Mail.app in Sierra accumulating Gmail drafts

Just now using MacOs Sierra's Mail client. Compared to what happened on El Cap, which worked fine. It seems that now Gmail is accumulating drafts, in other words, once the email is sent, there may be one or many drafts of the email in the drafts folder. Probably corresponding to how many autosaves happened.  Can I stop this from happening?


Multiple bibliographies without repetitions

I know of multibib and some related packages but, as far as I understand, they do not seem to fit perfectly my needs.   I would like to do the following. A main bibliography would list all items cited in the main text. A second bibliography will list all items cited in footnotes (and, ideally, in other designated environments, such as remarks). The basic idea is to have a short bibliography containing vital references and a longer one containing other references that are not vital but may be intersting.  This is not overly difficult using multibib. My main problem is that I would like to have items cited in the main text and in footnotes to be listed only once in the main bibliography.  Here is a pseudo-code of what I would like to have.  \documentclass{article} % Here a definition of the \citespecial command. \begin{document} Some text \cite{a,b} and there a footnote\footnote{\citespecial{b,c,d}} \bibliographystyle{plain} \bibliography{mybib} \end{document}    The result should have a, b in the main bibliography and c, d in the second one but not b since it already appears in the main bibliography.  I am currently a bibtex user but I can consider using biblatex.  For the record, here is a MWEusing multibib  \documentclass{article} \usepackage{filecontents,multibib} \usepackage{multibib} \newcites{secd}{Secondary References} \begin{filecontents}{essmult.bib} @ARTICLE{a,   author       = "Doe, J.",   title        = "Title, Part 1",   journal      = "Interesting Journal 1",   year         = "1991",   volume       = "1",   pages        = "1--11", } @ARTICLE{b,   author       = "Doe, J.",   title        = "Title, Part 2",   journal      = "Interesting Journal 2",   year         = "1992",   volume       = "2",   pages        = "2--22", } @ARTICLE{c,   author       = "Doe, J.",   title        = "Title, Part 3",   journal      = "Interesting Journal 3",   year         = "1993",   volume       = "3",   pages        = "3--33", } @ARTICLE{d,   author       = "Doe, J.",   title        = "Title, Part 4 ",   journal      = "Interesting Journal 4",   year         = "1993",   volume       = "4",   pages        = "4--44", } \end{filecontents} \begin{document} Some text \cite{a,b} and there a footnote\footnote{\protect\citesecd{b,c,d}} \bibliographystylesecd{plain} \bibliographysecd{essmult} \bibliographystyle{plain} \bibliography{essmult} \end{document}    giving the following result, showing the unfortunate repetition that I am trying to avoid


When should end punctuation go inside quotes?

I have been/am being taught that end punctuation should always go inside quotes. For example, you are supposed to write:     Marvin thought it was "awful."   The problem is I do not see how does this make sense. Intuitively, I always wrote:     Marvin thought it was "awful".   as that makes more logical sense — you want a quote to be an exact replication of what somebody else said, so why should you add punctuation inside?  I always thought it made more sense to not touch the quote and add anything after or before if it must be added.  So, why should I put end punctuation inside quotes?


If a hot beverage in a cup gets stirred, the sound of the spoon changes. You can easily hear this if you repeatedly cling the spoon to the cup ground after stirring. The cling sound will raise in tune for quite a long time.  This even happens if the fluid motion is (almost) stopped after stirring, eg. by using the spoon to do so.  What is the reason for this effect? Why it last so long after stirring?


How does one evaluate a prediction confidence for an SVM?

For an SVM classifier, how can I get the confidence of each prediction ? I thought of adding a "unknown" class, but I don't quite see how to do it ( what values ?)  While theory is highly appreciated, I would be glad if you can give me hint(s) on how to do it in scikit-learn.


How do I return two values from a function?

How do I design a function prototype that would allow a single function to find and return simultaneously both the lowest and the highest values in an array? Thank you.


is there any force on a tennis ball that is being thrown in the forward direction after it leaves the persons hand?

is there any force on a tennis ball causing it to go forward after it leaves the person hands. Any help is much appreciated


How can I use sed to delete lines two (or any number) after a match but not including the match and lines in between?  For example:  Enter command below > login Command valid Enter your password at the below prompt Remember to make sure no-one is looking at your screen > mysecretword Password accepted   I want to only delete the line "> mysecretword" on account of it being two lines after the line "Enter your password at the below prompt". I can't use absolute line number positions, because the match could appear any number of lines after the start of the file.  Searching online I find a lot of solutions like sed '/Enter your password.*/,+3d' filex, but this would also remove the "Enter your password..." line and the following line, which is not what I want. I only want to remove one line, which is a certain number of lines after a match.  How can I do this with sed (or indeed any other commonly-available tool)?


