Invisible region on screen is blocking mouse cursor

In the bottom right corner of my Macbook Pro (running MacOS 10.15.3 Catalina with a second screen connected as main), sometimes, there is a region (invisible) where I just can't move the cursor to. I need to restart the MacBook Pro to let me access the region with my mouse cursor. The cursor just won't pass this region, just as if the screen has ended there. I have added a screenshot below and drawn the region. I read about applications that might behave weird and cause such an issue, but the problem persists even when all apps are closed. What could this be? Are there any known issues? Or yet better, known solutions? ... Update 1:  I have appended a screenshot of my arrangement and drawn a yellow box of the area which is not accessible.  Update 2:  The cursor is blocked from reaching the region in the third screenshot (I cannot reach the Files folder for example).  Update 3:  Today (2020/05/25, using Mac OS 10.15.4), the problem re-occured, but the non-accessible area has changed to the top-left, with the available height only being as much as the system menu and a width of 90%. (For example, I have a window in full height/width and I can no longer move the mouse cursor to the 'minimize' or 'close' window buttons).  Update 4:  2020/10/30, (using macOS 10.15.7) I returned my 15" MacBook Pro, because I thought the problem only appears on them. I encountered the same problem on a 13" MacBook with completely different apps installed. I suspect more and more that it's a very rare (race) condition / scaling bug in the OSX core that handles multiple display screens. The problem also happens on macOS 11.1 Big Sur.      Note: In the , someone has posted a video screenshot of what happens.


I would like to show user friendly whiptail menu.  My goal in whiptail is this:  Choice1 Choice2 Choice3 Choice4   I have array consist of:  Choice1 Choice2 Choice3 Choice4   I run array through loop for like this:  for value in ${value[@]} do     echo "$value" done   I could not add whiptail inside echo because I get 4 another menus.  I tried script like this:  $val=$(whiptail --title "xx" --menu "choose" 16 78 10 for value in ${value[@]} do     echo "$value" done 3>&1 1>&2 2>&3)   After run above mentioned script my shell looks horrible.  shell after script:    Is there anybody who solve my problem?


Link up the excellent search engine that gives "Questions that may already have an answer" with the search box

The search engine that works behind the scenes to generate the "Questions that may already have your answer" is staggeringly amazing; even this first draft at a not very good title brings up exactly the question I was going to ask as the first result:   On the other hand, the search bar doesn't do quite such a good job:   So I'd like to propose that a little of the "New question screen" magic go into the search bar. Or to propose this in a little less wishy-washy way; that (in addition to normal search results) top results from the "Questions that may already have your answer" box go into the search box as if the search had been phrased as a new question. This will help casual users who may search but may not (attempt to) ask. This will additionally be helpful for experienced users because (due to draft saving) you cannot have two independent new question pages open at once. As such, I can't use the new question-based search while also drafting a question


Would you please help me with adjectives?

Could anybody possibly kindly explain me what is the difference between these?- in meaning.  They are all 10 years old  They are all ten-year-olds


What is the proof for kinetic energy $= mv^2/2$?

What is the proof for kinetic energy $= \dfrac{mv^2}{2}$?


What's the best way to do a backwards loop in C/C#/C++?

I need to move backwards through an array, so I have code like this:  for (int i = myArray.Length - 1; i >= 0; i--) {     // Do something     myArray[i] = 42; }   Is there a better way of doing this?  Update: I was hoping that maybe C# had some built-in mechanism for this like:  foreachbackwards (int i in myArray) {     // so easy }   Update 2: There are better ways. Rune takes the prize with:  for (int i = myArray.Length; i-- > 0; ) {         //do something } //or for (int i = myArray.Length; i --> 0; ) {     // do something }   which looks even better in regular C (thanks to Twotymz):  for (int i = lengthOfArray; i--; ) {         //do something }


Can you explain why it is 6 * (3/9) ,Why don't we add 5kΩ resistance too, How is this a current division,what is the formula for this.Thanks..


Is export of QGIS layer styles to mapnik possible?

Is it possible to export layer styles to mapnik xml from QGIS?  As I understand it, it used to be possible once by means of quantumnik plug-in, which is discontinued now.  I see this issue  two years ago but to no avail.  Is that it? No other ways to do it? I refuse to believe it is not possible.  It's rather frustrating to have a map ready in QGIS and to be unable to export the styles to mapnik sitting on the same data!  You may call it a "duplicate question", but 4 years have passed since it was asked last time, so maybe something has changed?


How co prime numbers can be used to form any number beyond a number

Suppose we have two co prime numbers a and b. Then it is always possible to form any number greater than or equal to a*b - a - b +1 by using the given co primes only that is  ax + by where x and y will be non negative integers. I can't seem to find the logic behind it? How it is happening and why?


Topology generated by those subsets of $X$ which are preserved by images of nets in that subset by a function

$\mathbf {The \ Problem \ is}:$ Let, $\mathcal N(X)$ be the set of all nets in a topological space $X$, and $\mathcal P(X)$ be the power set of $X.$ Let, $L : \mathcal N(X) \to \mathcal P(X)$ be a function such that $L\{x_{\sigma}\}_{\sum} = L\{y_{\gamma}\}_{\Gamma}$ whenever one of $\{x_{\sigma}\}_{\sum}$ and $\{y_{\gamma}\}_{\Gamma}$ is a subnet of the other . Define,  $\tau =\{V \subset X | L\{x_{\sigma}\}_{\sum} \subset V^c \text{for every net}  \{x_{\sigma}\}_{\sum}    \text{in} V^c\}$ Show that $\tau$ is a topology on $X.$ $\mathbf {My \ Approach }:$ Actually, I am having problem in showing that $V_1 \cap V_2$ is in $\tau$ when both of them are in $\tau.$ I tried by contradiction, let $\{x_{\sigma}\}_{\sum}$ is in $(V_1 \cap V_2)^c$  and let there exists $p \in J=L\{x_{\sigma}\}_{\sum}$ such that $p \in V_1 \cap V_2$ , then $L\{p\} \subset J \cap V_1 \cap V_2$ as $\{p\}$ is a constant net. Then, I tried to show there must be a subnet $\{y_{\gamma}\}_{\Gamma}$ of $\{x_{\sigma}\}_{\sum}$ such that $K=L\{y_{\gamma}\}_{\Gamma}$ is disjoint from $V_1\cap V_2.$ But, I can't show this . A small help is very much required at this time, thanks in advance .


A very urgent question :  Please simplify this logic expression for me with helping boolean algebra :  A'C'D + A'BD + BCD + ABC + ACD'  I know that must use consensus theorem .  my solve :  STEP 1 : Terms 1 & 3 ---eliminate---> Term 2  STEP 2 : Terms 3 & 5 ---eliminate---> Term 4  STEP 3 : Terms 2 & 4 ---eliminate---> Term 3  But truth table said step 3 is incorrect . but why ?   please tell me why step 3 is Wrong ?  and tell me What is the simplest form of it ?


I use mouse with left-hand. My system is shared with other people who are right handed. So, I need frequently to switch mouse button.  I would like to know how to swap mouse button using AppleScript? I am using default mouse come with my iMac machine.


Blender gets very slow to draw a scene having large number of plane?

I have a very simple python script to generate planes in the scene. I want to generate 50000 planes in a scene, to compensate for unavailability of POINT primitive, so that i can render a point cloud.  It runs at a good pace till 2000 th plane is added , then starts slowing down, and gets very slow. My computer's config is - i7 3.4 GHz, 16GB RAM, GeForce 9800 GTX graphic card.  here is the python script-  import bpy  from math import * import random  for i in range(2000):     x=random.uniform(0,100)     y=random.uniform(0,100)     z=random.uniform(0,100)     bpy.ops.mesh.primitive_plane_add(location=(x,y,z))     #bpy.context.active_object.scale=(100,100,100)     print("\n",i)   Any Help on  why it is slowing down? How can this be fixed ? Any alternate approach to render point cloud in blender? would be much appreciated...  Thanks for your time and attention


Why is an accepted answer not counted in the Score of a Next tag badge?

Why is the score of a tag not counted after you get an accepted answer?  If I answer a question with a support tag, why does this not count in the Next tag badge?


Prove that if $\langle Tx,x\rangle =0$ for all $x \in X$, then $T = 0$

This is exercise 10 in section 3.2 of Kreyszig's Introductory Functional Analysis with Applications:     (Zero Operator): Let $T:X \to X$ be a bounded linear operator on complex inner product space $X$. If $\langle Tx,x\rangle =0$ for all $x \in X$, show that $T=0$.    I had solved little kindly guide me further       Solution:   Let $\langle Tx,x\rangle =0$ for all $x \in X$. Let $x=u+av$ where $v,u$ belong to $X$ and $a$ be the scalar then  $$ \langle Tx,x\rangle =\langle T(u+av), u+av\rangle $$ since $T$ is linear then  \begin{align} \langle Tx,x\rangle &=\langle Tu+aTv, u+av\rangle \\     & =\langle Tu,u\rangle +\overline{a}\langle Tu,v\rangle +a\langle Tv,u\rangle +a\overline{a}\langle Tv,v\rangle \\     & =\overline{a} \langle Tu,v\rangle +a\langle Tv,u\rangle  \end{align}


Is there any nice explanation of why the complex exponential function has no roots in the complex plane?

Here I am not looking for an explanation that uses basic properties that complex exponential function has, such as $e^{z+w}=e^ze^w$ or $e^0=1$ or any other, if this fact can be explained by using those basic properties.  I am seeking for some explanation that has to do with the positions and number of the roots of the truncated exponential function and suppose that we only know how Taylor series for $e^z$ looks like, so in fact I seek for an explanation in which we do not know that complex exponential function has the basic properties it has.  Suppose that we truncate complex exponential function and define a function $e_{k}{(z)}=\sum_{i=0}^{k} \dfrac {z^i}{i!}$.  Because of the fundamental theorem of algebra we have that $e_{k}{(z)}$ has $k$ complex roots so bigger the $k$ the more roots we have.  But when we pass to the limit $\lim_{k\to\infty} e_{k}{(z)}=e^{z}$ somehow all the roots "disappear", and instead of maybe expected an infinite number of roots we have none.     How to explain this?


Command activated items of negative energy ray or Repair light damage

A command activated item costs caster level X spell level X 1800 (for an instantaneous spell).  So imagine this: A belt or something of negative energy ray (caster lvl 1, spell lvl 1 x 1800=1800) and a caster with tomb tainted soul allowing him to use the ray to heal himself as a standard action.  Or a construct (intelligent item) with a command activated item of repair light damage (caster lvl 1, spell level 1 x 1800=1800), once again this creature can heal itself as a standard action.  But looking at a spell like cure light wounds, there is no way you would make an item of cure light wounds as command activated costing only 1800.  So I suppose my question is balance based. It is obvious to me that an item that can cure just about anyone for only 1800 is out of the question, but an item that can heal because you took a feat or because of your creature type I could reasonably see costing 1800 as standard actions are precious in combat.


Example code required for how to access embedded .Net image resources in C#

It's very easy to mark an image file to become an embedded resource however how does one access the image thereafter. Please can I have some example code?


