In this case of a second order linear homogeneous ODE with constant coefficients and repeated roots:  $ay'' + by' + cy = 0 $ (and $r1 = r2$)  why is the solution $y_1(t) = e^{-b/2a}$ not enough? in other words, why do we need a second equation?

Assuming I have the following homogeneous ODE equation: $$a\cdot y'' + b\cdot y' + c \cdot y = 0$$ Why for $(b^2 - 4\cdot a\cdot c=0) \quad $,(meaning, when $m_1=m_2$) then the solution is: $$y = C_1\cdot e^{m_{1}x} + C_2\cdot x \cdot e^{m_{2}x}$$ Why isn't it simply: $$y = C_1\cdot e^{m_{1}x} + C_2 \cdot e^{m_{2}x}$$ ? Also, why did they choose to multiply $C_2$ with $x$? Why not having a totally different approach for the solution when $(m1=m2)$ (e.g. diving the equation with $x$)?


Or any other silver surface? Perfect silver "colour" just seems to be "reflecting gray", so something that absorbs all wavelengths by the same fraction and reflects everything else specularly. When I scratch it, it gets gray.  So a mirrors are gray and specular reflectors and therefore the colour we commonly call silver is, also, simply gray and specular. Is that correct or am I heading in the wrong direction here?

Why do most metals (iron, tin, aluminum, lead, zinc, tungsten, nickel, etc.) appear silver or gray in color? (What atomic characteristics determine the color?)  What makes copper and gold have different colors?


I'm trying to create a "simple" script that I'm going to use to create some documentation for Unix/Mac machines.  I've successfully received the information I need, but it seems like I can't send it over to a webserver I've created with CURL because it gives some whitespaces and characters in the information output. I've tried with very many methods but nothing seems to work correctly..   This is the URL output that the script will send over to curl:   "ip.ip.ip.ip/documentation/index.php?avdelning=XX&user=XXX&hostname=XXX&model=ModelName:MacminiModelIdentifier:Macmini4,1&RAM=Memory:8GB&CPU=ProcessorName:IntelCore2DuoProcessorSpeed:2.4GHzNumberofProcessors:1&CPUCORES=TotalNumberofCores:2&MACADDRESS=etherxx:xx:xx:xx:xx:xx&SERIALNUMBER=SerialNumber(system):XXXXXXXX&LASTLOGGEDIN=XXXXX   Using only the following string will work if I do it directly with CURL and will not give me any errors and I receive the information on the webserver.   But when I use the script it does not work. The script:   #!/bin/bash  STR_RAM=$(/usr/sbin/system_profiler SPHardwareDataType | grep Memory: | sed 's/ //g'); STR_MODEL=$(/usr/sbin/system_profiler SPHardwareDataType | grep Model | sed 's/ //g'); STR_CPUNAME=$(/usr/sbin/system_profiler SPHardwareDataType | grep Processor | sed 's/ //g'); STR_CPUCORES=$(/usr/sbin/system_profiler SPHardwareDataType | grep Cores: | sed 's/ //g'); STR_SERIAL=$(/usr/sbin/system_profiler SPHardwareDataType | grep Serial | sed 's/ //g'); STR_MACADDR=$(ifconfig | grep en0 -A3 | grep ether | sed 's/ //g'); STR_LOGGEDIN=$(finger | tail -1 | sed 's/ //g'); STR_HOSTNAME=$(hostname | sed 's/ //g');  STR_URL=ip.ip.ip.ip/documentation/index.php?avdelning=$1\&user=$2\&hostname=$STR_HOSTNAME\&model=$STR_MODEL\&RAM=$STR_RAM\&CPU=$STR_CPUNAME\&CPUCORES=$STR_CPUCORES\&MACADDRESS=$STR_MACADDR\&SERIALNUMBER=$STR_SERIAL\&LASTLOGGEDIN=$STR_LOGGEDIN;   STR_URL2=$(echo $STR_URL | sed 's/ //g' | awk '{printf("\"%s\"\n", $0);}'); curl $STR_URL2;   As you can see I've added a bunch of probably unnecessary editing with sed and awk but nothing seems to work.   I get these error messages:  After I added the awk to add double quotes before and after the URL string I get:  Could not resolve "ip.ip.ip.ip   Which is very strange since I can run the curl command directly in terminal without that error. And If I do not remove the spaces etc I receive multiple lines that the URL can not be resolved. I've tried with urlencoding in perl and bash but that does not seem to fix the problem either.  I'm running this on a Mac now. Usage: sudo sh script.sh randomstring randomstring  EDIT: Output of new script   sudo sh script2.sh IT Denniz curl: (3) Illegal characters found in URL xx.xx.xx.xx/documentation/index.php?avdelning=XX&user=Denniz&hostname=admins-Mac-mini-2.local&model=ModelName:Macmini ModelIdentifier:Macmini4,1&RAM=Memory:8GB&CPU=ProcessorName:IntelCore2Duo ProcessorSpeed:2.4GHz NumberofProcessors:1&CPUCORES=TotalNumberofCores:2&MACADDRESS=  etherXX:XX:XX:XX:XX&SERIALNUMBER=SerialNumber(system):XXXXXXXXXXX&LASTLOGGEDIN=adminadmins008Jun10:21

Or, an introductory guide to robust filename handling and other string passing in shell scripts.  I wrote a shell script which works well most of the time. But it chokes on some inputs (e.g. on some file names).  I encountered a problem such as the following:   I have a file name containing a space hello world, and it was treated as two separate files hello and world. I have an input line with two consecutive spaces and they shrank to one in the input. Leading and trailing whitespace disappears from input lines. Sometimes, when the input contains one of the characters \[*?, they are replaced by some text which is is actually the name of files. There is an apostrophe ' (or a double quote ") in the input and things got weird after that point. There is a backslash in the input (or: I am using Cygwin and some of my file names have Windows-style \ separators).   What is going on and how do I fix it?


I have a task to calculate sum of digits in C#. In this case as an example. I like to calculate the sum of "12345" which is: 1+2+3+4+5 = 15. But the result coming after the execution of code is: 53. What is the mistake in the code?  static void Main(string[] args) {     string inputNumber = "12345";      int sum =0;     Console.WriteLine("Please Enter Your Desired Number");      for (int i = 0; i < 5; i++)     {         Console.WriteLine(inputNumber[i]);         sum = sum + Convert.ToInt32(inputNumber[i]);          Console.WriteLine(sum);     } }

I have a char in c#:  char foo = '2';   Now I want to get the 2 into an int.  I find that Convert.ToInt32 returns the actual decimal value of the char and not the number 2.  The following will work:  int bar = Convert.ToInt32(new string(foo, 1));   int.parse only works on strings as well.    Is there no native function in C# to go from a char to int without making it a string?  I know this is trivial but it just seems odd that there's nothing native to directly make the conversion.


Is it safe to use 19V 6.32A 120W Laptop Charger / Adapter , because I lost my 20V 7.5A 150W adapter and the only one I could find locally is the 19V 6.32A 120W , currently using the laptop for Gaming and not Rendering (yet)..?

I'm using a common charger for both of my laptops.  The charger is specified at 20 Volts and 3.25 Amperes. My other laptop has a specification of 19 V and 3.42 A.  Is it safe to charge my laptop with chargers whose specifications exceed or are not equal to the mentioned specifications?  I have read somewhere that it may cause some damage if the voltage or amperage is not matching the specs.


Can I expand all \newcommands without doing anything else in LaTeX?  Edited: My true goal is standardizing math papers in plain text so that theorems and definitions can be accurately and easily extracted without losing mathematical symbols.

Is it possible to have LaTeX (or another program) to expand a the macros in a .tex file, and output the expanded LaTeX source?   If no such program exists: are LaTeX macros processed simply as string substitutions, before the document is interpreted? If so, it might be easy enough to write my own such converter.  Edit: The reason I ask is journals which don't accept LaTeX submissions with macros. It would be useful to be able to develop with my usual macros, and convert automatically to the 'macro-expanded' format for submission.


I asked how to solve this optimization . I found this approach by combining @Royi's idea in his  with KKT's conditions. Personally, I feel my formulation is clearer and easier to understand.  Could you please verify if my proof is correct or contains logical mistake? Thank you so much!     Let $[\![ p ]\!]:=\{1,\ldots,p\}$ and $(x_1,\ldots,x_p) \in \mathbb R^p$. Solve the constrained optimization problem $$\begin{align*} \text{min} &\quad \frac{1}{2}\sum_{i=1}^p (y_i-x_i)^2 \\ \text{s.t} &\quad \sum_{i=1}^p y_i - 1 &&=0\\            &\quad\forall  i \in [\![ p ]\!]: -y_i &&\le 0  \end{align*}$$   $\textbf{My attempt}$ Define $$\begin{aligned} f(y) &= \frac{1}{2}\sum_{i=1}^p (y_i-x_i)^2 \\ h(y) &= \sum_{i=1}^p y_i - 1 \\ \forall i \in [\![ p ]\!]: g_i(y) &= -y_i  \end{aligned}$$ We have $f,g_i$ are convex and $h$ is linear. Let $a =(1/p, \ldots, 1/p)$. Then $h(a)=0$ and $g(a) <0$ for all $i \in [\![ p ]\!]$. It follows that Slater's condition is qualified. By Karush-Kuhn-Tucker conditions, we have $$\begin{aligned} \begin{cases} \forall i \in [\![ p ]\!]:\mu_i &\ge 0 \\ \forall i \in [\![ p ]\!]: g_i(y) &\le 0\\ h(y) &=0 \\ \forall i \in [\![ p ]\!]:\mu_i g_i(y)&=0 \\ \nabla f (y)- \lambda\nabla h (y)+ \mu_i \nabla g_i (y) &=0 \end{cases} &\iff \begin{cases} \forall i \in [\![ p ]\!]:\mu_i &\ge 0 \\ \forall i \in [\![ p ]\!]:-y_i &\le 0\\ \sum_{i=1}^p y_i - 1&=0 \\ \forall i \in [\![ p ]\!]: -\mu_i y_i &=0 \\ \forall i \in [\![ p ]\!]: (y_i - x_i) -\lambda - \mu_i &= 0 \end{cases} \end{aligned}$$  If $x_i+\lambda = 0$ then $y_i=\mu_i =0$ and thus $y_i = (x_i+\lambda)_+$. If $x_i+\lambda > 0$ then $y_i>0$ and thus $\mu_i=0$. Then $y_i = (x_i+\lambda)_+$. If $x_i+\lambda < 0$ then $\mu_i>0$ and thus $y_i=0$. Then $y_i = (x_i+\lambda)_+$. As such, we always have $y_i = (x_i+\lambda)_+$.  Then $\sum_{i=1}^p y_i - 1=0 \iff \sum_{i=1}^p (x_i+\lambda)_+ - 1=0$. Notice that $(x_i+\lambda)_+ = \max \{x_i+\lambda,0\}$ is continuous in $\lambda$ for all $i \in [\![ p ]\!]$. Hence $\psi(\lambda) = \sum_{i=1}^p (x_i+\lambda)_+ - 1$ is continuous in $\lambda$. Let $\alpha = -\max_{i \in [\![ p ]\!]}|x_i|$ and $\beta =1+ \max_{i \in [\![ p ]\!]}|x_i|$. It follows that $\psi(\alpha)<0<\psi(\beta)$. By Intermediate Value Theorem, the equation $\psi(\lambda)=0$ has a solution. Notice that $\psi$ is strictly increasing, so such solution is unique. We can also solve that equation by applying Intermediate Value Theorem on the interval $[\alpha , \beta]$.