Number ways to distribute $k$ identical objects between $n$ people so that a special group of $a$ people receive odd number of objects among them

Suppose there is a group of $n$ people, and we need to choose exactly $k$ among them to give $k$ identical prizes. Also, exactly $a$ of these $n$ people are special. The problem is to calculate, how many ways are there to choose the $k$ people in such a way that, an odd number of special people are included in the choice? For example, if $n = 5,\ k = 3,\ a = 3$ then there are $4$ possible ways. WLOG, we assume that the first $3$ people $p_1,\ p_2,\ p_3$ are special. Then the possible ways are: $$ (p_1, p_2, p_3)\\ (p_1, p_4, p_5)\\ (p_2, p_4, p_5)\\ (p_3, p_4, p_5) $$ I know the solution to a similar problem where the constraint of odd special people are not present, so we can pick any number of people from the $a$ special ones and the remaining from the $n - a$ non-special ones. There is bijection argument which shows the answer is simply ${n \choose k}$. But I can't seem to find any way to adapt this solution for the above problem with the odd constraint.


What about allowing things like  [Edit this question][edit] [What's on topic?][help/on-topic] [The proposal site][a51]   So they look like                  To reduce answers' and comments' (raw) length.    Oh, there's another thing. Can we have the text auto-generated so that we don't have to write  [Allow custom text for magic links](https://meta.stackexchange.com/questions/296051/allow-custom-text-for-magic-links)   but simply [/q/296051]? That'd be convenient (especially in comments)!


If A is a countable set, how can I show that A has countably many finite subsets?

Lets say that A is a countable set. How would I go about showing that A has countably many finite subsets? I need to show that for every $n \in N$, the set $P^n(A)$ of finite subsets - with exactly $n$ elements - of A is countable. How would I then show how the union $U_{n \in N} P^n(A)$ of all these sets is countable?


How can I make oily material like Nyx Assassin?

One of the characters of the Dota2 that Is called  has an interesting material effect If you look In below gif at the body and feet you can see this effect.It looks like .I like to know how can I make something like this In blender:    I downloaded the  and tried to Implement it but I couldn't do it.    After reviewing the textures , I found a texture as specular wrap It seems that this texture has been used for this effect.I used this texture as specular but not work , I think special shader used to make this effect.


How to handle WordPress Plugin Front-end AJAX Call

I'm developing a custom plugin. The plugin provides a shortcode that outputs some HTML to the front-end, wherever it is called.  For the sake of example, this HTML includes a form button and textfield. When the button is clicked on the front-end, I want to use jQuery to make an AJAX call to fetch some data and populate the textfield. The data is calculated and returned from one of my plugins functions.  What request URL should I use for my AJAX request?  I could create an ajax-handler.php script, place this inside my plugin directory, require the plugin php class, and access its functionality that way, but I am unsure if this is the best practice...  Is there a more efficient / native WordPress way of handling plugin AJAX requests on the front end?


JavaScript: parseInt(1.15*100) = 114 WHY?

So the behavior of parseInt here seems to me to be so bad that I just don't know what to think...  parseInt(1.15*100) = 114


How can I find the determinant of a $n\times n$ square matrix whose all diagonal elements are equal to $a$ and off-diagonal elements are equal to $b$?

How can I find the determinant of this type of square matrix of $n\times n$ $$\begin{vmatrix} a&b&b&b& \ldots&b\\b&a&b&b&\ldots&b\\b&b&a&b&\ldots&b \\ \vdots&b&b&a&\ldots &b \\ b&b&b&\ldots &a&b \\b&b&b&b&\ldots &a \end{vmatrix}_{n\times n}=?$$ I have applied elementary operation: $C_1\to C_1+C_2+C_3+\ldots+C_n$ $$\begin{vmatrix} a+(n-1)b&b&b&b& \ldots&b\\a+(n-1)b&a&b&b&\ldots&b\\a+(n-1)b&b&a&b&\ldots&b \\ \vdots&b&b&a&\ldots &b \\ a+(n-1)b&b&b&\ldots &a&b \\a+(n-1)b&b&b&b&\ldots &a \end{vmatrix}_{n\times n}$$ Applied, $C_2\to C_2-C_3$, $C_3\to C_3-C_4$, $\ldots$, $C_{n-1}\to C_{n-1}-C_n$ $$=(a+(n-1)b)\begin{vmatrix} 1&0&0&0& \ldots&b\\1&a-b&0&0&\ldots&b\\1&0&a-b&0&\ldots&b \\ \vdots&0&0&a-b&\ldots &b \\ 1&0&0&\ldots &a-b&b \\1&0&0&\ldots &b-a&a \end{vmatrix}_{n\times n}$$ $$=(a+(n-1)b)(a-b)^{n-1}\begin{vmatrix} 1&0&0&0& \ldots&b\\1&1&0&0&\ldots&b\\1&0&1&0&\ldots&b \\ \vdots&0&0&1&\ldots &b \\ 1&0&0&\ldots &1&b \\1&0&0&\ldots &-1&a \end{vmatrix}_{n\times n}$$ I got stuck here. I can't find the way to solve this. However the answer is $(a+(n-1)b)(a-b)^{n-1}$. your help will certainly be appreciated. thank you.


