What is the expected number of peaks in an array of length $n$ with each number randomly drawed from $[0, 1]$?

Suppose we randomly draw a real number from $[0, 1]$ for $n$ times, and get an array: $a_1, a_2, ..., a_n$. If for some integer $i$ such that $2<=i<=n-1$ and $a_{i-1}<a_i$ and $a_i>a_{i+1}$, we call $a_i$ a peak in the array.  The question is: what is the expected number of peaks in the array $a_1, a_2, ..., a_n$?  For example, in array $[0.6,0.3,0.7,0.4,0.9,0.8]$, there are $2$ peaks: $0.7$ and $0.9$.


Find a continuous function $f$ that satisfies...

Find a continuous function $f$ that satisfies  $$ f(x) = 1 + \frac{1}{x}\int_1^x f(t) \ dt $$  Note: I tried differentiating with respect to $x$ to get an ODE but you get one that contains integrals - likely difficult to solve.


What is the words for the relationship between pounds and pence, or dollars and cents?

A pound is a higher denomination than pence. I'm looking for the word that describes the relationship between a small denomination and a large one, or potentially between denominations in any direction.


Classes and lessons at Hogwarts are presumably scheduled at fixed times of day. The first class might start, for example at nine in the morning.  To be on time for one's lessons, it is therefore crucial to know the current time but we know that electric watches of course do not work at Hogwarts because of all the magical interference. Are there magic watches? Is there maybe a spell to tell the time?  How do people at Hogwarts usually tell the time?


What is the effect of the number of cross-type focus points on sharp focus?

Canon claims that EOS 6D has special capability to focus in low light, but it has only one cross-type sensor and overall only 11 focus points. Does only one cross-type focus point in the Canon EOS 6D affect its ability to focus in low light? Is it correct to assume that more cross-type focus points produce more accurate and sharper focus?


See below example:  $ ls -1p appledir/ applefile orangedir/ orangefile $ find . -type f -name apple\* ./applefile $ find . -type f -name orange\* ./orangefile $ find . -type f -name apple\* -o -name orange\* ./applefile ./orangedir ./orangefile $ find . -type f \( -name apple\* -o -name orange\* \) ./applefile ./orangefile $    I was surprised to discover I needed the parentheses for this to work as expected; apparently I haven't internalized the rule of precedence by which find evaluates its arguments.  How can I easily predict when I will and when I will not need to use parentheses to explicitly group find primaries?  Put another way, what are the rules by which I can imagine find inserting parentheses into the commands I give it, which will allow me to accurately predict how it will evaluate ungrouped expressions?


What is the verb used to indicate that you have travelled from point A to B by motorboat?

Please consider the following and fill in the blank.  This has driven me crazy ever since I moved to florida.  How would somebody say the travel often by a boat without any sails.   I drove from New York to California.  <-- By Car I flew from New York to California. <-- By plane I sailed from New York to London. <-- by Sailboat I blank from New York to Florida <-- by motorboat


Show that $\exists $ a $3\times 3$ invertible matrix $M\neq I_3$ with entries in $\mathbb Z_2$ such that $M^7=I_3$.  My try:  Consider the space $X=GL_3(\mathbb Z_2)$ .Now $|GL_3(\mathbb Z_2)|=168$.By Sylow's Theorem $X$ has a Sylow-$7$ subgroup of order $7$ say $H$ .Since $H$ is cyclic so $H$ has an element  of order $7$.Hence $\exists  A$ such that $A^7=I_3$.  But how to find the matrix $A$? I can't proceed further.  I found that this question has been asked before.I don't want  a hit and trial method for solving this question.Is there a definite way?


I am trying to import a CSV file but cant seem to align the points. I made sure the csv is in UTF-8 and using the project projection but cant seem to align the points no matter after trying multiple projections. What am I missing here?


The lifetimes of a colour TV picture tube

The lifetimes of a color TV picture tube is normally distributed, with a mean of $8$ years and a standard deviation of $2$ years.  (i) What is the probability that a picture tube will last more than $10$ years?  (ii) If the firm guarantees the picture tube for $4$ years, what percentage of the tubes sold will have to be replaced?


Formula to return just the Column Letter in excel

I am looking for a formula I can use in any cell that will return the column LETTER of the column the formula is in,  I can get the LETTER and ROW number using the below, but I cant get it without the ROW information  =ADDRESS(CELL("row"),CELL("col"))   I don't mind using vba to work it out if there isn't a formula that can achieve this.  NOT A DUPLICATE OF  I only want the COLUMN and not the line number !


I try to sign in on Minecraft and it keeps on saying "Unknown Password or Username." And when I try to reset my password, the user name says "Player Not Found." even though I put in the correct name. Why is this happening?


Using Ubuntu 14.04.1LTS. While trying to install VLC, it's throwing this error: "Package dependencies cannot be resolved" - it seems some packages are missing in order to install VLC.


Surjectivity of right and left translations implies semigroup is in fact group

I want to show a set of statements on a semigroup $G$ are equivalent. The left and right translations are given by $l_g(h)=gh$ and $r_g(h)=hg$ respectively.   $G$ is a group For all $g \in G$ both $l_g$ and $r_g$ are bijective For all $g \in G$ $r_g$ is surjective and there exists an $f\in G$ s.t. $l_f$ is surjective   The implications from 1. to 2. and 2. to 3. I managed. But I'm struggling with proving 3. implies 1. I think I only need to show the existence of the neutral and inverse elements, as $G$ is by assumption a semigroup and thereby closed.    A neutral element for each element must be in $G$ as $r_g$ is surjective so in particular $\forall g\in G: \exists e\in G$ s.t. $g=r_g(e)$. How can I show that this e is the same for all $g$?  I still don't see how I can show the inverse elements lie in $G$


Should some badges come with added reputation?  For example: Civic Duty gives you +100 reputation.  I'm not advocating reputation for every badge just a select few.


This excercise was part of an exam of a second course on linear algebra. I'm studing for my exam so I'm trying to do the old ones. It goes as follows:  Let $V$ be a real finite-dimensional vector space. Let $S$ and $T$ be operators in $V$ such that $$TS-ST=T$$ a) Prove that for any integer $k \geq 1$ the following equTion holds: $$T^kS-ST^k=kT^k$$ b)Prove $T$ is nilpotent (hint: consider the linear operator $\phi:End(V)\to End(V)$ given by $\phi(H)=TH-HT$)  I've managed to prove part a) by induction but I'm completly stuck with b) because I don't understand how to use the hint or any other fact. At first I tried to prove there exist some non-zero $k$ such that $T^kS=ST^k$ but I think the proof of b) should be independent of the order of nilpotence of the operator so that proof would not be a direct proof and reasoning by contradiction took me nowhere. It doesn't feel neither there's some polynomial approach. Of course I also tried to use the hint and made the following computations:   $\phi(S)=T$   $\phi^2(H)=T^2H-2THt+HT^2$   $T[\phi(H)]=T^2H-THT=\phi[T(H)]$   (and some more that I belive are useless)   The last equality seems to be an important fact but I just don't know where to go from here. I also tried to prove that $\phi$ is nilpotent, which I don't know if its true, but even if it were true I don't know how I would use it.  I feel terrible because I've studied the whole content of the program and I've done most of the excercises from the problem sets but with this excercise it seems I'm missing something important and don't know what it is. Any guidence of hint will be much appreciated.


java array pass by reference does not work?

I thought almost all languages, including java, pass array into function as reference (modifiable).  But somehow it does not work here, and the testArray is still 1,2,3 with size of 3.  Strange enough, when if I change result[i] = 2 to a[1] =2 it works. It did pass by reference.  What is wrong with this code?   At the end, I had a = result; (which update the a). Did result get removed from stack. Is that why I still get to the original a?   I am confused.  Thanks!  class Test {    public static void main(String[] args)    {        int[] testArray = {1,2,3};       equalize(testArray, 6);        System.out.println("test Array size :" + testArray.length);       for(int i = 0; i < testArray.length; i++)          System.out.println(testArray[i]);    }     public static void equalize(int[] a, int biggerSize)    {       if(a.length > biggerSize)          throw new Error("Array size bigger than biggerSize");        int[] result = new int[biggerSize];      // System.arraycopy(a, 0, result, 0, a.length);      // int array default value should be 0       for(int i = 0; i < biggerSize; i++)          result[i] = 2;        a = result;    } }


I have a class and I would like to capture a keystroke. I know there are events in a WinForm application for keypresses. I want my class to be able to capture a keystroke, without using WinForms. I know I can create a keyboard hook, but I would prefer not to use that method, as it involves importing other Windows libraries and I would like this to work under Mono, as well as Windows. All I need is the ASCII code of the key pressed. I don't need to capture modifiers, such as ctrl, alt, shift, etc...  Any suggestions?


I have installed windows 8.1 alongside with ubuntu 14.04. I had to reinstall the ubuntu like I did many times but this time when I installed ubuntu and started notebook it does not show Grub menu it boots directly to windows. I have to press F12 or special button on my notebook go to boot menu choose ubuntu to show the grub menu. Could anyone tell me how to fix that, please? Also, I feel like my notebook is really loud it is not like it used to be.  notebook specs:  lenovo ideaPad y50-70 nvidia gtx 980 4gb intel i7 4720 HQ haswell Windows 8.1 + Ubuntu 14.04   I somewhere read that I should add # before GRUB_HIDDEN_TIMEOUT=0, but it was set by default like that.  #GRUB_HIDDEN_TIMEOUT=0


XeTeX: What happened to \mathcal and \mathscr?

Recently I switched from pdflatex to xelatex to be able to use OpenType fonts. I like to use variables highlighted using \mathcal for specific variables, while I used to use \mathscr-typeset variables for matrices. But when I compile with XeLaTeX they look exaclty the same.  Old code  \documentclass{standalone} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        New code  \documentclass{standalone} \usepackage{unicode-math} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Broken code  I tried to get back the glyphs from mathrsfs, but it failed this way.  \documentclass{standalone} \usepackage{unicode-math} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Question: How can I get back the behaviour? In principle I'd like to have the old \mathcal letters from the pdflatex-version of Computer/Latin Modern.    Alternate solutions (Addendum 2016/05/11)


Java: "Type mismatch: cannot convert from Byte[] to byte[]"

I'm getting this odd error in my Java and I'm completely stuck.  private List<byte[]> sharedWorlds = Collections.synchronizedList(new ArrayList<byte[]>());  Byte[] y = sharedWorlds.toArray(new Byte[0]);  try{      //this line won't compile!     Utilities.writeByteArray(outStream, sharedWorlds.toArray(new Byte[0]));  }catch(Exception e){     System.out.println("Error!"); }      Type mismatch: cannot convert from Byte[] to byte[]   The second parameter to "writeByteArray" needs to be a byte[] and not a Byte[]...  I could loop through a new byte[] and copy every element, but this seems unclean and inefficient?  I tried casting  (byte[]) sharedWorlds.toArray(new Byte[0])   but this errors with      Cannot cast from Byte[] to byte[]   My Java is rusty, but I have no idea what's going on here.


