For an ideal gas, we can relate temperature to the average kinetic energy of the gas molecules.  What if we view a container of this gas from a reference frame that is translating at constant speed relative to the container.  $$E[X^{2}] = Var[X] + E[X]^{2}$$  The distribution of speeds is the same, but since the mean is larger (it is zero in the rest frame of the container), then the observer would view a higher average kinetic energy. Does the moving observer say that the container of gas is hotter?  If bulk translation doesn't relate to temperature, is there some hidden zeroing that's not present in the simple statement of "average kinetic energy"?
In ideal gas model,  is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becomes hotter? Do we need to distinguish the random vibration KE and KE in one direction?  Furthermore, if we accelerate a block of metal with ultrasonic vibrator so that the metal is vibrating in very high speed with cyclic motion, can we say the metal is hot when it is moving but suddenly become much cooler when the vibration stop?
Air gap on isolation space The below photo belongs to a PSU. I wonder what was the reason of placing air gaps on the 8 mm isolation. Is it to improve the isolation or provide a thermal relief (although there is no component below the red circled air gap)? Is “ ’s ” ever correct for pluralization? A relatively modern dictionary (I don’t know which one, because we’ve cut out the pages and used them as wallpaper in our bathroom, but I know it’s less than 20 years old) indicates that R’s is one correct pluralization of R, as is Rs, but whichever dictionary this is, it’s kind of a no-name brand, so I’m not sure I trust it.  I’ve always wondered what the best way was to pluralize single letters or numerals, like 2’s or 2s.  What’s correct? I have an Samsung Galaxy S3 Neo.  Bus 002 Device 042: ID 04e8:6860 Samsung Electronics Co., Ltd GT-I9100 Phone [Galaxy S II], GT-I9300 Phone [Galaxy S III], GT-P7500 [Galaxy Tab 10.1]   The keyboard &amp; language setting is português.  I today installed Android Device Manager and to test it's functionality I locked the phone with the password: "abcd" (4 letters were required).  After entering the password and confirming with the "OK" button of my keyboard, the phone showed me that the password is wrong. "Senha incorreta".  I reset the password after some tries to "123456" and the phone reloaded the lock screen. Again the password showed up to be wrong. I also tried the alphabetic password: "abcdefg" - same error.  I changed the language of my Google account from German to Portuguese and reset the password to "123456" again and I tried to really reboot my phone and unlock the SIM card again. But anyways I can not get through my lock of the Android Device Manager.  I tried to enter the password 35 times wrong with hope to get a chance to authenticate with my Google Account login.  I also tried to connect the phone with adb but it does not show up in this state with:  adb devices   So what can I do to get access to my phone again? Preface: Every couple of days there comes a question of this type, which is easy to solve with sed, but takes time to explain. I'm writing this question and answer, so I can later refer to this generic solution and only explain the adaption for the specific case. Feel free to contribute.  I have files with variable definitions. Variables consist of uppercase letters or underscore _ and their values follow after the :=. The values can contain other variables. This is Gnom.def:  NAME:=Gnom FULL_NAME:=$FIRST_NAME $NAME FIRST_NAME:=Sman STREET:=Mainstreet 42 TOWN:=Nowhere BIRTHDAY:=May 1st, 1999   Then there is another file form.txt with a template form:  $NAME Full name: $FULL_NAME Address: $STREET in $TOWN Birthday: $BIRTHDAY Don't be confused by $NAMES   Now I want a script which replaces the variables (marked with $ and the identifier) in the form by the definitions in the other file, recursively, if necessary, so I get this text back:  Gnom Full name: Sman Gnom Address: Mainstreet 42 in Nowhere Birthday: May 1st, 1999 Don't be confused by $NAMES   The last line is to ensure that no substrings of variables get replaced accidentally. Self-Studying Measure Theory and Integration As the title says, I'm interested in reading about measure theory and integration theory on my own time, and was hoping for book recommendations, prerequisites, and things like that.  As for my background, I've taken introductory analysis, where we covered the "typical" subjects up until some theorems about differentiable functions.  I'm taking intermediate real analysis now; we talked about metric spaces in general for a while, but lately we've focused solely on $\mathbb{R}^n$. Now we're working towards a proof of the implicit function theorem in $\mathbb{R}^n$.  