Salesforce email says I'm connecting via TLS 1.0 but that protocol does not appear in login history

I received an email recently that reads:     Your org has been identified as having users or integrations still   connecting to Salesforce using TLS 1.0 encryption protocol during the   month of February.   That led me to ask an initial question around how I can figure out who is using TLS 1.0:   Unlike that question, this one is about the email I received from Salesforce, that seems to contradict what I am seeing in the login history. It's not about how I can pull the login history in the first place.  I pulled the login history from Sep 2016 through Apr 2017, and all of my users (and API calls) have been using TLS 1.2. So the email appears to contradict what the logs say. I downloaded all logs available and I filtered on the protocol column in Excel and it only has TLS 1.2. There are zero instances of TLS 1.1 or 1.0 in the log file. The log file includes activity.  Is it safe to assume that I'm only using TLS 1.2 since that is what the logs say? I'm just concerned about the Salesforce email stating otherwise.


What are my options for sending email from my VPS with a Blacklisted IP

I have postfix and dovecot running on debian 7, I can send mail fine, but it keeps going to my spam folder when sent to google accounts. Another user who doesn't use gmail said it was delivered to his inbox. When I send a test message to myself I get the following headers:  Delivered-To: chaoskreator@gmail.com Received: by 10.170.37.203 with SMTP id 194csp288892ykf;         Fri, 29 Aug 2014 21:45:25 -0700 (PDT) X-Received: by 10.236.70.105 with SMTP id o69mr20864964yhd.25.1409373925239;         Fri, 29 Aug 2014 21:45:25 -0700 (PDT) Return-Path: <webmaster@beansworthy.fluidvector.com> Received: from fluidvector.com ([2605:f700:100:400::875a:4b61])         by mx.google.com with ESMTPS id s36si567167yhp.30.2014.08.29.21.45.24         for <chaoskreator@gmail.com>         (version=TLSv1.2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128);         Fri, 29 Aug 2014 21:45:24 -0700 (PDT) Received-SPF: softfail (google.com: domain of transitioning webmaster@beansworthy.fluidvector.com does not designate 2605:f700:100:400::875a:4b61 as permitted sender) client-ip=2605:f700:100:400::875a:4b61; Authentication-Results: mx.google.com;        spf=softfail (google.com: domain of transitioning webmaster@beansworthy.fluidvector.com does not designate 2605:f700:100:400::875a:4b61 as permitted sender) smtp.mail=webmaster@beansworthy.fluidvector.com Received: from localhost (localhost.localdomain [127.0.0.1])     by fluidvector.com (Postfix) with ESMTP id 725E7123A0C9F     for <chaoskreator@gmail.com>; Sat, 30 Aug 2014 00:45:23 -0400 (EDT) X-Virus-Scanned: Debian amavisd-new at fluidvector.com Received: from fluidvector.com ([127.0.0.1])     by localhost (fluidvector.com [127.0.0.1]) (amavisd-new, port 10024)     with ESMTP id oI9bUVMx6Thv for <chaoskreator@gmail.com>;     Sat, 30 Aug 2014 00:45:19 -0400 (EDT) Received: by fluidvector.com (Postfix, from userid 33)     id 17DA0123A0CA1; Sat, 30 Aug 2014 00:45:19 -0400 (EDT) To: =?UTF-8?B?dGVzdA==?= <chaoskreator@gmail.com> Subject: =?UTF-8?B?V2VsY29tZSB0byAiQmVhbnNXb3J0aHki?= X-PHP-Originating-Script: 1000:messenger.php From: <webmaster@fluidvector.com> Reply-To: noreply@fluidvector.com   I notice the lines   Received-SPF: softfail (google.com: domain of transitioning webmaster@beansworthy.fluidvector.com does not designate 2605:f700:100:400::875a:4b61 as permitted sender) client-ip=2605:f700:100:400::875a:4b61;     Authentication-Results: mx.google.com;            spf=softfail (google.com: domain of transitioning webmaster@beansworthy.fluidvector.com does not designate 2605:f700:100:400::875a:4b61 as permitted sender) smtp.mail=webmaster@beansworthy.fluidvector.com   which I assume means there's an issue with my SPF TXT DNS record: v=spf1 a:fluidvector.com ~all, even though pySPF says it's good.  I've looked up on mxtoolbox.com and found that for some reason, my IP (which I obtained from my VPS provider) is apparently blacklisted on Barracuda and spamcannibal. I've contacted my VPS provider, but they didn't seem to be able to do anything for me. So, at this point I assume I'm limited to just contacting the black lists and pleading to have my IPs removed? What are my options here? Can I get gmail to let mail from my servers be delivered to inbox instead of the spam folder without the headache of trying to get unlisted?