How one can define right vector space over Division ring $R$ ?  What properties it lack than the vector space over field? One thing which it lack is definitely commutative properties but what other properties it lacks?


Adjust color temperature with Intel HD graphics

Is there any way to install Intel HD graphics in Ubuntu  If yes then how? If no then how I reduce blue color from my lcd


Is it possible in C# to have a Struct with a member variable which is a Class type?  If so, where does the information get stored, on the Stack, the Heap, or both?


Why must I put the command read into a subshell while using pipeline

The command df . can show us which device we are on. For example, me@ubuntu1804:~$ df . Filesystem     1K-blocks    Used Available Use% Mounted on /dev/sdb1       61664044 8510340  49991644  15% /home  Now I want to get the string /dev/sdb1. I tried like this but it didn't work: df . | read a; read a b; echo "$a", this command gave me an empty output. But df . | (read a; read a b; echo "$a") will work as expected. I'm kind of confused now. I know that (read a; read a b; echo "$a") is a subshell, but I don't know why I have to make a subshell here. As my understanding, x|y will redirect the output of x to the input of y. Why read a; read a b; echo $a can't get the input but a subshell can?


I can create a collection of pictures giving a 360-degree view from a certain spot, just taking a bunch of photographs from the same spot but in a different direction.  However, what software could I use (on Windows) to stitch these images together to get one big image?  I prefer something that would stitch them together without showing any seams.


Connect Apple 30" Cinema Display to new MacBook USB-C

I noticed in this thread the OP successfully managed to connect a 30" cinema display to the new Macbook Pro USB-C, with full resolution:    I have the official Apple dual DVI adapter, going to a displayport > USB-C adapter like yours, however the screen does not fire up.  I then tried a multi adapter instead of the single displayport > USB-C, which worked but only at 1280 resolution:    Would the official Apple Dual DVI adapter not work?


Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?

I know that if A and B are square nxn matrices, then AB and BA have the same characteristic polynomial and thus the same eigenvalues (and same algebraïc multiplicity).   I'm wondering though if this can be generalized: if A is a nxm matrix and B a mxn matrix, then AB is a nxn matrix and BA a mxm matrix.  So my question is: will the eigenvalues of AB and BA, that differ from zero, have the same algebraïc multiplicity?


While working with PHP I used output buffer as a way to "combine" multiple method outputs and ex. write buffet to a file.  Example:  ob_start(); print $foo->bar(); print $anotherFoo->anotherBar(); $output= ob_get_contents(); ob_end_clean(); file_put_contents("output.html",$output);   Is there an equivalent in C#?


Consider:  The supermassive black hole in a galactic core.  A neutron star of nearly maximum mass does a very close flyby (remember, galactic black holes don't have the incredibly vicious tides of an ordinary one--it can get awfully close without crossing the Roche limit.)  Now, a neutron star can easily have an escape velocity of half of lightspeed.  What happens when it flies past at 86% of c (Lorentz factor = 2).  An observer sees it with half the radius in the line of motion and twice the mass--it's escape velocity is above lightspeed.  Thus the observer sees the object as a black hole.  It completes it's flyby and slows back down--the observer sees it go from being a black hole to being a neutron star--but that can't be.


If the electric field is the gradient of the potential, then can we say that whenever potential is zero, the electric field is zero?

For example, in a dipole, at the center of the two charges making up the dipole, the potential is zero but the electric field is non-zero. But if $E = -\operatorname{grad}V$, then why is $E$ not zero?  Another example: In the case of two positive charges, the electric field is zero at the mid-point of line joining them, but potential is non-zero. What am I misunderstanding here?


Is it possible to copy a comment text in markdown to the clipboard?  E.g., if the comment text in markdown is blah $x$ and http://stats.stackexchange.com/questions/221704/results-of-softmax-regression-on-mnist-dataset, I will get  blah xx and stats.stackexchange.com/questions/221704/… if I select then copy the comment text (assuming latex is activated), whereas I want to have the comment text in markdown.  The edit button is only present for five minutes and for one's own comments.


How to redirect all variations of a domain to https version?

Google has started punishing non https sites both in SEO and their browsers. So I guess we must make sure that all our clients are using https    Assuming that I have a domain example.com I would like to redirect all the variations of this domain to the https version.   There can be six variations example.com, www.example.com, http://example.com, http://www.example.com, https://example.com, https://www.example.com.   I want to make sure that all these variations redirect to https://www.example.com.


Everything working fine i got this error at the end please give solution. I have tried each and every solution, I don't know what to do.. please give the exact solution trying from past 2 days but i can't solve the problem..  Thanks in advance  public double calculatedDistance(DataSnapshot dataSnapshot ) {           HashMap<String, Object> values = (HashMap<String, Object>) dataSnapshot.getValue();          double lati = Double.parseDouble(values.get("latitude").toString());         double longi = Double.parseDouble(values.get("longitude").toString());          double xSquare = Math.pow(lat-lati, 2);         double ySquare = Math.pow(lng-longi, 2);         double distance = Math.sqrt(xSquare + ySquare);          //double dist = distance;          textViewdistance.setText(String.valueOf(""+distance+""+"km"));         return distance;      }   Error in Logcat  E/AndroidRuntime: FATAL EXCEPTION: main     Process: com.example.ambulance, PID: 17399     java.lang.NullPointerException: Attempt to invoke virtual method 'double java.lang.Double.doubleValue()' on a null object reference         at com.example.ambulance.MapsActivity.calculatedDistance(MapsActivity.java:451)         at com.example.ambulance.MapsActivity$2$1.onChildAdded(MapsActivity.java:178)         at com.google.firebase.database.core.ChildEventRegistration.fireEvent(com.google.firebase:firebase-database@@19.2.0:79)         at com.google.firebase.database.core.view.DataEvent.fire(com.google.firebase:firebase-database@@19.2.0:63)         at com.google.firebase.database.core.view.EventRaiser$1.run(com.google.firebase:firebase-database@@19.2.0:55)         at android.os.Handler.handleCallback(Handler.java:907)         at android.os.Handler.dispatchMessage(Handler.java:105)         at android.os.Looper.loop(Looper.java:216)         at android.app.ActivityThread.main(ActivityThread.java:7625)         at java.lang.reflect.Method.invoke(Native Method)         at com.android.internal.os.RuntimeInit$MethodAndArgsCaller.run(RuntimeInit.java:524)         at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:987)


Prove the following:  $\displaystyle\prod_{n=1}^{180}\left(\cos{\left(\dfrac{n\pi}{180}\right)}+2\right)=\displaystyle\sum_{n=0}^{89}\binom{180}{2n+1}\left(\dfrac{3}{4}\right)^n$.  We can state this as $\displaystyle \binom{180}{1}\left(\dfrac{3}{4}\right)^0+ \binom{180}{3}\left(\dfrac{3}{4}\right)^1+\cdots+\binom{180}{179}\left(\dfrac{3}{4}\right)^{89} = \left(\cos\left(\dfrac{\pi}{180}\right)+2\right)\left(\cos\left(\dfrac{2\pi}{180}\right)+2\right) \cdots \left(\cos\left(\dfrac{180\pi}{180}\right)+2\right)$   The problem I am encountering is that there is no general result we can prove about this for $n$ it seems. I tried using induction on $n$ to prove this but it fails for the base case. Also, combinations and cosines seem unrelated, so how could I prove the equation is true?


I created regular expression for nodejs aggaregate query. But can not create it.  Here, is my code.      var device = "HPM220";     var expression = /^[device].*/i;     console.log(expression);   My device name is "HPM220". but my output is /^[device].*/i. It is wrong output.  The output should be /^[HPM220].*/i  What mistake i did here?


Are black holes an infinite source of energy?

Black holes are considered particularities because in a determined point in time they are pointless, as consequence there are some mass in a null space so the density become infinite. Finally if energy is equal to mass, that is mean a black hole has an infinite energy? Is that possible?


Research statement ideas got used by interviewing committee

Last year, I applied to a university which is in Europe so a research statement is a crucial part of the application. I was interviewed by two faculty members and then finally got a rejection letter.    In my research statement, I had a particular idea and described a roadmap for it, though I did not get into technical details. But the idea was there and clearly stated. Recently, I came across a publication where the title is the same as my idea (wording is a little bit different) and is co-authored by one of the members of the interview panel.  The publication has technical details which were not part of my research statement. I believe there is no clear proof here whether my ideas got used or not.    My questions are:   Is this suspicious?   Is this valid and acceptable?


Can or could, which is correct, or at least better? Why?

She has forgotten how she could open the window.  Vs  She has forgotten how she can open the window?   In a sentence like this, which is correct or better ? could  or can? Why? Thanks!


Well, I got (I think) a pretty basic question.  I'm new in Ubuntu, and I'm wondering how do I backup all I've installed and my GUI settings and tweaks.  I'm not pretty much interested in backing up info (as Ubuntu Official Backup seems to be oriented to), since I work everything in dropbox or google drive, but better in all the drivers, programs (or packages as it is called in ubuntu... btw, It's difficult to get used to terms, programs in windows, apps in macos, packages in ubuntu... well)  So, long question made short: I want to backup my nvidia driver, Appearence and Mouse and Display settings, and overall all I've installed in my machine such as Skype, Chrome, Synapse, etc etc etc.  Any help or guidance is welcome! :)


Inequality: showing that $p(1-p)\leq \frac{1}{4}$ if $0<p<1$.

I was wondering if there was another way to derive the inequality shown in the title of this question apart from calculus.  Doing it with calculus is pretty straightforward:   Let $f:(0,1)\to\mathbb R$ be a function defined by $f(p)=p(1-p)$. Taking the first derivative $f'(p) = 1-2p=0\Rightarrow p=1/2$ is a critical point. Then the maximum is $1/4$ and it is reached when $p=1/2$. Hence $p(1-p)\leq 1/4,$ $\forall p\in(0,1)$.


Everything I read about this spell leaves me with more questions than answers.  Does a simulacrum have the personality of its target? How would that reconcile with a target that is fiercely independent?  If it had no orders, does it attempt to entertain itself, or does it just sit there waiting for orders as an emotionless husk? Does it beg for orders like Mr Meeseeks?  Does it perform its orders and nothing else? If you order it to wait for someone, does it sit motionless until the person arrives, or will it engage in small talk to keep itself occupied?  How specific does an order need to be? Will it follow the letter or the spirit of the order?


I've made a 2-module project where one module is completely denoted to a library that I've made and I'm accessing that library from the other module(which contains the MainActivity.java) of the project. Now I want to push only my library to the GitHub so that anyone can use it for their need. I know how to push the entire project to GitHub but How can I extract the library ( module ) from the project and push only that. Thanks in Advance!


Optimal Dragonborn Warlock for DPR/AC with Blade pact and Fiend patron

How can I get the highest Damage-Per-Round (both melee and ranged using pact weapon and Eldritch Blast) and AC possible (with DPR being more important than AC) with a Dragonborn Warlock taking the Pact of the Blade and a Fiend as otherworldly patron? Assume the character has the standard ability array or uses point-buy and prioritizes STR, CHA, and CON in that order. Also assume multiclassing and feats are allowed.


