisewi2
Use $\mathrm{ln}a-\mathrm{ln}b=\mathrm{ln}\left(\frac{a}{b}\right)$ and continuity of ln.
$\underset{n\to 00}{lim}\left(\mathrm{ln}\left(n+1\right)-\mathrm{ln}\left(n\right)=\underset{n\to \infty }{lim}\mathrm{ln}\left(\frac{n+1}{n}\right)$
$=\mathrm{ln}\left(\underset{n\to \infty }{lim}\frac{n+1}{n}\right)$
$=\mathrm{ln}\left(1\right)=0$
Note that
$\underset{n\to \infty }{lim}\frac{n+1}{n}=\underset{n\to \infty }{lim}\frac{\overline{)n}\left(1+\frac{1}{n}\right)}{\overline{)n}\cdot 1}$
$=\frac{1+0}{1}=1$
Do you have a similar question?
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Chemistry by Skanda - 10
Chemistry Level 1
Calculate the volume occupied by $$\ce{1 mole}$$ of an unknown gas at a temperature of $$\ce{300 K}$$ and pressure of $$\ce{1 atm}$$
(Molar volume of the gas at Standard Temperature and Pressure $$(STP)$$ = $$22.4\text{ L}$$.
Note: The volume must be in terms of liters.
×
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# Time-Resolved Fluorescence Wiki
### Site Tools
howto:separation_of_2_species_with
# Separation of 2 Species with Different Lifetimes Using FLCS
## Summary
This tutorial shows step-by-step, how the FLCS analysis can be used to calculate separate autocorrelation curves for the two components of a mixture of ATTO655 and Cy5 based on their different lifetimes.
## Background Information
The two fluorophores ATTO655 (ATTO-Tec, Germany) and Cy5 (GE Healthcare) have almost identical spectral properties and are thus excited with the same wavelength (e.g. 635 nm) and detected at the same spectral range. As also their molecular weight is comparable, the diffusion constant is too similar to distinguish between both dyes in a mixture by means of standard FCS.
Nevertheless, the autocorrelation curves of both dyes differ in the microsecond range. ATTO655 shows practically no photophysical fluctuations. Therefore, FCS curves of ATTO655 can be fitted with the simplest 3D diffusion model, making it very suited for calibration. Cy5 on the contrary, exhibits a distinct bunching term on its FCS trace originating from photophysical processes, i.e. cis/trans isomerization.
The fluorescence lifetime of both dyes differ significantly (~1.8 ns for ATTO655 and ~1 ns for Cy5). In FLCS (Fluorescence Lifetime Correlation Spectroscopy), the lifetimes are used to create specific photon filters allowing to calculate FCS autocorrelation curves for each lifetime component. The aim of this script is to demonstrate, how two FCS traces are calculated from the same dataset, a nanomolar solution of a mixture of both components.
Since the dye separation is based on fluorescence lifetime measurements via TCSPC, this script can only be applied, if at least one fluorophore is excited with a pulsed laser.
## Step-by-Step Tutorial
### Select a file and start the script
• Start SymPhoTime 64 software.
• Open the “Samples” workspace via “File\open Workspace” from the main menu.
Note:
The “Samples” workspace is delivered with the SymPhoTime 64 and on the DVD-ROM and contains example data to show the function of the SymPhoTime 64 data analysis. If you haven't installed it on your computer, copy it from the DVD onto a local drive before going through this tutorial.
Response: The files of the sample workspace are displayed in the workspace panel on the left side of the main window.
• Highlight the file ATTO655+Cy5_diff_FCS+FLCS.ptu by a single mouse click.
• Select the “Analysis” tab and in there, open the drop down menu “FCS”.
Note:
The drop down menu can be opened and closed by clicking on the grey button on the left side of the header of the drop down menu:
• Start the FLCS script by clicking on “Start”.
Response: The FLCS script is applied to the file ATTO655+Cy5_diff_FCS+FLCS.ptu. Thereby, a new Window opens:
Note:
The window contains three different regions:
1. Left: Analysis and display options. For explanation of the different parameters, place the mouse cursor over this part of the window and press <F1> to open the corresponding help page.
2. Upper center/right: Intensity time trace. The display can be changed using the “trace display settings” of the analysis options. The large window shows the inset of the complete trace above highlighted in green. The photon counting histogram on the right displays the frequencies of the different intensity values. Usually, this trace is used to check, whether the signal is stable during the measurement. Also, large intensity spikes originating from aggregation of the fluorescent sample can be detected in this graph.
3. Lower center/right: FCS trace window. As first the FCS correlation criteria have to be defined and the curve needs to be calculated, this graph does not contain any trace at this stage.
• In this file, the light was evenly splitted onto two detectors. Therefore, select both detectors in the definition of “Channel A”:
• Before calculating the FLCS trace, the FLCS filters for the individual components must be defined. The software offers two ways to define these filters:
• If the different dyes have been measured separately, and TCPSC curves of the two components are available, it is possible to load these TCSPC histograms as patterns for the filter definition. This is called “Pattern Matching” approach.
• If the individual TCSPC histograms are not available, or a dye is analyzed that changes its fluorescence lifetime under certain conditions, a lifetime fit can be performed of the TCPSC histogram of the measurement. The FLCS filters can be calculated from the fitted lifetime components. This approach called “LT (lifetime) fitting” can only be employed, if the two components that should be separated have a practically single exponential decay behavior.
Note:
As a prerequisite for both approaches the lifetime patterns of the two components must be sufficiently different. The next steps demonstrate both ways to define the FLCS filters. In practice, apply the better suited option according to the sample.
### Definition of the FLCS Filters via Pattern matching (Option 1)
• In the “FLCS” drop down menu, click on “Create Filters\Pattern Matching”.
Response: The FLCS pattern matching windows pops up.
Note:
This window consists of different sections:
1. Left: Controls for importing and fitting the patterns. Click on the “Help” button to learn about the meaning of the different parameters.
2. Upper center: TCSPC histogram of the imported patterns. As we haven't loaded any pattern yet, this graph doesn't contain any data.
3. Upper right: TCPSC curve of the measured data.
Lower center/right: FLCS filter curve. As no filter has been calculated yet, this graph is still empty.
• Click: “Import”.
Response: Another window pops up containing the measurement files from the workspace.
• Select the file Cy5_diff_IRF+FLCS-pattern.ptu and click “OK”.
Response:
• The TCSPC histogram for this file appears in the “Patterns” graph in the upper center.
• A few parameters are added in the parameter display on the left.
• Click “Import” again to load the pattern for the second dye.
Response: A new window pops up containing the measurement files from the workspace.
• This time, select the file ATTO655_diff_FLCS-pattern.ptu and press “OK”.
Response:
• The TCSPC histogram for this file is added to the “Patterns” graph in the upper center. This window contains now the TCSPC curves of both dyes.
• A few parameters are added in the parameter display on the left.
• Press “Initial FIT” to fit these patterns to the decay of the FCS measurement.
Response:
• The two patterns are fitted into the decay and appear in the graph on the upper right, as well as a fitting curve. The residuals of this graph are evenly spread around 0, indicating that the decay is well described as a sum of both patterns.
• Fitting values are added to the Fitting table. The χ² value close to 1 indicates that no further pattern is needed to fit the data.
• Three FLCS filters are generated, which are named after the two files containing the loaded TCPSC patterns. The third pattern is the background. Note that for the pattern fit, the background in the TCSPC curves of the individual components is subtracted.
• As now the patterns are successfully calculated, click “OK”.
Response:
• The pattern definition window is closed.
• The FLCS filter functions are displayed in the graph on the left in the FLCS script main window. As the Cy5 pattern was loaded first, this pattern is active.
• Press “Calculate”.
Response:
• The FLCS curve for this filter function is calculated. As the filter function is calculated from the Cy5 pattern, it practically contains the autocorrelation of only the Cy5 dye. The photophysical component (cis/trans isomerization) at short correlation times is clearly visible.
• Save this curve by clicking “SaveResult”.
Response:
• The result file is stored as FLCS.pqres. In order to remember its contents, we rename it: Cy5-FLCS.pqres. Files can be renamed by clicking slowly twice onto the file name and typing in the new name.
• Now the FLCS autocorrelation curve for the second dye, ATTO655, must be calculated. Therefore, select this pattern in the FLCS main window and press “Calculate”.
Response:
• The FLCS curve for this filter function is calculated. As the filter function is calculated from the ATTO655 pattern, it practically contains the autocorrelation of only the ATTO655 dye. The photophysical component at short correlation times which was pronounced in the Cy5 correlation is now missing.
• Click on “Save result” to save this curve. Rename the generated file as ATTO655-FLCS.
• These curves can now be fitted by selecting “Transfer to fit”. The process of how to fit a FCS curve is explained in the tutorial Calculate and Fit FCS Traces with the FCS Script.
### Definition of the FLCS Filters via Lifetime Fitting (Option 2)
• In the “FLCS” drop down menu, click on “Create Filters\LT-FItting”.
Response: The TCSPC fitting window pops up.
Note:
This window contains different sections:
1. Left: Controls for fitting the TCSPC curve and the filters. Click on the “Help” button to learn about the meaning of the different parameters.
2. Upper center/right: TCPSC curve of the measured data.
3. Lower center/right: FLCS filter curve. As no filter has been calculated yet, this graph is still empty.
• To avoid wasting photons, select the “n-Exponenial Reconvolution” Fitting Model.
• As the sample contains two dyes, select 2 exponential components.
• Click “Initial Fit” (marked in orange).
Response: The TCSPC curve is fitted. A χ² close to 1 and nicely spread residual indicate a sufficiently good fit.
• Click “Create FLCS Filters”.
Response:
• Three FLCS filter curves are calculated and displayed in the lower graph. These filter curves correspond to the lifetime component of ~0.8 ns (Cy5), the lifetime component of ~1.8 ns (ATTO655) and the background, mainly caused by dark counts and detector afterpulsing.
• As now the patterns are successfully calculated, click “OK”.
Response:
• The pattern definition window is closed.
• The FLCS filter functions are displayed in the graph on the left in the FLCS script main window. As the ~1.8 ns component was assigned to lifetime 1, this pattern is active.
• Click “Initial Fit” (marked in orange).
Response:
• The FLCS curve for this filter function is calculated. As the filter function is calculated from the ~1.8 s (pattern of ATTO655), it practically contains the autocorrelation of only the ATTO655 dye. The curve only shows diffusion and no further bunching term as for Cy5.
• Save this curve by clicking “SaveResult”.
Response:
• The result file is stored as FLCS.pqres. In order to remember its contents, rename it as ATTO655-FLCS.pqres. Files can be renamed by clicking slowly twice onto the file name and typing in the new name.
• Now the FLCS autocorrelation curve for the second dye (Cy5) must be calculated. Therefore, select this pattern (corresponding to ~0.8 ns) in the FLCS main window and press “Calculate”.
Response:
• The FLCS curve for this filter function is calculated. As the filter function is calculated from the Cy5 pattern, it practically contains the autocorrelation of only the Cy5 dye. The photophysical component at short correlation times is now clearly visible.
• Click on “Save result” to save this curve. Rename the generated file as “Cy5-FLCS”.
• These curves can now be fitted by selecting “Transfer to fit”. The process of how to fit a FCS curve is explained in the tutorial Calculate and Fit FCS Traces with the FCS Script.
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# Math Help - [SOLVED] trig question
1. ## [SOLVED] trig question
so had my AS core 1 exam today - dont think i did very well, bugger. anyway the question is...
You are given that $tanA=\frac{1}{2}$ and the angle A is acute. show without using a calculator that $cos^2A=\frac{4}{5}$
ta
2. ## Re :
Originally Posted by coyoteflare
so had my AS core 1 exam today - dont think i did very well, bugger. anyway the question is...
You are given that $tanA=\frac{1}{2}$ and the angle A is acute. show without using a calculator that $cos^2A=\frac{4}{5}$
ta
Note that tan A is in the first quadrant . Draw a triangle ..
From there you will be able to find that $cos A = \frac{2}{\sqrt 5}$
Squarring it , you should get the results ...
3. ## sorry to be...
....stupid but i dont understand this as of yet and require it to be explained more if at al possible, the book is just confusing me!
ta
4. ## Re :
Originally Posted by coyoteflare
....stupid but i dont understand this as of yet and require it to be explained more if at al possible, the book is just confusing me!
ta
Alright , it is ok . Firstly , do u know that when you are given the value of a trigo function , ie
$tanA=\frac{1}{2}$
you can draw a triangle and find cos A and sin A as well ?
If u do , well , the question tells us that A is an acute ( smaller than 90 ) , so we know that tan A is in the first quadrant and everything is positive here .
Note that $(cos A)^2=cos^2A$
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# In A ‘Luvvy’ Recovery, Digital Hits 28 Percent Of WPP Sales
Earlier this year, the world’s biggest advertising group said new media would make up two thirds of its income in three or four years.
Today it stands at 28 percent, WPP said, as it reported first-half-of-year pre-tax profit up 36 percent to £244 ($379.46) million, on three percent better revenue of £4.44 ($6.91) billion.
CEO Sir Martin Sorrell, over the last year, has cautiously refrained from embracing a 2010/11 upturn away from the recession.
But the latest WPP earnings statement does dare to say: “The results reflect the recovery in the world economy … “The group
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# How to specify a Diff-In-Diff Regression with multiple time periods?
I'm working on analysing experimental data for a thesis project. The data consists of subjects performing the same task over five rounds, and I'm interested in the difference in trends between subjects in two different treatments. The two treatments are identical until round 3.
I planned on using a diff-in-diff model to estimate the difference of Effort levels of subjects across these treatments. The problem is, I have five rounds, two of which are before-treatment and three of which are after-treatment. Currently, I'm using this specification, but I'm not sure if it's correct:
$$Effort_{it}=\beta _{0} + \beta_{1}Treatment_{i}+\sum_{n=2}^{5}\beta _{n}Roundn_t+\beta_6Treatment*After_{it}$$
Where treatment is a dummy for being in the treatment groub, Roundn is a dummy for being in Round N, and Treatment*After is an interaction dummy for being in the treatment group after round 2 (when the treatment "begins").
I'm confused mostly on what to do with the different time periods. Would it be best to use dummies for each round like above, or to just include a Round variable that is equal to the number of the round. Also should I just include one interaction term, or one for each round?
I am a bit confused because you said there are two treatments. I presume that one "treatment" group is the control group and the other is the treatment group. (I don't think you have a separate control group.) I am also confused because you said the treatment is identical until round 3 but then the treatment begins in round 2. I presume that there is no treatment in rounds 1 and 2, and the treatment group is treated differently thereafter in rounds 3, 4 and 5.
Your $Roundn$ dummy variables for $n=2,\ldots 5$ make sure that you handle the "round effects" (for the control group) properly in a nonparametric way. This looks fine to me. If you include only the $After$ dummy, it means that there is no trend within each of the "before" and "after" periods. You would not want that.
A single $round$ variable means that there is a linear trend in $Effort$ in the control group. You could try that, but I would wonder where the linearity belief comes from. Also, you lose only 3 more degrees of freedom by including the round dummies comparing to the linear trend model. That's not a big deal unless you have a really small sample. I would be happy with the full round dummies.
Your model assumes that the treatment effects (measured by diff-in-diff) are identical in all rounds 3, 4 and 5 (because you have only one interaction term). If you believe it is true, that's fine. If you believe otherwise, you can include three interaction terms $Treatment * Round3$, $Treatment * Round4$ and $Treatment * Round5$ instead of the single interaction term. If you want, you can test if those treatment effects are identical across rounds.
• Thanks for the help! Sorry for the wording issues, but you did interpret what I was saying correctly. One thing I have read was to specify it using fixed effects for each round, and then interaction terms for all rounds but one. Doing this, I wouldn't have to include the Treatment dummy correct? I think having interaction terms for each round would eliminate the need for that. – econra2017 Nov 13 '16 at 21:34
• Yes. Fixed effects for each round contain Treatment dummy, so you need not include the treatment dummy separately. But if you include interaction terms for all rounds, it means that there is a nonzero "treatment effect" in Period 2 as well, while there was no "treatment" in that period. – chan1142 Nov 15 '16 at 14:01
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Home / Arithmetic Aptitude / Problems on Ages :: Discussion
### Discussion :: Problems on Ages
1. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
2. A. 2 times B. 2$$\frac { 1 } { 2 }$$times C. 2$$\frac { 3} { 4 }$$times D. 3 times
Explanation :
Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) =$$\frac {5 } { 2 }$$(x + 8)
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio =$$\frac { (4X+16 )} { (X+16 )}=$$$$\frac { 48 } { 24 }$$=2
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# DTIME
DTIME
In computational complexity theory, DTIME (or TIME) is the computational resource of computation time for a deterministic Turing machine. It represents the amount of time (or number of computation steps) that a "normal" physical computer would take to solve a certain computational problem using a certain algorithm. It is one of the most well-studied complexity resources, because it corresponds so closely to an important real-world resource (the amount of time it takes a computer to solve a problem).
The resource DTIME is used to define complexity classes, sets of all of the decision problems which can be solved using a certain amount of computation time. If a problem of input size n can require f(n) computation time to solve, we have a complexity class DTIME(f(n)) (or TIME(f(n))). There is no restriction on the amount of memory space used, but there may be restrictions on some other complexity resources (like alternation).
## Complexity classes in DTIME
Many important complexity classes are defined in terms of DTIME, containing all of the problems that can be solved in a certain amount of deterministic time. Any proper complexity function can be used to define a complexity class, but only certain classes are useful to study. In general, we desire our complexity classes to be robust against changes in the computational model, and to be closed under composition of subroutines.
DTIME satisfies the time hierarchy theorem, meaning that asymptotically larger amounts of time always create strictly larger sets of problems.
The well-known complexity class P comprises all of the problems which can be solved in a polynomial amount of DTIME. It can be defined formally as:
$\mbox{P} = \bigcup_{k\in\mathbb{N}} \mbox{DTIME}(n^k)$
P is the smallest robust class which includes linear-time problems $\mbox{DTIME}\left(n\right)$ (AMS 2004, Lecture 2.2, pg. 20). P is one of the largest complexity classes considered "computationally feasible".
A much larger class using deterministic time is EXPTIME, which contains all of the problems solvable using a deterministic machine in exponential time. Formally, we have
$\mbox{EXPTIME} = \bigcup_{k \in \mathbb{N} } \mbox{ DTIME } \left( 2^{ n^k } \right) .$
Larger complexity classes can be defined similarly. Because of the time hierarchy theorem, these classes form a strict hierarchy; we know that $\mbox{P} \subsetneq \mbox{EXPTIME}$, and on up.
## Machine model
The exact machine model used to define DTIME can vary without affecting the power of the resource. Results in the literature often use multitape Turing machines, particularly when discussing very small time classes. In particular, a multitape deterministic Turing machine can never provide more than a quadratic time speedup over a singletape machine (Papadimitriou 1994, Thrm. 2.1).
Multiplicative constants in the amount of time used do not change the power of DTIME classes; a constant multiplicative speedup can always be obtained by increasing the number of states in the finite state control. In the statement of Papadimitriou (1994, Thrm. 2.2), for a language L,
Let L $\in$ DTIME(f(n)). Then, for any $\epsilon$ > 0, L $\in$ DTIME(f'(n)), where f'(n) = $\epsilon$ f(n) + n + 2.
## Generalizations
Using a model other than a deterministic Turing machine, there are various generalizations and restrictions of DTIME. For example, if we use a nondeterministic Turing machine, we have the resource NTIME. The relationship between the expressive powers of DTIME and other computational resources are very poorly understood. One of the few known results[1] is
$\mathsf{DTIME}(O(n)) \neq \mathsf{NTIME}(O(n))$
for multitape machines. If we use an alternating Turing machine, we have the resource ATIME.
## References
1. ^ Paul Wolfgang, Nick Pippenger, Endre Szemeredi, William Trotter. On determinism versus non-determinism and related problems. doi: 10.1109/SFCS.1983.39
Wikimedia Foundation. 2010.
### См. также в других словарях:
• DTIME — In der Komplexitätstheorie steht DTIME(f) oder auch kurz TIME(f) für die Menge der Zeitkomplexitätsklassen in Bezug auf eine deterministische Turingmaschine. Wird eine konkrete Funktion f angegeben, so bedeutet dies: DTIME(f) ist die Klasse… … Deutsch Wikipedia
• DTIME — En teoría de la complejidad computacional, la clase de complejidad DTIME(f(n)) (también llamada TIME(f(n))) es el conjunto de los problemas de decisión que pueden ser resueltos en una máquina de Turing determinista en tiempo O(f(n)), y espacio… … Wikipedia Español
• DTIME — En teoría de la complejidad computacional, la clase de complejidad DTIME(f(n)) (también llamada TIME(f(n))) es el conjunto de los problemas de decisión que pueden ser resueltos en una máquina de Turing determinista en tiempo O(f(n)), y espacio… … Enciclopedia Universal
• Time hierarchy theorem — In computational complexity theory, the time hierarchy theorems are important statements about time bounded computation on Turing machines. Informally, these theorems say that given more time, a Turing machine can solve more problems. For example … Wikipedia
• Teorema de la jerarquía temporal — En la teoría de complejidad computacional, los teoremas de jerarquía temporal son declaraciones importantes sobre cómputo de tiempo acotado en máquinas de Turing. Informalmente, estos teoremas dicen que con más tiempo, una máquina de Turing puede … Wikipedia Español
• Computational complexity theory — is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. In this context, a… … Wikipedia
• Time complexity — In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O… … Wikipedia
• Complexity class — In computational complexity theory, a complexity class is a set of problems of related resource based complexity. A typical complexity class has a definition of the form: the set of problems that can be solved by an abstract machine M using… … Wikipedia
• Liste von Komplexitätsklassen — Dies ist eine Liste von Komplexitätsklassen, die in der Komplexitätstheorie betrachtet werden. Die Klassen verwenden in ihren Definitionen verschiedene Maschinenmodelle. Die wichtigsten Modelle sind Turingmaschinen; diese können deterministisch,… … Deutsch Wikipedia
• Lückensatz von Borodin — Der Lückensatz von Borodin ist ein 1972 von Allan Borodin veröffentlichter Satz der Komplexitätstheorie in der theoretischen Informatik. Er besagt, dass es in der Hierarchie von Komplexitätsklassen beliebig große Lücken gibt. Formal: Für totale,… … Deutsch Wikipedia
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# Definite Integration
Printable View
• Jul 24th 2007, 08:53 AM
dekar
Definite Integration
Hi,
Could somebody please help me in getting a closed form expression for integrating the following expression:
(1+(x^m))^n
limits of integration are from 0 to 1. Integration is to be done with respect to x and m and n are positive real numbers.
Is it to do with the incomplete beta function, but the upper limit is coming out to be -1, which should lie in the interval 0 to 1.
Thanks in anticipation.
Dekar
• Jul 24th 2007, 09:15 AM
galactus
It appears to be hypergeometric. I ran it through Maple and it gave me.
$\int{(1+x^{m})^{n}}dx=xhypergeom\left([\frac{1}{m},-n],[1+\frac{1}{m}],-x^{m}\right)$.
• Jul 24th 2007, 09:19 AM
dekar
Thanks Galactus,
Can you please help me in getting the expansion of this function?
Thanks
Dekar
• Jul 24th 2007, 09:41 AM
topsquark
Quote:
Originally Posted by dekar
Thanks Galactus,
Can you please help me in getting the expansion of this function?
Thanks
Dekar
See here.
-Dan
• Jul 24th 2007, 09:41 AM
ThePerfectHacker
Quote:
Originally Posted by dekar
Hi,
Could somebody please help me in getting a closed form expression for integrating the following expression:
(1+(x^m))^n
limits of integration are from 0 to 1. Integration is to be done with respect to x and m and n are positive real numbers.
I think the following works for $n,m>0$.
$\int_0^1 (1+x^m)^n dx$
Let $t=x^m \implies t' = mx^{m-1}$
Thus,
$\frac{1}{m}\int_0^1 (1+t)^n t^{-1 +\frac{1}{m}}dt= \frac{1}{m}\mbox{B}\left( n+1, \frac{1}{m} \right)$
• Jul 24th 2007, 09:57 AM
dekar
Hi,
It won't work because it is (1+t), to have it to get reduced to the beta function we need (1-t),
Thats why I guess, It may go to Incomplete Beta Function if we substitute say p=-t at this stage, but the upper limit then becomes -1.
Dekar
• Jul 24th 2007, 10:00 AM
ThePerfectHacker
Quote:
Originally Posted by dekar
Hi,
It won't work because it is (1+t), to have it to get reduced to the beta function we need (1-t),
Thats why I guess, It may go to Incomplete Beta Function if we substitute say p=-t at this stage, but the upper limit then becomes -1.
Dekar
Yes, I made a mistake.
You can see more here.
• Jul 24th 2007, 10:06 AM
dekar
So isn't there a better (a less messy) way to arrive at the closed form solution other than that hypergeometric?
I need it a program friendly way to code this.
Any help is highly appriciated.
Thanks
Dekar
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# Var..Do
Release: 4.6 • 5.0 • 5.1 • 5.2 • 5.3 • 5.4 • 6.0 • 6.1 • 6.2 • 6.3
The Var is now deprecated. We recommend you use Local..Do instead.
## Local x := expr Do body
Declares a local value with identifier «x», so that the identifier «x» refers to the value obtained by evaluating «expr». The identifier «x» can then be referred to within the «body» expression. The expression «body» is said to be the lexical context of «x», since outside of the lexical context, the identifier «x» is not recognized.
Local q:=F(a,I) Do q / Sum(q,I);
q+1 { error -- q is no longer in lexical context }
Local is often used in a procedural syntax, where the declaration is followed by a semi-colon and the Do keyword is omitted, such as:
Local x := Sum(A, I);
Local y := Sum(B, I);
(x + y) * (x - y)
With this syntax, the lexical context for «x» extends from the expression immediately following the semi-colon to the end of the sub-expression that the Var..Do declaration is embedded in. For example, in the following expression the lexical scope of a is shown in green.
1 + (Local a := b^2; Local c := a/b; c^2 - a - c - 2) + 5
You can declare multiple local identifiers on the same line by separating them with commas. All have the same lexical scope.
Local a:=J, b, c, d:=2;
When the :=«expr» is omitted, the local is initialized to Null. So in the preceding example, b and c are set to Null.
When a function has multiple return values, you can capture these into separate locals by placing the local names in parentheses. For example, the function SingularValueDecomp returns 3 matrix values.
Local (u, w, v) := SingularValueDecomp(a, I, J, J2);
## Dimensionality Declaration
The allowed dimensions of a local value can be declared using the syntax:
Local «x»[«indexList»] := «expr» Do «body»
an equivalent anachronism (considered deprecated) is
Local «x» := «expr» in each «indexList» Do «body»
There are some situations where the extra information about which indexes are allowed is required in order to ensure that the «body» expression will array abstract correctly when new dimensions are added to a model later.
When the allowed indexes are declared, Analytica will ensure that when «body» is evaluated, the value of «x» will not have any indexes not listed in «indexList». If the original value assigned to «x» has indexes beyond those found in «indexList», Analytica will automatically iterate, evaluating «body» multiple times one slice at a time.
Note: You should not make any assumptions about the order of the iteration, or an assumption that every index value will actually be visited. Our spec for Local allows the leeway for the expression compiler to re-order iteration order, to skip cases that it can prove will not impact the final result, or even to evaluate multiple cases concurrently. Speed optimizations like these have no detectable effect on your result except in the case where «body» has side-effects. Side-effects may include user-interactions (like MsgBox), writing/logging to files, or assignment. In contrast, the For..Do declaration also iterates while also guaranteeing sequential ordered and complete visitation of all cases. Because a Local declaration allows the expression compiler extra leeway to apply speed optimizations, Local..Do declarations are usually preferred to For..Do since they are declarative and faster, unless, of course, you rely upon procedural programming style side-effects within «body». You may find it conceptually convenient to imagine Local..Do iterating over each non-allowed index combination, which is logically equivalent to what actually happens as long as you have no assignments or other side-effects within the «body».
If the result of «expr» does not already have all the indexes declared in «indexList», the missing indexes are NOT added to «x».
