My family will buy a car, so to minimise the car's air conditioning and heating (and thus fuel)  costs, how should we choose a car exterior's colour and the interior's colour and material (eg fabric vs leather)?   For example, if my aunt lives in Toronto, Canada, which is cold from Sep to May (9 months), then does it make sense to choose a darker colour which apparently absorbs more heat?  Sadly, I know no physics so don't understand .
How does the color of a car influence its inner temperature change over time when parked outside in windless, hot and sunny regions?  I know what's the common idea about that: black cars are supposed to build up high temperatures faster because black objects absorb radiations instead of reflecting them off. Is it true? And then, what happens during the steady state? Some claim the black car will stay hotter, some others claim it will be the same whatever the color. Do all cars have the same temperature inside in the long run, or are some of them hotter?  I've Googled it but the best I could find was . It claims to be based upon ~20 articles. But there's not even a mention of absorption or emission spectrums. A priori, a black car could absorb all visible radiations and emit it as infrared while reflecting all of the Sun's infrared. And it's still only qualitative. I've found nothing on Physics stackexchange, the closest being .
Proof that a Combination is an integer From its definition a combination $\binom{n}{k}$, is the number of distinct subsets of size $k$ from a set of $n$ elements.  This is clearly an integer, however I was curious as to why the expression  $$\frac{n!}{k!(n-k)!}$$ always evaluates to an integer.  So far I figured:  $n!$, is clearly divisible by $k!$, and $(n-k)!$, individually, but I could not seem to make the jump to proof that that $n!$ is divisible by their product. How do I tunnel and browse the server webpage on my laptop? I run a web app in one of my lab servers, and I have already setup X11 Forwarding on those machines. Other lab members can tunnel through SSH, and browse that web app on their local browser at home.  I can't. Last time I checked with them, there is almost nothing I need to do.  When I type 192.168.1.113/webapp I get nothing.   Any tips?  THanks.    I ended up using the second method :)  ssh -L 8080:&lt;server-ip-address&gt;:80 &lt;username&gt;@&lt;remote-addr&gt; -N Preventing itemize environment to insert initial vertical space I'm using itemize and tables like the following  \begin{tabularx}{\textwidth}{&gt;{\ttfamily}llX}  \toprule  \textbf{\rmfamily Operator} &amp; \textbf{Typen} &amp; \textbf{Regel} \\  \midrule  = &amp; Alle Typen &amp;   \begin{itemize}    \item This is how we roll    \item Maybe we can talk?   \end{itemize} \\  \bottomrule \end{tabularx}   But it keeps inserting a vertical space before the itemized list. How can I prevent it from doing so? How is MSE divided by $\sigma^2$ always a chi-square distribution? Can a professor influence the graduate admissions committee if he or she is interested in a particular student? Does the Lunatic Cultist spawn on iPad? I was searching for more answers on the internet. I kept searching, and I found one thing that help me a little. I went back to Terraria and tried it out, but the Lunatic Cultist didn’t spawn.  Does the Lunatic Cultist spawn on an iPad? Get text between two strings Regex VB.Net I'm trying to solve a question where I need to write $\frac {1}{1+z^2} $ as a power series centered at $z_0=1$  I'm not allowed to use taylor expansion. So my first thought was to rewrite the function in a form where I can apply the basic identity:  $$ \frac{1}{1-x} = \sum_{n=0}^\infty x^n $$  So let's rewrite the original function $f(z) = \frac {1}{1+z^2} $ and use above identity:  $$\frac {1}{1+z^2} = \frac {1}{1-(-z^2)} $$ But observe that I need to center it at $z_0=1$ so I rewrote it to:  $$\frac {1}{1-(-z^2)}=\frac {1}{2z-(-(z-1)^2)} $$  I can factor out $\frac {1}{2z}$ and use the basic identity to get : $$\frac {1}{2z}\frac {1}{1-\frac{(z-1)^2}{2z}} = \frac {1}{2z}\sum_{n=0}^\infty \left(\frac{-(z-1)^2}{2z}\right)^n =\frac {1}{2z}\sum_{n=0}^\infty \frac{(-1)^n(z-1)^{2n}}{(2z)^n} = \sum_{n=0}^\infty \frac{(-1)^n(z-1)^{2n}}{(2z)^{n+1}}$$  The problem is if I ask wolfram alpha: power series$ \frac{1}{1+z^2} $centered at z = 1 it will give me a different answer that doesn't match the sum I found.  Can anyone help me figure this one out? What am I doing wrong? Expectation of the maximum of gaussian random variables Cyrillic monospaced font in XeLaTeX I've installed full TexLive 2011 using "install-tl" script in Ubuntu 12.04.  When I was using TexLive 2009 from repositories the following file was compiled without any errors.  \documentclass{article} % XeLaTeX \usepackage{xltxtra} \usepackage{xunicode}  % Fonts \setmainfont{Arial} \newfontfamily\cyrillicfont{Arial} \setmonofont{Courier New}  % Lang \usepackage{polyglossia} \setmainlanguage{russian} \setotherlanguage{english}  \begin{document} English normal.  \texttt{English monospace}.  Русский обычный.  \texttt{Русский моноширинный}.  % Text in Russian \end{document}   But XeLaTeX from TexLive 2011 gives this error:     ERROR: Package polyglossia Error:       --- TeX said ---   The current roman font does not contain the Cyrillic script!   Please define \cyrillicfont with \newfontfamily.      See the polyglossia package documentation for explanation.   Type  H   for immediate help.    ...                                                    l.17 ...nglish normal.  \texttt{English monospace}                                                     .   In spite of this error the output PDF is correct.  The error remains if comment out \setmonofont{Courier New}.  Using Courier New as main font gives no error on normal text (without \texttt, \textbf and so on).  Using DejaVu Sans Mono as monospaced font gives no error too.  I've been searching for solution few hours but there aren't any.  Maybe this is a bug in Polyglossia or Fontspec? What is "it" in the following sentence: It is clear that Bob likes doughnuts MCMC in a frequentist setting I have been trying to get a sense of the different problems in frequentist settings where MCMC is used. I am familiar that MCMC (or Monte Carlo) is used in fitting GLMMs and in maybe Monte Carlo EM algorithms. Are there more frequentist problems where MCMC is used? I thought the way to undo a \def was to define it to \relax, but that does not appear to work.  Also, am not sure why this produces no output if I try to use \def instead of \let in my attempt to do an undef.  \documentclass{article}  \begin{document}  \def\CaseA{}%  \ifdefined\CaseA%     \def\ProcessCaseA{}%     % Do stuff that uses \ProcessCaseA     %\def\ProcessCaseA\relax% no output if use this, and comment next line     \let\ProcessCaseA\relax% no output if comment this, and use above line \fi  % Now do stuff that requires \ProcessCaseA NOT be defined \ifdefined\ProcessCaseA     ERROR: \textbackslash ProcessCaseA is still defined \else     SUCCESS: \textbackslash ProcessCaseA is not defined \fi  \end{document} Any good application for data usage monitor? I was wondering if there are any good applications to monitor how much data I use on my laptop in a month. My net connection has a restriction of how much data I can use after which the speed goes down considerably. I saw ntop, but I just wanted to ask if there are any other good options or suggestions regarding this. Regards. Does anyone know whether there are only finitely many of primes of the form $6^{2n}+1$, where $n$ zero or any natural number? Is there a free site to play Yu-Gi-Oh? British placement of punctuation relative to inverted commas Someone who just thinks they know what they're talking about I've removed the poll style answers in favour of open discussion.  I realise now this isn't the best way to have a proper discussion about this issue - sorry to anyone who commented/voted.    This is mostly a followup on this question:    As I've answered, the reason this is happening is that the root database (in the production Stack Exchange database server) is still called StackExchange.Programmers - a database name that propagates to SEDE and through it to the data dump.  The question here is what to do about it - the current situation is somewhat broken for users of the data dump.  These are the options we have:   Do nothing Update the root database name (requires downtime - so very undesirable) Update the update scripts so the SEDE database name is the new name, change will flow to the data dump export (breaks any queries using the old name) Update the export to the data dump so only it gets the new name Something else we haven't thought about   I have added all of these options as answers below - please vote on the one you most prefer, we will try to accommodate the top voted answer. How do I make an object face the mouse position, but only on one plane? I want a game object to turn and look towards where the mouse was clicked (in world space).  It works well when considering all 3 dimensions, but I really only care for the plane formed by the x and z axis, not the y.  I've tried to fix this by setting the y of the directionTarget to the y of the object's position, but that gives weird results.  My code looks like this:  Quaternion rotationTarget;     float rotationLerpProgress;     float rotationLerpDuration = 1f;      // Use this for initialization     void Start ()     {      }      // Update is called once per frame     void Update ()     {             if (Input.GetMouseButtonDown (0)) {                     var ray = Camera.main.ScreenPointToRay (Input.mousePosition);                     RaycastHit rayHit;                      if (Physics.Raycast (ray, out rayHit)) {                             var rayHitPoint = rayHit.point;                              var rotationDirection = transform.position - rayHitPoint;                                                            rotationDirection.Normalize ();                             //rotationDirection.y = transform.position.y;                             rotationTarget = Quaternion.LookRotation (rotationDirection);                             rotationLerpProgress = Time.deltaTime;                     }                     //targetPosition = Camera.main.ScreenToWorldPoint (Input.mousePosition);                                     }              if (rotationTarget != transform.rotation) {                      transform.rotation = Quaternion.Lerp (transform.rotation, rotationTarget, rotationLerpProgress / rotationLerpDuration);                     rotationLerpProgress += Time.deltaTime;                       if (rotationLerpProgress &gt;= rotationLerpDuration) {                              transform.rotation = rotationTarget;                     }              }      }   I must be missing something. How do I do this right?