I have a slide show use setInterval 5sec, each slide should stop 5 sec.  When user click previous button, slide will go back previous image.  My problem is when user click previous, time still counting. (previous image only stop 3sec not 5sec)  Is any way to reset time when user click?  setInterval(function(){   //start slide... },5000);   $('#previous').click(function(){     //go back to previous slide and reset time });


I am creating case through trigger,but i am getting the   UNABLE_TO_LOCK_ROW, unable to obtain exclusive access to this record:  can anybody help me...


Probability of a player winning before another

Given a 7 sided dice, 2 players roll it independantly simultaneously and when a player rolls a '6' he gets a prize.  What is the probability of the first player getting a prize before the second?  So my solution is to sum over all the turns j in which player 1 could win, and make the second player lose all these turns:  $$P(A) = \sum_{i=1}^{\infty}(6/7)^{j-1}*(1/7)*(6/7)^j = 0.461$$ My question is if my solution is correct, and if so, why is the probability so low? It seems to me that either player 1 wins before the 2nd or the other way around, and the probability of them playing forever is 0, so it should be 0.5?


Drawing arrows in the following latex picture

\documentclass[a4paper,12pt,twoside]{report} \usepackage{pgf,tikz} \begin{document}  \begin{figure}[hbt!]     \begin{center}          \begin{tikzpicture}[scale=0.95,             thick,             acteur/.style={                 circle,                 fill=black,                 thick,                 inner sep=2pt,                 minimum size=0.2cm,scale=0.65             }             ]              \node (a1) at (0,0) [acteur,label=left:\footnotesize{}]{};                           \node (a2) at (1.5,0)  [acteur,label=left:\footnotesize{}]{};                                     \node (a3) at (1.5,1.5) [acteur,label=left:\footnotesize{}]{};                               \node (a4) at (0,1.5) [acteur,label=left:\footnotesize{}]{};                                       \node (a5) at (.75,3) [acteur,label=left:\footnotesize{}]{};                                                \draw [green]  (a1) -- (a2);              \draw  [blue](a2) -- (a3);              \draw [green]  (a3) -- (a4);             \draw  [red](a4) -- (a1);             \draw [blue] (a4) -- (a5);             \draw [red]  (a5) -- (a3);         \end{tikzpicture}     %   \caption{ Candidate for maximizing algebraic connectivity in $\mathcal{B}_4$}\label{F2}     \end{center} \end{figure}  \end{document}  In this graph, I want to place arrows in the green edges, that is, I want to replace the green edges with directed edges with green color. How to do that.


What similarity index should I use with relative abundance data for a PERMANOVA?

I have data on the relative abundance (0 to 1 ratio) of 5 land covers for different landscapes (analogous to species composition). These landscapes are grouped into three geographic areas and I want to test for differences in the composition of the landscapes between those three areas and between two years (I have the compostion of land covers for 2000 and 2010). For this I thought to make a permanova with a year nested in the geographic region. However, I don't know what distance of dis(similarity) I should use to test for differences between groups. Is it okay to use Bray-Curtis simmilarity index or will Spearman-rank correlation be better? Do you recommend any other index?


Set of limit points of a subset of a Hausdorff space is closed.

Let $X$ be a Hausdorff space and $A\subset X$.  Define $A'=\{x\in X\mid x\text{ is a limit point of }A\}$.  Prove that $A'$ is closed in $X$.  Relevant information:  (1.) Every neighborhood of a point $x\in A'$ contains a point $y\in A'$ distinct from $x$ (in fact, in a Hausdorff space, every neighborhood of $x$ contains $\infty$-many points of $A$ distinct from $x$)  (2.) In a Hausdorff space, every sequence has a unique limit.  On first glance, it should be an easy proof, but I've made little progress.  I was planning on showing $\overline{A'}=A'$.  Firstly, $A'\subset \overline{A'}$ trivially.  To show $\overline{A'}\subset A'$, proceed by contradiction.  Assume there exists $x\in\overline{A'}$ such that $x\not\in A'$.  This should yield an easy contradiction but I don't see it.  In particular, I'm unsure if the fact that $x\in\overline{A'}$ implies that there actually exists a sequence in $A'$ converging to $x$.  By (2) we know all sequences have unique limits, but do we know that elements in the closure are limits of sequences?  If this is true, it should yield an easy contradiction.  Any help?


The M1 and M2 lines in Lille, France have a confusing . It's 7 days per week, but it looks like it's "running" basically 24h hours per day (minus some ten-minute delay). I never took the metro later than 11 PM when I was in Lille last year, but people told me that it stops just before midnight. But... it looks like it starts right back up again immediately, after about 10 minutes.  What are the actual hours of the Lille M1 and M2 lines? I have a hard time believing that they're 24/7...


Does Ubuntu support touchscreen laptops?

Is it possible to use a touchscreen display on a laptop with Ubuntu, as in like, being able to scroll with my touchscreen and stuff?


Why doesn't the alien kill Ripley in the shuttle craft?

In the last scene of Alien, Ripley escapes in a shuttle craft. She screams when she sees that the alien is onboard. Why didn't the alien kill her immediately when she boarded the shuttle craft? Is it sleeping? How deaf would a 'perfect' species have to be to not hear someone scream at the top of her lungs right next to you?


$\lim_{n \to \infty} \mid a_n + 3(\frac{n-2}{n})^n \mid^{\frac1n} = \frac35$. Then find $\lim_{n \to \infty} a_n$.

Let $\{a_n\}$ be a sequence of real numbers such that $$\lim_{n \to \infty} \mid a_n + 3(\frac{n-2}{n})^n \mid^{\frac1n} = \frac35$$  Then find  $\lim_{n \to \infty} a_n$.  Tried very hard yet not able to crack it. Help Needed.  Anyone able to do the sum??


Ubuntu 19.04 Disco Dingo umlauts and accents. I have searched, yet not found. Anywhere

I have searched far and wide, yet I am confronted in GNOME on 19.04 with the fact that I cannot get umlauts etc to work. I have 2 kali (KDE) machines, on which I can get it to work quite easily. However, in this case, under Settings - devices - typing column - to find the "compose" key - is not there... I've edited etc/default/console-setup to include  XKBOPTIONS="compose:Shift+AltGr" but I am sort of afraid to reboot, in fear that I might break something. Also it does not seem like the correct way since setting this functionality has been standard on previous versions of ubuntu etc.   This question has been asked many times, and has been solved many times, which is how I solved the umlaut problem on Kali/KDE too (since I am quite new on linux). Have tried linux many times in the past but only now it sticks. Any problems I have had up to now I have been able to solve without asking but this one is beyond me.   Am going to reboot now anyway, I guess I will have to.   If I don't return shortly, something broke. Otherwise, I'll be back soon ;-)  Thanks!  returned, system did not break aaannndd.... trying... e  No joy. Pressing the AltGr key just shows the firefox menu bar.  I'm lost.


Limit exercise from Rudin: $\lim\limits_{n \to \infty} \sqrt{n^2+n} -n$

This is Chapter 3, Exercise 2 of Rudin's Principles.  Calculate $\lim\limits_{n \to \infty} \sqrt{n^2+n} -n$.  Hints will be appreciated.


Would like to ask if someone could help me draw this tree diagram using Latex. Any assistance will be much appreciated. Thanks


Tikz: purely vertical arrow from nodeA.south to nodeB.north

I have the following tikz code  % compilation command: pdflatex --jobname=Diag-f1 Diag.tex \documentclass{book} \usepackage{tikz} \pgfrealjobname{Diag} \begin{document} \beginpgfgraphicnamed{Diag-f1} \begin{tikzpicture}[node distance=3em] \node(G)[rectangle,fill=red!5,draw=red,text width=5cm]{}; \node(H)[below of=G]{H}; \node(H1)[left of=H]{H1}; \node(H2)[right of=H]{H2}; \draw[->](G.south)-|(H1.north); \draw[->](G.south)--(H.north); \draw[->](G.south)-|(H2.north); \end{tikzpicture} \endpgfgraphicnamed \end{document}     but I am not happy with the two arrows going from G.south to H1.north and H2.north. Because of the -| command, there is a spurious horizontal line. How can I achieve the same result without this annoying horizontal line? \draw[->](G.south)--(H1.north); is not a solution. There are available tricks but I may have missed an obvious solution here.


Tax questions - Working from India for US company

I am working from India for a US company and as per my knowledge I am not liable to pay any tax to US govt.  My first question is can I have them deposit my pay check in US account without any deduction of taxes. I think I need to fill W8-BEN form for this. Please advise.  My second question is what kind of taxes I need to pay in India as I am working as a independent contractor ? DO i need to fill any paperwork and how these taxes will be calculated ?  Please advise.


How to transfer data between a replacement SSD and old SSD?

My plan is to replace my laptop's current 256GB SSD with a 1 or 2 TB SSD. This means that the new SSD will be completely empty without any OS, or my data... I am using Windows 10 on the subject computer.  I have the ability to create a "Windows backup Image" (I do this weekly anyway) of my old SSD and put it on one of my external drives and I was hoping to "restore" this backup image onto the new SSD after it is installed into the laptop, so I can resume exactly how I'd left off but with more space. However, does Windows need to already be on that new SSD in order to do this? If so, are there any other solutions which solve the problem of needing to transfer data/OS image from current SSD to new SSD?  Please Note: This is not a request for a software recommendation. I am wondering about the method for which to go about this. For example, is it possible to restore an image to the SSD after the drive has been installed when the computer now has no current OS installed on it? Without an OS, how is this achieved?


Is there any tool in QGIS that traces a line like the trace tool (Editor Toolbar) in ArcGIS? I want to draw a line and trace this line back so that I get the beginning and the end of the line at the same position. Any suggestions?


How can I share my iMac's internet connection with my iPad?

i have an iMac, that has internet access via cable (no WiFi).  I know, that my iMac has Wi-Fi access point.  How can I share the internet connection of iMac with iPad?


Trademark names that start with a lowercase letter -- do we cap the lowercase letter when it starts a sentence?  E.g.:  iTunes is a hot spot in the app store.  Not: ITunes is a hot spot ...  iPhone sales have plummeted since the inception of the Samsung S5.  Not:  IPhone sales have plummeted since the inception of the Samsung S5.


Include graphic with white background as transparent

I am trying to create a graphic with pstricks and want to include a logo which has some white colored background. But I want this white background to be transparent.  I have tried to change the white background to transparency with gimp and save it as ps file but I think ps cannot deal with transparency. Unfortunately I cannot use png or pdf as far as I know, because I have to use latex -> dvips -> ps2pdf when using pstricks.  Hopefully somebody can help me.  \documentclass{standalone} \usepackage{pstricks} \usepackage{graphicx}  \begin{document} \begin{pspicture}(0,0)(1,1) \psframe[fillcolor=red, fillstyle=solid, linecolor=red](0,0)(1,1) \rput[lb](0,0){\includegraphics[width=1cm]{logo.ps}} \end{pspicture} \end{document}   Since my background is not a simple red filled rectangle, it does not help me to color the white background of the logo in gimp (which would be the most simplest solution).


Command Prompt in Administrator mode doesn't see mapped drives

I am not sure but when I start my Command Prompt in Administrator mode, I can't switch to a mapped drive.  I can do so if I am not in Administrator mode.  Am I missing something simple?


Can I be my own trusted CA via an signed intermediate certificate?

Can I get a certificate from a root CA that I can then use to sign my own web server certificates? I would, if possible, use a signed certificate as an intermediate to sign other certs.  I know that I would have to configure my systems in a certain way with "my" intermediate certificate in order to supply information about the chain of trust to my clients.   Is this possible? Are root CAs willing to sign a certificate like this? Is it expensive?  BACKGROUND  I'm familiar with the basics of SSL as it pertains to securing web traffic over HTTP. I also have a basic understanding of the way the chain of trust works, in that web traffic is secured "by default" if you encrypt with a certificate that has a valid chain all the way back to a root CA, as determined by the browser/OS vendor.  I am also aware that many of the root CAs have begun signing certificates for end users (like me) with intermediate certificates. That may require a bit more setup on my end, but otherwise, those certificates will work fine. I guess this has to do with protecting their all-valuable private key for the CA and the disaster that it would be if i were ever compromised.  EXAMPLES        Now, we are definitely not the size of any of those organizations, but they seem to be doing something like this. It would definitely make the management of these certificates a lot more palatable, especially considering one way we are expanding the reach of our e-commerce platform.


question about contractive and hereditary property

A topological space is $T_B$ if each compact subset  is closed.  A topological space is called a US-space provided that each convergent sequence has a unique limit.  A topological property $\mathcal{R}$ is contractive if $(X,\tau)$ has property $\mathcal{R}$ and if $\tau^{\prime} \subset \tau$, then (A, $\tau^{\prime}$) has property $\mathcal{R}$.  A topological space is called a C- C-space provided that  the  compact subsets  are precisely the closed sets.     Is property C-C , US contractive,  hereditary?      Is property $T_B$  contractive?


Evaluating $\lim\limits_{x \to \infty}x\left(\left(1+\frac{1}{x}\right)^x-e \right)$

I'm trying to find the limit of: $$\lim\limits_{x \to \infty}x\left(\left(1+\frac{1}{x}\right)^x-e \right)$$  I tried to use L'Hôpital but it lead me nowhere. Any ideas?


I've done some searching here and have not found what I'm looking for.  I've got a form that gets filled out, upon submitting it adds it to an SQL database (using PHP). However, if someone puts an apostrophe or single quote, it will blow up...I need to be able to either parse each text field to check for single quotes to escape them out or find some other way for this to work.  Here is my SQL statement...if it helps.  $query = "INSERT INTO workshopinfo (Year, Presentername, email, bio, arrival, title, description, costyn, matcost, schedlimit, additionalinfo, typeofws, verified)" . "VALUES ('$year', '$presentername', '$email', '$bio', '$arrival', '$title', '$description', '$costyn', '$matcost', '$schedlimit', '$additionalinfo', '$typeofws', '$verified')";   So of course a single quote will blow it up, as will a double quote...it fails every time.  There is likely an easy solution to this.


Evaluating the integral $\int_0^\infty\frac{x^3}{e^{ax}-1}dx$

When describing black body radiation in Physics, one comes across an integral of the form $$I(a)=\int_0^\infty\frac{x^3}{e^{ax}-1}dx \tag1$$ for $a>0$. In our lecture, we were given that this integral evaluates to $$I(a)=\frac{\pi^4}{15a^4}$$ without a derivation of this result. While reviewing my course notes over the Christmas break, I came across this integral and have tried to evaluate it myself, but I have not been successful so far. My first step, of course, was to substitute $u:=ax$, which gives us $$I(a) = \frac{1}{a^4}\int_0^\infty\frac{u^3}{e^u-1}du \tag2$$ but beyond that, I'm stuck. I've tried differentiation under the integral sign on the original integral in $(1)$, which lead to the integral $$\int_0^\infty\frac{\log^4 u}{(u-1)^2}du$$ which I also no have no clue how to tackle. I've also thought about using contour integration, but I'm unsure as to what would be an appropriate contour to consider. I know that the integrand has singularities at $z=2\pi ik$ for $k\in\mathbb{Z},k\neq 0$ but I'm not even sure how one would go about calculating the residues at these singularities due to the peculiar form of the denominator, which is unlike any I have previously encountered.  How would one go about deriving that $$\int_0^\infty\frac{x^3}{e^{ax}-1}dx = \frac{\pi^4}{15a^4}$$ is true?


Short story: Man with wings who flew over a farm and was shot down by the farmer

I read this a long time ago as a child. It was in a collection of short stories, maybe some kind of scifi anthology.  It was about a man with wings who flew over a farm and was shot down by the farmer, mistaking him for some bird, I think. His daughter nursed the man back to health, they ended up getting married but he had to cut off his wings. Some time in the future, his wings begin to grow back and he decides to fly but his wings are not strong enough to support him. He ends up falling into a lake (or some body of water) and the story ends.


The school provides services of art teacher. or School provides the services of art teacher. which one is correct


Is there any way to make a hotkey turn the screen off?

How can I make a script (or make some changes) to allow me to turn the screen off in Ubuntu (12.04) whenever I want, the way thevscreen can be turned off in Cellphones?  And how can I make a combination of keys (a shortcut) to execute that script?  I want to conserve power.  I've seen this question    but there is no hotkey for it.  Moreover, in the answer, it is said that there are many ways to accomplish this so I'd like to know more.


LaTeX: optional arguments with square brackets

LaTeX is trying to add a missing $ that I don't want to the following code. Minimal working example:  \documentclass[letter,12pt]{article}  \newcommand{\monkeyBeans}[2][]{   \parbox{4in}{#1} }  \begin{document}  \parbox{4in}{$[a, b]$}   \monkeyBeans[$[a, b]$]{yo monkey}  \end{document}   If I try any of the following lines in my document instead of the call to monkeyBeans, there is no error:  \parbox{4in}{$[a, b]$}  \monkeyBeans[yo monkey]{$[a, b]$} \monkeyBeans[$(a, b)$]{yo monkey} \monkeyBeans{$[a, b]$}{yo monkey}   What is the deal with square brackets in optional arguments?


Are my arms pulled outwards when I sit on a rotating office chair?

Suppose I am sitting in an office chair in a room. Now someone just starts to rotate the chair. The chair is now rotating quite fast. I think my arms will be   pulled outwards.  Now from my point of view I am sitting still but the room and chair base is being rotated the same axis. Why do I feel my arms getting pulled still?


In season 7 Cersei attacks      House Tyrell and gets all their gold,   in order to pay the debts to the Iron Bank and then ask their help to hire some mercenaries. But before the gold is back in King's Landing      they're attacked by the Dothraki and a dragon, and (apparently) lose the gold.   It made me think that the support from the Iron Bank was lost too. But, in the last episode, it appears they still have the support of the Bank to hire the mercenaries.  So the question:       Did she recover the gold after the defeat or does the Iron Bank help her without having recovered the gold?


Add an image at footer and show the page numbers using beamer

I want add an image to my footer and then I want show the number of current page / total pages:  So I added this three lines:  \setbeamertemplate{footline}[text line]{      \includegraphics[width=\paperwidth,height=1cm]{footer}      \insertframenumber{} / \inserttotalframenumber\hspace*{2ex}      }   But as result I can't see the numbers.  How can I fix it?  This is my entire configuration of beamer:  \documentclass[smaller]{beamer}  \usepackage{xcolor} \usepackage{comment} \usepackage{multirow} \usepackage{colortbl} \usepackage{xspace} \usepackage{textpos} \usepackage{tikz} \usepackage{csquotes}  \usepackage{graphicx} % already used by beamer \graphicspath{{img/}} \DeclareGraphicsExtensions{.png,.jpg}  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % BEAMER CONFIGURATION - START %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  \hypersetup{pdfpagemode=FullScreen} \beamertemplatenavigationsymbolsempty  \usetheme{Singapore}    % red, quite simple \usecolortheme{orchid}  % Make margines wider \setbeamersize{text margin left=1em,text margin right=1em}  % Select itemization and enumeration style: default, ball, circle % \setbeamertemplate{enumerate subitem}[default] \setbeamertemplate{enumerate items}[square] \setbeamertemplate{itemize items}[triangle]  %%% The navigation bar on top \setbeamertemplate{headline}{} % \setbeamertemplate{headline}[infolines theme]  \definecolor{UofTBlue}{RGB}{0,47,101} \setbeamertemplate{frametitle}{%     \nointerlineskip%     \begin{beamercolorbox}[wd=\paperwidth,ht=2.8ex,dp=.9ex]{frametitle}         \hspace*{1ex}\insertframetitle%     \end{beamercolorbox}% }  \setbeamercolor{structure}{fg=UofTBlue} \setbeamercolor{frametitle}{fg=white,bg=darkgreen} \setbeamercolor{section in head/foot}{fg=white,bg=UofTBlue}    %\makeatletter %\setbeamertemplate{footline} %{ %  \leavevmode% %  \hbox{% %  \begin{beamercolorbox}[wd=1\paperwidth,ht=2.25ex,dp=1ex,right]{date in head/foot}% %%     \usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em} %    \insertframenumber{} / \inserttotalframenumber\hspace*{2ex}  %  \end{beamercolorbox} %  }% %  \vskip0pt% %} %\makeatother  \setbeamertemplate{footline}[text line]{ \includegraphics[width=\paperwidth,height=1cm]{footer}  \insertframenumber{} / \inserttotalframenumber\hspace*{2ex}  }  \end{document}


What are some efficient ways to combine two structures in MATLAB?

I want to combine two structures with differing fields names.  For example, starting with:  A.field1 = 1; A.field2 = 'a';  B.field3 = 2; B.field4 = 'b';   I would like to have:  C.field1 = 1; C.field2 = 'a'; C.field3 = 2; C.field4 = 'b';   Is there a more efficient way than using "fieldnames" and a for loop?  EDIT: Let's assume that in the case of field name conflicts we give preference to A.


We have quite a couple of domains where the rightful owner is us, but the nameserver is managed by a third party (subcontractor), who doesn't allow us to change the zone files.  Thus, we are moving to our new nameservers, which we can manage on our own, namely DigitalOcean's free DNS service.  Is it possible and if yes, what disadvantages would it bring if instead of requesting the nameserver change at the registrar for DO's nameservers, I would request a change for ns1.example.com, then I'd create a CNAME record that ns1.example.com points to ns1.digitalocean.com? Would that work?  In that case, if we ever have to move our DNS service from DigitalOcean to some other service, the registrar wouldn't need to change a hundred domains at once with all the administrative hassle, we could simply modify the abovementioned CNAME record.


Does the Windows 7 Notepad understands the different line-endings of Unix, Mac and Windows?