#### Example
The following computes the standard deviation across only the time periods that are profitable:
Local earnings[Time] := revenue-expenses;
LocalIndex profitTimes := Subset(earnings > 0);
SDeviation(earnings[Time = profitTimes], profitTimes)
Without the dimensional declaration restricting earnings to the Time index, Subset would complain that earnings has more than dimension in the event that revenue-expenses has an index in addition to Time. The dimensional declaration here allows the expression to fully array abstract if new dimensions are added to the model.
The above expression is meant to be illustrative, but for completeness we also note an alternative expression for the same computation that does not require iteration:
Local earnings := revenue - expenses Do SDeviation(earnings, Time, w: earnings > 0)
### Atomic Declarations
A special case of the dimensional declaration is the declaration that a local value must be atomic -- i.e., a single non-array value. In this case, the we simply specify a zero-length list of allowed indexes:
Local «x»[] := «expr» Do «body»
Then inside «body», «x» is guaranteed to be atomic.
#### Example
The following computes the log-factorial of a number in an array-abstractable fashion (i.e., works even if n is originally an array:
Local n[] := n do Sum(Ln(1..n))
Note: The local value can have the same identifier as a global variable, and the value of the global can appear within «expr» since that is outside the local identifier's lexical scope. Inside «body», the identifier always refers to the local value. Having two local values with the same identifier is not allowed.
### Atomic..Do syntax
Analytica also recognizes the following syntax for declaring a local value as atomic:
Atomic «x» := «expr» Do «body»
This syntax is equivalent to Local «x»[] := «expr» Do «body»
## Explicit Iteration
The following syntax:
Local «x» := «expr» In «I» Do «body»
evaluates «expr», then iterates over each element of index «I», setting «x» to the «expr»[«I» = i] slice while «body» is evaluated. In a sense, this is a dual to the dimension declaration -- here we are specifying the dimensions that are not allowed in «x», while the Local «x»[«I»] := ... syntax specifies the dimensions that are allowed. However, in this syntax, only a single index can be specified.
This dual style iteration is very rarely used.
## Assignment
Although side-effects are generally prohibited from within Analytica expressions (due to dependency-maintenance and Analytica's adherence to the principle of referential transparency), you can change the value of a local value using the assignment operator, :=. For example:
Local n := 27;
Local steps := 0;
While (n > 2) Do (
steps := steps + 1;
n := If Mod(n, 2) Then n/2 Else 3*n + 1
);
steps
Assignment always resets the value of «x», even if «x» contains a handle. In other words, when you assign to a local value, you are resetting the value that the local identifier refers to, as opposed to changing the value of the object pointed to by the local value. See more in the section below on Meta-Inference.
### Slice assignment
You can also assign to individual slices of a local value. This is described in detail at Slice assignment.
## Evaluation Mode
A local value refers to a value, not an object. Hence, the terminology "local value" (or just "local") should be used and it should not be called a "local variable". A local value is not a variable -- a variable in an object that has attributes, has a separate mid-value and sample-value, and usually appears on an influence diagram. A local value has no attributes, does not appear in the global namespace, and does not maintain a separate Mid- and Sample-value.
When the local value is declared, «expr» is evaluated in the current Evaluation mode. From that point on, «x» becomes an alias for the value that resulted from that evaluation, whether or not the identifier «x» appears in Mid- or Sample- context. This can be a source of confusion. Consider the following example:
Local u := Uniform(0, 1);
SDeviation(u)
When this expression is evaluated in Mid mode it is not equivalent to SDeviation(Uniform(0, 1)). The later evaluates to 0.29, while the former results in 0. This is because u is assigned Mid(Uniform(0,1)), which is 0.5, and then the result is SDeviation(0.5), which is zero.
You can, of course, call Sample() or Mid() explicitly from «expr» when desired, e.g.:
Local u := Sample(Uniform(0, 1));
SDeviation(u)
This confusion can be avoided by adhering to and conceptualizing the terminology that «u» is a local value, not a local variable.
## Meta-Inference and the use of handles
Most models built in Analytica make no use of handles, and so the considerations described here impact only the most advanced modelers. Inference involving handles provides a mechanism for meta-Inference -- that is, reasoning about or altering your model from within Analytica itself. Advanced uses of meta-Inference can be used to extend Analytica's capabilities in many ways, creating functionality in your model beyond what is offered directly by the Analytica interface.
A handle is essentially a pointer to an Analytica object, such as a Variable, Index, or Module object. Meta-inference implementations usually need to store handles inside local values, assign handles to local values, read information about the objects pointed to by these handles, and manipulate the objects pointed to by these handles.
When implementing meta-inference algorithms, you should never use Var..Do to declare locals, but instead should use Local or LocalAlias..Do. The older Var..Do syntax suffers from several inconsistencies with how handles are treated, which is why is new deprecated (as of Analytica 5.0).
• LocalAlias «x» := «expr» Do «body»
or equivalently, Alias «x» := «expr» Do «body»
• Local «h»[«indexList»] := «expr» Do «body»
When LocalAlias..Do is used to assign a handle to «x», then «x» is treated everywhere as an alias of the object pointed to. If you were to copy the expression and substitute the object's identifier everywhere «x» appears (assuming the object is in the global namespace), you would get the identical result. Once the local «x» is assigned a handle, you can no longer change the handle (i.e., change which object is pointed to), since an assignment, «x» := z, would be interpreted as an assignment to the object pointed to, rather than changing what «x» refers to. You cannot declare dimensions in a LocalAlias..Do or Alias..Do declaration.
When a handle is assigned to a local value declared as Local, then the local identifier refers to an atomic value that has a data type of "handle". Operations such as «h»+1 do not make sense, since this would be attempting to add 1 to a handle value, rather than adding 1 to value of the variable pointed to by the handle. Your local value may contain a handle, or an array of handles, as well as other data types.
When a handle is assigned to a local «x» declared using Var..Do, it acts as a hybrid between a LocalAlias and a Local, which is confusing, so that we recommend that you do not use Var..Do with values containing handles. In a value context, «x» acts as an alias to the object. However, in an assignment context (an L-value context), it a acts like a local value, in which the local «x» changes to refer to the new value, rather than causing the object pointed to by «x» to be changed. Consider:
Var x := Handle(A);
x := x + 1
Here x is first assigned a handle to A. In the assignment operation, when the right-hand side of the assignment is evaluated, x + 1 refers to the value of A plus 1. Hence x acts as an alias to A. The assignment changes what the value the local identifier refers to, but does not alter A. After the assignment, the local x contains a numeric value (or perhaps array of numeric values) and no longer points to the variable A.
Suppose in the above example that A evaluates to a self-indexed array. The right-hand side of the assignment is a value context, so in this case, x refers to the array-value of A. If we wanted x to alias the index value of A, rather than the array value, we could use the following instead:
Var x := Handle(A, asIndex: true);
x := x + 1
When you assign a handle to a local identifier that has been declared using Local, the value itself has a data type of Handle. This can be contrasted with locals declared using LocalAlias, for which the identifier is the identifier of the object. Consider this example
Local h := Handle(Va1); h := 2 LocalAlias x := Handle(Va3); x = 3
After this code is evaluated, the object Va1 remains unchanged, the local h now has a value of 2 instead of a handle, and the Definition of the global variable Va2 has been changed to 3. The local x still refers to the same variable as the global identifier Va3. The last line is only allowed in a context that allows side-effects to global variables, such as from a button script.
When you have a handle to an object in a Local, and you want to use it as if it were a global variable, you do this by using LocalAlias as illustrated here
Local h := Handle( I ); { The local with the handle to an object, in this case an index } LocalAlias J := h; Sum( a, J )
## History
There has been a long history of changes and enhancements to the Analytica language's syntax and treatment of local variables, which has lead to a proliferation of different constructs for declaring local variables, with subtle distinctions between them, and many of the distinctions really just required to support backward compatibility for models created in older releases of Analytica. Starting with Analytica 5.0, this complexity has been simplified, so that now there are only three ways you need to know for declaring locals:
Local v := ...; LocalAlias x := ...; LocalIndex I := ...
In addition, you may want to use For..Do in some occasions, which also introduces a local identifier.
The Local keyword was introduced in Analytica 5.0 as is equivalent to MetaVar..Do. MetaVar..Do was introduced (in release [fill in]) to correct inconsistencies in Var..Do. Var..Do still has those inconsistencies, which can make it confusing to use when writing code that involves handles, but it continued to be used extensively since MetaVar..Do had such an unnatural name. In Analytica 1.0, local variables were declared via a Using..Do construct, now considered very archaic and seldom seen.
Analytica 5.2 introduced several enhancements to local declarations. These include the ability to omit the «expr» value for a local (so that it defaults to Null, and to declare multiple identifiers in the same declaration, both of which are illustrated by
Local a, b, c;
It also introduced reduced dimensionality qualifier, and the ability to capture multiple return values.
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Czechoslovak Mathematical Journal, Vol. 67, No. 3, pp. 579-608, 2017
# On boundary value problems for systems of nonlinear generalized ordinary differential equations
## Malkhaz Ashordia
#### Received May 3, 2011. First published July 11, 2017.
Malkhaz Ashordia, A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 6 Tamarashvili St., Tbilisi 0177, Georgia, and Sukhumi State University, 12, Politkovskaya St., Tbilisi 0186, Georgia, e-mail: ashord@rmi.ge
Abstract: A general theorem (principle of a priori boundedness) on solvability of the boundary value problem ${\rm d} x={\rm d} A(t)\cdot f(t,x),\quad h(x)=0$ is established, where $f\colon[a,b]\times\mathbb{R}^n\to\mathbb{R}^n$ is a vector-function belonging to the Carathéodory class corresponding to the matrix-function $A\colon[a,b]\to\mathbb{R}^{n\times n}$ with bounded total variation components, and $h\colon\operatorname{BV}_s([a,b],\mathbb{R}^n)\to\mathbb{R}^n$ is a continuous operator. Basing on the mentioned principle of a priori boundedness, effective criteria are obtained for the solvability of the system under the condition $x(t_1(x))=\mathcal{B}(x)\cdot x(t_2(x))+c_0,$ where $t_i\colon\operatorname{BV}_s([a,b],\mathbb{R}^n)\to[a,b]$ $(i=1,2)$ and $\mathcal{B}\colon\operatorname{BV}_s([a,b],\mathbb{R}^n)\to\mathbb{R}^n$ are continuous operators, and $c_0\in\mathbb{R}^n$.
Keywords: system of nonlinear generalized ordinary differential equations; Kurzweil-Stieltjes integral; general boundary value problem; solvability; principle of a priori boundedness
Classification (MSC 2010): 34K10
DOI: 10.21136/CMJ.2017.0144-11
Full text available as PDF.
References:
[1] M. T. Ashordiya: On solvability of quasilinear boundary value problems for systems of generalized ordinary differential equations. Soobshch. Akad. Nauk Gruz. SSR 133 (1989), 261-264. (In Russian. English summary.) MR 1040252 | Zbl 0686.34022
[2] M. Ashordia: On the correctness of linear boundary value problems for systems of generalized ordinary differential equations. Georgian Math. J. 1 (1994), 343-351. DOI 10.1007/BF02307443 | MR 1262572 | Zbl 0808.34015
[3] M. Ashordia: On the stability of solutions of a multipoint boundary value problem for a system of generalized ordinary differential equations. Mem. Differ. Equ. Math. Phys. 6 (1995), 1-57. MR 1415807 | Zbl 0873.34012
[4] M. T. Ashordiya: Criteria for the existence and uniqueness of solutions to nonlinear boundary value problems for systems of generalized ordinary differential equations. Differ. Equations 32 (1996), 442-450. (In English. Russian original.); translation from Differ. Uravn. 32 (1996), 441-449. MR 1436980 | Zbl 0884.34029
[5] M. Ashordia: Criteria of correctness of linear boundary value problems for systems of generalized ordinary differential equations. Czech. Math. J. 46 (1996), 385-404. MR 1408294 | Zbl 0879.34037
[6] M. T. Ashordiya: A solvability criterion for a many-point boundary value problem for systems of generalized ordinary differential equations. Differ. Equations 32 (1996), 1300-1308. (In English. Russian original.); translation from Differ. Uravn. 32 (1996), 1303-1311. MR 1601505 | Zbl 0894.34012
[7] M. Ashordia: On the correctness of nonlinear boundary value problems for systems of generalized ordinary differential equations. Georgian Math. J. 3 (1996), 501-524. DOI 10.1007/BF02259778 | MR 1419831 | Zbl 0876.34021
[8] M. Ashordia: Conditions for existence and uniqueness of solutions to multipoint boundary value problems for systems of generalized ordinary differential equations. Georgian Math. J. 5 (1998), 1-24. DOI 10.1023/B:GEOR.0000008135.69001.48 | MR 1606414 | Zbl 0902.34013
[9] M. Ashordia: On the solvability of linear boundary value problems for systems of generalized ordinary differential equations. Funct. Differ. Equ. 7 (2000), 39-64. MR 1941857 | Zbl 1050.34007
[10] M. Ashordia: On the general and multipoint boundary value problems for linear systems of generalized ordinary differential equations, linear impulse and linear difference systems. Mem. Differ. Equ. Math. Phys. 36 (2005), 1-80. MR 2196660 | Zbl 1098.34010
[11] R. Conti: Problèmes linéaires pour les équations différentielles ordinaires. Math. Nachr. 23 (1961), 161-178 French. DOI 10.1002/mana.1961.3210230304 | MR 0138818 | Zbl 0107.28803
[12] J. Groh: A nonlinear Volterra-Stieltjes integral equation and a Gronwall inequality in one dimension. Ill. J. Math. 24 (1980), 244-263. MR 0575065 | Zbl 0454.45002
[13] T. H. Hildebrandt: On systems of linear differentio-Stieltjes-integral equations. Ill. J. Math. 3 (1959), 352-373. MR 0105600 | Zbl 0088.31101
[14] I. T. Kiguradze: Boundary-value problems for systems of ordinary differential equations. J. Sov. Math. 43 (1988), 2259-2339. (In English. Russian original.); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Novejshie Dostizh. 30 (1987), 3-103. DOI 10.1007/BF01100360 | MR 0925829 | Zbl 0782.34025
[15] I. T. Kiguradze, B. Půža: On boundary value problems for functional-differential equations. Mem. Differ. Equ. Math. Phys. 12 (1997), 106-113. MR 1636865 | Zbl 0909.34054
[16] I. T. Kiguradze, B. Půža: Theorems of Conti-Opial type for nonlinear functional-differential equations. Differ. Equations 33 (1997), 184-193. (In English. Russian original.); translation from Differ. Uravn. 33 (1997), 185-194. MR 1609904 | Zbl 0908.34046
[17] I. T. Kiguradze, B. Půža: On the solvability of nonlinear boundary value problems for functional-differential equations. Georgian Math. J. 5 (1998), 251-262. DOI 10.1023/B:GEOR.0000008124.88849.7c | MR 1618364 | Zbl 0909.34057
[18] I. T. Kiguradze, B. Půža: Conti-Opial type existence and uniqueness theorems for nonlinear singular boundary value problems. Funct. Differ. Equ. 9 (2002), 405-422. MR 1971619 | Zbl 1048.34108
[19] I. T. Kiguradze, B. Půža: Boundary Value Problems for Systems of Linear Functional Differential Equations. Folia Facultatis Scientiarum Naturalium Universitatis Masarykianae Brunensis. Mathematica 12. Brno: Masaryk University (2003). MR 2001509 | Zbl 1161.34300
[20] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter. Czech. Math. J. 7 (1957), 418-449. MR 0111875 | Zbl 0090.30002
[21] Z. Opial: Linear problems for systems of nonlinear differential equations. J. Differ. Equations 3 (1967), 580-594. DOI 10.1016/0022-0396(67)90018-6 | MR 0216068 | Zbl 0161.06102
[22] Š. Schwabik: Generalized Ordinary Differential Equations. Series in Real Analysis 5, World Scientific, Singapore (1992). DOI 10.1142/1875 | MR 1200241 | Zbl 0781.34003
[23] Š. Schwabik, M. Tvrdý: Boundary value problems for generalized linear differential equations. Czech. Math. J. 29 (1979), 451-477. MR 0536070 | Zbl 0424.34014
[24] Š. Schwabik, M. Tvrdý, O. Vejvoda: Differential and Integral Equations. Boundary Value Problems and Adjoints. Reidel, Dordrecht, in co-ed. with Academia, Publishing House of the Czechoslovak Academy of Sciences, Praha (1979). MR 0542283 | Zbl 0417.45001
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# Understanding the elliptic curve equation by example
I'm trying to follow this tutorial and wonder how the author get the list of points in the elliptic curve. For example, why when you input x=1 you'll get y=7 in point (1,7) and (1,16)?
on intuitive level, I'll do:
x=1, 1^3+1+1 mod 23
= 3mod23 = 3 so why we get (1,7) & (1,16).
• What's wrong with the obvious: because $y^2=3\bmod23$ has two solutions: $y=7$ and $y=16$, as verified by $7^2\equiv49\equiv3\pmod{23}$ (the other follows by taking the opposite, $-7\bmod23=23-7=16$)?. If you want a method to solve that other than by trial and error, in the general case there's Tonelli-Shanks; or since here we have $23\equiv3\pmod4$ you can use $y=\pm3^{(23+1)/4}\bmod23$ – fgrieu Jul 13 '17 at 16:36
• ohhhh, got it. I totally ignored the y^2. so 7^2≡3mod23 & 16^2≡3mod23 – adhg Jul 13 '17 at 16:38
As fgrieu already mentioned, you forgot that the $y$ term in the elliptic curve equation is squared, so for $x= 1$ you have $y^2 = 1^3 + 1 + 1 = 3 \text{ mod } 23$. In order to solve the congruence $y^2 = n \text{ mod } p$ (where $p$ is a prime) you can use the following algorithm (Tonelli-Shanks):
1. Factor the powers of $2$ out of $p-1$, so in your case write $p-1 = 22 = Q2^S = 11 * 2^1$
2. Pick a value $z$ that is not a quadratic residue modulo $p$ i.e. there exists no $x$ such that $z = x^2 \text{ mod } p$. I picked $7$ at random and verified it's not a quadratic residue via Euler's criterion ($7^{\frac{23-1}{2}} = 22 = -1 \text{ mod } 23$)
3. Set the following values (all calculations done modulo $p$): $$M \gets S(=1)$$ $$c \gets z^Q(7^{11}=22)$$ $$t \gets n^Q(3^{11}=1)$$ $$R \gets n^{\frac{Q+1}{2}}(3^{\frac{11+1}{2}}=16)$$
4. This step involves looping until $t = 1$, which in our case is already true going into this step, so we have $y = R = 16$ as one of our solutions. The other solution can be found by computing $p - R = 23 - 16 = 7$.
Hence we have the two solutions $y = 16, y = 7$ when $x = 1$, yielding the points $(1, 16), (1, 7)$ as expected.
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IMR Press / RCM / Volume 23 / Issue 11 / DOI: 10.31083/j.rcm2311364
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Type 2 Diabetes Incidence and Mortality: Associations with Physical Activity, Fitness, Weight Loss, and Weight Cycling
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1 College of Health Solutions, Arizona State University, Phoenix, AZ 85004, USA
*Correspondence: Glenn.gaesser@asu.edu (Glenn A. Gaesser)
Academic Editors: Fabio Angeli and Brian Tomlinson
Rev. Cardiovasc. Med. 2022, 23(11), 364; https://doi.org/10.31083/j.rcm2311364
Submitted: 13 June 2022 | Revised: 21 August 2022 | Accepted: 6 September 2022 | Published: 25 October 2022
This is an open access article under the CC BY 4.0 license.
Abstract
Cardiometabolic diseases, including cardiovascular disease (CVD) and type 2 diabetes (T2D), are the leading cause of death globally. Because T2D and obesity are strongly associated, weight loss is the cornerstone of treatment. However, weight loss is rarely sustained, which may lead to weight cycling, which is associated with increased mortality risk in patients with T2D. Meta-analyses show that weight loss is not generally associated with reduced mortality risk in T2D, whereas weight cycling is associated with increased all-cause and CVD mortality. This may be attributable in part to increased variability in CVD risk factors that often accompany weight cycling, which studies show is consistently associated with adverse CVD outcomes in patients with T2D. The inconsistent associations between weight loss and mortality risk in T2D, and consistent findings of elevated mortality risk associated with weight cycling, present a conundrum for a weight-loss focused T2D prevention and treatment strategy. This is further complicated by the findings that among patients with T2D, mortality risk is lowest in the body mass index (BMI) range of ~25–35 kg/m${}^{2}$. Because this “obesity paradox” has been consistently demonstrated in 7 meta-analyses, the lower mortality risk for individuals with T2D in this BMI range may not be all that paradoxical. Physical activity (PA), cardiorespiratory fitness (CRF), and muscular fitness (MF) are all associated with reduced risk of T2D, and lower risk of CVD and all-cause mortality in individuals with T2D. Reducing sedentary behavior, independent of PA status, also is strongly associated with reduced risk of T2D. Improvements in cardiometabolic risk factors with exercise training are comparable to those observed in weight loss interventions, and are largely independent of weight loss. To minimize risks associated with weight cycling, it may be prudent to adopt a weight-neutral approach for prevention and treatment of individuals with obesity and T2D by focusing on increasing PA and improving CRF and MF without a specific weight loss goal.
Keywords
obesity
metabolic syndrome
cardiorespiratory
cardiovascular disease
exercise
weight fluctuation
body weight variability
Figures
Fig. 1.
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Math Calculators, Lessons and Formulas
It is time to solve your math problem
mathportal.org
# T-Test calculator
The Student's t-test is used to determine if means of two data sets differ significantly. This calculator will generate a step by step explanation on how to apply t - test.
Two sample t-test calculator
One or two tails, equal or unequal variances, paired or unpaired + steps.
show help ↓↓ examples ↓↓
0123456789.,del
Use data grit to input values
Groups Have Equal Variance (default) Groups Have Unequal Variance (Welch t-test)
Two Tailed Test (default) One Tailed Test
0.05 (default) 0.01 0.001
Unpaired T Test (default) Paired (Dependent) T Test
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One sample t-test calculator
Compare the mean of a dataset to some fixed value to determine if the data mean is significantly different from that value.
show help ↓↓ examples ↓↓
0123456789.,del
0.05 (default) 0.01 0.001
Two Tailed Test (default) One Tailed Test
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examples
example 1:ex 1:
Twelve younger adults and twelve older adults conducted a life satisfaction test. The data are presented in the table below. Compute the appropriate t-test.
$$\begin{array}{c|cccccccccc} \text{older} & ~12~ & ~16~ & ~10~ & ~19~ & ~20~ & ~11~ & ~14~ & ~25~ & ~16~ & ~12 \\ \text{younger} & ~10~ & ~9~ & ~12~ & ~15~ & ~14~ & ~15~ & ~13~ & ~12~ & ~21~ & ~15 \end{array}$$
example 2:ex 2:
Are the means between two data sets are significantly different at level $\alpha < 0.05$.
$$\begin{array}{c|cccccccccc} \text{group 1} & ~5.1~ & ~4.3~ & ~3.1~ & ~4.6~ & ~3.9~ & ~4.3~ & ~4.7~ & ~3.8~ & ~4.1~ & ~5.0 \\ \text{group 2} & ~2.1~ & ~3.4~ & ~1.8~ & ~3.5~ & ~4.0~ & ~2.5~ & ~2.1~ & ~3.5~ & ~2.8~ & ~1.9 \end{array}$$
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# Relation between Torque and Speed
## Introduction
There relation of torque with the speed of an object is an important part of physics as it is integrally connected to the motion and rotating capability. The relation between these two components is integrally and very much connected to the power of the object. The value of torque is often extracted by “Power/ Speed.” This statement is the most basic and necessary information to know about the relation between speed and torque.
## What is Torque?
Torque is a significant product of the radius of rotation and force. As a result, in the case of an increasing radius, the torque is also found to increase (Lenzo et al. 2018). This finally results in torque. Torque is also known as the rotational equivalence of an object’s linear force.
Images Coming soon
Torque is a measure of force that is the reason behind leading an object to rotate. Angular acceleration is also found to be a result of torque. Description of torque also includes a moment of force (Okoroha et al. 2019).
The lever arm and moment arm are the two most important terms that are connected to the relation of torque and speed. Torque is presented by the symbol ‘T’. Si unit of Torque is N.m (Newton Meter). Dimension and SI base units are $\mathrm{ML^{2}T^{-2}}$ and kg.$\mathrm{m^{2}.s^{-2}}$. There are main two types of torque in physics and these are dynamic and static torque. Static torque is found to produce any kind of angular acceleration. As an example, cycling can be mentioned in which no such kind of acceleration is found.
## What is Speed?
The speed of an object is used to measure the total distance that is covered within a particular unit of time. The speed of an object is considered a scalar unit of quantity in physics. In the time of determining the speed of an object, there is no need to establish the proper direction of an object’s movement (Andrade et al. 2020). The term and meaning of velocity possess a very significant difference. Velocity is a vector quality. It can also be described as the speed of an object that is moving in a particular direction.
The measurement of an object’s speed is presented by both CGS and SI units. In CGS mode, the speed is presented with cm.s-1 and in SI mode, the unit becomes $\mathrm{ms^{-1}}$(Osawa et al. 2019). There are four significant types of speed and these are instantaneous, average, uniform, and variable speed.
## Relationship between Torque and Speed
There is an integral relation between torque and speed based on which the differences in motion of an object can be determined. The relation between speed and torque is significantly proportional to each other. In the case of presenting the torque of a rotating object, the ratio between angular velocity and power is important.
In the case of a rotational motion, the torque is often expressed as the multiplication of force value with radius value (Sun et al. 2019). As a result, the value of force is the value in which torque is divided by the value of radius. The power value can be calculated by multiplying linear distance and force and then dividing the result by time. The multiplication of torque and angular velocity extracts the value of power.
Images Coming soon
## Relation between Speed and Torque: Derivation
Being a rotatory motion, it s very easy to derive the significant and unique relation between torque with power. Comparison of linear equivalent is important for this derivation. The covered angle is to be multiplied by a radius of movement for extracting the value of linear displacement. The circumference of a wheel is integrally connected to the linear displacement of an object (Artetxe et al. 2018). The formula of Linear distance is “Linear distance= Radius* Angular velocity* time”. As per this related mathematical formula, force is inversely and significantly proportional to the value of speed, also known as angular velocity.
## The difference between Torque and Speed
Torque Speed
It is related to rotational force. It is related to the rotation rate of an object.
The output of torque helps an object to increase its speed. Speed can be calculated by considering (Revolutions per minute) RPMs.
## Conclusion
The calculation of Torque is done by following a formula in which torque is equal to the result in which the power of the object is divided by that object’s speed. The value of power is a relevant part, based on which the torque of an object can be calculated. Comparison of the linear equivalent is also a mentionable part. In the equation of torque and speed, the value of velocity and speed are interchangeable in nature. The most important reason behind this is the torque that always possesses the speed in a stable, particular, and confirms direction.
## FAQs
Q.1. What is meant by linear displacement?
Ans. Linear displacement is the particular amount of distance that is covered by an object within a specific time. The circumference of an object’s rotation is also related to the concept of linear displacement. The value of a product’s angle with radius is also related to the concept of linear displacement.
Q.2. What is defined by angular speed?
Ans. Angular speed is used to define the speed at which a central angle of a rotating body is found to change in respect of different times. Angular speed is expressed by “$\mathrm{\omega =\theta t}$”.
Q.3. What are the two most important components with which the rotational motion can be characterized?
Ans. The value of speed and torque are the two most important components with which the value of rotational motion is characterized. Rotational motion is also related to the power which is acquired by multiplying speed and torque.
Q.4.What is the relation between torque and output speed?
Ans. An incensement in torque results in decreasing value of output speed. These two components are related inversely.
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Browse Questions
# The $E_{cell}$ in which the reaction :$MnO_4^-+Fe^{+2}+H^+\rightarrow Mn^{+2}+Fe^{+3}+H_2O$ occurs is 0.59V at $25^{\large\circ}C$.The equilibrium constant for the reaction is
$\begin{array}{1 1}(a)\;50\\(b)\;10\\(c)\;10^{50}\\(d)\;10^5\end{array}$
For the given half-cell reaction
$-nFE^0_{cell}=-RTln K_{eq}$
$-5\times 96500\times 0.59=-2.303\times 8.314\times 298 \log K_{eq}$
$K_{eq}=7.8\times 10^{49}\approx 10^{50}$
Hence (c) is the correct answer.
