Is it possible to pagebreak aligned equations?

The report I'm writting features a lot of long, multiple lines equations. To reduce visual polution I've been using an aligned environment nested inside equation. This way (unlike just using an align environment) I get only a single label for all the lines.  The problem is that so many long equations often need to be broken into two pages, otherwise I get lots of blank vertical space in the document. However the aligned environment does not allow the \displaybreak command.  Is there an alternative way to achieve a pagebreak inside an aligned equation?  Here's a sample ofthe equations I'm using  \begin{equation}     \begin{aligned}     ...\\     ...\\  %I need to pagebreak here     ...\\ \end{aligned}\end{equation}


How do I resize hard disks on ubuntu 14.04 lts?

After having installed Ubuntu on to my Toshiba Satellite laptop, I realised that I had mistakenly set up the boot partitioning wrong after experiencing lagging issues. Instead of having 200gb of storage I have just under 20gb. This is the only thing spoiling my experience and I was hoping someone would know how to sort it without too much complication. I'm currently dual booting wind pre-installed Windows 8.1 with UEFI/EFI and I don't want to risk corrupting either my windows or ubuntu operating system.


How to down-weight older data in time series regression

In a regression fit of vectors varying with time $t$ $\qquad y \sim [x_t\ x_{t-1}\ x_{t-2}\ ...] \cdot [c_t\ c_{t-1}\ c_{t-2} \ ...] $ , how can one down-weight the older $x_t$ to model "older is less relevant" (than the regression gives) ? Say that rows in data matrix $X$ are observables (stocks, market segments ...) and columns are times. Correct me,   weights rows; how does one weight columns, times ?  Added: Down-weighting older data in time series looks complex, much more so than linear least squares with i.i.d. errors in rows (observations) -- just divide through by $\sigma_i$; or classification  with i.i.d. errors in columns (e.g. features) -- just centre each column. Can anyone say either   yes, I downweight time series; here are some examples on the web no: down-weighting time series is complex, not for novices.   (  discussed this question 10 years ago, mentioning Kalman filters and hierarchical Bayes, but with no examples.)


What is a word to accompany horizontal and vertical?

If 'horizontal' follows the horizon, and 'vertical' ascends from the horizon, is there a word for a line from the viewer to the horizon? Otherwise, is there a broadly accepted business term for describing data where there are two horizontals, but one is an iterative representation of the first?  Specifically, this word would be used in a business sense to represent a second horizontal of accompanying data that would be something of a Y axis to an X axis. (This is not immediately for purposes of verbal presentation.) Is there a specific term that describes this relation in a business context? I want a word that won't alienate listeners unfamiliar with unrelated fields of study.  While 'longitudinal' is helpful in , this does not differentiate itself from 'horizontal', which is a common term used in business to describe a broad area, as opposed to a 'vertical' describing a focused area of specialization.  Alternatively, is there a business construct that addresses horizontality, verticality, and adds the ability to describe depth that can be utilized instead that relies on these concepts?


When an image is inserted in a pdf with the graphicx package, a right click on the image in the output gives the possibility to copy the image. My question is how can one block this possibility?   I guess there is an option in the graphicx package to do so, but I couldn't find it in the package manual (I find this manual not very helpful, especially for the neophyte).  As requested, here is a Minimal Example (where image is any image .jpg):  \documentclass{article}  \usepackage{graphicx}   \begin{document}      \begin{center}      \includegraphics{image}    \end{center}   \end{document}


Output the number of pairs that are in the wrong order in an array?

For example I have the array:  int IDs[]={1,21,5,3,12,23,2};   The number of pairs that are in the wrong order is 9. The pairs are: (21, 5) (21,3) (21, 12) (21,2) (5,3) (5,2) (3,2) (12,2) (23,2).  So , my algorithm for this implies two for's:     for(int i=0;i<IDs.length;i++)     {         for(int j=i+1;j<IDs.length;j++)         {             if(IDs[i]>IDs[j])                  wrong++;                      }     }   The problem is that this has a complexity of n2 and I should have a complexity of maximum n*log n.


Is Transit visa required for Doha layover?

My fiance is traveling from Dubai back to the USA with a layover in Doha, Qatar for two hours.    Does he need a Transit visa?


So I am just trying to create a simple draw view where a user can draw on the screen. However after hours of research I still seem to be having trouble solving why, when I call canvas.drawPath() in my onDraw() method, the app crashes. (I have omitted touch methods here)  public class DrawTing extends View{  private Bitmap bm; private Canvas canv; private Path path; Context context; private Paint paint1; private Paint paint;  public DrawTing(Context c) {     super(c);     this.context = c; }  public DrawTing(Context c, AttributeSet attrs) {     super(c, attrs);     this.context = c; }  public DrawTing(Context c, AttributeSet attrs, int defStyle) {     super(c, attrs, defStyle);     this.context = c;      path = new Path();      paint = new Paint();     paint.setDither(true);     paint.setAntiAlias(true);     paint.setColor(Color.GREEN);     paint.setStyle(Paint.Style.STROKE);     paint.setStrokeJoin(Paint.Join.ROUND);     paint.setStrokeWidth(10f);  }  @Override protected void onSizeChanged(int w, int h, int oldw, int oldh) {     super.onSizeChanged(w, h, oldw, oldh);      bm = Bitmap.createBitmap(w, h, Bitmap.Config.ARGB_8888);     canv = new Canvas(bm); }  @Override protected void onDraw(Canvas canvas) {     super.onDraw(canvas);     canvas.drawPath(path, paint);      //NPE here      //Things I have tried along with canvas.drawPath()      //canvas = this.canv     //canvas = canv;     //canvas = new Canvas();     //canvas.drawRect(0,0, getWidth(), getHeight(), paint);     //canvas.drawColor(0xFFAAAAAA);     //canvas.drawBitmap(bm,0,0, paint);  }   My logcat is displaying this error message:   FATAL EXCEPTION: main                                                               Process:   com.ting.cian.ting, PID: 7989   java.lang.NullPointerException: Attempt to read from field 'boolean   android.graphics.Path.isSimplePath' on a null object reference                                                                   at   android.graphics.BaseCanvas.drawPath(BaseCanvas.java:295)                                                                   at   android.graphics.Canvas.drawPath(Canvas.java:1652)                                                                   at   com.ting.cian.ting.DrawTing.onDraw(DrawTing.java:124)                                                                   at   android.view.View.draw(View.java:19119)                                                                   at   android.view.View.updateDisplayListIfDirty(View.java:18069)                                                                   at   android.view.View.draw(View.java:18847)                                                                   at   android.view.ViewGroup.drawChild(ViewGroup.java:4214)                                                                   at   android.view.ViewGroup.dispatchDraw(ViewGroup.java:4000)                                                                   at   android.view.View.updateDisplayListIfDirty(View.java:18060)                                                                   at   android.view.View.draw(View.java:18847)  ...   Thanks for your time!


I do not want the section numbered, i.e., Roman number I. (as the following figure show). How can I do this?


okular snap package doesn't appear in applications and command 'okular' is not recognized

I've installed okular from snap  snap list Name              Version  Rev   Developer  Notes core              16-2.30  3887  canonical  core kde-frameworks-5  5.37.0   13    kde        - okular            16.12.3  3     kde        -   when enter command okular in shell  okular The program 'okular' is currently not installed. You can install it by typing: sudo apt install okular   It also doesn't appear in the application list. the only way to launch okular is from software center.


Why is my Ubuntu so slow on Virtual Box? (MacBook Pro)

I recently downloaded Virtual Box and Ubuntu to do some quant trading and ran into some issues with the installation process of Ubuntu in Virtual Box itself. I googled some solutions but have run into some problems with some of them while some others have worked but Ubuntu is still slow.   1) I enabled 3D acceleration which made it a little faster but still quite slow.   2) I tried to install CompizConfig via Homebrew but it wouldn't install. brew install compizconfig-settings-manager && ccsm is what I tried but I found get a "No formulae found in taps error".   Could someone suggest what is going wrong with this process? How should I make my Ubuntu run faster in my virtual machine? Will assigning more RAM to it help?  Edit- Just to be clear, my Ubuntu's screen goes black due to unresponsiveness during the installation process itself.   Thanks in advance!


Why do we need a safelight in the darkroom?


Show that $\sum_{n=0}^\infty \binom{n+2}{2}x^n$ converges for $|x|<1$ and calculate its sum

Show that $\sum\limits_{n=0}^\infty \dbinom{n+2}{2}x^n$ converges for $|x|<1$ and calculate its sum.  My attempt: $$\sum\limits_{n=0}^\infty \dbinom{n+2}{2}x^n=\sum\limits_{n=0}^\infty \frac{(n+2)(n+1)}{2!}x^n=\frac{1}{2}\sum\limits_{n=0}^\infty (n^2+3n+2)x^n$$ We look for absolute convergence of the power series: $$\lim\limits_{n\longrightarrow\infty}\left|\frac{((n+1)^2+3(n+1)+2)x^{n+1}}{(n^2+3n+2)x^n}\right|<1$$ $$|x|\lim\limits_{n\longrightarrow\infty}\left|\frac{n^2+5n+6}{n^2+3n+2}\right|<1$$ $$|x|*1<1\Longleftrightarrow|x|<1$$ The power series converges $\forall x \in \mathbb{C}:|x|<1$ $\Box$ Now we calculate its sum: $\frac{1}{2}\sum\limits_{n=0}^\infty (n+1)(n+2)x^n$ First of all, we know (for $|x|<1$): $$\sum\limits_{k=0}^\infty x^k=\frac{1}{1-x}$$ Since the power series converges in a radius of $\rho=1$ we can differenciate elementwise: $$\sum\limits_{k=0}^\infty \frac{d}{dx}x^k=\sum\limits_{k=0}^\infty kx^{k-1}=\frac{1}{(1-x)^2}$$ Differenciating another time gives us: $$\sum\limits_{k=0}^\infty \frac{d}{dx}kx^{k-1}=\sum\limits_{k=0}^\infty k(k-1)x^{k-2}=\frac{2}{(1-x)^3}=\sum\limits_{k=-2}^\infty (k+2)(k+1)x^{k}$$ This gives us: $$\frac{1}{2}\sum\limits_{n=0}^\infty (n+1)(n+2)x^n=\frac{1}{2}\left(\frac{2}{(1-x)^3}\right)=\frac{1}{(1-x)^3}=\sum\limits_{n=0}^\infty \dbinom{n+2}{2}x^n$$  It would be great if someone could look over it and check if my work is correct :) thank you


Light fixture with a switch that has an outlet

I hope this explains it better: in this room there is a switch with one set of wires and only the black one went through the hole in it, and another black one in the other hole, and is hooked to the outlet by being wrapped around the screw terminals. The ground is cut short and not grounded.  Now on to the outlet: the wire from the switch is connected to the top screw - but it's on the side that says "white".   There are two more sets of wires that connect to the outlet as follows:   the two black ones are on the the other screw terminal on the bottom (one on the "white" side)  the grounds are grounded to the screw terminal below that  the white ones are connected by the one from the switch to the bottom (black side), with one of the white ones from the other set on the screw terminal, and the one from the other cable is on the top screw terminal on the "white" side.   Now to the light: there are the black and white that come out of the box, and that is the set that has the ground cut short.  The original light fixture was a single 660w/250v rated socket.  The one my friend put up was a fixture with two 660w /250v sockets.  At the light only black and white connected, not ground... It worked then made noise and this is where I'm at.  When I wire test them, the black one from the switch and the white ones from either sets nothing...  but all the other ones light up.....!