Let $x = (x_1,\ldots,x_p) \in \mathbb R^p$. I'm solving the constrained optimization problem     $$\begin{align*} \text{min} &\quad \sum_{i=1}^p (y_i-x_i)^2 \\ \text{s.t} &\quad \sum_{i=1}^p y_i - 1 &&=0\\            &\quad\forall  i = \overline{1,p}: -y_i &&\le 0  \end{align*}$$   My attempt:  Let $f(y) = \sum_{i=1}^p (y_i-x_i)^2$, $h(y) = \sum_{i=1}^p y_i - 1$, and $g_i(y) = -y_i$ for all $i = \overline{1,p}$.  We have $f,g_i$ are convex and $h$ is linear. Let $\alpha =(1/p, \cdots, 1/p)$. Then $h(\alpha)=0$ and $g(\alpha) <0$ for all $i = \overline{1,p}$. It follows that Slater's condition is satisfied. By Karush-Kuhn-Tucker conditions, we have $$\begin{aligned} \begin{cases} \forall i = \overline{1,p}:\mu_i &\ge 0 \\ \forall i = \overline{1,p}: g_i(y) &\le 0\\ h(y) &=0 \\ \forall i = \overline{1,p}:\mu_i g_i(y)&=0 \\ \nabla f (y)+ \lambda\nabla h (y)+ \mu_i \nabla g_i (y) &=0 \end{cases} &\iff \begin{cases} \forall i = \overline{1,p}:\mu_i &\ge 0 \\ \forall i = \overline{1,p}:-y_i &\le 0\\ \sum_{i=1}^p y_i - 1&=0 \\ \forall i = \overline{1,p}: -\mu_i y_i &=0 \\ \forall i = \overline{1,p}: 2(y_i - x_i) +\lambda - \mu_i &= 0 \end{cases} \\ \end{aligned}$$  Then I'm stuck at solving the last system of equations.  How can I proceed to solve it? Thank you so much!


I have been trying to learn OO JS. I was playing with different patterns, wrote following example.  var obj = function() {      this.a= function() {         return 'a';     }  }  obj.prototype.b = function() {     return 'b'; }    var instance = new obj();  console.log(instance.a()); console.log(instance.b());    Is there any difference here in function a and b?

What's the difference between  var A = function () {     this.x = function () {         //do something     }; };   and  var A = function () { }; A.prototype.x = function () {     //do something };


Why is the Area 51 site no longer showing up on the More Stack Exchange Communities list? Prior to today, the More Stack Exchange Communities list in the top bar contained a link to Area 51. However, when I hit the link to the Stack Exchange Communities on the top right corner of my screen, I have noticed that the Area 51 community link is missing now. Why is this so? Is it due to a bug in the system, or is it intentional that it was removed? Perhaps a new series of protocols are in place that I am unaware of? This has just recently happened. After all Area 51 is a Stack Exchange Community! Is there any official explanation for this?

As you see. What can be the reason? I added it to communities list about a week or two ago.


I remember reading a book about people with special abilities a while back (early-mid 2000's) in which there was a girl and her brother.  There were certain people in the book who had abilities and had to go fight a war against other people with abilities.  I think the girl's power was talking to animals (bugs etc...)  and her brother I think had the power of persuasion in that he would always seem to get people to do things for him...  something along those lines?  I also remember there was a group of men from the kingdom who tracked down people with special powers, one of them having the ability to find said people as his power...

I read this novel when I was young. It is probably a children's or young adult novel. I think I read it in 1997 or earlier. I remember very much enjoying it, but the title and most of the details are unfortunately quite hazy for me. Here is what I have:   The main character was a girl in her early teens (I think) She was sent to live with a man who was some sort of master of dragons She may have been related to this man (his niece, perhaps), but I also may have made that up The man wore gloves at all times. When he removed them and touched someone he could see something about them. Their future, I think?   Sound familiar to anyone?   Update: Thinking back on it some more, I think I remember that the dragon lord guy and the heroine ended up in some kind of romantic relationship (making it less likely that he was her uncle). Also, he did at one point take off his gloves and touch her, seeing her future (I think).  'nother Update: It's possible that I'm confusing dragons with volcanos. Or, there may have been both. And I think they lived on an island, or a coastline?


I am trying to type linguistic formulas in LateX. An example would be smilar to this:

I'm trying to (more or less) replicate this phonological rewrite rule:    I'm using the package , and what I manage to accomplish is this:  \documentclass{article} \usepackage{phonrule} \begin{document}  \phonc     {\phonfeat{$-$cnt\\ +hi}}     {[$\alpha$grv]}     {\oneof{%         \phonfeat{$-$cnt\\ $\alpha$grv}\phold\\         \phold\phonfeat{$-$cnt\\ $\alpha$vce}%     }}  \end{document}     My main problem here is what appears after the "when" slash:  (1) The package only provides a left curly bracket - how can I add a right one as well?  (2) The two options within the curly brackets are not well aligned. I think comparing the two pictures themselves says it better than what I could do with words.


I am struggling with computing the following sums:     $$\sum_{k=1}^{n}k\binom{n}{k}=\binom{n}{1}+2\binom{n}{2}+...+n\binom{n}{n}$$   and     $$\sum_{k=0}^{n}\frac{1}{k+1}\binom{n}{k}=\binom{n}{0}+\frac{1}{2}\binom{n}{1}+\frac{1}{3}\binom{n}{2}+\dots+\frac{1}{n+1}\binom{n}{n}$$   At first, I tried just rewriting the general terms in a form where the Binomial Theorem could be applied, but could not do so. ($k$ should be in the exponent of something with $n-k$ in the exponent of something else.)  Then, for the first sum, I re-wrote it in the following manner:  \begin{align} S &=\binom{n}{n}+\dots+\binom{n}{3}+\binom{n}{2}+\binom{n}{1}\\ &+\binom{n}{n}+\dots+\binom{n}{3}+\binom{n}{2}\\ &+\binom{n}{n}+\dots+\binom{n}{3}\\ &\quad\vdots\\ &+\binom{n}{n} \end{align}  Noting that:  $$\binom{n}{0}+\binom{n}{1}+\binom{n}{2}+\dots+\binom{n}{n}=\sum_{k=0}^{n}\binom{n}{k}1^k1^{n-k}=(1+1)^n=2^n,$$  I can rewrite the first line in $S$ as $2^n-1$ (the $-1$ is there because I'm over-counting the $\binom{n}{0}=1$).  Then I tried to say that if all the "blanks" were filled (if all the lines were like the first line), since there are $n$ lines, then I have $n(2^n-1)$. From this point, we should have:  $$S+\text{blanks}=n(2^n-1)\Longrightarrow S=n(2^n-1)-\text{blanks}$$  However, the problem of finding the value of "blanks" seems as hard as the original problem and I can't get to the right answer of $n2^{n-1}$ (according to WA). In one of my attempts, I ended up with a geometric series but that still didn't work.  I have not spent much time on the second sum as I feel I should be able to do the first one before even tackling the second one. Am I going in the right direction with this? Is there a more intelligent way of working this out?  Thanks in advance for any help/hints.

Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$ ?    I know that $\sum_{k=0}^{n}\binom{n}{k}= 2^{n}$ and so, $\sum_{k=1}^{n}\binom{n}{k}= 2^{n}-1$ but how to deal with $k$ ?


I am interested in getting into the Star Wars Expanded Universe, and was wondering what would be the best place to start.

I've been a fan of the Star Wars movies since I was a kid, but I've never read any of the books. Every time I've thought about reading them, I change my mind because there is so many books, I don't know where to start.      I don't live anywhere near a public library, and I don't have a lot of money to spend on 200+ books. I'm going to be buying the books for my e-reader with Christmas gift cards.   I've heard about The Thrawn Trilogy by Timothy Zahn, and The Darth Bane Trilogy by Drew Karpyshyn. The Thrawn Trilogy sounds really good, but since Bane isn't in the movies, is it worth it reading about characters I don't know? Is that one of those books I would have to read more in the universe before reading? Is it any good?  I'm interested in learning more about the characters in the original trilogy and the prequels. So, my question is, how do I read them? Do I read them in chronological order? Will I be completely lost if I read them out of order?


select * from zones z where st_intersects(z.geom, st_Buffer(ST_SetSRID(ST_Point(2.336031, 48.863172), 3857),1));   It looks like the 1 in the st_buffer is being interpreted as degrees, I need to find geometries within n meters of a given point.  I did find a reference to a new function (st_Buffer_Meters) but that didn't seem to do anything different.

I'm trying to find the points within a certain distance, in meters, from another point.  I'm using the function ST_Buffer, but I don't get how to express the distance in meters.  I'm trying with something like this:  select 1 as cartodb_id, ST_Buffer(   ST_Transform(     ST_GeomFromText(       POINT(-58.38145 -34.60368)'       , 4326     )     , 3857   )   , 500 ) as the_geom_webmercator   I have the coordinates from google maps (in wgs84, 4326) then I transform them to webmercator (3857) and then I pass 500 as parameter, and I get something that looks like the desired area, but after comparing it with what google maps says it falls short for a non neglectable distance.  Is this the right way to achieve it?   note: you can try the sql query in cartodb  --  From this question:  I came with the following code (I use SRID 31997 to calculate the buffer, and then go back to webmercator)  select 1 as cartodb_id, ST_Transform(   ST_Buffer(     ST_Transform(       ST_GeomFromText(         'POINT(-58.427185 -34.624592)'         , 4326       )       , 31997     )     , 2000   ), 3857 ) as the_geom_webmercator   Now if falls short for no more than 20 meters. I thought mercator (EPSG 3857) was in metric units.


Say I have something like  var T = Type.GetType("System.Nullable`1[[System.DateTime, mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089]]");   which is a nullable datetime.   T.FullName gives me:   "System.Nullable`1[[System.DateTime, mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089]]"   How can I extract DateTime? or Nullable<DateTime> as a string representation from the Type?

I am working on code generation and ran into a snag with generics. Here is a "simplified" version of what is causing me issues.  Dictionary<string, DateTime> dictionary = new Dictionary<string, DateTime>(); string text = dictionary.GetType().FullName;   With the above code snippet the value of text is as follows:   System.Collections.Generic.Dictionary`2[[System.String, mscorlib, Version=2.0.0.0,   Culture=neutral, PublicKeyToken=b77a5c561934e089],[System.DateTime, mscorlib,   Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089]]   (Line breaks added for better readability.)  Is there a way to get the type name (type) in a different format without parsing the above string? I desire the following result for text:  System.Collections.Generic.Dictionary<System.String, System.DateTime>


I know that it is true that $5\geq  -2$, but I really do not understand why. Let me explain how I think.      $5\geq -2$ means that $5$ is greater than or equal to $-2$. I am perfectly fine with the fact that $5$ is greater than $-2$. I am not so fine with the fact that $5=-2$, as $5\neq -2$. I think that I have misunderstood something in the concept of inequalities.    With consideration to what I have written in the quote, why is it true that $5\geq -2$?

