What's the best way to get constructive critique of your photographs?

Whats the best what to get constructive critique of your photographs?  I'm thinking along what site or online community provides such things, but I'm open to all answers.    If I have a photograph that I think is nice, what's an effective way to get somebody (apart from friends and family) to offer "good" advice?  Posting it to a site like this one with a general "what can I do better?" isn't helpful, and on sites like Flickr only the photographs that are already good get noticed.


Ping requests time out for specific packet sizes

After having VPN problems with my new internet provider on LTE router Huawei B315s-22, found out such interesting behavior:  ping bite.lv -f -l 1436 -n 1 -----> Reply from 213.226.139.45: bytes=1436 time=48ms TTL=57 ping bite.lv -f -l 1437 -n 1 -----> Request timed out.                    .... ping bite.lv -f -l 1472 -n 1 -----> Request timed out. ping bite.lv -f -l 1473 -n 1 -----> Packet needs to be fragmented but DF set.   Seems for packet size range 1437—1472 ping request always times out.  Changing MTU size on the router to 1400 does not help.


$.post('image.php', {     image:form.image.value   }   <form id="form" enctype="multipart/form-data"> <input type="file" id="image" name="image"/>   PHP->isset($_FILES['file'])  How to use $.post() to post $_FILES inside of form tag? Do I still need include enctype or do I need use AJAX, and how can I do that?


Combinatorial proof of $k\binom{n}{k} = n\binom{n-1}{k-1}$

I'm trying to prove this combinatorially. $$k\binom{n}{k} = n\binom{n-1}{k-1}$$ I know the first step is to relate a question to the equation. My question was if you have $n$ friends how many ways can you choose $k$ of them. I know this isn't correct because that would be the question if the left side wasn't being multiplied by k. Can anyone help me figure out what multiplying ${n \choose k}$ by $k$ means?


8GB USB drive reduced to 3MB, how can I recover the correct size?

After trying to copy a software from another system, my 8GB USB flash drive reduced to 3MB.  I checked the Disk Manager, it looks like this:    I couldn't see any unallocated space there..  Can I resize my drive?


Calculate bearing between two decimal GPS coordinates

I'm building a virtual tour application that uses custom panoramas in conjunction with Google's StreetView service.  With StreetView, you can have 1 to n links at each particular location to move to, and these links are based on compass bearings.  Each panorama has an associated GPS location to six decimal places acquired via .  My issue is when I calculate the compass bearings from each link location, it returns a bearing that is a tiny (as in 0.00001 degree difference) from true north.  Given a map like                         4                        |                        |                        |                        2                        |                        |                        |                        1   where each number is a location and has the following values:  1- 43.682213, -70.450696 2- 43.682194, -70.450769 4- 43.682179, -70.450837   What I'd like is a method to determine programatically that the bearing from 1 to 2 and 2 to 4 is 70 degrees, and 2 to 1 is 250 degrees.  Using the code from  as a starting point, I wrote the following function  //starting lat/long along with converting degrees to radius     var endLat = location.lat();  //for rhumb calc     var endLong = location.lng();      //loop over response, calculate new headings for links and add link to array     for(var i=0; i<data.length; i++){       //this link's lat/long coordinates       var startLat = data[i].lat;       var startLong = data[i].lon;        //get the delta values between start and end coordinates       var dLong = endLong - startLong;        //calculate rhumb bearing to       var dPhi = Math.log(Math.tan(endLat/2+Math.PI/4)/Math.tan(startLat/2+Math.PI/4));       if (Math.abs(dLong) > Math.PI ) dLong = dLong > 0 ? -(2*Math.PI-dLong) : (2*Math.PI+dLong);       var bearing = (toDeg(Math.atan(dLong, dPhi)) + 360) % 360;   Using the above function and substituting  location for position 2 data[0] for position 1 data[1] for position 4   I get the bearings  359.9958174081038 degrees to 4 (should be 70 degrees)   and   0.0038961130024404156 degrees to 1 (should be 250)   Why is this function returning such different values than expected?


How to find $ \displaystyle \int_0^{\pi/2} \frac{1}{1+(\tan x)^e}dx $?

How to find $$\displaystyle \int_0^{\pi/2} \frac{1}{1+(\tan x)^e}dx $$Substitution seems not to work.


Alternative(?) definition for normalizer

Let $G$ be a group and $H$ be a subgroup. Consider the following set: $$\hat{N}(H):=\left\{g\in G: g^{-1}Hg \subset H\right\} $$ The normalizer of $H$ is usually defined as $$N(H):=\left\{g\in G: g^{-1}Hg=H\right\} $$ My question is: are these two sets equal? If $H$ is finite, then the answer is certainly positive. The map $x\mapsto gxg^{-1}$ is an injective map from $H$ onto $H$, so if $H$ is finite, it is also invertible. Thus $g^{-1}Hg\subset H$ implies $g^{-1}Hg=H$, and $\hat{N}(H)=N(H)$.   In the general case, my guess would be no. The normalizer is a subgroup of $G$, whereas $\hat{N}(H)$ possibly isn't. While $1 \in \hat{N}(H)$ and $g,h \in \hat{N}(H)\Rightarrow gh \in \hat{N}(H)$, if $g\in \hat{N}(H)$ i cannot deduce that $g^{-1}\in \hat{N}(H)$.  I couldn't find any counterexample, though. I know that $H$ would have to be infinite and nonabelian (otherwise $g^{-1}Hg=gHg^{-1}$). I tried to use some subgroups of $\operatorname{GL}_2(\mathbb{C})$, but all the ones I could construct had the whole $\operatorname{GL}_2(\mathbb{C})$ as their normalizer.


Method Throws java.lang.NullPointerException after calling it

I have a Class Sample and I call the method calcValues in my main class. But if I call calcValues, it throws a Null Pointer Exeption. But I do not know why...  Here is the code:  Class Sample:  public List<Float> calcValues(List<Float> inputValues)  {     List<Float> outValues = new ArrayList<>();      for (Float value : inputValues) //causes the error     {         SensorDataResult res = this.mySensorData.computeAverage(value);          System.out.print("Ergebnis: ");         System.out.print(res);         if(res != null)          {             // TODO Maybe check for Alarms             outValues.add(res.getValue());         }     }     return outValues; }   Class Main:  public static void main(String[] args)  {     Sample newSample = new Sample();     List<Float> inputValues = new ArrayList<Float>();     inputValues.add(10.0f);       newSample.calcValues(inputValues); //causes the error in main class }   Why does this method (calcValues) throw an error when I call it?  The StackTrace:      Exception in thread "main" java.lang.NullPointerException       at at.axtesys.idr.Sample.calcValues(Sample.java:29)       at at.axtesys.idr.TCPServer.main(TCPServer.java:24)


Uniformly continuous functions sequence $f_n(x)$ converges uniformly to a uniformly continuous function $f(x)$?

We know that if continuous functions sequence $g_n(x)$ converges uniformly to $g(x)$, then $g(x)$ is continuous function.  But what if uniformly continuous functions sequence $f_n(x)$ converges uniformly to $f(x)$? Does that imply $f(x)$ is uniformly continuous function?   If so - how do we prove it? what $\delta$ should we take for $f(x)$? We can't simply choose $\min\{ \delta_n \}$.  And what if $f_n(x)$ converges pointwise to $f(x)$. Will $f(x)$ be continuous? uniformly continuous? Or pointwise convergence is not enough?


How can I upload music from an iPhone to a PC without iTunes?

I am looking for an app that will let me transfer media from iPhone 5 to a PC without iTunes sync.  It has 3 atributes that I like:   works on any Windows upload media with no iTunes sync multiple iOS management


How can I access volumes encrypted with LUKS/dm-crypt from Windows?

The answer to this question used to be FreeOTFE (); sadly, the project has not been updated for three years and its website () is no longer online.  Is there any software available now that can be used to access LUKS/dm-crypt volumes from Windows, now that FreeOTFE is no longer maintained/available?


Sanitizing SQL query with PDO and replacing deprecated mysql_real_esape_string to keep PHP code secure

How can I replace mysql_real_escape_string in PDO to keep my code still secure:  (mysql_real_escape_string no longer supported in PHP v7.x)  I would appreciate if somebody could provide an example for this code line: "ORDER BY " . mysql_real_escape_string($order) . " LIMIT :numRows";"  Full code below:   public static function getList( $numRows=1000000, $order="pageID ASC" ) {     $conn = new PDO( DB_DSN, DB_USERNAME, DB_PASSWORD );     $sql = "SELECT SQL_CALC_FOUND_ROWS *, UNIX_TIMESTAMP(pagePublicationDate) AS pagePublicationDate FROM web_pages             ORDER BY " . mysql_real_escape_string($order) . " LIMIT :numRows";      $st = $conn->prepare( $sql );     $st->bindValue( ":numRows", $numRows, PDO::PARAM_INT );     $st->execute();     $list = array();      while ( $row = $st->fetch() ) {       $article = new cmsEngine( $row );       $list[] = $article;     }      // Now get the total number of website pages that matched the criteria     $sql = "SELECT FOUND_ROWS() AS totalRows";     $totalRows = $conn->query( $sql )->fetch();     $conn = null;     return ( array ( "results" => $list, "totalRows" => $totalRows[0] ) );   }


Why do photons follow specific path after reflection from a mirror surface if they can be emitted in any direction by electrons of mirror surface?

The electron absorbs the energy of photon(with specific frequency)and re-emits the photon.The photon can be emitted in any direction. So why do they get re-emitted in a specific direction after reflection? On hitting normal to surface the photons follow path in reverse normal direction and hitting at an angle it follows V path.


Why does the same query run faster the second time I run it?

I noticed when running a SQL query it is faster the second time than the first. So my question is, in Oracle SQL Developer where can you see the statistics that explain this behaviour?


Dual boot when Windows installed after Linux

I made the mistake of installing Windows 10 after installing Linux (Kubuntu 18.04).  How can I make Grub the controlling boot loader at this point without disturbing either of the existing installations?  Most of the discussion of this subject seems to assume that one or the other of the systems has been installed, but not both.  If the existing setup boots into Windows, how do I get Grub installed?  (I also have a live Kubuntu on a memory stick.)  Update: I've been able to get into my Kubuntu system by pressing Esc on power-up, which on this particular machine (HP Pavilion) gives me a choice of where to boot from.  Kubuntu and Windows are the two important choices.   But I still can't get the machine to boot directly into grub.  I've installed and run Boot-Repair.  It completed successfully but didn't solve the problem.  Further Update: I've finally gotten the dual boot to work, but I did it the scorched-earth way: I completely cleared the disk by installing a new partition table with gparted, reinstalled Windows 10 and then reinstalled Kubuntu 18.04. My conclusion is that if you're in a bad initial state, fixing the problem is almost impossible unless  you have specialized knowledge.  Most of the fixes proposed in this forum are dependent on a favorable initial state.


How to copy file/folder permissions and ownerships from one folder to another (recursively)

How do I copy all the folder, subfolders and files permissions (recursively) from /www_03062018 to my new /www ?  I came across .  chmod --reference=RFile file   Which didn't help much, it did apply a change for the main folder /www but didn't apply on its subfolders and files.    I have tried:   chmod -R --reference=/www_03062018 /www   and it didn't work.   My situation:   I have 2 folders on my Ubuntu machine: /www and /www_03062018.   /www is a "git clone" from the production machine.   /www_03062018 is my old directory that i used to work on and upload files via FTP.   I started to use GIT and when I clone a directory its folder ownerships and file accesses settings don't get cloned along with it.


