Electromagnetic radiation: Why lower energy radiation( like radio waves) penetrates walls and higher energy radiation(like visible light) doesn't?
Electromagnetic wave properties of light vs radio waves
Confirmation that someone is listening to another person's speech When someone is telling you a very long and detailed story he usually wants to hear some "confirmations" (or response) that you are listening to his story. In Russian we often use something like "tak" (which has a meaning of "ok" and "well, proceed further"), "a-ha" or "uh-huh".  What word serves the same purpose in English and American English? I have a hierarchical category tree and checkboxes next to each item that allow to enable/disable the correpsonding category.    I assume it is an expected default behavior that all subategories of natural environment become checked when I check the natural environment category. But what about unchecking it again: Should this automatically uncheck all subcategories or restore the previous state in case some were checked already?  Furthermore... Should unchecking one of the subcategories cause the parent category to become unchecked? Can my friend and I play minecraft together with different mods? I have come across these three definitions of the limit superior (or upper limit) and the limit inferior (or lower limit) of a sequence of real numbers and I wonder how to establish the equivalence of these.    Walter Rudin: PRINCIPLES OF MATHEMATICAL ANALYSIS, 3rd edition:  Definition 3.16: Given a sequence $\{s_n\}$ of real numbers, let $E$ be the set of numbers $x$ (in the extended real number system) such that $s_{n_k} \to x$ for some subsequence $\{s_{n_k}\}$. This set contains all subsequential limits ..., plus possibly the numbers $+\infty$, $-\infty$. We now ... put  $$s^{*} = \sup E,$$ $$s_{*} = \inf E.$$ The numbers $s^{*}$, $s_{*}$ are called the upper and lower limits of $\{s_n\}$; we use the notation  $$ \lim_{n \to \infty} \sup s_n = s^{*}, \, \, \, \lim_{n \to \infty} \inf s_n = s_{*}.$$ Tom M. Apostol: MATHEMATICAL ANALYSIS, 2nd edition:  Sec. 8.3: Definition 8.2: Let $\{a_n\}$ be a sequence of real numbers. Suppose there is a real number $U$ satisfying the following conditions:    i} For every $\epsilon &gt; 0$ there exists an integer $N$ such that $n &gt; N$ implies $$a_n &lt; U + \epsilon.$$ ii) Given $\epsilon &gt; 0$ and given $m &gt; 0$, there exists an integer $n&gt; m$ such that $$a_n &gt; U - \epsilon.$$ Then $U$ is called the limit superior (or upper limit) of $\{a_n\}$, and we write $$U = \lim_{n \to \infty} \sup a_n.$$ Statement (i) implies that the set $\{a_1, a_2, a_3, \ldots \}$ is bounded above. If this set is not bounded above, we define $$\lim_{n\to\infty}\sup a_n = +\infty.$$ If the set is bounded above but not bounded below and if $\{a_n\}$ has no finite limit superior, then we say $\lim \sup_{n\to\infty} a_n = -\infty$. The limit inferior (or lower limit) of $\{a_n\}$ is defined as follows: $$\lim_{n\to\infty}\inf a_n = -\lim_{n\to\infty}\sup b_n,$$ where $b_n = -a_n$ for $n= 1, 2, 3, \ldots$.    Robert G. Bartle and Donald R. Sherbert: INTRODUCTION TO REAL ANALYSIS, 3rd edition: Exercises for Section 3.3: Problem 10: Let $(x_n)$ be a bounded sequence of real numbers, and for each $n\in \mathbb{N}$ let $s_n \colon= \sup \{x_k \colon k \geq n\}$ and let $t_n \colon= \inf \{x_k \colon k \geq n\}$. Prove that $(s_n)$ and $(t_n)$ are monotone and convergent. Also prove that if $\lim (s_n) = \lim (t_n)$, then $(x_n)$ is convergent. [One calls $\lim (s_n)$ the limit superior of $(x_n)$ and $\lim (t_n)$ the limit inferior of $(x_n)$.]   Now how can one show that the above three definitions are equivalent (i.e. these three definitions are of the same pair of numbers)? This week I've read two news stories about two different camera lenses that can magnify things that are very far away.  The first is the , which is a point-and-shoot camera that costs $600, has an 83x optical superzoom lens ("the same field of view as a 2,000mm lens on a full-frame camera"), and lets you see the craters of the moon.  The second is the , which weighs 36 pounds, costs $180,000, and can take portraits of people a half mile away.  A non-photographer might ask, "Why would somebody spend their life savings on a gigantic telescope of a lens when you could take far away pictures with a handheld camera for 1/300th the price?"  Well, I am basically a non-photographer, and I would like to ask that question. What does the big one give you that the little one doesn't provide? I understand that small changes in lenses can make a big difference in size and price, but this seems to be of a different scale entirely.   What is going on with the optics of the lenses that makes the small one able to be so small and the big one have to be so...big?   I'm trying to get a basic intuition for what makes lenses different, and I realize I don't understand enough about how lenses work to even know how to compare these apples and watermelons. LaTeXiT is cropping the pdf I am using LaTeXiT (pierre chachatelier, www.chachatelier.fr) - latex equation editor for Powerpoint for mac.  