When can Eisenstein's Criterion never be used?
Irreducibility check for polynomials not satisfying Eisenstein Criterion.
Power set equivalency of Axiom of Choice Restoring Windows XP PATH variable I installed an application that screwed my PATH variable. Now I cannot run anything from the command prompt. Is there any way I can restore PATH variable? Does app review rejection list all issues? Our app was rejected recently with reason Google+ signin, which we understood is not according to Apple policy and need to fix.  While discussing about this issue we came across an interesting question with Apple review process, does Apple review team list all issues (if more than one exists) while rejecting app (or) would they stop reviewing other areas as soon as they found an issue (in our case Google+ signin)? I noticed a peculiar behavior of my Ubuntu 13.04 (although possibly it's also present in previous versions): when my system freezes completely (I do not ask for troubleshooting this) so that even X does not respond to Ctrl+Alt+FX keys, the CapsLock toggle diode on my keyboard blinks (with frequency of ~1Hz), although the system is completely unresponsive.   What is the cause of this phenomena? Is it caused by some internal kernel mechanisms? Is this specific to Ubuntu (is it caused some custom Ubuntu additional software)? Does it has anything to do with HAL? What is the purpose of it? Can I customize this behavior on Ubuntu? symmetric functions vs symmetric polynomials I am doing my thesis related with symmetric functions and representations.   It is for this reason that I am reading MacDonald's book Symmetric Functions and Hall Polynomials.  When reading chapter 1.2. The ring of symmetric functions, he also talks about symmetric polynomials. And he compares both notions and sometimes treats them as equivalent but sometimes not. Does anyone have a clearer explanation about what is the difference (if there are differences)?  So, what is the difference between symmetric functions and symmetric polynomials? Back-transformation of regression coefficients I'm doing a linear regression with a transformed dependent variable. The following transformation was done so that the assumption of normality of residuals would hold. The untransformed dependant variable was negatively skewed, and the following transform made it close to normal:   $$Y=\sqrt{50-Y_{orig}}$$  where $Y_{orig}$ is the dependent variable on the original scale.   I think it makes sense to use some transformation on the $\beta$ coefficients to work our way back to the original scale. Using the following regression equation,   $$Y=\sqrt{50-Y_{orig}}=\alpha+\beta \cdot X$$  and by fixing $X=0$, we have   $$\alpha=\sqrt{50-Y_{orig}}=\sqrt{50-\alpha_{orig}}$$  And finally,  $$\alpha_{orig}=50-\alpha^2$$  Using the same logic, I found  $$\beta_{orig}=\alpha\space(\alpha-2\beta)+\beta^2+\alpha_{orig}-50$$  Now things work very well for a model with 1 or 2 predictors; the back-transformed coefficients resemble the original ones, only now I can trust the standard errors. The problem comes when including an interaction term, such as  $$Y=\alpha+X_1\beta_{X_1}+X_2\beta_{X_2}+X_1X_2\beta_{X_1X_2}$$  Then the back-transformation for the $\beta$s are not so close to the ones from the original scale, and I'm not sure why that happens. I'm also unsure if the formula found for back-transforming a beta coefficient is usable as is for the 3rd $\beta$ (for the interaction term). Before going into crazy algebra, I thought I'd ask for advice... biblatex broken overnight As late as last week my setup for biblatex worked fine. Going back to the same project today not even a minimal file compiles:  \documentclass{article}   \usepackage{biblatex} %\addbibresource{biblatex-examples.bib}   \begin{document}  test%foo\nocite{*}    %\printbibliography  \end{document}   but breaks off with   /usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.sty:3776: LaTeX  Error: Missing \begin{document}.  See the LaTeX manual or LaTeX Companion for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.3776   australian,newzealand} ?  /usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.sty:3776: Math f ormula deleted: Insufficient symbol fonts. \expandafter -&gt;american|  l.3776   australian,newzealand}   And keeps repeating the last one until    (That makes 100 errors; please try again.)   when I ignore it.  Files without biblatex work as expected.  Using tlmgr to go my two backup versions of biblatex back in time to 1st Jan I still get the same errors.  Could this be another update from the last week or so that causes this?  