In versions earlier than 7, Notepad interprets CRLF as a newline. While on Mac/Unix newline is just LF. Have they(MS) added this essential feature in the new Notepad??  PS: Don't have a Win 7 machine around, otherwise would have checked out myself.


markdown editing in comments, 5 minutes only and paragraphs

If I answer as an 'answer' I get the good-looking UI to help me do all the things I want, BUT if I am in comments I am helpless. Would it take much resources to have the same same UI to keep sanity in answers too ?    The other query is, is there a way to test the output/look as we do when framing a question? For people who are not so good at markdown will appreciate if this can be done.   Lastly I tried retext and saw the preview there of the comment till I was happy with. Copying and pasting it there makes it a jumble.   $ aptitude show retext Package: retext                           State: installed Automatically installed: no Version: 5.0.0-1 Priority: optional Section: editors Maintainer: Dmitry Shachnev <mitya57@gmail.com> Architecture: all Uncompressed Size: 417 k Depends: python3-markups, python3-pyqt5, python3-pyqt5.qtwebkit, python3:any (>= 3.3.2-2~) Recommends: docutils-common (>= 0.10-3~), python3-enchant, python3-markdown | python3-docutils, shared-mime-info (>= 0.91) Breaks: retext-wpgen (< 4.0~) Replaces: retext-wpgen (< 4.0~) Description: Simple text editor for Markdown and reStructuredText  ReText is a simple editor for Markdown and reStructuredText markup languages.    ReText supports tabs, live text preview and syntax highlighting. Supported export formats: HTML, ODT, PDF. It is also possible to write custom  export extensions.    It is written in Python using Qt libraries. Homepage: http://retext.sourceforge.net/   Hoping people can help.   The comment in question for now is  but there have been other comments where I had same issues.


In the following: float n1= 3.0; double n2 = 3.0; long n3 = 2000000000L; long n4 = 1234567890L; printf("%f %Lf %ld %ld\n", n1, n2, n3, n4);   3.000000 1.200000 2000000000 1234567890  Why is 1.2 printed for the second value and not 3.0? I suppose maybe I'm screwing up the float prints -- with float, double, and long double, or what's the reason why the above prints an incorrect result? Is this the correct way to print all decimal-types? float n1= 3.0F; double n2 = 3.0; long double n3 = 3.0L; printf("%f %f %Lf\n", n1, n2, n3);


Can't search unanswered questions with multiple tags

I've searched for this specific answer with no luck. I want to be able to filter unanswered questions with [tag1] AND [tag2], but it doesn't seem to work for unanswered.  When I use a link like this:   Even though it has a "+", it still treats it as an OR. I want unanswered questions containing both tags. Is this possible? Unclear if this is a possible bug/feature/ or user error.


Beginner resources for character modelling in Blender 2.8

I'm a beginner in Blender 2.8. I have been following random tutorials on YouTube and even rendered my own project, but they've all been objects, while I started Blender with the aim of modelling characters. And now I feel like I've just been going all over the place and doing whatever looked cool without actually working towards my goal. Where should I start character modelling with Blender 2.8? It'd be really helpful if someone could point me in the right direction and guide me towards useful resources. Thanks!


Custom thumbnailers don’t work on Ubuntu 18.10 and 18.04

Recently I had a bunch of my own scripts for the thumbnails in Nautilus: , , office documents and so on.  Seems like either I’m doing something wrong (thumbnail generation behavior changed), or custom thumbnailes don’t work in latest GNOME at all, even my previous scripts, which worked smoothly on previous versions of Ubuntu.  I’ve done some research, tried to run a simple script (see below) and it didn’t work out.  My test thumbnailer in /usr/share/thumbnailers/z.thumbnailer:  [Thumbnailer Entry] Exec=/home/maximal/thumb.sh %s %i %u %o MimeType=image/webp;image/x-webp   Where /home/maximal/thumb.sh is:  #!/bin/bash echo $0 >> /home/maximal/thumb.log echo $1 >> /home/maximal/thumb.log echo $2 >> /home/maximal/thumb.log echo $3 >> /home/maximal/thumb.log echo $4 >> /home/maximal/thumb.log   Then, when I remove thumbnail cache rm -rf ~/.cache/thumbnails and restart Nautilus nautilus -q, my log file doesn’t contain anything and ~/.cache/thumbnails/fail/gnome-thumbnail-factory contains all the failed thumbs (looks like corrupted/empty PNGs):    So, apparently, Nautilus even didn’t try to execute my thumbnailer script. When I try to run thumb command itself, it works perfectly. For example convert through cwebp|dwebp package:  convert -thumbnail 256x256 file.webp png:file.webp.png   When I wrap this command to a thumbnailer, it looks like it wasn’t even requested to run by Nautilus.  [Thumbnailer Entry] Exec=convert -thumbnail %sx%s %i png:%o MimeType=image/webp;image/x-webp;   Exactly the same situation occurs with other my thumbnailers: audio waveforms, office documents, photoshop files and so on.  Could anyone help?


It's famously unknown whether the natural log of 2 is rational or not.  How about the natural log of other numbers. Is it known/unknown whether these are rational?  Obviously ln(1) is 0, and ln(2^n) is n*ln(2) (and is thus rational iff ln(2) is rational), but how about other cases?


Xpath expression with multiple predicates

I am trying to build a complex xpath expression which will answer the following condition.  From the XML data below, returns the User entity which:   His loginname is "user1" His name is "User 1" He has 2 different profiles values which are "operator" and "admin" (I don't know the exact order ahead)         <user>   <login>user1</login>   <name>User 1</name>   <profile>     <value>admin</value>     <id>2</id>     <description>admin users</description>   </profile>   <profile>     <value>operator</value>       <id>1</id>     <description>Operator</description>   </profile> </user>  <user>   <login>user2</login>   <name>User 2</name>   <profile>     <value>admin</value>     <id>4</id>     <description>admins users</description>   </profile>   <profile>     <value>poweruser</value>       <id>5</id>     <description>power users</description>   </profile> </user>  </root>    Can someone please supply an example for such a case?  EDIT: Added a complex profile entity


Batman's Rule: Is it thrown out the window in the new DC Universe?

So, some stick-in-the-mud dredged up this question:    It got me thinking about the  movie, which (presumably) is going to set in motion DC's version of the MCU since it involves a few new players who will have their own origin movies hitting theaters soon.  And in B v S, there's a scene where Batman goes into a warehouse and essentially kills everyone in it.  He's throwing bombs, he's throwing grenades, he's breaking people's necks, etc...  So, historically Batman has had his "No Kill" rule.  Which, some theorize, is actually a "No Murder" rule.  But, this is clearly premeditated murder, because he came armed to the teeth and knew people were going to die.  And I'm curious if anyone knows how that's justified in Batman's ethos, or if Batman in this new DCEU (DC Extended Universe) is going to not necessarily live by this rule.


Why is there quality loss on my image styles?

This is the original image (610x405)    This is the image after applying image style (scale and crop) to 290x190.    Both image have the same aspect ration, yet there is visible quality loss on downsizing. Am I applying the right image style? What should I be doing?


Geometric intuition of the dimension of Grassmannians and flag manfolds

I wish to understand geometrically (not just algebraically) why the dimension of the Grassmanian $G(k,n)$ is $k(n-k)$ and the dimension of a flag manifold $F(k_{1},k_{2},...,k_{n},N)$ is $\sum_{i=1}^{n}k_{i}(k_{i-1}-k_{i})+Nk_{n}$ (in fact with understanding the Grassmanian case it would be enough because the flag are just "nested" Grassmanians).  I am thinking in a spatial way in the well known $G(2,5)$ but I am unable to see geometrically how the space of all $2$-planes in $\mathbb{P}^{5}$ can be $6$-dimensional...


I am trying to prove that for all $n$, $S_n$ is isomorphic to a subgroup of $A_{n+2}$.  Say $S_n$ acts on $\{\alpha_1,...,\alpha_n\}$ and $A_{n+2}$ acts on $\{\alpha_1,...,\alpha_n,\alpha_{n+1},\alpha_{n+2}\}$.  Let $\sigma \in S_n$ and let $\phi: S_n \to A_{n+2}$ be given by $\phi(\sigma)=\sigma$ if $\sigma$ is an even permutation, and $\phi(\sigma)=\sigma(\alpha_{n+1}\alpha_{n+2})$ if $\sigma$ is an odd permutation.  This way $\phi(\sigma) \in A_{n+2}$.  Now, let $\sigma, \rho \in S_n$.  Then $\phi(\sigma \rho)=\sigma \rho (\alpha_{n+1}\alpha_{n+2})$.  Also, $\phi(\sigma)\phi(\rho)=\sigma(\alpha_{n+1}\alpha_{n+2})\rho(\alpha_{n+1}\alpha_{n+2})=\sigma\rho$.  So, $\phi(\sigma \rho)$ does not seem to equal $\phi(\sigma)\phi(\rho)$.  But the idea is that we want $\phi(S_n) \cong S_n$, and $(\alpha_{n+1}\alpha_{n+2})$ does not permute any members of $\{\alpha_1,...,\alpha_n\}$, so $\phi(\sigma \rho)$ and $\phi(\sigma)\phi(\rho)$ are equal as permutations on this (sub)set.  This feels a little subtle to me and I'm not sure if my idea is valid or not.  If it is not, can this proof still be saved?  I appreciate any thoughts on this.  Thanks.


How can I show tasks only of current virtual desktop in Ubuntu dock?

Is there way I can only show the tasks which are running in the Ubuntu dock which are running on the current virtual desktop instead of showing all the tasks?   I'm on Ubuntu 20.04.


Match everything inside a "method call" string with possibly nested parentheses

I'd like to write a python regex to replace the string FARM_FINGERPRINT() and anything inside that method call with the string '0'. For example, for the string:  s = 'FARM_FINGERPRINT(stuff(more stuff()), even more stuff), another_thing()'   The regex should replace it with '0, another_thing()'.  I'd be open to non-regex solutions as well.


$\lim_{n\to \infty}\frac{1}{n} \sum_{k=1}^n x_k =x\;$ given $\;\lim_{n\to \infty} x_n= x\;?$

I have a question which is giving me a hard time.    I want to show that $$ \lim_{n\to \infty}\frac{1}{n} \sum_{k=1}^n x_k =x$$ given that $\lim_{n\to \infty} x_n= x$.


Prove the quartic polynomial $x^4-20x^2+16$ is irreducible over rationals

Question: Check whether the polynomial $x^4 - 20 x^2 + 16$ is irreducible over the rationals. Eisenstein's criterion cannot be applied here and I couldn't come up with any other method to check whether this is irreducible or not. Any help in getting this done is much appreciated.


Possible Duplicate:          The FAQ specifies that:     Use your downvotes whenever you encounter an egregiously sloppy, no-effort-expended post, or an answer that is clearly and perhaps dangerously incorrect.   But if I find a correct question, closed (or not yet) as duplicate, is downvote a correct behavior for Stack Overflow policy?


Show that a is a quadratic residue modulo $p$ iff $ind_{r} (\mathbb{a})$ is even.

Let $p$ be an odd prime with primitive root $r$. Let $\mathbb{a}$ be an integer with $gcd(\mathbb{a},p) =1$ and $ind_{r} (\mathbb{a})$ denote the index of $\mathbb{a}$ relative to $r$. Show that $\mathbb{a}$ is a quadratic residue modulo $p$ iff $ind_{r} (\mathbb{a})$ is even.  Could anyone give me a hint for solving this, please?  For the index of an integer w.r.t quadratic residue, Please follow the .


What is this little (3mm) spotted insect in Northern Italy?

Every now and then I find one or two of these tiny bugs in my kitchen. They are about 3-4 mm long and seem to be very static on hard surfaces (furniture or walls). They rarely, if ever, more. The one in the picture was found dead on the floor so I was able to take close-up pictures. The insect seems to have a very regular pattern of spots and presumably wings. I tried to look online for Italian websites of "household bugs" but I could not find it. Is it problematic, i.e. does it ruin food or something? Location: Northern Italy, province of Vicenza


Ubuntu 16.04 keeps asking screen password after installation of Radeon graphics driver

I am using Ubuntu 16.04 on dell 5559 with radeon graphics. I downloaded the package from AMD and installed it. After restarting it keeps on asking the password even after a put the right password. Once I put the password, it read and again return back and asking password.   Now I can't login the system. Anyone kindly assist, how can I open it?