Well, probably this might seem a really simple question (and it might be so too!), but off late me and my friends have been debating quite hard over this question.     Is $3 \ge 1$ or is it just $3 > 1$?   Actually it all started here: if functions $f$ and $g$ satisfy $f>g$ then do they also satisfy $f \ge g$? All of us agreed. (are we wrong here itself?). After all, the $\ge$ symbol is basically 'greater than' OR 'equal too'. So if a function $f$ takes values greater than $g$, then definitely it satisfies the $\ge$ relation.  But then somehow the above mentioned question came up. My friends say that $3 \ge 1$ is absolutely wrong. Their reasoning: "under no circumstances can 3 be equal to 1", so $3 \ge 1$ is wrong.  My argument: $3 \ge 1$ is a mathematical statement which can either be true or false. It states that 3 is either greater than OR equal to 1. One of the conditions is satisfied and the two conditions are linked by an 'OR'. So $3\ge 1$ is true.  Who's right?  (please edit or add tags as i don't know what to tag the question as!)


In the sentence "people like us never wash […] hands", should the pronoun be "our" or "their"?

Question:     A man like you should not do this, _______?   Which question tag should I use in the blank space?   should he? should you?   Which would be grammatically correct? I think 1 is true.


Is there  any way now of installing a version of Pages or iWork on a Mac running High Sierra 10.13.6?

I uninstalled my iWork tools - Keynote, Numbers and Pages - from my MacBook Air.      Unfortunately, I don't want to upgrade my MBA to Mojave/Catalina in order to install.  I looking for the working iWork version for 10.12 Sierra.  Is there some repository for old versions of iWork?


So everywhere I'm looking I'm seeing BAB bonuses beyond a certain level start being formatted as such +10/+5 at level 10. I understand that once you reach a +6 BAB you get an extra attack as well as at +11, but what are the second and third numbers for? and why are they divided if the amount of attacks I get is always based on the first number?

I've been reading the PF core rulebook, but confused over some of the data in the Character tables, and not found anywhere in the book that explains it, so wondering if someone could explain it?  Taking the Monk class table for example:     Level | Base Attack Bonus | ..... | Flurry of Blows Bonus      1st       |       +0          |   ....    |        -1/-1      2nd       |       +1          |   ....    |        +0/+0      ...      ...      16th  |       +12/+7/+2   |   ....    |        +14/+14/+9/+9/+4/+4/-1      17th  |       +12/+7/+2   |   ....    |        +15/+15/+10/+10/+5/+5/+0      18th  |       +13/+8/+3   |   ....    |        +16/+16/+11/+10/+6/+6/+1   What do the slashes between the bonuses mean?


I have been using the metric for quite a while now and I never thought about it. Why does the time coordinate always have an opposite sign to the space one?  In other words, why does the metric have this form(in free space)? $$ ds^2= -dt^2+d\vec{x}^2 $$

I've looked up  and on Griffths' didatic Introduction to Electrodynamics, but, still, am struggling to understand why time has the opposite sign of the space coordinates. Any insights are welcome.


Does $\frac1{1+|z|^2}$ have a power series at $z=1$? If not, why not? How can we generally say that a function has a power series?

How can I show that $\frac{1}{1+|z|^2}$ isn't analytic at $z=1$? I thought: $\frac{1}{1+|z|^2}=\frac{1}{1+x^2+y^2}$ (substituting $z=x+yi$). We calculate the Cauchy-Riemann equations and we get that $u_x=-2x$, $u_y=-2y$, $v_x=v_y=0$. So this function is only analytic at $z=0$. Is this right?


I have a few standard MagSafe 2 chargers left and want to use it with my new MacBook 12.  Are there any adapters I can use to convert these Magsafe chargers into USB-C chargers that work with the MacBook 12" or 2016 Macbook Pro?

I have a 2015 MacBook Pro with a MagSafe 2 charging cable. My wife has a new MacBook Pro from 2016 with USB-C. I was wondering whether I could technically (in the matter of electronic feasability) use her charging cable on my MacBook and vice versa with some sort of adapter / dongle, and, if so, where I would get one?


I often use mv ./* DEST or cp -r ./* DEST to move/copy all files and directories from the current directory to another. But what if I want to move/copy all but one file/directory?

There are plenty of situations where the use of a * is virtually inevitable - e.g. rm -rf * in a folder that holds thousands of subfolders and files.  But what if you want to exclude just one or two files or folders from the rm command? I've googled my way around and only found quite complicated solutions like find . -depth -not \( -name 'one' -o -name 'two' \ -o -name 'three' \) -exec rm {} \; as stated .  Is there a possibility to do this in an easier way - without that detour to find? E.g. rm -rf --exclude='one' --exclude='two' --exclude='three' * like in rsync or just rm -rf -e 'one','two','three' *?  Maybe even a general possibility to exclude things from * (so other commands like cp, mv, ... don't have to implement their own)? Something like *{'one','two','three'} or so?


I am in big trouble since last few weeks... I am getting 100% disk utilization on my Windows, while I can see no process is significantly using the disk. The issue is faced by many as you can see there are many many threads on this:   on  on    This is how it looks like:    100% disk usage    No process is significantly using the disk    Also I created a thread on   to ask where to find the registry key to tweak HDD driver as recommended by microsoft's site. But of no use.  I tried, stopping many services, clean boot, running process explorer to checks whats using disk the most, as suggested by many online threads. In fact, I formatted by C: drive and installed clean Windows 10. But issue came back!!!  Let me tell me something about my machine: its Dell XPS 15 L502X. Its 2011 edition. It has 16 GB RAM, quad core i7 2630QM. This machine worked perfect with Windows 7,8 and 10 for so many years but now its failing. As I told above I tried everything thats noted in various sites, but nothing helped.   Now I recalled that few months back I was trying to copy paste some big video file to pendrive and I was getting another famous error "Cannot read from source file issue". I didnt paid much attention to it. Left those video files as is. I remember I tried running chkdsk with no success. Now I started feeling that the issue was aggravated. I felt this must be due to  bad sectors. So I cut pasted all files in the drives to external hard disk using TeraCopy software. It gives list of files that failed to copy. So I deleted those files when TeraCopy was not able to move them and then recovered those files using EASEUS recovery tool. Then I hard formatted (not quick format) thinking that it will fix bad sectors. This worked for E: drive.  But while doing same for F: drive, it got all screwed. First while recovering files, I was getting . So I left those files unrecovered and went on to hard format the drive. But now after almost 5 hours its barely 30% done.   One more observation, many times after random killing of processes (mostly onedrive which had folder in F: drive), my disk utility used to come to normal after few minutes.  Q1. So should I conclude its hard disk which is culprit here?    Q2. Will this formatting of F: drive ever complete?  Q3. If completed will my machine be fixed, that is will my machine be free from 100% disk utilization?   Q4. Will my hard disk be safe to use in future for no data loss...  Q5. Should I buy new hard disk?  Q6. Does hard formatting fix bad sectors at all?  Q7. Should I do the same for C: drive too? While installing Windows I did quick format, not hard format.  Sorry for so many questions...but I have wasted many weeks on this. And no thread online is of help to me.

After startup for 5 minutes my system is very slow. The Task Manager shows that the disk usage is at 100%. (Later this number is around 2-4 %, but sometimes for 1-2 minutes go up again at 100%.)  I searched a lot on Google. For example I read , and also other pages. I opened two topic on Microsoft answer.  and one in Hungarian.  But I didn't found the solution yet. So I would like to ask Community's help. :)  Here the steps I already done:   I disabled everything at startups (including services) and the issue is the same.  I disabled Prefetch and Superfetch, the Baground Intellingent Transmission, Windows Search and Windows Defender but the issue is still persists. I made a health check on HDD, I made defrag and file system error check, but there are no errors. Also I tried to reinstall the HDD's driver. I made a full hardware check up, with no errors. The Windows and all the drivers are up-to-date. I tried a clean start. The issue is the same. I deleted Dropbox and all antivirus. I turned of the MSI mode.      I using also Linux, where this error is not occurs. Good to know, that Windows had 4 partitions, but I deleted 2 of them for the Linux. I don't know what partitions was these but both was only 10 - 20 MB.  I using a Dell Inspiron 15R SE 7520 with Windows 10 Home.  Personally I think it can be the Intel Rapid Store Technology "driver", because the problem started around when I installed it. (However I'm not sure.) And my hardware not supported yet by Intel, so I have no the newest driver. However I deleted Intel's software and driver and the issue is the same.    Thank you in advance for your assistance!


In my research I am using an OLS multiple linear regression like: $$ y_i = x_i^T\beta + \varepsilon_i $$    $y_i$ and $x_i$ are some 2-by-1 matrices (forecasts from 2 different models).  Now I want to perform OLS (which I am able to). The problem is that the elements of the $\beta$ can be negative and the sum is not necessarily $1$. Do you know any reference or algorithm to impose these restrictions?   $$\sum \beta = 1\text{  and  }\beta_j\ge 0\ \   \forall j$$

I would like to estimate a multiple linear regression model $N$ observations (with $\beta$ of length $k$):  $$Y = X \beta + \epsilon$$  subject, however, to some linear constraints on the coefficients. I.e a constraint of the form  $$M \beta = 0$$  where (at least in my case) $M$ is of dimension $2 \times k$ but more generally can be expressed as  $$M \beta = c$$ where $M$ is of dimension $p \times k$ with $p < N$ and $c$ of dimension $p \times 1$.  I have not been able to find much about this online and would appreciate references to read up on this..  Thanks


I've never seen people use StackExchange like this.  A few questions:   First, does anyone use it like this? Second, what was the original intention behind this option? What was the vision?   Thanks.

I showed up here to write a perfectly normal rant about misaligned pixels, and there's a big fat checkbox cluttering up the "Ask" page:    WHAT THE EEEEK IS THIS NEW ABOMINATION?


How can I return the top 10 rows for each category?  Say I have a table named xyz. It has a column called state, in the political unit sense of the word.  I want the top 10 rows from each state. Do I use case so that one can see from which state the row is?  I am using SQL Server 2012.  The top 10 would be from FCFS, the order in which they are entered.  Columns are  FirstName, LastName, Address, city, state, zip, phone etc.   For example, I have rows in my table from states AL, CT, NY etc. I want the top 10 rows based on FCFS from each state.

I often need to select a number of rows from each group in a result set.  For example, I might want to list the 'n' highest or lowest recent order values per customer.  In more complex cases, the number of rows to list might vary per group (defined by an attribute of the grouping/parent record). This part is definitely optional/for extra credit and not intended to dissuade people from answering.  What are the main options for solving these types of problems in SQL Server 2005 and later? What are the main advantages and disadvantages of each method?  AdventureWorks examples (for clarity, optional)   List the five most recent recent transaction dates and IDs from the TransactionHistory table, for each product that starts with a letter from M to R inclusive. Same again, but with n history lines per product, where n is five times the DaysToManufacture Product attribute. Same, for the special case where exactly one history line per product is required (the single most recent entry by TransactionDate, tie-break on TransactionID.