Does the Oathbow count as a magical source of damage?

Does the  count as a magical source of damage to bypass resistance/immunity to nonmagical attacks?   While it is in the Magic Items section of the DMG, it does not actually state  that it is a magical weapon like they did with the .


How to add myself to sudoers when accidently remove main user out of the sudo group

I was trying to create a public and private share directory using samba and I ended up accidently relocated my main user to smbshare group and can no longer use sudo commands or log in as root. I will not be able to get into recovery mode.


"I have no question"--> "Me, too" or "Me, either"?

Ok, at the end of an English class, the teacher says "Do you have any questions?"  Student A:  I have no question Student B:  Me, too / Me, either  So, the Student B should say "Me, too" or "Me, either"? I know that "Me, either" is American English: "Me, either" is American English: . EDIT (after comments): So, we can't use "Me, too" in this case? Note: my question is unique. I know the rule of using "Me, too" or "Me, either". "Me, too" for positive sentence & "Me, either" for negative sentence.  Ex: I have a question. Me, too Ex2: I don't have a question. Me, either.  So if we say "I have no question" then  which one we should use "Me, too" or "Me, either"?


Single-User-Recovery-Mode on High Sierra 10.13.6

Before the High Sierra update to 10.13.6 I was able to boot in single-user-recovery mode by holding Cmd-R-S at startup, but after the latest software update booting while holding Cmd-R-S just enters the regular Single-User Mode on the root volume (like if I pressed only Cmd-S).  Is there a new method or alternative key combination to boot the RecoveryOS in Single-User Mode?  EDIT: booting while holding Cmd-Option-R-S also starts in Single-user mode (not Single-user-recovery mode).


How often is total score for a tag calculated

How often is my total score for a particular tag calculated. I've gotten several recent upvotes under android but my total score hasn't seem to have gone up. When I say total score, I mean like the total score displayed on this .


Is intentionally producing a lower quality TV release unique to anime?

A lot of shows nowadays are significantly censored or badly drawn for TV release. When the home media versions come out, they are uncensored and in some cases redrawn in certain areas.    Kagerou Project TV - BluRay Comparison  Part of this is of course the rush to release, but when the BluRays / DVDs come out, these are some of the main selling points of the shows in order to engage previous viewers.   Tokyo Ghoul TV - BluRay Comparison  Is this something unique to anime and its market? I haven't seen anything like it in Western media


I purchased a wifi thermostat and cannot located the common wire. My unit is old and is a Coleman 70 with no terminals inside labeling the wires.     As you can see in the second image, there is a blue wire that is not being used that goes to my thermostat. I am trying to use this as a common wire, I am just unable to determine where this wire connects to.  THank you for the help.


Bibliography headline in capital letters using classicthesis and biblatex

I use LyX with classicthesis. I just switched from natbib/bibtex to biblatex/biber, because I need some of the functionalities. Everything works fine, but now the word "Bibliography" does not appear as "BIBLIOGRAPHY" in all capital letters in the headline as it should in classicthesis.  How can I change this behaviour?


I threw a coin in a well that [was] or [is] in the forest

Which statement is correct and why?  I threw a coin in a well that was in the forest.  vs  I threw a coin in a well that is in the forest.  Also, is the "is/was" before "in the forest" called a linking verb?  Lastly, is the phrase "that [was/is] in the forest" an adjectival phrase that is describing forest?


Understanding boolean operators in bash script

phone_missing=false echo "missing $phone_missing"  if [ ! $phone_missing ] then         echo "Lost phone at $readabletime"         $phone_missing=true fi   I just can't understand this.  The line   echo "missing $phone_missing"   echos missing false, I would expect the statement   if [ ! $phone_missing ]   to be true and enter the if clause, but it doesn't? What am I missing here!?


I'm unable to add the tag bug to a question (but was able to do that a couple of months ago) - I get an error that says "'bug' tag not allowed". I couldn't find any information about that change - what is the rationale behind it?


Why is the electric field between two conducting parallel plates not double what it actually is?

According to here:   We can treat two parallel plates as being a single conductor which has an electric field of $\frac{\sigma}{\varepsilon_0}$. They say that equivalently, we can consider the system to be two charge sheets, each one contributing an electric field of $\frac{\sigma}{2\varepsilon_0}$.  My question is, why is the electric field between two parallel conducting plates not $\frac{2\sigma}{\varepsilon_0}$? Shouldn't each plate be considered to be a conductor (not merely a charge sheet)? In that case, each plate contributes $\frac{\sigma}{\varepsilon_0}$, for a net electric field of $\frac{2\sigma}{\varepsilon_0}$. Why must we consider each conducting plate to be a charge sheet and not a conductor?


Is a Russian driver's license valid in the U.S.? Is an IDP needed?

I have a Russian relative who will be visiting the U.S. for a short time (less than a month) and I would like him to be able to drive my car while he's here.  Will he need an , or will his license be valid by itself?  (I would appreciate authoritative answers with links to government websites on these points, as my searches didn't turn up anything authoritative.  It seems like the license is valid but an IDP is recommended, but it's not clear.)  This is about California specifically if it varies at the state level.


Why can't I log in after unistalling Python 2.7 and installing Python 3?

I uninstalled the Python 2.7 package to try and upgrade to Python 3. I uninstalled Python 2.7, and noticed some of my launcher items were completely gone. At this point I had installed Python 3. Now on reboot, I can't log in and the background for the log-in screen is black with white dots. Any help would be greatly appreciated.  P.S. - This is running 11.10 Oneiric Ocelot. I still have the same version Live CD.  EDIT: Thanks for the feedback! But I can't boot into text mode, only boot from the Live CD, and I can't connect to the internet because I installed the Debian .tar.gz package usb_modeswitch for Mobile Broadband. Is there a way to copy the Python 2.7 parts of the OS from the Live CD and inject them into my system? The only thing I can think of is get a 12.04 Live CD and click 'Upgrade from 11.10 to 12.04' option, but for reasons I won't go into this is impractical for me.


Triangle of least perimeter for a given area is the equilateral.

I want the opposite of , i.e., a proof that the equilateral triangle has the least perimeter of all the triangles with a given area. If possible I'd prefer an answer without Lagrange multipliers. I tried to differentiate Heron's formula with respect to $a$ and $b$ mantaining the area constant, but didn't get anything good. Any help would be appreciated. Thanks.


How can I list all user names and/or home directories?

I want to list all the users dirs on the machine.Usually, I will do:  ls -l /home   But I use it in a script that will be deployed on others machines and maybe on that machines they don't call it home (e.g. myHome). So I want to generalize it to ls -l ~. But it just lists my users home dirs instead of all users home dirs name (basically I want to get a list of the users names on the machine). How can I generalize it?


Kerckhoffs’ principles – Why should I make my cipher public?

As I understand it, the less people know about the internals of my protocol or cipher, the more secure the protocol is. However  states that     A cryptosystem should be secure even if everything about the system, except the key, is public knowledge.   To be more precise, it's the 2nd principle that states     It must not be required to be secret, and it must be able to fall into the hands of the enemy without inconvenience;   Of course I understand why I should keep the key secret, but publishing my protocol's internals seems counter-intuitive. Why should I do it? Wouldn't that give the advantage to the attacker?


MySQL Syntax error message "Operand should contain 1 column(s)"

I tried running the following statement:  INSERT INTO VOUCHER (VOUCHER_NUMBER, BOOK_ID, DENOMINATION) SELECT (a.number, b.ID, b.DENOMINATION)  FROM temp_cheques a, BOOK b WHERE a.number BETWEEN b.START_NUMBER AND b.START_NUMBER+b.UNITS-1;   which, as I understand it, should insert into VOUCHER each record from temp_cheques with the ID and DENOMINATION fields corresponding to entries in the BOOK table (temp_cheques comes from a database backup, which I'm trying to recreate in a different format). However, when I run it, I get an error:  Error: Operand should contain 1 column(s) SQLState:  21000 ErrorCode: 1241   I'm running this in SQuirrel and have not had issues with any other queries. Is there something wrong with the syntax of my query?  EDIT:  The structure of BOOK is:  ID  int(11) START_NUMBER    int(11) UNITS   int(11) DENOMINATION    double(5,2)   The structure of temp_cheques is:  ID  int(11) number  varchar(20)


qed symbol missing in Springer document classes (llncs and svjour3)

I'm currently using the two Springer document classes llncs and svjour3. Both define their own theorem environments (not using amsthm), including their own proof environment. However, this proof environment does not automatically generate a qed symbol (box) at the end of each proof, as the proof environment of amsthm does. What's the proper way of automatically generating a qed symbol while using the theorem/proof environments provided by the Springer document classes?


Manipulating expression $(\frac{1}{4}+\frac{1}{2^{n+1}})(1-\frac{1}{2^{n+1}})$ in inductive step.

My question concerns the inductive step of the proof below. I've typed out the work I've done so far. If anyone has any suggestions on how to proceed thanks in advance.  If $n\in\mathbb{N}$, then $(1-\frac{1}{2})(1-\frac{1}{4})(1-\frac{1}{8})(1-\frac{1}{16})\cdots(1-\frac{1}{2^n})\ge\frac{1}{4}+\frac{1}{2^{n+1}}$.  $Proof.$ We use mathematical induction.  Base Case. For $n=1$ we see that $1-\frac{1}{2}\ge\frac{1}{4}+\frac{1}{4}$ since $\frac{1}{2}\ge\frac{1}{2}$.  Inductive Step. Let $n>1$. Assume our statement is true for $n$. Now observe that  $\begin{align}(1-\frac{1}{2})(1-\frac{1}{4})(1-\frac{1}{8})(1-\frac{1}{16})\cdots(1-\frac{1}{2^{n+1}})&\ge\\ \left((1-\frac{1}{2})(1-\frac{1}{4})(1-\frac{1}{8})(1-\frac{1}{16})\cdots(1-\frac{1}{2^{n}})\right)(1-\frac{1}{2^{n+1}})&\ge(\frac{1}{4}+\frac{1}{2^{n+1}})(1-\frac{1}{2^{n+1}}) \end{align}$  My question is: How do we get from $\begin{align} (\frac{1}{4}+\frac{1}{2^{n+1}})(1-\frac{1}{2^{n+1}}) \end{align}$ to $\frac{1}{4}+\frac{1}{2^{(n+1)+1}}$?  Most of what I've attempted has led to tedious calculations that do not simplify to the desired result. I've also tried making the argument that $(1-\frac{1}{2^{n+1}})$ must be $\ge$ to $\frac{1}{2}$ but then I'm stuck with $\frac{1}{8}+\frac{1}{2^{(n+1)+1}}$... Is my approach incorrect here?