If I swich back to TL 16 things work as expected. (For my work I need TL 17 because of packages.) Suppose that $ f $ is entire and that for each $ z $, either $ |f(z)| \leq 1 $ or $ |f^\prime (z) |\leq 1 $. Prove that $ f $ is a linear polynomial. My question is in the title. I'm a little lost in how to solve this problem. There is a hint associated with the problem that states the following:   Use a line integral to show that $ |f(z)| \leq A + |z| $ where A = $\max\{1, |f(0)|\}$  Thanks for the help. Specifying geography with cardinal directions So here in America we are in "the West".  Would this become "the Western world" or "the western world? "  I'll assume the same applies to "the East" (Asia). I received $1000 and was asked to send it back. How was this scam meant to work? Possible Australianism - netbank = a website + app by which an Aussie can do their banking, including transferring money to other people.  A while ago, I ended up with $1000 transferred into my account, which in the description looked like a netbank transfer, not like a cheque, cash deposit etc, and which looked like it had already cleared and landed in my account. Usually when something is still working through the bank's system it displays as 'pending', but did not in this case.  I received a phone call from someone, saying that they had accidentally typed in the wrong account number, and wanting me to send them the same amount of money back via netbank.   Surely bank account numbers have a checksum, which make it relatively difficult for a typo to result in a payment going to the wrong person? What are likely sources of them being able to find my phone number to call me? Obviously, the bank either being hacked, or giving it out in response to a query from this person (but surely the bank is unlikely to tell me my own mobile number if I claim to have forgotten it?). Presumably either my phone, or the phone of someone I have sent money to/received money from could be compromised. Has anyone heard of any instances of this happening?  I then went to my bank, explained the situation and said that I did want to refund the money through the officially sanctioned methodology. After the laughter died down, the bank told me to ask the person to fill out a form, then they would get me to fill out a form that would authorize undoing that exact payment.  I rang up the person to tell them this, and over the course of about a week received an increasingly elaborate story about how that wasn't working, they needed the money immediately, there was a fee to fill out that form and they couldn't afford to pay it etc.  After that, I never heard back from them again. I check my netbank for several weeks after, expecting the money to magically disappear, but it did not. This was probably a year ago, and I'm pretty vague with money so may not have noticed if it disappeared more recently. How were they expecting to benefit?  Were they hoping to get the transfer from me, and undo the transfer to me, to leave them $1k up? If so, how can an internet banking transfer be 'undone' once it has already shown as 'received'. Or was this to do with money laundering? The account they requested me to send money to was the same as the one that the money appeared to come from. This was a scam, right? Dealing with bundle/omnibus/list-of-questions question that consists of rather distinct questions I have looked at the various help pages but I couldn't find a clear guideline for the following issue: often enough someone will ask in the same post (i.e. in the same SE-question) a whole bunch of questions (in the plain English sense of the word), which while may be about the same topic are nevertheless sufficiently distinct that each may require several paragraphs of text to answer adequately.   I can see an upside for leaving related questions grouped together from the asker's perspective: "there's a thread (on SE) answering all my questions about topic T!" On the other hand, from the perspective of organizing questions by having a clear heading/title for each (actual) question and so forth, i.e. from the perspective of SE being a fairly structured database of Q&amp;As instead of being a more like a collection of forum threads "I'm confused about topic T", the omnibus question-list approach seems clearly sub-optimal.  