Proof that $\gcd$ divides $\operatorname{lcm}$

Show that the following conditions are equivalent:  i) There exist positive integers $a, b$ such that $\gcd(a,b)=d$ and $\operatorname{lcm}(a,b)=m$.  ii) $d\mid m$


Do the rules that apply to a lava block apply to the run off from the lava block?

I was wondering if the rules that apply to lava blocks (they can catch things on fire from blocks away and can travel through one block) apply to the lava that is not on/in the block of lava.


Why is the verb to be in the infinitive in 'Praise be to God.'?   Other sentences that look similar are:  'May you be always in our presence.'  'May you be forgiven.'  But May + sub + infinitive of be is used to make a wish and 'Praise be to God' is more of a informative statement rather than a wish.


How could you copy the contents of an HDC to a bitmap?


Why is plain-hash-then-encrypt not a secure MAC?

It seems that even in MAC-then-encrypt systems like SSL, something like HMAC is used rather than a plain hash. Why?   Suppose we use some stream cipher; then why can't we use $Encrypt(m | H(m))$ as the MAC-then-encrypted version of the message? Assuming no bad relations between $Encrypt$ and $H$, what are the possible weaknesses? It seems that in this case we are encrypting the hash with part of a secretly keyed stream cipher keystream, and the hash is secure; does this not fulfil an approximation of the ideal MAC?  This must be somehow bad, since no secure protocol seems to use it. Why?


I would like to understand the term white balance. My camera has settings for white balance with the following options:   Auto white balance Daylight Cloudy Shade Flash Incandescent lights White set1 / White set2 White balance K set   Can anyone throw some, well, light on this? Also, is there any relation of white balance with the exposure while taking snaps? This is, if the exposure is high, then do we need to set white balance to low, or something like that?


Is it true that $x_n$ is a Cauchy sequence in some Hilbert space if and only if:  for all $m \in \mathbb{N}$, for all $\epsilon > 0$, there exists $N=N(m) \in \mathbb{N}$ (so the $N$ can depend on $m$) such that $$\lVert x_{n+m}-x_n \rVert \leq \epsilon \quad\text{ if $n \geq N(m)$}.$$  Is that correct?


Unable to detect my Home wifi after installing Ubuntu 16.04

I recently installed LTS 16.04 as a dual boot with my windows 7. Post installation i am unable to connect to my home wifi. The broadcom driver is installed and working. The wifi connection works as expected on the Windows OS and on the ubuntu i am able to connect to the same home wifi if i tether it via my mobile phone. Also i am able to see my neighbours wifi in the list and a whole bunch of other networks except my home's network .Has anyone faced this issue.. any help would be great.  $ sudo lshw -C network *-network                       description: Network controller        product: BCM4313 802.11bgn Wireless Network Adapter        vendor: Broadcom Corporation        physical id: 0        bus info: pci@0000:03:00.0        version: 01        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress bus_master cap_list        configuration: driver=bcma-pci-bridge latency=0        resources: irq:17 memory:f3500000-f3503fff   *-network        description: Ethernet interface        product: AR8162 Fast Ethernet        vendor: Qualcomm Atheros        physical id: 0        bus info: pci@0000:04:00.0        logical name: enp4s0        version: 10        serial: f0:de:f1:f4:95:d7        capacity: 100Mbit/s        width: 64 bits        clock: 33MHz        capabilities: pm pciexpress msi msix bus_master cap_list ethernet physical tp 10bt 10bt-fd 100bt 100bt-fd autonegotiation        configuration: autonegotiation=on broadcast=yes driver=alx latency=0 link=no multicast=yes port=twisted pair        resources: irq:31 memory:f3400000-f343ffff ioport:2000(size=128)   *-network        description: Wireless interface        physical id: 3        logical name: wlp3s0b1        serial: 08:ed:b9:96:ef:1b        capabilities: ethernet physical wireless        configuration: broadcast=yes driver=brcmsmac driverversion=4.4.0-21-generic firmware=610.812 ip=192.168.43.121 link=yes multicast=yes wireless=IEEE 802.11bgn


Is it enough a 100Mbps LAN for a server rack?

My website is growing and growing. So now i'm considering moving to a 2-server virtual rack (in ThePlanet). Im thinking on using one server for the DBMS and the other for the Webserver (currently I have both things on one single machine).  Given that setup, would it be enough 100Mbps for the server-to-server link?? or should I consider having a 1 Gbps rack ??    More info: By now my site have a little more than 1 million pageviews a day and on the peak hours (from 14:00 to 18:00) about 85 thousand pageviews each hour. Also, on the peak hours the traffic associated to the web content (html, css, images, etc..) reaches between 50 and 60 Mbps, for a total of about 200GB a day.  What I really dont know is whether a 100Mbps ethernet link will perform as good as a socket file (MySQL) for the dbms-webserver comunication.


My brother started a character on destiny on my dads profile but now he has made his own profile an wants to play on his profile with that character even though he has made another character he still wants the other. Both profiles are on a home Xbox so is there any way he can play his character on his profile?


How do you debug PHP scripts?  I am aware of basic debugging such as using the Error Reporting. The breakpoint debugging in PHPEclipse is also quite useful.  What is the best (in terms of fast and easy) way to debug in phpStorm or any other IDE?


How to get input from user and apply calculation in Python?

I am just starting python.  I want to get the input from user and calculate it.  Example: I want to get the time flight of projectile motion by t =(v sin(theta))/g  import math print "this program will find time flight of projectile motion" g = 9.8 ##get the velocity and angle ##calculate it ##print time with some text


I'm trying to save the find output to a variable in this manner:   a=find /Users/Downloads/DTI_allsites/subprojects/*/UII_0077 -name "dti_preprocessed" -type d   But I keep getting the following message:   -bash:      /Users/Downloads/DTI_allsites/subprojects/UII_B/UII_0077:   is a directory   whenever I try to use the command, to echo the path using:       echo $a  I don't get anything saved in the variable.  How can I fix this?


Error: iptables: No chain/target/match by that name

I am trying to configure proxy server on RHEL Server 6.5 using Squid and iptables. Below is the command I executed and the error message it displayed:  vzlptest01 root [root] > iptables -A INPUT -i eth0 -m state --state ESTABLISHED,RELATED -j ACCEPT iptables: No chain/target/match by that name.   Some more details:  vzlptest01 root [root] > cat /proc/net/ip_tables_matches limit state length ttl tcpmss multiport multiport tos tos dscp icmp udplite udp tcp  vzlptest01 root [root] > cat /proc/net/ip_tables_targets DNAT SNAT LOG TOS TOS DSCP TCPMSS REJECT ERROR   How to deal with this issue?


Why Does the Median Minimizes the Sum of Absolute Deviations?

Apparently, the mean is the value that minimizes the sum of the squares of deviations, and this made sense to me because the sum of the squared differences can be represented as an equation:   (a - x)^2 + (b - x)^2 + (c - x)^2 + ...  This function has a minimum when we take the derivative and solve it when it's equal to zero:  0 = -2(a – x) + -2(b – x) + -2(c – x) + ...  Some more arithmetic will allow us to arrive at the conclusion:  x = (a + b + c + ...) / N  However, I'm having trouble finding a similar way to solve for the median, although I suspect my rusty calculus or arithmetic is behind it.  The sum of absolute deviations would produce the equation:  |a-x| + |b-x| + |c-x| + ...  I think the derivative function would be:  0 = -(a-x)/|a-x| + -(b-x)/|b-x| + -(c-x)/|c-x|  But I am not sure how to continue from here.


Error:  E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   Hi everyone I get the above error whenever I try to install something. I am still new on Linux so I don't really know whats going on. I was actually trying to install git.


Why are objects (such as planets) in motion and not static?

I am just curious, why are all the planets, rocks etc in motion? Would they fall into objects with larger gravity if they were not in motion? What is stopping the earth from falling into the sun or moon from falling into earth? Is motion the reason why air crafts can remain in air? what are the mechanics behind this? Or perhaps I am mixing up too many things?


How to keep ArcMap Toolbar in a nice order?

I`m having an issue with my ArcMap. Every time I open it the tool bar is really messy, so I always have to start re-organising the tool bar first. Does anyone have an idea of how can I keep it in order without rearranging it every single time I use it?


I am using Ubuntu GNOME 16.04 and my terminal looks like this.    Is there a way to get that purple background terminal like this?


NOTE : By perpendicular component of $\vec{F}$, I mean a vector which is a component of $\vec{F}$, but perpendicular to it.  In the image above, the red vectors are a possible set of rectangular components of $\vec{F}$, and blue vector is the sine component of cos component of $\vec{F}$, ie,  perpendicular component of $\vec{F}$. Now, logically, the perpendicular component of $\vec{F}$ should be zero, since its projection is zero. But if we consider the image above, the Perpendicular component, $|\vec{F}|\cos\theta\sin\theta$, is not zero. What is the cause of this discrepancy, and how to take components properly?


I found out black heats up the most and white the least, as I expected. The question I had is that despite black reflecting all the wavelengths of the visible spectrum, and hence giving the black material its colour, why is it not the coolest?  I mean, even blue. It's reflecting the higher frequencies, which are at a higher energy acc. to E=h*f (f is frequency), why does it get heated more than red?


Do I need to apply for a visa to enter South Korea as a tourist on an Australian passport?

Do I need to apply for a visa to enter South Korea as a tourist for a few days when travelling on an Australian passport? Or will I be able to get one on arrival?


How can I be more visible to have an answer at my question?

By curiosity, is there a way to get attention to obtain an answer by someone, if nobody answered or even comment ?   It could be by placing this question on the top of the active questions, by an action of the user.  I think some questions deserve to be answered and can help other people.


Let the random variables $\xi_1, \xi_2, \ldots, \xi_n$ be independent, have an exponential distribution and expectation of each is 2. Are $\sum_{i=1}^{n} \xi_i / i$ and $\max\xi_n$ equally distributed?


Evaluate $\int^1_0 \log^2(1-x) \log^2(x) \, dx$

I have no idea where to even start. WolframAlpha cant compute it either.  $$\int^1_0 \log^2(1-x) \log^2(x) \, dx$$  I think it can be done with series, but I am not sure, can someone help a little so I can get a start??  Thanks!


$$\int_0^\infty\frac1{(x^2+1)(\ln^2(x)+\pi^2)}$$  Prove the convergence of this integration.


Just wonder whether subprograms can be totally muted in ways other than just deleting it. I ask bacause:  For example, I tried to setup a loop in another nodetree, Then disable auto execution for that nodetree. However, it can still be invoked in other nodetrees, because subprograms seem to be kinda "global" data.  In some cases I want to mute the subprogram to improve overall performance by disabling the execution. Is that helpful? Can I do that? Or other better solutions? Thanks!


Whenever I try to add an image to my JPanel I get an NPE. (The error is when I initialize a new ImageIcon!) What I've tried:  Class loader Main class's get resource '/' before path and without '/' before path  Code in main class: public class Main {     public static void main(String[] args) {         GameWindow game = new GameWindow();          game.setSize(1280, 720);         game.center();          game.addImage(new ImageIcon(Main.class.getResource("player.png")).getImage(), 0, 0);          game.setVisible(true);     } }  Inside the engine GameWindow class: public class GameWindow {     private final JFrame frame = new JFrame("Game Window");     private final JPanel board = new JPanel();      public GameWindow() {         frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);     }      public void addImage(Image image, int x, int y) {         board.getGraphics().drawImage(image, x, y, null);     }      public void center() {         frame.setLocationRelativeTo(null);     }      public void setVisible(boolean visible) {         if (visible) {             if (!board.isVisible()) {                 board.setVisible(true);                 frame.add(board);             }         }         frame.setVisible(visible);     }      public void setSize(int x, int y) {         frame.setSize(x, y);     } }  Here's what the file path looks like before building it into a JAR and running it.  Any help would be appreciated, I've spent so long (1 day + 1/2) trying to find an answer.


