I am currently on Ubuntu 14.04 in VMware Workstation12. I tried install cmake 3.6.2 at first, while I get the error   Could NOT find CURL (missing: CURL_LIBRARY CURL_INCLUDE_DIR)   Then I searched it on the Internet, get this answer , when run  sudo apt-get upgrade, get   E: GPG error: http://ubuntu.cn99.com precise InRelease: Clearsigned file isn't valid, got 'NODATA' (does the network require authentication?)   I looked into multiple solution on the Internet including these     , and  .   All doesn't work for me.  How to solve the problem? Thanks, allanna.  I don't wanna re-install Ubuntu, now I can't install any software. When I type   apt-get update, I get  E: GPG error:  precise InRelease: Clearsigned file isn't valid, got 'NODATA' (does the network require authentication?)

I can use my mobile broadband to access Internet with Firefox but when I want to install any package from terminal or make 'apt-get update' command I got the following error:  got 'NODATA' (does the network require authentication?)   apt-get update output:  Get:1 extras.ubuntu.com trusty InRelease [213 B] 98% [1 InRelease gpgv 213 B] [Connecting to archive.ubuntu.com] Splitting up /var/lib/apt/lists/partial/extras.ubuntu.com_ubuntu_dists_trusty_InRelease into data Ign extras.ubuntu.com trusty InRelease E: GPG error: extras.ubuntu.com trusty InRelease: Clearsigned file isn't valid, got 'NODATA' (does the network require authentication?)    output of `cat /var/lib/apt/lists/partial/extras.ubuntu.com_ubuntu_dists_trusty_InRelease  <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <html> <head> <title>404</title> <meta http-equiv="Cache-Control" content="no-cache"/> </head> <body> <p> Not Found </p> </body> </html>   output of wget:  wget -O - http://extras.ubuntu.com/ubuntu/dists/trusty/InRelease  --2014-06-01 09:23:35--  http://extras.ubuntu.com/ubuntu/dists/trusty/InRelease Resolving extras.ubuntu.com (extras.ubuntu.com)... 91.189.92.152 Connecting to extras.ubuntu.com (extras.ubuntu.com)|91.189.92.152|:80... connected. HTTP request sent, awaiting response... 200 OK Length: 213 [text/html] Saving to: ‘STDOUT’   0% [                                       ] 0           --.-K/s              <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <html> <head> <title>404</title> <meta http-equiv="Cache-Control" content="no-cache"/> </head> <body> <p> Not Found  </p> </body> </html>


When I load up  the Interesting tab is selected by default.  I'm not complaining, because they are all, by and large, very interesting but many of these questions have either no answers, no upvotes or both, so I am interested to know how you define interesting? Is this automated or are questions marked as Interesting by experienced moderators? If it is automated, what properties does a question needs to have to be classed as Interesting?

I asked , but within minutes, it was off the question list even though the question list went back an hour in time.  Is this some form of moderation?  If so, it seems weird that no comment was made within the thread that the question was deleted, moved, or otherwise removed from the question list.


I am trying to label the angles of a triangle. I can't figure out why my code is kicking the name to the outside. My apologies for any formatting issues; this is my first post here. \documentclass{article}   \usepackage{tkz-euclide}   \usetkzobj{all}   \begin{document}   \begin{tikzpicture}[dot/.style={fill,circle,inner sep=1.5pt}]   \path     (80:5) node [dot,label=above left:$A$]{} coordinate (A)     (20:9) node[dot, label=right:$B$]{} coordinate (B)     (0:0) node[dot,label=below left:$C$]{} coordinate(C);    \path coordinate (Q)at($(C)!(A)!(B)$) node at (Q)[]{} ;     \draw[-]  (A)--(C);    \draw[-] (C)--(B);    \draw[-] (A)--(B);    \draw[purple!70!black] (A)--(Q);    \tkzMarkRightAngle(A,Q,C);    \draw[|<->|] ($(P)!-7mm!90:(B)$)--node[fill=white,sloped] {$x$} ($(B)!-7mm!-90:(P)$);   \draw[|<->|] ($(Q)!-4.9mm!90:(A)$)--node[fill=white] {$10$} ($(A)!-3mm!-90:(Q)$);    \tkzMarkAngle[size=0.75cm,color=black,label=$\alpha$](B,C,A);   \tkzMarkAngle[size=1cm,color=black,label=$\beta$](A,B,Q);   \tkzMarkRightAngle(B,A,C);   \end{tikzpicture}   \end{document}

I am trying to label the angles of a triangle. I can't figure out why my code is kicking the name to the outside. My apologies for any formatting issues; this is my first post here. \documentclass{article} \usepackage{tkz-euclide} \usetkzobj{all} \begin{document} \begin{tikzpicture}[dot/.style={fill,circle,inner sep=1.5pt}] \path (80:5) node [dot,label=above left:A]{} coordinate (A) (20:9) node[dot, label=right:B]{} coordinate (B) (0:0) node[dot,label=below left:C]{} coordinate(C);  \path coordinate (Q)at((C)!(A)!(B)) node at (Q)[]{} ;  \draw[-] (A)--(C); \draw[-] (C)--(B); \draw[-] (A)--(B); \draw[purple!70!black] (A)--(Q);  \tkzMarkRightAngle(A,Q,C);  \draw[|<->|] ((P)!−7mm!90:(B))--node[fill=white,sloped] {x} ((B)!−7mm!−90:(P)); \draw[|<->|] ((Q)!−4.9mm!90:(A))--node[fill=white] {10} ((A)!−3mm!−90:(Q));  \tkzMarkAngle[size=0.75cm,color=black,label=α]; \tkzMarkAngle[size=1cm,color=black,label=β]; \tkzMarkRightAngle(B,A,C); \end{tikzpicture} \end{document}  I am trying to fit $\beta$ inside the triangle instead of its current location.


Show from the definition of a Cauchy Sequence that Xn=ln(n) is not a Cauchy Series

I read in the book Applied Analysis by Hunter and Nachtergale that     the sequence $x(n)=\log(n)$ is not Cauchy since $\log(n)\to\infty$   But that seems to be irrelevant to the definition of a Cauchy sequence which I understand is as follows:     A sequence $x(n)$ is said to be Cauchy if for every $\epsilon > 0$  there exists an $N$ such that $\lvert x(m)-x(n)\rvert < \epsilon$ for all $m,n>N$.   This sequence $(\log n)$ seems to meet the definition. So how come it is not considered Cauchy?


I am wanting to sell my MacBook Air 2014 and decided to try factory reset it. -I used Mac recovery mode and followed the steps from apple support site () When I turned back on my computer there was no software installed at all and the Mac started up to a question mark.  I had to use Mac internet recovery this time and reinstalled software, OS X Mavericks 10.9.5. Since then I have tried to update from Mavericks to Catalina with no success. When Catalina downloaded it said "Corrupt image". My thinking then was to download earlier software updates, Sierra, Yosemite etc etc. I have tried to download from Apple support website and the App store too as this was recommended to try. Still unsuccessful. I can now access recovery mode but my only option is to reinstall Mac OS and not Big Sur.  Can anyone offer advice of how to update to newest software?

Sometimes it's hard to search for older versions of macOS & OS X  on the App Store.  This is an attempt to provide the canonical QA for this issue, as per the Meta QA -  I expect it to be modified over time to hopefully become a complete information resource.  How can I get any older version of a Mac OS to be able to run as a VM, or to reinstall on my Mac?


In my Oppo A3s, in the settings app, there is an option to clear image cach(approx. 900mb).  I just want to know, if it will delete the image from the device(or sd card) or not.  Thanks.

I have an OPPO A3s where there is an option to clear image cache approx. 900 mb. size.  I want to know if clearing it will delete my pictures or not?


You go to official site to download ISO image. There is only one "Download" button. No option to choose between 32 or 64 bit. My PC is 64 bit, I don't want to download 32 bit version.

Why is there no 32 bit ISO for the new Ubuntu 18.04?


I get a NullPointerException in production that I cannot reproduce locally. The stack trace is meaningless to me, because it references a NullPointerException to a member declaration. java.lang.RuntimeException:    at android.app.ActivityThread.performLaunchActivity (ActivityThread.java:3430)   at android.app.ActivityThread.handleLaunchActivity (ActivityThread.java:3614)   at android.app.ActivityThread.handleRelaunchActivityInner (ActivityThread.java:5527)   at android.app.ActivityThread.handleRelaunchActivity (ActivityThread.java:5418)   at android.app.servertransaction.ActivityRelaunchItem.execute (ActivityRelaunchItem.java:69)   at android.app.servertransaction.TransactionExecutor.executeCallbacks (TransactionExecutor.java:108)   at android.app.servertransaction.TransactionExecutor.execute (TransactionExecutor.java:68)   at android.app.ActivityThread$H.handleMessage (ActivityThread.java:2199)   at android.os.Handler.dispatchMessage (Handler.java:112)   at android.os.Looper.loop (Looper.java:216)   at android.app.ActivityThread.main (ActivityThread.java:7625)   at java.lang.reflect.Method.invoke (Method.java)   at com.android.internal.os.RuntimeInit$MethodAndArgsCaller.run (RuntimeInit.java:524)   at com.android.internal.os.ZygoteInit.main (ZygoteInit.java:987) Caused by: java.lang.NullPointerException:    at org.catrobat.paintroid.MainActivity.onCreate (MainActivity.java:122)   at android.app.Activity.performCreate (Activity.java:7458)   at android.app.Activity.performCreate (Activity.java:7448)   at android.app.Instrumentation.callActivityOnCreate (Instrumentation.java:1286)   at android.app.ActivityThread.performLaunchActivity (ActivityThread.java:3409)   at android.app.ActivityThread.handleLaunchActivity (ActivityThread.java:3614)   at android.app.ActivityThread.handleRelaunchActivityInner (ActivityThread.java:5527)   at android.app.ActivityThread.handleRelaunchActivity (ActivityThread.java:5418)   at android.app.servertransaction.ActivityRelaunchItem.execute (ActivityRelaunchItem.java:69)   at android.app.servertransaction.TransactionExecutor.executeCallbacks (TransactionExecutor.java:108)   at android.app.servertransaction.TransactionExecutor.execute (TransactionExecutor.java:68)   at android.app.ActivityThread$H.handleMessage (ActivityThread.java:2199)   at android.os.Handler.dispatchMessage (Handler.java:112)   at android.os.Looper.loop (Looper.java:216)   at android.app.ActivityThread.main (ActivityThread.java:7625)   at java.lang.reflect.Method.invoke (Method.java)   at com.android.internal.os.RuntimeInit$MethodAndArgsCaller.run (RuntimeInit.java:524)   at com.android.internal.os.ZygoteInit.main (ZygoteInit.java:987)  It is strange to me because the NullPointerExeption does not give a line where where I use a variable, rather it points at the declaration of a variable. public class MainActivity extends AppCompatActivity {     public static final String TAG = MainActivity.class.getSimpleName();     public ToolReference toolreference;   <---- NullpointerException at this line ?!?! (this is MainActivity:122)  @Override public void onCreate(Bundle savedInstanceState) {     setTheme(R.style.MyTheme);     super.onCreate(savedInstanceState);      setContentView(R.layout.activiy_main);      toolRefence = new ToolReference();     ...     }      ... }  The code snippet is a little bit simplified. Full code . I do understand why NullPointerExceptions happen, but it never happened to me that it says to me the variable declaration is a problem

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


The following was a midterm exam question in an abstract algebra course I was not able to solve:     Let $z \in \mathbb{C}$ with $\left| z \right| = 1$ and $z \neq -1$.   Show that the following holds true:      $z = \left(\frac{1 +z}{\left|1 + z\right|} \right)^2$      Hint: This is a possible definition for a "principal root" of $z$.   In the exam, I tried to attack this using the fact that if $\left| z \right| = 1$ holds true, I can write $z$ as $\exp(it)$ for some $t\in \left[0, 2\pi \right[$. I tried to work on the left side of the equation using the properties of $\exp$, but didn't know how to deal with the norm in the denominator.  In hindsight, how can this be solved? Is the hint actually helpful?