It's producing pdf that appear to be "cropped" on top (see attached) - I've tried already with changing the "margins" option (Preferences>General) but unsuccessfully - don't think that's the problem.   Any hint?   Thanks $G \times H \cong G \times K$ , then $ K \cong H$ I already know that if groups $G,H,K$ are finitely generated abelian groups, following is true.  If $G\times K$ is isomorphic to $H\times K$, then $G$ is isomorphic to $H$. I prove this by uniquness of factorization of finitely generated abelian groups.  My questions are   If group $G$ is finite,$G\times K$ is isomorphic to $H\times K$, then $G$ is isomorphic to $H$? Can you give me a easiest proof and it can be proved by projection function on external direct product? If $G,H,K$ are groups.  If $G\times K$ is isomorphic to $H\times K$, then $G$ is isomorphic to $H$. This statement is false. What is a counterexample?   *$\times$ is external direct product Prove that every idempotent element is not nilpotent element. Let $R$ be a ring. Prove that every idempotent element is not nilpotent element.  I've got a problem with proving this question. I was be grateful, if somebody would be help me. In The Force Awakens, we see Rey pouring some flour-like polystarch rations into water so that the flour amazingly transforms into something that looks like bread. What are these rations? Is there any documentation of the fictional chemistry and biology that makes the starch rations behave as they do? command to display time (duration) in human readable form I spent 3 hours trying to write a command to format a time (duration) expressed as a floating number (in seconds) in a nice form as follows:  if the time is &lt; 60 write as a float with 3 decimals (i.e. milliseconds)  else let h,m,s be the hours, minutes and seconds corresponding to the time      if h=0 then write as m:ss (ss always with 2 digits, m can have only 1)      else write h:mm:ss (mm and ss with 2 digits, h can have only 1)   So 1.25678 gives 1.256, 125.35 gives 2:05, 18249 (which equals to 5*3600+4*60+9) gives 5:04:09.  I tried several packages for the comparison/formatting. No success. Can someone help me ? Thanks ! What do "watched tags" and "ignored tags" do? What is the most elegant way to solve this:   open a file for reading, but only if it is not already opened for writing open a file for writing, but only if it is not already opened for reading or writing   The built-in functions work like this  &gt;&gt;&gt; path = r"c:\scr.txt" &gt;&gt;&gt; file1 = open(path, "w") &gt;&gt;&gt; print file1 &lt;open file 'c:\scr.txt', mode 'w' at 0x019F88D8&gt; &gt;&gt;&gt; file2 = open(path, "w") &gt;&gt;&gt; print file2 &lt;open file 'c:\scr.txt', mode 'w' at 0x02332188&gt; &gt;&gt;&gt; file1.write("111") &gt;&gt;&gt; file2.write("222") &gt;&gt;&gt; file1.close()   scr.txt now contains '111'.  &gt;&gt;&gt; file2.close()   scr.txt was overwritten and now contains '222' (on Windows, Python 2.4).  The solution should work inside the same process (like in the example above) as well as when another process has opened the file. It is preferred, if a crashing program will not keep the lock open. Is there a Google Drive client available? Community♦ user edit: How does it know what to edit? Overlapping matches in Regex I can't seem to find an answer to this problem, and I'm wondering if one exists. Simplified example:  Consider a string "nnnn", where I want to find all matches of "nn" - but also those that overlap with each other. So the regex would provide the following 3 matches:   nnnn nnnn nnnn   I realize this is not exactly what regexes are meant for, but walking the string and parsing this manually seems like an awful lot of code, considering that in reality the matches would have to be done using a pattern, not a literal string. New breaker and panel: What's the brown goo where they connect? How to resolve merge conflicts in Git repository? I want to resolve merge conflicts in my Git repository. How to do that ? JQ (GET ID based on NAME) I get a long list of such arrays  {     "id": "byu6g6c4cjys5mdkg5znh8ju8c",     "create_at": 1511875272294,     "update_at": 1511875272294,     "delete_at": 0,     "display_name": "BMA",     "name": "BMA",     "description": "",     "email": "aleksandar.ivanov@random.com",     "type": "O",     "company_name": "",     "allowed_domains": "",     "invite_id": "gdgz1tbxuinntx1fbr1ax7kehy",     "allow_open_invite": false,     "scheme_id": null   }   I want to get by JQ only the ID where the name is BMA. At the moment I parse " jq -r '.[]["name"]" and I can filter the output from curl by name and I will get "BMA" and also 100 other names, but I need to filter only the ID where name is =BMA. Any ideas? Say I have the titanic kaggle competition, but I'm not interested in the competition for predicting survival for each individual. Instead I want the most accurate estimate of total survivors on the titanic. Would this be achieved by using a probabilistic model, then adding the probabilities for each individual? For example, if I have 3 people and 1 survived, but my model produced 0.4, 0.4, and 0.4 probabilities for each person to survive, I calculate 0 survived. But if I add 0.4 for each person, I get 1.2, which is closer to the actual. Does this make sense? CSS background opacity with rgba not working in IE 8