How to create a String with the result of a drop down menu?

I've created a JFrame window with a JComboBox. I can select things but they don't do anything. I thought that event was a String, but it isn't. What is the solution for this?  import java.awt.FlowLayout; import java.awt.event.ItemEvent; import java.awt.event.ItemListener;  import javax.swing.Icon; import javax.swing.ImageIcon; import javax.swing.JComboBox; import javax.swing.JFrame; import javax.swing.JLabel;  public class Gui extends JFrame {     private JComboBox box;     private JLabel picture;      private static String[] filename = {"", "b.png", "x.png"};      public Gui() {         super("the title");         setLayout(new FlowLayout());         box = new JComboBox(filename);         box.addItemListener(                 new ItemListener() {                     public void itemStateChanged(ItemEvent event) {                         if(event.getStateChange()==ItemEvent.SELECTED){                             System.out.println("test");                             if(event=="b.png") {                                 System.out.println("test2");                             }                         }                     }                 });         add(box);     } }


How to use 'apt' to get source code and then do separate compile

I want to get the source code for a project and then build it the same way that apt would.  E.g. I want the working source code and be able to run 'make' or similar command on the source.  How can I do that?  Specifically I want to get this source 'icedtea-6-jre-jamvm'


Vim editor and it's difference and how to repair these editor

What is difference between  Vi  and Vim in Ubuntu,Because when you type some text in vi it's much differ from what you type in vim . thank you


I-dem or Id-em ? And po-tent or p-t'nt ?  I've commonly heard the two combinations: I-dem-po-tent and Id-em-p-t'nt.  It looks like idempotent comes from the root for the words identical and potency so the first should be "right" (in British English locale), or at least make sense with our existing words...?


I want to purchase an ND filter and ND grad filters for my cameras.  For lack of better terminology, I want the square ones.  My lens sizes are 67mm and 77mm.  I realize that I can use an adapter so that I only have to purchase one set of filters, but am not sure which adapter size to buy.  Should I buy a set made for 77mm, and then buy a step-up adapter so that I can use them on my 67mm?  Any help will be much appreciated.


Is it possible to make QGIS 3 portable with changed location for Qgis setup parameters folder.  For QGIS 2 it looked like this in qgis.bat file:     qgis --optionspath "X:\qgis" --configpath "X:\qgisini"   For QGIS 3 it doesn't work. Setup parameters are default placed in:      C:\Users\xxx\AppData\Roaming\QGIS


I am having the same trouble as others getting my Atheros AR8131 Ethernet card recognised by Ubuntu 12.10 on my new HP Pavillion P7-1449 PC. I found the same question where the answer suggested the following:   Download Tarball compact-wireless-3.6.8-1-snpc Run  ./scripts/driver-select alx make sudo make install    The problem is when I run the make command I get the following:  make -C /lib/modules/3.5.0-21-generic/build M=/home/chris/Downloads/compat-wireless-3.6.8-1-snpc modules make: *** /lib/modules/3.5.0-21-generic/build: No such file or directory.  Stop. make: *** [modules] Error 2   Found a link to an alternative patch file (compat-wireless-2012-09-25-pc) but then I get the similar error:  make -C /lib/modules/3.5.0-21-generic/build M=/home/chris/Desktop/compat-wireless-2012-09-25-pc modules make: *** /lib/modules/3.5.0-21-generic/build: No such file or directory.  Stop. make: *** [modules] Error 2   Any help you could provide would be greatly appreciated.


Downgrading from iOS 7 to a recent full backup of iOS 6.1.3

I have a device (iPhone 4S) that is running iOS 7, but I was wondering: Is it possible to restore a full backup of the same device running iOS 6.1.3.  I'm not worried about losing data from the iOS 7, but I would like to restore the device to its previous state under iOS 6.  Is this possible?  Again, to reiterate: I'm not looking for clean downgrade/install of iOS 6, I wish to restore a full back-up containing an earlier iOS. Thanks.


Description list with aligned descriptions

is exactly what I'm looking for. I want my description environment to produce this:  Label is long   text  lab2            blalballalaa label3          possible second rule label four      hello world   Someone offered this:  \newenvironment{mydescription}[1]                                                   {\begin{list}{}%    {\renewcommand\makelabel[1]{##1:\hfill}%    \settowidth\labelwidth{\makelabel{#1}}%    \setlength\leftmargin{\labelwidth}    \addtolength\leftmargin{\labelsep}}}   {\end{list}}   Which works great (the parameter is the longest label), except I think the enumitem should be able to do this. Unfortunately, the documentation for it is extremely confusing to me. Could someone show me how to achieve the same result with enumitem?


Someone sent to rescue brother, find out what happened to him?

I recall a book I read back in middle school (ca. 1981), where humanity had sent an astronaut to check out signs of an intelligent race or something like that, but he disappeared.  Earth then sends his younger brother to see what happened, but using an older spacecraft because the first mission used the only up-to-date one Earth had.  Also they refuse to let him take any weapons, to avoid any possible provocation.  On the way something impacts his windshield, punching a hole through it.  He thinks either it was a meteoroid, or a laser beam--but no Earth laser beam could punch a hole that small from more than 1000 miles away.  He later finds the aliens, who are blobs with tentacles or something like that (my memory's hazy), and he's out in his space suit.  He doesn't have a laser to defend himself with, so he uses his communicator (or something like that), setting it to CODE, its most intense setting.  That seems somehow to disable the alien, and soon it's in trouble.  He comes out to it and tries to pull it away from danger, but of course with nothing to push/pull against, his efforts are in vain--but it turns out that convinces the aliens that humanity really means them no harm, so he returns to Earth a hero.  That's as best I can remember the story.  Does it ring any bells for anyone?


changing excel data formatting from vertical to horizontal

I'm not sure what this is called, but I want to reformat excel data from this;    to this;    In other words, loop though the column headers and add each of the data points in a new grouping. And display the results on a new tab.


How can I specify the home directory in Ubuntu, like I can specify %APPDATA% in Windows? I know about $HOME, but that doesn't seem to work when I try changing the default GNOME screenshot save location on Ubuntu 20.10 using dconf Editor. Any help would be greatly appreciated :D Edit: Also, when I change settings in dconf Editor, are they changed at the root level for everyone or just for me?


Proof of the First Isomorphism Theorem for Groups

The statement is the First Isomorphism Theorem for Groups from Abstract Algebra by Dummit and Foote. This proof was left as a exercise, so I'd like to check if all is ok. In particular, I'm a bit worried about the (*) line. It looks a bit awkward, but is it too bad? Any suggestions?    Theorem: If $\varphi : G \rightarrow H$ is a homomorphism of groups, then $ker \varphi \trianglelefteq G$ and $G/ker \varphi \cong \varphi (G)$.  Proof: Let $\varphi:G \rightarrow H$ be a group homomorphism. If $g \in G$ and $h \in ker \varphi$, then we have that $ghg^{-1} \in ker \varphi$ because $$\varphi (ghg^{-1})= \varphi (g) \varphi (h) \varphi (g^{-1})= \varphi (g) \varphi (g^{-1}) = \varphi (gg^{-1}) = \varphi (1) =1,$$ so that $ker \varphi \trianglelefteq G$. Now, define $\phi: G/ker \varphi \rightarrow \varphi (G)$ by $$\phi (g(ker \varphi))=\varphi(g),$$ for each $g(ker \varphi) \in G/ker \varphi$, for some $g \in G$. This is well defined because if $g' \in g(ker \varphi),$ then $$\phi (g'(ker \varphi))= \varphi(g')= \varphi(g)= \phi (g(ker \varphi)).$$ Also, this is a group isomorphism because for each $\varphi (h) \in \varphi (G),$ for some $h \in G$, we have $$(*) \ \phi^{-1}\{\varphi(h)\}= \phi^{-1} \varphi[g(ker \varphi)]= \phi^{-1} \varphi(\pi^{-1}\{g(ker \varphi)\})= \{g(ker \varphi)\},$$ a set with a single element of $G/ker \varphi$, so that it is a bijection, and for every $g(ker \varphi), g'(ker \varphi) \in G/ker \varphi$, for some $g,g' \in G$, we have $$\phi [g(ker \varphi) g'(ker \varphi)]=\phi [(gg')(ker \varphi)]=\varphi(gg')=\varphi(g) \varphi(g')=\phi [g(ker \varphi)] \phi [g'(ker \varphi)],$$ so that it is a group homomorphism.


Probability : At least one boy vs Exactly one boy

Part A. a company is holding a dinner for working mothers with at   least on son. Ms. Smith, a moher of two children is invited. What is   the probability that both children are boys?   ANS：P(both boys | at least 1 boy ) = 1/3     Part B. Your new colleague Ms. Parker also have two children. You see   her walking with one of her children and that child is a boy. What is   the probability that both of them are boys?   ANS: P(both boys | one boy ) = 0.5  I don't understand Part B. If you know one of her children is a boy, does this implies that Ms. Parker has $\geq1$ boy? In mathematical terms, this means that Ms.Parker has at least one boy, true? How come it is different from Part A. Confuse!


Just installed 14.04. It seems to be converting all my screen touch gestures to mouse gestures. And it only supports one point touch. It is supposed to support ten touch points (tested with windows 8.1).  Am I missing something here? Do I have to install some kind of package? Or is it just not supported?  Test - being able to draw here:


Remove page-breaks after chapters in the report class?

So I am using the report class, and every time I try to create a new \chapter it creates it on a new blank page with just the title. I have tried using \usepackage{etoolbox} but I keep getting Latex Error: Float(s) lost and will not compile. I want to start my chapter on the same page, but I can not figure out how.  Link to full .tex file:   \documentclass[12pt, letterpaper, twocolumn]{report} \usepackage{fullpage} \usepackage[pdftex,hypertexnames=false,linktocpage=true]{hyperref} \hypersetup{colorlinks=true,linkcolor=blue} \usepackage{etoolbox} \begin{document} \title{TITLE} \author{RPBruiser} \date{April 13, 2015} \maketitle \begin{abstract} Stuff is here. \end{abstract} \renewcommand{\chaptername}{} \chapter{Introduction} Context of Chapter 1 \chapter{Methods} \section{Housing} Information 123525 -------------HERE IS WHERE I WANT TO BE ON SAME PAGE------------- \begingroup \renewcommand{\clearpage}{} \chapter{results} \endgroup \end{document}


Infinite Series vs Integral Representation of State Vectors in QM?

Shankar's Principles of Quantum Mechanics, pg. 57-59 subsection Generalisation to Infinite Dimensions states that state vectors defined as,  $$|f_n\rangle = \sum_{i} f_n(x_i) |x_i\rangle, \tag{1}$$  exist within a space of dimension $n$ which is 'unspecified but assumed to be some finite number'. The text then goes on to say that for $n\rightarrow\infty$ the series must be replaced with an integral such that the inner product remains finite, i.e.  $$\langle f|f\rangle = \int |f(x)|^2 dx.$$  What I'm trying to understand is when one can let $n\rightarrow\infty$ without assuming one has a continuous basis, i.e. that the $x_i$ remain distinct and the series description (1) is still valid. The inner product,  $$\langle f|f\rangle = \sum_i^\inf |f(x_i)|^2,$$  must be finite which restricts $f$, so does this just define some restricted function space? How does all this link in with the notion of countably infinite and uncountably infinite Hilbert spaces?


How to create a cross product with tikz?

