It doesn't snow a lot where I live, but whenever it does and I go outside, the air feels warmer than I would expect on an clear day with an equivalent temperature, even though thermometer on my car reads -1 C° which is colder than most clear days. Does this have anything to do with humidity?
I sometimes hear stories where people compare their feelings in winter in different places in the world.  It goes like     in city X the temperature was the same as in city Y, but the humidity made me feel much colder...   or      oh well, -20°C would be cold, but the humidity was low, so it felt OK   so it implies that humidity somehow makes it feel colder. I am talking about temperatures below freezing (-30...0°C).  Does this have any physical explanation, or is it some sort of ?
Applied boolean modifier leaving shading artifacts with flat shading I tried to manipulate a cube with the Boolean modifier. I tried to cut out an edge of the cube with a cylinder. Also, the shading result looks awful in FLAT SHADING mode, so I turned on SMOOTH SHADING.   Has anyone an idea how to achieve a better result. (I also cut out a Sphere first, this made the result less awful).   I used Blender Internal and rendered with smooth shading for smoothness.  Using flat shading looks okay, except the "round" cutouts :/  Face normals are okay.  First image is smooth shading.    EDIT: User Pisurquatre suggested the EdgeSplit modifier, works perfect to me (Maybe a little tweaking here and there): If I set multiple Alarms, can I tell them apart? What does "rc" in .bashrc stand for? Is it "resource configuration", by any chance? Durrett Example 1.9 - Pairwise independence does not imply mutual independence? The example in question is from Rick Durrett's "Elementrary Probability for Applications", and the setup is something like this:     Let $A$ be the event "Alice and Betty have the same birthday", $B$ be the event "Betty and Carol have the same birthday", and $C$ be the event "Carol and Alice have the same birthday".   Durrett goes on to demonstrate that each pair is independent, since for example,   $P(A \cap B) = P(A)P(B)$.   However, he concludes that $A, B$, and $C$ are not independent, since   $P(A \cap B \cap C) = \frac{1}{365^2} \neq \frac{1}{365^3} = P(A)P(B)P(C)$.  I understand the reasoning here, and that one can generally show that arbitrary events $X$ and $Y$ are not independent by showing that $P(X\cap Y) \neq P(X)P(Y)$.   I am a little new to probability, though, and don't understand why exactly $P(A \cap B \cap C) = \frac{1}{365^2}$.   My progress so far:   I do see why $P(A) = P(B) =P(C) = \frac{1}{365}$, and thus why $P(A)P(B)P(C) = \frac{1}{365^3}$.  It seems like the sample space $\Omega = \{ (a, b, c) \mid a,b,c \in [365] \}$ -- i.e., all of the possible triples of numbers from 1 to 365, where 1 denotes January 1st, 2 denotes January 2nd, etc. From that, I can conclude $|\Omega| = 365^3$, but I'm not sure where to go from here.   It seems like once a single birthday is chosen, the rest are completely determined if they're all equal to each other - is this a good direction to go in? What are best practices for choosing and pairing fonts? I've always found font selection to be a little bit of a mystery. What factors should be considered when choosing a font? How does one successfully incorporate two fonts into a design?  I realize that some factors will include things like:   Legibility Scalability Appropriateness/Mood/Emotion   However, how does one objectively judge legibility or appropriateness? Are there objective principles that can be applied for font selection? If possible, please list resources or examples in your answers. Studies focused on the effectiveness of different fonts would also be extremely useful. How to reduce the number of hyphenation? Sometimes, assume our document contain many long words, TeX may generate some hyphenation at the end of line. But it really hinder our smooth reading. Although I know we can add the hyphenation rule at the preamble. It can't reduce hyphenation number but effect the hyphenation position. It is said that microtype package can give us more compact output. But it require expert level to tuning the parameter. Can Button[] generate output without using Print[]? I used the inbuilt dataset stackloss here. I used following R code for creating the multiple regression model.  &gt; head(stackloss)   Air.Flow Water.Temp Acid.Conc. stack.loss   1        80         27         89         42   2        80         27         88         37   3        75         25         90         37   4        62         24         87         28   5        62         22         87         18   6        62         23         87         18  &gt; fit &lt;- lm(stack.loss ~ .,data=stackloss) &gt; plot(fit)   And when I plot the model, the four following graphs are displayed.      How to interpret these graphs? What are the significance of these graphs? How to use these graphs? Why do paintbrush loops get thicker at the top in Illustrator? When I do swirls in Illustrator with the paintbrush tool I often get this result (see image).    The loops doesn't get perfectly rounded, instead sometimes some of them gets thicker at the top of the loop... It tends to happen more if I paint small with low brush sizes. Why is this happening? At the start of Harry Potter and the Philosopher's/Sorceror's Stone Voldemort's Killing Curse backfires      due to Lily's sacrifice protecting Harry from Voldemort.   leaving Harry with his scar      and a loose piece of Voldemort's soul   and Voldemort as a loose soul, self-described as "Less than a ghost".  