I have a query like this: update T_table set detail = 'XXXX' where num = 155;  which on my php file looks like this: $sql = "update T_table set ".$_GET['field']." = '".$_GET['value']."' where num = ".$_GET['num']; $output = mysql_query($sql);  I would like to know if it is possible to inject SQL where the XXXX are in the query. Because they will be replaced by a sting from $_GET, and if it is possible how would you do? Important: My MYSQL database is not allowing double pipes (||) as a concatenation operator.

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


First, I know this question has been asked already  but was never answered. I am applying for an assistant professorship position (in CS) and due to overloaded teaching duties over the last years, I did not produce many papers. Currently, I am trying to compensate for this by submitting a lot of papers, which are under review. In my CV, I want to show the selection committee that I am actively working on research and actively submitting papers by listing these papers but I am not sure how they will be considered. If you were a member of the committee, how would you receive this?

Assume a search committee is reading my CV and in the publication section they notice some of my papers are only submitted or claimed to appear in a journal (or accepted for publication in a journal). Sometimes the journal which has accepted the paper for publication lists the title of accepted articles before actually publishing them, but in the rest of cases there is no evidence to prove that the referee process of the paper is over and the journal has accepted the paper for publication. Also assume preprints of my papers are available in ArXiv. So, my questions are:   How a search committee interprets and evaluates those papers which are just submitted or are claimed to appear?  Does a search committee consider these types of publications less valuable than the published ones (assuming the same quality)?  Does a search committee refer to my preprints in ArXiv to evaluate my submitted or accepted papers?


I recently gave a bad answer using the android app and I immediately noticed that it is bad since it doesn't answer the question. I wanted to delete it but I can't see that option in the android app. And I had no access to my laptop, therefore I received downvotes.   How to delete questions and answers from the android app?

Currently, the only way to vote to delete (and undelete, since you can't see deleted posts) in the Android app is to open the post in a browser, and then vote to delete from there.  Can we get delete vote functionality within the app, as well as the ability to delete our own posts?  Worth to mention: users , so it's possible in the API.  Related:


From a  question it seems there are fully refundable tickets. Are such tickets there in economy class also ?   I tried some options on akbartravels.com but in most flights two-thirds costs seem to be surcharges and taxes which I guess would be non-refundable.   Am I reading it right ?

I'm an Indian. I'm planning to book a journey from Mumbai to Johannesburg, South Africa and back (conference visa). I looked at refundable tickets, while they are priced higher, they give you half your money back, for instance if the to and fro flight costs INR 40,000 they give you INR 20,000 . But this is if you are cancelling for some reason.   What if you have to cancel because your visa application or the transit visa application got rejected. As far as I understand the procedure is :-  a. Buy airline tickets   b. Apply for Visa   c. Wait between 1-6 weeks to get update about your visa application, for both visa and transit visa (although transit visa should be shorter I guess.)  d. If visa is granted then move on to planning other things about the trip.   Now in case, if the visa application fails (for whatever reason ) what recourse does the traveler have ?  Are there any airlines who are better understanding than others about this situation ?  In non-refundable tickets, I guess that all is lost or is there some way to save money there too.   Lastly, I read travel insurance can help in this case. How does travel insurance help in the above scenario ?  Edit :- One of the pre-conditions of getting the visa is   Proof of a Valid Return or onward ticket or purchase of ticket. This is from   and


Fortunately, I can still login with this email address that I have lost access to.  I have been searching around here for a way to update it to the current one I use.  I have found many answers.  But they all give instructions to click on something not displayed or in one case, a page that prompts me to login via another email I no longer have the password for. I need current up to date instructions on how to change my email address or add another email-based login for this same user name that I am posting this with.

How do I remove login credentials (emails or OpenIDs) from my account?     For more information, see "" in the .


I'm using the svjour3 class to write journal article in Springer.  But I found there is one weird feature: The math are forced to be italic.  For example, with code  \RequirePackage{fix-cm} \documentclass[twocolumn]{svjour3}  \smartqed   \journalname{blah blah} \begin{document} \title{blah}  \author{blah} \institute{blah}  \date{Received: date / Accepted: date} \maketitle  \begin{equation} \Gamma(x) \end{equation}  \end{document}   I will get    well, in normal case, it should be     Why the Gamma is italic in svjour3? Is this a required feature in this class? How to hack it and make it normal?

I am using svjour3 class to draft my manuscript and have many \usepackage in it. The capital greek letters are rendered italic in the output. svjour3 could be obtained from   Following is a example (the symbols are italic even when no extra packages are loaded)  \documentclass{svjour3} \usepackage{amsmath}  \begin{document} This is just the beginning. \\ This is $\Sigma, \Theta$ in italics and I don't want them to be.  \end{document}     How to avoid this? Please do not suggest \usepackage{upgreek}.   PS: This manuscript I am writing constitutes of abstracts from my thesis, these symbols render correctly in my thesis Latex draft. There would be many other manuscripts and reports simultaneously going on and I want consistency in all. I believe the problem is created by the class file.


I have been studying about the human eye and it's working in school for some time. I came across something. I have been taught that the image formed on the retina of the eye by the lens is inverted and the image is made erect by the brain so as for correct perception. But how does the brain know what is erect or inverted? Why doesn't it just keep the image as it is? Please note that I am asking why the brain reverses the image and not about the nature of image formed on retina.

Why do we turn images upside down again rather than dealing with them directly, still vertically rotated after passing through our lens?   I don't see how that would cause any problems, and how we'd ever be able to figure out if we are presented with flipped images after getting used to interacting based on visual input, whether flipped or not.   What am I missing?


A couple days ago I decided to try Blender.    Why on screen do some faces have a different color and some "scratches"? How do I make all of the 3d model one color? And after rendering I have some artifacts (see screenshot). What is the reason of this?

For instance, here I have two cubes that are offset only on the x-axis. When I render them (using Blender's internal renderer), the overlapping faces interfere with each other and the result looks awful. A quick and easy solution would be to offset them by just a smidget, but is there another solution that allows faces to overlap and not exhibit this graphical glitch?


Let, S be a set defined such that $ S =\{n \in \mathbb{N}:$ if $A_1,A_2,...,A_n$ are finite sets, then $\bigcup_{i=1}^{n} A_{i}$ is finite$ \} $.  Let n = 1 and assume $A_n = A_1 $ is finite. Then, $\bigcup_{i=1}^{n} A_{i} =A_1$,which means $\bigcup_{i=1}^{n} A_{i} =A_1$ is finite. Therefore, $1\in S$. Suppose for some $n \in \mathbb{N}$ that $n \in S$. Then, the predicate if $A_1,A_2,...,A_n$ are finite sets, then $\bigcup_{i=1}^{n} A_{i}$ is finite is true for $n$. Suppose, $A_{n+1} $ is finite. Then, $\bigcup_{i=1}^{n+1} A_{i} = \bigcup_{i=1}^{n}  \cup A_{n+1}$. Since, $\bigcup_{i=1}^{n}$ is finite by our induction hypothesis and since $A_{n+1}$ is finite, it follows that  $\bigcup_{i=1}^{n+1} A_{i}$ is finite. Therefore, $n+1 \in S$. By the principle of induction it follows that $S= \mathbb{N}$  please critique my proof and give any advice. Thank you!

Prove : If $A_{1},A_{2},...,A_{n} \text{ are finite sets, then }  $$$ \bigcup_{i=1}^n A_{i} \text{ is finite.} $$   Proof:  (I) Basis Step : $p(1)$ is true because it is true because it is finite. There is a first one and a last one.  (II)  Induction Step: Suppose $p(k)$ is ture.  $$ \bigcup_{i=1}^k A_{i} \text{ is finite.} $$  Show : $P(k+1)$ is true LHS.   $$ \bigcup_{i=1}^{k+1} A_{i} \text{ is finite.} $$  Here is where I get stuck because I do not know what the right hand side of this problem is. I also do not know if you are to multiply or add to the original left hand side. How does one prove this is true for all $n \in \Bbb N ?$


I use the following pattern for regex match in grep (zgrep, as searching within compressed files) as  zgrep -P '(?<=start).{20,120}(?=end)' *   I need to add some terms with OR operator in the middle, but this pattern does not work  zgrep -P '(?<=start)[first|second|third].{20,120}(?=end)' *   How can I introduce first|second|third in the middle of the matching string?

How can I introduce a conditional OR into grep?  Something like, grepping a file's type for (JPEG OR JPG), and then sending only those files into the photos folder.  For example.  I know how to send the file where I want it, and get the file type, I just need some help with the grep part.  I'm on OS X, which IMO seems to have modified/customized *nix utilities than what I'm used to in a *nix environment.  So hopefully the answers can be as generic/portable as possible.


Hey this is my first rigging experience and I tried rigify and now the old method and I get stuck in the same area basically, a little further with rigify but in the end the same issue.  Here's a video of my issue ->   Updated Issue (for those that don't want to watch the video): - Bone heat weighting failed to find one or more bone - Now in riggify it finds the head neck and spine bones, but not the limbs - In the old fashion method it finds no bones - I have the limbs detached but still all acting as 1 mesh - My friend said I need to actually have each limb have its on mesh. - This character I'm using was imported into blender via .obj file from magicavoxel   here's the file ->     *After removing duplicated vertices, I still get the same issue when using riggify:    only the mid bones work and not the limbs.

Here is the .  Picture:   It's nothing special but I cant figure out why I get problems rigging this mesh. It would be important and a great Help! Thanks for reading and I know there are a lot of guides answering this question but I tried all and it doesn't seem to work.


Is there any explanation or evolutionary advantage to the endometrium constantly cycling between the proliferative and menstrual cycle? Wouldn't it be more advantageous if it kept always fully thickened? I imagine it is less energetically expensive than to be always producing and losing all those cells, blood vessels, etc.

When I watch wilderness specials for more than a few minutes, I notice a familiar pattern: predators are depicted as being alerted by the scent of blood. Wounded animals seem to make the best prey and predators seem to have a heightened awareness for the smell of blood.   It would seem that it would then be a disadvantage to evolutionary survival for female organisms to menstruate. How do females of a species not attract predators to the signal of menstrual blood?   Do female organisms in the wild actually menstruate? If so, is there a difference in the composition of menses that does not alert predators? How would this not at the very least give predators an idea of the general vicinity of the female?  If wild animals excrete their menses, do they have ways in which they are able to mask the evidence of its release or are they somehow internalizing the tissue so that they are not released?  If female organisms in the wild do menstruate, then why is this not a survival disadvantage?


I just purchased a Windows 8 desktop and set about installing ubuntu.  The installer couldn't read the hdd, so I installed ubuntu to a separate drive.  Now I can't boot into windows, says grub can't find the path, and the only way to boot into ubuntu is to keep the usb stick in, I assume the EFI partition is on the stick, but I've tried installing it to the drive and haven't found any success.  I ran boot repair, says all is good, but the problem persists.  I've tried googling for a similar problem and have come up empty handed.  Any suggestions?  edit: boot repair got ubuntu to boot with the usb stick, however windows 8 still won't load.  Says it can't find the drive or the efi file.  Is grub not mounting the disk windows is installed on?