Let $X$ and $Y$ be independent random variables such that $X\sim\mathrm{Poisson}(\lambda_1 = 5)$ and $Y\sim\mathrm{Poisson}(\lambda_2 = 15)$. Let $Z = X + Y$ . Compute $\mathrm{Corr}(X, Z)$.  Answer:  $\mathrm{Var}(X) = \lambda_1 = 5$  $\mathrm{Var}(Y) = \lambda_2 = 15$  $\mathrm{Cov}(Z) = \mathrm{Cov}(X, X+Y) = \mathrm{Cov}(X, X) = V(X) = 5$  $\mathrm{Var}(Z) = \mathrm{Var}(X + Y) = V(X) + V(Y) = 5 + 15 = 20$  $\mathrm{Corr}(X, Z) = \dfrac{\mathrm{Cov}(X, Z)}{\sqrt{\mathrm{Var}(X)} \sqrt{\mathrm{Var}(Z)}} = \dfrac{5}{\sqrt{5 \cdot 20}} = 0.5$    I get most of the solution but I'm confused on how they got $\mathrm{Cov}(Z)$  $\mathrm{Cov}(Z) = \mathrm{Cov}(X, X + Y) = \mathrm{Cov}(X + Y, X) = \mathrm{Cov}(X, X) + \mathrm{Cov}(X, Y) \neq \mathrm{Cov}(X, X)$   Could someone explain how they got $\mathrm{Cov}(Z)$?


Should profane user names be prohibited?

I know that profanity is discouraged in SO posts.  However I recently saw a user with the F-word in his name.  Just out of curiosity, I searched for other users with the same word and found many hits - see below.  Personally this does not offend me.  I just wonder how others feel about it, and if it is something that SO should try to prevent.  Apologies if I've offended anyone by posting this image.  Edit - This questions is similar to, but not the same as: .  That question asks about a particular name and if it is genuine or not.  I am asking if SO should be doing anything to prevent users from creating accounts with potentially offensive names.


What is Animation Nodes addon used for? Where can I find more information about it?


How to find Mac admin password not reset Mac admin password

I am not a administrator and I would like to find the administrator password. I would not like to reset it however. Is there anyway to find and not reset the administrator password?


Problem : $(1+z)^n=(1-z)^n$ $\Rightarrow $ $Re(z) =0$

I am trying, but I found $im(z) =0$ I want to know where is my mistake My attempt : $(1+z)^n=(1-z)^n$ We put $z =e^{i\theta}$ $(1+e^{i\theta})^n=(1-e^{i\theta})^n$ $\Leftrightarrow $$(-e^{-i\pi} +e^{i\theta})^n=(-e^{-i\pi} - e^{i\theta})^n$ $\Leftrightarrow $$(e^{\frac{i\theta-\pi}{2}}(e^{\frac{i\theta+\pi}{2}}-e^{\frac{-i(\theta+\pi) }{2}}) ) ^n=(-((e^{\frac{i\theta-\pi}{2}}(e^{\frac{i\theta+\pi}{2}}+e^{\frac{-i(\theta+\pi) }{2}}) ) ^n$ $\Leftrightarrow $$(e^{\frac{i\theta-\pi}{2}}(e^{\frac{i\theta+\pi}{2}}-e^{\frac{-i(\theta+\pi) }{2}}) ) ^n=(e^{-\pi} ((e^{\frac{i\theta-\pi}{2}}(e^{\frac{i\theta+\pi}{2}}+e^{\frac{-i(\theta+\pi) }{2}}) ) ^n$ $\Leftrightarrow $ $ (sin (\frac{\theta +\pi}{2}) e^{i\frac{\theta}{2}}) ^n=(cos(\frac{\theta+\pi}{2})(e^{i\frac{\theta-\pi}{2} - \pi})^n$ $\Leftrightarrow $$-sin(\frac {\theta}{2}) =cos(\frac {\theta}{2}) $ and $e^{i\frac{\theta}{2}}=e^{i\frac{\theta-\pi}{2} - \pi}$ $e^{i\frac{\theta}{2}}=e^{i\frac{\theta-\pi}{2} - \pi}$$\Rightarrow $$cos(\frac {\theta}{2})  +isin(\frac {\theta}{2}) =cos(\frac{\theta-\pi}{2} - \pi) +isin(\frac{\theta-\pi}{2} - \pi)  $ $\Rightarrow $ $cos(\frac {\theta}{2})  +isin(\frac {\theta}{2}) =-cos(\frac {\theta-\pi}{2})  - isin(\frac {\theta-\pi}{2})$ $\Rightarrow $ $cos(\frac {\theta}{2})  +isin(\frac {\theta}{2})=-sin(\frac {\theta}{2}) +icos(\frac {\theta}{2})$ We know that:$-sin(\frac {\theta}{2}) =cos(\frac {\theta}{2}) $ So $2 isin(\frac{\theta}{2}))= 0$ $\Rightarrow $ $im(z) =0$


Why does the "Marked as Duplicate" block not give link(s) to the duplicate question(s)?

I often find pages which are marked as duplicate in a block just below the question, and it looks something like this:     marked as duplicate by ..., ..., ... Jan 31 '17 at 23:59      This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.   Why are there no links in the marked as duplicate block pointing to those duplicate questions? (F:A) (or a single link helping you point to those questions, see below)  It is quite frustrating that you have to think of similar questions (or try to rephrase your question) yourself and then look them up, if it could also supply those apparently known duplicate links.  When a user marks a question as duplicate, then I guess that user knows about the duplicate question in question (no pun intended) and might as well supply a link to that other question with little effort, so other users don't have to get creative to find it. (F:A)      (Sorry, the question grew very long. Please focus on above first before reading further)  As I am writing this I notice that when asking a new question (the window I am currently in) there are already functionalities showing similar questions as the one I am typing:     "Questions that may already have your answer" (F:E) a block with links to existing questions just below your new question title. "Similar Questions" (F:F) a pop-up block with links to existing questions in the sidebar. (only visible when your input focus is in the question-description-textarea)     Perhaps an alternative or additional feature could be to put general links in that "Marked as duplicate"-block, which give the same functionality (generated links) as I see here in the ask a new question window:     "See other questions that may have your answer" (F:B)   "See Similar questions" (F:C)     Come to think of it, those general links might also be useful for questions which aren't yet marked as duplicate.      There is already a sidebar "Related" (F:G) which seems to show links which also could be interpreted as "Similar Questions". If the links below "Related" are generated in the same way perhaps the title might be rephrased to "Related, similar or possible duplicate questions", so you know where to look. And put a "See Related" (F:D) #anchor link in the "Marked as duplicate" block which helps focus your attention on that Related block.    If the "Related" questions are generated differently then it might help to add a new block with "Similar (or possible duplicate) questions".    To make replies to this question a bit more managable let's mark mentioned features for easier reference:    Feature (F:A) : (new) when marking as duplicate, supply a link to the duplicate, and show that in de "Marked as duplicate box. Feature (F:B) : (new) a general "See other questions that may have your answer" link. Feature (F:C) : (new) a general "See Similar questions" link. Feature (F:D) : (new) a "see Related" link. Feature (F:E) : (existing) the "Questions that may already have your answer" list of links as seen on the asking a new question page. Feature (F:F) : (existing) the "Similar Questions" sidebar list of links as seen on the asking a new question page. Feature (F:G) : (existing) the "Related" sidebar list of links as seen on an existing question page.     Meta-meta:  Sorry for the wall of text, I was thinking about how to split this up but couldn't figure out how without losing cohesion on how all these things relate to eachother.  Wanted to add tag "question-linking" but not allowed to add new tags yet.  Ofcourse... only after typing all this I find duplicate questions to mine: (only showed up on the next page for my search for questions...) -     I Still feel my question covers more than the "duplicate question" mentioned above, so I thought it might be better to start this new question as a seperate question "thread" to cover all new mentioned options.


Script failing for restoration of database, as unable to proceed further

I want to include * as mentioned below in double inverted commas, but i am not able to find the file. When i remove the inverted double inverted commas it works.   $CONTROL=/bkp/Test/back/13_Mar_2018/ ls -lrt "$CONTROL\*controlfile";


How do I get other resolution option other than default one in full screen?

I want to get my 1366x768 monitor to have other screen resolution 800x600 or 1240x768 in full screen.   What option do I have? Thanks.  Here what I did,        shaharil@busuk:~$ xrandr   Screen 0: minimum 8 x 8, current 1366 x 768, maximum 8192 x 8192   VGA-0 disconnected (normal left inverted right x axis y axis)   LVDS-0 connected primary 1366x768+0+0 (normal left inverted right x axis y axis) 309mm x 174mm      1366x768       60.0*+   HDMI-0 disconnected (normal left inverted right x axis y axis)      shaharil@busuk:~$ cvt 800 600 60    # 800x600 59.86 Hz (CVT 0.48M3) hsync: 37.35 kHz; pclk: 38.25 MHz   Modeline "800x600_60.00"   38.25  800 832 912 1024  600 603 607 624 -hsync +vsync      shaharil@busuk:~$ xrandr   Screen 0: minimum 8 x 8, current 1366 x 768, maximum 8192 x 8192   VGA-0 disconnected (normal left inverted right x axis y axis)   LVDS-0 connected primary 1366x768+0+0 (normal left inverted right x axis y axis) 309mm x 174mm      1366x768       60.0*+   HDMI-0 disconnected (normal left inverted right x axis y axis)      shaharil@busuk:~$ xrandr --newmode "800x600_60.00"   38.25  800 832 912 1024  600 603 607 624 -hsync +vsync      shaharil@busuk:~$ xrandr --addmode LVDS-0 800x600_60.00   X Error of failed request:  BadMatch (invalid parameter attributes)     Major opcode of failed request:  140 (RANDR)     Minor opcode of failed request:  18 (RRAddOutputMode)     Serial number of failed request:  27     Current serial number in output stream:  28


Buying shares when the price goes down 2% and selling shares when it goes up 2%

Suppose I have 50,000 in a tracker.  Because it's an aggregate of the share index, it can obviously go up or down but what it certainly does is fluctuate up or down.   What is the problem, if any, of selling when it goes up 2% and then buying back in when it goes down 2%? Every time you clear 1000 allows you to then buy more shares. Surely you could do this many times a year? Barring crashes in the market, which means you hold for recovery, I can't see a downside myself. Any older, wiser heads out there?


Why are my posts omitted from Google search results when my site is listed in it?

My domain is not new at all, in fact I have waited for quite a long time now for Google to show some love. If I do a search for my domain name, it shows the website is listed, but if I try to search for even a year-old post on Google, using my website name too, it never returns it. Instead it says some results have been omitted and asks if those omitted results should be included in the search results.  The following is the message it returns:     In order to show you the most relevant results, we have omitted some   entries very similar to the 8 already displayed. If you like, you can repeat the search with the omitted results included.   Why are my posts are never returned in search results even though I have original and ample content on my website?


Is there any way to prove that:  $$ \sum_{n=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90} $$  Using Euler's original proof of equating coefficients?


Dystopian future, an old novel where everyone only has a three day memory?

I'm trying to find the name and/or author of a story I read in the 1990s (I think) about a future where everyone takes 'memory loss' pills. It means you only remember three days of short term stuff, though you remember all the basic skills like talking and tying your shoelaces, and who your family is. If you don't take the pills you have to live in an exile community. This boy takes the pills, and is looking after a small shrub, but he doesn't know for how long he's been looking after it. Something like that.  Anyone read something even remotely like this and could point me in the right direction?  Much appreciated.


How does this Makefile makes C program without even specifying a compiler?

I was using a Makefile from the book " (2001)". It was strange for me to see that GNU make does compile the code correctly, without even specifying a compiler in the Makefile. It's like baking without any recipe!  This is a minimal version of the code:  test.c  int main(){}   Makefile  all:            test   and make really works! This is the command it executes:  cc     test.c   -o test   I couldn't find anything useful in the documentation. How this is possible?    P.S. One additional note: Even the language is not specified; Because test.c is available, GNU make uses cc. If there exists test.cpp or test.cc (when there is no test.c), it uses g++ (and not c++).