I am making half adder circuit for my school project but I saw their datasheet and it says maximum supply volate is 5.25v and I have 9v battery, How do I use it if I want to test my circuit without burning ICS? I watched this video to complete my project but he didn't specify the battery he used. Pls help Video link -: . Thank you IC I used : Ic 7408(SN74LS08N) , IC 7432 (SN74LS32N), IC 7404 (SN74LS04N) . thank you

I have been looking around for an easy way to convert 12V to 5V. I have seen some people saying that a simple resistor is all that is needed.  $$ Volts = Ohms \cdot Amps $$ $$ Amps  = \frac{Volts}{Ohms} $$ $$Ohms  = \frac{Volts}{Amps}$$  So applying a resistor will diminish the voltage of the circuit. That should mean that an appropriately sized resistor could simply be placed in the path of a 12V circuit, converting it to 5v.   If this is the case how would one reduce amps? Would series vs parallel make a difference in this area?   I have seen designs that include a regulator IC and some capacitors, but if a simple resistor/fuse/diode setup will do the trick, I would really prefer that.


$$\int_0^5 e^{-2t}\sin(t) \,\mathrm{d}t$$   I know I should be able to integrate this by parts but I can't seem to get the parts I choose to make the result any easier to integrate.

Is there a general formula for finding the primitive of $$e^{ax}\sin(bx)?$$  I've done this manually with $a=9$ and $b=4$ using Euler's formulas. But it takes a bit of time. Is there a pattern here?


I would like to set up Ubuntu to switch between workspaces when pressing Super+Number (ie: Super+1 goes to workspace 1, etc etc)  I have the correct shortcuts set in the Keyboard settings, but instead of switching workspaces it opens up the app from the drawer on the left. For the life of me I cannot figure out how to disable the default Super+Number shortcut in 16.04.  There's been multiple post and links I've found regarding much older installs of Ubuntu (12.XX~ish), they recommend modifying compizconfig, but I don't know if that's still relevant to 16.04.  Additionally, I found another question regarding 17.10:   However, the suggestion there to try gsettings set org.gnome.shell.extensions.dash-to-dock hot-keys false returns No such schema 'org.gnome.shell.extensions.dash-to-dock'  Any help that anyone can offer would be a huge help!

In 12.04 (and prior, I believe), + (like Windows+1) will switch to the first app in the launchbar. Can I disable this somewhere? I like to use Super+Number to switch between workspaces.


I know that the algebraic closure of $\mathbb Q_p$, which I'll denote $\overline{\mathbb Q_p}$, is not metrically complete: there are $p$-adic Cauchy sequences that do not converge. (The example I know is $\sum_{n > 0, (n,p) = 1} \zeta_n p^n$ where $\zeta_n$ is a primitive $n^{th}$ root of unity; there are plenty of others).   However, there is a proof via Krasner's Lemma - mentioned on Wikipedia , with a reference to Proposition 8.1.5 of Neukirch, Schmidt, and Wingberg's Cohomology of Number Fields - that the $p$-adic completion of the separable algebraic closure of a global field $k$ is equal to the separable algebraic closure of its completion. That is, for $k = \mathbb Q$, $\overline{(\mathbb Q_p)} = (\overline{\mathbb Q})_p$.   Why doesn't this mean that the algebraic closure of $\mathbb{Q}_p$ is complete? The example I gave above, $\sum_{n > 0, (n,p) = 1} \zeta_n p^n$ is a $p$-adic Cauchy sequence in $\overline{\mathbb{Q}}$, so it should converge to an element of $(\overline{\mathbb{Q}})_p$.   EDIT This is answered . For reference, $(\overline{\mathbb{Q}})_p$ denotes the union of all completions of number fields with respect to valuations extending the $p$-adic valuation on $\mathbb{Q}$.

The following corollary of Krasner´s Lemma says:  Let k be a global field and p a prime of k. Then $(\overline{k})_p=\overline{k_p}$. Im wondering if $(\overline{k})_p$ means the completion of $\overline{k}$ because i know that $\overline{\mathbb{Q}_p}$ is not complete. So i think it means  $\bigcup L_{ip}$ with the $L_{ip}$ ranging over all finite extensions of k. In particular $\bigcup L_{ip}$ doesn´t need to be complete. Am i correct with that? Thx for any help given!  You can find the corollary for example in Neukirch´s cohomology of number fields, 8.1.5.


Compute the eigenvalues of the $n\times n$ matrix M defined by $$(m_{ij}) = \begin{cases} 1 - 1/n & \text{ if } i = j  \\ -1/n & \text{ otherwise.} \end{cases} $$  Using Wolfram Alpha, I found a pattern: for an $n \times n$ matrix, the eigenvalues are $0$ (with multiplicity $1$) and $1$ (with multiplicity $ n - 1)$. But how can I prove this fact? I didn't get anywhere with induction.  For example, in the $n = 2$ case, we have that $\text{trace M } = 1$, and $\text{det} M = 0$. So the product of the eigenvalues is $0$ (which means one eigenvalue is $0$) and the sum is $1$, so the other one must be $1$. This doesn't really work for higher orders though.

I want to find the rank of this $n\times n$ matrix \begin{pmatrix} 1 & a & a & \cdots & \cdots & a \\ a & 1 & a & \cdots & \cdots & a \\ a & a & 1 & a & \cdots & a \\ \vdots & \vdots & a& \ddots & & \vdots\\ \vdots & \vdots & \vdots & & \ddots & \vdots \\ a & a & a & \cdots  &\cdots & 1 \end{pmatrix}  that is, the matrix whose diagonals are $1's$ and $a$ otherwise, where $a$ is any real number.  My first observation is when $a=0$ the rank is $n$ and when $a=1$ the rank is $1.$ Then I can assume $a\neq 0, 1$ and proceed row reduction to find its pivot rows. I obtain  \begin{pmatrix} 1 & a & a & \cdots  & a \\ 0 & 1+a & a & \cdots & a \\ 0 & a & 1+a & \cdots & a \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & a & a & \cdots  & 1+a \end{pmatrix} by subtracting the first row multiplied $a$ for each row below the first, and then divides the factor $(1-a)$,  and stuck there. Any hints/helps?


I am crafting applications for US faculty positions and Californian universities require diversity statements. Now, the problem is I have no idea what to write in it, since diversity can mean literally anything. I've seen various examples that are all based on personal struggles by people belonging to minority groups or active in some program related to mentoring/teaching to minorities, which makes writing such a statement much easier.  Now, I've never been involved in any "program" of this type. There's no research/teaching about minorities in my field (science). I'm no minority, since I'm a white european. I've lived here and there for various years (outside of my homeland) in my early life and to work these last 5-6 years, so I'm technically an emigrant, but I guess it'd be offensive to people emigrating due to serious reasons to pick on this to develop the statement.  I was wondering whether anybody can give me a solid to develop something tasteful. I thought about something about multidisciplinarity since I've worked and studied in various fields, but I think the purpose of such statement is to address racial/gender/sex diversity.

Some job ads of US schools require a "statement on diversity". I am not based in the US, and have never written one before. What should one say in a statement on diversity anyway? Am I supposed to state how I would increase the (ethical, scientific, or with regards to other aspects) diversity of the faculty? Would something like "Since I come from Africa, I would make a big contribution to your diversity since currently all faculty members at your department are white" usually be expected?


If $A$, $B$ and $C$ are the angles of a triangle, prove that:  $$sin\frac {A}{2}+sin\frac {B}{2}+sin\frac {C}{2}=1+4sin\frac {B+C}{4}.sin\frac {C+A}{4}.sin\frac {A+B}{4}$$  My attempt;  Here, $$A+B+C=\pi$$  Now,  $$L.H.S=sin\frac {A}{2}+sin\frac {B}{2}+sin\frac {C}{2}$$ $$= 2sin\frac {\frac {A}{2}+\frac {B}{2}}{2}.cos\frac {\frac {A}{2}-\frac {B}{2}}+sin\frac {C}{2}$$ $$=2sin\frac {A+B}{4}.cos\frac {A-B}{4}+sin\frac {C}{2}$$ $$=2sin\frac {\pi-C}{4}.cos\frac {A-B}{4}+sin\frac {C}{2}$$  Now, from here I could not.continue, please help me to.complete the proof..

To prove  $$\sin\frac A 2+\sin\frac B 2+\sin\frac C 2-1=4\sin\frac{\pi -A}4\sin\frac{\pi -B}4\sin\frac{\pi-C}4$$  My approach :   $$ \begin{align} \text{L.H.S.} & = \sin\frac{A}{2}+\sin \frac{B}{2}+\sin\frac{C}{2} -1 \\[8pt] & = 2\sin\frac{A+B}{4}\cos\frac{A-B}{4}+\cos\left(\frac{\pi}{2}-\frac{C}{2}\right)-1 \\[8pt] & = 2\sin\frac{\pi -C }{4}\cos\frac{A-B}{4} - 2\sin^2\left(\frac{\pi -C}{4} \right) \\[8pt] & =2\sin\frac{\pi -C }{4}\left\{ \cos\frac{A-B}{4} - \sin\left(\frac{\pi -C}{4} \right)\right\} \end{align} $$  Unable to move further please help. thanks.


I have some data which includes a bunch of bracketed codes, sometimes multiple on one line.  Lorem ipsum  (ABC123) dolor sit amet consectetur adipiscing elit (BCD234) sed do  (345CDE) eiusmod tempor (8675309) incididunt   All my attempts to pull out the bracketed strings (grep -P -i -o "(?<=\().*(?=\))" and grep -E -i -o "\(CAS.*\)") have resulted in an output like:  ABC123 BCD234 345CDE) eiudmod tempor (8675309   whereas what I need is :  ABC123 BCD234 345CDE 8675309   How should I go about this?  I'm using GNU grep.  I bonus would not be broken by unmatched brackets and pull out ABC123  from ut labore (et dolore (ABC123) magna aliqua but that's not too important.

I have this gigantic ugly string: J0000000: Transaction A0001401 started on 8/22/2008 9:49:29 AM J0000010: Project name: E:\foo.pf J0000011: Job name: MBiek Direct Mail Test J0000020: Document 1 - Completed successfully  I'm trying to extract pieces from it using regex. In this case, I want to grab everything after Project Name up to the part where it says J0000011: (the 11 is going to be a different number every time). Here's the regex I've been playing with: Project name:\s+(.*)\s+J[0-9]{7}:  The problem is that it doesn't stop until it hits the J0000020: at the end. How do I make the regex stop at the first occurrence of J[0-9]{7}?


