Syncronize method call on parameter value in java

I need to synchronize this method on id argument value. I was thinking about using string pool reference, is there a better way?  static void f(Number id) {   String s = String.valueOf(id).intern();   synchronized (s) {    // syncronize this block by id value   } }


I would like to add a small quotations as we can find in books before a chapter.  Is there a simple command to do this ?  I use Xelatex and biblatex, with author-year style


Let $A=\mathbb{Z}[x]_{deg\leq n}$ denote the set of all polynomials in $x$ with degree less than or equal to $n$. Show that A is denumerable. I know that set of all polynomials with integer coefficients is countable but how can I prove this problem ?


How can Quicksilver run with someone without injuring them?

If Quicksilver can go that fast, if he didn't hold the person’s neck while running with them would his sudden burst of speed snap their neck? Or would they just have whiplash like in X-Men: Days Of Future Past?


BasicTeX - how to identify packages that need to be added after an upgrade

I'm using the BasicTeX distribution on OS X and recently upgrade from the 2011 to the 2012 distribution. This forces me to add the packages that I had added over time to the BasixTeX 2011 installation by pulling them from the online repository with tlmgr. Is there a good way to list these packages that are not part of BasicTeX but are part of the complete TeXLive?


I used the following    \usepackage[a4paper,width=150mm,top=25mm,bottom=25mm,bindingoffset=6mm]{geometry} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhead{} \fancyhead[RO,LE]{Systemic Crisis: Visualizing Vulnerability} \fancyfoot{} \fancyfoot[LE,RO]{\thepage} \fancyfoot[LO,CE]{chapter \thechapter} \fancyfoot[CO,RE]{Raisul Islam} \renewcommand{\headrulewidth}{0.4pt} \renewcommand{\footrulewidth}{0.4pt}    I am writing my thesis. i have the warning     Package Fancyhdr Warning: \headheight is too small (12.0pt): Make it   at least 14.49998pt. We now make it that large for the rest of the   document. This may cause the page layout to be inconsistent, however.   Please help


On my rooted Nexus 5, when I open any file manager the sdcard shows empty. Some apps however are able to read from it and I can see it is intact when I connect it to my PC. This means I can't access the files on my sdcard (virtual sdcard in the case of N5) and also evernote fails to sync as it can't create a database.   I have tried chmod777 on the sdcard through recovery to try to set permissions right which failed. Restarting the device also fails. Clearing the dalvic cache also fails.   Any help would be appreciated!


Are there any decent picture editing programs in Ubuntu like Ifran View?

XnViewMP could be fine but how can I instal it? I can't understand the forums sort  of coding. I can't do it.


Conditional formatting on whether something is a formula in Google Sheets?

Is there a way, in Google Sheets, to have conditional formatting of some sort, to change the background color of a cell based on whether the cell contains a formula or a plain value?


Place parentheses around a cross-reference

Is possible to surround a cross-reference with brackets or parentheses? For example when I write a command like some text \ref{some label} then when compiled the output was some text (12) without manually placing parentheses in latex  command, like some text (\ref{some label}).


Why does explorer.exe has an established connection to a microsoft server?

This seems a bit odd. Using netstat -a -b -n I've found the following:  TCP 192.168.1.X:1150   157.56.124.76:443 ESTABLISHED [Explorer.EXE]   It turns out that the ip 157.56.124.76 which resolves to db3wns2011017.wns.windows.com is a static ip from .  Moreover, using tcpView from  I can see that it's a TCP connection over https.  I tried closing the connection and after a second it was back on. Initially a kb of data was sent and nothing after that..  What is this all about and why is it Established?  I have windows 8.1 enterprise. I don't have OneDrive or any other microsoft cloud stuff installed. This is persistent, and is there after booting.  update  After finding out that this is related to Windows Push Notifications, I followed the steps  to disable such notifications, but the connection remains.


Pgfplots: Two legends for scatter plot with multiple plots and classes

I need to create a detailed scatter plot. It contains two different plots, each with several classes - each plots can contain upward of 1000 coordinates with varying levels/classes in each. There may also be more than 2 plots.  After lots of searching I got the colors and classes right, but now I would like to split the legend into one for the classes, and one representing each plot.  I am only getting one of two scenarios:  Either I can have eq. \addlegendentry{A} after my plot,which then shows A and B in a legend - but does not specify the marker type (figure 1).     Or if I comment out and only specify the class legend entries, I get the correct legend with the different class colors (figure 2).    What would like to see is both legends, seperately, but with the A/B legend in black and showing the marker style. Something in the line of the following:    I am aware that I could modify the classes to A1 ... A10, B1 ... B10, but this would result in a long list of legend entries. I would prefer it to keep it simplified.  Any help will be tremendously appreciated!  MWE:  \documentclass{article} \usepackage[a4paper, left=1.5cm, right= 1.5cm, top=1.5cm, bottom = 1.5cm]{geometry} \usepackage{pdflscape} \usepackage{pgfplots} \pgfplotsset{compat = 1.3} \usepackage{tikz} \usetikzlibrary{pgfplots.dateplot,calc,plotmarks}  \definecolor{grey2}{RGB}{100, 100, 100} \definecolor{blue1}{RGB}{99, 190, 255} \definecolor{blue2}{RGB}{0, 128, 192} \definecolor{blue3}{RGB}{82, 15, 191} \definecolor{green1}{RGB}{135, 255, 66} \definecolor{green2}{RGB}{42, 173, 40} \definecolor{yellow1}{RGB}{255, 245, 66} \definecolor{orange1}{RGB}{255, 160, 66} \definecolor{pink1}{RGB}{255, 99, 174} \definecolor{purple1}{RGB}{187, 99, 255} \definecolor{red2}{RGB}{255, 66, 66}  %------------------------- \begin{document} \begin{landscape} \begin{center} \begin{tikzpicture}     \begin{axis}         [width = 10cm, height = 10cm,      scatter,         only marks,         scatter src=explicit symbolic,             scatter/classes={                            1={grey2},                 2={blue1},                 3={green1},                 4={green2},                 5={yellow1},                 6={orange1},                 7={red2},                 8={purple1},                 9={pink1},                 10={black}             },             legend style={             at={(0.5,-0.135)},                 anchor=north,                 inner sep = 0.2cm,             },             legend columns=10,             legend entries={1,2,3,4,5,6,7,8,9,10},             tick pos = left,             ymin = -0.1,         ]         \addplot [mark size=2.5pt, mark=*] coordinates { (5.8, 5.7) [4] (4, 5.4) [4] (4, 5.6) [3] (4.2, 5.5) [3] (3.9, 5.4) [2] (2.1, 2.6) [1] (2.4, 2.6) [1] (2.3, 7.3) [5] (2.4, 7.3) [5] (5.5, 7.2) [6] (6, 10.1) [8] (7.3, 10) [8] (10, 9.2) [7] (3.8, 9.3) [7] };                   %\addlegendentry{A} %when this is commented out, I get only the classes         \addplot [mark size = 3pt, mark=square] coordinates { (2.4, 5.7) [4] (3.6, 5.5) [3] (3.5, 4.1) [2] (8.7, 3.5) [2] (6.0, 2.7) [1] (5.2, 8.3) [6] };                  %\addlegendentry{B}  %when this is commented out, I get only the classes \end{axis} \end{tikzpicture} \end{center} \end{landscape} \end{document}


What are the requirements for the larger images for community ads?

On the meta posts that collect community ads (), I see ads in two sizes, 300x250px and 600x500px.  (Everything renders the same when ads are actually used on the sites, as you would expect.)  The requirements for ads include:     The image that you create must be 300 x 250 pixels, or double that if high DPI.   I assume "high DPI" is a property of the software used to create the ads, or perhaps some "image export" property.  I'm not a graphics person; the ads I've made have usually started out as photos or similar art that I crop and scale to 300x250 using low-end software (Paintbrush on Mac, Paint on Windows, that kind of thing).  Should I be making them double size?  I haven't because nothing in my software says anything about "high DPI" so I assume it doesn't apply to me.  In a few months we'll be doing the next round of ads on my sites, and if I should be doing something different to make better images, I'd like to know.


Why is script with " xp_cmdshell " in comment failing with a transport level error?

When executing the following batch that is part of a large script:  ... GO ----------------------------------------------------------------------------------------------- -- Removed the xp_cmdshell for deleting the backup file  ----------------------------------------------------------------------------------------------- if exists (select * from dbo.sysobjects where id = object_id(N'[dbo].[PR_MyProc]') and OBJECTPROPERTY(id, N'IsProcedure') = 1) drop procedure [dbo].[PR_MyProc] GO ...   We get the following error on a remote SQL Server:      Msg 121, Level 20, State 0, Line 0 A transport-level error has   occurred when receiving results from the server. (provider: TCP   Provider, error: 0 - The semaphore timeout period has expired.)   When we remove "xp_cmdshell" from the comment, the batch succeeds. This error only occurs on some of our SQL servers. We are running the script remotely. The version of SQL Server that fails is:      Microsoft SQL Server 2014 - 12.0.2000.8 (X64) Feb 20 2014 20:04:26 Copyright (c) Microsoft Corporation Standard Edition (64-bit) on Windows NT 6.2 (X64) (Build 9200: ) (Hypervisor)    On another server the same script succeeds. That server has this version:     Microsoft SQL Server 2014 - 12.0.2000.8 (X64)   Feb 20 2014 20:04:26   Copyright (c) Microsoft Corporation  Standard Edition (64-bit) on Windows NT 6.1 (X64) (Build 7601: Service Pack 1) (Hypervisor)    Both servers have xp_cmdshell enabled. The failing server is running Windows 2012 R2 and the server that succeeds is running Windows Server 2008 R2 SP1. If we run the script on the server locally it succeeds. If we run the script remotely from another virtual server, it fails. We also found that the script only fails if the comment has "(space) xp_cmdshell (space)".  Can anyone tell me why this script fails? And why does it fail on some servers and not others?  There is no antivirus running on the server. SQL Server Management Studio is connected, changing the comment to remove xp_cmdshell always succeeds and the original script always fails.


Will I lose a badge if I remove the question I earned it on?

Let's say I get a Popular Question badge on one of my questions. If I remove that question, will I lose that badge?


How does a circular lens produce rectangular shots?

Is it something like the sensor captures a circular image and then what we get is the cropped version?  Something like this:    Or did I get it completely wrong?


Let $m \geq 3$ be an odd integer. Prove that for any $a \in \mathbb{F}_{2^m}$, the equation $x^6+x+a=0$ has a zero or two distinct solutions in $\mathbb{F}_{2^m}$.  I have proven the following facts:  Let $a>1$ be an integer. For any positive $n,d\in \mathbb{Z}$, $\,$ $d$ divides $n$ if and only if $a^d-1$ divides $a^n-1$. In particular, $\mathbb{F}_{p^d}\subseteq \mathbb{F}_{p^n}$.   Let $\phi$ denote the Frobenius map $x\mapsto x^p$ on the finite field $\mathbb{F}_{p^n}$. Then $\phi$ gives an isomorphism of $\mathbb{F}_{p^n}$ to itself. Also, $\phi^n$ is the identity map and no lower power of $\phi$ is the identity.   For any prime $p$ and any nonzero $a \in \mathbb{F}_p$ prove that $x^p-x+a$ is irreducible and separable over $\mathbb{F}_p$.   I don't know if any of these facts will help me prove this. I am currently studying Chapter 13 from Dummit and Foote. Any help on how to prove the statement is greatly appreciated, thank you.  ***My question is not exactly the same as the post in   because I found a counterexample for $x^2+ax+1=0$ having the same number of solutions as $x^6+ax+1=0$ in $\mathbb{F}_{2^m}$ whenever $m \geq 3$ is odd.