Suppose $z\neq -1$ is a complex number of norm 1m $(|z| =1)$. I know that $z= n + mi$, what is the most straightforward way of solving this problem? I was also given the following sketch for a possible approach.


So i read this book in mid to late 2000s. Future dystpoian setting  I remember the main characters were at least a boy and a girl. The boy at least, idk if the girl was aswell, was owned by a pharmacutical corporation and was used as a test subject. Specifically i remember him saying that his legs burned and i think he was on a treadmill all day so possible deoderant test kinda thing happening.  He slept in a big room with the other children and slept in a cot matrix that was very tall so like 10 cots connected to poles maybe.   He escapes.  The girl is a master mechanic for street racing gang, shes like 13 and a badass. The gang has glowing body modifications and cyborg muscle mods. Modding themselves as much as there cars.  The are escaping from or fighting the government and he shoots an rpg down the barrel of a tank at the split second the safety guard opens to fire a round at him and destroys the tank.  Still gets captured.  Thats all i remember, please help.

I can't really remember how long ago it was, but I think the book was marketed towards children/teens.  All I remember is the basic premise of the story.  Some story about these unusual little blue electric critters that only certain people could see, and these kids took it upon themselves to go about destroying them since they fed off energy or something like that.  Not sure whether they fed off people or off electricity... or both maybe?  I think the dominant method of destroying them was an electric baton that was taken from law enforcement.  I wanna call them buzz batons, but that's probably thanks to Artemis Fowl.


Looks like 6,12,18,24 etc. are peaks compared to their near neighbors. Any insights why? Click on   to see Bar Chart

Out of the 78499 prime number under 1 million. There are 32821 prime gaps (difference between two consecutive prime numbers) of a multiple 6. A bar chart of differences and frequency of occurrence shows a local maximum at each multiple of 6. Why is 6 so special?


What is the syntactic function of the non-finite clause "called a typedef" in the sentence "C provides a facility called a typedef."?

A new study has shown that millions of pieces of junk floating in  space could be a big hazard for satellites orbiting Earth.   Is there an implicit 'which are' in front of floating in space? Why is 'which are'  not written?


I know that Bentham sacrificed himself to save Luffy so that he can escape from Impel Down.  He disguised as Magellan to open the gates for Luffy, but later the real Magellan came and it seems like the two fight each other (not in screen).  My friends believed that he's dead at that fight. But when I read , it is stated that he's currently become the new queen of Newkama Land.     Bentham, alias Mr. 2 Bon Kurei, is a former officer agent of Baroque   Works and an okama (a Japanese slang term for a transvestite). While   he was once an enemy of Luffy's as a part of the Baroque Works, the   two became quick friends, leading Bon Kurei to sacrifice himself for   Luffy both at Alabasta and later at Impel Down.    He is currently the new Queen of Newkama Land.   So I want to know, is Bentham or Bon Kurei dead or alive after Impel Down arc? If he alive, have he shown in comics ar anime after Impel Down arc?

SPOILER ALERT: Contains spoilers for those who have not read or watched the end of Impel Down arc.  In the anime episode 451, Bon Clay disguises himself as Magellan to help Luffy and the prisoners escape on the Marine ship. Magellan gets very angry when he finds out, and attacks Bon Clay.    The episode ends after a few seconds, and the subsequent episodes do not show what happened next. Does it imply that Bon Clay was killed offscreen, or is this left as a suspense?


't Hooft showed that Yang Mills theory with spontaneous gauge symmetry breaking Higgs potential is still renormalizable.  Is the Standard Model fully renormalizable?   The potential issues to addressed in your answer are:   Includng the electroweak and strong interaction sectors The issue of chiral gauge theories.   (previous answer  does not address the last issue on chiral gauge theories.)

This question is inspired from  Ron Maimon says that standard model is renormalizable, and though there seems to be conflicting (?) answers. Is this because each answer differs in what "renormalizability" means? Furthermore, what paper Ron Maimon is referencing to by saying "'t Hooft proved it"?  Also, in  it says standard model is renormalizable. So standard model is renormalizable?


This is a dynamic programming solution to the minimum change problem in python from .  I don't understand what's going on in the elif block in general.  More specifically, what is the [:] doing in this line   table[i] = table[i - coin][:]   Could this be written with a dictionary instead of the table memoization list?    def solve_coin_change(coins, value):     """A dynamic solution to the coin change problem"""      table = [None for x in range(value + 1)]     table[0] = []     for i in range(1, value + 1):         for coin in coins:             if coin > i:                 continue             elif not table[i] or len(table[i - coin]) + 1 < len(table[i]):                 if table[i - coin] != None:                     table[i] = table[i - coin][:]                     table[i].append(coin)      if table[-1] != None:         print('%d coins: %s' % (len(table[-1]), table[-1]))     else:         print('No solution possible')  coins = [1, 2, 4] value = 11  solve_coin_change(coins, value)

I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.


I'd like to refer to the same footnote (possibly avoiding \ref) in the following manner:  First note  First note  Second note  First note  I tried to do this, but in the last row (above) I got Second note instead of First note:  \documentclass[11pt]{article} \begin{document}   First note here \footnotemark, First note here \footnotemark[\value{footnote}]. Second note here\footnote{Nota normale} First note here \footnotemark[\value{footnote}].   \footnotetext{Questa è una nota utilizzata più volte.}   \end{document}     Thank you so much in advance.

I am trying to put the same footnote on to two different places - saving and re-using the footnote counter. Here is what I want to do (part of a larger doc - a paper out of my dissertation):  %Start LateX snippet%  $\Delta$ Age\footnote{\FNTabAge}         \newcounter{savetmp01} \setcounter{savetmp01}{\value{mpfootnote}} %Save "a"%  Grade\footnote{\FNTabGrade} \newcounter{savetmp02} \setcounter{savetmp02}{\arabic{mpfootnote}} %Save "b"%  Grade\footnotemark[\arabic{savetmp02}] x Non-English %Reuse "b" - works%  $\Delta$ Age\footnotemark[\arabic{savetmp01}] x Non-English %Reuse "a" - does not work. Instead it shows "b"%   I want to save the footnote counter first when defining $Delta$ Age, and then again when explaining Grade.   The first re-use works perfectly well (both show the same footnotemark "b"), but the second re-use does not work - I am getting "b" again, instead of "a" as I want it.  Any ideas? Already tried using \thesavetmp01 or \value{savetmp01}, but no luck.


Is it possible to return the label value of the selected option using an inputSelect? <ui:inputSelect label="Staff Package: " class="dynamic" aura:id="staffPackageInputSelect" change="{!c.onStaffPackageSelect}"/> Controller: onStaffPackageSelect: function(component, event, helper) {     helper.getSelectedFilteredPicklistOption(component,event); }  Helper: getSelectedFilteredPicklistOption: function(component, event) {     var selectedItem = event.getSource().get("v.value");     component.set("v.selectedFieldValue", selectedItem); }  I've got the value, but I also need to get the selected label value.

I would like to get the value of the label of the selected drop down item.  In this case, the label is the Name of the Contact.  <aura:component>  <aura:attribute name="contacts" type="Contact[]"/>  <lightning:select label="Contact" aura:id="contactList" name="contactList">     <aura:iteration items="{!v.contacts}" var="c" indexVar="index">        <option value="{!c.Id}">{!c.Name}</option>    </aura:iteration>  </lightning:select>  </aura:component>   I know how to get the value:  component.find("contactList").get("v.value");   But how do I get the label?


How to generate a random alphanumeric string that's limited to 10 character in netbeans, im trying to save an attachment file as a random alphanumeric filename.

I've been looking for a simple Java algorithm to generate a pseudo-random alpha-numeric string.  In my situation it would be used as a unique session/key identifier that would "likely" be unique over 500K+ generation (my needs don't really require anything much more sophisticated).    Ideally, I would be able to specify a length depending on my uniqueness needs. For example, a generated string of length 12 might look something like "AEYGF7K0DM1X".


Hi I'm trying to show that  $$ I=\int_0^1 \frac{\arctan\big(\sqrt{x^2 + 2}\big)}{\sqrt{x^2 + 2}(x^2 + 1)}dx=\frac{5\pi^2}{96}. $$ We can try the substitution $u=(x^2+2)^{1/2}, du=x(2+x^2)^{-1/2}dx$ but that didn't help me much because of the (x^2+1) piece.  Any ideas?  Thanks.

The following integral  \begin{align*} \int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{dx}{x^{2}+1} = \frac{5\pi^{2}}{96} \tag{1} \end{align*}  is called the  and became famous since its first discovery in 2002. Fascinated by this unbelievable closed form, I have been trying to generalize this result for many years, though not successful so far.  But suddenly it came to me that some degree of generalization may be possible. My conjecture is as follows: Define the (generalized) Ahmed integral of parameter $p$, $q$ and $r$ by  \begin{align*} A(p, q, r) := \int_{0}^{1} \frac{\arctan q \sqrt{p^{2}x^{2} + 1}}{q \sqrt{p^{2}x^{2} + 1} } \, \frac{pqr \, dx}{(r^{2} + 1)p^{2} x^{2} + 1}. \end{align*}  Now suppose that $p q r = 1$, and define its complementary parameters as  \begin{align*} \tilde{p} = r \sqrt{\smash{q}^{2} + 1}, \quad \tilde{q} = p \sqrt{\smash{r}^{2} + 1}, \quad \text{and} \quad \tilde{r} = q \sqrt{\smash{p}^{2} + 1}, \tag{2} \end{align*}  Then my guess is that  \begin{align*} A(p, q, r) = \frac{\pi^{2}}{8} + \frac{1}{2} \left\{ \arctan^{2} (1 / \tilde{p} ) - \arctan^{2} ( \tilde{q} ) - \arctan^{2} ( \tilde{r} ) \right\}. \end{align*}  Plugging the values $(p, q, r) = (1/\sqrt{2}, \sqrt{2}, 1)$, the corresponding complementary parameters become $(\tilde{p}, \tilde{q}, \tilde{r}) = (\sqrt{3}, 1, \sqrt{3})$. Then for these choices, the original Ahmed's integral $\text{(1)}$ is retrieved:  \begin{align*} \int_{0}^{1} \frac{\arctan \sqrt{x^{2} + 2} }{\sqrt{x^{2} + 2} } \, \frac{dx}{x^{2} + 1}  &= \frac{\pi^{2}}{8} + \frac{1}{2} \left\{ \arctan^{2} \frac{1}{\sqrt{3}} - \arctan^{2} 1 - \arctan^{2} \sqrt{3} \right\} \\ &= \frac{5\pi^{2}}{96}. \end{align*}  In fact, I have a more generalized conjecture involving dilogarithms depending on complementary parameters. But since this specialized version is sufficiently daunting, I won't deal with it here.  Unfortunately, proving this relation is not successful so far. I just heuristically calculated and made some ansatz to reach this form. Can you help me improve the situation by proving this or providing references to some known results?    EDIT. I finally succeeded in proving a general formula: let $k = pqr$ and complementary parameters as in $\text{(2)}$. Then whenever $k \leq 1$, we have  \begin{align*} A(p, q, r)  &= 2\chi_{2}(k) - k \arctan (\tilde{p}) \arctan \left( \frac{k}{\tilde{p}} \right) \\ &\quad + \frac{k}{2} \int_{0}^{1} \frac{1}{1-k^{2}x^{2}} \log\left( \frac{1+\tilde{p}^{2}x^{2}}{1+\tilde{p}^{2}} \times \frac{1+\tilde{q}^{2}x^{2}}{1+\tilde{q}^{2}} \times \frac{1+\tilde{r}^{2}x^{2}}{1+\tilde{r}^{2}} \right) \, dx. \end{align*}  Then the proposed conjecture follows as a corollary. I'm planning to gather materials related to the Ahmed's integrals and put into a combined one. You can find an .