How can I create a cross product like the one in the picture.    \documentclass{article} \usepackage{tikz} \begin{document}  \begin{tikzpicture}[line width=.7pt] \draw [->] (-.2,0)node[below]{$o$}--(4.5,0)node[below]{$x$}; \draw [->] (0,-.2)--(0,2)node[left]{$y$};  \end{tikzpicture}  \end{document}


How to hide/proxy port 8080 via HTTPS/443 with Apache?

I have a non-encrypted service running separate to apache on 8080. I'd like to hide it and redirect all traffic to it via SSL.  I have successfully setup proxy/reverse proxy so all requests to www.example.com go to port 8080.  However, I can still directly access the service if I go to . And it goes via http, not https. I can't block that with the firewall, since the service includes some of the links in the form . I have tried adding a virtualhost on :8080 and listen on 8080 but that doesn't work (and also breaks the proxy on *:443).  Could anyone suggest what I am doing wrong? All services run on the same ip address.  <VirtualHost *:80>     ServerName example.com     ServerAlias www.example.com     Redirect permanent / https://www.example.com/ </VirtualHost>  <VirtualHost *:8080>     ServerName example.com:8080     ServerAlias www.example.com:8080     Redirect permanent / https://www.swapsk.in:443/ </VirtualHost>  NameVirtualHost *:443 <VirtualHost *:443>     ServerName example.com     ServerAlias www.example.com      ServerAdmin webmaster@localhost     DocumentRoot /var/www/html      SSLEngine on     SSLCertificateFile /root/cert.crt     SSLCertificateKeyFile /root/key.key     SSLCACertificateFile /root/ca.ca-bundle      ProxyRequests     Off     ProxyPreserveHost On     AllowEncodedSlashes NoDecode     <Proxy *>         Order deny,allow         Allow from all     </Proxy>     ProxyPass         /phpmyadmin !     ProxyPassReverse  /phpmyadmin !     ProxyPass         /  http://localhost:8080/ nocanon     ProxyPassReverse  /  http://localhost:8080/     ProxyPassReverse  /  http://www.example.com/     RequestHeader set X-Forwarded-Proto "https"     RequestHeader set X-Forwarded-Port "443"  </VirtualHost>


Let $R$ be the ring of all continuous functions from the closed interval $[0,1]$ to $\mathbb {R}.$

Let $R$ be the ring of all continuous functions from the closed interval $[0,1]$ to $\mathbb {R}$  and for each $c \in [0,1]$ let $M_c = \{f \in R |f(c) = 0\}.$       (a) Prove that if $M$ is any maximal ideal of $R$ then there is a real number $c \in [0,1]$ such that $M = M_c.$   (b) Prove that if $b$ and $c$ are distinct points in $[0,1] $ then $M_b\neq M_c.$      (c) Prove that $M_c$ is not equal to the principal ideal generated by $x — c.$      (d) Prove that $M_c$ is not a finitely generated ideal.    (a) I know that $M_c$ is maximal ideal of $R.$  Since $M$ is a maximal ideal of $R$ then $M$ is prime ideal. I am unsure how to proceed.  (b) Assume that  $b\neq c$ and $M_b=M_c.$ Let $f \in M_c.$  Then  $f \in M_b.$ Thus, $ M_c$ is not  maximal ideal of $R.$  (c) and (d) I have no idea how to start it.  Help me, please!


I have to make this method round up a double which is fine but I need it to only round up the first number after the first decimal.   Example 83.2839783214 would be 83.3 here is the code I have so far I can't seem to figure out how exactly to implement it.   public double getPercentFull(){  double percent;  double p = (storage / capacity) * 100;  percent = (double)Math.round(p);   return percent;


Are there any MySQL functions to get all rows with with a start or end date that fall between a given start and end date?

I have a table of events with a recorded start and end time as a MySQL DATETIME object (in the format YYYY-MM-DD HH:MM:SS. I want to find all events that occur in a specific date range. However, events can span multiple days (and go outside of my date range, but I want to return them if they even overlap by 1 second or more with my date range).  Suggestions?


How do I go about backing up/saving installed device drivers in Windows?

I want to reinstall Windows on a machine which has some very obscure drivers. I don't much fancy having to hunt round for them (that's if I'm able to locate them at all). Is it possible to save or backup already installed drivers? If so, how do I do this? How do I then go about installing these 'saved' drivers?


I have a list of dicts like below:  [  {'init_time': datetime.time(14, 0), 'end_time': datetime.time(19, 0), 'value': 5.2},   {'init_time': datetime.time(17, 0), 'end_time': datetime.time(18, 0), 'value': 6.5},  {'init_time': datetime.time(15, 0), 'end_time': datetime.time(17, 0), 'value': 2.5} ]   How can I sort this list by the value of each dict's init_time? Usually with sorted one is able to sort a dict based on either key or value, but in my case, I'm not interested in sorting the dict but the list, using the dict's values.  For example, the output of the above would be:  [  {'init_time': datetime.time(14, 0), 'end_time': datetime.time(19, 0), 'value': 5.2},   {'init_time': datetime.time(15, 0), 'end_time': datetime.time(17, 0), 'value': 2.5}  {'init_time': datetime.time(17, 0), 'end_time': datetime.time(18, 0), 'value': 6.5}, ]


Can not login to MacBook Pro... strange boot screen

Problem: My 2015 retina MacBook Pro is currently stuck booting up to this screen. It happened after I tried following some troubleshooting tips as my MacBook started to freeze up. I’m afraid I made it worst. This occurred after trying SMC reset and I can’t get back any other screen.   It seems to be asking me to turn it off with a switch? But I don’t have a switch on the side of my Mac. Is there a way to fix this before I take it to get checked out at the store? ;(


Difference between epoch and batch size in neural network

I am beginner in machine learning and I came across these terms while going through code of cnn, I want to know how to what exactly they mean and other question is that when the weights of network change? after each batch size or after every epoch? Thank you.


Let $a, b\geq 0$, then prove or disprove $$(a+b)^{r}\leq a^r+b^r$$ where $r \in [0, 1]$.


Can someone identify a resistor with only markings on it see TP?

I am trying to repair circuit boards that fried on my hydraulic anchors (Power Poles) on my boat.  Both have the same resistor fried. I have found the same one elsewhere on the board, see pic.  I tested on my multimeter and get .9 ohm.  The only marking on it is TP.  Anyone know where I can get these?


When I go to upgrade the system with apt-get upgrade the message appears: E: The package linux-hwe-5.4-headers-5.4.0-56 needs to be reinstalled, but I can't find an archive for it. I am a new user in Ubuntu, I need a step by step on how to solve it, please.


How are AUROC scores computed with just two vectors of actual and predicted values as input?

In the R package ModelMetrics, the auc score as shown in the documentation takes only two inputs;  aucScore <- auc(actual=actuallabels, predicted=predictedlabels)  where the inputs are pretty self explanatory. However, how is the AUC score even calculated here? From my understanding, do we not need the class "probabilities" (scores) produced from the model in order to graph the ROC curve in the first place? Each point on the ROC curve is the TPR vs. the FPR, at varying thresholds of class "probabilities" to trigger a "positive" prediction, if my understanding is correct. So how can we chart the ROC curve and find the area under said curve if we don't have the class probabilities to derive each point on the ROC curve itself? Based off labels alone, I would find that it would be impossible to find this unless there's some underlying estimation going on.  I've also noticed that many other packages also compute the area under the ROC curve by taking only two vectors of labels with seemingly no class probabilities.  Thanks.


Must one have a knowledge of fine art to be a Graphic Designer? Should all Graphic Designers know how to draw?

Is it true that nice design comes with a nice  drawing?  Do designers have to know how to draw to be a good designer or not?


A mirror reflects all electromagnetic waves that fall on it in the visible spectrum. How does the mechanism of reflection work? Is it because when a photon hits an electron, the electron jumps to a higher energy level and then to come back to its initial energy level, it emits a photon.  If the energy levels of an atom are quantized, how can a mirror absorb all e.m waves in the visible spectrum? Shouldn`t it absorb only specific wavelengths?


Outputting a parseInt value to two decimals?

I'm new to javascript, and really did try to find a solution but I don't know how to apply it to my specific code.  I have two range fields on a form which I want to use as a loan calculator. So, value1 is for the 'loan amount', value2 is for the 'repayment period'. So value1 needs to be divided by value2, and then it needs to output it into an ID called #fullvalue so that I can show the repayment installment value on the form. My code below is working great, however, I can't for the life of me get it right to output the #fullvalue amount to two decimal places. So that it shows like $79.50 instead of something like $75.56789555  $(window).on('load', function() { $("form :input").change(function() { var value1 = $('form #value1').val(); var value2 = $('form #value2').val(); var fullvalue = parseInt(value1, 10) / parseInt(value2, 10); $('form #fullvalue').val(fullvalue); }); });


Why do cosmic bodies such as planets, stars, satellites revolve? What made them to revolve after the formation of universe?


How to properly render smoke on a transparent background?

When rendering volumes with Film > Transparent enabled, the alpha appears to be the wrong type (premultiplied/straight). In the 3D view it works as expected:    This is a known .  Is there any way to work around this?


SObject row was retrieved via SOQL without querying the requested field - In visual force Commanlink action

I am having issues with Merge fields not working with the visualforce page I created.   This is the code where it is having issue;   <apex:commandLink target="_blank" action="https://na99.salesforce.com/a2g/e?CF00N0A000000Okji={!Account_Plans__c.Name}" value="New Key Business Initiative"/>    It is not querying this field; CF00N0A000000Okji={!Account_Plans__c.Name}  Any help is appreciated.   Thanks!


Simple Automation of Car Path Finding Between 2 Points

I would think that it would be simple to have a car drive from A to B, but apparently I haven't been able to figure it out. My goal is to have a car begin at a certain position and angle, calculate the best path to another position with another angle, and then travel there.  Please keep in mind that this car has a minimum turning radius, so it can't simply change angles by spinning. Also, I would like to see what I can do with the car only traveling in a single direction, ie. no reversing.  I have read over many grid-based algorithms, but I don't see how I can translate those to what I need, which is most likely a series of arcs and straight lines.  The closest thing I have have found is Dubins Interval, which seems closest to what I need, though I believe it is old and has probably long since been replaced. I have sketched out paths using this method, but have had trouble translating it to programmatic form (C++). I believe the rough idea is to line up the minimum steering circles of the start and goal, start turning from the start until you are on the line, head towards the goal, and then either simply go onto the goal circle and curve it, or project an additional circle on the same line and use it to end up on the goal circle in the opposite direction.  If anyone knows of any examples, code preferred, of simple car driving path examples, I would appreciate it.


HTML encoding strikes again (but with a twist) - Chat messages inbox notifications aren't looking good

I just noticed this in my inbox:        Same appears in the global inbox of the network profile.  This looks like  , with the difference that it happens only if the word containing the special character is the last when truncating the message.  Can it please be fixed? Since it's hard to know which word will be the last, it's hard to reproduce hence not sure if it affects only chat notifications or other types of notifications as well.


We know that Hogwarts is in Britain, and all students speak English. Thus all the spell we have seen have English dialect. But what about the wizards of countries outside Britain?   Like when Hermione went to France and Ron went to Egypt. I am sure none of those wizards cast their spells in English... but somehow this thing was never discussed or mentioned?  Does this mean that every spell one cast in English has its counter spell in other languages? Each one of the spells in each one of the languages? Then what about the spells that one wizard invents himself and never discloses in  public, like Sectumsempra (Invented by Snape and there could be tons of others from other wizards)?  Does this also mean that other wizards of other countries may have invented spells of their own, in their own language which somehow they have kept secret? There should be a check on things like this. Does the ministry keep track of such spells? If yes then how?