Earth occupation/invasion book I read in the 90s

I remember a TON of details, but I can't for the life of me find the title of this book.  The story takes place during Earth's occupation by a race of red-skinned, black-eyed, three-fingered aliens, and involves an attack on the planet by other aliens that resemble Swiss army knives. That race's name starts with an H.  The protagonists are a young boy whose mother works for the chief of the occupying race and the chief's daughter.  It was a hardcover book. The cover featured both protagonists. The boy was in a blue shirt with a V neck, very 60s era Trek looking. The female protagonist was described as wearing a cloak and was possibly depicted that way on the cover. Her three-fingered hand was DEFINITELY depicted on the cover. And yes, the invading aliens were described as resembling army knives or multitools, but the exact term swiss army knife might not have been used. All of the occupying alien structures were described as open domes. The female protagonist mentioned that her ancient people lived on open plains ...while ancient humans lived in caves, and that's why modern humans lived in houses and this alien race preferred domes. This is a paraphrase of an exact exchange between the two protagonists (taken from comments. Ooops!)  I'm located in the US. I read this book in junior high between fall of 1996 to spring of 1997, but it was not a new book. If I had to guess, based on 20-year-old memories, it felt like, or I remember it looking like, it was published in the 70s. But I can't be certain.  The cover, on top of featuring both protagonists, may have also featured geometric shapes: cones, spheres, cubes. But I watched a LOT of UPN in those days.  Has anybody ever heard of this book?


How is the trace of the adjoint of Lie algebra elements defined?

Consider an element $X\in\mathfrak g$ of some Lie algebra $\mathfrak g$. I understand that $\mathfrak g$ can be represented via its action on other elements of the same algebra, as $\operatorname{ad}(X)Y\equiv[X,Y]$, so that $\operatorname{ad}(X)\in\operatorname{GL}(\mathfrak g)$.  One often considers things such as the trace of these objects (e.g. when considering the Killing form), or more generally the "matrix elements" of operators such as $\operatorname{ad}(X)$.  However, I usually don't see any direct mention of the inner product with respect to which these things are defined. To properly define what something such as $\operatorname{ad}(X)_{ij}$ is, don't I need to be able to define uniquely the coefficient of the generator $X_i$ in the decomposition of $[X,X_j]$ (denoting with $\{X_i\}$ the elements of some basis for the algebra)?  Is there a canonical choice of such inner product? And on a similar note, do we just usually assume that the basis of the Lie algebra is orthonormal (or at least orthogonal) with respect to this inner product?


Splitting a list or collection into chunks

I have a program that will read the contents of a file into some sort of list or array.  This list/array could contain any number of items.  I need to split it into smaller groups, say of 50 items each and then do some processing on each item in each group.  List<string> stuffFromFile = new List<string>();  while ((line = fileReader.ReadLine()) != null)       {            stuffFromFile.Add(line);       }   I have been looking through some examples online about how to chunk stuff but to be honest, I don't really understand the examples and some of them seem overly complex.  I just need something simple that will chunk/split/break the original list of items into groups of 50 and then let me iterate through each item in each group until the processing is complete.  The total number of items read in will most likely not be a number that I can divide evenly by 50 so most likely the last group may contain less than 50 items, but would still need to be processed just like the rest.  Can anyone help here?  It sounds like it should be simple but I don't really know how to do it.  I've seen example about using LINQ but I don't understand it either.


When Luke went to look for Yoda on the planet Dagobah, he   landed/crashed quite close to Yoda's home.  This implies Dagobah is a rather small planet. I mean, if it was as big as the Earth or Mars, I guess it would be rather unlikely to   find Yoda that quickly. Luke would have to fly above the planet's surface until he either senses a force-sensitive entity (that might be a first test of how good Luke is in using the force) or Yoda made himself recognizable somehow.  I'd say Dagobah can't be much bigger than Pluto. And given the fact that it has an Earth-like surface gravity it seems to be very dense too. Dagobah's atmosphere doesn't seem to be very high either and it's fully cloudy/foggy which again implies a small and dense planet. Wookieepedia claims the planet is 14,410 kilometers (8,954 miles) in diameter but that seems unlikely.   How would Luke find Yoda otherwise that quickly on an entire planet bigger than Earth?


The order of adjectives: Is it exactly the same in GB, the USA, and elsewhere in the English-speaking world?

When learning the order of adjectives in a sentence, I thought up a word "saSHcomp" standing for the  order.   Later, I  found out that there's a slightly  where the shape of a noun comes before its age.  So, both "an old round thing" and "a round old thing"  are correct and the order of the adjectives depends on the variant of the English one's using, British or American.  My question is as follows:  Might the confusion of these orders influence negatively the results of English grammar level tests taken in Great Britain or in the USA?   Can the use of this or that order manifest, in one single sentence, the origin of the writer, British or American, or, to be more exact, where they lived when they came to school?   Do native English speakers themselves ever confuse this order in the writing?   What's the order of these two adjectives that is used in the English-speaking world beyond GB and the USA — especially in Canada, Australia, and South Africa?