So, I made a stardew valley.desktop and add this shortcut to favorites.  But when I start the game, the game creates a new icon and replaces mine with that one instead.    How I can fix this?


Puzzle: Betting on basketball games strategy

This is a question I saw as an interview question, that I cannot figure out.  Devise a method for betting on the individual games of a basketball series so that if your team wins the series, you win \$100, and if they lose the series, you lose \$100.  Series' are 7 games, and the first team to win 4 games wins the series (so a team could win after 4,5,6, or 7 games). The problem is, how do we devise a strategy for individual games, so that no matter the sequence of games, you get a predictable amount at the end? I cannot think of anything...


A Rogue dilemma: to roll for Stealth, or not to roll?

I need some guidance about how to best use Stealth checks for a campaign.   When it comes to Stealth, say of a Rogue*, would it be better to allow players to roll for their own Stealth skill check, or, for the DM to roll for them?  The hook is whether allowing players to roll for Stealth takes away the potential drama and infuluences their decisions.   SCENARIO: The party comes into what looks like an abandoned castle atop a hill. They enter the great hall and notice that on the floor there is fresh blood. The wind whistles through the broken rooftop. The party had heard back at the local tavern, the "Ditches & Riches", that rumours have it that there is an undead creature lurking in the hills and the ruins of the old castle. The party decides to investigate. The Rogue decides to go ahead and use their Stealth to find out what they might be dealing with. They make a plan: an ambush! They agree on an ambush point; the Rogue will find the undead and report back; they will then purposely make some noise to attract the undead and set the speedy Monk as bait to lure the undead into the ambush point.  The Rogue sets off to look for the undead creature...   First Option: The Rogue rolls for Stealth and after bonuses had a confident score of 28.  Second Option: The Rogue rolls badly and ends up with a miserly score of 12.  Third Option: The DM rolls for the Rogue and does not tell the player.    The implications here are different and it affects game-play. If the Rogue rolls a very high score for Stealth they will be confident about exploring the chambers around the main hall looking for this undead, maybe going a bit further afield from where the party are hiding even. If the Rogue's roll is dire, then they are likely to overly cautious just peak as they know that if the undead is powerful, their passive perception will likely reveal the Rogue's position and possibly could end up in death. If the DM rolls and does not declare the result, the Rogue will investigate regardless, but be aware that there is a chance of being discovered, so it could create a sense of intrigue and actual peril in the players.  DM strategy: My question is specifically about whether allowing players to roll their own Stealth checks takes away some of the potential fun in the game? How can you add a sense of intrigue and peril into the campaign when players are investigating an unknown area when they already know what their Stealth check was?  Please put on your DM hats on for this question. Thank you.    (*) I used a Rogue in my question because Rogues tend to be the PCs that most often use/require Stealth checks, but this could apply to any class using Stealth.


I want to generate a list of basic monomial from x^0 to x^n (in particular, n=9) using Sympy. My quick solution is a simple list comprehension combined with Python's lambda function syntax:  import sympy as sym x = sym.symbols('x')  monomials = [lambda x: x**n for n in range(10)]   However, when I verify that monomials is constructed as expected, I find that:  print([f(x) for f in monomials]) >>> [x**9, x**9, x**9, x**9, x**9, x**9, x**9, x**9, x**9, x**9]   If I redefine monomials without using the lambda syntax, I get what I would otherwise expect:  monomials = [x**n for n in range(10)] print(monomials) >>> [1, x, x**2, x**3, x**4, x**5, x**6, x**7, x**8, x**9]   Why do I get this behavior?    Specs:   Python 3.5.1 Sympy 1.0   I am using the Anaconda 2.5.0 (64-bit) package manager.


How to get ride of 50 GB of other storage on mac when tried everything?

I've tried everything to find and delete these 'other' files:  rebuilding spotlight index using ncdu using "professional" disk utility apps like omnidisk disabling/deleting local snapshots deleting my cloud drive (I use pCloud and I really thought this was the issue as currently spotlight can't access its files, so it would have put them in other) repair disk through disk utility  Any other advice? I have a 2015 mac pro.


How to make the below arrows in latex    The suggested duplicate is a vertical tree and I don't need that I just need a horizontal two arrows


Can I damage my camera's lens mount by lifting it with a super-tele lens attached?

I have been taking the D850 with the Sigma 150-600 (1.9kg) for a walk in the wild. Normally I use the strap on the lens to carry the camera hanging from my shoulder.  I realized that in many situations I was raising the gear on the camera only for the first moment until I could grab the lens with my other hand.  On a podcast by Tony and Chelsea Northrup on wildlife photography with a 500mm prime lens they mentioned that holding the camera only with a bigger lens attached may damage the mount.  Will raising the gear on the camera only damage the mount?


prove that $\gcd(n^2+n ; n+2) = 1$ or $2$

As stated in the title, I need to prove that $\gcd(n^2+n ; n+2) = 1$ or $2.$ What I have tried: -let $d = \gcd(n^2+n ; n+2)$ $$\implies \begin{cases} d \mid n^2+n \\ d\mid n+2 \end{cases}$$ $$\implies \begin{cases} d \mid n(n+1)   & \quad \text{product of 2 consecutive numbers} \\ d\mod n+2 \end{cases}$$ $d \mid n(n+1) \implies d\mid 2  \quad \text{because product of 2 consecutive numbers is always even}$ now idk how I prove that $d\mid 2 \quad and\quad d\mid n+2$ I'm just bad at number theory, thanks for help in advance.


Find when new hardware is connected on FreeBSD

How can I find out when a device is connected to my FreeBSD machine? Lets say I plug in a USB device, HDMI device, Bluetooth or something like that.  Can I have a console output to say [device] and gives some output about the device?


How do I transfer a file to my server using PuTTY?

when calling SCP in PuTTY on my Win7 box, it doesn't let me use C:/, but I also have no idea where on my local machine it will look for files by default. None of program directory or user directory worked. For example, I saved file.txt next to PuTTY.exe, and also in C:\Users\Me but calling SCP file.txt file.txt in PuTTY failed both times with      cp: cannot stat 'file.txt'   So, how do I transfer a file to my server using PuTTY?  EDIT: Also, calling SCP file.txt myserver:file.txt gives a similar error: file.txt: No such file or directory


I was browsing through the apt folder to try my proxy settings and I was unable to find the apt.conf file in Ubuntu 11.04. Is there any alternative file for it?  Adding proxy settings to 99-synaptic in apt.conf.d does not help as it gets overwritten everytime I restart the system.


Why didn't the agents take over Neo's body?

Apparently, when someone sees something strange or unusual in the Matrix, it triggers some kind of red flag that tells the agents "come here and take over that body". We see it a few times during the movie, like in the subway station, with an old hobo, for example.  Couldn't the agents add Morpheus's and/or Trinity's faces to the list of triggering elements? If not, what about a self-repairing mirror?  My point is: why didn't the agents simply take over Neo's body? They had many opportunities before he was out of the Matrix. Can't they see through his eyes?  Plus, on a purely cinematic level, imagine how dramatic the scene would have been. Morpheus would have had a dilemma: getting rid of the agent would mean killing the potential One.


Returning to the US after previous overstay

I travelled to the US as a tourist and lived there illegally for almost 9 years. I was never arrested, or had any trouble with the law. I was never deported. I paid my taxes (had a TIN), had a job, bank account, etc.. About 9 years ago I decided to leave as I was tired of living like that, not able to be legal, in fear of deportation and loosing everything.  Will I be allowed to enter US now, as I hold a different passport other than the one I overstayed with?


I am in doubt with an exercise - I need to calculate  $$\left(205\mid853\right)$$  I would use the fact Legendre's symbols are multiplicative, but then I would have something like   $$\left(5\mid853\right)\left(41\mid853\right)$$  and it would not help much with Gauss lemma, since it would mean having sequences $(853-1)/2$ longs to multiply, to operate $\mod 853$, and so on.   Is there a faster trick I don't see?  Thanks in advance.


Square of largest area inscribed in a right triangle

I was solving a question while I was stuck at a point. The question wanted me to find the length of the side of the square of largest possible area that can be inscribed in a given right triangle. But I was thinking whether how to prove that the square with largest area is the one whose two of the sides coincide with the legs of the right triangle. I've tried proving that but I couldn't figure any way out.  Can someone help me prove it in an easy way?  The answer that is being linked to it as duplicate does not give specific proof for a right triangle.


These seem to get marked as duplicate... but there is an easily available piece of information that I had to do quite a bit of perusing to find that I think most users asking would like to see:  Per the   "Users of 12.04 LTS will be offered the automatic upgrade when 14.04.1 LTS is released, which is scheduled for July 24th."  I'm only posting this in case some other frustrated user is looking for this information, and like me, is not finding it in the other answers the "duplicates" are being referred to.


Multiplicative Inverse for Elements in an Integer Ring

In the book I'm reading it says that there exist elements with multiplicative inverses in a integer ring if $gcd(a,m)=1$ where $a$ is the element and $m$ is the modulo.   The inverse $a^{-1}$ is defined such that $a \times a^{-1} \equiv 1$ mod $m$  Also it says that if an inverse exist for $a$ we can divide this element since $b/a \equiv b  \times a^{-1}$ mod $m$   I'm confused as to what $b$ is in this case? My guess right now is that it is another member in one of the equivalence classes for the modulos $m$.


I want to make one of my favorite white bread sandwich loaves, but I'm out of sugar. What I do have is honey. How much honey should I use to replace 3 Tbs of granulated sugar? How much should I reduce the water in the recipe to compensate?


17.10 Software installed in software center, but not accessible

In Ubuntu 17.10 I installed applications from the software center. At first everything worked fine, but after a few days they kind of disappeared. They are neither found when searching in the dash, nor when the executable name directly in the terminal. However, the software center shows them still as installed and they can be launched from there. Any help to fix this strange behavior is appreciated.


Writing function definition in header files in C++

I have a class which has many small functions. By small functions, I mean functions that doesn't do any processing but just return a literal value. Something like:  string Foo::method() const{     return "A"; }   I have created a header file "Foo.h" and source file "Foo.cpp". But since the function is very small, I am thinking about putting it in the header file itself. I have the following questions:   Is there any performance or other issues if I put these function definition in header file? I will have many functions like this. My understanding is when the compilation is done, compiler will expand the header file and place it where it is included. Is that correct?


Is there a "continuous product" which is the limit of the discrete product $\Pi$, just like the integral $\int$ is the limit of the summation operator $\sum$? Thanks!


Probability Brownian motion is positive at two points

Let $0<s<t$ and $(B_r)_r$ is Brownian motion. Does anybody know what $P(B_s>0,B_t>0)$ is? I think I remember it was some $arctan$-law but I don't know the exact form. So I do not need a proof, stating the result would be completely sufficient, but I could not find it using google.  Thank you for your help.


How do I disable notifications in my personal profile for activity on pages I am an admin of?

I'm an admin of several pages on Facebook (for technical stuff like RSS imports, etc.), but neither do I contribute content nor do I care about their content.  Still, as an admin, I get notifications (upper left hand, the globe icon) about activity (someone liked this, someone posted that) on those pages in my personal (!) profile .  Does anyone have the same issue? Is there any way to explicitly disable notifications for certain pages?  (This behavior seems to be new, by the way; I'm only seeing those notifications for a few weeks now.)