How can I remove multiple segments from a video using FFmpeg?

I am trying to delete a few sections of a video using FFmpeg.  For example, imagine if you recorded a show on television and wanted to cut out the commercials. This is simple with a GUI video-editor; you just mark the beginning and ending of each clip to be removed, and select delete. I am trying to do the same thing from the command-line with FFmpeg.  I know how to cut a single segment to a new video like so:  ffmpeg -i input.avi -ss 00:00:20 -t 00:00:05 -map 0 -codec copy output.avi   This cuts a five-second clip and saves it as a new video file, but how can I do the opposite and save the whole video without the specified clip, and how I can I specify multiple clips to be removed?  For example, if my video could be represented by ABCDEFG, I would like to create a new one that would consist of ACDFG.


Let $R=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and $I=(f_1,\ldots,f_q)$  a monomial ideal of $R$. If $f_i$ is homogeneous of degree $d\geq 1$ for all $i$, then prove that  $$ R[It]/\mathfrak m R[It]\simeq K[f_1t,\ldots, f_q t]\simeq K[f_1,\ldots,f_q] \text{ (as $K$-algebras).} $$ $R[It]$ denotes the Rees algebra of $I$ and $\mathfrak m=(x_1,\ldots,x_n)$.


We have to show that the degree sequence (n,n,n-1,n-1,...,3,3,2,2,1,1) is graphic for all n bigger or equal to 1. I used the technique where you delete the first degree (n) in the sequence and then for the next n degrees you substract one, but I get stuck at actually subtracting 1 from n degrees. Not sure if I’m on the right path.


Agile extension tester certification mock tests

I am giving ISTQB Agile extension tester certification exam in next 2 days. I could see single mock test paper roaming around internet. I would like to solve few more mock papers. Can i get these test papers for free anywhere please?  Note:  This exam is different from ISEB foundation level exam.


Assume $A$ is diagonalizable. Show that $A$ is similar to $A^T$  Any help would be very appreciated. I know for a matrix to be diagonalizable it has to be a square matrix so the # of rows and columns stay the same for $A^T$.


"We maybe have a problem" or "Maybe we have a problem"? Do we put "maybe" before a verb?

Maybe is an adverb.  Normally, people put "Maybe" at the beginning of a sentence.  Ex: Maybe we have a problem  My question is:  Do we put "maybe" before a verb? Ex: "We maybe have a problem" it sounds very strange.  It is very good if your answer includes some referencing source.


Prove that $\mathbb{R}\not\cong X\times X$ for any $X$

Prove that $\not\exists$ a topological space $X$ such that $\mathbb{R}$ is homeomorphic to $X\times X$.  My approach was to prove by contradiction: say $f:\mathbb{R}\rightarrow X\times X$ be such a homeomorphism. Then we look at $g_i:=\pi_i\circ f$ for $i=1,2$. So, $f=g_1\times g_2$. We know both $g_1$ and $g_2$ are open surjective maps. Clearly $g_i$ can't be one-one but I can't advance from here. If we can show that $\exists r_1,r_2\in \mathbb{R}$ such that $g_i(r_1)=g_i(r_2)$, then we are done. Any help? Any algebraic topology answer is most welcome as well.


Find correlation between binary variable and discrete variable

My background is not in stats but I did do some in school. You're help is really appreciated.  I'm wondering what is the best way to find some correlation between a binary variable and a discrete variable with a range between 1 and 5 (inclusive).  For example, let's say the binary variable is whether an employee was working at a lemonade stand at a specific time.  The discrete variable ranges from 1 to 5 and equates to how a customer rated the lemonade at a specific time.  Data example:  Time  | Rating | Bill Worked? | Susy Worked?  10:00 |   5    |       0      |       1  10:35 | 3 | 1 | 0  etc.  I'd like to see if certain employees impact the rating of the lemonade by a significant amount.  Not even sure if correlation is the best way to do this...  Thanks very much in advance!  Edit: The distribution of the "customer rating" appears to be lognormal...  1: 300  2: 70 3: 330 4: 1100 5: 3000  I ran a linear regression but I'm worried that the results will be insignificant.


Number of irreducible monic polynomials of degree $3$ over $\Bbb F_p$, $p$ prime

Good morning :)  So I had an exercise, which asks "how many monic irreducible polynomials are there of degree 3 over the finite polynomial ring $\Bbb F_p[X]$, where $p$ is some prime?"  I was wondering if you can do this via counting?  I know that there are $ p(p-1)/2$ monic irreducible polynomials of degree 2 over $\Bbb F_p[X]$.  And then I counted how many reducible polynomials of degree 3 there are, which is:  A reducible polynomial of degree 3 has to have at least one linear factor.  Then we have 4 options:  1) $(X-a)(X^2 + bX + c)$, where the quadratic term is irreducible. => There are $p^2(p-1)/2$ polynomials of this form.  2) $(X-a)^3$ => p polynomial of this form.  3) $(X-a)^2*(X-b)$, where $a$, $b$ distinct => $p(p-1)/2$. polynomials of this form.  4) $(X-a)(X-b)(X-c)$, where $a, b, c$ pairwise distinct => $p(p-1)(p-2)/6$ polynomials of this form.  And in total I have $p^3$ possible monic polynomials of degree 3 with coefficients in $\Bbb F_p$.  So then the number of irreducible, monic polynomials of degree $3$ over $\Bbb F_p$ is  $p^3 - (p^2(p-1)/2 + p + p(p-1)/2 + p(p-1)(p-2)/6) = p(p-1)(p+3)/3$ when I count it.  However I know the correct solution is supposed to be $(p^3 - p)/3$. Now I do not see where I made the mistake, if anybody here can spot my mistake I would be very thankful.  Thank you in advance. :)


I've got two Ubuntu boxes running who have both developed the same problem.  They keep throwing up error messages about how I'm out of space.   Error: BrokenCount > 0    Tried to run sudo apt-get -f install:  dpkg: error processing archive /var/cache/apt/archives/linux-image-4.4.0-83-generic_4.4.0-83.106_amd64.deb (--unpack):  cannot copy extracted data for './boot/System.map-4.4.0-83-generic' to '/boot/System.map-4.4.0-83-generic.dpkg-new': failed to write (No space left on device) No apport report written because the error message indicates a disk full error                                                                               dpkg-deb: error: subprocess paste was killed by signal (Broken pipe) Examining /etc/kernel/postrm.d . run-parts: executing /etc/kernel/postrm.d/initramfs-tools 4.4.0-83-generic /boot/vmlinuz-4.4.0-83-generic run-parts: executing /etc/kernel/postrm.d/zz-update-grub 4.4.0-83-generic /boot/vmlinuz-4.4.0-83-generic Preparing to unpack .../linux-image-4.4.0-93-generic_4.4.0-93.116_amd64.deb ... Done. Unpacking linux-image-4.4.0-93-generic (4.4.0-93.116) ... dpkg: error processing archive /var/cache/apt/archives/linux-image-4.4.0-93-generic_4.4.0-93.116_amd64.deb (--unpack):  cannot copy extracted data for './boot/vmlinuz-4.4.0-93-generic' to '/boot/vmlinuz-4.4.0-93-generic.dpkg-new': failed to write (No space left on device) No apport report written because the error message indicates a disk full error                                                                               dpkg-deb: error: subprocess paste was killed by signal (Broken pipe) Examining /etc/kernel/postrm.d . run-parts: executing /etc/kernel/postrm.d/initramfs-tools 4.4.0-93-generic /boot/vmlinuz-4.4.0-93-generic run-parts: executing /etc/kernel/postrm.d/zz-update-grub 4.4.0-93-generic /boot/vmlinuz-4.4.0-93-generic Preparing to unpack .../linux-image-4.4.0-96-generic_4.4.0-96.119_amd64.deb ... Done. Unpacking linux-image-4.4.0-96-generic (4.4.0-96.119) ... dpkg: error processing archive /var/cache/apt/archives/linux-image-4.4.0-96-generic_4.4.0-96.119_amd64.deb (--unpack):  cannot copy extracted data for './boot/System.map-4.4.0-96-generic' to '/boot/System.map-4.4.0-96-generic.dpkg-new': failed to write (No space left on device) No apport report written because MaxReports is reached already                                                               dpkg-deb: error: subprocess paste was killed by signal (Broken pipe) Examining /etc/kernel/postrm.d . run-parts: executing /etc/kernel/postrm.d/initramfs-tools 4.4.0-96-generic /boot/vmlinuz-4.4.0-96-generic run-parts: executing /etc/kernel/postrm.d/zz-update-grub 4.4.0-96-generic /boot/vmlinuz-4.4.0-96-generic Errors were encountered while processing:  /var/cache/apt/archives/linux-image-4.4.0-97-generic_4.4.0-97.120_amd64.deb  /var/cache/apt/archives/linux-image-4.4.0-83-generic_4.4.0-83.106_amd64.deb  /var/cache/apt/archives/linux-image-4.4.0-93-generic_4.4.0-93.116_amd64.deb  /var/cache/apt/archives/linux-image-4.4.0-96-generic_4.4.0-96.119_amd64.deb E: Sub-process /usr/bin/dpkg returned an error code (1)   Deleted a load of files, still wouldn't fix my dependencies.  How'd my pipe break and what should I do to fix this?   df:     Filesystem                  1K-blocks     Used Available Use% Mounted on udev                          3529056        0   3529056   0% /dev tmpfs                          710068    17808    692260   3% /run /dev/mapper/ubuntu--vg-root 953106324 11889680 892778580   2% / tmpfs                         3550320      800   3549520   1% /dev/shm tmpfs                            5120        4      5116   1% /run/lock tmpfs                         3550320        0   3550320   0% /sys/fs/cgroup /dev/sda2                      483946   474540         0 100% /boot /dev/sda1                      523248     3664    519584   1% /boot/efi tmpfs                          710068       84    709984   1% /run/user/1000 /home/frank/.Private        953106324 11889680 892778580   2% /home/frank   Any help would be appreciated, thanks!


In Arkham Horror, do 'leftover' successes after triggering a doom token removal still count?

In a 2-investigator game, if he rolls 3 successes, does the remaining success get accumulated toward the next doom token removal? Along the same vein, if he rolls 4 successes, does he remove 2 tokens?


RegEx: to capture numbers in lines, one line at a time

I am using a commercial scraper with some light RegEx support, and I want to capture data (the odds, 3.13, 14.69 etc. etc.) from the text as seen below:  I have to match one variable at a time (it is how the scraper works), save it, repeat. The problem is that I can't match some numbers as seen above; for some reason the first digit before the decimal place is not captured. However ([\d]+.[\d]+) correctly matches everything. Any suggestions?


How can I add new packages to archive.ubuntu.com?

I found that some of the software downloaded by "apt-get" is now out of date. I compiled the new versions into .deb packages. Now, how can I add them into the software center or archive.ubuntu.com? I just want to make everyone convenient.


general solution sum of two uniform random variables aY+bX=Z?

is there a general solution to that? I have seen simple examples for Y+X=Z but I was wondering how this would be with rescaling?