"Aura Integration Service Error" When installing a private package

Our clients see this error when they try to install a new version of our package. I read  and  that this is because our package is not publicly listed on AppExchange. We don't want to list it yet but want to be able to install upgrades. As of now, no matter what we do, the installation link forwards to the (nonexistent) landingpage. How can this be resolved?


Why would an incorrect password attempt take a lot longer to process than a correct one?

The most prominent place I've noticed this is when SSH-ing at work, but I feel like I've observed this behaviour elsewhere too.  When I try to log into Linux servers from my Windows desktop at work, I've noticed that if I mis-type my password, it takes a good 5 seconds or so before I get "Access Denied" back. Then when I type my password correctly, the login (along with welcome messages etc) is virtually instant.  Is there any logical reason for this, or would it be down to some odd configuration that's specific to the machines here at work?


Redirect loop when trying to login to /wp-admin/

Stuck in an infinite loop when trying to log in to my wordpress site. I type in the URL/wp-admin and then it loops me back to the regular website, not the admin login page.   I have tried with http and https to no luck...


Tunneling data over SSH is pretty straight-forward:  ssh -D9999 username@example.com   sets up port 9999 on your localhost as a tunnel to example.com, but I have a more specific need:   I am working locally on localhost host1 is accessible to localhost host2 only accepts connections from host1 I need to create a tunnel from localhost to host2   Effectively, I want to create a "multi-hop" SSH tunnel. How can I do this? Ideally, I'd like to do this without needing to be superuser on any of the machines.


Find matrix of linear transformation in the standard basis

I have a linear transformation $A$.  In basis ${(1,1),(1,2)}$  $A= \begin{bmatrix} -1 & -1\\4 & 6 \end{bmatrix}$  Find $A$ in the standard basis ${(1,0),(0,1)}$  The teacher told us the answer, but i have no idea how to get it:  $A= \begin{bmatrix} 1 & 2\\3 & 4 \end{bmatrix}$


A little bit of context, I read the sentence below after the system - a computer application - has been subject to a certain kind of update:     The system will be able to not create a record of that movement   anymore.   I think they are trying to stress the new behavior of the system compared to the previous one, hence that sentence construction.  Firstly, would it sound better if we changed the sentence for something like this where we get rid of the split infinite:     The system will be able not to create a record of that movement   anymore.   At least for me that sentence construction seems a little bit odd and something an English native speaker would not say, do you agree with me or is it perfectly acceptable?


How to sort a Google Sheets Query by a custom ordering

I have a table of choir members with a “name” and a “voice type” column. How can I write a query that orders them by decreasing pitch level of the voice type (i.e. soprano > contralto > tenor > bass)?  Is there in the  something similar to ?  I also tried the , but it does not seem to have an option for custom ordering, either.


If $x^2+ax+b=0$ has a rational root, show that the root is an integer.

So far I have  Assume $a,b,x,y$ are integers; $\frac xy$ is rational; and that $\frac xy$ is in simplest form.  WTS: $\frac xy$ is integer  So $(\frac xy)^2 + a(\frac xy) + b = 0$;  ${x^2\over y^2} = -b - a(\frac xy)$;  $x^2 = -by^2- axy$;  $x^2 = y(-by - ax)$;  so $y$ divides $x^2.$  I am having trouble on how to show that $\text{gcd}(x,y)=1.$


How does shutting down require sudo except when done through a GUI?

If I want to shut down my machine programmatically or on the terminal, I must do sudo poweroff or sudo shutdown.  If I want to shut down my machine through my window manager and desktop environment, I navigate to my application menu and click "shut down".  This does not require my password.  How is this implemented?


I am working on AIX unix and trying to remove non-printable characters from file the data looks like Caucasian male lives in Arizona w/ fiancÃÂÃÂÃÂÃÂÃÂ in file when I view in Notepad++ using UTF-8 encoding. When I try to view file in unix I get ^▒▒^▒▒^▒▒^▒▒^▒▒^▒▒ instead of the special characters.  I want to replace all those special characters with space.  I tried sed 's/[^[:print:]]/ /g' file but it does not remove those characters.My locale are listed below when I run locale -a  C POSIX en_US.8859-15 en_US.ISO8859-1 en_US   I even tried sed -e 's/[^ -~]/ /g' file and it did not remove the characters.  I see that others stackflow answers used UTF-8 locale with GNU sed and this worked but I do not have that locale.  Also I am using ksh.


question about cyclic groups and quotient groups

Is a quotient group always cyclic.  I see nothing on the internet that tells me it's the case, but since a quotient group: $\Phi : G \rightarrow G/H$ such that $\Phi(g) = gH$ Its kernel is H therefore intuitively, this implies the notion of cyclic groups