What is the correct way to read color codes?

For example,    The resistor above has four colors. Green, blue, red, gold.   My calculation says its value is 562 ohms +-10%. But this page says its value is 5.6K-1/4W. What is my mistake?


In British English, when speaking of, or to medical doctors, when does Mr denote a higher rank than Dr?

My knowledge of the nuances of British English come from reading authors such as P.D.James, but I have the impression that Dr. Smith is a less eminent medical doctor than Mr. Smith.  Was this so, and if so, it is still the case?  When does it take for Dr. Smith to become Mr. Smith?  And, if the eminent medical doctor is a woman, is she referred to as Mrs. Smith whether or not she is married?  Ms. Smith or Miss Smith seems unlikely, but, as I say, I don't understand the nuances.  (Sorry not to have a specific quote.)


How do animal perceive distances with their eyes and ears

I am studying how animals (including the human beings) can perceive distances thanks to their eyes and their ears. I am focusing on the fact that they always go in pairs: two eyes, two ears, etc.  About the sight, I think our eyes use the parallax. But is this enough? Is this the only way we can perceive distances with them?  About the sounds, I think it is merely by interferometry, but I am not convinced, because the distances between our ears and the wavelength are not always comparable to one another.  What do you think about it? Thanks in advance,  Isaac


RegEx to check first character as + and others are only numbers

My use case is to validate a String only consists of + and the numbers. I have tried with so many regexes but couldn't able to fix my issue. I have used /^[0-9]+$/ regex but it is failed in the 2 nd and 3rd(Obviously it is because it is having A Character) input. My need is, if the input is 00000094777216903 - TRUE if the input is +947777216903     - TRUE (+ is fine if it is in the beginning of the string) if the input is +947777216903A    - FALSE if the input is 0000777216903A    - FALSE  Can anyone help me to achieve my need in JS.


How to Label and Caption a Tikzpicture inside a tabular environment

What is the correct way to label and captionize a tkizpicture inside a tabular environment? (Since figures are not allowed inside a tabular)  Excerpt from my .tex:  \begin{tabular}{l r}  &    \begin{tikzpicture}    ... % I want to label this tikzpicutre and give it a nice caption    \end{tikzpicture} \end{tabular}   Outside the tabular I would have done it like this:     \begin{figure}    \begin{tikzpicture}    ...     \end{tikzpicture}    \label{fig:...}\caption{...}    \end{figure}   Basically I want to create a page that looks like this:  ---------------------------- |Text Text    TKIZ    TKIZ | |TextText     TKIZ    TKIZ | | Text Text   Figure X: ...| |                          | |This text is under the    | |table and references above| |TKIZ Figure with \ref{..} | ----------------------------


How to prove the property of the Lemoine point of a triangle?

From Wolfram , I know there is a Lemoine point of triangle, also called symmedian point, the sum of squared distances of this point to all the three sides is algebraically minimum.    How to prove such a property?


We know that surprisingly enough, $i^i=\frac1{e^{\frac\pi2}}$.  But what about finding the value of ${i^i}^{i\cdots}$? Is it possible?  My attempt: Let $${i^i}^{i\cdots}=x$$ $$i^x=x$$ Or $$\left(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}\right)^x=x$$ $$e^{\frac{\pi}{2}ix}=x$$ But can we take the $\log$ of both sides?  Even if we take, $$\frac{\pi}{2}ix=\log x$$ Now how to solve this equation?  Edit: OKay, as pointed by @JackD'Aurizio, that we have to first check whether the given sequence converges or not. But I have no idea for how to check that? (Please answer in elementary terms)


Mathematical physics text with plenty of applications

I'm looking for texts on mathematical physics. I've seen various other threads, but the texts recommended in those threads were mathematical methods of theoretical physics texts, that is to say those texts focused on the math methods useful for physicists and assumed the applications of those methods would be covered in some other text. What I'm looking for is a book which introduces some math and then looks at its applications (back and forth) rather than a text which just goes over some math. (Example of books which are NOT what I'm looking for: Mathematics for physicists by Dennery, Math methods for physicists by Weber and Arfken etc)  I've taken courses in multi-variable calc, linear algebra, real analysis, and I'm currently taking a course in abstract algebra. But so far I've only seen applications of multi-variable to physics. I'm looking for books which look at the applications of the other subjects mentioned above to physics, of course books which cover subjects beyond those mentioned are also welcome.   So far I'm liking the flavor of the text "A Course in Modern Mathematical Physics" by Szekeres, but I'd prefer a text which got to the physics side of things more quickly (in the Szekeres text the first eight chapters are strictly on pure math).   After some amazon searching it looks like Theoretical Physics by Joos, Mathematical Physics by Henzel, and Physical Mathematics by Cahill may be good bets?


Add "Computer" item to Nautilus sidebar on Ubuntu 17.10

On Ubuntu 17.10 there's no longer link to root partition in sidebar, called "Computer" on earlier Ubuntu versions. Is there any way to add "Computer" item to Nautilus sidebar?


How to compare entries in a java phone book using link list

How would I compare an object that I created using scanner. To an object stored of the same class that I placed in the java link list.  This is where I get the object stored in the phone book class where my java link list is.  //this is the class I will use to   //create an object to store in the objects of link list   //here I will store the records      public class Person {     private String firstName;      private String lastName;     private String phoneNumber;      public Person()     {     firstName="";     lastName="";     phoneNumber="";      } public Person(String nombre,String last, String number) {     firstName=nombre;     lastName=last;     phoneNumber=number;      StringBuilder str =new StringBuilder(phoneNumber);     str.insert(3,"-");     str.insert(7,"-");     phoneNumber=str.toString();   }  public Person(String nombre, String last) {     firstName=nombre;     lastName=last;     phoneNumber="";   }   } //this will see if the two object are equal without comparing phone numbers public boolean same(Person waco) {     boolean perro=false;      if(firstName == waco.firstName && lastName == waco.lastName)     {         perro =true;      }         return perro; }   This is how I add entry to my link List.    //santiago is the link list       if( input == 'n')     {         System.out.println("you have chose to add an entry");         String first; //this will hold the firstName         String last; //this will hold the last Name         String phone; //this will hold the phoneNumber          System.out.println("enter the first name");         first=keyboard.nextLine();          System.out.println("enter the last Name of this person");         last=keyboard.nextLine();           System.out.println("insert phone in the following form without dashses xxx-xxx-xxxx");         phone = keyboard.nextLine();         keyboard.nextLine();          santiago.add(new Person(first,last,phone));   }   Now what I am trying to do is see how a Person object I put into my list, is equal to a new Person item I created using scanner in this following part of the code          if( input == 's')         {              System.out.println("enter a first Name");             String first = keyboard.nextLine(); //put in here the first name             System.out.println("enter a last name");              String last  =keyboard.nextLine(); //put in the last Name              Person agustin = new Person(first ,last);               Person maria = santiago.get(0);              System.out.println(agustin.same(maria));       }   Now if santiago and maria objects have the same first and last Name the same method should return true  But my program returns to it to me as false. I am not sure why?


Looking for CART/ML model that works with relative data

I am a beginner at AI and ML. I have been given a dataset, where I have noticed the columns are relative to one another. So is there any CART or ML model that can work with relative data ? For example in Decision Tree, the tree looks like :   if X[0]<192:      if X[1]>24:        if X[2]<12:        ...  I'm looking for a Decision Tree, that works like this :   if X[0]>X[1]:    if X[1]<X[2]:       ...  Is there any such Machine Learning Model ?


Why is the last pgfplots tick label not shown in one of my groupplots?


Not every left  ring is left . Take $\mathbb{Z}$ as a quick example.  But:     : a left Artinian ring is left Noetherian.   I find this quite amazing. I find this asymmetry shocking. It just seems plain unreasonable that there are rings where every ascending chain of ideals stabilizes but not every descending chain stabilizes, and at the same time  every ring with stabilizing descending chains has stabilizing ascending chains.  I know asymmetries abound in ring/module theory, but this one strikes me as more elementary and uncanny.  My question is:     Why does this happen?   Of course, this question is at an informal level; I'm not asking for a proof of the theorem. I just want to understand why one chain condition implies the other, but not the other way around. At first glance, it just seems so symmetrical, that I would have expected the conditions to be equivalent, or to have neither condition implying the other.  My very naive first observation is that for noetherian rings, we have the characterization "every ideal is finitely generated", but for artinian rings there is not (that I know of) a simple analog, which is perhaps the first spark of an asymmetry...


Deleted ~/.Skype but chat history persists

The title says it all; I deleted the ~/.Skype dir, restarted Skype, agreed to the T&Cs and added my sign-in information, yet my chat history still remains whenever I click any contact I have spoken with.  How do I remove chat history?


I created an empty read-only directory: mkdir -m 400 ~/Desktop/hello  As per the octal permission, it indicates the directory has read only permission. But contrast to that when I am using the following command the directory was deleted: rmdir ~/Desktop/hello  How is this possible to delete the directory when it is read only?


How to enter password only once in a bash script needing sudo

Data   I want operator users on this machine to mount their own cifs shares The sudoers file already contains the /bin/mount -t cifs //*/* /media/* -o username=* command for all operators I want the users to mount a cifs share through a script typing the password only once, not twice. The sudo password and the cifs password are identical.   What I already have  This script works:  #!/bin/bash sudo 'mount -t cifs //192.168.1.1/home /media/$USER/home -o username=$USER'   ...but it requires the users to type the same password twice!     Once for sudo Once for the mount itself   This would also work:  #!/bin/bash echo -n Password:  read -s szPassword echo $szPassword | sudo -S sh -c 'echo $szPassword | mount -t cifs //192.168.1.1/home /media/$USER/home -o username=$USER'   ...but this would require me to allow all operator users to be able to sudo sh (major security problem)  Question  How to mount a cifs share in bash¹ without putting sh in the sudoers file nor creating a permanent/temporary file???  Note 1: no python, perl, C, Go, ... please? Note 2: I know I can just remove the password through the sudoers file, but I'm trying to tighten security, not loosen it, without giving up convenience...


I can't open Eclipse from Dash Home although it shows its icon. Eclipse was properly installed using apt-get.  When I launch Eclipse from Dash Home it doesn't open. It opens only through Terminal. How can I open it from the dash?


How to add memtest86 entry to grub2 menu?

I want to test new memory, but can't find memtest86 entry in grub2 menu. I looked at script /etc/grub.d/20_memtest86+ and found this lines  # We need 16-bit boot, which isn't available on EFI. if [ -d /sys/firmware/efi ]; then   exit 0 fi   The directory /sys/firmware/efi exists. Why memtest menu entry not added, if /sys/firmware/efi exists?


how to force unity to avoid picking up a random object twice

I have a simple enemy wave based survival game the spawn system have an array of enemy AIs and Spawn Points, I want the spawned prefabs to be removed from the enemies array to avoid getting spawned again, is there a way to do so, here's my code: public Transform[] spawnPoints; public GameObject[] enemies;   Pos= spawnPoints[Random.Range (0,spawnPoints.length)]);  AI = Instantiate (enemies[Random.Range (0, enemies.length)]) , Pos);


Would "mid-to-late" and "low-to-mid" hyphenated as compound modifiers?

Would "mid-to-late" and "low-to-mid" be hyphenated as compound modifiers?  Examples:  Temperatures are expected to be in the low-to-mid 60s.  Joe, I think, is in his mid-to-late 80s.  He was in his middle-to-late 40s.  She was in her middle-to-upper 60s.  Temperatures are expected to be in the lower-to-middle 70s.  Are all correct?  Thanks!!!


