Why the Entry class in HashMap is static in java
Static nested class in Java, why?
Let $G$ be a group with $|G| = n$ and let $ \emptyset \ne S \subseteq G$.   I want to show that $S^n$ is a subgroup of $G$ where by $S^n$ I mean the set $\lbrace s_1\cdots s_n \; | \; s_i \in S\rbrace$. Renting a car in Ireland when under 25? My friend and I are planning a vacation to Ireland later this year. We'll be there for a week, flying into Dublin and then renting a car and driving around the country.  Both of us are 23. Are there any age restrictions on renting cars in Ireland? What would be the cheapest/best option for us? I've searched online, but I have not found any clear instructions how to permanently add .sty files to my TeXShop installation. I'm using a Mac with OSX (TeXShop is a mac only program).  What is the best way of doing this? The one comprehensive set of instructions I found .   I've got as far as extracting the files (running LaTeX on the .ins and . dtx files) but after that I don't know what to do. I also don't understand how to update the index of my distribution, and whether there are particular OSX specifics (the instructions are for Windows). I am going to change my machine: from a laptop with Ubuntu to another laptop where I am going to install Ubuntu...  I am quite happy with the current system, what I am afraid of is having to rebuild everything from 0.  So what do people often do to clone an Ubuntu system? That may include the data, packages, shortcut settings, etc... Is it possible to delete multiple elements from a list at the same time? If I want to delete elements at index 0 and 2, and try something like del somelist[0], followed by del somelist[2], the second statement will actually delete somelist[3].  I suppose I could always delete the higher numbered elements first but I'm hoping there is a better way. I have been wanting to understand how to find the sum of this series.   $$1^p + 2^p + 3^p +{\dots} + n^p$$  I am familiar with Gauss' diagonalised adding trick for the sum of the first $n$ natural numbers.  I can prove the formulas for  $$\begin{align}   \sum_{1}^{n} k^2 &amp;= \frac{n(n+1)(2n+1)}{6}\\  \sum_{1}^{n} k^3 &amp;= \frac{n^2(n+1)^2}{4}\\ \sum_{1}^{n} k^4 &amp;= \frac{n(n+1)(2n+1)(3n^2+3n-1)}{30} \\ \end{align}$$  With mathematical induction. But, beyond that even proofs with mathematical induction are difficult.  I'm interested in learning the theory and the proof behind Faulhaber's formula. What is the knowledge required to understand this proof ? Sending an HTTP request using QNetworkAccessManager Execute command from file in current shell I want to executed command from file (which is script) in current shell in terminal.  Example: I have file ch_dir contains following:  #!/bin/bash cd /usr   Now if I execute file usually as following then it executes commands in different shell:  pandya@pandya-desktop:~$ ./ch_dir pandya@pandya-desktop:~$   Here cd /user is executed in different shell.  But I want to execute in Current shell. How do I do that?  Note: Here cd is only used to explain. Question's aim is to execute any command in current shell I want to be able to pull in the error log from BIOS across a network I want to be able to pull in the error log from BIOS across a network. Looking at Win32_BIOS in MSDN I did not see anything defining the error log. Would love to do this in C# with WMI, but am open to suggestions. Is it possible?  Win32_BIOS does not have a property (don't know if that is the right term) that contains the BIOS error log. Is there a library, API, etc. that I can use to pull this information locally or from the network? Can $\pi$ or $e$ be a root of a polynomial with algebraic coefficients? Since $\pi$ and $e$ are transcendental, neither can be the root of a polynomial with rational coefficients. However, it is easy to construct a polynomial transcendental coefficients (with $\pi$ or $e$ as one of it's roots), namely $(x-\pi)$ and $(x-e)$. However, is it possible to construct a finite polynomial (one of whose roots is $\pi$ or $e$) with only algebraic coefficients? (i.e. something such as $y=x^5-(\sqrt 2 -1)x^2+x$ .) A polynomial with only radical coefficients would be the best.  P.S. The polynomial doesn't necessarily need to have BOTH $\pi$ and $e$ as it's roots, just one is interesting enough. Derive Fourier transform of sinc function We know that the Fourier transform of the sinc function is the rectangular function (or top hat). However, I'm at a loss as to how to prove it. Most textbooks and online sources start with the rectangular function, show that   $$\int_{-\infty}^\infty \text{rect}(x)e^{i\omega x}dx=\int_{-1/2}^{1/2}e^{i\omega x}dx=\left.\frac{e^{i\omega x}}{i\omega}\right\vert_{-1/2}^{1/2}=\text{sinc}(\omega/2)$$  and then just invoke duality and claim that the Fourier transform of the sinc function is the rectangular function. Is there any way of deriving this directly? i.e., starting with the sinc function?   I've tried, but I'm not sure as to how to proceed. I know that the sinc is not Lebesgue integrable and only improper Riemann integrable. Some vague recollection of these being important in the Fourier transform hinders my thought process. Can someone clear things up for me? Distance learning: taken seriously? I'm currently in the first year of a six year bachelor's degree aiming for astrophysics. The course is a home/distance learning setup run by the Open University. While I am enjoying it thoroughly, I am aware of the academic politics that can dog professional science. So my question is thus: Upon soldiering on with the degree, then masters, and then PhD, will I be taken seriously within a professional setting given my inability to reference a leading university for my education? Will the format for my studying be "pitied"?   