The Durbin-Watson statistic to detect autocorrelation in the error terms ranges from 0 to 4. Currently, I am working out why it cannot exceed 4 analytically. The lower boundary case is obvious considering the actual statistic which is   $$DW =  \frac{\sum\limits_{t=2}^{T}(\hat{\epsilon}_t - \hat{\epsilon}_{t-1})^2}{\sum\limits_{t=1}^{T} \hat{\epsilon}_t^2};$$   but for the upper boundary case, i.e. DW < 4, I ran in one particular difficulty. After expansion of the numerator I get   $$\sum\limits_{t=2}^{T}(\hat{\epsilon}_t - \hat{\epsilon}_{t-1})^2 = \sum\limits_{t=2}^{T} \hat{\epsilon}_t^2 - 2\hat{\epsilon}_t\hat{\epsilon}_{t-1} + \hat{\epsilon}_{t-1}^2 = \sum\limits_{t=2}^{T} \hat{\epsilon}_t^2 -2 \sum\limits_{t=2}^{T} \hat{\epsilon}_t\hat{\epsilon}_{t-1} + \sum\limits_{t=2}^{T} \hat{\epsilon}_{t-1}^2.$$   Obviously the last and first term are both less or equal than $\sum\limits_{t=1}^{T}\epsilon_t^2$ since they miss a non-negative term. Hence,   $$\sum\limits_{t=2}^{T} \hat{\epsilon}_t^2 + \sum\limits_{t=2}^{T} \hat{\epsilon}_{t-1}^2 \leq 2\sum\limits_{t=1}^{T} \hat{\epsilon}_t^2.$$   What I can't seem to figure out analytically is why necessarily   $$-2\sum\limits_{t=2}^{T}\hat{\epsilon}_t\hat{\epsilon}_{t-1} \leq 2 \sum\limits_{t=1}^{T} \hat{\epsilon}_t^2$$   must hold, i.e. why   $$0 \leq \sum\limits_{t=1}^{T} \hat{\epsilon}_t^2 + \sum\limits_{t=2}^{T} \hat{\epsilon}_t\hat{\epsilon}_{t-1},$$   considering that the error terms might be negative? Surely, there is some kind of estimation that yields the result but what is it?


How to find Ubuntu which is already installed?

How to find Ubuntu which is already installed, I have dual operating system in my COMPUTER as per windows XP and Ubuntu, a few day ago I have formatted my computer & install win 7 operating system, but I have formatted C: drive only (win xp on c: drive) but not uninstall Ubuntu, now I start computer but I can not find Ubuntu which is already installed!! I have not more idea for Ubuntu, please anyone tell me how I can find Ubuntu in my computer, My computer only show windows 7 operating system.


I have two Date values. I need to find number of weeks between them. I want to do it Apex Class. Not looking for formula fields.  So far I tried:  Integer numberofweeks = (projectStartDate - opp.Project_Start_Date__c)/7;    I receive this error:     Date arithmetic expressions must use Integer or Long arguments


InfoPath rules for two related fields(Edited)

I have an InfoPath form that has signature and status fields and I want to make a condition that when the signatures field is not blank, the status field will show a message.  Basically, when signer 1 done then I need status to show Ready for signer 2. And when signer 2 is done I need the status to show Ready for signer 3.  Is it possible in InfoPath designer I have difficulty to applied the action is that b/c the control is signature?  Note: My Signature is Digital signature (Not input category)


Looking for a story about identical people in identical houses, with kids bouncing balls

My sister was assigned to read this book in elementary school so it must have been a sci-fi classic.  Anyway, there is this planet that has this street with identical houses and driveways and at the same time of the day all the identical kids from all of the houses come out and play or bounce a ball. It reminded me of looking into a mirror in a restaurant bathroom where your face repeats forever.


I have come up with a theorem. (It probably doesn't qualify as a theorem, but I don't know what else to call it) This is what it states:  If  $$\lim_{x\to\infty}f'(x)$$ exists (is finite), then $$\lim_{x\to\infty}\frac{f(x)}x=\lim_{x\to\infty}f'(x)$$ I have yet to find a counterexample, and it just seems to make sense to me, but I can't actually prove it.  This "theorem" is crucial to an answer to a question that I was asked to give, but my answer won't be a very good one if I can't prove why it works.    What I've tried:  I have been able to prove it if $f(x)$ has a linear asymptote (I think my terminology is correct).  If:  $$\lim_{x\to\infty}f(x)=\lim_{x\to\infty}mx+b$$  Then:  $$\lim_{x\to\infty}\frac{f(x)}x=\lim_{x\to\infty}\frac{mx+b}x=m$$  But that doesn't work if there is no asymptote. Take $f(x)=\ln(x)$ for example. the $b$ in $mx+b$ would be infinite.


How to keep the rank in google search engine database when changing ip address

I am a newbie in the field of website making. I currently made a website using Django and host it using digital ocean, I learn all of it by myself and I am very interested. However, I would like to learn google search engine optimization now and let people have a higher chance of visiting my website. And I wonder, because I am just testing my website status so I use Digital Ocean, what if in the near future, I change the hosting location ,and thus the ip address change, could google still keep the rank of the website when searching a particular website.


Should this:     We believed the issues which would be on the agenda were too problematic at the time"   Be like this?     We believed the issues that would be on the agenda were too problematic at the time.


what is the value of the acceleration of a bar magnet falling through a coil?

when a bar magnet is made to fall through a closed circular coil kept horizontally,according to Faraday's law an emf is induced in the coil,which again according to Lenz law,will oppose the downward motion of the magnet.Therefore the value of the acceleration changes.What is the value of this acceleration,or what is the equation describing the motion of the magnet?


Why didn't the ghosts and the portraits know about the Basilisk?

The ghosts of Hogwarts have been around the castle for a very long time, and possibly should remember the first time this happened, 50 years ago, when Tom Marvolo Riddle opened the Chamber and killed Myrtle. Harry could've gathered a lot of information about these events from these figures.      Why didn't Harry enquire about the Basilisk to any of the ghosts or the paintings?   Come to think of it, why didn't Dumbledore ask the ghosts about the Basilisk sightings? Also, even if he was in a position where he was able to do anything about it, why didn't he find the Chamber entrance himself?      And what about the paintings? The paintings of various teachers, headmasters and other figures flood the walls of Hogwarts. Is there a possibility that they could be petrified? Also, couldn't these paintings bear witness to the events? I know they sleep at night, but wouldn't they wake up to such events?      NOTE:  My knowledge on the series is highly limited, so please excuse any mistakes I may have made.


I have a HP 530 laptop with Ubuntu 12.04 installed. With Windows Vista, I could use its wireless hardware, but now it doesn't work. I have tried using the command: sudo rfkill unblock all  Does anyone know what I should do?  Edit: I have a Broadcom wireless network card.


How to get Explorer sort by Name to sort folder and folder shortcuts together?

Here Explorer sort by Name separates folder and folder shortcuts.     How can I remedy this i.e. get it to sort them together?  EDIT: Clarification: I want the sorting to remain otherwise unchanged, i.e. not to change the sorting of folders with respect to non-folder-shortcut files.


Running 5.1.1 lolipop on android s5 with 0.29.3 version Pokémon Go.  Periodically there will be a bug or the game freezes and if I reload my game it will get stuck at 20%.  It won't reload unless I connect to WiFi.  If I'm with a friend I can connect to a hotspot and get it to reload and work (sometimes I need to restart my phone depending on the friends network).  It isn't a server outage since it will work again if I connect to wifi and everyone else around me is playing without issue. It isn't a 4G or network error since speed tests are consistent and everything else works perfectly fine, others can use my hotspot and have no problems, if I connect to wifi and it loads past the 20% it will continue to load correctly if I disconnect the wifi, it only gets stuck until there's a wifi connection.  Force stop and clearing cache, clearing data, uninstalling and reinstalling nothing else will get it to work.  Any suggestions on a fix?


I am a recently graduated graphic designer. I would like to know if there are any worthwhile websites that I could present my portfolio and receive or look for job offers.  I have came across the following freelancewebsites by searching the web that seem to meet my criteria:       (the most famous website for people seeking for employers and employees)   I've also found two articles providing reviews on these types of sites:       I am new to the online freelance market. As a result, I don't have any clue which websites are mainstream for graphic designers and illustrators (which are my specialties). It's not immediately discernible to me which sites are the ones that are not a scam and are also good place for establishing myself.  I'm mainly looking for the resources that experienced designers are familiar with. I'm looking to narrow it down to the ones that have been used by those established in the industry. As a result I decided to consult the matter here and ask for input.


Will there always be integer solutions for $x$ and $y$ in $3^y = 2^x - 1$?

Is there a way to find the solutions of $3^y=2^x-1$ where $(x,y)$ are integer coordinates (maybe within a certain interval)? Are there an infinite number of integer coordinate pairs for this equation? Is it possible to even determine this? I'm not quite sure the difficulty of this problem, but substituting $x$ or $y$ values into this equation to find integer pairs is time consuming and not very promising.


The goal that I am trying to get to is having user input the name of a movie along with the release date. To do this I have set up separate classes.   Movie cameronsMovie = new Movie("Sin City", 2005);     Movie [] movieList = new Movie [9];     movieList[0] = cameronsMovie;      for (int i = 0; i < movieList.length; i++) {         System.out.print("Please enter a movie Title: ");         String title = GetInput.readLine(); //Get movieTitle         System.out.print("Please enter the year it was released: ");         int releaseDate = GetInput.readInt(); //Get year         // creating a new ojbect         Movie userMovie = new Movie(title, releaseDate); /* calls the          constructor from Movie class         */         movieList[i] = userMovie;     }      System.out.println(movieList.toString());   This is the code that I am using to call the other classes and the problem that I am having is with my last line of code printing out a result of [LMovie;@2a139a55  In my classes file I have this code   public String toString() {         String temp = new String();        temp = "Movie title: " + getTitle() + "\nYear of Release: " +                       getYear();        return(temp);         }   to return my string. Is there something wrong with the way my toString() is set up or is there another place where I am making a mistake


Do items downgrade when repaired after being damaged?

In Divinity: Original Sin, if an item's durability goes down to 0 and then the item is repaired, is it as good as new or does it become worse (and if so, to what extent)?


I am trying to translate a piece of French material (in English) and here is my codes:  \documentclass[12pt]{article} \usepackage[english]{babel} \usepackage{amsmath,amsthm,amssymb,amsfonts} \usepackage{geometry}\geometry{margin=1in} \usepackage{paracol}   \begin{document}  \newpage \begin{sloppypar}  \begin{paracol}{2}    1. Il y a plus de 50 ans que l'ingénieur Heaviside introduisit  ses règles de calcul symbolique, dans un mémoire audacieux où des calculs mathématiques fort peu justifiés sont utilisés pour la solution de problèmes de physique.\\   \switchcolumn   \end{paracol} \end{sloppypar}  \end{document}   But when I run the codes in TeXStudio, the accented letters completely disappear. (For instance, "ingénieur" in the first sentence becomes "ingnieur".)    Is there a quicker way to fix this than manully typing the accented letters as in this ?