Limit of $\lim\limits_{x \to \infty}\frac{1}{\cosh(x)}+\log\left(\frac{\cosh(x)}{1+\cosh(x)}\right)$ without l'hopital

I've got this function and I need to find the limit. I have tried multiple things. I've replaced $\cosh(x)$ with $e^x+e^{-x}$ and calculate on that. But it seems like no matter what I do, I always gets a problem with $\infty$.  Here is the function: $\lim\limits_{x \to \infty}\frac{1}{\cosh(x)}+\log\left(\frac{\cosh(x)}{1+\cosh(x)}\right)$


Need of terminal emulator in unix systems

I am trying to understand the concept of virtual terminals in unix and I am not able to figure out the need of terminal emulator and concept of virtual consoles clearly. I was going through a video  on youtube and the lecturer says that now a days we do not have a terminal as we have full fledged setup of monitor, keyboard and mouse. Why we can not consider them as terminal ? According to the  of a terminal, it is a set of hardware used to communicate with processes. Then why the author says that we do not have terminals now a days ?  Why do we need terminal emulator ? Lecturer says that the terminal emulator sits between "x window system server" and the processes talk to the output devices using terminal emulator. But in case of GUI processes talk directly to "x window system server" which in term communicates with device drivers for stdin/stdout. But why do we need terminal emulator in case processes are capable to talking to "x window server" directly. Is it the case that for "x window server" does not support CLI and for command line interaction, terminal emulator acts as an adapter between process and "x window server" ?  EDIT:-  I went through the answer below and some other resources and here is what I got. Display can work in both  as well as  mode. When we use command line interface, the system expects terminal character device files for I/O. Now when we are already running a GUI which means we have display in non character mode, and we open up a CLI, that session expects a terminal character file to communicate, which is not there. So, we need terminal emulators which creates pseudo terminal character files and also communicates with x-window-server and acts like an adapter. Kernel also have some device specific actual terminal character files which come into play when we connect it to any display using text mode. When we are using GUI there is no need of terminal character files. Is the correct or I have got it wrong ?


Chronologically, when does the Death Star scene of Revenge of the Sith take place?

This is basically all Revenge of the Sith spoilers, so read on at your own peril.  The second to last scene of Revenge of the Sith features Darth Vader and the Emperor overseeing the construction of the first Death Star. Several things imply this takes place some time after the film's main narrative.   The Star Destroyers have been remodeled.       The Republic Navy has transitioned into the Imperial Navy and the officers have received new uniforms.       Vader has gotten used to his armor and the Imperial officers have gotten used to Vader.     How much time has passed?  Edit: Some people are claiming my question is a duplicate of this . However, all the linked question's answers state is that the Death Star was in construction during the Clone Wars. They do not mention any of the clues that this scene takes place at a later date, nor do they state when the scene actually takes place.


As the title reveals, I want to prove (based on the axioms of field) that $$-a=(-1)\cdot a$$ I've been trying for a while now, but couldn't think of a way to do it and it got me thinking that maybe its does not require a proof, but it doesn't feel right. Any ideas?


How do I create an Ubuntu live USB using a Mac?

I'd like to create an Ubuntu live USB stick on a Mac to use to install Ubuntu on another machine. How do I accomplish this?


Can someone please explain Maximum Likelihood Estimation in very lay-man terms? I understand that the Likelihood function is obtained by multiplying all the probabilities in the distribution. Or if I am wrong, please correct.


Python unresolved reference error in a function

I am quite new to python so this may be a stupid question. a = 0 def example():          a = a + 1     print(a)  example()  Why is a unresolved when it seems to be above?


Windows Media Player Missing after Creators Update

My copy of Windows 10 N Professional recently installed the "Creators Update", and after rebooting, Windows Media Player is missing and no videos will play on my web browser.  How can I restore this functionality?


Covering estate tax on US assets for non-resident alien

I am a non-resident alien holding a brokerage account in the USA but residing outside the USA. My country does not have an estate tax treaty with the USA. So my estate is liable for a significant estate tax up to 40%. Is there any way to avoid or to cover this tax? I thought of buying term insurance for myself, but I am not sure whether US companies will sell term insurance to a non-resident. I want to buy insurance from a US company because I want the death benefit to be in USD. Can someone suggest as to what the best way to approach this issue is?


I want to solve following problem  Let $f,g : (-1, 1) \rightarrow \mathbb{R}$ be $C^{\infty}$ functions, and suppose that $f^{(n)}(0)= g^{(n)}(0) $ for $n=0,1,2,\cdots, $. Is there some $\delta>0$ such that $f(x) = g(x)$ for all $x \in [-\delta, \delta]$?  Naively, from taylor series expansion of $C^{\infty}$ functions, I suspect that there is $\delta>0$ but I don't know how to prove this rigorously.


How does one find which files are taking up 80% of the space on a Linux webserver?

The drive is constantly filling up. You've hunted down all the spare and random files you can. grep'd for coredump files and even removed some of the un-needed backups...  What would be your next move.  The actual server in question has 10GB of website files and the OS shouldn't take any more than 10GB so how do you track down what's filling a 50GB (virtual) drive?


Why is $\Bbb{Z}_2 \times A_5$ not solvable?

We can write $\Bbb{Z}_2 \times A_5 > 1 \times A_5 > 1$ as a composition series, but why is $\Bbb{Z}_2 \times A_5$ not solvable? I know that $A_5$ is not solvable, but it is enough? I'm really having a bad time with this. Thanks in advance!


Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $

How can I prove that $${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $$  I tried the following:  We use the :  $$y^{\underline k}=\underbrace{y(y-1)(y-2)\ldots(y-k+1)}_{k\text{ factors}},$$ so that $\binom{y}k=\frac{y^{\underline k}}{k!} .$   Then  $${x +y+n- 1 \choose n} = \frac{(x +y+n- 1)!}{n! ((x +y+n- 1) - n)!} =  \frac{1}{n!}. (x +y+n \color{#f00}{-1})^{\underline n} $$  And  $$ {x+n-k-1 \choose n-k}{y+k-1 \choose k}$$ $$\frac{1}{(n-k)!}.(x+n-k-1)^{\underline{n-k}}.\frac{1}{k!}.(y+k-1)^{\underline{k}}$$ $$\frac{1}{k!.(n-k)!}.(x+n-k-1)^{\underline{n-k}}.(y+k-1)^{\underline{k}}$$ $$\sum_{k=0}^n{n \choose k}(x+n-k-1)^{\underline{n-k}}.(y+k-1)^{\underline{k}}$$  According to the Binomial-coefficients:  $$ ((x+n-k-1) + (y+k-1))^{\underline{n}}$$ $$ (x+y+n\color{#f00}{- 2})^{\underline{n}}$$  What is wrong ? und How can I continue?  :/


Homebrew putty installation does not make the putty command recognisable

I would like to instal  with use of Homebrew. I'm performing the following command:  brew install putty   which gives the seemingly correct output:  ==> Downloading https://homebrew.bintray.com/bottles/putty-0.67.el_capitan.bottle.tar.gz Already downloaded: /Users/thisuser/Library/Caches/Homebrew/putty-0.67.el_capitan.bottle.tar.gz ==> Pouring putty-0.67.el_capitan.bottle.tar.gz 🍺  /usr/local/Cellar/putty/0.67: 11 files, 1.5M   However, the putty command is not recognised:  thisuser-541/41:~$ putty -bash: putty: command not found


A program's output seems to be neither stdout nor stderr?

I got a program vsftpd which output doesn't seem to be either stdout or stderr (if that's even possible?)  My terminal output is:  ~# vsftpd 500 OOPS: SSL: cannot load RSA private key   I tried to redirect to a file but I get nothing in the file and the output still goes to the console:  ~#vsftpd > /tmp/out.txt 500 OOPS: SSL: cannot load RSA private key  ~#vsftpd &> /tmp/out.txt 500 OOPS: SSL: cannot load RSA private key  ~#vsftpd 2> /tmp/out.txt 500 OOPS: SSL: cannot load RSA private key   I'm actually trying to call this program from .Net Core from which I'm not able to get the StdOut/StdErr neither. And .Net Core crashes with The process cannot access the file because it is being used by another process. unless I enable StdIn-redirect, which I don't understand, I'm not parsing anything to StdIn and I never experienced this before with any other program calls.


Solving functional equation $f(x)f(y) = f(x+y)$

I'm having some trouble solving the following equation for $f: A \rightarrow B$ where $A \subseteq \mathbb{R}$ and $B \subseteq  \mathbb{C}$  such as:  $$f(x)f(y) = f(x+y) \quad \forall x,y \in A$$  The solution is supposed to be the form $f(x) = e^{kx}$ where k can be complex but I don't see how to show it.  Note: I'm trying to solve this equation to find irreductible representation of U(1) but it doesn't really matter I think


I'm having an interesting (albeit frustrating) issue with Python.   I'm attempting to populate a 2d array called plaintexts based on some calculations, and I've found that all of the entries in this array are duplicated. Ie, plaintexts[0] == plaintexts[1] == ... == plaintexts[n]. I assumed I messed up value assignment so I tried to halve my code to find the issue, but after a fruitless hour I assigned a value to plaintexts[0][3] at the end of my code and lo and behold, that same value popped up in every other row.   Below is my relevant code:  placeholder = ['0'] * 33 plaintexts = [placeholder] * len(ciphers)  for i in range(2):      for j in range(1, 2):          for k in range(0,len(ciphers[0])-1,2):             .             .             .             .             if charType == '010':                 if(plaintexts[i][k/2] != '0'):                    .                   .                   .                   .                 else:                     plaintexts[i][k/2] = (' ', xorstr.lower())                   .                   .                   .                   .  plaintexts[0][3] = '13414113133' print plaintexts[0][3] print plaintexts[1][3] print plaintexts   I'd appreciate any help in figuring out the issue.


Browser back leaves page after going fullscreen in stack snippet

Opening a Stack Snippet in full screen should use history.pushState() to add an entry to the browser history stack. Clicking back will then close the snippet rather than leave the page completely.


Evaluate the following complex integral $\frac{1}{2\pi i}\int_{|z|=1}\frac{\overline{f(z)}}{z-a}\,dz$

Let , $f$ be analytic for $|z|<2$. Show that $$\frac{1}{2\pi i}\int_{|z|=1}\frac{\overline{f(z)}}{z-a}\,dz=\begin{cases}\overline{f(0)} &\text{ if } |a|<1\\\overline{f(0)}-\overline{f(1/a)}&\text{ if }|a|>1\end{cases}$$   By putting $z=e^{i\theta}$ , $\displaystyle\int_{|z|=1}\frac{\overline{f(z)}}{z-a}\,dz=\int_0^{2\pi}\frac{\overline{f(e^{i\theta})}}{e^{i\theta}-a}ie^{i\theta}\,d\theta=i\int_0^{2\pi}\frac{\overline{f\left(\overline{e^{-i\theta}}\right)}}{1-ae^{-i\theta}}\,d\theta$.  Now putting , $e^{-i\theta}=t$ , it becomes $\displaystyle =-\int_{|t|=1}\frac{\overline{f(\bar t)}}{1-at}\,dt$. As $f(t)$ is analytic so $\overline{f(\bar t)}$ is also analytic. Now we can apply the residue theorem and finally I got the desire integral $=-\overline{f(0)}$ when $|a|<1$.     My problem is about the sign. I got an extra negative sign. Please verify my proof & detect where I made mistake ...