I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this?


The option or button to transfer Pokemon's to the professor has disappeared? Droid Phone. Is there a limit of transfers?

After downloading the July 30th update, I noticed the ability to Transfer my Pokemon was gone.    Is this a bug or is everyone experiencing this?


I am learning to use Leaflet. I tried to add a layer from  . My code looks like this:  var wms = L.tileLayer.wms("https://wms.nlsc.gov.tw/wms", {     layers: 'EMAP2',     format: 'image/png', }).addTo(map2);   But the layer didn't show on the map. When I checked what is being returned by the developer's tool, I found they were xml files and not images! So this may be the problem, but I don't know how to fix it. Other things I've tried:   Checking with another layer, "CITY". Doesn't work. Still no layer is showing. Check if something is really wrong with my code by trying to load a layer from another source by changing the url to "", and layer to "OSM-WMS". This works! Check if something is something is wrong with the coordinates by loading the 'EMAP2' from the first source and "OSM-WMS" layer from the second source in QGIS. I set the CRS to EPSG:3857 for both. This works! They overlay just fine. Check what request the browser is sending using developers tool. For the "EMAP2" layer, this is a sample of what is being requested (as there are multiple request):

I am trying to create a map in both Leaflet and OpenLayers 3 which displays the  layer EMAP8 from the WMS http://wms.nlsc.gov.tw/wms. I can't get it to work. I can open the layer in QGIS, but when I try to use it in Leaflet like this:  var overlay_taiwanemapen0 = L.tileLayer.wms('http://wms.nlsc.gov.tw/wms', {     layers: 'EMAP8',     format: 'image/png',     transparent: true,     continuousWorld : true, });   or in OpenLayers 3 like this:  var lyr_taiwanemapen = new ol.layer.Tile({     source: new ol.source.TileWMS(({         url: "http://wms.nlsc.gov.tw/wms",         params: {"LAYERS": "EMAP8", "TILED": "true"},     })),     title: "taiwane-map(en)", });   I get nothing displayed. I can see layers being requested, and data being transferred, but nothing on the map.  What am I doing wrong?


if I write "there exists x for all y (statement)" vs " for all y there exists an x (statement)" . does it make any difference?  does the first statement mean that there is an x which makes the (statement) valid for all the y? does the second statement mean" for any given y, there will be an x which makes the (statement) true? Or do the statements mean same?

Existential-universal quantifier:     there exists $y$ in $U$ s.t. for every $x$ in $V$, $A(x,y)$   Universal-existential quantifier:     for every $x$ in $V$ there exists $y$ in $U$ s.t. $A(x,t)$   Could you please explain, why existential-universal implies the universal-existential, but not vice versa? Some examples are desirable.  Thank you for your help in advance.


I want to upgrade my laptop by adding a SSD. I have two plans:   First, putting SSD in place of cd-rom by a caddy if both HDD and cd-rom have same type of connectors. Or, if the speed of cd-rom connector is limited in compare to the HDD connector, then I should replace the current HDD by SSD and then I will put the HDD in place of the cd-rom.   So, I need to find type of their connectors!  ls -l /sys/block/sd?  lrwxrwxrwx 1 root root 0 Oct 17 17:29 /sys/block/sda -> ../devices/pci0000:00/0000:00:1f.2/ata1/host0/target0:0:0/0:0:0:0/block/sda lrwxrwxrwx 1 root root 0 Oct 17 19:23 /sys/block/sdb -> ../devices/pci0000:00/0000:00:1f.2/ata2/host1/target1:0:0/1:0:0:0/block/sdb

I have a Samsung NP300e5Z i5 laptop. I am using Ubuntu 14.04 in this laptop.  my system RAM is 4GB and i want to increase it but i am not sure how many memory slots are available in my system. so, how to check    how many memory slots available? how many slots my system is currently using? what is maximum RAM size that I can increase to?   any suggestion will appreciated


My laptop is hp pavilion g4 1303au and Processor- AMD A4-3330MX APU (Dual Core Processor with 2200 Mhz). I have a problem with Ubuntu 20.04 latest version. When I installed Ubuntu 20.04 it goes ok and I spent some time on it. But when I tried to reinstall windows 7 then on the partition section it said that windows cannot be installed on this drive. It has no option to delete the ubuntu drive. So I cancelled the process and removed my pendrive from laptop and restarted it. But it won't restart and stuck with black screen with blinking horizontal cursor on it. I pressed alt+f2 alt+f1 enter But nothing is working. Please help sir.

I installed Windows 7, which ate Ubuntu's boot file. When starting up the computer, it now goes straight to Windows, without giving me the option of booting Ubuntu.   How can I get Ubuntu back?


I have made a clean install of Ubuntu 14.04 LTS Desktop and now want's to convert it into a kiosk with a full screen webbrowser.  This was previously done in 10.04 and worked perfect, but due to hardware changes (graphics) we are forced to use version 14.04.  I have created a kiosk.desktop in /usr/share/xsessions and a shell script called kiosk.sh that launches firefox with r-kiosk installed. The shell script is executable. A user called "kiosk" is set to autologin (in /etc/lightdm/lightdm.conf).  But now i'm stuck. I'm want the kiosk.sh to be run when the kiosk user session is started.   In previous versions this could be done in the GUI tool "Login Screen Settings" or in /usr/share/lightdm/lightdm.conf.d/50-ubuntu.conf.  I have changed 50-ubuntu.conf to "user-session=kiosk" but it doesn't start. The "Login Screen Settings" tool can't be found. Has it been replaced by another utility in 14.04?  Placing a kiosk.sh.desktop in ~/kiosk/.config/autostart works, but the gnome-desktop is shown before firefox starts in fullscreen mode making it possible for the users to interact with the desktop.  What is to correct/best way to start firefox in fullscreen after user autologin?  Thanks  Thomas

I would like to customize ubuntu for a library, they only want to display a web browser with their site in full screen.  No address bar, no button user can only click the link on the page.  If library's staff enter admin user name and password they can change any settings in ubuntu.  Any suggestion or usefully link is much appreciated.


How can I cut off (delete) the excess parts of the logs sticking through the roof in my picture?  Note: The sloped roof is just a rotated plane; not sure if this affects how you might do it.

I have a quick question. Looking at the next GIF that I made, what is the quickier way you can come up with to delete the excess material that goes beyond the wall? It is basically the attachment of the handrail to the wall what is giving me this "problem".    My solution would be using the boolean modifier with a cube or something, so obviously I know how to do it. But I'm looking for the best solution, i.e., does Blender let me select the excess material in any way? For example, is there a quick way to intersect those planes? I read about intersecting planes in Blender and seems like a difficult task (not worth it in this case). So I discarded that solution.  Thanks.


Suppose that, for given integers $a$ and $b$, there exist integers $x$ and $y$ satisfying $ax + by = 6$. What are all the possible values of $\gcd(a, b)$?  Progress, we know that since $ax + by = 6$, then $x = (6 - by)/a$. In order for $x$ to be an integer, $6 - by$ must be some multiple of a. Similarly, $y = (6 - ax)/b$, so $6 - ay$ must be some multiple of $b$. Then for some integer $q$, $aq = 6 - by$. For some integer $r$, $br = 6 - ay$. Then $b = (6 - ay)/r$ and back substituting gives us $y = (6 - ax)/[(6 - ay)/r] = r(6 - ax)/(6 - ay)$. Thus $6y - ay^2 = r(6 - ax)$ and so we have the quadratic... I'm in a mess, any help and/or advice would greatly be appreciated.

Let $a,b,c$ be positive integers.  Verify that Diophantine equation $ax + by = c$ has integer solution $x_0, y_0$ if and only if $GCD(a,b)|c$. Attempt Diophantine $ax + by = c$ has integer solution $x_0, y_0$ implies $GCD(a,b)|c$. Factoring out $ GCD(a,b)$ from each side gives $$\frac{1}{GCD(a,b)}(ax + by) = \frac{1}{GCD(a,b)}c$$ which must still have an integer solution as $GCD(a,b)$ obviously divides both $a$ and $b$.  If $GCD(a,b)$ does not divide $c$ there is no integer solution. That $GCD(a,b)|c$ implies that $ax + by = c$ has integer solution $x_0, y_0$. Let $c = GCD(a,b)d$, where $d$ is integer. $ax + by = GCD(a,b)d$;  divide both sides by $GCD(a,b)$: Obtain $mx + ny = d$ with $GCD(m,n) = 1$.  If $d$ is an integer and $GCD(m,n) = 1$ then $x,y$ must be integers as $mx + ny$ cannot be further divided evenly. or $ax + by = c$ has no solution implies $GCD(a,b)$ does not divide c. $c = GCD(a,b)(\frac{ax}{GCD(a,b)} + \frac{by}{GCD(a,b)}) + r$ with $GCD(a,b) > 0, 0<r<GCD(a,b)$, r integer $\frac{c}{GCD(a,b)} = \frac{ax + by}{GCD(a,b)} + \frac{r}{GCD(a,b)}$


The only reason why I install Banshee on my new ubuntu distros is because i cannot seem to be able to add my favorite radio station to Rhythmbox.  I would like to add this radio station to Rhythmbox http://live-icy.gss.dr.dk:80/A/A05H.mp3  I press add radio and enter the radio URL in this box:    Now when i try to start the radio nothing happens  Any help appreciated   edit 1  Ubuntu 13.10  Rhythmbox 2.99.1

The stream does not play in Rhythmbox nor totem. It played fine before the upgrade; it looks like a regression from . The streams play in mplayer and play fine when downloaded with wget and then opened in totem. I suspect there is either a bug in gstreamer, or I am missing some component of gstreamer, somehow.   Is this a known bug: if so where can I help debug it? What part, package or addong for gstreamer manages streaming of mp3? Is rhythbox using gstreamer at all? If not, I am probably looking in the wrong direction.


In an Inn, while trying to speak with someone I accidentally picked up an item, stealing it. The Inn's owner and wife immediately began attacking and chased me out of town. Every time I go back into the Inn, the two immediately recognize me and chase me out of town again.  Is there anything I can do to get forgiveness in the Inn?

I accidentally killed a noble, now every guard wants to kill me. Is there any way I can get rid of the bounty?


I am creating a game where I am calculating the user points on the basis of user activities. Everything working fine I got the sum of points and on the basis of points I calculated the rank. I have two columns for points calculation PointsUp (contains up points) and pointsdown (contains down points)  select Sum(PointsUp-PointsDown) as points from table1 t1   join table2 t2 on t2.Id = t1.id where t1.ActivityTime BETWEEN '2015-01-01' AND '2016-01-01' Group By t1.Id order by points desc   Everything is fine but the problem come when I have to rank the users with same points then I have to consider the registeration date of user who register first will come up on ranking. The registeration date is in another table table3 i have tried to join third table but the sum is behaving odd showing wrong sum calculation  Can anyone help, please?