Prove that $n! > n^{3}$ for every integer $n \ge 6$ using induction

Proof.  Base case. When $n = 6$, LHS = $6! = 720$ and RHS = $6^{3} =  216$. Thus LHS > RHS.  Inductive step. Assume that $m! > m^{3}$ for some fixed integer $m$ such that $m \ge 6$. We must show that it also holds true for $(m+1)$, i.e, $(m+1)! > (m+1)^{3}$. Observe that   \begin{align*} (m+1)! &= (m+1) \cdot m! \\ &> (m+1) \cdot m^{3} \text{$\quad$(by the inductive hypothesis)}\\ \end{align*}  (still unfinished)    I know it boils down to showing that $(m+1) \cdot m^{3} > (m+1)^{3}$ but I'm unsure on how to proceed.


How can I get a call stack listing in Perl?

Is there a way I can access (for printout) a list of sub + module to arbitrary depth of sub-calls  preceding a current position in a Perl script?  I need to make changes to some Perl modules (.pm's). The workflow is initiated from a web-page thru a cgi-script, passing input through several modules/objects ending in the module where I need to use the data. Somewhere along the line the data got changed and I need to find out where.


XeLaTeX update [20201004] and item ball in Beamer

Beamer item balls go missing while compiling in XeLateX since yesterday's TeXlive update, however, the same code works with pdfLaTeX. Any solution, please. Here is my MWE: \documentclass{beamer}  \setbeamertemplate{itemize item}[ball] \setbeamertemplate{enumerate item}[ball]  \begin{document}  \begin{frame} \frametitle{A tested title} text \begin{enumerate}     \item this is an item \end{enumerate} text3 \begin{itemize}     \item this is an item \end{itemize} \end{frame} \end{document}


What is a good book to self-teach optics?

I'm interested in camera lenses and how things like barrel distortion and lens flare happens, but know that one cannot just start there.  I'm a math major and I've worked out of Strauss PDE book so I know about the wave equation and some stuff beyond as well.  Are there any good books out there for me to self-teach so I can at least begin to understand all this?


Estimate of n factorial: $n^{\frac{n}{2}} \le n! \le \left(\frac{n+1}{2}\right)^{n}$

on our lesson at our university, our professsor told that factorial has these estimates  $n^{\frac{n}{2}} \le n! \le \left(\dfrac{n+1}{2}\right)^{n}$  and during proof he did this  $(n!)^{2}=\underbrace{n\cdot(n-1)\dotsm 2\cdot 1}_{n!} \cdot \underbrace{n\cdot(n-1) \dotsm 2\cdot 1}_{n!}$  and then:  $(1 \cdot n) \cdot (2 \cdot (n-1)) \dotsm ((n-1) \cdot 2) \cdot (n \cdot 1)$  and it is equal to this  $(n+1)(n+1) \dotsm (n+1)$  why it is equal, I didn't catch it. Do you have any idea? :)


"Enchantment Creatures" and "Enchanted Creatures"

Is a enchantment creature card considered to be a creature that is enchanted? I need to know for , which destroys all creatures that aren't enchanted.


Prove that the series with terms $a_n$ diverges.

where the series has the nth term given by $$a_n = \frac {1\cdot3\cdot5\cdot\cdots\cdot(2n-1)}{2\cdot4\cdot6\cdot\cdots\cdot2n}$$  I managed to show that $$a_n = \frac {(2n)!} {4^n (n!)^2}$$  But it doesn't really help.. I'd like to compare it with something since the ratio test doesn't work.


Group isomorphism of the nonzero real numbers

$G$ is set $\{x \in \mathbb{R} : x \neq -1\}$ with group operation $x\circ y=x+y+xy$.  Show that $f(x)=x-1$  is an isomorphism from the multiplicative group $\mathbb{R}^*$ to $G$.


Integer solutions to $m+n=\text{gcd}(m,n)+\text{lcm}(m,n)=9!$

Recently, I have found this problem:  Given two natural numbers $m$ and $n$, find the number of tuples $(m,n)$ such that: $$m+n=\text{gcd}(m,n)+\text{lcm}(m,n)=9!$$  I hav completely no idea of how to do it because I am used to operate with the formula $\text{gcd}(m,n)\cdot\text{lcm}(m,n)$ and not with the sum $\text{gcd}(m,n)+\text{lcm}(m,n)$. In order to escape from this problem, I have tried to set $n=9!-m$ and then substitute for $n$, but here I am stuck agian because I have to work with: $$\text{gcd}(m,9!-m)+\text{lcm}(m,9!-m)$$ Any idea of how to proceed? Thanks.


At what age should my baby be expected to support her own head?

I have a 4-month old daughter.  Each time she is awake she gets some "tummy-time" where we put her on her stomach on a play-mat, to build up her neck muscles.  She doesn't like it that much and usually ends up crying after a few minutes of this.  Also, when we hold her so she is facing us, against our chest, she often jerks her head back like she doesn't enjoy being held that way.  While we have noticed her neck support getting stronger, there's still a small amount of wobble there and we have to support it.  At what age should we expect her to be able to support her head without any support?  Is there any other exercises other than tummy-time we can do to improve her strength?  Update  My daughter will be 5 months in about a week's time and we have noticed a big improvement in her head control/strength over the past few weeks.  I would say she has about 90% head control now.  Thanks for all of your great answers!


Two-part question: Neural Networks(NN) can be looked at as stacked units of logistic regression classifiers (LRC). A basic requirement of an activation function is to be non-linear. When LRC is a neuron, sigmoid function is the activation function and is said to bring non-linearity to NN. Q1:) If this is true, why is LRC still a linear classifier even when it uses non-linear sigmoid function? Further, if the activation function is a linear function(e.g. an identity function), the NN can no longer learn non-linear decision boundaries. Q2:) Does this mean that the depth of a neural network plays no role in making it non-linear? I have scanned similar threads for this question. But not convinced yet!


Reputation does not update after community wiki is removed from a post, and does not match the value displayed in the reputation audit

If votes were cast on a post while it was community wiki, and a moderator removes wiki from that post, the votes should count towards reputation again. However, while this is visible in a reputation audit, , and the reputation score needs to be recalculated to reflect the change.  Can someone fix this?


my program counts and prints out the number of files of folder and the total size in bytes of all files but i have error ("Exception in thread "main" java.lang.NullPointerException")  import java.io.*; public class Ex5 {     public static void a(String s) throws IOException{          long size=0;         File f=new File(s);         File [] a=f.listFiles();         System.out.println("the number of files in this folder :"+a.length);         for(int i=0;i<a.length;i++){         if(a[i].isFile()){             size=size+a[i].length();          }else             a(a[i].getName());          }     System.out.println("the folder size is :"+size);     }     public static void main(String[] args) throws IOException {         // TODO Auto-generated method stub       a("C:\\Users\\hackour\\Documents\\javablue\\applet");     }  }


Terminal name changed to 'Name@dhcp-xx-x'

I have no idea what dhcp means, so I don't know why instead of just showing 'Name ~' as the beginning of each terminal line, it started showing 'Name@dhcp-xx-x' as the format of my username. Is this a virus or did I just accidentally change this? How do I undo it?


Specifying element type for DXF creation using ogr2ogr

I am trying to create a DXF from a Polygon Shapefile using ogr2ogr:  ogr2ogr -f DXF parcels.dxf parcels.shp   The problem is that the polygons are written as hatch elements.    How do I specify that ogr2ogr should create LWPOLYLINE elements (Or any other )?  I have tried this from command line and from QGIS 'save as' option with the same result.  I don't remember this being an issue in the past, but seems like it started with GDAL version 1.10.x.


Windows 7 entry missing from grub after 12.04 installation

I've read several answers to related questions here, but have not found one that matches my situation.  I assisted a colleague to reinstall Windows 7 from a recovery partition. We then booted into Windows, shrank the Windows partition (/dev/sda3) and the installed Ubuntu 12.04 (we partitioned the remaining space into / (sda5), /home (sda6), /swap (sda7) and free space for another Windows drive later.) I specified GRUB to install to /dev/sda. /dev/sda1 and /dev/sda2 were recovery/system partitions.  After rebooting, grub showed the Ubuntu boot options in the menu, and an option for a Windows recovery on /dev/sda1 and a similar one for /dev/sda2. It did not show an entry for Windows 7 on /dev/sda3. I booted into Ubuntu and ran sudo update-grub, but this failed to detect Windows on /dev/sda3. I checked the contents of /dev/sda3 and Windows is still there.  I hope I can resolve this soon, as this is not a good first impression of an LTS release to someone who has just decided to start using Ubuntu/GNU/Linux!


How can i find all ways to color a planar graph with four colors?

I was wondering whether there are any heuristics on how to find all the ways to color a planar graph with four colors. What I tried so far: With a given coloring I looked at all vertices that are connected with less than three colors and used the cross product to find all other color combinations. This gives me many more ways to color a planar graph but not all. I would be very grateful if you had any idea.


On the factorial equations $A! B! =C!$ and $A!B!C! = D!$

I was playing around with hypergeometric probabilities when I wound myself calculating the binomial coefficient $\binom{10}{3}$. I used the definition, and calculating in my head, I simplified to this expression before actually calculating anything $$ \frac {8\cdot9\cdot10}{2\cdot3} = 120 $$ And then it hit me that $8\cdot9\cdot10 = 6!$ and I started thinking about something I feel like calling generalized factorials, which is just the product of a number of successive naturals, like this $$ a!b = \prod_{n=b}^an = \frac{a!}{(b-1)!},\quad a, b \in \mathbb{Z}^+, \quad a\ge b $$ so that $a! = a!1$ (the notation was invented just now, and inspired by the $nCr$-notation for binomial coefficients). Now, apart from the trivial examples $(n!)!(n!) = n!$ and $a!1 = a!2 = a!$, when is the generalized factorial a factorial number? When is it the product of two (non-trivial) factorial numbers? As seen above, $10!8$ is both.


rewrite script to use wp_remote_get instead of file_get_contents_curl

I have a script that pulls the facebook likes via facebook graph and writes them in my DB. However it uses file_get_contents_curl for the request and this is causing problems, so I'd like to use the wp_remote_get() command. I've tried to change it but somehow I can't do it (I don't really have PHP knowledge).  Here's the part of the script:  foreach($posts as $post)     {          $fb = json_decode(file_get_contents_curl('http://graph.facebook.com/?id='.get_permalink($post->ID)));         if( !isset( $fb->likes) && isset($fb->shares) )         {             $fb->likes = $fb->shares;         }         //$fb->likes = isset($fb->likes) ? $fb->likes : 0;         $myfblikes = sprintf("%04s", (int)$fb->likes);         update_post_meta($post->ID, 'fb_likes', $myfblikes);     }


how to search wordpress database for slug names

I'm trying to rename one of my pages to 2017 and the slug to 2017 as well.  When i click save the slug is renamed to 2017-2.  To me this means something else is using this slug, but i'm not sure how to find what is using it.    I tried going to my phpmyadmin and doing a database search for 2017, but nothing shows up there besides 2017 being a larger part of a number (ie 30382017)    I've also tried going to that page www.example.com/2017 and get a page not found error.  is there a way to find out what may be using this and why i can't rename to just 2017?


Would using varchar(5000) be bad compared to varchar(255)?

Since varchar anyways allocate space dynamically, my question is whether using varchar(255) be more efficient or save more space compared to using varchar(5000).  If yes, why?