Voldemort was not dead, but had no physical body (until he got better in book 4).  What happened to his body?  Did it disappear?  Or was it left in the rubble of the house, alongside the bodies of James and Lily? I understand that \bf and \it are now obsolete in LaTeX and that \textbf and \textit are proper, as they produce more sophisticated (in particular, cumulative and properly kerned) changes to font style. I have read the  and I understand the rules and their reasons, as well as the several other commands that are affected.  However, I find it convenient to use LaTeX for notetaking during lectures, and in that rushed environment, shortening a command by any number of keystrokes helps keep me from falling behind. \bf and its two-letter kin are still very useful to me for that reason, and once a presentation is finished I can go through and replace all appearances of \bf et al. with \textbf et al.  My question is this: is there a plan eventually to replace the short font style commands like \bf with the implementations of \textbf etc. some day, or should I expect \bf always to remain in existence but obsolete, for reasons of backward compatibility with original TeX? Original TeX has been greatly improved on in countless ways, but in the heat of transcription I sometimes miss its conciseness. How can I get the DateTime for the start of the week? How to prevent book class from vertically justifying the contents? If we use the book class, the output looks like the following screenshot.    But if we use the article class, the output looks better as follows.    The MWE is given as follows. Note: please enable -shell-escape!  \documentclass[12pt]{article}% please change to article and compare the output.  \usepackage{filecontents} \begin{filecontents*}{"article sample.tex"} \documentclass{article} \usepackage{lipsum} \begin{document} \lipsum[1-20] \end{document} \end{filecontents*}  \usepackage{showexpl}  \lstset {     breaklines=true,     breakindent=0pt,     tabsize=2,     columns=flexible,     language={[LaTeX]TeX},     basicstyle=\small\ttfamily\hbox{}, }  \newcount\x  \newcommand\MyLTXinputExample[2][2mm]{% % #1: length of gap, % #2: filename with .tex,      \lstinputlisting[caption=\url{#2.tex}]{"#2.tex"}     \bgroup         \parskip=#1\relax         \fboxsep=0pt         \pdfximage{#2.pdf}%         \x=0         \loop             \ifnum\x&lt;\pdflastximagepages                 \advance\x by 1                 \noindent\hfill                 \fbox{\includegraphics[width=0.5\dimexpr\linewidth-4\fboxrule-#1\relax,page=\x]{"#2"}}%                                  \ifnum\x&lt;\pdflastximagepages                 \advance\x by 1                 \hfill                 \fbox{\includegraphics[width=0.5\dimexpr\linewidth-4\fboxrule-#1\relax,page=\x]{"#2"}}%             \fi                 \hfill\null\par         \repeat     \egroup }  \PassOptionsToPackage{obeyspaces}{url} \usepackage{hyperref}  \begin{document} \immediate\write18{pdflatex "article sample"} \MyLTXinputExample{article sample} \end{document}   How to prevent book class from vertically justifying the contents? In other words, I want to use the book class but its output (only the justification is under consideration) must look like the output that article class produces. I have enabled storing Desktop &amp; Document Folders in iCloud. I keep my Xcode projects on Desktop. Every hour or so, iCloud will store files, inside of Pods folder present alongside the Xcode Project in iCloud. This is very tedious as I then have to click on each one of them one-by-one to re-download.  How can I prevent iCloud from downloading my files in this manner, for this specific Xcode project?  I have tried disabling iCloud for Desktop, but this results in me losing all my Desktop folders/files, so I could rather not go this route. How do you deserialize json properties that are reserved words in apex? The Cartesian product of a family $(A_i\mid i\in I)$ is defined as $$\prod\limits_{i\in I}A_i=\{f:I\to\bigcup A_i\mid f(i)\in A_i\}$$ Let $I_n=\{i \in \mathbb N \mid i \le n\}$ for $n\in \Bbb N$ and $A_i$ be countable for all $i\in I_n$. Then $\prod\limits_{i\in I_n}A_i$ is countable.   My attempt: Lemma 1: $(\prod\limits_{i\in I_n}A_i) \times A_{n+1}$ and $\prod\limits_{i\in I_{n+1}}A_i$ are equinumerous for all $n \in \mathbb N$. (I presented a proof ) Lemma 2: If $A$ and $B$ are countable, then $A \times B$ is countable. (I presented a proof ) I will prove the theorem by induction on $n$. The theorem is trivially true for $n=0$. Assume that the theorem is true for $n=k$, then $\prod\limits_{i\in I_k}A_i$ is countable. Since $\prod\limits_{i\in I_k}A_i$ is countable (by inductive hypothesis) and $A_{k+1}$ is countable, then by Lemma 2 $(\prod\limits_{i\in I_n}A_i) \times A_{n+1}$ is countable. Furthermore, by Lemma 1 $(\prod\limits_{i\in I_k}A_i) \times A_{k+1}$ and $\prod\limits_{i\in I_{k+1}}A_i$ are equinumerous, then $\prod\limits_{i\in I_{k+1}}A_i$ is countable too. Thus the theorem is true for $n=k+1$. This completes the proof.   Does this proof look fine or contain gaps? Do you have suggestions? Many thanks for your dedicated help! For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$ I need to have one column as the primary key and another to auto increment an order number field. Is this possible?  EDIT: I think I'll just use a composite number as the order number. Thanks anyways. How is ** implemented in Python? I'm wondering where I find the source to show how the operator ** is implemented in Python.  Can someone point me in the right direction? How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime