Does a linear operator obeying Leibniz rule imply it is a differential operator?

At the moment I'm studying manifolds and in the definition of tangent space, the notion of derivation was used in the material I'm reading. I asked here about the matter and it was told me that it's not necessary to have a complete background in abstract algebra to proceed but instead just understand the definition of a derivation. If I understood well a derivation is a way to extract the main properties of a differential operator: linearity and obeying the product rule. This line of thought leads me to a doubt: every differential operator should obey the product rule, but if a operator is linear and obey the product rule is possible to conclude it's a differential operator (it can calculate rates of change, be used to construct the taylor approximation to the function and every other properties we expect from a derivative)?


How many zeros are there in $25!$?  I don't know how to really calculate it the number of zeros in the right hand can easily find by .  That gives us:  $\lfloor{\frac{25}{5}}\rfloor+\lfloor{\frac{25}{25}}\rfloor=5+1=6$  But I got stuck with finding the zeros between.Any hints?


I am new in concurrency in Java, but I have problems in understanding the work of the executor service.   My problem: I'm executing below code separately and I wonder that array of threads faster then executor service (3s vs 30s, by System.currentTimeMillis()).  public class SimpleExample { private static final int THREAD_COUNT = 10; private final AtomicInteger cnt;  private SimpleExample() {     cnt = new AtomicInteger();     cnt.set(0); }  public static void main(String[] args) throws IOException, InterruptedException {     // threads();     // service(); }  private static void threads() throws InterruptedException {     SimpleExample example = new SimpleExample();     ParallelTask task = new ParallelTask(example);     Thread[] threads = new Thread[THREAD_COUNT];     for (int i = 0; i < threads.length; i++) {         threads[i] = new Thread(task);     }      long a = System.currentTimeMillis();     for (Thread thread : threads) {         thread.start();     }      for (Thread thread : threads) {         thread.join();     }     System.out.println("time: " + (System.currentTimeMillis() - a)); }  private static void service() {     SimpleExample example = new SimpleExample();     ParallelTask task = new ParallelTask(example);     ExecutorService service = Executors.newFixedThreadPool(THREAD_COUNT);      long a = System.currentTimeMillis();     Future future = service.submit(task);     while (!future.isDone()) {         // do nothing     }     service.shutdown();     System.out.println("time: " + (System.currentTimeMillis() - a)); }  void run() {     while (cnt.get() < 300) {         try {             Thread.sleep(100);             System.out.println(cnt.get());             cnt.incrementAndGet();         } catch (InterruptedException ignore) {}     } }  static class ParallelTask implements Runnable {     private final SimpleExample example;      ParallelTask(SimpleExample example) {         this.example = example;     }      @Override     public void run() {         example.run();     } }   }  How it's possible? Thanks.


If $G \times G \cong H \times H$ must $G \cong H$?

If $G$ and $H$ are both groups and $G \times G \cong H \times H$, is it required that $G \cong H$?


How can I tell how much storage space my console has?

I have an older Xbox 360 with Kinect but need to work out how big the hard drive is. I no longer have the original box. Can anyone tell me how to do this please?


How do we identify if an org is using NPSP

We are developing an appexchange product and there is a functionality which needs to be different if its a Non profit vs the rest of the licenses.  Is there a way we can identify if the org uses NPSP?  Thanks


How to expand a drive partition using unallocated space?

I'm trying to expand dev/sda7/ space using unlocated memory[587GB]. I'm not able to expand dev/sda7/ to unlocated memory resize option won't show the memory of unlocated. Is there a way to push unlocated memory into extended partition and resize dev/sda7 memory from there?


Everytime I'm in the math mode and there already is a \ typed and I type another one, TeXstudio replaces the old one with the new one instead of let me having a \\ typed. This is annoying me and I would like to disable it, but I can't find where to do it. Can someone help?


A word for someone that loves learning/ curious, has wonder about the world In general

I need a word that describes the love of learning, discovering, or it could even be a word that describes a curious person.


why so? heap, shows one thing and then another

I'm trying to learn c ++, doing some tests, I have the following questions, which, in a way shows one thing and the other works as expected, I will try to explain as best I can, "sorry for my English," I have a base class that is more or less so I think this is the important part;  class Basefptr { public:     Basefptr();     virtual ~Basefptr();     virtual void funcPtr1(); };  inline void Basefptr::funcPtr1(){     std::cout << "funcPtr1" << std::endl; } #endif /* BASEFPTR_H_ */   and in the derived class that other;  #include "Basefptr.h"  class Derivada : public Basefptr { public:     Derivada();     virtual ~Derivada();     virtual void funcPtr1(); };  inline void Derivada::funcPtr1(){     std::cout << "funcPtr1_de_Derivada" << std::endl; } #endif /* DERIVADA_H_ */   that this is the main;  #include "Basefptr.h" #include "Derivada.h" #include <vector> #include <algorithm>  int main(int argc, char* argv[]){  Basefptr* base     = new Basefptr; Derivada* derivada = new Derivada;  std::vector<Basefptr*> poli;  poli.push_back(base); poli.push_back(derivada);   std::for_each(poli.begin(), poli.end(),[](Basefptr* b){      b->funcPtr1(); });   Basefptr base1; Derivada derivada1;  std::vector<Basefptr> poli1;  poli1.push_back(base1); poli1.push_back(derivada1);   std::for_each(poli1.begin(), poli1.end(),[](Basefptr b){      b.funcPtr1(); });  return 0; }   this the shell out;   funcPtr1   funcPtr1_de_Derivada   funcPtr1   funcPtr1   The first two lines are as expected, but the second is not what I expected, because he believed that would be like the first, can someone explain me, the reason this is so, if you please. or am I doing something wrong greetings and thanks for reading.


Rhetorical device - listing rejected answers

Is there a name for the rhetorical device whereby you ask a question and then list the rejected answers? For example:     "What was it then? It wasn't x, nor y, nor z. No, in fact it was . . .."   The Cicero De Imperio passage is as follows:  How was it, do you suppose, that he was able to display that excessive rapidity, and to perform that incredible voyage? For it was no unexampled number of rowers, no hitherto unknown skill in navigation, no new winds, which bore him so swiftly to the most distant lands; but those circumstances which are wont to delay other men did not delay him. No avarice turned him aside from his intended route in pursuit of some plunder or other; no lust led him away in pursuit of pleasure; no luxury allured him to seek its delights; the illustrious reputation of no city tempted him to make its acquaintance;


alias for executing the same command with sudo credentials

I am trying to create some alias for executing the same command but with sudo credentials. In the ultimate case I want to be something like:  alias !!='sudo !!'   But when I source /.bashrc file this particular alias doesn't work for some reason.


How to show $\lim_{n\to\infty}n\left\{\sum_{k=1}^n\frac{1}{(n+k)^2}\right\}=\frac{1}{2}$

Show that $$\lim_{n\to\infty}n\Bigg\{\dfrac{1}{(n+1)^2}+\dfrac{1}{(n+2)^2}+\dfrac{1}{(n+3)^2}+\cdots+\dfrac{1}{(2n)^2}\Bigg\}=\dfrac{1}{2}.$$  Proof:     We can rewrite $$\lim_{n\to\infty}n\Bigg\{\dfrac{1}{(n+1)^2}+\dfrac{1}{(n+2)^2}+\dfrac{1}{(n+3)^2}+\cdots+\dfrac{1}{(2n)^2}\Bigg\}=\lim_{n\to\infty}n\Bigg\{\sum_{k=1}^n\dfrac{1}{(n+k)^2}\Bigg\}$$      Which looks astoundingly similar to the form in Corollary 8.3, where $\dfrac{b-a}{n} = n\implies b-a = 2n$.     Corollary 8.3: Let $f$ be a continuous function on an interval [a,b]. Then $$\int_a^bf(x)dx=\lim_{n\to\infty}\dfrac{b-a}{n}\sum_{k=0}^{n-1}f\Bigg(a+\dfrac{k}{n}(b-a)\Bigg)$$    That would mean the term in Corollary 8.3 would morph into      $$f\left(a+\dfrac{k}{n}(b-a)\right)=f\left((b-2n)+\dfrac{k}{n}(2n)\right)=f(b-2n+2k)$$     We need $f(b-2n+2k)$ to look like $\dfrac{1}{(n+k)^2}$. This would imply that $f$ is  ... but then I get stuck. I am unsure how to find $f$ or even if I need to find $f$.


Is it really impossible for Bumblebees to fly?

According to some source or other (I forget which now) it is theoretically impossible for bumblebees to fly by virtue of their size/bulk/aerodynamic properties. Is this old adage apocraphyal or true? And if its true, how come they do fly?


Story about a guy who intentionally becomes ultimate bad guy to trigger societal change

I read it a long, long time ago, I think it was just a short story.  The plot was that society had lost it's way, accepting that everyone was equal, and therefore no advances were being made, as smart people just 'pretended' to align with the mediocre.  One guy decided this was not good, and fashioned himself into the ultimate bad guy, triggering society to change to recognise greatness/intelligence where it arose. Eventually society recognised that some people were better than others, in some ways, and scientific advances were made.  In the end I think he climbed into an engine nozzle, so he'd be entirely destroyed and no one would know what happened to him.


Unsupervised classification of large binary/boolean dataset

I have a large dataset of binary data.  I have ~15,000 rows and ~2000 columns, wit the data itself consisting of a binary variable.  I would like to classify all 15,000 rows into n groups, by using their 2,000 values across the columns.  I have considered using random forest classification, as well as running a PCA and seeing which groups of rows co-vary with the first few principle components, but neither of these approaches seem ideal.  I am wondering if there is some other machine learning technique that is best when dealing with binary/boolean data.  I'm very comfortable in R, and would especially appreciate any recommendations of specific packages.


Allow user to use sudo to execute anything, only one executable as nopassword

I have a Linux user that needs to be able to execute any command with sudo, but it should ask for their password for all apart from one executable. Currently my sudoers files looks like:  # # This file MUST be edited with the 'visudo' command as root. # # Please consider adding local content in /etc/sudoers.d/ instead of # directly modifying this file. # # See the man page for details on how to write a sudoers file. # Defaults        env_reset Defaults        mail_badpass Defaults        secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"  # Host alias specification  # User alias specification  # Cmnd alias specification  # User privilege specification root    ALL=(ALL:ALL) ALL  # Members of the admin group may gain root privileges %admin ALL=(ALL) ALL  # Allow members of group sudo to execute any command %sudo   ALL=(ALL:ALL) NOPASSWD:/bin/switch.sh  # See sudoers(5) for more information on "#include" directives:  #includedir /etc/sudoers.d   So I have added my user to the sudo group, however I think I have the syntax wrong as now I can only execute switch.sh with sudo and no others


Java: Type mismatch: cannot convert from int to char

char c = '1';  char res = '0' + '1'; // no error char res2 = '0' + c; // compile error   The last line will throw compile error. Each part of the expression is char, why the expression itself is promoted to an int?   Thanks  Edit: Found why the 3rd statement failed. The reason is explained in    But the knowledge that char + char = int does not explain why the 2nd of your three examples does compile. Any ideas?


I can't seem to hook up everything to the same power grid and I am getting so frustrated. I set it up so many different ways now to see if I could get it to work and it just won't. I've tried hooking up all my generators to the beam emitter and then to the relay dish and the control console and that didn't work. I've tried using a power pylon with the generators and that didn't work. I'm totally over this. any suggestions? (I'm building with the Minutemen on top of an old housing structure btw)


While reading about slicing in Python I came across this interesting example which doesn't make sense.  let a be a list    a = [1,2,3,4,5,6,7]  a[1:4] = [0,0]  print(a)   output>> [1, 0, 0, 5, 6, 7]   a = [1,2,3,4,5,6,7]  a[1:6:2] = [0,0]  ValueError: attempt to assign sequence of size 2 to extended slice of size 3   Why do we get ValueError in the second case? The description says size 2 to extended slice of size 3 but in first case we are assigning the sequence of size 2 to a slice of size 3 and it works.


Ubuntu server system (no X installed) that runs several networking daemons.  It's been headless for years but I recently attached a monitor to it and installed some cli monitoring utilities (glances and pysensors) as this server is also my NAS gateway.  Been on this horrific easter-egg hunt searching for how-to disable the screen-blanking / powersaver mode for the terminal.    I'm hesitant to remove acpi as a package because of unknown/future interdependencies.  Somewhere, there's some obscure config setting that will prevent the monitor from blanking.  I've disabled the sleep option in the monitor's firmware - and, of course a key-press on the kb will awaken the screen...but not sleeping at all is optimal.  thanks...


How to automatically kill a process using script?

How to write a script that kills a java process?  From console it looks like  root@ubuntu-s-1vcpu-1gb-ams3-01:~# lsof -i tcp:8080 COMMAND  PID USER   FD   TYPE  DEVICE SIZE/OFF NODE NAME java    9657 root   26u  IPv6 4694148      0t0  TCP *:http-alt (LISTEN) root@ubuntu-s-1vcpu-1gb-ams3-01:~# kill 9657   How should it be implemented in .sh file?


copy/paste of large amount of text to terminal leads to scrambled/missing characters

I work with TextMate and R over the terminal. When pasting a lot of code (CMD+C/CMD+V, e.g. 60 lines) it sometimes happens that few characters in the code are scrambled, which then leads to error messages and wrong code execution.  For example:     col <- ifelse(...   is turning into      col < col < cse(...   or      onlyDF   is turning into     oalyDF   These character-replacements seem very random and it is difficult to predict when it happens.  The problem is also described here for iterm2:   The explanation provided there is that it is a bug in bash that can lead to buffered input to get lost due to paste speed.   Has anyone experienced these problems and found a work-around for the native terminal app in Mac OS? (e.g. by modifying the paste speed, if that is possible in terminal)


Hello I would like to find a file called lyxpipe (which is used by the program lyx). However, I don't have a idea where the program is installed.  I typed  locate lyx lyx: /usr/bin/lyx2.0 /usr/bin/X11/lyx2.0 /usr/share/lyx2.0   However, when I try to navigate to the folders I can type  pwd home/Theodor   where Theodor is my username.  But there is no other folder bin in this directory. Can somebody tell me how to access these paths?


GeoTools Geometries lost when storing features to shapefile

As you know, the geometry column name of schema for saving into a shapefile must be "the_geom". I have a SimpleFeatureCollection with a schema, geometry name of which is not "the_geom"; It is "geometry". I want to save this collection into an esri shapefile. But I loose geoemetries when storing.    Attribute table before save:  |  FeatureIdentifier  | name | people |     geometry     | ---------------------------------------------------------- | jahan_0             | ali  | 23     | POINT(67.0 35.0) | | jahan_1             | gh   | 245    | POINT(67.2 34.4) |  ---------------------------------------------------------   Attribute table after reading shapefile:    |  FeatureIdentifier  | the_geom | name | people | -------------------------------------------------- | mesal_0             |          | ali  | 23     | | mesal_1             |          | gh   | 245    |   -------------------------------------------------   How can I save my feature collection into shapefile without loosing geometries?  The problem is on storing. I tested the saved shp file by QGIS and saw geometries lost.    more code on saving shapefile:    DataStore dataStore = ...; // shapefile data store // My FeatureCollection containing two features SimpleFeatureCollection collection = ...;  dataStore.createSchema(schema); String typeName = dataStore.getTypeNames()[0]; SimpleFeatureSource fs = dataStore.getFeatureSource(typeName); MyUtil.saveToFeatureStore(collection,(FeatureStore) fs);   MyUtil.java:  public class MyUtil{   public static void saveToFeatureStore(SimpleFeatureCollection collection, FeatureStore featureStore){     Transaction tx = new DefaultTransaction("create");     featureStore.setTransaction(tx);     try{       featureStore.addFeatures(collection);       tx.commit();     } catch(Exception ex){       tx.rollback();     } finally{       tx.close();     }   } }   My problem is: How to save features into shapefile by GeoTools. There is no question about storing features by GeoTools at this site.


How long can you store uncooked cut fries?  Tried to make some other day, didn't finish. Had quite a bit left over.....am currently storing them in water in refrigerator.  How long will they be safe to fry and eat? Or, can they?  Would estimate it's been at least 4-5 days.  Thanks


Export settings for a sharp logo in Illustrator

I want to export a logo which I made in Illustrator (CC 2015) for a customer and import it into Word so it can be used as a standard template for their letters. The logo in Illustrator is created in a 300 ppi document setting. It contains text with a non standard font. I am working on a retina screen MacBook.  My problem is (and I know I'm not the only one) that no matter what I try: the file becomes just terrible after importing it in Word. With 'terrible' I mean: it loses all of it's crisp and smoothness. The lines of the logo but especially the text parts just become totally pixelated and blurry. Presenting it like this to my customer would not be professional in any kind of way.  This is a screenshot of the logo in Illustrator:   This is how I export it to PNG for example:       The result isn't all that bad actually:    ...but wait and see what happens after I import the PNG into Word:      The end result:    I am aware that it's practically not possible to get the same kind of quality after exporting the file as a PNG or JPEG (or even importing an .AI file directly into Word, I already tried that) since Illustrator is vectors and PNG of JPEG files become pixels. Still like I wrote before; I can't imagine it can't be done in a way resulting in an acceptable logo quality, at least I do believe there are ways to do it better than I am doing it right now :)  I think Word has a built in compression setting which I know can be turned off on a Win machine but as far I as I can see I can't find that option in the Mac version of Word.  What would you recommend I do?


GPG error KEYEXPIRED when using sudo apt-get update (Ubuntu 15.04)

Reading package lists... Done W: GPG error: http://deb.opera.com stable InRelease: The following signatures were invalid: KEYEXPIRED 1435908620 KEYEXPIRED 1435908620 KEYEXPIRED 1435908620 The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 63F7D4AFF6D61D45 trevor@trevor-Latitude-D620:~$


Disk space available: Finder shows way less than System Information

The Finder currently shows only 81GB available (at the bottom of a folder's window) whereas System Information > Storage shows 455GB available.  Why does the Finder show so much less space available?  FYI: I'm running macOS 10.15.4 on an iMac with a 500GB drive.


As Taylor's series give $e^x = 1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...$  Similarly, can someone please help me to find expansion of the term $\frac{1}{(1 - e^{-x})}$? Where $0 < e^{-x} < 1$  Thank you.


Bayesian approach: ignoring the denominator leads to the conditional density equaling the joint density?

I know there are a lot of questions here about ignoring the denominator in a Bayesian approach, but I don't think mine is a duplicate of any of them.  I am reading the book "Pattern recognition and machine learning" by Cristopher Bishop.  Imagine we have a set of N observations of a (single) variable, which we collect in a vector $\mathbf{x} \in \mathcal{R}^N$. We would like to find the mean $\mu$ of the probbility density function that generated that data, using a Bayesian approach. Thus, we first need to find the posterior probability $p(\mu|\mathbf{x})$  We can write:  $p(\mu|\mathbf{x}) = p(\mathbf{x}|\mu) \cdot \dfrac{p(\mu)}{p(\mathbf{x})}$  Now as the book says, we can ignore the denominator because it is just a normalizing factor  $p(\mu|\mathbf{x}) \propto p(\mathbf{x}|\mu) \cdot p(\mu) = p(\mathbf{x}, \mu) $  where the last equation follows from the product rule, or the defition of conditional density for $p(\mathbf{x}|\mu)$ if you want.  So we are approximating a conditional distribution with a joint distribution? How is that even possible?  For one, $p(\mu|\mathbf{x})$ whould be a function of $\mathbf{x}$, while $p(\mathbf{x}, \mu) $ whould be a function of both $\mathbf{x}$ and $\mu$, right?


iCloud Drive taking up space on local drive?

My computer seems to be keeping a local copy of my iCloud Drive folder. Is there any way to disable this?  I know this because in my "Library" folder, there is another folder called "Mobile Documents" that links to the contents in my iCloud Drive folder.  Also, when I click on "About This Mac", under "Storage", it includes the iCloud Drive folder's contents.  Is there a way for me to not keep a local copy of the iCloud Drive folder? I don't want it taking up space on my hard drive...


I'm using latest debian relese and i need to do some port forwarding, but i dont know how.I have 2 stream sources coming to my server on the same udp port from 2 diferent ip-s  192.168.1.2:1003 via udp to 192.168.1.4 (server)   192.168.1.3:1003 via udp to 192.168.1.4 (server)   My qestion is: how to forward this port 1003 coming from 1.2 to some other port 1004 for example?


Delete subdirectories leaving a given one

I need to delete all sub directories and their contents in a given folder, whilst leaving a particular sub directory. Is there a way to do this using bash or a shell script? The file structure is shown below.  container_dir │ ├── delete_this_dir │   ├── file1.txt │   └── file2.txt │ ├── delete_this_dir │   ├── l1.txt │   └── l2.txt │ └── keep_this_dir     ├── file1.txt     ├── file2.txt     └── file3.txt


Log of mounted/unmounted devices in Unix

Apologies in advance for the basic question.  I need to identify the log of mounted/unmounted devices in Unix (including the timestamps when these actions where performed).  I noticed that using the mount command is not very helpful for this purpose, since there is no indication of the timestamps when the mount/unmount operations where performed. Can anyone indicate me a possible alternative?  Thank you in advance! :-)


How to split parameter in stored procedure

This is the stored procedure:  CREATE PROCEDURE [dbo].[StoredProcedure]     @FILTERNAME varchar(100) = '' AS     IF @FILTERNAME <> ''     BEGIN         SELECT              CODE, NAMEen, NAMEkr          FROM              (SELECT                   OT.CODE, OT.NAMEen, OT.NAMEkr, OT.Sortkey               FROM                   OptionTable OT              INNER JOIN                   ConditionTable CT ON OT.CODE = CT.CODE              INNER JOIN                   MasterTable MT ON CT.DevCode = MT.DevCode                                   AND CT.PlanCode = MT.PlanCode               WHERE                   MT.ProductName LIKE '%' + @FILTERNAME + '%'              GROUP BY                   OT.CODE, OT.NAMEen, OT.NAMEkr, OT.Sortkey) TBL         ORDER BY              Sortkey     END   This stored procedure is called from vb6. I cant touch the vb6's code so I need to fix this.  Until now, the parameter was like 'XXX', but it's going to be like 'A,BB,CCC,ZZZZ'.  I need to split the parameter's string by , and change the condition like this: when the parameter is something like this 'A,BB,CCC,ZZZZ', then use this WHERE condition:  WHERE MT.ProductName LIKE '%' + A + '%'    or MT.ProductName LIKE '%' + BB + '%'    or MT.ProductName LIKE '%' + CCC + '%'    or MT.ProductName LIKE '%' + ZZZZ + '%'   Can someone help me? Thanks.


Is there any way to bookmark some questions in Stack Overflow?

I would like to recollect some questions. Some time after I find them, I have to refer them. When my first search used some keyword, which is not in my mind after some time. So I would like to keep those links in my profile and refer them later. Is there any way to bookmark such things in Stack Overflow itself, like Browser BookMarks?


I'm using Ubuntu Studio - Xenial Xerus 16.04.3 LTS and want to install Skype for Linux.  When I drag the Skype installer to the terminal I get the following message:  serafims@SATELLITE-C50-B:~$ '/home/serafims/Downloads/skypeforlinux-64.deb'  /home/serafims/Downloads/skypeforlinux-64.deb: line 1: syntax error near unexpected token `newline' /home/serafims/Downloads/skypeforlinux-64.deb: line 1: '!arch'   What can I do to resolve this issue?


Ffmpeg. How to replace black bars by zoomed image

In some videos there zoomed part of the same video instead of black bars. Like this one:


Using this   OF=$(ps fax | grep 'php-fpm: master process' | awk '{print $1}')   IDX=`expr index $OF ' '`   I get an error. The results of the $OF variable are:  27797 27495   What is the error here? I think it has to do with how the variable is being passed into the expression. Also, have tried putting ' quotes around the $OF variable to no avail. That just returns 0 as not found.


How many times to roll a die before getting two consecutive sixes?

Basically, on average, how many times do you have to roll a fair six-sided die before getting two consecutive sixes?


Find a set of limit point of $A=\{ \frac{1}{m}+\frac{1}{n} : m,n \in \Bbb{N} \}$ in $\Bbb{R}$ by using the following way.

Find the set of limit points of $A=\{ \frac{1}{m}+\frac{1}{n} : m,n \in \Bbb{N} \}$ in $\Bbb{R}$.   I want to solve this question by the following way, but I need help.  We know that $0< \frac{1}{m}+\frac{1}{n} \leq 2$, for all $m,n \in \Bbb{N}$.   If $x<0$, then $x\notin A’,$ because $(x-1,0)$ is a neighborhood of $x$ and $(x-1,0) \cap A=\emptyset$ If $x>2$, we have $(2,x+1)\cap A=\emptyset$, so $x\notin A’$. If $x=2$, $(\frac{3}{2},3) \cap (A\setminus \{2\})=\emptyset $, then $x\notin A’$. If $x=\frac{1}{n}$, where $n\in \Bbb{N} \setminus \{1\}$, let $\epsilon =\min \{x,1-x\}>0$, then we have $x+\frac{\epsilon}{2}\in (x-\epsilon,x+\epsilon)\cap (A\setminus \{x\}) \neq \emptyset$, so $x\in A’$.   What about other cases:   If $x=0$ If $0<x<1$ and $x\neq \frac{1}{n}$ If $x=1$ If $1<x<2$   Thanks.


Given $A$ and $B$ is the subset of $C$ and $f:C\mapsto D$, $$f(A\cap B)\subseteq f(A) \cap f(B)$$ and the equality holds if the function is injective.  But why for the inverse, suppose that $E$ and $F$ is the subset of $D$, $$f^{-1}(E \cap F) = f^{-1}(E) \cap f^{-1}(F)$$ without saying that the inverse function is injective. So if  $$x\in f^{-1}(E) \cap f^{-1}(F)$$ $$x\in f^{-1}(E) \text{ and } x\in f^{-1}(F)$$ This means that there exists elements $y_1 \in E$ and $y_2 \in F$. So here how do we know that these two elements are equal.  I am independent learner so I hope I can get an explaination in more details.


The sign of $d\mathbf{r}$ when integrating the universal gravitational force in order to define gravitational potential energy

I am trying to find gravitational potential energy by integrating the gravitational force:  $$\mathbf{F}(\mathbf{r}) = - \ G \frac{Mm}{|\mathbf{r}|^2} \ \hat{\mathbf{r}}$$  where $\mathbf{r}$ is the vector from the centre of the Earth with mass $M$ towards the point of a mass $m$, and $\hat{\mathbf{r}}$ is the unit vector pointing towards the vector $\mathbf{r}$.  The potential energy at a point of the distance $|\mathbf{r}|$ can be found from  $$U(\mathbf{r}) = -\int_{\infty}^{r} - \ G \frac{Mm}{|\mathbf{r}|^2} \hat{\mathbf{r}} \ \cdot \ d\mathbf{r}$$  Then, removing the minus signs the expression becomes  $$U(\mathbf{r}) = \int_{\infty}^{r}  \ G \frac{Mm}{|\mathbf{r}|^2} \hat{\mathbf{r}} \ \cdot \ d\mathbf{r}$$  However, look at the picture below that I drew.   Since I am integrating from infinity to a point r, I thought $d\mathbf{r}$ should be directed towards the opposite direction of $\hat{\mathbf{r}}$, but actually, if I calculate in that way I get  $$U(\mathbf{r}) = \frac{GMm}{r},$$ in which the minus sign is omitting.  From a mathematical perspective, either of $\hat{\mathbf{r}}$ and $\mathbf{r}$ direct towards the same direction, hence the scalar product should be a positive value.  But I still do not understand why $\hat{\mathbf{r}}$ and  $d\mathbf{r}$ should be considered the same direction whenever I am calculating. This is perhaps not accounting for the upper and lower bounds.  Can anybody explain please?


Make annoying executable invisible to bash tab completion (cd-it8 etc)

When using the command line, cd is one of the most frequently used shell commands. I've gotten used to the ability to type cd, pressing tab, and then pressing tab again to see what directories there are to cd into. Ubuntu has recently started including the colord package and its tools start with cd. Now if I press cd and tab, I get this: $ cd cd                 cd-fix-profile     cd-it8              cd-create-profile  cd-iccdump           How can I make sure all those cd-* executables don't show up when I'm using the command line? I assume they are necessary for the OS, so I can't just move them out or rename them; however, I don't want them to be completed or even visible when I'm in bash. Note that this is under bash 4.4.20(1) which is what comes with Ubuntu 18.04. As an aside: are those executables still included in Ubuntu 20.04?


Proof that there are infinitely many primes of the form $4m+3$

I am reading a proof of there are infinitely many primes of the form $4m+3$, but have trouble understanding it. The proof goes like this:    Assume there are finitely many primes, and take $p_k$ to be the largest prime of the form $4m+3$. Let $N_k = 2^2 \cdot 3 \cdot 5 \cdots p_k - 1$, where $p_1=2, p_2=3, p_3=5, \dots$ denotes the sequence of all primes. We find that $N_k$ is congruent to $ 3 \pmod {4}$, so it must have a prime factor of the form $4m+3$, and this prime factor is larger than $p_k$ — contradiction.  My questions are:   Why is $N_k$ congruent to $3 \pmod{4}$? Why must $N_k$ have a prime factor of the form $4m+3$ if it's congruent to $3 \pmod{4}$?   It seems that those should be obvious, but I don't see it. Any help would be appreciated!


How to "cd" between directories using a python script

I'm writing a test script that is supposed to cd from the current directory into a new one if that path is confirmed to exist and be a directory  serial_number = input("Enter serial number: ") directory = "/etc/bin/foo" if os.path.exists(directory) and os.path.isdir(directory):    #cd into directory?    subprocess.call(['cd ..' + directory])   My dilemma is that I don't know how to properly pass a variable into a subprocess command, or whether or not I should use call or Popen. When I try the above code, it comes back with an error saying that No such file or directory "cd ../etc/bin/". I need is to travel back one directory from the current directory so then I can enter /etc and read some files in there. Any advice?


What is the relationship between the sum of squares of all weights and lambda in the ridge regression

Currently I am reading  chapter 8, regression.  And I feel quite confused about the following paragraph(see picture below), does it mean in ridge algorithm, the sum of all weights will be less than lambda?  As I see from the execution result, it is impossible. Assume that we set a small value for lamda, and weights will be nearly same as regular least squares regression. Such this constriaint will not be met.  So how should I understand the following sentence?


Calculating $\int_{0}^{\infty} x^{a-1} \cos(x) \ \mathrm dx = \Gamma(a) \cos (\pi a/2)$

My goal is to calculate the integral  $\int_{0}^{\infty} x^{a-1} \cos(x) dx = \Gamma(a) \cos (\pi a/2)$,  where $0<a<1$, and my textbook provides the hint: integrate $z^{a-1} e^{iz}$ around the boundary of a quarter disk.   However, I couldn't figure out how to control the integral over the quarter arc. Any hints?


The series $\sum_{n=2}^{\infty }\frac{1}{\log (n!)}$

I'm trying to find out whether this Series $\sum_{n=2}^{\infty } a_{n}$ converges or not when $$a_{n}=\frac{1}{\log (n!)}$$  I tried couple of methods, among them: d'Alembert $\frac{a_{n+1}}{a_{n}}$,   Cauchy condensation test $\sum_{n=2}^{\infty } 2^{n}a_{2^n}$, and they both didn't work for me.  Edit: I can't use stirling, and integral.  Thank you


I'm coping file to xclip  cat file.txt | xclip  I'm pasting without problem with  xclip -o  When I want to paste it to Firefox with Ctrl+V it pastes old text (that shouldn't already be in the clipboard).  When I go back to terminal and run xclip -o it pastes the correct text.  Why is there a problem with pasting to Firefox?


Withdrawing a Schengen visa (business class) application

I recently applied for a business Schengen visa to Switzerland (from India). However my visa approval is delayed and the purpose of the trip, which was to attend some crucial meetings, is not applicable any more. My client and I do not feel it is necessary to make the trip anymore and would like to withdraw/cancel my visa application.   Is this easy to do? Will canceling my application reflect poorly on me and hamper my future chances of traveling to the EU region or to Switzerland?


Resetting a for-loop when removing elements from a list

How do I reset a for-loop while looping through a list? For example, I want the for-loop to reset i.e. (i=0 and j=1) when there are duplicates in a list .  In this piece of code, I want the duplicates removed and the for-loop reset when subsequent entries in the list are equal. For instance, we have   list1 = [east, west, west, east]   I want the resultant list1 to be equal to an empty list.   This is because, When both "west" entries are eliminated, this results in the list updating to [east,east]. Since this is also a duplicate, the result must hence be an empty list [].   j=1; for (int i=0;i<(list1.size()-1);i++){     if((list1.get(i)==list1.get(j))){         list1.remove(i);         list1.remove(i);         i=0;         j=1;     }else{         j++;     } }


What is the usefulness of a screensaver on a computer using a LCD monitor?

Old computers were using CRT monitors and when an image was continuously displayed on the screen, it became marked. So, screensaver where invented to avoid screen burn-in.   Laptops and modern computers almost all uses LCD display now and, AFAIK, they are not affected by this effect.  So, should I completely deactivate this feature and use power management instead or I am wrong?


I'm very curious about how light is created.    I'm trying to get back to some type of real understanding about why everything on the sub-atomic level vibrates and the implications for the preservation of both the conservation of energy and conservation of momentum.  How is light created at the atomic level?


Adding angular momenta in quantum mechanics

When there are two spin-1/2 particles, the possible states can be grouped into a singlet and a triplet.   When there are three spin-1/2 particles, there are two possible values for the total angular momentum number, j. These two values are j=s=3/2 and j=s=1/2. How do I determine the possible states for this three particle system in the {j,m} basis, where j is the total angular momentum of the system, and m is the total z component of the angular momentum of the system? Can I treat the j=1/2 case as if there is only one spin 1/2 particle, or is it necessary to still consider all three particles for the j=1/2 case? Note that I am not considering orbital angular momentum at all. Also, for the j=3/2 case, how many particles are involved in this situation? I know that m ranges from -j to j in integer steps, so then for the j=3/2 case, the m value takes on values of -3/2, -1/2, 1/2, and 3/2.   Is there--for the j=3/2 situation of the three particle system--a tricky singlet and triplet grouping as in the case of the two spin-1/2 particle case mentioned at the beginning of this question?  In summary, I am confused about how many particles to consider for each value of j, for the system of three spin-1/2 particles, with j taking on two different values.   Thank you!


Can I add styles to footer with $wp_styles->add_data?

I'm working on a script to easily move js and css scripts to the footer using the add_data function in $wp_scripts and $wp_styles. I know for scripts that if the group is greater than 0 the script call will be moved to the footer (first foreach below does that). However, setting the group for styles doesn't have the same effect (and group is set properly with second foreach). Is there a way to move styles to the footer with the same method, or should I be looking for an alternative?  function mod_scripts(){     global $wp_scripts, $wp_styles;     foreach($wp_scripts->queue as $script){         if ( ! $wp_scripts->get_data( $script, 'group' ) ){             $wp_scripts->add_data( $script, 'group', 1 );         }     }     foreach($wp_styles->queue as $style){         if ( ! $wp_styles->get_data( $style, 'group' ) ){             $wp_styles->add_data( $style, 'group', 1 );         }            } }   EDIT: The reason for the request is that I'm trying to remove blocking css to make a page load faster. The recommended method is basically to just embed the css directly into the page, but that's never worked out well. And now I realize that the question as I asked it is flawed. I'm just looking for an effective way to load styles that still maintains proper compatibility with plugins.


Don't know what 'this' keyword reference

I don't understand what this keyword reference in this example: public class Game extends Canvas implements Runnable{      /* some code.. */         private Thread thread;     private boolean running=false;      private synchronized void start(){         if(running) return;         running = true;         thread = new Thread(this,"Thread");         thread.start();     }  }  First, I thought it could be written as : thread = new Thread(new Game(),"Thread"); but it doesn't work.


Using Kaiser rule to select the best principal components: pros and cons

Is the Kaiser rule (choosing only PCs with eigenvalues >1) a suitable method to select the best principal components? What are its pros and cons?


I am trying to download vlc to play movies but it is not working. When i go to software center and try to install vlc it says "Package dependencies cannot be resolved"  I am not to ububtu and linux can some one guide what needs to be done?


Send an email with attachments through a workflow

I have been looking for a solution to my issue, but I can't find anything.  The matter is the following: - I set up a workflow to start manually to send an email to a specific distribution list, whenever an engineer wants to send a start of test for a vehicle (an item in the list). - When starting the workflow, the engineer will fill out a form (parameters) and then start the workflow.   Is it possible to browse for an attachment when filling out the form, adding in the parameters, and then have it send it in the email through the workflow? I am not able to add the attachment in the workflow. The attachments are in .pdf file and they are located in the engineers' desktop.   Not sure if I am making much sense, please let me know if you would like me to explain myself better.  Any help please?  Thank you


Please help to identify an animated movie: a boy lost on a jungle planet (80-90-s)

I remember watching an animated movie (part of, because it was incomplete) on a videotape in the 90's. It was a full-length movie, not likely a series. Please help to identify.   The movie was French (with English subtitles) The protagonist is a little boy lost on a jungle planet. His parents have perished before. A rag-tag rescue team travels in a spaceship to save him. The team includes a captain, some rogue prince and an old balding man with a patch on his head (and some other people I do not remember) The boy communicates with the team using an odd, egg-shape 2-way transmitter. The old man knows the planet where the boy is stranded pretty well The team lands on some planet which is populated with faceless people. They try to subvert the team, but the Rogue Prince rebels and the power of the faceless people is disrupted, giving the team a chance to fly away. The boy makes friends with some elephantine local creature.   Then the tape ended. It did not include any title or opening credits either, as someone tried to jam in as many films on the tape as possible.


PHP PDO prepare statement, using variable for column SET

how can insert variable to a prepared PDO statement? I don't know which column will be modified. the code is (throws error):   private function deleteData($column, $id)   {     $stmt = $this->db->prepare('UPDATE table SET $column = "" WHERE id = ?'); // $column variable has 1 out of 4 values, and it changes dynamically      $stmt->bind_param('i', $id);     $stmt->execute();   }  Error:  Fatal error: Uncaught mysqli_sql_exception: Unknown column '$column' in 'field list' in  as I understood from the topic linked the only option is to make a switch? switch ($column) {     case 'column1':        $stmt = $this->db->prepare('UPDATE table SET column1 = "" WHERE id = ?');     break;     case 'column2':        $stmt = $this->db->prepare('UPDATE table SET column2 = "" WHERE id = ?');     break;     and so on...


Find the value of: $\frac{\sqrt{45} + \sqrt{18}} {\sqrt{7+2\sqrt{10}}}$

Find the value of:$$\frac{\sqrt{45} + \sqrt{18}} {\sqrt{7+2\sqrt{10}}}$$      I need help solving this question. Every reply is appreciated.  Thanks!


Does a List guarantee that items will be returned in the order they were added?

Does a List<T> always guarantee that items will be returned in the order they were added when enumerated?  Updated: Thanks for all the answers folks, puts my mind at ease. I had a quick poke around the List<T> class with .NET Reflector (should've probably done that in the first place) and indeed the underlying store is an array of T (T[]).


apt-get to install a package and its first level dependencies only?

Is there a way I can use apt-get install command to install a package and its first level dependencies only instead of all the dependencies recursively?  EDIT:  I am dealing with ROS and would like to install a single package with only its first level dependencies. I don't actually want to install or update the system dependencies that this ROS package depends on, "recursively". During running a particular application if any 'dependency-not found' error is thrown, I would like to see what exactly is missing. I hope this helps.  PS: Also, it seems that there is an apt-get command to install only the first-level dependencies but couldn't find any. Any help is greatly appreciated.


Irreversible process with $dS=0$ (isolated system)

Is there an irreversible process, where the entropy of the isolated system does not change?


Why can't using 2 separate measuring instruments to measure position and velocity work?

According to Heisenberg uncertainty principle, position and velocity cannot be measured accurately at the same time. What if we use 2 separate measuring instruments to measure position and velocity at the same time? One for measuring velocity and another one for measuring position. Would this solve the Heisenberg problem? I am sure there are smarter people who have thought of it, so I don't think it will work. May I ask why not?


I am trying to create a shortcut whose path is something like:  apps\bin\myapp.exe --userdir apps\conf\_user    This own't work because Windows wants a absolute path but this shortcut is stored on a USB stick and therefore I cannot hardcode the thing to C: or D: as it will change each time the USB is inserted into a new PC.  I am currently using a *.bat file to work around this but the CMD.EXE windows stays visible until it's physically closed -- kind of a PITA.  Any ideas???


How should I transform non-negative data including zeros?

If I have highly skewed positive data I often take logs. But what should I do with highly skewed non-negative data that include zeros? I have seen two transformations used:   $\log(x+1)$ which has the neat feature that 0 maps to 0. $\log(x+c)$ where c is either estimated or set to be some very small positive value.   Are there any other approaches? Are there any good reasons to prefer one approach over the others?


Ubuntu google authenticator only for ssh not physical machine

I set up google authenticator for ssh login, and it works fine.  However, when restart the computer and login form the physical machine, it requires the google autheticator code also - is it possible to change it so this is ONLY for ssh?


Can I use a regular for loop to delete certain objects from an ArrayList?

Let's say we have an ArrayList of Cats.   This is our cat:  public class Cat{    String color;    int age;    public Cat(String color, int age){        this.color = color;        this.age = age;    }  }   We have a cat and each cat has a color. Somewhere else in our code, we have the following:   ArrayList<Cat>cats = new ArrayList<Cat>();  cats.add(new Cat("white",5);  cats.add(new Cat("black",6);  cats.add(new Cat("orange",10);  cats.add(new Cat("gray",3);  System.out.println(cats.size()); prints out 4   So now are cats ArrayList has 4 cats in it. What if I want to remove all cats that are over 5 years old, shouldn't I be able to do the following?  for(int index = 0; index<cats.size(); index++){     if(cats.get(index).age > 5){         cats.remove(index);     } }   Now after that runs, I print out the size of the cats ArrayList and it says 3, even though it should remove 3 Cats and leave one.  So, shouldn't this work? I don't understand why it wouldn't. What other ways are there to remove objects with specific values from a List/Array?


Show that $\{ f \ast f: f \in \mathcal{E}'(\mathbb{R}^n) \} \subsetneq \mathcal{E}'(\mathbb{R}^n)$

I wonder if somebody could help me understand the following solution:  $\textbf{Problem:}$ Let $F=\{ f \ast f: f \in \mathcal{E}'(\mathbb{R}^n) \} \subset \mathcal{E}'(\mathbb{R}^n)$. Show that $F \neq \mathcal{E}'(\mathbb{R}^n)$ ($f\ast f$ is the convolution of $f$ with it self and $\mathcal{E'} $ is the space of distributions with compact support in $\mathbb{R}^n$).  $\textbf{Solution:}$ Assume the contrary. Then $\delta_1 -\delta_0 \in F$ so there is an $f \in \mathcal{E'}$ such that $f \ast f= \delta_1 -\delta_0$ Since $f \in \mathcal{E'}$ such the Fourier transform of $f$, $\hat{f}$, is complex analytic. Then $ (\hat{f}(\xi))^2= e^{-i\xi}-1 \in \mathcal{O}({\xi}) \implies \hat{f}(0)=0$.  I fail to see why this is a contradiction (also I don't get the last implication). Does anybody understand this?


How to access custom REST controller in managed package via Site

I had a custom Apex REST controller which was made available by a Site    But now I've added the Apex class into a managed package, I cannot access the REST controller anymore? How do I access the REST endpoint?


Squared Error vs Absolute Error loss functions

The two most popular types of loss functions are  1) squared error: $L(y,f(x))=(y-f(x))^2$ --> best estimate is the $E(Y|x) $ 2) absolute error: $L(y,f(x))=|y-f(x)|$ --> best estimate is the $median(Y|x)$  I have two questions.  1) Why do people use the squared error method? The absolute error method makes much more intuitive sense. You get the difference between the actual and the estimate. Plain and simple. If you square the difference, then won't you get "warped" values depending on the size of the difference?  2) This also got me thinking about what is "expected value." Expected value is defined as the mean. However, the best estimate under the absolute error loss function is the median. So is the "expected value" the median? I would very much appreciate it if someone can help me clarify my thinking. Thanks.


Can the information entered into a Cognito Form be automatically sent to an email address upon submission?

I have build a website for a finance company.  The Cognito Form is on the website as an application form.  I would like the information sent automatically to the finance company's email address (as soon as the form is submitted) without having to log into Cognito Forms. The finance company needs to know the exact moment the application for finance comes in. The finance company can not possibly log in to Cognito Forms 24/7 to check if there are any finance applications.


Difficult inequality : $\sum_{n} |z_{n}|\le \pi \left|\sum_{k} z_{n_k}\right|$

Given a family of complex numbers $(z_n)_n$ prove that there exists a subsequence $(z_{n_k})_k$ such that   $$\sum_{n} |z_{n}|\le \pi \left|\sum_{k} z_{n_k}\right|$$  I ailled to find a counter example of this inequality. what tricky me here is the constant $\pi$. How does that constant appears here? How can I prove this inequality?   Any hint or idea?


What does the ./ mean (dot slash) in linux?

For example, I can do the following  touch a  or  touch ./a  Then when I do ls I can view both, so what exactly is the ./ for?


I have a string with hex values, for example:  01 02 03 AA BB CC FF 09 65 AA BB DE F2   And my need is take part of this string before first AA BB. I try do it with regular expressions. My ideas are around something like this:  (([0-9A-F]{2} )+(AA BB )){1}   And after match take first group. But it's not works. Could somebody help me with this task, please?


Converting time field omitting time and returning null values?

I have a time field in my shapefile that is formatted as HH:mm:ss.s It is a text field, and I want to convert it to a date so I can calculate time elapsed across rows (if there's a better way to do this let me know). Basically, each row is a point on a route, and I want to use the time field to calculate the amount of time elapsed between the first and last points on the route.   I tried using the convert time field tool, setting the input format as HH:mm:ss.s, and the output type as DATE. The output field however only shows values of 01/01/2001 for some rows and  for other rows.   time is the input field and time_c is the output field  I'm not sure what's going wrong here, here is what shows up in the geoprocessing results window:    I tried adding the date data to the field as well to make the format yyyy-MM-dd HH:mm:ss.s, but it still didn't work:


AirPlay turned off and can't be turned on

I have a MacBook Air and with no apparent reason the AirPlay icon has dissapeared from the desktop. When I go to System Preferences → Displays, the status of AirPlay shows "Off" and there's no way to change it since it doesn't show the "On" option.


Linux Mint 19 Tara - can only install without EFI

For the past week I've been trying to create a dual boot with Windows 10 and Linux Mint 19 Tara.  The base setup, as intended is supposed to be a simple 1 operating system per SSD:     /dev/sda (250GB SSD) - Windows 10       /dev/sdb (250GB SSD) - Linux Mint 19 Tara   All other data disks are disconnected (for the time being).  I started with installing Windows 10 (onto /dev/sda) making sure I boot of USB using UEFI. Everything went fine and looking at the partitions, I can clearly see an EFI partition.  I then proceeded to boot the Mint USB in the same manner and started install (using ERASE, Encrypt and LVM).  At some point I get prompted with:     The 'grub-efi-amd64-signed' package failed to install into /target/. Without the GRUB boot loader, the installed system will not boot.   This results in a GRUB command-line at boot-time. When I type 'exit' it will then go on to boot Windows.  So, I started researching and found tons of articles and guides all explaining me to do exactly what I've been doing, including disabling 'Secure Boot' and 'Fast Boot' etc in the BIOS.  In my ASUS BIOS there isn't an option to disable 'Secure Boot' directly and I originally simply set the OS Type to 'Other', which works perfectly fine for installing Fedora 28 and Kali. (which I had previously installed on /dev/sdb)  This change was not enough though. So after some more research I found that in order to completely disable 'Secure Boot' I need to delete the key in BIOS. Once I had done that, 'Secure Boot' showed as disabled. Still, Linux Mint installation gave me the exact same error message and failed to install GRUB.  I then started experimenting some more including various approaches to manually setting up partitions. None of it worked and always resulted in the same issue. I eventually found that I seemingly can't install using EFI at all. The only installation that went through properly was, when I booted of the USB without UEFI (while 'Secure Boot' is disabled, obviously).  This clearly isn't what I want though and I've grown extremely frustrated. As a result of failed experimentation, I've had to reinstall Windows several times as well and we all know that's never fun, as it takes the better part of a day to fully update Windows.  I've really started to enjoy Linux Mint on my other (older) system and simply want it on my main system as well, but I'm relatively new to linux and I'm at a loss.  I sincerely hope somebody has some suggestion(s).  Please let me know if you need more information, but keep in mind that I'm fairly new to Linux in general, so be specific with any queries.  Thanks.  Update: I've tried 'Boot Repair' as suggested to some Ubuntu users with similar issues, but I still only get a GRUB command-line at start up.  Update 2: I decided to try another download of Linux Mint from a random mirror and noticed that today the downloaded is is called 'linuxmint-19-cinnamon-64bit**-v2**.iso'. Hopefully EFI install will work now. Will post back with results.  FIXED That did it. After creating a new bootable USB from the now available 'linuxmint-19-cinnamon-64bit-v2.iso', the system installed just fine using EFI. Awesome! :)


How to find the Range of function  $$f(x)= \frac{x^2-3x-4}{x^2 - 3x +4}$$ I tried to equate the expression to $y$, then cross multiplied  $$ y= \frac{x^2-3x-4}{x^2 - 3x +4}$$ $$ y(x^2 - 3x +4)= x^2-3x-4 $$ bought the terms to one side so it becomes a quadratic and made Discriminant to zero , but i cant seem to reach anywhere.. Any suggestions?


Recently,I have found out, that if we consider the speeds at which stars or other space objects move from the point of view of the Earth, we can calculate that they would be faster than light, because they do full revolution in 24 hours, and in that time they do more than a light year of distance. But SR tells us that speed of light is the upper limit for speed of objects in the universe. My question is what is the explanation for this "contradiction"?


I try to install Ubuntu 16.04 next to Windows 10. Windows is installed on legacy bios and then upgraded to Windows 10. When I try to install Ubuntu from USB stick, it shows a message titled "Force UEFI installation?". It says that the machine's firmware started the installer in UEFI mode but there is an OS installed using BIOS compatibility mode. If I force installation I won't be able to boot Windows.  How can I start the installer in legacy mode?  BIOS of the machine supports legacy and UEFI modes. Legacy support is enabled. But USB disk is always recognized as EFI. USB disk's name is shown as "EFI USB Disk" in BIOS. I cannot change that. I burned the USB with both startup disk creator on ubuntu 14.04 and pendrive software on Windows. Same result.  Thanks.


I need to show that: $$\lim_{n \to +\infty}\sum_{k=0}^{k=n-1}\left(\frac{n-k}{n}\right)^n = \frac{e}{e-1}$$I observed that taking the limit term by term gives the result, but of course this is not justified. This exercise assume no prior knowledge on uniform convergence of series. (I am new to series but I remember from calculus a result on limits that is justified in this case.) So I should be able to prove it following another path.   It also appears that a conversion to a definite integral is unfeasible. What do you suggest?


Is there a term for a question that is only a question because of a question mark?

I sent a friend a question in the form:     Just trying to remember how we know each other?   That is a "statement" without the question mark at the end. Is there a term for this? Since it does not begin with a "How", "Why", "Where" etc..


Create a new document and rename it directly (in one step) in Ubuntu 18.04

I know this is some how silly and ridiculous, but it is really annoying! I recently installed Ubuntu 18.04.. With Ubuntu 16.04, I was able, when I create a new empty document, to rename it directly: I didn't need to :     step1:  create the document. step 2: click on it with the right button and choose rename    Everything was done in one step. However, in Ubuntu 18.04, I can not do this (creating and renaming) in one step: every time I want to create an Empty document, I have to:   Create the empty document Right click on it then choose rename.   Is there anyone who faced the same problem? And is there a fix for this?  PS: It is not about how to create an empty document in Ubuntu 18.04, it is about how to create and rename, in one step, an empty document.


User should not allow to submit 2 entries on the same week in sharepoint list

i am new to sharepoint online. i am creating a timesheet in sharepoint list. Please help me with the below requirement.  Solution required:  I have two fields called week start and week end. User should not allow to submit 2 entries on the same week (Week start and week end).and the production hour should be more than 45 hrs.  Request your help on this. Techies..


'None is' or 'none are', when the antecedent is plural?

Jacob Rees-Mogg MP, speaking by the invitation of the Speaker of the House of Commons in a , quoted a Financial Times article and, in passing, 'corrected' its grammar.  Quoting the article, Rees-Mogg said of entries on a Wikipedia list (of entries in a table) that 'none are' from Europe and then corrected the article saying that it should be 'none is'.  'None' may refer to 'not one' in which case I would say it is singular. But 'none' may also refer to 'not any' in which case I would suggest it is plural.  Thus I think that Mr Rees-Mogg is not correct in correcting the FT article.  'None of the entries' (that is, not any of the entries) are from Europe' seems quite correct to me.  'Not one of the entries is from Europe' is also correct, I would say.  Is Mr Rees-Mogg correct ?     entry for 'none' :     a. Not any (one) of a number of people or things. Also: neither of two persons or things (now regional).   ======================================  EDIT : I have read the suggested duplicates and they are inconclusive. I was hoping for a definitive (and thus an academic), decisive answer to the question.  =======================================


Deleting your question only to re-ask it

In , the OP admitted to deleting his question and then reposting it. I feel like this user has successfully "gamed" the system. His post is not technically a dupe (since he deleted the original), and it's not offensive (in content) or spam, so it's not flag-worthy.  I left a comment attempting to educate the user. But what else can be done here? I would hate to see this catch on as a way of getting more attention for your post.


Switching between virtual console and GUI

How to switch between virtual console and GUI in Ubuntu? I wanted to see what key functions would allow me to switch between the two.


Wireshark problem. Can't select default interface

I downloaded Wireshark from the Ubuntu 11.10 software center and when I start it and want to select default interface for capture in the list of interfaces are blank. I can't select default interface. Please help me.


Why C++ Don't Use Parent Class Constructor?

I wondering why in c++ can't use parent class constructor for an specific signature, in case that derived class miss that?  For example in below sample, I can't initialize dd object with std::string.  #include <iostream>   class Base {     int num;     std::string s; public:     Base(int _num){ num = _num;}     Base(std::string _s){ s = _s;} };  class Derived : public Base { public:     Derived(int _num):Base(_num){} };  int main() {     Base b(50);     Derived d(50);     Base bb("hell");     Derived dd("hell"); // <<== Error     return 0; }   With Inheritance I expect to extend a class and not losing previous functionality but here I feel losing some.  In a more practical example, I create my version of std::string but It doesn't behave like a std::string in some cases :  #include <string> #include <iostream>   class MyString: public std::string { public:     void NewFeature(){/* new feature implementation*/} };  int main() {     MyString s("initialization");   // <<== Error: I expect to initialize with "..."     cout<<s;                        // <<== Error: I expect to print it like this.     return 0; }   Can somebody give some explanation ?