I created a java project and when I run it from NetBeans it runs correctly and does what is supposed to but when I move it on the Linux server it gives me this error:   Exception in thread "main" java.lang.NoClassDefFoundError: org/apache/log4j/Logger     at arhivare.Arhivare.<clinit>(Arhivare.java:29) Caused by: java.lang.ClassNotFoundException: org.apache.log4j.Logger     at java.net.URLClassLoader.findClass(URLClassLoader.java:382)     at java.lang.ClassLoader.loadClass(ClassLoader.java:424)     at sun.misc.Launcher$AppClassLoader.loadClass(Launcher.java:349)     at java.lang.ClassLoader.loadClass(ClassLoader.java:357)     ... 1 more   It has to to with log4j library which I included in the project (it runs in Netbeans). What am I missing ?

I am getting a NoClassDefFoundError when I run my Java application.  What is typically the cause of this?


Let $f(x) = 2x + \cos{x}$.    Calculate $f^{-1}(1)$; Supposing that $f^{-1}$ is differentiable, show that $(f^{-1})^{\prime}(1) = \dfrac{1}{2}$.   Thanks for the help :]

I don't know how to attack this problem. The last I've tried is using a differential equation, but I don't know how to solve it.  Let $y$ be $f^{-1}(x)$. Knowing that $x=f(y)= 2y + \cos(y)$ and derivating I obtained the following non-linear first order differential equation: $y' \cdot (2-\sin(y))=1$  I would thank you if you can help me.  Edit: I haven't said, but it is trivial to check that the function is injective, so it has an inverse, because $\forall x \in \mathbb{R}$ $f'(x) \neq0$


I Have the full name of a type as string and I would like to use this string to tell type of a generic method. see this        string typeStr ="Dll.NameSpace.MyType";       var list = new List<Dll.NameSpace.MyType>();//should put typeStr here       var result = call.SomeGenericMethod<...>(obj);//should put typeStr here    didn't help me. If you try visiting , it does not satisfy my needs.  EDITS:  The generic method I'm trying to call is an extension one. I have unsuccessfully tried the following code,  method remains null       var result = repo.Get();      Type elementType =               Type.GetType("x2o_Care.Models.ViewModels.PatientViewModel");      MethodInfo method =typeof(AutoMapper.QueryableExtensions.Extensions)                        .GetMethod("ProjectTo", new[] { typeof(IQueryable)});         MethodInfo generic = method.MakeGenericMethod(elementType);          var model = generic.Invoke(result.OrderBy(e => true).Take(20), null);

I have a string variable that represents the name of a custom class. Example:   string s = "Customer";   I will need to create an arraylist of customers. So, the syntax needed is:  List<Customer> cust = new ..    How do I convert the string s to be able to create this arraylist on runtime?


Suppose we have an ordinary balance where equal weights are put in both sides. Now one side is slowly held down. When this force is not applied anymore, the balance tends to achieve horizontal position.  But when one side is held down, the moment of force due to both weights are equal in magnitude and opposite in direction. Also, the potential energy of the system remains same (As the height lost by one weight is equal to the height gained by another). So why does the balance try to regain horizontal position?    Here $r$, $F (=mg)$ and $\sin \theta$ are equal

I'm talking about a Weighing Balance shown in the figure:    Press & Hold on onside of the horizontal beam and then release it. It makes some oscillations and comes back to equilibrium like shown in the figure.  Both the pans are of equal equal masses. When the horizontal beam is tilted by an angle using external force, the torque due to these pan weights are equal in magnitude & opposite in direction. Then why does it come back to it position? What's making it to come back?


I have gotten several files from various sources on the net to learn from. When they load the UI is completely changed from what I am used to in the Default view when you first create a new blender scene.  I am looking at the file now and there is no default view selection anyway in it. Since I am very new to blender I like to use the default view that is standard with blender as it helps me find things I need.    Thanks in advance for the assistance.

Is there a way to open files without changing the UI layout?  Sometimes in older files the layout will be in the old 2.4x style, which can be annoying.  One way would seem to be appending everything in, but that gets tedious with having to do it over again and again for objects, materials, textures, etc.


I want to read a single character from the keyboard (like BASIC GET, FORTH KEY or C getchar. It looks as if to do this with python I have to load a package and extract a module from this. Surely there is an easier way? Can't I just read stdin?

Is there a way of reading one single character from the user input? For instance, they press one key at the terminal and it is returned (sort of like getch()). I know there's a function in Windows for it, but I'd like something that is cross-platform.


Structured Data error for “Missing: homeLocation” i have try setting all i could but still this error is still showing please how and where can i solve this issues  someone should help me out pls  and all my post has duplicate title and duplicate description please a guide line to fix it too. please help me.

Although we didn't do any changes, this new error appeared in the GSC Structured Data section:    I don't really get what it means. There are many fields for Schema.org, is homeLocation suddenly a required field? Does that make any sense?


We have a set of parameters configured in Parameter Manager that are applied to all links in our emails from that BU. Is it possible to selectively prevent those parameters from being applied to a URL?

A client recently went live with a Commerce Cloud website / Marketing Cloud integration. Marketing Cloud is sending a Shipping Confirmation triggered email.  The tracking link in the Shipping Confirmation email won't resolve properly because of the WAC string.  Is there a way to disable the WAC string for a specific link using AMPscript or by any other method? Any other potential workarounds?


I am quite the beginner in XNA. I have only recently started using GameComponents. I have a multiplayer game called Better Pong. I move the ball (which is an object) by incrementing the Vector2 (the position) of the ball by the velocity Vector2 and updating the hitbox Rectangle.  However, by having very large speeds (such as (12,12)) the ball might go through the paddle since it just skips through the Paddle's Rectangle "hitbox".  Is there a way to make the ball make smaller movements, so it doesn't go through the paddle (but still move fast)?

I'm creating a 2d sidescrolling shooter, and I'm having a little trouble with collision detection for the bullets. Everything including the bullets are objects with their own polygons / update methods.  The trouble is that bullets go fast, and at 60 frames per second (what the game runs at) a bullet will often skip right through a wall -- since it moves more than the width of the wall during in the update interval -- and continue happily on its way since the polygons will never actually overlap.  What can I do about this? The only thing I've been able to come up with is to draw a line from the old position to the new position and do collision detection on that, but line drawing for collision detection is recommended against by the slick2d documentation. How can I solve this?


(Reading database ... 166 files and directories currently installed.) Preparing to unpack .../libc6-dbg_2.26-6_i386.deb ... Unpacking libc6-dbg:i386 (2.26-6) over (2.25-5) ... dpkg-deb (subprocess): decompressing archive member: lzma error: compressed data is corrupt dpkg-deb: error: <decompress> subprocess returned error exit status 2 dpkg: error processing archive /var/cache/apt/archives/libc6-dbg_2.26-6_i386.deb (--unpack):  cannot copy extracted data for './usr/lib/debug/.build-id/b7/d4c76439e3e67b30d081161328b4388778aee6.debug' to '/usr/lib/debug/.build-id/b7/d4c76439e3e67b30d081161328b4388778aee6.debug.dpkg-new': unexpected end of file or stream Errors were encountered while processing:  /var/cache/apt/archives/libc6-dbg_2.26-6_i386.deb E: Sub-process /usr/bin/dpkg returned an error code (1)   What should I do?

Firefox fails to update due to corrupted download (deb)  Preparing to unpack .../firefox_32.0+build1-0ubuntu0.14.04.1_i386.deb ... Unpacking firefox (32.0+build1-0ubuntu0.14.04.1) over (31.0+build1-0ubuntu0.14.04.1) ... dpkg-deb (subprocess): decompressing archive member: lzma error:  compressed data is corrupt dpkg-deb: error: subprocess <decompress> returned error exit status 2 dpkg: error processing archive  /var/cache/apt/archives/firefox_32.0+build1-0ubuntu0.14.04.1_i386.deb (--unpack):  cannot copy extracted data for './usr/lib/firefox/libxul.so' to '/usr/lib/firefox/libxul.so.dpkg-new':   unexpected end of file or stream Please restart all running instances of firefox, or you will experience problems.


I'm trying to put some code into a function but I get an Unbound Local Error - I sort of understand why, I just don't know how to fix it.  edit: specifically I was told not to use global because global "is a bad idea". Surely there must be another way?  In the overall code I have multiple variables which need to be altered by user_input and those altered values then need to be passed through one or more different functions (repeatedly (with new values) until a certain conclusion is drawn).  How can I use the variables in multiple functions (cleanly)? If I define them in one function then they're only available there, right? And I can't alter their values from/to elsewhere?  Thank you for any help.  This is a sketch of the code I want to put in a function:  #variables that need to be used (and altered) within multiple functions Var1 = #a_number Var2 = #a_number Var3 = #a_number  def a_function(): #created Unbound Local Error     output() #prints original vars     while True:         inp = float(input("Enter a number: "))          Var1 += inp         Var2 -= inp         Var3 *= inp         output() #prints new values for vars          if/elif/else....         #when Vars are a certain number new calculations are done         #on them. Regardless, there is always only one output of         # the 3 Vars         #some Var vals trigger certain functs which print those new value         #or functions which may even manipulate the values further

How can I create or use a global variable in a function?  If I create a global variable in one function, how can I use that global variable in another function? Do I need to store the global variable in a local variable of the function which needs its access?


I have created a web application which uses Database as MSACCESS, one of the column name in MSACCESS is separated with space something like "Employee Name".  My c# code is failing and not able to read the column name which has space between two words. I cannot change the column name as it was used by many applications.  Can i dynamically add underscore or remove the space in a specific column.  Or can someone suggest the best approach for this.  SELECT      Format([empdate],'mm') AS Month,      Sum([Time]) as MyTime      Format([empdate],'yyyy') as CurrYear  FROM Table  where empName ='" + AND ManagerName='XYZ'  Group by Format([empdate],'mm') ,Format([empdate],'yyyy')    in the query say empdate is emp date and ManagerName is Manager Name - i am getting exception while executing in c#

What do the brackets do in a sql statement?  For example, in the statement:    insert into table1 ([columnname1], columnname2) values (val1, val2)  Also, what does it do if the table name is in brackets?