Can a human being live without any carbohydrates?

Nowadays low-carb is in fashion, but what I recently wondered is whether a human can live without any carbohydrates at all?  Of course this would be hard to do in reality, as most food will contain proteins as well as carbohydrates, but let's assume it would be possible to circumvent any carbohydrates.


How did evolution support sports, fun, entertainment etc

We know that many animals entertain themselves by playing games. But sports actually increases risks of death,or at least accidents. So why did evolution choose it? And why did evolution decide to make us look for entertainment every now and then?


Why is this substring problem returning false?

Why is this coming out as false?   public class practice  {    public static void main(String [] args)     {       System.out.println(startHi("hi "));    }     public static boolean  startHi(String str)     {        System.out.println(str.substring(0,2));        if(str.length() < 2)         {           return false;        }        else if(str.substring(0,2) ==("hi"))         {           return true;        }        else         {          return false;        }    } }


Can I open terminator with one windows with bash and another with fish?

So I am running terminator 0.98. I like fish shell but for some task it is handy to have bash (like for virtualenvwrapper). So I now have two windows that open when I start terminator. But I would like to have one that opens with fish and one with bash. Is this possible, if so: how?  I start terminator with my custom layout by changing my config file located ~/.config/terminator/config.   In the layout section of the config file I used this code.  [layouts]   [[default]]     [[[child0]]]       fullscreen = False       last_active_window = True       maximised = True       order = 0       parent = ""       size = 1280, 985       type = Window     [[[child1]]]       order = 0       parent = child0       position = 490       ratio = 0.5       type = VPaned


Is there a difference in these two sentences, and if so, what is the difference?   Immediately afterwards I remembered having met her. I remembered having met her immediately afterwards.   I think there is a difference but cannot identify what it is.


Why does it use typename in "typename Operation::second_argument_type(x)"?

This is the bind2nd definition:   template <class Operation, class T>     binder2nd<Operation> bind2nd (const Operation& op, const T& x)     {       return binder2nd<Operation>(op, typename Operation::second_argument_type(x));     }   And the key word typename can be used to:   In a template declaration, typename can be used as an alternative to class to declare type template parameters. Inside a declaration or a definition of a template, typename can be used to declare that a dependent name is a type.   So, I think typename is used to declare that Operation::second_argument_type is a type, but I want to know why we need to use typename here ?Can't we use it ? What is the advantage to use it ?


How to install utorrent.tar.gz on ubuntu 13.10?

I know to install software from terminal using some sudo apt-get stuffs but I can't install utorrent by terminal. So, I download .tar.gz from their website. So please instruct me how to install .tar.gz or say the way to install it from terminal friends.


So on several websites, including phys.org and physics.stackexchange, I have read that photons do not experience time. And that if you travel at the speed of light, time and distance shrink to 0.  Is this really the case? Or is this simply one of those analogies gone wrong type thingy?  If this is the case, I have a couple of questions:   If light emitted from a star x lightyears away reaches earth, has it truly not experienced time, or any change?  Does this mean that from its point of view, as soon as it left x, the earth was already there? This seems very counterintuitive, since then for light the future is already set in stone, leading to a deterministic universe? What happens if at the time it leaves x, I put something in its path to earth? Yet before it reaches it, I put it away again. Will that object never have existed? How does it deal with the time it took me to put the obejct there and remove it?  Given 3, is there simply no space and time between begin and endpoint? Does it simply not exist between these points? Since speeds are relative, one could just as easily take a perspective that the photon is fixed in space and everything else is moving relative to it.. So where does from its perspective the earth get its energy from to attain this speed? What is a good book to read on relativity, or about the maths needed to understand this? Because I get a feeling it's always the case that the explanations are faulty when there was no math involved. Can we even take the reference frame of a photon? Because since it appears if we can it would lead to all these problems above, so I'm guessing for some reason we can't? If so, why not?   Feel free to answer one, multiple or all questions. I'm not afraid of math although my understanding is lacking, so explanations in that regard would be much appreciated. :)  Bonus question (really out there and more philosophical what-if than semi-serious pondering): 8. If all reference frames are equally valid (perhaps not the photon), and assuming spacetime is grainy at the planck scale, could this not lead to an apparent continuous spacetime since all dilations and contractions would be equally valid? In a sort of integer to rational numbers type difference?


When iterating through a list in python, how can I get the current number of "i"?

I have a list and am iteratively performing a function on each item. I am trying to print out how far through the iteration the script is. The problem is that I can't easily get the position.  Here is what I have so far, but it generates a ValueError: 'item' is not in list.:  that_number = len(mylist) for i in mylist:       this_number = mylist.index(i)      print this_number, " out of ", that_number      DO SOMETHING print "Done!"   I am aiming for the output:  1 out of 3 2 out of 3 3 out of 3 Done!    is related in that it is trying to find the position in a list, however is there a valid way of getting the element position without using enumerate?


What is the meaning of axe in: "Axe me a question!"   Thank you for your time.


Windows Server 2008 R2: *Show* all users at login screen

This question is essentially the opposite of:   In my case, I'm trying to convince Windows 2008 R2 to show all (or, at least 2) users.  Previously, I did have registry entries under:  HKEY_LOCAL_MACHINE\Software\Microsoft\Windows NT\CurrentVersion\Winlogon\SpecialAccounts\UserList  However, at this point the SpecialAccounts key has been deleted.   Within gpedit.msc, under:Computer Configuration\Windows Settings\Security Settings\Local Policies\Security OptionsMy current "Interactive Logon" settings are:   Display user information when the session is locked: User display name, domain and user names Do not display last user name: Disabled Do not require CTRL+ALT+Delete: Enabled   With these settings, upon first logging in all I get is text fields for Username and Password; no click-able icons.  ...perhaps there's a setting elsewhere that I need to adjust in order to get click-able user icons for all users to show up on the logon screen?  Thanks in advance,  Nathan


Why can't you use the word "me" before a proper noun?

As per the title, I don't understand why it is grammatically incorrect to say "me and John went to the park" as opposed to "John and I went to the park." Is any help on this available?


How can the discrete atomic spectrum be observed?

My teacher told me that in an atom (assume hydrogen), as soon as the single electron absorbs a photon with the right amount of energy, it jumps up to another energy level, and instantly falls back down to the initial one, releasing a photon with the same wavelength as the one it absorbed. So, if I place a source of white light, and in front of it a sample of hydrogen, and then a prism, according to what I have read so far, the screen should show an absorption spectrum, but why would it? Since the electrons are falling back down in all the hydrogen atoms almost instantaneously, they should give out the specific wavelengths of light which form the emission spectrum, which, I think, would combine with the previous one (absorption spectrum) to give a continuous spectrum? TL;DR: If a sample of hydrogen atoms is excited by white light, why don't the electrons getting excited and coming down instantly give absorption and emission spectrums respectively, which would combine to give a continuous spectrum? **NOTE:**I would have the same question regarding emission spectrums, but I assume all the atoms in the discharge tube would be excited (so no room for further absorption and production of an absorption spectrum), which would give out just the emission spectrum of hydrogen.


For a language $L$ is $Double(L)=\{w: ww\in L\}$ regular?

Given a language $L$, let $Double(L)=\{w: ww\in L\}$ and $NotDouble(L)=\{w: ww\notin L\}$  If L is regular, are $Double(L)$ and $NotDouble(L)$ regular? I tried using the closure properties of $L_{reg}$ but I figured out that $Double(L) \cup NotDouble(L)$ are not complementing  of $L$. I tried thinking about the regular expression of $L$ but I couldn't get anywhere with it. I saw this question but I couldn't understand the answers. Is there a way to prove this using regular expressions, automata and closure properties only?


Solve $y^2=x^3-4$ in $x,y\in \mathbb{Z}$

I am having trouble solving the diophantine equation given in the title. This is how far I came:  We can factor in $\mathbb{Z}[i]$ $y^2+4=x^3\Rightarrow (y+2i)(y-2i)=x^3$. I want to show now that their gcd is a unit so in $\{\pm 1,\pm i\}$. Suppose $d=u+vi$ is the gcd, then $u+vi\text{ | }2y$ and $u+vi\text{ | }4i$. Now taking the norm, we find $u^2+v^2\text{ | }4y^2$ and $u^2+v^2\text{ | }16$. From the second part we find that $d=u+vi\in\{\pm 1,\pm i, \pm 4,\pm 4i,\pm 1\pm i,\pm 2\pm 2i\}$. Obviously $\pm 4$ and $\pm 4i$ cannot divide $y\pm 2i$. I don't know how to show it for the others.   If we assume that $y+2i$ and $y-2i$ are coprime and using the equation $(y+2i)(y-2i)=x^3$ we find that $y-2i=\epsilon \alpha^3$ and $y+2i=\delta \beta^3$ where $\epsilon$ and $\delta$ are units. From here on it is straightforward to find what $\alpha$ and $\beta$ can be. My only problem is showing that $y-2i$ and $y+2i$ are coprime.


prove that $\lim_{n\to∞} \frac{n!}{n^n}=0$

any sugestions?, by Stolz–Cesàro?. The trouble says that first try with $k<n$ and then for a particular $k<\frac{n}{2}$ I try by definition of $\epsilon$ but it doesn't help


What is a simple way to let a command run for 5 minutes?

Is there an easy way to let a specific command (only terminable through Ctrl-C) run for 5 minutes automatically?  For example:  minute-command 5-minutes ping www.google.com   or any other command that does not terminate itself.  I'd like to be able to specify a time limit, not only 5 minutes.


Define the color of an imported .svg picture, using TikZ

I use TikZ to create drawings. They are composed of text, arrows, and svg-icons (e.g. coming from the ). These icons (svg files) are mono-color only (i.e. black & transparent). What I'm used to do is to download them, change their color using Inkscape (i.e. black -> blue), and then import them as a node:   \node (my-picture) at (13,17) {\includegraphics[width=210pt]{myPicture.svg}};   However, if I want to change one color (e.g. let the main color of my document be green, and not blue anymore), I need to manually edit each .svg file.  Question: Would it be possible to include the raw .svg-file and specify its color as a TikZ option? E.g. \node [svgcolor=orange] (my-picture) at (13,17) {\includegraphics[width=210pt]{myPicture.svg}};


Why directory with large amounts of entries does not shrink in size after entries are removed?