What is the word for "knowledge of words?"

I remember that there was a word that meant being knowledgeable about many words, but I've forgotten what the word was.


I want to boot ubuntu but i dont know how to add the ext4 partition to my boot menu

So , i used UNetBootin to install Ubuntu 18.04 on my pc , i installed it on a parititon i created from my hard drive     i opened the installer i think it was something like Ubuntu 18.04 Installer it was on the desktop i partitioned the drive on the partition i created 100 gbs i set it to ext4 then installed told me to restart now i dont know how to get into it   What do i do then ! Thanks  EDIT : Dual boot : I have windows 10


Lightning URL hack issue with prepopulating fields on Page Load

I have Visualforce Page which redirects to standard accounts edit page with prepoulated value for record Type. The record type is getting populated using URL hack. But since URL hacks dont work in lightning experience this functionality is not working and the record type is not populated.  Is there any other workaround to redirect to a standard page with pre-poulated values in Lightning?


What made us think that Earth moves around the Sun?

Trying to observe the night sky for a few weeks, the motion of the Sun and the stars pretty much fits into the Geocentric Theory i.e. All of them move around the Earth.  What then, which particular observation, made us think that it could be the other way around, that all the planets move around the Sun?


I got into a small confusion of numerical calculation.   in C#:  > 44.5 + (((5220886 / 2) - 2496118) / 897211) * 9 < 44.5   in JS:  > 44.5 + (((5220886 / 2) - 2496118) / 897211) * 9 < 45.646803817608124   Which one is correct? Can anyone help me to understand why this is happening?  P.S: Though there is one post in SO which is dealing with , my question is a little bit different as I am not doing anything with strings. This is pure numerical calculations.


upgrading an O.S. affects which file systems?

I will be upgrading my O.S. from Ubuntu 13.04 to Ubuntu 13.10. As its recommended to take back-up before doing that, I'm interested to know which file systems are affected by upgrading so that I need to take back up of those only.  When I installed my O.S. I had created these 4 partitions:  / /boot /home swap   Then later I had created 3 more partitions sda9, sda10 and sda11 by utilizing the unallocated space. I have taken some back-ups on these 3 newly created partitions. Now, may I presume that these 3 partitions won't be affected at all by the up gradation?  I have a related post of mine  but couldn't get resolved there.


Is it damageful to disallow *.txt in robots.txt?

Does someone know if disallowing *.txt in robots.txt can be a problem? I fear a little that robots can't even access to robots.txt in this case.


Why is the localization of a commutative Noetherian ring still Noetherian?

This is an unproven proposition I've come across in multiple places.   Suppose $A$ is a commutative Noetherian ring, and $S$ a multiplicative subset of $A$. Then $S^{-1}A$ is Noetherian.  Why is this? I thought about taking some chain of submodules $$ S^{-1}M_1\subset S^{-1}M_2\subset\cdots $$ and pulling back to a chain  $$ M_1\subset M_2\subset\cdots $$ of submodules of $A$ which must eventually stablize. Is there more to it than this? I kind of wary of assuming all submodules of $S^{-1}A$ have form $S^{-1}M$ for $M\leq A$.


Integral $\int_{-\infty}^{\infty} \frac{c(\theta)}{(1 + x^2)^\theta} dx $

I want to calculate this integral:$\int_{-\infty}^{\infty} \frac{c(\theta)}{(1 + x^2)^\theta} dx $  it's easy to do, when $\theta$ is given: For example when $\theta$ is 1, then integral is equal to $\pi$  But how to calulate integral, when \theta is not given?  And $c(\theta)$ is a constant, that is dependent on $\theta $


Do I need "the" when refer to something that has its name or label?

I get confused about academic writing. Is it grammatically correct to say:  We will propose the X test. The equation (1) is used for solving the problem. The X test is defined in the equation (1). According to the equation (1), ...  I would like to know if the word "the" is used correctly. Any help would be appreciated. ============update============== Here is what the equation will look like(The image is from google)


How can I typeset the reduced Planck constant (ℏ)?

How can I typeset the symbol for the  (from quantum theory)? It consists in an italic "h" whose upper part is crossed by a small "slanted" bar:     For information, this slanted bar also occurs quite often with the letter "l" (ell) in Polish. Example: the Polish word for "word" is "slowo", where the letter "l" bears a slanted little bar.  Is there a package that provides that symbol?  Second question: please tell me where to look for and how to correct the LaTex PDF warning  overfull/underfull \hbox or \vbox


I cant send or receive anything after connecting to FTP, but can remove files. I know that I didn't do a 'good job' with the iptables and now I need help.  Here is the output from iptables -L -n -v  Chain INPUT (policy DROP 16184 packets, 4360K bytes)  pkts bytes target     prot opt in     out     source               destination           930  149K ACCEPT     all  --  *      *       127.0.0.1            0.0.0.0/0             4672 3279K ACCEPT     all  --  *      *       0.0.0.0/0            0.0.0.0/0            state RELATED,ESTABLISHED     1    71 ACCEPT     udp  --  *      *       0.0.0.0/0            0.0.0.0/0            udp dpt:53     1    60 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:20000    90  5200 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:10000    28  1632 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:443    39  2140 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:80     1    60 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:993     1    60 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:143     1    60 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:995     3   160 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:110     1    60 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:53     1    60 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:587     1    60 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:20     5   300 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:21    21  1240 ACCEPT     tcp  --  *      *       0.0.0.0/0            0.0.0.0/0            tcp dpt:25  Chain FORWARD (policy ACCEPT 0 packets, 0 bytes)  pkts bytes target     prot opt in     out     source               destination           Chain OUTPUT (policy ACCEPT 6260 packets, 4251K bytes)  pkts bytes target     prot opt in     out     source               destination     If i change the input policy to accept everything works again but I dont want to do that. I tried to enable all the states for port 21 but still didn't work.


Which LaTeX package provides this text typeface?

The typeface is the same as the one here:   I have copied the image from that post here.    Thanks in advance.


Let $X$ be a set and $\{Y_\alpha\}$ is infinite system of some subsets of $X$. Is it true that: $$\bigcup_\alpha(X\setminus Y_\alpha)=X\setminus\bigcap_\alpha Y_\alpha,$$ $$\bigcap_\alpha(X\setminus Y_\alpha)=X\setminus\bigcup_\alpha Y_\alpha.$$ (infinite DeMorgan laws)  Thanks a lot!


Is the space of smooth sections of a vector bundle finitely generated as a $C^\infty$-module?

Given a smooth finite-dimensional vector bundle $E\to M$ on a smooth manifold $M$, is the space of smooth global sections $\Gamma(E,M)$ always a finitely generated $C^\infty(M)$ module? This amounts to asking whether there exist finitely many smooth sections $s_1,...,s_m$ such that every $s\in \Gamma(E,M)$ can be written as $s=f_1 s_1+...+f_m s_m$ with smooth functions $f_1,...,f_m$.


How did the planets (in the Solar System) start to revolve around the sun if they were attracted towards the Sun via the gravitational force?

The planets in the Solar System revolve around the Sun in almost circular paths called orbits. The Sun pulls the planets with the gravitational force,but the planets do not get drawn to the Sun but remain at certain distance because of the centrifugal force which acts in the outward direction (as the planets are revolving around the Sun). How did the planets start to revolve around the sun if they were attracted towards it (via the gravitational force)?


An equality about infinite sums involving squared harmonic numbers

I found the following equality. But I forgot the source as well as the solution.  If you give the proof, I appreciate it.  $$\sum_{k=1}^\infty \frac{1}{k^2}\left( 1 + \frac12 + \dots + \frac1k \right)^2 = \frac{17\pi^4}{360} = \frac{17}{4} \sum_{k=1}^\infty \frac{1}{k^4}$$


How can I use Einstein's field equations?

Every time I try to find the answer to this question I get redirected to different pages that ultimately do not end up answering my question. I have some understanding of Riemannian geometry but have no idea how to link it to the presence of a mass with .  Could someone provide an example, either linked or typed and submitted as answer, of a simple question with an object of defined mass?


Why and When Do We Need Standardization for Machine Learning

When and why do we need standardization for machine learning? What's the benefit for doing so?   For example,  we replace $y_i$ with $(y_i - u_y)/ \sigma _y $ we also replace $x_i$ with $x_ij - u_j / \sigma_j$  It would be great if someone provides me some intuitions.


What are some good time series classification methods where we have a single time series of some motor and a labelled training data indicating at what points did the motor fail, the rest are normal working. The time series classification model should be able to tell motor state normal or fail based given a set of time series features.


How to calculate the intersection of two planes?

How to calculate the intersection of two planes ?  These are the planes and the result is gonna be a line in $\Bbb R^3$:  $x + 2y + z - 1 = 0$  $2x + 3y - 2z + 2 = 0$


\printbibliography doesn't work with Biblatex and Texmaker

I'm using for the first time biblatex  The main file is similar to the following:  \documentclass[12pt,a4paper]{report}  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage{amsmath} \usepackage{amssymb} \usepackage{mathtools} \usepackage{bm} \usepackage{booktabs} \usepackage{graphicx} \usepackage{rotating} \usepackage{lscape}   \usepackage[space]{grffile}%para os directórios com espaços não darem problemas  \usepackage{float}% para os floats, aka imagens e tabelas, ficarem onde queremos. Usar [H] em vez de [h] \graphicspath{ {Imagens/} } \usepackage{algorithm} \usepackage{algpseudocode}  \floatname{algorithm}{Algorithm} \renewcommand{\algorithmicrequire}{\textbf{Input:}} \renewcommand{\algorithmicensure}{\textbf{Output:}}   \usepackage{tikz} \usetikzlibrary{automata, positioning, arrows,shapes} \usetikzlibrary{decorations.pathreplacing}  \tikzset{ ->, % makes the edges directed >=stealth', % makes the arrow heads bold node distance=3cm, % specifies the minimum distance between two nodes. Change if necessary. every state/.style={thick, fill=gray!10}, % sets the properties for each 'state' node initial text=$ $, % sets the text that appears on the start arrow }  \newtheorem{theorem}{Theorem}[subsection] \newtheorem{corollary}{Corollary}[theorem] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{property}{Property} [subsection] \newtheorem{definition}{Definition} [subsection]  \usepackage{hyperref} \hypersetup{     colorlinks=true,     linkcolor=red,     filecolor=red,           urlcolor=red,     pdfnewwindow %para o comando href não fechar a apresentação ao abrir novos pdf's }  %%%%%%%%%%%%%%%%%%%%%%%%%%%% %\usepackage{xcolor}%Comment out before printing %\pagecolor[rgb]{0,0,0}%Comment out before printing %\color[rgb]{1,1,1}%Comment out before printing %%%%%%%%%%%%%%%%%%%%%%%%%%%%  \usepackage[backend=biber]{biblatex} \addbibresource{Bibliography.bib}  \begin{document} \input{titlepage}  \chapter*{Abstract} \input{Abstract/Abstract}  \chapter*{Dedication} To    \chapter*{Declaration} I declare that..  \chapter*{Acknowledgements} I ack  \tableofcontents  \chapter{Towards a First Chapter}   \chapter{Dealing with a Second Chapter}   \printbibliography  \cite{Stuart10} is a testing crucible  \end{document}   The .bib file has the following text:  @article{<Stuart10>,     author        = {Stuart},     title         = {Some Very Difficult Problems},     journaltitle  = {Numerology},     year          = {1820},     volume        = {1},     pages         = {451-559} }   However, when I compile, every thing appears fine except for the Bibliography section which never appears... There's no error warning, and everything is compiled smoothly.