I am developing a plugin which finds buffer. In that i am using lineedit for getting distance from the user and pass it to the buffer function. My current code throws an error "'QLineEdit' object has no attribute 'Value'. I had also attached my code for reference.   def run(self):     """Run method that performs all the real work"""     # show the dialog     self.dlg.show()     # Clear the QcomboBox before loading layers     self.dlg.Statecombo.clear()     self.dlg.Citycombo.clear()     self.dlg.DistancelineEdit.clear()     layers = self.iface.mapCanvas().layers()     for layer in layers:         if layer.type() == QgsMapLayer.VectorLayer:             idx = layer.dataProvider().fieldNameIndex( 'name_1' )  #this field contains state names             uv = layer.dataProvider().uniqueValues( idx )              """Adding the state names to the combo box"""             for i in uv:                 if i:                     self.dlg.Statecombo.addItem(str(i))               QObject.connect(self.dlg.Statecombo, SIGNAL("currentIndexChanged(int)"), self.findTheCityNames)             QObject.connect(self.dlg.Citycombo, SIGNAL("currentIndexChanged(int)"), self.calcDistance)  # Run the dialog event loop     result = self.dlg.exec_()     # See if OK was pressed     #if result:     if result:         distance = self.dlg.DistancelineEdit.value()         new_distance = distance         number = self.dlg.number_buf.value()         QgsGeometry.buffer(new_distance , 2)                     pass  def findTheCityNames(self):     self.dlg.Citycombo.clear()     ct = self.dlg.Statecombo.currentText()     st = "name_1='"+ct+"'"     exp = QgsExpression(st)     fidAndVal = {}             #QMessageBox.information(self.iface.mainWindow(), "info", st)       layer = self.iface.activeLayer()      iterFeat = layer.getFeatures()      for f in iterFeat:         val = exp.evaluate(f)         if bool(val):             attrs = f.attributes()             idx = layer.fieldNameIndex('name')             cityName = f.attributes()[idx]             fidInt = f.id()             fidAndVal[fidInt] = cityName      for x in fidAndVal.keys():         self.dlg.Citycombo.addItem(fidAndVal[x])   def calcDistance(self):     pass

I am writing a simple plugin that finds buffer. My gui has 2 combo box and 1 Line edit. The first combo box will have a drop down of values  from column 'States' and 2nd combo will have a drop down of values from column 'Cities'. Note that the Cities will be filtered in the combo box depending on the states selected. And 3rd Lineedit gets a distance from the user. As a result, I want buffer for the cities (from the 2nd combo box) with the user specified 'distance value' given in the lineedit box.I tried QgsGeometryAnalyzer().buffer() function in QGIS API. But the first argument is a layer for the above mentioned function. Instead i want my gui to take value from the city combo and lineedit and find buffer. How to accomplish. Sorry for the lengthy post.


I am kinda new to Guice injection. And I got nullptr exception in my project. I suspect it is because I do not set up Injecting dependencies correctly. After investigation, it is caused by invokeSomeMethod in S3Driver.java file, specifically lambdaHelper.invokeSomeMethod(). Could you shed some hints about what went wrong? Thank you S3Driver.java // Constructor public S3Driver() {              Injector injector = createInjector(new LambdaHelperModule(), new S3Module());              this.lambdaHelper = injector.getInstance(LambdaHelper.class); }  ... lambdaHelper.invokeSomeMethod(); // Nullptr Exception  This is my project setup: LambdaHelper.java // Constructor public LambdaHelper(S3Class s3Class) {   this.s3Class = s3Class; }  S3Class.java ... // Constructor public S3Class(S3Presigner p, S3Client s) {this.p = p; this.s = s;};   LambdaHelperModule.java public LambdaHelper provideLambdaHelper() {              S3Class s3Class = S3Class.builder()                                          .s3Presigner(S3Presigner.builder().build())                                          .s3Client(S3Client.builder().build())                                          .build();              return new LambdaHelper(s3Class); }  S3Module.java public S3Class provideS3Class() {              return new S3Class(S3Presigner.builder().build(),                                  S3Client.builder().build()); }

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


Okay, someone tasked me to make a leaderboard for their game. However, the one I have right now is really insecure. All it does is check if someone is in the top 100, and if they are, post the score to the server, where the server will completely trust the client to give a real score.  My question is: How would I make it harder, or better, impossible, to send a fake high score, because right now they can just post a value to an easy-to-find endpoint.  Clarifications: The game is running in an interpreted environment, therefore obfuscation is not practical, and the game has a lot of input (an hour's worth at least), so sending that to the server is also impractical.

Browser and mobile games commonly have global highscore tables. It's also common for those tables to contain scores of 2,147,483,647 — where people have figured out the webservice call that reports scores and used it to record a fictitious score.  For simple puzzle games, we can defend against this by including a record of every move the player made (and any random seeds used to generate the level) with the score-reporting call. The entire game can then be reproduced and verified on the server.  However, this quickly becomes infeasible for anything larger than Pac-man.  How else can cheating of this kind be prevented?


I've been playing this game for a long time but I cannot recall if there has ever been an iconic group of monsters of neutral good (or for that matter chaotic good or true neutral) alignment native to the other planes in the way that other alignments have their iconic creatures (5e names used - they have had other aliases):  \begin{array}{c|c c c}  & \text{Lawful} & \text{Neutral} & \text{Chaotic} \\ \hline \text{Good} & \text{Angels} & ? & ? \\ \text{Neutral} & \text{Modrons} & ? & \text{Slaadi} \\ \text{Evil} & \text{Devils} & \text{Yugoloths} & \text{Demons} \end{array}  Can anyone fill in the blanks?

In my D&D 5e game, I have a custom cosmology, and I'm currently working on a concept for an afterlife plane where any sentient creature who enters is sorted by alignment and guided to the afterlife. While in this afterlife plane, a character begins to take on a form that represents its alignment. This visually distinguishes each alignment from one another (making them easier to sort) but also provides a cool transformative aesthetic that my players have expressed interest in seeing.  In order to prevent this from being opinion-based, answers must entail specific monsters that have canonically been declared to be representative of their respective alignment, or creatures that have another narrative connection with their alignment or alignment-based plane. I will accept any creature from the history of D&D and Pathfinder as long as you can cite its close ties with its respective alignment.  I understand that there may be more than one correct answer (for example, Monster X may be the perfect NE monster in D&D 4.0 while it might be Monster Y in Pathfinder. An answer is considered correct as long as it is backed by the lore of its system.


I can very well see that all prime numbers satisfies this condition.  But what about other numbers, does there exist other solutions?  How do I find them?  Any help will be truly appreciated.

I'm asked to find all integers $n$ such that $\phi(n)+\sigma(n)=2n.$ I know that when $n$ is a prime, $\phi(n)+\sigma(n)=(n-1)+(n+1)=2n.$ My guess is that $n$ can be primes only, and I want to derive a contradiction when $n$ is a composite number. But I can only show that when $n=pq$ ($p$, $q$ distinct primes), $\phi(n)+\sigma(n)=2pq+2=2n+2.$ How do I generalize from here?


I'm wondering if lists comprised of similar or related words/phrases can be shortened by omitting the root/suffix/word that they have in common except in the last item in the list.   Examples:    "We were best-friends through elementary, middle, and high school." "I received checks in amounts of five-, six-, and seven-thousand dollars." "He works with para and quadriplegic patients."    I feel if any of the examples is permissible, it would be example 1.  In example 2, although riding the line of ambiguity as to the amount on the checks (it could be "$5, $6, and $7,000" OR "$5,000, $6,000, and $7,000") it seems to be a reasonable sentence that would be easy to understand in context. However, I am unsure my use of hyphens would be proper in this sentence.  In example 3, the prefix "para" is isolated from "paraplegic"   I don't think the sentence in example 3 is anywhere close to proper but I read it in a document that was sent to me for work and it prompted me to ask questions concerning similar language situations. Thanks for any replies!  -Ian

If multiple hyphenated terms share the same latter half, and I wish to list them without repeating that latter half, how should the hyphens be placed?  For example:     I will be investigating control issues in ground-based, water-based, and air-based robots.   If I do not want to repeat based, could I write:     I will be investigating control issues in ground-, water-, and air-based robots.   Is it correct to just leave a hyphen dangling after ground and water?  If not, how should it be written? I know the original sentence doesn't sound too bad, but I really just want to know the punctuation rule (or the convention in American English if there is no rule).


I want to replace the original jack from my notebook with a new one since it is broken (and I would like to avoid to replace it with the same as the original). The original AC adapter supplies 19V and a bit less than 3Amp. However I can't find on Internet a DC jack (for pannel-mounting use) whose rated voltage is 19 V. All I find are 12V DC / 3Amp MAX jacks.  So what would happen if I use my AC Adapter with that new power DC jack (so 12V 3Amp) ? Will it overheat or is it safe?  Thanks (and sorry if that's a duplicate).

Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device.


How can I open a new Stack exchange section to talk about art. In general.  About questioning, history, philosophy, infringement with technology.

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


I need to loop recursively through files in specific folders (to add them to git skip-worktree). I've made a script for that: #!/bin/bash  scan_recursively () {     echo "Doing $1"     if [ -f "$1" ]; then         echo "git update-index --skip-worktree $1" >> output.txt     else         for f in $1/*; do             scan_recursively "$f"         done     fi }  echo "" > output.txt for folder in fol1 fol2 file1.txt #fol\ 11 do     scan_recursively $folder done  And it works fine, but when I uncomment fol\ 11 it breaks into an infinite loop and in the console I see repeatedly: Doing fol/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*/*  With the number of /* growing until I stop the program. Same happens when a sub folder contains space in it's name

Or, an introductory guide to robust filename handling and other string passing in shell scripts.  I wrote a shell script which works well most of the time. But it chokes on some inputs (e.g. on some file names).  I encountered a problem such as the following:   I have a file name containing a space hello world, and it was treated as two separate files hello and world. I have an input line with two consecutive spaces and they shrank to one in the input. Leading and trailing whitespace disappears from input lines. Sometimes, when the input contains one of the characters \[*?, they are replaced by some text which is is actually the name of files. There is an apostrophe ' (or a double quote ") in the input and things got weird after that point. There is a backslash in the input (or: I am using Cygwin and some of my file names have Windows-style \ separators).   What is going on and how do I fix it?


I see many articles and posts about javascript objects and primitives passed by refference vs passed by value. Though I don't see topic covering functions. Are they passed by value or refference. Therefore I made test myself to check it out.   Cosnider this example:    function sayHello() {  console.log("Hello") }  function changeSayHello(func) {  func = function() {   console.log("Good Bye");  }  func(); }   sayHello(); // >>  Hello  changeSayHello(sayHello); // >> Good Bye sayHello(); // >>  Hello      You can see the result by running the snippet. From this example I conclude that functions in JavaScript are passed by value. What is your comment.  * EDIT * May be this better explains what I ment. And it shows that function is passed by refference?     var Obj  = function() {  this.a = 5; }  var change = function(func) {  func.prototype.b = 8; }  var first = new Obj();  console.log(first.b); //undefined  change(Obj);  console.log(first.b);// 8     I don't see why this is marked as duplicate. I saw the proposed answer and there is no example about functions being passed as an argument.

The primitive types (number, string, etc.) are passed by value, but objects are unknown, because they can be both passed-by-value (in case we consider that a variable holding an object is in fact a reference to the object) and passed-by-reference (when we consider that the variable to the object holds the object itself).  Although it doesn't really matter at the end, I want to know what is the correct way to present the arguments passing conventions. Is there an excerpt from JavaScript specification, which defines what should be the semantics regarding this?


I created a simple bash script which contains the command ifconfig. In general I want to execute such a privileged script to run as non-root user. I have tried hown root:users ./path/to/script.sh followed by chmod 4550 ./Desktop/dhcp_client.sh I tried even 4755. I want to use bash scripts to include some privileged commands then I must run the script that contains them as non-root. Then I must invoke these scripts from an application which is run as non-root.