In python how to check inequality to "float("inf")"?

I have following simple code. Just confused why the second evaluation is True. Could anyone explain to me? So what is exactly the difference between "is" and "=="?  a = float("inf") print a != float("inf") print a is not float("inf") # why is this True?  b = 1 print b != 1 print b is not 1  c = int(1) print c != int(1) print c != int(1)   Output:  Python 2.7.10 (default, Jul 14 2015, 19:46:27) [GCC 4.8.2] on linux  False True False False False False


How would I go about fixing this error? I have pycharm installed through a ppa that I have been using for years in various computers.  W: GPG error: http://ppa.launchpad.net/mystic-mirage/pycharm/ubuntu xenial InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY DD969F10A7E2BCD2 W: The repository 'http://ppa.launchpad.net/mystic-mirage/pycharm/ubuntu xenial InRelease' is not signed. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. W: There is no public key available for the following key IDs: DD969F10A7E2BCD2


What are the odds of the following:  Great Grandmother was born January 14 (1/14)  My Grandfather was born April 11 (4/11)  I was born on January 14 (1/14)  My son was born on April 11 (4/11)   FYI: My Great GrandMother lived to be 100 years old.  She passed just a few years ago.


Heap Overflow And Stack Overflow examples

I need help in understanding heap and stack overflow, so it would be a lot helpful if I had few examples to understand the concept well


I'm using a Surface Pro 3 running Windows 10 and I have 14GB Free on my C:\ drive. But whenever I shrink it it only says I have 941MB avalible to shrink.


How can I fix QGIS PostGIS Manager error 'shp2pgsql' is not recognized?

I have QGIS 1.8.0 installed via OSGeo Installer and work on win 7. All I need is to upload the shapefile to the database via this plugin. Unfortunately I am receiving an error:  Something's wrong: ["'shp2pgsql' is not recognized as an internal or external command,\n", 'operable program or batch file.\n']   How to install and configure shp2pgsql to make this plugin work fine?


How to prove Binet theorem, namely $\det ( AB ) = \det (A ) \det ( B )$?

I've tried with the formulation of two arrays $2 \times 2$, but could not.


Prove that: $e^{-\frac{|t|}{2}}= \int_{\mathbb R} \frac{e^{ixt}}{1+x^2} dx.$

I need help for prove that $$e^{-\frac{|t|}{2}}= \int_{\mathbb R} \frac{e^{ixt}}{1+x^2} dx, \quad \forall t\in \mathbb R.$$ Thank you in advance


Buying a camera specifically for wide angle photographs

I am a real estate agent. My only need for the camera that I purchase, is to have the best wide angle photos. I was looking at DSLR and point and shoot cameras. What is the best point and shoot camera (i'm not sure if this is the correct term, I'm speaking of something like the canon coolpix)? Also, are there some cheaper options for DSLR cameras with the attachments? I saw a canon ef-s 10-18mm that was priced pretty well but I don't know what kind of camera I would need to attach this to. Any help would be appreciated. Thank you!!


How to make WordPress keep me signed in?

When I log in to my WordPress blog, there's a checkbox that says Remember me.  But whether or not I check this, if I come back in a day or two I have to log in again, so it doesn't appear that this checkbox does anything.  (My Google account, by contrast, hasn't ever once asked me to re-login on this computer, for more than a year now.)    How do I make WP actually remember me?


I've had this question on my mind for quite a while and looking at the web, I couldn't find an answer to this question.  I've had a lot of physics experiments involving springs, unintentionally dismantled a hair clipper once, helped my dad repair his car, and all of them have very identical springs.   Here's an image of a variety of springs that are used for multiple purposes:     So, what's with the spiral/helical shape? And why are they "curled"  in circle-like shapes. Why not triangle, square or any other geometric shape? What exactly is the physics behind this.


How to prove "eigenvalues of polynomial of matrix $A$ = polynomial of eigenvalues of matrix $A$ "

Title looks a little bit twisted. What I want to say is the following:  $A\in\mathbb{R}^{n\times n}$, polynomial of matrix $A$: $P(A)=\displaystyle \sum_{k=0}^{n} c_k A^k$. $\lambda(A)$ is the set of eigenvalues of $A$.   So, we want to prove $\lambda(P(A))=P(\lambda(A))$  So far, I can prove it when $A$ is diagonalisable, but when $A$ is not diagonalisable, it seems we can't just simply use Jordan normal form to prove it. (Or this statement won't hold when it's not diagonalisable?)  Can anyone suggest me something and help me out? Thanks!


How to create vertices/edges/faces at the intersection of an object and a plane?

I have a cubic object and a bigger plane that 'cuts' it. My objective is to create a face on the cube where the plane is cutting it without removing anything from the cube mesh, so I can't use the boolean operators. Until now, I used the Knife tool, but its accuracy leaves a lot to be desired.  I tried to use both 'Mesh > Faces > Intersect' options from the bottom dropdown menu, but neither is satisfying, Intersect Knife plainly not working and Intersect Boolean removing my entire cube.  Is there a simple solution on Blender 2.77a that involves no Python scripts and no extensions whatsoever? Thanks in advance.


Still no fictional geographies in some GIS format?

I'm actually reviving  from 2011 as I'm hoping the Game of Thrones fever has boosted people's interest in drawing fictitious countries in some GIS format (e.g. .shp) from 2011 until now, so that others can improve or modify.  Alternatively, does anyone know of an easy way to transform a bitmap map such as the one below to a vector map?  Source: .


$$ \int_{0} ^ {\pi/4} \frac {\tan^2x}{1+x ^2} dx$$  I have tried using $x=\tan \theta$. But in my opinion i am finding that this might not be closed  form. Please help.


How should I install a partition wall perpendicular to a finished exterior wall?

I wish to install a partition wall with a header made of 2x8s (7 feet long). The header will run perpendicular to ceiling joists. I know the no-nonsense approach is to cut channels in the ceiling drywall and exterior wall drywall to anchor the header and end stud. Unless I am extremely lucky I will have to install some blocking between exterior wall studs to anchor the end wall stud (implies opening a couple spots to install blocking and repairing vapour barrier and drywall). Is the opening of existing drywall overkill?


How to extract elements from dictionary and append to list

I have a dictionary below: a = {'Developer': [{'id':1, 'name':'a', 'age':'11'}, {'id':2, 'name':'b', 'age':'33'}, {'id':3, 'name':'c', 'age':'34'}]}  Expected  output one: [{'id':1, 'name':'a'}, {'id':2, 'name':'b'}, {'id':3, 'name':'c'}]  Expected  output two, list of ids only: [1, 2, 3]  Code: list_ = [] for i,j in a.items():     d = {}     for m in j:         d['id'] = m['id']         d['name'] = m['name']         list_.append(d)          list_  My current out: [{'id': 3, 'name': 'c'}, {'id': 3, 'name': 'c'}, {'id': 3, 'name': 'c'}]


Who cares about Transpiled Circuit Text?

At any result of a job in this last version of the Circuit Composer, at the OpenQasm tab inside the Circuit Diagram, I am unable  to use the tradicional copy or ctrl-c to get the transpiled circuit selected text for further studies.  Is this an error or it is functioning correctly, because in before versions it was possible doing it?


Apache2: ReWrite rule not showing up in address bar?

I have a domain, example.com.  Here is my apache2 ReWrite rule:  RewriteEngine on RewriteRule ^([^/.]+)/?$ index.php?uname=$1 [L]   When I go to ,  appears in the address bar of my browser.  I want  to appear in the address bar! (my javascript needs to parse the GET arguments)  Is this possible?  Many thanks in advance,


StackExchange drop down hiding chat, blog and log out, concerns

Took a few seconds to find how to get back to chat on SO. I quickly found that it was hiding inside the StackExchange drop down along with Blog and Log out. Having these links inside the "site switcher" seems a tad out of place and calls for concern personally.   Any ideas for an alternative to these objects location?


The list of sources could not be read as type 'universe' is not known while updating

When I run sudo apt-get update in Terminal of my Ubuntu 19.04, I get this:  E: Type 'universe' is not known on line 35 in source list /etc/apt/sources.list E: The list of sources could not be read.


Where are 3rd party jars deployed in a maven system

New to Maven...  I have succeeded in creating a jar for my app. I'd like to run the app from this jar "java -jar foo.jar MyClass" but I have no idea where to get (and package) all the dependencies. Does maven have a goal to do this? If not, do I use something like proguard? And then how do I thread that into the maven goals?  Thanks in advance


Solving ODE with negative expansion power series

Since on Mathematics stackexchange I didn't get an answer, I'll try it here, since people here are more familiar with this topic (general relativity related).  I am reading a dissertation of Porfyriadis "Boundary Conditions, Effective Action, and Virasoro Algebra for $AdS_3$", and I am trying to solve a system of DE to get the appropriate diffeomorfism (page 31 onward).  I am trying to solve a system of ODE, such that each DE is equal to some degree of term that I'm expanding to. For instance, one DE is this:  $\xi^r\partial_r g_{rr}+2g_{tt}\partial_t\xi^t=\mathcal{O}(r)$  which you get by taking a Lie derivative of background metric and setting it equal to certain $\mathcal{O}(r^n)$ terms.  $g_{ij}$ are given, from metric ofc. I need to assume that the solution (since I'm looking for components of $\xi^\mu$( which is a vector with components $\xi^t, \xi^r, \xi^\phi$) is given with power series of the form:  $\xi^\mu=\sum\limits_{n}\xi^\mu_n(t,\phi)r^n$,  and this is to be seen as expansion around 1/r (expansion around $r=\infty$).  Now when I plug this in the ODE I get this  $\frac{2}{l^2}\sum_n\xi^r_nr^{n+1}+2\sum_n\xi^t_{n,t} r^n+\frac{2}{l^2}\sum_n\xi^t_{n,t}r^{n+2}=\mathcal{O}(r)$, where  $\xi^\mu_{n,i}$  is the derivative with the respect to i-th component.  What troubles me is, how to expand this? Do I set n=0,-1,-2,... until my O(r) terms cancel each other out? Or?  I'm kinda stuck, at this seemingly easy point.  In the thesis he gets 6 equations with coefficients, first one should be:  $\xi^r_{n-1}+l^2\xi^t_{n,t}+\xi^t_{n-2,t}=0,\ n\ge 2$,  But I am not getting this. What am I doing wrong?    EDIT: For further clarity: The metric is that of $AdS_3$ given with line element:  $ds^2=-\left(1+\frac{r^2}{l^2}\right)dt^2+\left(1+\frac{r^2}{l^2}\right)^{-1}dr^2+r^2 d\phi^2$,  and the differential equations in question are given by solving $\mathcal{L}_\xi g_{\mu\nu}=\mathcal{O}(r^n)$, where $\mathcal{O}(r^n)$ are the fall off conditions. In the dissertation, he took the deviation of nonzero components of the metric to be subleading, that is:  $\mathcal{L}_\xi g_{tt}=\mathcal{O}(r)$ $\mathcal{L}_\xi g_{rr}=\mathcal{O}(r^{-3})$ $\mathcal{L}_\xi g_{\phi\phi}=\mathcal{O}(r)$, while others are $\mathcal{O}(1)$.  Solving Lie derivative gives me 6 equations, which I should solve by plugging in the above ansatz ($\xi^\mu=\sum\limits_{n}\xi^\mu_n(t,\phi)r^n$), but this is the part I get stuck.  ADDENDUM:  I was looking at other components, and have noticed that I have $g_{rr}$ factor with some of them. That term in metric is:  $g_{rr}=\left(1+\frac{r^2}{l^2}\right)^{-1}$  Now, is it legitimate thing to expand this around $r=\infty$ so that I can put $r$ terms inside the sums (assumed solution)?