Given a fairly simple regex, I'd like to match a text between to delimiters:  ___MANUAL_TICKET___  ###_CLIENT_START_### TEST ###_CLIENT_END_###  ###_PROBLEM_START_### TEST2 ###_PROBLEM_END_###  ###_EMAIL_START_### xyz@test.com ###_EMAIL_END_###   To get the client I am using this regex:      ###_CLIENT_START_###\s(.*?)\s###_CLIENT_END_###   which works as seen .  But when I use it in my PHP Code it does not find any matches:  preg_match('@###_CLIENT_START_###\s(.*?)\s###_CLIENT_END_###@', $source, $matches);  (tried different regex delimiter such as / and ~, same result)  What am I doing wrong?


I would like to create a new race which you can play as a PC without it being too overpowered for normal game settings. I would like one with wings, but are wings (even wings with clumsy maneuverability) (or gills or claws or a prehensile tail) potentially game-breaking? And what about racial traits and size categories and spell-like abilities-which ones are acceptable for PC use?


Four cards are drawn from a pack of 52 cards. What is the chance that no two cards are of equal value? Each belongs to a different suit? My try-- Total probability =$^{52}C_4$ In the pack of 52 cards there are 4 aces, 4 1s and so on. So, there will be 13 groups of 4 cards containing same value. $\therefore$ Probability that no two cards are of equal value =$\frac{^{13}C_4\times ^4C_1}{^{52}C_4}=\frac{44}{4165}$ But given answer is=$\frac{2816}{4165}$ I think I did it wrong, please help me. I also couldn't solve the 2nd problem.


List of PDOStatement::bindParam data_type parameters

Is there a list describing all of the data_type parameters you can use in PDOStatement::bindParam() ? If none, what do you commonly use, and for what type of field ?  According to PHP manual: data_type Explicit data type for the parameter using the PDO::PARAM_* constants.   I know about the PDO::PARAM_INT and PDO::PARAM_STR . I've heard of PDO::PARAM_LOB but I wasn't sure how and when to use that, though. (for date ?)


I want to delete colors added in Terminal

I added color on the gnome-terminal as in the picture and now I want to delete the custom colors added    I want to have the colors as in this picture


Why can't we have algebraic formulas for $5^{th}$ degree (and higher) polynomials?

If we have a formula for $0=x^4-3x^2-2x+1$, exactly what characteristic of the equation changes when I add an $x^5$ term to only the RHS (and not the entire equation) so that $0=x^5+x^4-3x^2-2x+1$ cannot be solved in a general algebraic way? Please try to keep the answers at a low level (beginning calculus) if possible. Thanks.


after installed ubuntu 17,10 ,unable to use gparted

i installed Ubuntu as only operating system, i used the default partitioning scheme using the complete hard drive and now i want to add another partition for data? i used gparted, after input data, but there is no option to resize.


Can filecontents write an external file in a parent directory?

Reading  got me thinking about the potential of .tex files for harbouring malicious code.  The filecontents package is used to write external files from within a LaTeX document. According to my tests, it can be used to write external files in an existing path down the directory tree. In other words, it can create a file in the directory in which the input .tex file is located, or in any of its subdirectories. For instance, the following code works as expected,   \documentclass{article}  \usepackage{filecontents}  \begin{filecontents*}{./myfolder/myfile.txt} Hello World \end{filecontents*}  \begin{document} test \end{document}   as long as     ./myfolder   is a valid path (i.e. the "myfolder" subdirectory already exists):  Is writing an external file up the directory tree possible?  All of my attempts so far have been unfruitful. I'm guessing that it's not possible; otherwise, that would represent a potentially very malicious exploit, without even requiring --shell-escape; malevolent people would have used that exploit long before I asked myself this question, and LaTeX would have become infamous for it.  So, is writing an external file up the directory tree possible or not? If the answer is yes, how do you do it? If the answer is no, what exactly forbids it?


On all Stack Exchange sites where I have review privileges, the review queue menu icon has a red dot. No matter what I try, it doesn't go away.     on Meta Stack Overflow might or might not be related.


What is the speed of one photon of a beam of light with respect to the other photon of the same beam?

as according to special relativity the relative speed is $u'=\frac{(u-v)}{1-(uv)/c^2}=\frac{0}{0}$ because $v=c$ the speed of second photon with respect to any inertial observer and $u=c$ speed of first photon with respect to same observer so $u'$ the speed of first with respect to second photon should also be $c$ according to second postulate of special relativity but how


I am currently re-reading the Lord of the Rings. While reading the chapter "In the House of Tom Bombadil", where the four hobbits meet Tom and Goldberry, I thought a lot about the speculations and questions about who Tom Bombadil actually is. Then the question "Who exactly is Goldberry?" struck me. From the description in the book I am not able to deduce if she is an elf or maybe a Maia, or - like Tom - probably something different entirely.   So who exactly is she? And what else is known about her, apart from the (little) information given in FotR?


70s UK science fiction TV show with time travel and telepathic cat

I'm trying to identify a science fiction series on UK TV during the 70s, but I can only recall the following:   A party of adults and children. There was a woman with a telepathic bond to her cat: she could look into its eyes to see what it had seen. Time travel was involved. I think it may have been inadvertent or uncontrolled time travel. On one occasion the party encountered an Elizabethan seaman who demanded to know if Elizabeth was still queen. They party replied "err... yes" because they didn't want to have to explain time travel.


I am currently in the process of modifying one biblatex style to conform to another, and that includes adding a new datatype. I have added the code below to my style.bbx  \DeclareFieldFormat[datatype]{title}{{#1}\addperiod} \DeclareFieldFormat[datatype]{foo}{{#1}\addperiod} \DeclareFieldFormat[datatype]{bar}{#1}   When using \DeclareBibliographyDriver{datatype}, \printfield{title} is the only one that prints anything. \printfield{foo} and \printfield{bar} do not produce anything.   Changing foo to another field already in use (such as journaltitle) seems to work, but I'd like to avoid a hacky solution like that if possible.


How do I rename lots of files on a directory without changing their extensions?

I have a problem! I have a bunch of image files with extensions. Jpg and. Png. I wrote a script that renames the files, changing their names in a pattern followed by a number like this:  ... arquivo_1.jpg arquivo_2.jpg ...   And following this sequence, but it needs to know the extension, in this case I used the extension. Jpg.  I was wondering how do I optimize the script so that it renames but keeping the original extension of the file and keep doing the sequence I described above. Can someone help me?


In one of my worlds I built a house on the top of a mountain. When starting to build a wheat farm, I found out that the water keeps freezing, and I have to break the ice blocks:    Does wheat grow even if it is near ice instead of water? If not, how can I prevent the water from freezing?


Should I store RAW file or DNG for backing up

I have decided to store my photos for back-up. I am struggling with file type. Should I store the RAW file that comes from camera or  DNG file where all my editing has been stored.


How can I set cookies on my posts so that I can get view count of that post

Can anyone help with the solution? This is my post and I have created a custom column to get view counts on my single post. I'm want to keep a track of views for every single post. I'm trying to set a cookie when a user opens a single post. Please provide an example so that it will be easy to understand.


I'm trying to write a minimax algorithm for connect 4 in Java, but am getting an error while trying to iterate through a list of possible moves.   It says that      Exception in thread "main" java.util.ConcurrentModificationException     at java.util.ArrayList$Itr.checkForComodification(Unknown Source)   at   java.util.ArrayList$Itr.next(Unknown Source)   I've looked around online, and have found some things (about updating an object within the iterator), but am not quite sure what to do.  Here is my code.  public class AI {        public Move minimax(Board board, int depth, int alpha, int beta, String           player, Move move) {          if(depth == 0 || board.getScore() >= 512) {             return move;         }          else if(player.equals("computer")) {             Move maxMove = new Move(0,0);             maxMove.moveScore = -1000000;             Iterator<Move> it = board.possibleMoves.iterator();             while(it.hasNext()) {                 Move m = it.next();                 board.putPiece(player, m.yMove);                 m.moveScore = board.getScore();                 if (board.getScore() < minimax(board, depth-1, alpha, beta,      "human", m).moveScore) {                     maxMove = m;                 }                 else {                     maxMove = minimax(board, depth-1, alpha, beta, "human",     m);                 }                 board.removePiece(m);                 alpha = Math.max(alpha, maxMove.moveScore);                 if (alpha >= beta) {                     break;                 }              }              return maxMove;         }          else {             Move minMove = new Move(100, 100);             minMove.moveScore = 1000000;             for(Move m : board.possibleMoves) {                 board.putPiece(player, m.yMove);                 m.moveScore = board.getScore();                 if (m.moveScore < minimax(board, depth-1, alpha, beta,      "computer", m).moveScore) {                     minMove = m;                 }                 else {                     minMove = minimax(board, depth-1, alpha, beta,     "computer", m);                 }                 board.removePiece(m);                 beta = Math.min(beta, minMove.moveScore);                 if(alpha >= beta) {                     break;                 }              }              return minMove;         }     } }   Any and all help is appreciated.   Thanks,


Different methods for constructing the same empty nested list in python results in inconsistent behaviour

I'm using Python 2.7.12.  I'm having a problem that I think is best explained through example.  Why does the .append() behaviour of c differ from a and b?  #Three different but equivalent methods to construct empty list:  a = [] for i in range(10):     a.append([])  b = [[] for _ in range(10)]  c = [[]]*10  print a print b print c  #Check to make sure they're equivalent. They are. print a==b print b==c print a==c  #Carry out the same operation on all lists a[1].append(6) b[1].append(6) c[1].append(6)  #Woah!  c is now different than a and b! print a print b print c  print a==b print b==c print a==c   OUTPUT:  [[], [], [], [], [], [], [], [], [], []] [[], [], [], [], [], [], [], [], [], []] [[], [], [], [], [], [], [], [], [], []] True True True [[], [6], [], [], [], [], [], [], [], []] [[], [6], [], [], [], [], [], [], [], []] [[6], [6], [6], [6], [6], [6], [6], [6], [6], [6]] True False False


Find a meromorphic function $f$ with poles at $\dots,-3,-2,-1$

I need help with the following problem:  Find a meromorphic function $f:\mathbb{C}\longrightarrow \mathbb{C}$ whose only singularities are simple poles at $\dots,-3,-2,-1$ with residues $n$ at $z=-n$.  Any hint would be appreciated.


I'm tutoring for a college math class and we're doing putnam problems next week and this one stumped me:      Find the minimum value of $|\sin x+\cos x+\tan x+\cot x+\sec x+\csc x|$ for real numbers $x$.


Are the WotC archives of d20 Character Optimization forum forever lost?

I was looking for the Wizard Handbook but all the links were broken.  Somewhere on the handbooks of other classes (on other forums) I saw a      This was archived by WotC, here's the link   But the link leads to the welcome page of WotC (since it's broken).  Is there a way to get all that info back? Do you know where to get it from? The Wayback Machine did not archive the forums.


How to find a density matrix of a qubit?