I have been using Lubuntu on my netbook for a while without any problems, but I have just upgraded to 17.10 and now it will not boot properly.  I think that the display driver is problematic for some reason as I have used GRUB to load recovery mode and it works fine.  I have tried dpkg and fsck but they have not made any difference.  I cannot post a screenshot as I am a new user, but after the normal boot cycle, the right hand 20% of the screen is more or less OK and the rest of it is black with corrupted text.  Any help gratefully appreciated.  Thanks  BB


Limit of $b_n$ when $b_n=\frac{a_n}{n}$ and $\lim\limits_{n\to\infty}(a_{n+1}-a_n)=l$

I have the following problem.   I have to find the limit of $b_n = \frac{a_n}{n}$, where $\lim\limits_{n\to\infty}(a_{n+1}-a_n)=l$  My approach:  I express $a_n$ in terms of $b_n$, i.e. $a_n=nb_n$ and $a_{n+1}=(n+1)b_n$  We look at the difference: $a_{n+1}-a_n=(n+1)b_{n+1}-nb_n$  Assuming that $b_n$ converges to a real number m, we see that:  $l=(n+1)m-nm$, from where I conclude that $m=l$.  What I'm left with is proving that $b_n$ is convergent which I'm not sure how to do.  Thanks in advance!


is there a bijection for $f: \mathbb R \to \mathbb C$?

I imagine no since the dimensions do not match  but they have the same cardinality $|\mathbb R |= |\mathbb C|$?


I would like to enable bitlocker on my C: drive, but I dont understand the following message:    If it's the hardware, which part exactly? I have a recent asus motherboard with UEFI. How can I find out if my motherboard supports TPM?


How does a change in Constitution affect an NPC/monster/wild-shaped druid's hit points?

If an effect or spell changes an NPC's Constitution (e.g. the  or the fortitude ), how does it affect that creature's max HP? I'm interested in Constitution decreases as well.   I have a player who wants to wear his dwarf belt as a collar when in wild shape, (which I could say no to) but the ioun stone seems entirely possible.  I'm also curious about how Con changes from such items/sources affect a druid in , if that creature can use the item.  I assume I'd modify by hit dice or CR? But that doesn't seem right.  If a wild Direwolf ((37hp(5d10+10) CR 1, CON 15 (+2)) was affected in a specific way, then should it be any different from a druid wild shaping into a Direwolf?  I was maybe thinking player level would affect this, but player level doesn't affect HP of Wild Shape. Also, if it's a level 3 druid Wild Shaped as a Direwolf, then technically that Direwolf is level 3?  I've read () that Wild Shaped druids (that are high enough level to maintain their form) CAN use their beasts hit dice and Con mods during short rests, leading me to believe that Con IS affected by hit dice, but it seems too easy to be correct.  Spells like polymorph and true polymorph match CR with level, but it doesn't seem like something tied to CON


When I go to the WiFi Settings in Camera (Canon 70D) all I see is:  Connection:   Exit Confirm Set Error Details (greyed out)   I can't recall the password or find any way to reset it. Some I found () say the Camera should say Infrastructure mode. Inside the Confirm Settings I can see on page 3 it shows:     Connect'n method: Camera access point mode   But again I see no way to change this.  On my Smartphone EOS Remote app there's a Connection Guide with completely different menus from what I'm seeing on the Camera.  Any idea how I can reset the WiFi Name and Password on the Canon 70D?


why is there a difference in the usage of "neither...nor" in similar sentences?

look at these two sentences:  neither the coach nor the players are going to the beach.   neither the players nor the coach is going to the beach.  why does one sentence use "are" while the other has "is"?  does it have something to do with the arrangement of subjects or is there any other reason?


How to get a closed form for $\sum m f(n,m)$ where $f(n,m)$ is number of weak compositions?

First, consider how many $n$-dimensional vector of non-negative integers $(x_1,x_2,\cdots,x_n)$ are there whose sum of all entries satisfies $x_1+x_2+\cdots+x_n=m$?  For example for $n=2,m=2$, there are $(2,0),(1,1),(0,2)$, so $f(2,2)=3$.  For $n=3,m=2$ there are $(2,0,0),(0,2,0),(0,0,2),(1,1,0),(0,1,1),(1,0,1)$, so $f(3,2)=6$.   How about for general $m,n$? What I know is $f(n,m)\le$ n+m choose n by   --  Then, I would like a closed form solution for $$\sum_{m=0}^Mf(n,m)$$


what would you call a guy everybody picks on?

Let's say we have a guy who is stupid and weak and everybody picks on him and mocks him all the time. What would we call this guy?  I found timid in the dictionary but I am looking for a colloquial word.


Let $U\subset\mathbb R^3$ be an open set, and $f:U\to \mathbb R$ be a smooth function. Suppose that the level set $S=f^{-1}(\{0\})$ is non-empty, and that at each $p\in S,$ the gradient $\overrightarrow \nabla f(p)$ is not the zero vector. Then $S$ is a smooth two-dimensional surface in $U$, and $p\mapsto \overrightarrow \eta(p)=\frac{1}{||\overrightarrow \nabla f(p)||}\overrightarrow \nabla f(p)$ defines a smooth unit-length normal vector field along $S$. At each $x\in U,$ write $H(f)_{(x)}$ for the $3\times 3$ Hessian matrix specified by $$(H(f)_{(x)})_{ij}=\frac{\partial^2f}{\partial x_i\partial x_j}(x).$$   Show that, at each $p\in S$, the second fundamental form $II_p: T_p(s)\times T_p(s)\to \mathbb R$ is the symmetric bilinear map    $$II_p(\overrightarrow v,\overrightarrow w)=\frac{-1}{||\overrightarrow \nabla f(p)||}\overrightarrow v\cdot H(f)_{(p)}\overrightarrow w,$$for all $\overrightarrow v ,\overrightarrow w \in T_p(s)$.       (Here, we view the tagent space $T_p(S)$ as the two-dimensional subspace $(span\{ {\overrightarrow \eta(p)}\})^{\bot}$ of $\mathbb R^3$.      Edit: Actually my question is why the second fundamental form under the usual definition can be written in this way.      Definition: The quadratic form $II_p$, defined in $T_p(S)$ by $II_p(v)=-<d  N_p(v),v>$ is called the second fundamental form of $S$ at $p$, where $dN_p:T_p(S)\to T_p(S)$ is the differential of the Gauss map.   Hopefully, I express this problem explicitly. I was just wondering how to prove this statement.   I took a diffrential geometry class last semester, and when I organized my notes this morning, I found this statement, but there was no proof...  Looking forward to an understandable explaination. Thanks in advance.     Edit 2:Furthermore, show that, at each point $p\in S$, the expression   $$\phi_p(z)=det\pmatrix{-H(f)_{(p)}-zI_{3\times 3} & \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)& 0}$$   (the underlying matrix here is $4\times 4$) defines a second-degree polynomial whose roots $\lambda_1$ and $\lambda_2$ are $||\overrightarrow \nabla f(p)||k_1$ and $||\overrightarrow \nabla f(p)||k_2$, where $k_1$ and $k_2$ are the principal curvatures of $S$ at $p$.      Also, if a non-zero vector $\pmatrix {\overrightarrow v \\c}$ lies in the kernel of the $4\times 4$ matrix $$\pmatrix{-H(f)_{(p)}-\lambda_jI_{3\times 3} & \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)& 0},$$   then $\vec v$ is a non-zero element of $T_p(S)$ and lies in the "principal direction" corresponding to $K_j$.


How to change unity side laucher position from left to right ubuntu 14.04

Is there any method available using which we can change the position of side bar laucher from left to right. I have installed the unity tweak tool but it only allows to auto hide the launcher. There are many tutorials which teaches about how to move launcher to the bottom but i am unable to find any links pertaining the position change to the right   P.S. not to confuse with any other launcher i am uploading this picture


What might be an effective way to universally block or auto-accept common cookie warning banners before the web browser shows them to the user?  Eg. does a userscript (Greasefire/Tampermonkey) exist to find and thwart most cookie-warning implementations, perhaps via a regex search? Or at least can this be accomplished with an extension? (Trying not to bloat the browser with yet another extension, though.)  This applies to many outdated UK and EU websites, especially now that the .


What is the maximum number of downvotes a question can have

I was just wondering what the maximum number of down votes a question can have before it is removed from StackOverflow.


php string comparison not giving expected results

I have a small code snippet has below  $duration = 0; if ($duration == 'daily') {     $duration = '+1 DAY'; }  echo $duration;   I am expecting 0 has output but end results are +1 DAY. i am not able to understand why above conditions is success?  But we i use === returning expected results.  I have checked in php 7 and php 5.5. both versions are giving the 0 as output.


How do I suppress a warning or error message for site users?

drupal_set_message() on certain conditions. Even with visible errors messages disabled, anonymous users see this. Indeed, the comment in the code even has a TODO to change it to an exception.  Obviously I don't wish to hack core. Is there a clean way to suppress this for anonymous and non-administrator users?  Notably, the message is in a t() function, so I could use the  module, but this would affect all users (including site administrator), so it's a bit problematic.


How to tune disk parameters in hdparm.conf by UUID?

I have a disk that was spinning down too fast and   /dev/sda {     apm_battery = 254 }   per  helped. The problem is that I plan on switching the disk in future. How can I make sure that apm_battery will affect only that specific disk?


Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$

Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}.$   I'm currently trying to finish a task that requires me to use mathematical induction to prove that $2^{3^n}+1$ is divisible by $3^{n+1}$. This is the first time that the divider is not a simple integer and I'm having trouble trying to prove it.   This is what I managed to do:     First step:      For $n=1$:      $2^3+1=9$      $3^2=9$      $L=P$      Second step: I assume that for some numbers $n>=1$  $2^{3^n}+1$ is divisible by $3^{n+1}$      Third step: (induction hypothesis):   $2^{3^{n+1}}+1$ is divisible by $3^{n+1}$   I'm getting stuck here, trying to do some algebra and simplify the dividend:     $2^{3^{n+1}}+1 = 2^{3^n*3}+1$


I've heard a variety of opinions regarding the pros and cons of using responsive web design recently and was wondering whether it was necessary for small businesses that target small geographical areas to implement responsive web design?   Some sub-questions I have regarding this include:   Is it better to use responsive web design as opposed to having separate code utilized for different dimensions/devices? Can it potentially affect SEO (positively or negatively)? What are the main problems I could run into when optimizing a website for a business using this design method?