If P a polynomial of degree n let M=Max |f(z)| if Z ∈ D(0,1) prove if |z|>1 then P(z)<=M.|Z|^n Maybe we can use the maximum modulus principle and consider 𝑞(𝑧)=𝑧^n P(1/𝑧)


Just something I ran into and couldn't think of a proper explanation. If I create an empty *.txt file on my PC and then look at its size, it shows 0. But how is that possible? I mean even if the file itself is empty, it still must have some size, just to store its own name. How can this be explained? (Non OS specific)


How to detect if a player has killed a mob? Minecraft 1.15.2

So I am making a function for a video, and I need a way to set a player's score to 1 when they kill a bat.  I was thinking I could just summon an invisible armor stand on every bat in the overworld, and use that to detect if a bat died near a player. However that could be very buggy, and may lag some users games.  Anyone got any alternatives?


Is there functionality to convert from UTC time to local time using country name?

I have searched the method here but there is no case for me.  Is there functionality to convert from UTC time to local time using country name from excel ?  Example :  string CurrtTime = DateTime.UtcNow.ToString("yyyy-MM-dd HH:mm:ss");   I would like to create a variable for localtime which receive value ( country name ) from Excel. How to do ?  string localtimenow = ____________.(CurrtTime).(Thailand) string localtimenow2 = ____________.(CurrtTime).(Australia)  Expected results.  UTC TIME => yyyy-MM-dd 08:18:xx  BKK TIME => yyyy-MM-dd 15:18:xx  SYD TIME => yyyy-MM-dd 18:18:xx


Now that we have a shiny new top bar, have there been any changes in plans to make it visible in the chat rooms? The responses in old threads I've found seem to defer or decline the option due to issues which may have been resolved by now, completely side-step the problem, or refer to third-party solutions.     Some third-party solutions and a non-answer that addresses the chat index, but not chat rooms.      Acceptance of the general concept seems unconfirmed. "It has come up before, though, and was deferred. I'll ask around, to see if that has changed..." Based on that same answer, it appears this request was rejected because the suggested refresh rate was too often. The new top bar automatically updates, so this should no longer be an issue.   I'm interested to find out what the current status is with regards to implementing this directly on the SE chatrooms, without the need for client-side plugins or scripts.


Solve $$I=\int_0^1\frac{ln(1+x)}{1+x^2}dx.$$  After let $x=\tan t$, $I=\int_0^{\pi/4}ln(1+\tan t)dt$ and I stuck here.


Is grammatically correct to say: "Jewish is the nation that Jesus came from"?

Is correct grammatically to say      "Jewish is the nation that Jesus came from!"   as a declarative sentence ?  I ask my question because of that's strange to me to see the end of the sentence ends with preposition (as you can understand by yourself, I'm not English native speaker...)


Travelling to using two passports where one is not ok with dual citizenship

I have two passports where one of them is not OK with with dual citizenship. As suggested by previous questions posed that I should fly to a neutral country - "C" which does not need visa as transit and then fly into the single citizenship country -"B" -entering using B passport.   However on my return to A (dual citizenship) country via the neutral country using my A  passport, would it not be strange not to have an B country exit stamp on the A passport especially you just flew out from B country? (As you enter and leave your (single citizenship) B country using its own passport) Would the neutral country's immigration question this and report to your  B country?


Executing multiple commands from a Windows cmd script

I'm trying to write a Windows cmd script to perform several tasks in series. However, it always stops after the first command in the script.  The command it stops after is a maven build (not sure if that's relevant).  How do I make it carry on and run each task in turn please?  Installing any software or configuring the registry etc is completely out of the question - it has to work on a vanilla Windows XP installation I'm afraid.  Ideally I'd like the script to abort if any of the commands failed, but that's a "nice to have", not essential.  Thanks.


Syntax Error in etc/sudoers and can't edit it in terminal

I was/am trying to run terminal commands without having to use sudo first and must have broke the file. Now I'm trying to fix it and it's giving me this error when I try to edit with the same sudo visudo command.  /etc/sudoers: syntax error near line 62 <<< sudo: parse error in /etc/sudoers near line 62 sudo: no valid sudoers sources found, quitting sudo: unable to initialize policy plugin  I'm on a Mac using Terminal Is there a way to edit this file and remove what I added or reset it without harming or removing other files?


Syntax Error when attempting to /give a player a named diamond sword?

I am attempting to give a player a named diamond sword using this command: /give @p diamond_sword 1 0 {display{name:"Burn"}}  But I'm getting the following error: Syntax error: Unexpected "{": at "0 {display>>{<<name:"Burn"  This happens on both Minecraft Pocket Edition and Minecraft PC. Can someone help me fix this? I really want to know how to use these and I haven't used command blocks untill now.


How to fix `sudo apt-get update` on Ubuntu 16.04?

I'm new to Ubuntu. Got this error while installing ppa:


Simple Mersenne prime divisibility proofs

From "Fundamentals of Number Theory" by William J. LeVeque:     $M_n=2^n-1$.      Show that if $n=rs$, $M_r$ divides $M_n$.   My proof is:     $(M_n=2^n-1)+(n=rs) => (M_{rs}=2^{rs}-1)=>(M_{rs}=(2^r)^s-1)$      $(M_r=2^r-1)=>(M_r+1=2^r)$      $M_{rs}=(M_r+1)^s-1$      In the expansion of $(M_r+1)^s$, all components are of the form $M_rX$, except for the product of all ones. This follows from the combinatorial constraints. Therefore $M_n$ is of the form      $M_n=M_{rs}=M_r(X_1+X_2+...)+1-1$.      Thus $M_r|M_n$.     I have two questions:   1) Is this proof correct/acceptable?  2) In what other ways can this problem be solved? Specifically I am interested in what other kinds of algebraic/logical/mathematical manipulations could be used.  Thanks in advance!


How to set a label's position relative to its pin?

Consider the following LaTeX manuscript featuring a TikZ picture of an empty node with an attached pinned label.  \documentclass[tikz]{standalone} \begin{document} \begin{tikzpicture}   \node [draw,pin=x] {}; \end{tikzpicture} \end{document}   The resulting image is                                                                    (This is not quite the image you'd get from the above code: I enhanced the pin's visibility a little, for the reader's convenience.)  I know how to adjust the angle and length of the pin (this is described in section 17.10.3 'The Pin Option' of the TikZ & PGF manual for version 3.0.1a on p. 241), but how can I adjust the position of the lable (angle, distance, and label anchor) with respect to the head of the pin?


Let $R$ be a ring with finitely many maximal ideals such that $R_{\mathfrak m}$ ($\mathfrak m$ maximal ideal) is noetherian ring for all $\mathfrak m$. Is $R$ noetherian?   I think $R$ has to be noetherian. Let $p_1 \subset p_2 \subset \cdots \subset p_n \subset \cdots$ be an infinite ascending chain of prime ideals in $R$, then I claim that there exist a maximal ideal $m$ which will contain all the prime ideals in this chain (from finiteness of the maximal ideals), this will give a chain of prime ideals in $R$ localised at $m$, but since that has to be finite (the local ring $R_m$ is noetherian) so the chain pulled back will terminate in $R$.


Landau's derivation of a free particle's kinetic energy- expansion of a function?

I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact that the Lagrangian of this particle must be the same (or at most, differ by the total time derivative of a function of co-ordinates and time) in different inertial frames.     We have $L'=L(v'^2)=L(v^2+2\mathbf{v}\cdot\boldsymbol{\epsilon}+\boldsymbol{\epsilon}^2)$. Expanding this expression in powers of $\boldsymbol{\epsilon}$ and neglecting terms above the first order, we obtain    $$L(v'^2)=L(v^2)+\frac{\partial L(v^2)}{\partial (v^2)}2\mathbf{v}\cdot\boldsymbol{\epsilon}.$$   I think I'm ok with all the physics in this section. What I don't get is just the part I quoted above (so maybe this post is better suited for the math site, but since this is book is so physics-y I thought I'd post it here). My math is pretty rusty, so I'm not really sure- how do the authors expand the function to arrive at the above expression? It reminds me a bit of a Taylor expansion, but not very much. What's the process used to arrive at it?


Force process and kernel module to one core exclusively

I'm just in the phase of evaluating new possibilities, so this question may be a bit strange. I have a Quad-Core CPU which has to do some realtime tasks (it has access to some GPIOs, so this is definitely possible). Instead of using a Realtime Linux (which is more a soft realtime), I want to implement a hard realtime application. So my idea is this:   on bootup force all components of the operating system to two of the CPUs cores load one kernel module which uses the third core exclusively and therefore can do some nasty things like bit-banging the GPOs in realtime later start one process which uses the remaining core and sends data to the kernel module   My questions: is it possible to configure a Linux Kernel/System in this way? If yes: how can I ensure two cores are left unused and how can I put a kernel module and a process to them?  Every idea and hint is welcome :-)


I used composer create-project drupal-composer/drupal-project and have happily been using composer install composer require and composer update to keep my development system up-to-date and moving it around different development machines.  However, the upgrade to Drupal 8.1.0 from 8.0.6 was clumsier that I'd expected. Is there a slicker way of upgrading all the symfony dependencies than this?  composer require drupal/entity:8.1.0-alpha2 drupal/core:8.1.0 \     symfony/process:~2.8 symfony/console:~2.8 symfony/event-dispatcher:~2.8 \     symfony/yaml:~2.8 symfony/translation:~2.8 symfony/validator:~2.8 \     symfony/serializer:~2.8 symfony/routing:~2.8  symfony/http-foundation:~2.8 \     symfony/http-kernel:~2.8 symfony/dependency-injection:~2.8 \     symfony/class-loader:~2.8  drush @mysdevsite updb  drush @mydevsite cr   BTW This current (25 April) sole answer to the duplicate question didn't work for me. e.g. - drupal/entity 8.0.1 requires drupal/system <8.1.0 -> satisfiable by drupal/core[8.0.6, 8.0.x-dev]. caused Your requirements could not be resolved to an installable set of packages. So I had to require each of 8.1.0's dependencies in turn just the same as without the --update-with-dependencies option. Painful.


How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?

I'm working on a practice exam for my masters quals and I am having difficulties with the following limit. According to wolfram alpha, it's value is 1/2. Does anyone know how to find this limit?   $$\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right].$$


Relationship Between Circles Under Inversion

Considering the inversion $w=\frac{1}{z}$ Consider two unshaded circles $C_{r}$ and $C_{s}$ with radii $r>s$ that touch at the origin of the complex plane. The shaded circles $C_{1}$,$C_{2}...C_{7}$ (labeled in counterclockwise direction sequentially) all touch $C_{r}$ internally and $C_{s}$ externally. $C_{1}$ also touches the real axis and $C_{i}$ and $C_{i+1}$ touch for $i=1...6$.  Let $r_{i}$ denote the radius of $C_{i}$. Then show that for $i=1,2...,$ $r^{−1}_{i}+3r^{−1}_{i+2}=3r^{−1}_{i+1}+r^{−1}_{i+3}$.    I'm struggling to begin with this problem. I know that under inversion the two circles touching at the origin $C_{r}$ and $C_{s}$ will be mapped to straight lines and that the other circles will be mapped to circles, however I'm struggling to see how I would obtain the $r^{-1}_{i}$s. Any help would be much appreciated.