I am creating a game where I am calculating the user points on the basis of user activities. Everything is working fine - I got the sum of points and on the basis of points I calculated the rank. I have two columns for points calculation: pointsup (contains up points) and pointsdown (contains down points)  select sum(pointsup - pointsdown) as points  from table1 t1 join table2 t2      on t2.Id = t1.id where t1.ActivityTime BETWEEN '2015-01-01' AND '2016-01-01'  group by t1.id  order by points desc   Everything is fine, but the problem comes when I have to rank the users with same points. In this case, I have to consider the registration date: who registers first will come up first on the ranking. The registration date is in another table table3. I have tried to join this third table but the sum is behaving oddly, showing wrong sum calculation.  Can anyone help please?


public class Tester{   public static void main (String args[]){    String word="sandwich";   char newWord[]=word.toCharArray();    System.out.println(word.equals(transform(newWord)));   if (word.equals(transform(newWord))){       System.out.println("same");}       else{         System.out.println("not");       }    }   public static String transform(char [] newWord){     for(int i=0; i<newWord.length;i++)     {       System.out.print(String.valueOf(newWord[i]));       //System.out.print(""+newWord[i]);      }    return "";   }     }   RESULT>> sandwich false          sandwich not  Is there a way to convert a concatenated 'string' of characters to a string literal?

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?


I have windows 7 and task mgr shows about 20 conhost.exe's running???????

The process conhost.exe started showing up on Windows 7, and searching Google doesn't reveal an explanation of what this process is and why it shows up.  What is the conhost.exe process?


So I got the following SDE to solve:  $$dX_t=\alpha\, dt + \sigma X_t \,dB_t, X_0=x_0$$  This is what I've tried:  Using Ito's I should get the following relations:  $$X_t=f(s,x)$$ $$\alpha = \frac{1}{2}\frac{d^2f}{dx^2}+\frac{df}{ds}$$ $$\sigma X_t=\frac{df}{dx}$$  The second equation, which seems to be a ODE:  $$\frac{df}{dx}-\sigma X_t=\frac{df}{dx}-\sigma f=0$$ Using the integrating factor: $$I = e^{\int -\sigma \,dx}=e^{-\sigma x + g(s)}$$ $$\frac{df}{dx}I-\sigma fI=0$$ $$(fI)'=0$$ $$f=CI^{-1}$$ Using the initial value: $$f(0,0)=x_0=C$$ $$f=x_0e^{-\sigma x + g(s)}$$ The problem for me is now to solve $g(s)$.  Differentiating by $x$ twice and $s$ once gives: $$\frac{df}{ds}=g'(s)f$$ $$\frac{d^2f}{dx^2}=\sigma^2f$$ $$\alpha = \frac{1}{2}\frac{d^2f}{dx^2}+\frac{df}{ds}$$ $$\frac{1}{2}\sigma^2f+g'(s)f=\alpha$$  At this point I'm quite unsure on what to do.

Solve the SDE: $dX(t) = udt + \sigma X(t)dB(t)$  Provided Question  The SDE is $dX(t) = udt + \sigma X(t)dB(t)$. Find $X(t)$, where $X(t)$ is some stochastic process and $B(t)$ is a Wiener process. Both $u$ and $\sigma$ are constants.  Hint: Multiply both sides by the "integrating factor" $e^{-\sigma B(t) + \frac12 \sigma^2 t}$.  Current Progress  Multiplying both sides by the appropriate integrating factor:  $$ \exp{\big( -\sigma B(t) + \frac12 \sigma^2t\big)}dX(t) = \exp{\big(-\sigma B(t)+\frac12\sigma^2t\big)}(udt + \sigma X(t)dB(t)) $$  Then set $f(t,x,b):=\exp{\big( -\sigma B(t) + \frac12 \sigma^2t\big)}X(t)$ and apply Ito's formula. Some of the required results before actually applying Ito's formula:  $ \frac{df}{dt} = \frac12\sigma^2 X(t)e^{-\sigma B(t) + \frac12 \sigma^2t} \\ \frac{df}{dx} = e^{-\sigma B(t) + \frac12 \sigma^2t} \\ \frac{df}{db} = -\sigma X(t)e^{-\sigma B(t) + \frac12 \sigma^2t} \\ \frac{d^2f}{dx^2} = 0 \\ \frac{d^2f}{db^2} = \sigma^2 X(t) e^{-\sigma B(t) + \frac12 \sigma^2t} \\ \frac{d^2f}{dxdb} = -\sigma e^{-\sigma B(t) + \frac12 \sigma^2t}  $  Given this, we need to know the following derivatives of the quadratic variations and co-variations:  $ d\langle B\rangle_t = dt \\ d\langle X,B\rangle_t = ??? $  My Request  Please instruct me on what $d\langle X,B\rangle_t$ is equal to so that I may progress further with this problem.


I've noticed on a acer travelmate 5720, that runs Ubuntu 13.04, it doesn't show or pickup the latest 13.10 version. I did check die update settings and it is set pickup/show the latest updates. But with the necessary settings set, it doesn't pickup the latest version. And it does have access to full free internet. Is there some solutions? Or can I update via terminal?

I would like to know how to upgrade from my current version of Ubuntu to the next stable from the Command line interface?


So I know in order to prove a function is bijective, you need to prove that it is both injective and surjective. I know that to prove it is an injection, I need to make $f(x) = f(y)$, and try to get $x=y$ from that, but I can't seem to manipulate the equations to do so.   Also, how would I prove that this is surjective?

Prove that the function $f: R\to R$ given $f(x)=x\cdot |x|$ is a bijection  Proof 1: f is injective  Suppose $$f(a) = f(b) \implies a\cdot |a| = b\cdot |b|$$ $$\implies (a\cdot |a|)^2 = (b\cdot |b|)^2$$ $$\implies a^4 =b^4$$ $$a=b$$ Thus, f is injective  Proof 2: f is surjective  Pick $n\in R$, we want to show $n=f(x)$ for some $x\in R$  $$\implies n= a\cdot |a|$$ for some $a\in R$  I dont know how to complete the surjective proof


Here's two examples (note that in first example, backticks also had no effect, for some reason):   include/db.php:      $attribs =               array(                     PDO::ATTR_PERSISTENT => $config['db']['persistent'],                     PDO::ATTR_ERRMODE => $config['db']['errormode']             );       $db = new PDO(             $config['db']['uri'],             $config['db']['user'],             $config['db']['pass'],             $attribs     );     $db->query("SET NAMES 'utf8'");     $db->query("SET CHARACTER SET 'utf8'");   } catch (PDOException $e) {         print "Error!: " . $e->getMessage() . "";         die(); }  function dbGetEngine() {         global $config;         return substr($config['db']['uri'], 0, strpos($config['db']['uri'], ':')); } ?> include/config.php:     It gets worse, try adding space prior to the asterisk :/  Just removing the asterisk fixes stuff up. Thing is, I believe it looks nicer with the asterisk ... and it's definitely a bug :-)

Consider the following piece of Markdown code:  This is some regular text.      >>> def factorial(n):     ...     return 1 if n < 2 else n * factorial(n - 1)     ...   * This is a list item.      >>> def factorial(n):     ...     return 1 if n < 2 else n * factorial(n - 1)     ...    Notice that the second code block is preceded by a list item.   Why is the factorial code not properly formatted under these circumstances? To demonstrate the problem, I'll insert the Markdown code show above:    This is some regular text.  >>> def factorial(n): ...     return 1 if n < 2 else n * factorial(n - 1) ...     This is a list item                 def factorial(n):       ...     return 1 if n < 2 else n * factorial(n - 1)       ...               This applies to numbered as well as unnumbered lists.


As most Minecraft command blocks makers know, if we use the /say command to output text, this will happen:     [@]Lorem ipsum   The [@] is actually very annoying, how can I remove it?

I've looked it up, and apparently there is not a way to. But, there's an NPC in my map where I have it "talking" with a /say command. So, is there a way to make it say something like [(NPC Name)] (Text) without mods?


Instead of trying to find the square root of square numbers, I try to find the square root of numbers that aren't square numbers like 12 and 35, but it seems hard to do it with pencil and paper, so I use a calculator to figure those out.  I wonder how I can find the square root of a not-square number ONLY with paper and pencil.

I was reading Richard Feynman biography when I read that one time he was able to calculate the  cube root of large number in his brain by just using simple facts of everyday life. So my question is there a way to calculate square root or cube root by using just a pen a paper, I mean a systematic way not by trial and error.


I have file called -l in my directory  now I tried to do  for i in *; do stat -c "%s %n" "$i"; done   it lists all files with sizes but in the middle of the output there is something like  395 koko.pub stat: invalid option -- 'l' Try 'stat --help' for more information. 2995974 list.txt   so it can not process -l as normal filename, how do I get desired behavior from stat?

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?


Prove that there do not exist any positive integers $x,y$ and $z$ that satisfy $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=1$   My attempt:-     Since $x,y $ and $z$ are positive integers, we can assume without loss of generality that $x\le y\le z$  . Hence we have  $\frac{z}{y}$ and $\frac{y}{x} \ge 1$. This implies, $$\frac{x}{y}+\frac{y}{z}+\frac{z}{x}\gt 2$$. Therefore, there do not exist any integers $x,y $ and $z$ satisfying the above equation. Does this look good? Can this be solved using divisibility or any other technique ?

Are there any positive integers $x,y,z$ such that $$\frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 1?$$ Prove/Disprove.   I've plugged in random positive integers for $x,y,z$ and I have not been able to get the equation to equal $1$.


Check this extremely simple html structure. One div inside another, the inner (green) div has margin-top: 100px, the outer (red) div has no margin-top. The outer div is twice (200px) as high as the inner div (100px).   So what would you expect the result to look like? If you're like me, you get the opposite of what you'd naturally expect to get.  My question is NOT how to prevent this. My question is WHY ist this happening this way consistently across all browsers? I mean, this obviously must be the way it's inteded to work, but to me it's strongly counter-intuitive.    .red {     background-color: #a00;     height: 200px; }  .green {     background-color: #0a0;     margin-top: 100px;     height: 100px; }

So essentially does margin collapsing occur when you don't set any margin or padding or border to a given div element?


I am trying to upgrade my the core/jquery library from 3.2 to 3.4.1 in the core. How can I update the assets/vendor/jquery/jquery.min.js defined in core.libraries.yml to a further jquery version? I can not currently update my drupal to v8.9, which comes with v3.5 of jQuery. I am using drupal 8.6 So far I have tried looking at  but the recommended module doesn't seem to be available for drupal 8 and above.

In my theme's libraries.yml file, after the global-styling section, i'm trying to replace one JavaScript file from the core Toolbar module (it's addition of padding-top to body interferes with our theme, so just changing that to margin-top).    libraries-override:   toolbar/toolbar:     js:       js/views/BodyVisualView.js: js/views/BodyVisualView.js   I repeatedly get the error:     Drupal\Core\Asset\Exception\IncompleteLibraryDefinitionException:   Incomplete library definition for definition 'libraries-override' in   extension 'mythemename' in   Drupal\Core\Asset\LibraryDiscoveryParser->buildByExtension() (line 93   of   /vagrant/web/core/lib/Drupal/Core/Asset/LibraryDiscoveryParser.php).