I want to center the content of MAIN horizontally and vertically on the page, but whichever solution I tried, it didn't work. I'm absolutely frustrated atm, because I got it to work, then I changed a lot and it reset itself.  Maybe someone could look over it and give me a hint where I'm wrong. Thank you.    html, body, div, span, applet, object, iframe, h1, h2, h3, h4, h5, h6, p, blockquote, pre, a, abbr, acronym, address, big, cite, code, del, dfn, em, img, ins, kbd, q, s, samp, small, strike, strong, sub, sup, tt, var, b, u, i, center, dl, dt, dd, ol, ul, li, fieldset, form, label, legend, table, caption, tbody, tfoot, thead, tr, th, td, article, aside, canvas, details, embed,  figure, figcaption, footer, header, hgroup,  menu, nav, output, ruby, section, summary, time, mark, audio, video {  margin: 0;  padding: 0;  border: 0;  font-size: 100%;  font: inherit;  vertical-align: baseline; } /* HTML5 display-role reset for older browsers */ article, aside, details, figcaption, figure,  footer, header, hgroup, menu, nav, section {  display: block; } body {  line-height: 1; } ol, ul {  list-style: none; } blockquote, q {  quotes: none; } blockquote:before, blockquote:after, q:before, q:after {  content: '';  content: none; } table {  border-collapse: collapse;  border-spacing: 0; }  /********** LANDINGPAGE.CSS **********/ /**********  **********/ *, header, footer { font-family: 'Roboto', sans-serif; font-size: 1vw; color: #4c4c4c; letter-spacing: 0.05em; text-decoration: none; }  h1 { font-family: 'Lato', sans-serif; font-weight: normal; font-size: 4vw; }   /********** SITE **********/ .wrap_site { max-width: 100%; margin: 0 5%; }  .wrap_content { display: flex; align-items: center; justify-content: center; }  .button { border: 1px solid #4c4c4c; display: inline-block; cursor: pointer; font-size: 1vw; padding: 8px 18px; background-color: white; }  .button:hover { transition: background-color 0.5s ease; color: white; background-color: #4c4c4c; }   /********** HEADER **********/ .wrap_header { left: 0; right: 0; top: 0; border-bottom: 1px solid #4c4c4c; padding-top: 1rem; padding-bottom: 1rem; }  header { display: flex; justify-content: space-between; }   /********** FOOTER **********/ .wrap_footer { position: absolute; left: 0; right: 0; bottom: 0; margin: 0 5%; border-top: 1px solid #4c4c4c; padding-top: 1rem; padding-bottom: 1rem; }  footer { display: flex; justify-content: space-between; }  <!DOCTYPE html>

This website is currently under construction.

Hi, my name is x. Welcome to my website.

你好, 我叫 x。欢迎来到我的网站。

ABOUT ME

       contact@x.com 📧     ⚖ Imprint


Let $f$ be a continuous function on $\Bbb R$ satisfying $f(f(f(x)))=x ;\ \forall x \in \Bbb R$. Then is $f$ the identity function?

I don't know what the answer is but I tried to get some information from the hypothesis and have reached till the result that $f$ is an homeomorphism.  This is because $f$ is bijective and continuous as well as it's inverse is also continuous because $f \circ f=f^{-1}$ and composition of continuous functions is continuous.  What should be my next step? or this is not the way to reach the answer?


Variation of the BASE Current with the COLLECTOR Current in CE config?

So can anyone explain me how the collector voltage(V (output)) will vary with variation in base current with respect to the following figure?         – Schematic created using


Now that too localized is gone should we embrace the "typo questions"?

The old "too localized" closing reason included "questions that are unlikely to help future visitors".   , that if a question resulted from a typo in the OP code those questions should be closed with "too localized" reason.  The current off-topic reason does not cover that.  Should these questions remain open now, as they do not really fall into any current closure category?  UPDATE  I marked  for diamond moderator attention to be deleted as Robert Harvey hinted below, only to get the flag declined as "declined - flags should only be used to make moderators aware of content that requires their intervention".  Can you confidently tell me that this is a useful question that helps the goal of SE?


Numbering all environments within chapter with the same counter?

I want to number my definitions, lemmas, examples, etc. as "chapter"."number of environments"... For example:  1. Chapter One         1.1 Env. A     1.2 Section One         1.2 Env. B         1.3 Env. A     1.3 Section Two         1.4 Env. C         1.5 Env. B   But at the moment I am only able to get  1. Chapter One         1.1 Env. A     1.2 Section One         1.1 Env. B         1.2 Env. A     1.3 Section Two         1.1 Env. C         1.2 Env. B ...   I know that I can use  \newtheorem{A}{A}[chapter] \newtheorem{B}[A]{B}   if I want that B has the same counter as A, but this way only works if I start all my chapters with the same enviroment...  Is there a simple way so that ALL enviroments share the same counter within a chapter?  Sorry for the bad format, but I hope you still get my problem!


I have a galaxy s 5 and want to know if putting ubuntu phone on it if it will brick or work? If it bricks I can all ways upgrade to the note 4, which leads me to my next question. Would it work on the note 4? I think the desktop on the note 4 would be pretty awesome to have. I love that you guys are trying to put pc power on phones. Keep it up. Please.


Riemann and Darboux Integral of a product of two functions

I'm studying the Darboux definition of integrability, which I completely explained . There's an exercise that asks me to prove that the Darboux Integrability is equivalent to Riemann Integrability, but this Riemann integral is defined as the following:  It first defines a 'pointed' partition (I don't know how to say it in ensligh) by the following: a 'pointed' partition $[a,b]$ is a pair $P^*=(E,ξ)$, where $P=\{t_0, t_1, \cdots, t_n\}$ is a partition of $[a,b]$ and $ξ = (ξ_1, \cdots, ξ_n)$ is a list of $n$ chosen numbers such that $t_{i-1}\le ξ_i\le t_i$ for each $i=1,\cdots ,n$.  Now, the Riemann Integral is defined as:  $$\sum(f,P^*) = \sum_{i=1}^n f(ξ_i)(t_i-t_{i-1})$$  (I didn't understand the notation for the left hand side of the equation, by the way)  Finally, I'm asked to prove the following: given $f,g:[a,b]\to \mathbb{R}$ integrable functions, for the entire partition $P=\{t_0, \cdots, t_n\}$ of $[a,b]$ let $P^* = (P,ξ)$ and $P^{\#} = (P, η)$ be pointed partitions of $P$, then:  $$\lim_{|P|\to 0}\sum f(ξ_i)g(η_i)(t_i-t_{i-1}) = \int_a^b f(x)g(x) \ dx$$  I guess here I need to prove that the Riemann Integral of the product of two functions if the darboux integral of $f(x)g(x)$, but it seems too obvious, I just need to verify that $f,g$ are integrable, then their product is too, isn't it? I'm pretty sure this should be a hard question. Is there another interpretation that I'm missing?


I'll throw you a party    What does the above sentence means and how it is different from the sentence given below?     I'll give you party


Prove that s is finite and find an n so large that $S_n$ approximate s to three decimal places.

$$S=\sum_{k=1}^\infty\left(\frac{k}{k+1}\right)^{k^2};\hspace{10pt}S_n=\sum_{k=1}^n\left(\frac{k}{k+1}\right)^{k^2}$$ Let $S_n$ represent its partial sums and let $S$ represent its value. Prove that $S$ is finite and find an n so large that $S_n$ approximate $S$ to three decimal places.   Solution: first of all, I think that we Will use L'hopital rule and then use root test while starting to solve this. But how?


macOS Terminal find most recent file in directory

I'm writing (what I thought would be) a quick little bash function to identify the most recent photo imported into Apple's standard Photos.app from a DSLR.  So far it looks something like this:  find ~/Pictures/Photos\ Library.photoslibrary/Masters -type f  Pretty simple. As it is, it lists the entire library of imported photos. My first instinct was to simply | tail -n 1, but the files aren't listed in any discernible order.   I considered | sort -V, but it's not unusual for the filenames (i.e. IMG_0123.CR2) to become out of order.  FYI: This BSD version of find doesn't support the -printf option found in the GNU version.


How to group applications using terminal or configuration file?

In the "Show Applications" tab in Ubuntu it is possible to group icons together using the create a folder and then add to folder option in the Ubuntu Software (which is described in detail )  However, since I often reinstall my system, I was wondering if it were possible to do this using terminal, or by editing menu's configuration file hidden in depths of the system folders? This would automate the whole thing and save me a lot of time by not doing it manually.


Classical algorithm with complexity similar to Shor's discovered: Are there more efficient quantum algorithms than Shor's?

In the article  the author claims that he discovered classical algorithm for factoring integers in polynomial time. The Quantum Report mentioned  that it has similar performance to Shor algorithm which is often considered to ignite interest in quantum computers. Of course, the new classical algorithm has to be examined closely before it is confirmed that it is really so fast as claimed. However, I would like to know if there are other quantum algorithms besides Shor and quantum binary optimization based. Has it been proven that Shor algorithm is optimal or could there be another even faster quantum algorithms for integers factoring?


Do I need a telephoto lens to make objects in the distance appear closer?

I have seen some photos where a far-away object looks much bigger compared to nearby objects. Apparently this is called lens compression and it has to do with the focal length of a lens. How can I achieve this effect? How does it work?


How to complete a circular shape using an array modifier?

How would I use the array modifier to duplicate this pattern all the way around the top and bottom circle faces? Whenever I try to use the array modifier, the pattern just copies next to itself. Its hopefully going to be a grenade. Ive added the blend file in case anyone can help. Thanks


\begin{vmatrix}  a & b & b & \dots & b \\   b & a & b & \dots & b \\   b & b & a & \dots & b \\  \vdots & \vdots& \vdots & \ddots & \vdots\\  b & b & b &   & a\\  \end{vmatrix}  I still have no idea how to solve this determinant, please help me if you can:)


Use of "which" directly after a word that it is not pointing to

My question is about the following sentence:     We have created a system to support operations of the devices, which processes and sends out data.   Would you say this use of "which" is OK? I'm not sure because the "which" comes directly after the word "devices" which it is not pointing to, instead the "which" is pointing to "system". I wondered if there was some kind of rule about that.


We have the search box on our ListViewWebPart - via Display Search Box - and the searches time-out (rarely it works straight-away), with the icon just going around in circles.  Interestingly, if we visit the list view page itself (e.g. by clicking on the ListViewWebPart header), the search works every time.   Could there be some script or other issue on the Site Masterpage vs the System Masterpage that could be causing the problem? Our masterpages aren't too different.