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# Generative adversarial networks and image-to-image translation
Yet another post about generative adversarial networks (GANs), pix2pix and CycleGAN. You can already find lots of webs with great introductions to GANs (such as here, here, here or here), pix2pix (here, with kittens, code and an interactive demo) and CycleGAN (here). Anyway, here are my two cents.
## Generative modeling and sampling
One of the most fundamental problems in machine learning is estimating the true distribution given a collection of samples. If we effectively discover this true distribution wich a machine learning model, we could do many things, such as sampling from that distribution. Not surprisingly, this type of models are often known as generative models. Estimating a model is relatively easy in low dimensional spaces or if we have significant prior information about the structure of the probability distribution (e.g. thermal noise is known to follow Gaussian distributions, we just need to estimate the mean and variance). However, things get complicated for complex distributions in high dimensional spaces. That is the case in image generation.
In the example above, we want to learn an approximation $\hat p\left(x\right)$ of the true probability distribution $p\left(x\right)$ of all the 64×64 color images that represent (realistic) faces (we have a dataset with a number of samples from $p\left(x\right)$, i.e. real faces). If images are vectorized we have $x\in \mathbb{R}^{12288}$, since 64x64x3=12288. Even a small 64×64 image lies in a very high dimensional space of 12K dimensions. Now think of all the possible 64×64 images that represent faces and all the possible combinations of pixel values in 64×64 images. The former is just a tiny fraction of the latter, just like a needle in a haystack. And that is precisely our objective: to discover the tiny manifold embedded in a very high dimensional space where face images lie in. Current state-of-the-art generative models can generate realistic 1024×1024 images of faces (3M-dimensional space!!, check here). On a side remark: many of the generated faces look like real people, but they don’t exist in reality… disturbing, right?.
Another problem is that the distribution is very complex and we cannot assume a simple parametric model (e.g. a mixture of Gaussians). Together with high dimensionality, this makes it very difficult to be modeled directly with density estimation models. Only recently some new approaches have started to obtain good results. The most notable are variational autoencoders (VAE), autorregressive models (such as PixelCNN, PixelRNN) and generative adversarial networks (GANs). We will focus on the last one.
Instead of assuming a complex parametric model from which we generate new samples, many generative models use an indirect sampling approach. In this case, images are not sampled from the target high-dimensional space $\hat p\left(x\right)$, but from a simple distribution (e.g. a normalized Gaussian) in a low-dimensional space known as latent space. Each latent vector $z$ in this latent space is transformed into an image using a function $G_\theta\left(z\right)$. With this indirect sampling mechanism the objective is now to learn the parameters $\theta$ of the transformation, in such a way that the distribution of the transformed samples approximates $p\left(x\right)$. As you can imagine, the family of transformations is implemented as a trainable neural network.
A possible way to solve that problem is learning a model that memorizes the training data in the parameters $\theta$ and simply retrieves random training samples as output. In principle, that is something we want to avoid, because we are interested in $p\left(x\right)$ rather than in the empirical distribution given by the training set. In other words, after training we would like to sample realistic yet unseen images.
GANs are based on an adversarial setup where two networks, the generator $G_{\theta_g}\left(z\right)$ and the discriminator $D_{\theta_d}\left(x\right)$, compete to optimize their own objectives. The generator tries to generate images as realistic as possible. The discriminator tries to tell apart fake images coming from the generator and real images coming from the training set. Note that the generator never sees the training data directly. The game is formulated as the following minimax objective
$$\min_{\theta_g}\max_{\theta_d}\left[\mathbb{E}_{x\sim p_{data}\left(x \right)}\log D_{\theta_d}\left(x\right) + \mathbb{E}_{z\sim p\left(z \right)} \log \left(1 - D_{\theta_d}\left(G_{\theta_g}\left(z\right)\right)\right) \right ]$$ This can be addressed by alternatively optimizing the generator and the discriminator. The corresponding problem for the discriminator is
$$\max_{\theta_d}\left[\mathbb{E}_{x\sim p_{data}\left(x \right)}\log D_{\theta_d}\left(x\right) + \mathbb{E}_{z\sim p\left(z \right)} \log \left(1 - D_{\theta_d}\left(G_{\theta_g}\left(z\right)\right)\right) \right ]$$ and for the generator
$$\min_{\theta_g}\left[\mathbb{E}_{z\sim p\left(z \right)} \log \left(1 - D_{\theta_d}\left(G_{\theta_g}\left(z\right)\right)\right) \right ]$$ The authors (Goodfellow et al.) observed that optimizing this objective for the generator may lead to flat gradients (i.e. which carry very little information to update the generator and therefore learning will be difficult). They propose the following alternative that seems to provide more informative gradients and works better in practice
$$\max_{\theta_g}\left[\mathbb{E}_{z\sim p\left(z \right)} \log D_{\theta_d}\left(G_{\theta_g}\left(z\right)\right) \right ]$$
Optimizing this minimax problem is difficult and often unstable. However, many improvements have been proposed, including architectural improvements (e.g. DCGANs), better losses (e.g. Wasserstein distance), and better training strategies (e.g. PG-GANs). Current GANs are more stable to train and can generate images with larger resolutions.
## Conditional GANs
So far so good, we can sample a random realistic image of a, say, animal. But we cannot control what kind of animal. Wouldn’t it be nice to tell the network the animal we want, e.g. a dog?
That is precisely the idea of conditional GANs, where an additional input is added to restrict the sampled images to those satisfying certain properties. For simplicity, we now focus on the semantic category $c$ as condition (assuming that the training images are annotated with the corresponding category label). The task is now learning the joint distribution $p_{data}\left(c,x\right)$ of labels and images, and then be able to sample from the conditional distribution $p_{data}\left(x\vert c\right)$. This is achieved by modifying the original minimax objective to include the condition $c$ in both the generator and discriminator (and also while sampling training/generated data)
$$\min_{\theta_g}\max_{\theta_d}\mathcal{L_\textnormal{cGAN}}\left( \theta_g,\theta_d\right )=\min_{\theta_g}\max_{\theta_d}\left[\mathbb{E}_{c,x \sim p_{data}\left(c,x\right)}\log D_{\theta_d}\left(c,x\right) + \mathbb{E}_{c\sim p_{data}\left(c\right),z\sim p_z\left(z \right)} \log \left(1 - D_{\theta_d}\left(c,G_{\theta_g}\left(c, z\right)\right)\right) \right ]$$
Another popular framework is Auxiliary Classifier GANs (AC-GANs), where in addition to the real/fake discrimination task, the discriminator network is augmented with an additional classification task: the generated imaged conditioned to a given category $c$ should be classified as the same $c$.
Here we have considered categories as conditions. The power and flexibility of conditional GANs (or any other conditional image generation model) is that almost anything could be used as condition (in general we prefer conditions that can be represented as fixed-length vectors). Examples of problems that can be tackled with conditional GANs are image-to-image translation, text-to-image synthesis and attribute-to-image synthesis (where the conditions are image embeddings, text embeddings and attribute embeddings, respectively). We discuss the first one in the next sections.
## Image-to-image translation
Most tasks in image processing and computer vision can be seen as transforming one input image into an output one (e.g. filtering, edge detection, image enhancement, colorization, restoration, denoising, semantic segmentation, depth extraction). The term image-to-image translation has been used recently to refer to general purpose methods that learn transformations directly from datasets with pairs of input and output images. These are some examples
For example, let us consider the problem of color to grayscale conversion. The solution to that problem is very simple, just average the RGB values of each pixel. Now let us consider the inverse problem of grayscale to color conversion (known as colorization). This is more complex, since there are many color values with the same grayscale value. In general, we need to figure out which of those colors are plausible, given the input grayscale image. But we need to resort to some high-level understanding of the image. For instance, if we understand the image is showing a face, then we can imagine the plausible skin colors that a particular face may have, obtained by our experience of having seen many faces during our life. Similarly, a colorization algorithm can learn to infer colors in grayscale faces after being trained with a dataset of color faces.
Another example is superresolution, which consists of upsampling a low resolution image to a realistic higher resolution one. Note that downsampling is trivial, by simply dropping high frequency information, but upsampling requires inferring those details. As in the previous example, the prior for these details can be learned from a suitable dataset.
These translations are not limited to photos, they could include other modalities and even translations between modalities (i.e. cross-modal translation). For example, semantic segmentation, where each RGB pixel is transformed to a semantic label. The inverse problem is photo image synthesis. As in the previous examples, the former is often a many-to-one problem (yet still challenging), while the latter is usually one-to-many (e.g. a region with the semantic label ‘car’ could have many RGB solutions, differing in color, texture, details, etc., yet all plausible).
## Paired image-to-image translation
In many cases we can collect pairs of input-output images. For example, we can easily get edge images from color images (e.g. applying an edge detector), and use it to solve the more challenging problem of reconstructing photo images from edge images, as shown in the following figure
Now observe that we can consider the edge image as an input condition and then use a conditional GAN to generate the output image. This is the idea of pix2pix. The generator now is a bit more complicated, since it consists of an encoder followed by a decoder (implemented as a convolutional network followed by a deconvolutional network).
But that the optimization problem is exactly the same as in the category-conditional GAN described previously
$$\min_{\theta_g}\max_{\theta_d}\mathcal{L_\textnormal{cGAN}}\left( \theta_g,\theta_d\right )=\min_{\theta_g}\max_{\theta_d}\left[\mathbb{E}_{c,x\sim p_{data}\left(c,x\right)}\log D_{\theta_d}\left(c,x\right) + \mathbb{E}_{c\sim p_{data}\left(c\right),z\sim p_z\left(z \right)} \log \left(1 - D_{\theta_d}\left(c,G_{\theta_g}\left(z\right)\right)\right) \right ]$$ In addition to the conditional GAN loss, the authors also include a $L_1$ loss that forces the generated image for a given input to remain as similar as possible to the corresponding paired output ground truth image. This provides faster convergence and more stable training. This additional loss is
$$\mathcal{L_\textnormal{L1}}\left( \theta_g\right )=\mathbb{E}_{c,x \sim p_{data}\left(c,x \right ),z\sim p_z}\left \|x- G_{\theta_g}\left(c, z\right) \right \|_1$$ and the combined problem
$$\min_{\theta_g}\max_{\theta_d}\left[\mathcal{L_\textnormal{cGAN}}\left(\theta_g,\theta_d\right )+\lambda \mathcal{L_\textnormal{L1}}\left( \theta_g\right )\right]$$
## Unpaired image-to-image translation
Now let us think of a more exotic translation, for example, horses to zebras. Given an image of a horse, can we get find the image of a zebra with the same background, same pose and aligned exactly with the original horse image? Probably not, so we cannot create an (input,output) pair, and therefore we cannot apply paired image-to-image translation.
However, if we relax the requirements and just collect a set of images with horses and a set of images with horses we can create a pair, but at the set level (in this case corresponding to two domains: horse and zebra).
In pix2pix we can generate an output image conditioned on the input one and compared with the corresponding output ground truth. In this case that is not possible. CycleGAN (and similar concurrent works, such as DiscoGAN and DualGAN) address this problem by learning at the same time the translation in both directions. Since images are generated in both domains, there are also two discriminators.
The main idea is to observe that transforming in one direction and then in the other back to the original domain (i.e. a cycle), ideally, the final image should be the same as the original. Therefore, we can compare both images and penalize when the difference is large (this is known as cycle consistency loss). Since we cannot compare with a reference output image, the reconstructed image is compared to the original input one (see figures below). The images generated are also evaluated by a discriminator for that particular domain.
For convenience we refer to images $x\in X$ from domain $X$ (e.g. horses) and images $x\in X$ from domain $Y$ (e.g. zebras ). Let us illustrate the training process for the cycle horse-zebra-horse ($X\rightarrow Y\rightarrow X$). We also drop the random vector $z$ used in previous cases. Now we have two translations $y=G^\textnormal{XY}_{\theta_{xy}}\left(x\right)$ and $x=G^\textnormal{YX}_{\theta_{yx}}\left(y\right)$ implemented using two generators $G^\textnormal{XY}_{\theta_{xy}}$ and $G^\textnormal{YX}_{\theta_{yx}}$. The objective in this cycle is
$$\mathcal{L}^\textnormal{XY}_\textnormal{cGAN}\left( \theta_{xy},\theta_{yx},\theta_y\right )=\mathbb{E}_{y\sim p_{data}\left(y\right)}\log D^\textnormal{Y}_{\theta_y}\left(y\right) + \mathbb{E}_{x\sim p_{data}\left(x\right)}\log \left(1 - D^\textnormal{Y}_{\theta_y}\left(G^\textnormal{XY}_{\theta_g}\left(x\right)\right)\right)$$
and the corresponding cycle consistency loss is
$$\mathcal{L}^\textnormal{XYX}_\textnormal{cyc}\left( \theta_{xy},\theta_{yx}\right )=\mathbb{E}_{x\sim p_{data}\left(x\right)}\left\| G^\textnormal{YX}_{\theta_{yx}}\left(G^\textnormal{XY}_{\theta_{xy}}\left(x\right)\right)-x \right\|_1 + \mathbb{E}_{y\sim p_{data}\left(y\right)}\left\| G^\textnormal{XY}_{\theta_{xy}}\left(G^\textnormal{YX}_{\theta_{yx}}\left(y\right)\right)-y \right\|_1$$
Similarly, the other cycle also has the corresponding losses $\mathcal{L}^\textnormal{YX}_\textnormal{cGAN}\left( \theta_{xy},\theta_{yz},\theta_x\right )$ and $\mathcal{L}^\textnormal{YXY}_\textnormal{cyc}\left( \theta_{xy},\theta_{yx}\right)$. The full objective combines the four losses. And voila, here is your horse in zebra skin.
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# Why is $(T-\lambda I)^pT(x) = T(T-\lambda I)^p(x)$?
Definition. Let $$T$$ be a linear operator on a vector space $$V$$, and let $$\lambda$$ be an eigenvalue of $$T$$. The generalized eigenspace of $$T$$ corresponding to $$\lambda_1$$ denoted $$K_\lambda$$, is the subset of $$V$$ defined by
$$K_\lambda$$ = $$\{x \in V: (T-\lambda I)^p(x) = 0$$ for some positive integer $$p\}$$.
To show that $$K_\lambda$$ is $$T$$-invariant, consider any $$x \in K_\lambda$$. Choose a positive integer $$p$$ such that $$(T-\lambda)^p = 0$$. Then
$$(T-\lambda I)^pT(x) = T(T-\lambda I)^p(x) = T(0) = 0$$
I wanted to know how we go from $$(T-\lambda I)^pT(x) = T(T-\lambda I)^p(x)$$?
• Induction on $p$? Or write $T$ as $(T-\lambda I)+\lambda I$? – Angina Seng Aug 4 '18 at 15:42
• Take both expressions and expand out $(T-\lambda I)^p$ using the binomial theorem. After simplifying, you will find there are equal. – Mike Earnest Aug 4 '18 at 15:42
Since $T$ commutes with both $T$ and $\lambda\operatorname{Id}$, $T$ commutes with $T-\lambda\operatorname{Id}$ and therefore it comutes with any power of $T-\lambda\operatorname{Id}$.
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# IBDP Physics 3.1 – Thermal concepts: IB Style Question Bank -SL Paper 1
### Question
When 40 kJ of energy is transferred to a quantity of a liquid substance, its temperature increases by 20 K. When 600 kJ of energy is transferred to the same quantity of the liquid at its boiling temperature, it vaporizes completely at constant temperature. What is
for this substance?
A. 15
B. 15 K
C. 300
D. 300 K
Ans: D
SPECIFIC HEAT CAPACITY
It is the amount of heat required to raise the temperature of unit mass of substance through 1 degree.
Specific heat capacity,
Latent heat of vaporisation : It is the quantity of heat required to convert unit mass of liquid into vapour at its boiling point.
$$Q=mL$$
now
$$40 \;kJ=m\times c\times \Delta T$$ where $$\Delta T =20 K$$
$$600 \;kJ = m \times L$$
$$\therefore \frac{m \times L}{m\times c\times \Delta T} =\frac{600 \;kJ}{40 \;kJ}$$
or
$$\frac{L}{c} =\frac{600 \;kJ}{40 \;kJ}\times \Delta T =300 K$$
### Question
Which aspect of thermal physics is best explained by the molecular kinetic model?
A The equation of state of ideal gases
B The difference between Celsius and Kelvin temperature
C The value of the Avogadro constant
D The existence of gaseous isotopes
Ans: A
The kinetic molecular theory can be used to explain each of the experimentally determined gas laws.
Any sample of a gas is made of molecules. A molecule is the smallest unit having all the chemical properties of the sample. The observed behaviour of a
gas results from the detailed behaviour of its large number of molecules. The kinetic theory of gases attempts to develop a model of the molecular behaviour
which should result in the observed behaviour of an ideal gas.
### Question
Molecules leave a boiling liquid to form a vapour. The vapour and the liquid have the same temperature.
What is the change of the average potential energy and the change of the average random kinetic energy of these molecules when they move from the liquid to the vapour?
## Markscheme
B
During a phase change, temperature of the substance remains the same. Average kinetic energy of the molecules of the substance does not change during phase change but average potential energy changes.
Heat supplied at phase change is used in increasing internal energy of molecules. Internal energy of a given body in vapour phase is larger than that in liquid phase
### Question
Which of the following is equivalent to a temperature of –100°C?
A. –373 K
B. –173 K
C. 173 K
D. 373 K
### Markscheme
C
TºK = (tºC + 273) or tºC = (TK – 273)
Hence –100°C in K is –100+273 = 173K
### Question
A sample of solid copper is heated beyond its melting point. The graph shows the variation of temperature with time.
During which stage(s) is/are there an increase in the internal energy of the copper?
A. P, Q and R
B. Q only
C. P and R only
D. Q and R only
### Markscheme
A
When a solid melts, its molecules move apart against the strong molecular attraction. This needs energy which must be supplied from outside. Thus, the internal energy of a given body is larger in liquid phase than in solid phase. Similarly, the internal energy of a given body in vapour phase is larger than that in liquid phase.
### Question
A pure solid is heated at its melting point. While it is melting the
A. mean kinetic energy of the molecules of the solid increases.
B. mean potential energy of the molecules of the solid increases.
C. temperature of the solid increases.
D. temperature of the solid decreases.
## Markscheme
B
during Phase change (melting) there is no change in Temperature and hence Kinetic Energy remain constant. heat supplied $$Q=mL$$ is used to increase internal potential energy.
### Question
Equal masses of water at 80°C and paraffin at 20°C are mixed in a container of negligible thermal capacity. The specific heat capacity of water is twice that of paraffin. What is the final temperature of the mixture?
A. 30°C
B. 40°C
C. 50°C
D. 60°C
$$ms_w(80-t)=ms_p(t-20)$$
$$(80-t)\times 2s_p=s_p(t-20)$$
$$160-2t=t-20$$
$$t=60^{\circ}C$$
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Continuity of an inverse function
1. May 7, 2008
ohreally1234
1. The problem statement, all variables and given/known data
Prove that the a continuous function with compact domain has a continuous inverse. Also prove that the result does not hold if the domain is not compact.
2. Relevant equations
3. The attempt at a solution
I tried using the epsilon delta definition of continuity but didn't get anywhere.
This is supposed to be a pretty standard proof in any real analysis book but unfortunately the one I'm using has it listed as an exercise...
2. May 7, 2008
Dick
First, you need to add that the function is 1-1 to your premises. I'll give you a hint as to why you need compactness by giving you the usual counterexample f:[0,2*pi)->R^2 defined by f(x)=(cos(x),sin(x)). Why does that show the result doesn't hold without compactness?
3. May 7, 2008
ohreally1234
Hmm, how do I prove the first part (that it is continuous)
4. May 7, 2008
Dick
Think about it. Suppose f:X->Y. A function is continuous if for every convergent sequence in X, x_n->x that f(x_n)->f(x). f^(-1) is continuous if for every convergent sequence y_n->y in Y that f^(-1)(y_n)->f^(-1)(y). You want to show f^(-1) is continuous given f is continuous, 1-1, and X is compact. Hint: define x_n such that f(x_n)=y_n. Does the sequence x_n have a limit point? Why?
5. May 7, 2008
ohreally1234
But isn't f(x) = (cos(x), sin(x)) not a 1-1 function (because it's a circle)?
6. May 7, 2008
Dick
No. Why? Show me two values of x that map to the same value of (cos(x),sin(x)) in the domain [0,2*pi).
7. May 7, 2008
ohreally1234
oh sorry, i also forgot to add that
f:[a,b] => R
I got the continuity part down (your hint really helped!), but I'm having trouble with the compact part.
8. May 7, 2008
Dick
What kind of 'trouble with the compact part'? You are given that the domain is compact, you don't have to prove it.
9. May 7, 2008
ohreally1234
I'm having trouble with giving a counter example of a continuous 1-1 function f:[a,b] => R whose inverse is not continuous (does it even exist)?.
10. May 7, 2008
Dick
You won't find one for f:[a,b]->R. [a,b] is compact. You are going to have to be more creative and pick a non-compact domain.
11. May 7, 2008
ohreally1234
If the domain is non-compact, does such a function exist?
12. May 7, 2008
Dick
Yes. Pick the domain X to be [0,1) union [2,3]. Notice the open end on the first interval. Can you define a SIMPLE function f:X->R whose inverse isn't continuous? Concentrate on using the open endpoint.
13. May 7, 2008
ohreally1234
sorry im stumped... i tried playing with functions such as f(x)=1/(x-1) but im not sure what to do
14. May 7, 2008
Dick
Try f(x)=x on [0,1) and f(x)=x-1 on [2,3]. Since I just gave that to you, for free, you have to explain to me why it works. Is it continuous? What's the range? Is it 1-1? Finally give me a formula for the inverse (like the one for f) and tell me why it's discontinuous.
15. May 7, 2008
ohreally1234
ooo that makes so much more sense:
range of f is [0,2] but the inverse f^-1: [0,2] => [0,1) U [2,3] is clearly discontinuous at x=1.
thanks so much
16. May 7, 2008
Dick
Sure, but can you help a little more next time, and show some more of approaches you have tried?
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# Generators for the radical of an ideal
I am interested in finding a generating set of the radical of an ideal given a set of generators for the ideal itself, but after a lot of thought I cannot figure out a good way to do it. Specifically:
Let $k$ be an algebraically closed field, and $I \subset k[x_1, ..., x_n]$ an ideal. If $I = (f_1, ..., f_m)$, is there any good way to find a set of generators for $\text{rad}(I)$?
Edit: One may assume that $f_1, ..., f_m$ form a Gröbner basis for $I$. (Given any set of generators for an ideal in $k[x_1,..., x_n]$ it is always possible to find a Gröbner basis, so this assumption is without loss of generality.)
There are algorithms that find the generators for the radical of an ideal, e.g.: Gianni, P.; Trager, B.; Zacharias, G.: Gröbner Bases and Primary Decomposition of Polynomial Ideals. J. Symb. Comp. 6, 149–167 (1988).
Note though that these methods are non-trivial; as far as I know, there is no simple characterization of the generators of a radical ideal. The construction by Connor only gives a subset of a generating set.
• I won't say "a subset of a generating set", and my example under his answer shows why. – user26857 Dec 15 '15 at 11:05
If each $f_i$ is a product of powers of irreducibles, I think the generator for rad$(f_i)$ will be the product of the irreducibles for $f_i$ raised only to the first power. Do this for each $f_i$ and you have a generating set for rad$(I)$.
• I see what you're saying, that sounds like a good idea. Do you know of any good way to factor the $f_i$ into irreducibles? – Eric Haengel May 17 '12 at 2:18
• That's always tough... I don't know a straightforward method for an arbitrary polynomial, especially in multiple variables. Eisenstein's criterion can be very helpful in some cases for determining if a given factor is irreducible. – Connor May 17 '12 at 2:24
• I think acoustician's method is wrong. Consider $I = (x + y^2, x + 2 y^2)$, its generators are irreducible, but $I$ is not radical: $y \notin I$ and $y^2 \in I$. However acoustician's method works for monomial ideals. – Andrea May 18 '12 at 7:56
• You're definitely right, Andrea. Can you think of a description for non-monomial ideals? I'm stumped. – Connor May 19 '12 at 1:03
• @Andrea: Right, that is an important example, but I think the problem is that while $x+y^2$ and $x+2y^2$ generate $I$, they are not a grobner basis. Instead we can write $I = <x, y^2>$, where $x$ and $y^2$ do form a grobner basis, and it is true that $\text{rad}(I) = <x, y>$ is generated by the square-free part of each generator. So, I think what acoustician was saying works if we start with a grobner basis for $I$. – Eric Haengel May 24 '12 at 17:14
one way to solve the problem ( of finding generating set for radical ideal ,having the generator set of ideal ) is either to reduce it into principal ideal (by means of finding its reduced groebner basis) or factorizing it into power monomials). Then for example: if having I=< xy, x^2+xy> , applying the routine leads to G={xy} as the reduced groebner basis for I. (x^2+xy is eliminated since it's monomial xy € LT (xy) ) Now we use the theorem that says : Radical(f)= f/ GCD(f,df/d x1,d x2,...) So: Radical(I)=xy/y=x considering Lex ordering x>y Thus Radical(xy,x^2+xy)=x
• Please take a minute to learn a bit of TeX. If you're familiar with it, please use it. Regards, – Pedro Tamaroff Jan 31 '15 at 13:55
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# Self Esteem
## Would you like to be seen as:
• Total voters
25
• Poll closed .
Status
Not open for further replies.
#### Perseus
##### Prolific Member
Would you like to be seen as:
physically desirable
physically irresistible
a beautiful mind
a beautiful soul
#### Jordan~
##### Prolific Member
Who wouldn't like to be seen as both physically irresistable and a beautiful mind?
#### Ermine
##### is watching and taking notes
I've got enough looks to get by and my mind is well above average. My soul, however, needs some work. Is this adding to what we already have, or choosing only one?
#### PreAlgebra
##### Member
Looks although important, seem to be more trivial than the mind or soul. Being viewed as having a beautiful soul would be great but I think greater achievements are made with the mind. So that is how I would like others to see me only being able to choose one.
#### Perseus
##### Prolific Member
I could have put, what do other people see you as? It would not have been right though. That would depend on their NT. I think the Artisans see my soul, but miss out on the intuitive mind. It means I get on with them OK and they are warmer people than the Rationals.
However, I do not want to chase the Bear (ISTP) girls into the woods. Too physical.
#### Fleur
##### Prolific Member
Im going to be direct and frank.
Your poll is called "Would you like to been seen as...", but the thread is called "Self esteem".
Are going to put the answers of poll in some certain level of self esteem?
#### Perseus
##### Prolific Member
Im going to be direct and frank.
Your poll is called "Would you like to been seen as...", but the thread is called "Self esteem".
Are going to put the answers of poll in some certain level of self esteem?
If you are rational, intuitive and imaginative, I'm sure you can work out why ?! Maybe you need to be experienced as well ?
nieVe - eXperience continuum
#### Ogion
Well, she is right in pointing out a difference. Self-esteem is what i think about myself. "To be seen by others as..." is something different, and it implies that our self-esteem depends on others opinion of us...
Ogion
#### Perseus
##### Prolific Member
I made it clear that it is what we most relish, rather than what others want.
But it may well be that self esteem is boosted by the self being treated properly. The rational might not like being chased into the woods by a rampant bear!
#### Fleur
##### Prolific Member
If you are rational, intuitive and imaginative, I'm sure you can work out why ?! Maybe you need to be experienced as well ?
Your polls just brings me associations with lab rats.
#### Perseus
##### Prolific Member
Your polls just brings me associations with lab rats.
Interesting. Maybe the intuition does cross the Pond? (=North Atlantic) i.e. dependent on culture (or lack of).
#### Fleur
##### Prolific Member
There were some threads, when you told, that you swift between types. Why couldnt I do that either?
#### Perseus
##### Prolific Member
Lot of ugle ducklings, it seems.
#### Fleur
##### Prolific Member
Yep, the elephants dont like to be chased around and they tend to be unforgiving, unlike the gold-fishes, who gives their heart into action too rushly.
But ostriches dont mind either.
Last edited:
#### Perseus
##### Prolific Member
There were some threads, when you told, that you swift between types. Why couldnt I do that either?