If we are given a state of a qubit, how do we construct its density matrix?


Find the coefficient of the term $x^2$ in $\left(x+\frac 2x\right)^{4}$

Find the coefficient of the term $x^2$ in $$\left(x+\frac 2x\right)^{4}$$   This is what I have done so far.  We know $a$ = $x$ and $b$ = $\frac2x$ and $n$ = 4  So what I have done is $4c2$ x $(x)^2$ x ($\frac2x$)$^2$  As we know that $^2$ + $^2$ = 4, and 4 is the $n$ value.  The answer is one though?  What have I done wrong?   P.S.  was the tutorial that helped me.


Grammar difference between "Drive Home" vs" "Drive to Work"

I was configuring my navigation recently and came across this thought and I'm not sure I understand the grammatical rules as to why it is proper to say "Drive Home" but not "Drive to Home". It seems to make sense to say "Drive to My Home" but certainly not "Drive My Home".  Likewise, why is it "Drive to Work" but not "Drive Work" (aside from the obvious different meaning). I get that "Go Work" is different here since Work is also a verb, but "Go to Home" doesn't sound right.  It makes sense to me that "to" should be required as a preposition to a destination, but what makes "Home" different?


If $\sum a_n$ converges does it imply $\sum a_n^3$ converges?

As title says does the converges of $\sum_{i=0}^\infty a_i$ imply that $\sum_{i=0}^\infty (a_i)^3$ converge?


I already ask how to print a map without screwing the "sync" between my map and the Openlayers background. I have tried 2.6.0 and 2.8.1 versions getting only deep frustration. I have used the scale suggested to have optimal results, getting a wonderful series of failures. On the screen the map looks perfect, once printed on PDF it slides out of sync. I want to think I am doing something wrong because is hard to believe after so many years we have still to deal with this bug. I love QGIS and what it allows me to do, but not been able to print my maps really make me @#$%$#@@#$##$@#@@#$&*%^%. Help please.


I'm trying to answer the following exercise: Suppose that $f$ is twice differentiable on $[0,+\infty)$.      Show that if $\lim\limits_{x \to \infty} f(x)$ exists and $f''$ is bounded, then $\lim\limits_{x \to \infty} f'(x)=0$.   If $\lim\limits_{x \to +\infty} f'(x)$ exists then I know how to prove that this limit is equal to 0 (by using the mean value theorem).       But how can I show that this limit exists?    Counterexample: Let us consider  $f(x) = x \sin\frac{1}{x}$. Then $$f'(x) = \sin\frac{1}{x} - \frac{1}{x} \cos\frac{1}{x}$$ and $$f''(x) = -\frac{1}{x^2}\cos\frac{1}{x} + \frac{1}{x^2}\cos\frac{1}{x} - \frac{1}{x^3} \sin\frac{1}{x}.$$ This example shows that the hypothesis that there exists $\lim\limits_{x \to \infty} f(x)$ is essential.


I am using drupal 7 contact form in my site and I want to rename  some field names, like  "Subject" to "Emne" etc..


Possible to lock focal length on zoom lens? (SELP1650)

(This could turn out to be a bone, practical, product-specific query, but this is the internet so the worst that could happen is a 0 rather than a 1.)  Anyhoo: is it possible to lock a zoomable lens to a certain focal length? Is this a typical feature for a lens?  I want to keep my SELP1650 at X mm to help with some creative experiments, but the thing shifts whenever I move my hand against the lens ring. Does SELP1650 (or the body, Sony A6000) specifically have this option?  Or... is there a reasonably non-goofy DIY trick I could pull off, without bricking the thing? (anticipating a sarky 'duct tape' suggestion)


How can I select body outside an element using jquery

I need the exact functionality what jQuery light box does. In my project in a loop, I have a hidden element for every item. When a visitor will click on the element, he/she will see the hidden element. Then, when the visitor will click outside the element (new), the element will hide again. But, the element has an anchor tag. So, if the visitor will click on the element, he/she can go to the link. I have to find out how I can select the area which is outside of the element.  I am giving here a simple HTML.

                  WDZ
   Javascript:     Now I need the code by I can implement:  "When a visitor clicks outside of id="two", it will show div id="one" again and div id="two" will hide. But, if he/she clicks inside div id="two", it has another functions.


Spacelike interval and length contraction

I am having a serious trouble finding an agreement between the two facts in Special Relativity:  (1) given two events $A$ and $B$ in spacetime separeted by a spacelike interval $s$, the distance in space between the two events will be the shortest in the reference frame which the two events occur simultaneously:   The invariance of the interval says $s^2=(\Delta x)^2-(c\Delta t)^2$ and $\Delta x$ is minimum when $\Delta t=0$  (2) the length contraction says $L=\dfrac{L_0}{\gamma}$ where $\gamma=(1-(v/c)^2)^{-1/2}$ , $L_0$ is the proper length of an object in a reference frame which the object is at rest and $L$ is the length of the object in a reference frame which the object moves with speed $v$ in the $x$ direction.  This says that the lenght of the object in the $x$ direction is the largest in the comoving reference frame of this object.  The question is: According to (1), the reference frame in which two events $A$ and $B$ occur simultaneously is the reference frame that gives the shortest distance in space between the two events. Let $A$ and $B$ be the two end points of a meter stick in a reference frame in which the stick is at rest and at time $t=0$. This two events occur simultaneously, so the distance in space between the two is the shortest acording to (1). But according to (2) shouldn't this distance be the largest?  What is wrong?


Extending a monomorphism $K \to E$ to an automorphism of $E$

Suppose $E$ is a splitting field of a polynomial $f(x)$ over $F$ and $K$ a subfield of $E/F$. Can any monomorphism of $K \to E$ be extended to an automorphism of $E$?


Capitalising the definite article in names

When I was a youngster some mumble-mumble-mumble decades ago, I was taught that, in the instances of names of persons, places, and things which carried the definite article the, the article wasn’t capitalised.  Hence, the Batman, the Empire State Building, the Medal of Honor.  In the last twenty years or so, I have seen the capitalisation of the in names proliferate.  Now, it’s The Batman, The Empire State Building, The Medal of Honor.  When I point this out as an error, I’m generally met with the argument, “No, those are names, and all words in a name are capitalised.”  Did I get it wrong, way back when?  Or is it one of those things in which style has trumped rule, and now the standard is to capitalise the definite article in names?


Render result does not appear when file is reopened

I can't find the rendered image result. The render work perfectly but when I reopen the file there is only a blank grey screen. This has not happended before.Please help.


There exists (glorious) users on various StackExchange sites with more than 1000 badges. This makes the formatting of the user profile at the bottom of questions/answers a little odd, as the badge information overflows to the next line.        Would it make sense to summarize badge counts larger than 1000 in a similar way to reputation? Using the above screenshot as an example, the users's badge count would instead be:  * 109  * 1k  * 1k  This is a nitpick and low priority, but maybe it would make a good on-boarding task for a new hire?


Can I switch off built in laptop keyboard on boot up because it’s faulty

Some of my laptop’s keyboard keys are ‘acting as if pressed’ even though they’re not been pressed, and this is interfering with the boot up of Ubuntu. I have an external usb keyboard, so I want to switch off the internal keyboard before boot up, ie., before it gets the chance to cause boot up problems.  Can anyone help?  Quack


Today I've realized that when voting for closing questions, some of them have have an account for some reasons I can't see. For instance:    So I read that question, see that it lacks sufficient information and I'm voting for its closing. In the first menu I see there are 3 votes:    But once I click on the "Offtopic" submenu I can see just 2 votes:    I can't see the third reason which I assume has only one vote (code must demonstrate a minimal understanding of the problem being solved). The same I've noticed for this one:     off-topic: Questions concerning problems with code you've written must describe the specific problem — and include valid code to reproduce it — in the question itself. See SSCCE.org for guidance.    Why is that I can't see those reasons as options nor the votes for them?


Finding the number of non-negative integral solutions of $x + y + z = 10$

I realize that this question has been asked multiple times and I do not really want to know how to do it, I understand how to solve it, my issue is somehow I have used the distribution and I am not getting the right answer.  Method of Solving: I solved this in the first go by directly applying the distribution formula that is $$\binom {n+r-1}{r-1} $$ By using, $n = 10, r= 3$ we get, $$\binom{12}{2} = 66$$ however the answer given is $$\binom{12}{3} = 220$$ Next, I tried to solve by taking multiple cases that is, setting any variable, $x,y$ or $z$ to values from $0,1,2,3...10$, so for example if $x = 0$ then we get, $$y+z=10$$ now it is simple enough to distribute this even without the formula, we get $$\Bigl((0,10),(1,9),(2,8)(3,7),(4,6)\Bigl) \cdot 2,(5,5)$$ which gives us $11$ cases, that can be verified using the formula $$P_0 = \binom{11}{1}.$$ Now taking cases till $x=10$ we get, the final result as $$\sum _{n=0} ^{n=10} P_n = 11+ 10 + 9 + 8+ \ldots +1 = 66$$ Please tell me where I am going wrong or of it simply a case of the answer in the text being wrong, and if the second method is correct.


How to make a command line executable an application?

I have a command line executable (specifically JMeter), which opens a GUI application when launched from the terminal.  However, I would like to create a link to it that would wrap it up to become a proper Mac application (included in /Applications directory and all that).  How do I do that?


No operating system found Ubuntu 14.04 Dual Boot

So my laptop is dual booted with Windows 10 and Ubuntu 14.04 on a 240GB SSD (aftermarket).  It has worked fine for months.  I never use the Windows partition unless I have to, and haven't used it for weeks.  Today I was working in Ubuntu, when my status bar at the top seemed to be shifted over to the right and I was unable to click anything.  The computer appeared to be freezing up so I held the power button to shut down.  Upon startup, I got the "No Operating System Found" message.    I popped in the Ubuntu 14.04 Live DVD and booted into the tryout mode in order to run boot repair.  I went through the process of installing boot repair and when I run it I don't get an option to do the "Recommended Repair".  The button is nonexistant.  The only option it gives me is the boot report, which gave me this report:    I looked over it quickly and see that no boot loader is installed, no partitions were found, and this message at the bottom:     The default repair of the Boot-Repair utility would not act on the   MBR. Additional repair would be performed:  repair-filesystems   I attempted to reinstall GRUB2, so I ran gparted to see my partitions.  Only two show up:    /dev/sda1, FileSystem:unknown, Size: 8.02GB unallocated, Size: 14.35GB   I'm guessing this is reading from the smaller onboard SSD intended for the operating system (originally meant to be used for Windows speed boot, or whatever it's called).  It appears that it can't find the 220GB SSD?  I tried mounting the partition (the only partition available) I get this:     mount: block device /dev/sda1 is write-protected, mounting read-only   NTFS signature is missing. Failed to mount '/dev/sda1': Invalid   argument The device '/dev/sda1' doesn't seem to have a valid NTFS.   Maybe the wrong device is used? Or the whole disk instead of a   partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   I have a really bad feeling about all of  this, and I have no idea what has gone wrong.  Any Ideas?  Thank you all in advance!