Quantum mechanics and gender of unborn baby

Having a debate with my other half here, I'm currently pregnant and we have not had any scans or tests to determine gender of the baby.   I'm seeing this as similar to a  in that my baby is both male and female until it is determined either way. However my partner believes that it is unequivocally fixed because the sperm and egg determined the gender, the fact that it has not yet been observed is irrelevant.   I know that this is all mainly theory but I wanted to get a physicist's opinion. How determined is my baby's gender right now?


I have the following string that I want to split on the "\n" but I need to remove/replace all of the occurances of multiple "\n\n";   Here is my sample string:  "\n01:05 PM\n901\nNew York Mets \n\n\n\n\n\n\n\n\n \n+125\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"   So that I end up with an array like  1:05 PM  901 New York Mets +125  I've tried,   string adjRow = row.InnerText.Replace("\n", "");   Is there a single Regex Pattern that will work?  Added the following and seems to work.       RegexOptions options = RegexOptions.None;                     Regex regex = new Regex("[\n]{2,}", options);                     string adjRow = regex.Replace(tempRow, "\n");   Here is the result,     "\n01:05 PM\n901\nNew York Mets \n \n+128\n \nOv\n8½\n-113\no\n"


I have a direct mapped cache of size S with the line size L. The cache is physically indexed and tagged. The physical address is 50 bits, numbered from 0 to 49 (with 0 being the least significant bit). The machine has a word size of 4 bits and the memory is byte-addressable. Which bits of the 50 bits are compared with the address tag?


Intuition for Euclidean Distance as a measure of spread (Standard Deviation)

I've been studying descriptive statistics and am having a hard time understanding the actual intuition behind standard deviation. I'm trying to get a practical feeling for it and so I'm trying to draw conclusions from it using a distribution of 20 numbers, from 1 to 20. I know the mean is 10.5 and the absolute average deviation is 5, which is pretty intuitive.   Now when taking the standard deviation I get the value 5.77 which still makes some sense if I think about it as the average euclidean deviation from the mean. So I imagine adding orthogonal distances and then averaging them $\frac{\sum(x_i-\bar x)^2}{n}$ and taking the square root of that at the end to get the actual average distance. The formula makes sense from an euclidean perspective. So all that being said, my questions:  1) Why would an euclidean average distance be more accurate than an absolute deviation from the mean? I actually think absolute average deviation is more accurate since it doesn't infer any direction of the values. When taking the euclidean distance, I'm pretty much saying every value is placed at a 90° angle from each other. That does not sound right. So why the Euclidean distance? (I'm aware of this article but If someone could actually explain what efficiency is that would be very helpful: )  2) If The advantage of using SD is because of all the math we have developed around normal distribution shapes (68%, 95%, 99,7%...) wouldn't it be better to just rewrite that model with the new average deviation?  3) Ill probably post another question in the future about this, but when calculating standard error, this standard deviation seems to get even worse, since we need corrections for finite populations. Does this make any sense?


Which vegetables we should not store in the fridge and why?

I've read that some vegetables should be never stored in the fridge.  Is that apply to most of the vegetables, some specific group or specific ones (which one)? What's general rule?


Does the wood elf's Mask of the Wild trait allow them to basically "disappear" in front of their opponent if in an area lightly obscured by foliage?

The rules on  state, in part (PHB, p. 177):  You can't hide from a creature that can see you clearly, [...]  The description of the 's Mask of the Wild trait says (PHB, p. 24):  You can attempt to hide even when you are only lightly obscured by foliage, heavy rain, falling snow, mist, and other natural phenomena.  Can a wood elf in melee combat with a creature in a wooded area surrounded by light bushes simply use their movement to move 5 feet into an area lightly obscured by foliage, then use their action to hide right in plain sight of his opponent (5 feet away)? Then continue their movement using the cover of the light foliage to escape? I am looking for a RAW ruling on this; all interpretations must be traced back to specific words in official written rules or official WotC rule clarifications.


Hiding get mobile app button on SP online communication site collection

For one of the clients, I have spin up a modern communication site collection and on the landing page of the same, I am seeing 'Get the mobile app' showing up, I was able to hide the 'feedback' button using css but no luck with Get the mobile app button.  Can someone please share css to hide 'get mobile app' button, appreciate the help.


True or false: If $A^3 = 0$ , $A$ is not invertible. Justify answer.

can you help me with my homework:  If $A^3 = 0$ , is $A$ not invertible? and please justify why.


Showing remaining review count while reviewing

I think when a user is reviewing it would be useful if they can view their remaining review count in review-bar, such as 14 of 20.    Can this be implemented?


I am relatively new to Java, and often find that I need to sort a Map<Key, Value> on the values.  Since the values are not unique, I find myself converting the keySet into an array, and sorting that array through array sort with a custom comparator that sorts on the value associated with the key.  Is there an easier way?


Cite references in figure caption without appearing in list of figures

Problem: Citation appearing in the list of figures.  Minimal Working Example:  \begin{figure}[H]     \centering     \includegraphics[scale=0.6]{phases-analyse-predictive.png}     \caption{Phases de l'Analyse prédictive \citep{Imanuel2014}}     \label{phases-analyse-predictive} \end{figure}   Current outcome:    Desired outcome:  The reference to appear in the  figure caption but not in the list of figures.


There are    around about getting Ubuntu LTS working with Nvidia 960M cards. Given that there's no definitive answer, I want to offer the following: after testing several distros, Knoppix and Kali both worked without any problems.   So, my questions:    What is different about Ubuntu that Nvidia drivers don't work out of the box? More importantly, is there an easy way (for an end user) to import whatever's working into Ubuntu 16.04?   Edit: Here's what I tried:   Purged nvidia-* and reinstalled 364 drivers. Got login loop, followed answers  (chown, chmod, rm .Xauthority, and  /tmp) Reinstalled xorg and unity. Went to  and found the  version that works with my card (opted for the Long lived branch). Purged nvidia* (no dash, following a tip in a comment), and reinstalled 367 drivers. Purged nvidia*, reinstalled 370 drivers. Currently stuck at login loop, after following instructions from 2.


Easiest way to prove that $2^{\aleph_0} = c$

$\aleph_0$ is the cardinality of the set of natural numbers, $\aleph_0 = |N|$. $c$ is the cardinality of the continuum, i.e. the set of real numbers $c = |R|$.  I know that $|P(A)| = 2^{|A|}$. This means that the cardinality of the power set of a set is 2 raised to the power of the cardinality of that set.  This basically means that to prove  $2^{\aleph_0} = c$, I need to prove $c = |P(N)|$. I've seen the Cantor diagonal argument, although I have no idea on how to use it to prove this.   Could anyone suggest ideas of the simplest way to prove that $2^{\aleph_0} = c$?


Overzealous spam filter triggers on Chinese characters in the "Help and Improvement" queue

It seems the spamfilter on the "Help and Improvement" queue has some problem. From  (from the review of  question).  I think,   Well, "there are" happens quite often in spams, also often in hams :-) Maybe in the case of a 3k+ user it is not really probable he would try to spam.   On my tries it seems, the first word of the edited message is considered always spammy.


they would've got away with/would've gotten away with it

Which is right:   They would’ve got away with it. They would’ve gotten away with it.   I am interested in what we would say in the United Kingdom of Great Britain and Northern Ireland, not in the United States of America.


Why does my query run fast in Environment A, but slow in Environment B?

I have a piece of SQL that seems to run really fast in Environment A, but the exact same query runs really slow in Environment B!  Environments are supposed to be the same, so what should I do and/or where should I look in order to see why the query doesn't perform the same?


Generalizing Cauchy-Schwarz for more than two vectors

For a complex inner product space, $X$, Cauchy-Schwarz inequality states $$ | \langle x,y \rangle |^2 \leq \langle x,x\rangle \cdot \langle y, y\rangle , $$ for any $x,y \in X$.  Equality holds if and only if $x$ and $y$ are linearly dependent.  I noticed that this can be restated as: $$ \left|\begin{array}{cc}  \langle v_1, v_1 \rangle & \langle v_1, v_2\rangle \\ \langle v_2, v_1 \rangle & \langle v_2, v_2\rangle \\  \end{array}\right| \geq 0$$  with strict equality if $\{v_i \}$ is linearly independent.  Does this (somehow) generalize for $n$ vectors?  That is, does the following hold:  $$ \left|\begin{array}{cccc}  \langle v_1, v_1 \rangle & \langle v_1, v_2\rangle & \cdots &\langle v_1, v_n \rangle \\ \langle v_2, v_1 \rangle & \langle v_2, v_2\rangle & \cdots &\langle v_2, v_n \rangle \\ \vdots & \vdots & \ddots & \vdots \\ \langle v_n, v_1 \rangle & \langle v_n, v_2\rangle & \cdots &\langle v_n, v_n \rangle  \end{array}\right| \geq 0$$   At the very least, can we prove that the above determinant is non-zero if $\{v_i \}$ is linearly independent?  I came across this working on a functional analysis problem set, but this isn't a homework problem.    EDIT: For those tagging it as a duplicate, I see this as different because this question specifically concerns inequality, and not just proving that the determinant is non-zero if they are linearly independent.  Additionally, this post specifically suggests a connection to Cauchy-Schwarz that isn't mentioned in the other post.    As a commenter (Algebraic) pointed out, this matrix is called the Gram matrix of the vectors $\{v_i\}$; Wikipedia states that this matrix if positive semi-definite, and is positive definite in the case where they are linearly independent.  This proves that the determinant is indeed greater than or equal to zero for arbitrary $\{v_i\}$ and is strictly positive in the case where the $\{v_i\}$ are linearly independent.


Are there graphs for which $G \cong Cay(Aut(G), S) $?

I'm looking for graph $G$, $V(G) >2$, such that$G \cong Cay(Aut(G), S) $, where $Cay$ is the Cayley graph (considered as undirected graph) and $S$ is minimal generator of $G$.  I've written a GAP code that looped through $\Gamma$ groups, and formed $G'=Cay(\Gamma)$ and $G''=Cay(Aut(G')) $. After it checked if $G' \cong G''$ is true. It happened to be false for the first 1000 groups, except when $\Gamma$ is the trivial group and when it is isomorphic to $C_2$.  Now, I am not even sure what generator set was used by GAP. Is it possible that for other generator set it would work? Maybe if it isn't minimal?  Thanks in advance!


How to calculate "interference weight" between 20MHz, 40MHz and 11ac 80MHz APs?