Close vote notice: While the linked duplicate asks same question, the comments and the only answer do not provide an answer which draws from authoritative source. The , does in fact provide the answer I've been seeking. Thus the proposed duplicate isn't helpful, however Thomas's answer here is proper.  According to the  and personal account , directories that have large amount of entries get to a size over 4096 bytes (which can be seen with ls -l output), but once the entries are removed - the number never goes down.   The question is "why" ? Is it due to how ext4 filesystem configured to retain directory metadata ? Obviously removing the directory and recreating it isn't a solution, since it deletes original inode and creates a new one. What can be done to decrease the number manually ?


Do our eyes act as observers at the quantum level?

This is a very high level question. I was just thinking about the idea than in quantum physics, the act of observing has a "strange" effect on some properties (e.g. double slit).  If I'm staring at a light bulb, are my eyes having an effect similar to the sensor that plays the role of an observer in the quantum interference experiment?


Having trouble with the brackets using /summon command, can someone please help?

I'm working on a map with my friend and I recently stumbled into a problem, neither me nor my friend know which brackets to change in this command:  /summon zombie ~ ~1 ~ {     HandItems:[     {Count:1,id:iron_hoe,tag: {display:{Name:"Grim Reaper's Scythe"},     ench:[{id:16,lvl:5},{id:19,lvl:2}]}}, {Count:1,id:book, tag:{display:{Name:Magical Book}}}],ArmorItems:[{Count:1,id:leather_boots, tag:{display:{Name:"Grim Reaper's Weak Boots"}}},{Count:1,id:leather_leggings, tag:{display:{Name:"Grim Reaper's Weak Pants"}}},{Count:1,id:leather_chestplate, tag:{display:{color:3157807, tag:{display:{Name:"Grim Reaper's Weak Tunic"}}}},{Count:1,id:skull,Damage:3, tag:{SkullOwner:Grimreaper}}],CustomName:Grim Reaper,Visible:1,HandDropChances:[0.2f,0.1f]}   I am fairly sure it has to do with the tag to color the chestplate.


review queue -- same edit different stages (Approve or Reject?)

Often I'm working my through suggested edits and I'll come across a suggested edit to a tag-wiki.  I read through it, it looks good so I say "Approve!".  Then I work through a few other suggestions only to discover the same tag-wiki (edited by the same person), but it is generally much shorter.  In other words I'll see something like (assume for the sake of argument that these are good edits and that foobar originally had no info attached to the tag):  tag-wiki foobar    foobar is a term that programmers use a lot.  Nobody really knows why but wikipedia   has some info you can check out.                      edited by mgilson   ...work through some more edits here...  tag-wiki foobar    foobar is a term that programmers use a lot.                    edited by mgilson   What is going on here?  Is it just that the user made multiple edits?  Why don't they all get lumped together? (Maybe that should be a feature request)?  More importantly, should I reject the second because I already approved the first, or does the approval of the first somehow depend on the approval of the second?


How can I proof-read my own work more effectively?

After an article/book has finally reached the pre-publication stage, the authors have to check the proofs for errors (introduced by themselves or during type-setting). I find this one of the least enjoyable aspects of my work and also think I might not be particularly efficient. It varies with the length of the manuscript. A five-page article in conference proceedings is obviously less of a problem than a monograph.   When proof-reading my own contributions, it is the umpteenth time that I am reading the same text. I find it exceedingly boring, which might make me ineffective (taking a long time to read the text, and potentially overlooking errors). The delay between the actual research and publication of the work can be quite extensive. After such a long time, I am less likely to recall all the details of the analysis, making me more likely to overlook errors in the manuscript.   Asking colleagues to help with this also seems ineffective. They might be less bored while reading the text, but (a) might not be very attentive because they have more pressing issues at hand and (b) can only spot clear inconsistencies, but not other errors you can only notice if you did the research yourself.  How can I make my proof-reading more effective and enjoyable/increase my motivation?


Two-sided ideal generated by subset of not commutative ring

Let $R$ be a non-commutative ring, and $S\subset R$  some subset. Let $I_S$ be the smallest two-sided ideal of $R$ such that $I_S\supseteq S$. Is it true that (if $R$ is unital ring) $I_S$ consist only of elements of the form: $$\sum_{s\in S}\left(\sum_{k=1}^{N_s}x_{k}sy_{k}\right),$$ or (if $R$ isn't unit ring) $I_S$ consist only of elements of the form: $$\sum_{s\in S}\left(m_{s}s+xs+sy+\sum_{k=1}^{N_s}x_{k}sy_{k}\right),$$ where $N_s\in\mathbb{N}$, $m_{s}\in\mathbb{Z}$ and $x, y, x_{k}, y_{k}\in R$.  Thanks a lot!


How to decide on which site to ask a question (deciding between stackoverflow, superuser and unix & linux)

I'd like to ask a question, whether it's possible to create patches using git format-patch against a remote git repository (i.e. not from a local clone/checkout).  As this is not necessarily about programming itself and does not require knowledge of a programming language, it doesn't fit that well at , but might still be interesting and valuable for programmers. But then, should it be asked better at  or on  and is there some way to distinguish between those three sites in general for new questions?   Took a look at the respective tour pages, and for some more generic question I have to admit there is some slight overlap, especially between superuser and unix stackexchange.  Took a look at    on this topic but didn't quite help on this matter.


To What Extent are Magnetism and Gravity Related and Unrelated?

I find many people (especially UFO-ologists) are quick to say there is an interplay between magnetism and gravity, especially when explaining antigravity of UFOs.   On the other side, I see those who are disciplined in science and  reasonably sceptical are quick to refute the relationship of the two forces.   Hence my question:   To what extent are magnetism and gravity related and unrelated?  I've already seen .  I'd like to know what modern science has to say between the both the relationship and difference between the two forces. A summary, some formulas, and modern references would be greatly appreciated.


Convergence in probability: show sequence converges

I am having trouble figuring out how to work with convergence in probability questions. I will give a self-study example from Casella and Berger's Statistical Inference Below.      Let $X_{1}...X_{n}$ be a sequence of random variables that converges   in probability to a constant a. Assume that $\mathbb{P}(X_i > 0 ) = 1$   for all i. Verify that the sequences defined by $Y_{i}^{'} = a/X_{i}$   converge in probability.   I will give the solution to this problem below and then point out where I am having trouble.   $\mathbb{P}(|a/X_{i} - 1| \leq \epsilon)$ $=$ $\mathbb{P}({{a}\over{1+\epsilon}} \leq X_{i} \leq {{a}\over{1 - \epsilon}})$ = $\mathbb{P}(a-{{a\epsilon}\over{1 + \epsilon}} \leq X_{i} \leq a + {{a\epsilon}\over{1 - \epsilon}})$  ( ** In the step above, why is 1 chosen in the expression $(|a/X_{i} - 1|)$? Also, why is $(a - {{a\epsilon}\over{1 + \epsilon}})$ used? I know that since we know $X_{n} \longrightarrow a$ in probability, we're probably trying to rewrite the expression in such a way to use that fact.... but I'm not sure how to just "pull it out of my hat" essentially; ie, in a testing situation. ** )   Use $(1 + \epsilon)^{-1} < (1 - \epsilon)^{-1}$ and continue  $\mathbb{P}(|Y_{i} - a^{1/2}| > \epsilon)$ $\geq$ $\mathbb{P}(a-{{a\epsilon}\over{1 + \epsilon}}$ $\leq$ $a + {{a\epsilon}\over{1 - \epsilon}}) = \mathbb{P}(|X_{i} - a|$ $\leq$ $\epsilon{{a}\over{1 + \epsilon}})$ $\longrightarrow 1$ as i $\longrightarrow$  $\infty$   ( ** In the above, why is the constant being used now $a^{1/2}$ ?? )  Is there some better, more systematic way to approach these problems? I want to be able to encounter any convergence problem and instantly know the steps to employ, rather than try to rewrite the problem in a tricky way.


What does "...from nonmagical attacks not made with silvered weapons" mean?

I'm sure your first thought is, that's perfectly clear.  Unfortunately my group who aren't normally rules lawyers disagree.  Party encounters a  (MM p.211).  It has:     Damage Immunities: bludgeoning, piercing, and slashing from nonmagical   attacks not made with silvered weapons.   My reading of that is if the weapon has to be magical and silvered to hurt it.  So a +1 silver dagger will hurt it, but a +1 regular dagger or a +0 silver dagger won't.  The group's interpretation was that all three of those weapons would hurt and only a +0 regular dagger would be ineffective.    I would also note my interpretation would mean something like blade barrier would also not harm it since you could argue they're magical blades but nothing indicates that they're silvered.    This also appears to be the same wording for some undead so I'm not looking for a lycanthrope specific interpretation but something general for every time that wording is used.    Thanks in advance.


how to determine cumulative probability, i.e. the probability of the variable X being less than µ + σ when we do not know X, µ or σ

Let's say that you need to find the cumulative probability for a random variable X which is normally distributed. You do not know what the value of X is or, for that matter, what the value of µ and σ is. You only know that X = µ + σ. Can you find the cumulative probability, i.e. the probability of the variable being less than µ + σ?


Problems exporting a mesh with an alpha mask into another program

I've used an alpha mask (grey is visible instead of just black) as well as projection painting to achieve the result of Image 1 in blender, but I want to export this gun into Roblox Studio. When exporting it, either as fbx or obj, the alpha mask is lost in the process and I end up with this (black, not grey) in Image 2. I've tried messing around with the export settings, but to no avail. Node setup and export settings (fbx) below


Can I remove a failed audit from my record if I pushed the wrong button accidentally?

What is accident forgiveness? To me, it is the act of understanding that we are humans, and we make mistakes, so a person who makes a mistake should not be quickly judged or ridiculed. But rather, people should show that person empathy, compassion, and possibly humor.  I was reviewing some suggested edits on SO, and I came to a post that I didn't fully understand. I thought it should probably be rejected because the edit didn't make too much sense, but instead I was just going to skip over it. However, I was thinking about something else, and when I went to click "skip", I accidentally clicked "improve".   Right when it happened, time slowed down, and everything was slow motion. My brain automatically knew I made a mistake and I of course saw the "stop and pay attention" message yelling at me. I don't want this to be on my record forever. Is there anyway to get some accident forgiveness?