I have a big binary file (which can be as large as 2^32 bytes). I intend to perform multiple writing and reading operations on it constantly throughout my program (the contents of the file are constantly being updated). I am considering both performance and ease of use.  I looked up a bit and found that people have quite different opinions on it. Some people say that memory-mapping is not beneficial in this case, the others say that memory-mapping is more efficient.  I haven't written any code yet. I am still considering which approach I should use.  I would like to know which approach is more efficient and easier to use. I know that if I use memory mapping I can use memcpy, memset etc. to modify my memory and they will be reflected in the actual file. However, I am new to C so there might be counterparts of these function when using a stream.

POSIX environments provide at least two ways of accessing files.  There's the standard system calls open(), read(), write(), and friends, but there's also the option of using mmap() to map the file into virtual memory.  When is it preferable to use one over the other?  What're their individual advantages that merit including two interfaces?


They tend to fluctuate as I move the model around:

I don´t know if this is a bug only to me or a common problem, for I don´t know why it occurs.  I had a problem once before where some edges of my model got jagged with black holes when switching to rendered mode (or actual rendering). Answers I got said that I modeled in too much detail or too small, and used the combination Subdiv Modifier/Auto Smooth/sharp edges wrong.  Now I have a way more problematic thing. I have a really simple scene, but most of the edges have this annoying jagged problem. I build this model in a higher scale (since the last one was too small).  I used the Subdiv Modifier/Auto Smooth/sharp edges again, but if I toggle on/off the Subdiv Modifier/Auto Smooth/sharp edges/seams, shade smooth/flat, won´t help at all. These artifacts just keep showing.  Does anyone know why this occurs?  Shaded Flat and zoomed in for a better look on the artifact.      My hardware specs are   GPU: Asus M5A78L-M LX3 GPU: NVidia GTX 750 StormX OC CPU: AMD FX6300 @ 3,5 GHz 8 GB RAM Windows 7 Professional 64-bit


This evening I had cause to log in to , a site I hadn't visited before, and I found myself unable to login.  After clicking on log in with Stack Exchange I wait and wait and the username and password boxes never appear.    Thinking it was my browser, I cleared out my cache, and tried again, with the same result. The browser itself is Chrome 23.0.1271.95 m, on Windows 8, which claims to be up to date.  I then visited a few other SE sites. On sites I've logged in to before, I was logged back in automatically, click here to refresh the page. On sites I haven't logged in to before, such as , I got the same result as Cross Validated.  At that point I did a global logout and then cleared any remaining cookies I could find. When I went back to attempt to log in again, I could no longer log in to any Stack Exchange site.  On the computer which is failing to log in, I hit F12 and looked at the Network tab. When I click log in with Stack Exchange a number of requests fly by; the last one being POST /users/login/global, which returns a 404 Not Found.  I also see the following additional error in the console:  Port error: Could not establish connection. Receiving end does not exist. chromeHidden.Port.dispatchOnDisconnect   I suspect these may be related to my problem.  (I am posting this from a different browser from which I was already logged in; I'm quite afraid to attempt logging out... And I'm just a sysadmin, not that much of a developer anymore, so if I forgot anything important, please let me know.)

I recently noticed that, when  is enabled in Firefox, the login process on Stack Exchange sites stopped working. (Symptom: after clicking "log in", then clicking on the "log in with Stack Exchange" logo", the login process just spins forever and doesn't continue. If it's relevant, I login with Stack Exchange as my OpenID provider.) Disabling Adblock Plus makes the login process start working again.  Is there any workaround that allows me to have Adblock Plus enabled (for example, for other sites) while still allowing login on Stack Exchange sites to work properly?


There is this "weird" bonus xp that pokemon go gives when catching a Pokémon. Doesn't say why either in the game.    So why is it given ?

I found , earlier, and found out that I can throw a curveball at pokémon to earn an increased experience bonus.  I have since noticed two more bonuses: "Great" and "Nice". I had assumed the bonuses were for throwing a pokéball with the 'catch circle' closer to the center, which according to the FAQ, increases the chances of actually catching the pokémon.  However, I have since noticed that the 'catch circle' is actually bigger in cases where I have earned a "Great" bonus. Despite appearing to be a less powerful throw, I earn more experience than when I earn a "Nice" bonus. "Great" nets me 50 experience, while "Nice" only nets 10 experience.  What are the possible catch bonuses, and how much experience do they reward?  For bonus points, every so often I am awarded an additional 10 experience points that are not accounted for on the experience screen. The screen lists my bonuses, and tells me how much experience I have earned, but I am clearly rewarded additional experience when it is added to my player. Assuming this is another catch bonus, what could this be?


The first time Gollum had attempted to kill the Hobbits didn't go as plan, as the Hobbits were aware of his presence and were able to trick him into thinking that they were asleep.  However, Gollum had many other opportunities once he had agreed to take them to Mordor to have killed them in their sleep and take the ring from Frodo. This isn't the case though, and he seems to remain loyal (to an extent) and doesn't really seem to attempt anything until the final film, where he leads them into Shelob's lair.  Why is this?

I'm only basing this question on the LotR movies, since I haven't read the books.  Gollum starts following Frodo and Sam, and then one night jumps out and tries to kill them and take the Ring. They subdue him, but only because they expected him and were thus able to defend themselves. From then on he kind of decides to help them get to Mordor to destroy the Ring.  During this period he seems to have split personalities: Gollum vs. Smeagol, with Gollum wanting to kill them and Smeagol seeming to be at least neutral towards them, from the conversations the movie shows between the two.  At some point though, Gollum seems to win over Smeagol and convince him to lure them to Shelob to kill them.  But why didn't he just kill them while they were sleeping? In the movie, he has dozens of opportunities where he could definitely cut one hobbit's throat, bash their head in with a big rock, push them off a ledge, etc.


From time to time I lose 10 rep points for a "User was removed" reason. I'm really curios to know in what way I helped that user, that is, what was his\her question, and what did I answer? Currently, there's no way to know that and trace back my answer.  Can SO add a link for the origin of the Rep points lost?

Understanding , it'd be nice to know specifically where that reputation was lost from.  Reputation changes typically cite where reputation was gained or lost; however, it's difficult to reference the origin of where it was lost when a user is removed:        Already labeled as removed, a link to the question would indicate the source of the loss, as in:     -10     6 hours ago     removed     List component to bring up InputText boxes   Perhaps there's greater complexity here than I realize, such as the question itself being deleted; however, actions such as removing an upvote to a question or answer could be linked.


I am familiar with PCA from  where you either normalize the data (to standard normal or centered?) and construct a covariance matrix or just construct the correlation matrix, eigendecomposition, sort eigenvalue/vector pairs by eigenvalue in descending order (the ratio of these eigenvalues to their sum is the explained variance), and finally, transform the original data to be projected onto the new eigenvalue axes matmul(X, sorted_eigenvectors.T)  This makes sense to me but WHAT IS PRINCIPAL COORDINATE ANALYSIS?  I understand you use a distance matrix instead of a correlation matrix.  What does this mean in terms of eigenvectors?  In PCA, the eigenvectors are in the direction of maximum variance but what about in a distance matrix space?   Here's some Python 3 code I made to do PCA.    import numpy as np import pandas as pd from sklearn.datasets import load_iris from sklearn.preprocessing import StandardScaler from sklearn import decomposition  np.random.seed(0)  # Iris dataset DF_data = pd.DataFrame(load_iris().data,                         index = ["iris_%d" % i for i in range(load_iris().data.shape[0])],                        columns = load_iris().feature_names)  Se_targets = pd.Series(load_iris().target,                         index = ["iris_%d" % i for i in range(load_iris().data.shape[0])],                         name = "Species")  # Correlation matrix (Note: StandardScaler of data and then covariance = correlation) DF_corr = pd.DataFrame(np.corrcoef(DF_data.T),                        index = DF_data.columns,                       columns = DF_data.columns)  # Eigendecomposition Ve_eig_vals, Ar_eig_vecs = np.linalg.eig(DF_corr)  # Sorting eigenpairs eig_pairs = [(np.fabs(Ve_eig_vals[j]), Ar_eig_vecs[:,j]) for j in range(DF_data.shape[1])] eig_pairs.sort(); eig_pairs.reverse() Ar_components = np.array([x[1] for x in eig_pairs])  # Projection matrix Ar_Wproj = np.array([x[1] for x in eig_pairs]).T  DF_transformed = pd.DataFrame(np.matmul(DF_data.as_matrix(),Ar_Wproj),                               columns=["PC_%d" % k for k in range(1, Ar_Wproj.shape[1]+1)]) #          PC_1      PC_2      PC_3      PC_4 # 0    2.669231 -5.180887 -2.506061 -0.115201 # 1    2.696434 -4.643645 -2.482874 -0.105533 # 2    2.481163 -4.752183 -2.304354 -0.102643 # 3    2.571512 -4.626615 -2.228277 -0.276660 # 4    2.590658 -5.236211 -2.409756 -0.153814 # 5    3.008099 -5.682217 -2.456525 -0.221893 # 6    2.490942 -4.908714 -2.106376 -0.181431 # 7    2.701455 -5.053209 -2.444074 -0.209103   Can I literally just replace the correlation matrix (DF_corr) w/ a distance matrix?   from scipy.spatial import distance  Ar_MxMdistance = distance.squareform(distance.pdist(DF_data.T, metric="braycurtis")) DF_dism = pd.DataFrame(Ar_MxMdistance, index = DF_data.columns, columns = DF_data.columns)

How are PCA and classical MDS different? How about MDS versus nonmetric MDS? Is there a time when you would prefer one over the other? How do the interpretations differ?


I am trying to tie together some pieces of grammar here. Specifically: What is proper full-stop and comma notation in combination with parentheses?  The issue shows when abbreviations are involved as in these sentences:     He measured all the properties (though not height, width, depth etc.).      He measured all the properties (though not height, width, depth etc.), which might be of use.   At the closing parenthesis, there are the weird-looking .). and .), constructions. Is this actually correct notation?   The answer on  concludes that the full-stop in the first sentence can both be inside or outside the parenthesis depending on which part of the text, it is tied to. I would therefore keep it outside in the example above.

Example:     It's all about apples, oranges, bananas, etc.   VS.     It's all about apples, oranges, bananas, etc..   Update  What happens if the abbreviation is inside parentheses, do you place a dot after and before the closing parenthesis?     It's all about fruit (apples, bananas, etc.).


While I am doing stuff... doesn't seem to matter what, my USB mouse just stops working... sometimes it will be the keyboard as well but usually not as often. Ubuntu forces me to press my power button to recover my mouse again.  Any ideas?  Let me know if you need more information.  This is a dual boot system and only happens on Ubuntu, and it works fine under Windows

All operating systems freeze sometimes, and Ubuntu is no exception. What should I do to regain control when...   just one program stops responding? nothing at all responds to mouse clicks or key presses? the mouse stops moving entirely? I have an    In what order should I try various solutions before deciding to pull the power plug?  What should I do when starting up Ubuntu fails?  Is there a diagnostic procedure I can follow?