I've read that the sequence $\left(e_n\right)_{n \in \mathbb{N}}$ $$ e_0=1\text{ and } \ e_n=e_{\left\lfloor \,n/2 \right\rfloor}+e_{\left\lfloor \,n/3 \right\rfloor}+e_{\left\lfloor \,n/6 \right\rfloor} $$ satisfies the beautiful equality $$ \frac{e_n}{n} \underset{n \rightarrow +\infty}{\rightarrow}\frac{12}{\ln\left(432\right)} $$ I read the proof of Erdös himself but he proves the general case. Is there an easier way to prove this equality ? I would be curious to see it !

Nice problem:  Let $a_{0}=1$ and $$a_{n}=a_{\left\lfloor n/2\right\rfloor}+a_{\left\lfloor n/3 \right\rfloor}+a_{\left\lfloor n/6\right\rfloor}.$$  Show that  $$\lim_{n\to\infty}\dfrac{a_{n}}{n}=\dfrac{12}{\log{432}},$$  where $\lfloor x \rfloor$ is the largest integer not greater than $x$.  It is said this problem was created by Paul Erdős, and I can't find this problem's solution, does anyone have any nice methods? Thank you.


I have a desktop (Ubuntu 13.04 & Win 7 Home Premium) and a Laptop (Ubuntu 12.04), both having WiFi adapters. I also have a WiFi router connected to internet which both my computers can access.  I want to share files between my desktop and my laptop using WiFi (similar to Homegroup on Windows 7 but without using Ethernet cables).  How do I set-up that?  I want to share files using both OSs, if anyone have have information about sharing files with any of the OS please answer!

I wanna transfer some files from this PC with Ubuntu to a PC with Windows 7 I don't care how to do it (ftp, samba or whatever) I wanna know the steps, I searched a lot but I can't find anything that works. Thank you.


I've had a setup that's been working for several months. My laptop has been connected to a Dell dock that's been connected to two Dell monitors. The laptop has been running Ubuntu 18.04 with the lid closed.  As of some hours ago, when I connect the dock, first all three screens appear to work, but after a few seconds all of the three screens turn black. After that, the computer keeps running but the screens stay black. Even if I disconnect the dock the laptop screen will stay black, and I have to restart it by pressing its physical button.  I haven't done anything sophisticated recently AFAIK, the only thing I can think of is that I deleted some .gz files in the var/logs folder (`sudo rm *.gz), but that should be safe.   How can this be fixed? Is there any way to regain control of the computer after disconnecting the dock without restarting it?   I can connect one of the monitors directly to the laptop via HDMI and that works, but I don't have ports enough to connect both of the monitors in that way.

I have a Lenovo T480s that I connect to my dock at work every day. Today all of a sudden my monitors remain black after I'm prompted for the encryption key for my disk. Usually, the login prompt should turn up.   Booting my machine without the dock works fine. Any ideas to how I can fix this? Any help is appreciated.


I'm trying to code MergeSort algorithm myself but I got to the point, when I'm not sure what is wrong so the algorithm is not working. I basically do everything like goes in mergesort algorithm, finding mid, splitting and merging. Code goes here:  void merge(int *aux1, int *aux2, int *array) {     int p1 = 0, p2 = 0, i;     //debug     printf("MERGE! sizeof aux1:%d, aux2:%d", SIZEOF_ARRAY(aux1), SIZEOF_ARRAY(aux2));     printf(" MERGE!sizeof array:%d\n", SIZEOF_ARRAY(array));      for (i = 0; i < SIZEOF_ARRAY(array); i++) {         if ((aux1[p1] > aux2[p2]) && (p2 != SIZEOF_ARRAY(aux2))) {             array[i] = aux2[p2];             p2++;         } else {             array[i] = aux1[p1];             p1++;        }    }   }  void mergeSort(int *array, int l, int r) {     if (l < r) {         int m = (l + r) / 2; //finding mid of array          int aux1[m - l + 1], aux2[r - m]; //create temporary arrays         int i;         //debug         printf("MERGESORT sizeof aux1:%d, aux2:%d\n", SIZEOF_ARRAY(aux1), SIZEOF_ARRAY(aux2));          //split arrays         for (i = l; i <= m; i++)             aux1[i - l] = array[i];          for (i = m + 1; i <= r; i++)             aux2[i - (m + 1)] = array[i];          mergeSort(aux1, l, m);         mergeSort(aux2, m + 1, r);          merge(aux1, aux2, array);     } }   The issue with the code is that when I try to debug it and I get to the point when mergeSort stops and it comes to merge the very first 2 elements of the array, in merge function, the macro SIZEOF_ARRAY(aux1) or SIZEOF_ARRAY(aux2) shows, that they (aux1[] and aux2[]) are 2 elements long, while in mergeSort function the same macro shows they have only 1 element which is correct. I totally don't know what is happening because I'm using the same temporary arrays, but macro shows different lengths. Macro code is:  #define SIZEOF_ARRAY(a) (sizeof( a ) / sizeof( a[ 0 ] ))   Any help would be appreciated. THANKS!!!

First off, here is some code:  int main()  {     int days[] = {1,2,3,4,5};     int *ptr = days;     printf("%u\n", sizeof(days));     printf("%u\n", sizeof(ptr));      return 0; }   Is there a way to find out the size of the array that ptr is pointing to (instead of just giving its size, which is four bytes on a 32-bit system)?


I'm using the following line of code to match search word in my data list. But Contains is case-sensitive if I search for "search" it doesn't match with "Search" or "seArch".  What are my alternatives to Contains? How Can I replace it with IndexOf?  IEnumerable<Compound> allCompounds = _context.Compounds.ToList(); IEnumerable<Compound> filteredCompounds; if (!string.IsNullOrEmpty(param.sSearch)) {     filteredCompounds = allCompounds              .Where(c => c.CompoundName.Contains(param.sSearch)                          ||                          c.RI.Contains(param.sSearch)                           ||                          c.MolecularWeight.Contains(param.sSearch)                          ||                          c.MolecularFormula.Contains(param.sSearch)                          ); }

Is there a way to make the following return true?  string title = "ASTRINGTOTEST"; title.Contains("string");   There doesn't seem to be an overload that allows me to set the case sensitivity.. Currently I UPPERCASE them both, but that's just silly (by which I am referring to the  issues that come with up- and down casing).  UPDATE This question is ancient and since then I have realized I asked for a simple answer for a really vast and difficult topic if you care to investigate it fully. For most cases, in mono-lingual, English code bases  answer will suffice. I'm suspecting because most people coming here fall in this category this is the most popular answer.  answer however brings up the inherent problem that we can't compare text case insensitive until we know both texts are the same culture and we know  what that culture is. This is maybe a less popular answer, but I think it is more correct and that's why I marked it as such.


In the new interface I don't see where the listing of popular questions from all Stack Exchange sites has gone.  Has it been moved or is it no longer available?  If the latter, why?

Since the new top bar has been rolled out - a number of different people, established and new users alike, have asked questions on where a specific link has disappeared to with the new top bar design. Where has the link to <X> gone?


So I was forced to work with old technology and got stuck. With flexbox this wouldn't have been an issue, but I can't seem to get it right without it. Here is an example of what I want:    It's supposed to be straight forward, but being accustomed to flexbox made me a cave animal when it comes to old ways of aligning. Here is what I tried based on suggestions online, but the box and text still aren't aligned vertically. Can someone save me? (the green border is for better showing if it is centered)

 test  test2

I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers?

testing...


so I've been recently studying recursion in Java, and while i fundamentally understand it, I don't quite have a grasp on what is happening behind the code. So for example, finding the factorial of 4.  public static long factorial(int n) {     if (n == 0) // Base case         return 1;     else          return n * factorial(n - 1); // Recursive call }   Can someone explain to me how the code would run. How does n* factorial(n-1) know what factorial(n-1) is equal to as it just recalled itself? I'm quite confused, any explanation would be appreciated, thanks!

One of the topics that seems to come up regularly on mailing lists and online discussions is the merits (or lack thereof) of doing a Computer Science Degree. An argument that seems to come up time and again for the negative party is that they have been coding for some number of years and they have never used recursion.  So the question is:   What is recursion? When would I use recursion? Why don't people use recursion?


What advances are being tested in Canary?  How is feedback from users/testers received and responded to?

As the question title says it all, I read Google support, I read few things here and there, the only thing they say is it's for developers and it is updated at a rapid speed, but how exactly is Chrome Canary different from Google Chrome?


Consider the following Ruby code  sleep 10 puts "Foo is #{ENV['foo']}"   Saving this file to envtest.rb  Running this from the shell:  export foo=bar ruby envtest.rb & export foo=baz ( ... 10 seconds later ... ) => Foo is bar   It appears that the environment is evaluated when the ruby interpreter is launched. Is it possible to update environment variables during execution and have those changes reflected in running processes? If so, how?

On Unix, is there any way that one process can change another's environment variables (assuming they're all being run by the same user)? A general solution would be best, but if not, what about the specific case where one is a child of the other?  Edit: How about via gdb?


I am applying for graduate physics and I was wondering to work with a well-known professor in Caltech. He is a pioneer in the field that I am interested in. I have a kinda outstanding background, however, I am not sure if the professor is looking for exotic genius students who have completed their master at 18 or something! In this sense, I am very ordinary. How should I send an email to the professor and finally understand if I have any chance to do my PhD under his supervision or not?  P.S. I just want to know how one should contact a professor to make themselves sure that whether the professor is willing to accept them as a graduate student. I do not ask please decide on behalf of me.