The following formula returns the correct result:  =if(S3,if(J3>=NRealGames,0,min(max(NRealGames-J3,0),S3)/S3),)   This one returns the same result:  =if(S3:S,if(J3:J>=NRealGames,0,min(max(NRealGames-J3:J,0),S3:S)/S3:S),)   But this one returns the wrong result:  =ArrayFormula(if(S3:S,if(J3:J>=NRealGames,0,min(max(NRealGames-J3:J,0),S3:S)/S3:S),))   What is wrong with my ArrayFormula?  EDIT  This question is not duplicated of  because I am asking about ArrayFormula, not about Clamp (why was it marked as duplicated??)


Using a comparison test, test series for convergence / divergence

Test series for convergence / divergence using a comparison test:  $$\sum_{n=1}^\infty\frac{n+2^n}{n+3^n}$$  According to symbollab website, this series converges. I guess I need to compare it with following geometric series (which converges) $$\sum_{n=1}^\infty(\frac{2}{3})^n$$ as less than or equal to, but I don't know how to get rid of n in numerator / denominator.


Verification of solution for $\lim_{x\to 1} \frac{x\cdot \sin\{x\}}{x-1}$

Can you verify the solution to the following (very simple) problem $$\lim_{x\to 1} \frac{x\cdot \sin\{x\}}{x-1},$$ where $\{\}$ is the fractional part function. LHL = $\lim_{h \to 0^+}\frac{(1-h)\cdot \sin(1-h)}{-h} = \lim_{h \to 0^+}\frac{(1)\cdot \sin(1)}{-h}=-\infty$ RHL = $\lim_{h \to 0^+}\frac{(1+h)\cdot \sin\{1+h\}}{h} = \lim_{h \to 0^+}\frac{(1)\cdot \sin(h)}{h}=1$ Since $LHL \neq RHL$ hence limit does not exist. Is it correct to say that LHL does not exist? Or should I say LHL exists and is $-\infty$?


How did Will Byers know where the letters were on the wall in Stranger Things?

In the first season of Stranger Things, communication between the real world and the upside down seems to have some interesting properties. Initially communication only seems possible as echoes of voice from the real world to the upside down (and this is demonstrated several times, but the reverse is not possible except at near breaches/gates).   Eventually it is shown that Eleven can use radios to hear things in the other side and then Joyce Byers develops a method for Will to communicate as well. However,    How did Will know the specific locations for the different letters?   In the final episode of season 1 we see that recent changes such as the bear trap or any of the Christmas lights are missing from the Byers home within the Upside-Down. Joyce Byers doesn’t say anything out loud while writing the letters (and anything spoken would be extremely hard to localize that well).   Did Will even know he was turning lights on?


How to add custom basemaps to BasemapGallery

I would like to add my own custom basemaps to the BasemapGallery. Is there any way I can create my own BasemapGallery with only my maps? I am using the ArcGIS API for javascript.  EDIT: for clarity  I have already created a custom basemap that the answer  describes. The issue is that I would like to create a  but with my own basemap, not ArcGIS's. I hope this makes a little more sense now.


Can I use a HDD on my PS3 if I have already used another on the same console?

I'm thinking of changing the Hard Disk of my PS3 (Slim 120GB), but I am unsure of what will happen to the data on the one I previously had if I do this:   PS3 has some data in the HDD. I turn off PS3, change HDD, install OS on new HDD. I download some data on new HDD from PS Plus.   Let's imagine I forgot to back something up...   I turn PS3 off, change HDD back.   Can I still use the old hard drive without needing to format it again?


I have a folder (let's name it main-folder and it's mounted via smb) that contains lots of files and subfolders. I want to copy half of the contents of main-folder to a local subfolder (let's call it my-folder). My problem is that one folder is common between main-folder and my-folder. And even though I have pressed the option key, I do not get the merge option.  I know I can use rsync and other similar commands which I've done lots of time. EXCEPT I can't use it this time as I am only copying half of the files/folders. Too tedious to write an exception list.  I was hoping for a similar behaviour when dragging files/folders in Windows Explorer.  Any ideas on how to make it work? Thanks a lot


In Selenium 2 - Java, what's the difference between  ChromeDriver driver = new ChromeDriver();  and  WebDriver driver = new ChromeDriver();  ? I've seen both of these used in various tutorials, examples, etc and am not sure about the difference between utilizing the ChromeDriver vs WebDriver objects.


Unexpected update result on the quickly nested list in Python

Why couldn't the first element but the whole column be updated below?  >>> x=2*[2*[1]] >>> x [[1, 1], [1, 1]] >>> x[0][0]=2 >>> x [[2, 1], [2, 1]]


How do I find on the Internet hits for a word with a dash in the middle?

Background: I tried to find information about the tool python-config, but a Google search brought up mainly hits for python's config module.  Digging a bit deeper, the issue is that Google treats the character "-" in search terms as a stop character and word separator. So even with a Google Advanced search I was not able to find only pages contain "python-config" (with the dash). Then I tried briefly Bing and Yahoo with no more success.  On this site here I found , but the search engine suggestions contain mainly code search sites.  So my question remains: How do I find with Google hits for a word with a dash in the middle, e.g. "python-config". What is the best way to do this?  ps: Meanwhile I did find out what the python-config tool is for - by reading through the python.org documentation, but not by searching the python.org site, because it uses a custom google search...


Is it possible to find all DNS subdomains for a given domain name?

This question exists because it has   historical significance, but it is not   considered a good, on-topic question   for this site, so please do not use it   as evidence that you can ask similar   questions here.      More info:    Anyone knows if it's possible to find all A records, CNAME or subzone records configured for a domain name?  For example, domain.com:  www IN CNAME domain.com. subdomain1 IN CNAME domain.com. subdomain2 IN CNAME domain.com.   subdomain1 IN A 123.4.56.78. subdomain2 IN A 123.4.56.79.    I want to keep a sub-domain private where I'll run an admin application (it will be password protected and on a special port, but I would prefer to keep it as private as possible).


After executing cd %TEMP% i was taken to C:\Users\KRISWE~1\AppData\Local\Temp I have never seen the folder KRISWE~1 before, does anyone know what this is? It seems to be exactly identical to my regular user folder. It doesn't show up as a hidden folder, and i can only access it via cd. I noticed it's exactly 8 characters long, so i was thinking it might be some sort of hidden legacy system. Does anyone know?


Chain rule misunderstanding : two different use of it give two different answers...

I am studying G.R an I have a mistake by using chain rules (yes probably very basic mistake) that I don't get.  Take the following quantity (there is Einstein convention here, the $X$ and $V$ are vectors and $\{x\}$ and $\{y\}$ are two different system of coordinates.):  $$ X^{\beta} V^{\sigma} (\frac{\partial y^{\mu}}{\partial x^{\beta}}\frac{\partial x^{\alpha}}{\partial y^{\mu}}\frac{\partial^2 y^{\rho}}{\partial x^{\alpha} \partial x^{\sigma}})$$  I need to "simplify" it.  I can  do it in two different ways.  First, I can use the summation over $\mu$ :   $$ \frac{\partial y^{\mu}}{\partial x^{\beta}}\frac{\partial x^{\alpha}}{\partial y^{\mu}}=\frac{\partial x^{\alpha}}{\partial x^{\beta}}=\delta^{\alpha}_{\beta} $$  I also could use the summation over $\alpha$ (other "method" to simplify it):  $$\frac{\partial x^{\alpha}}{\partial y^{\mu}}\frac{\partial^2 y^{\rho}}{\partial x^{\alpha}x^{\sigma}}=\frac{\partial x^{\alpha}}{\partial y^{\mu}}\frac{\partial}{\partial x^{\alpha}}\frac{\partial y^{\rho}}{\partial x^{\sigma}}=\frac{\partial y^{\rho}}{\partial y^{\mu} \partial x^{\sigma}}=\frac{\partial}{\partial x^{\sigma}}\frac{\partial y^{\rho}}{\partial y^{\mu}}=\frac{\partial}{\partial x^{\sigma}}\delta^{\rho}_{\mu}=0$$  Thus, if I use the first thing I will end up with :  $$ X^{\beta} V^{\sigma} (\frac{\partial y^{\mu}}{\partial x^{\beta}}\frac{\partial x^{\alpha}}{\partial y^{\mu}}\frac{\partial^2 y^{\rho}}{\partial x^{\alpha} \partial x^{\sigma}})=X^{\beta} V^{\sigma} (\frac{\partial^2 y^{\rho}}{\partial x^{\beta} \partial x^{\sigma}}) \neq 0$$  And if I use the second method I end up with :  $$ X^{\beta} V^{\sigma} (\frac{\partial y^{\mu}}{\partial x^{\beta}}\frac{\partial x^{\alpha}}{\partial y^{\mu}}\frac{\partial^2 y^{\rho}}{\partial x^{\alpha} \partial x^{\sigma}})=0$$  It is probably a very stupid mistake or a more deep incomprehension thing but I really don't see it.  Could you help me figure this out ?


I'm wondering where I find the source to show how the operator ** is implemented in Python.  Can someone point me in the right direction?


I do have an overlapping polygon shapefile of different radius. I want to clip a polyline for each fid individually. How is that possible in ArcGIS?


The added button is invalid. Want to achieve the same functionality on the newly added element

I want to implement the addition and deletion of forms.Each new element contains two buttons to delete itself and add the same elements as itself.But in fact only the first one is valid, after the page is loaded itself. How can I fix it? Why?  Just started using jquery and javascript  JavaScript and Jquery code show below.    $(document).ready(function() {   var num_ac = 0   $(".add_ac").click(function() {     num_ac++     // Determine if the user enters a valid value     var select_option = $(this).parent().parent().find("select option:selected")[0].index;     var hr = parseInt($(this).parent().parent().find("input").val());      if ((select_option > 0) && (hr > 0)) {       var temp = $("#ac_row_1").clone().attr({         id: "ac_row_" + num_ac       });       temp.appendTo($("#activity_list"));     } else {       alert("Should input value");     }    })    // Can't delete the first one   $('.del_ac').click(function() {      var row_id = $(this).parent().parent().attr("id");     if (row_id !== "ac_row_1") {       $(this).parent().parent().remove();     } else {       alert("Cannot remove Because This is the first row")     }    })  })

       <select class="form-control ac_select">         <option value="0">Choose Activity</option>         <option value="1">Swimming</option>         <option value="2">Walking</option>         <option value="3">Runing</option>       </select>

              <input type="text" class="form-control" placeholder="Hour per week?" onkeyup="this.value=this.value.replace(/\D/g,'')">

       <button type="button" class="btn btn-danger del_ac">Delete</button>       <button type="button" class="btn btn-primary add_ac"> +Add</button>


Symbol for square bracket with only one horizontal line

The way cycles in permutations are written in my country's textbooks (Serbia) is with square brackets [ and ], but with only one horizontal line at the top to denote the beginning of the permutation, and only one horizontal line at the bottom at the end.  Is there a symbol in LaTeX for this?