Hello I was wondering how you could do the following in python Suppose we have these lists ["Apples","Pears","Oranges","Grapes"] ["Apples","Pears","Oranges","Grapes","Strawberries"] ["Apples","Pears","Oranges","Pumpkins","Cherries","Lemons"]  And I wanted to extract to extract the 4th element and beyond. So... ["Grapes"] ["Grapes","Strawberries"] ["Pumpkins","Cherries","Lemons"]  The lists will all have more than 3 elements. How would I do this?

I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.


What’s that word that describes the feeling when something you see/hear/smell reminds you of someone? For example if you go to the park and you see the place where you had a first kiss with someone and that place makes you miss that person? It isn’t something that you do voluntarily, it’s more like a thing that pops out in your head and you can’t get it out. (I remember my English teacher talking about it I just don’t know what it is)  “I went to the park today and that bench triggered my ____”

Is there a noun that precisely describes the emotion of missing someone/something?  There is longing, but I don't think that's quite right. You can feel longing for something without missing it. I know this word exists in another language (Hebrew - געגוע), but I'm not sure if there is an equivalent in English.


I have a 32 length hex string in Java and need to make an IV to encrypt. I know dart has a function IV.fromBase16, and I need something like that in Java.   I tried reverse engineering through flutter, but nothing made sense. I'm new to this part of development.   I already tried codec jar but it was worthless. I googled for questions to transform 32 to 16, but all that I have found was how to transform a string in hex values.   Also, I need to use AES and CBC, but I'm not aware if this is possible in Java due to the string length.

I am looking for a way to convert a long string (from a dump), that represents hex values into a byte array.  I couldn't have phrased it better than the person that posted .  But to keep it original, I'll phrase it my own way: suppose I have a string "00A0BF" that I would like interpreted as the  byte[] {0x00,0xA0,0xBf}   what should I do?  I am a Java novice and ended up using BigInteger and watching out for leading hex zeros. But I think it is ugly and I am sure I am missing something simple.


Not sure what is going on.  I have ran Process Explorer and I dont' see any of the usual culprits.  I have consistent 70-90% CPU usage.  It's often within the services process due to Windows Update. I typically just disable the windows update service and I'm good to go.  But over the last couple days, ntoskrnl.exe has been chewing away at my performance big time.  My computer starts slowing down more and more and more, and eventually practically comes to a halt.  Oddly enough, sometimes it will slow down to a grind even though the CPU usage only says it is at 50%.  A couple months ago I upgraded the RAM to 16GB, which seemed to help but now it seems whatever issue I am dealing with has finally caught back up.  I don't see anything particularly insightful to me within process explorer, and none of the help articles I googled are helpful.  Any tips?

I have noticed that from some time my system is freezing and its probably caused by the high CPU usage which is caused by the system process.  All applications I'm running is the Skype, TeamSpeak and Chrome so it definitely shouldnt eat that amount of CPU.  You can see the problem itself and running processes in the screenshot below:    Sometimes CPU usage is reaching 90%, but the average usage is like 40-65%.  My PC parameters:   Windows 8 (customer preview) Intel Core i3 - 2350M 8 GB RAM   I'd appreciate any help attempt! Regards.  --UPDATE--  As the user below posted a great answer, I have noticed that the process that is eating the most CPU in the system is called Arthurx.sys, simple google tells that it's a TPLink driver (an wifi adapter, I have bought like 2 weeks ago!) drivers has been installed from the Windows MSDN, but also tried to install the drivers from the attached CD, but it doesn't help. From the system start, it is using like 5% of the CPU only, but after 2-4 hours of working it is growing up and reaching 40-60% of the CPU usage.  Device name: TPLink WN722N


If $A$ and $B$ are proper ideals of a ring with no zero divisors, show that $A\cap B \neq \{0\}$    Ideals:  A subset $I$ of a ring $R$ is called an ideal if   $I$ is a subring of $R$ For all $a\in I,r\in R$ $ar\in I$ and $ra\in I$.     $A$ and $B$  both satisfy the above. How to show that $A\cap B \neq 0$?

$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.  I have no idea how to solve it. please help.


In the books, Dumbledore was wearing a ring on his finger, giving him a curse in the 6th book.  My question is: did he have to wear that ring on his finger? Couldn't he, like, chain the ring and wear it as a medallion, as the trio did with the locket in book 7, so that he wouldn't get cursed?  It just makes me wonder whether there was a canon reason for that, or whether Rowling just had to make a reason/excuse to rid of Dumbledore faster.

So I was wondering and going back to Harry Potter recently and I was trying to figure out why Dumbledore put Marvolo Gaunt's Ring. The ring that Dumbledore had expertly deduced was an Horcrux was already heavily guarded by Voldemort in Little Hangleton and the only possible solution would be destroy it which Dumbledore eventually did with the Sword of Gryffindor.  It seems extremely careless and stupid of him to do such a thing. Why would the headmaster try a ring that would eventually kill him, as pointed out by Severus Snape?


I am using windows 10. I have some tutorials which requires to run on internet explorer 6.0 + .   when i try to run those tutorials it runs on Microsoft Edge. after a spash screen it shows the message that it requires IE 6.0 +.  Is there any way to download and install IE 6.0 + on win10.  or Is there any to make Microsoft Edge behave like IE 6.0  Thanks. - Shahid

I have Microsoft Edge, but I need Internet Explorer 7 as a web site I am accessing will only open with this.  I downloaded Internet Explorer 7 and it said it was not compatible.  How do I make this work?


I'm visiting St. Maarten from Sri Lanka. I have a Caribbean visa from the Netherland Embassy. Transit period in Amsterdam Airport is 4 hours. Do I need a transit visa to go through Amsterdam?

I found many related questions on this site but I am still not sure about the rules. How can I decide if I need a visa to transit? Schengen members as of May 2021 are as follows:  Austria Belgium Czech Republic Denmark (excluding Greenland and the Faroe Islands - but an open border with the Schengen Area is maintained) Estonia Finland France (excluding overseas departments and collectivities) Germany Greece Hungary Iceland Italy Latvia Liechtenstein Lithuania Luxembourg Malta Netherlands (excluding Aruba, Curaçao, Sint Maarten and the Caribbean Netherlands) Norway (excluding Svalbard) Poland Portugal Slovakia Slovenia Spain (except Ceuta and Melilla) Sweden Switzerland


Let V be the vector space F(ℝ,ℝ). Which ones of the following subsets are vector subspaces of V ? Justify your answer! (a) {f ∈ V | f(1) = 0}  (b) {f ∈ V | f(0) = 1} (c) {f ∈ V | f only has a finite number of zeros} (d) {f ∈ V | f has infinitely many zeros}  I do not know how to proceed. Could you please give me a hint? Thank you in advance.

Determine which of the following sets is a vector space.  $V$ is the line $y=x$, in the $xy$-plane: $V =\{[x,y]: \; y=x\}$  $W$ is the union of the first and second quadrants in the $xy$-plane: $W=\{[x,y]: \; y\geq0\}$  $U$ is the line $y = x+1$ in the $xy$-plane: $U=\{[x,y]: \; y=x+1\}$    I know that the answer is that "$V$" is the only vector space. However how do I come up with a quick proof to show that $V $is a vector space and that the other $2$ aren't?


I have created a small program to understand Java Volatile keyword:  public class MultiThreadedCounter implements Runnable {      private volatile int counter = 0;      public void run() {          increment();         decrement();      }      private void decrement() {         counter = counter - 5;         System.out.println("dec = " + counter);     }      private void increment() {         counter = counter + 5;         System.out.println("inc = " + counter);     }      public static void main(String[] args) throws InterruptedException {         MultiThreadedCounter m = new MultiThreadedCounter();         Thread[] t = new Thread[100];         int count = 0;         while (true) {             if (count >= 100) {                 break;             }             Thread t1 = new Thread(m);             t[count] = t1;             count++;         }          for (int i = 0; i < t.length; i++) {             t[i].start();         }     }  }   Now in this program, I am seeing different set of results when I run the program multiple times.  Then I tried removing the volatile keyword for counter variable and observed similar results. i.e I am seeing different results when I run the program many times.  How Volatile helps in this program? When we need to use this keyword, I have gone through some material ans SO posts but I am not getting clear picture of the usage of this keyword.

At work today, I came across the volatile keyword in Java. Not being very familiar with it, I found . Given the detail in which that article explains the keyword in question, do you ever use it or could you ever see a case in which you could use this keyword in the correct manner?


Suppose there is a parallel plate capacitor with distance between plates $d$ and it is charged to a potential difference $V$ and then charging battery is disconnected. Then the plates are further separated by a distance $d$. We need to calculate work done in doing this.  Now, I did this problem in two different ways, and they are giving contradictory results.  The first solution involves finding change in electrostatic energy of the capacitor and accordingly find the work done which is $CV^2/2$. This gives the right answer.  But, here's another solution which I think is perfectly justified and want your help in finding what is the fault in this approach.  Consider one plate to be at rest and the other one moving. Now the change in potential is from $V$ to $2V$ as the distance is doubled while field is same between the plates. Therefore, the work done should be the charge on capacitor plate times the potential difference, i.e  $QV$. Now $Q=CV$ which gives the work done as $CV^2$.  Now, I know that this answer is incorrect, but even after spending quite a time on this, I cannot figure out the fault.  So, please help.  Thanks.

If a capacitor is charged by a source with constant voltage, $V$, the energy, $W$, stored by a capacitor of capacitance $C$ is given by:  $$ W = \frac{1}{2} QV = \frac{1}{2} V^{2}C = \frac{Q^{2}}{2C} $$  where $Q$ is the charge stored on the plates.  If the capacitor is now disconnected, and its capacitance is changed by increasing the distance between the plates, its energy must increase since work is being done by moving charge under the influence of an electrical field. Furthermore, since the plates are not connected to anything, it can be assumed that charge is conserved.  The method for calculating the change in energy that I have seen in textbooks and on the internet is to calculate $Q$ for the pre-separated case, calculate $C$ for both cases, then use:  $$ W = \frac{Q^{2}}{2C} $$  to give $$ \delta W = \frac{Q^{2}}{2} \left( \frac{1}{C_{2}} - \frac{1}{C_{1}} \right) $$  where $C_{2}$ is capacitance post-separation, $C_{1}$ is capacitance pre-separation and $\delta W$ is the change in energy.  This seems naive to me. That formula was for the process of charging a capacitor from a constant voltage with the $\frac{1}{2}$ arising from the potential difference that charge is raised by decreasing as more charge is deposited.  With constant $Q$, we can say that:  $$ dW = QdV $$  and integrate to give:  $$ \delta W = Q(V_{2} - V_{1}) $$  where $V_{2}$ is the post-separation voltage and $V_{1}$ is the pre-separation voltage. Substituting $Q = CV$ then gives:  $$ \delta W = Q^{2} \left( \frac{1}{C_{2}} - \frac{1}{C_{1}} \right) $$  i.e. double the textbook answer.  Am I missing something?


The individual tag badge descriptions are all stating 80 as the minimum number of answers:    This is incorrect.  80 is only the minimum for the silver badge, as shown on the :     Bronze Badge  You must have a total score of 100 in at least 20   non-community wiki answers to achieve this badge.   50.3k awarded      Silver Badge You must have a total score of 400 in at least 80   non-community wiki answers to achieve this badge.   9.1k awarded      Gold Badge You must have a total score of 1000 in at least 200   non-community wiki answers to achieve this badge.   2.7k awarded   This affects Stack Overflow as well as other sites such as .