This is the analogue of closed graph theorem for compact space          Suppose that $X$ and $K$ are metric spaces, that $K$ is compact, and that the graph of $f: X \rightarrow K$ is a closed subset of $X \times K$. Prove that $f$ is continuous.      Because metric space is first countable, all we need is to prove that if $x = \lim_{n \rightarrow \infty} x_{n}$, then $f(x) = \lim_{n \rightarrow \infty} f(x_{n})$. Suppose $x = \lim_{n \rightarrow \infty} x_{n}$, then because $K$ is compact, sequence $\{f(x_{n})\}$ has a subsequence $\{f(x_{n_{i}})\}$ converge. Because the graph of $f$ is closed, we must have $\lim_{n \rightarrow \infty}\{f(x_{n_{i}})\} = f(x)$. All we need to prove now is $\{f(x_{n})\}$ converge to $f(x)$, but I can't prove that. Can any one help me. I really appreciate. Thanks


Evaluting sum $\sum \limits_{n=0}^\infty\frac{n^k}{n!}$

Inspired by this ,I was interested if the following sum has a closed form.Looking for $k$ integer I found the  so that the sum when $k$ is natural number is $e\cdot B_k$ where $B_k$ is the $k$-th Bell number.I am interested if it's known whether the sum $$\sum_{n=0}^\infty\frac{n^k}{n!}$$ has a closed form for some other values of $k$.


how do I view a file strictly by the date it was accessed/created/downloaded

I am looking for a command that I can use to locate a file by the date a file was created on my computer


My company is building a product. It's going to be versioned by SVN. It's a webapp so basically there will never be a version out which doesn't have some features in them and thus could always be labeled as beta. But since it's going to be a corporate product I really don't want the "unstable watchout" on there. So how would you go about versioning? Is 1.0 stable? Should the build date be in the version number? Tell me what you guys think!


Why did Voldemort need to drink Unicorn blood?

"[...] it is a monstrous thing, to slay a unicorn. Only one who has nothing to lose, and everything to gain, would commit such a crime. The blood of a unicorn will keep you alive, even if you are an inch from death, but at a terrible price. You have slain something pure and defenceless to save yourself, and you will have but a half-life, a cursed life, from the moment the blood touches your lips."      - Firenze, Harry Potter and the Philosopher's Stone   In the first Harry Potter book/movie, we found Voldemort drinking Unicorn blood. Why did he need Unicorn blood to stay alive? Maybe, a unicorn blood works on undead soul, but wasn't he already protected by his Horcruxes in terms of being kept alive?


I have downloaded Adobe Flash player 11.2, but can't install it.   I am using Ubuntu 13.04. Can anyone help me?  I don't know which program it will open with.


Why are the values of upvotes for simple and complex questions equal?

I found several very-close-to-duplicate questions/answers. However, I want to restate some questions and discuss the answers from these questions.  Here the questions which I found:         I find it quite unfair that super simple questions and their answers upvote give the same amount of reputation points per upvote as complex questions. I think reputation points should be much closer linked to contribution. And I think that contribution in answering/asking a simple question (both in time, value and time saved to other developers) is way less than for some more complex questions.   Why doesn't Stack Overflow change this?  I saw several common answers:     if you change the game, then the only result is that people will game it differently.   I agree only partly with this. Sure, people will always game the system. However, any improvement can be rejected based on this argument. I believe if there is an obvious problem, it makes sense to fix it. And it looks like this question was asked number of times (meaning that it's not only me thinking that it should be changed).     Reputation is NOTHING more than an INCENTIVE to contribute.   Again. I agree only partly. Reputation doesn't have any real value (it can't be converted to anything). However, let's be honest. People are competitive and people like to have some measurement stick and most of software developers want to have a fair game. Based on this, reputation isn't NOTHING, reputation is very important tool which makes Stack Overflow popular. Calculating reputation one way or another way may lure or discourage people from participating.     Esoteric questions are only of interest to people working with that item.   I believe one of the biggest values of Stack Overflow that it contains a lot of information which is hard to find somewhere else.  So, sure, there are some rare questions which aren't valuable to the whole community. But, I would say that a question which saves 25 people a day of work (complex question) is more valuable than a question which saves a 1000 people 3 minutes of googling (simple question).  My summary:  I believe it makes sense to change a system a little bit. The simplest way would be the ability to mark a question as trivial. If some number of people marked the question as trivial (let's say 10), all upvotes for this question/answers become less valuable (for example, 1 or 2 points, instead of 5). This will close this gap.


How does $\sum_{n=1}^{\infty}a_n$ diverge?

Let $a_n=1-2^{\frac{-1}{n}}$, $b_n=\frac{1}{n^p}$. If $p=1$, then if I want to compare $\sum_{n=1}^{\infty}a_n$ with $\sum_{n=1}^{\infty}b_n$, does it converge or diverge by comparison? To answer this question, I think it's obvious that $b_n$ diverges, without a doubt. But the real question is am I able to draw this conclusion from comparing it with $b_n$? I know that sometimes these comparison tests do not work, so this is the main problem that i am concerned with.


I have the following question:  Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$?  Note: the symbol $\cong$ denotes a homeomorphism between topological spaces  What I think:  I think that in fact there is a homeomorphism between those spaces, because is possible to express the lexicographic order as union of vertical lines with open extremes, I mean this is a basis for the lexicographic order. If I consider the Identical function I have the homeomorphism. Am I right?


I came around this question:  Show that if $a$, $b$, and $c$ are integers such that $(a, b) = 1$, then there is an integer $n$ such that $(an + b, c) = 1$,   in the Chinese Remainder Theorem section of my textbook and wasn't too sure how I could break that up so I could use the CRT to solve it.  Any hints would be greatly appreciated thanks!


Why can't an argument for the Riemann Zeta function be 1? What happens if we take Re(s)=1?

If $s=1$, then the series equals to $\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...\to \infty$  This certainly does seem to be a convergent series. Why doesn't it have a limit?


(NBHM_2006_PhD Screening Test_Analysis)     The curve $x^3− y^3= 1$ is asymptotic to the line $x = y$. Find the   point on the curve farthest from the line $x = y$   how should i solve this problem


Precise definition of limits and $\lim_{x\to-1}\frac1{\sqrt{x^2+3}}=\frac12$

Prove using the epsilon-delta definition,   $$ \lim_{x\to-1}\frac1{\sqrt{x^2+3}}=\frac12 $$   what I came up so far was:  $0<|x+1|<δ$ implies $\left|\frac1{\sqrt{x^2+3}} - \frac12\right|<ϵ$  \begin{align} &\frac1{\sqrt{x^2+3}} - \frac12 \\ &=\frac{2\sqrt{x^2+3}-(x^2+3)}{2(x^2+3)} \\ &= \frac{2\sqrt{(x+1)^2-2(x+1)+4} - ((x+1)^2-2(x+1)+4)}{2[(x+1)^2-2(x+1)+4]}  \end{align}  I'm unable to proceed because there are no real roots for $y^2-2y+4$  Can some please help me with this question? Thanks!


How to make Windows Update not to use all the internet band?

Is there a way to make Windows Updates not ot use up all the internet band?  I use Windows 8.1 Home Edition (64 bits).


Adding existing style while publishing a new layer in GeoServer using REST API

I have a function which publishes a layer in GeoServer with the REST API. Now I want to add an existing style in the layer while publishing it.  Anyone has any idea where I write the style name or call the 'style.sld' while publish the layer?  const publish = function (layerName) { return new Promise((resolve, reject) => {     axios({         method: 'POST',         url: `http://${GEOSERVER_IP}:${GEOSERVER_PORT}/geoserver/rest/workspaces/workspaceName/datastores/datastoreName/featuretypes.xml`,         auth: {             username: `${GEOSERVER_ADMIN_USER}`,             password: `${GEOSERVER_ADMIN_PASS}`         },         headers: {             'Content-Type': 'text/xml'         },         data: `<featureType>                 <name>${layerName}</name>                 <srs>EPSG:4326</srs>             </featureType>`     })         .then(response => {             resolve({                 ok: 1,                 message: `Layer has been published.`             })         })         .catch(err => {             reject({                 ok: 0,                 message: err.response.data,             })         })  }) }


Are certification courses like ISTQB necessary in testing career and if so, to what extent?

How will certification help in a testing career and up to what extent will it help?


Execute PowerShell Script from C# with Commandline Arguments

I need to execute a PowerShell script from within C#. The script needs commandline arguments.  This is what I have done so far:  RunspaceConfiguration runspaceConfiguration = RunspaceConfiguration.Create();  Runspace runspace = RunspaceFactory.CreateRunspace(runspaceConfiguration); runspace.Open();  RunspaceInvoke scriptInvoker = new RunspaceInvoke(runspace);  Pipeline pipeline = runspace.CreatePipeline(); pipeline.Commands.Add(scriptFile);  // Execute PowerShell script results = pipeline.Invoke();   scriptFile contains something like "C:\Program Files\MyProgram\Whatever.ps1".   The script uses a commandline argument such as "-key Value" whereas Value can be something like a path that also might contain spaces.  I don't get this to work. Does anyone know how to pass commandline arguments to a PowerShell script from within C# and make sure that spaces are no problem?


Lorentz invariance of Action or Lagrangian?

For what I know, the Action should be Lorentz-invariant in accordance to the axioms of SR. For example for a free particle the Action would be the integral of the proper time, which of course is invariant. Now my doubt is the following: does that mean that the Lagrangian should be Lorentz-invariant as well? In some texts I've read it is often stated that the Lagrangian should be a Lorentz scalar, but how does this assures the Action to be Lorentz-invariant too? For example, once one gets the Lorentz-invariant Lagrangian for the EM field $\mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}$, why should its action:$$\int -\frac{1}{4}F^{\mu\nu}F_{\mu\nu} d^4x$$ be Lorentz invariant too? Aren't we integrating a scalar over a specific set of  coordinates which are not Lorentz-invariant?


I have a dual boot with Ubuntu and Windows and I trying to make a Linux partition bigger, but I can't.


Probabilistic argument to evaluate $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k = 0}^n \frac{n^k}{k!}$

I'd like to come up with a probabilistic argument to evaluate the following limit: $$\lim_{n\to\infty} e^{-n} \sum_{k = 0}^n \frac{n^k}{k!}$$  The reason is that, if $X \sim \mathrm{Poisson}(n)$, the limit translates to $$\lim_{n\to\infty} F_X(n)$$ where $F_X$ is the cumulative distribution function of $X$. I know that it can be expressed by resorting to the gamma function and its incomplete counterpart, but I don't think I'll be able to evaluate the limit if I substitute that expression.  Is there a simpler probabilistic argument in this case? In the meantime, I confirmed the limit indeed exists, and it's $1/2$:    import scipy as sp, matplotlib.pyplot as plt  F_X = lambda n: (sp.stats.distributions.poisson.rvs(n, size=100000) <= n).mean() ns = np.logspace(0, 6, 30) fig, ax = plt.subplots(figsize=(10, 6)) ax.semilogx(ns, list(map(F_X, ns)), marker='o') ax.set_xlabel('$n$', fontsize=16) ax.set_ylabel('$F_X$', fontsize=16)


What has happened with the broom riding class in the Harry Potter books?

Aside from the very first novel I didn't find any mentioning of the broom riding classes. In the first book Malfoy taunts Harry in this class to get into the air with him, which after a series of events results in Harry ending up in the Quidditch team. However this class will never be mentioned again as far as I'm concerned throughout the books nor the movies.  Was it just a 1-2 hours long introduction? Is there no PE class at the school?


