String.split on dot doesn't work as expected
String.split() *not* on regular expression?
Term for words like Snowmageddon, Nipplegate and even cheeseburger? In any Pythagorean triplet at least one of them is divisible by $2$, $3$ and $5$. Show that if $x$, $y$, $z$ are integers such that $x^2 + y^2 = z^2$, then at least one of them is divisible by $2$, at least one is divisible by $3$, and at least one is divisible by $5$.  I know that $x,y,z$ are sides of a right-angled triangles. If I start putting values, then I can show, but have no clue about mathematical approach.  How do I solve it mathematically, using modular arithmetic? I want to prove that $xe^{-x}$ is bounded by some constant for all the $x \in [0, \infty)$. So I take derivative of this guy, and found that on $x \in [0, \infty)$, its derivative is positive from $[0, 1)$, $0$ at $x=1$, and negative from (1, in infinity). So  $xe^{-x}$ achieves its maximum in $[0, \infty)$ at $x=1$, which is $1/e$. However, to prove that it's bounded by $1/e$, I need to prove that as $x$ goes to infinity, $xe^{-x}$ converges to $0$. Because otherwise, if it went to some value below $(-1/e)$, $xe^{-x}$ would not be bounded by $1/e$. How can I prove that $xe^{-x}$ converges to $0$? I mean, as $x$ goes to infinity, $e^{-x}$ converges to zero, but at the same time, x diverges to infinity. How can I formally prove that the product term converges to $0$? Do I need to use the epsilon definition of convergence to prove it?  Could you just show me the formal proof of $xe^{-x}$ converges to $0$? Or is there's any other way to approach this question? My professor suggested that I should use the power series for $e^{-x}$...?   Your help is greatly appreciated! Thank you so much!  I hope you enjoy your Saturday! Which Standard Visitor visa should I apply for? I have a shapefile with 3800 polygons representing the smallest administrative areas in Ireland. Many of these, in rural areas, have tiny populations, under 100 people. In urban areas, all would have adequate populations.  For each area I have a population figure, and various other attributes, all of which can be intelligently summed to give valid results for areas produced by combining the smaller areas.  I need to merge the areas to get say, 500 or 600 areas of reasonable population. I need to leave the larger (in population) areas alone, where possible. I would greatly prefer to do this automatically. This is necessary for model fitting purposes, primarily.  I've looked at a number of the dissolve questions here:   'Batch Dissolve Polygons based on Attributes in QGIS or FWTools' I think would require me to know which areas to merge, when this is what I need to calculate. 'Practical way of managing polygons and unions of them' and 'How do dissolve polygons from shapefile using open source tools?' have the same issue.   Any suggestions? Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$ I found this problem in a book and while I understand the given solution, I don't quite understand how somebody would arrive at this solution unless they did out the casework and happened to make the right guesses to solve the problem. Any guidance on solving this from scratch would be greatly appreciated! I'm trying to understand at a deeper level the ubiquity of log-likelihood (and perhaps more generally log-probability) in statistics and probability theory.  Log-probabilities show up all over the place: we usually work with the log-likelihood for analysis (e.g. for maximization), the Fisher information is defined in terms of the second derivative of the log-likelihood, entropy is an expected log-probability, Kullback-Liebler divergence involves log-probabilities, the expected diviance is an expected log-likelihood, etc.    Now I appreciate the many practical and convenient reasons.  Many common and useful pdfs are from exponential families, which leads to elegantly simplified terms when log-transformed.  Sums are easier to work with than products (esp for differentiating).  Log-probs have a great floating point advantage over straight probs.  Log-transforming a pdf often converts a non-concave function into a concave function.  But what is the theoretical reason/justification/motivation for log-probs?  As an example of my perplexity, consider the Fisher information (FI).  The usual explanation for intuiting the FI is that the second derivative of the log-likelihood tells us how "peaked" the log-likehood is:  a highly peaked log-likelihood means the MLE is well-specified and we are relatively sure of its value, while a nearly flat log-likehood (low curvature) means many different parameter values are nearly as good (in terms of the log-likelihood) as the MLE, so our MLE is more uncertain.   This is all well-and-good, but isn't it more natural to just find the curvature of the likelihood function itself (NOT log-transformed)?  