Increase volume of /home partition with unallocated space

I have been trying to resize my /home partition (/dev/sda5) with the unallocated space (325 GiB), I tried gparted but it seems that I can't add the unallocated space.    The fdisk -l output:    Can someone help me?


Ubuntu 15.10 freeze on Acer E11/Bay Trail CPU

I went ahead and upgraded from Mint 17.2 to Ubuntu 15.10 on my Acer ES1-511-P1T9 with Bay Trail n3530 CPU and so far am having amazing performance over Mint 17.2 (almost 70-80% performance increase) however the system has started freezing.  It seems to be when hitting the 4gb+ of memory in use (8gb installed).  I've run a full memtest (about 3-4 hours) on the 8gb stick and am not seeing any errors.  I've read a few things about issues with the new Intel HD linux drivers causing issues, has anyone else seen this with the Bay Trail CPUs?  I'm hesistant to pull the 8gb and reinstall the 4gb as its such a pain removing the whole motherboard to do so lol if there is any chance that it's something else.  Edit:  Under 8.1 Pro x64 system is fully stable.  Under 15.04 system is fully stable however performance is horrible (actually worse than under Win8.1).  Fresh install of 15.10 yields a freeze usually within 10 minutes even with 0 applications running and wifi disabled.  This sucks :( I don't want to use Win8.1 lol


Showing there is a natural map between coim$(f)$ and im$(f)$ in an abelian category

We defined an abelian category as one who is (i) additive, (ii) every morphism has a kernel and a cokernel,  (iii) and every monomorphism is a kernel and every epimorphism is a cokernel.  I'm given a morphism $f: A \rightarrow B$ is an abelian category $\mathcal{C}$.  I need to show that there is a natural (isomorphism) map $\overline{f}$ between the image and the coimage of $f$.  Attempt: I know the image of $f$ is the kernel of its cokernel, and the coimage of $f$ is the cokernel of its kernel.  So I have arrows $$ \ker(f) \xrightarrow{k} A \xrightarrow{f} B \xrightarrow{q} coker(f). $$ I also have maps $$c: A \rightarrow coim(f) = coker(k)$$ and $$ m: im(f) = ker(q) \rightarrow B. $$   Now we know that $f \circ k = 0$, since $k$ is the kernel of $f$. Since $c$ is the cokernel of $k$, by def. of cokernel there exists a unique factorization such that $f =  \psi \circ c. $   Since $q$ is the cokernel of $f$, we have $q \circ f = 0$. Since $m$ is the kernel of $q$, we have a unique factorization $f = m \circ \phi$.   Now I'm stuck. I have these two unique morphisms $\psi: coim(f) = coker(k) \rightarrow B$ and $\phi : A \rightarrow im(f) = ker(q)$.   But how do I construct a morphism $\overline{f} : coim(f) \rightarrow im(f)$ ?? And how do I show it is an isomorphism?  Thank you for any help.


How to remove a particular link from the autocomplete list of desktop Google Chrome?

Sometimes after I visit a wrongly inputed page more than once, Chrome will weirdly store it in the autocomplete bar from the location form (address bar? the one get focused when you click CMD+L on Mac).  What can I do to remove one from the list? Here in the red outline is the one I want to remove.


Generate two correlated ARMA(1,1) processes

How can I generate two correlated ARMA(1,1) data series where  $d_{1,t}=\mu+\phi_{1}d_{1,(t-1)}-\theta_1(e_1(t-1)+e_1(t))$  $d_{2,t}=\mu+\phi_{2}d_{2,(t-1)}-\theta_2(e_2(t-1)+e_2(t))$  and $\rho_{12}$ is desired correlation between $e_1$ and $e_2$?


Proof by the Principle of Mathematical Induction

I'm trying to do my Maths assignment but I can't get this done. I'm a novice, so it's a bit hard to know which steps I need to follow in this one. $$(1−x)(1+x+x^2+⋯+x^n)=1−x^{n+1}$$ My usual first step is to proof it when $n = 1$ and then when $n = k$. But the problem is that I don't know what $x$ is. I usually solve problems that only have $1$ variable.


Why does my circuit work on a breadboard, but not on a perfboard? I am new to soldering

I'm a total beginner when it comes to soldering, and recently I've been trying (and failing) to solder together a simple circuit I put together for a Raspberry Pi sensor.    Although it works fine on the breadboard, when I solder it onto one of my , the sensor no longer turns on.    Here is a topdown view of my soldered circuit:    Here is a view of the connections (the red block is just covering up old connections from past attempts):    More pictures of the connections.  What might I be doing wrong?


I have this simple treeset.   TreeSet<Fruit> treeSet = new TreeSet();     try {         treeSet.add(pear);         treeSet.add(apple);         treeSet.add(orange);         System.out.println(treeSet);     } catch (Exception e) {         System.out.println(e.getMessage());     }   when this compiles it prints it all out on the same line. How can i make it so it prints each object out on a different line?


What does the star and doublestar operator mean in a function call?

What does the * operator mean in Python, such as in code like zip(*x) or f(**k)?   How is it handled internally in the interpreter? Does it affect performance at all? Is it fast or slow? When is it useful and when is it not? Should it be used in a function declaration or in a call?


When a children appear in a movie that has a scene or two depicting sexuality (R rated material), is it the norm to let these children know what kind of movie they are participating in? Or are they kept in the dark until they grow up and find out?  What if they wanted to see the movies they acted in? Are they even allow to watch the full R-rated film they helped make?  Is there any kind of formality or agreement between the child and the movie/TV-show producers/directors, in which the child's approval is obtained? Or is it the parent's approval that counts?  Case in point: In the movie Ken Park (2002), we see a little girl watching something inappropriate on TV (maybe she was not really watching anything, and they edited it out like that), but the whole movie is R rated and is inappropriate for ages below 18 to watch. Does the actress child know what kind of movie is she in?


running scripts that have sudo in it as sudo at startup?

I have a script that I want to run on startup.  This script launches vms using sudo VBoxManage.  How can I a) Execute this vm start script on the computer startup and b) make sure the sudos don't need me to actually type in a password.    I figured rc.local somehow but not sure how to handle the fact that it requires sudo to run VBoxManage with


How to dynamically creating chatter groups in Apex?

It looks like ConnectApi.ChatterGroup is abstract. Is there really no way to create Chatter groups via connect in Apex?   Is the solution to call the chatter REST API from APEX?   UPDATED based on answer below:   public static Id createGroup(String groupName, List<User> users) {      CollaborationGroup g = new CollaborationGroup(Name=groupName, CollaborationType='Public');     g.OwnerId = UserInfo.getUserId() ;     insert g;      List<CollaborationGroupMember> groupMembers = new List<CollaborationGroupMember>();      for (User user: users) {         CollaborationGroupMember member = new CollaborationGroupMember();         member.MemberId = user.Id ;         member.CollaborationGroupId = g.Id ;         groupMembers.add(member);     }      insert groupMembers;     return g.Id ; }


$a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$

I just need to check the reasoning in my proof is correct, I think it is valid although I'm not totally convinced because I can't follow the logic; does proving that $x$ is an integer prove that $ac|bd$?  Theorem: Let $a$, $b$, $c$, $d$ be integers. If $a|b$ and $c|d$, then $ac|bd$.  Proof: $aj=b$ and $ck=d$ for integers $j$, $k$. Then, $ac|bd$ implies $acx=ajck$ and thus $x=jk$ for some $x$. Since the product $jk$ is an integer, $x$ is an integer and thus $acx=ajck$ and thus $ac|bd$.


How to test something in Multi-Threaded Environment using Java

How do I test something like this in multithreaded environment. I know it's gonna fail, cause this code is not thread-safe. I just wanna know how can i prove it? Creating bunch of threads and trying to add with those different threads? This code is intentionally not written properly cause of testing purposes !!!   public class Response_Unit_Manager {  private static HashMap<String, Response_Unit> Response_Unit_DB =         new HashMap<> ();  /**  *   * This subprogram adds a new Response_Unit to the data store.  The  * new response unit must be valid Response_Unit object and it's ID must be   * unique (i.e., must not already exist in the data store.  *   * Exceptions Thrown:  Null_Object_Exception  */ public static void Add_Response_Unit (Response_Unit New_Unit)          throws Null_Object_Exception, Duplicate_Item_Exception {     String Unit_ID = New_Unit.Unit_ID ();      if (New_Unit == null)         throw new Null_Object_Exception ();      else if (Response_Unit_Exists (Unit_ID))         throw new Duplicate_Item_Exception (Unit_ID);      else         Response_Unit_DB.put (Unit_ID, New_Unit); } //end Add_Response_Unit


I have a question , why decibels are useful for electrical engineers ?? I still can't figure out why it is useful to use decibels in expressing power ratios , gain and other things ?


How to remove the textured background from a handwritten text document?

I'm using Adobe Photoshop.  I noticed that there are other questions similar to this one.   However, the reason I'm posting my question is, when I followed the instructions in the  about removing the background from a signature, it was not working for me on this document. I needed to select several times for each letter. Many times I was also getting parts of the background with the letters.  Is there some shortcut?  It looks like it will take me a whole day to select all the text, letter by letter.  Perhaps the reason the Magic Wand tool is not working well is because the text is handwritten and the edges are not well defined?  So, here's the picture.  (I thought I uploaded it the first time, I'm trying again now)    Basically, I would like guidance on how to remove the background and put the text on a solid white background. (If possible in an easier more efficient manner than selecting each letter one by one)  P.S. For those curious, this is a handwritten marriage document in the Hebrew language written on parchment with a quill.


How to formulate a likelihood ratio test for an exponential distribution?

Find the form of the likelihood ratio test of $H_0 : \lambda = \lambda_0$ against $\lambda\neq\lambda_0$ when $X_1,X_2,...,X_n$ is a random sample from $Ex(\lambda)$. Simplify it as much as possible.   I've started as follows, where $\lambda_1$ is some alternative parameter  $$ \frac{L_0}{L_1}=\frac{\prod f(x;\lambda_0)}{\prod f(x;\lambda_1)} $$  I think the p.d.f. for an exponential is $\lambda e^{-\lambda x}$ so  $$ \frac{L_0}{L_1}=\frac{\prod \lambda_0 e^{-\lambda_0 x_i}}{\prod \lambda_1 e^{-\lambda_1 x_i}} $$  $$ =(\frac{\lambda_0}{\lambda_1})^n\frac{\prod e^{-\lambda_0 x_i}}{\prod e^{-\lambda_1 x_i}} $$  Which I think can be simplified like this by taking logs  $$ =n log(\frac{\lambda_0}{\lambda_1})\frac{e^{-\sum\lambda_0 x_i}}{e^{-\sum\lambda_1 x_i}} $$  Not sure about this but, I think that becomes  $$ =n log(\frac{\lambda_0}{\lambda_1}) e^{-\sum x_i ({\lambda_0}-{\lambda_1})} $$  Am I right so far? Not sure where to go from here. I think the critical region is where the above is less than some constant.


I have a separate machine Dell 1545 laptop. I was wondering how to have  a full install using 12.04 LTS on my Vista machine? Can I just put the burned ISO disc in the disc tray and restart then go into Bios- selecting Boot from CD or is it more different than that? I Do Not want to Dual Boot!  Thanks.


disabled all msconfig services can't get logged in

I was trying to fix red dead redemption ii I went into msconfig and accidentally disabled all the services I restarted my computer and it won’t let me login can someone help me fix this


How can I convert many images into a movie?  I have about 12000 images, and I want to create a movie based on the timestamps of the images. The timestamp is also the filename. I tried using convert but it crashes my PC when I try to do it. What is a good command-line way to solve this problem?