I'm trying to calculate the total number of counts a raster contains using python script. When I ran the script, I didn't get any error. However, I also didn't get the number of counts for each row in the attribute table.  Code:  import arcpy  #To overwrite output arcpy.env.overwriteOutput = True  #Set environment settings arcpy.env.workspace = "C:/Subhasis/Test/raster-read"  #Build Raster Attribute Table arcpy.BuildRasterAttributeTable_management("sti-9", "Overwrite")  # loop through attribute table Rows = arcpy.SearchCursor( "sti-9" )   for row in Rows:     count = row.getValue( "COUNT" )      print count


In India, we often receive SMSs which do not actually have a number, but instead, have a name like 'VK-AMSWAN'. SMS blockers like Truecaller don't have any facility to recognise such senders, and keep asking for a number to block.  How do I block such senders? I cannot blanket block all unknown SMSs because even banking information comes from such named senders.  Edit: When using third party SMS apps like chomp SMS, there is an option to show contact number below contact name. Guess what it shows for the spam?  VK-AMSWAN (name)  VKAMSWAN (where the number shows up for other contacts)  -_-  Edit 2: Thank you so much for your suggestions, guys. :) But it seems SMS blocking isn't as well developed as call blocking is. Truecaller actually rejects spam calls without you ever knowing about them. No SMS blocker I've seen has this facility so far. All they do is receive the messages and hide them. If someone can locate a method to fully block spam SMS, please do tell. :)


In Candy Box 2, how do I find and use the teleport feature to get out of the hole with my stuff?

When I searched on Arqade how to get out of The Hole in Candy Box 2 with all of my stuff, I found two answers. I didn't know how to find or use the teleport, so I went with the second option and found the pogo stick. Now, I have the desert bird feather with allows me to jump higher with the pogo stick, but it's still not high enough to make it completely out of the hole. The only option left is the teleport. I don't know if the teleport feature is something everyone has right off the bat or if it's something I have to find, but I can't find it on my screen. So... uh, where is it please?


I need to arrange my pictures on the way shown in the attached figure. Please any help from you.


Implement numbering scheme like A,B,C... AA,AB,... AAA..., similar to converting a number to radix26

I want to implement numbering scheme like Microsoft Word uses for numbering.  first one gets = A,next is  B, next is C, .... then AA, then AB,....and so on.  as shown below   A        B  C  .   .  AA  AB  AC  .  .  AAA  AAB  ....   '=>' here means converted to.  some examples:       1 => A 26 => Z 27 => AA 52 => AZ 53 => BA   and heres the code for it:     var convertToNumberingScheme = function(n){         var x = n-1,             r26 = x.toString(26),             baseCharCode = "A".charCodeAt(0);          var arr = r26.split(''),             len = arr.length;          var newArr =arr.map(function(val,i){             val = parseInt(val,26);              if( (i === 0) && ( len > 1)){                 val = val-1;             }              return String.fromCharCode(baseCharCode + val);         });         return newArr.join('');     }   It seems to work fine, but any ideas if there are some potential bugs or ways to  optimize this.


how to get 3D vertex bounding box around the object in python

I have a vehicle model, the 3D bounding box of the vehicle model contains the 3D coordinates of each vertex.  My question is would it possible to get the 3D bounding box coordinates, which is a 8 vertex vector [8,2] directly from python. With this bounding box coordinates, I want to do two things, firstly calculate the pose of the object, secondly find a way to calculate the image pixel coordinate corresponding to each 3D vertex.  I have found some related work, this  shows how to get 2D bounding box coordinates around the image, however it is 2D bounding box.   Furthermore,  can show us how to display the 3D bounding box around the object, it doesn't tell me how to get vertex in python.


How to create a polygon from a data CSV file with coordinates using QGIS?

Having the following information in a CSV file:    I want to build a polygon with all the points where the Group name is the same.   For example I want to join all the points where the group is T101 and form a polygon.  How can I achieve it using QGIS?


while reading NYT's review on the Gladwell's last book I stumbled upon a rather strange passage:     In the weeks I spent listening to Malcolm Gladwell’s podcast, I   learned that lobsters have serotonin, that Elvis Presley suffered from   parapraxis and that Mr. Gladwell adheres to a firm life rule that he   drink only five liquids: water, tea, red wine, espresso and milk.   Why the author uses "he drink" here? Is it a legal thing to do? Are there cases when you should use it?


I am using Koma-script for a report.  \documentclass[titlepage,12pt,a4paper,toc=bibnumbered,numbers=endperiod]{scrreprt}   I would like to give multiple option to "toc" option such as bibnumbered, flat, chapterentrywithdots etc. instead of just one.   How can I do this?   I am a newbie so please bare with me...


Start for a proof of the fundamental theorem of algebra

Let $p(z)=a_o+\dots+a_nz^n$, with $n\geqslant 1$ and $a_n\neq0$. Let $f:\mathbb{C}\rightarrow\mathbb{C}$ be defined by $f(z)=1/p(z)$.   I need to show that there is an $R>0$ such that \begin{equation}\left|z\right|>R\quad\rightarrow\quad\left|z^nf(z)\right|<2/\left|a_n\right|.\end{equation}  I have no clue how to do this...


I have this puzzle "A woman went to the market and a horse broke the eggs she had in her basket. The owner of the horse offered her to pay for the damage caused. He asked her how many eggs were broken by his horse. She said she didnt knew , but remebered that when she arrenged them in pairs, there was one left. Same thing happened when she arrenged them in groups of 3, 4, 5 and 6. But when she arrenged them in groups of 7 there was none left. what is the minimum quantity of eggs that were in the basket?" I tried showing the equations  2a+1=x 3b+1=x 4c+1=x 5d+1=x 6e+1=x 7f=x  But I really dont know what to do with them


Why is it "geometric" but "theoretical"?

I just came across a course name: Geometric and Theoretical Optics. The mismatched endings bug me. Why do we have both -ical and -ic endings?   Is there any difference in meaning between, say, theoretic and theoretical? I know that acoustic and acoustical mean slightly different things, but is this difference inherent in the words, or is it just usage — we happen to use the former for sound, and the latter for ceilings?


In a bash script I have several arrays which I need to access in a gnuplot code:  #!/bin/bash ... # fill array a[*] and b[*] ... gnuplot <<EOF   do for [j=0:10] { # access ${a[j]} and ${b[j]} } EOF   The problem is that ${a[j]} in the gnuplot code is not interpreted as element j of the array a.  How can I solve that?


Method to determine outliers with a skewed dataset

How can we find outliers in a dataset with a (highly) skewed distribution? With a normal distribution, is it well documented to use 2 x Standard Deviation or the upper boundary of the box plot (1.5 x IQR). However, for something like a conversion rate, where the distribution is severely positively skewed, how can we find the high conversion rates that are outliers?  I have done a lot of research around this topic and is a big business problem for us, but I can't find much at all about it.


I'm wondering why we use entities for some cases, when we can use nodes. When we use nodes we can use lots of modules to use for almost any purpose.. The above sentence is my main question, while I was planning to make an election system. Here is my case: I want to write a simple voting system that users become candidates, then an admin authenticate them, then for a period of time othef users come and vote to number of candidates(number of candidates is defined by admin)  The structure I planned is to make outside of drupal world is to have three tables 1. A table for elections, containing information about the election itself for example election for choosing manager this year! 2. A table for candidates containing election reference( no 1 ), user id , accepted status, and votes. 3. A table for keep track of election containing the voter id, and candidate id , and election id.  I was thinking these can be fields of nodes, that we only work with these values by php codes in template for example. But I want to make a drupal module. But I'm confused that what is the best DRUPAL WAY to do that?  Thanks


i was asking for a good explanation to explain to me why use binding in sql i read that it helps against sql injection but i couldn't get it clear can anyone explain it for me thanks


In Windows there is an option to disable auto detection of headphones so speakers won't auto mute but I am unable to find such option in Ubuntu. How can I activate such feature?


Why does an IP address range scan not scan the 255 address by default?

The  starts with a default scan range of 192.168.1.1 to 192.168.1.254 (presumably this changes dependant what C level IP the gateway is set to.   Is there a technical reason the scanning range isnt set to 192.168.1.0 to 192.168.1.254 (note the 0 not 1 at the beginning and 255 not 254 at the end) ?  Is the x.x.x.0 and x.x.x.255 address not commonly used for some reason ?


cpp - why didn't guardian protect me from multiple definitions?

I'm more into JAVA, but when HI-Perf is in the requirements list C/C++ must come on the table. And so it did. And, as expected, I'd stumbled upon something I cannot understand and cannot dig out in SO. So can anyone explain me why didn't guardian in a header below work?  // a0a.h  #ifndef _A0A #define _A0A  class State { public:     static State* A; }  State* State::A = new State(); /* this is going to be troublesome */  #endif   .  B.h // #include "a0a.h" C.h // #include "a0a.h"  XXX.h // #include "B.h" XXX.h // #include "C.h"   and compilation gives me a multiple definitions error on the line pointed out above.  I've made it work by moving that line away to a .cpp source file, but I still want to understand why didn't guardian protect me from shooting my own foot here?  I hope I do not have to tell that this is just a dummy code reflecting what I did -- not the actual code I was writing.  EDIT   does not explain WHY. I mean I do not get the picture from any of those answers -- they just give suggestions (none of which I need).  Of course I can dive into books and probably learn how all of this makes compiler sneeze in my console, but asking is SO is much faster and will most likely help someone else to understand.


How to check if a string is a valid integer?

I have:   op1 = Integer.parseInt(jTextField1.getText());  op2 = Integer.parseInt(jTextField2.getText());   However, I want to check first whether the text fields' values can be assigned to integer variables. How do I do that?  I've been going through this for a long time, so, if this was already asked here, forgive me


please, can you put the numbering of my expression to the end of a row after the fraction. I tried 2 different ways, but it is stiil not good enough. These equations are the same, so enough change just one of them.  Thanks in advance  First equation:  \begin{fleqn} \begin{equation} \begin{split} t^{\text{same rode}}_{j} = \frac{-(speed_j - speed_0) \pm \sqrt{\left(speed_j - speed_0\right)^2 \pm 2\cdot\left(accel_j - accel_0\right)\cdot \left(r-d^{\text{between 0 and j}}\right)}}{accel_j - accel_0} \end{split} \end{equation} \end{fleqn}   Second equation:  \begin{fleqn}   \begin{equation} \label{eq1}     \begin{split}       \MoveEqLeft\mathrlap{t^{\text{same rode}}_j =}\\        & = \frac{-(speed_j - speed_0) \pm \sqrt{\left(speed_j - speed_0\right)^2 \pm 2\cdot\left(accel_j - accel_0\right)\cdot \left(r-d^{\text{between 0 and j}}\right)}}{accel_j - accel_0}     \end{split}   \end{equation} \end{fleqn}


How can i remove a item from a list whilst creating another list with the removed items?

Hey guys i'm scraping an website which ultimately led me to an list consisting of First and last name of the users...I would like to separete every 2 items of this said list,group them and store them in another list that will contain all the first and last names grouped.  For example: ['Jhon', 'Doe', 'Joey', 'Santos']  Desired output : list1 = ['Jhon','Doe']                  list2 = ['Joey','Santos']  Is there a way of automating this?


Assume I want to allocate only 256 bytes memory blocks  char * memory = new char[256];   than I use placement new to create a FooBar object (sizeof(Foobar)<=256)  FooBar * obj = new (memory) FooBar();   does  delete obj; //this also calls the destructor of FooBar   delete all the 256 bytes of memory?  Does the standard guarantee that the whole "memory" buffer is deallocated by just "deleting obj"? Or it is based on the type "FooBar" and therefore this operation has undefined behaviour?  Assumption: FooBar is the only object in the memory buffer.  This is not duplicate question, please first understand the question. It is not immediately evident what this code does.


