Why does deflating baloon spurting through the air make circular motion?
Why does a balloon spiral in the air instead of moving in a straight line?
Future humans build using dirt, go to war over small amounts of it I am looking for a short story that I read in the 1970s (It may have been published in the 60s) about humans using the Earth's dirt to make stuff; as a result the Earth has shrunk and is smaller than the moon; also how nations go to war over a country's amount of dirt; Microcosmic God was in the same book.  Bought book through a science fiction book club; a collection of short stories. Internet through wireless hotspot, intranet through wired network - can I use both at the same time? Here are some examples.  "Until the Son of God appear" What I was taught: Subjunctive of indefinite future.  "It is required that the applicant be 18 years old and possess a valid driver's license." What I was taught: mandative subjunctive.  "Where be ye going," said the false knight on the road?" What I was taught: subjunctive of direct discourse.  "If I were you, which we both are thankful I am not, I wouldn't do that. What I was taught: The subjunctive mood is used for supposition contrary to fact.  "I dreamed I were a fireman in my Maidenform bra." What I was taught: The subjunctive mood can be used with words like dream.  "God bless you." I don't remember, so obviously I wasn't taught.  I can live with Pluto's not being a planet, but I must say it's irksome to find that so much of what I was told about English turns out to be nonsense. How can I list the contents of a .zip folder in c#? How can I list the contents of a zipped folder in C#? For example how to know how many items are contained within a zipped folder, and what is their name? Clarification for non-answers One of my flags for "non-answer" was declined and I was wondering if I misunderstood what "non-answer" means. I saw someone post an answer that was just a block of code, with nothing in it that was even the slightest related to the question, it was just a random block of code with no explanation. Should I have not used the "not an answer" tag even though the description explicitly says that it should be used when answers "do not attempt to answer the question"? Animation Blending Basics Say I have a framework with characters that can run and walk and of course, stand still.  Am I right in thinking that animation blending is the process of smoothly transitioning between these by generating dynamic animations at runtime?  If so, what is the basic theory of how this works, and how would I implement it? Evaluate the following limit of finite sum Evaluate the limit $$\lim_{n\to \infty}\frac{1}{n}\sum_{k=0}^{[n/2]}\cos \left(\frac{k\pi}{n}\right)$$  I tried through considering two cases : (i) When $n$ is even (ii) when $n$ is odd.  When $n$ is even then the limiting value is $\frac{1}{\pi}$. But when $n$ is odd then ??  Case 1 : $n$ is even..  Then , take $n=2p$ where $p$ is positive integer. Then $$\lim_{n\to \infty}\frac{1}{n}\sum_{k=0}^{[n/2]}\cos \left(\frac{k\pi}{n}\right)$$  $$=\lim_{p\to \infty}\frac{1}{2p}\sum_{k=0}^{p}\cos\left(\frac{k\pi}{2p}\right)$$  $$=\frac{1}{2}\int_0^1\cos(\pi x/2)\,dx$$  $$=\frac{1}{\pi}.$$  Case 2 : When $n$ is odd.  Take, $n=2p+1$ , where $p$ is a positive integer. Then ,   $$\lim_{n\to \infty}\frac{1}{n}\sum_{k=0}^{[n/2]}\cos \left(\frac{k\pi}{n}\right)$$  $$=\lim_{p\to \infty}\frac{1}{2p+1}\sum_{k=0}^p\cos\left(\frac{k\pi}{2p+1}\right)$$  From here how I proceed ? Connectivity, Path Connectivity and Differentiability I have two questions which pertain to differentiability, connectivity and path connectivity. Ocasionally, I will encounter an author who defines connectivity in the following way:   An open subset $U$ of $\mathbb{R}^n$ is said to be connected if and only if given two points $a$ and $b$ of $U$ there exists a differentiable mapping $\phi: \mathbb{R} \rightarrow U$ such that $\phi(0) = a$ and $\phi(1) = b$.   