Does the Galaxy Far Far Away have a name?

The galaxy we live in has a name: The Milky Way.  Does the galaxy where Star Wars takes place have a name?


Continuing on from the  I also received 3 separate waybill numbers however additionally I was sent 2 SMS messages each wanting me to pay £17 import duty. Each SMS lists one of the waybill numbers I've been emailed.  I have just received my watch and the waybill number it has is the third one, i.e the one that has no invoice associated with it.  What should I do about the two £17 invoices? Seaching for them on DHL's system indicates they do exist and are against my name.


Show that the equation $\cos(\sin x)=\sin(\cos x)$ has no real solutions.

The following problem was on a math competition that I participated in at my school about a month ago:      Prove that the equation $\cos(\sin x)=\sin(\cos x)$ has no real solutions.   I will outline my proof below.  I think it has some holes.  My approach to the problem was to say that the following equations must have real solution(s) if the above equation has solution(s):  $$ \cos^2(\sin x)=\sin^2(\cos x)\\ 1-\cos^2(\sin x)=1-\sin^2(\cos x)\\ \sin^2(\sin x)=\cos^2(\cos x)\\ \sin(\sin x)=\pm\cos(\cos x)\\ $$  I then proceeded to split into cases and use the identity $\cos t = \sin(\frac{\pi}{2} \pm t\pm y2\pi)$ to get   $$ \sin x=\frac{\pi}{2} \pm \cos x\pm y2\pi\\ $$  and the identity $-\cos t = \sin(-\frac{\pi}{2}\pm t\pm y2\pi) $ to get   $$ \sin x=- \frac{\pi}{2}\pm \cos x \pm y2\pi.\\ $$  where $y$ is any integer.  I argued that $y=0$ was the only value of $y$ that made any sense (since the values of sine and cosine remain between $-1$ and $1$).  Therefore, the above equations become   $$ \sin x=\frac{\pi}{2} \pm \cos x\implies \sin x \pm \cos x=\frac{\pi}{2}\\ $$  and   $$ \sin x=- \frac{\pi}{2}\pm \cos x\implies \cos x\pm\sin x= \frac{\pi}{2}.\\ $$  Then, by a short optimization argument, I showed that these last two equations have no real solutions.  First, does this proof make sense?  Second, if my proof makes sense, then I feel that it was not very elegant nor simple.  Is my approach the best, or is there a better (i.e., more elegant, shorter, simpler) proof?


Chrome: Overcoming "file not commonly downloaded" warning

We are a software publisher. Our installer EXEs are signed with our code signing certificate issued by Thawte. Recently, our installers are being flagged as "####.exe is not commonly downloaded and could be dangerous" --the call-to-action being discard.  These files do not have any malware in them. VirusTotal lists no error for the files. These files were created newly but were signed using our certificate that is in use for the past 1 year  On what grounds is Chrome flagging this as "dangerous". How many downloads does it need to be completed before it is no more "uncommon"?  How can we prevent such a dialog from appearing in the future?


I have a very peculiar problem with my ubuntu 18.04 LTS. I press Ctrl+Alt+F1 to go to tty1 as always. And there is the classic screen that you have to login as always. But when I try to login this happens:  I put my username and click enter. Then the password field shows up but the terminal clicks return automatically before me being able to enter my password. Then of course it asks for password again, and then terminal clicks return again. Then the whole login thing resets and asks for username again but terminal keeps clicking return and at some point it completely resets and it stops as if I had just pressed Ctrl+Alt+F1.  Anyone have any clues?   Thanks


In how many ways can $500$ indistinguishable students select books from $10$ titles if no more than $20$ copies of one particular text are selected?

Assume that there are an arbitrarily large number of copies of ten diﬀerent discrete math books (which we will call titles) for cmsc250. Each student must choose one title as the course text book. Assume that the ﬁve hundred students taking the course are indistiguishable.  How many diﬀerent ways can the students choose titles, if Epp must be chosen by at most twenty students?   I understand that this is a stars and bars problem where the formula would be ${n+r-1}\choose{r-1}$, but whats throwing me off is the "at most" parameter of the problem. My answer is ${480+9-1}\choose{9-1}$ My reasoning was that we now have one less "bar", and that should be shown by lowering $r$ by 1  Am I approaching this the right way?


General solution of $x$ if $\sin x+\cos x=1$

General solution to the equation $\sin x+\cos x$=$1$ is found to be $x=2n\pi$ and $x=2n\pi+\pi/2$, Pls refer   My Approach: $$ \sin x+\cos x=1\implies \sin x\frac{1}{\sqrt{2}}+\cos x\frac{1}{\sqrt{2}}=\frac{1}{\sqrt{2}}\\\implies\sin x\cos(\pi/4)+\cos x\sin(\pi/4)=\sin(\pi/4)\implies \sin(x+\pi/4)=\sin(\pi/4)\implies x+\pi/4=n\pi+(-1)^n [\pi/4]\implies x=n\pi+(-1)^n\frac{\pi}{4}-\frac{\pi}{4} $$ How do I check both the results are the same, without inputting the values for $n$ ?


Can a MAC address be altered, or is it like a computer's fingerprint and remains unique to that computer only? If a person has the computer's MAC address, can it be used to identify that computer proving ownership? I'm asking this because I had two laptops stolen and I'm going to go with the police to retrieve them. However, I'm sure the person who stole them will try to say they belong to him. I still have access to the antivirus programs, which also shows the Mac address for all devices registered. That's why it's important that I'm able to somehow prove ownership.


Why Such discouraging and limiting policies for opinion based questions?

I have observed several times, whenever I ask something that relates or compares two things, moderator puts it on hold saying that it will invite chatty discussion.  But why are there such policies? Sometimes, questions are so genuine and unique that very rare or no attention is previously concentrated. But just because they compare two things they are put on hold.   A very recent incident is this: . This question is very genuine and almost rarely concentrated before. But just because it compares Java and OpenMP, it is put on hold. And I observed this mostly happens when Java is compared with some other technology. I suspect sometimes Stack Exchange is biased towards Java and it really doesn't allow to find pitfalls in it.   Doing this I think Stack Exchange discourages people from asking questions. Instead why don't you dedicate one site to such questions?   Being a leading technology forum, I never expected this from Stack Exchange. And I must admit that Stack Exchange is limiting its scope of exploring various technologies and their interdependency, superiority comparisons etc.   If Stack Exchange isn't built for such questions, then where should we post such questions? Because I don't find any other discussion forum as robust and complete as Stack Exchange.


How many onto group homomorhisms are there from $\mathbb Z_2\times \mathbb Z_4$ onto $\mathbb Z_2\times \mathbb Z_4$?

I am trying find the number of onto group homomorphisms from $U(20)$ onto $U(15)$ where $U(n):=\{1\leq r\leq n: (r, n)=1\}$.   Here is what I tried.  Since $U(20)\cong \mathbb Z_4\times \mathbb Z_2\cong U(15)$, it follows that only we need to find the number of onto group homomorphisms from $\mathbb Z_2\times \mathbb Z_4$ onto $\mathbb Z_2\times \mathbb Z_4$. Let $f$ be one such onto group homomorphism. Then by first isomorphism theorem we must have $$\frac{\mathbb Z_2\times \mathbb Z_4}{\ker f}\cong \mathbb Z_2\times \mathbb Z_4.$$  This tells that $|\ker f|=1$ and hence $f$ is an isomorphisms.   NOW ?  How many isomorphisms are there from $\mathbb Z_2\times \mathbb Z_4$ to $\mathbb Z_2\times \mathbb Z_4$: is it a valid question ? If so, what should I reply ?  Can someone show me what I am doing wrong please ?


Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$

Prove via induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$ Having a very difficult time with this proof, have done pages of work but I keep ending up with 1/(k+2).  Not sure when to apply the induction hypothesis and how to get the result $1- \frac{1}{(n+2)!}$.  Please help! thanks guys, youre the greatest!


won't instead of using' wouldn't' is possible?

I had asked a question  in which@Jay also answered.But He used "wouldn't" in the following sentences while answerimg my question:   Here, you wouldn't say, "May I ask you what is your name?" Though we break this rule for questions sometimes Well, someone might say that in informal speech, but you wouldn't write it or use it in formal speech. "May I ask you what's your name?" is awkward; a fluent speaker wouldn't say that.   I had asked  question in ELL and I have also received answers for it. But there is one thing that I'm still confused about.  Do the meanings of the sentences above change if we use 'won't' instead of using 'wouldn't' ? can we use 'won't' in the place of 'wouldn't' without changing the meanings of the sentences above?  Note:This question is all about wouldn't vs won't or are they interchangeable or not)


My school needs me to use office 365 but the online version is broken. Is it possible that I can get office 365 on ubuntu?   Leave a answer below.


As one of my friend got refusal for visit visa and they give him reason that "Your intention to leave the territory of the member states before expiry of the visa could not be ascertained. My question is if he wants to appeal , he has to take appointment again for german embassy to submit letter in person and in the letter that he received they mentioned information regarding appeals that " an action with the Administrative Court in Berlin" , what does that mean ?  Which is the best way to get a visa as soon as possible - by appeal or applying again?


How to make a real bootable Ubuntu USB disk?

So far all of the instructions out there only seem to explain how to make a "trial" version of Ubuntu on a bootable USB disk. I don't want that. Here is what I am looking for:  I have a Windows laptop with no space on it to install a dual-boot of Ubuntu. I am going away on a month long business trip and need my laptop, but I also have a few linux programming projects I am working on and would like to take them with me. I want to install linux onto a USB drive, then copy over my source code. When I have time to work on my projects, I want to be able to simply insert the USB drive, boot to linux and have a fully functioning development environment available to me. When I change my source code, I want that source code to get saved to the USB drive and for it to be persistent so that the next time I boot to linux all of my changes are still there.  When I install the Ubuntu ISO to my USB drive, I can boot to linux, but when I create any source code on it, the source code is gone next time I boot. This will not work. I must have a persistent development environment.  So far I found one thing claiming to give me what I want - a tool called Linux Live or "lili" for short. I used it on two different USB drives and for some unknown reason (even they do not seem to know what is happening) the final step of the install process wipes my USB drives. o_O  Is there truly no way to install a persistent linux development environment onto a bootable USB drive? There must be a way to do it. Can someone please point me in the right direction?  Thank you.


What is the difference between above two sentences?  Would you let me know, why did you go there? Could you let me know, why did you go there?  I guess would is kind of  expecting a yes or no answer, whereas  could is asking for an explanation as an answer. Am I right with my guess?


I have a prolog code for searching a book. It is a simple game. I want to make interfaces with C#. But i don't know how to connect prolog into c#. Please help me. How to conncet prolog with C#.


How to recover data I lost while installing Ubuntu 18.01?

While installing Ubuntu 18.01 I lost all the data in my hard disk. Previously the system was dual booted with Ubuntu 16.01 and Windows 10.   Is there is any possibility to recover my data? If so kindly suggest the way to do it.