I want to know how to calculate the "interference weight" in the combination of APs running on different channel frequencies.  Lets say I have 10 APs in different operating modes, such as 11a, 11a/n and 11ac.  If an 11a AP is running a 20MHz channel say (36), and some 11a/n APs are running 40MHz channels (36 and 40), and some 11ac APs are running with 80MHz channels (36, 40, 44, 48).  Now how do these frequencies interfere with each other and how can I calculate the interference weight among these frequencies?  "Interference weight" means, like how much percentage that a channel is interfering with other channel. Like, AP1 and AP2 are running on channel say 48, we can say that they are highly interfering. And if they are running with little adjacent channels like (AP1 at 44 and AP2 at 48), there is partial interference, and if they are running in away channels there is no interference.  By this we can achieve a channel for an AP with less interference with reference to neighbors, we can select that channel as an automatic channel for that AP.


proof of the second generalized mean value theorem for integrals

Let $f,g,g´$ be continous on $[a,b]$ and $g$ monotone on $[a,b]$; then there exist $c\in (a,b)$ so that $$\int_{a}^{b}f(x)g(x)dx=g(a)\int_{a}^{c}f(x)dx+g(b)\int_{c}^{b}f(x)dx$$  Ineed to apply the first generalized mean value theorem for integrals i.e. $$\int_{a}^{b}f(x)g(x)dx=f(c)\int_{a}^{b}g(x)dx$$ to $g´$and $\int_{a}^{x}f(x)dx$ but I don´t know how please I would appreciate your help


How can you detect if users have created sock puppet accounts?

How many users have created more than one profile on SO to vote themselves on their other original profile? There are some benefits when you have more reputation and sometimes you don't want a single -1 vote on your question or answer. In this case you may have an extra account to convert that -1 vote into 0 vote and  upvote for each of your questions and answers to gain reputation. I think it is not a good thing to do as a good developer.  Is there any way to recognize this situation? I think there should be some stats in each user's profile about how many votes are posted by each user on him/her or something like that.  So how many users have more than one profile? How to handle this situation? I have not created one yet but............ I don't think so :)


If I remote wipe my iPhone, can I still locate it remotely?

If I lose my iPhone, and I use remote wipe to prevent my confidential data from being stolen, then can I still use Find My iPhone to locate it on a map?  I'm assuming not (since it resets to factory settings), but I wanted to double-check.


I am answering a question regarding the simplicity of a group of order 380 and wondering if my approach is okay.  380 = 2^2 * 5 * 19, so the Sylow 5 subgroups have order 5, are cyclic, and if there are more than 1 of them, then we must have 76 of them. Hence, we have (5-1)*76=304 elements of order 5. Now, looking at the Sylow 19 subgroups, if there are greater than 1 of them there must be 20, but we don’t have enough space for all of those elements in the group, hence there is only one Sylow 19 subgroup, a normal subgroup, and so the group is not simple.


Can't start Ubuntu after interrupted upgrade

I was trying to upgrade Ubuntu from 16.04 to 16.10, but during the upgrade process an error popped up (it said something like 'there is an error in system files' but I don't remember exactly).   The upgrade window froze and I forced quit.   Now, after restart Ubuntu is stuck at purple screen. What should I do to reach the login screen? I have important files in my system and now I can't reach them also. I also have windows 8 installed pc and I can start windows normally, if that's any use.


Figuring out algorithm/formula for item scaling in WoW

I am trying to figure out the algorithm/formula for item stat scaling in WoW. If you play in battlegrounds or arenas, your item's stats increase to the highest possible level in that bracket. So if you're level 10 your items will be boosted to level 19 in that bracket. 20 will be 29 and so on.  I have an example here:    This item is level level 20 and has 10 armor, 7 agility, and 7 stamina. When you join the arena or battleground, it will increase to this:    I am trying to figure out this algorithm/formula, so I can enter any item's item level and stats, which will then figure out the stats when in a battleground or arena. How would I approach that? I've tried a few isolation equations, but it won't really work :( Thanks in advance!


Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$

In general, the group $\mathbb Z_{mn}$ under addition $\bmod mn$ is isomorphic to the direct product $\mathbb Z_m \times \mathbb Z_n$ if and only if $\gcd(m,n)=1.$ This is easy to see since $\mathbb Z_{mn}$ is generated by the element $(1,1)$, and if $\gcd(m,n)=1$, then this will only be zero if it is multiplied by itself $mn$ times (resulting in the cyclic group).   However I'm interested in constructing an isomorphism between the two groups as an explicit expression. I've been playing around a bit with some examples, one of which is the function $\phi : \mathbb Z_2 \times \mathbb Z_3 \to \mathbb Z_6$ where $\phi(a,b) = 3a + 4b \pmod 6$, which gives us the desired isomorphism. I'm interested here in the relationship between the integers $2$, $3$, and the coefficients $3, 4$ of $a$ and $b$. After playing around in Wolfram|Mathematica, I managed to obtain the following isomorphisms $\phi_{m,n} : \mathbb Z_m \times \mathbb Z_n \to \mathbb Z_{mn}$ for coprime $m,n$ in $\{1, 2, \dots, 10\}$.   First of all, the following results seem to hold in general.  $$\phi_{1, n}(a, b) = a + b \qquad \text{for all $n$}$$  $$\phi_{m, 1}(a, b) = a + b \qquad \text{for all $m$}$$  $$\phi_{2, n}(a, b) = na + (n + 1)b \qquad \text{for all $n$}$$ $$\phi_{m, n}(a, b) = K a + L b \iff \phi_{n,m}(a, b) = L a + K b \qquad \text{for all $m, n$}$$  Beyond this point, I could not spot a general pattern. The isomorphisms I obtained are:  $$\phi_{3, 4}(a, b) = 4a + 9b$$ $$\phi_{3, 5}(a, b) = 10a + 6b$$ $$\phi_{3, 7}(a, b) = 7a + 15b$$ $$\phi_{3, 8}(a, b) = 16a + 9b$$ $$\phi_{3, 10}(a, b) = 10a + 21b$$ $$\phi_{4, 5}(a, b) = 5a + 16b$$ $$\phi_{4, 7}(a, b) = 21a + 8b$$ $$\phi_{4, 9}(a, b) = 9a + 28b$$ $$\phi_{5, 6}(a, b) = 6a + 25b$$ $$\phi_{5, 7}(a, b) = 21a + 15b$$ $$\phi_{5, 8}(a, b) = 16a + 25b$$ $$\phi_{5, 9}(a, b) = 36a + 10b$$ $$\phi_{6, 7}(a, b) = 7a + 36b$$ $$\phi_{7, 8}(a, b) = 8a + 49b$$ $$\phi_{7, 9}(a, b) = 36a + 28b$$ $$\phi_{7, 10}(a, b) = 50a + 21b$$ $$\phi_{8, 9}(a, b) = 9a + 64b$$ $$\phi_{9, 10}(a, b) = 10a + 81b$$ If you want to try and generate a few yourself, here is the Mathematica function I implemented. I'm sure it can be optimised, but for the first 10 coprime integers it sufficed.  isomorphism[{m_, n_}] :=       Module[{x = Null},       For[i = 1, i < m*n,           i++, (If[#[[2]] == Table[i, {i, 0, m*n - 1}],           x = ToString[#[[1]][[1]]] <> "a+" <> ToString[#[[1]][[2]]] <>          "b"; Break[]] &) /@       Table[{{i, j},       Mod[i #[[1]] + j #[[2]], m*n] & /@       Table[{Mod[i, m], Mod[i, n]}, {i, 0, m*n - 1}]}, {i, 1,      m*n}, {j, 1, m*n}][[i]]]; x];   I'd appreciate if anyone can help me find the pattern to determine $\phi_{m, n}$ in general.


How do I map cones on a grid using 5e standard distance?

I am making spell templates for 5th editions standard distance rules, and I am puzzled on cones. How do you map large cones on a grid using the standard diagonal squares = 5ft rule?   I am mostly confused as to when the width equals the distance. The PHB just says "A cones width at a given point along it's distance is equal to that points distance from the origin.". I assume it is either the mid or end point, but either one has issues. If I choose the mid point it makes the cone huge, if I choose the end point the shape is off.   Either way, I know things like this are kept vague on purpose, but this seems a little to vague.


I unplugged everything from my computer a couple of days ago because I had to move it. After half an hour later I plugged everything back but my computer wouldn't start. It's a HP desktop. Here are the things I noticed or have done.        The power button's light used to be lit when power cord is plugged in and it isn't anymore.   I pressed the power button and nothing happened.   The power supply has a green light. When I plugged in the power cord, the green light is on.   I followed steps posted on the internet to test if a power supply is still working. I unplugged all lines that are connected to the   power supply and used a pin to connect green and blank wire and   plugged in the power cord of the power supply. The fan was running   fine.   I changed the cmos battery.


Why are Flash applications so sluggish/crashy?

I've noticed that Flash applications tend to be more sluggish under Ubuntu than they do under Windows on the same machine. This is particularly noticeable when watching HD video or playing graphics/physics-heavy games. Are there any ways of improving the performance of Flash under Ubuntu, or is this just an issue with the Linux version that I will have to live with?  Currently I'm just cutting down on the number of tabs open, blocking flash ads, and closing other programs, but I'm looking for ways to affect Flash itself.  Other things I have already been doing include using Youtube's HTML5 feature and playing videos straight from /tmp in VLC. I was wondering if there was some way of streamlining Flash itself though. Perhaps not.  More Specific Question: Is there anything I can do in mms.cfg to boost performance?


How would i create a multi value Dictionary in c#?  E.g. Dictionary<T,T,T> where the first T is the key and other two are values.  so this would be possible: Dictionary<int,object,double>  Thanks


Which version of NFS is my NFS server using?

I'm mounting a NFS filesystem on my machine.  How do I figure out what version of the NFS protocol the server uses?  I don't have access to the NFS server machine, but I do have root on my client machine.  Is there anything I can run on my client machine to identify what version of the NFS protocol is being used by the server, or what versions it supports?  I wasn't able to find any useful information in /var/log/messages or kernel debugging output (dmesg).  I have tried running nfsstat, but I'm not sure if it is giving me any useful information.  However, when I run nfsstat -s to request information about the server, I don't see anything useful:  # nfsstat -s Server rpc stats: calls      badcalls   badfmt     badauth    badclnt 0          0          0          0          0          When I run nfsstat -c to request information about the client, I do see some information about Client nfs v3, but I'm not sure how to interpret this.  Does this tell me anything about the protocol being used between my client machine and the NFS server?  Does it mean I am currently using v3 of the NFS protocol?  Does it tell me anything about what versions of the NFS protocol the server supports, e.g., NFS v4?


How to run a Desktop graphical application just once under sudo?

For example, I'm trying to run Archive Manager from Ubuntu Desktop (10.04) under sudo otherwise it won't let me extract a Software Development Kit into /usr/local  Update: I don't want sudo to be a permanent change to launching the application; only to run it under sudo when I choose, until it's quit.


What is the best way to root a 2012 Nexus 7 running 5.1.1 Lollipop?

I have had my N7 for about 5 or 6 months now, and I am considering rooting it. I would like to know the best one click rooting methods to use. I've heard of kingoroot, but I don't know if it roots 5.1.1 yet. Thank you


How can I check if the pairs of letters T and K , E and W are homeomorphic or not?


I can use computers. I know how to use a computer.   Why?  And what about the followings. Which of these is the natural sentence to say?   He can teach how to use a computer. He can teach how to use computers.


Usage of 'the' with an adjective in superlative degree when there is no noun

Should I put 'the' before an adjective in superlative degree when there is no noun.  For example:  I am (the) strongest. You are (the) best.


If $n\in N$,then prove that $2\sqrt n-2<1+\frac{1}{\sqrt2}+\frac{1}{\sqrt3}+....+\frac{1}{\sqrt n}<2\sqrt n-1$  How should i prove this inequality,neither AM-HM nor any other inequality theorem is working here.