Constructing an explicit isomorphism between finite extensions of finite fields

Suppose $K$ is a finite field, $K = \mathbb F_{p^s}$. If we take an irreducible polynomial $f$ of degree $d$ over $K$, then the splitting field $L$ of $f$ is $K(\alpha)$ where $f$ is the minimal polynomial of $\alpha$. But then $L = \mathbb F_{p^{sd}} $. Since $\mathbb F_{p^{sd}}$ is unique, we see that this is the splitting field of every irreducible polynomial of degree $d$ over $K$.   Take $K = \mathbb F_2$ and let $P(X) = X^3 + X + 1$, $Q(X) = X^3 + X^2 + 1$. Let $L$ be the splitting field of $P$ and $L'$ be the splitting field of $Q$. The above tells us that $L$ and $L'$ are isomorphic. I would like to construct an explicit isomorphism between $L$ and $L'$.   I know that $L \cong \mathbb F_2[X] /(X^3 +X + 1)$ and $L' \cong \mathbb F_2[X] / (X^3 + X^2 + 1)$. Intuitively, I want to find an isomorphism $\phi : \mathbb F_2[X] \to \mathbb F_2[X]$ such that $\phi((X^3 + X + 1)) = (X^3 + X^2 + 1)$. A little playing around gives me $\phi(X) = X+1$. It now feels like I'm falling at the last hurdle: how do I finish the construction of an isomorphism between $L$ and $L'$? I don't think $\phi$ makes sense as a map from $L$ to $L'$, yet it seems the map I want.


How do I trigger just once and not multiple times if I the Player enters the Trigger?

I wanna trigger just one time and not multiple times. I have a Health System and I want that the Player takes damage from an GameObject if he enters the Trigger but it directly triggers like 65 times in a sec. how can I trigger just once ?  I dont have a Script attached to the GameObject what should give the Player Damage, it just have a Box Collider 2D. The Code for the Trigger enter has the HealtScript that is attached to the Player.  Here is my HealthScript  public Image Bar; public float maxHealth = 100f; public float currentHealth = 0f;   // Use this for initialization void Start ()  {     currentHealth = maxHealth;     InvokeRepeating ("decreaseHealth", 0f, 2f); }   void decreaseHealth() { //  currentHealth -= 5f;     float calchealth = currentHealth / maxHealth;     SetHealth (calchealth); }  void SetHealth (float myhealth) {     Bar.fillAmount = myhealth; }  void OnTriggerEnter2D (Collider2D other) {     if (other.gameObject.tag == ("Damage"))     {         currentHealth = -5f;     } }   }


Start menu and "action center" cannot be opened in Windows 10

After about 2 months from updrading from Windows 7 Home Premium to Windows 10 I am having weird issues: When I click Windows icon, nothing happenes - Windows menu is not opened.  The same happens when I press the (Win) key on keyboard - Windows menu is not opened.  Also clicking on sound menu does not do anything - sound control does not appear.  The same with Action Center: Clicking the icon does nothing.  Restart of computer helps, but temporarily: After some time the icons do nothing. Is there something I can check or do in order to fix this?  Edit: Microsoft Windows [Version 10.0.10586] is the build of the system


error LNK2019: unresolved external symbol template

I am learning how to use template in c++ language ,my program is just simple linear search program which i use just for understanding purpose while compiling the program compiler constantly giving me this linker error   Error   1   error LNK2019: unresolved external symbol "public: __thiscall searching<int>::searching<int>(int)" (??0?$searching@H@@QAE@H@Z) referenced in function _main C:\Users\Sachin\Documents\Visual Studio 2012\C++\template\template\Source.obj   template Error   2   error LNK2019: unresolved external symbol "public: __thiscall searching<int>::~searching<int>(void)" (??1?$searching@H@@QAE@XZ) referenced in function _main    C:\Users\Sachin\Documents\Visual Studio 2012\C++\template\template\Source.obj   template Error   3   error LNK2019: unresolved external symbol "public: void __thiscall searching<int>::set_data(void)" (?set_data@?$searching@H@@QAEXXZ) referenced in function _main   C:\Users\Sachin\Documents\Visual Studio 2012\C++\template\template\Source.obj   template Error   4   error LNK2019: unresolved external symbol "public: void __thiscall searching<int>::get_data(void)" (?get_data@?$searching@H@@QAEXXZ) referenced in function _main   C:\Users\Sachin\Documents\Visual Studio 2012\C++\template\template\Source.obj   template   Header.h  #include<iostream> using namespace std; typedef int BOOL; #define TRUE 1 #define FALSE 0  template <class t> class searching { private :     t *ptr;     int isize;     BOOL sort;  public:     searching(int);     searching(searching &);     ~searching();      BOOL linearsearch(t);     BOOL linearsearchbi(t);     BOOL binarysearch(t);     void set_data();     void get_data();     BOOL chechsorted();  };   main.cpp  #include "Header.h"  int main() {      searching <int>obj1(10);     //searching <float>obj2;       obj1.set_data();     obj1.get_data();     obj1.linearsearch(5);     return 0; }   helper.cpp  #include"Header.h"  template <class t> searching <t>::searching(int ino) {     isize =ino;     ptr= new <t> [isize]; }  template <class t> searching <t> ::searching(searching  &ref) {     isize=ref.isize;     ptr=new <t>[isize];      for(int i=0;i<isize;i++)     {         ptr[i]=ref.ptr[i];     } }  template <class t> searching <t>::~searching() {     delete []ptr; }  template <class t> void searching <t>::set_data() {     cout<<"Enter "<<isize<<" element"<<endl;     for(int i=0;i<isize;i++)     {         cin>>ptr[i];     } }  template <class t> void searching <t> ::get_data() {     cout<<"Eelements are :"<<endl;     for(int i=0;i<isize;i++)     {         cout<<ptr[i]<<endl;     } }  template <class t> BOOL searching <t>::linearsearch(t value) {     int i=0;      for(i=0;i<isize;i++)     {         if(ptr[i]==value)         break;     }     if(i==isize)     {         return FALSE;     }     else     {         return TRUE;     } }   I have tried moving all the definitions from the helper.cpp to header under class but compiler still gives me error is there any thing i need to change in this code please guide me. Thanks in advance.