A Skylark (INFJ) turns into a Swift (INFJ variant) to avoid the Hawk (INTJ) attack. Type changers are called morph-shifters. It can be chemically induced as well, by morphine (this is pathological to me). This chemical is favoured by the Horse (ESFJ). I am not sure why, but these types are usually adversial to me; the worst.
Morph shifting can be to variants or to completely another type.
I cannot change much beyond ENTP, INFP, INTP, Snake, Dragon and Eagle. Eagle is more socially acceptable and the most successful, but I suspect under stress I revert to Dragon. I suppose I can temporarily try a bit of INTJ (Hawk) as circumstances dictate. I have been on TV, but I am not really a Performer (ESFP) the Butterfly.
In our society, the use of thinking component requires opportunity. It is no use being a Legal Eagle without training and the opportunity may only be available to the higher income classes (England).
This is Snake (ENTP) mode. You know what the Unicorns (ESFJ variant) think of that! Horses get spooked.
#### Ogion
Wow, Fleur, now you sounded like Perseus.
Perseus, you are saying that the types can show behaviour of the other types from time to time as well? I wouldn't disagre with you there, because, staying in the theory, everybody has every 'function', just in different strength, so anybody can show other behaviour.
But following your post is not easy, so much 'animals'
Ogion
#### Perseus
##### Prolific Member
Wow, Fleur, now you sounded like Perseus.
Perseus, you are saying that the types can show behaviour of the other types from time to time as well? I wouldn't disagre with you there, because, staying in the theory, everybody has every 'function', just in different strength, so anybody can show other behaviour.
But following your post is not easy, so much 'animals'
Ogion
I expect most people inahbit the middle ground. It just so happens that I am an extreme NP. I only have bad trouble when I meet an extreme Guardian (SJ) and then trouble really does occur. Extreme NPs do not have a name. At least, the book has not yet been written to my knowledge.
There is room for a new plot. Surely, a film must have been made? In Tortilla Flat, the vagabonds were probably SPs.
However, extreme Horseman (ESFJ) are likely to be wife bashers or husband bashers and rapists if they do not get exactly what they want. Plenty of films about these types.
#### Kuu
I cannot change much beyond ENTP, INFP, INTP, Snake, Dragon and Eagle. Eagle is more socially acceptable and the most successful, but I suspect under stress I revert to Dragon. I suppose I can temporarily try a bit of INTJ (Hawk) as circumstances dictate. I have been on TV, but I am not really a Performer (ESFP) the Butterfly.
I think you are soooooo misguided. Mirroring or acting out some other type's common behaviour patterns does not make you that type. The way your mind works is still pretty much the same, and that is what is important to type. External appearances are just the consequences.
#### Perseus
##### Prolific Member
I think you are soooooo misguided. Mirroring or acting out some other type's common behaviour patterns does not make you that type. The way your mind works is still pretty much the same, and that is what is important to type. External appearances are just the consequences.
It is not an overlay pattern. I can (as circumstances disctate, choose to make an early judgement, for the short time I believe in it, I could say I have transferred to INTJ). Alas, as new information comes in I revert to INTP, as P is my strongest suit 11/12 (A smaller species of Eagle: a Falcon say)
I can apply my mind (headache) over a difficult problem and raise my thinking status upwards from 7/12 to complete an IQ test, but I would not want headaches all the time. INTP with a greater T variant (from Dragon to Eagle, less fantastic, more realistic)
Extraversion is rather easy for short periods and only after a time exhaustion sets in and I need a recharge period. ENTP. (Eagle to Snake) My Intraversion is 8/12 so the gap is smaller). ENFP to Ferret is possible and would be rather useful if I could sustain it.
Intuitive thoughts sometimes have to be checked by sensing information (for others), and this is hard work from 10/12 downwards. However, the work of collection sensing information is long lasting. I would not chase the Bear (ISTP) girls into the woods though. Too much. I would get lost. Especially not the S 8 and above on the Paragon test.
The change to Butterfly would be an act. Role play performance for a short period. This is ESFP. This involves a traumatic alteration in consciousness. I am not going to be a TV star as it is really an act. (I have turned down appearances.)
I think I probably work on ENFP, with the Beaver charisma if I can pull it off. Maybe, my talks do not go down all that well?
Mirror would be change to a Horse (ESFJ) which I cannot do. I cannot drive a car, so I cannot be a Petrolhead.
Mostly, relationships involve using techniques to minimise type conflicts.
#### Kuu
I don't think you'll ever get it, Perseus...
Maybe being physically irresistible would also make you constantly harrassed by people you don't care about. And that might make your beautiful mind go insane, or not capable or working... We're introverts... we need people to stfu, leave us alone and let us think. So having both would ironically be like having none...
#### Jesin
##### Prolific Member
Perseus, you're not speaking the same language as the rest of us. You're not using the same conceptual framework. Put down Keirsey and your animal typing for a moment and try to understand MBTI type theory. Otherwise you'll never be able to get your point across.
#### loveofreason
##### echoes through time
I have trouble separating mind from soul... my mind is my soul.
#### Jordan~
##### Prolific Member
I don't think you'll ever get it, Perseus...
Maybe being physically irresistible would also make you constantly harrassed by people you don't care about. And that might make your beautiful mind go insane, or not capable or working... We're introverts... we need people to stfu, leave us alone and let us think. So having both would ironically be like having none...
If you were really irresistible enough, you could just tell them to go away and they would. Besides, why bother leaving home when the fruits of your beautiful mind can pay servants to go out and do all the menial day to day tasks for you?
#### Ex-User (221)
##### Member
I'm not exactly a top contender in any catagory...
#### Gorgrim
##### Active Member
I have trouble separating mind from soul... my mind is my soul.
Isnt soul quite a subjective word?
I went with soul because I liked it better.
Mind....
Mind and Body? I hear it like that sometimes, as seperate things. My Soul, or Brain-connections, I think you could say. Is what really determines how everything I do or AM works.
Its the essence of me, my kind of "soul" determines everything about me - thus I find that it describes me the best. Atleast, I don't find either Mind or Soul wrong, but what really sets them apart is abit unclear to say the least. Because Im just as much as product of my mind - and enviroment too, as I am a product of my soul. In terms of how i see it
#### nihilen.
##### Active Member
What does this poll have to do with self-esteem. That's more like others-esteem.
#### loveofreason
##### echoes through time
Isnt soul quite a subjective word?
Absolutely.
What does this poll have to do with self-esteem. That's more like others-esteem.
You'll find that unexplained jumbling of concepts and highly unique definitions are a hallmark of Perseus' threads.
If you want to challenge your N to find hidden relationships by all means read them.
If it's at all likely to irritate you, then don't.
#### sagewolf
Isnt soul quite a subjective word?
Mind....
Mind and Body? I hear it like that sometimes, as seperate things. My Soul, or Brain-connections, I think you could say. Is what really determines how everything I do or AM works.
Its the essence of me, my kind of "soul" determines everything about me - thus I find that it describes me the best. Atleast, I don't find either Mind or Soul wrong, but what really sets them apart is abit unclear to say the least. Because Im just as much as product of my mind - and enviroment too, as I am a product of my soul. In terms of how i see it
[/CENTER]
Haaah... the way I see it, my soul is what is irreducibly me: but I don't know what that is. It might be my creativity, or my determination to be independent, or my indifference to interpersonal relationships, or all of that, or none of that... but I don't remember ever being just a soul and nothing else, so I don't know how my soul might be defined, except in these loose terms.
My mind is the expression of my soul to other people and the outer world in general-- and, indeed, my own perception of myself-- through the conduit of my brain, with the sum total of all the values and experiences and collected ideas and information that that brain holds. When I die, I might well lose all that information and revert to being just a soul, or my soul might have been coloured by the filter it passed through so many times, or it might be able to adapt and change.
...I sense a story idea coming on. Anyway, is it clear that I would prefer a beautiful mind, as that's what others see of me? If I were physically attractive, people would pay attention to me. Can't have that. I'm an I.
#### Waterstiller
##### ... runs deep
I put "beautiful mind" but I also find it hard to discern between mind and soul. I'd say that I presently think I'm all of the options aside from "irresistibly" attractive.
As far as what people perceive of me, the people I'm closest to seem to appreciate my mind/soul a lot. I'm seen as attractive to the average person, I suppose.
I have good self-esteem at this point in time.
#### Perseus
##### Prolific Member
Still having appalling difficulties relating to other people, especially mates and partners. Tormented to the edge of madness.
If they clicked on beautiful mind meets beautiful soul, the most blatant difficulties would be alleviated.
#### myexplodingcat
##### thwriterislurking
Mind and soul are more important than looks.
##### Member
Physically Irresistible.
Because the effort to get there is too fucking much.
#### JarNew
##### Banned
new category:
evolutionarily iresistable
Status
Not open for further replies.
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# Converting SVG into PNG
This post is post 4 of a (so far) 4-part series on "Scalar Vector Graphics (SVG)".
1. Ways to use SVG in your html pageFebruary 25, 2021
2. How to embed SVG images on MediumMarch 31, 2021
3. Making speech bubbles in SVGAugust 05, 2021
4. Converting SVG into PNGAugust 12, 2021
In one of my previous posts I mentioned that I was still looking for the best way to convert SVG into PNG. If you just Google “Convert SVG to PNG” you will get hundreds of hits, from Inkscape, to online tools, to photo editors that can import SVGs (I know Pixelmator Pro claims to support SVG imports). For simple SVGs these options may work, but I’m tend to explore the boundaries of what is possible in SVGs. Also, if you offer to convert an SVG to an PNG, you better (at least) offer me a way to specify the resolution that I want my PNG to be; you cannot just assume that the viewBox of the SVG says anything about the resolution it’s meant to be shown at.
Today I’m happy to announce that I found my way to do this: script Firefox to screenshot an SVG, with the exact boundaries I want, at the exact resolution I want.
The tool is also available as docker container, just build it from the GitHub repository.
Update: after using this method for a while, I found one drawback: it does not export transparency properly; it just gives your SVG a white background. This is a shame; Safari does export the background transparency (but then has problems rendering the SVGs….). To be continued!
## What is it
A command line script that one can run, give some parameters like width and height, or even custom JavaScript that needs to be run before the conversion, and that outputs a PNG file.
The main reason that I need this, is that I like using SVGs in these blog posts, however many websites (like Facebook and LinkedIn, consumers of the Open Graph image I serve with each blog post) don’t support SVG. So I need a tool to convert it to PNG, preferably automatically.
## Why Firefox
Over all my time with SVGs, Firefox has consistently been the best renderer. As a small example, the following SVG:
This is not a full comparison of all converters and which support which features; rather my point is: Firefox is in my experience the best.
## Scripting Firefox
There are multiple ways to script Firefox. A common one is to use the WebDriver protocol, through a small program called geckodriver. The simplest way to use WebDriver is through Selenium, a tool that is primarily for automating web applications for testing purposes, but is certainly not limited to just that (from the Selenium website. Using the Selenium WebDriver bindings for Python I built a first version, that did exactly what was needed. The problem: too many moving parts – you need geckodriver and a pip install selenium.
As a second version, I experimented with directly making “WebDriver” calls to geckodriver using curl:
curl -X POST "localhost:4444/session" --data '{"capabilities": {"alwaysMatch": {}}}' -H "Content-Type: application/json; charset=utf-8"
curl -X POST "localhost:4444/session/d6b5812e-962d-9f46-8d70-cf4ec999293a/url" --data '{"url": "file:///Volumes/Work/reinhrst.github.io/assets/images/2021/08/10/results-js-and-go-speedup.svg"}' -H "Content-Type: application/json; charset=utf-8"
It works, but takes quite some overhead, and still requires geckodriver.
It turns out that geckodriver is not much more than a translation between WebDriver on the one end, and the Firefox Marionette protocol on the other end; so if we learn to speak “Marionette”, we should be able to get rid of geckodriver.
### Marionette
The Marionette protocol is not well documented, however since all of Firefox is open source, if you know where to look, you can find it. I documented my findings in this StackOverflow answer:
• each message is a length-prefixed json message without newline (so for instance, when you connect telnet localhost 2828, you’re greeted by 50:{"applicationType":"gecko","marionetteProtocol":3}, the 50 meaning the json is 50 bytes long.
• each message (except for the first one) are a json array of 4 items:
• [0, messageId, command, body] for a request, where messageId is an int, command a string and body an object. Example (with length prefix) 31:[0,1,"WebDriver:NewSession",{}]
• [1, messageId, error, reply] for a reply. Here messageId is the id the reply was to, and either error or result is null (depending on whether there is an error). E.g. 697:[1,1,null,{"sessionId":"d9dbe...", ..., "proxy":{}}}]
• A full list of all commands can be found in the Marionette source code, and it seems to me that all functions there are pretty well documented. For one thing, it seems that they expose all WebDriver functions under WebDriver:*.
In the linked Marionette source code, there is a list of all commands, and to which JavaScript function they map. The arguments that are valid for that function (which are well documented) are exactly what you can give as arguments in the Marionette call.
The last part of the puzzle is how to start a (hidden) Firefox session to connect to (by default Marionette uses port 2828, which obviously leads to problems if you try to start more than one in parallel. The solution is to start FireFox with a profile that has a user preference for marionette.port set to 0. Then when it starts Firefox will choose a random free port, and write this to the user preferences file. A proof of concept in bash:
TEMPD="$(mktemp -d)" echo 'user_pref("marionette.port", 0);' > "${TEMPD}"/prefs.js
/Applications/Firefox.app/Contents/MacOS/firefox-bin --marionette --headless --no-remote --profile "${TEMPD}" & MARIONETTE_PORT="" while [ -z "$MARIONETTE_PORT" ]; do
sleep 1
MARIONETTE_PORT=$(cat "${TEMPD}"/prefs.js | grep 'user_pref("marionette.port"' | grep -oE '[1-9][0-9]*')
done
echo "Marionette started on port \$MARIONETTE_PORT"
fg
## Putting it all together
I wrote it all up in a less-than-200-line python file. It starts Firefox, opens a url (this can be a file:/// url; but actually also works fine with a remote SVG file, or even a whole webpage), runs some custom JavaScript to set the width and height, or other properties if you want to. And finally asks Firefox to save a screenshot of the :root element to a PNG file. And, because it’s all in python, it should be easy to add custom things, delays, waiting for a specific event, etc.
It turns out that headless Firefox is also very happy to run in a Docker container, so a Dockerfile is provided as well.
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# Tag Info
60
What you suggest is possible, but the solution is a major problem, for larger reasons. We have sent probes to crash into Jupiter. It is physically possible to send waste into a gas giant. Just as it is theoretically possible to send waste now into the Sun. However, the primary issues encountered commonly with waste is economic and logistical. Waste is not ...
57
It would lose speed due to drag and fall in. If you're thrusting to maintain speed, just fly like a plane and don't try to orbit. The hypersonic speed of orbital velocity would be conspicuous anyway, not a good way to hide. Do you have any idea how fast orbital velocity is? Low Earth orbit is about 17500 miles per hour. Imagine doing that while still ...
41
Analyzing Jupiter First off, since Jupiter doesn't have a surface, the 1 bar pressure altitude is commonly referred to as the surface. Surface temp (from a NASA fact sheet) is, in that case, around 165 K; cold but not cold enough that you couldn't insulate it trivially. So in this region, pressure and temperature are not a major concern. At this altitude ...
38
Like JDługosz wrote, what will cause problems in the scenario you describe isn't so much your orbit as the fact that you are within the gas giant's atmosphere. I'm going to use Jupiter here to have some specific gas giant to use for examples. Feel free to look up the relevant data for any other gas giant, or come up with your own. For the case we are ...
34
We have already found exo-planets matching this criteria. For example HD_100777_b has a mass just slightly higher than Jupiter and orbits its star at the same distance from the sun that our earth does. (The star is a similar size to our sun but I didn't check the brightness so I don't know for sure if it's in the habitable zone). You can explore the known ...
34
Io and Jupiter have a very special relationship. Io is a volcanic moon, which ejects charged particles. Due to its relatively low gravity (~0.18g), the particles escape, but they get trapped by Jupiter's immensely powerful magnetic field and form a plasma torus. The density of the plasma is higher close to and ahead of Io. Saturn is like a smaller Jupiter, ...
30
Skimming various gasses from the Jovian atmosphere or using superscience to extract metallic hydrogen from deep below the surface only taps a small amount of the potential resources available. Since you explicitly said "Jupiter" and not the Jovian system, I will set aside the 67 moons or thousands of asteroids on the L4 and L5 trojan points. Jupiter has a ...
23
It's possible, but heat generated by the Kelvin-Hemlholz mechanism may be too variable to complex life to develop solely as a result of this source of heat. This paper suggests that the temperature of Jupiter, when it first finished an initial phase of contraction, was quite high, at around 25000K. At this temperature, it would have a small habitable zone ...
23
Mining metallic Hydrogen might be a possibility, but I am unsure what happens when you move it out of the pressure and what goes on from there. Second and probably more fun for a story...Helium-3. Most Helium on Earth is Helium-4 (two neutrons and two protons at its center)...on Earth it's a silly ratio of 99.999986% Helium 4. However Jupiter has a ...
18
The problem is energy Since you're on the moon orbiting the gas giant, both you and the trash are moving at the moon's orbital speed around that gas giant. And it takes a lot of energy/fuel to slow the trash down and get it out of the planet's orbit, allowing it to fall into the atmosphere. As long as you have cheap and plentiful energy resources and ...
17
For the TL;DR, see the bottom of this answer. Okay, so first of all, the orbital period of the gas giant around its star is $256 \times 24$ hours, and I'd like to establish the distance from the planet to its star. Since you haven't specified anything about the star itself, I'll go with our Sun for simplicity's sake. Also for simplicity's sake (or to retain ...
15
First, it's important to discuss what radiation belts are and how they form. Radiation belts are formed by charged particles that are trapped by a planet's magnetic field and, due to the shape of that field and their own initial velocity, tend to collect in certain regions. The main source of charged particles in e.g. Earth's Van Allen belts is the solar ...
13
Absolutely. This would only take a few simply steps, and a small bit of luck. Here's how it could happen: A protostar forms from a collapsing gas cloud. A giant sphere of gas and dust collapses upon itself. The pressure is so great that the sphere begins nuclear fusion, and it beings to emit light. An accretion disk forms. The protostar begins to collect ...
13
Jupiter's magnetosphere encompasses all of its Galilean satellites Jupiter's magnetosphere has a dipole moment 18,000 times greater than Earth's and encloses all four of its major moons. Callisto's orbital semi-major axis is 1.8 million km; so this gives a wide range of potential orbits for an Earth-sized planet. A planet larger than Jupiter, perhaps one ...
12
Yes, but for a different reason. This is basically what happened with the Cassini probe, which was sent to crash into Saturn in 2017. However, the reason the probe was successfully disposed of wasn't because Saturn's a gas giant; it's because the spacecraft burned up upon entering Saturn's atmosphere. The same things happen with meteors, and would happen ...
11
First off, I'd like to plug JoeKissling's answer here, which I used as a basis for mine. Radiation pressure Hawking radiation emitted from a black hole acts as blackbody radiation, emitted equally from the surface area of the event horizon. Based on Wikipedia's 'crude analytic estimate', the equivalent temperature $T$ is given by $$\frac{\hbar c^3}{8\pi ... 11 The solution you are looking for is a mass driver. In essence, they are a giant electromagnetic gun that would accelerate a mass past escape velocity and send it to space. They were proposed decades ago as a cheaper method of sending cargo to space. The main benefit against rockets is that, as most of the energy is provided by the mass driver, the ship won't ... 11 No, it's not possible for the moon to always be between the planet and the sun. For the moon to be in a stable orbit around the planet, and always be in front of the sun, two things must be true (We'll ignore the situation of putting the Moon at the L1 Lagrange Point, it wouldn't be in orbit around the planet, and L1 is not long-term stable): The Moon's ... 10 I have one major point to make: A good portion of Jupiter does not complete one rotation in 9.8 hours. Jupiter isn't like a giant ball of rock. It's called as "gas giant" for a reason, which is that it has a large, massive, turbulent atmosphere that's constantly moving and changing. This means that its atmosphere undergoes differential rotation, a ... 10 Hydrogen, water, ammonia, all skimmed from the atmosphere rather than mined from the surface. Ammonia contains nitrogen, so with the water and a carbon asteroid you can start building greenhouses. Helium-3. Getting it out of Saturn's more shallow gravity well would be smarter, but if you're in the area anyway ... 10 Let's look at some key Jovian atmospheric characteristics: Density at P=1\text{ bar} (i.e. the surface): \rho_J=0.16\text{ kg m}^{-3} Temperature at P=1\text{ bar}: T=165\text{ K} Mean molecular weight: \mu=2.22 Primary atmospheric constituents: H (89.8%), He (10.2%) In other words, if you want to float close to the surface, you're in a cold, ... 10 Why are transits so rare? Essentially, you want a low relative orbital inclination. A body's orbital inclination is the angular difference between its orbital plane and a reference plane. In the Solar System, this reference plane is the the ecliptic, such that Earth's orbit is contained in this plane (and thus it has an inclination of zero). Most of the ... 9 Take a look at this question. Apparently Jupiter doesn't have enough mass to sustain a fusion reaction; it requires a lot more mass even for a small star. If heated enough it would even lose mass as atoms reached escape velocity. Assuming your type-2 civilization started a fusion reaction, the fusion wouldn't continue unless they actively kept it going, ... 9 We can go with an old disproven explanation that I found in an outdated science textbook I saw in high school: Star Farts During star formation, as the star's spin increases, it throws off matter for its equator in bursts. The heavier elements don't travel as far and form the inner rocky planets. The lighter elements travel farther, forming the ... 8 Really awesome answer by ckersch. I want to add in some math to get an idea of how large this kind of habitable zone would be. Formulas are from here and here, if you want to investigate them further, though I'll try to explain them here. We may assume that the source of energy is gravitational potential energy, defined as$$U_g = -G \frac{M_p m_s}{r} ...
8
Since you want this planet to be more or less Earth in orbit around a gas giant, let's do that, as a gedankenexperiment, and see what shakes out. Currently, Earth is in the "Goldilocks Zone" of radiant energy from its star. too close and it would be too hot; too far, too cold ("too hot" and "too cold" generally having the ...
8
So, what you want is a planet where there's very little light, but it isn't terribly cold. There's an easier way to get this, and it's more interesting. Take a normal F- or G-type star, pretty much like the Sun. Put your planet in orbit round it. Don't make it a moon of a gas giant, that gets complicated. Have an unusual feature: a large belt of fine dust ...
8
The spins of all large moons in the Solar System are locked to their host planet, meaning that they always show the same face to the planet. This is sometimes called "tidal locking", and it's pretty much unavoidable for the case of a large moon (even in systems with many moons, like Jupiter's Galilean satellites). It looks something like this: If you were ...
8
Your world is the equivalent of Jupiter's moon Io, which has tidally induced heating and volcanism. Then when the volcanoes go off, the charged particles they blast out provoke huge auroras on Jupiter. https://www.space.com/29248-jupiter-auroras-volcanic-moon-io.html Jupiter's auroras, which are sparked by particles from the planet's moons as well as ...
8
What you've described is the most expensive way possible to rid a world of waste, but yes, it can be done. However, human nature (with regrettably rare exception) is to use the simplest, cheapest solution possible. So unless your story includes an explanation of either... Why it's cheaper and more efficient to ship waste to Saturn over, say, dumping it ...
Only top voted, non community-wiki answers of a minimum length are eligible
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# as.POSIX*
0th
Percentile
##### Date-time Conversion Functions
Functions to manipulate objects of classes "POSIXlt" and "POSIXct" representing calendar dates and times.
Keywords
utilities, chron
##### Usage
as.POSIXct(x, tz = "", ...)
as.POSIXlt(x, tz = "", ...)
"as.POSIXlt"(x, tz = "", format, ...)
"as.POSIXlt"(x, tz = "", origin, ...)
"as.double"(x, ...)
##### Arguments
x
An object to be converted.
tz
A time zone specification to be used for the conversion, if one is required. System-specific (see time zones), but "" is the current time zone, and "GMT" is UTC (Universal Time, Coordinated). Invalid values are most commonly treated as UTC, on some platforms with a warning.
...
further arguments to be passed to or from other methods.
format
character string giving a date-time format as used by strptime.
origin
a date-time object, or something which can be coerced by as.POSIXct(tz = "GMT") to such an object.
##### Details
The as.POSIX* functions convert an object to one of the two classes used to represent date/times (calendar dates plus time to the nearest second). They can convert a wide variety of objects, including objects of the other class and of classes "Date", "date" (from package date), "chron" and "dates" (from package chron) to these classes. Dates without times are treated as being at midnight UTC.
They can also convert character strings of the formats "2001-02-03" and "2001/02/03" optionally followed by white space and a time in the format "14:52" or "14:52:03". (Formats such as "01/02/03" are ambiguous but can be converted via a format specification by strptime.) Fractional seconds are allowed. Alternatively, format can be specified for character vectors or factors: if it is not specified and no standard format works for all non-NA inputs an error is thrown.
If format is specified, remember that some of the format specifications are locale-specific, and you may need to set the LC_TIME category appropriately via Sys.setlocale. This most often affects the use of %b, %B (month names) and %p (AM/PM).
Logical NAs can be converted to either of the classes, but no other logical vectors can be.
If you are given a numeric time as the number of seconds since an epoch, see the examples.
Character input is first converted to class "POSIXlt" by strptime: numeric input is first converted to "POSIXct". Any conversion that needs to go between the two date-time classes requires a time zone: conversion from "POSIXlt" to "POSIXct" will validate times in the selected time zone. One issue is what happens at transitions to and from DST, for example in the UK
as.POSIXct(strptime("2011-03-27 01:30:00", "%Y-%m-%d %H:%M:%S"))
as.POSIXct(strptime("2010-10-31 01:30:00", "%Y-%m-%d %H:%M:%S"))
are respectively invalid (the clocks went forward at 1:00 GMT to 2:00 BST) and ambiguous (the clocks went back at 2:00 BST to 1:00 GMT). What happens in such cases is OS-specific: one should expect the first to be NA, but the second could be interpreted as either BST or GMT (and common OSes give both possible values). Note too (see strftime) that OS facilities may not format invalid times correctly.
##### Value
as.POSIXct and as.POSIXlt return an object of the appropriate class. If tz was specified, as.POSIXlt will give an appropriate "tzone" attribute. Date-times known to be invalid will be returned as NA.
##### Note
Some of the concepts used have to be extended backwards in time (the usage is said to be ‘proleptic’). For example, the origin of time for the "POSIXct" class, ‘1970-01-01 00:00.00 UTC’, is before UTC was defined. More importantly, conversion is done assuming the Gregorian calendar which was introduced in 1582 and not used universally until the 20th century. One of the re-interpretations assumed by ISO 8601:2004 is that there was a year zero, even though current year numbering (and zero) is a much later concept (525 AD for year numbers from 1 AD).
If you want to extract specific aspects of a time (such as the day of the week) just convert it to class "POSIXlt" and extract the relevant component(s) of the list, or if you want a character representation (such as a named day of the week) use the format method.
If a time zone is needed and that specified is invalid on your system, what happens is system-specific but attempts to set it will probably be ignored. Conversion from character needs to find a suitable format unless one is supplied (by trying common formats in turn): this can be slow for long inputs.
DateTimeClasses for details of the classes; strptime for conversion to and from character representations.
Sys.timezone for details of the (system-specific) naming of time zones.
locales for locale-specific aspects.
##### Aliases
• as.POSIXct
• as.POSIXct.default
• as.POSIXct.POSIXlt
• as.POSIXct.date
• as.POSIXct.dates
• as.POSIXct.Date
• as.POSIXct.numeric
• as.POSIXlt
• as.POSIXlt.Date
• as.POSIXlt.date
• as.POSIXlt.dates
• as.POSIXlt.POSIXct
• as.POSIXlt.factor
• as.POSIXlt.character
• as.POSIXlt.default
• as.POSIXlt.numeric
• as.double.POSIXlt
##### Examples
library(base) ## These may not be correct names on your system as.POSIXlt(Sys.time(), "America/New_York") # in New York as.POSIXlt(Sys.time(), "EST5EDT") # alternative. as.POSIXlt(Sys.time(), "EST" ) # somewhere in Eastern Canada as.POSIXlt(Sys.time(), "HST") # in Hawaii as.POSIXlt(Sys.time(), "Australia/Darwin") windows cols <- c("code", "coordinates", "TZ", "comments") tmp <- read.delim(file.path(R.home("share"), "zoneinfo", "zone.tab"), header = FALSE, comment.char = "#", col.names = cols) if(interactive()) View(tmp)
Documentation reproduced from package base, version 3.3, License: Part of R @VERSION@
### Community examples
jimrothstein@gmail.com at Nov 25, 2016 base v3.3.1
## example * Using system time * Create and Compare 3 objects from system time r now<-Sys.Date() d1<- as.Date(now) class(d1) type(d1) d2<-as.POSIXct(now) d3<-as.POSIXlt(now)
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# Problem with numeric integration
I am having trouble with the UnitStep function as in the title. My problem is very simple, but I am not able to get a numerical result.