At first glance the emphasis on the log-transform seems arbitrary and wrong.  Surely we are more interested in the curvature of the actual likelihood function.  What was Fisher's motivation for working with the score function and the Hessian of the log-likelihood instead?  Is the answer simply that, in the end, we have nice results from the log-likelihood asymptotically? E.g., Cramer-Rao and normality of the MLE/posterior.  Or is there a deeper reason? Is Switching the Neutral OK? What’s the worst that can happen if i put a switch in the neutral instead of the phase?   I just found out that 3 light bulbs sockets in my home  are connected this way, it first came to my mind to fix it but then I recalled the flow of current from positive to negative is just a convention since the electrons are charged negatively and they actually flow from N to L so i cant really find an solid excuse to mess with the wiring for the next 2 hrs How to change file extension at runtime in Java Execute shell script or command on idle time I'm searching for the possibility to execute a shell script or command based on idle time in the bash shell.  As an example, if I'm in a SSH session to a server of mine and after X minutes of inactivity in the terminal, I want a command to start a desired program like cmatrix, and when I come back and press a key I will get back where I left. Templated check for the existence of a class member function? Does an Action Surge grant a second bonus action? We were trying to understand how the "Action Surge" rule works, and after some discussion we came to a standstill.      Starting at 2nd level, you can push yourself beyond your normal limits for a moment. On your turn, you can take one additional action on top of your regular action and a possible bonus action   The keyword "possible" is what threw us off. Half the group thought it meant "additional action or bonus action", and the other half thought it was "additional action and bonus action".  So which is it? Why is the direction of cross products of two vectors perpendicular to the plane? The function auto.arima in the forecast package of R is a powerful tool to identify the best ARIMA(p,d,q) model for a given data series. In the   of the function, they report the following:  auto.arima(y, d=NA, max.p=5, max.q=5, max.order=5, max.d=2, start.p=2, start.q=2, ...)   According to the above function it seems that, by default, auto.arima tries to find the best model among all the combination having:   p equal or lower than 5 q equal or lower than 5 d equal or lower than 2 order equal or lower to 5, i.e. p + q + d  ≤ 5.   However, why does the default code stops at these conditions? Is there any particular reason why p, q and d should be equal or lower than 5, 5 and 2 and their sum lower than 5? Using Regular Expressions to Extract a Value in Java I have several strings in the rough form:  [some text] [some number] [some more text]   I want to extract the text in [some number] using the Java Regex classes.  I know roughly what regular expression I want to use (though all suggestions are welcome). What I'm really interested in are the Java calls to take the regex string and use it on the source data to produce the value of [some number].  EDIT: I should add that I'm only interested in a single [some number] (basically, the first instance). The source strings are short and I'm not going to be looking for multiple occurrences of [some number]. Pivot rows into multiple columns It's really hard to get started on Stack Overflow I have been on Stack Overflow for some time.  It is an AMAZING resource and don't know if I would've got through the past 18 months without it.  I love it!  Problem is that I have "1" reputation.  All of my questions have already been asked and answered.  My "new user restrictions" mean: - I can't vote up answers that were helpful. - I can't comment on answers.  I sometimes have a question to ask one of the users that answered someone else's question but I can't.  This is hard!  How do I get a break?  Do I have to troll for a couple of days/weeks/months to answer enough questions in the hope someone votes some of them up just so I can do some basic functions?  Perhaps the number of site visits and length of membership could count for something? What are Extension Methods? What are extension methods in .NET?    EDIT: I have posted a follow up question at How do the review limits work? I got the brand new Custodian badge today for reviewing posts. Inspired by that, I reviewed some more suggested edits. Now I ran into a limit:     You have no more suggested edit votes today; come back in x hours.   How is that limit calculated? I made 61 reviews today which seems to be some calculated limit.  I searched for an answer on meta but found nothing helpful. Can spells be cast through a Wall of Force?