How to perform natural (lexicographic) sorting in R?
How to sort a character vector where elements contain letters and numbers in R?
Consider a hypothetical situation: In which a time traveler travels in a spaceplane at close to speed of light circling the earth and I get a live telecast of inside of that plane to my television. How time dilation will effect him and what will I observe sitting next to the tv seeing him live. Considering time runs slower at speed of light, will he be looking like a slow motion video? (Or let he also watching live streaming of us at earth, what it will look to him) P.S. I'm not sure if it even makes some sense but if it does kindly explain in logical details. Sorry for the the bad english, I'm not a native speaker. When "etc." is at the end of a phrase, do you place a period after it? Example:     It's all about apples, oranges, bananas, etc.   VS.     It's all about apples, oranges, bananas, etc..   Update  What happens if the abbreviation is inside parentheses, do you place a dot after and before the closing parenthesis?     It's all about fruit (apples, bananas, etc.). A generalized version of the second Borel-Cantelli lemma says     Theorem 5.3.2. Second Borel-Cantelli lemma, II. Let $\mathcal F_n, n \ge 0$ be a filtration   with $F_0 = \{\emptyset, \Omega\}$ and $A_n , n \ge 1$ a sequence of events with $A_n ∈ \mathcal F_n$ . Then   $$ \{A_n \,i.o.\} = \left\{\sum_{n \ge 1} P (A_n |\mathcal F_{n−1}) =\infty \right\}. $$   An exercise of this lemma is     Exercise 5.3.6. Show    $\sum_{n \ge 2} \mathbb P (A_n | \cap_{m=1}^{n−1} A_m^c ) = \infty$ implies $P (∩_{m \ge 1} A_m^c ) = 0$.   I think we can actually prove that $\cap_{m \ge 1} A_m^c = \emptyset$. My proof is like this: Let $B_n = \cup_{m = 1}^n A_n$. Let $\mathcal F_n = \sigma(A_1,\dots,A_n)$, which forms a filtration. It is easy to verify that $$ \mathbb P (A_n | B_{n-1}^c ) = \mathbb P (A_n | \mathcal F_{n-1})(\omega) $$ when $\omega \in B_{n-1}^c$.  Assume there exist $\omega \in \cap_{m \ge 1} A_m^c$. It follows from the previous lemma that $$ \omega \in \left\{\sum_{n \ge 1} P (A_n |\mathcal F_{n−1}) =\infty \right\} = \{A_n \,i.o.\}. $$ In other words, $\omega \in \cap_{m \ge 1} \cup_{n \ge m} A_n$, which contradicts $\omega \in \cap_{m \ge 1} A_m^c$.  Is this the right proof? What is the appropriate statistical test when calculating the busiest day of the week? We have 10 years of data and Monday is the busiest (most visits to the hospital) on average. If we wanted to assess whether that is true and report a p-value, what is the appropriate statistic?   We believe the answer is chi-square as we found a peer-reviewed medical article from the Annals of Emergency Medicine (highest circulating journal for that specialty) that used chi-square for this very calculation.   If chi-square is appropriate, what values do we use for observed and expected values for chi-square? One approach would be to list all the values for Monday as observed values, or all the means for Mondays averaged across a month, or all the means for Mondays averaged across a year.  If there were no busiest or least busy days, we would assume that the visits would be the same every day of the week. That means our "expected values" for Chi-Square would be the mean of the visits for any given week. Disabling IPv6 on Mint and Debian How does one disable IPv6 completely (for all interfaces, resp. for the whole machine?  Keep in mind, I don't want any kind of GUI solution.    OS in question:   Linux Mint 18.x Cinnamon 64-bit GNU/Linux Debian 9.x Cinnamon 64-bit Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular. Can I enter Croatia with single entry visa Schengen? How exactly does time slow down near a black hole? How exactly does time slow down near a black hole? I have heard this as a possible way of time traveling, and I do understand that it is due in some way to the massive gravity around a black hole, but how exactly does that massive gravity slow down time? LM317 getting hot Should an LM317 (specifically a ) rated for 500ma output current really be getting hot to touch when only pulling 170ma at 5V?  Package is SOT-223, input is 9V.  Is this normal? Chromatic polynomial properties I have some properties which I do not understand how to form a proof for. Most of them are by induction, which is not my strong point Any help would be fantastic.   Looking at the chromatic polynomial $$P_G(k)=P_{G-e}(k) - P_{G/e}(k)$$  Properties   1.If G has n  vertices then $ P_g(k)$ has degree n and the coefficient of $k^n $ is 1   The signs of $P_g(k) $ alternate If G has q components the smalles non-zero term of $P_g(k)$ is the term in $k^q$ A person who speaks kindly. Sometimes she might be hard, but fair.   What is an adjective to describe such person? I have this picture:  (I have the original in Pixen and could export it to several different formats. I went with PNG though since it's lossless.)  