When needing to ask a professor about something important and potentially delicate, what is an appropriate way to phrase the question or write the email?  Examples include:   Requesting a recommendation letter Asking for exceptions to policy (e.g., ignoring a course prerequisite, rescheduling an exam) Asking if you can do research with them, join a group, get into a program Scheduling a meeting, exam, or defense Letting them know about a change of plans Letting them know about a life event affecting your work or studies (e.g., wedding, funeral, sickness, vacation)


Anyone know of a good program or way to list Programs/Softwares installed, wanting to upgrade from Ubuntu 18.04 to Ubuntu 20.04 but need a list of the things I've installed so I can reinstall them on 20.04?

I need to reinstall my Ubuntu 18.04 and I want to backup and restore all installed snap packages including all installation settings.   With snap list I get the list of installed packages. However, the list is not in a suitable format for reinstalling all the packages. I need something like apt-clone that would work for snap packages the same way it works for apt installed packages.


To be more clear, right now the volume and brightness keys are used and I have to hold 'fn' in order to execute an F1, F2, F3, F4, F5... command. Can I reverse this so it's function key by default and holding 'fn' enables the volume and other special controls?

I am using an Apple keyboard. To get the default functionality of the function keys, I need to press fn+Function key. This is quite annoying since I frequently use the function keys for debugging. Is there any way I can get the default functionality out of the function keys, i.e., get the effect of pressing the Fn key without having to actually press it?


If I am instructing someone to make a number negative, is there a verb I can use?  Negitivise? Negify? Negate, for me, does not work as this is to cancel out, rather than turn a number into the negative equivalent.

I am doing some programming with math. I have written a tidy function which turns any positive number to negative or any negative number to a positive.  I would like to name this function in the most informative way so that if someone else were to look at my function; they would understand, straight away, what it does (and expect what it says on the tin).  The best word I can come up with is 'flip' but I feel that it fails at being obvious.  The function belongs to the Math object so it looks like this:  answer = Math.flip(number)   The results might be  -1 = Math.flip(1)   or  1 = Math.flip(-1)   How can I best describe this act?


Alternative viewpoint of the coupon collectors problem In the coupon collectors problem we draw from a collection of $n$ coupons, with replacement and ask the question how many draws $K$ it takes to collect all or a subset of size $l$ of the coupons (ie, draw $l$ of them at least once). Thus $K$, the number of draws, is the random variable for which a distribution is derived. In this problem we have the the number of draws, $k$, fixed and ask the question how many, $L$, unique coupons we have selected in those draws. Thus $L$, the number of unique coupons, is the random variable. Relation between the two We can relate these two quantitites via the cumulative distribution functions. The probability that we obtain $l$ or less coupons, given $k$ draws, is equal to the probability that we need to draw more than $k$ times to obtain $l+1$ coupons. $$P(L \leq l|k) = 1 - P(K \leq k| l+1)$$ Question So basically this question can be answered indirectly with the answer to the coupon collectors problem. That problem has an intuitive and straightforward , since the distribution of the number of times to collect $l$ coupons is equal to the sum of $l$ geometric distributed variables. Question: Can we also describe a similar straightforward derivation more directly for $P(L=l|k)$ by not using the equation $P(L \leq l|k) = 1 - P(K \leq k| l+1)$?

I've just played a game with my kids that basically boils down to: whoever rolls every number at least once on a 6-sided die wins.  I won, eventually, and the others finished 1-2 turns later. Now I'm wondering: what is the expectation of the length of the game?  I know that the expectation of the number of rolls till you hit a specific number is  $\sum_{n=1}^\infty n\frac{1}{6}(\frac{5}{6})^{n-1}=6$.  However, I have two questions:   How many times to you have to roll a six-sided die until you get every number at least once?  Among four independent trials (i.e. with four players), what is the expectation of the maximum number of rolls needed? [note: it's maximum, not minimum, because at their age, it's more about finishing than about getting there first for my kids]   I can simulate the result, but I wonder how I would go about calculating it analytically.    Here's a Monte Carlo simulation in Matlab  mx=zeros(1000000,1); for i=1:1000000,    %# assume it's never going to take us >100 rolls    r=randi(6,100,1);    %# since R2013a, unique returns the first occurrence    %# for earlier versions, take the minimum of x    %# and subtract it from the total array length    [~,x]=unique(r);     mx(i,1)=max(x); end  %# make sure we haven't violated an assumption assert(numel(x)==6)  %# find the expected value for the coupon collector problem expectationForOneRun = mean(mx)  %# find the expected number of rolls as a maximum of four independent players maxExpectationForFourRuns = mean( max( reshape( mx, 4, []), [], 1) )  expectationForOneRun =    14.7014 (SEM 0.006)  maxExpectationForFourRuns =    21.4815 (SEM 0.01)


The latest bizarreness of Skype I noticed recently:  When there is an unread message and a notification in the systray icon and I doubleclick it, two Skype windows appear. They have the same content. If I click an item, like a recent chat, both windows show the selected chat. They are like mirrors. Both fully functional.  The same thing happens when I open the Skype windows by clicking the new message notification (it is Windows 10).  I can close one window and continue using the remaining, so unlike other problems this one is not serious at all. Nevertheless comments are welcome.  OS: Windows 10 Pro, up to date Skype Desktop App version 8.55.0.131

I have a weird experience with Skype installed on one of my Windows 10 1903-based computers.   Whenever:   I have Skype opened and minimised to tray bar (notification area / clock), I see some Skype notification and click it,   Skype brings back its window and then opens another one, an exact copy, over that one:    The second "copy" of main Skype windows (opened after clicking notification) is not operable at all.  I cannot:   react with any image (clicking "react to this message" brings no effect), switch to another chat using left sidebar (clicking brings no effect), write anything in current chat, etc.   This happens only:   on one of my PCs, all others (with the same Skype and Windows version) works OK and opens only one copy of main Skype window after clicking a notification, when Skype is minimised to tray bar (works just fine, if it is minimised to task bar).   I don't know, if this is relevant, but I have also noticed that when I have Skype minimised to tray bar then, after clicking its tray bar icon:   it takes 2-3 seconds of wheel spinning before main Skype window displays any content, Skype always open on "Welcome name instead of the chat, I've been in recently.   I have configured my Skype to minimise to task bar on clicking "minimise" and to notification area on clicking "close" (I have disabled minimising Skype directly to notification area), if that matters.  Is there anything I can do with this? Is this some sort of bug? I must admit that it is pretty confusing and irritating that I have to close the second, not operative "copy" of main Skype windows (that appears after each click on Skype notification) to be able to interact with Skype in any way.  Edit: I have Skype for Windows 10 downloaded from Microsoft via Microsoft Store app, so this is not Skype for Desktop.


For example:   a vampire feeds their blood a human in order to give them some of the vampires' powers. one gains some of the vampires' powers after surviving a fight with them one get cursed and receives some of the vampiric powers as the result   How does one gain vampiric powers without becoming a vampire? I am looking for a permanent solution, that wouldn't be lost in antimagic fields or by dispelling magic. Is there anything in Dungeon and Dragons 3.5 or any other edition(it will be converted into 3.5 material) that could give those?  Dragon Magazine and Dungeon Adventures are also acceptable.

I know I've ran across this in one of my 3.5 books recently and I cant remember the book or much about it, and am having trouble re-locating this. There was an entry towards the front of the book for a vial of vampiric blood. It gave similar stats as a barbarians rage but you were also considered under the control of the vampire while its effects lasted.   About the book: If i recall correctly, the book was focused more on monsters; but not the monster manual. I believe the passage where it talked about the vials was also talking about how a vampire could make a human its servant without changing it to a spawn or charming it. I really cant recall much about the book itself...  i believe it was in one of the thinner books ( <250 pages) but i cant be sure as I've spent three days going through these books now and cant locate it.  If it helps my 3.5 collection consists of : Exalted Deeds, Vile darkness and VD more archfiends, Complete adventurer, complete arcane, complete divine, complete warrior, draconomicon, DMG, PHB, Monster Manual, Expanded Psionics, Ghostwalk, and Unearthed Arcana.  And i also have other books, incase I'm wrong about it being a 3.5 thing...  Monster Manual 2, tome and blood, sword and fist, song and silence, oriental adventures, Masters of the wild druids grove and MotW barbariands druids and rangers, manual of the planes, fiend folio, Defenders of the faith, arms and equipment, and... uh..  the book of erotic fantasy.  =)   I know that its a long shot for someone to pin-point this as I'm having issues finding it with my books in front of me or with google...  but I appreciate any information or help on finding this ruling.


In the graphics/graphicx packages there are commands \rotatebox, \resizebox, \scalebox and even \reflectbox. But how can I slant/skew something in the same way? (I'm missing a \skewbox command.)  (Incidentally I looked in the PostScript manual (736 pages). The word "slant" never appears in it, and the word "skew" appears three times, one of them in the sentence "The operators in this group manipulate the CTM to achieve any combination of translation, scaling, rotation, reflection, and skewing of user coordinates onto device coordinates", which proves that at some time some Adobe engineer thought of skewing, but in fact never documented it or wrote any code. Fortunately in the PDF manual version 1.7 there is mention of skewing and even an illustration, on page 118 (the transformation matrix is [1 tan a tan b 1 0 0], I'm interested in horizontal skewing, so that a is 0), so this time Adobe took it seriously. How come this operator has never been included in graphicx? or maybe I overlooked it? Is it because there is no "native" PostScript support for it?)

Using the graphicx package, I can make any arbitrary box rotated using the \rotatebox{...}{...} command. Is there a comparable command in any package that lets me shear a box, i.e., producing a kind of general slanting?


Which one has more correct way to put, and what are the differences found on those two sentences?

I saw him crossing the road.   I saw him cross the road.   Which one is correct and why?


I have a function that takes an array of strings and map each string to a Date instance. The function boils down to the following code.   Private Function ParseDates(dates() As String) As Date()   Dim res() As Date   Dim i As Integer    If UBound(dates) >= 0 Then     ReDim res(UBound(dates)) As Date   End If     For i = LBound(dates) To UBound(dates)     res(i) = #01/01/2000#   Next i   ParseDates = res End Function   The function works just fine as long as the argument dates is nonempty. When dates is empty res is not given a dimension. As a result, the returned value is not enumerable causing to users of this function to crash if the result is enumerated in a loop.  parsedDates = ParseDates(input)  For i = 1 To UBound(parsedDates) ' Suscription out of range   ...   How do I instantiate and return an empty array, when dates is empty?   If you call Split("",".") you receive an object with type String(0 to -1). I need my function to return a object of type Date(0 to -1) as Date() is not an actual array.   I have tried with ReDim res(-1) this causes an Subscript out of range error.

Passing an undimensioned array to the VB6's Ubound function will cause an error, so I want to check if it has been dimensioned yet before attempting to check its upper bound.  How do I do this?