Choosing right set of variables for Logistic regression and decision tree

I am a beginner in R. I am doing logistic regression using around 80 independent variables using glm function in R. The dependent variable is churn which says whether a customer churned or not. I want to know how to identify the right combination of variables to get a good predictive logistic regression model in R.  I also want to know how to identify the same for making good decision tree in R ( I am using the ctree function from the party package). So far, I had used drop1 function  and  anova(LogMdl, test="Chisq") where LogMdl is my logistic regression model to drop unwanted variables in the predictive model.  But maximum accuracy I was able to achieve was only 60%.   Also I am not sure if I am using the drop1 and anova functions correctly. I dropped the variables with lowest AIC using drop1 function.  Using anova function, I dropped variables with p value > 0.05  Kindly help me how to identify the right set of variables for both logistic regression and decision tree models to increase my model's predictive accuracy to close to 90% or more than that if possible.     library(party) setwd("D:/CIS/Project work") CellData <- read.csv("Cell2Cell_SPSS_Data - Orig.csv") trainData <- subset(CellData,calibrat=="1") testData <- subset(CellData,calibrat=="0") # validation or test data set LogMdl = glm(formula=churn ~ revenue  + mou    + recchrge+ directas+                 overage + roam    + changem +                changer  +dropvce + blckvce + unansvce+                 custcare+ threeway+ mourec  +                outcalls +incalls + peakvce + opeakvce+                 dropblk + callfwdv+ callwait+                months  + uniqsubs+ actvsubs+  phones  + models  +                eqpdays  +customer+ age1    + age2    +                 children+ credita + creditaa+                creditb  +creditc + creditde+ creditgy+ creditz +                 prizmrur+ prizmub +                prizmtwn +refurb  + webcap  + truck   +                 rv      + occprof + occcler +                occcrft  +occstud + occhmkr + occret  +                 occself + ownrent + marryun +                marryyes +marryno + mailord + mailres +                 mailflag+ travel  + pcown   +                creditcd +retcalls+ retaccpt+ newcelly+ newcelln+                 refer   + incmiss +                income   +mcycle  + creditad+ setprcm + setprc  + retcall,                 data=trainData, family=binomial(link="logit"),                control = list(maxit = 50)) ProbMdl = predict(LogMdl, testData, type = "response") testData$churndep = rep(0,31047)  # replacing all churndep with zero testData$churndep[ProbMdl>0.5] = 1   # converting records with prob > 0.5 as churned table(testData$churndep,testData$churn)  # comparing predicted and actual churn mean(testData$churndep!=testData$churn)    # prints the error %   Link for documentation of variables:   Link for Dataset (.csv file) :    I could not produce the output of dput since the data size is more than 5 MB. So I have zipped the file and placed in the above link.   Description of important variables: * churn is the variable that says whether a customer churned or not..... * churndep is the variable that needs to be predicted in the test data (validation data) and has to be compared with the churn variable which is already populated with actual churn. For both churn and churndep, value of 1 means churned and 0 means not churned.


Help with trigonometry identity derivation

Can someone help me with a complicated trigonometry derivation with only basic trigonometric identities:  $$\csc^2 \bigg(\frac{\pi}{7}\bigg) + \csc^2 \bigg(2\frac{\pi}{7}\bigg) + \csc^2 \bigg(3\frac{\pi}{7}\bigg) = 8$$  Thanks...


Are there any positive integers $a, b, c, d$ such that both $(a, b, c)$ and $(b, c, d)$ are Pythagorean triples?

Pythagorean triple is a triple of integers $(a, b, c)$ such that $a^2+b^2=c^2$. Is there any Pythagorean triple such that, not only $a^2+b^2$, but also $b^2+c^2$ is a square number? If not, how to prove it?  I tried to prove non-existence the following way: If true, it would mean that there is a pair of integers such that both sum and difference of their squares is a square number. Let's call these integers $a$ and $b$ and $a<b$. Then, there are integers $c$ and $d$ such that: \begin{align} &a^2+b^2=c^2 \\ &a^2-b^2=d^2 \end{align}  Multiplying those equations gives: \begin{equation} a^4=(cd)^2+b^4 \end{equation}  This is similar to Fermat's Last Theorem for $n=4$, but using it only shows that $cd$ can't be square number, not that there are no integer solutions.


On Ubuntu 14.04, the internet kept disconnecting. So, I decide to restore connection ability, but I am new to linux. I typed:  sudo apt-get purge network-manager   The wifi icon on the top right was disinterested and I left with no internet. Since I have lots of software installed on my machine, I don't want to reinstall ubuntu. What would be the cure in this situation? FYI, I have another windows PC, so I can download.


I have built a new PC and had to buy Windows from retailer store.   During the installation I entered the 25 digit key.  Created only local account.  Now I was curious about the installation process and saw: Windows is activated with a digital license.  Why is it activated using a digital key? I did use the 25 digit key from inside the bought Windows box. Went something wrong?


If the bounded operators $X\to Y$ form a Banach space in the operator norm, is $Y$ necessarily Banach?

that if $Y$ is Banach, the set $B(X,Y)$ of bounded linear operators from $X$ to $Y$ is Banach in the operator norm. I was now wondering about the converse. Is it true? More precisely:     Suppose $B(X,Y)$ is a Banach space, where $X,Y$ are two normed space. Is $Y$ then necessarily Banach?   I do not really know where to start, neither in trying to prove, nor in trying to find a counterexample.


"What did you say?" or "What did you said?"

I was teaching my son and I always get confused which verb I should use, as English is our second language, I asked my son to put the word 'said' in example and he come up with this:     what did you said?    but know there's something wrong so I come a cross this website, so if anyone is reading this can we say :  I know that we can say "what do you say", but i need to know if we can use "what do you said?"


I have a 500+ lines stored proccedure which I am writting and testing using the Microsoft SQL Management studio. Today I encounter the following 'strange' case. My query (in pseudocode) look like the following  create table #TempTable1 (Name varchar(30))  -- Some queries involving #TempTable1  drop table #TempTable1  -- Some queries  declare MyCursor cursor fast_forward for  select ......  open MyCursor  fetch next from MyCursor into @CursorValue while @@fetch_status = 0    begin         create table #TempTable1 (Name varchar(30))         -- Some queries involving #TempTable1         drop table #TempTable1          fetch next from MyCursor into @CursorValue      end  close MyCursor  deallocate MyCursor    My query fails with an error in the second create table     There is already an object named '#TempTable1' in the database.   I know that due to query optimizations the commands are not running in the sequence I am typing them. However this error still seems strange to me. I can put some go commands to force the execution, but this will create some other problems in my code e.g. I will have to redeclare some variables e.t.c. Renaming the tables will solve the problem but it will harm a little the readabillity of the code. So it is more 'curiocity' than an 'actual problem'.  Any suggestions on why this is happening and how I can avoid it?


Proof of $(ab)^n=a^nb^n$ is fulfilled when it is true for $n = 2$

Prove that for given elements $a,b$ from group $G$, equation $(ab)^n = a^nb^n$ is fulfilled for all $n∈ {\displaystyle \mathbb {Z} }, $ if and only if equation is true for $ n=2 $.  I have no idea how to prove it. I would be gratefulfor any help.


Single word for a person who is addicted of using internet

I want to know a single word for a person who is greatly addicted of using internet. Please don't answer the word internetmaniac. I already have this one.


How to make a bootable USB. I am using UBUNTU 13.04 LTS and want to make a bootable usb to install windows  Suggest any Ubuntu based usb creators to make a bootable Windows Flash drive.


arp table contains addresses asigned to 00:00:00:00:00:00 mac address

What mean 00:00:00:00:00:00 MAC address in arp table? On my OpenWRT router on interface connected to ISP I have seen 24 entries with this MAC address and on local network there are 7 entries. What these entries means or indicate?


Suppose that $l_1 = \{ (x_n)_{n \in \mathbb{N}} | \sum|x_n| < \infty \}$ and $l_{\infty} = \{ (x_n)_{n \in \mathbb{N}}| \sup|x_n| < \infty \}$.  Show that $(l_1)^* \cong l_{\infty}$, where $(l_1)^*$ is a dual space of $l_1$.  My attempt: Define a map $L: l_{\infty} \rightarrow (l_1)^*$ given by  $$L(x)(y) = \sum_{n \in \mathbb{N}}{x_ny_n}$$  where $y = (y_n)_{n \in \mathbb{N}} \in l_1$.   My aim is to show that $L$ is an isometric isomorphism.   Clearly $L$ is linear and and injective (choose $y = e_n$ for all $n \in \mathbb{N})$.  How to show that $L$ is a surjection and isometry?


What is the difference between procfs and sysfs?  Why are they made as file systems? As I understand it, proc is just something to store the immediate info regarding the processes running in the system.


How do I enter Unicode characters in LaTeX?  What packages do I need to install and what escape sequence do I type to specify Unicode characters in an ASCII source file?


Term for words which change meaning when a space is added

Taking this example,     Everyday is an adjective that means commonplace, ordinary, or normal.      Every day means "each day."   or numerous other similar words which have a different meaning when extra spaces are added, is there a particular term to describe these?  E.g. psychotherapist and psycho the rapist have two very different meanings, maybe and may be, or between and be tween.  I know that some of these words can be homophones, homographs, or homonyms, but the closest I can find is something like , which describes words that share the same spelling but have different meanings when capitalised e.g. polish/Polish, march/March.  Is there a particular term to describe words which look the same, but change meaning (and perhaps pronunciation) when a space is added?


BAT file will not run from Task Scheduler but will from Command Line

I'm trying to run a BAT script from Task Scheduler in Windows 2008 R2 and it runs for 3 seconds and then stops.  It says it successfully completes but I know it doesn't.  I can run this script from the command line directly, and it runs just fine.  The bat file I'm running actually deletes files older than 7 days using "forfiles" then I'm mapping a network drive, moving the files across the network using robocopy, and then closing the network connection.  I have taken the network and copy options out of the file and it still does the same thing.  Here is how my file looks:  rem This will delete the files from BBLEARN_stats forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN_stats" -m *.* -d -17 -c "cmd /c del @file"  rem This will delete the files from BBLEARN_cms_doc forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN_cms_doc" -m *.* -d -14 -c "cmd /c del @path"  rem This will delete the files from BBLEARN_admin forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN_admin" -m *.* -d -10 -c "cmd /c del @path"  rem This will delete the files from BBLEARN_cms forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN_cms" -m *.* -d -10 -c "cmd /c del @path"  rem This will delete the files from attendance_bb forfiles -p "E:\BB_Maintenance_Data\DB_Backups\attendance_bb" -m *.* -d -10 -c "cmd /c del @path"  rem This will delete the files from BBLearn forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN" -m *.* -d -18 -c "cmd /c del @path"  rem This will delete the files from Logs forfiles -p "E:\BB_Maintenance_Data\logs" -m *.* -d -10 -c "cmd /c del @path"  NET USE Z: \\10.20.102.225\coursebackups\BB_DB_Backups /user:cie oly2008  ROBOCOPY E:\BB_Maintenance_Data Z: /e /XO /FFT /PURGE /NP /LOG:BB_DB_Backups.txt  openfiles /disconnect /id *  NET USE Z: /delete /y   This is happening on 2 servers when trying to run commands from inside a BAT file.  The other server is giving an error if (0xFFFFFFFF) but that file is running a CALL C:\dir\dir\file.bat -options and I've used commands like that before in Server 2003.  Here is the file for this file:  call C:\blackboard\apps\content-exchange\bin\batch_ImportExport.bat -f backup_batch_file.txt -l 1 -t archive  NET USE Z: \\10.20.102.225\coursebackups\BB_Course_Backups /user:cie oly2008  ROBOCOPY E:\ Z: /move /e /LOG+:BB_Move_Course_Backups.txt  openfiles /disconnect /id *  NET USE Z: /delete /y


When I create a new document, everything is showed in Points not in mm despite that I have configured Illustrator to use mm instead of inches:     How can I change that ?


How to find the number of non-isomorphic binary trees with $n$ nodes?

A binary tree can have at most two children.  Two trees are called isomorphic if one of them can be obtained from other by a series of flips, i.e. by swapping left and right children of a number of nodes. Any number of nodes at any level can have their children swapped. Two empty trees are isomorphic.  The idea is to create an array of integers whose $i^{th}$ term will store number of such tree with $i$ nodes.