I get a null pointer exception error every time that I try to get an offline player

Every time that I try to right-click a head with the name of an offline player, it just returns a console error and nothing happens. If the target player of the player head is online, the event will work perfectly.  Error:  org.bukkit.event.EventException         at org.bukkit.plugin.java.JavaPluginLoader$1.execute(JavaPluginLoader.java:305) ~[spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at org.bukkit.plugin.RegisteredListener.callEvent(RegisteredListener.java:62) ~[spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at org.bukkit.plugin.SimplePluginManager.fireEvent(SimplePluginManager.java:502) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at org.bukkit.plugin.SimplePluginManager.callEvent(SimplePluginManager.java:487) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at org.bukkit.craftbukkit.v1_8_R1.event.CraftEventFactory.callPlayerInteractEvent(CraftEventFactory.java:226) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at org.bukkit.craftbukkit.v1_8_R1.event.CraftEventFactory.callPlayerInteractEvent(CraftEventFactory.java:193) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at org.bukkit.craftbukkit.v1_8_R1.event.CraftEventFactory.callPlayerInteractEvent(CraftEventFactory.java:189) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at net.minecraft.server.v1_8_R1.PlayerConnection.a(PlayerConnection.java:1153) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at net.minecraft.server.v1_8_R1.PacketPlayInArmAnimation.a(SourceFile:22) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at net.minecraft.server.v1_8_R1.PacketPlayInArmAnimation.a(SourceFile:8) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at net.minecraft.server.v1_8_R1.PacketHandleTask.run(SourceFile:13) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source) [?:1.8.0_231]         at java.util.concurrent.FutureTask.run(Unknown Source) [?:1.8.0_231]         at net.minecraft.server.v1_8_R1.MinecraftServer.z(MinecraftServer.java:696) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at net.minecraft.server.v1_8_R1.DedicatedServer.z(DedicatedServer.java:316) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at net.minecraft.server.v1_8_R1.MinecraftServer.y(MinecraftServer.java:634) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at net.minecraft.server.v1_8_R1.MinecraftServer.run(MinecraftServer.java:537) [spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         at java.lang.Thread.run(Unknown Source) [?:1.8.0_231] Caused by: java.lang.NullPointerException         at net.milkbowl.vault.economy.AbstractEconomy.getBalance(AbstractEconomy.java:20) ~[?:?]         at me.rarfiles.hyrushbounties.Events.onItemClick(Events.java:69) ~[?:?]         at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) ~[?:1.8.0_231]         at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source) ~[?:1.8.0_231]         at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source) ~[?:1.8.0_231]         at java.lang.reflect.Method.invoke(Unknown Source) ~[?:1.8.0_231]         at org.bukkit.plugin.java.JavaPluginLoader$1.execute(JavaPluginLoader.java:301) ~[spigot-1.8-R0.1-SNAPSHOT-latest.jar:git-Spigot-c3c767f-33d5de3]         ... 17 more   My main code:


I have a web application I have been developing locally on my computer, I have recently launched it on my web server with the exact same settings for MySQL, but for some reason I am encountering a character encoding issue where "smart quotes" (’) are being displayed as black triangles with question marks (�), but only on the server. This is on the HTML: <meta http-equiv="content-type" content="text/html; charset=utf-8" />  My local MySQL database (without character issues) is MySQL 5.7.26 with an InnoDB table with UTF8MB4 encoding and a table collation of utf8mb4-unicode-ci My server MySQL database (with character issues) is MySQL 5.5.5-10.3.21 with an InnoDB table with UTF8MB4 encoding and a table collation of utf8mb4-unicode-ci Perhaps there is a PHP setting somewhere I am missing? Edit: if I run this script on my computer is works perfectly, but if I run the same script on my server with the same data in the database, it give me the character encoding issue: error_reporting(E_ALL);  include 'dbconfig.php';  $id = 19;  try {     $pdo = new PDO("mysql:host=$servername;dbname=$dbname", $username, $password);     $pdo->setAttribute(PDO::ATTR_ORACLE_NULLS, PDO::NULL_TO_STRING);     $pdo->setAttribute(PDO::ATTR_DEFAULT_FETCH_MODE, PDO::FETCH_ASSOC);     $sql = $pdo->prepare("SELECT * FROM products WHERE id=:id");     $sql->execute(['id' => $id]);       var_dump ($sql->fetch());      while ($row = $sql->fetch()) {         $data[] = $row;     }      echo json_encode($data);  } catch(PDOException $e) {     //echo "Error: " . $e->getMessage();     echo "Database Error"; } $conn = null;


How can I concatenate regex literals in JavaScript?

Is it possible to do something like this?  var pattern = /some regex segment/ + /* comment here */     /another segment/;   Or do I have to use new RegExp() syntax and concatenate a string? I'd prefer to use the literal as the code is both more self-evident and concise.


If LaTeX tools implement the TeX features from scratch

I just asked about , which lead to  which pointed out some tools such as . I also have heard of LuaTeX, , , and others.  I am not familiar with how these different "LaTeX tools" work, which is what this question is about. I am wondering if they actually implement TeX from scratch. That is, they somehow read the  and implemented all the algorithms without resorting to some standard / central TeX library. By standard / central TeX library I mean some central code repository that implements all the algorithms from the research papers. If all these tools are all implementing the research from scratch then that would be a useful learning tool.  If the tools I listed (and others similar) are just wrappers around a central TeX library, then wondering what that central library is. I have seen , but given that , I am not sure if that would be considered tex-core. This question  leads to  (also , looks like it's written in , and ), but not sure if everything is using that. If instead there are multiple different implementations of the TeX research, that would be helpful to know as well.


how to install ubuntu and applications in separate partition

I what to format my computer such that both the os and all additional applications are going in one partition and all of my person files in a second one. The reason for that is that I can then create a ghost based on the first partition only and therefore save a lot of space. Alternatively, I would like some help on how to create a ghost that doesn't consider specific folders under my home directory (i.e. my personal files). Any ideas?


.NET OpenSource projects and strong named assemblies?

I am currently thinking about open-sourcing a project of mine and am in the process of preparing the source code and project structure to be released to the public. Now I got one question: how should I handle the signature key for my assemblies? Should I create a new key for the open-source version and publish it along with the other files to the SVN repository? Should I leave the key out and everyone who wants to compile the code should generate his own key?  How do you handle this? I feel a little bit uncomfortable with releasing a signature key to the public.


how can I make my animated robot pick up an object (a pole) during an animation

how can I make my animated robot pick up an object (a pole) without making two separate animated key signatures one for the robot and one for the object?


How do you use the /testfor command in 1.5.2?

I play in 1.5.2, and right now I'm working on using commands. I see that there's a /testfor command when I write /help, but what does this even mean? What is it and how do I use it? Edit: This question is not a copy: 1.5.2 commands could very possibly be different than the latest version.


The sum of a vertible element and a nilpotent element is vertible

Let $R$ be a commutative ring with $1$. Let $a\in R^\times$ and $b\in\text{Nil}(R)$. Show that $a+b\in R^\times$.   Attempts:  Suppose $b^n=0$.  I've tried to figure out a "simple" case as $n=2$;  I've tried to develop the expressions $(a+b)^2=a(a+2b)$ and $a^{-1}(a+b)=1+a^{-1}b$ but nothing came up.  Also $\exists x,y\in R$ s.t. $1=xa+yb$ but it doesn't help because we get $x=a^{-1},y=0$.  Another direction i've failed is to show $\langle 0\rangle=R/\langle a+b\rangle$.


Is the equipartition theorem derivable from more basic principles

Is the equipartition theorem really a theorem and derivable from more basic assumptions or is it just a hypothesis.  Some of the ways energy is partition is not to squared quantum numbers (e.g. vibration) although translation and rotation are


I have a 2D grid of $M \times N$ points. I need to find the total number of lines (not line segments) passing through these points including the diagonals. For example:   $M=2,N=2$: Number of lines $= 6$ (2 horizontal, 2 vertical, 2 diagonals)  $M=2,N=3$: Number of lines $= 11$ (2 horizontal, 3 vertical, 6 diagonals)  $M=3,N=3$: Number of lines $= 20$ (3 horizontal, 3 vertical, 14 diagonals)  $M=2,N=4$: Number of lines $= 18$ (2 horizontal, 4 vertical, 12 diagonals)  $M=3,N=4$: Number of lines $= 35$ (3 horizontal, 4 vertical, 28 diagonals)   Can someone help me in finding a general formula to find this?


A term or phrase meaning "to explain in simple words"?

How do you ask someone to explain something in very simple words, understandable by everyone from general public? In Russia we say something, that can be translated like "explain on fingers". What's the correct English for this?


Which of the following is correct?        I request that my proposal is communicated to the team for necessary action.   I request that my proposal be communicated to the team for necessary action.      I would appreciate further discussion on the topic so that I do not make similar mistakes or face this indecision in future.


I am new to probability. I am working on this problem, but I am not sure if my approach is right. I'd really appreciate it is someone could please help me. Here is the problem:  A bag contains a pen which is either red or blue. I put a red pen inside the bag and shake it. Then, I take a pen out of the bag which is red. You are supposed to guess the color of the pen remained in the bag. What is the probability that the pen remained in the bag is also red?  So I think there are two different possibilities here:    the pen which we took from the bag, is the one when put inside, in that case the probability that the pen remained in the bag is also red, is 1/2.  The pen which we took from the bag, is not the one we put inside. So the probability that the pen remained in the bag is red, is 1.    Now if we add this to possibilities, we get 1.5 > 1 and it's clearly wrong! I don't understand why though.


I've just started recieving the following error on my WP site, when I publish a page update:  Missing argument 2 for wpdb::prepare(), called in /home/greenfin/public_html/wp-content/plugins/auto-image-field/auto-image-field.php on line 98 and defined in/home/greenfin/public_html/wp-includes/wp-db.php on line 992  The page still publishes correctly but I have to back/forward out of the error screen to see anything. I'm concerned it may cause ongoing issues. Any ideas on how to update?


by the following command we can print the duplicate lines from file  uniq -d string file.txt   but how we can do it on csv file ?  we need to print the duplicate lines only on fields 1,2 from csv file - not include field 3  FS - ","  for example:   spark2-thrift-sparkconf,spark.history.fs.logDirectory,{{spark_history_dir}}  spark2-thrift-sparkconf,spark.history.fs.logDirectory,true  spark2-thrift-sparkconf,spark.history.Log.logDirectory,true  spark2-thrift-sparkconf,spark.history.DF.logDirectory,true   expected results:   spark2-thrift-sparkconf,spark.history.fs.logDirectory,{{spark_history_dir}}  spark2-thrift-sparkconf,spark.history.fs.logDirectory,true   second:  how exclude the duplicate lines from the csv file ( I mean to delete only the duplicate lines on fields 1,2   expected output:   spark2-thrift-sparkconf,spark.history.Log.logDirectory,true  spark2-thrift-sparkconf,spark.history.DF.logDirectory,true


How to solve this integral: $\int_0^\infty x^a e^{-bx}dx$?

How do i integrate the following definite integral :  $\int_0^\infty x^a e^{-bx}dx$. Any hint is appreciated. where $a$ and $b$ are non-negative integers.


What is the ultimate postal code and zip regex?

I'm looking for the ultimate postal code and zip code regex. I'm looking for something that will cover most (hopefully all) of the world.


"I gave him + INDIRECT OBJECT" vs. "I gave + INDIRECT OBJECT+ to him"

Consider these two sentences: "I gave him a pencil," and, "I gave a pencil to him."  Is it correct that the important part of the sentence is placed at the end? When we want to emphasize the pencil that I gave him, must we say, "I gave him a pencil?" When we want to emphasize that it is him to whom I gave a pencil, must we say, "I gave a pencil to him?"