See these three pages:          All three of them say:     Earned at least X total score for at least 20 answers in the  tag.   This same text also appears on the tooltip for the tag badge:   Also note the double colon after 'gold badge'  As well as on these pages:          But the  clearly states:        Bronze Badge:  You must have a total score of 100 in at least 20 non-community wiki answers to achieve this badge.   Silver Badge: You must have a total score of 400 in at least 80 non-community wiki answers to achieve this badge.   Gold Badge: You must have a total score of 1000 in at least 200 non-community wiki answers to achieve this badge.        Edit:  It has been noted in the comments that other users see different numbers in these pages, but in all cases it appears they see the same number of answers are required for all tag badge description, regardless of the badge's type.


How to see that the circle $\mathbb{S}^1:=\{x \in \mathbb{R}^2 \mid x^2+y^2=1\}$ is homeomorphic to the quotient space $\mathbb{R/Z}$ that is given by $x \sim y : \Leftrightarrow x-y \in \mathbb{Z}$?

An equivalence relation on $\mathbb{R}$ is given by   $$ x\sim y\Leftrightarrow x-y\in\mathbb{Z}. $$   Show that the quotient space $(\mathbb{R}/{\sim},\tau_1)$ is homeomorphic to $(S^1,\tau_2)$, where $\tau_1$ is the quotient topology and $\tau_2$ the induced topology.   I have to find a bijective continuous function $$ f\colon \mathbb{R}/{\sim}\to S^1 $$ with $f^{-1}$ continuous.  Do you have an idea how to find such a function?


I read  about voltage dividing. Let's look at this image for the discussion:  Ok so we have 2 resistors in the circuit, and Vout is of lower voltage. But I don't understand - voltage is always a difference between two points.  So, with respect to what point is Vout has a lower voltage? If you say with respect to ground - then, why in  it says:  Keep in mind not to use a voltage divider to reduce the voltage to supply a device or load because you have to remember that an external device will result in a parallel circuit with R2.  So actually if you take Vout, connect it to the + terminal of a device, and the - terminal to GND, the voltage of this circuit will be dependent on the resistance of the device. So what is this arrangement of voltage dividing good for? I'm actually asking this because I want to supply my ESP8266 with power from a 9V battery, so I thought of using resistors to divide the voltage. But for this, I need to know the resistance of my ESP8266, which is not shown in the datasheet.

When would you use a voltage regulator vs a resistor voltage divider?  Are there any uses for which a resistor divider is particularly bad?


I'm trying to write some provisioning shell scripts for Vagrant dev environment. I'm used to start bash scripts as follows   #! /bin/bash   But after surfing through some git repos I found out that in most cases guys use   #! /usr/bin/env bash    So the question is: what the difference and what is the most decent way to start a bash script? (any alternatives are also appreciated)

I notice that some scripts which I have acquired from others have the shebang #!/path/to/NAME while others (using the same tool, NAME) have the shebang #!/usr/bin/env NAME.  Both seem to work properly.  In tutorials (on Python, for example), there seems to be a suggestion that the latter shebang is better.  But, I don't quite understand why this is so.  I realize that, in order to use the latter shebang, NAME must be in the PATH whereas the first shebang does not have this restriction.  Also, it appears (to me) that the first would be the better shebang, since it specifies precisely where NAME is located.  So, in this case, if there are multiple versions of NAME (e.g., /usr/bin/NAME, /usr/local/bin/NAME), the first case specifies which to use.  My question is why is the first shebang preferred to the second one?


Is there a plugin out there that will split a polyline at vertexes?  My arcgis license isn't high enough to run the tool.  I'm using 2.2.

I want to automatically split all lines in a QGIS layer at their vertices (). I've done a Google search and found , which is quite close but the workflow is complicated. Because I'll have to train my co-workers (who are unfamiliar with GIS) to use this tool, I want something as simple as a plugin or something that doesn't require GRASS. Since it's been a long time from 2010 - the time of , I wonder if there is any better way to achieve the same result?


I am trying to produce a type of "Calligraphic L" using LaTeX. Please see the image below. The wobbles are down to me, possibly too much sugar over the Christmas holiday period.    This type of "L" is used in Abramowitz and Stegun , see the reference , in particular in result 9.6.26 which gives recurrence relations for modified Bessel functions.  So, how might I produce this type of "L" using LaTeX?  Other Info.  I have searched using Google, with the search string "latex fancy L" and also used "Detexify" on a mobile phone but did not find anything useful. I also considered other "Math Alphabets" the packages "eufrac" and "rsfso" do not appear to give the type of "L" I am looking for. I have also searched on StackExchange using a mobile phone.  The "L" I want is like that in the package "calrsfs", like the symbol given by the command \mathcal{L} but with an extra  loop at the top left of the symbol and a little crossing line part way up the main stem of the symbol.  Reference Handbook Of Mathematical Functions, ninth Dover printing,  Ed M. Abramowitz and I.A. Stegun, Dover Publications, Inc., New York.  Response to duplicate issues.  How to look up a symbol or ...  I recomend the post in question. I think that is where I found out about Detexify from. Apparently the advice in this post should have led to an answer to my question. It's over to the powers that be now ...  How to do the 'curvy L' ...  My question is about a particular symbol, one that appears in an equation in Abramowitz and Stegun. This symbol is not a symbol normally used to represent the Lagrangian or a Laplace transform. In fact it is not even an "L".  Scanned Symbol

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


I am a researcher (doing my PhD) in Computational Biology. I have submitted a manuscript to an Elsevier journal 3 months before. One day after my submission editorial status changed to 'With Editor'. But after that no further change (change to 'Under Review') has been noticed. I already has one publication with Springer Verlag. In that case within a week of being 'With Editor' the status changed to 'Under Review'. This time this is opposite. Is it likely of being 'With Editor' status for long 3 months?

What steps does a manuscript typically go through from submission to publication (or rejection) in a typical journal? How are these steps referred to, in particular by editorial systems, and how long do they each typically take?  Note that this question is about the typical situation and hence not about:   Journals with an atypical workflow, e.g. those that allow for an instantaneous reviewer–author interaction. Exceptional steps or rare occurrences such as withdrawal or .   This is a canonical question on this topic as per . Due to its nature, it is rather broad and not exemplary for a regular question on this site. Please feel free to improve this question.


I'm trying to install ubuntu 13.04 to a 32gb usb stick so I can bring It to and from school. I've install about three time now using the something else install method And every time I install it says something like this "Installation complete please restart your computer". When i restart the computer and hold down alt (Due to the fact that I'm on mac) The usb doesn't show up as a bootable thing. When i go to reinstall it to the usb useing a cd it says that it is installed on it. So I want to know how to fix this   NOTE (I don't want the iso on the usb thats on the cd. I want the os on the USB so i can bring to and from school)  computer specs for home and school they are macs  if they were pc this would be SOOO much easier saying how I've installed it on pc before but not mac and a usb together

If you are hurrying to reply, System → Administration → StartUp Disk Creator -- no, that's not what I'm talking about.   I want to try Ubuntu 11.04's Unity without touching my existing Ubuntu install.  To do this, I need to install the nVidia drivers first (sigh).  To do this, I need changes to persist a reboot.  To do this, I need to really install Ubuntu on a USB key.  How do you do that?    What I tried   I tried to make a USB key from , then boot from it, then choose "Install Ubuntu." The installer refused to install to the installation media itself. I tried, from my installed copy of Ubuntu:  sudo kvm /dev/sdb --cdrom .cache/testdrive/iso/ubuntu_natty-desktop-i386.iso   ...but the installer didn't detect the disk properly.


states that: $$ \int_0^1x^{-x}dx=\sum_{n=1}^\infty n^{-n} $$ and $$ \int_0^1x^{x}dx=-\sum_{n=1}^\infty(-n)^{-n} $$ A friend of mine noticed that numerically: $$ \int_0^1\int_0^1(xy)^{xy}dxdy\approx  0.7834... \approx \int_0^1x^{x}dx $$ Are these two integrals really equal?

Show that $\int_{0}^{1}\int_{0}^{1}(xy)^{xy}dxdy = \int_{0}^{1}y^{y}dy$  I have tried the method used in the Gaussian integral, polar coordinates, exp(.) and ln(.) of both sides of the integrand...  Gaussian integral:   I have also looked at the sophomore dream function, but I am not sure how to proceed that way in this case.  Sophomore dream function:    Now I am stuck. Any help would be appreciated.


I see an example for standardizing data value . For better illustration, the table is shown below  I did the same thing in excel and as you can see, the results are different.  For mean and variance, I used AVERAGE and VAR formulas, respectively in Excel. The standardized values are calculated as: 0  ->  (0-2.5)/3.5 = -0.714 ...  What is wrong then?

Why does dividing a dataset by sigma make the sample variance equal to 1? Assuming a zero mean for simplicity.  What's the intuition behind this?  Dividing by the range (max-min) makes intuitive sense. But standard deviation does not.


I have a few domains with Dreamhost where I have set a load of records using their web based domain name system, and I've like to move them to another provider that lets me enter info directly as a text file for their name server, bind 9 to use. (If you're interested, I'm moving them to Gandi.net).  Previously when I used a cpanel based system to do something similar, there was a tool that let me simply enter a domain name, and any available domains were automagically entered into a system, saving me typing it myself (and bringing down sites with silly typos in the process).  What open source tool can I use to query a domain for all the relevant subdomains and records and list them in a format like a zone file, that I can use with other name servers?

I want to see what nodes exist under a certain domain from within the domain. Short of querying every valid IP address within that domain, is there a way to get all records/map the network?


Consider the ordinary differential equation $$y'=y(y-1)(y-2)$$ Then which of the following statements is true?      1)If $y(0)=0.5$ then $y$ is decreasing      2) If $y(0)=1.2$ then $y$ is increasing      3) If $y(0)=2.5$ then $y$ is unbounded      4) If $y(0)<0$ then $y$ is bounded below   Using partial fractions I get   $$\big( \dfrac{1}{2y} -\dfrac{1}{y-1}+\dfrac{1}{2(y-2)}\big)dy=dx$$ which upon integration gives  $$ \dfrac{y(y-2)}{(y-1)^{2}}=C e^{2x}$$  Can anyone help me how to rule out the options?

Consider the Ordinary Differential equation $y' = y(y-1)(y-2)$. Then from the different initial conditions, can we derive properties of the function $y$ ?  I thought of finding the solution to this differential equation, which I tried to use Partial fractions!, (any other easier or efficient method to solve this ODE?). After doing Partial fractions  I got  $0.5 \ln|y| - \ln|y-1| +0.5 \ln|y-2| = x + c$. Now if $y(0) = 0.5$, is the function $y$ decreasing?, well I thought of substituting value of $y(0)$ into the ode to get $y' = 0.5(0.5-1)(0.5-2)>0$, implying $y$ is decreasing (is this the correct way?). Also if $y(0) =1.2$ then using the above criteria I think $y$ is increasing? Also if $y(0) = 2.5$ then can we say anything about the boundedness of $y$ ? If $y(0)<0$, can we say $y$ is bounded below?.