Show that $\lim_{x\to \infty}\left( 1-\frac{\lambda}{x} \right)^x = e^{-\lambda}$

Based on the definition of $e: = \lim_{x\to\infty} \left(1+\frac1x \right)^x$, how can we show that   $$\lim_{x\to \infty}\left( 1-\frac{\lambda}{x} \right)^x  = e^{-\lambda}?$$  So far I've tried changing variables, $\eta = \frac{-x}{\lambda}$, so $=\lim_{\eta \to -\infty}\left( \left( 1 + \frac1\eta \right)^\eta \right)^{-\lambda}$. But then we would need to show $\lim_{\eta \to -\infty}\left( 1 + \frac1\eta \right)^\eta =e$.


I'm new at blender and I'm trying to animate a ferris wheel. But blender is still very difficult for me and I'm stuck. I made the base and the little cars separately but I have no idea how to let them rotate properly.    Anyone who wants to explain me how to do that?  Many thanks!


I know that the generator for $(\Bbb Z,+)$ is $<1>$, because you can get any number in $\Bbb Z$ as a sum of $1's$ and $-1's$. But what about $(\Bbb R, +)$ how can one find a generator for this group , or is it impossible ?


Mesh always faces User Perspective when added

Whenever I try adding a new object in my scene, it always starts off facing towards the user perspective. How can I make it so that it's aligned to the grid (like the default cube) rather than my view without rotating the object?  Here is a cube that I just added using Shift-A. Unlike the default cube, it faces where my view port is pointing.    Vs. Default cube orientation


It is common to say "What happened to him (or somebody)?" to inquire about somebodies' whereabouts. But is it right?   In my opinion, it should be "What was happened to him?" or "What did happen to him?", even it can be "What had happen to him (before today)?" Am I wrong in this understanding?


Something massivly slows down my internet

Soo I have this problem that has been going on for a few weeks now and I can't find a fix or a thing that would help me. the problem is that my PC is 90% under some virus / spyware that incredibly slows down my PC sometimes. Sometimes it's fine but from second my download speed goes to 0.20MB/s I usually have around 20MB/s it's pretty random and weird, I don't know what to do,I tried reinstalling OS - didn't work. try installing some anti spywares didnt work either. I'm pretty sure it's PC fault not provider. cuz as Soon as I have these weird internet slowing down I tend to speedtest my internet and viola 1MB/s after I turn off the PC and test it again on mobile its fine around my usuall 20MB/s. I really don't know what to do anymore if someone knows and open to any possible fixes thanks!


I have searched a lot about it but could not get an answer. I read somewhere that linux Ubuntu has 6 or 7 terminals.   We can start them by pressing -  Ctrl+Alt+(F1-F6)   and to get back to GUI-  Ctrl+Alt+F7   So what i want to know is what is the difference between these 6 different terminals , and how can we use them as per to different purposes??


Can I normalise IP4/6 addresses to IP6 in PHP without string-hacking?

There are lots of posts here and elsewhere about  addresses in PHP.  I want to write code which will normalise all IP addresses, regardless of their representation, to IP6 format.  I can do that by piecing together various bits of advice and doing some string hacking, but has best practice moved on from that?  Are there built-in functions in modern PHP which will do this correctly for all cases, without any conditional logic in my application code?


DNS keeps resetting after reboot. Ubuntu 17.10

So I see there are lots of issues on this.  I've read through all the posts,  but cant seem to find a permanent solution on this.  I have Ubuntu 17.10 and everytime my computer reboots,  I have to reset the dns servers.  The only solution that seems to work for me is to:   Add google's DNS servers to my /etc/resolv.conf file.  Verify they are listed in my network manager gui Restart network manager.  (sudo systemctl restart NetworkManager)   Im not sure why adding the dns servers to resolv.conf works, only to have it overwritten,  but I'f I dont.  My DNS doesn't work.   I know this is not the proper way,  but every other method I've tried seems to fail.  The other issue I have is, I have several other computers on the local network (raspberry pi's)  I can't ssh into them using their names.  I can with their IP address.  Here's my current resolv.conf  # Generated by NetworkManager nameserver 127.0.1.1   Here's my /etc/hosts  127.0.0.1   localhost 127.0.1.1   Bootes64 192.168.1.101   homeassistant 192.168.1.102   media 192.168.1.103   wdnas 192.168.1.120   security  # The following lines are desirable for IPv6 capable hosts ::1     ip6-localhost ip6-loopback fe00::0 ip6-localnet ff00::0 ip6-mcastprefix ff02::1 ip6-allnodes ff02::2 ip6-allrouters   Is there a permanent solution to this?  EDIT   This has been marked as a duplicate of a similar issue,  However That is one of the first questions I ran across with google.  NONE of the suggestions there work.  and Seeing as the last update was in 2014,  I have some serious misgivings that it will work on a 17.10 machine.


Why doesn't bit shift work for -1 in java?

I tried to do -1 >> 1 in java, but the result printed was still -1 At the beginning, I thought this is because of sign extending nature of arithmetic right shift. But through additional tests, I found that -1 >> [0, 64] is -1. Why is this happening?


Validate user credentials against windows login

I've read a couple of posts on SO regarding user authentication on Windows and it seems that one is able to retrieve the username, but not the password of the logged-in user, as it is hashed in one direction.   My question is: Is it possible to validate the username/password provided in the Windows Form app as a Windows login?   Essentially, my goal is to ask the user to provide once again his Windows password (username would be prompted automatically), and to check somehow if those credentials would pass as a Windows login. If so, how?   I know I can retrive the username like so: Environment.UserName; But beyond that I'm lost.


Is there a modal command for MakeLowercase?

Analog to  question I've been wondering WHAT is to \lowercase as \bfseries is to \textbf? (... and for uppercase, or \MakeLowercase and MakeUppercase, etc., which also seem to be text-block commands as explained .)  Is there a "switch"/"declaration"/"modal command" (what is the correct term here?, is there a difference between them?) that would allow one to turn something into lowercase/uppercase in the same way that one would use \scshape for example, i.e., not as text-block command with the curly braces?  Or how to create such a command?  I couldn't find any clue on the forum.


Questions about networking theory in a 2d shooter game

So currently I am starting to work on a 2d top down space shooter game, and I have just got to networking. So far the client can draw a ship at a desired x, y and rotational coordinate with any set of vertex data (referenced from pre-existing vectors of data). The problem I am having is just the main idea of how the game loop should revolve around the networking. My idea was have each loop of the game set to 1000/60ms, and then ask the server for some data, render it and sleep for the remaining time in the frame. Problem with that is that I realised a normal ping to a game server is around 100ms, meaning the game would only be getting around 10fps. The solution I assume is to only receive events 10 times a second versus the 60 refreshes the game is getting, but how would you render and be polling to receive data at the same time? Finally I am using enet as the networking library if anyone is interested because it seems to be pretty simple in its concept, but if there is a better one for this type of game out there it would be nice to know. (I did try googling all of this stuff but its kind of hard to describe exactly what I am confused about, so thanks for any help).


After I began Pokemon go, I clicked "no" if you want the camera to be on. I don't want to make a new account to activate it, so is there anyway to activate it after initially declining to use it? If not, should I make a new account?


Is it possible to create dummy column while fetching in SOQL Like  select 'Dummy Column Text' as DUMMYCOL from MY_TABLE


How to match only alphanumeric with regex

I'm trying to match alphanumeric with the regex below, but still matched the result that I don't need.  ([0-9a-z_]+|[0-9a-z]+)   What I really want to match are  Example: abc123 abc_123   What I don't want to match are  Example: abc 123 123_123 abc_abc


Geometry Nodes - Incremental increases & controls

I found  which shows exactly what I'm trying to do. At about the 10 second mark of the linked video, he shows controls working as integers. That in a nutshell is what I want to do.  I'm trying to figure out how to use Geometry Nodes but I'm starting at a pretty low level of understanding. There is a project I want to develop that I've broken down into a bunch of simpler tasks that I need to learn how to do. This is one of them. I'm using Blender 2.93 beta. I want to be able to translate and scale by specific increments. Attached is a screen capture showing my node tree and the modifiers tab. I've used the Math node "Snap" to set an increment of 1 unit for scaling. That actually does what I want, only adjusting the cube by 1 unit increments. Success!.... however, the X (Width), Y (Depth) and Z (Height) are connected to the Group Input to give me a control for each under Geometry Nodes in the Modifiers Tab but these controls don't conform to the 1 unit increment. Currently they increase by 0.001 units at a time not by 1. Is there a way of making those controls conform?   Re:  answer, This in some ways produce something which is another way of doing the same thing I already did with the snap function plus have added an offset which could be useful. This isn't what I was trying to resolve though. I've attached another pic. On it I've written the length of each of the sides, w=3, D=2 and H=1,but the controls on the right hand side say something different they say W= 3.37 etc These are the pre snapped sizes. I want the controls on the right hand side (Width, Depth, Height) to say the actual size not the pre.snapped size. In other words the controls themselves should reflect the snap/rounding that is set inside the geometry node tree. Can this be done?


doctors appointments or doctor's appointments or doctors' appointments

Not sure this was properly addressed before but question was where to put the "'" on the s. In the question it was about having multiple appointments that day, each appointment with a different doctor. So when you state you have multiple appointments that day with different doctors what should it be? My guess is i have doctors appointments. Is that right?


Does the Tough feat's hit point bonus apply to a Druid's wild shapes?

A Druid in Wild Shape takes on all the wild shape creature's physical ability scores, and those creatures have a number of listed Hit Dice, so does the Druid get to add the additional 2 hp per hit dice from the Tough feat to their wild shape forms?


How can I convert timestamps in a column to a date?


Is $g \circ f$ invertible if both $f$ and $g$ are invertible?.  I know that $f: A \rightarrow B$ and $g: B \rightarrow C$.   This is what I have so far:   If $f$ is invertible, $f^{-1} : B \rightarrow A$, $f^{-1} \circ f = id_A$. And if $g$ is invertible,  $g^{-1} : C \rightarrow B$, $g^{-1} \circ g = id_B$.  Given all of this information, however, I am not sure how this proves that $g \circ f$ is invertible.


I have to find out a normal transformation that is neither hermitian nor unitary.  gives me the answer. However, I would like to know how to find it out mathematically, not just guess and test. Can I go from the properties of eigenvalues of hermitian and unitary to get the answer? For example: eigenvalues of a hemitian must be real, then I choose (i,-i,0) as eigenvalues of the required matrix. Those eigenvalues satisfy the condition that the required matrix is not unitary whose eigenvalues are |1|. From those, I have characteristic equation has the form of x(x^2+1)= 0 which leads to the form of the required matrix has the trace =0 and det = 0.  Can I do it?


Name and origin of writing with period after each word

It may be limited to the web ecosystem, but I've read a lot of those sentences lately, where each word is followed by a period. Examples:  Oh. My. God. Best. Job. Ever. No. F***ing. Way.  Putting each word on its own hints the readers should give their full attention to each and every one of them. Does this technique have a name? Can its origin be traced back to a book or article?


Hypernym for different time sections of a day

In a day, we have different names for different times of it. For example, morning, afternoon, night, evening, noon.  I need a hypernym for them all. What word should I use?


Proof By Induction: Summation of Polynomial

Prove by induction (weak or strong) that:    $$\sum_{k=0}^{n-1}(k + 1)^2= \frac{n(n + 1)(2n+1)}{6}$$  My base case is:    $n = 1$, which is true.  In my Inductive Step, I assume that: $$S(n)=\frac{n(n + 1)(2n+1)}{6}$$ holds for an arbitrary value of $n$.    Proving it then holds for $n+1$: $$ S(n+1)=\frac{(n+1)((n+1)+1)(2(n+1)+1)}{6}$$ $$ \phantom{S(n+1)}=\frac{(n+1)((n+2)(2n+2+1)}{6}$$ $$ \phantom{S(n+1)}=\frac{(n+1)((n+2)(2n+3)}{6}$$ $$ \phantom{S(n+1)}=\frac{2n^3+9n^2+13n+6}{6}$$  but can't see how my definition of $S(n)$ can be substituted into this final equation?  [EDIT] This isn’t a duplicate because the original summation of $(k+1)^2$ is what I’m originally provided with. The apparent duplicate question also doesn’t have a correct proof by induction answer associated with it.