Okay, so I was trying to uninstall a program called Kodi. I ran the following commands in terminal:  sudo apt-get update sudo apt-get remove kodi* sudo apt-get purge kodi*   I was reading it on this site:   So, the next thing it says to do is this:  rm -r ~/.kodi/   After this, I'm not sure what the terminal output was, something about the command not being able to do that because of something.   Then, Ubuntu welcome pops up, just like when you first install it. I went to desktop, it was empty, all my files gone. I restarted the PC, only to come to realize that it's a fresh installation of Ubuntu.   Can someone explain what the heck is going on?


Is the word 'It' in 'It's a pity' a referential pronoun?

Reopen note:  This question has been marked as a duplicate of a question about so-called weather-it. This question here has nothing to do with weather it. It seems from one of the answers that it might be from an extraposition construction, or from a referential usage. This has nothing to do with 'weather-it' at all.    Question:  Is the word 'It' in:        It's a pity       a pronoun? Or does it just serve as a filler because otherwise there isn't a subject in the sentence?   Is the situation different in the sentence:   It's a pity you cannot come.


100 tickets numbered 1,2,3...,100, are sold to 100 different people for a drawing...

I found the answer to these questions but I want someone could give explaination $100$ tickets numbered $1,2,3...,100$ are sold to $100$ different people for a drawing. Four different prizes are awarded, including a grand prize (trip to Tahiti). How many ways are there to award the prizes if:  a) There are no restrictions? Answer: $94109400$  b) The person holding ticket 47 wins the grand prize? Answer: $941094$ c) The person holding ticket 47 wins one of the prizes? Answer: $3764376$  d) The person holding ticket 47 does not win a prize? Answer: $90345024$  e) The person holding ticket 19 and 47 both wins prize? Answer: $114072$


How to calculate the force in an "impulse based reaction model"?

I have a sphere moving forward with v (pre collision) = v1i  A second sphere colliding with the first one has its own pre collision velocity = v2i  The collision should be not totally inelastic (like, you know, the case of two human bodies colliding each other), but for my purpose I think I can consider the coefficient of restitution = 0  Using the formula   $$ I  = mv_f - mv_0$$   and replacing I with F * (delta)t I woul like to know how can I compute that F, since I don't know what will be v(post collision) because it is my final unknown to compute. And I think that force should be computed with the relative velocity of the two spheres, but I have no idea at the moment on how to proceed. Any suggestion will be strongly appreciated.  UPDATE  Thank you for your suggestion ja72.  So in that case can I write something like this?  $$  F *\Delta t = \frac{ (\epsilon+1) \left(v_2-v_1\right)}{\frac{1}{m_1}+\frac{1}{m_2}} $$   But in this case, how am I supposed to evaluate final velocity of the two spheres?


Security Updates - The package system is broken

tried to update recently, and have this result from Update Manager:  The package system is broken If you are using third party repositories then disable them, since they are >a common source of problems. Now run the following command in a terminal: apt-get install -f The following packages have unmet dependencies: libk5crypto3: Depends: libc6 (>= 2.14) but 2.15-0ubuntu10.12 is installed libk5crypto3:i386: Depends: libc6 (>= 2.4) but 2.15-0ubuntu10.12 is installed  Have tried: apt-get install -f as suggested also tried apt-get clean & i think dpkg --configure -a I also tried after trying to sort the problem with Synaptic, but nothing has made any difference. I don't have any third party repositories enabled Any help would be great, thank you! System is: Ubuntu Release 12.04 (precise) 64-bit following Alexs suggestion: Alex, thank you. After sudo apt-get install -f  I got Get:1 http://gb.archive.ubuntu.com/ubuntu/ precise-updates/main libk5crypto3 i386 1.10+dfsg~beta1-2ubuntu0.7 [77.4 kB] Fetched 77.4 kB in 0s (173 kB/s)   dpkg: error processing libk5crypto3:i386 (--configure):  libk5crypto3:i386 1.10+dfsg~beta1-2ubuntu0.6 cannot be configured because libk5crypto3:amd64 is in a different version (1.10+dfsg~beta1-2ubuntu0.7) dpkg: error processing libk5crypto3 (--configure):  libk5crypto3:amd64 1.10+dfsg~beta1-2ubuntu0.7 cannot be configured because libk5crypto3:i386 is in a different version (1.10+dfsg~beta1-2ubuntu0.6) No apport report written because MaxReports has already been reached                                                                     Errors were encountered while processing:  libk5crypto3:i386  libk5crypto3 E: Sub-process /usr/bin/dpkg returned an error code (1)


Sum of binomial coefficients when lower suffices is same in the series: ${m \choose m}+{m+1 \choose m}+{m+2 \choose m}+...+{n \choose m}$

I want to find out sum of the following series: $${m \choose m}+{m+1 \choose m}+{m+2 \choose m}+...+{n \choose m}$$ My try: ${m \choose m}+{m+1 \choose m}+{m+2 \choose m}+...+{n \choose m}$ = Coefficient of $x^m$ in the expansion of $(1+x)^m + (1+x)^{m+1} + ... + (1+x)^n$  Or, Coefficient of $x^m$ $$\frac{(1+x)^{m}((1+x)^{n}-1)}{1+x-1}$$ $$=\frac{(1+x)^{m+n}-(1+x)^{m}}{x}$$ But, how to proceed further?  Note: $m≤n$


What equipment should I have to kill the Eye of Cthulhu?

I just manually summoned the Eye of Cthulhu, going into battle with copper armour, tungsten broadsword, gold bow, jester arrows and plenty of lesser healing potions. I came rather close to death but I managed to stay alive. However, the Eye took off when I had his health down to ~1700. I'm assuming this means you only have a few minutes to finish it off after a certain point. Is there any equipment I'm missing to help kill the Eye faster and to help my survivability? If it's relevant, my current life is 120.


How to Install Ubuntu on a pre-existing D drive?

Unlike  question, I have 5  already-formatted partitions (Each are "Logical" and "N.T.F.S" style) in the hard disk, and all are being used for specific type of documents. (C drive being used for Windows)  I want to install   on the pre-existing drive D; and without interfering any pre-existing partitions and their contents. I have downloaded the ISO file. Please guide me with flow charts.


How would I go about creating a 3D MMORPG Mouse Look? I have created a 3D Space Rpg that is almost finished with success so far. However, I didn't have a clue, how I would attempt to make a Mouse Look method where if a user right clickes and then holds the right mouse button and moves it around the camera moves around with the mouse. The camera can not move away from your character/ship, it should act as if the character/ship is it's origin and that it rotates all around the origin.  I don't mind coding this with python either. Advice is welcome!


Is $( \mathbb{R} , T)$ connected if T is finite complement topology on $\mathbb{R}$

This question is number 6 of 3.1 of wayne patty topology.  Let  T be finite complement topology on $\mathbb{R}$. Is ($\mathbb{R} , T)$ connected?  Attempt: I took $\mathbb{R}=U \bigcup V$ , U ,V both open. Now I have to see if $\bar U \bigcap {V } = \bar {V} \bigcap U = \phi $ . But I am not able to undestand what closure of U will be in Finite complement topology. Can you please help in that?


Reagarding skype for linux 32bit machine

How and from where can I download skype for ubuntu 16.04 32bit machine and how can I install it?


Reporting Results of Mann-Whitney U Test - Means vs Medians

I had a question  that I got a bunch of great responses on.  I have, hopefully, a quicker question here.  There is a debate in the literature regarding reporting means vs medians in a Wilcoxon-Mann-Whitney test.  See  and also .  I would like to report means in my table, since I only have four possible values (0 through 3), rendering medians less effective as the differences are not pronounced.  If I do report means in the table, would I just put an asterisk saying that means are reported for the Mann-Whitney test because the medians don't show the differences effectively?  I feel like I need to explain why I used means and not medians to describe my ordinal data and show significance (even though a Mann-Whitney is comparing the distributions and not the medians, as some think).  Are there are any references out there that show this as a precedent?  As always, advice/help is greatly appreciated!


Running nginx on AWS and accessing the website over plain old http

Two days ago I've started using AWS in order to serve my web applications. I've subscribed to the t2.micro and formed an Instance and then installed nginx on it from scratch using ./configure --prefix=/usr/local/nginx-1.16.1 --without-http:rewrite_module --with-http_ssl_module --with-openssl=~/Downloads/openssl-1.1.1i  and I've edited the nginx.conf the relevant section to read: server {     listen 80;     server_name enginx.strangled.net;     <truncated>     location / {          root html;          index index.html index.htm;     } <truncated>  On the web terminal screen of AWS, under the Instance page this is written: Public IDs: 100.26.187.63 Private IPs: 172.31.92.210 I take from these writings that my instance has a publicly accessible unique  IP of 100.26.187.63 so I got a free DNS enginx.strangled.net at freedns.org and edited the Type A record to have 100.26.187.63 as the Destination. I start nginx and it starts without any errors. ps -aux | grep nginx outputs 2 lines nginx master and worker appropriately. I enter http://enginx.strangled.net on a browser but it can't connect to any nginx server and it ends up with The connection has timed out The server at enginx.strangled.net is taking too long to respond.  What could be missing in this setup? How to connect to the nginx server over http or is it not possible at all connecting to any server over http on AWS?


I have been assigned a project to be done in Windows PowerShell. I am familiar with shell scripting but it's a new technology. I was told that its similar to shell except few syntax changes.  I have one week time to learn and understand the basics.  I tried looking for an emulator but couldn't find one. I don't have a dual system on my laptop. Help me out here.  Do I need to install Windows on my laptop so that I could practice those commands at home or there is a solution available in Ubuntu without making changes to my operating system.


I'm setting up a server for backing up my desktop box remotely. I want to prevent remote password access to the server, permitting only users with private keys (AKA my desktop box) to access it. How can I block remote password access while allowing physical password access to the server?


My question is about suid! The logic behind that is to grant root permission when a privileged command is executed by a user. For example, passwd has such a feature.  $ ls -l /usr/bin/passwd  -rwsr-xr-x 1 root root 54224 Aug 21  2017 /usr/bin/passwd   I have written a piece of code which opens a zsh. So, I manually add suid to my executable.   $ chmod u+s myzs $ ls -l myzs -rwsr-xr-x 1 mahmood mahmood  7360 Jul  6 21:34 myzs   However, when I run the binary, the shell opens for the current user (me) and not the root. What is the difference between my binary file and passwd? both have suid.  $ ./myzs  % whoami                                                                                mahmood


How can I display just a portion of an image in HTML/CSS?

Let's say I want a way to display just the the center 50x50px of an image that's 250x250px in HTML. How can I do that. Also, is there a way to do this for css:url() references?  I'm aware of clip in CSS, but that seems to only work when used with absolute positioning.


Integrals involving reciprocal square root of a quartic

For two integration below, what is the ratio of them?  $$I_1 = \int_0^1\frac{dt}{\sqrt{1-t^4}}$$  $$I_2 = \int_0^1 \frac{dt}{\sqrt{1+t^4}}$$ What is the ration $\frac{I_1}{I_2}$? I do not have any thoughts for solving this question so could anyone give me some hints? Thank you!!