Exporting OpenStreetMap data to shapefile

I want to have river paths and Parks/natural/Landscape shapefiles in our region:   How should I export this layer to a shapefile?  Before this I googled it a lot but I couldn't find anyway.


Change new tab to about:blank in chrome without any extension

Can we change new tab to about:blank without installing any extension for latest chrome versions?


Help on Surjection, Injection, and Bijection

I am a undergraduate majoring in CS. In preparation for a discrete mathematics exam coming up next week, I am looking through problems I got wrong on the homework. A concept I don't understand are surjections, injections, and bijection. From lecture, for a function to be a bijection, it has to be both an injection and a surjection. So say I proved a function is not a surjection, why couldn't I say that it has to be injection since we know it can't be a bijection by definition?   So my homework problem is in the link below.        Problem 4.26. Let $A$, $B$, and $C$ be sets and let $f\colon B\to C$ and $g\colon A\to B$ be functions. Let $h\colon A\to C$ be the composition, $f\circ g$, that is, $h(x)::=f(g(x))$ for $x\in A$. Prove or disprove the following claims.         (a) If $h$ is surjective, then $f$ must be surjective.   (b) If $h$ is surjective, then $g$ must be surjective.   (c) If $h$ is injective, then $f$ must be injective.   (d) If $h$ is injective and $f$ is total, then $g$ must be surjective      I got  a) True b) False c) True d) False  When the answer is supposed to be  a) True b) false c) false d) true  I think the reason why I got them wrong is because I assumed that if a function is not surjective, then it has to be injective and vice versa. Could someone help me understand this concept? That would be much appreciated!


Simple yet much debated question inside my study circle. Please explain with reasons.


What is the historical origin of a "Silver Stag"? Why do Golden dragons remain in circulation after Robert's Rebellion?

In Westeros there are three coins:   Copper Stars (The Seven-Pointed Star is the symbol of the Faith of the Seven.) Silver Stags (The Stag is the sigil of house Baratheon.) Gold Dragons (The Dragon is the sigil of house Targaryen.)   Was the Stag already on the silver coin before Robert became king?  If so, why? Was house Baratheon that important?  If not, what was on the silver coin during the reign of the Targaryen kings?  Why is the sigil of house Targaryen still on the gold coin after Robert took the crown?  Robert hates the Targaryens so much, even murdering innocent children is OK for him.   Keeping this in mind I find it especially strange, that he doesn't change the sigil on most valuable coin.


Implication and its consequences for real world

I assume implication is the operator that is most of the times used in mathematics, am I right? (i.e. whenever if/then construct is used)  If yes, then I think it is known that it has some   Merely that implication is true if premise is false. Which doesn't make sense in real world because I could say: if pigs can fly, then we can cure any illness. But this is not true in the way we understand if/then in real life, isn't it? Because we can't cure any illness so far.  So my question is more philosophical in nature, if we agree that mathematics is using an operator implication which is problematic from philosophical point of view and doesn't very well align with the real world meaning of if/then, then doesn't this cause problems for mathematics when we try to apply some results of mathematics to real world? More particularly because the operator (implication) that was used in math may not be the one that reflects the one in real life? This means we can't use some results from math which relied on implication, in real life?


Can I use my iPhone as a "remote" for my iPad?

iPhones and iPads both have several apps aimed to be remotes for the PC/Mac -- mostly geared towards specific apps.  That's not what I'm asking about.  I'm interested in any way of using my iPad and iPhone/iPod touch side-by-side where the iPhone presents a menu of commands to control the iPad -- things like shortcuts, or better yet, buttons that invoke user-definable macros.  Does it exist?  Does the iPad have any way of being scripted through an API?  Note: VNC is irrelevant to this question.


What is the difference between normal Select query and a Select query inside Common Table Expression(CTE)?

I'm having a table 'Products' and if Execute this query  SELECT TOP 1000 [ProductID]       ,[ProductDesc]       ,[ManufacturingDate]       ,[ExpiryDate]       ,[Price]   FROM [TestSat].[dbo].[Products]   I got the output:    and If I use this select query:  SELECT ProductDesc,Price   FROM [Products]   WHERE Price>20.00   I got this output:    If I use CTE-Select like this:   ;WITH ProductsCTE(ProdName,Price) AS ( SELECT ProductDesc,Price   FROM [Products]   WHERE Price>20.00 )   I got this output:    The only difference I found between this simple Select Query as well as CTE Select query is the Column name (ProductDesc as ProdName).  Does it is the only difference between normal Select query as well as CTE Select query?


PostgreSQL: How to backup only One Schema from a database and restore it to other schema having same name of database?

I have a database named "A" which has three schemas "B","C" and "D". I want to take backup of schema "C"  and restore the data to Schema "B"? not sure how to do this as I am new to Postgres. pls help with commands.


broadcom dw1530 wifi doesn't work anymore

My wifi worked great on Ubuntu, until today where my wifi doesn't work anymore after turning on my pc. I don't see the wifi tab in the settings. I am running a dual boot and wifi still works on Windows. Wi-fi card: broadcom dw1530 wireless-n wlan half-mini card Which steps should I take to troubleshoot and fix this?


Evaluate $ \lim_{x \to 0} \left( {\frac{1}{x^2}} - {\frac{1} {\sin^2 x} }\right) $

$$\lim_{x\to0}\left({\frac{1}{x^2}}-{\frac{1}{\sin^2x}}\right)$$  Using the L'Hospital Rule I obtained the value $-1/4$, but the answer is given to be $-1/3$. I can't find the mistake. Here's what I did; please point out the mistake.  \begin{align} \lim_{x\to0}\left({\frac{1}{x^2}}-{\frac{1}{\sin^2x}}\right)&=\lim_{x\to0}\frac{(\sin x+x)(\sin x-x)}{(x\sin x)(x\sin x)} \\[1ex] &=\lim_{x\to0}\left(\frac{\sin x+x}{x\sin x}\right)\lim_{x\to0}\left(\frac{\sin x-x}{x\sin x}\right) \\[1ex] &=\lim_{x\to0}\left(\frac{\cos x+1}{\sin x+x\cos x}\right)\lim_{x\to0}\left(\frac{\cos x-1}{\sin x+x\cos x}\right) \\[1ex] &=\lim_{x\to0}\:(\cos x+1)\,\lim_{x\to0}\left(\frac{\cos x-1}{(\sin x+x\cos x)^2}\right) \\[1ex] &=\lim_{x\to0}\frac{-\sin x}{(\sin x+x\cos x)(2\cos x-x\sin x)} \\[1ex] &=-\lim_{x\to0}\left[\frac{1}{1+\cos x\left(\frac{x}{\sin x}\right)}\right]\left(\frac{1}{2\cos x-x\sin x}\right) \\[1ex] &=-\frac{1}{2}\left[\lim_{x\to0}\,\frac{1}{1+\cos x}\right] \\[1ex] &=-\frac{1}{4} \end{align}


Linear Matrix Inequality of a matrix $T$ with $\| T \|_2 < \rho$

Assume $T \in \mathbb{R}^{d\times d}$. Let $\rho(T)$ be the spectral radius of $T$ and $\rho \ge 0$. Prove that  $\rho(T) < \rho$ if and only if there exists a $P \succ 0$ satisfying $T^TPT - \rho^2 P \prec 0$.  I can prove the Necessity: If $P = I$, for any $x \in \mathbb{R}^d$,   \begin{equation} x^T T^T P T x - \rho^2 x^T P x = \| Tx \|^2 - \rho^2 \| x\|^2 < 0 \end{equation} so $T^T PT - \rho^2 P \prec 0$  I get stuck in proving the Sufficiency.


Can someone please explain the Riemann Hypothesis to me... in English?

I've read so much about it but none of it makes a lot of sense. Also, what's so unsolvable about it?


Why do I get syntax error when I try to run my C++ program after compiling it?

I am trying to learn C++, but I can't even make the first (hello world) example from cplusplus.org work with g++ command or c++. I created a file just like the example and ran g++ myfile, then ./myfile.  I get a permission problem, then I use chmod +x myfile and the permission problem is gone but this problem happens:  gzuspower@gzuspower:~/Desktop$ ./4 ./4: line 1: //myfirst: No such file or directory ./4: line 4: syntax error near unexpected token `(' ./4: line 4: `int main ()'   I called my file 4 because it is my 4th attempt. This is on Xubuntu 16.04.The duplicate question answer did not work i tried .c ,.cpp ,as file extension and tried firstc++ (my first attempt file) instead of 4(my fourth attempt file) and nothing works. i'm going to try different form of hello-world code.


I'm a fresh graduate student, and I want to write a resume using Latex, what is the best way to do it ?


"Home" is not translated on localized sites

This reads "Home" on esSO, ptSO, ruSO and rus. Strangely enough, the text on jaSO is in Japanese and it's the only site with translation.


Can I change the Lock On switching? Using the keyboard and mouse it's really annoying when fighting more than one enemy.


I can't seem to be able to wrap my head around the definitions I find on the web.  From what I can gather, these are shadows that YOU paint onto your mesh?  Why is it a good idea to have static shadows?  Don't shadows change all the time? For example if I paint ambient occlusion on my model, it's only going to get darker, even if I put lights where they are, isn't that unrealistic?


find a number $aabb$ such that is full square

I know that  I can write $aabb=1000a+100a+10b+b$, $a,b\in \{0,1,2,3,4,5,6,7,8,9\}, a\neq 0$, so $aabb=1100a+11b=m^2$, where $m\in \mathbb N$, I notice that $m^2=11(100a+b)$ so I need to find some number that $11\mid m^2$ and $11\mid m$,$1100<m^2<9999$ or $33<m<99$ so I just put number in calculator and 88 is answer, so $aabb=7744$, but is there any other better solution?


Find all solutions $f:\mathbb R \to \mathbb R$ to the functional equation $g(f(x+y)) = g(f(x)) + g(f(y))$

Let $g:\mathbb R \to \mathbb R$ be continuous and such that $g(0) = 0$ and $g(x)g(−x)>0$ for any $x > 0$. Find all solutions $f:\mathbb R \to \mathbb R$ to the functional equation $$g(f(x+y)) = g(f(x)) + g(f(y)),\quad x,y \in \mathbb R $$  I have deduced that (if $f$ is continuous) we must have $g(f(x)) = \lambda x$, because $g \circ f$ is a continuous linear function and all such functions must be of that form. I am then tempted to say that $f(x) = g^{-1}(\lambda x)$ but I cannot do this because I do not know that $g$ is bijective. Unfortunately I do not understand the significance of the conditions $g(0) =0$ and $g(x)g(-x)>0$ for $x > 0$. Any help would be appreciated.


Can I use a photo of me taken by AFP/Getty Images?   I am applying for a Apple WWDC Scholarship. I want to use this image in a app that will not be distributed. Only Apple employees will see this. I could potentially receive a ticket (no monetary value). Does this count as commercial?


How to use jQuery.bind on dynamically created items

I have this:  $(".sf_sub_accordian, .sf_find_container").bind("click", function(event) {     event.stopPropagation(); });   But it stops working when I add content dynamically via ajax-call.  How to make bind work with dynamically created content?  Edit: Without success I have already tried this:  $(document).on("click", ".sf_sub_accordian, .sf_find_container",function(event) {         event.stopPropagation(); });   In fact, it doesn't work at all if I do it like that.


I have been trying to show that if $f:[a,b]\rightarrow \mathbb{R}$ is a continuous function then $$\lim_{n \rightarrow \infty} \prod_{k=1} ^ n  \left( 1+ \frac{1}{n}f\left(\frac{k}{n}\right)  \right)= e^{\int_0 ^1 f(x)dx} $$ I have tried some approaches to prove this but couldn't find a way. Can someone kindly help me out. Thank you.