I have
f1[y] = 1/(E^((-1 + y)^2/2)*Sqrt[2*Pi])
g1[y] = (1.0028877725946312*^6*UnitStep[-7.963235463105154 - y])/
E^((-1 + y)^2/2) + (0.12147136083763578*UnitStep[-7.963235463105154 + y])/
E^((-1 + y)^2/2) +
1.001393070562657*
(0.3484061634773921*Sqrt[E^(-(-1 + y)^2/2)] +
0.3484061634773921*Sqrt[E^(-(1 + y)^2/2)])^2*
(-UnitStep[-7.963235463105154 + y] + UnitStep[7.963235463105154 + y])
and I want to solve the problem
$$N\left[\frac{1}{2}\int_{-\infty}^{\infty}\left(\sqrt{f1[y]}-\sqrt{g1[y]}\right)^2dy\right]$$
However, I did not get any result although I waited for a long time. I can plot $g1$ without any problem as well as $f1$, but I can not calculate the simple integral.
-
there is a syntax error in your definition. Try f1[y_] = instead of f1[y] = – Thies Heidecke Feb 27 '13 at 20:37
@ThiesHeidecke You mean f1[y_]:=, but as long as the NIntegrate uses y, that actually doesn't matter. I suspect the real problem is trying to use N[Integrate[...]] instead of NIntegrate. – Xerxes Feb 27 '13 at 20:39
@Xerxes: in this case Set and SetDelayed are both fine. But you have a point with the N[Integrate[...]] construct. – Thies Heidecke Feb 27 '13 at 20:41
@ThiesHeidecke even if I change to the other syntax I still have the same problem. – Seyhmus Güngören Feb 27 '13 at 20:41
Ah, got it. Well, you have your answer. When you wrap N outside of an integral, it first tries to evaluate it symbolically and only after it realises it can't (or until it succeeds), it tries numerical. Using NIntegrate it is done numerically from the start. The symbolic attempt is what takes long – Rojo Feb 27 '13 at 20:46
Using your definitions (using the placeholder pattern f1[y_] instead of the absolute pattern f1[y] is usually a good idea if you want to use it as a function that works with numerical values, too. Also using := (SetDelayed) instead of = (Set) inserts the left hand side value y into the definition every time you use it, which is closer to the behavior you would expect from a function):
f1[y_] := 1/(E^((-1 + y)^2/2)*Sqrt[2*Pi])
g1[y_] := (1.0028877725946312*^6*UnitStep[-7.963235463105154 - y])/
E^((-1 + y)^2/2) + (0.12147136083763578*
UnitStep[-7.963235463105154 + y])/E^((-1 + y)^2/2) +
1.001393070562657*(0.3484061634773921*Sqrt[E^(-(-1 + y)^2/2)] +
0.3484061634773921*
Sqrt[E^(-(1 + y)^2/2)])^2*(-UnitStep[-7.963235463105154 + y] +
UnitStep[7.963235463105154 + y])
you could compute the integral via
(1/2) NIntegrate[(Sqrt[f1[y]]-Sqrt[g1[y]])^2, {y,-\[Infinity], \[Infinity]}]
(* 0.10271 *)
Using NIntegrate can save a lot of time, since Mathematica then knows that you are interested in a numerical solution from the start and doesn't waste time trying to find an analytical solution (Thanks to Xerxes and Rojo for pointing that out).
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great! So my mistake was using the symbols. I guess in this case mathematica is searching first the algebraic solution and then trying to convert it to numerical value. Thanks alot. – Seyhmus Güngören Feb 27 '13 at 20:49
Unless you Clear[y] prior to running this code, it is not safe to use Set instead of SetDelayed. Consider y=banana;f[y_]=y;f[0.1]. (* banana *) – Xerxes Feb 27 '13 at 20:51
good point, i'll change the code for robustness. – Thies Heidecke Feb 27 '13 at 20:52
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GEORGE (programming language)
7:24
GEORGE (General Order Generator) is a programming language invented by Charles Leonard Hamblin in 1957.[1][2][3][4]
It was designed around a push-down pop-up stack for arithmetic operations, and employed reverse Polish notation.[5]
The language included loops, subroutines, conditionals, vectors, and matrices.
Algebraic expressions were written in reverse Polish notation; thus, ${\displaystyle a+b}$ was written `a b +`, and similarly for the other arithmetic operations of subtraction, multiplication, and division.
The algebraic expression ${\displaystyle ax^{2}+bx+c}$ was written `a x dup × × b x × + c +`, where '`dup`' meant 'duplicate the value'.
Following the reverse Polish form, an assignment statement to evaluate the formula ${\displaystyle y=ax^{2}+bx+c}$ was written as `a x dup × × b x × + c + (y)`.
The computer evaluated the expression as follows: the values of `a`, then `x`, were pushed onto the top of the accumulator stack; '`dup`' caused a copy of the top-most value (`x`) to be pushed onto the top of the accumulator stack; Multiply (`×`) caused the top two values, namely, `x` and `x`, to be removed (popped) and multiplied, returning the product to the top of the accumulator stack. The second multiply (`×`) then caused the top two values on the stack (namely, `a` and `x**2`) to be popped and multiplied, and the product (`a×x**2`) to be pushed onto the top of the accumulator stack. And so on the remaining components of the expression. The final operation, namely (`y`), returned the value of the expression to storage without changing the status of the accumulator stack.
Assuming that the value on the top of the accumulator stack was not required immediately, it would be removed (cleared) by using the operator (`;`).
The following program reads in eight values and forms their sum:
```0,
1, 8 rep (j)
R +
]
(P)
```
The first line initialises the sum by pushing the value zero onto the top of the accumulator stack.
The second line introduces a loop, is spoken as "for 1 to 8 repeat for j", and is terminated by the square bracket.
In the third line, R causes one number to be read in and pushed onto the top of the accumulator stack, and the plus sign (+) causes that value to be added to the (partial) sum, leaving only the partial sum on the top of the accumulator stack.
After the loop terminates, the (P) causes the final sum to be punched on a card.
Manipulation of vectors and matrices requires subscript notation. In GEORGE, the subscript(s) preceded the vector or matrix name. Thus A(j) was written `j | A`. The following program reads in vector a of 10 values, then forms the squares of those values, and finally prints those values.
```1, 10 R1 (a)
1, 10 rep (j)
j | a dup * j | (a) ;
]
1, 10 P1 (a)
```
In the program, the first line is a vector read that reads in the ten values into a(1) through a(10).
The second line introduces a loop to run through the ten values of j.
The third line fetches a(j), duplicates it, multiplies those two values giving the square, and then stores it in a(j). Note the semicolon (;), which clears (or cancels) the top entry in the accumulator stack. Were this not done, the accumulator would gradually fill up with the squares of the values.
The final line is a vector punch (i.e., print) to write out the ten squares.
GEORGE coding table[6]
1 2 3 4 5 6 7 8 15
0 / 0 16 a q (a) (q) log R
1 , // 1 17 b r (b) (r) exp (P)
2 ; ~ 2 18 c s (c) (s) pow
3 * & 3 19 d t (d) (t) rem
4 4 20 e u (e) (u) sqrt
5 + ] 5 21 f v (f) (v) sin
6 - 6 22 g w (g) (w) cos
7 × 7 23 h x (h) (x)
8 ÷ rep 8 24 i y (i) (y) R1
9 neg I 9 25 j z (j) (z) P1
10 mod 10 26 k α (k) (α) R11
11 max 11 27 l β (l) (β) P11
12 dup 12 28 m γ (m) (γ)
13 rev 13 29 n λ (n) (λ)
14 = 14 30 Θ μ (Θ) (μ)
15 > 15 31 p ω (p) (ω)
The above GEORGE coding table assisted in transcribing a program onto punch cards.
Conditional operations were written as jumps, as follows: if a > 0 go to 5 (which transfers to label 5 if a is greater than zero) would be written
`0 a > 5 ↑ `
Label 5 was indicated by including *5 elsewhere in the program. Unconditional transfers were written 5↑
Subroutine calls were made with the down arrow, .g., to call subroutine labelled 17, write 17↓, where the label 17 was encoded using column 3 of the above table.
Historical note
In the first version running by May 1957 on an English Electric DEUCE, all values were stored in binary fixed-point form in a 32-bit word, with 16 binary places.
In the second version introduced by 1958, values were held in floating-point form, with one value per word: 22 bits for the mantissa and 10 bits for the exponent.
Some form of coding table was needed because the printing equipment of the time provided only 26 letters of the alphabet, a decimal point, plus sign, minus sign, and slash.
References
1. ^ Hamblin, Charles Leonard (May 1957). An Addressless Coding Scheme based on Mathematical Notation (Typescript). New South Wales University of Technology.
2. ^ Hamblin, Charles Leonard (June 1957). "An addressless coding scheme based on mathematical notation". Proceedings of the First Australian Conference on Computing and Data Processing. Salisbury, South Australia: Weapons Research Establishment.
3. ^ Hamblin, Charles Leonard (1957). "Computer Languages". The Australian Journal of Science (20?): 135–139; Hamblin, Charles Leonard (November 1985). "Computer Languages". The Australian Computer Journal (Reprint). 17 (4): 195–198.
4. ^ Hamblin, Charles Leonard (1958). GEORGE IA and II: A semi-translation programming scheme for DEUCE: Programming and Operation Manual (PDF). School of Humanities, University of New South Wales, Kensington, New South Wales. Archived (PDF) from the original on 2020-04-04. Retrieved 2020-07-27.
5. ^ Beard, Bob (Autumn 1997) [1996-10-01]. "The KDF9 Computer — 30 Years On" (PDF). Resurrection - The Bulletin of the Computer Conservation Society. No. 18. Computer Conservation Society (CCS). pp. 7–15. ISSN 0958-7403. Archived (PDF) from the original on 2020-07-27. Retrieved 2020-07-27. […] The KDF9 is remarkable because it is the believed to be the first zero-address instruction format computer to have been announced (in 1960). It was first delivered at about the same time (early 1963) as the other famous zero-address computer, the Burroughs B5000 in America. Like many modern pocket calculators, a zero-address machine allows the use of Reverse Polish arithmetic; this offers certain advantages to compiler writers. It is believed that the attention of the English Electric team was first drawn to the zero-address concept through contact with George (General Order Generator), an autocode programming system written for a Deuce computer by the University of Sydney, Australia, in the latter half of the 1950s. George used Reversed Polish, and the KDF9 team were attracted to this convention for the pragmatic reason of wishing to enhance performance by minimising accesses to main store. This may be contrasted with the more `theoretical' line taken independently by Burroughs. Besides a hardware nesting store or stack - the basic mechanism of a zero-address computer - the KDF9 had other groups of central registers for improving performance which gave it an interesting internal structure. […] [1] (NB. This is an edited version of a talk given to North West Group of the Society at the Museum of Science and Industry, Manchester, UK on 1996-10-01.)
6. ^ Programming Course. School of Electrical Engineering, The University of New South Wales. n.d. p. 24.
By: Wikipedia.org
Edited: 2021-06-18 18:13:08
Source: Wikipedia.org
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Plotting a ECDF in R and overlay CDF
I need to plot a ECDF in R and overlay a CDF. In my case I have to do this with the gamma distribution where alpha = 2, beta = 3, and for example, with a sample size of 40, so it is pretty straightforward.
plot(ecdf(rgamma(40, 2, 1/3)))
lines(x, pgamma(x, shape = 2, scale = 3), type="l", col = "red")
I'm not sure, but I think that the above should be correct (I read somewhere that rgamma use lambda as parameter, so that's why it's 1/3 and scale refers to beta according to what I read, so it's just 3).
The result is the following plot:
I wonder if what I did is okay, if it is... then the only thing I don't understand is, why does the red line reaches until x has a value of 12 or 13?
• Maybe the red and black line overlay each other after 13?
– kristang
May 23, 2015 at 8:52
• You don't say what's in x (give minimum reproducible example, please), but I bet max(x) is right where the red line stops. It did what you told it to do ... if you want it to draw higher, give it higher values to draw. May 24, 2015 at 0:41
Yes, what you have done is ok. You were right to worry about the default parameters of the Gamma distribution, because if you do not specify the scale, then R defaults to rate which is 1/scale.
When it comes to the graph though, might I suggest though an upgrade to ggplot2? The picture becomes much clearer this way.
library(ggplot2)
set.seed(235)
x<-rgamma(40,2,scale=3)
p<-qplot(x,stat="ecdf",geom="step")+theme_bw()
p<-p+stat_function(fun=pgamma,color="blue",args=list(shape=2,scale=3))
p<-p+labs(title="ECDF and theoretical CDF")
p
As you can see the two curves are reasonably close, even with 40 samples. And they are more discernible as well. If you like then, there are many tutorials on ggplot2 out there that you can follow.
• +1 - the reason the base plot is hard to read though is because of the extreme aspect ratio - which has nothing directly to do with using ggplot or base graphics. May 25, 2015 at 13:24
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# Intel Optane Persistent Memory and kdb+
Intel® Optane™ persistent memory, herein called Intel Optane PMem, is a new hardware technology from Intel.
Intel Optane PMem is based on a new silicon technology, 3D XPoint, which has low latency (memory like) attributes and is more durable than traditional NAND Flash.
Intel Optane technology was first unveiled in 2017, in the form of Intel Optane SSD. By packaging 3DX Point in a Solid State Drive (SSD), Intel created a product with speeds faster than the other SSD devices (largely based on NAND Flash) that preceded it. However, the scale of performance improvement of 3DX Point brought another target into Intel’s sights – main memory.
The technology that dominates main memory, DRAM, is order of magnitudes faster to access, but smaller in size and more cost per Byte than NAND flash. Storage (whether SSD or spinning disk) is large and cheap, but orders-of-magnitude slower to access. This has led to a significant gap in the memory-storage hierarchy:
SRAM CPU cache L1, L2, L3
DRAM main memory
SSD storage
HDD archival
Intel Optane PMem introduces a new category that sits between memory and storage. In newly designed system boards, capable of supporting Intel Cascade Lake CPU chip set, or later, the memory sits in the same DDR4 DIMM slots (and memory bus) as DRAM. Persistent memory sits close to the CPU, and allows applications to directly address it as memory.
SRAM CPU cache L1, L2, L3
DRAM main memory
>> Optane Memory
>> Optane SSD
SSD storage
HDD archival
## What are the advantages?
By combining storage and memory, Intel Optane PMem is at once high-performance, high-capacity, and cost-efficient.
### High-performance
Intel Optane technology is faster than existing storage media, as shown by Intel Optane SSDs. Intel Optane PMem offers another advantages, due to - Direct CPU access to individual bytes, rather than blocks, at a time. - Minimal latency and maximal throughput via the memory bus, versus PCIe connections for SSDs.
### High-capacity
While DRAM currently caps at 258 GiB per module, Intel Optane PMem is current generation of Optaen (aka Apache Pass) is available in capacities of 128 GiB, 256 GiB, and 512 GiB. On Cascade Lake designs, six Intel Optane PMem modules can be used per socket, users can address 10+ TB of optane memory space on a single 4 socket system.
### Cost-efficient
The retail prices of Intel Optane PMem are intended to sit between the price per GiB for DRAM and NVMe Intel Optane storage. This can be one consideration for a kdb+ solution, especially if it uses a lot of active memory for streaming or real-time analytics, or if it needs extremely fast access to hot data in a HDB. This may make such a solution more affordable than just using DRAM. The increased memory size also provides an opportunity to consolidate workloads onto fewer nodes, leading to an even lower TCO through reduced hardware, software, datacenter and operations costs.
## How can kdb+ users benefit?
Some advantages that Intel Optane PMem provides to databases are:
• On-disk databases will run faster using expanded Intel Optane PMem as storage because some or all of the space does not need fetching from disk
• In-memory databases will scale using Intel Optane PMem as a larger memory space
A typical kdb+ application uses a combination of memory and storage to gather, persist and analyze enormous datasets. Kdb+’s structured use of on-disk data allows efficient access to databases up to petabyte scale. The size of in-memory datasets, however, is primarily restricted by the size of the accessible memory space.
Once datasets grow beyond the available memory capacity, users have three main options:
• read/write data from storage
• scale horizontally
• scale vertically
### Read/write data from storage
Kdb+ on-disk databases are partitioned, most commonly by date, with individual columns stored as binary objects within a file system. The result is a self-describing database on disk, mapped into memory by a kdb+ process and presented to users as if it resides in memory. The limiting factor with most queries to on-disk data, is the latency and bandwidth penalty paid to jump from storage to DRAM-based memory.
### Scale horizontally
Adding more machines into the mix allows users to add more memory by scaling out. Processes across a cluster communicate via IPC and work on calculations as a single logical unit. The success of this approach depends largely on the inherent parallelization of the task at hand, which must be balanced against the increased complexity and costs of hardware.
### Scale vertically
Vertical scaling is the preferred method of scaling for most kdb+ applications, as users aim to keep as much hot data as possible close to the CPU. If everything would fit in memory, and we could afford it, we’d probably put it there. However, traditional memory (DRAM) is expensive and, even if funds were unlimited, is limited in capacity on a per-socket basis. Intel Optane PMem presents opportunities to address these issues, through faster form of block storage or through significantly scaled-up memory capacity.
## How can kdb+ users deploy Intel Optane PMem?
Intel Optane PMem can be deployed in a number of ways, depending on the design of users’ existing applications. There are three modes by which Intel Optane PMem can be used by kdb+.
• Memory mode
• App Direct Mode
• Storage over App Direct
### Memory mode
In Memory mode, the DRAM acts as a cache for frequently-accessed data, while the Intel Optane PMem provides large memory capacity. When configured for Memory Mode, the applications and operating system perceive a pool of volatile memory, no differently than on DRAM-only systems. In this mode, no specific persistent memory programming is required in the applications. This dramatically increases the amount of memory seen by the kernel and hence available to kdb+. DRAM mixes its memory address space with Optane.
For larger datasets, this increased memory space avoids the costs and complexity of horizontal scaling.
Vertical-vs-horizontal scaling
A common solution for overly-large in-memory datasets, is to split the data across multiple machines. Data is usually split based on some inherent partition of the data (e.g. ticker symbol, sensor ID, region), to allow parallelization of calculations. Horizontal scaling allows users to add memory, but comes at a cost. Average perfomance (versus a single machine) is reduced due to the cost of IPC to move data between processes. There is also an increase in complexity as well as hardware, datacenter and operations costs.
Intel Optane PMem, in Memory mode, creates a new opportunity to scale vertically. A significantly extended memory space enables calculations on a single machine, rather than a cluster. This removes or reduces the complexities and performance cost of IPC, allowing users to run simpler, more efficient analytics.
### App Direct Mode
Kdb+ 4.0 contains support for App Direct Mode, in which the applicaitons and operating system are explicitly aware there are two types of direct load/store memory in the platform, and can direct whihch type of data read or write is suitable for DRAM or Intel® Optane™ persistent memory. Kdb+ sees Intel Optane PMem and DRAM as two separate pools, and gives users control over which entities reside in each. As a result, users can optimize their applications and schemas, keeping hot data in fast DRAM while still taking full advantage of the expanded memory capacity.
Horizontal partitioning
e.g. Keep ‘recent’ historical data in Intel Optane PMem, allowing multi-day queries in memory
Vertical partitioning
e.g. Different tables/columns residing in DRAM/Intel Optane PMem
### Storage over App Direct
Storage over App Direct Mode is a specialized application of App Direct Mode, in which Intel Optane PMem behaves like a storage device accessible via a filesystem. As the filesystem is explicitly optimized for the underlying technology, it offers better operational latencies. With extremely low read/write speeds, data is passed quickly between storage and memory, enabling faster queries. Intel Optane PMem is particularly fast at small, random reads, which makes it particularly effective at speeding up kdb+ historical queries.
Storage over App Direct Mode was recently benchmarked, publicly, using the STAC M3 industry-standard benchmarks. Tests ran on Lenovo ThinkSystem servers with Intel Optane PMem, 2nd Generation Intel® Xeon® processors, and kdb+ 3.6.
Using a 2-socket server:
• Intel Optane PMem was faster in 16 of 17 STAC-M3 Antuco benchmarks, relative to 3D NAND SSD
• In 11 of the benchmarks, Intel Optane PMem was faster by more than 2×
Using a 4-socket server:
• Intel Optane PMem was faster in 8 of 9 STAC-M3 Kanaga benchmarks, relative to 3D NAND SSD
• In 6 of the benchmarks, Intel Optane PMem was faster by more than 2×
Compared to all publicly disclosed STAC-M3 Antuco results:
• For 2-socket systems running kdb+, this solution set new records in 11 of 17 mean response-time benchmarks.
• For 4-socket systems running kdb+ this solution set new records in 9 of 17 mean response-time benchmarks.
Write speeds are also improved using Intel Optane PMem, allowing higher throughput when logging and writing database partitions.
## Summary
Intel Optane persistent memory is a game-changing technology from Intel, which allows kdb+ users to increase the performance and capacity of their applications. Through reduced memory costs and infrastructure consolidation, Intel Optane PMem should also reduce TCO.
Earlier versions of kdb+ are already compatible with Intel Optane PMem through Memory Mode (BIOS settings required) and Storage over App Direct Mode, providing improvements for both in-memory and on-disk datasets. From version 4.0 onwards App Direct Mode gives users control over Intel Optane PMem, taking optimal advantage of the technology to suit their applications.
KX has created a new technology and marketing partnership with Intel, around Optane Memory. By working closely with Intel’s engineers, we ensure kdb+ takes full advantage of the features of Intel Optane PMem. We also have a team of engineers ready to help customers evaluate Intel Optane PMem. Through a POC, we can determine the optimal way to deploy the new technology to new and existing use cases. Please contact optane@kx.com to coordinate any such POC, or for any technical questions.
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TL;DR
On with TASK #2 from The Weekly Challenge #130. Enjoy!
# The challenge
You are given a tree.
Write a script to find out if the given tree is Binary Search Tree (BST).
According to wikipedia, the definition of BST:
A binary search tree is a rooted binary tree, whose internal nodes each store a key (and optionally, an associated value), and each has two distinguished sub-trees, commonly denoted left and right. The tree additionally satisfies the binary search property: the key in each node is greater than or equal to any key stored in the left sub-tree, and less than or equal to any key stored in the right sub-tree. The leaves (final nodes) of the tree contain no key and have no structure to distinguish them from one another.
Example 1
Input:
8
/ \
5 9
/ \
4 6
Output: 1 as the given tree is a BST.
Example 2
Input:
5
/ \
4 7
/ \
3 6
Output: 0 as the given tree is a not BST.
# The questions
My question about the definition is whether the leaves are considered only the empty left/right nodes of a node that has a key. Another question would be whether a node with a key always has two non-empty left and right children.
All in all, anyway, it doesn’t really matter for the implementation I have in mind… so it’s more curiosity than anything else.
# The solution
The most straightforward approach is, for me, to go recursive. In this case, in each node we will have to consider the following quantities:
• the key of the node itself;
• the minimum key and the maximum key of the left child, which we will call $lmin and $lmax;
• the same quantities for the right child, respectively $rmin and $rmax.
At that node, we have the following:
• if either the left or the right child don’t comply with the BST rules, then the whole tree does not either. Hence, we have to make sure that they do.
• At the specific node, we must check that the key is greater than $lmax (i.e. the maximum value on the left side) and that it is also less than $rmin (i.e. the minimum value on the right side).
If both apply, then this particular node is good, and we can go back to the parent node, reporting a success and also $lmin and $rmax as the overall minimum and maximum values.
In case the tree is not perfectly assembled (e.g. a node only has a left or a right side) we will have to cope with the fact and act accordingly.
Perl goes first this time:
#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';
sub check_bst ($root) { state$checker = sub ($node) { return 1 unless$node;
my $key =$node->{key};
my ($lsub,$lmin, $lmax) = __SUB__->($node->{left});
return 0 unless $lsub; ($lmin, $lmax) = ($key, $key - 1) unless defined$lmin;
my ($rsub,$rmin, $rmax) = __SUB__->($node->{right});
return 0 unless $rsub; ($rmin, $rmax) = ($key + 1, $key) unless defined$rmin;
return 0 if $key <$lmax || $key >$rmin;
return (1, $lmin,$rmax);
};
return ($checker->($root))[0];
}
sub n ($k,$l = undef, $r = undef) {{key =>$k, left => $l, right =>$r}}
say check_bst(n(8, n(5, n(4), n(6)), n(9)));
say check_bst(n(5, n(4, n(3), n(6)), n(7)));
I guess that these two lines deserve some additional explanation:
($lmin,$lmax) = ($key,$key - 1) unless defined $lmin; ... ($rmin, $rmax) = ($key + 1, $key) unless defined$rmin;
In case a leg is empty, we get nothing from it (i.e. undef). This inherently means that the sub-tree on that side is compliant, hence:
• to make the test succeed, we set $lmax to be smaller than the key ($key - 1), and $rmin to be greater than it ($key + 1).
• on the other hand, the missing extreme is set to be equal to $key, because this is the value we want to send back to the parent’s call. Time for Raku now, which is a simple translation: #!/usr/bin/env raku use v6; sub check-bst ($root) {
my sub checker ($node --> Array()) { return 1 unless$node;
my ($key,$left, $right) =$node<key left right>;
my ($lsub,$lmin, $lmax) = checker($left);
return 0 unless $lsub; ($lmin, $lmax) = ($key, $key - 1) unless defined$lmin;
my ($rsub,$rmin, $rmax) = checker($right);
return 0 unless $rsub; ($rmin, $rmax) = ($key + 1, $key) unless defined$rmin;
return 0 if $key <$lmax || $key >$rmin;
return (1, $lmin,$rmax);
}
return checker($root)[0]; } sub n ($k, $l = Nil,$r = Nil) {(key => $k, left =>$l, right => \$r).hash}
put check-bst(n(8, n(5, n(4), n(6)), n(9)));
put check-bst(n(5, n(4, n(3), n(6)), n(7)));
And with this… it’s all for this post, I hope you enjoyed it and stay safe anyway!
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# If two vectors $$\vec{r}.\vec{n_1}=d_1$$ and $$\vec{r}.\vec{n_2}=d_2$$ are such that $$\vec{n_1}.\vec{n_2}$$=0, then which of the following is true?
Category: QuestionsIf two vectors $$\vec{r}.\vec{n_1}=d_1$$ and $$\vec{r}.\vec{n_2}=d_2$$ are such that $$\vec{n_1}.\vec{n_2}$$=0, then which of the following is true?
Editor">Editor Staff asked 11 months ago
If two vectors \vec{r}.\vec{n_1}=d_1 and \vec{r}.\vec{n_2}=d_2 are such that \vec{n_1}.\vec{n_2}=0, then which of the following is true?
(a) The planes are perpendicular to each other
(b) The planes are parallel to each other
(c) Depends on the value of the vector
(d) The planes are at an angle greater than 90°
This question was posed to me in semester exam.
I want to ask this question from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options
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# MATLAB Really Simple Question
This is so easy I am sure...but I have no idea how to look it up.
I want to execute a loop from i = 1 to N
During each iteration I want to prompt the user for the i-th input. Let's say, I want to ask for
x1, x2, x3, ..., xN.
I should be able to write something like:
Code:
for i:N
x(i) = input(' Enter value of x' & i)
next
But the '&' does not seem to be the proper way to do this.....
Anyone know this one?
Thanks!
matonski
for i = 1:3
x(i) = input([' Enter value of x' num2str(i) ': ']);
end
Wow! You're my hero right now matonski!