Is it possible to connect to the Subsystem for Linux in Windows 10 using SSH

Now that Windows 10 has the Windows Subsystem for Linux is it possible to connect to it remotely via SSH?  With the Bash shell up and running I tried connecting Putty (running on the same Machine) to localhost but the connection was refused.  Has anyone gotten this to work?


Anyone knows what software tool is used to draw these circuit schematics

I was reading online and found this site:   I was very curious how this professor drew all these circuit diagrams in his lecture notes (such as this one: ). They just look very very good.   And example is shown below:      To be more specific about what I mean, by "publication quality" I mean the following:   The software must output vector graphics, such as eps, or windows meta files. It would be good to have control over the style of the graphics, such the style of the components, line width, figure size, etc. It would be good to have a graphical user interface. I understand LaTeX is very powerful but it's just too painful to write a 100 line script to generate a circuit diagram.   So in short, I'm not really looking for a schematic capture program. I'm looking for a program that can generate pretty circuit schematic illustrations so that I can put them in papers and presentations.  (I am aware of other posts on this forum, such as this one: .  None of the software mentioned in that post seems to get you publication quality figures.)


"no 'operator++(int)' declared for postfix '++' [-fpermissive]" on enums

I have got the enum  enum ProgramID {     A = 0,     B = 1,     C = 2,     MIN_PROGRAM_ID = A,     MAX_PROGRAM_ID = C,  } CurrentProgram;   Now, I am trying to increment CurrentProgram like this: CurrentProgram++, but the compiler complains: no 'operator++(int)' declared for postfix '++' [-fpermissive]. I think there IS such an operator that increments "enums", but if there is not, how do I get the successor of one of these values?


How to call 911 for my home area when overseas?

I have my house wired up with security cameras. When traveling others countries, I still can get phone alerts that there is movement in the house, and can access the security feeds on-line to see if there are burglars. But if I want to ring the police to go to my house, how can I call them? I can use a long distance phone card, but I think 9-1-1 won't work as usual in this situation.


I'm very new to Ubuntu and I want to know: what is the exact use of /etc/hosts?   Lets say I'm adding this into it :  127.0.x.x mydomain   What does that mean?


Can't put more than 10 digits into one variable in c++

Im suppose to create a loop that takes in a string input number and turn it to a integer variable so i could add 1 to the number and then turn it back to a string and print it out 5 times with 1 added to the number per print.The problem is, it only works up to 9 digits. if you put more then 9 then it starts giving other different numbers like -125346543.   if you put 9 digits 101010101. it will print it out 101010101 -> 101010106, but if you put 10 digits like 1010101010. it will print out -128764798 -> 128764804. I need it to print a least up to 13 digits  #include <iostream> #include <string> #include <sstream>  int main() {     int l=0;     int x=0;     string nope;     cout<<"please provide 13 digit code : ";     cin>>nope;                                // ask for 13 digit code for(i=0; i < 5 ; i++) {     stringstream geek(nope);                 // turn string to Int     geek>>x;     l = x + 1;                               // add 1 to Int     stringstream ss;                         // turn it back to string     ss << l;     string q = ss.str();     nope = q;     cout<<nope;                              // prints out }


Losing attribute table when working remotely

Because of the pandemic my work is strictly remote. I remote into my work computer via laptop. I have two monitors connected to that laptop. Sometimes when I move the ArcMap desktop program from one screen to another my attribute table is lost beyond the visual monitors and it takes a while to get it back. Online I found that unplugging and plugging my desktop from my monitors is the only thing that works. However it is only a stroke of luck that I can click on the attribute table before it disappears again. Every time this happens I loose a good 20 minutes. Does anyone have a better solution that doesn't involve randomness/luck or me going to the office to change my remote computer settings (we are not allowed in the office until May).


How do we know that light is made up of electric and magnetic fields?

What are the experiments that prove that light consists of electric and magnetic field oscillating perpendicular to each other. What are the experimental evidence we have for this theory of light ?


Almost every language has polite ways to say that someone is old and that someone is getting ones. Are they usual in English? If so, which is the most usual euphemism in English to express these two ideas nowadays? Below are the ones I am familiar with:  to be old   He is advanced in age. He is advanced in years. He is of advanced age. (less usual)   to get old   Aunt Betty is getting along in years


Ok, here is what I think. Please correct me if I am wrong. $$\sqrt{9} \neq 3$$ and also $$\sqrt{9} \neq -3$$  Now let's assume, that above statements are false, then we have $-3 = \sqrt{9} = 3$ and since $3 \neq -3$ the assumption must be wrong. Ok, square root must be equal to 3 and -3 at the same time. As of my understanding a set of numbers is not a number itself and that leads to a conclusion, that a square root of a number is not a number. Right?  Both answers are of the same importance - neither of them is superior. Then here is the question - when we plot $f(x) = \sqrt{x}$, why do we always plot positive answers? Can someone give me a proof, that plotting negative answers is not allowed?


Infinite product $\prod_{n=1}^\infty\frac{2}{1+\pi^{2^{-n}}}$ calculation problem

To calculate the infinite product $$\prod_{n=1}^{\infty}\frac{2}{1+\pi^{\frac{1}{2^n}}},$$ I found that $\sum_{n=1}^{\infty}\ln\left(\frac{2}{1+\pi^{\frac{1}{2^n}}}\right)$ converges, so as $\prod_{n=1}^\infty\frac{2}{1+\pi^{\frac{1}{2^n}}}.$   The task though is asking to calculate the product  and not just verify the convergence. Is there a mathematical way to calculate this product, or calculate this limit : $$\lim_{n\rightarrow\infty}\frac{2^n}{\left(1+\pi^{\frac{1}{2}}\right)\left(1+\pi^{\frac{1}{2^2}}\right)\cdots\left(1+\pi^{\frac{1}{2^n}}\right)}$$  Thank you for your time


I want to create a DEB file manually. I would like to just provide a folder which contains data to install, and a script to be executed after installation.  Is this possible?


How do I change the Wi-Fi hotspot channel?

Is it possibe to change the channel my phone broadcasts its Wi-Fi hotspot on?   Right now it's using the same channel as my neighbour (6). My router is reporting several unused slots.


I'm a new Ubuntu user.  I've installed Ubuntu 13.10 on my desktop alongside windows 7.  When I try to play any mp3 file with Parole Media player (which I believe is the default) , it says :     Parole needs MPEG-1 Layer 3(MP3) decoder to play this file. It can be   installed automatically.   Then I click Install and it gives error like Required plug-in could not be found.  Even when I am connected to the Internet .  I read many solutions on this very forum , but none of them seemed to work .   The last thing I tried was to manual download and install the MP3 plug-in package . It installed successfully, but I still can't play Music.


proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$

If $k$ is a positive integer, how to prove that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$


Food safety concerns regarding cooked steak stored in the fridge

I'm thinking of cooking some steak and storing it for later use in a cold salad. If I cook it to medium rare and cut it into strips and store it in the firdge, will it be safe to eat later? I know any bacteria mostly grows on the surface of the meat so that should be killed when cooked, but is there a higher danger of contamination on the now exposed, less cooked surface area?   If I put it in a clean container I'm guessing the pink parts are just as prone to further contamination as the outer surface.   If kept in this condition, how long should I expect this meat to stay good for in the fridge?  What would be different if we were talking about a partially eaten steak stored for later consumption?


WKT: What is the reasoning behind the concept of a POINT EMPTY?

In data formats like WKT and WKB, we have ways of representing "empty" geometries. That all pretty much makes sense: a "LINESTRING EMPTY" is a LINESTRING type with 0 vertices. Same with a MULTIPOINT, POLYGON, etc.  But what about POINT EMPTY? For starters, there is no WKB representation for a POINT EMPTY, only WKT. GeoJSON also doesn't define this case in its specification.  According to the Wikipedia definition of a , "points do not have any length, area, volume, or any other dimensional attribute". So how can it be empty, and why does the WKT specification allow this?


Jquery dynamically added forms are not clickable and do not allow any input (all the ui elements can not be focused or clicked)

I created a container to add elements to it as follow

 <button class="add-button" value="Add" />
   then on button click  $(".add-button").click(function () {     add($(this).parent().find(".form-container:first").prop("id"), getID()); });  function getID(){ var d = new Date(); return d.getYear().toString() + d.getMonth().toString() + d.getDate().toString() + d.getHours().toString() + d.getMinutes().toString() + d.getSeconds().toString() + d.getMilliseconds().toString(); }  function add(id, parentid){ var form = "
";  form += "
"; form += "
"; form += "<select><option value='1'>Item 1</option></select>"; form += "
" form += "
"; form += "<input type='text'/>"; form += "
" form += "
"; form += "<input type='checkbox' id='ck" + id + "'/>Only"; form += "
" form += "
";  form += "
"; form += "

"; form += "<button class='add-button' value='Add'/>"; form += "
";  form += "
"  $("#" + parentid).append(form); }   when click add button the ui created but i can't select from the dropdown list, the check box also is not clickable and text box does not allow input (all the ui elements can not be focused or clicked).  All UI displayed as image


Deep networks vs shallow networks: why do we need depth?

The  states that a feedforward neural network (NN) with a single hidden layer can approximate any function over some compact set, provided that it has enough neurons on that layer.   This suggests that the number of neurons is more important than the number of layers.  But in practice deep learning is obviously very successful at various prediction tasks. Why is that? Shouldn't all deep NNs be equivalent to single layered NNs with enough neurons? Why do we need depth?


mysterious error: \pdfendlink ended up in different nesting level than \pdfstartlink

I ran into the "mysterious"  \pdfendlink ended up in different nesting level than \pdfstartlink   error.  According to , "this happens when hyperref is used under pdftex and a citation splits across a page boundary".  The given solution is to manual fix the citation to not split across the page boundary.  However, this workaround isn't feasible for me, as the documents are automatically generated on a server with no user interaction.  Is there any solution to the problem known, perhaps an experimental hyperref action or a patch to pdftex?  (Probably, one could use luatex to solve the problem, but for other reasons, luatex is not an option in this project.)  MWE:  \documentclass[%draft               ]{article} \usepackage{hyperref} \setlength{\textwidth}{3cm} \setlength{\textheight}{3cm}  \begin{document} Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna \href{http://www.tug.org/errors}{aliquyam erat, sed diam voluptua.} \end{document}


Every continuous function on Q can be extended to R continuously. ls it true or false?

If I take $f(x)=1,\ \forall x \in \Bbb Q$ , then since $\Bbb Q$ is dense in $\Bbb R$, $f(x)=1,\ \forall x \in \Bbb R$. In this the answer should be true, but I don't understand that why the answer is given false.


I have a valid b1/b2 visa I obtained for the purpose of a conference last year, unfortunately I couldn't attend the conference for some family issues. Now I wish to use the visa this year, would that be allowed knowing that the conference has passed?