This particular example is from Edward's Advanced Calculus of Several Variables p 84. Now, this is obviously not the standard definition we learn from topology which has nothing to do with differentiability but rather whether there exists two nonempty open subsets that comprise a separation. It also seems to me that what the author is really defining what it means for a space to be "smoothly path connected", which of course implies connectivity and, it seems to me, considerably more.  My first question is: Is "smoothly path connected", as defined above actually equivalent to "connected", in the topological sense, in $\mathbb{R}^n$?  Next, in Vector Calculus by Baxandall and Liebeck on p 150 the authors state the existence of a continuous path $\alpha$ from the closed interval $[0,1]$ to an open subset $D$ of $\mathbb{R}^n$ where $\alpha (0) = a \in D$ and $\alpha(1) = b \in D$ guarantees the existence of a differentiable path with the same properties. This claim is stated without proof.   My second question is: Can someone provide a reference to a proof of the above claim or explain why it is so? In the biblatex doc, it says ( Version 1.7, p.11):     thesis      A thesis written for an educational institution to satisfy the   requirements for a degree. Use the type field to specify the type of   thesis.      Required fields: author, title, type, institution, year/date      Optional fields: subtitle, titleaddon, language, note, location,   month, isbn, chapter, pages, pagetotal, addendum, pubstate, doi,   eprint, eprintclass, eprinttype, url, urldate   I would like to know if there is any "canonical" way to add the name of the supervisor(s) in a field of the .bib file (no .bbl manipulation please, I want my bibliography to be usable "as it" in several documents).  The expect result could be something like  :     Meand Myself. “A brilliant result, explained”. PhD thesis**, under the   joint supervision of Pr. Toto and Pr. Tata**. Université Paris 24,   Nov. 2013.   The "under the (joint) supervision" could be a string that would be declined in four ways:   under the supervision of  under the joint supervision of and the abridged forms New line in Sql Query Matrix Group induction proof and order of elements question $H$ is the set of the matrices $A$ of the form $$A= \begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}$$  where $0\leq \theta &lt; 2\pi$  is a group with respect to matrix multiplication.  Question part (1) Prove by induction that  for any $\theta$ and any positive integer $n$,  $$\begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}^{n} = \begin{pmatrix} \cos(n\theta) &amp; \sin (n\theta) \\ -\sin (n\theta) &amp; \cos (n\theta)\end{pmatrix}$$   When $n =1$ we have $$\begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}^{1} = \begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}$$   and clearly this holds for the base case.   Now I'm going to assume true when $n=k$ and try and prove for $k+1$. So we have   $$\begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}^{k}\begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}^{1} = \begin{pmatrix} \cos(k\theta + \theta) &amp; \sin (k\theta + \theta) \\ -\sin (k\theta + \theta) &amp; \cos (k\theta + \theta)\end{pmatrix}$$   Now I'm sure I can cheese this, but is there some clever way to pull this apart? I want to just be able to say something like the determinant of the left side is $1^{k+1}$ and its the same on the right ...  Question part (2) Find an element of $H$ of order 5.  Here I'm totally lost, I seem to think that every element is of order 1 cause the determinant is 1.  Question part (3) Find an element of $H$ of infinite order.  Again I'm lost; I want to somehow make the determinant 0 for this but it can never be 0 for any $\theta$. How to hide title bar in Firefox 57 Quantum? I used to use an extension to hide/show the title bar in Firefox, but since Firefox 57 was released most of the extensions were disabled.  In Chrome I just uncheck the option "Use system title bar and borders" and it's done.  Are there any ways to do that? Filtering questions by multiple tags I know you can select a tag and then click on unanswered to view the unanswered questions for that tag.  But is there a way to view questions only for a certain set of tags > 1 tag?  