Could anyone tell me what energy really is? I searched for it, and some people said that energy doesn't exist physically and it is not fundamental, but it is a relationship between other fundamental things, and there is not energy by itself, so it should be related to something else.  So could anyone help me understand it?
The simplistic undergrad explanation aside, I've never really understood what energy really is. I've been told that it's something when converted from one kind of something to another kind, or does some "work", as defined by us, but what is that something?  Moreover, if the total amount of energy in the universe is finite and we cannot create energy. Then, where did it come from? I've learned from thermodynamics where it goes, but where does it come from?  I know this sounds like something trivially simple, but there is so much going on in the physical universe and I just can't grasp what it is. Maybe it is because I lack the mathematical understanding that I can't grasp the subtle things the universe is doing. Still, I want to understand what it is doing.  How do I get to the point of understanding what it's doing?  (Note: What prompted me to ask this was . I'm afraid that it just puzzled me further and I sat there staring at the screen for a good 10 minutes.)
Primary ideals in Noetherian rings For an $R$-module $M$ I have the following definition for a submodule $N\subset M$ to be $\mathfrak{p}$-primary: this is the case when $\text{Ass}(M/N) = \{\mathfrak{p}\}$, that is, $M/N$ is coprimary or $(0)$ is a primary submodule.  Now for an ideal $\mathfrak{q} \subset R$ this definition gives that $\mathfrak{q}$ is $\mathfrak{p}$-primary iff $\text{Ass}(R/\mathfrak{q}) = \{\mathfrak{p}\}$. It can be shown that this is equivalent with $\mathfrak{p}^n \subset \mathfrak{q}$ for some $n\in \mathbb{N}$ and the condition \begin{align*} \forall r,s \in R: rs \in \mathfrak{q}, r\not\in \mathfrak{p}\Rightarrow s \in \mathfrak{q}. \end{align*}     Now I suspect that if $R$ is Noetherian, and if $\mathfrak{q}$ is $\mathfrak{p}$-primary, then we have $\sqrt{\mathfrak{q}} = \mathfrak{p}$. I have shown this for PID's, but does this generaly hold?    And if so, is every ideal $\mathfrak{q}\subset R$ then $\sqrt{\mathfrak{q}}$-primary?   Many thanks. I'm making a mini game (bomb squad) and the armor needs to be enchanted. I know that armor can be enchanted through command blocks and that is what I intend to do. I am wondering if it is possible to enchant armor twice in one command block or should I need multiple command blocks as I have done in the past? Answer appears automatically converted as a comment Avoiding "(Not Responding)" label in windows while processing lots of data in one lump I occasionally need to process a large amount of data from one package off the network, which takes sufficiently long that when the user tries to interact with the application windows adds the "(Not Responding)" string to the window title. I am aware this is because the processing is being done within a call to handle a message (some way up the stack) and therefore is blocking the message pump. I'm also aware the ideal way to deal with this is to process the data asynchronously in a separate thread so the pump can continue running, however this is a LARGE desktop application which is single threaded from top to toe and safely spinning this processing off is not feasible in our time frame.  So with that in mind, is there by any chance a way I can at least avoid the "not responding" moniker (which to most users reads as "has crashed") by telling windows my application is about to be busy before I begin the work? I believe there is something along these lines when responding to a request to close, one can keep asking windows for more time to avoid it proclaiming that your not "closing in a timely fashion"  I should add this is a C++ MFC application. I've implemented AStar in Java and it works ok for an area with obstacles where the chosen destination is reachable.  However, when the destination is unreachable, the calculated "path" is in no way to the closest location (to the unreachable location) but is instead some random path.  Is there a feasible way to tweak AStar into finding the path to the closest location to an unreachable destination? Why don't researchers request payment for refereeing? Are two norms equivalent if they induce the same topology on a vector space? A word for someone who you share a half-sibling with This is probably best explained with an example.  Alice and Bob have a child, Erin. Bob and Carol have a child, Frank. Carol and Dan have a child, Grace. Clearly, Erin and Frank are half-siblings, because of their father, Bob. Similarly, Grace and Frank share their mother, Carol.  Erin and Grace have no parents in common, and are thus not half-siblings. However, is there a term for their relation? What are bitwise shift (bit-shift) operators and how do they work? I've been attempting to learn C in my spare time, and other languages (C#, Java, etc.) have the same concept (and often the same operators) ...   What I'm wondering is, at a core level, what does bit-shifting (&lt;&lt;, &gt;&gt;, &gt;&gt;&gt;) do, what problems can it help solve, and what gotchas lurk around the bend? In other words, an absolute beginner's guide to bit shifting in all its goodness. A common mistake for beginning group theory students is the belief that a quotient of a group $G$ is necessarily isomorphic to a subgroup of $G$.  Is there a characterization of the groups in which this property holds?  If this question is too broad, I might ask if such a characterization exists for $p$-groups.    History: I originally posed the opposite question, regarding groups for which $\exists N\unlhd G\,:\, \not\exists H \unlhd G\, \text{  s.t. } H \cong G/N$, and crossposted this to .  I received an answer there to the (now omitted) peripheral question about probability, which shows that most finite groups probably have this property.  After this, I changed the question to its current state, as this smaller collection of groups is more likely to be characterizable. When hyperref is loaded I receive the following error:     TeX capacity exceeded, sorry [input stack size=5000].   