How to place amsmath equations at top of page ignoring \topskip?

I need every amsmath equation to place at the top of the page. So I use \noindent to do that. Everything is fine except equation+split environment. Than formula is placed a bit higher (by \vskip-\lineskiplimit (it's -3pt) from asmmath.sty \@display@init macro). align+split is ok. The glue is discardable item but it's in a box so it's not discarded.  ....\glue(\topskip) 0.0 ....\hbox(21.00012+16.0001)x430.00462, direction TLT .....\vbox(21.00012+16.0001)x430.00462, direction TLT ......\glue -3.0 ......\glue 0.0   MWE:  \documentclass{article} \usepackage[showframe,paperwidth=10cm,paperheight=5cm]{geometry} \usepackage{amsmath}  \begin{document}  \noindent \[ \begin{split} \left(a^{B^{B^{B}}}\right) \\ bb \end{split} \]  \clearpage \noindent \begin{align} \begin{split} \left(a^{B^{B^{B}}}\right) \\ bb \end{split} \end{align}  \end{document}   Result:   Questions:   Is there a way to test am I on the top of page? Then I could fix that \vskip. I tried leaders but its very tricky.  Is there an other way to place formulas forcing \topskip?


How to print the element in a list with index?

I'm trying to print the element with the index of every element in the list   But my implement prints every element with index 0 and every element with index 1 until the last index  can anyone fix it, I'm stuck here?  if __name__=="__main__":      r = [6, 5, 3, 3]     diff = [[(i,j)for i in r]for j in range(5)]     print(diff)   Actual output:  [[(6, 0), (5, 0), (3, 0), (3, 0)], [(6, 1), (5, 1), (3, 1), (3, 1)], [(6, 2), (5, 2), (3, 2), (3, 2)], [(6, 3), (5, 3), (3, 3), (3, 3)], [(6, 4), (5, 4), (3, 4), (3, 4)]]   Desired output:  [(6, 0),(5, 1),(3, 2),(3, 3)]


Batch replacing white background with a colour

I need to batch replace the white background on several thousand images. Is there a better way of doing this aside from setting up an action, selecting the white background and filling in colour?


Unknown column in 'where clause' in mysql

I have a query in sql which returns me some rows . Now when i want to search  based on some condition ,it says "unknown column in where clause"  SQL Query   SELECT    SUM(     CASE       WHEN otd.passenger_type = 'adult'        THEN 1        ELSE 0      END   ) AS 'Adult_count',   SUM(     CASE       WHEN otd.passenger_type = 'child'        THEN 1        ELSE 0      END   ) AS 'child_count',   CASE      WHEN p.branch = 'EBIZ'     THEN 'EBIZ'     ELSE 'LTOB'    END     AS 'passenger_branch_new' ,   t.tour_code AS TOUR_CODE,   ot.optional_tour_name,   p.BRANCH,   tum.login,   t.Region_name,   t.start_date ,   CONCAT(u.first_name,' ',u.last_name) Tname FROM   tour t     INNER JOIN tour_user_mapping tum      ON tum.tour_sub_code = t.tour_sub_code        INNER JOIN USER u   ON u.login = tum.login     INNER JOIN main_optional_tour_mapping motm      ON motm.main_tour_code = t.tour_code    INNER JOIN      (SELECT        tour_code,       tour_name AS optional_tour_name,       child_rate,       adult_rate,       region      FROM       optional_tour      WHERE delete_flag = 'F') AS ot      ON ot.tour_code = motm.optional_tour_code    INNER JOIN optional_tour_details otd      ON otd.optional_tour_code = ot.tour_code    INNER JOIN passenger p      ON (       p.passenger_id = otd.passenger_id        AND p.tour_code = t.tour_code        AND p.tour_sub_code = t.tour_sub_code        AND motm.main_tour_code = p.tour_code     )  WHERE t.delete_flag = 'F'    AND tum.delete_flag = 'F'    AND tum.role_id = '3'     AND Tname = 'Sunny Thangaraj' GROUP BY t.tour_sub_code,   motm.optional_tour_code,  passenger_branch_new ORDER BY t.created_on DESC            Now when i search using Tname i get Unknown column 'Tname' in 'where clause' Is there something wrong with syntax ? Please help me with this Also when i try to search using 'passenger_branch_new' i get the same error of unknown column But in Group By clause i have used 'passenger_branch_new' and it works fine .


How to change to default the selected dropdown

I'm making three dropdowns on HTML and I make a JavaScript program to alert when there has a duplicate selected value. What should I do If after the alert the selected dropdown return its default value after the alert.    function hey() {    var count = document.getElementsByClassName('data').length;   //var cars = document.getElementsByClassName('data')[0].value;   var arr = [];   var text = "";   var i = 0;   while (i < count) {     if ((document.getElementsByClassName('data')[i].value) == "") {} else {       arr.push(document.getElementsByClassName('data')[i].value);     }     i++;   }   document.getElementById("demo").innerHTML = arr;   var uniqueval = arr.filter(function(itm, i, arr) {     return i == arr.indexOf(itm);   });   if (arr.length > uniqueval.length) {     alert("Has duplicate")   } }
   <select name="type" class="data" onchange="hey()">     <option value="">---select---</option>     <option value="teacher">Teacher</option>     <option value="student">Student</option>     <option value="students">Students</option>   </select>   <select name="class" class="data" onchange="hey()">     <option value="">---select---</option>     <option value="teacher">Teacher</option>     <option value="student">Student</option>     <option value="students">Students</option>   </select>   <select name="class" class="data" onchange="hey()">     <option value="">---select---</option>     <option value="teacher">Teacher</option>     <option value="student">Student</option>     <option value="students">Students</option>   </select>

When I select another dropdown and its been already selected
  Theres have an alert message and when I click OK I want to return its default value which is --select--
     I want to return the --select-- value after the alert of the selected dropdown.


It is well known that a parametric form of the parabola $y^2=4ax$ is $(at^2, 2at)$.      What are possible parametric forms of the general parabola   $$(Ax+Cy)^2+Dx+Ey+F=0$$   ?


$S^{-1}R\cong \frac{R[x]}{(sx-1)}$ for $S = \langle s^k\rangle\ $ [fraction ring as quotient ring]

Few Definitions: Let $R$ be a nonzero commutative ring which does not necessarily contain identity. Let $S$ be a multiplicatively closed subset of $R$ such that $S$ does not contain the zero element and zero divisors.  Define an Equivalence relation $\sim$ on $R\times S$ by setting $(r, s) \sim (r',s')$ if $rs' = sr'$. and denote the equivalnece class of $(r, s)$ by $\frac{r}{s}=\{(a,b)|a\in R, b\in S \enspace \text{and}\ rb=as\}$.  Now, the set $S^{-1}R$ is the set of equivalence classes under $\sim$.  Define multiplication and addition on $S^{-1}R$ by  $$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd} \enspace \text{and}\ \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$$  My Question:     Let $R$ be a commutative ring with $1\neq 0$. Let $s$ be a nonzero   divisor of $R$ and $S$ denote the multiplicatively closed subset   $\{1,s,s^2,...\}$.Then prove that $$S^{-1}R\cong \frac{R[x]}{(sx-1)}$$   My Idea: Define $$\varphi:R[x]\rightarrow S^{-1}R\\r\mapsto r \enspace \forall \enspace r\in R\\x\mapsto \frac{1}{s}\enspace \forall \enspace s\in S$$ Now, I need to show that this map is surjective ring Homomorphism and need to determine its kernel. Then, I will use First Isomorphism Theorem for Rings to get the result.  It is easy to note that $\varphi$ is a ring homomorphism under the above definition.  Now, any element $\alpha \in S^{-1}R$ is of the form $\frac{a}{s^m}$ for some $m\in \mathbb{N}\cup\{0\}$, where $a\in R$ and $s^m\in S$. Now, $$\frac{a}{s^m}=a\times \frac{1}{s^m}= a\times (\frac{1}{s})^m\\=\varphi(a)\times (\varphi(x))^m\\=\varphi(a)\times \varphi(x^m) =\varphi(ax^m)$$ Therefore,  $\varphi$ is a surjective ring homomorphism.    But I don't know how to compute its Kernel.  Can Anyone please help me and show me a proof?


How should I print types like off_t and size_t?

I'm trying to print types like off_t and size_t.  What is the correct placeholder for printf() that is portable?  Or is there a completely different way to print those variables?


Is there a limit to how hot an object can be?

We know that speed of physical object cant exceed speed of light, a body cant be cooler than 0k, thus does there exist a limit to hotness of an object?


Why does the rod rotate only about its center of mass after being hit anywhere except its center of mass? Can it be proved mathematically? In case I'm wrong then show about which point the rod will rotate after being hit at any point other than the center of mass (mathematically). I don't need any physical interpretation cause its been discussed with logical support previously, please try to show it mathematically.[The rod is kept unhinged on a smooth horizontal plane]


i have database:     so result it:    frome this code:     <?php        $dbhost = '?';     $dbuser = '?';     $dbpass = '?';       try {          $dbh = new PDO("mysql:host=localhost;dbname=?", "?", "?");           $dbh->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);         $result = $dbh->query("SELECT * FROM DATACC");       mysql_set_charset("UTF8");   header('Content-type: text/html; charset=utf-8');       } catch(PDOException $e) {         echo $e->getMessage();     }   echo "";       echo "
";         foreach($result->fetchAll() as $row){    echo "
";      echo "
";      echo "" . $row["MaCC"] . "	";      echo "" . $row["HoVaTen_VN"] . "	";      echo "" . $row["NgaySinh"] . "	";      echo "" . $row["NoiSinh"] . "	";                echo "
";    echo "
";      }     echo "</talbe>";    echo "";     $dbh = NULL;  ?>     can you help me fix this code! (i tried many way i can to fix this error, so still fail). Thanks for this!


Why can posts never have a number as the link?

Here's something interesting I noticed today - it is not possible to name a post a number - no matter what theme you use, and even if you name a post a long number that has no tag or post-name or category name conflicts, you will still get 2015 or 1826628 renamed as 2015-2 or 1826628-2.  I assume this isn't a bug, but I also don't see why you can't have mysite.com/20 or similar as a permalink to a post, when you have it named "20", and permalinks are set to postname.


I have to find a combinatorial proof to prove that  $$k=\frac{(10!)!}{(10!)^{9!}}$$  is an integer number.  I really don't know where to start from. I thought that another way of saying it might help more: prove that $(10!)! \pmod {(10!)^{9!}} \equiv 0$.


Why do I get 1 as an answer when I got (j>1) as a condition?

#include <stdio.h> #include <stdint.h> #include <stdlib.h>  double rand_double() {     return ( ((double)rand())/ ((double)RAND_MAX) ); }  int main(){     double i=rand_double();     double j;     do {         i=(i*0.5);         j=(1+i);         printf("%lf\n", j);     }     while(j>1);     return(0); }


If I am a divination wizard, and I have someone take 5 for their saving throw, can they spend a luck point from their lucky feat to roll something else?  It seems like they can I just want to make sure.


Find community text partially obscured in the edit box

The current community top bar menu contains an edit named "Find a SE community". The text in this edit is partially obscured on the top and on the bottom:        I'm using FF 58.0.2.


Non-Uniform Scaling during UV unwrap. What is this?