Proving that for $|G|= p^n$, that some subgroup $N$ is normal in G, where $|N|=p^{n-1}$

Basically what the title says. If $|G|=27$ for example, how would one prove that $N$ is normal in $G$ if $|N|=9$


Would improvised weapons work with cantrips like Green-Flame Blade and Booming Blade?

Green-Flame Blade:      As part of the action used to cast this spell, you must make a melee   attack with a weapon against one creature within the spell's range,   otherwise the spell fails.   This states that so long as the attack is a melee attack made with a weapon, you may use this cantrip and apply its affects. I realize improvised weapon has weapon in the name, and is under the weapons category, but it would also mean that I can use a mug as an improvised weapon with Booming Blade. I see no reason why this would not work, but  I'm still curious to see how others may interpret this.


Calculate the sum of this series ?$$\sum_{n=0}^{\infty}\frac{(\frac{2}{7e})^n(-1)^n}{{((\frac{2}{7e}) n+1)}^{n+1}}=?$$ I need to calculate the sum of this series to find the integral found here


Assume that $ 1a_1+2a_2+\cdots+20a_{20}=1, $ where the $a_j$ are real numbers and that these values minimize...

Assume that $\ 1a_1+2a_2+\cdots+20a_{20}=1, $ where the $a_j$ are real numbers and that these values minimize  $[1a_1^2+2a_2^2+\cdots+20a_{20}^2.]$ Find $a_{12}$.  Any help would be greatly appreciated. Thanks!


Who cooked and served food for the prisoners of Azkaban?

As far as I remember, there were only inmates and Dementors mentioned as Azkaban inhabitants. Were there servants or house elves who cooked?  (The question is inspired by a silly comic strip with a dementor holding a tray).


How to keep part of a spreadsheet always visible during navigation

I want to apologize in advance for asking something that's clearly available on the web. Unfortunately, I don't know the appropriate terminology though.  I'm looking to keep certain rows/columns always shown in excel. For example, in a worksheet with a lot of columns, I always want to see the name that exists on the far left. More importantly, how do I turn this off?


remove lines from file using linux command/script have multiple condition to remove a single line

HI I want to remove line from file have below lines starting with # and have Apache/apache. Please find below file content which I want to manipulate and remove :  ---------------------------------------------------------- # Apache configuration # This is apache configuration This is not Apache configuration ----------------------------------------------------------   Please suggest...


What is the point of .cpp files if I can use header files with the same use?

I may be thinking/using header files the wrong way, but currently I'm using 1 .cpp file and the rest are all in header files. I have things like a screen which is an array of characters in a header file, I have the function to draw the screen to the terminal in a header file, I have all my global variables in a header file, but I have game.cpp where all those files will be used. I am doing this wrong? I feel like at this point there's no reason to use .cpp files. Header files seem to be so much better because I avoid the issue of redeclaration.


the number of positive-integer solutions that satisfy $x_1\cdot x_2\cdot x_3\cdot x_4=1,000,000$?

I can't solve the following:  Find the number of positive-integer solutions that satisfy $x_1\cdot x_2\cdot x_3\cdot x_4=1,000,000$.  Thanks.


How to calculate variance or standard deviation for product of two normal distributions?

For example if I have two multiplied distributions a * b:  d = np.random.normal(1,2,150000) * np.random.normal(1,3,150000) mean_d = np.mean(d);  print(mean_d, '\t- mean d') std_d = np.std(d);  print(std_d, '\t- std d') var_d = np.var(d);  print(var_d, '\t- var d')  d = np.random.normal(0,2,150000) * np.random.normal(0,3,150000) mean_d = np.mean(d);  print(mean_d, '\t- mean d') std_d = np.std(d);  print(std_d, '\t- std d') var_d = np.var(d);  print(var_d, '\t- var d')  d = np.random.normal(2,4,150000) * np.random.normal(3,6,150000) mean_d = np.mean(d);  print(mean_d, '\t- mean d') std_d = np.std(d);  print(std_d, '\t- std d') var_d = np.var(d);  print(var_d, '\t- var d')   Result:  1.00402910382297    - mean d 7.006851762786954   - std d 49.09597162567064   - var d  -0.010013854223866369   - mean d 5.98944114495835    - std d 35.873405228919985  - var d  6.015273009526654   - mean d 29.412059046178683  - std d 865.0692173359013   - var d   Mean of the product calculated by multiplying mean values of each distribution mean_d = mean_a * mean_b. What is the formula for calculating variance or standard deviation?  Calculating using this formula:  def std_prod(x,y):   return np.sqrt(np.mean(y)**2*np.std(x)**2 + np.mean(x)**2*np.std(y)**2 + np.std(y)**2*np.std(x)**2)   gives slightly different results:  7.004889924524913   - std d 6.983597750949972   - std_prod d  5.9967239637288525  - std d 5.9877281028408005  - std_prod d  29.315982668663818  - std d 29.305068878687155  - std_prod d


setting a program to run as admin in a standard account

I am managing a few computers and there is a program on them that must be run as an admin to work. There are multiple standard users and one admin user (me) on the computers. Is there a way to set only that program to run as an administrator without needing to enter in admin credentials every time on a standard account?


Oi, eu utilizo o LaTeX para o desenvolvimento dos meus trabalhos e afins, e uso o Mozilla Firefox como meu programa  padrão para abrir PDF. Gostaria de saber se tem como inserir tais dados expostos no screenshot para que, caso seja aberto as propriedades do meu documento, aparacem: Título, Autor, Assunto, Palavra-chave.


I am always unsure about the position of "only" in the sentence. For example:      This ticket only costs 5 dollars.   This ticket costs only 5 dollars.    Are there any difference? Which one is better?


Function Equation Question Involving $f(xy)=f(x)f(y)-f(x+y)+1$

Let $\mathbb{Q}$ denote the set of rational numbers. Find all functions from $\mathbb{Q}$ to $\mathbb{Q}$ which satisfy    $f(1)=2$; and  $f(xy)=f(x)f(y)-f(x+y)+1$.   I know that $f(x)=x+1$ satisfies the equation but I don't know how to prove if this is the only such function. This question was in the 'Induction' section of my textbook.   Any hints?


Hibernate and SQL Server - time mismatch between Java and database with Java 8 types

I got the following situation. My software operates on a database with tables autogenerated by Microsoft Dynamics NAV 2009. The database runs on an MS SQL Server 2012. We created a new table in NAV that has several datetime fields. NAV stores these to SQL Server using datetime columns (I know this tyoe should not be used today, but NAV 2009 does and I can't change that).  My software receives data from external partners and writes it into this table, so that NAV can read it and work on it. NAV only reads that table, never writes to it.  But for some reason weird things happen when storing the time values to the database. My software is a Spring Boot 5.1 application that uses Hibernate 5.3.7 for ORM. My JPA entity uses the Java 8 type Instant to map the date and time values to the database table.  @Entity @Table(name = "Nav Company$My Table") public class MyTableEntity implements Serializable {      /* some more fields here... */      @Column(name = "Our Timestamp", updatable = false, nullable = false)     private Instant ourTimestamp;      @Column(name = "Partner Timestamp", updatable = false, nullable = false)     private Instant partnerTimestamp;      /* getters and setters here */ }   When data from a partner comes in, my software reads the provided timestamp as LocalDateTime, adds timezone information to it to get a ZonedDateTime,  extracts the Instant and stores it in the database using the entity.  My logs show that the time calculation in the software is correct. The last line is the Instant that is written to the database.  2019-01-22 09:00:01 [...] : navTimestamp[LDT]: ldt =    2019-01-22T09:00:01.015597300 2019-01-22 09:00:01 [...] : navTimestamp[LDT]: zoneId = Europe/Berlin 2019-01-22 09:00:01 [...] : navTimestamp[LDT]: zdt =    2019-01-22T09:00:01.015597300+01:00[Europe/Berlin] 2019-01-22 09:00:01 [...] : navTimestamp[ZDT]: zdt =     2019-01-22T09:00:01.015597300+01:00[Europe/Berlin] 2019-01-22 09:00:01 [...] : navTimestamp[ZDT]: instant = 2019-01-22T08:00:01.015597300Z   But when I SELECT the data from the table using SQL Server Management Studio, it shows that the database stored 2019-01-22 09:00:01.017 instead of 2019-01-22 08:00:01.017 as I would have expected (remember: column type is datetime, not datetimeoffset). When NAV reads that value, it even adds another hour to convert it into local time (GMT+1), thus showing 2019-01-22 10:00:01.  So I guess somewhere between my application and the SQL Server, Hibernate does some weird things and does not transmit the UTC time stored in the Instant but instead converts it to local time first and then stores it in the database.  How can I make sure that the UTC time is stored in the database and not local time?


Error in .getText() in a parseInt in Java

I know the title might not be that helpful. I do apologize. My problem is that I am trying to create a simple MPG application to help me get used to GUI. I have a gallons and a miles JTextField. I also have an ueditable JTextField to display the MPG. I am trying to convert the user input to an integer then divide the gallons and miles input for the result of the miles per gallon, which will be displayed.  I have the parseInt as displayed below:      int mil = Integer.parseInt(miles1.getText());     int gal = Integer.parseInt(gallons1.getText());   then the MPG:  int mpg = gal / mil;   It shows no error in the code, but once I go to run the application I get these errors:  java.lang.NullPointerException at app.<init>(app.java:40) at app$1.run(app.java:26) at java.awt.event.InvocationEvent.dispatch(Unknown Source) at java.awt.EventQueue.dispatchEventImpl(Unknown Source) at java.awt.EventQueue.access$200(Unknown Source) at java.awt.EventQueue$3.run(Unknown Source) at java.awt.EventQueue$3.run(Unknown Source) at java.security.AccessController.doPrivileged(Native Method) at java.security.ProtectionDomain$1.doIntersectionPrivilege(Unknown Source) at java.awt.EventQueue.dispatchEvent(Unknown Source) at java.awt.EventDispatchThread.pumpOneEventForFilters(Unknown Source) at java.awt.EventDispatchThread.pumpEventsForFilter(Unknown Source) at java.awt.EventDispatchThread.pumpEventsForHierarchy(Unknown Source) at java.awt.EventDispatchThread.pumpEvents(Unknown Source) at java.awt.EventDispatchThread.pumpEvents(Unknown Source) at java.awt.EventDispatchThread.run(Unknown Source)   Does anybody know what is causing this?


How to combine two JSON objects together

I have two JavaScript obj like so: const objOne = {   "firstname": "xzxz",   "lastname": "xzxzxzx" };  const objTwo  = {   "title": [     {       "name": "foo",       "table": "First"     },     {       "name": "bar",       "table": "Second"     }   ] };  and I want to combine them like below (not sure if "combine" is the appropriate word but hopefully make sense) {   "firstname": "xzxz",   "lastname": "xzxzxzx",   "title": [     {       "name": "foo",       "table": "First"     },     {       "name": "bar",       "table": "Second"     }   ] }  so far I tried the below    let result = [];      results.push(objOne);      results.push(objTwo);  but surely the result is not the one I want and it make sense as I create an array and I push into both objects. [   {     "firstname": "xzxz",     "lastname": "xzxzxzx"   },   {     "title": [       {         "name": "foo",         "table": "First"       },       {         "name": "bar",         "table": "Second"       }     ]   } ]