Mainly I'd like the union of tag1 with tag2 with tag3 with tag4. But also the intersection of tags would be nice as well. tabular input by columns (i.e. transpose a table) I would like to be able to transpose a tabular(x) table like in the following example. It is not necessary to be completely automated, but I don't want to change the data order, which is a painful and stupid. By "not completely automated" I mean that e.g. the headers can be done seperately etc.  Let's see the MWE:  \documentclass{article}  \usepackage{booktabs} \def\Midrule{\midrule[\heavyrulewidth]}  \begin{document}  \centering  \begin{tabular}{*6c}\toprule \bfseries Name &amp; Alice &amp; Bob &amp; Chuck &amp; Dave &amp; Eve\\\Midrule \bfseries Sex &amp; Female &amp; Male &amp; Male &amp; Male &amp; Female\\\midrule \bfseries Age &amp; 18 &amp; 19 &amp; 20 &amp; 21 &amp; 22\\\bottomrule \end{tabular}  \bigskip  Which I want to look like  \bigskip  \begin{tabular}{*3c}\toprule \bfseries Name &amp; \bfseries Sex &amp; \bfseries Age\\\Midrule Alice &amp; Female &amp; 18\\\midrule Bob &amp; Male &amp; 19\\\midrule Chuck &amp; Male &amp; 20\\\midrule Dave &amp; Male &amp; 21\\\midrule Eve &amp; Female &amp; 22\\\bottomrule \end{tabular}   \end{document}     Note: I know that , but I would like to get it without expl3 (mostly because people would might use my code quite often have an old LaTeX installed and I cannot be convincing them to change this). How to understand the memory usage and load average in linux server I am using a linux server which has 128GB of memory and 24 cores. I use top to see how much it is used. Its output is pasted at the end of the post. Here are two questions:  (1) I see that each of the running processes occupies a very small percentage of memory (%MEM no more than 0.2%, and most just 0.0%), but how the total memory is almost used as in the fourth line of output ("Mem:  130766620k total, 130161072k used,   605548k free,   919300k buffers")? The sum of used percentage of memory over all processes seems unlikely to achieve almost 100%, doesn't it?  (2) how to understand the load average on the first line ("load average: 14.04, 14.02, 14.00")?   Thanks and regards!  Edit:  Thanks!  I also really like to hear some rough numbers based on used percentage of memory to determine if a server is heavily loaded, since I once became the one who cramed the server without understanding the current load.  Is swap regarded as almost the same as memory? For example, when memory and swap are almost of same size, if the memory is almost running out but the swap is still largely free, may I just view it as if the used percentage of memory + swap is still not high and run other new processes?  How would you consider together CPU or memory (or memory + swap) usage? Do you become worried if either of them reaches too high or both?  Output of top：  $ top    top - 12:45:33 up 19 days, 23:11, 18 users,  load average: 14.04, 14.02, 14.00 Tasks: 484 total,  12 running, 472 sleeping,   0 stopped,   0 zombie Cpu(s): 36.7%us, 19.7%sy,  0.0%ni, 43.6%id,  0.0%wa,  0.0%hi,  0.0%si,  0.0%st Mem:  130766620k total, 130161072k used,   605548k free,   919300k buffers Swap: 63111312k total,   500556k used, 62610756k free, 124437752k cached    PID USER      PR  NI  VIRT  RES  SHR S %CPU %MEM    TIME+  COMMAND  6529 sanchez   18  -2 1075m 219m  13m S  100  0.2  13760:23 MATLAB 13210 timothy   18  -2 48336  37m 1216 R  100  0.0   3:56.75 absurdity 13888 timothy   18  -2 48336  37m 1204 R  100  0.0   2:04.89 absurdity 14542 timothy   18  -2 48336  37m 1196 R  100  0.0   1:08.34 absurdity 14544 timothy   18  -2  2888 2076  400 R  100  0.0   1:06.14 gatherData  6183 sanchez   18  -2 1133m 195m  13m S  100  0.2  13676:04 MATLAB  6795 sanchez   18  -2 1079m 210m  13m S  100  0.2  13734:26 MATLAB 10178 timothy   18  -2 48336  37m 1204 R  100  0.0  11:33.93 absurdity  12438 timothy   18  -2 48336  37m 1216 R  100  0.0   5:38.17 absurdity 13661 timothy   18  -2 48336  37m 1216 R  100  0.0   2:44.13 absurdity 14098 timothy   18  -2 48336  37m 1204 R  100  0.0   1:58.31 absurdity 14335 timothy   18  -2 48336  37m 1196 R  100  0.0   1:08.93 absurdity 14765 timothy   18  -2 48336  37m 1196 R   99  0.0   0:32.57 