I've got a problem while unwrapping UVs. When I'm unwrapping UVs it showing me this message.     Why is this happening?


Yesterday I upgraded Ubuntu from 11.04 to 11.10.  There is a nice effect of alt tab switcher with windows preview in 11.10 but with my system only simple alt tab switcher is working without effects.  I have Nvidia 1GB graphics card. I was using ubuntu classic with 11.04 as driver was not working with it but with 11.10 now nvidia driver is working and I want all unity effects.  I have installed compiz setting manager but can't able to enable alt tab switcher effects from anywhere.


What is the length and breadth of ONLY the screen in the Nexus 7?

I'm not asking the diagonal values, but the length and breadth ones of the Nexus 7. And only of the LCD screen, not the entire hardware.


Itemize not giving correct result. It is omitting % sign

I am creating a list of items using 'itemize'. The lines in the item have the sign "%" after a figure. The given lines are:   The revenue has increased by 27% YOY and that has resulted in increase of income by 15%. This impact has resulted in increase of the MOM growth by 20% and WOW growth by 10%.   Now, 'itemize' is omitting everything after % sign. So the output is coming out to be:   The revenue has increased by 27 This impact has resulted in increase of the MOM growth by 20   Can someone explain why? And how do I correct this?  The code I am using is:  \begin{itemize} \item The revenue has increased by 27% YOY and that has resulted in increase of income by 15%. \item This impact has resulted in increase of the MOM growth by 20% and WOW growth by 10%. \end{itemize}


Mathematics of quantum mechanics for beam splitter

I'm reading a book where quantum interference is explained with a common experiment, where photons are thrown to some apparatus formed by two beam splitters:    Describing the problem using linear algebra, we could assign some vectors for the two possible paths that the photon could take after the first beam splitter, for example  $$ \text{Red path} \equiv \left(\begin{array}{c}1\\0\end{array}\right) \quad \text{Green path} \equiv \left(\begin{array}{c}0\\1\end{array}\right) $$  Then, if we say that the photon starts in the state of the red path, the quantum state after the first beam splitter is  $$ \lvert\psi\rangle = \dfrac{1}{\sqrt{2}} \left(\begin{array}{cc}1&i\\i&1\end{array}\right)\left(\begin{array}{c}1\\0\end{array}\right) = \dfrac{1}{\sqrt{2}}\left(\begin{array}{c}1\\i\end{array}\right) = \dfrac{1}{\sqrt{2}}\left(\begin{array}{c}1\\0\end{array}\right) + \dfrac{i}{\sqrt{2}}\left(\begin{array}{c}0\\1\end{array}\right) $$  Mathematically, this is nice because it gives 50% of probabilities for the photon to be found in each path since  $$ \left|\dfrac{1}{\sqrt{2}}\right|^2 = \dfrac{1}{2} \quad \text{and} \quad \left|\dfrac{i}{\sqrt{2}}\right|^2 = \dfrac{1}{2} $$  However, I don't see why the book represents the beam splitter using the imaginary number $i$. Wouldn't it be the same physically speaking (in terms of the resultant probability) if we represent the beam splitter with the usual Hadamard's gate  $$ \dfrac{1}{\sqrt{2}} \left(\begin{array}{cc}1&1\\1&-1\end{array}\right) $$  Is there any reason (historical, physical, ...) that could make the author choose the matrix with the $i$ components?


When I click on new button then I uploaded the file using lightning file upload now if i'm clicking on cancel button, then I'm again click on new button then the previous uploaded file is there. How can i reset that uploaded file after clicking on cancel button. Uploading a file
                                *Upload Medical Certificate                                              <lightning-file-upload name="fileUploader" accept={acceptedFormats} record-id={myRecordId} onuploadfinished={handleUploadFinished}>                             </lightning-file-upload> {docName}
    Cancel button <button type="button" class="slds-button slds-button_destructive" onclick={closeSuspendModal}>Cancel</button>  JS closeSuspendModal() { this.isShowSuspendModel=false;    }  get acceptedFormats() {         return ['.pdf', '.png', '.docx', '.jpg', '.jpeg'];     }      handleUploadFinished(event) {         // Get the list of uploaded files         const uploadedFiles = event.detail.files;         this.docId=uploadedFiles[0].documentId;         this.docName=uploadedFiles[0].name+' uploaded successfully';         console.log('1111'+uploadedFiles[0].documentId)         console.log('1111'+uploadedFiles[0].name)              }


I tried to define (my first! - I'm a LateX newbie) command to insert notes in the margins of my text, but it introduces gaps wherever I insert the command :-( The code for my command is:  \newcommand{\mnote}[1] {   \mbox{}\marginnote{\color{red}\footnotesize#1} }   And I use it for example like this:  \subsection{Differentiable Manifold} \mnote{This is the central object in differential geometry.}A differentiable manifold is   but lo and behold, this has the unpleasant effect of adding white space before the letter of the paragraph:    How can I restore proper alignment for the initial letter of the paragraph?


Will extracting data from salesforce remove all data from salesforce

If I extract data from salesforce for an object using dataloader.io or dataloader, would it remove data too for that object from salesforce.


Questions can be merged into other questions.   What is a merged question? When should questions be merged? Who can merge questions? How do I request it? What happens to merged posts? Anything else I should know about merged questions?


Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$

Any hints on how I can prove the inequality:     $$|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$$   Thank you.


Example of decreasing sequence of sets with first set having infinite measure

I was wondering if someone could please give me an example of a sequence of decreasing sets where the first set has infinite Lebesgue measure; i.e., $\{B_{n}\}_{n=1}^{\infty}$ such that $m(B_{1}) = \infty$ but $m(\cap_{n=1}^{\infty} B_{n}) \neq \lim_{n \to \infty}m(B_{n})$?  thank you.


How do I make all subdomains to redirect to the domain directly in nginx?

I want to redirect url's like:  to   How do I do this?


Looking for information about a problem of a least subset of vectors modulo 2 summing to another vector

I'm quite interested in the following algorithmic problem, on which I can't find any information. Phrased as a decision problem:  Given a set of vectors $V$ in $\text{GF}(2)^n$, a vector $\mathbf u$ in $\text{GF}(2)^n$, and an integer $k$, decide whether there exists a subset $S \subseteq V$ such that $|S|\leq k$ and  $\sum_{\mathbf v\in S} \mathbf v = \mathbf u$.  Note that despite sounding similar to the subset sum problem, it's actually quite different – in particular without the $|S|\leq k$ restriction it's basic linear algebra. My attempts to google the problem have failed so far. Is this a problem already explored in some papers? Is it equivalent to another well-known problem? Is it solvable by a practical algorithm? Is it NP-complete? I would be surprised if there was no literature about this problem at all given the short formulation. What I figured out by myself is that this problem could be polynomially reduced to the problem of  Given a set of vectors $V$ in $\text{GF}(2)^n$, a vector $\mathbf u$ in $\text{GF}(2)^n$, and an integer $k$, decide whether there exists a subset $S \subseteq V$ such that the vector $\mathbf u+\sum_{\mathbf v\in S} \mathbf v$ consists of at most $k$ ones.  Maybe this one is better-known?


I need to parse an html so any one tell me how to do this in objective-c?


Multiplication of adjacency matrix of two graphs

Consider two $N \times N$ adjacency matrices $A$ and $B$  belonging to different graphs(unweighted and undirected). What does their product $AB$ represent? I know that the powers of the adjacency matrix gives the number of paths between any two vertices of length equal to the power. But I am having trouble extendeding this logic to the above problem


Unable to SSH to my virtual machine via Windows Power Shell ISE

Well, I have a Linux virtual machine running in my vmWare. And I would actually love to use my Linux in Windows Power Shell. So I usually use it by doing an SSH to my VM. Recently I came across the "Windows Power Shell ISE" where you can have the feature of opening multiple tabs and other cool stuff.  Here comes the actual problem, when I try to do SSH to my virtual machine, the SSH Operation is being stucked and it is not showing me any further console or message. I am having an SSH Client that comes with GIT, Windows 8.1 and vmWare Workstation 10.  PS C:\> ssh esis@192.168.255.142 ssh : Warning: Permanently added '192.168.255.142' (RSA) to the list of known hosts. At line:1 char:1 + ssh esis@192.168.255.142 + ~~~~~~~~~~~~~~~~~~~~~~~~     + CategoryInfo          : NotSpecified: (Warning: Perman...of known hosts.:String) [], RemoteException     + FullyQualifiedErrorId : NativeCommandError


QGIS Spatial join many points to single vector

I've got two shape files, one contains many point coordinates and the other vector shapes. There are many point coordinates contained within each vector shape.  I would like to perform a spatial join and create a new shapefile of the coordinates but with the attributes of the overlying vector shape.  QGIS spatial join does not seem to work for this. Any ideas? Also setting up a spatial database would be the ideal solution but is not possible in the time frame required.  Thanks Richard


I have a single layer of polygons (drawn around every zip code). I have a CSV file with territory numbers and the zip codes in each territory. I joined these and was able to color each territory (multiple zip codes) instead of each individual zipcode. What I'd like to do now is get rid of the zip code boundaries to only have the territory boundaries, but I can't figure out how to do this.


For curve secp256k1 prime modulus is $2^{256}-2^{32}-977$ and order is smaller number but has near half of starting bits set. If I draw number to be private key, it must be less than order. All field operations are modulo prime modulus and it means they must be smaller than modulus but can be  >= order? (or not?). Coordinates of public key point can exceeds order? A very interesting case is in signing and verifying: in pseudocode:  is modulo order.  * if (nonce outside range [1, order-1]) return false  * p = nonce * G  * r = p.x % order  * if (r == 0) return false  * s = nonce^-1 * (msgHash + r * privateKey) % order  * if (s == 0) return false  * s = min(s, order - s)  This means, operations are done, first modulo modulus p, next modulo order?


What does it mean to be in the fast lane in California?

I don't think I've ever understood this.   I travel frequently across the State of California by car.  And I often take the highway to get to many places.  One thing I don't understand is how fast lanes and slow lanes work.  I was recently travelling on a fast lane near San Francisco driving at the speed limit, when I noticed a cop who was travelling behind me honk at me, presumably because I was going slowly? I noticed there was a long line of cars behind me.    So I moved into the slow lane.  But even weirder is that cars in the slow lane drive at the speed limit, and cars that drive in the fast lane drive way past the speed limit, even cops.  And I have never seen anybody get arrested for going faster than the speed limit, except for really fast drivers.  So I don't understand, even with 6 years of driving throughout California under my belt.  I understand the fast lane is for fast cars, but doesn't driving at the speed limit constitute fast? I really don't understand.  I talked to a local officer and they said that if there are cars tailgating you or lining up behind you, you should change lanes to a slower one, but if I'm already driving at the speed limit, how can I go any faster?


Estimate ARMA coefficients through ACF and PACF inspection

How do you estimate the appropriate forecast model for a time series by visual inspection of the ACF and PACF plots? Which one (i.e., ACF or PACF) tells the AR or the MA (or do they both)? Which part of the graphs tell you the seasonal and non-seasonal part for a seasonal ARIMA?  Consider the ACF and PCF functions displayed below.  They are from a log transformed series that's been differenced twice, one simple difference and one seasonal (, ).  How would you characterize the series? What model best fits it?