Find the number of triples $(x,y,z)$ of real numbers satisfying the equation $x^4+y^4+z^4+1=4xyz$

QUESTION Find the number of triples $$(x,y,z)$$ of real numbers satisfying the equation $$x^4+y^4+z^4+1=4xyz$$  I have tried to solve this problem but can't quite understand how to manipulate the given data to reach a clear result. Could someone please explain how I should approach and solve this problem.Thanks :)


The group $[G, G]$ generated by the set of all commutators is normal in $G$

I'm doing this exercise in textbook Algebra by Saunders MacLane and Garrett Birkhoff  A commutator in a group $G$ is an element of the form $g^{-1} h^{-1}g h$. Then the group $[G, G]$ generated by the set of all commutators is normal in $G$.  I showed in  that $N$ is normal in $G$ if and only if $\forall (n,g) \in N \times G: n^{-1} g^{-1} n g \in N$. Then it follows directly that $[G, G]$ is normal in $G$. Now I try the the straightforward approach as follows. For $x = (g^{-1} h^{-1}g h)(a^{-1} b^{-1}a b) \in [G, G]$, our goal is to show $kxk^{-1} = kg^{-1} h^{-1}g ha^{-1} b^{-1}abk^{-1} \in [G, G]$. Then I'm stuck. Could you please elaborate on how to proceed?


How can I remove the Guest account from my admin account? Because there is no use of have a password for the admin account will the guest is open to anyone.


I'm sorry if this question seems extremly dumb or/and pathetic. I'm quite new to electronics. For one of my electronics projects, I want to buy a power supply like , but it says Output: 12V 2A and I know that 2 amps is dangerous for the human body. So what does it mean? Will I hurt myself if I touch the two cables or is it fine? I don't really understand this. I'm sure you all know the answer and if so, please explain why. Thank you!  EDIT: My question has been marked as a duplicate but it's different. The other question is about what voltages / currents are dangerous but I do now that. However, I'm asking if the 2A power supply always outputs 2 amps or if it is the maximum current it CAN output.


Add the ability to search for my unanswered questions across all sites

I know how to search for my unanswered questions in a given site:     user:me hasaccepted:no   But I would like to do this across all sites.  How can this be done, if it's possible?  If not, then could this be a feature request?    Edit:  The conclusion at , which all the dupes point to (directly or indirectly), seems to be: No, it's not possible. So I guess I'm proposing a feature request. How do I do that?


Does one fill out a form or does one fill in a form? I've gotten different answers from the people I've asked.  Google search results:          fill in a form — 14,200,000   fill out a form — 7,000,000


What is this symbol that looks like an epsilon and \in symbol?

I came across this symbol that  looks like an epsilon and \in symbol.  Can someone tell me what it is?  I dont know how to make TeX display on this page (unlike MathSE).


Python transforming one dimensional array into two dimensional array

I have a list [1,2,3,4,5,6,7,8] I want to convert this as [[1,2,3,4][5,6,7,8]] in python. Can somebody help me with this


my xgboost model accuracy decreases after grid search with

I tried grid search for hyperparameter tuning in XGBoost classifier but the best accuracy is less than the accuracy without any tuning   // this is the code before the grid search xg_cl = xgb.XGBClassifier(objective='binary:logistic', seed = 22) xg_cl.fit(x_train, y_train) y_pred = xg_cl.predict(x_test) print(metrics.confusion_matrix(y_test, y_pred)) print(metrics.accuracy_score(y_test, y_pred)) [[11  1] [ 1 26]] 0.9487179487179487   also, worth mentioning that the dataset shape is (195, 11) after PCA, and i am trying to classify whether a patient has a parkinsons disease or not.   // this is the grid search code clf_xgb = xgb.XGBClassifier(objective = 'binary:logistic') params__grid = {     'n_estimators' : range(50,150,10),     'max_depth': range(2, 12),     'colsample_bytree': np.arange(0.5,1,0.1),     'reg_alpha' : np.arange(0,0.6,0.1),     'reg_lambda' : np.arange(0,0.8,0.1)   } search = GridSearchCV(estimator=clf_xgb, param_grid=params__grid, scoring = 'accuracy',                             cv = 4 ) search.fit(x_train,y_train)  print('best score:/n',search.best_score_) print('bestparams:/n' ,search.best_params_)  best score: 0.9038461538461539  best params: {'colsample_bytree': 0.5,      'max_depth': 7,      'n_estimators': 50,      'reg_alpha': 0.2,      'reg_lambda': 0.1}   then I used these parameters to build and train a new classifier  clf_xgb_1 = xgb.XGBClassifier(objective = 'binary:logistic', max_depth = 7, n_estimators = 50, reg_alpha = 0.2 ,                               reg_lambda = 0.1, colsample_bytree = 0.5 ) clf_xgb_1.fit(x_train,y_train) y_pred_2 = clf_xgb_1.predict(x_test) print('accuracy:/n', metrics.accuracy_score(y_test,y_pred_2)) print('confusion matrix:/n', metrics.confusion_matrix(y_test,y_pred_2))  accuracy: 0.8974358974358975  confusion matrix: array([[ 9,  3],        [ 1, 26]], dtype=int64)   How come my results are worse? I would expect that GridSearch would improve on the results.


Is "that" needed in "I saw that you were waiting..."?

Can someone confirm with me for these sentences   "I saw you were waiting for the bus"  —    incorrect "I saw that you were waiting for the bus"  — correct   Am I right?


Question: What is a good method for conducting post hoc tests of differences between group means after adjusting for the effect of a covariate?  Prototypical example:   Four groups, 30 participants per group (e.g., four different clinical psychology populations) Dependent Variable is numeric (e.g., intelligence scores) Covariate is numeric (e.g., index of socioeconomic status) Research questions concern whether any pair of groups are significantly different on the dependent variable after controlling for the covariate   Related Questions:   What is the preferred method? What implementations are available in R? Are there any general references on how a covariate changes procedures for conducting post hoc tests?


Is there a composite integer $n \geq 9$ such that $n \nmid (n-1)!$?  If we are not talking about composites then by Wilson's theorem we have $n \nmid (n-1)!$.


I want to install ubuntu on vmware, I have downloaded the OS file from ubuntu web site, how to go ahead. Like for RHEL 6 do I have to download an ISO image file so as to install it or is there some other unique technique?


How to rename a group of files with what looks like a Windows file path in their names

I got a bunch of files with the filename messed up. All the file names have the same beginning which appear to be windows file directories. The problem is there are 700+ files and I really don't want go through and manually rename all of them. These are examples of the file names (Note: None of these have file directories):  G:some\really\long\file\path\then\the\name1.jpg G:some\really\long\file\path\then\the\name2.png G:some\really\long\file\path\then\the\filename.txt G:some\really\long\file\path\then\the\file_name.mov ...   The important take away is that each file has G:some\really\long\file\path\then\the\ before the file name that I would like.   So I would want the above files to look like:  name1.jpg name2.png filename.txt file_name.mov   I've tried the rename command and was not successful. I am still new with Linux and really am not sure on how to go about it or really what to google. Any help would be appreciated.


I am working on an invitation design for a charity. I am wondering which one of these is correct, Young Men's Committee or Young Mens Committee


Why is Lamarck's evolutionary theory considered incorrect?

Many sources postulate without much argumentation that Lamarck's evolutionary theory is "obviously incorrect". A classic example provided in such sources is the one with giraffes, in which Lamarck argued that the necks of these animals became long as a result of continually stretching to reach high foliage. This mechanism for adaptive change in response to the environment is considered wrong.  Now the counterargument to Lamarck's ideas comprises modern findings in genetics. So it is stated that organisms pass down traits through predetermined genetic information, not based on environmental adaptations during their lifetime. Furthermore, genetic research shows that living organisms cannot alter their genetic material as needed.   Doesn't the latter contradict the evolutionary theory itself, which states that nature (i.e. environment) shapes species through natural selection in the environmental milieu? If it is not the environmental/natural factor that is responsible for genetic evolution, then what is? If genetic material were to be unchangeable, then how would adaptation to the environment and consequent evolutionary change would ever be possible? The genotype (following this logic) would remain the same. And lastly, maybe giraffes do not develop long necks at such a rapid pace (as Lamarck probably thought) by simply stretching their necks in one generation; however, what, if not neck stretching, is responsible for their consistently longer necks throughout thousands or millions of years? Hadn't the environment gradually shaped their genotype? Similarly, if I run more often, maybe my children will not become more fit, but isn't it just a matter of time (thousands of years) that if all of us consistently run a lot, then our offspring will eventually become more fit? Wouldn't our voluntary efforts eventually enhance our genetics? I do not see any problem with Lamarck's logic at all, except probably the time frame.


How should I prioritize my emergency fund, down payment, and retirement?

How should I prioritize my savings between enlarging my emergency fund, saving for retirement, and saving up for a down payment on a house (financial aspects of buying vs renting aside, I would prefer to own my home)?  Details:   I have no debt besides my credit cards (which I pay in full every month) and a car lease.  I already have an small emergency fund of approximately 2 months of expenses. I am married with 2 small children Neither my spouse nor I have access to a 401K plan right now, but this may change in the future   Edit:  It has been suggested that this question is either a duplicate of  or . I looked at the answers to these questions, but they don't really help:   Most of the answers to the  deal with investing strategies in and not prioritization of savings goals. Even the answers to the  don't seem to mention saving for a down payment at all (unless you assume that saving for a down payment is a perfect equivalent of paying of a mortgage early. Most answers I find about saving priorities on this site, or on the web in general place one of the highest priorities on "401K contributions up to your match", but don't explicitly give alternative priorities for when a 401K isn't available.


I can use the following proposition:  Proposition A: For a measurable function $f:S\to\overline{\mathbb{R}}$ the following are equivalent:   i) $f$ is integrable. ii) $\left|f\right|$ is integrable.   Now, let $f,g:S\to\overline{\mathbb{R}}$ be measurable functions.  Exercise: Show that $f$ is integrable iff $\sum\limits_{n\in\mathbb{Z}}2^n \mu(\{x\in S:2^n< \left|f(x)\right|\leq2^{n+1}\})<\infty.$  Solution: Let $A_n = \{x\in S:2^n < \left|f(x)\right|\leq 2^{n+1}\}$ for $n\in\mathbb{Z}$. Then the $(A_n)_{n\in\mathbb{Z}}$ are disjoint. Let $C:=\sum\limits_{n\in\mathbb{Z}}2^n\mu(A_n)$. Let $g:=\sum\limits_{n\in\mathbb{Z}}2^{n+1}\mathbb{1}_{A_n}$ and $h:=\sum\limits_{n\in\mathbb{Z}}2^n\mathbb{1}_{A_n}$. Then $h\leq f\leq g$. Moreover, $$\int_Shd\mu=C\,\,\text{ and }\int_Sgd\mu = 2C.$$  From monotonicity we see that $C\leq \int_S \left|f\right|d\mu\leq 2C$, and the required equivalence follows from proposition A.  There's a lot of things about this proof that I don't understand:  Questions:   How do we know that $f(x)\leq g(x)$? I understand that this is true if $x \in A_n$ for some $n\in\mathbb{Z}$, but isn't it possible that there exists an $x$ such that $x\notin A_n$ for any $n\in\mathbb{Z}$? If it's not possible that would mean that $\bigcup\limits_{n\in\mathbb{Z}}A_n = S$, right? But how do we know this is the case? Why do we have that $\int_S hd\mu = C$? $h$ is not a simple function right? Why do we know that from monotonicity we have that $C\leq \int_S \left|f\right|d\mu\leq 2C$? Isn't this supposed to be $C\leq \int_S fd\mu\leq 2C$, as we know that $h\leq f\leq g$?  If I accept that the steps that I questioned above are true, I'm still not done. While I understand that constructing functions $h$ and $g$ in the way that is done in the solution would imply that $f$ is integrable, I don't understand how this proof shows the if and if only part of the exercise. Could you explain why this is the case?   I understand that this is a lot to answer; feel free to present your own explanation that doesn't not directly answer any of the particular questions I posed, but explains the solution in a more general way.  Thanks in advance!