absurdity 13445 timothy   18  -2 48336  37m 1216 R   99  0.0   3:01.37 absurdity 28990 root      20   0     0    0    0 S    2  0.0  65:50.21 pdflush 12141 tim       18  -2 19380 1660 1024 R    1  0.0   0:04.04 top  1240 root      15  -5     0    0    0 S    0  0.0  16:07.11 kjournald  9019 root      20   0  296m 4460 2616 S    0  0.0  82:19.51 kdm_greet     1 root      20   0  4028  728  592 S    0  0.0   0:03.11 init     2 root      15  -5     0    0    0 S    0  0.0   0:00.00 kthreadd     3 root      RT  -5     0    0    0 S    0  0.0   0:01.01 migration/0     4 root      15  -5     0    0    0 S    0  0.0   0:08.13 ksoftirqd/0     5 root      RT  -5     0    0    0 S    0  0.0   0:00.00 watchdog/0     6 root      RT  -5     0    0    0 S    0  0.0  17:27.31 migration/1     7 root      15  -5     0    0    0 S    0  0.0   0:01.21 ksoftirqd/1     8 root      RT  -5     0    0    0 S    0  0.0   0:00.00 watchdog/1     9 root      RT  -5     0    0    0 S    0  0.0  10:02.56 migration/2    10 root      15  -5     0    0    0 S    0  0.0   0:00.34 ksoftirqd/2    11 root      RT  -5     0    0    0 S    0  0.0   0:00.00 watchdog/2    12 root      RT  -5     0    0    0 S    0  0.0   4:29.53 migration/3    13 root      15  -5     0    0    0 S    0  0.0   0:00.34 ksoftirqd/3 Command substitution: splitting on newline but not space I know I can solve this problem several ways, but I'm wondering if there is a way to do it using only bash built-ins, and if not, what is the most efficient way to do it.  I have a file with contents like  AAA B C DDD FOO BAR   by which I only mean it has several lines and each line may or may not have spaces.  I want to run a command like  cmd AAA "B C DDD" "FOO BAR"   If I use cmd $(&lt; file) I get  cmd AAA B C DDD FOO BAR   and if I use cmd "$(&lt; file)" I get  cmd "AAA B C DDD FOO BAR"   How do I get each line treated a exactly one parameter? I am trying to perform centrality analysis with sDNA with ArcGIS Pro (ver. 2.7.1). However, I have failed to run the Preparation &amp; Integral Analysis in sDNA with the same reason. What is the problem and What should I do? In school, I have always seen sets. I was watching a video the other day about functors, and they started talking about a set being a collection, but not vice-versa. I also heard people talking about classes. What is their relation? Some background would be nice.   It has to do with something called Russell's paradox, but I don't know what that is.   I think that the difference between a family and a set is that the former is a function and the latter is a set. Is this right? What is a good data plan for Internet surfing in northern Italy? I've checked the webpages of some their providers, but franly, just like in the case of those in my own language, I literally cannot find my way around them. So if you wouldn't mind sharing a word of two or advice.  I'm looking for a good solution for mobile internet surfing in northern Italy, that can be connected to a laptop (you know, that usb stick with a SIM card inside kind of thing). 15 Gb or so at some decent speed. Can you perhaps give a recommendation or two of what to get?    Edit: Just to define what I'm looking for exactly. A data plan of 15 Gb with an internet key (usb stick into which a SMS card goes) that you plug into a laptop. Preferably non-contractual, so I can cancel when I leave. I am not interested in surfing on my mobile phone since due to size I still prefer the smaller Nokia-like models for calls (smaller to carry) - no internet on them. Evaluate $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$$  All i could do was to see that $$\frac{1}{3}=\frac{1}{2.1+1},\frac{1}{5}=\frac{1}{2.2+1},\frac{1}{7}=\frac{1}{2.3+1},\dots$$  SO, we should be able to write   $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots=1+\sum_{n=1}^{\infty}\frac{1}{2n+1}.\frac{1}{4^n}$$  This is what i could simplify the given question to...   But, this is doing me no good.. I could not go any further..  I would be thankful if some one can help me to clear this.  I would request users who are trying to help me to just give necessary hints but not post it as answer.  Thank You.