ESTA and multiple nationalities + using different passports at check in and immigration

Just signed up and this is my first question.   I have recently become a citizen of Australia and will be traveling back to the US again soon. I already have an ESTA on my European passport however now that I am Australian too I have to use this passport when traveling in and out of Australia (this is apparently mandatory for AUS immigration). Do I have to apply for a new ESTA on my Australian passport to now travel to the US or can I use my existing one on my EU passport? Am I able to check in with the airline when leaving Australia on my EU passport but then show my AUS passport at Immigration when exiting the country and then show my EU passport when landing in the US? Or do I need to use the same passport for both?   There seems to be conflicting info online. A similar question was already asked on here but the only answer to that did not offer clear explanation. My question also refers to checking in with the airline on one passport and showing immigration another passport and whether that is ok or not.


What are integers $x$ and $n$ such as $ x^4+x^3+x^2+x+1 = n^2$?

What are the integer numbers $x$ such as $x^4+x^3+x^2+x+1$ is the square of an integer?  $0$ and $-1$ are obvious answers, but how many are there?


Different ways of Arranging balls in boxes

This question is generalization of different cases of  combinatorics problems that are generally asked.  We will find general way of arranging $n$ balls in $r$ boxes. Cases :    Identical Balls. Distinct Balls. Order considered. Distinct Balls. Order not considered.   Two cases arise in each case :    Empty boxes allowed. Empty boxes not allowed.   Please feel free to add any other cases or minor variations you might think can be generalized.


Computing the quotient of SL(2,Z) by its commutator subgroup

So far, I know the matrices $$S=\left( \begin{matrix} 0&-1\\ 1&0 \end{matrix} \right), \quad T=\left( \begin{matrix} 1&1\\ 0&1 \end{matrix} \right) $$ generate SL$(2,\mathbb{Z})$. $S^2=(ST)^3=-I$. I also know the matrices $$X=\left( \begin{matrix} 1&1\\ 1&2 \end{matrix} \right), \quad Y=\left( \begin{matrix} 2&1\\ 1&1 \end{matrix} \right) $$ with their inverses $X^{-1},Y^{-1}$ generate SL$(2,\mathbb{Z})'$, the commutator subgroup. I'm interested in what the quotient $SL(2,\mathbb{Z})/SL(2,\mathbb{Z})'$ is. In general, how would I go about computing the quotient of two matrix groups? I'm trying to use GAP but I'm having a lot of trouble!


How to limit read speed from a tcp socket

I would like to read some data from server. But I want to limit the receiving speed. What is the best way to do that?  Only solution that comes to my mind is to measure how many bytes I received in a certain period of time, calculate speed and then make a decision whether or not to continue reading from socket or to stop for some time.  But I think that it would lead to the fact that for the first part of certain period of time (in which I measure amount of bytes received) speed would tend to a maximum bandwidth and then drop to zero for the remaining part of the period. But I want it to be stable.


Trouble showing that $a_{n+1}=\frac12\left(a_n+\frac{2}{a_n}\right)$ is monotone given $a_1=2$

I've tried induction firstly by showing that $a_1>a_2$ - then assuming the expression for some $k$ I failed to make proper use of the assumption in the inductive step and I get stuck with the expression $2 < (a_n)^2$.  Next I tried directly computing both $a_{n+1}-a_n$ and $a_{n+1}/a_n$ which yielded nothing of particular use.  The most promising but failed attempt was when I tried induction on $a_{n+1}/{a_n}$ starting from the base case $a_2/a_1=3/4<1$, assuming $a_{k+1}/a_k<1$ and then making some use of the assumption in the inductive step however not being able to reach $a_{k+2}/a_{k+1} < 1$.  All of this is an attempt to show convergence of the given sequence by showing monotonicity and boundedness.


Why do American people use simple past instead of present perfect with "ever"?

I would say British English seems to adhere to English grammar books that I learned in school more than American English.  For example, I was taught that we use present perfect with "ever" because the time is unspecified or something which happened in the past which is important now.  See  say:     Present perfect simple: uses      We use the present perfect simple to refer to events in the past but   which connect to the present.      We often use present perfect for talking about something which   happened in the past which is important now.      we often use general time expressions like ever, never, before, in my   life, so far, up until now with this use of the present perfect   simple:      We often use ever, not … ever and never when we talk about   experiences:      Have you ever tried to write your name and address with your left hand?      American English      In American English the past simple is often used instead of the   present perfect simple, often with already and yet.      American English Did you eat (yet)? Did you finish (already)?      British English Have you eaten (yet)? Have you finished (already)?    confirms this:     The Present Perfect Tense in British and American English      British and American grammar differences – present perfect vs. simple past      In American and British English, we can also use ‘just’ with the   simple past to talk about recent events. So what’s the difference   about the way American and British people use ‘just’? When we’re   giving news in British English we generally use the present perfect.      Oh, your mother’s just called.       Oh, what did she want?      When we’re giving news in American English, we often use the simple   past.      Your sister just called.       Oh really? What did she want?      So both these sentences are possible in both varieties. It’s just that   we use the present perfect more frequently in British English.      The words ‘yet’ and ‘already’ indicate a time up to now or until now.      That relation to the present time means we commonly use them with the   present perfect. That’s true in both British and American English. In   American English, especially spoken English, you’ll often hear us use   these words with the simple past, too.      I’m going outside to practice soccer.       Wait a sec.       Did you do your homework yet?      Yeah, I already did it.       OK.      In British English, these sentences would be unusual. With ‘yet’ and   ‘already’ we usually use the present perfect, not the simple past. So   when do Americans use the present perfect and when do they use the   simple past? In written English and when we’re speaking carefully, we   often use the present perfect with ‘yet’ and ‘already’. But when we’re   speaking informally, we often use the simple past. ‘Did you do it   yet?’ sounds a little more informal than ‘Have you done it yet?’,   especially if we use the less careful pronunciation ‘Did ja do it yet?.   And there’s something else. My theory is ‘Did you do it yet?’ can   sound just a little more urgent in American English than ‘Have you   done it yet?’   And I guess that usage may apply to "ever" as well  Have you ever watched the film? ( we use present perfect because we don't know the time the that person watched the film or the specific time that that action happened is not important or its result is important now, ie I just want to know if you have watched it, the time is not important)  But American people will say:  Did you ever watch the film? (I feel strange when hearing it, why would the asker want to know the specific time right at the beginning)  Is that how American people say daily? or  American grammar is not as strict as British English?


Expectation of the maximum of gaussian random variables

Is there an exact or good approximate expression for the expectation, variance or other moments of the maximum of $n$ independent, identically distributed gaussian random variables where $n$ is large?  If $F$ is the cumulative distribution function for a standard gaussian and $f$ is the probability density function, then the CDF for the maximum is (from the study of order statistics) given by  $$F_{\rm max}(x) = F(x)^n$$  and the PDF is  $$f_{\rm max}(x) = n F(x)^{n-1} f(x)$$  so it's certainly possible to write down integrals which evaluate to the expectation and other moments, but it's not pretty. My intuition tells me that the expectation of the maximum would be proportional to $\log n$, although I don't see how to go about proving this.


Given a 3D model, I want to define different regions and fill each region with solid color (to distinguish)  Is there an easy way to do it?   My current solution is to first select faces under edit mode, then switch to vertex paint mode and paint use a brush. I changed some properties of the brush(large radius, reduce edge softness) but I can't make regions in solid color as I expected..  Please Help.


Using File Geodatabase coded domain with ArcGIS Online?

I created a File GDB and set up a domain, and the domain was assigned to a field in a feature class. The domain behaves as expected on ArcGIS Desktop (dropdown list when editing the content of that field).  But if I zip up the FGDB and upload to ArcGIS Online to created a feature layer and edit the layer online, there is no dropdown when editing.  I don't see any additional step in this tutorial, other than a different mechanism of getting data to ArcGIS Online. I don't think I can do it the same way in ArcGIS 10.0:   Anyone has any idea what's going on?


Kuratowski's Theorem using Axiom of Choice

I can't seem to be able to prove Kuratowski's Theorem using the Axiom of Choice, although they are equivalent assertions. Kuratowski's Lemma: Every partial order has a maximal chain. Axiom of Choice: For every set X of disjoint nonempty sets there exists a set Y such that for every set $Z \in X, Y \cap Z$ is a singleton. My attempt: Consider any chain $C_0$ of the partial order. If $\exists x \in X \setminus C_0$ which is comparable with some element of $C_0$, let $C_1 := C_0 \cup \{ x \}$. Iterate this process . If at some point we cannot find such an x, then we have found a maximal chain. Suppose we can find such an $x$ infinitely, then the sets $i\geq 1 \Rightarrow X_i := C_{i+1} \setminus C_i$ are disjoint singletons. Hence by axiom of choice there exists $Y$ for which $X_i \subseteq Y$. Inorder to finish the proof, I need to prove something of the form "If a is comparable with some element of $C_0$, then $\exists j$ s.t. $a \in C_j$". I can't seem to prove this. P.S: x is comparable with y iff $x R y \lor y R x$.


Background: I was working on a project and was having a colleague of mine proof-read a piece of documentation. He said that one sentence was ambiguous because he couldn't determine what the antecedent was (actually he knew because of the context, but said that to somebody else it might be ambiguous).   Sentence:     The server picks up the emitted fax via ModuleA, which forwards it to ModuleB.   To me it's clear that the which of the sentence refers to ModuleA, but apparently other people may be confused as to whether it's the server or ModuleA that does the forwarding. In my experience I've always made the assumption that the noun that's closer is the implied antecedent, but I couldn't find any rules to follow in determining the antecedent to use.   Question: Are there rules that unambiguously determine what antecedent is referred to by a pronoun without having any contextual information?


How do I get a python reference to the viewport camera?

I want do draw a line from one point to another using the blender opengl functions provided in bgl. Both points are in world coordinate system. I found a function in bpy_extras.object_utils called world_to_camera_view which needs a scene, a camera and a Vector of the point as a parameter.  I can get the scene from   bpy.context.scene   but how do I get the viewport camera?   Background: What I want to do is, to write a modal operator which lets the user move, rotate and zoom the camera in the viewport and the lines between the points in the viewport are drawn correctly. Its just an operator to learn drawing with bgl.


Java class with method that accepts list of any object

I want to create a class that can be made without any parameters, and has a method that takes a list of any object and behaves like this:  List<String> list1 = Arrays.asList(new String [] {"a","b"}); List<String> result1 = myClass.myMethod(list1);  List<Integer> list2 = Arrays.asList(new String [] {1,2}); List<Integer> result1 = myClass.myMethod(list2);   Here's my attempt after reading briefly about Java generics:  public class myClass<T> {  public List<T> myMethod(List<T> input) {   ...    return input; // just an example }   Why doesn't this work?


How did Gared (Night's Watch man) get back from behind The Wall?

The surviving Black Brother, Gared, from the prologue of A Game of Thrones is apparently the deserter who is beheaded in the beginning of the book.   But how did he manage to get to Winterfell from the other side of The Wall? Or did the show throw me off track and in the book there weren't any survivors, so the deserter is someone else?


Prove that any polynomial function is continuous

I am expected to prove by induction that any polynomial function is continuous. In which "direction" would you advise to make induction?   e.g. Taking $x^n$ and making induction on $n$ is not sufficient. By polynomial I understand, $\sum^{m}_{n=1}a_n x^n$. How do I prove it's continuity using epsilon delta notation? And further do I make an induction on $n$ only? Is not $a_n$ a variable as well?  It seems complicated. If you have any suggestion, I would be obliged.