Why not make .txt file executable instead of .sh file to run scripts?

I was wondering what's the need to put executable commands inside a .sh file to make a single script, since I can do the same by putting the commands inside a .txt file and making it executable using chmod.   I'm assuming this can be done with any of the file extensions. So, I am quite confused about the need for .sh extension. Any help would be much appreciated.


apt update: Could not handshake: An unexpected TLS packet was received

I had problem doing sudo apt update for manually added repositories (I had problem with nodejs and docker) with my Ubuntu 17.10 VM running in VirtualBox. The error I get is Could not handshake: An unexpected TLS packet was received.  The following are steps that I took when trying to add docker repository and the output. The same thing happened when I tried to add nodejs as well.  sdnc-dev@sdncdev-VirtualBox:~/tools/idea-IC-173.4674.33/bin$ curl -fsSL https://download.docker.com/linux/ubuntu/gpg | sudo apt-key add - OK sdnc-dev@sdncdev-VirtualBox:~/tools/idea-IC-173.4674.33/bin$ sudo apt-key fingerprint 0EBFCD88 pub   rsa4096 2017-02-22 [SCEA]       9DC8 5822 9FC7 DD38 854A  E2D8 8D81 803C 0EBF CD88 uid           [ unknown] Docker Release (CE deb) <docker@docker.com> sub   rsa4096 2017-02-22 [S]  sdnc-dev@sdncdev-VirtualBox:~/tools/idea-IC-173.4674.33/bin$ sudo add-apt-repository "deb [arch=amd64] https://download.docker.com/linux/ubuntu $(lsb_release -cs) stable" [sudo] password for sdnc-dev:  sdnc-dev@sdncdev-VirtualBox:~/tools/idea-IC-173.4674.33/bin$ sudo apt update  Ign:1 https://download.docker.com/linux/ubuntu artful InRelease Err:2 https://download.docker.com/linux/ubuntu artful Release   Could not handshake: An unexpected TLS packet was received. Hit:3 http://us.archive.ubuntu.com/ubuntu artful InRelease Get:4 http://security.ubuntu.com/ubuntu artful-security InRelease [78.6 kB] Get:5 http://us.archive.ubuntu.com/ubuntu artful-updates InRelease [78.6 kB]        Get:6 http://us.archive.ubuntu.com/ubuntu artful-backports InRelease [72.2 kB] Get:7 http://us.archive.ubuntu.com/ubuntu artful-updates/main amd64 Packages [226 kB] Get:8 http://us.archive.ubuntu.com/ubuntu artful-updates/main i386 Packages [222 kB] Get:9 http://us.archive.ubuntu.com/ubuntu artful-updates/main Translation-en [101 kB] Get:10 http://us.archive.ubuntu.com/ubuntu artful-updates/universe i386 Packages [91.9 kB] Get:11 http://us.archive.ubuntu.com/ubuntu artful-updates/universe amd64 Packages [92.8 kB] Get:12 http://us.archive.ubuntu.com/ubuntu artful-updates/universe Translation-en [52.9 kB] Reading package lists... Done               E: The repository 'https://download.docker.com/linux/ubuntu artful Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.   Here is the details of my setup:     VM: Ubuntu 17.10    VirtualBox 5.2.8 r121009 (Qt5.6.2)    I am behind corporate proxy.   Does anyone know how to fix this?


What does "likelihood is only defined up to a multiplicative constant of proportionality" mean in practice?

I'm reading  where the authors are leading from a discussion of maximum likelihood estimation to Bayes' Theorem, ostensibly as an introduction for beginners.  As a likelihood example, they start with a binomial distribution:  $$p(x|n,\theta) = \binom{n}{x}\theta^x(1-\theta)^{n-x}$$  and then log both sides  $$\ell(\theta|x, n) = x \ln (\theta) + (n-x)\ln (1-\theta)$$  with the rationale that:     "Because the likelihood is only defined up to a multiplicative constant of proportionality (or an additive constant for the log-likelihood), we can rescale ... by dropping the binomial coefficient and writing the log-likelihood in place of the likelihood"   The math makes sense, but I can't understand what is meant by "the likelihood is only defined up to a multiplicative constant of proportionality" and how this allows dropping the binomial coefficient and going from $p(x|n,\theta)$ to $\ell(\theta|x,n)$.  Similar terminology has come up in other questions ( and ), but it still not clear what, practically, likelihood being defined or bringing information up to a multiplicative constant means. Is it possible to explain this in layman's terms?


System settings application is missing I was deleting some apps from Ubuntu. Afterwards, I realized that I don't have the settings application installed. What should I do to re-install it? I don't know whether I deleted the system settings app - I don't think that's possible. I tried installing KDE system settings but that's not the right application. Any help would be appreciated.


Off-topic questions - users breaching the rules still gain reputation off them

Please take a look at this question and answer: .  It's clearly off-topic as it's a request for a recommendation of an external library. I voted to close the question and put a comment to OP. OP replied to my comment but still left the question.  Then another user put an answer. I put the comment for the answer as well but the answer stayed and was later accepted.  Moreover, both the question and answer were upvoted once.  I downvoted both the question and answer as there was no response from OP and answerer.  Now, the rep changes were:   OP better of by 5 rep (+5 upvote, -2 downvote, 2 accepted an answer). Answerer better of by 23 (+10 upvote, -2 downvote, 15 accepted answer). me down by 1 (-1 downvote on answer)   The question was later put on hold but it doesn't change the rep gains and losses.  I'm not complaining about my lost rep. I just feel that the reward for asking and answering off-topic questions exists in the system. That gives a wrong  indication of hat behaviour is desired in SO.  Maybe when a question is put on hold for off-topic reasons, the reputation gains (only gains) should be reversed?  UPDATE  Aziz Shaikh has a valid point that the rep changes will be reversed once the question is closed and deleted (see ). The problem is, with the way closing queue is going, that may take very long (up to forever).


I've got a set of files in a directory, all of the format test[0-9][0-9].txt. If I run  find . -regex ".*/(test)[0-9][0-9]\.txt"   then all the files are shown, but if I run  find . -regex ".*/(test)[0-9]{2}\.txt"   then none are shown. What am I doing wrong?!  I've had a search through previous similar questions to this, but can't find a particularly relevant answer


Deciphering the RSA encrypted message from three different public keys

I have three different 1024-bit public keys with common exponent $e$ but different moduli. A message $m$ is encrypted (without padding) using the three keys, which results in three different encrypted messages.  Given the three pairs of public keys $(N_i,e)$ and the encrypted messages $c_i=m^e\bmod N_i$ , how do I decipher the original message $m$ ?


This question   Has a canonical URL of   Which is an encoded form of ��  It should instead have a canonical URL of   Which is a correct encoded form of 💩.


Exercise with automorphisms of rational functions field

Let $E $ be the field of rational functions over $\mathbb Q $ and consider the six automorphisms $$\alpha_1:f (x)\mapsto f (x), \;\alpha_2:f (x)\mapsto f (1/x)$$ $$\alpha_3:f (x)\mapsto f (1/(1-x)), \; \alpha_4:f (x)\mapsto f (1-x)$$ $$\alpha_5 : f (x)\mapsto f (x/(x-1)),\; \alpha_6:f (x)\mapsto f ((x-1)/x).$$ I have to prove that they form a group of authomorphisms $G $ (hence $|G|=6$), and that, named $F=$Inv $G $, $[E:F]\ge 6$. The first point is quite easy, however it is unclear to me why $[E:F]$ is not equal to $6$: a theorem states that if $E $ is a field and $G $ is a finite group group of authomorphisms of $E $, then $E/$Inv $G $ is a Galois extension (theorem 4.7 of Basic Algebra I). This should imply precisely$[E:F]=|G|$, so I must be wrong somewhere; thanks for any explanation.


I am trying to include a DC jack on one of my PCBs. I am just setting up the footprints now, and I am not quite sure which pin is which. What do the symbols on the drawing mean?  I have included a snap of the schematic below, it has been taken directly from the .


How to check another column value to be the highest to determine the latest record that occurs multiple times in Oracle SQL Developer?

I have a table called ro_main_table which stores details of productions such as serial_nr, pr_date_time, machine_nr, record_key etc. I would like to get the distinct machine_nr and record key from ro_main_table where pr_date_time is in last 6 hours. For this I do: select machine_nr, record_key, pr_date_time from ro_main_table where pr_date_time >= SYSDATE - 6/24;  Which gives me the table below:     MACHINE_NR RECORD_KEY PR_DATE_TIME     54 9809 17-DEC-20 04.02.35.000000000 AM   55 9811 17-DEC-20 04.58.22.000000000 AM   55 9817 17-DEC-20 09.17.50.000000000 AM   54 9814 17-DEC-20 07.57.24.000000000 AM   50 9818 17-DEC-20 09.45.22.000000000 AM     However, as you see there might be machines which are started twice during this time (i.e. machine_nr occurs multiple times). If this is the case, I will choose the record which has the highest record_key. For example, for machine 55 it is 9817. How can I achieve this? Thank you very much in advance!


Why is using std::string still needed after #include ?

In order to use strings I need to include the string header, so that its implementation becomes available. But if that is so, why do I still need to add the line using std::string?  Why doesn't it already know about the string data type?  #include <string>  using std::string;  int main() {     string s1; }


Character limits on textarea fields - pros and cons and best practices?

Some of our form fields have character limits. We're debating whether we should reflect the current size of data entry, or to simply hard-limit and inhibit data entry beyond that size.  In HTML, simple <input> elements can have a maxlength attribute that inhibits further entry, but <textarea> has no built in option. Character limits in <textarea> can easily be imposed via javascript.  Twitter shows the remaining available characters, and will let you type more than that in but shows it as an error (and disables the action button).     We're looking at proactively showing the number of allowed characters for a limited field, and showing the number of characters remaining. If the user exceeds the limit then an inline form invalidation message appears.     A counter argument is that users don't even notice the little numbers updating, and that the user might well end up expending a great deal of effort typing something which they then need to trim.  What are some of the pros and cons of using these character counters?


I was working in my terminal, when I misspelled while cd to root (/). Accidentally, I typed // and I got in terminal:  root@weblocalhost://#   When i type pwd, i get response // but when I type ls -s i got same list as in / directory.  When you type more than 2, i.e. /// you get:  root@weblocalhost:/#   Always 1 / except for 2. Is there any difference and what is // for?