Most efficient way to repeat a cutout pattern

Trying to figure out the best way to take this alternating circle cutout pattern and duplicate it around the surface of this cylinder.  This is a file that was given to me- I did not make the initial cutouts.


Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?

I am using hierarchical clustering to analyze time series data. My code is implemented using the Mathematica function DirectAgglomerate[...], which generates hierarchical clusters given the following inputs:   a distance matrix D the name of the method used to determine inter-cluster linkage.   I have calculated the distance matrix D using Manhattan distance:  $$d(x,y) = \sum_i|x_i - y_i|$$  where $i = 1,\cdots, n$ and $n \approx 150$ is the number of data points in my time series.  My question is, is it ok to use Ward's inter-cluster linkage with a Manhattan distance matrix?  Some sources suggest that Ward's linkage should only be used with Euclidean distance.  Note that DirectAgglomerate[...] calculates Ward's linkage using the distance matrix only, not the original observations.  Unfortunately, I am unsure how Mathematica modifies Ward's original algorithm, which (from my understanding) worked by minimizing the error sum of squares of the observations, calculated with respect to the cluster mean.  For example, for a cluster $c$ consisting of a vector of univariate observations, Ward formulated the error sum of squares as:  $$(\sum_j||c_j - mean(c)||_2)^2$$  (Other software tools such as Matlab and R also implement Ward's clustering using just a distance matrix so the question isn't specific to Mathematica.)


My GM has created a Mary Sue NPC. What can I do to persuade the GM to make her less powerful?

My GM has created a Mary-Sue-type NPC. She is a demigod with thousands of years of experience, and was once an enemy, but is now an ally of the party, though really of only a few favourite players. She is literally undefeatable, and I actually mean literally, not figuratively. Any attempts to defeat her will be vetoed.  To compound the problem, she is also pretty much a jerk, though to the GM's credit he has actually given some attempt to give her a heart of gold. The invulnerability and jerkishness don't combine well, e.g. a nother player character tried to become friends with her and make up for previous grudges—denied and his head is being used as a football.  This situation will only be worsened by the problem that our next game will be in the same setting, except that our new characters will be nerfed, due to the fact that our whole group agrees our last characters were too OP.  The Mary Sue, of course, will stay on the same power level.  This is making the game quite a bit less fun for me, though I don't know about the other players. It is quite seriously ruining it, due to the fact that she has an extremely short fuse and will kill anyone who annoys her.  What can I do to persuade the GM to make her less powerful/obnoxious? Please help!


Difference between "./" and ". " for running a script/application?

I always ran scripts using ./      For example ./script.sh   I recently learned that you can also type . script.sh   Is there any difference?   The second is much easier for me since my keyboard doesn't have a key for / but I need to press SHIFT -.


Consider a Hilbert Space $H$ such that $\sum_{n=0}^\infty \|x_n-y_n\| 0$ then $z=0$

Let $H$ be a separable Hilbert space and $(x_n)_{n\in \mathbb{N}}$ a   complete orthonormal set.  If $(y_n)_{n \in \mathbb{N}}$ is a sequence   such that $$\sum_{n=0}^\infty \|x_n-y_n\| < 1.$$ Show that if $z\perp y_n$ with $\forall n>0$ then $z=0$   Hi, can you help me with this exercise, I think in resolve it with Parseval's identity.


Printing an array to a file with each element of the array in a new line in bash

I am trying the contents of an array into a file with each element of the array in a new line in the file.  IFS=$'\n'    echo "${mtches[@]}" > sample1.txt     The content of mtches is "qwe" and " asd". But the sample1.txt file contains qwe asd in a single line. Why is it not taking IFS value into the picture?


Question on kinematics and theory of relativity

If two particles A and B travel in opposite directions with the velocity of 0.6c and 0.7c respectively, the particle A sees particle B moving with a speed of 1.3c in the opposite direction (c is the speed of light). Is this possible?


Why are strings declared as an array "char word[5] = "hello" modifiable but not strings declared as pointer (char *word = "hello")?

I was under the impression that      char word[5] = "hello";   is the same as       char *word = "hello";    because arrays always decay into a pointer?


Is it possible to skip onPause() method of BaseActivity in MainActivity when latter extends former?

MainActivity.java  public class MainActiviy extends BaseActivity {      @Override     public void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_main);     }      @Override     public void onPause() {         super.onPause()         // Can I avoid BaseActivity's onPause()?     } }   I just want to call onPause() in MainActivity skipping BaseActivity.  I cannot edit BaseActivity as it is part of a library that I'm using and removing super.onPause() in MainActivity gives error.  Maybe this is possible or maybe not so workarounds are most welcome.


How to prove that $c_0I+c_1A+..+C_nA^n$ is singular if $(v,Av,A^2v,...,A^nv)$ is linearly dependent, $v \in \mathbb{F^n}$ and $A_{n \times n}$?

Given that the sequence $(v,Av,A^2v,...,A^nv)$ is linearly dependent (1), $A_{n \times n}$, over $\mathbb{F^n}$ prove that scalars $c_0,c_1,..,c_n$ exist (such that not all of them are zeroes) such that the matrix $M=c_0I+c_1A+..+c_nA^n$ is singular.    First I'm not sure how (*) can be used here exactly. We can say that the sequence $(c_0I,c_1A,..,c_nA^n)$ resembles the sequence (1) where $v=I$. But here we have scalar $c_i$ so it's not exactly the same sequence.   Maybe I could say that the sequence $(c_0I,c_1A,..,c_nA^n)$ is linearly dependent because it has $n+1$ elements while over $dim\mathbb{F^n}=n$ $\quad$(2).  Intuitively I understand that suppose we sum all the matrices $c_iA^i$ and then in the last sum operation we get to some $c_jA^j$ and if it's a linear combination of other matrices then we can have such a $c_j$ that: $$ c_oI+\sum_{i=1}^{n-1} c_iA^i+c_jA^j=0 $$ But I don't think this is enough to prove.


We just moved into a new house with some iron fencing around the backyard and a large double gate to allow access to the backyard. Unfortunately one side of the gate was damaged at some point in the past and the two sides don't meet anymore and the latch doesn't close. Even worse the gap is big enough for my dog to slip through.    How can I bend that one bar back closer to true so that the two sides meet and my dog won't be able to run away? Trying to save myself the large expense of having to get a whole new gate.  My first thought was to use my car's scissor jack as recommended in , but I don't think I could get it to fit in between the two bars in the right spot. The clamp spreader I feel is probably a good option, but I'm not sure how to use anything that spreads while preventing the bar next to it from bending instead -- which seems like the most likely outcome given the inward bent.


My iPhone 4 has just stopped charging -- what could be wrong with it?

I have had this iPhone4 for about over three years now but it suddenly won't charge. It comes on at 1% and than turns straight back off and it keeps doing that whilst on the charger. I don't even have enough time to turn off my phone.  Could someone please tell me if I need a new phone or a new battery ? what is wrong with it it has all my contacts and details in it and I need it fixed.


Do 3rd party camera apps really improve picture quality?

I've got a Samsung Galaxy Grand Neo (Jelly Bean). It has a 5 mp camera but I'm not satisfied with the picture quality. Will it help if I use another app like Camera Zoom FX or anything? If yes, then which app should I use?


How Do I Make a Custom Texture Pack For Minecraft? (16x16)

I've been toying with the idea of creating a custom texture pack for Minecraft, just to see how successful I'll be at it.  Problem is, I have no idea how to go about doing this.    Where do I begin, what steps do I take, and what do I do once I'm finished?


Setting a DBGrid column format in Delphi

I am using a DBGrid component in Delphi. I wonder how I can set the format of a column.  I have real values that I want to be displayed as currency in the grid.    Someone knows how?


How do you attack a specific player in Clash of Clans?

I want to play against my friend in Clash of Clans. Is there a way to attack a specific player by username?


I have a DELL inspiron 5537 i5 laptop with Ubuntu 14.04. When I use Google Hangouts on Google Chrome, my mic just doesn't work. When I open the secure info setting it shows that the mic is allowed.  Works in Windows.  I have tried to add the Hangouts plugin and it also doesn't work.  Is there any to solve the problem?


Confused with a result of a for...in statement JS output

I was just testing out the Java Script for...in ( just a newbie :P :D ).  I tried the following code:  var arr=[]; arr['n1']='name1'; arr['n2']='name2'; arr['n3']='name3'; arr['n4']='name4';  var i,j;  for(i in arr) {     for(j in i)         document.writeln(j+"-"); }   and the output was:   0- 1- 0- 1- 0- 1- 0- 1-   I was wondering why am I getting an output like this.  The for...in loop if tried to output the 'i' instead of 'j' I'm getting the index names.  When I checked the typeof 'j' I got it as String.  Please help me understand the output.


I need to check whether the String is an Integer. And I found such solution:  private boolean isInteger(String str) {     try {         Integer.parseInt(str);         return true;     } catch (NumberFormatException e) {         return false;     } }   Is there a more beautiful and proper way to do this without try/catch clause?


I am trying to find the last digit of $3^{5^7}$ (or $3^{(5^7)}$, if you will) using modular exponentiation. Here's what I've figured out:  The value I want is $3^{5^7} \mod 10$.  $5^n \mod 10 = 5$ (if $n$ is a positive natural number).  The residues of $3^n \mod 10$ repeat themselves every time $n$ increases by $4$. The pattern is $1, 3, 9, 7, 1, 3, 9, 7, \ldots$ for $n = 0, 1, 2, 3, 4, 5, 6, 7, \ldots$  Now, I don't know how to use these facts to get what I need. I know that the answer $3$ (via WolframAlpha) but I don't know how to connect the dots here. Any help would be appreciated.  Thanks!


A single word for "not seeing the big picture"

I am looking for a word that would describe being obsessed with the details of a larger entity such that the "looker" neglects to see the whole or (perhaps more importantly) the purpose of the whole.  Basically, "not seeing the big picture".  What can [more] succinctly describe this?  Edit: I just found this post: . I think I want the exact opposite.


providing a list of figure filenames used in tex file

Is there a simple way of getting a list of figure filenames from a tex file? for example if I have included 10 png, 5 pdf and 3 eps files, is there a script that can output the filenames to a list so I can make sure they all get kept/moved to a different directory together? I've looked at the extract package, but that produces a tex file with the figure code extracted. I guess I can use 'grep', such as cat my.tex | grep eps, but just checking there isn't a standard tex command to do this.


Using Bernoulli's Inequality to prove an inequality

Using Bernoulli's Inequality show that $$\left(1+\frac{1}{k+1}\right)\left(1-\frac{1}{(k+1)^2}\right)^k\geq 1$$for all $k\in\mathbb{Z^+}$.   My initial thought was to start be noting that \begin{align*}1-\frac{1}{(k+1)^2}&\geq 1-\frac14 \text{ for all natural $k$}\\\implies\left(1-\frac{1}{(k+1)^2}\right)^k&\geq\left(1-\frac14\right)^k\geq1-\frac k4,\end{align*}by Bernoulli's Inequality. Multiplying both sides by $(1+1/(k+1))$ gives the required expression on the left hand side, but the expression on the right hand side is not always greater than or equal to one. So my approach is clearly flawed.   However, if I use Bernoulli's Inequality as follows $$\left(1-\frac{1}{(k+1)^2}\right)^k\geq1-\frac{k}{(k+1)^2}$$ and multiply both sides by $(1+1/(k+1))$ I get an expression greater than or equal to one. However, this seems to me completely false; isn't Bernoulli's inequality $$(1+x)^k\geq1+xk$$ supposed to work for a variable real $x>-1$ and a fixed natural $n$?  Any help will be appreciated.