Let be $f:\mathbb{C} \to \mathbb{C}$  entire function such as $f(z)=f(z+i)=f(z+1)$ for all $z$. Show that $f$ is constant.  Can you help me?


Group of even order contains an element of order $2$ (Explanation)

I am working on the problem:     If G is a group of order 2n, show that the number of elements of G of order 2 is odd.   which already has solution (in the link below), please explain the solution in that link


How can I add mp3 files as podcasts to my iPhone using iTunes?

I am using iTunes 12.5 on Windows 10 with an iPhone 5s.  Sometimes I download hour-long .mp3 files that I want to put onto my iPhone as podcasts, so that it automatically remembers where I am in my listening if I have to stop in the middle.  I know how to transfer .mp3 files to my iPhone, where they show up as Music.  I also know that I can right click on any song, choose 'Get Info' and under Options change the media kind to 'Podcast.'  But when I change the file to a podcast, it disappears from iTunes, though it does show up on my device when I open the Podcasts app.  How can I transfer an .mp3 file to my iPhone as a podcast, and still have that podcast show up in iTunes when I look there to see what podcasts are on my device?


I need to import and specially export in 3DS format. I know that I can import a file in 2.79 and the copy-paste to 2.8, but then when I copy-paste it back to 2.79 I'm having problems with textures missing. Is there any way to import/export 3ds in 2.8 without using any other version or software like we did in 2.79? The extension is missing in the add-ons repository either.


Why do physicists believe that particles are pointlike?

String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories.   So why is it that it's popular belief that particles are 0-dimensional points? Was there ever a proposed theory of them being like this? And why?   What reason do physicists have to believe that particles are 0-dimensional points as opposed to 1-dimensional strings?


How many distinct Boolean operators are there that take three inputs?

From what I know, boolean operators are the likes of AND, OR, XOR, NOT, NAND and NOR. So does this mean that there are actually 6 distinct boolean operators that can take three inputs?


I recently bought shares on a market where I normally buy and we're confirmed at asked price sorry not bid please see attached pictures and number of shares were confirmed and a congratulations note sent as normal but at open time price was changed but I screenshot my buying price each time. Can they do that Ask one price and confirm number of shares when you buy but later changed it? What is want to know is that legal?


How to fetch Root namespace defined in a .NET Assembly using Reflection

I have loaded a Assembly using following code  Assembly.LoadFrom(ProjectDllPath);   Now this asssembly contains only one namespace and some classes in that namespace and I want to fetch the name of that Namespace . What is the syntax to fetch that name.


Elegant way to locate all large files (files over 200 or so megs) on Windows 7?

Basically, I'm running out of hardrive space and I've looked at the usual culprits -- downloads, media, large programs etc.  There seems to be hidden files or maybe log files that could be taking up a lot of space and I don't know how to locate them.


What does the last line stand for in this Python function?

def f(x):     xs=str(x)     if len(xs) == 1:         return int(xs)     n = int(xs[0]) + int (xs[1])     if len (xs) == 2:         return n     else:         return n+f(xs[2:])   Speciffically, what does f(xs[2:]) do?


Meaning of legend value in Kernel Density?

I have done some analyses on the spatial distribution of traffic signs using kernel density, I used SQUARE_KILOMETERS in area unit, the output is good and clear, but I don't understand the meaning of the legend.


Herbert in his book "Elements of set theory" on page no 3 says that      we can form the set $ \{ \emptyset \} $ whose only member is $\emptyset $. Note that $ \{ \emptyset \} \neq  \emptyset $, because $ \emptyset \in \{ \emptyset \} $ but $\underline{ \emptyset \notin \emptyset} $·   By the last argument $\emptyset \notin \emptyset$, is he saying that empty set is not a member of or does not belong to empty set  OR  it is a typo and he wanted it to be $ \{\emptyset \} \notin \emptyset $, that set containing empty set is not a member of empty set


Understanding the diagrams of electromagnetic waves

I'm having trouble understanding the diagrams of elctromagnetic waves.  I have no problem with any concept in classical mechanics, and I think this can be answered without any relativity (which I don't know yet). I hope for an answer which is as intuitive as possible but any answer will be good.  So in the common diagram of an electromagnetic wave:     What exactly do the vectors represent? The wave is propagating though an eletromagnetic field. Are the lines just the field created by a particle?  We learned in physics that a charged particle creates a field in all of space, Is this a picture of changes in the field when it moves? And if so, how does it move? does it move up and down with the amplitude of this wave?  Lastly, It's not clear to me why the E-field part is not in the direction of the motion of the wave, because usually an electric field is depicted as so:    i.e it is in a direction "outwards" from the source of the charge.  This is really running through my mind for some time, so thanx for reading this!


Where to find the Mac OS X Lion security configuration guide?

Most Mac OS X releases have very nice , but Lion is not in the list. Is this document available somewhere else on Apple's site, or is there a roughly-equivalent document available somewhere on their site under another name?


Article Usage in Standard American English

Here is the text:  "This is a 29-year-old Arn Anderson, who looks much older than that. It seems the stress of keeping the crowds entertained every night got to him and aged him much quicker than the average person."  According to the rules, in the last phrase, it should be "an average person" because the meaning is any average person. Why did they use the?


What is the difference between the dot (.) operator and -> in C++?


When you have a link from lets say twitter that is t.co/foo that links back to your website how does that effect SEO and how do the major search engines handle Shortened URLs?


this is quite a simple question, however I'm finding it tricky. I want to treat a char* as if it were a std::string, for instance:      char *p = ...; // read a huge chuck from a file      std::string s(p); // this is not what I want   So, if I use the constructor, I get a copy of p, which is a waste of memory and time. Is it possible somehow to avoid this, and "assign" the std::string content to a pre-existing address?  Any other idea is more than welcome!  Thanks!


Travel from South East Asia to Europe by land

Does anyone have experience or know about travelling from South East Asia to Europe, all by land? I'd be happy to catch a quick flight here and there but would prefer to do the entire trip by land.  I really don't know much about making the trip and would love to receive some first-hand advice. I really don't have to stick to any plan/time constraints, but I'll ideally start the trip in Thailand and end up anywhere in Europe.   What's the best route? How long should it take? What sort of monthly budget would I need?   Thank you!


Archimedes Classic Proof for Area of Circle: Love it but can't grasp one aspect...

The proof assumes that:...  The perimeter of any CIRCUMSCRIBED regular polygon is GREATER than the circumference of the circle.  ie:  !  Is this an axiom? Is there a fundamental property I'm missing? Does the answer to this depend on the definition of how one measures a circumference?  Please advise! :)


I'm creating a news app with NEWSAPI's API. whenever i'm clicking the news it crashes

Whenever I click to the news it crashes, below is LOGCAT  java.lang.NullPointerException: Attempt to invoke virtual method 'long java.util.Date.getTime()' on a null object reference                                                                                at com.jimdo.saifstudios.lynknews.Adapter.ListNewsAdapter.onBindViewHolder(ListNewsAdapter.java:105)                                                                                at com.jimdo.saifstudios.lynknews.Adapter.ListNewsAdapter.onBindViewHolder(ListNewsAdapter.java:70)  ListNewsAdapter  class ListNewsViewHolder extends RecyclerView.ViewHolder implements  View.OnClickListener {  ItemClickListener itemClickListener;  TextView article_title; RelativeTimeTextView article_time; CircleImageView article_image;  public ListNewsViewHolder(View itemView) {     super(itemView);     article_image =  (CircleImageView)itemView.findViewById(R.id.article_image);     article_title = (TextView) itemView.findViewById(R.id.article_title);     article_time = (RelativeTimeTextView)  itemView.findViewById(R.id.article_time);      itemView.setOnClickListener(this); }  public void setItemClickListener(ItemClickListener itemClickListener) {     this.itemClickListener = itemClickListener; }  public void setArticle_title(TextView article_title) {     this.article_title = article_title; }  public void setArticle_time(RelativeTimeTextView article_time) {     this.article_time = article_time; }  public void setArticle_image(CircleImageView article_image) {     this.article_image = article_image; }  @Override public void onClick(View view) {     itemClickListener.onClick(view,getAdapterPosition(),false);  } }  public class ListNewsAdapter extends  RecyclerView.Adapter<ListNewsViewHolder>  { private List<Article> articleList; private Context context;  public ListNewsAdapter(List<Article> articleList, Context context) {     this.articleList = articleList;     this.context = context; }  @Override public ListNewsViewHolder onCreateViewHolder(ViewGroup parent, int viewType)  {     LayoutInflater inflater = LayoutInflater.from(parent.getContext());     View itemView = inflater.inflate(R.layout.news_layout,parent,false);     return new ListNewsViewHolder(itemView); }  @Override public void onBindViewHolder(ListNewsViewHolder holder, int position) {      Picasso.with(context)             .load(articleList.get(position).getUrlToImage())             .into(holder.article_image);     if (articleList.get(position).getTitle().length() > 65)      holder.article_title.setText(articleList.get(position).getTitle().substring(0,65)+"...");     else         holder.article_title.setText(articleList.get(position).getTitle());      Date date=null;     try     {         date = ISO8601Parse.parse(articleList.get(position).getPublishedAt());     }catch (ParseException ex)     {         ex.printStackTrace();     }     holder.article_time.setReferenceTime(date.getTime());      // Set event click     holder.setItemClickListener(new ItemClickListener() {         @Override         public void onClick(View view, int position, boolean isLongClick) {             Intent detail = new Intent(context,DetailArticle.class);             detail.putExtra("webURL",articleList.get(position).getUrl());             detail.setFlags(Intent.FLAG_ACTIVITY_NEW_TASK);             context.startActivity(detail);            }     });  }  @Override public int getItemCount() {     return articleList.size(); } }


"Having said that" vs. "That being said"

I want to know the meanings of these phrases Having said that and That being said, the difference between them, and in which context I can use both of them.   According to my first understanding of these expressions, I think they are equivalent to the phrase "Considering what was said before" or in "reference to what has already been said". I am not sure of the meaning, but hope to find its exact meaning.


Today when i opened Stack overflow i saw this :    So i thought some problem with net ,  I asked the person sitting near me to open SO but he was having same issue.  I want to know is it because anything wrong in our network or anything else?  While searching i found below errors.    It might be because our System Admins might have removed some permission to access something?  Because 403 is there.


I need help setting the attributes of objects inside a List

Let's get to the point. I'm using a LinkedList to store some info about the objects it store. The thing is, I can't set all the attributes of the objects right when I create it, so I need to access them later. In fact, this is the piece of code where I access it.  listaNodos.get(esteNodo(nodoActual)).caminoVuelta.getLast().setFin(currentGrid);                      listaNodos.get(esteNodo(nodoActual)).caminoVuelta.getLast().setPath(caminoVuelta);  Just as a clarification: caminoVuelta is also a LinkedList. So, can I modify the atributes of the instances stored in caminoVuelta by simply accessing them with getLast() method from LinkedList and then using the set() methods? Or will this change never happen to the original object?  For some reason, (and it only happens for the first node(Nodo) I create) it returns a NullPointerException.   I hope it's clear enough. Thanks.