When I open my picture in Preview (OS X) and zoom in, it looks fine. The characters have extremely sharp boarders between them and the background. However, when I put it into my LaTeX document, compile it to a PDF (using TeXShop) and then zoom in, it suddenly have gotten blurry (see screenshot: ).  Minimal working example:  \documentclass[12pt]{article} \usepackage{graphicx} \begin{document} \includegraphics[scale=1]{fig1.png} \end{document}   In the end, I would like to be able to scale the picture freely without there being any blurring at all. what is the difference between - I make it to go and I make it go? What is the difference between sentences like these:     I make it to go.   I make it go.   or     You make me to cry.   You make me cry. Find all roots of $\,x^2\!\equiv x\pmod{\!900}$, i.e all idempotents in $\Bbb Z_{900}$ I need the idempotent elements of $Z_{900}$ $2^2\cdot 3^2\cdot 5^2=900$ Of course there's $$0 \pmod 4 \\ 0 \pmod 9 \\ 0 \pmod {25} \\ $$ and $$ 1 \pmod 4 \\ 1 \pmod 9 \\ 1 \pmod {25} \\ $$ I found the answers by making a C++ program to test all numbers, but I don't know how to quick solve on paper. This is the output of the program $(0, 0, 0) \rightarrow 0 \\ (1, 1, 1) \rightarrow 1 \\ (0, 0, 1) \rightarrow 576 \\ (0, 1, 0) \rightarrow 100 \\ (1, 0, 0) \rightarrow 225 \\ (1, 1, 0) \rightarrow 325 \\ (0, 1, 1) \rightarrow 676 \\ (1, 0, 1) \rightarrow 801 \\$ I'm runing 15.04 on a dell xps 13 bluetooth recognises devices when i  try to add them but won't let me connect to them Here is the results from my terminal.  ~ $ uname -a; lspci -nnk | grep -iA2 net; lsusb; dmesg | grep -i bluetooth; dmesg | grep -i firmware; lsmod | grep bluetooth  Linux aaron-XPS-13 3.19.0-15-generic #15-Ubuntu SMP Thu Apr 16 23:32:37 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux 02:00.0 Network controller [0280]: Broadcom Corporation BCM4352 802.11ac Wireless Network Adapter [14e4:43b1] (rev 03)     Subsystem: Dell Device [1028:0019]     Kernel driver in use: wl Bus 003 Device 002: ID 8087:8001 Intel Corp.  Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 003: ID 0bda:5682 Realtek Semiconductor Corp.  Bus 001 Device 002: ID 0a5c:216f Broadcom Corp.  Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub [    8.164048] Bluetooth: Core ver 2.20 [    8.164065] Bluetooth: HCI device and connection manager initialized [    8.164069] Bluetooth: HCI socket layer initialized [    8.164073] Bluetooth: L2CAP socket layer initialized [    8.164079] Bluetooth: SCO socket layer initialized [    8.353160] bluetooth hci0: Direct firmware load for brcm/BCM20702A0-0a5c-216f.hcd failed with error -2 [    8.353166] Bluetooth: hci0: BCM: patch brcm/BCM20702A0-0a5c-216f.hcd not found [   20.289452] Bluetooth: BNEP (Ethernet Emulation) ver 1.3 [   20.289455] Bluetooth: BNEP filters: protocol multicast [   20.289459] Bluetooth: BNEP socket layer initialized [   20.310897] Bluetooth: RFCOMM TTY layer initialized [   20.310907] Bluetooth: RFCOMM socket layer initialized [   20.310912] Bluetooth: RFCOMM ver 1.11 [  886.399085] Bluetooth: hci0 urb ffff8800d8c15e40 failed to resubmit (2) [  895.471190] Bluetooth: hci0: BCM: patching hci_ver=06 hci_rev=1000 lmp_ver=06 lmp_subver=220e [  896.113983] Bluetooth: hci0: BCM: firmware hci_ver=06 hci_rev=1624 lmp_ver=06 lmp_subver=220e [    8.353160] bluetooth hci0: Direct firmware load for brcm/BCM20702A0-0a5c-216f.hcd failed with error -2 [  896.113983] Bluetooth: hci0: BCM: firmware hci_ver=06 hci_rev=1624 lmp_ver=06 lmp_subver=220e bluetooth             491520  22 bnep,btusb,rfcomm ~ $ Word or phrase for mere coincidence that brings happiness Reload the page on hitting back button Say you have a stick which breaks randomly into three pieces (we can choose the points randomly). What is the probability that the area is greater than or equal to $0.4$?   I can see it has something to do with Heron's formula but I just can't put t together. Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$ Suppose $(M,d)$ a metric space. I want to show that      If every continuous real-valued function on $M$ attains a maximum, then $(M, d)$ is compact.   I was trying to do this by assuming $M$ non-compact and showing explicitly a function which does not attain a maximum. If $M$ is not bounded it's enough to take the distance from a fixed point as we can always find a sequence which "exits" every compact and pushes the distance at infinity. But what if $M$ is bounded? I'm new to both JavaScript and . In YUI library examples, you can find many uses of this construct:  (function() {     var Dom = YAHOO.util.Dom,     Event = YAHOO.util.Event,     layout = null,         ... })();   I think the last couple of parentheses are to execute the function just after the declaration.  ... But what about the previous set of parentheses surrounding the function declaration?  I think it is a matter of scope; that's to hide inside variables to outside functions and possibly global objects. Is it? More generally, what are the mechanics of those parentheses?