Now maybe I can get a little extra out of you? I am used to using
Code:
For i = 1:3
x(i) = input(' stuff ')
end
Can you tell me litle about your syntax? Why are the '[' brackets now required? as in your syntax
Code:
for i = 1:3
x(i) = input([' Enter value of x' num2str(i) ': ']);
end
Thanks again!!!
matonski
Since i is a number, I had to use num2str to convert it to a string. Then, the brackets are used to concatenate the separate strings.
Since i is a number, I had to use num2str to convert it to a string. Then, the brackets are used to concatenate the separate strings.
Excellent! So brackets are used to concatenate strings. Perfect!
Thanks again
I want to assign the value 5 to the variables x1,x2,x3 so I would like to be able to do something to the effect of
Code:
for i = 1:3
[x num2str(i)] = 5
Thanks!
EDIT: I just tried
strcat(x, num2str(i))= 5
and Horrible things happened! Haha...
matonski
Horrible things happened because you are trying to assign a number to a string. It's like trying to assign 5 to the number 4.
I suggest not naming variables that way and simply using x(1), x(2), etc. There's a way using the function eval, but that's generally frowned upon. Besides, using arrays lets you make use of all matlab's matrix functionality very simply and straightforwardly.
For example, if you wanted to just set x(1) through x(3) to 5, you could just do x(1:3) = 5
Mentor
Alternatively, you could do this:
Code:
do i=1:3
x(i) = 5
end
This is longer than the way matonski suggested, but it's more in line with many other programming languages.
do i=1:3
end
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My Math Forum Related rates - inscribed
Calculus Calculus Math Forum
November 9th, 2017, 01:42 PM #1 Newbie Joined: Nov 2017 From: Canada Posts: 4 Thanks: 0 Related rates - inscribed A rectangle is inscribed in a semicircle of a radius 5m. Estimate the increase in the area of the rectangle using differentials if the length of its base along the diameter is increased from 6m to 6 1/6 m ?
November 9th, 2017, 06:39 PM #2 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,280 Thanks: 931 Show your work you lazy Canuck!!
November 10th, 2017, 03:15 AM #3 Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 A rectangle "inscribed in a circle" can't have its base "along the diameter". Your question makes no sense.
November 10th, 2017, 03:45 AM #4 Global Moderator Joined: Dec 2006 Posts: 19,697 Thanks: 1803 The problem states "inscribed in a semicircle", not "inscribed in a circle", so it does make sense.
November 10th, 2017, 03:56 AM #5 Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 Right. Thanks, I misread it. Igorrrawr, set up a coordinate system with the origin at the center of the semicircle, the x-axis along its base. We can write the semi-circle as $y= \sqrt{25- x^2}$. The vertices of the rectangle on the semi-circle are of the form $\left(x, \sqrt{25- x^2}\right)$ and $\left(-x, \sqrt{25- x^2}\right)$ for some positive x. The area is given by $A= 2x\sqrt{25- x^2}$. Initially, the base is 6 so x= 3 and $A= 6\sqrt{25- 9}= 6(4)= 24$. Differentiate the formula for A to find dA in terms of x and dx, then set dx= 1/6. Thanks from igorrrawr
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# American Institute of Mathematical Sciences
## Path prediction model of county urban growth boundary based on BP neural network
1 School of Management, Xi'an University of Architecture and Technology, Xi'an 710055, China 2 School of Public Administration, Shaanxi Radio and Television University, Xi'an 710068, China
* Corresponding author: Huiqin Wang
Received April 2019 Revised May 2019 Published January 2020
The city is the center of the regional system and the most influential space-time composite system. The spatial expansion of its land has become one of the main features of land use change in China. The problem of marginal growth of county cities is studied in depth in this paper. Firstly, the county urban land use information extraction method based on probabilistic neural network is used to obtain the geographic data of the county city. Then, through the optimized multi-feature fusion acquisition algorithm, the collected geographic data features of county cities are multi-featured. Finally, based on the characteristics of county city geographic data, the BP neural network-based path prediction model of the county urban growth boundary is established to predict the path of county urban growth boundary. The analysis shows that when the random variable is 1.1 and the threshold is 0.7, the prediction accuracy of this model is 99$\%$, which can effectively predict the growth boundary path of county cities. Compared with the similar prediction model, the prediction accuracy of this model is 99.87$\%$, which makes more accurate prediction of the future development of the city and can provide the basis for urban planning.
Citation: Zhiyuan Sun, Huiqin Wang, Ke Wang, Aorui Bi. Path prediction model of county urban growth boundary based on BP neural network. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020254
##### References:
[1] C. Bradley, N. Joyce and L. Garcia-Larrea, Adaptation in human somatosensory cortex as a model of sensory memory construction: A study using high-density eeg, Brain Structure and Function, 221 (2016), 421-431. doi: 10.1007/s00429-014-0915-5. Google Scholar [2] Y. Chen, Prediction algorithm of pm2.5 mass concentration based on adaptive bp neural network, Computing, 100 (2018), 825-838. doi: 10.1007/s00607-018-0628-3. Google Scholar [3] M. Colombo, D. Cumming and S. Vismara, Governmental venture capital for innovative young firms, Journal of Technology Transfer, 41 (2016), 10-24. Google Scholar [4] T. Cong, J. Hong and O. Dong, Ntb branch predictor: Dynamic branch predictor for high-performance embedded processors, Journal of Supercomputing, 72 (2016), 1679-1693. Google Scholar [5] M. Di, M. Mottolese and B. Di, The cytoskeleton regulatory protein hmena (enah) is overexpressed in human benign breast lesions with high risk of transformation and human epidermal growth factor receptor-2-positive/hormonal receptor-negative tumors, Clinical Cancer Research, 12 (2016), 1470-1478. Google Scholar [6] M. Dorado-Moreno, A. Sianes and C. Hervás-Martínez, From outside to hyper-globalisation: An artificial neural network ordinal classifier applied to measure the extent of globalization, Quality and Quantity, 50 (2016), 549-576. doi: 10.1007/s11135-015-0163-7. Google Scholar [7] G. Frana, M. Almeida and S. Bonnet, Nowcasting model of low wind profile based on neural network using sodar data at guarulhos airport, brazil, International Journal of Remote Sensing, 39 (2018), 2506-2517. Google Scholar [8] X. Fu, F. Wang and J. Shang, Optimized bp neural network algorithm based on multi-child genetic algorithm, Computer Simulation, 33 (2016), 258-263. Google Scholar [9] J. Gao, X. Wu and W. Gao, Review on inductive contactless power transfer technology, Journal of Power Supply, 15 (2017), 166-178. Google Scholar [10] M. Guerrero, D. Urbano and A. Fayolle, Entrepreneurial activity and regional competitiveness: Evidence from european entrepreneurial universities, Journal of Technology Transfer, 41 (2016), 105-131. doi: 10.1007/s10961-014-9377-4. Google Scholar [11] E. Jenelius and H. Koutsopoulos, Urban network travel time prediction based on a probabilistic principal component analysis model of probe data, IEEE Transactions on Intelligent Transportation Systems, 19 (2018), 436-445. doi: 10.1109/TITS.2017.2703652. Google Scholar [12] M. Joshanloo and W. Dan, Religiosity reduces the negative influence of injustice on subjective well-being: a study in 121 nations, Applied Research in Quality of Life, 11 (2016), 601-612. doi: 10.1007/s11482-014-9384-5. Google Scholar [13] S. Kim, K. Um and H. Kim, Hospital career management systems and their effects on the psychological state and career attitudes of nurses, Service Business, 10 (2016), 87-112. doi: 10.1007/s11628-014-0257-7. Google Scholar [14] W. Peng and Q. Huang, Research on complex information system evolution process, Journal of China Academy of Electronics and Information Technology, 12 (2017), 37-42. Google Scholar [15] B. Song, Study on construction technology and engineering management of water conservancy and hydropower projects, Automation and Instrumentation, 10 (2017), 170-171. Google Scholar [16] I. Szcs, B. Schlegelmilch and T. Rusch, Linking cause assessment, corporate philanthropy, and corporate reputation, Journal of the Academy of Marketing Science, 44 (2016), 376-396. doi: 10.1007/s11747-014-0417-2. Google Scholar [17] J. Tremblay and I. Abi-Zeid, Value-based argumentation for policy decision analysis: Methodology and an exploratory case study of a hydroelectric project in québec, Annals of Operations Research, 236 (2016), 233-253. doi: 10.1007/s10479-014-1774-4. Google Scholar [18] H. Uzun, Z. Yldz and J. Goldfarb, Improved prediction of higher heating value of biomass using an artificial neural network model based on proximate analysis, Bioresource Technology, 234 (2017), 122-130. doi: 10.1016/j.biortech.2017.03.015. Google Scholar [19] H. Wang and X. Zhang, Game theoretical transportation network design among multiple regions, Annals of Operations Research, 249 (2017), 97-117. doi: 10.1007/s10479-014-1700-9. Google Scholar [20] Y. Wang, S. Hu and F. Cao, Research prospect of cathode materials for lithium ion battery, Chinese Journal of Power Sources, 41 (2017), 638-640. Google Scholar [21] S. Xu, Z. He and R. Long, Impacts of economic growth and urbanization on co2 emissions: Regional differences in china based on panel estimation, Regional Environmental Change, 16 (2016), 777-787. doi: 10.1007/s10113-015-0795-0. Google Scholar [22] J. Zhou and X. Hu, Knowledge sharing and life satisfaction: The roles of colleague relationships and gender, Social Indicators Research, 126 (2016), 379-394. Google Scholar
show all references
##### References:
[1] C. Bradley, N. Joyce and L. Garcia-Larrea, Adaptation in human somatosensory cortex as a model of sensory memory construction: A study using high-density eeg, Brain Structure and Function, 221 (2016), 421-431. doi: 10.1007/s00429-014-0915-5. Google Scholar [2] Y. Chen, Prediction algorithm of pm2.5 mass concentration based on adaptive bp neural network, Computing, 100 (2018), 825-838. doi: 10.1007/s00607-018-0628-3. Google Scholar [3] M. Colombo, D. Cumming and S. Vismara, Governmental venture capital for innovative young firms, Journal of Technology Transfer, 41 (2016), 10-24. Google Scholar [4] T. Cong, J. Hong and O. Dong, Ntb branch predictor: Dynamic branch predictor for high-performance embedded processors, Journal of Supercomputing, 72 (2016), 1679-1693. Google Scholar [5] M. Di, M. Mottolese and B. Di, The cytoskeleton regulatory protein hmena (enah) is overexpressed in human benign breast lesions with high risk of transformation and human epidermal growth factor receptor-2-positive/hormonal receptor-negative tumors, Clinical Cancer Research, 12 (2016), 1470-1478. Google Scholar [6] M. Dorado-Moreno, A. Sianes and C. Hervás-Martínez, From outside to hyper-globalisation: An artificial neural network ordinal classifier applied to measure the extent of globalization, Quality and Quantity, 50 (2016), 549-576. doi: 10.1007/s11135-015-0163-7. Google Scholar [7] G. Frana, M. Almeida and S. Bonnet, Nowcasting model of low wind profile based on neural network using sodar data at guarulhos airport, brazil, International Journal of Remote Sensing, 39 (2018), 2506-2517. Google Scholar [8] X. Fu, F. Wang and J. Shang, Optimized bp neural network algorithm based on multi-child genetic algorithm, Computer Simulation, 33 (2016), 258-263. Google Scholar [9] J. Gao, X. Wu and W. Gao, Review on inductive contactless power transfer technology, Journal of Power Supply, 15 (2017), 166-178. Google Scholar [10] M. Guerrero, D. Urbano and A. Fayolle, Entrepreneurial activity and regional competitiveness: Evidence from european entrepreneurial universities, Journal of Technology Transfer, 41 (2016), 105-131. doi: 10.1007/s10961-014-9377-4. Google Scholar [11] E. Jenelius and H. Koutsopoulos, Urban network travel time prediction based on a probabilistic principal component analysis model of probe data, IEEE Transactions on Intelligent Transportation Systems, 19 (2018), 436-445. doi: 10.1109/TITS.2017.2703652. Google Scholar [12] M. Joshanloo and W. Dan, Religiosity reduces the negative influence of injustice on subjective well-being: a study in 121 nations, Applied Research in Quality of Life, 11 (2016), 601-612. doi: 10.1007/s11482-014-9384-5. Google Scholar [13] S. Kim, K. Um and H. Kim, Hospital career management systems and their effects on the psychological state and career attitudes of nurses, Service Business, 10 (2016), 87-112. doi: 10.1007/s11628-014-0257-7. Google Scholar [14] W. Peng and Q. Huang, Research on complex information system evolution process, Journal of China Academy of Electronics and Information Technology, 12 (2017), 37-42. Google Scholar [15] B. Song, Study on construction technology and engineering management of water conservancy and hydropower projects, Automation and Instrumentation, 10 (2017), 170-171. Google Scholar [16] I. Szcs, B. Schlegelmilch and T. Rusch, Linking cause assessment, corporate philanthropy, and corporate reputation, Journal of the Academy of Marketing Science, 44 (2016), 376-396. doi: 10.1007/s11747-014-0417-2. Google Scholar [17] J. Tremblay and I. Abi-Zeid, Value-based argumentation for policy decision analysis: Methodology and an exploratory case study of a hydroelectric project in québec, Annals of Operations Research, 236 (2016), 233-253. doi: 10.1007/s10479-014-1774-4. Google Scholar [18] H. Uzun, Z. Yldz and J. Goldfarb, Improved prediction of higher heating value of biomass using an artificial neural network model based on proximate analysis, Bioresource Technology, 234 (2017), 122-130. doi: 10.1016/j.biortech.2017.03.015. Google Scholar [19] H. Wang and X. Zhang, Game theoretical transportation network design among multiple regions, Annals of Operations Research, 249 (2017), 97-117. doi: 10.1007/s10479-014-1700-9. Google Scholar [20] Y. Wang, S. Hu and F. Cao, Research prospect of cathode materials for lithium ion battery, Chinese Journal of Power Sources, 41 (2017), 638-640. Google Scholar [21] S. Xu, Z. He and R. Long, Impacts of economic growth and urbanization on co2 emissions: Regional differences in china based on panel estimation, Regional Environmental Change, 16 (2016), 777-787. doi: 10.1007/s10113-015-0795-0. Google Scholar [22] J. Zhou and X. Hu, Knowledge sharing and life satisfaction: The roles of colleague relationships and gender, Social Indicators Research, 126 (2016), 379-394. Google Scholar
Diagram of the Relation between Urban Growth Expansion and Economic Development at County Level
Modular structure of BP neural network
Prediction accuracy of models with different parameter settings
Contrast chart between predicted growth boundary path and actual growth boundary path of a city in 2015
Prediction of Urban Land Growth Change in the County in 2015 Based on Different Parameter Combinations in the Model
Land type (a, T) 2015 -$\infty$, 0.7 1.1, +0.7 1.6, +0.7 2.1, +0.7 1.1, 0.8 The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ Live 2399.59 2482.3 3.44 2620.82 9.21 2820.92 17.55 2943.3 22.65 2614.72 8.95 Comm ercial clothing 256.35 287.69 12.21 257.4 0.4 256.84 0.18 257.42 0.41 257.42 0.41 Working condi tion clothing storage 65.78 71.76 9.08 67.98 3.34 67.84 3.12 68.66 4.37 67.98 3.33 Road traffic 81.77 81.76 -0.01 82.62 1.03 84.19 2.95 82.6 1 82.61 1.02 Public manage ment and services 514.43 518.13 0.71 519.4 0.96 521.28 1.32 519.8 1.04 518.75 0.83 Waters 1.34 1.32 -1.71 1.4 4.58 1.4 4.47 1.44 7.24 1.4 4.24 Public green space 22.89 22.65 -1.05 22.78 -0.47 22.74 -0.65 22.63 -1.11 22.85 -0.18 Other 1722.61 1592.47 -7.54 1568.3 -8.95 1549.05 -10.07 1528.2 -11.3 1572.85 -9.68
Land type (a, T) 2015 -$\infty$, 0.7 1.1, +0.7 1.6, +0.7 2.1, +0.7 1.1, 0.8 The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ Live 2399.59 2482.3 3.44 2620.82 9.21 2820.92 17.55 2943.3 22.65 2614.72 8.95 Comm ercial clothing 256.35 287.69 12.21 257.4 0.4 256.84 0.18 257.42 0.41 257.42 0.41 Working condi tion clothing storage 65.78 71.76 9.08 67.98 3.34 67.84 3.12 68.66 4.37 67.98 3.33 Road traffic 81.77 81.76 -0.01 82.62 1.03 84.19 2.95 82.6 1 82.61 1.02 Public manage ment and services 514.43 518.13 0.71 519.4 0.96 521.28 1.32 519.8 1.04 518.75 0.83 Waters 1.34 1.32 -1.71 1.4 4.58 1.4 4.47 1.44 7.24 1.4 4.24 Public green space 22.89 22.65 -1.05 22.78 -0.47 22.74 -0.65 22.63 -1.11 22.85 -0.18 Other 1722.61 1592.47 -7.54 1568.3 -8.95 1549.05 -10.07 1528.2 -11.3 1572.85 -9.68
Comparison of Prediction Accuracy of Thirteen Models
Direction Range left ($\bullet$) Area Covered by Real Growth Path($km^{2}$) Paper model Cellular Automata model Multi-agent model Predicted value ($km^{2}$) Area matching value D ($\%$) Predicted value ($km^{2}$) Area matching value D ($\%$) Predicted value ($km^{2}$) Area matching value D ($\%$) East 0-90 109.5 109.4 99.91$\%$ 103.1 94.16$\%$ 101.1 92.33$\%$ West 90-180 72.34 72.33 99.99$\%$ 70.21 97.06$\%$ 68.22 94.30$\%$ South 180-270 88.23 88.21 99.98$\%$ 85.34 96.75$\%$ 81.23 92.07$\%$ North 270-360 87.34 86.99 99.60$\%$ 85.23 97.58$\%$ 81.23 93.00$\%$ Whole 0-360 357.41 356.93 99.87$\%$ 343.88 96.21$\%$ 331.78 92.83$\%$
Direction Range left ($\bullet$) Area Covered by Real Growth Path($km^{2}$) Paper model Cellular Automata model Multi-agent model Predicted value ($km^{2}$) Area matching value D ($\%$) Predicted value ($km^{2}$) Area matching value D ($\%$) Predicted value ($km^{2}$) Area matching value D ($\%$) East 0-90 109.5 109.4 99.91$\%$ 103.1 94.16$\%$ 101.1 92.33$\%$ West 90-180 72.34 72.33 99.99$\%$ 70.21 97.06$\%$ 68.22 94.30$\%$ South 180-270 88.23 88.21 99.98$\%$ 85.34 96.75$\%$ 81.23 92.07$\%$ North 270-360 87.34 86.99 99.60$\%$ 85.23 97.58$\%$ 81.23 93.00$\%$ Whole 0-360 357.41 356.93 99.87$\%$ 343.88 96.21$\%$ 331.78 92.83$\%$
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2018 Impact Factor: 0.545
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# Name the series: a) sum_(n = 0)^oo (f^n xx a)/(n!) xx (x – a)^n
Armorikam 2021-08-18 Answered
Name the series:
a) $$\displaystyle{\sum_{{{n}={0}}}^{\infty}}\frac{{{f}^{{n}}\times{a}}}{{{n}!}}\times{\left({x}–{a}\right)}^{{n}}$$
b) $$\displaystyle{\sum_{{{n}={0}}}^{\infty}}\frac{{{f}^{{n}}\times{0}}}{{{n}!}}\times{x}^{{n}}$$
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## Expert Answer
rogreenhoxa8
Answered 2021-08-19 Author has 16313 answers
a) $$\displaystyle{\sum_{{{n}={0}}}^{\infty}}\frac{{{f}^{{n}}\times{a}}}{{{n}!}}\times{\left({x}–{a}\right)}^{{n}}$$ is a Taylor series.
b) $$\displaystyle{\sum_{{{n}={0}}}^{\infty}}\frac{{{f}^{{n}}\times{0}}}{{{n}!}}\times{x}^{{n}}$$ is a Maclaurin series.
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# Question 79d9a
You want the value of $5.05 {\left(1.06\right)}^{3}$.
This is equal to $5.05 \times \left({1.06}^{3}\right)$, or $5.05 \times 1.06 \times 1.06 \times 1.06$.
This can be put into a calculator for a rounded value of \$6.01#.
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Last edited by Vuramar
Tuesday, November 17, 2020 | History
2 edition of Learning, self-learning, and pattern recognition. found in the catalog.
Learning, self-learning, and pattern recognition.
Leonas Kacinskas
# Learning, self-learning, and pattern recognition.
Written in English
Subjects:
• Pattern perception.
• Edition Notes
Classifications The Physical Object Series ATD report, 67-64, ATD report ;, 67-64. LC Classifications Z663.23 .A2 no. 67-64 Pagination iii l., 94 p. Number of Pages 94 Open Library OL5391451M LC Control Number 72602911
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### Learning, self-learning, and pattern recognition. by Leonas Kacinskas Download PDF EPUB FB2
Learning, self-learning, and pattern recognition (ATD report) [Kacinskas, Leonas] Learning *FREE* shipping on qualifying offers. Learning, self-learning, and pattern recognition (ATD and pattern recognition.
book Leonas Kacinskas. Remedying this deficiency, Machine Learning: An Algorithmic Perspective, Second Edition helps students understand the algorithms of machine learning.
It puts them on a path toward mastering the relevant mathematics and statistics as well as the necessary programming and experimentation/5(33). The full texts of all the presented papers except two t are included. The papers cover a great variety of topics related to learning processes and systems, ranging from pattern recognition to systems identification, from learning control to biological modelling.
In order to reflect the actual content of the book, the present title was selected. Children begin using their senses to recognize patterns and categorize things at a young age ' skills that play an important role in early learning.
This tip sheet provides some simple activities, as well as recommended books, that parents can use to help their kids build pattern recognition and categorization skills in science and math. Self-Learning Neural Networks Basic Concepts.
We have explained the structures and utilized programs to demonstrate how a neural network utilizes a teacher’s guidelines for pattern recognition and comparison to complete its tasks.
This chapter will detail network learning without a teacher. Pattern Recognition and Machine Learning. This completely new textbook reflects these recent developments while providing a comprehensive introduction to the fields of pattern recognition and machine learning.
It is aimed at advanced undergraduates or first-year PhD students, as well as researchers and practitioners. Get Deep Learning: Practical Neural Build and run intelligent applications by leveraging key Java machine learning libraries.
About This Book. Apply the code generated in practical examples, including and pattern recognition. book forecasting and pattern recognition; In Detail.
Machine learning applications are everywhere, from self-driving cars, spam. book or to fill in gaps in your knowledge of Information Theory and related material. MacKay outlines several courses for which it can be used including: his Cambridge Course on Information Theory, Pattern Recognition and Neural Networks, a Short Course on Information Theory, and a Course on Bayesian Inference and Machine Size: KB.
Pattern Recognition and Machine Learning (Information Science and Statistics) The above book by Christopher M. Bishop is widely regarded as one of the most comprehensive books on Machine Learning.
At over pages, it has coverage of most machine learning and pattern recognition topics. It is considered very rigorous for a machine and pattern recognition. book (data science). Rogers and Girolami, A First Course in Machine Learning, (Chapman & Hall/CRC Machine Learning & Pattern Recognition), Chris Bishop's book, or David Barber's both make good choices for a book with greater breadth, once you have a good grasp of the principles.
Self-Learning Study Material Basic. Linear Algebra Gilbert Strang; Probability & Statistics basics; Hands On Machine learning Book; Piyush Rai Self-learning, IIT-K [ ] Advanced.
Elements of Statistical Learning Theory; Pattern Recognition & Machine ; Learning llow; Reinforcement Learning; Time Series [ ] Software implementations of brain-inspired computing underlie many important computational tasks, from image processing to speech recognition, artificial intelligence and deep learning by: This book contains the Proceedings of the US-Japan Seminar on Learning Process in Control Systems.
The seminar, held in Nagoya, Japan, from August 18 to 20,was sponsored by the US-Japan Cooperative Science Program, jointly supported by the National Science Foundation and the Japan Society Author: King-Sun Fu.
Pattern recognition is the automated recognition of patterns and regularities in has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine n recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use.
Schlesinger, M. Vzaimosvjaz obuchenija i samoobuchenija v raspoznavaniji obrazov; in Russian (Relation between learning and self-learning in pattern recognition). Kibernetika, (2)– Google ScholarAuthor: Michail I.
Schlesinger, Václav Hlaváč. Listing one book that Nishant’s comprehensive list already covers. * Deep Learning. This online version is free, but you can get a print version from Amazon Deep Learning Ian Goodfellow, Yoshua Bengio, Aaron Courville For self-learning, particular.
1. Socratic by Google – An indispensable app for high school and University students that helps you find the best online resources for you to learn new concepts and getting help on any subject. Nearpod – a student engagement platform built to make teaching with technology easy with VR Field Trips, game-based activities, and collaboration.
Special Book Collections This paper studies pattern recognition and image processing, proposes a method to implement limited length and limited weight cutting with pattern recognition and image processing technique.
In particular, we consider a self-learning algorithm for visual recognition and system of automatic generation that based. Neural networks and deep learning currently provide the best solutions to many problems in image recognition, speech recognition, and natural language processing.
This book will teach you many of the core concepts behind neural networks and deep learning. For more details about the approach taken in the book, see here. The top machine learning videos on YouTube include lecture series from Stanford and Caltech, Google Tech Talks on deep learning, using machine learning to play Mario and Hearthstone, and detecting NHL goals from live streams.
Synopsis Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and /5(49).
The term machine learning was coined in by Arthur Samuel, an American IBMer and pioneer in the field of computer gaming and artificial intelligence.
A representative book of the machine learning research during the s was the Nilsson's book on Learning Machines, dealing mostly with machine learning for pattern classification.
Interest related to pattern recognition continued into the. Unfortunately none of the answers mentioned here pertains to the original question. Read all other recommendations and you’ll become ML expert, I don’t challenge that.
However you’ll still be struggling with market data which is unlike any other s. In order to reflect the actual content of the book, the present title was selected.
All the twenty-eight papers are roughly divided into two parts--Pattern Recognition and System Identification and Learning Process and Learning Control.
It is sometimes quite obvious that some papers can be classified into either part. Advanced Machine Learning: Machine Learning Course at Cornell University. Unfortunately, there are no videos, only courseware. The part about actual combat is good. The Elements of Statistical Learning: Classic ESL; Pattern Recognition and Machine Learning: A Classic Book; 5.
Application. Information extraction and search. Curious about Machine Learning and its many applications. Artificial intelligence and machine learning are among the most significant technological developments in recent history.
Especially ML has. Information theory and inference, often taught separately, are here united in one entertaining textbook. These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography/5(10).
A self-learning visual pattern explorer and recognizer using a higher order neural network to improve the efficiency of higher-order neural networks was built into a pattern recognition system. In this paper we will be discussing about the concepts of Deep Learning (DL).Deep learning has become an extremely active research area in machine learning and pattern recognition society.
Part of the book is about the Weka toolkit, but a good chunk is really a gentle introduction to the ideas behind machine learning, the various types of classifiers, feature selection algorithms, etc.
level 1. Although deep learning nets had been in existence since the s and backpropagation was also invented, this technique was largely forsaken by the machine-learning community and ignored by the computer-vision and speech-recognition communities, Hinton shared in a journal.
It was widely thought that learning useful, multistage, feature. Recognition of patterns aims at classifying objects based on statistical data collected for the purpose of extracting features of objects based on a priori information or using self-learning.
Classified objects are usually groups of measurement or observation results defining the location of corresponding points in the multidimensional space of Author: Andrzej Zak. A system of computer programs discriminates between pictorial patterns by determining a substantial number of numerically encoded pattern properties.
Supervised learning is used to find both an optimum decision sequence and the thresholds for decision rules. These are applied to patterns from an object set to test the consistency of the classification procedure. Deep learning is a subfield of ML that uses algorithms called artificial neural networks (ANNs), which are inspired by the structure and function of the brain and are capable of self-learning.
ANNs are trained to “learn” models and patterns rather than being explicitly told how to solve a problem. pattern recognition, associative memory, learning engines. 1: INTRODUCTION In this paper, we introduce an algorithm using Mirroring Neural Networks (MNN) which performs a dimension reduction of input data followed by mapping, to recognize patterns.