How to change row color? and to stop hover on row color

I need to change the color of the row in the table to red instated of gray color. i have used the playground but i cannot change it,     If you open this above link(Playground)the table ll be row with gray color but my requirement is it should be red color.there is any resolved solution to be red color row?   in this table row with gray color but i need lite red color . if i apply t1 to slds-theme_error , red colr came but hover on row color  if you open that link it ll show like this picture  There is anyway to avoid hover in slds table


How to install ubuntu alongside installed windows 8.1?

I am trying to dual boot windows 8.1 and ubuntu, but i don't know exactly how to do it, since i tried it once and it went really wrong. Now, as i said, i have windows 8.1 installed, and in system information, it appears "BIOS mode: legacy". However, i don't know if i need to install ubuntu in uefi mode or legacy mode. I already have Ubuntu on a usb stick ready to boot. I really am not very experienced in this kind of things. Can you help me? I really need ubuntu for university, but i also need windows. Thank you :)


Proving that $f(x) = \ln(x)$ is uniformly continuous on $[1, \infty)$

I was given the hint of using the Mean Value Theorem. I've gone over the definitions but am having a hard time seeing what to do.


What registry access can you get without Administrator privileges?

I know that we shouldn't being using the registry to store Application Data anymore, but in updating a Legacy application (and wanting to do the fewest changes), what Registry Hives are non-administrators allowed to use?    Can I access all of HKEY_CURRENT_USER (the application currently access HKEY_LOCAL_MACHINE) without Administrator privileges?


Where should I put the application icon for the application menu?

I've created an application entry for an app in /usr/share/applications/, just like this:  [Desktop Entry] Type=Application Encoding=UTF-8 Name=Sample Application Name Comment=A sample application Exec=/opt/application Icon=application.png Terminal=false Categories=Application   I noticed that many apps's Icon part in /usr/share/applications was just a file name, like application.png in the sample above. I guessed it should be a relative path. So where did most apps store its icon? If I want to follow the rule, which path should I put my icon in?


Filling back & front of text with different colors

Hi Im trying to make something similar to the image above, How can I color front and back with two different colors? Thank you!


**forgot my password which is needed for installation .cant download gnu plot now. please rescue my password.**I tried so many times.


Is there any way to enable Ctrl+L to clear screen when 'set -o vi' is set?

When you press Ctrl+L in bash default mode the screen is cleared. But when I run set -o vi and press Ctrl+L the keystroke is printed (^L). Is there any way to keep this behavior?


I have problem, I use this code:  \pagestyle{empty} \begin{center} \includegraphics[scale=0.8]{hahaha.png}\\ \vspace{1cm} \end{center}   But when I compile, the picture doesn't show.    What is the problem?


How to delete a file with a bad file name?

I had a file downloaded from torrent by a media center device on an external hard disk. The file has an invalid filename such as "Movie ** 480p ** NEW.wmv" (without the quotes). I cannot delete or rename the file in any way probably because of the asterisks "**" in the file name. Do you have any ideas what I can do?  Details: The external drive uses an NTFS file system. I tried Windows, Windows command line, OSX terminal, Ubuntu but could not delete it. I can see the file by "dir" or "ls" commands, but when I try to delete or rename I get "No such file or directory" or a similar error. So the file can be shown but cannot be operated on by all OSs I mentioned above. I thought I deleted it with Ubuntu Terminal commands but the file and the folder it is in is only moved to ".Trash" folder and it is stuck there.  I tried various suggestions in various forums:   rm -r rm * del * rmdir rmdir -r dir /x (does not work on Windows 8.1) find . -inum number_here -exec rm -i {} \; shell scripts in Linux to delete files rm "Movie ** 480p ** NEW.wmv" rm -- 'file_name_here' (and variants) chkdsk f: (This actually ended up with an error) Using 7Zip   ...and many other suggestions on different forums to similar problems, none of them work. My last option is using a hex editor and change the file name manually on disk but that may mess up the Master File Table. In addition, I could not locate what sector the MFT is.  One user on  solved this problem by connecting his drive to an Android system but my Android devices do not have USB connections and the original media center device cannot delete or rename the file either.  Any other suggestions?


I've always wondered about this and never found a good solution.  But  reminded me of it.  When I have a URL on my website it can be displayed and accessed any of the following ways:  http://www.somesite.com/subdirectory http://www.somesite.com/subdirectory/ http://www.somesite.com/subdirectory/index.htm http://www.somesite.com/subdirectory/index.html http://www.somesite.com/subdirectory/index.php http://www.somesite.com/subdirectory/index.asp http://www.somesite.com/subdirectory/some-relevant-keywords http://www.somesite.com/subdirectory/some-relevant-keywords.htm http://www.somesite.com/subdirectory/index.php?page=some-relevant-keywords http://www.somesite.com/subdirectory/?page=some-relevant-keywords http://www.somesite.com/subdirectory/?page=some-relevant-keywords&even=more-keywords   etc...   Now, I can understand the merits of adding keywords in the URL. Even the most basic SEO guide will mention to do just that. ... but for the sake of sanity, clarity, ease of reading, ease of use, and so on, including web compliance ...  Is it preferred to have a file-extension or not?  Really, deep down my logic tells me: yes, it should. The reason being is this stems back to the days of the past when the internet was mostly USENET, FIDONET, FTP and GOPHER.   See, if a URL has no filename, then it normally is considered a directory. This is where index.htm came about, because this by default lists the directory if no index file is found. However, soon enough, web programmers started overriding this and using index.htm to actually serve the content of that web directory as a page. The main difference, was markup language was added in, and this was parsed in the browser. With this markup language, the Content-Type:text/html; tag in the response header became the indicator to what filetype it was for any file. HTML seems to be the only "filetype" that just doesn't have consistently named extensions, except for when they are saved.  Unfortunately, once web pages became the main thing, it became a security error to actually display the directory contents, so everything stayed hidden with only the actual URL content being displayed.   Not to mention the cross-platform file-naming wars.. windows based require a 3 or less digit extension, and unix/mac can have more. So should it be .HTM or .HTML or NONE and let the platform decide?  So in essence, I guess what I am trying to figure out is beyond SEO and dealing more with aesthetics and web compliance.


I wrote this statement in the main method  the Exception will be in the (GuaranteeYears) so i put it in the try block.  First in the main I make a Store object and pass number 4 in parameter, in the Store class I will have a array called arrProduct that will have the length 4:  boolean flag1 = true; while (flag1) {     try {         System.out.println("Ente GuaranteeYears");         int GuaranteeYears=read.nextInt();          StrongDevice s = new StrongDevice(code,type,price,Model,Capacity,GuaranteeYears); //the object          flag1 = false;         x.addProduct(s);      }   and this is my add method  public boolean addProduct(Product p) {     if(arrProduct.length==NumOfProduct)         return false;      arrProduct[NumOfProduct]=p;     NumOfProduct++;     return true; }   My question is: when I make the object and add it to the array it gives me NullPointerException - why that happened?


when user click the ok button of windows alert box the meassage is copied to users clip board using jquery

I have copied the div element to the alert box. Now when I pressed ok button is it possible the text is copied to the user's clipboard.  Here is the code for reference:  $(document).ready(function(){     $("#bn").click(function(event){         $(alert($('#demo').text())     }); });


Let $S$ be a ring with subring $R$, both PIDs.  Let $a, b \in R$ with gcd $r \in R$.  If $s \in S$ is the gcd of $a$ and $b$ when considered in the larger ring $S$, prove that $r = su$ for some unit $u \in S$.  I am trying to exploit the fact that the ideal $(a, b) = (s)$ and any other generator of the ideal $(a, b)$ is a unit multiple of $s$.  It is clear from the definition of gcd that $r | s$ which implies that $(s) \subset (r)$.  These ideals are generated in $S$, I have given some thought as to what I get from considering them as ideals of $R$.  Still I can not see how to proceed.  Any suggestions are appreciated.  Thanks in advance.


Constants of proportionality in Force Equations/ Physics in General

I was in physics class and we were talking about the gravitational constant G (6.67 x 10^-11 Nm^2/Kg^2). The question came up:      "Why does $F= (GMm)/r^2$ have a constant of proportionality and not $F=ma$?"   Our teacher said that it had to deal with the way we define our base unit of measurement for force, the Newton, but didn't explain it much beyond that.  The following is my solution to the question. Please tell me if you agree with my logic.  In physics, we first realized force was proportional to the multiplcation of mass and acceleration so we decided to measure force this way. We defined our basic force unit, the Newton, so that 1 newton is the force that causes a 1 kg object to accelerate at 1m/s^2. When we plug these numbers into our proportionality for force, F=kma, and solve for k, k=1, and the equation turns to f=ma.  We also realize that there are other proportionalities for force, for example: F is proportional to (Mm)/r^2 or F is proportional to (Qq)/r^2. These can be rewritten in the form F=(kMm)/r^2 and F=(kQq)/r^2.   In order to solve for each of these constants of proportionality, we need to have one number for the right hand term and one for the left.  For example: When we measure the force of gravity between two 1 kg objects 1 m apart, the resulting force is 6.67 x 10^11 times smaller than the force accelerating a 1 kg object at 1 m/s^2. This is just the nature of the universe. Different types of forces have different strengths. If we called the latter force 1 newton, like we've defined it, then the gravitational force is 6.67 x 10^-11 N. Thus, in F=(kMm)/r^2, k must have a value of 6.67 x 10^-11.  However, we could've defined our units for force in terms of gravity. If we called the force of grav. between two 1kg objects 1m apart a Newton, then in this situation, G would equal 1.  This would also change our constants of proportionality in other equations. For example, F=ma would now be F=6.67 x 10^11 ma. This is because the force accelerating a 1 kg object at 1m/s^2 is 6.67 x 10^11 times greater than our gravitational force in the previous example which we named a newton. Therefore, using our new definition of the newton, this applied force is 6.67 x 10^11 N and k in f=kma must = 6.67x10^11.  From these examples, I draw some conclusions:  The way we define our unit of force determines our constants of proportionality in all our relations for force. Additionaly, changing the units we measured in would also change our k values. This would give us different values for the right and left hand terms of our proportionalities and thus k would change in those proportionalities.   Does my logic seem correct? I also have one more question: can we generalize the previous statement? Is it fair to say that the way we define any unit of measurement for any physical quantity determines the k values in all the equations for that physicaly quantity?


How to install "libqt5webview5-dev" on Ubuntu 16.04 LTS?

I'm not an expert, I'm on Ubuntu 16.04 LTS, and I'm trying to install Stremio by following this tutorial "https://github.com/Stremio/stremio-shell/blob/master/DEBIAN.md" from source codes. So in order to make it work, I have to install the "libqt5webview5-dev" package, but unfortunately I get the error "Unable to locate package libqt5webview5-dev". (sorry the following terminal outputs are in Fench) $sudo apt-get install -y libqt5webview5 Lecture des listes de paquets... Fait Construction de l'arbre des dépendances        Lecture des informations d'état... Fait E: Impossible de trouver le paquet libqt5webview5  I tried to add the "universe" repository but it was already enabled. $sudo add-apt-repository universe Le composant de distribution « universe » est déjà activé pour toutes les sources.  Maybe my distribution is too old ? Can you help me ? Thanks!