The energy of photon is given by the equation $E=hf$, where $h=$ Planck's constant, and f=frequency of radiation. Is f quantized, or can it assume any value?   If it can assume any value, then wouldn't this mean that the energy of photons is not quantized? If f can be any value from a continuous series, this would mean that for any number you imagine, there will always be another number that when multiplied by h gives you that first number. So $E$ could assume any value.   However, we know that $E$ is indeed quantized, so could someone please point out the flaw in my reasoning?   PS: I don't believe this question is a duplicate, since it addresses wether radiation frequencies are discrete in the context of an equation. The answers, therefore, aren't limited to "no, the EM spectrum is not quantized" but also explain that for a given frequency, the photons' energy is quantized. In other words, while the questions are similar, I believe that both the question and the answers have angles that are different enough to justify not being duplicates. For example, if the answers to this question had not addressed the photon energy, I would still be confused as to why so many textbooks say that energy is quantized. This isn't the kind of answer that the duplicates would require, however. Thank you for linking the other posts, though, as they could be useful for someone looking for a different answer.

I'm just starting to learn physics and I have a question (that is probably stupid.)  I learned that energy levels that the bound electron can have are discrete. I also learned that when an electron transitions from one level to another, a photon with a specific wavelength (energy) is created and released into the wild.  My question is this: are there holes in the electromagnetic spectrum, values of frequency that the created photon can't possibly have?


Suppose $A$ is a square matrix (over $\mathbb{R}$ or $\mathbb{C}$, take your pick) such that $(I-A)^{-1}$ exists. Then is it necessarily true that  $$I + A + A^2 + \dots + A^n + \dots = (I-A)^{-1}$$ ?  There is a well known theorem which claims that if $||A|| \lt 1$ then $(I-A)^{-1}$ exists and the above is true.   What I am asking is something like the converse of that theorem. My hunch is that this is false, but I am unable to come up with a counter-example.

If $X$ is a Banach space, and $T:X \to X$ is a bounded linear operator with norm < $1$, then $I-T$ has a bounded inverse defined by $(I-T)^{-1} = \sum_{n=0}^\infty T^n$.   Thinking in terms of a converse, if $T$ is any bounded linear operator defined on $X$, then does the existence of a bounded inverse $S=(I-T)^{-1}$ imply that $S$ can be represented as $S=\sum_{n=0}^\infty T^n$?


Very Hard: Suppose I have a polynomial $g(x)=x^p $+ lower order terms. Asymptotically the inverse is  $g^{-1}(x) \sim x^{1/p}$ for large $|x|.$ What is a bound of the error of this asymptotical approximation explicitly  in terms of $|x|$? Any help would be amazing

Suppose $f(x) = x^p + $ lower order terms. Then Asymptotically $f^{-1}(x) \sim x^{\frac{1}{p}} $ for large $|x|$. How can we bound the error in this asymptotic approximation in terms of $|x|$


So I have say two meshes, A and B. In some plases, both meshes may have similar surfaces and in other cases they don't. Is there an addon to compare the meshes and determine to what degree they match. I know we can simply keep the two meshes on each other and look for extrusions but I am looking for something else, such as a procedure which can compare the faces, the orientation etc.  I have a (yet to be working) 3D camera system which will provide me with 3D models and I wanted to compare the meshes.  Thank you in advance.

Is there a way in Blender to compare two pieces of mesh or two meshes to its similarity? Maybe with some script or an addon.  What I mean: there is a stone or brick broken into half for example:   This is a kind of forensic or architectural task. The goal is to prove that those 2 pieces have similar surfaces and may be connected to each other with some threshold or they were a one piece before. I know of "select similar" in Blender, similar face area in this case, but it doesn't work quite well for such a task.  I am not a coder so I can't figure out a possibility of solving this. So what is the way to do it?


I want to add an 'active' class to the sections when the user scrolls the section into the viewport so it shows the user what section they are in.  I have written the code below but it does not work.  Help please.   const sections = document.querySelectorAll('section');  window.addEventListener('scroll', function scrolling() {     sections.forEach((section) => {         if (isInViewport(section)) {             section.classList.add('active');         } else {             section.classList.remove('active');         }     }); });

Section 1

Lorem ipsum dolor sit amet.

Aliquam a convallis justo. .

Section 2

Lorem ipsum dolor sit amet.

Aliquam a convallis justo.n.

Is there an efficient way to tell if a DOM element (in an HTML document) is currently visible (appears in the viewport)?  (The question refers to Firefox.)


I recently got a paper rejected at a very good journal. Reading the reviewers comments, I think the suggested scores were:  Reviewer 1: Accept Reviewer 2: Major revision Reviewer 3: Major revision Reviewer 4: Reject  Reviews 3 and 4 were not good reviews (review 4 length was 2 lines...) and partially based on a common misunderstanding on my field. Nevertheless, the editor decided to reject the paper. So, I don't plan to appeal and I cannot resubmit due to the journal policy not allowing it. Instead, I'll try another journal. My question is: should I submit also my comments to this reviewers in the new submission? Even if I clarified even more in the paper the common misunderstanding, I feel like new reviewers may misunderstand again, while having the answers to the previous comments may help. Is this acceptable? May this penalize my submission because I disclose it has been already rejected elsewhere?

I submitted my paper in IEEE Transcations of XXX and got a rejection. But the comments were really helpful and has helped me a lot in improving the paper. But, unfortunately, I cannot resubmit that paper to this same journal again and now I am looking for another journal.   I am writing a proper response again every comment and thinking to submit the response letter as part of the submission to the new journal. The basic idea is to let the reviewers know that this paper has been reviewed (by reviewers of another journal) and improvements has been made. Will it somehow improve the chances of acceptance. (as I am in the final stages of my PhD now)  What does the community say?


Consider following inequality:     $|z_1 + z_2|\ge|z_1| - |z_2|  \  \ \ \ \ \  z_1,z_2 \in \mathbb{C}$   Is that true always? I tried many examples and it was correct but I don't know how to prove that if it's right.

Is the inequality $\lvert z_1 + z_2 \rvert \ge \lvert z_1 \rvert - \lvert z_2 \rvert$ incorrect, where $z_1$ and $z_2$ are any two complex numbers? I need an example to prove that it is. And in case it is correct, can you please give the proof? Thanks for any help.


Suppose $X$ has a uniform distribution on $(-1,1)$, and let $Y = X^2$. How do we find $f_Y$?

$X\sim U[0,1]$ and $Y\sim U[-1,1]$ are two uniform-distributed R.V.'s. Are $X^2$ and $Y^2$ still uniform? Do they have explicit probability density funtion?


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

Are there any sort of configuration options for specifying the default save location for gnome-screenshot, or is this hard-coded into the source code? It used to be ~/Desktop, which seems to have changed to ~/Pictures (in 12.04). The only possible solution I've seen is about  (as it includes time stamp information now instead of simply 'Screenshot#'), but that solution doesn't really seem ideal to me. Also,  post suggested that the last save location is remembered the next time you take a screenshot, but in my experience, this doesn't seem to be the case. And in any case, following on from that, that entry in gconf-editor doesn't even seem to accurately reflect the last location, so more than likely an entry related to an older version of gnome-screenshot. Table of contents:


Briefly the up- and downvotes on my last question where shown twice (see image). Is that as it should be?    It has happened again twice:    and:

I have six upvotes for the one question with no intervening history. They have been summarised into two groups - one with 4 events and one with 2 events. However, when you expand either, both show all 6 events. Minor I know, just letting you know.


Where is the output is displayed or piped? like when simply doing :  print('test')  i can't see any result in any window? not in console etc. So where is the output has been sent to ?

I'm trying to debug a Python script by placing a print("foo=" + foo) statement in my code.  But where does the output appear?     It doesn't appear on the Python Console, and it doesn't appear on the area that appears when you drag the lower edge of the infobar downwards (what is the name for this area? My script errors show up in red here.)


For example:I Have following List.  ｌist1=["a","b","c","d"]   How to get both iterator number(in below code that is iteration) and item of list in the same for loop.I can write with following two loop .  for iteration in len(list1):     for each_item in list1:         #logic related to each_item

How do I access the index in a for loop like the following?  ints = [8, 23, 45, 12, 78] for i in ints:     print('item #{} = {}'.format(???, i))   I want to get this output:  item #1 = 8 item #2 = 23 item #3 = 45 item #4 = 12 item #5 = 78   When I loop through it using a for loop, how do I access the loop index, from 1 to 5 in this case?


Given an lambda expression, I need a way to store a compiled delegate in a dictionary, so i don't need to compile them each time.  My first attempt was caching delegates by expression converted to string:  class ExpressionEqualityComparer : IEqualityComparer<Expression> {     public bool Equals(Expression a, Expression b)     {         return a.ToString().Equals(b.ToString());     }     public int GetHashCode(Expression e)     {         return e.ToString().GetHashCode();     } } void Main() {     var e1 = (Expression<Func<object, string>>)(o => ((Model)o).Prop);      Console.WriteLine(e1.ToString());      d.Add(e1, e1.Compile());      var e2 = (Expression<Func<object, string>>)(o => ((Model2)o).Prop);     try     {         d.Add(e2, e2.Compile());     }     catch     {         // ArgumentException. An element with the same key already exists in the Dictionary< TKey, TValue >.     }     Console.WriteLine(e2.ToString());        Console.WriteLine(d.Count); } Dictionary<Expression, System.Func<object, string>> d = new Dictionary<Expression, System.Func<object, string>>(new ExpressionEqualityComparer()); class Model {     public string Prop { get; set; } } class Model2 {     public string Prop { get; set; } }   Output:  o => Convert(o).Prop o => Convert(o).Prop 1   This approach does not work because Expression.ToString() is not detailed enough to provide equality, and it's not reliable since there is no guarantee about the ToString implementation in general.  How to implement Equals(Expression, Expression) and GetHashCode(Expression) correctly without visiting the expression nodes?  If it's not possible with expression instance, is it possible with some other language construct, wrapping the original expression, which can be used to obtain the said expression?  The absolute requirement, which makes this question different from duplicates: Working in constant amortized time proportional to average size of the expression, which is the requirement to keep original hash function algorithmic properties.

Given a method signature:  public bool AreTheSame<T>(Expression<Func<T, object>> exp1, Expression<Func<T, object>> exp2)   What would be the most efficient way to say if the two expressions are the same? This only needs to work for simple expressions, by this I mean all that would be "supported" would be simple MemberExpressions, eg c => c.ID.  An example call might be:  AreTheSame<User>(u1 => u1.ID, u2 => u2.ID); --> would return true


I have set up  $ echo $EDITOR emacs -nw   I was wondering why it is not found here, and how I can solve the problem? Thanks.  $ sdiff -o sdiff.out f1 f2 1 2 3                                 | 2 3 4 %e1 sdiff: subsidiary program 'emacs -nw' not found   I don't know why an option in $EDITOR is a problem, and where it is required in sdiff source code? I guess it is here   prog = getenv ("EDITOR"); if (prog)   editor_program = prog;   and here   execvp (editor_program, (char **) argv);   or  and . I am not sure what the program is doing.  For comparison, the following works perfectly fine:  $ eval "$EDITOR"

I'm using Zsh and some CLI's such as Google's gcloud load files via $EDITOR.    For me, I have set this as:  export EDITOR="/usr/local/bin/mvim"   With aliases for that editor using the -v flag which loads vim in the terminal:   mac_vim="$EDITOR -v"  alias vi=$mac_vim  alias vim=$mac_vim  alias v=$mac_vim   That works but when the gcloud CLI calls $EDITOR it does not have the -v flag so it opens in a new terminal.  I thought I could change that by instead adding the -v flag here:  export EDITOR="/usr/local/bin/mvim -v"   However, when I try and run that on the command line I get:  $EDITOR text.html zsh: no such file or directory: /usr/local/bin/mvim -v   Is it possible to include a flag when exporting my $EDITOR?