There have been many investigations done on pattern recognition, a few of. Deep Learning is used by Google in its voice and image recognition algorithms, by Netflix and Amazon to decide what you want to watch or buy next.
Pattern Recognition and Machine Learning Signals and Systems I Signals and Systems II. Labs Advanced Topics Lab Communications Lab Embedded Signal Processing Lab Real-time Signal Processing Lab System Theory Lab. Seminars Medical Signal Processing Speech and Audio Processing Underwater Signal Processing.
Student Projects. Theses. Information theory and inference, often taught separately, are here united in one entertaining textbook. These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography.
This textbook introduces theory in Cited by: Brain and Nature-Inspired Learning, Computation and Recognition presents a systematic analysis of neural networks, natural computing, machine learning and compression, algorithms and applications inspired by the brain and biological mechanisms found in nature.
Sections cover new developments and main applications, algorithms and simulations. I am currently learning from Christopher Bihops's Pattern Recognition and Machine Learning book about posterior distributions for the Normal distribution whenever both $\mu$ and $\tau$ (the precision term) are unknown by using the Normal-Gamma distribution as a conjugate prior.
Self-learning pattern recognition and neural network approaches encountered combinatorial complexity (CC) of learning requirements. Various ways of overcoming CC in neural networks include techniques like pruning, regularization, weight by: The ultimate objective is to build self-learning systems to relieve human from some of already-too-many programming tasks.
At the end of the course, students are expected to be familiar with the theories and paradigms of computational learning, and capable of implementing basic learning systems.
Pattern Recognition and Machine Learning.a. Data Link: Enron email dataset. b. Project Idea: Using k-means clustering, you can build a model to detect fraudulent activities.K-means clustering is an unsupervised Machine learning algorithm.
It separates the observations into k number of clusters based on the similar patterns in the : Rahul Patodi.
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# Christoph's last Weblog entries
### Entries from May 2011.
30th May 2011
At April 30, I took over maintenance of of Debian's kFreeBSD autobuilders. Means getting something like 4,5k e-Mails this month (gladly no need to sign all those 4k successful builds any more!), filling nearly 30 RC Bugs (quite a lot of which got fixed just within hours after filling, wow!), investigating some of the more strange build failures and such stuff. In general it turned out to be quite some fun.
Quite interesting which libraries turn out to be rather central to the Archive. I wouldn't have guessed that a uninstallable libmtp would prevent a reasonable fraction of the builds to fail -- including packages like subversion.
Packages builds failing because the disk space is exhausted may be something most of us have already witnessed, especially those here that use one of these small notebook hard drives. Build failures caused by a lack of RAM might certainly be imaginable as well, especially on highly parallel builds. But have you ever seen gcc fail because the virtual address space was exhausted on 32 bit architectures?
Also there's a interesting lot of packages with misspelled build dependencies which sbuild can't find and therefore can't build the package. Maybe having a lintian check for some of these problems would be a good idea?
I'm also regularly seeing build failures that look easy enough to fix -- like some glob in a *.install for some python package matching lib.linux*. I try to fix some of these as I see them but my time is unfortunately limited as well. Someone interested in quick&easy noticed about these kind of issues? I could put URLs to build-logs on identi.ca or somewhere on IRC.
There are also some really strange failures like llvm, which builds flawlessly on my local kFreeBSD boxes all the time, inside and outside schroot but hangs all the time in the same testcase when building on any of the autobuilders (any hints welcome!) or perl failing on kfreebsd-amd64 selectively but all the time.
Tags: debian, foss, kfreebsd, porting.
17th May 2011
Imagine you have a old postgresql database. Further imagine it has it's encoding set to something like LATIN-1 but some PHP web application has put in UTF-8 strings. Now what would you do if you have some python application actually respecting the encoding and recoding the db content from latin-1 to UTF-8 giving you garbage. Seems you can easily trick postgresql to now believe it is UTF-8:
UPDATE pg_database SET encoding = 6 WHERE datname = 'foo';
For a summary of these magic numbers the PostgreSQL Manual is usefull.
Tags: dbs, postgresql, programmieren.
12th May 2011
## From the java point of view
Recently I had to get some Scala Tool working correctly. Unfortunately there are basically no packages in the Debian Archive at all so I had to use maven to install these (or download + install manually). Being a highly paranoid person downloading and executing code from the internet without any cryptographic verification at all one after the other practically drove me nuts. Looking a bit deeper I noticed that some of the software in maven's repository have some signatures next to them -- signed by the author or release manager of this specific project.
## Why secure sources matters
With my experience in mind I got some Input from other people. One of the things I was told is that some scala tools just aren't security critical -- they're only installed and used as the current user. In my opinion this is, for my desktop system, totally wrong. The important things on my private Computers are my GPG and SSH keys as well as my private data. For messing with these no super user access is needed at all.
## Comparing to the Common Lisp situation
Being a Common Lisp fan of course I noticed basically the same problem for installing Common Lisp libraries. Here the situation in Debian is quite a bit better -- and I'm working in the pkg-common-lisp Team to improve this even more. Common Lisp has some maven-alike tool for downloading and installing dependency trees called quicklisp -- without any cryptographic verification as well. However there's light at the end of this tunnel: There are plans to add GPG verification of the package lists really soon.
## Comparing the maven and the quicklisp model
So there are basically two different approaches to be seen here. In maven the software author confirms with his signature the integrity of his software while in quicklisp the distributor confirms all users get the same software that he downloaded. Now the quicklisp author can't and won't check all the software that is downloadable using quicklisp. This won't be doable anyway as there's way to much software or a single person to check.
Now in some kind of perfect World the maven way would be vastly superior as there's a End-To-End verification and verification of the full way the software takes. However there's a big problem: I don't know any of these Authors personally and there's no reason I should just trust any of them.
Now comparing this to the Distribution / quicklisp model. Here I would just have to trust one person or group -- here the quicklisp team -- to benefit from the crypto which might be possible based on karma inside the using community. However here I don't gain the possibility that the software is integer.
However idealized if some of these pieces of software was forged between upstream and the quicklisp team and attacker would also intercept me downloading the software from the same address so I get the source from upstream matching the checksum from quicklisp -- assuming the quicklisp team does indeed know the correct website. Additionally I get the confirmation that all other quicklisp users get the same source (if the quicklisp guys are fine of course) so no-one inside the community complaining is a good indication the software is fine. For this to work there's of course a relevant user-base of the distributor (quicklisp) necessary.
## Relevance for Debian
So how do conventional Linux Distributions like Debian fit in here. Ideally we would have maintainers understanding and checking the software and confirming the integrity using their private key or at least know their upstreams and having at least a secured way getting the software from upstream and a trust relationship with them. Of course that's just illusionary thinking of complex and important software (think libreoffice, gcc or firefox for example). Maintainers won't fully understand a lot simpler pieces of software. And loads of upstream projects don't provide a verified way of getting the correct source code though that's a bit better on the real high-impact projects where checksums signed by the Release Manager are more common than in small projects.
## A misguided thought at the end
As I'm a heavy emacs user I like to have snapshots from current emacs development available. Fortunately binary packages with this are available from a Debian guy I tend to trust who is also involved upstream so adding the key from his repository to the keyring apt trusts. Now my first thoughts were along the lines "It would be really nice if I could pin that key to only the emacs snapshot packages" so this guy can't just put libc packages in his repository and my apt would trust them. Now thinking of it again a bogus upload of the emacs snapshot package could just as well put some binary or library on the system at some place in front of the real on in the system path which would be rather similar bad.
b
Tags: debian, foss, linux, security, web.
6th May 2011
So this is a collection of things I came about when trying to get a Debian GNU/Hurd virtual machine running with kvm. Most of it is properly documented if you manage to find that particular piece of information.
### Kernel Version
Due to a bug in linux 2.6.37 and .38 hurd will only boot if you supply -no-kvm-irqchip which is not that easy if you are using libvirt. A wrapper kvm script in the PATH will do, as will using a 2.6.39 kernel.
### sudo
sudo will hang before returning from executing some command. I'm now using screen and sudo -i which keeps you a working tty gets you root and hasn't caused mayor trouble yet
### sshd
openssh-server won't come up complaining about missing PRNG – and indeed there's no /dev/{u,}random in the default install. fix is to install random-egd from ports.
Tags: debian, howto, hurd, porting.
Created by Chronicle v4.6
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# What is the tension on the line when the elevator is accelerating
1. Mar 21, 2006
### superdave
An elevator weighs 10000N. What is the tension on the line when the elevator is accelerating upwards at 3 m/s?
2. Mar 21, 2006
Well, acceleration is in $\frac {m}{s^2} [/tex]. Is that a typo? Also, what is newtons first law? 3. Mar 22, 2006 ### sporkstorms And after you recall Newton's first law, be sure to draw a force diagram before solving the problem. This will help ensure that you get the signs correct (arrows pointing in opposite directions will have opposite signs). 4. Mar 22, 2006 ### nrqed I agree with drawing a free body diagram (this should always be the first step in that type of question) but I think that everybody meant Newton's *second* law... Patrick 5. Mar 22, 2006 ### Hootenanny Staff Emeritus I'm sorry to be pedantic but the units of acceleration are not [itex]m/s$, they are $m/s^2$.
There are two questions that you should ask yourself when doing this question;
(1) What is the tension in the wire when the elevator is stationary? I.e. what force is required to balance the weight of the elevator?
(2) What additional force is required to accelerate the elevator at $3 m/s^2$? Hint: For this one you will need to use Newton's second law as nrqed said.
Hope this helps
-Hoot
6. Mar 22, 2006
### sporkstorms
Whoops. I was like a sheep, following right over the edge of a cliff.
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### point not inside the domain in auto-adaptive
169
views
1
10 months ago by
Hi, I am solving time dependentproblem using auto-
adaptive, Once mesh is adated , I am getting error: Unable to evaluate function at point. The point is not inside the domain.
solver_disp = AdaptiveLinearVariationalSolver(problem_disp, MF)
solver_disp.parameters["error_control"]["dual_variational_solver"]["linear_solver"] = "cg"
solver_disp.parameters["error_control"]["dual_variational_solver"]["symmetric"] = True
solver_alpha = LinearVariationalSolver(problem_alpha)
# inside the time loop
solver_disp.solve(TOL)
unew.assign(u.leaf_node())
Any idea to fix this issue.
FEniCS version: 1.6.0
Thanks for the help
Community: FEniCS Project
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# Let $f,g: X \rightarrow Y$ be continuous and $Y$ be Hausdorff. Prove that $\{x | f(x) = g(x)\}$ is a closed subset of $X$.
I realize this question has been asked, But i just wrote up this proof and it's a little different so I was hoping somebody would check it.
Let $$f,g: X \rightarrow Y$$ be continuous and $$Y$$ be Hausdorff. Prove that $$Z=\{x | f(x) = g(x)\}$$ is a closed subset of $$X$$.
Proof: Let $$x \in X-Z$$
Then $$f(x) \neq g(x)$$, and since $$Y$$ is hausdorff this implies that $$\exists U_1, U_2$$ open in $$Y$$ s.t. $$f(x) \in U_1$$, $$g(x) \in U_2$$ and $$U_1 \cap U_2 = \emptyset$$.
Since $$f$$ is continuous and $$U_1$$ is open in $$Y$$, we have $$f^{-1}(U_1)$$ is open in $$X$$ and $$x \in f^{-1}(U_1)$$.
Since $$g$$ is continuous and $$U_2$$ is open in $$Y$$, we have $$g^{-1}(U_2)$$ is open in $$X$$ and $$x \in g^{-1}(U_2)$$.
Claim: $$g^{-1}(U_2) \cap f^{-1}(U_1)$$ is a neighborhood of $$x$$ contained in $$X-Z$$.
Suppose $$z \in g^{-1}(U_2) \cap f^{-1}(U_1)$$, then $$f(z) \in U_1$$, $$g(z) \in U_2$$. But $$U_1 \cap U_2 = \emptyset$$ and so $$f(z) \neq g(z)$$ and thus $$z \in X-Z$$.
Thus $$X-Z$$ is open and thus $$Z$$ is closed
• Seems to be a correct proof – RMWGNE96 May 11 '19 at 12:30
• Perfectly right. A useful corollary is that if $Y$ is Hausdorff and $f:X\to Y,\,g:X\to Y$ are continuous and agree on a dense subset of $X$ then $f=g.$ For example, in the proof of the Jones Lemma. – DanielWainfleet May 12 '19 at 5:42
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# Circular arrow in tikz-cd
How do I draw a circular arrow (to indicate commutativity) in tikz-cd, similar to the one in the middle of the following diagram?
(Image from this question.)
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Use of PDFlatex or XeLaTeX with $\circlearrowleft$ from amssymbol/amsmath with scalable size.
Code
\documentclass[border=2pt]{standalone}
\usepackage{amssymb,amsmath}
\usepackage{tikz-cd}
\usetikzlibrary{arrows}
\usepackage{tikz}
\begin{document}
%\tikzset{commutative diagrams/.cd, arrow style=tikz,diagrams={>= latex}}
\begin{tikzcd}[row sep=2cm,column sep=2cm,inner sep=1ex]
\bar A \arrow[thick,swap] {d}{\bar F_q}
&
\bar A_E \arrow[thick,swap]{l}[name=U]{\pi^\star}
\arrow[thick]{d}{\bar F_{q,E}}
\\
\bar A & \bar A_E \arrow[thick]{l}[name=D]{\pi^\star}
\arrow[to path={(U) node[midway,scale=3] {$\circlearrowleft$} (D)}]{}
\end{tikzcd}
\end{document}
-
You can draw an arc using the option -> following the syntax described in the documentation in the Arc Path Reconstruction.
\draw (starting point x, starting point y) arc (starting angle:ending angle:radius);
For instance this code will produce an arrow like the one requested
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw[step=1cm,gray!50,very thin] (-1.9,-1.9) grid (5.9,5.9);
\draw[very thick,->] (0,0) -- (4.5,0) node[anchor=north west] {\bf{x axis}};
\draw[very thick,->] (0,0) -- (0,4.5) node[anchor=south east] {\bf{y axis}};
\foreach \x in {0,1,2,3,4}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\mathbf{\x}$};
\foreach \y in {0,1,2,3,4}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\mathbf{\y}$};
\draw[thick, ->] (3,2) arc (0:270:1cm);% syntax (starting point coordinates) arc (starting angle:ending angle:radius)
\end{tikzpicture}
\end{document}
-
At least an explanation of how to include this into tikz-cd would be great. – Manuel Jul 9 at 8:42
If you are willing to use Lua- or XeLaTeX:
% arara: lualatex
\documentclass{article}
\usepackage{tikz-cd}
\usepackage{unicode-math}
\begin{document}
\begin{tikzcd}[row sep=5pt, column sep=5pt]
\overbar{A} \arrow[swap, "\overbar{F}_q"]{dd} & & \overbar{A}_E
\arrow["\overbar{F}_{q,E}"]{dd} \arrow[swap, "\pi^\ast"]{ll} \\
& \cwopencirclearrow & \\
\overbar{A} & & \overbar{A}_E \arrow["\pi^\ast"]{ll}
\end{tikzcd}
\end{document}
`
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# Thread: Trouble with integrating trig functions
1. ## Trouble with integrating trig functions
I have two trig functions that i cannot seem to find a way to integrate. They are:
INTEGRAL of: 31(1+cos(x))^2
This one looks pretty simple but whenever i check my answer my taking the derivative of it, it never comes out right.
and
INTEGRAL of: 27(sin(x)/(cos(x))^3
Im suppose to have my answer in terms of tangent. Which messes me up because usually i would do a trig substitution to cancel out the sine. If its not possible to express it in terms of tangent then what is it in terms of sine and cosine.
2. Hello,
Originally Posted by fogel1497
I have two trig functions that i cannot seem to find a way to integrate. They are:
INTEGRAL of: 31(1+cos(x))^2
This one looks pretty simple but whenever i check my answer my taking the derivative of it, it never comes out right.
$(1+\cos(x))^2=\underbrace{1+2 \cos(x)}_{\text{easy to integrate}}+\cos^2(x)$
Now note that $\cos^2(x)=\frac{1+\cos(2x)}{2}$
and
INTEGRAL of: 27(sin(x)/(cos(x))^3
Im suppose to have my answer in terms of tangent. Which messes me up because usually i would do a trig substitution to cancel out the sine. If its not possible to express it in terms of tangent then what is it in terms of sine and cosine.
Substitute u=cos(x)
get your answer and it'll be ok if you want to transform into tangent, use the identity 1=sin²(x)+cos²(x)
then transform sin(x)/cos(x)=tan(x)
but it's not necessary
3. Hello, fogel1497!
$\int \frac{27\sin x}{\cos^3\!x}\,dx$
We have: . $27\int\frac{\sin x}{\cos x}\cdot\frac{1}{\cos^2\!x}\,dx \;=\;27\int \tan x\sec^2\!x\,dx$
Now let: $u \:= \:\tan x\quad\Rightarrow\quad du \:= \:\sec^2\!x\,dx$
Got it?
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
We could get a different (but equivalent) answer . . .
We have: . $27\int \sec x \,(\sec x\tan x\,dx)$
Let: $u \:=\:\sec x \quad\Rightarrow\quad du \:=\:\sec x\tan x\,dx$
Substitute: . $27\int u\,du \:=\;\frac{27}{2}u^2 + C$
Back-substitute: . $\frac{27}{2}\sec^2\!x + C$
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## Happy (late) October 1st
China just had their national day (called GuoQinJie I’m told) on October 1st. It was their 60th anniversary so there was a pretty big parade. Which is actually a bit frustrating since I was in Tienanmen Square last October 1st and there was nothing but a bunch of tourists milling around (the rest of the trip was great anyway so no big deal). Apparently if you’re ever planning on visiting Beijing on National Day, you need to make sure it’s in a year ending in 9 or 4. Anyway, my wife came across this pretty cool time lapse video of the parade (the video page has it in HD):
## Tab Indented Standard Input Redirect in Bash
I managed to forget how to redirect standard input (when you want to feed a bunch of lines to a program) in a bash script while still indenting and had to go digging around for it. So I figured I'd make a note here so I don't forget again and for anyone else in the same boat. It's just <<- instead of <<. For example if you want to keep indentation within a loop:
BASH:
1. for i in 1 2 3 4;do
2. cat<<-EOF
3. This is loop \$i
4. More advanced stuff could go here
5. EOF
6. done
You can use whatever you want to indicate the end of the input instead of EOF if it floats your boat (as long as you use the same thing both times) but unfortunately <<- doesn't work with spaces for indentation (although I'm a tab man myself).
## The Birds and the Bees of Leatherbacks
When I was writing up the last post on the Great Turtle Race, I came across this Wikipedia page that has details on every Colbert report ever (what doesn't Wikipedia have?). It included this quote on Stephen Colbert's leatherback:
Stephen is unhappy at the fact that Stephanie Colburtle The Turtle did not win The Great Turtle Race, after being bested by another turtle named Billy. He claims Billy is a male, and demands a re-race. (After explaining that one can tell the sex of a turtle by the concavity of its plastron, Stephen says that he checks the plastron on "all [his] dates, and if it's not concave, [he is] outta there." However, a concave plastron denotes a male turtle.)
Now I'm not totally sure the concave plastron bit works with leatherbacks since they're more barrel-shaped than turtle-shaped but I guess it's possible. But on the topic, I just thought I'd share a couple tips for determining leatherback sex.
First, is it on a beach? If so, it's female. Healthy male leatherbacks never return to land after their initial crawl from the nest to the ocean. That makes research programs that catch turtles at sea the only way to look at male leatherbacks.
Second, does it have a long tail that trails well behind the shell? Then it's a male. Leatherbacks (and other sea turtles) store their penis in their tail. The tails of female turtles barely extend past their shell. The tails of male turtles, shall we say, hang low and wobble to and fro. I couldn't dig up a picture of a male leatherback but here's a picture of a male green sea turtle tail (from seaturtle.org courtesy of Daha Diew and Alain Gibudi) that should give an idea (that's its rear flippers in the left edge of the picture).
And now you know.
## Great Turtle Race
I'm a bit late on this one (I don't know how I managed to miss it since I had to put the data together) but National Geographic and Conservation International had a Great Turtle Race with a bunch of leatherback turtles tagged by my old adviser. They took data from turtle tracked from Nova Scotia to South America and had a big two-week event watching which turtle reached the Caribbean first. They have a pretty cool animation of the satellite tracking (although of course not quite as good as mine) and some cute leatherback artwork (complete with leathery back instead of shell, although why are they green?).
That site also has the first leatherback game I've ever seen. The artist did a really good job since the view is pretty much identical to the view we get from a shoulder mounted turtleCam. Unfortunately, the game turtle handles like a tank which really doesn't do justice to the maneuvering ability of leatherbacks. They're huge animals but in the water they're really quite graceful and they can turn on a dime (as I quickly found out when we were trying to catch them).
Anyway, it looks like the turtle named Backspacer (it's weird to see all the interesting names since we always call the turtles by their tag ID number), sponsored by Pearl Jam, yes that Pearl Jam, won the race. Turtle Cali won the diving portion of the race and received an Iron Turtle Award. Here's a nice post-race summary and also Olympic swimmer (and turtle coach) Jason Lezak's take on it. It's great to see so much public interest in leatherback turtle tracking and National Geographic and Conservation International did a great job promoting and running the event.
## Displaying Code in LaTeX
gioby of Bioinfo Blog! (an interesting read by the way) left a comment asking about displaying code in LaTeX documents. I've sort of been cludging around using \hspace's and \textcolor but I've always meant to figure out the right way to do things so this seemed like a good chance to figure out how to do it right.
LaTeX tends to ignore white space. This is good when you're writing papers but not so good when you're trying to show code where white space is an essential part (e.g. Python). Luckily there's a builtin verbatim environment in LaTeX that is equivalent to html's <pre>. So something like the following should preserve white space.
\begin{verbatim}
for i in range(1, 5):
print i
else:
print "The for loop is over"
\end{verbatim}
Unfortunately, you can't use any normal LaTeX commands inside verbatim (since they're displayed verbatim). But luckily there a handy package called fancyvrb that fixes this (the color package is also useful for adding colors). For example, if you wanted to highlight "for" in the above code, you can use the Verbatim (note the capital V) environment from fancyvrb:
\newcommand\codeHighlight[1]{\textcolor[rgb]{1,0,0}{\textbf{#1}}}
\begin{Verbatim}[commandchars=\\\{\}]
\codeHighlight{for} i in range(1, 5):
print i
else:
print "The for loop is over"
\end{Verbatim}
If you really want to get fancy, the Pygments package in Python will output syntax highlighted latex code with a command like: pygmentize -f latex -O full test.py >py.tex The LaTeX it outputs is a bit hard to read but it's not too bad (it helped me figure out the fancyvrb package) and it does make nice syntax highlighted output.
Here's an example LaTeX file with the three examples above and the pdf it generates if you're curious.
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# Some basic derivative-integral issues
1. Dec 14, 2005
### Robokapp
It's not really homework, although that is where I encountered this first time.
I had to evaluate the integral from zero to whatever of 3^x.
I realized...while dy/dx of e^x=e^x the dy/dx of any number not equal to e does not follow the same pattern. It has a different formula.
Same for Log base e (the natural log)...so I'm asking, isn't e and any number n constants? why does the derivative or integral of e^x differ from n^x ?
Also, why is log base e (natural log) different in formul than any other log?
I don't understand why a constant won't act like the others. Is it that e was discovered this way purposelly? Or e was already known and it just hapepned to work this way?
I know I'm splitting hairs here, but it would be useful to understnad how they work, in interest of saving brain capacity...
~Robokapp
2. Dec 14, 2005
### incognitO
its because $\log e=1$...
look at it this way....
$$\begin{array}{c}a^x=y(x) \\ \\x \log a=\log y(x) \\ \\ \dfrac{d}{dx}(x \log a)=\dfrac{d}{dx}\log y(x) \\ \\ \log a =\dfrac{y'(x)}{y(x)} \\ \\ y(x) \log a =y'(x)\end{array}$$
wich means
$$\frac{d}{dx}a^x=a^x \log a$$
$e$ is not different from any other constant, just $\log e=1$
Last edited: Dec 14, 2005
3. Dec 14, 2005
### d_leet
The natural log of e equals one, in other words log base e of e is one but thats the same for any number
suppose we have a
then log base a of a is 1because a^1 is a.
For integrating and differentiating a number n^x we know that
n^x = (e^ln n)^x which is the same as e^(x*ln n) and since ln n is a coinstant the integral would be (e^(x*ln n))/(ln n) which is (n^x)/(ln n)
differentiating is similar.
4. Dec 15, 2005
### hypermorphism
e was discovered to be the base of the natural logarithm, where the natural logarithm was found by studying the break in behavior of the integrals $$\int x^n dx$$ when x=-1. The integral was found to behave exactly like a logarithm, and thus the integral $$\int_1^x \frac{dt}{t}$$ was defined to be the natural logarithm with the natural base e, Euler's number.
It is also fascinating to know that the only family of functions whose derivative returns the same function is f(t) = A*et. This property makes e pop up in a ridiculous amount of places (it is as ubiquitous as $\pi$). You can find out more about the history of e in the book "e: the Story of a Number" by Maor.
Last edited: Dec 15, 2005
5. Dec 15, 2005
### Robokapp
Well...talking about that, I'll probably feel like an idiot for stating the obvious, but did anyone notice that the derivative of y=ln(n x) where n is any constant number is always 1/x
I wonder...how does that work? I mean ln (1000x) shouldn't raise/fall at same rate as ln (0.001x) right? but because of Chain Rule they have equal derivatives. The constant goes in front and cancels out with the one inside Ln.
I understnad the math, but how reasonable is it?
6. Dec 16, 2005
### d_leet
Well if you remember the properties of logarithms specifically this one
log(ab) = log a + log b
then that means you can expand ln(1000x) as ln x + ln 1000 and since
ln 1000 is just a constant you will get just 1/x as the derivative, the same follows for ln(.001x)
7. Dec 16, 2005
### Robokapp
oh. Yea...forgot about that. you have a 1/ times dx/dx or times 1 and a 0 times dx/dx or 0*1+1*x^-1=dy/dx
I knew it's something really insignifficant...just didn't think it trough. :surprised
oh also about e wasn't e supposed to be calculated by the formula
(1+1/x)^x for large numbers? The problem with that is that it's never quite defined as a constant. If you plug in the graph of (1+1/x)^x for a range from 0 to 10^25 (Yea, I got a lot of free time to mess up with my TI83) you'd see it goes up, down, up again and then it keeps on growing until it gets out of range. Also if you take the derivative of (1+1/x)^x you'll lnotice that it indicates a behaviour far from constant...
plug in
y1=e
y2=(1+1/x)^x
for x-max = 100 and you'll see them be undistinctively overlapped.
go to x=10^20 and you'll see the y1 go up and down across the y2
Last edited: Dec 16, 2005
8. Dec 16, 2005
### d_leet
Are you attempting the product rule on that, dont even bother. suppose we have
ln ax
d/dx[ln u] = du/u
so if u = ax
the du = a
and u = ax
so we have ln ax = a/ax = 1/x.
As top the second part of your post e is defined as hypermorphism showed earlier, however e is also equal to
the limit as n goes to infinity of (1 + 1/n)^n which is precisely what you had. You can find that this limit is e using l'hospital's rule but it's a somewhat circular definition since the best way to find that limit is using the natural logarithm.
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Analysis of Grounding Resistance for Zero Energy Town Floating PV System Using Underground Wiring
Title & Authors
Analysis of Grounding Resistance for Zero Energy Town Floating PV System Using Underground Wiring
Ko, Jae-Woo; Lim, Jong-Log; Kim, David K.; Cha, Hae-Lim; Kim, Si-Han; Lee, Chang-Koo; Ahn, Hyung-Keun;
Abstract
Floating PV system is installed on the water such as artificial lake, reservoir, river for the purposes of zero energy town and/or large scale of PV station. There are electrical gains from cooling effect by water and reflection of water surface. Particularly, floating PV power station with high efficiency solar cell modules receives a lot of attention recently. Floating PV system is installed on the water, which means grounding method to the frame of solar cell and electrical box such as connector band and distribution panelboard should be applied in different way from grounding method of PV system on land. The grounding resistance should be 10[$\small{{\Omega}}$] in case the voltage is over 400[V] in accordance with Korean Standard. The applicable parameters are the resistivity of water in various circumstances, depth of water, and length of electrode in order to meet 10[$\small{{\Omega}}$] of grounding resistance. We calculated appropriate length of the electrode on the basis of theoretical equation of grounding resistance and analyzed the relation between each parameters through MATLAB simulation. This paper explains grounding system of floating PV power station and presents considerations on grounding design according to the resistivity of water.