The setuid permission bit tells Linux to run a program with the effective user id of the owner instead of the executor:  > cat setuid-test.c  #include <stdio.h> #include <unistd.h>  int main(int argc, char** argv) {     printf("%d", geteuid());     return 0; }  > gcc -o setuid-test setuid-test.c > ./setuid-test  1000  > sudo chown nobody ./setuid-test; sudo chmod +s ./setuid-test > ./setuid-test  65534   However, this only applies to executables; shell scripts ignore the setuid bit:  > cat setuid-test2  #!/bin/bash id -u  > ./setuid-test2  1000  > sudo chown nobody ./setuid-test2; sudo chmod +s ./setuid-test2 > ./setuid-test2  1000     Wikipedia :     Due to the increased likelihood of security flaws, many operating systems ignore the setuid attribute when applied to executable shell scripts.   Assuming I'm willing to accept those risks, is there any way to tell Linux to treat the setuid bit the same on shell scripts as it does on executables?  If not, is there a common workaround for this problem? My current solution is to add a sudoers entry to allow ALL to run a given script as the user I want it run as, with NOPASSWD to avoid the password prompt. The main downsides to that is the need for a sudoers entry every time I want to do this, and the need for the caller to sudo some-script instead of just some-script


I was trying to free up some space on my ubuntu ext4 partition using GParted to install Windows 7. However, when I right-click the partition, most options to edit it are greyed out. There is a symbol of a key next to the partition name. There's about 29 GB free space on the partition. I am using ubuntu 13.04 and GParted 0.12.1.

Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?


I am a Blood Hunter (Critical Role class ) with the Sharpshooter and Crossbow Expert feats wielding two hand crossbows. My Crimson Rite allows me to deal an additional 1dx magical damage of some element when I make an attack with a targeted weapon. Sharpshooter simply says that you can add 10 damage to the attack, but it doesn’t specify type. I see a direct comparison to Jeremy Crawford’s ruling on , implying I could choose the damage type of the extra damage. Am I missing some rule that contradicts my assumption?

Sneak Attack has the same type , this is easy, unless there are multiple damage types.  A Flame Tongue does slashing (or piercing) damage, and fire. Can I chose the Sneak Attack damage in this case to be fire too?


So i have  $A + B + C = \pi$  $$\frac{A}{2} + \frac {B}{2} + \frac{C}{2} = \frac{\pi}{2}$$  $$4\cos\left(\frac{-B-C + \pi}{2}\right)\cos\left(\frac{-A -C + \pi}{2}\right)\cdots$$  And I doubt this leads to anywhere.  So then I tried,  $\sin\left(\frac{-B-C + \pi}{2}\right)\cdots$ and this didn't go anywhere either.  I don't know what to try, and I've seen other people's solutions and they do something like: $\sin(C) = \sin(A + B)$, $\cos(C/2) = \sin(\frac{A + B}{2})$ but i don't see where they got this part from. Other people use Euler's formula or whatever but I haven't learned that yet so I can't use it.

Prove that $\sin(2A)+\sin(2B)+\sin(2C)=4\sin(A)\sin(B)\sin(C)$ when $A,B,C$ are angles of a triangle   This question came up in a miscellaneous problem set I have been working on to refresh my memory on several topics I did earlier this year. I have tried changing $4\sin(A)\sin(B)\sin(C)$ to  $$4\sin(B+C)\sin(A+C)\sin(A+B)$$ by making substitutions by reorganizing $A+B+C=\pi$. I then did the same thing to the other side to get $$-2(\sin(B+C)\cos(B+C)+\sin(A+C)\cos(A+C)+\sin(A+B)\cos(A+B))$$ and then tried using the compound angle formula to see if i got an equality. However the whole thing became one huge mess and I didn't seem to get any closer to the solution. I am pretty sure there is some simpler way of proving the equality, but I can't seem to figure it out. Maybe there is a geometric interpretation or maybe it can be done using just algebra and trig. Any hint's would be appreciated (I would prefer an algebraic approach, but it would be nice to see some geometric proofs as well)


I have a computer with only one harddrive but I have a spare harddrive that I can temporarily use.  I can't format my computers harddrive because I still need to use the operating system every day and to setup, install and update all my works programs it would take over 24 hours so to prevent downtime I want to install the operating system and programs to a second harddrive and then once it's setup correctly I need to wipe the first harddrive and copy the entire os, files...etc back over to the first, now clean drive.  Is there a way to do this or is it better to do it with partitions or something?  Any ideas?

Can anyone recommend a cheap/free utility that can do this without very much effort?  My preference is that it would be really easy.    Boot into Windows Pick drive to move Pick target drive It copies everything over, and reboots to the correct partition.


Supposed I have a project that is intended to be open-source, but it depends on a static library that I also wrote (and I don't want open-source). If I distribute the library with the other code to be compiled together, could the library be somehow decompiled so the original source is recovered? I know disassembling is possible, but the output of that is somewhat cryptic still.

I have a program in which I've lost the C++ source code.  Are there any good C++ decompilers out there?  I've already ran across .


How does Distinct() work on a List<> of anonymous type? will it just do a property compare? or will it always return the same list?  example:   List<SomeObject> list;  ....  ....   var result = list            .Where(i => i.Condition)            .Select(i => new                 {                   Name = i.Name,                   Date = i.Date                });            .Distinct()            .ToList()     Please note I applied the distinct on the anonymous-type list.

So I have a collection of objects.  The exact type isn't important.  From it I want to extract all the unique pairs of a pair of particular properties, thusly:  myObjectCollection.Select(item=>new                                 {                                      Alpha = item.propOne,                                      Bravo = item.propTwo                                 }                  ).Distinct();   So my question is:  Will Distinct in this case use the default object equals (which will be useless to me, since each object is new) or can it be told to do a different equals (in this case, equal values of Alpha and Bravo => equal instances)?  Is there any way to achieve that result, if this doesn't do it?


I tried to program in swift but somehow I can't build my code. I am using VSCode . I read that you have to install sourcekit-lsp, but I am unsure if I installed it correctly.  Then I did the following command to check the version:  $ swift -version /snap/swift/5/bin/swift: error while loading shared libraries: libatomic.so.1: wrong ELF class: ELFCLASS32    but as you can see, there is something wrong with libatomic.so.1.  I then tried to install libatomic library but it is already installed.  I also tried the answers in this post ->   ,but that didn't solve the problem neither.  What do I have to do to be able to code in swift in VSCode?

According to  its supported platforms are:   Ubuntu 14.04 Ubuntu 16.04 Ubuntu 18.04   Is there any way to install it on a machine running Ubuntu 19.04?


So, as I understand it, computable numbers are countable since you can order the set of Turing machines that compute a number based on their Gödel number and thus count the numbers they compute. This means there are "as many" numbers that cannot be computed by a Turing machine as there are real numbers. Further, I noticed that the description or the definition of a real number is also finite (or at least can be, I haven't gone down the mental rabbit hole of figuring out what it means to have a non-finite definition for something). This means you can Gödel number them, order them, and then count all the numbers that can ever be described or defined with finite means, which then means there are again "that many" real numbers that can't ever be defined (which also means "most" real numbers can't ever be thought of or known to exist individually).  I was thinking whether there are numbers that can't be computed, but can be described and I found one. Order all Turing machines by their Gödel number and assign a natural number to each of them. Define the number  h ∈ [0, 1] as having a 1 as its i-th decimal/binary digit if the i-th Turing machine halts and 0 otherwise. Then h is a unique real number, but evidently non-computable, since the halting problem cannot be decided.  I'd like to know whether I've made any mistakes anywhere in my reasoning. Otherwise I'd like to know if such a set of numbers already has a name, what other numbers or sets of numbers does it contain that are not computable, if this bears any significance at all or if it makes any sense to define this set and what other sets can be naturally thought of as being steps following rational, transcendental and computable number on the way to the reals.  Any improvements on this post are welcome.

Reading  Wikipedia page I found this definition:     A real number $a$ is first-order definable in the language of set   theory, without parameters, if there is a formula $\phi$ in the   language of set theory, with one free variable, such that $a$ is the   unique real number such that $\phi(a)$ holds in the standard model of   set theory.   A few lines later we find the statement:     Assuming they form a set, the definable numbers form a field....   But, since they are a subset of the set of real numbers, why shouldn't they be a set?   Coming back from this question to the definition, I've another doubt: if ZFC is consistent this does not means that every set-theoretic object (and so any real number) is definable in some model?  Reading the whole article does not lessen my confusion .... and the ''talk'' is too difficult for me and it does not help.  More generally, this Wikipedia article is "disputed" ad has many "!" So I doubt that it is not reliable.  A brief surf on the web give me many pages on this subject but I've  found nothing that I can understand and give a response to the question: we can well define what is a definable real number?


Is their an elegant way to prove the product of two Levi Cevita tensors is equivalent to a determinant of a matrix of Kronecker deltas? I know that the anti-symmetry and cyclic nature should be easily proved via determinant row-interchange laws, but is the proof inelegant when it comes to showing it zeroes out when two indices are repeated?  The property in mind is: $$\epsilon_{ijk}\epsilon_{lmn}=\det\left|    \begin{array}{cccc}       \delta_{il}   & \delta_{im}  & \delta_{in}   \\       \delta_{jl}   & \delta_{jm}  & \delta_{jn}   \\       \delta_{kl}   & \delta_{km}  & \delta_{kn}       \end{array} \right| $$

In order to prove the following identity: $$\sum_{k}\epsilon_{ijk}\epsilon_{lmk}=\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl}$$ Instead of checking this by brute force, Landau writes thr product of Levi-Civita symbols as: $$\epsilon_{ijk}\epsilon_{lmn}=\det\left|    \begin{array}{cccc}       \delta_{il}   & \delta_{im}  & \delta_{in}   \\       \delta_{jl}   & \delta_{jm}  & \delta_{jn}   \\       \delta_{kl}   & \delta_{km}  & \delta_{kn}       \end{array} \right| $$  The proof that the equalty holds is quite straightforward if you consider what values the indices can take. But I've been told that there's a much more profound and elegant demonstration based on the representation of the symmetric group.  Does anybody know this approach based on group theory?


As of today, Google Instant Search . This is what it used to look like:    I never cared much for the instant display of results while I typed. However, I did use, hundreds of times a day, the keyboard shortcuts it allowed.  For those that never used it - with instant search turned on, you could:   Press enter after a search, and use the up/down keys to move a 'pointer'  down through the results Then press 'enter' to open a search result being pointed at At any point in time, typing letters/numbers on the keyboard would refocus on the search bar Pressing enter with a result highlighted could be combined with the ctrl modifier to open a result in a new tab.   I find the mouse quite difficult to use and try to avoid it when possible. Is there a tool or script I could use to replicate the keyboard behaviour that instant search used to give me?  Previous questions have asked (and been answered) in the era of instant search (e.g. ,  and my previous question ), while I'm looking for a non-google replacement with the same functionality.  I am using Chrome on Ubuntu 15.01.

As the title says; I used to be able to press Tab+Enter in Chrome to take me to the first search result. This now only works if I am not signed in to my Google account. When signed in, I can't do it. It works fine (signed in and not) on Firefox.  I believe this may have stopped working since a system update.  I'm using:   Ubuntu 12.10 Chrome 23.0.1271.64   Is this to do with a setting within Google, or is it something within Chrome? Because it works in Firefox, it suggests it is a Chrome problem. I tried disabling all extensions, but no joy.