I have noticed in my .bashrc that some lines have export in front of them, such as  export HISTTIMEFORMAT="%b-%d  %H:%M  " ... export MYSQL_HISTFILE="/root/.mysql_history"   whereas others don't, such as   HISTSIZE=100000   I am wondering if, first, this is correct, and second what the rule is for using export in .bashrc.


I know how to set up KDE so that I can initially login without a password.  But is there a way to enable login without a password following a logout?


What keeps electrons on a negatively-charged conductor from leaving?

Imagine a negatively charged conductor in a vacuum. The excess electrons will be spread out over the surface such that the net electric field inside the conductor is zero.  What keeps these extra electrons bound to the conductor?   For the case of a neutral conductor, I could intuitively understand some sort of Coulomb force being responsible. But for a negatively charged conductor, I don't understand what (net?) positive entity is exerting the attractive force.   Is there an explanation based only on classical electrodynamics (say, at the level of Jackson). If not, is the explanation purely quantum mechanical?   Basically, how does one model this phenomenon?


Travelling through UK - H1B (Visa stamp expired) but have a UK visitor's visa

I am an Indian citizen. I am going to India on a vacation. I am planning to have my flight via London. I've a layover there at London for almost 5-6 hours. I have a visitor's visa for UK but not planning to visit the city this time, my concern is that my H1 stamp on my passport has expired.    Can I pass through London with expired US visa stamp on my passport as I have UK visitor's visa on my passport?


I know that the proof that every vector space has a basis uses the Axiom of Choice, or Zorn's Lemma. If we consider an axiom system without the Axiom of Choice, are there vector spaces that provably have no basis?


I have the following style:     Anderson, E. (1988), 'Transaction costs as determinants of opportunism in integrated and independent sales forces', Journal of Economic Behavior & Organization Vol. 9 No. 3, pp. 247-264.   How do I make changes to get the following punctuation format?     Anderson, E. (1988), “Transaction costs as determinants of opportunism in integrated and independent sales forces”, Journal of Economic Behavior & Organization, Vol. 9 No. 3, pp. 247-264.   I use the following codes to import from JabRef  \bibliographystyle{agsm} \bibpunct{(}{)}{;}{a}{,}{,}


In academic papers, 'We evaluated X' vs. 'X is evaluated'

As far as I know, it would be better to follow these two rules when writing an academic paper:   Avoid using passive voice. Keep the object of interest in the subject position.   But often I encountered the situations where those two rules contradict each other. For example, in my research field, the typical first sentence of 'evaluation' section (same as the 'experiment' section in other fields) starts with 'We evaluated the system X..', but some people prefer to write it like 'The system X is evaluated..'. To follow rule 1, one should put 'we' in the subject position, but it contradicts rule 2 as the object of interest is 'the system X' rather than 'we'. In such kind of cases, which rule should come first?


Here is my question:  Is a homeomorphism, that is, a continuos function whose inverse function is also continuous, always bijective?


How do I play local SWF files in ubuntu 14.04

today I just upgrade my ubuntu 12.04 to 14.04.  The problem is that I cannot play local swf files.  Even after installing flash player you cannot play swf files.   I can play online flash games in browser but not swf files when you have them downloaded in your computer  Any fix for this problem?  I tried gnash but that won't open swf in browser so the data that I have saved in cookies for that specific swf file won't restore.  This problem is same for all browsers I have tried. (chrome, chromium, firefox)  what I have tried is this command:    sudo update-pepperflashplugin-nonfree --install and this one:    sudo apt-get install flashplugin-nonfree-extrasound  just installed flash plugin for chrome still not fixed this is what I did: downloaded a tar file from adobe then these 3  commands:  sudo mkdir /opt/google/chrome/plugins sudo cp libflashplayer.so /opt/google/chrome/plugins sudo cp –r usr/* /usr   the internal flash player for chromium is activated:   and also I tried gnash which didn't open my file. you can download the swf file from this site:       there is a free version  Temporary solution for this problem is to upload your swf file to a website (then you can view it from browser). I use


I am having a little trouble getting my update manager to refresh. There is an error message ('$ept2nd2006' is not known on line 1 in source list /etc/apt/sources.list.d/eduke32.list):  E:The list of sources could not be read.  Go to the repository dialog to correct the problem. E:_cache->open() failed, please report.    When I try to open the GDebi package installer I get a error:     Software index is broken"(This is a major failure of your software   management system. Please check for broken packages with Synaptic   Package Manager, check the file permissions and correctness of the   file 'etc/apt/sources.list' and reload the software information   with:'sudo apt-get update' and 'sudo apt-get install -f'   I got the same error message when I opened SPM and it closed automatically.  For a brief history of what I initially did. I was following the command script to install eduke32 via the  in the first line of command script, where the long vertical line is, I pressed enter a finished the line of script and then entered my password.   How do I correct this problem?


Solving $k$ element subsets with no two consecutive elements using recurrence relations and generating functions

The problem of $k$ element subsets of an element set such that no two elements are consecutive can be solved using stars and bars approach. But, can it be also solved using recurrence relations and generating functions? Note that the problem of any element subsets can be solved using recurrences which gives a fibonacci number answer. But what about this problem? I think this is not duplicate problem. Any hints? Thanks beforehand.


Claim: The difference between two rational numbers always is a rational number  Proof: You have a/b - c/d with a,b,c,d being integers and b,d not equal to 0.   Then:   a/b - c/d ----> ad/bd - bc/bd -----> (ad - bc)/bd   Since ad, bc, and bd are integers since integers are closed under the operation of multiplication and ad-bc is an integer since integers are closed under the operation of subtraction, then (ad-bc)/bd is a rational number since it is in the form of 1 integer divided by another and the denominator is not eqaul to 0 since b and d were not equal to 0. Thus a/b - c/d is a rational number.


I have a problem with theorem numbering. If anyone has solutions, please help me.  My document has two chapters. In 2nd chapter, one theorem is written and numbering like Theorem 2.1.1. Now I want to state the same theorem with the same number in chapter 1 like I want Theorem 2.1.1 in chapter 1. Please, if anyone has solutions or suggestions, let me know.  I am using the following packages and running the file in LaTeX+DviPs+PDF Viewer+Ps2Pdf setting  \documentclass[12pt]{book} \usepackage[pdftex]{graphicx} \usepackage{epstopdf} \usepackage[centertags]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm} \usepackage{bm} \usepackage{mathrsfs} \usepackage{newlfont} \usepackage{pdfpages} \usepackage[]{cite} \usepackage{booktabs} \usepackage{multirow} \usepackage{rotating} \usepackage{xcolor} \usepackage{fancyhdr} \usepackage{multicol} \usepackage{notoccite} \usepackage{acro} \usepackage{subfiles} \usepackage{import} \usepackage{tabularx} \usepackage{tikz} \usepackage{tkz-graph} \usepackage{longtable} \usepackage{hyperref} \usepackage{breakurl} \usepackage{tabularx,ragged2e,booktabs,caption} \theoremstyle{plain} \usepackage{nomencl} \makenomenclature \renewcommand{\nomname}{List of Symbols} \usepackage[usenames,dvipsnames]{pstricks} \usepackage{pstricks-add} \usepackage{epsfig} \usepackage{pst-grad} % For gradients \usepackage{pst-plot} % For axes \usepackage[space]{grffile} % For spaces in paths \usepackage{etoolbox} \usepackage{threeparttable,placeins,caption,stfloats} \usepackage{enumerate} \usepackage{enumitem} \usepackage{floatrow} \usepackage{mathtools,relsize} \usepackage{latexsym} \usepackage{subfigure,makecell,stfloats} \usepackage{algorithm} \usepackage[noend]{algpseudocode} \usepackage[capitalize,nameinlink]{cleveref} \usepackage{lipsum} \usepackage{xfrac} \usepackage{braket} \usepackage{soul} \usepackage{enumitem} \newlist{symb}{itemize}{1} \setlist[symb,1 {label=,labelwidth=1in,align=parleft,itemsep=0.1\baselineskip,leftmargin=!}


If I have a Java class return escapeHTML format data. Then I want to unescape the information is a JSP script, is there such a way to do so?   only has escapeXml attributes.


Removing WordPress version number from included files

I am trying to remove the WordPress version number from the file extensions for security purposes. Some of the enqueued files include the WordPress version number on the end of them, which can be seen from the inspector. For example:  <link rel="stylesheet" id="admin-bar-css" href="http://sitename.com/wp-includes/css/admin-bar.min.css?ver=3.8.1" type="text/css" media="all">  As you can see, ver=3.8.1 was apended. I've come across a few filters that remove the WordPress version number from the header and footer etc, but not from the included files. That filter looks like:  function remove_version() {     return '';  } add_filter('the_generator', 'remove_version');   But that does not remove the version number from linked files. Does any one know of a way to remove this version number??  Thanks


Can $s_n=1+x+x^2+x^4+x^8+\ldots+x^{2^n}$ be simplified?

Is there a closed form for a finite sum $s_n=1+x+x^2+x^4+x^8+\ldots+x^{2^n}$? I apologize if this has been already discussed. Is there some literature on this I can take a look at?


Can I say "I concur with something" instead of "I agree with something"?

Hi I'm still learning English and I rather have problems with grammar.  So my question is can I use     I concur with this statement   instead of      I agree with this statement   Is it weird? Does it sound unnatural?


error when adding user to wheel group in CentOS 7

I am trying to grant sudo privileges to a user of a CentOS 7 devbox by typing gpasswd -a user wheel, but the attempt is failing.  What am I doing wrong?    Here is what I typed:    I discovered that the user is not in the wheel group as follows:    [user@localhost git]$ sudo yum install git [sudo] password for user:  Sorry, try again. [sudo] password for user:  Sorry, try again. [sudo] password for user:  user is not in the sudoers file.  This incident will be reported.   I then logged in as root and typed the following to add the user to the wheel group:    [user@localhost git]$ su - Password:  Last login: Thu Aug 20 17:11:31 PDT 2015 on pts/0 [root@localhost ~]# gpasswd -a user wheel Adding user user to group wheel [root@localhost ~]# exit logout   I finally tried to use the sudo command again but it failed as follows:    [user@localhost git]$ sudo yum install git [sudo] password for user:  user is not in the sudoers file.  This incident will be reported. [user@localhost git]$


I have tried to do apt-get update in my ubuntu system and has got the following error:  Please help  Hit:17 https://packagecloud.io/slacktechnologies/slack/debian jessie InRelease  Reading package lists... Done                                                    E: The repository 'http://ppa.launchpad.net/ubuntu-wine/ppa/ubuntu artful Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.


Why do some people place the differential at the beginning of their integral?

I've seen several times on this site people writing integrals like  $ \int \! dxf(x) $. This seems confusing to me, especially in an iterated integral or next to a long integrand and it's nonstandard compared to my own personal experience. I'm wondering what are the reasons people use this notation swap and if it has broader support than I'm aware of.


Applying with minors for UK Standard visit visa

I am applying for the UK standard visit visa. I have filled my application and also entered details of my children traveling with me (it suggested that they still need to have separate applications filled)  Now I have started filling my 11 years old daughter's application, and there are few things the form is asking which are a bit confusing:     What is the ownership status of your home   Shall I choose 'other' and highlight that she is not renting it?     How much money are you personally planning to spend on your visit to the UK? (Required)    Should I put the same amount for my daughter as well which I entered for myself?      What is the total amount of money you spend each month? (Required)    Not sure what to fill here, it does not allow me to enter 0, is it OK to enter pocket money amount?