i don't have much knowledge about dns records and devops things. I'm just trying to achieve ;  I have an Ec2 instance on amazon. I create a CNAME record for and successfully redirected to ec2 instance.  I would like to know is it possible to subdomain to given port number for ec2 instance i mean; I have 2 node.js applications are running on my ec2 server one of them is listening to 80 port which is providing web content. CNAME record is just working fine with that application.  My other application is listening to 5575 port. i would like to have . that is point to ec2's 5575 port. is it possible to have something like that. I found SRV record thing but i'm not sure if it's correct record type for me.


Why is my function returning NaN although I've used Number() function?

I am trying to create a very simple multiplier function.  Although I've used Number() function, I still get NaN upon calling the function.      let x = prompt("1. sayı"); let y = prompt("2. sayı"); let num1 = Number(x); let num2 = Number(y);   function multiply(num1, num2) {   let result = num1 * num2;   alert(result); }  multiply();


Where does Linux get Swap partitions to mount

I have recently added a second swap partition for my third system (Two of which are Linux).  My aim was to have a single dedicated swap space for each of the systems so that it would not cause any problems when swap-sharing.  Making the appropriate changes to /etc/fstab, I rebooted... Only to have the first system load both of the available swap partitions.  My question is, are there any other ways a system can mount a partition other than those listed in /etc/fstab?  cat /etc/fstab output  UUID=9034-ACC1  /boot/efi       vfat    umask=0077      0       1 UUID=ece74c78-21b5-4c37-ad97-2dcbd98c1d50 /home           ext4    defaults        0       2 UUID=78ab45f8-1a54-49b3-b7a9-48afc6a95054 none            swap    sw              0       0 /dev/sr0        /media/cdrom0   udf,iso9660 user,noauto     0       0 UUID=de651abc-dcc4-472a-8bb6-64d0e89cdc30 /tmp ext4 defaults,noauto 0 2 UUID=f5019f7b-d758-4aee-8261-424ca5813b75 /var ext4 defaults,noauto 0 2 UUID=477bf58b-c602-4116-afea-7e8914adbf56 / ext4 errors=remount-ro,noauto 0 1   Yet cat /proc/swaps yields  Filename                Type        Size    Used    Priority /dev/sda15              partition   6291452 0       -2 /dev/sda8               partition   6179836 0       -1   fdisk -l  Disk /dev/sda: 931.5 GiB, 1000204886016 bytes, 1953525168 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disklabel type: gpt Disk identifier: E7779D9B-ADD0-40D7-A257-C1DEF6AC0E35  Device     Type                         UUID /dev/sda1  Windows recovery environment 84D97802-5484-4905-85D5-39A6C394635F /dev/sda2  EFI System                   FF3F087C-3E1F-428B-A3A6-3083444059F9 /dev/sda3  Microsoft reserved           0BE8D02B-398F-4D93-9A71-8C1AE98FBF20 /dev/sda4  Microsoft basic data         8F0537C3-D0CF-413C-9417-FA2436FF1583 /dev/sda5  Windows recovery environment 7CC71CC6-F1D9-4693-AB32-5DB177867815 /dev/sda6  Linux filesystem             A20F3F7B-4EA3-4749-9601-B9D879B19498 /dev/sda7  Linux filesystem             5829D354-8018-43FD-9738-B31A82C0073B /dev/sda8  Linux swap                   F8FCB0F2-38EC-4A3C-92CB-7196DC7AEAF0 /dev/sda9  Linux filesystem             31174EC2-06E4-4963-8302-273994431B65 /dev/sda10 Linux filesystem             BC658257-DBE5-40D0-9CD1-CEC46E1913BC /dev/sda11 Linux filesystem             E1E3A130-EA53-48B4-A130-4CF349964A41 /dev/sda12 Linux filesystem             359F6EC1-D937-43E6-A3E3-DDC8E457C0CC /dev/sda13 Linux filesystem             82092B42-981D-4F67-977F-6A3F034B365E /dev/sda14 Linux filesystem             278ACACC-B8CC-4169-8A79-E9812F59B035 /dev/sda15 Linux swap                   33BF80B8-A409-4AD5-B778-836974BAA8C3  Partition table entries are not in disk order.   I tried repacking the initramfs, checked that the resume variable is not set wrong, and only one of the two systems does this.