However, when I remove hyperref package it compiles successfully. I traced it back and found that \maketitle causes the error but don't know how to fix it. Is there any way to use hyperref in my setup.   Code:       %!TEX TS-program = xelatex     \documentclass[journal,transmag,]{IEEEtran}      \usepackage[hyphens]{url}     \usepackage{hyperref}      \usepackage{xunicode}      \usepackage{fontspec}      \usepackage{polyglossia}     \setmainlanguage{english}     \setotherlanguage{arabic}     \newfontfamily\arabicfont[Script = Arabic]{Amiri} % Replace 'Simplified Arabic' with a font from your system       \begin{document}     \title{A Very Nice Title}      \author{\IEEEauthorblockN{             John Doe\IEEEauthorrefmark{1}}%,~\IEEEmembership{Member,~IEEE}         \IEEEauthorblockA{\IEEEauthorrefmark{1}My address}         % &lt;-this % stops an unwanted space         \thanks{Manuscript received mm dd, 20xx; revised mm dd, 20xx.               }     }      % The paper headers     \markboth{headers...}%     {Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for IEEE Transactions on Magnetics Journals}      \IEEEtitleabstractindextext{%         \begin{abstract}My Abstract.\end{abstract}          % Note that keywords are not normally used for peerreview papers.         \begin{IEEEkeywords}             Key 1, Key 2     \end{IEEEkeywords}}      \maketitle       \IEEEdisplaynontitleabstractindextext     % \IEEEdisplaynontitleabstractindextext has no effect when using     \IEEEpeerreviewmaketitle       \section{Introduction}     English Text      \begin{Arabic}      السَلَامُ عَلَيكُمْ     \end{Arabic}       \end{document} Where does the energy required to stop a moving body come from and go? For a long time, I have been thinking about this: In order to stop a moving body, I have to apply impulse to change the existing momentum to $0$. For the impulse I have to impart force on the moving body . That means I have to eliminate all the kinetic energy associated with the moving object in order to bring it to a halt. Thus, work is done on the object, right? If work is done, energy must be given by me...  Here is where my confusion arises:   If I eliminate the associated kinetic energy of the body, where does this energy go? The work(?) done by me on the moving object to stop it obviously uses energy from me. Again, where does this energy go? Vertical uniform circular motion.. can it really be uniform? This is the picture in my mind:    For centripetal force, I learned that: $T-mg\cos\theta= \frac{mv^2}{r}$  In vertical circular motion, the velocity is naturally going to decrease as kinetic energy is converted to potential energy as the particle moves up the circle- and thus resulting into a non-uniform circular motion.  However, I was told that if tension changes accordingly, the velocity will remain constant(as from the equation). What I do not get about this part of the explanation is that which force will balance mgsinθ (tangential force in the diagram  )? In FreeBSD and also in Linux, how can I get the numerical chmod value of a file? For example, 644 instead of -rw-r--r--? I need an automatic way for a Bash script. How to add custom C++ keywords to be recognized by Minted? What are path and contour integrals? I am very confused on what path and contour integrals actually represent. I tried looking for an answer on Google but the only examples were related to Quantum Mechanics. For instance, real Riemann integrals can be thought as &quot;the area under the curve&quot;. What about path/contour integrals? Also, is there a difference between path and contour integrals, or are they the same thing? I've been thinking of contour integrals as path integrals where the path is a &quot;closed loop&quot;, but I'm not sure if that's the case. It's all so confusing, and not being able to visualise these concepts makes it feel like I'm just memorising formulas and theorems without any reason. I have been thinking about path integrals as integrating over a curve in three dimensions. For example, in an $xyz$ coordinate system (with $y$ pointing “up”), we have a path on the $x$-&quot;$z$&quot; plane and integrate over that path. That is, instead of integrating over and along &quot;$y=0$&quot;, we integrate over a certain path. But I don't know if this is a correct way to think of path integrals. This issue has been frustrating me a lot because I'm now studying theorems that involve path/contour integrals and I just can't understand what they really do or mean. By path integral I mean $$\int_{\gamma\vert_{[a,b]}}f(z)\hspace{0.2em}dz = \int_{a}^{b}f(\gamma(t))\cdot\gamma'(t)\hspace{0.2em}dt$$ where $f:U\subseteq\mathbb{C}\rightarrow\mathbb{C}$ is a function that satisfies all conditions for complex integration and $\gamma:[a,b]\rightarrow U\subseteq\mathbb{C}$ is at least a piece-wise regular path. Any help would be appreciated. Java Generics: List, List, List Finding Value of the Infinite Product $\prod \Bigl(1-\frac{1}{n^{2}}\Bigr)$ While trying some problems along with my friends we had difficulty in this question.   True or False: The value of the infinite product $$\prod\limits_{n=2}^{\infty} \biggl(1-\frac{1}{n^{2}}\biggr)$$ is $1$.   I couldn't do it and my friend justified it by saying that since the terms in the product have values less than $1$, so the value of the product can never be $1$. I don't know whether this justification is correct or not. But i referred to Tom Apostol's Mathematical Analysis book and found a theorem which states, that    The infinite product $\prod(1-a_{n})$ converges if the series $\sum a_{n}$ converges.   This assures that the above product converges. Could anyone help me in finding out where it converges to? And,   Does there exist a function $f$ in $\mathbb{N}$ ( like $n^{2}$, $n^{3}$) such that $\displaystyle \prod\limits_{n=1}^{\infty} \Bigl(1-\frac{1}{f(n)}\Bigr)$ has the value $1$? See YouTube videos in Anaglyph mode How to see a YouTube video in  from a non-3D Android device? I am not able to enable Anaglyph mode from the YouTube application. How to prevent page breaking for lstinputlistings?