Here is my virtual host :  <VirtualHost *:80>     ServerAdmin webmaster@localhost     ServerName policy.domain.com     ServerAlias www.policy.domain.com     DocumentRoot /policy     ErrorLog /policy/error.log     CustomLog /policy/custom.log combined     <Directory /policy/>         Options  +IncludesNOEXEC         AllowOverride None         Order allow,deny         allow from all          # redirect non www to www         RewriteEngine On  RewriteCond %{REQUEST_FILENAME} !-d RewriteCond %{REQUEST_FILENAME}.php -f RewriteRule ^(.*)$ $1.php [L]  RewriteCond %{HTTP_HOST} !^www\. [NC] RewriteRule ^(.*)$ http://www.%{HTTP_HOST}/$1 [R=301,L]        </Directory>   </VirtualHost>   I have tried various settngs, but pages at www doesn't seem to appear. Though, the php removal works well when I remove non-www to www condition. To be specific, apache is redirect non www to www but at www it shows server not found error.

This is a  about Apache's mod_rewrite.   Changing a request URL or redirecting users to a different URL than the one they originally requested is done using mod_rewrite. This includes such things as:   Changing HTTP to HTTPS (or the other way around) Changing a request to a page which no longer exist to a new replacement. Modifying a URL format (such as ?id=3433 to /id/3433 ) Presenting a different page based on the browser, based on the referrer, based on anything possible under the moon and sun. Anything you want to mess around with URL   Everything You Ever Wanted to Know about Mod_Rewrite Rules but Were Afraid to Ask!  How can I become an expert at writing mod_rewrite rules?   What is the fundamental format and structure of mod_rewrite rules? What form/flavor of regular expressions do I need to have a solid grasp of? What are the most common mistakes/pitfalls when writing rewrite rules? What is a good method for testing and verifying mod_rewrite rules? Are there SEO or performance implications of mod_rewrite rules I should be aware of? Are there common situations where mod_rewrite might seem like the right tool for the job but isn't? What are some common examples?   A place to test your rules  The  web site is a great place to play around with your rules and test them. It even shows the debug output so you can see what matched and what did not.


Let $K$ be the subgroup of $S_4$ such that $K = \{e, (1,2)(3,4), (1,3)(2,4), (1,4)(2,3)\}$.  I'm not sure if the first part of the question is related, but it asks to show that $K \triangleleft S_4$.  I believe I've shown that $K \triangleleft S_4$.  For any $g \in S_4$, $g$ can be expressed as a product of transpositions  The definition of normal means we need to show $gKg^-1 = K$  So suppose we represent $K$ as arbitrary transpositions then: $K = \{e, (a,b)(c,d), (a,c)(b,d), (a,d)(b,c)\}$  Then for an arbitrary transposition in $S_4$:  $$(a,b) \{e, (a,b)(c,d), (a,c)(b,d), (a,d)(b,c)\} (a,b)$$ $$= \{e, (a,b)(c,d), (a,c)(b,d), (a,d)(b,c)\}$$ $$ = K$$  So $K$ is normal.     Now I need to show that $S_4/K\cong S_3$.   I'm pretty sure that I have to find a map $\phi:S_4 \rightarrow S_3$ that is a homomorphism such that $\ker(\phi) = K$, but I'm not sure how to do this.

If $G:=S_4$ and $H:=\{id,(12)(34),(13)(24),(14)(23)\}$ Show that $G/H$ has order $6$ and all of its elements have order less than or equal to $3$ (so by the classification of the groups of order 6 up to isomorphism, $G/H\cong S_3$)   $H$ is normal, since left- and right cosets are equal, There are $6$ cosets:  $\{id,(12)(34),(13)(24),(14)(23)\},\ \{(12),(34),(1423),(1324)\},\ \{(13),(24),(1234),(1423)\}$  $\{(123),(134),(243),(142)\},\ \{(14),(23),(1243),(1342)\},\ \{(132),(143),(234),(124)\}$  What does it mean: All elements of $G/H$ have order less than or equal to $3$?  Each element is a set of 4 permutations, what is the order here ?  $G/H\cong S_3$: How can I construct an isomorphism, since the cosets are disjoint, can I just pick an element from each group and compare them with $S_3$ ?  Thanks in advance.


Every time I want to write on a new line I press Shift+Enter. In the Editor it goes to new line, but on the Preview it stays on the same line.  So I have to make 2 new lines in order to get some separation.  Why can't I just make a new line without having a whole other blank line in between?

When I post a question and want to add a new line, I have to press Return two times, or else the next text will appear on the same line.  Is this really supposed to behave this way? If so, why?


Not exactly sure how to approach. Cannot do telescoping, or break up the sum into two parts either, cannot find a way to express division as the sum here. Although, if it was something like $\frac{1}{n(n+1)}$ we could write $\frac{1}{n}-\frac{1}{n+1}$. Would like to solve this with simple/clever arithmetic.

How can I evaluate $$\sum_{n=1}^\infty\frac{2n}{3^{n+1}}$$? I know the answer thanks to , but I'm more concerned with how I can derive that answer. It cites tests to prove that it is convergent, but my class has never learned these before. So I feel that there must be a simpler method.  In general, how can I evaluate $$\sum_{n=0}^\infty (n+1)x^n?$$


I am currently learning C and I have written many small programs. However, I have noticed that the main function could start as      main()     {        //code     }   or      int main()     {       //code       return 0;     }   or      int main(void)     {        //code        return 0;     }   Which option should I use? Thanks!

What is the correct (most efficient) way to define the main() function in C and C++ — int main() or void main() — and why? And how about the arguments? If int main() then return 1 or return 0?  There are numerous duplicates of this question, including:       — For C++, with a very good answer indeed.     Related:


Lets assume,in picture blow, the current be in its peak voltage moment. then when the current begins to fall (assume a moment after the peak moment) we know the current is blocked by diodes (actually two diodes) and then the cap discharge its stored charged to load. my question is why diodes block this current? Why the diode doesn't allow the rest of falling voltage current to go into the load? Is this because of the fast rate of voltage chaining for this falling voltage current?

I was reading about full-wave rectifiers and came across the schematics below which the capacitor C can smooth its voltage, but I didn't understand one case:  We know that when the rectifier's voltage begins to falling from its peak, the cap C starts to send its charge to load. Where does the falling current coming from FW rectifiers go? (The current from peak to zero and that one who rises from zero to the point which the cap starts to charge in diagram) Is it blocked, by diode or capacitor? Why?


I Have a map of custom metadata type Map<String,error_mdt> error  error=[select id, DeveloperName from error_mdt].How can we Use meta data types in test class to get code coverage.  I have already checked on the solution given my salesforce creating testcase in metadata type but Is there any other solution we can have without creating TestCase__C field.

I have three questions that I'd like to be clarified.   Is their anyway we could create Custom Metadata in Test Classes? I tried to create on my Test Class but I got an error saying the fields of the metadata could not be writable.  If not, then does that mean we should declare real values in our Custom Metadata and use that instead in our test classes? If (2) is correct, then does this mean we have to create the Custom Metadata in the environment we'll be deploying our code before doing the actual deployment?


Where and when did the infection start? I'm curious because it isn't explained in The Walking Dead. If it was then I will have to start it all over again.

I'm wondering where and why the zombie outbreak began?


Suppose that m, n, and l are integers such that                             m^2+n^2=l^2       Then   At least one of the integers m, n and l is divisible by 3.   My idea is to use prove by contradiction, so I set m=3p+1 or 3p+2, n=3q+1 or 3q+2 but i have no idea how to continue

Let $l,m,n$ be any three positive integers such that $l^2+m^2=n^2$   Then prove that $lm$ is always a multiple of 3.


I switch between my left and right hand for my mouse a lot, and every time I do, I have to go to System Preferences > Mouse > and switch the Primary mouse button. Is there any way I can create a keyboard shortcut to toggle this setting? I'm willing to figure out AppleScript if that would help me

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


I was trying to learn new terminal commands. Then I tried to write command to test what happens.  Strangely, looks like it's a valid command, but what does it do? It didn't return anything.

Recently I found command: command which has no manual entry but help displays as follows:  $ help command command: command [-pVv] command [arg ...]     Execute a simple command or display information about commands.      Runs COMMAND with ARGS suppressing  shell function lookup, or display     information about the specified COMMANDs.  Can be used to invoke commands     on disk when a function with the same name exists.      Options:       -p    use a default value for PATH that is guaranteed to find all of         the standard utilities       -v    print a description of COMMAND similar to the `type' builtin       -V    print a more verbose description of each COMMAND      Exit Status:     Returns exit status of COMMAND, or failure if COMMAND is not found.   Is command -v is alternative of which?  What arguments are accepted by this command and how/when to use command?


So I'm creating a simple grep command that gets only the last logged in people who's username starts with 161 and has 3 digits next to it:  last | grep "^161[0-9]{3}"   However it doesn't print anything even though it has these usernames on the list. Whats even more weirder is if I do egrep instead of grep  last | egrep "^161[0-9]{3}"   The command works.  Can anyone explain what is the difference?

I wrote a regular expression which works well in a certain program (grep, sed, awk, perl, python, ruby, ksh, bash, zsh, find, emacs, vi, vim, gedit, …). But when I use it in a different program (or on a different unix variant), it stops matching. Why?


I've only been using Linux for a few weeks (I'm a recent convert) and in my system, I have several drives, an SSD with Windows 10 on, and an HDD I use for mass storage. Both of these drives have padlock symbols on every folder and file and I can't move files around. I believe that the permissions for both are set to read/write. Any help would be very gratefully appreciated.