The omnibus approach also makes the issue of accepting answers (and perhaps reviewing such actions) difficult: if two different users give replies to different parts/sub-sets of the question-list, which one is the most adequate one? Even upvoting all partial answers seems iffy because it actually penalizes the user(s) who provides(s) the most complete answer to the question-list: since a user can only give at most one upvote to another user's answer, if user X provides answers to A &amp; B in the same SE-answer, he can only get at most one upvote from user Y, whereas if these were two different SE-answers, he could get two upvotes from user Y.  So, given the above problems, which I think are real enough, is there anything in the SE system addressing list-of-questions question splitting? Why is the Sun approximated as a black body at ~ 5800 K? Get two letter country code in Apex method I want to write an Apex method that takes a country name as input and returns the equivalent two letter country code (ISO A2). Is there a way to write it without explicitly hard coding all countries and code in the method? I discovered that you can start your variable name with a '@' character in C#.  In my C# project I was using a web service (I added a web reference to my project) that was written in Java. One of the interface objects defined in the WSDL had a member variable with the name "params". Obviously this is a reserved word in C# so you can't have a class with a member variable with the name "params". The proxy object that was generated contained a property that looked like this:  public ArrayList @params {     get { return this.paramsField; }     set { this.paramsField = value; } }   I searched through the VS 2008 c# documentation but couldn't find anything about it. Also searching Google didn't give me any useful answers. So what is the exact meaning or use of the '@' character in a variable/property name? How do I make the method return type generic? Consider this example (typical in OOP books):    I have an Animal class, where each Animal can have many friends. And subclasses like Dog, Duck, Mouse etc which add specific behavior like bark(), quack() etc.  Here's the Animal class:  public class Animal {     private Map&lt;String,Animal&gt; friends = new HashMap&lt;&gt;();      public void addFriend(String name, Animal animal){         friends.put(name,animal);     }      public Animal callFriend(String name){         return friends.get(name);     } }   And here's some code snippet with lots of typecasting:  Mouse jerry = new Mouse(); jerry.addFriend("spike", new Dog()); jerry.addFriend("quacker", new Duck());  ((Dog) jerry.callFriend("spike")).bark(); ((Duck) jerry.callFriend("quacker")).quack();   Is there any way I can use generics for the return type to get rid of the typecasting, so that I can say      jerry.callFriend("spike").bark(); jerry.callFriend("quacker").quack();   Here's some initial code with return type conveyed to the method as a parameter that's never used.   public&lt;T extends Animal&gt; T callFriend(String name, T unusedTypeObj){     return (T)friends.get(name);         }   Is there a way to figure out the return type at runtime without the extra parameter using instanceof? Or at least by passing a class of the type instead of a dummy instance. I understand generics are for compile time type-checking, but is there a workaround for this? A typical $L^p$ function does not have a well-defined trace on the boundary Adjective Used as an Adverb? That cake looks good.    In formal proper grammar, may good (adjective) get used as an adverb? Or, may you read it as, That cake (noun phrase, nominal[?], argument[?]), looks (verb, predicate[?]), good (subject compliment[?].? How may I discern this, grammatically? Find $\int \frac{x^3}{x^2-1} \:\mathrm{d}x$ Find $\displaystyle \int \dfrac{x^3}{x^2-1} \:\mathrm{d}x$.   I think there are a few ways to do this. We could just break this up using long division or break it up into partial fractions then use long division. My homework says to break this up into its roots so that's why I brought up partial fractions. Is that the best way to do it here? Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$ Is there an intuitive way, though I am not sure how to find a conceptual proof either, to establish the following identity: $$\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$$ for all natural numbers.  I am thinking about binomial formula $$\sum_{k=0}^n\binom nk x^{n-k}y^k=(x+y)^n$$ but I'm not sure how to use it.  I find this problem tantalizing because it looks as if there should be some sort of intuitive way so that is why I share it here. I am looking for an answer like  if possible. Can you find one? I have a question regarding the two QGIS Versions 2 and 3. When I load exactly the same raster file into QGIS 2 and QGIS 3 I get different min/max values, how is this possible? I have used the same coordination system.