Can Polymorph be used to give a druid new Wild Shape forms?

After my group's last session, it was pointed out that Polymorph does not require the caster to have ever seen the creature they are attempting to transform the person into. This has spawned a conversation between our Wizard and Druid.  Polymorph states:     The new form can be any beast whose challenge rating is equal to or   less than the target's (or the target's level, if it doesn't have a   challenge rating).   There is, as far as I can tell, no other restrictions. It must be a beast, and it must be CR lower than or equal to the character's level. You need not have any knowledge of the creature, other than knowing it exists at all.  Druid's Wild Shape states:     Starting at 2nd level, you can use your action to magically assume the   shape of a beast that you have seen before.   So, the Wizard and Druid player in the party began thinking this over. Wild Shape only requires that the druid has seen the animal before, but Polymorph has no such restriction.  The DM has been enforcing the "must have seen it before" rule on the Druid's wild shapes, but now the druid is coming up on 9th level and will be able to shift into CR3 beasts. Issue being, he hasn't ever seen one.  As far as I can tell, there is nothing stopping the wizard from polymorphing a willing ally into a beast that the druid hasn't seen before, which would enable the druid to then wild shape into it as long as the level requirement is met. Is there any rule preventing this, or any other reason why it wouldn't work?


This always nags me... I would prefer a logical as well as a grammatical explanation of it.      We enjoyed each other's company.     We enjoyed each others' company.    Which one is correct? Why is the other not?


I am a novice using C# to scrape sites. I understand how to find hrefs and how to handle really simple tables.  Now I want to parse this .. and just pick out the first text i.e. 'office manager' and the href.
   Office Manager	   Office & Admin	   Cambridge	   Find out more

   Find out more
   Also can folk recommend a site where I can learn my way into the world of nodes, tds and trs?


Let , $y(x)$ be a continuous solution of the initial value problem $y'+2y=f(x)$  , $y(0)=0$ , where, $$f(x)=\begin{cases}1 & \text{ if } 0\le x\le 1\\0 & \text{ if } x>1\end{cases}$$Then, $y(3/2)$ equals to (A) $\frac{\sinh(1)}{e^3}$ (B) $\frac{\cosh(1)}{e^3}$ (C) $\frac{\sinh(1)}{e^2}$ (D) $\frac{\cosh(1)}{e^2}$  Integrating both sides we get , $$\int_0^xd(y(x))+2\int_0^xy(x)\,dx=\int_0^xf(x)\,dx$$ $$\implies y(x)+2\int_0^xy(x)\,dx=\int_0^xf(x)\,dx=1$$ $$\implies y(x)=1-2C$$where , $$C=\int_0^xy(x)\,dx=(1-2C)x\implies C =\frac{x}{1+2x}$$ Then , $y(x)=\frac{1}{1+2x}$ and so, $y(3/2)=1/4$.  But no option match..Please help..


Is is possible to download older versions of Android applications?   Is there some kind of online archive for all versions of Android apps? Like how you can find older versions of some Windows app.


Is this correct approach to proving $xy=0$?

Is this a sufficient way of proving that for for all real numbers $x$ and $y$, if $xy=0$ then $x=0$ or $y=0$?   My attempt:   $$xy=0$$  $$y=\frac{0}{x}$$  $$x=\frac{0}{y}$$  Is this a correct approach using axioms of real numbers?


How to apply the same rules to several locations with Nginx?

In a project I have very large nginx configuration with a lot of redundant lines.  The current state is like the following  location ~ /loc1/ {     common rules; } location ~ /some/other/location/ {     common rules; } location ~ /yet/anotherone {     common rules; }  etc .....   What I'd like to have is seperated way where there is a generic rule template and a list of locations.  In other related questions people have used regex to match several locations like so  location ~ (/loc1/|/some/other/location/|/yet/anotherone) {     common rules; }   In my case this would result in a huge line which would be very ugly to maintain.  Is there another cleaner way to do this?  Thank you very much.


When I try to run Maya from the terminal, I get:  error while loading shared libraries: libtiff.so.3: cannot open shared object file: No such file or directory.   How do I solve this?  Note: Maya is a third-party software.


Can I install Ubuntu fully on usb thumb drive? NOT LIVE USB

Can I install Ubuntu on usb during installation by setecting "something else"? And is it safe for my usb somebody said it destroys your usb after a while?


I have the following list of objects:  { DomainName="my-corp-1", GroupName="group-x", Desription="my group x" }  { DomainName="my-corp-2", GroupName="group-x", Desription="my group x - follow up with admin" }  { DomainName = "my-corp-1", GroupName="group-y", Description="my group y" }   If an object with the same GroupName exists in both domains then I should keep the object which exists in my-corp-1 and filter out the object with the same GroupName associated with my-corp-2.   For example, in the list of objects above, the second object in the list should be filtered out b/c the GroupName already exists for group-x in the first object.  What would be a clean way to implement this filtering routine in C#?


Submit an HTML form with empty checkboxes

I have an HTML form - with PHP, I am sending the data of the form into a MySQL database. Some of the answers to the questions on the form have checkboxes. Obviously, the user does not have to tick all checkboxes for one question. I also want to make the other questions (including radio groups) optional.  However, if I submit the form with empty boxes, radio-groups etc, I received a long list of 'Undefined index' error messages for each of them.  How can I get around this? Thanks.


Why byte[] comparison differs from hex comparison? I am computing a hash value of the same string with return type of byte[]  byte[]  hash1 = md5sum('3078RUR26') byte[]  hash2 = md5sum('3078RUR26')   I get  [B@7852e92 and [B@4e25154f respectively.  However, if I use the same function and do bitwise Integer.toHexString on hash1 and hash2 afterwards, I get 5ddff3704bc83a675f3f51671da9c2c for both statements. Why?


Are changes in the tax code for individuals usually retroactive to the beginning of the year, or not?

With the new administration, there is a potential for changes in the tax code.  The one that interests me the most is the possibility that the rate for long-term capital gains (now 20%, maximum) will be raised to the rate for ordinary income which might be as high as 39.6%. I seem to remember that changes in tax rates were not retroactive to before the change was proposed in the bill.  Was this usually the case, and is it likely to be the case in 2021, or is it a coin toss at this stage?


Are German "Dr.med." and USA PhD equivalent?

Where can I find information if the german Dr.med. is corresponding to the USA PhD? Did anyone with Dr.med. apply for USA PhD equivalent?  Thanks for the comments. Actually I don’t really think this has been answered here. I read the mentioned topics and they don't answer my question. MD in USA is a title students get after finishing medical school. In Germany this turns you in a Physician, but you don't have the title "Dr.med."  To earn the title you have to write and defend a doctoral thesis. That's why MD in US and Dr. med. in Germany are not the same.  About transfer from US to Germany it says (Grundsätze für die Regelung der Führung ausländischer Hochschulgrade (PDF) auf kmk.org.):  “Inhaber von folgenden Doktorgraden …Vereinigte Staaten von Amerika: „Doctor of Philosophy“ Abk.: „Ph.D.“,…können anstelle der im Herkunftsland zugelassenen oder nachweislich allgemein üblichen Abkürzungen die Abkürzung „Dr.“ jeweils ohne fachlichen Zusatz und Herkunftsbezeichnung  führen.”  This is what I find on Wikipedia, but I hesitate to huse this as my only source:  "There are a variety of doctoral degrees, with the most common being the Doctor of Philosophy (PhD), which is awarded in many different fields, ranging from the humanities to the scientific disciplines. There are also some doctorates in the US, such as ... Doctor of Medicine (MD) ..., which are generally regarded internationally as professional degrees rather than doctorates, as they are not research degrees and no defense of any dissertation or thesis is performed. ...  ...Doctorate degrees in Germany are research doctorates and are awarded via a process called Promotion ("promotion"). The concept of a US-style professional doctorate as an entry-level professional qualification does not exist. ...  ...In German-speaking nations; most Eastern European nations..., the corresponding degree to a Doctor of Philosophy is simply called "Doctor" (Doktor), and the subject area is distinguished by a Latin suffix (e.g., "Dr. med." for Doctor medicinae, ...)."


Calling an overloaded function from a derived class

C++ newbie here.  Is there a way to call an overloaded function in a base class from the same function name with the same signature in a derived class?  In Smalltalk, I can do it the "super" keyword.  Is there any C++ equivalent?  class MyBaseClass {   void initialize() { doSomething(); } };  class MyDerivedClass : public MyBaseClass {   void initialize() {       super initialize(); // first, call MyBaseClass::initialize()       doLocalInitialize(); // now initialize non-inherited members }   Thanks, Norm


How to write an expression that adds text month to numerical value?

I have a report which returns number of doors sold in a month from 2 locations. The month is displayed as a value 1-12.... I would like to return 1-Jan, 2-Feb etc.    EDIT  I am using:  datepart(MONTH, DeFactoUser.F_ST_Transaction.STTR_DATE) to get the month number, I have tried:  datepart(MONTH, DeFactoUser.F_ST_Transaction.STTR_DATE) + '-' + datename(MONTH, DeFactoUser.F_ST_Transaction.STTR_DATE) to get the name appended to the number. I get an error Conversion failed when converting the nvarchar value 'September' to data type int.  Obviously doing something silly.... any clues would be good.


I do factorization by just plugging in simple numbers to check whether they are factors, using long division and also using synthetic division. But, how to do it in the case of complex equations. For eg: Factorize $x^6+5x^3+8$  Putting $v=x^3$ I get $v^2+5v+8$. But, this equation has complex roots. So, how to continue?


Find answer of $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=4$

If I had a very shallow question, then I am sorry. $x,y,z\in\mathbb{N}^{+}$ and$$\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=4$$find $x,y,z$.  I try with AM-GM, just get$$ \frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}\geq\frac{3}{2}$$  This means that the equation must have a real solution, but can not be sure there is an integer solution.  Let: $x=ay=abz$, then the equation becomes:$$\frac{ab}{a+b}+\frac{b}{ab+1}+\frac{1}{a^2+ab}=4$$  Which makes the problem become non-homogeneous, and seems to become more difficult. I have no more ideas. Could anyone help me? Thanks a lot.


Can't figure out how $\sin\left(\tan^{-1}(x)\right)=\frac{x}{\sqrt {x^2+1}}$

Simplify the expression $$\sin\left(\tan^{-1}(x)\right)$$ Using a triangle with an angle $\theta$, opposite  is x and adjacent is 1 meaning the hypo. is ${\sqrt {x^2+1}}$   Now because the problem has sin after the $\tan^{-1}(x)$ that means that the opp. being x, is put on top of the hypo. giving us the answer, but I feel like I'm missing something because I haven't incorporated the $\tan^{-1}x$


Can I apply a different GTK3 theme from the main one to an individual application?

For example, can I keep Ambiance as main theme but assign elementary theme to elementary's app?