Until recently both my Windows Partition (C:) and my Data Partition (E:) would mount as read/write. Now both seem to only mount as read-only.    GParted Resize (Error)  ntfsresize v2.0.0 (libntfs 10:0:0) Device name : /dev/sda4 NTFS volume version: 3.1 Cluster size : 4096 bytes Current volume size: 86207623680 bytes (86208 MB) Current device size: 86207627264 bytes (86208 MB) New volume size : 78662066688 bytes (78663 MB) Checking filesystem consistency ... Accounting clusters ... Space in use : 62126 MB (72.1%) Collecting resizing constraints ... Needed relocations : 1606868 (6582 MB) Schedule chkdsk for NTFS consistency check at Windows boot time ... Resetting $LogFile ... (this might take a while) Relocating needed data ... ERROR: Extended record needed (1032 > 1024), not yet supported! Please try to free less space.   chkdsk Output:     Checking file system on E: The type of the file system is NTFS. Volume label is Data.  A disk check has been scheduled. Windows will now check the disk.                            99482 file records processed.   495 large file records processed.                        0 bad file records processed.                            0 EA records processed.                                  0 reparse records processed.                             104412 index entries processed.                          0 unindexed files processed.                             99482 security descriptors processed.                    2466 data files processed.                              CHKDSK is verifying Usn Journal...   4479208 USN bytes processed.                                      Usn Journal verification completed. Windows has checked the file system and found no problems.  84187132 KB total disk space.   60479688 KB in 69969 files.      15520 KB in 2467 indexes.          0 KB in bad sectors.     174336 KB in use by the system.      65536 KB occupied by the log file.   23517588 KB available on disk.       4096 bytes in each allocation unit.   21046783 total allocation units on disk.    5879397 allocation units available on disk.  Internal Info: 9a 84 01 00 00 1b 01 00 fc 1a 01 00 00 00 00 00  ................ 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................ 42 00 00 00 52 73 5c 77 b0 e7 1d 00 b0 df 1d 00  B...Rs\w........   fstab  # /etc/fstab: static file system information. # # Use 'blkid' to print the universally unique identifier for a # device; this may be used with UUID= as a more robust way to name devices # that works even if disks are added and removed. See fstab(5). # # <file system> <mount point>   <type>  <options>       <dump>  <pass> proc            /proc           proc    nodev,noexec,nosuid 0       0 # / was on /dev/sda5 during installation UUID=8213cc89-2438-41b9-899f-13b4c5b299af /               ext4    errors=remount-ro 0       1 # swap was on /dev/sda6 during installation UUID=45873767-d9ae-4f0c-baab-ffc2726ac24e none            swap    sw              0       0   Checked the drive in GParted, GSmartControl and with ntfsfix, all completed successfully, no change.  Partitions  dev/sda1 NTFS WinRE dev/sda2 NTFS Windows C: dev/sda3 Extended dev/sda4 NTFS Data E: dev/sda5 EXT4 Ubuntu dev/sda6 linux-swap    I am looking for an explanation of:    Internal Info: 9a 84 01 00 00 1b 01 00 fc 1a 01 00 00 00 00 00  ................ 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................ 42 00 00 00 52 73 5c 77 b0 e7 1d 00 b0 df 1d 00  B...Rs\w........   and    Resetting $LogFile ... (this might take a while) Relocating needed data ... ERROR: Extended record needed (1032 > 1024), not yet supported! Please try to free less space.


During an interview of Antonin Scalia by Charlie Rose, Scalia criticized the grammar he heard on a commercial flight:      "It's required that your luggage is under the seat in front of you"   Would it be more correct to say:     "It's required that your luggage be under the seat in front of you"?   Why or why not? Thanks.

Why is this sentence correct?     She suggested that he go to the cinema.   I would definitely use goes instead of go.


Consider differential function $f:\mathbb{R} \to \mathbb{R}$ with the property that for all $a,b \in \mathbb{R}$   we have  $$f(b)-f(a)=(b-a)f'(\frac{a+b}{2})$$  Then show that every such function is polynomial of degree less than or equal to two.  i was thinking of applying Roll theorem. but got nowhere.please  provide a hint   Thanks in advanced

Every differentiable function $f:R \rightarrow R$ with the property that $(2h)f′(x) =f(x+h)−f(x−h)$ for all $x \in R$ and all $h$ has the form $f(x) =ax^2+bx+c$.  I would like to get some help on this one. Taking partial derivatives was an idea, but is that legal?


When we see atoms under an electron microscope, what exactly are we seeing? I mean, these spheres that we know as atoms are electron clouds and that is what we are seeing, am I right?     Can you please explain to me, how exactly our eyes are able to see those spheres that we know as atoms? Like photons are hitting those constantly moving electrons and then they reflect back and hit the retina of our eyes where it gets absorbed. That’s fine. But I want to know, how exactly photons are interacting with those constantly moving electrons of an atom of an object from which they are being reflected?

The "equal angles" law of refection on a flat mirror is a macroscopic phenomenon. To put it in anthropomorphic terms, how do individual photons know the orientation of the mirror so as to bounce off in the correct direction?


(I wrote this using the assumption that the graviton exists, which I know is not necessarily true; this is asked from a theoretical standpoint)  It is my understanding that General Relativity states all massive and/or energetic particles must be affected by the curvature of spacetime; this stipulation aligns with all known elementary particles. I understand that the graviton, being a particle that reliably interacts with photons, is going to be virtually impossible to detect experimentally. It is almost certainly massless and of a remarkably low energy, but it must possess energy nonetheless. As such, shouldn't gravitons themselves be affected by gravity, creating a paradox in which (increasingly virtual ?) gravitons must interact with other gravitons? Also, assuming that our conception that massless particles always travel at the speed of light holds true for gravitons, wouldn't gravitons themselves not be able to escape from a black hole, annulling the gravitational force of the black hole in the process?

I always thought the non-linearity of Einsteins field equations implies that there should be direct graviton-graviton interactions. But I stumbled upon  which argues:     If gravitons exist, then, like photons and unlike gluons, gravitons do   not interact with other particles of their kind. That is, gravitons   carry the force of gravitation but are not affected by it. This is   apparent due to gravity being the only thing which escapes from black   holes, in addition to having an infinite range and traveling in   straight lines, similarly to electromagnetism.   Is Wikipedia correct? If not, why not? And what then are the arguments that there must be graviton-graviton interactions?    (As of this question being asked, the above paragraph has been removed from Wikipedia.)


I have a problem trying to install Geant4 on  Linux system.  $ cmake .. CMake Error at CMakeLists.txt:13 (find_package):   By not providing "FindGeant4.cmake" in CMAKE_MODULE_PATH this project has   asked CMake to find a package configuration file provided by "Geant4", but   CMake did not find one.    Could not find a package configuration file provided by "Geant4" with any   of the following names:      Geant4Config.cmake     geant4-config.cmake    Add the installation prefix of "Geant4" to CMAKE_PREFIX_PATH or set   "Geant4_DIR" to a directory containing one of the above files.  If "Geant4"   provides a separate development package or SDK, be sure it has been   installed.   -- Configuring incomplete, errors occurred! See also "/home/dell/Desktop/geant4/geant4.9.6/examples/basic/B1/build/CMakeFiles/CMakeOutput.log".   I tried:  apt-get install g++   But I get:  E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?

I get this error whenever I try to install programs using the terminal:  home@ubuntu:~$ apt-get install myunity E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   Also I'm unable to install updates using the terminal.


I have a loop in the script below. It is not working as I want. I need to put the $LINE value in front of each column. While it puts "$LINE" instead of it is value:  cat list | while read LINE ; do sed 's/^/$LINE\t/g' $LINE.alf > $LINE.joined done

I want to do:  cat update_via_sed.sh | sed 's/old_name/new_name/' > new_update_via_sed.sh   in my program.  But I want to use variables, e.g.  old_run='old_name_952' new_run='old_name_953'   I have tried using them but the substitution doesn't happen (no error). I have tried:  cat update_via_sed.sh | sed 's/old_run/new_run/' cat update_via_sed.sh | sed 's/$old_run/$new_run/' cat update_via_sed.sh | sed 's/${old_run}/${new_run}/'


Can I repair my hard disk?      I am a beginner with Ubuntu and I don't know how I can fix my hard drive or if it can be repaired.

I want to run the check file system tool, but for that I need to unmount the volume, I have just one partition, should I go ahead with unmount and repair. I am new to Ubuntu, so please help.(Image)


Let $H$ be an inﬁnite dimensional separable Hilbert space with orthonormal basis $(e_n)_n≥1$. Let $f_N = \frac{1}{N} \sum^{N^2}_{n=1} e_n$, $\forall N ≥ 1$.   I am trying to show that $e_n → 0$ weakly, as $n →∞$ and $f_N → 0$ weakly, as $N →∞$, while $ \|f_N\| = 1$, $\forall N ≥ 1$.

Let $H$ be a Hilbert space with ONB $\{b_1, b_2, \cdots \}$.     I want to prove that the sequence $x_n = \frac{1}{n}\sum_{i=1}^{n^2}  b_i$ converges weakly to $0$.   Notice also that $\|x_n\|=1$.  The claim is easily verified on the basis elements, i.e. for large $n$  $$\langle x_n, b_i \rangle= \frac{1}{n}\to 0$$  but I fail to see why it is true for an arbitrary element $y = \sum_i \langle y, b_i \rangle b_i$. Why does  $$\langle x_n, y\rangle = \frac{1}{n} \sum_{i=1}^{n^2} \langle y, b_i \rangle$$  converge to $0$?


I'm a new user here and regularly check Super User. I find many questions related to Microsoft Excel so I was thinking maybe we can have a separate SE site for Microsoft Office products.

I have an idea or subject that should have a Q&A, and want to propose a new site. How can I do this?  Related:


According to  documentation, we must use JavaScript (Perl 5) regular expressions : . What pattern do you use for email validation in Dart? Is there any different way than JavaScript to achieve this in Dart?

Is there a regular expression to validate an email address in JavaScript?


Is it grammatically correct to use the word "and" as the first word in a sentence? Why or why not?

Since I first learned English, I have been holding this understanding that "and", as a conj. but unlike "but",  can only connect two clauses, not two sentences ended with periods.  But recently, I have seen so many prints, either in entertainment or in academia, where "And" is popularly used in the beginning of a sentence. It seems like the author is trying to connect the sentence just right before and the sentence following "And" in some intended meaning which I don't quite get.  I was wondering if I have been wrong all the time, or if there is a new trend that I fail to understand and accept? How to understand such usage of "and" in rigorous English grammar? If I am right, why it is used differently from "but" in terms of what I mentioned at the beginning of this post?


I heard "This may be the case" in the seminar many times. But I still don't know what that means.  Could someone explain the meaning of this sentence? And it would be really appreciated if you give more examples of similar expressions.

What does a person mean when they ask this question: "Why would that be the case?"


Although some authors require a covering map to be surjective by definition, I am, in particular, talking about the definition given by Hatcher:     A covering space of a space $X$ is a space $\tilde X$ together with a map $p:\tilde X\to X$ satisfying the following condition: There exists an open cover $\{U_\alpha\}$ of $X$ such that for each $\alpha,\ p^{-1}(U_\alpha)$ is a disjoint union of open sets in $\tilde X$, each of which is mapped by $p$ homeomorphically onto $U_\alpha$. We do not require $p^{-1}(U_\alpha)$ to be nonempty, so $p$ need not be surjective.   I don't understand the remark made at the end. Since $\{U_\alpha\}$ covers $X$ and each member is the homeomorphic image of some open set in $\tilde X$, $p$ should be surjective. How come that it is possible that $p$ is not? Or did the author mean that $p$ only maps some part of $p^{-1}(U_\alpha)$ onto $U_\alpha$ whenever $p^{-1}(U_\alpha)$ is nonempty?  What is an  example of a nonsurjective covering map?

So, Hatcher defines a covering space as      A covering space of a space $X$ is a space $\tilde{X}$ together   with a map $p:\tilde{X}→X$ satisfying the following condition: Each point $x\in X$ has an   open neighborhood $U$ in $X$ such that $p^{−1} (U)$ is a union of disjoint open sets in $\tilde{X}$ ,   each of which is mapped homeomorphically onto $U$ by $p$.   Also he says      We allow $p^{−1} (U)$ to be empty, the union of an empty collection of sheets over $U$ , so $p$   need not be surjective.   But then, if the definition is satisfied for every $x \in X$ wouldn't that mean that $p$ maps $\emptyset$ onto some $U$? That doesn't make sense! And if it just means "for all $x \in p(\tilde{X})$" then why say "for all $x \in X$"?  Can someone please explain this to me?