Whenever I click on my chrome shortcut I get a new window (as expected) but I also get a new Unity entry with a different icon (one from an iconset I had been using before upgrading to 14.04 - don't really remember the name). The new unity entry does not seem to originate from a correct .desktop entry because all the submenus are missing from it (New incognito window, New Window etc.) and it has a permanent tag '(1) Facebook' no matter the window title (see attached picture).  I have uninstalled and reinstalled chrome in hope that it would help which it did until restart but now I get the same behaviour.  Note that I haven't altered any .desktop files regarding chrome and I can only find one file:  /usr/share/applications/google-chrome.desktop which seems to be correct (with submenus etc.)


1) $D$  is a positive integer, find all rational solutions of Pell's equation  $$x^2-Dy^2=1$$  2) What about $D\in\Bbb Q$ ?


Are "most" continuous functions also differentiable?

Let $A$ be a nonempty open subset of $\mathbb{R}$.   Consider a function $f : A \rightarrow \mathbb{R}$. Given that $f$ is continuous, what is the probability that it is differentiable? I suspect it is $0$.


Why were the effects of the ring instant for Smeagol and not for Bilbo?

I am wondering why after Smeagol first saw the ring, without even touching it, he was immediately prepared to kill his friend to get it. Bilbo had the ring for many years and yet he was willing to give it up after some minor persuasion from Gandalf. I just thought there might be an explanation written somewhere that I haven't seen.  edit:     This question is not a duplicate. This question is predicated on 'first contact' with the ring, not the effects after 'longstanding possession' of it that the other question is asking. We can see that Aragorn and Faramir, both mortals, resisted the 'call' of the Ring and wouldn't take it, much less by force even when they easily could have. Yet others are so enthralled without ever touching it that they would kill their own mother to possess it.


What is this closed off pipe under my kitchen sink?

This pipe has a very slow leak. What is the pipe for and what is the best way to stop the leak?


Inserting a table in latex having 23 columns

I  have to insert a table which has 23 columns and 400 rows. I tried by using method of inserting simple tablle. But when i compiled the pdf does not show some columns on the page.how can i fix it?


How to bind data-src attribute for the image in the post using jquery?

I'm trying to use  for responsive image in the wordpress blog. For that I have to add the data-src attribute in the place of src in the  tag.  Or I have to get the url from the image in the post and need to bind my new  tag near the old  tag and wrap that old  tag in  tag. I don't have any idea how to do it.  Basically it must looks like this:


For the following SQL Server datatypes, what would be the corresponding datatype in C#?  Exact Numerics  bigint numeric bit smallint decimal smallmoney int tinyint money     Approximate Numerics  float real     Date and Time  date datetimeoffset datetime2 smalldatetime datetime time     Character Strings  char varchar text     Unicode Character Strings  nchar nvarchar ntext     Binary Strings  binary varbinary image     Other Data Types  cursor timestamp hierarchyid uniqueidentifier sql_variant xml table   (source: )


Let $U =\{ p\in \mathbb{P_4}(\mathbb{R}): p(6) = 0 \}$. Find a Basis of $U$.

LADR 3rd ed. S.Axler|Section 2.C|problem 4. page.48  Let $U = \{ p\in \mathbb{P_4}(\mathbb{R}): p(6) = 0 \}$.  I take the general form of a polynomial of degree 4 :  $p(x)=e+dx^1+cx^2+bx^3+ax^4$ and then I tried to narrow the form down to one that represents polynomials of degree 4 with the property that p(6)=Zero  $0=e+d6^1+c6^2+b6^3+a6^4$ $e=-d6^1-c6^2-b6^3-a6^4$  $p(x)=e+dx^1+cx^2+bx^3+ax^4$ turns into: $p(x)=d6^1-c6^2-b6^3-a6^4+dx^1+cx^2+bx^3+ax^4$ $p(x)=d(x-6)+c(x^2-6^2)+b(x^3-6^3)+a(x^4-6^4)$  According to a worked-out solution I found on the net, $\{(x-6),(x^2-6^2),(x^3-6^3),(x^4-6^4)\}$ is indeed supposed to be a basis for the subspace described above.  What I fail to understand is how $\{(x-6),(x^2-6^2),(x^3-6^3),(x^4-6^4)\}$ can be linearly independent and thus a basis for the subspace(assuming the answer is correct).   $0=p(\textbf{6})=d(\textbf{6}-6)+c(\textbf{6}^2-6^2)+b(\textbf{6}^3-6^3)+a(\textbf{6}^4-6^4)$  If x=6, then p(x) is zero, but the coefficients do not have to be zero.   Thank you.


SQL Server service start automatically only after Windows Shutdown, how can I make restart automatically without batch file?

I am using MS SQL Server 2014, When I restart my Pc the SQL Server Service does not start automatically, however, it does after Windows Shutdown and run again, how can I make it restart automatically ? Without using batch file


I asked a  recently, looking for examples of an online tool. Per the , I answered my own question with a few examples that I had already found. I did this so that these examples would be included in the answers, along with the rest.  The question has received only down votes and insults saying that this shouldn't be done.   Should I not answer my own questions?


Latex environment for makrdown like lists

Is there any environment for making lists (similar to ennumerate or itemize), that would support markdown/wikitext like syntax.  Currently, it is a tedious task to write lists, as one has to write \item for each item (rather than # or * as in wikitext and markdown).  Syntax gets even nastier when you want have nested lists. I only know outline, but writing \1 (for item at the first level) or \2 (for secound level) is also ugly.  Maybe someone managed to hack around listings support for .md, to render */# not as code but as items?


Is past perfect necessary in 'It had been here before we came.'?

Would you use past perfect in following sentence or would you rather go with other tense?     It had been here before we came.


PHP file gets download instead of getting executed when browsed in any browser

I have a phpinfo.php file which I am trying to run by browsing to it using browser but the browser downloads the file instead of executing it.  phpinfo.php  <?php    phpinfo(); ?>   I followed following  post, added following lines to my /etc/apache2/httpd.conf and restarted apache but invain. phpinfo.php still gets downloaded.     AddType application/x-httpd-php .php> .phtml   AddType application/x-httpd-php-source .phps   Have I added these line to the correct file?  On an openSuSE forum following was mentioned. I followed this too but still no success. Same problem is persisting.     In case the browser wants to save your   php files instead of displaying the   content, you should enable php support   in the /etc/apache2/mod_userdir.conf   file. Add the following line to it,   just after the  line and restart   the server.      Include /etc/apache2/conf.d/php5.conf


Prove using the basic properties of a sequence that $\lim \frac{n}{2^n} = 0$  I tried to prove this using the standard epsilon-definition of a limit but the math got really hard, so I stopped. Then, I tried to represent the sequence as a quotient or a product of two sequences, but those sequences were not convergent. Thus, I've got no more ideas on how to tackle this problem. Any suggestions would be most appreciated.


What are all the differences between all the editions of the first book of the Dark Tower series?

Wad Cheber had said (in ) that there are differences between each version of the first book (I understand there is a large gap between books 1 & 2 being written):     Like, there are two (or three) editions of Book I (The Gunslinger): The original serialized version in which it appeared in SF&F magazine, which I've never read; the original limited edition print novel version (and reprints of it) which was slightly altered from the serialized version; and the significantly different "Revised and Expanded Edition" which was released in the early 00's, when Book V came out.   What are all the differences?


Understanding floating point multiplication under different representations

I was multiplying a floating point number by hundred, only to see it round it off. The same does not happen when multiplying by 10 or 1000.  546.55 * 100 = 54654.99999999999  546.55 * 10 * 10 = 54655.0  546.55 * 1000 = 546550.0 (this is something I tried just to see how it behaves on powers of 10 greater than 100)  Shouldn't multiplication by 100 and multiplication by 10*10 have the same result? Will an interpreter understand 100 and 10*10 as different?


What legendary shiny pokemon are legitimately obtainable as of Sword/Shield?

Within a few months, Nintendo will launch the first DLC of Pokemon Sword / Shield. As I understand it, in that DLC, they will introduce all the remaining legendary pokemon.  One of my goals is to try to get every legendary Pokemon in their normal and shiny form. But some of them are not legitimately available in shiny form.  I know that the first three legendary birds and Mewtwo are legal, since in Pokemon Let's Go you can get them by doing soft reset. But I'm not sure about other legendaries.  Therefore, I would like to know which are legitimately available as shiny (or which are not), and how to obtain them.


In many fonts I come across, I see that the glyph uppercase i - I is same as lowercase l.  Why is it so? Why don't font designers add a differentiating factor between the two glyphs?  This specially creates a problem with the word 'Ill'. Whether to read it roman 3 or short for 'I will'.    Extra  I am asking this because I am making a font, so I want to know if I should stick to this standard design, or use different glyphs for the two... Also, see my .  P.S. I don't know if this should goto SuperUser, but I can't post questions there.


I have an ISO file on a Linux machine for which I don't have root access. I am looking for some command or software that would allow me to extract all the files on the ISO without the need for root. Any ideas?


So code blocks in questions and answers on the android app (inline included) seem to be scared of me putting my finger in them. When I poke them, they only move over two columns!  (For clarity, these are the code blocks that overlap the TextArea view because they've been eating too much)  The intended behaviour here is that when I press my finger into a code block, the touch event should register a drag; at current, I try to scroll inside a code block and I end up switching to question or answer view instead, over and over.  EDIT:  Something tells me this is status-bydesign because the text is deliberately cut off (probably inviting you to click on the code block and expand it; UX Decision?):


Can be used only in preamble occurs when using \usepackage command

Whenever I am trying to use the subfigure or the algorithm2e package using \usepackage command, it is showing   LaTeX Error: Can be used only in preamble.    What is the problem and how to get rid of it. If there is any substitute for the two packages without using the above ones, kindly let me know.


$\mathbb{R} [ X ] / ( X^ 2 + 2 )\cong \mathbb{C}$?

I am puzzled since in my eyes I cannot prove that there can be a function which is homomorphic regarding multiplication. Do you know any functions that could be?  I was thinking that the quotient field has the format:   < ax+b | x^2 = -2>   Am I missing something?


How to disable super or subscripting in text mode

Writing a report with some part numbers, for example "partname_123". I want to write the underline as a underline and not as sub-scripting. How do I disable the super/sub-scripting in a regular text? is there a general command I can use or just a command for the specific word, like: \ignore-super-sub-scripting{partname_123}  -Using a sharelatex template that I found: Business report (version 1)


constract a sequence of functions on [o,1] each of which is discontinous at every point on [0,1] and which converges uniformly to a function that is continous at every point


I'm quite new to electronics and I'm having a hard time understanding the "pull-up resistor" principle. I have read a lot of articles about that, and I think I've got it but I'm not 100% sure so I have a question. In , after the first image, it says:     When the momentary button is pressed it connects the I/O pin to Vcc and the microcontroller would register the input as a high.   But I don't get it. Where is VCC? From what I see, there is no power source on this schema, just a microcontroller wired to a button that are both wired to ground so how can there be any voltage at all in this circuit?