I haven't learned any of the theory behind Riemann integration, unfortunately. Is it important to be familiar with this first? What is the "continue" keyword and how does it work in Java? I saw this keyword for the first time and I was wondering if someone could explain to me what it does.   What is the continue keyword? How does it work? When is it used? Headphones microphone is not working I'm trying to use my headphones with my Ubuntu 13.10. My headphones are Nokia BH-905i, which can be connected via Bluetooth or green+pink wires.  If I use bluetooth, voice quality is terrible or microphone doesn't work. If I try to choose "Headset" option from In and Out tabs in Sound Settings, they're disabling each together.  In Out tab, I'm using "High sound quality A2DP", because it betters voice quality.  How could I get my microphone working? Sound out works fine. Showing 2 Distributions are the Same Let $X_1, X_2, \dots$ be i.i.d. exponentially distributed RVs. For $n = 1,2,\dots$ consider: $Y_n := \max(X_1, X_2, \dots, X_n)$ $U_n := \sum_{i=1}^{n}\frac{X_i}{i}$ Show that $Y_n$ and $U_n$ have the same distribution   What I've tried: $P(Y_n&lt;y)= P(X_i&lt;y)^n = (1- e^{\lambda y})^n =&gt; P(Y_n=y) = n(1- e^{\lambda y})^{n-1}$ But I get stuck with $U_n$. I tried an MGF, $U_n$ evaluates nicely but then $Y_n$ gets messy. Any thoughts? I have a header file  x.h which is included by more than one *.c source files. This header file has some structure variables defined.  I have put multiple inclusion prevention guard at the beginning of the header file as:  #ifndef X_H #define X_H ... .. //header file declarations and definitons.   #endif//X_H   On building I get linker errors related to multiple definitions. I understand the problem.   Won't a multiple inclusion prevention guard at the top of header file as I have, prevent multiple inclusions of the header file x.h and thereby avoid multiple definitions of the variables that are there in x.h? #pragma once does not work on this particular compiler, so what is the solution?  Someone had posted  answer to a similar question. It doesn't seem to work for me. How does this solution work? Precedence of user and group owner in file permissions How Special Relativity causes magnetism Does this constitute a valid proof that $\frac{x^2}{1+x^4} \leq \frac{1}{2}$? As you can see on this screenshot of 's Guake he has a startup message of ASCII art when he opens it, and that's what I'd like to do, can someone help me? Once a world enters hardmode, corruption and hallows being spreading at an alarming rate, including the underground. Grass, which grows on dirt, succumbs easily to both. Jungles and glowing mushrooms grow on mud and provide unique and valuable items. Will corruption/hallows destroy these if left unchecked? If they do destroy mud-based life, how can I preserve these fragile ecosystems? Is it possible to change the color of a single bar when the bar plot is based on symbolic values? I am beginner in LaTeX, trying to use it for industrial documents. I wonder if there is a way to change the color of only one bar of the plot below, ie "TestDetails", to illustrate it is a local macro and not a LaTeX keyword. I have been trying to experiment with point meta, but could not find a way.  \documentclass{article} \usepackage{filecontents}  \usepackage{pgfplots}  \usepackage{pgfplotstable} \pgfplotsset{width=.95\textwidth, compat=newest}   \begin{document}  \begin{filecontents}{data.csv} {Occurences}, {keyword} 215, item 159, SI 134, subsubsection 106, TestDetails 58, caption \end{filecontents}  \pgfplotstableread[col sep=comma]{data.csv}{\datatable}  \begin{tikzpicture} \begin{axis}[ /pgf/number format/.cd,1000 sep={}, width=0.8\linewidth,height=6cm, xbar, xmin=30, xmax=250, xtick=\empty, enlarge x limits={value=0.1, upper}, enlarge y limits=0.1, ytick=data,  y dir=reverse, xlabel= {}, y tick label style={major tick length=0pt}, yticklabels from table={\datatable}{[index]1}, nodes near coords, nodes near coords align=horizontal, ] \addplot [draw,fill=blue!50]table[ y expr=\coordindex, x index=0]{\datatable}; \end{axis} \end{tikzpicture}  \end{document} Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$ Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $ Where is Ubuntu terminal located? I am trying to add terminal as external tool to compile javascript with node.js. I am following this  which is based on windows , and i am stuck at figuring out location of terminal application.  Where is the terminal located in Ubuntu? Multiplying Binomial Terms Track next Socratic badge progress Just got the  on StackOverflow and, since it can be awarded multiple times, wanted to start tracking progress to the next one, but, the badge is not shown in Available badges to track anymore:    Is it possible to track already awarded badges that can be awarded multiple times?