I have a canon EOS Rebel T2i with quite a few EF-S lenses. I would like to upgrade to the new Canon EOS Rebel T6s (or T6si (not sure the difference)). I was wondering if my EF-S lenses would work with the T6s(i) body or not. Thanks.


Election comments have no permalink link

There were   on this already, and  it’s also implemented by now. And when looking at the source, I can indeed see an ID being set for every comment on election pages.  However, unlike comments on questions, there is no actual link for the permalink for comments on election pages:    Could those be added please so we can actually link to comments easily?


I just bought macbook pro 16 and I get mild shock when charging and when I touch surface. Is this to be expected or do I need to have it serviced?


I searched for this error on StackOverflow but any topic seens to solve my problem. I have this code that opens a .txt file and inicialize objects variables and this error appears.  public void lerDoArquivo() {     try {         FileReader ler = new FileReader("Menu_de_itens.txt");         BufferedReader reader = new BufferedReader(ler);         String linha;          while ((linha = reader.readLine()) != null) {             processaEntrada(linha);         }          reader.close();     }      catch (IOException e) {         e.printStackTrace();     }   }   This is my stracktrace:  Exception in thread "main" java.lang.NullPointerException     at java.io.FileInputStream.<init>(FileInputStream.java:130)     at java.io.FileInputStream.<init>(FileInputStream.java:93)     at java.io.FileReader.<init>(FileReader.java:58)     at ItemMenuDAOTxt.lerDoArquivo(ItemMenuDAOTxt.java:22)     at ItemMenuDAO.<init>(ItemMenuDAO.java:16)     at ItemMenuDAOTxt.<init>(ItemMenuDAOTxt.java:14)     at ControleDeMenu.<init>(ControleDeMenu.java:21)     at FastFoodOO.main(FastFoodOO.java:11)


Is there to make the login screen appear on the external display in 18.04?

On Ubuntu 18.04, I have connected my laptop to an external display and I am able to set the external display as primary and external display only mode. But when I turn on my laptop or log out from my session the display login screen is displayed only on my(internal) laptop screen. But once I login the display switches to external only and my laptop screen turns off as expected. Is there a way I can make the login screen appear only on the external screen on bootup or on logout as in 16.04? Also the login screen does not follow my cursor as in 16.04.


Clarification regarding confidence intervals

In Example 5 , the authors discuss polling. Voting for candidate 'A' is given the numerical value of 1, and voting for 'B' has the value of 0. The CLT says that the average of a sample of $n$ people has the approximate distribution $$\overline{X} \approx N(p_0,\sigma/\sqrt{n}) $$ where $p_0$ is the true proportion of people who would vote 'A'. From this, and some general knowledge of the normal distribution they write:     This   means that we can conservatively say that in 95% of polls of $n$ people the sample mean   $\bar{X}$ is within $1/\sqrt n$ of the true mean. The frequentist statistician then takes the interval $\bar{X} ± 1/\sqrt n$ and calls it the 95% confidence interval for $p_0$.   I'm fine with this. However they write further     A word of caution: it is tempting and common, but wrong, to think that there is a 95%   probability the true fraction $p_0$ is in the confidence interval. This is subtle, but the error   is the same one as thinking you have a disease if a 95% accurate test comes back positive.   It’s true that 95% of people taking the test get the correct result. It’s not necessarily true   that 95% of positive tests are correct.   This remark has me puzzled. Earlier they said that in 95% of polls (of $n$ people) the confidence interval would contain $p_0$. Why doesn't this mean that $p_0$ would be in the interval with a probability of 95%?   Also, I can't see the analogy with the disease/test scenario (which sounds like the base rate fallacy). I'd appreciate some elaboration on that too.  Thank you!


Suddenly I cannot add any menu entry via the "Menu" settings option (....wp-admin/nav-menus.php).  Any new menu I set results in de-selecting the currently selected menu and saving a "null" menu structure in my homepage!  Any help would be greatly appreciated because my home page is affected/  Thank you


I'm pretty new to Ubuntu, been using it for about a week (I love it). Can someone tell me what the best way to install video drivers is? I've been having some troubles. I have a GeForce 750ti and am on 14.04. Thanks in advance.


Why to pass extern struct to function in C?

I have seen an example where someone has passed an extern struct to a function in C. Is there a good reason to do this instead of using the extern struct without passing it as a parameter? Is this solution more encapsulated?  //Test.h struct TEST_STRUCT {     int   member;                                                  }; extern struct TEST_STRUCT test_struct;   //Test.c struct TEST_STRUCT test_struct = {0};      Now I can decide to pass this test_struct to my function or to set my "member" variable in my function very comfortable like this:  test_struct.member = 10;


Decided to try to learn Blender, so started modelling new shelving using it.  Early on I had beveled a corner (not with a modifier) where the shelving goes from one wall to another.  We have since decided we would prefer it sharp.  I understand that the modifier would have been the better choice, but as I beveled with relatively few segments, I thought that it would be a good exercise to learn how one might manually remove the additional segments...so far though, no luck.  Can anyone suggest a course of editing to convert the two sections shown to 90 degree corners?


How do I take date as input and add +3 and set label with new date in java swings

How do I take date as input and add 3 in selected date then set label with updated date in java swings? My date format is YYYY-MM-DD.  eg if I enter 2016-04-04 then change date to 2016-04-07 and set a label to it.  i Tried this . .  gives me wring output. 1970-03-01 is ouput plz  help


Regex to match external block of brackets

I have found some regex to match textblocks between brackets. However, what if I have some String with nested brackets and I only want the most external part of it.   eg. "foo bar [first [second] [third]] asdf ]]]]"  I would like to be able to match the text between the first opening bracket and it's closing bracket, leaving everything inside intact.   Result would be: "[first [second] [third]]"


What are current pitfalls of using LuaTeX over pdfTeX

I know that there are several closely related older posts about LuaTeX.         As of recently I started entertaining the idea of switching my default engine form pdfTeX to LuaTeX. The main upshot as I see naively right now is the direct availability of a powerful scripting language from within my latex documents. That is related to my older questions about automatic document update as well as embedding animations into the presentation.  Before I make a leap of the faith I would like to know the current pitfalls of using LuaTeX over pdfTeX. How do people use PSTricks with LuaTeX? Any issues with Powerdot class? Are there any issues with bibtex or even commonly used packages for math publications?   Edit: I am still goofing off in front of the computer and testing LuaTeX engine. I tried on several complex documents with figures, bibliography files and similar. Works like a charm with the usual workflow for PSTricks  lualatex --output-format=dvi file.tex -> dvips file.dvi -> ps2pdf file.ps   I think I am going to edit my .profile and switch to lualatex unless I encounter a major problem.


What's a common interjection for the reaction to something creepy and disgusting (like some insects or spooky places, etc.)?

For example,  A: - Look! There is a centipede on the table!  B: - (interjection)!


Solve a congruence $1978^{20}\equiv x\pmod{125}$

I have checked the solution ($x=26$).  Solving modulo $5$ gives  $$1978^{20}\equiv 1978^{2\cdot 10}\equiv 1\pmod{5}$$  Solving modulo $25$ also gives $$1978^{20}\equiv 1\pmod{5}$$  How to evaluate the remainder $x$?


Python Match Regex works in tester but not in consol

This is pretty simple but I can't seem to figure this one out. What am I doing wrong here?  The online tester shows this works fine:   But I am getting nothing returned when I try it in the Python REPL:  test = """<speak><prosody volume=\"x-loud\">This text should match?<break time='500ms'/><mark name='punchline'/>\n\n<say-as interpret-as='interjection'>boing</say-as><break time='1ms'/>!\n</prosody></speak>""" rex = '(?<=<speak><prosody volume=\\\"x-loud\\\">)(.*)(?=<\/prosody>(?:<metadata>|<\/speak>))' m = re.search(rex,test)


Auto correlation function in R what are the error lines

If one invokes acf() function in R the estimated acf values are plotted together with blue error lines. What are they (the lines)?


Let $A,B,C,D,E$ be five points marked in clockwise direction on the unit crcle in the plane wth centre at origin.

Let $A,B,C,D,E$ be five points marked in  clockwise direction on the unit circle in the plane with centre at origin. If $f(P)=\alpha x+\beta y$ for $P=(x,y)$   If $f(A)=10,f(B)=5,f(C)=4,f(D)=10$. What is $f(E)$?  Please help on how to start


Got auto-granting bounty on a question that didn't get a true answer

I've put a large bounty on a question I really wanted an answer to, and yet all answers didn't have a working solution:    Sadly, some of them got upvoted, and the system decided to grant a bounty to one of them.  I didn't have the chance of extending the bounty period, or offer a larger bounty.  I tried to downvote all answers (because none had a working solution), but it still granted the bounty to one of them.  I also tried to flag the question to the moderator, to consider to extend my bounty, but it didn't work.  What should I do?


Q: how to adjust all my tables width to text document margins?

@LaTeX-class-file  filename        = "harvard-thesis.cls",  version         = "0.4",  date            = "4 April 2012",  codetable       = "ISO/ASCII"  As you can see in this example, my table exced the widht of the text document. My intention is to adjust the table widht to the text column in the whole doc.  \documentclass{harvard-thesis} \captionsetup{labelfont=\rmdefault, textfont=\rmdefault }  \begin{document}  \begin{table} \centering \begin{tabular}{@{}lll@{}}\toprule[1.5pt] \bf Periodista & \bf Medio & \bf Cargo \\\midrule  Sample name surname &  Sample medium & Other text. Responsable de Participación, redes y Comunidad \\  Sample name surname &  Sample medium & Other text. Responsable de Participación, redes y Comunidad \\  Sample name surname &  Sample medium & Other text. Responsable de Participación, redes y Comunidad \\  Sample name surname &  Sample medium & Other text. Responsable de Participación, redes y Comunidad \\   \bottomrule[1.25pt] \end {tabular}\par \captionof{table}{Periodistas participantes} \label{tab:periodistas} \end{table}  \end{document}


Python: float(var) conversion in Python wont work

this is my code:  def pmi(w1,w2):      x = float(1)      x = (bg_fdist[(w1, w2)])/(f_brown[(w1)]*f_brown[(w2)])      print x   the values entered will be:  >>> bg_fdist[('of','the')] 9781 >>> f_brown[('of')] 36412 >>> f_brown[('the')] 6997`   so i expect my x to be very small and between 0 and 1.  but i get as a return:  >>>> pmi('of','the') 0   i assume that might be, because x gets still handled as an integer? why is this? can anyone point out how i might get my expected result?  greetings!


How to convert the Current User Time from String to DateTime data type?

I have to populate the Current User Time-Zone DateTime in a DateTime field. I am trying this : String str = datetime.now().format(); DateTime d = Datetime.valueOf(datetime.now().format()); DateTime dtm =  (DateTime) DateTime.parse(str); system.debug('datetime.now().format() = ' + str); system.debug('Datetime.valueOf(datetime.now().format()) = ' + d); system.debug('DateTime.parse(str) = ' + dtm);  But the problem is that after using format() it is giving the String format and converting it into DateTime using valueOf() & parse() giving the PST time which is the ORG Timezone, whereas I want the Current User time-zone DateTime. How can I get the CurrentUser Time-Zone DateTime in DateTime Data Type?