I'm a student and I started my first portfolio. I'm doing some "fake jobs." I can do 3D and 2D (I'm not so good at drawing [yet]). In the future I hope to work with designing album covers, posters, and such.  What are some good projects for my portfolio?


How to check if a value exists in an object using JavaScript

I have an object in JavaScript: var obj = {    "a": "test1",    "b": "test2" }  How do I check that test1 exists in the object as a value?


Why would spacetime curvature cause gravity?

It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" to be experiencing gravitational acceleration. Do we also say along with it, that the object flying past in reality exeriences NO attraction force towards the massive object? Is it just following the spacetime geodesic curve while experiencing NO attractive force?  Now come to the other issue: Supposing two objects are at rest relative to each other, ie they are not following any spacetime geodesic. Then why will they experience gravitational attraction towards each other? E.g. why will an apple fall to earth? Why won't it sit there in its original position high above the earth? How does the curvature of spacetime cause it to experience an attraction force towards the earth, and why would we need to exert a force in reverse direction to prevent it from falling? How does the curvature of spacetime cause this?  When the apple was detatched from the branch of the tree, it was stationary, so it did not have to follow any geodesic curve. So we cannot just say that it fell to earth because its geodesic curve passed through the earth. Why did the spacetime curvature cause it to start moving in the first place?


Randomly generating the hallways between a network of rooms

So here's my base map:    (It won't necessarily be 5x5, just using this as an example.)  It's kinda boring the way it is with all the rooms connected. I want it to be more of a randomly generated labyrinth, where every room is accessible like so:    I've tried setting the hallways randomly:  foreach(Room r) {     r.northWall = randomBoolean();     r.southWall = randomBoolean();     r.eastWall = randomBoolean();     r.westWall = randomBoolean(); }   But that almost always ends up with rooms that you're unable to go to, like this:    And often some rooms have no hallways at all. I tried saying each room must have a minimum of 2 hallways, but it still doesn't fix the problem that sometimes there an inaccessible areas.  How should I go about doing this? I'm not too worried about the speed, as long as it's not ridiculously slow (Some levels will have 100+ rooms).


How to apply Cross Entropy on Rectified Linear Units

I am currently getting started with Machine Learning. However, I have some problem to derive formula and not able understand how to applied the Cross Entropy (CE) on Rectified Linear Units (ReLU).  I also try to search from website, but most of them either brief only few sentences or take sigmoid as examples. (maybe this is too obvious for them?)  The best that I can find is from this  which teach how to applied the CE error function on the Sigmoid Units. Therefore, I try learning from there and derive my own. Here is how I start,  Given   cross entropy $$C = - \frac{1}{n} \sum_x [y\ln{a} + (1-y)\ln{(1-a)}]$$  activation function $$a=\sigma(z)$$  weight sum input $$z = \sum_j w_ix_i + b$$  where $n$ is the total number of items of training data, the sum is over all training inputs, $x$, and $y$ is the corresponding desired output.  In this case, my activation function will be $$\sigma(z) = max(0,z)$$  Compute CE w.r.t weight $$\frac{\partial C}{\partial w_j} = -\frac{1}{n} \sum_x\bigg(\frac{y}{\sigma(z)} - \frac{(1-y)}{1-\sigma(z)}\bigg)\sigma'(z)x_j$$  Ok, the derivative of ReLU is (note that it is not differentiable on 0, put 0 instead) $$\sigma'(z) = \left\{      \begin{array}{lr}        1 & : z > 0\\        0 & : z \leq 0      \end{array}    \right. $$  When $z > 0$, $$\frac{\partial C}{\partial w_j} = \frac{y-z}{z(1-z)}$$  $z = 1$ is undefined  when $z \leq 0$ $$\frac{\partial C}{\partial w_j} = \frac{y-0}{0(1-0)}$$  which is undefined as well.  Can someone shed some light?


Question regarding the proof of $\pi$ is transcendental.

I was reading a proof of the fact that $\pi$ is transcendental over $\mathbb{Q}$, and the author mentioned that if $\pi$ is algebraic then so is $i \pi$, but I'm not particular sure why. Can anybody explain this to me? Thank you.


Number of nonzero Fourier coefficients for any $x$ can be at most countably many

I have been trying to prove Lemma 3.5 in "Introduction to Functional Analysis" by Kreyszig, which says that:  Any $x$ in an inner product space $X$ can have at most countably many nonzero Fourier coefficients $\langle x,e_k\rangle$ with respect to an orthonormal family $(e_k), k\in I,$ in X.  This is my attempt at proof using the hint provided in the book:  Let $n_m$ be the number of Fourier coefficients which are greater than $1/m$. By Bessel inequality: $$\|x\|^2\geq\sum_{k=1}^{\infty}\big|\langle x,e_k\rangle\big|^2> n_m\frac{1}{m^2}.$$ $$\implies n_m< m^2\|x\|^2. $$ This last inequality is clearly true for any $m=1,2,....$. Which implies that maximum number of nonzero Fourier coefficients $n_{\frac{1}{\infty}}<\infty.$  But I am stuck here. It is clear that number of nonzero coefficients might be infinite, but how does it imply $n_m$ is still countable.  The same question has been asked at: . But I don't understand the last sentence of the answer: Therefore there are only countably many i with $|\langle x,e_i\rangle|>0.$


"I don't buy no drinks." Grammatically correct?

I don't buy no drinks.   I saw this phrase in a song, and I'm not quite sure if it's correct I hope you'll help me find the answer. Thank you in advance.


Fixed field of automorphism $t\mapsto t+1$ of $k(t)$

I'm working on the following problem:     Determine the fixed field of the automorphism $t\mapsto t+1$ of $k(t)$. (Ex 7, section 14.1, Abstract Algebra by Dummit & Foote).    Here is my attempt of a solution:  Let be $\sigma$ the automorphism determined by $t\mapsto t+1$ and fixing $k$. An arbitrary element of $\alpha(t)\in k(t)$ has the form $\alpha(t)=\dfrac{p(t)}{q(t)}$ with $p,q\in k\left[ t\right]$. We can take $p,q$ such that $(p,q)=1$ and $q$ monic. If $\alpha$ is a fixed element by $\sigma$, then we have $\alpha(t)=\alpha(t+1)$, so that $\dfrac{p(t)}{q(t)}=\dfrac{p(t+1)}{q(t+1)}$ and finally $p(t)q(t+1)=p(t+1)q(t)$. As $(p,q)=1$, $q(t)$ must divide $q(t+1)$. By the same reason, $q(t)$ must divide $q(t+1)$, and as we took $q$ monic, we conclude that $q(t+1)=q(t)$, ie, $\sigma(q(t))=q(t)$. Now we note that, as $\sigma$ fixes both $\alpha(t)$ and $q(t)$, it must also fix $p(t)$.  Now I'm getting stuck. If the characteristic of the field $k$ is $0$, I can say both $p$ and $q$ have an infinite number of roots (if they're not constant polynomials), so both have to be constant. But if the characteristic is non-zero, I can't conclude in the same way. What can I say about the polynomials?  Thanks in advance!


Migration tool trying to deploy all /src when package.xml only specifices one custom object

I am trying to set up a Jenkins job which uses the migration tool to move code from a source control system to an org.  To test the job I created a new custom object  named aaaTest__c.  I changed my package.xml to the following:  <?xml version="1.0" encoding="UTF-8"?> <Package xmlns="http://soap.sforce.com/2006/04/metadata">     <types>         <members>aaaTest__c</members>         <name>CustomObject</name>     </types>     <version>31.0</version> </Package>   When my Jenkins job runs I see 1160 components that failed to deploy.  These include objects, workflows, triggers, classes and more.  The object errors appear to be for the custom fields on that object.  The errors all look like this:  workflows/Account.workflow (Account.Test_Task) -- Error: Not in package.xml   I don't understand why the migration tool is trying to deploy all of these components when I'm telling it just deploy one.  Any help will be greatly appreciated.


Re-entering Israel after Student Visa expires?

My multiple entry student visa was issued on June 25th, 2012 and expires on June 24th, 2013.  I entered Israel on August 26th, 2012.  I am planning to leave Israel on June 13th (to Poland) and return approximately a month later in order to take my return flight home to the United States (I am a U.S. citizen); staying in Israel no longer than a week.  Will I be able to re enter Israel in order to do so?


I am working on wsl2: OS: Ubuntu 20.04.1 LTS on Windows 10 x86_64 Kernel: 4.19.104-microsoft-standard Uptime: 2 mins Packages: 1329 (dpkg) Shell: zsh 5.8 Terminal: emacs CPU: AMD Ryzen 5 4500U with Radeon Graphics (6) @ 2.370GHz Memory: 201MiB / 12277MiB  When try to upgrade all apps, it report errors: ➜  gaowei sudo apt upgrade -y Reading package lists... Done Building dependency tree Reading state information... Done You might want to run 'apt --fix-broken install' to correct these. The following packages have unmet dependencies:  emacs-bin-common : Depends: emacs-common (= 1:26.3+1-1ubuntu2) but it is not insta lled  emacs-el : Depends: emacs-common (= 1:26.3+1-1ubuntu2) but it is not installed E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).  Unfortunately, it does not help to run --fix-broken but report errors: Preparing to unpack .../emacs-common_1%3a26.3+1-1ubuntu2_all.deb ... Unpacking emacs-common (1:26.3+1-1ubuntu2) ... dpkg: error processing archive /var/cache/apt/archives/emacs-common_1%3a26.3+1-1ubun tu2_all.deb (--unpack):  trying to overwrite '/usr/include/emacs-module.h', which is also in package emacs26 -common 26.3~1.git96dd019-kk1+20.04 dpkg-deb: error: paste subprocess was killed by signal (Broken pipe) Errors were encountered while processing:  /var/cache/apt/archives/emacs-common_1%3a26.3+1-1ubuntu2_all.deb  It report the errors repeatedly, whatever packages I tried to install. How could I solve the problem if not reinstall ubuntu on wsl? The emacs26 could not been removed: ➜  gaowei sudo apt remove --purge emacs26 Reading package lists... Done Building dependency tree Reading state information... Done You might want to run 'apt --fix-broken install' to correct these. The following packages have unmet dependencies:  emacs-bin-common : Depends: emacs-common (= 1:26.3+1-1ubuntu2) but it is not going  to be installed  emacs-el : Depends: emacs-common (= 1:26.3+1-1ubuntu2) but it is not going to be i nstalled E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).


In Avengers: Endgame, when Hulk initially uses the new Infinity Gauntlet, it takes a tremendous effort from him (in addition to almost burning his entire arm), in order to snap his fingers and restore the world as we knew it. Yet at the end of the movie, when Iron Man uses the Gauntlet, it seems very easy for him to snap his fingers.  How was Tony able to wield the stones with such ease when Hulk was clearly struggling with it?


I have Windows 7 and 8 installed on my laptop, I just installed Ubuntu.  It normally boots up in Windows 8, how do I change that?