I am an Iranian citizen travelling from Canada to Iran. I'm holding a Canadian work permit.  Do I need a transit visa if my flight goes through the US?

In Europe usually you don't need to go through immigration to change planes (unless you are entering/exiting Schengen). Is it the case in the US as well? May I catch a connecting flight on one of the US airports if I don't have US visa?


Could you provide an example of a random variable $X$ such that $|\mathbb{E}(\ln(X))|<\infty$ but $\text{Var}(\ln(X))=\infty$, if such a random variable exists at all? Related:  Motivated by .

It would be appreciated if the following examples could be given:   A distribution with infinite mean and infinite variance. A distribution with infinite mean and finite variance. A distribution with finite mean and infinite variance.  A distribution with finite mean and finite variance.   It comes from me seeing these unfamiliar terms (infinite mean, infinite variance) used in an article I am reading, googling and reading a thread on the , and not finding it a sufficiently clear explanation. I also haven't found any explanations in any of my own textbooks.


I am making a game that is like a combination of minecraft and unturned. It is like minecraft as it is very block based. It is like unturned because it has vehicles and other unturned functionalities. This is what the player model would probably look like:   The player model is very similar to minecraft's Steve. It does however have some major differences that make it unique. For instance the eyes are not stationary and can actually look around. The mouth has two sets of teeth which act as the jaw line and lips that represent the mouth. Both the teeth and the lips can be animated for a "Talking" animation. The eyes also have eyelids which can close and open with proper animating skill. The player model can also be customized in game, as the hair style, beard style, eye color, skin color, hair and beard color, can be changed during game play. Unlike minecraft's character, It is not restricted to just helmet, chest plate, leggings and boots for armor. This model can change its shirt, pants, helmet, hat, pants, leg armor, armor boots, chest plate, backpack (If he equips one), gloves, shoulder pads, elbow pads, and any other piece of armor and clothing that can be used in game.  My problem is, even with the major differences in the model, will it still be too similar to Steve? Or is this model too different to have me sued for copyright/IP infringement?  Thanks for any input.  I just started working on the model again, This time the player can hold things and also wears shoes:

Most games build on other games' successes and many are downright clones. Where is the limit of imitation before legal issues come into play? Is it down to literary or graphic work like characters and storyline that cause legal problems, or can someone actually claim to own gameplay mechanics?  There are so many similar clone games out there that the rules are probably very slack or nonexistent, but I'd like to hear the views of more experienced developers / designers.


I'm trying to create a brace on the bottom in Tikz Feynman, but no matter what I try, the brace remains on the bottom. This is what I have:  And this is what I want:  Sorry if the annotation was a bit bold; I forgot to change the brush width. Anyway, how do I turn this brace upside down? This is my current code:     \begin{tikzpicture}         \begin{feynman}             \vertex (i3) {\(u\)};             \vertex [above right=of i3] (i4);             \vertex [above left=of i4] (i5) {\(u\)};             \vertex [right=0.5cm of i3] (i6) {\(d\)};             \vertex [above right=of i6] (i7);             \vertex [above left=of i7] (i8) {\(d\)};             \vertex [right=0.5cm of i6] (a) {\(d\)};             \vertex [above right=of a] (b);             \vertex [above left=of b] (c) {\(u\)};             \vertex [above right=of b] (d);             \vertex [above right=of d] (e) {\(\overline{\nu}_e\)};             \vertex [right=of d] (f);             \vertex [above=0.2cm of f] (g) {\(e^-\)};             \diagram* {                 (i3) -- [fermion] (i4) -- [fermion] (i5),                 (i6) -- [fermion] (i7) -- [fermion] (i8),                 (a) -- [fermion] (b) -- [fermion] (c),                 (b) -- [boson, edge label=$W^-$] (d) -- [anti fermion] (e),                 (d) -- [fermion] (g)             };             \draw [decoration={brace}, decorate] (i5.north west) -- (c.north east) node [pos=0.5, above] {\large \(p^+\)};             \draw [decoration={brace}, decorate] (i3.south west) -- (a.south east) node [pos=0.5, above] {\large \(n^0\)};         \end{feynman}     \end{tikzpicture}  Would really appreciate any help!

How can I rotate a brace to make it appear ?  I'm currently using this code:  \documentclass[french]{beamer} \usepackage{tikz} \usetikzlibrary{fit,calc,positioning,decorations.pathreplacing,matrix} \begin{document} \begin{frame} \begin{tikzpicture}[decoration={brace}][scale=2]  \node [rotate=270] (A) {\fontsize{8}{8}\selectfont A};  \node [fit=(A)] (fit) {};               \draw [decorate,line width=1pt]    ([yshift=7pt]fit.south west) -- ([yshift=-7pt]fit.north west); \end{tikzpicture} \end{frame} \end{document}   Thanks in advance!


Given $A \in \mathbb{R}^{n \times n}$ and $\text{rank}(A) = 1$. By working only on real field, show that $A$ is diagonalizable if and only if $\text{tr}(A) \neq 0$. Here, $\text{tr}(A)$ is the sum of all eigenvalues of $A$.

Suppose $A=uv^T$ where $u$ and $v$ are non-zero column vectors in ${\mathbb R}^n$, $n\geq 3$. $\lambda=0$ is an eigenvalue of $A$ since $A$ is not of full rank. $\lambda=v^Tu$ is also an eigenvalue of $A$ since $$Au = (uv^T)u=u(v^Tu)=(v^Tu)u.$$  Here is my question:     Are there any other eigenvalues of $A$?   Added:  Thanks to Didier's comment and anon's answer, $A$ can not have other eigenvalues than $0$ and $v^Tu$. I would like to update the question:     Can $A$ be diagonalizable?


I purchased a number of these relay module boards off AliExpress. They consist of the following   16x relays, 12 volt coils A LM2596 setup as a buck converter 2x ULN2803A darlington arrays 16x 817C photocouplers Header for inputs (current sinks) Terminal for DC voltage input   There are some LEDs on the board as well but they don't really have any function other than convenience of display.  When I purchased these, I had some ideas about how they work. However, what I discovered is there is a terminal (blue) labeled "VCC" and "GND". If you feed this with 12 volts, the 12 volts is used by the LM2596 to make 5 volts. The 5 volts is actually measured at 4.83 VDC, but that doesn't matter here. It drives the   the "isolated" side of each 817C via some resistor. The 12 volt input is also carried to relay coil. So when one of the transistors in a ULN2803A pull a relay coil to ground, it closes the relay. Each 817C is normally high and if you sink current from the output pins it closes a relay.  The nominal "+5VDC" rail that is created by the buck converter is obviously not isolated. Measuring with a continuity tester confirms the ground of the entire board is common.   Do the photocouplers on this board actually accomplish anything when wired in this manner? I know they function as a logic inverter, allowing any current sink to actuate a relay. But that isn't really significant, for example a 2N3904 could do that.

Since the advent of the many microcontroller development boards, like Arduino, there have been a number of relay modules sold to drive mains AC loads.  A lot of these seem to use an optocoupler, driver transistor and a relay to drive the load (example on )  Why are they implemented like this?   Some of my thoughts:   Relays provide as good or better isolation than most optocouplers There is still a driver transistor present, so it is not component saving  There is still inductive kickback protection, so it is not component saving Optocouplers are not as cheap as transistors, so additional cost compared to just a driver transistor There is no need to meet any regulatory requirements as these are DIY products I have never seen small mains relays driven by optocouplers in commercial equipment A number of these boards don't seem to be designed brilliantly (no regard to clearance or creepage), so even if the optocoupler is simply to provide two layers of isolation, the board fails at this.


Prove by induction: $b^n-a^n=(b-a)\cdot \sum_{k=0}^{n-1}{a^k\cdot b^{n-1-k}}$ $\forall n\in \mathbb{N}$ and $a,b\in \mathbb{R}$  $\exists n\in \mathbb{N}:b^n-a^n=(b-a)\cdot \sum_{k=0}^{n-1}{a^k\cdot b^{n-1-k}}$  $\Rightarrow b^{n+1}-a^{n+1}=(b-a)\cdot \sum_{k=0}^{n}{a^k\cdot b^{n-k}}$  Base case: $n_0=1: b^1-a^2=(b-a)\cdot \underbrace{\sum_{k=0}^{1-1}{a^k\cdot b^{1-1-k}}}_{=1} \quad \checkmark$  Inductive step:  $b^{n+1}-a^{n+1}=(b-a)\cdot \sum_{k=0}^{n}{a^k\cdot b^{n-k}}$  The sigma sign is what stresses me out, how can I deal with it?

This question is from [Number Theory George E. Andrews 1-1 #3].     Prove that $$x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1}).$$   This problem is driving me crazy. $$x^n-y^n = (x-y)(x^{n-1}+x^{n-2}y+\dots +xy^{n-2}+y^{n-1)}$$  $(x^n-y^n)/(x-y) =$ the sum for the first $n$ numbers and then I added $(xy^{(n+1)-2}+y^{(n+1)-1})$ which should equal $(x^{n+1}-y^{n+1})/(x-y)$ but I can't figure it out    This is a similar problem in the book and I tried this method but it wasn't working out      $\quad$Thereom $\bf1$-$\bf2$: $\,\,\,\,$ If $\,x$ is any real number other than $1$, then $$\sum_{j=0}^{n-1}x^j=1+x+x^2+\ldots+x^{n-1}=\dfrac{x^n-1}{x-1}.$$    $\quad$Remark: $\displaystyle\sum_{j=0}^{n-1}A_j$ is shorthand for $A_0+A_1+A_2+\ldots+A_{n-1}.$     $\quad$Proof: Again we proceed by mathematical induction. If $n=1$ then $\displaystyle\sum_{j=0}^{1-1}x^j=x^0=1$ and $(x-1)/(x-1)=1$. Thus the theorem is true for $n=1$.  $\quad$ Assuming that $\displaystyle\sum_{j=0}^{k-1}x^j=(x^k-1)/(x-1)$, we find that $$ \eqalign{ \sum^{(k+1)-1}_ {j=0}x^j & = \sum^{k-1}_ {j=0}x^j+x^k=\dfrac{x^k-1}{x-1}+x^k \\ &= \dfrac{x^k-1+x^{k+1}-x^k}{x-1}\\ &= \dfrac{x^{k+1}-1}{x-1}. }$$   Hence condition $(\rm ii)$ is fulfilled, and we have established the theorem.    $\quad$Corollary $\bf1$-$\bf1$: $\,\,$ If $\,m$ and $n$ are positive integers and if $m>1$, then $n<m^n.$


I am stuck on this one, do not know where to start. Any hint would be appreciated.  What is the cardinality of $[P(\omega)]^{\omega}$? Is it equal to $|P(w)|$? How do I show that?

Let $A$ be a set with card($A$)=$a$. What is the cardinal number of the set of countably infinite subsets of $A$?   I see that this problem is equivalent to finding the cardinal number of the set of injective functions from $\mathbb{N}\rightarrow{A}$. I also know that the cardinal number of the set of bijections from $A\rightarrow{A}$ is $a^{a}$.   Hints and general heurisitcs would be greatly appreciated.