Edit: I suppose a bit more info may help. I'm 27,wife, 2 children, and I currently work as a full time chef, and self employed part time IT technician. I flunked my GCSEs, with no further education. The past 3 years have been a revelation for me, and I have discovered a before unexperienced love for academia; specifically, physics and astronomy. Last year I completed a 1 year OU maths brush up course, which at the time I really struggled with. This year I had a bout of madness and took the plunge for a BSc degree in astronomy. I am now loving the math within the physics so far (yet to hit calculus though!)  PhD, and even masters, is a long way off.  Also, since this original post I've improved my understanding of what a PhD actually entails. So I realise that if I get there, it may well not have anything to do with the OU!     It occurs to me that a lot of my initial queries could have been avoided with a better understanding of the educational and qualification system itself. I now have a greater appreciation as to what a PhD actually is, realising that its a long way off and not necessarily needed for a fulfilling career in research.  I think trying to repair my broken education and fight my way into a worthwhile (and productive!) career is enough of challenge at the moment. There will be plenty of time later for worries concerning doctorates.  It is good to hear that there is at least an open mind towards distance educated professionals.   As has been said, if you've got it, you've got it - you just have to be ready to prove it. Using "nor" in a list without "neither" This is the classic usage of neither/nor:     I would neither hide nor run away.   But is the following construction grammatical? (More than two choices, no neither)     I wasn't going to play dead.   I wasn't going to hide.   Nor was I going to run away. The temperature and pressure everywhere inside the Sun reach the critical point to start nuclear reactions - there is no reason for it to take such a long time to complete the reaction process.  Just like a nuclear bomb will complete all the reaction within $10^{-6}$seconds.  Why does most of the hydrogen of the Sun still not react even though it reaches the critical point, and why take stars billions of years to run out of fuel? Run bash script at login stored in the home folder? When I try to load a LaunchAgent plist from launchctl I can't find out how to run a script in the home directory.  My code is:  &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt; &lt;plist version="1.0"&gt; &lt;dict&gt;     &lt;key&gt;ProgramArguments&lt;/key&gt;     &lt;array&gt;         &lt;string&gt;bash&lt;/string&gt;         &lt;string&gt;~/script.sh&lt;/string&gt;     &lt;/array&gt;     &lt;key&gt;RunAtLoad&lt;/key&gt;     &lt;true/&gt;     &lt;key&gt;Label&lt;/key&gt;     &lt;string&gt;com.tyilo.test&lt;/string&gt; &lt;/dict&gt; &lt;/plist&gt;   I have tried both with and without bash and also replacing ~ with $HOME. I have also tried using bash -c without it working.  The error code is:   `com.tyilo.test: bash: ~/script.sh: No such file or directory` Lots of new batteries (for mobile devices, MP3 players, etc) have connectors with 3 pins. I would like to know what is the purpose of this and how should I use these three pins?    They are usually marked as (+) plus, (-) minus, and T. How do I identify an airport’s official free Wi-Fi network? While traveling in the Berlin Tegel airport (TXL), I wanted to get on Wi-Fi. I found three unsecured networks in addition to a number of password-protected networks.   _Free_TXL_WiFi airberlin Berlin Tegel Airport WiFi   I had no idea which of these were an official Wi-Fi network provided by the airport and which were provided by other people, potentially for malicious purposes like capturing my network traffic. Presumably the official one uses a captive portal to allow internet access.  Is there any way to determine which Wi-Fi network is the official one provided by the airport? Would airport staff such as at the ticketing booths know? Are there official lists available somewhere?  I’d like an answer that is applicable to airports generally, rather than specific to the Berlin Airport. Also, please don’t just give a blanket “don’t use any public Wi-Fi network” answer; I know there are risks associated with it, but sometimes it is a necessity and so I want to know how to identify the airport-provided one.   suggests there are no official Wi-Fi networks, but the answers are six years old, so it’s not clear if things have changed or if none of the networks I saw were official. If the velocity is a relative quantity, will it make inconsistent equations when applying it to the conservation of energy equations?  For example:  In the train moving at $V$ relative to ground, there is an object moving at $v$ relative to the frame in the same direction the frame moves. Observer on the ground calculates the object kinetic energy as $\frac{1}{2}m(v+V)^2$. However, another observer on the frame calculates the energy as $\frac{1}{2}mv^2$. When each of these equations is plugged into the conservation of energy, they will result in 2 distinct results (I think). Is there a function to round a float in C or do I need to write my own? Random point uniform on a sphere