Everywhere I look, the $ax^2+bx+c$ portion of the quadratic formula is listed as given.   Does anyone know where this comes from?  Edit  How can we prove that (x+y)^2 = ax^2+bx+c?

In algebra, all quadratic problems can be solved by using the quadratic formula. I read a couple of books, and they told me only HOW and WHEN to use this formula, but they don't tell me WHY I can use it. I have tried to figure it out by proving these two equations are equal, but I can't.  Why can I use $x = \dfrac{-b\pm \sqrt{b^{2} - 4 ac}}{2a}$ to solve all quadratic equations?


When I execute my code in eclipse maven environment, I am getting this error, as I am new to java don't know how to proceed further, any solution please.    Exception in thread "main" cascading.flow.FlowException: unhandled exception     at cascading.flow.BaseFlow.complete(BaseFlow.java:954)     at com.bitwiseglobal.engine.integration.BHSRuntime.execute(BHSRuntime.java:170)     at com.bitwiseglobal.bhse.utilities.BHSExecution.execute(BHSExecution.java:50)     at com.bitwiseglobal.bhse.utilities.BHSExecution.main(BHSExecution.java:29) Caused by: java.lang.NullPointerException     at java.lang.ProcessBuilder.start(ProcessBuilder.java:1010)     at org.apache.hadoop.util.Shell.runCommand(Shell.java:482)     at org.apache.hadoop.util.Shell.run(Shell.java:455)     at org.apache.hadoop.util.Shell$ShellCommandExecutor.execute(Shell.java:715)     at org.apache.hadoop.util.Shell.execCommand(Shell.java:808)     at org.apache.hadoop.util.Shell.execCommand(Shell.java:791)     at org.apache.hadoop.fs.RawLocalFileSystem.setPermission(RawLocalFileSystem.java:656)     at org.apache.hadoop.fs.RawLocalFileSystem.mkdirs(RawLocalFileSystem.java:444)     at org.apache.hadoop.fs.FilterFileSystem.mkdirs(FilterFileSystem.java:293)     at org.apache.hadoop.mapreduce.JobSubmissionFiles.getStagingDir(JobSubmissionFiles.java:133)     at org.apache.hadoop.mapreduce.JobSubmitter.submitJobInternal(JobSubmitter.java:437)     at org.apache.hadoop.mapreduce.Job$10.run(Job.java:1296)     at org.apache.hadoop.mapreduce.Job$10.run(Job.java:1293)     at java.security.AccessController.doPrivileged(Native Method)     at javax.security.auth.Subject.doAs(Subject.java:415)     at org.apache.hadoop.security.UserGroupInformation.doAs(UserGroupInformation.java:1628)     at org.apache.hadoop.mapreduce.Job.submit(Job.java:1293)     at org.apache.hadoop.mapred.JobClient$1.run(JobClient.java:562)     at org.apache.hadoop.mapred.JobClient$1.run(JobClient.java:557)     at java.security.AccessController.doPrivileged(Native Method)     at javax.security.auth.Subject.doAs(Subject.java:415)     at org.apache.hadoop.security.UserGroupInformation.doAs(UserGroupInformation.java:1628)     at org.apache.hadoop.mapred.JobClient.submitJobInternal(JobClient.java:557)     at org.apache.hadoop.mapred.JobClient.submitJob(JobClient.java:548)     at cascading.flow.hadoop.planner.HadoopFlowStepJob.internalNonBlockingStart(HadoopFlowStepJob.java:100)     at cascading.flow.planner.FlowStepJob.blockOnJob(FlowStepJob.java:248)     at cascading.flow.planner.FlowStepJob.start(FlowStepJob.java:172)     at cascading.flow.planner.FlowStepJob.call(FlowStepJob.java:134)     at cascading.flow.planner.FlowStepJob.call(FlowStepJob.java:45)     at java.util.concurrent.FutureTask.run(FutureTask.java:262)     at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1145)     at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:615)     at java.lang.Thread.run(Thread.java:745)   Either this error due to cascading issue or due to java null pointer exception. If any details needed please let me know.

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I read the documentation but there is no table parameter for center position. Only htbpH.  This is a problem because some of my tables are randomly at the top of the page, and others in the center. It makes reading them annoying.

How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference


Has anyone seen a case that url aliases or tokens end up replacing certain numbers in a url with the words node and entity. A UTC Timestamp in my url ended up replaced like this:  node4328522entityentity   I cannot find any errors in the watchdog table. It seems like it's trying to "encode" numbers, but those are numbers that shouldn't be encoded. Or another possiblitiy I've thought of is maybe it is trying to grab something out of a non-existent array at index 0 and 1?

I'm running Drupal 7 on Ubuntu 14.04 server, core and all modules up to date as of today (7th May). We have noticed today that zeros (0) are not displaying correctly in blocks that have a custom token. They are being substituted for the word 'custom'.  For example, "7,500" displays as "7,5customcustom".  I'm not sure how long it has been doing this, as we have only just noticed it today. In blocks without Custom Tokens, the zeros display correctly. This is a relatively recent issue, as it was not a problem a couple of months ago when our site was reviewed by our solicitors.  The source for the content is correct - so it appears to be a display issue. Any ideas?  As an aside, the zeros being replaced need not be in the Custom Token to be replaced (it happens whether they are part of the Custom Token, and when they are just plain text on the page).


I have been working on a server and want to add warps as can be typed in the chat without using /tp, somebody knows how?

Basically, I'm trying to recreate the Faction plugins /f map in my single-player without mods as my PC doesn't run them very well. (I know it sounds strange.) I am trying to use the /testfor to test if I have written '/f map' in chat, and if I have, it would show me a custom generated map. I don't know how to word this better xD Essentially what I want is for it to test if I have written a command in chat, and if I have, display something.


I bought an iphone 5 off kijiji and was able to restore it however the previous owner still had it connected to itunes therefore am unable to use it. Hiw do I completely wipe phone clean nd start fresh creating my own itunes account

I bought a used iPhone 4.  The previous owner re-set the phone, but did not remove the device from their iCloud.  It is asking me for their iCloud information when I try to set-up the phone.  I don't have contact with the previous owner anymore.  Is there a way to remove the device from their iCloud so I can use a new one?


My partner's son has a PS4 at his house with his mum. We are thinking of getting one for our place, and was wondering if he’d be able to use his PS4 account on both machines?  Also, he plays FIFA 20. Would we need to buy the game again or will he be able to play on our machine if he can log in with his user account?

Both myself and my boyfriend have PS4s.  Can I just get a single PSN account and sign both consoles into the same account, or do I need to get two separate accounts?


I'm not sure if the title is the correct description. What I want to do is basically like this: For example, if I have a binary sequence of 3-bits, I can have the following permutations:  1 -> [0,0,0]  2 -> [0,0,1]  3 -> [0,1,0]  4 -> [0,1,1]  5 -> [1,0,0]  6 -> [1,0,1]  7 -> [1,1,0]  8 -> [1,1,1]  But instead of binary sequence, I have a decimal array of integers upper bounded by some value N. Each of the digits can go from 0 to N.  So something like this:  1 -> [0,0,0]  2 -> [0,0,1]  3 -> [0,0,2]  ...  i -> [0,0,N]  i+1 -> [0,1,0]  ...  ...   Is there a closed-form solution to find the digits of any n-th permutation? Even a recursive solution? Or is iterative the only option?

I have an ordered set of symbols S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }. I want to find the 1,000,000-th permutation in lexicographic order of S. It is a programming puzzle, but I wanted to figure out a way without brute-forcing the task.  So my thinking was like this:  For 10 variable symbol positions, we have 10! permutations, obviously. Now we want to find the first symbol.  If we fix the first symbol, then the remaining 9 symbols can have 9! combinations.  That means that 0 or 1 cannot be the first symbol, because the highest possible position is 2*9! = 725,760, which is lower than 1,000,000.  The lowest position for a leading 3 is 3*9! + 1 = 1,088,641, so it can't be 3 or higher, either.  Therefore, the first number must be 2. 2*9! is the largest multiple of 9! no greater than 1,000,000, so I need the 2nd symbol (zero-based) from the current set.  So now the question becomes, of the remaining S := S \{2}, which permutation of these symbols is at lexicographic position (1,000,000 - 2*9!) = 274,240?  6*8! = 241,920 is the largest multiple of 8! which is smaller than 274,240, so I need the 6th-smallest symbol of the remaining set, which is 7. So the prefix should be 27 by now.  That way, I keep going and finally arrive at: 1,000,000 = 2*9! + 6*8! + 6*7! + 2*6! + 5*5! + 1*4! + 2*3! + 2*2! + 0*1! + 0*0!  which results in "2783905614" as my solution.  However, according to the , (free reg. req.) that is incorrect.  Where did I go wrong in thinking or applying?


The image below is of vineyard blocks on different soil types (four larger polygons - all different layers).    I would like to create a new attribute in the vineyard layer called soil type and fill it with the value from the four different soil type layer's attribute called description.  In the case where the soil types overlap the vineyard blocks, the attribute soil type should be where more than 50% of the block lies within the soil type. I have looked, but cannot find a answer.  I have tried geomwithin('Alluvial', 'Description') - a function I get in the field calculator after I installed the plugin refFunctions. However, this only works, of course, if the vineyard polygon is completely within the soil type. I have played around with Union, but I cannot see how that will help me.  Can someone please help me? I would prefer a expression, as I have no knowledge of scripting.

I've been working with qgis for a while but somehow I never fiured this out, so I thought it's time to ask.  I have 2 shapefiles.   a polygon layer from nearby fields (SHAPE1 (the red outlines)) a polygon layer, with different polygons than SHAPE1, that has soiltypes as an attribute (sand, clay etc.) (SOIL (the funky disco colors, each color represents a different soil type)   What I want to find out is what the main soiltype for each polygon in SHAPE1 is. (preferably by adding a field to SHAPE1 with the attribute from SOIL)  Is this possible?


While playing Diablo 3 today, I encountered an Elite monster named Nemisis several times. He popped up very randomly. I noticed he had a rune-like symbol under his name as well.He popped up twice in Act 1(I don't exactly remember what I was doing those times) and once in Act 2 (right before I went into the Witch's Den to fight her). He showed up probably a few hours in between his spawns. After being pulverized by him the first two times, the next time he showed up I was able to kill him. But an even stranger thing happened when I was about to kill him, as he had several shadows of myself attacking as well. He ended dropping a good bit of loot including a legendary item. What I want to know is his characteristics, like those rune-like symbols were, what triggers him to pop up, and anything else that would be helpful to know.

My friend and I were just playing Diablo 3 on Xbox One when we heard a weird sound in the Act I Spider Cave.  Then out of nowhere a red and black demon came out and ran for my friend! The name over the demon was "Hunter of (My friend's character name)". We had no idea what was happening and after my friend was killed the demon left? We have never seen that happen and I don't know if that was a Demon Hunter (my friend's character) thing or not?