I need to place the whole set of the Google web fonts in a single folder on my Ubunu 14.04 server.  I have downloaded the current snapshot from  which upon expansion gives me the structure  /fonts-master |  apache |  ofl |  ufl   Each of these sub folders in turn contains multiple folders - one for each font.  Each font folder contains one or more *.ttf files.  What I need to do is to grab each of these ttf files and place it in the folder /googlefonts.  I could write a PHP script that would do the job.  However, I suspect that there is a way to do the job via a few simple shell commands.  Roadblock: I know my way around BASH to do simple stuff like move & copy folders and files but that is about it.  I'd be grateful if someone here could tell me how/if this could be done.

In ~/my/path, I want to move all files that contain string "(J)" and have file type of ".foo" to ~/my/path/j  I'm trying:  [me ~/my/path]$ find -type f -name "*(J)*.foo" -print0 | xargs mv -0 j/  No luck :(


In Firefox I currently have as startpage 123.sogou.com, but I am not able to remove the website as my startpage. Every time I am changing the default page in Firefox back to Google, it automatically turns back to sogou after a restart. Any idea how to remove this?  I also tried the steps from , but it has not changed anything.

Firefox's default page is 123.sogou.com and I can't remove it. I've tried to reset and re-install it, but it keeps going back to sogou.


I'm looking for a way to store data on my client application.  I want to avoid using online database because there are just some variables to store.  I couldn't find any solution to simply cache data into the app.  The data should be accessible at the application start up and must be cleaned after 2 weeks (i guess we can store an expire date for such behavior.)

Question  I'm looking for a Java in-memory object caching API. Any recommendations? What solutions have you used in the past?  Current  Right now, I'm just using a Map:  Map cache = new HashMap<String, Object>(); cache.put("key", value);   Requirements  I need to extend the cache to include basic features like:   Max size Time to live   However, I don't need more sophisticated features like:   Access from multiple processes (caching server) Persistence (to disk)   Suggestions  In-Memory caching:    CacheBuilder - active development. See this .  - Config via API. No TTL. Not purpose built for caching.  - XML config. Mailing list. Last updated 2006.  - XML config. Documentation in Russian. Last updated 2006.   Enterprise caching:    - Properties config. Extensive documentation.  - XML config. Extensive documentation. By far the most popular according to Google hits.


I have observed at least one user who takes a very "ascetic" approach to rep: He awards bounties to questions he finds interesting, meritorious of more attention, and to reward/highlight exceptional answers.  Often to the point that his rep falls back to just double digits.  He does this on multiple sites where he is an outstanding contributor.  Just auditing his bounty activity on two sites: he has given away over 6,000 rep points, and I can find no indication of any nefarious or unintended consequences of the bounties.  I.e., he is using the bounty system as designed.  He is also revealing what I would consider to be a flaw: He is an Established User, but, due to his generous awarding of bounties, he is frequently toiling under the restrictions applied to inexperienced users.  E.g., it's silly to have his edits held up for review.  Though the implementation to change this might not be considered a priority, do people at least agree in principle that users should not lose privileges for spending their rep on bounties?  (.  Arguments for the status quo of losing privileges point out that there should be a cost to awarding bounties.  I would point out that loss of rep is a cost, and it is the right cost: You can't award more bounties than you earn in rep.)

Okay, I may as well mention straight off that the main reason I am asking this question is due to the upcoming reputation recalc.  It has always seemed silly to me how bounties affect privileges. After all, if rep is, as oft repeated, primarily a way of how much the system trusts you, bounties really shouldn't affect that. In terms of effects, this would lessen the pain from the rep recalc. One downside - this increase the number of bounties given out as users wouldn't be saving up their rep to gain privileges, so maybe it would be sensible to enforce a minimum reputation (500?) before you can post bounties.  PS. If people are worried about others gaming the system, the better way would probably be to make the extra reputation gained from bounties not count towards privileges, rather than removing privileges for posting bounties.


The company's annual revenues rose by 30%.  I'd like to ask if the preposition by there is indispensable. Is it wrong with it left out?

Which of the following sentence is correct ? If both are correct, do they have the same meaning ? The company's sales grew by 70% year-on-year to US$100 m. The company's sales grew 70% year-on-year to US$100 m.


My distro:  lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 19.10 Release:    19.10 Codename:   eoan   My kernel:  uname -a Linux n552vw 5.3.0-46-generic #38-Ubuntu SMP Fri Mar 27 17:37:05 UTC 2020 x86_64 x86_64 x86_64 GNU/Linux   Updates:       Ubuntu 20.04 has been officially released 4 days ago.  Trying to update  sudo do-release-upgrade -c Checking for a new Ubuntu release No new release found.   Questions   Are there any reasons why the system still does not prompt to update?   Notes   I DO NOT want the development version (the -d flag) - I want FINAL VERSION. Why the official page  the -d flag (update-manager -c -d)?

I followed these instructions to upgrade from 19.10 to 20.04:    I understand the  was 2 days ago. However, when I run the following as instructed:  Press Alt+F2 and type update-manager -c -d into the command box.    The popup shows:    I want the final release, not the development release.  I am following the official ubuntu instructions.  What am I doing wrong?  These are my update settings, which should just be LTS:


My iPad is running 7.0.2 and is jailbroken. It looks like Apple is not signing the 7.1.2 any longer.  Is there a way to upgrade iOS to 7.1.2 without letting iTunes contact its home (i.e. Apple's servers)?

I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this?


I stay 90 days in/90 days out of Sweden on a consistent basis to be with my fiance as much as possible while he finishes his studies (only 1 1/2 years left now, thank god!) We have been doing this dance for the last 2 1/2 years.  We booked this trip about 6 months ago, right before my last visit, as we always do. We do this because we like to stay one trip ahead to save money and decrease anxiety about booking tickets in time.  We must have miscalculated because upon checking with the Schengen calculator, it is saying that I am entering 1 day early. Basically, I stayed 89 days last time (June 18,2018-September 14,2018) and the day I return (December 13th, 2018) will be day 90 of staying in Sweden since my last date of entry (June 18, 2018). My timer resets on December 15th, so December 14th will be day 91.  I have been trying my very best to stay within the rules and regulations with absolutely no intention of breaking or disrespecting any of Sweden's immigration laws, and that would be obvious to anyone who looked at my passport history for the last 2+ years. I have not overstayed a single time, or if I have it was not intentional or to my knowledge, nor was it ever brought to my attention upon entering/exiting Sweden.  However, now that I have come across my first mistake, I am absolutely petrified of what the consequences might be when I arrive at passport control. I am hoping that nothing happens, but I would be totally understanding even if I had to pay a fine. Anything but a travel ban or deportation. Do you think I would be deported or banned for a miscalculation error (my first one in 2+ years at that)? I also have a return ticket already for March 13, 2019 (90 days after my date of entry) which I can easily present to the passport control officer if requested.  I really hope that someone here can ease my mind regarding this situation. I understand that laws are laws and I am in no way immune from following these laws. But do the immigration officers tend to allow a little wiggle room for human error in obvious cases of genuine mistakes like these?  Please, if anyone has any experience with a similar situation, let me know.

According to law, what are the consequences of a US citizen overstaying a Schengen visa?  In practice, how likely is one to be penalized for overstaying by a day, 10 days, and a month?  Are there countries that are more likely to enforce the rules on departure?


I installed the Ubuntu 14.04 and a Windows 7 in the same HD. And everything was working, but I created another partition in Windows to store data. And now I can't boot.  error unknown filesystem grub rescue >   How I can restore the grub?

When the bootloader (GRUB) is broken, I cannot access neither Ubuntu nor Windows.  I heard that an easy solution to fix this is to use the Boot-Repair tool from an Ubuntu liveCD (or liveUSB).  What are the steps to do this?


The condition is:     There exists homeomorphic metric spaces $(X,d), (X,d')$ such that only one of them is complete.   But is this possible?, If it is can someone give the example please?  Thanks a lot for the improvements, but the only thing that is changing is the metric not the space. And I think they are changing both in the answers :)   Thanks a lot in advance.

Does homeomorphic metric spaces preserves completeness?I mean two metric space which are homeomorphic and one of them is complete$\Rightarrow$ another one is also complete?


I have both Python 2.7.12 and 3.5 installed on my Ubuntu 16.04 system. I installed pandas using pip install pandas. When I import pandas in python 2 it works fine. But when I import pandas in python3 it throws an error saying:  ImportError: No module named 'pandas'   How do I install pandas for python3?

I'm trying to install pandas. When I do, it's automatically installing to the python installation for v 2.7.   How do I force pandas to install to the python 3.5 installation?


Source:   Take for example a bite attack. According to the table, a small bite does 1d4 damage, medium 1d6, large 1d8, huge 2d6, garg. 2d8, and col. 4d6. Presumably it'd continue 4d8, 8d6, etc.  However, if you look at the FAQ entry right below it, it says that as you increase the damage, the progression would be 1d4, 1d6, 1d8, 2d6, 3d6, 4d6, 6d6, 8d6, 12d6, etc.  So what is this supposed to mean? Does it mean for example that a gargantuan entity would do 2d8 damage with a bite attack, but a huge one enlarged to gargantuan would do 3d6?  This seems it might be a duplicate of  That question is 2 years old. Have we gotten any new information since then? Also, the newer chart is listed as a FAQ instead of an errata, which implies that the old chart might not be a mistake?

I am working on a druid character and just getting around to wild shapes natural attacks and I spotted what should be an error in its damage progression under the  which conflicts with the newer .  Official Damage Dice Progression Chart $$ \begin{array}{l|l} \text{Level} & \text{Dice}\\ \hline 0 & 0 \\ 1 & 1d1 \\ 2 & 1d2\\ 3 & 1d3\\ 4 & 1d4\\ 5 & 1d6\\ 6 & 1d8\\ 7 & 1d10\\ 8 & 2d6\\ 9 & 2d8\\ 10 & 3d6\\ 11 & 3d8\\ 12 & 4d6\\ 13 & 4d8\\ 14 & 6d6\\ 15 & 6d8\\ 16 & 8d6\\ 17 & 8d8\\ 18 & 12d6\\ 19 & 12d8\\ 20 & 16d6\\ \end{array} $$  Here we have the chart for Bite  $$ \begin{array}{l|l|l} \text{Size} & \text{Dice Level} & \text{Dice}\\ \hline Fine & 1 & 1d1\\ Diminutive & 2 & 1d2\\ Tiny & 3 & 1d3\\ Small & 4 & 1d4\\ Medium & 5 & 1d6\\ Large & 6 & 1d8\\ Huge & 8 & 2d6\\ Gargantuan & 9 & 2d8\\ Colossal & 12 & 4d6\\ \end{array} $$  Here we can clearly see that huge to gargantuan is only 1 and not 2, and from gargantuan to colossal is 3 instead of 2. If gargantuan was changed from 9 to 10 then the chart would be correct, its the only value that's off. So is this just a mistake or is this actually what its suppose to be?