Keywords
Floating PV system;Grounding method;Grounding resistance;
Language
Korean
Cited by
References
1.
J. Bione, O. C. Vilela, and N. Fraidenraich, Solar Energy, 76, 703 (2004). [DOI: http://dx.doi.org/10.1016/j.solener.2004.01.003
2.
J. Freilich and J. M. Gordon, Solar Energy, 46, 267 (1991). [DOI: http://dx.doi.org/10.1016/0038-092X(91)90093-C]
3.
C. Ferrer-Gisbert, J. J. Ferran-Gozalvez, M. Redon-Santafe, P. Ferrer-Gisbert, F. J. Sanchez-Romero, and J. B. Torregrosa-Soler, Renewable Energy, 60, 63 (2013). [DOI: http://dx.doi.org/10.1016/j.renene.2013.04.007
4.
T. Matsuo, K. Hanaki, and H. Satoh, In Advances in Water and Wastewater Treatment Technology (Elsevier, 2001) p. 109-117.
5.
F. Helfer, C. Lemckert, and H. Zhang, Journal of Hydrology, 475, 365 (2012). [DOI: http://dx.doi.org/10.1016/j.jhydrol.2012.10.008
6.
G. F. Tagg, Earth Resistances (London George Newnes Limited, 1964)
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Definition:Minimal Arithmetic
Minimal arithmetic is the set $Q$ of theorems of the recursive set of sentences in the language of arithmetic containing exactly:
$(\text M 1)$ $:$ $\ds \forall x:$ $\ds \map s x \ne 0$ $(\text M 2)$ $:$ $\ds \forall x, y:$ $\ds \map s x = \map s y \implies x = y$ $(\text M 3)$ $:$ $\ds \forall x:$ $\ds x + 0 = x$ $(\text M 4)$ $:$ $\ds \forall x, y:$ $\ds x + \map s y = \map s {x + y}$ $(\text M 5)$ $:$ $\ds \forall x:$ $\ds x \cdot 0 = 0$ $(\text M 6)$ $:$ $\ds \forall x, y:$ $\ds x \cdot \map s y = \paren {x \cdot y} + x$ $(\text M 7)$ $:$ $\ds \forall x:$ $\ds \neg x < 0$ $(\text M 8)$ $:$ $\ds \forall x, y:$ $\ds x < \map s y \iff \paren {x < y \lor x = y}$ $(\text M 9)$ $:$ $\ds \forall x:$ $\ds 0 < x \iff x \ne 0$ $(\text M 10)$ $:$ $\ds \forall x, y:$ $\ds \map s x < y \iff \paren {x < y \land y \ne \map s x}$
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# Local Langlands correspondence and Galois equivariance
The local Langlands correspondence $\text{rec}$ for $\text{GL}_{n}$ itself is not Galois equivariant (i.e. invariant under automorphisms of its field of definition) but rather its twist by contragradient and an unramified character is. In Carayol's article "Non-abelian Lubin-Tate theory" in Ann Arbor proceedings, this twist, which I will call $r_{\ell}$, is just referred as "Hecke correspondence," which makes me feel like there is something more about it. Is there a deeper reason to believe why not the local Langlands correspondence but its slight twist is the one that is Galois equivariant? More generally, is there an a priori reason why $r_{\ell}$ is the one that appears in geometric constructions?
• You may want to add link to the article and at least one top level tag. – Chris Ramsey Jan 8 '16 at 14:55
The reason $r_\ell$ appears in geometric constructions involving Shimura varieties is because Hecke operators act on the cohomology of a Shimura variety with coefficients in $\mathbb{Q}$; that's the source of the good behavior of $r_\ell$ with respect to automorphisms of the coefficient field.
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## Potential elastic energy problem in an incline
Question
A $$20.0$$ kg package is released on a $$50 ^\circ$$ incline, $$4.50 m$$ from a long spring with force constant $$150$$ N/m that is attached at the bottom of the incline. The block hits the spring, compresses the spring, and finally bounds back. The coefficient of kinetic friction between the package and the incline is $$\mu_k = .20$$. The mass of the spring is negligible
1. Calculate the maximum compression of the spring by the block.
2. How far does the block rebound back along the incline?
For the first part, I used work done by nonconservative force (W_nc) = $$E_f - E_i$$.
This translates into $$-f_k(d+x) = (1/2)(k)(x^2) - (mg)(d+x)(sin(\Theta))$$.
Plugging in known values, noting that x is the unknown results in: $$-(.20)(20.0)(9.80)(cos(50 ^\circ)(4.50 + x)=(1/2)(150)(x^2) - (20)(9.80)(4.50+x)(sin(50 ^\circ)$$.
Evaluating, $$-25.2(4.5+x)=75x^2 - 150(4.5+x)$$
$$0=75x^2 - 124.8(4.5+x)$$
$$x_1 = 3.69$$ m.
Is this procedure correct?
2. $$K_1 + U_1 + W_n = K_2 + U_2$$
$$W_n=U_2 - U_1$$.
$$-25.2x = (20.0)(9.80)(xsin(50 ^\circ) - (1/2)(150)(3.69)^2$$
$$-25.2x=150x - 1021$$
$$1021=175.2x$$
$$x=5.83$$ m
Is this procedure correct?
PhysOrg.com science news on PhysOrg.com >> Ants and carnivorous plants conspire for mutualistic feeding>> Forecast for Titan: Wild weather could be ahead>> Researchers stitch defects into the world's thinnest semiconductor
Both seem fine to me!
Thanks! I checked today and they were correct.
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• ### GravityCam: Wide-Field High-Resolution High-Cadence Imaging Surveys in the Visible from the Ground(1709.00244)
GravityCam is a new concept of ground-based imaging instrument capable of delivering significantly sharper images from the ground than is normally possible without adaptive optics. Advances in optical and near infrared imaging technologies allow images to be acquired at high speed without significant noise penalty. Aligning these images before they are combined can yield a 2.5 to 3 fold improvement in image resolution. By using arrays of such detectors, survey fields may be as wide as the telescope optics allows. Consequently, GravityCam enables both wide-field high-resolution imaging and high-speed photometry. We describe the instrument and detail its application to provide demographics of planets and satellites down to Lunar mass (or even below) across the Milky Way. GravityCam is also suited to improve the quality of weak shear studies of dark matter distribution in distant clusters of galaxies and multiwavelength follow-ups of background sources that are strongly lensed by galaxy clusters. The photometric data arising from an extensive microlensing survey will also be useful for asteroseismology studies, while GravityCam can be used to monitor fast multiwavelength flaring in accreting compact objects, and promises to generate a unique data set on the population of the Kuiper belt and possibly the Oort cloud.
• ### Olivine-rich asteroids in the near-Earth space(1803.04486)
March 12, 2018 astro-ph.EP
In the framework of a 30-night spectroscopic survey of small near-Earth asteroids (NEAs) we present new results regarding the identification of olivine-rich objects. The following NEAs were classified as A-type using visible spectra obtained with 3.6 m NTT telescope: (293726) 2007 RQ17, (444584) 2006 UK, 2012 NP, 2014 YS34, 2015 HB117, 2015 LH, 2015 TB179, 2015 TW144. We determined a relative abundance of $5.4\%$ (8 out of 147 observed targets) A-types at hundred meter size range of NEAs population. The ratio is at least five times larger compared with the previously known A-types, which represent less than $\sim1\%$ of NEAs taxonomically classified. By taking into account that part of our targets may not be confirmed as olivine-rich asteroids by their near-infrared spectra, or they can have a nebular origin, our result provides an upper-limit estimation of mantle fragments at size ranges bellow 300m. Our findings are compared with the "battered-to-bits" scenario, claiming that at small sizes the olivine-rich objects should be more abundant when compared with basaltic and iron ones.
• ### Pluto's atmosphere from stellar occultations in 2012 and 2013(1506.08173)
Aug. 14, 2015 astro-ph.EP
We analyze two multi-chord stellar occultations by Pluto observed on July 18th, 2012 and May 4th, 2013, and monitored respectively from five and six sites. They provide a total of fifteen light-curves, twelve of them being used for a simultaneous fit that uses a unique temperature profile, assuming a clear (no-haze) and pure N_2 atmosphere, but allowing for a possible pressure variation between the two dates. We find a solution that fits satisfactorily (i.e. within the noise level) all the twelve light-curves, providing atmospheric constraints between ~1,190 km (pressure ~ 11 \mubar) and ~ 1,450 km (pressure ~0.1 \mubar) from Pluto's center. Our main results are: (1) the best-fitting temperature profile shows a stratosphere with strong positive gradient between 1,190 km (at 36 K, 11 \mubar) and r = 1,215 km (6.0 \mubar), where a temperature maximum of 110 K is reached; above it is a mesosphere with negative thermal gradient of -0.2 K/km up to ~ 1,390 km (0.25 \mubar), where, the mesosphere connects itself to a more isothermal upper branch around 81 K; (2) the pressure shows a small (6 %) but significant increase (6-\sigma level) between the two dates; (3) without troposphere, Pluto's radius is found to be R_P = 1,190 +/- 5km. Allowing for a troposphere, R_P is constrained to lie between 1,168 and 1,195 km; (4) the currently measured CO abundance is too small to explain the mesospheric negative thermal gradient. Cooling by HCN is possible, but only if this species is largely saturated; Alternative explanations like zonal winds or vertical compositional variations of the atmosphere are unable to explain the observed mesospheric trend.
• ### Integral-field spectroscopy of (90482) Orcus-Vanth(1108.5963)
Aug. 30, 2011 astro-ph.EP
Aims. We seek to constrain the surface composition of the Trans-Neptunian Object (90482) Orcus and its small satellite Vanth, as well as their mass and density. Methods. We acquired near-infrared spectra (1.4-2.4 {\mu}m) of (90482) Orcus and its companion Vanth using the adaptive-optics-fed integral-field spectrograph SINFONI mounted on Yepun/UT4 at the European Southern Observatory Very Large Telescope. We took advantage of a very favorable appulse (separation of only 4") between Orcus and the UCAC2 29643541 star (R = 11.6) to use the adaptive optics mode of SINFONI, allowing both components to be spatially resolved and Vanth colors to be extracted independently from Orcus. Results. The spectrum of Orcus we obtain has the highest signal-to-noise ratio to date, and we confirm the presence of H2O ice in crystalline form, together with the presence of an absorption band at 2.2 {\mu}m. We set an upper limit of about 2% for the presence of methane, and 5% for ethane. Because the methane alone cannot account for the 2.2 {\mu}m band, the presence of ammonia is suggested to the level of a couple of percent. The colors of Vanth are found slightly redder than those of Orcus, but the large measurement uncertainties forbid us from drawing conclusions on the origin of the pair (capture or co-formation). Finally, we reset the orbital phase of Vanth around Orcus, and confirm the orbital parameters derived by Brown et al. (2010, AJ 139).
• ### "TNOs are cool": A survey of the trans-neptunian region. II. The thermal lightcurve of (136108) Haumea(1006.0095)
June 1, 2010 astro-ph.EP
Thermal emission from Kuiper Belt object (136108) Haumea was measured with Herschel-PACS at 100 and 160 micrometers for almost a full rotation period. Observations clearly indicate a 100-micrometer thermal lightcurve with an amplitude of a factor of ~ 2, which is positively correlated with the optical lightcurve. This confirms that both are primarily due to shape effects. A 160-micrometer lightcurve is marginally detected. Radiometric fits of the mean Herschel- and Spitzer- fluxes indicate an equivalent diameter D ~ 1300 km and a geometric albedo p_v ~ 0.70-0.75. These values agree with inferences from the optical lightcurve, supporting the hydrostatic equilibrium hypothesis. The large amplitude of the 100-micrometer lightcurve suggests that the object has a high projected a/b axis ratio (~ 1.3) and a low thermal inertia as well as possible variable infrared beaming. This may point to fine regolith on the surface, with a lunar-type photometric behavior. The quality of the thermal data is not sufficient to clearly detect the effects of a surface dark spot.
• ### "TNOs are Cool": A survey of the trans-Neptunian region I. Results from the Herschel Science Demonstration Phase (SDP)(1005.2923)
May 17, 2010 astro-ph.GA, astro-ph.EP
The goal of the Herschel Open Time Key programme "TNOs are Cool!" is to derive the physical and thermal properties for a large sample of Centaurs and trans-Neptunian objects (TNOs), including resonant, classical, detached and scattered disk objects. We present results for seven targets either observed in PACS point-source, or in mini scan-map mode. Spitzer-MIPS observations were included for three objects. The sizes of these targets range from 100 km to almost 1000 km, five have low geometric albedos below 10%, (145480) 2005 TB190 has a higher albedo above 15%. Classical thermal models driven by an intermediate beaming factor of $\eta$=1.2 or $\eta$-values adjusted to the observed colour temperature fit the multi-band observations well in most cases. More sophisticated thermophysical models give very similar diameter and albedo values for thermal inertias in the range 0-25 Jm-2s-0.5K-1, consistent with very low heat conductivities at temperatures far away from the Sun. The early experience with observing and model strategies will allow us to derive physical and thermal properties for our complete Herschel TNO sample of 140 targets as a benchmark for understanding the solar system debris disk, and extra-solar ones as well.
• ### Colors and taxonomy of Centaurs and Trans-Neptunian Objects(0912.2621)
Dec. 14, 2009 astro-ph.EP
The study of the surface properties of Centaurs and Trans-Neptunian Objects (TNOs) provides essential information about the early conditions and evolution of the outer Solar System. Due to the faintness of most of these distant and icy bodies, photometry currently constitutes the best technique to survey a statistically significant number of them. Our aim is to investigate color properties of a large sample of minor bodies of the outer Solar System, and set their taxonomic classification. We carried out visible and near-infrared photometry of Centaurs and TNOs, making use, respectively, of the FORS2 and ISAAC instruments at the Very Large Telescope (European Southern Observatory). Using G-mode analysis, we derived taxonomic classifications according to the Barucci et al. (2005a) system. We report photometric observations of 31 objects, 10 of them have their colors reported for the first time ever. 28 Centaurs and TNOs have been assigned to a taxon. We combined the entire sample of 38 objects taxonomically classified in the framework of our programme (28 objects from this work; 10 objects from DeMeo et al. 2009a) with previously classified TNOs and Centaurs, looking for correlations between taxonomy and dynamics. We compared our photometric results to literature data, finding hints of heterogeneity for the surfaces of 4 objects.
• ### Visible spectroscopy of the new ESO Large Program on trans-Neptunian objects and Centaurs: final results(0910.0450)
Oct. 2, 2009 astro-ph.EP
A second large programme (LP) for the physical studies of TNOs and Centaurs, started at ESO Cerro Paranal on October 2006 to obtain high-quality data, has recently been concluded. In this paper we present the spectra of these pristine bodies obtained in the visible range during the last two semesters of the LP. We investigate the spectral behaviour of the TNOs and Centaurs observed, and we analyse the spectral slopes distribution of the full data set coming from this LP and from the literature. We computed the spectral slope for each observed object, and searched for possible weak absorption features. A statistical analysis was performed on a total sample of 73 TNOs and Centaurs to look for possible correlations between dynamical classes, orbital parameters, and spectral gradient. We obtained new spectra for 28 bodies, 15 of which were observed for the first time. All the new presented spectra are featureless, including 2003 AZ84, for which a faint and broad absorption band possibly attributed to hydrated silicates on its surface has been reported. The data confirm a wide variety of spectral behaviours, with neutral--grey to very red gradients. An analysis of the spectral slopes available from this LP and in the literature for a total sample of 73 Centaurs and TNOs shows that there is a lack of very red objects in the classical population. We present the results of the statistical analysis of the spectral slope distribution versus orbital parameters. In particular, we confirm a strong anticorrelation between spectral slope and orbital inclination for the classical population. A strong correlation is also found between the spectral slope and orbital eccentricity for resonant TNOs, with objects having higher spectral slope values with increasing eccentricity.
• ### The CFEPS Kuiper Belt Survey: Strategy and Pre-survey Results(astro-ph/0510826)
Oct. 29, 2005 astro-ph
We present the data acquisition strategy and characterization procedures for the Canada-France Ecliptic Plane Survey (CFEPS), a sub-component of the Canada-France-Hawaii Telescope Legacy Survey. The survey began in early 2003 and as of summer 2005 has covered 430 square degrees of sky within a few degrees of the ecliptic. Moving objects beyond the orbit of Uranus are detected to a magnitude limit of $m_R$=23 -- 24 (depending on the image quality). To track as large a sample as possible and avoid introducing followup bias, we have developed a multi-epoch observing strategy that is spread over several years. We present the evolution of the uncertainties in ephemeris position and orbital elements as the objects progress through the epochs. We then present a small 10-object sample that was tracked in this manner as part of a preliminary survey starting a year before the main CFEPS project. We describe the CFEPS survey simulator, to be released in 2006, which allows theoretical models of the Kuiper Belt to be compared with the survey discoveries since CFEPS has a well-documented pointing history with characterized detection efficiencies as a function of magnitude and rate of motion on the sky. Using the pre-survey objects we illustrate the usage of the simulator in modeling the classical Kuiper Belt.
• ### Coordinated thermal and optical observations of Trans-Neptunian object (20000) Varuna from Sierra Nevada(astro-ph/0206486)
June 27, 2002 astro-ph
We report on coordinated thermal and optical measurements of trans-Neptunian object (20000) Varuna obtained in January-February 2002, respectively from the IRAM 30-m and IAA 1.5 m telescopes. The optical data show a lightcurve with a period of 3.176+/-0.010 hr, a mean V magnitude of 20.37+/-0.08 and a 0.42+/-0.01 magnitude amplitude. They also tentatively indicate that the lightcurve is asymmetric and double-peaked. The thermal observations indicate a 1.12+/-0.41 mJy flux, averaged over the object's rotation. Combining the two datasets, we infer that Varuna has a mean 1060(+180/-220) km diameter and a mean 0.038(+0.022/-0.010) V geometric albedo, in general agreement with an earlier determination using the same technique.
• ### The Color Distribution in the Edgeworth-Kuiper Belt(astro-ph/0206468)
June 26, 2002 astro-ph
We have started since 1997 the Meudon Multicolor Survey of Outer Solar System Objects with the aim of collecting a large and homogeneous set of color data for Trans-Neptunian and Centaurs objects [...] We have a combined sample of 52 B-R color measurements for 8 Centaurs, 22 Classicals, 13 Plutinos, 8 Scattered objects and 1 object with unidentified dynamical class. This dataset is the largest single and homogeneous published dataset to date [...]. A strong (color) correlation with mean excitation velocity points toward a space weathering/impact origin for the color diversity. However, thorough modeling of the collisional/dynamical environment in the Edgeworth-Kuiper belt needs to be done in order to confirm this scenario. We found also that the Classical TNOs consist in the superposition of two distinct populations: the dynamically Cold Classical TNOs (red colors, low i, small sizes) and the dynamically Hot Classical TNOs (diverse colors, moderate and high i, larger sizes). [...] Our specific observation strategy [...] permitted us to highlight a few objects suspected to have true compositional and/or texture variation on their surfaces. These are 1998 HK151, 1999 DF9, 1999 OY3, 2000 GP183, 2000 OK67, and 2001 KA77 and should be prime targets for further observations [...]. Our survey has also highlighted 1998 SN165 whose colors and dynamical properties puts it in a new dynamical class distinct from the Classicals, its previously assigned dynamical class.
• ### Visible-IR Colors and Lightcurve Analysis of Two Bright TNOs: 1999 TC36 and 1998 SN165(astro-ph/0205293)
May 17, 2002 astro-ph
We report on observations of two bright Trans-Neptunian Objects (TNOs) - 1999 TC36 and 1998 SN165}- during two observational campaigns, as part of the Meudon Multicolor Survey of Outer Solar System Objects. V-J color was measured for 1999 TC36 (V-J=2.34+/-0.18), which combined with previous measured colors in the visible, indicate a red reflectivity spectrum at all wavelengths. Photometric V-band lightcurves were taken for both objects over a time span of around 8 hours. We have determined a possible rotational period of P=10.1+/-0.8 h for 1998 SN165, making it the seventh TNO with an estimated period. From its lightcurve variation of Dm=0.151(+0.022/-0.030), we have inferred an asymmetry ratio of a/b >=1.148(+0.024/-0.031). For 1999 TC36, we did not detect any rotational period or periodic signal variation within the uncertainties, but the analysis of its lightcurve hints to a slight systematic magnitude decrease.
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# Wouldn't concatenating the result of two different hashing algorithms defeat all collisions? [duplicate]
Let's say I have three messages: A B C
And I run each of these through two different Hashing algorithms: MD5 and SHA1 for this example
MD5(A) = X
MD5(B) = Y
MD5(C) = Y
SHA1(A) = N
SHA1(B) = N
SHA1(C) = M
Notice the MD5 hash of B and C collide. And the SHA hash of A and B collide.
If I simply concatenate the digests, however, the results would be unique:
Combined Digest of A: XN
Combined Digest of B: YN
Combined Digest of C: YM
The underlying principle would be that whatever pair of messages could be found or constructed to form a collision with one hashing algorithm, wouldn't also form a collision with another hashing algorithm.
The combined digest length (for MD5/SHA1) would be 288 bits (128+160) -- but unless I'm missing something, this would be significantly more secure than a single hashing algorithm with a 288-bit digest.
Granted, in the example above I'm using MD5 and SHA1 which are both known to be effectively broken, but I'm hoping an answer exists that applies more conceptually to the premise than simply the choice of algorithms.
i.e., In a situation where collision resistance is critical, wouldn't the combination of SHA2-256 + SHA3-256 concatenated be more secure than a single iteration of SHA2-512, or SHA3-512?
• FYI, the closest question I found that is similar is this one: crypto.stackexchange.com/questions/81634/… But it didn't quite ask the exact premise of my question. Mar 1 at 18:52
• The short answer is no: a collision for MD5 || SHA-1 is almost as easy as a collision for SHA-1 alone — much worse than SHA-256 despite SHA-256 being slightly shorter, but unbroken. Mar 1 at 19:25
• No, it's not specific to MD5 and SHA1: the fact that the attack on the concatenation is basically only as hard as the attack on the longest hash is mostly generic. Mar 1 at 20:41
• What leads you to believe "whatever pair of messages could be found or constructed to form a collision with one hashing algorithm, wouldn't also form a collision with another hashing algorithm"? Mar 2 at 4:33
• The pigeon-hole principle alone tells us that collisions are still possible. Mar 2 at 16:16
No, concatenating the result of two different hashing algorithms does not defeat all collisions. You've overlooked the case where $$\text{MD5}(A)=\text{MD5}(B)=X$$ and $$\text{SHA1}(A)=\text{SHA1}(B)=N$$. In English, that's when a pair of inputs collides for both hash functions.
Furthermore, assuming a hash function's output is truly uniformly distributed for any given set of inputs (this isn't actually true, but for our purposes, it's close enough to true for modern cryptographic has functions), the collision resistance of $$\text{HASH}^P_\text{256-bit}(A) +\text{HASH}^Q_\text{256-bit}(A)$$ is exactly equal to the collision resistance of $$\text{HASH}_\text{512-bit}(A)$$.
Again, assuming a uniform distribution, the chance two inputs collide for an N-bit hash is $$\left(\frac{1}{2}\right)^N$$, or one in two for each bit of output. Assuming the chance that a pair of inputs collides for hash $$P$$ is independent of the chance of collision of the pair for hash $$Q$$, the chance a pair collides for both is the product of the chance it collides for each hash individually. Given this, it's clear the chance of collision is identical either way, since $$\left(\frac{1}{2}\right)^{256}\cdot\left(\frac{1}{2}\right)^{256}=\left(\frac{1}{2}\right)^{512}$$.
• Perhaps some people are sufficiently paranoid that they would prefer not to assume a uniform distribution -- e.g. if in the future it turns out that one of the hashing algorithms contains an exploitable flaw but the other algorithm does not, then using the concatenation of the two algorithms' output could be more resistant to exploitation than just using a single algorithm to generate twice the number of hash-bits? Mar 2 at 6:14
• This was the confirmation I was seeking. Thank you. Follow on question, is there a reason why doing a single 512-bit hash is "better" than concatenating two different 256-bit hashes (faster, more secure, simpler, lower cpu, anything)? Mar 2 at 15:44
• @Eddie This will depend entirely on the specific hash functions. For example, some processors implement hardware acceleration for specific hash functions, so one method may be significantly faster than the other on some hardware. In general though, assuming none of the hash functions have a known weakness, I don't think there's a strong technical reason to choose one or the other. That said, I think many people would find the decision to concatenate two cryptographic hashes perplexing in the absence of a strong technical reason, since it presumably increases implementation complexity. Mar 2 at 23:41
No, concatenating two hashes gives you at least the collision resistance of either but in many practical cases it will give you little more.
This is especially truely for MD hash functions where we know how to convert collisions into many way multi collisions. We can make 2^64 multi way sha1 collision and expect one will collide also in MD5.
• but in many practical cases it will give you little more -- could you expand on this a bit? And specifically speak to why it wouldn't give you an additional "the full collision resistance" of the other hashing algorithm? Mar 1 at 20:23
• try this question: crypto.stackexchange.com/questions/103630/… Mar 2 at 11:00
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## Quantitative Aptitude Quiz 83 for IBPS PO
1. A train travels for 7 hours at the speed of 27 km/hr. and for 9 hours at the speed of 38 km/hr. At the end of it driver finds he has covered 3/7th of total distance. At what speed the train should travel to cover the remaining distance in 24 hours?
1) 26.5 km/hr. 2) 27.5 km/hr. 3) 28.5 km/hr. 4) 29.5 km/hr. 5) 32 km/hr.
2. How many different words can be formed with the letters of the word "TRANSFER" so that the words begin with 'T'?
1) 40320 2) 20160 3) 5040 4) 2520 5) None of these
3. A bag contains 5 black and 3 white balls. A second bag contains 4 black and 2 white balls. One bag is selected at random. From the selected bag one ball is drawn. What is the probability that the drawn ball is black ?
4. Two pipes 'A' and 'B' would fill a tank in 36 hours and 45 hours respectively. If both pipes are opened together, find when the first pipe must be closed so that the tank may be just filled in 30 hours ?
1) 6 hours 2) 9 hours 3) 12 hours 4) 15 hours 5) 18 hours
5. A shopkeeper buys 5 tables and 8 chairs for 5000. He sells the tables at a profit of 12% and chairs at a loss of 8%. If his total gain is 80 then what price does he pay for a table and a chair ?
1) 480, 325 2) 450, 320 3) 400, 325 4) 425, 375 5) None of these
6. The area of a rectangular field is 4800% of its breadth. If the difference between length and breadth of the field is 28m. then what is its area ?
1) 5600 meter2
2) 8400 meter2
3) 9600 meter2
4) 1152 meter2
5) None of these
7. The length of a rectangle is thrice its breadth. If its length is decreased by 6m. and breadth is increased by 6m. the area of rectangle is increased by 132m2 . What is the length of rectangle ?
1) 27 meter 2) 33 meter 3) 36 meter 4) 42 meter 5) 48 meter
8. A square shape is formed from a wire, which encloses an area of 38.5 meter2. If the same wire is bent to form a circle then what will be its area ?
1) 42 meter2
2) 49 meter2
3) 56 meter2
4) 64 meter2
5) None of these
9. Twelve spherical balls of radius 4.5 cm. are melted and cast into a cylindrical rod of same radius. What will be the height of rod ?
1) 24 cm. 2) 36 cm. 3) 54 cm. 4) 60 cm. 5) 72 cm.
10. A rectangular tank is 45 metre long and 33 metre deep. If 1440 cubic metre of water be drawn from the tank, the level of water is goes down by 9 metre. What is the capacity of tank ?
1) 7240 cubic metre 2) 6810 cubic metre 3) 6260 cubic metre 4) 5750 cubic metre 5) 5280 cubic metre
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