My toshiba pen drive is now 4mb and i'm really freaking out. I have tried everything from easeus partition master, testdisk, hp usb disk utility. I've searched the entire web for help and nothing has worked. I even tried diskpart. When i go to the disk manager, there are no unallocated spaces. It's just the 4mb. I REALLY REALLY need help!!!

I have a brand new 32GB flash drive that was bought from Hong Kong but manufactured in China.  When I plug it in, it's detected, and when I examine the properties of the drive the size is reported to be 31.2 GB.  Windows forces me to format it but I have not manged to actually do that.  I then I browsed the internet and a forum told me to change the letter to L. After I did that I searched many programs that can help me format it, but when I checked it back, it is 4MB now.  Any idea what's happening with my drive?


I’m new here and I just found out who my biological father was.  Why I’m here is on ancestry.com a new dna match came up with 1,012 centimorgans with 36 segments longest segment is 100 centimorgans. No name just initials. Could this be a half sibling or first cousin or nephew? It is a male.

Given two tests that share some cM of autosomal DNA, how can I easily find the predicted relationships that such shared cM would suggest? For example, a 2,200 cM match suggests it could be either: grandparent, half-sibling, or grandchild.


The code below returns the following output:  Semaphore sema = new Semaphore(5,5,"sema_1"); for (int i = 0; i < 10; i++) {     ThreadPool.QueueUserWorkItem(delegate(object state)     {         sema.WaitOne();         Console.WriteLine(" = " + i);         sema.Release();     }); }     And just by adding the int j = i it completely changes the output to what I was expecting, which is the proper response reaching the limit of the Semaphore:  Semaphore sema = new Semaphore(5,5,"sema_1"); for (int i = 0; i < 10; i++) {     int j = i;     ThreadPool.QueueUserWorkItem(delegate(object state)     {         sema.WaitOne();         Console.WriteLine(" = " + j);         sema.Release();     }); }

I met an interesting issue about C#. I have code like below.  List<Func<int>> actions = new List<Func<int>>();  int variable = 0; while (variable < 5) {     actions.Add(() => variable * 2);     ++ variable; }  foreach (var act in actions) {     Console.WriteLine(act.Invoke()); }   I expect it to output 0, 2, 4, 6, 8. However, it actually outputs five 10s.  It seems that it is due to all actions referring to one captured variable. As a result, when they get invoked, they all have same output.  Is there a way to work round this limit to have each action instance have its own captured variable?


I have been trying this and i have no idea what i am doing , i think it will use for loop but i dont know how to use it      <script LANGUAGE="javascript">     function check(a)     {         if(a===list[a])     {     document.write("Number is Present");      }else{     document.write("Number is not Present");     }     }     </script>     <script LANGUAGE="javascript">     var list=[10, 20, 30, 40, 50, 60, 70, 80, 90, 100];     var n = prompt("Enter any Number");     check(n);     console.log(list);     </script>

What is the most concise and efficient way to find out if a JavaScript array contains a value? This is the only way I know to do it: function contains(a, obj) {     for (var i = 0; i < a.length; i++) {         if (a[i] === obj) {             return true;         }     }     return false; }  Is there a better and more concise way to accomplish this?


Prove the set $\Bbb Z^+ \times \Bbb Z^+ \times \Bbb Z^+$ is countable.   I know you can use diagonal processing to prove that $\Bbb Z^+ \times \Bbb Z^+$ is countable, but how would you go from there?

$Z$ is the set of non-negative integers including $0$. Show that $Z \times Z \times Z$ is countable by constructing the actual bijection $f: Z\times Z\times Z \to \mathbb{N}$ ($\mathbb{N}$ is the set of all natural numbers). There is no need to prove that it is a bijection.   After searching for clues on how to solve this, I found $(x+y-1)(x+y-z)/z+y$ but that is only two dimensional and does not include $0$.  Any help on how to solve this?


I know if I pump enough energy to a bunch of electrons so that they are all in their excited states, then I can introduce some photons to start off a chain reaction resulting in simulated emission. Can a star do so too?

Are there natural processes we've discovered which lead to laser light of some distinct wavelength?


I need UML modeling tool for Ubuntu such as . I need to design Sequences, Activity, UseCases for My Projects.

I just can't find a decent (and free) one. What can I use?


I saw the following in my flag list today:    Huh? This doesn't make sense. The only way a flag like this can be disputed is by being reviewed by a 10k+ non-moderator. However, if that is the case, then why does it say that a moderator reviewed it?

I know how disputed flags work. Today, I reviewed a "not an answer" flag and marked it as invalid.   I've later seen a disputed message with this reason:     invalid flag         disputed - a moderator reviewed your flag, but found no evidence to   support it   Given that disputed flags are in the ,  Is this message applicable only to my flag or is this message also for the original flagger?  Or put otherwise, are all disputed flags now shown this message (or similar decline reason)?  I've run out of flags for today to test this further.


Edit: I know this looks like a duplicate question, but it's very specific to the HTML5 drag events. I'm not having a problem adding in jQuery events, just the HTML5 drag and drop functionality.   I've used basic jQuery several times to add drag-and-drop functionality to a page, but I'd like to use the new HTML5 drag-and-drop feature for my current project. Drag works great for any element I include in the HTML, but I don't seem to be able to add elements dynamically and have them be draggable. I suspect this is because all the draggable event listeners are bound when the page is loaded, before my new elements are created. Has anyone had any luck using HTML5 to make dynamically added elements draggable? Or is there a way to re-bind event listeners without reloading the page?  Using .bind() with any of the HTML5 drag events doesn't seem to work. i.e,   $(newElement).bind('drag', function(e){   console.log('do you even drag, bro?'); });   won't ever fire, though .bind() with a click event works fine. I'm guessing this is because "drag" means nothing to jQuery. I am including the draggable="true" HTML tag in the new element, by the way.  So, anyone have success stories for binding the HTML5 drag events to dynamically created elements, or is it not possible? Thanks!

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


This is the method code:  public static void printMatrix(int[][] m, int i, int j) {     if (i == m.length ||j==m.length) {         System.out.println();     } else {         System.out.print("[" + m[i][j] + "]");          printMatrix(m, i, j++);         printMatrix(m, i++, j);     }  }   I don´t know why it just prints the first position of the array until a StackOverFlow error.  Thanks for the help.

What is a StackOverflowError, what causes it, and how should I deal with them?


Why there are no organisms that use cavities filled with lighter-than air substances (e.g. hydrogen) to fly and remain in air?  Given that there are a lot of fish and algae that use similar cavities to float, it is surprising that no organism utilized the same mechanism to fly.

If a trait would be advantageous to an organism then why hasn't it evolved yet?  Conversely, if a trait is not advantageous or mildly disadvantageous, why does it exist?  In other words why does evolution not make the organism more "perfect"?    This is a general question that would be applicable for any kind of trait. Please keep the answers precise and scientific.   Read this meta post for more information:


Is 13 going to be the first time (that we know of, obviously) that a Time Lord has changed genders during a regeneration? Preferably looking for in-canon or almost-canon, so anything other than the Curse of Fatal Death.

Is there anything that says The Doctor must be a man? I would love to see The Doctor come back as a ginger girl, and my friend tells me he thinks The Doctor cannot change gender. Is this true? If so where does it say that?


I'm trying to prove the following question from IMO 1972     Prove that for any positive integers $m,n$, $$\frac{(2m)!(2n)!}{m!n!(m+n)!}$$ is always an integer.   I tried thinking of a combinatorial argument, and came up with this: Imagine that there are two bags with $2m$ and $2n$ objects respectively. This expression is the number of ways of selecting $m$ objects from the first bag and $n$ objects from the second bag, such that the order in which you select these objects is not important. For instance, you can keep switching between bags, and also changing the order in which you select the objects.   However, I am not convinced that this is a correct argument. Where am I going wrong? Thanks

Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.  There is a answer given here to this question   I've seen how it can be proven using recurrence equations as well. When I was trying to solve this problem I was looking to represent it as the number of ways of counting something. Can anyone give such an example, thus proving the question another and very natural way?


I am using the following program for sending email through Java. When I use this program, I am not getting any error. At that same time I am not getting out it, means the mail is being not sent. I am trying to send message to Gmail. Are these smtp correct or not?  props.put("mail.smtp.host", "smtp.gmail.com");   props.put("mail.smtp.port", "465");  package mail;  import java.util.Properties;  import javax.mail.Message; import javax.mail.MessagingException; import javax.mail.Session; import javax.mail.Transport; import javax.mail.Message.RecipientType; import javax.mail.internet.AddressException; import javax.mail.internet.InternetAddress; import javax.mail.internet.MimeMessage;  public class mail4 {      private String from;     private String to;     private String subject;     private String text;      public mail4(String from, String to, String subject, String text){          this.from = from;         this.to = to;         this.subject = subject;         this.text = text;     }      public void send(){          Properties props = new Properties();         props.put("mail.smtp.host", "smtp.gmail.com");         props.put("mail.smtp.port", "465");          Session mailSession = Session.getDefaultInstance(props);         Message simpleMessage = new MimeMessage(mailSession);          InternetAddress fromAddress = null;         InternetAddress toAddress = null;         try {              fromAddress = new InternetAddress(from);             toAddress = new InternetAddress(to);         } catch (AddressException e) {             // TODO Auto-generated catch block             e.printStackTrace();         }          try {              simpleMessage.setFrom(fromAddress);             simpleMessage.setRecipient(RecipientType.TO, toAddress);             simpleMessage.setSubject(subject);             simpleMessage.setText(text);                         Transport.send(simpleMessage);           } catch (MessagingException e) {             // TODO Auto-generated catch block             e.printStackTrace();         }     } }     main class ***********  package mail; public class mail5 { public static void main(String[] args) {          String from = "xxx@gmail.com";         String to = "yyy@gmail.com";         String subject = "Test";         String message = "A test message";         mail4 sendMail = new mail4(from, to, subject, message);         sendMail.send();     } }

Is it possible to send an email from my Java application using a GMail account?  I have configured my company mail server with Java app to send email, but that's not going to cut it when I distribute the application. Answers with any of using Hotmail, Yahoo or GMail are acceptable.


I have a simple application with a main method that compares two literal strings:  public class App {     public static void main (String[] args) {         String first = "a";         String second = "a";         System.out.println(first == second);     } }   When I run this program in Eclipse, I get false as result. But when I compile and run this program by the command line, I get true.  The result should be true for both. Why does Eclipse return false?  I have tested it using JDK 7 and 8.    Note that I am aware that comparison with == compares for identity.  The JLS requires "a" to come out of the internal String cache, for both variables.  String first = "a";  // Creates instance, stores in cache and returns String second = "a"; // Should return instance from cache   However, if I run this from Eclipse I get false for the comparison, so both instances seem to be different although the JLS requires them to be the same.  Therefore, see :     Moreover, a string literal always refers to the same instance of class String. This is because string literals - or, more generally, strings that are the values of constant expressions () - are "interned" so as to share unique instances, using the method String.intern.

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?