To be specific, I have a solid background in college level math but I feel that I have trouble to understand what is number theory. As a first approximation, number theory studies integers. But it is of course not a complete answer. Somebody told me number theory in general studies "arithmetical properties" in algebraic systems. But this is not an answer for me but merely a paraphrase, since number theory=arithmetic. So what exactly number theory?  Let me put my question in another way, I cannot distinguish algebra from number theory.  Let me take geometry and topology as an example. These two areas are of course highly correlated. But I think I understand the difference: when we talk about geometry, the manifold should be equipped with metric. And curvature is extremely important in geometry. My understanding may be shallow here. But at least I find some key features like "metric", "curvature" geometrical but not topological.  But what's going on for number theory? I will greatly appreciate that someone can give a one sentence answer to distinguish number theory from algebra.  Edit: This question was marked as a duplicate of the question:  Subjects studied in number theory  They are similar but I think we are asking a question from different levels. I'm familiar with the basic number theory research subject such as prime distribution, zeta function, diophantine equation, etc.   But for the higher level number theory especially algebraic number theory, I fail to understand the key difference between number theory and general algebra.   For example, let me quote class field theory from wikipedia: "In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields and function fields of curves over finite fields and arithmetic properties of such abelian extensions." After reading this, I will say uh-oh, why abelian extensions is number theory? Wouldn't it be algebra? What properties would be considered as "arithmetic property"?


How do I use the ampersand (&) inside a foreach or conditional (or other group/environment) when building tables?

I am trying to build a table, and inside the tabularx environment I would like to have a loop, something like (here is a MWE):  \documentclass[10pt,a4paper]{article} \usepackage{tabularx} \usepackage{tikz} \newcommand{\nRows}{5} \begin{document}   \begin{tabularx}{\textwidth}{@{}>{\raggedright}p{2.2cm}@{}>{\raggedright}X@{}>{\raggedright}X@{}>{\raggedright}X@{}>{\raggedright}X@{}}     \foreach \r in {1,...,\nRows}{  % https://stackoverflow.com/questions/2561791/iteration-in-latex         \textbf{column1} & two & three & four & five      } \end{tabularx}  \end{document}   This doesn't work, because the ampersands (&) are causing problems. If I escape the &s, then the entire line gets printed in the first column, along with the literal ampersands, kind of like:  \documentclass[10pt,a4paper]{article} \usepackage{tabularx} \usepackage{tikz} \newcommand{\nRows}{5} \begin{document}   \begin{tabularx}{\textwidth}{@{}>{\raggedright}p{2.2cm}@{}>{\raggedright}X@{}>{\raggedright}X@{}>{\raggedright}X@{}>{\raggedright}X@{}}     \foreach \r in {1,...,\nRows}{  % https://stackoverflow.com/questions/2561791/iteration-in-latex         \textbf{column1} \& two \& three \& four \& five      } \end{tabularx}  \end{document}   This yields:  |column1 &      | | | | | two & three & | | | | | four & five   | | | |   Whereas what I want is:  |column 1 | two | three | four | five | |column 1 | two | three | four | five | |column 1 | two | three | four | five |   ....  Any ideas on how I can achieve this? I'm actually NOT looking to make identical rows - the rows will be different. This is just a MWE. Thanks!  Edit: I have tried implementing Herbert's answer as recommended in the comments section. It results in no output - just a blank PDF. Here is how I implemented it:  \documentclass[10pt,a4paper]{article} \usepackage{tabularx} \usepackage{tikz} \newcommand{\nRows}{5}  \makeatletter \newtoks\@tabtoks \newcommand\addtabtoks[1]{\@tabtoks\expandafter{\the\@tabtoks#1}} \newcommand*\resettabtoks{\@tabtoks{}} \newcommand*\printtabtoks{\the\@tabtoks} \makeatother  \begin{document}      \resettabtoks     \foreach \r in {1,...,\nRows}{  % https://stackoverflow.com/questions/2561791/iteration-in-latex         % \textbf{column1} \& two \& three \& four \& five          \addtabtoks{\textbf{column1} & two & three & four & five \\\hline}%     }  \begin{tabularx}{\textwidth}{@{}>{\raggedright}p{2.2cm}@{}>{\raggedright}X@{}>{\raggedright}X@{}>{\raggedright}X@{}>{\raggedright}X@{}} \printtabtoks \end{tabularx}  \end{document}   Any ideas on what I am doing wrong? Thanks!


Placing labels equidistant from a line segment

I have a display of similar triangles - one inscribed in another.  2.5mm below one line segment, the labels C and C_1 are positioned.  Actually, 2.5mm below the line segment, the centers of the nodes for C and C_1 are positioned.  The subscript on C_1 is preventing them from being equidistant from the line segment.  How do I make them equidistant?  \documentclass{amsart} \usepackage{amsmath} \usepackage{amsfonts}  \usepackage{tikz} \usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}   \usepackage{pgfplots} \pgfplotsset{compat=1.11}   \begin{document}     \begin{tikzpicture}  \coordinate (A) at (0,0); \coordinate (B') at (50:7.5); \path[name path=ray_k] (A) -- (B'); \coordinate (C') at (15:7.5); \path[name path=ray_ell] (A) -- (C');   %This command labels a point "B" 3.75cm from A on ray $k$. \coordinate (B) at (50:{15/4}); \draw (A) -- (B);  %These commands label the projection of AB onto \ell "C."  A line segment is drawn between %B and C, and a right-angle mark is placed at C. \coordinate (C) at ($(A)!(B)!(C')$);  \draw (B) -- (C);  %These commands draw a right-angle mark at C. \coordinate (U) at ($(C)!3mm!-45:(A)$); \draw (U) -- ($(C)!(U)!(A)$); \draw (U) -- ($(C)!(U)!(B)$);   %These commands draw an invisible line segment perpendicular to ray k from B to %ray $\ell$. The intersection is labeled C_1. \path[name path=perpendicular_line_segment_from_B] (B) -- ($(B)!3.5cm!90:(A)$); \coordinate[name intersections={of=perpendicular_line_segment_from_B and ray_ell, by={C_1}}];   %The following commands define B_1 as the intersection of k and a line segment %perpendicular to $\ell$ through C_1. A line segment is drawn between %B_1 and C_1, and a right-angle mark is placed at C_1. \path[name path=perpendicular_line_segment_from_C_1] (C_1) -- ($(C_1)!4cm!90:(C')$); \coordinate[name intersections={of=perpendicular_line_segment_from_C_1 and ray_k, by={B_1}}]; \draw (C_1) -- (B_1);  %These commands draw a right-angle mark at C_1. \coordinate (U_1) at ($(C_1)!3mm!-45:(A)$); \draw (U_1) -- ($(C_1)!(U_1)!(A)$); \draw (U_1) -- ($(C_1)!(U_1)!(B_1)$);   %This command draws the two sides of the triangle with a common vertex A. \draw (A) -- (B_1); \draw (A) -- (C_1);    %These commands draw an invisible line segment 2.5mm below AD for labels C and C_1. \coordinate (A_shift_for_labels) at ($(A)!2.5mm!-90:(C_1)$); \coordinate (C_1_shift_for_labels) at ($(C_1)!2.5mm!90:(A)$); \path[name path=path_for_labels_C_and_C_1] (A_shift_for_labels) -- (C_1_shift_for_labels); \coordinate (C_below) at ($(C)!-0.75cm!(B)$); \path[name path=path_from_B_to_C_below] (B) -- (C_below); \coordinate (C_1_below) at ($(C_1)!-0.75cm!(B_1)$); \path[name path=path_from_B_1_to_C_1_below] (B_1) -- (C_1_below); \coordinate[name intersections={of=path_for_labels_C_and_C_1 and path_from_B_to_C_below, by={C_label}}]; \coordinate[name intersections={of=path_for_labels_C_and_C_1 and path_from_B_1_to_C_1_below, by={C_1_label}}]; \node[green] at (C_label){$C$}; \node[green] at (C_1_label){$C_{1}$};  \end{tikzpicture}  \end{document}


I am trying to create a search form using javaFx and MySQL. But I get an Error when I run this code. java.lang.NullPointerException At row 55 String firstName = fname1.getText(); Maybe I missed something Please help me. public class FilteredEmployees implements Initializable {                @FXML         private TextField fname1;          @FXML         private TableView<Employee> table;                  @FXML         private TableColumn<Employee,String> fname;                    String firstName = fname1.getText();          String lastName = lname1.getText();                 public ObservableList<Employee> data = FXCollections.observableArrayList();              @Override         public void initialize(URL location, ResourceBundle resources) {                        try{                 String sql = "SELECT * FROM `employee` WHERE (fname LIKE '%?%') or (name LIKE '%?%')";                 Connection con = DBInfo.getConnection();                 PreparedStatement preparedStatement = (PreparedStatement)con.prepareStatement(sql);                 preparedStatement.setString(1, firstName);                 preparedStatement.setString(2, lastName);                                                                 ResultSet rs = preparedStatement.executeQuery();                                  while(rs.next()){                                      data.add(new Employee(rs.getInt(1), rs.getString(2), rs.getString(3),                              rs.getFloat(4), rs.getInt(5), rs.getString(6)));                                      }                                  con.close();             }catch(SQLException e){                 e.printStackTrace();             }                 }


How to show that $x^6-72$ is irreducible over the rationals?

An exercise states to (try to) prove that the polynomial $x^6-72$ is irreducible over the rationals.    As $72=2^33^2$, we cannot apply Eisenstein criterion without any additional trick. I was wondering if there is a neat way to show that this polynomial is irreducible? The only thing that comes to my mind is to deal with undefined coefficients and then solve polynomial systems, but maybe there is a more conceptual way?   [That there are no linear factors is obvious. Reductions modulo $2$ and $3$ give $X^6=0$. Reduction modulo $p=73$ gives (partial) factorization $X^6+1=(X^2+1)(X^4-X^2+1)$, but I am not sure if this  information is of any help here.]


While running  sudo apt-get update  it gives me the following error  alika@vilnisi:~$ sudo apt-get update [sudo] password for alika:  Hit:1 http: //deb.playonlinux.com precise InRelease Hit:2 http: //archive.ubuntu.com/ubuntu bionic InRelease                                      Ign:3 http: //ppa.launchpad.net/glasen/freetype2/ubuntu bionic InRelease                      Get:4 http:/ /archive.ubuntu.com/ubuntu bionic-updates InRelease [83,2 kB]                                                                            Hit:5 https: //dl.winehq.org/wine-builds/ubuntu bionic InRelease                                                                                Err:6 http: //ppa.launchpad.net/glasen/freetype2/ubuntu bionic Release                                                                                404  Not Found [IP: 91.189.95.83 80] Get:7 http: //archive.ubuntu.com/ubuntu bionic-backports InRelease [74,6 kB]             Get:8 http: //archive.ubuntu.com/ubuntu bionic-security InRelease [83,2 kB] Reading package lists... Done                                      E: The repository 'http:// ppa.launchpad.net/glasen/freetype2/ubuntu bionic Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.


Problem relating to circumscribing the escribed sircles

The triangle DEF circumscribes the three escribed circles of the triangle ABC. I have to prove that  $$\dfrac{EF}{a \cos A} = \dfrac{FD}{b \cos B}= \dfrac{DE}{c \cos C}.$$ Also, point D is opposite to A. E is opposite to B. F is opposite to C  I am not able to find the angles of the triangle DEF. Help me


For every real number $a$ there exists a sequence $r_n$ of rational numbers such that $r_n$ approaches $a$.

How to prove that for every real number $a$ there exists a sequence $r_n$ of rational numbers such that $r_n \rightarrow a$.


Why is the plural of “deer” the same as the singular?

Why is the plural version of deer identical to the singular version?  If mouse became mice, then why did the singular deer not change to something else in the plural?