Why do some bash built-ins (such as dirs, pushd or help) don't have manual entries?


Installing Tails on Ubuntu and get a disk error

I've been searching for hours and can't find an answer to this.  I open Tails installer through the application finder, click install and select "tails-i386-2.11.iso".  I then click the USB that I am using SanDisk Ultra Fit (124.2 GB) - /dev/sda.  I click Install Tails and I receive this error:  tails-i386-2.11.iso selected Unmounting mounted filesystems on '/dev/sda' GDBus.Error:org.freedesktop.UDisks2.Error.NotAuthorized: Not authorized to perform operation Tails installation failed! udisks-error-quark: GDBus.Error:org.freedesktop.UDisks2.Error.NotAuthorized: Not authorized to perform operation (3)   I have sudo -s enabled, and I have tried GNOME and it still will not load it up.


Contrabasson or contrabass in the begining of this Harnoncourt recording of Johannespassion, BWV 245, Part 1: "Herr, unser Herrscher"

== Cross-posted so  due to recommendation in the comments == Consider . I can't figure out if the very low notes at the very beginning are played by a (contra)basoon or a contrabass (or both). I don't know how to figure this out since there is is no guarantee that Harnoncourt adhered to the instrumentation of any sheet music of this piece that I can find. To me, the first note really sounds like a string being played, while the other ones could also be a woodwind instrument playing. As noted , there is a contrabasoon player in the , but unfortunately, this doesn't help us to answer the question either. I'd be grateful for anyone with a more precise ear than me and even more for someone with a source for the correct answer of this question.


How does SE manage their domains and determine the ones to renew?

Stack Exchange  that were used for .  However, there doesn't seem to be a uniform way in which SE handles their domains. Examples below.    Some of these domains currently redirect to their respective contest sites, though almost all the redirects are broken. The SSL errors are probably broken by SE's .    [SSL error] for   [redirect broken] for   [redirect broken] for   [SSL error] for   [redirect broken] for   [redirect broken] for   [redirect broken] for   [redirect broken] for   [redirect broken] for    Some of these domains were not renewed and no longer owned by SE (!!!)    for   for    Some domains don't seem to have been used before but are randomly redirected to the contest main page (which is perfectly alright but I'd just want to point out).         Of course, this list isn't exhaustive and I've missed out some.  So,   How does SE manage these special one-time-use event domains?  Can the broken redirects be pointed to the correct sites? How does SE decide which of these domains to renew? Did SE purposefully let the expired domains lapse or ...?   * Also related: .


Solutions for preventing/removing raindrops on glasses when riding in rain?

I have to wear glasses when riding by bike and when it rains it can become hard to see my surroundings.  Wiping them with my hand/glove makes things worse as it smudges everything.  Before I resort to wearing contact lenses, I thought I'd ask if anyone has any clever ideas on how to prevent this from happening.


Complex number being grater than $0$ in the definition of inner product

I was reading the definition of inner product  and they state the following:  Let $V$ be a vector space over a field $\mathbb F$ ( $\mathbb R$ or $\mathbb C$). A map $\left< \cdot , \cdot \right>: V \times V \to \mathbb F$ is called an inner product if, for all $x,y,z \in V$ and $\alpha \in \mathbb F$:  $\left< \alpha x , y \right> =  \alpha \left< x , y \right>$ and $\left< x + z , y \right> = \left< x , y \right> + \left< z , y \right>$ $\left< x , y \right> = \overline{\left< y , x \right>}$ $\left< x , x \right> > 0$, if $x \neq 0$.   My question is about property 3. Let $V$ be a vector space over $\mathbb C$, then $\left< \cdot , \cdot \right>: V \times V \to \mathbb C$, this means that for all $x \in V$, $\left< x , x \right>$ is a complex number. So what do they mean by $\left< x , x \right> > 0$? Do they mean that the inner product of $x$ with itself is allawys a real number, so if $\left< \cdot , \cdot \right>$ is an inner product then $\Im(\left< x , x \right>) = 0$? If not, what does it mean for a complex number to be greater than $0$ in this context?


Is there a way to use apostrophes in sed commands?

Is there a way to use apostrophes ' with the sed command?     I mean this: -    sed '-2 a\\ What's up?' text     I am talking about the apostrophe in "What's up". If I do it like this it gives me an error "Unmatched"    I tried to escape that apostrophe with \ OR \\ like this What\'s up?, but it doesn't work.


problem with initialization by default in class Assignment operator and vector in c++

Hi i am having problems storing default instances of a class in a vector, when i use no default constructor everything go fine.  this is the class structure:  #ifndef NEURO_H #define NEURO_H  #include<iostream> #include<fstream> #include<vector>  using namespace std;  class neurona { private:     double v_r; //potencial de reposo     double v_u; //potencial umbral     double v_d; //potencial alcanzado al disparar  public:     neurona(double=-65.,double=-55.,double=35.) ;     ~neurona()          ;     neurona(const neurona &)    ;     neurona & operator = (const neurona &);  };   neurona::neurona(double r,double u,double d):v_r(r),v_u(u),v_d(d) {}   neurona::~neurona() {}  neurona::neurona(const neurona &z) {     v_r=z.v_r;     v_u=z.v_u;     v_d=z.v_d; }  neurona & neurona::operator = (const neurona & z) {     if(this!=&z)     {     v_r=z.v_r;     v_u=z.v_u;     v_d=z.v_d;     }     return *this; }  #endif   and this is the main      int main()     {     neurona n1()        ;     neurona n2(3.,3.,3.)    ;     neurona n3=n2   ;      vector<neurona> v_neu(3)    ;  v_neu.push_back(n1);  //v_neu[0]=n1; //v_neu[1]=neurona2; //v_neu[2]=neurona3;    cout<<"okidoki"<<endl; }   i get the following error     neurona.cc: In function ‘int main()’:   neurona.cc:15:11: error: no match for ‘operator=’ (operand types are ‘__gnu_cxx::__alloc_traits >::value_type {aka neurona}’ and ‘neurona()’)     v_neu[0]=n1;   In file included from neurona.cc:1:0:   neurona.h:41:11: note: candidate: neurona& neurona::operator=(const neurona&)    neurona & neurona::operator = (const neurona & z)              ^~~~~~~   neurona.h:41:11: note: candidate: neurona& neurona::operator=(const neurona&)    neurona & neurona::operator = (const neurona & z)              ^~~~~~~   if instead of using n1 in the push_back() use n2 everything works fine, the same with n3.


How to put small numbers outside the pie slices without making a mess

I'm new to LaTeX and need some help with my figures. I would like to to put small numbers outside the pie slices without making a mess. Having found this thread , I tried it out, but didn't get all the way through with it. Right now, my pie looks like this:    I used the following code:  \usepackage{tikz,stackengine} \makeatletter  \tikzstyle{chart}= [legend label/.style={font={\scriptsize},anchor=west,align=left}, legend box/.style={rectangle, draw, minimum size=5pt}, axis/.style={black,thin,->}, axis label/.style={anchor=east,font={\tiny}}]  \tikzstyle{bar chart}=[ chart, bar width/.code={     \pgfmathparse{##1/2}     \global\let\bar@w\pgfmathresult}, bar/.style={thin, draw=black}, bar label/.style={font={\bf\small},anchor=north}, bar value/.style={font={\footnotesize}}, bar width=.75,]  \tikzstyle{pie chart}= [chart, slice/.style={line cap=round, line join=round, thin, draw=black}, pie title/.style={font={}}, slice type/.style 2 args={     ##1/.style={fill=##2},     values of ##1/.style={}}]  \pgfdeclarelayer{background} \pgfdeclarelayer{foreground} \pgfsetlayers{background,main,foreground}  \newcommand{\pye}[3][]{     \begin{scope}[#1]         \pgfmathsetmacro{\curA}{90}         \pgfmathsetmacro{\r}{1}         \def\c{(0,0)}         \node[pie title] at (270:1.3) {#2};         \foreach \v/\s in{#3}{             \pgfmathsetmacro{\deltaA}{\v/100*360}             \pgfmathsetmacro{\nextA}{\curA + \deltaA}             \pgfmathsetmacro{\midA}{(\curA+\nextA)/2}             \path[slice,\s] \c             -- +(\curA:\r)             arc (\curA:\nextA:\r)             -- cycle;             \pgfmathsetmacro{\d}{max((\deltaA * -(.5/50) + 1) , .5)} %%%              %\pgfmathprintnumberto{#3}{\fnum}  %\ifthenelse{\lengthtest{#3 pt < 10pt}} %{\path (O) -- ++ (\midangle:\radius) %node[inner sep=0,align=left,anchor=west,rotate=\midangle](nums#3)    {~~\fnum};} %{\path (O) -- ++(\midangle:\innerpos)  %node {\scalefont{#3}\beforenumber\fnum\afternumber};}           %%%                         \begin{pgfonlayer}{foreground}                 \path \c -- node[pos=\d,pie values,values of \s]{$\v\%$} +    (\midA:\r);             \end{pgfonlayer}             \global\let\curA\nextA}     \end{scope}}  \newcommand{\legend}[2][]{     \begin{scope}[#1]         \path         \foreach \n/\s in {#2}         {++(0,-5pt) node[\s,legend box] {} +(2pt,0) node[legend label]     {\n}};     \end{scope}}      \begin{document}         \begin{center}      \begin{figure}[H]     \centering \begin{tikzpicture} [pie chart, slice type={A}{black!0}, slice type={B}{black!10}, slice type={C}{black!20}, slice type={D}{black!30}, slice type={E}{black!40}, slice type={F}{black!50}, slice type={G}{black!60}, slice type={H}{black!70}, pie values/.style={font={\small}}, scale=2]  \pye{1994}{6.1/A, 2.9/B, 0.2/C, 54.3/D, 25.2/E, 1.4/F, 6.7/G, 3.2/H} \pye[xshift=2.2cm,values of coltello/.style={pos=1.1}]% {2005}{6.8/A, 3.0/B, 0.5/C, 52.3/D, 25.6/E, 1.8/F, 7.1/G, 2.8/H} \pye[xshift=4.4cm,values of caffe/.style={pos=1.1}]% {2015}{7.2/A, 3.1/B, 0.6/C, 50.6/D, 26.5/E, 2.3/F, 7.5/G, 2.2/H}  \legend[shift={(0cm,-1.5cm)}]{{A}/A, {B}/B}  \legend[shift={(1.4cm,-1.5cm)}]{{C}/C, {D}/D}  \legend[shift={(2.8cm,-1.5cm)}]{{E}/E, {F}/F} \legend[shift={(4.2cm,-1.5cm)}]{{G}/G, {H}/H} \end{tikzpicture} \end{figure}  \end{document}   This looks quite the way I want it to, only the small numbers should be placed outside the pies.  Thanks in advance :)


I have nearly 150 Panel pages and different template files. I generated lot of blocks using  module to be used in the Panel pages.   I guess this is causing memory issues in both MySQL and Apache configuration. Any solution for this memory issues?  My global memory_limit is 128M. Only after setting 512M in settings.php, my custom Drupal View is generating the output (otherwise, it generated a 502 error).  Is there a way so that I can set memory_limit only for my custom View?


{w| w ∈ {a, b} * is not a palindrome} Prove this language is not regular.

I've been doing some work to prove some languages are not regular. I have previously used pumping lemma to prove by contradiction. However I am used to questions which ask to prove languages such as {a^n b^m| n ̸= m} ⊂ {a, b}* are not regular. I would use pumping lemma for these but now I have come across this language.  {w| w ∈ {a, b} * is not a palindrome}  I'm unsure how to prove it is irregular. Can it be done with pumping lemma? Or another method?


Built-in card reader in MacBook Pro doesn't work

As the title says, the built-in card reader in my MacBook Pro doesn't work. It simply doesn't do anything when I instert an SD card. I'm using Mac OS X 10.6.8.  I guess one of the issues might be Parallels. I have it installed, but it's not running. In the properties of Parallels I've set that all USB devices should be loaded in Mac.


For the spell polymorph, it says that you keep your alignment and personality. Does that mean when an evil character polymorphs into a t-rex, he will attack his friends and team?


The Two Cultures: statistics vs. machine learning?

Last year, I read a blog post from  entitled  that discussed some of the differences between the two fields.  :  Simon Blomberg:      From R's fortunes   package: To paraphrase provocatively,   'machine learning is statistics minus   any checking of models and   assumptions'.   -- Brian D. Ripley (about the difference between machine learning   and statistics) useR! 2004, Vienna   (May 2004) :-) Season's Greetings!   Andrew Gelman:     In that case, maybe we should get rid   of checking of models and assumptions   more often. Then maybe we'd be able to   solve some of the problems that the   machine learning people can solve but   we can't!   There was also the  by Leo Breiman in 2001 which argued that statisticians rely too heavily on data modeling, and that machine learning techniques are making progress by instead relying on the predictive accuracy of models.  Has the statistics field changed over the last decade in response to these critiques?  Do the two cultures still exist or has statistics grown to embrace machine learning techniques such as neural networks and support vector machines?


I have an iPhone 4s running on iOS 8.1.3. I've owned it for about 2-3 years now and have taken good care of it physically and hardware wise. But recently my phone had died. I plugged it in to the charger no problem right? I come back about 20 minutes later to see nothing had changed... I tried adjusting the cord, trying to power down the device, rebooting, safe mode, and just letting it sit without the cord and retrying to charge it. Nothing worked; the phone just kept blinking the red battery logo even of 1 entire day of charging. What is there to do?


What is the meaning of Planet of the Apes(2001) movie ending?

In the last scene of the movie,       Leo gets into the pod and returns back to the electromagnetic field.  He is pushed back in time - the display of the pod starts somewhere  around 2700 and reaches somewhere around 2100. (The original time when  Leo left earth was 2029) The past earth seems to be now inhabited by  Apes and somehow Thade is considered a hero in this world.   How the heck did this happen? What is the meaning of this ending?


Linearity of complex-valued function from application of Liouville theorem

I am trying on problems from Bak and Newman's complex analysis. On the part of regarding Liouville's theorem, there were quite a number of problems concerns and an inequality and then ask you to prove that the complex-valued function is a linear one. An example is the following:  Suppose $f$ is entire and $|f(z)|\leq A+B|z|^{3/2}$ for constants $A,B$. Show that $f$ is a linear polynomial.  I hope someone can solve one of them for me. It will be helpful for me to understand problems of similar type once I understand this one!  Thanks in advance for answering.


Why do these Bootcamp windows look different?

On my Mac Mini Mid 2011, the Bootcamp window looks like this:  However on my Mid 2011 iMac - the computer where I want to make the install - the window looks like this:  Upon installing, the Mac Mini's window looks like this - and lets me select a disk image present on the hard drive or an external drive:  However on the iMac it doesn't allow me to select a .iso image:  And when I try to make the install on the iMac, I get a message saying:  Why are the steps in both High Sierra OS different? How do I proceed to install the .ISO of Windows 8.1 that I have on the iMac?


Draw cells in a 3D plot with only cell center data

I have data that is basically 3D (x,y, and temperature), a simple top view 3D plot in pgfplots  \documentclass{standalone}  \usepackage{tikz,pgfplots}  \begin{document}  \begin{tikzpicture}   \begin{axis}[view={0}{90}]    \addplot3[surf] coordinates {      (-1.5,-1.5, 20) (-0.5,-1.5,21)  (0.5,-1.5, 22) (1.5,-1.5,21)        (-1.5,-0.5, 21) (-0.5,-0.5,23)  (0.5,-0.5, 22) (1.5,-0.5,20)        (-1.5,0.5, 22) (-0.5,0.5,23)  (0.5,0.5, 24) (1.5,0.5,21)        (-1.5,1.5, 21) (-0.5,1.5,20)  (0.5,1.5, 21) (1.5,1.5,22)    };   \end{axis}  \end{tikzpicture} \end{document}   looks like this:    However, each of the points represents a 1x1 square, so the plot above should have 16 instead of 9 tiles, and span from (-2,-2) to (2,2).  How can I do that?


I have an object that is similar on one side and the other. However, the UV image editor UNwrapped it so that each half has slightly different vertex positions. How can I get it so that all the vertices line up?


Why am I getting a black spot in the cylinder. The scene is nothing special consists of few objects with no materials except for the cylinder, and lighting comes from the environment map.  The cylinder is smooth shaded and simply using a glossy material with the default settings.  Could this possibly have to do with render settings. I have tried re-adding the cylinder and creating a new glossy material but with the same results.


Windows 7 can not rename a file to 'aux.svg': "The specified device name is invalid"

I use Windows 7 x64. You can try this on your computer, too.  Go take any file. Try to rename it to 'aux.svg'. Windows will answer with     The specified device name is invalid.   I tried this on two different computers (also Win7 x64), with the same results. You can take any file you want. You can not rename it to 'aux.svg'. Dropbox will not download a file with that name. The browser will rename it to '_aux.svg' when downloading. This seems to happen in any directory I cared to try.  What the heck is happening here?


var directory showing its full via command 'df-h'

df -h shows:  df -h Filesystem     Size    Used   Avail Capacity  Mounted on /dev/ada0p2    1.9G    256M    1.5G    14%    / devfs          1.0K    1.0K      0B   100%    /dev /dev/ada0p4    804G     34G    706G     5%    /usr /dev/ada0p5     93G    3.5G     82G     4%    /var   but, du -sh shows:  du -sh /var 3.5G    /var   Why? df is telling me i have no space out of the 93G but when i check the file size of the /var/ directory it amounts to 3.5G?  Can any one explain why this is please?


What are the main differences between VirtualBox networking types?

I'm trying to use VirtualBox to host a couple of VMs.  Each VM should be able to connect to the Internet (this is needed primarily to install software) My Host browser should be able to connect to the Guest VMs.  Also I need to be able to ssh to the Guest VMs.     This is why I want each VM to have a static IP address.     This will also allow the VMs to connect to each other, say for database connectivity.  I have done this with VMware Fusion.  However, VMware has lately bitten me too often and destroyed so much work that I want to try VirtualBox.  But I'm not a network guru and don't know which type of networking I want.  So what I'm asking is simple:  What are the main differences between networking types. This could help me find out which type of networking I should use in my case.  And of course if anyone has a link to any documentation of how to do what I want, that would be greatly appreciated.  Thanks, ge


Could I attune a magical item to my pet cat? There don't appear to be any base requirements for attunement.


I am trying to add a geometry column to an existing table in PostgreSQL inside a plpgsql function using   EXECUTE format('ALTER table %I add column geom geometry(Point, 102003)', target_table);   Its raising an error "type "geometry" does not exist".   There is PostGIS extension installed in the database which I am running. Only thing is my table are not in public schema.


Best way to cite collaborators that are unaffiliated with an academic institution or business?

I am the lead author on a journal paper to the IEEE, and I'm trying to figure out how to cite other contributors in a way that makes sense.  Two of us are affiliated with a university, one contributor is a wonderful and knowledgable mathematician whose "real job" is in the service industry, and the other contributor is also a math nerd who is a barista in another country that did all of the proofs.  Would these non-conventional authors be "independent" or "unaffiliated" or some other term.  The affiliation is required by the journal.  Any suggestions (or a definitive source) of how to handle this issue would be appreciated.


Do we influence our emotions or do our emotions influence us?

The activities that we choose can influence our emotions such as doing a fun activity will make you happy, but our emotions also make us choose our actions such as a breakup could make you angry. Is one more likely than the other or are they equal?


Question on binomial expansion - divisibility

I am not able to solve this problem  Show that the integer just greater than $( \sqrt{3} + 1 )^{2m}$ contains $2^{m+1}$ as a  factor.  Any help would be thoroughly appreciated


In a problem based on selection of a team from the set of players ={R,S,T,U,V,W,X,Y,Z}, one the constraints is      Unless T and U are selected then V is selected.   I would like to know the propositional logic statement for this.  I understand "cond_A unless cond_B" logic but what does      Unless A then B mean?   Furthermore, in the specific scenario can T,U,V all be seleceted in the team?


Which site do Excel (or other spreadsheet) formulas belong on?

I just voted to close . The question, on Stack Overflow, is simply about an Excel formula. I felt it belonged on , so I voted to close.  Is my logic there correct, or would Excel-fu be acceptable on Stack Overflow? (This is a fairly easy formula, if that matters any.)


What is the difference between OpenOffice and the newly created LibreOffice?

What is the difference between OpenOffice and LibreOffice? I understand that LibreOffice is another fork that is going to be developed. I have used OpenOffice since v1 and am wondering if there is a definite advantage to uninstalling and trying LibreOffice.


"wire' in "Understand That People Are Wired Very Differently"

I am reading book "Principles: Life and Work" by Ray Dalio  In chapter 4 of Part II, Understand That People Are Wired Very Differently, “Because of the different ways that our brains are wired, we all experience reality in different ways and any single way is essentially distorted. This is something that we need to acknowledge and deal with. So if you want to know what is true and what to do about it, you must understand your own brain. ”  I am unable to grasp the meaning of 'wired' here.   is defined as a verb in OED as:   Install electric circuits or wires in. Provide, fasten, or reinforce with wires. Send a telegram or cablegram to. Snare (an animal) with wire. Obstruct (a ball, shot, or player) by a hoop.   I find none of them fit the context.  How to understand the 'wire' here?


I have a large set of images that I want to stitch the together and orthorectify. They have been taken from a small aircraft. The camera of the aircraft is tilted, thereby, although gps data is available, the image position and the gps position are different. I have tried some software such as Microsoft ICE and PTgui with no luck.  How could I proceed?


How can I use text-processing tools to insert a new line after every N lines?  Example for N=2:  INPUT:   sadf asdf yxcv cxv eqrt asdf   OUTPUT:   sadf asdf  yxcv cxv  eqrt asdf