Suppose $I$ is the ideal $(xy, yz, zx)$ in $R =\Bbb R[x, y, z]$. I want to compute the primary decomposition of $I$.    I have viewed many post on this topic, as I suspect, the primary decomposition of $I$ would be:  $$ (xy, yz, zx)= (x,y)\cap(x,z)\cap(y,z),$$  but I cannot show how.


Is it possible to draw graphs like the image below in LaTeX?


How to calculate the chance of two persons sharing the same birthday

I am reading a book and they state that "in a group of 23 people, the probability is 50.7% that two people share the same birthday"  How can this be?  Could somebody point to me how to calculate the 50.7% figure?  Many thanks in advance


An interesting inequality involving prime numbers

Could someone provide some help in how to  prove the following inequality involving prime numbers: $p_{n+1}\leq\ p_1p_2\cdots p_n + 1,\qquad(n\geq1)$ I tried induction(the base of induction is obvious: $3 = 3$ so it works). But in the case of induction step, I don't know how to proceed.


Why does adding more neutrons to an atom unstabilise it? Won’t adding more neutrons increase the strong force and thus knit the nucleus more tightly? Or is it because it’s being added in a particular place, the force is polarising part of the nucleus so it splits?


I want to learn ios development . I have read a few blogs and the first step seems to be learning Objective-C. Since I don't have a Mac, I want to find out if there is any way I can run objective-C on Windows& pc?


Evaluating the limit of $\lim_{x \to 9} \frac {x-9} {\sqrt{x} - 3}$

How do you evaluate the limit of  $$\lim_{x \to 9} \frac {x-9} {\sqrt{x} - 3}$$  by first principle? I was thinking of this way to evaluate but it seems to evaluate to $\frac {0} {0}$.  $$\lim_{x \to 9} \frac {x-9} {\sqrt{x} - 3} = \frac{\lim_{x \to 9} (x-9) }{\lim_{x \to 9}  {\sqrt{x} - 3}}$$  I mentioned that the limits do not exist because the function is not continuous at $ x=9$. Any idea on how to solve this question?


How can I create a link in Java Swing Application?

I wanted to create a Swing GUI , in which there should be a text which in event handling works as a JButton. import javax.swing.*; import java.awt.*; import java.awt.event.*; class Gui implements ActionListener { JFrame jf=new JFrame("Link"); JLabel jl=new JLabel("CLICK HERE"); Gui() { jf.setSize(400,400); jf.setVisible(true); jf.setDefaultCloseOperation(jf.EXIT_ON_CLOSE); jf.setLayout(null); Font f=new Font("Arial",) jl.setBounds(50,50,100,50); jf.add(jl); jl.addActionListener(this); } public void actionPerformed(ActionEvent ae) { JOptionPane.showMessageDialoge(null,"Clicked in link"); } public static void main(String arg[]) { new Gui(); } }  How can I create a text into a link in a Java Swing GUI? Please suggest a proper code.


Why when importing an obj file nothing appears even when zooming?

I have opened a new blender file and deleted the default cube, then imported an obj file . I did not see any thing so i selected it and i zoomed ,nothing appears.In the outliner i saw the object name ,But in the info panel i see that there isn't any verts/faces/edges.  When i opened the obj file in a text editor i found Mesh data in it. I tired this in all blender versions (2.78c/2.78.5/7.9). Can any one help how to view the mesh?


Question put on hold by moderators. Why was that since question has not met an answer?

It was me who asked  question. It was a duplicate but it had not satisfied any solutions of the original question. I mentioned it over comments and even then it was put on hold. A lot after that I found my exact solution over . So why was that put on hold even when it's not solved?


Does an Intel 1.80GHz quad core processor meet the 2GHz dual core processor system requirements?

My laptop has an Intel® Core™ i5-3337U CPU @ 1.80GHz × 4 processor. On the Ubuntu website, it says that I need a 2 GHz dual core processor as a requirement to install Ubuntu 18.04. Does this mean that I cannot install it?  Here are the full specs of my laptop:


QGIS: Delete information from rasters and shapes that are out of country borders

I am trying to make topographic maps for some countries and show only those countries. I already created reliefs from SRTM-data and imported lake and river data from Natural Earth. Now I want to delete all raster and shape information that is out of the country (in my example down there, Peru). The country is another shapefile from Natural Earth.  Long story short: How do I delete all the stuff out of Peru?


In the “community selection” drop down menu, my reputation on a particular meta site has been displayed 100 points smaller than the true amount for at least a week or so. The behaviour is consistent across different browsers on several devices, and independent of which SE site I use to view the drop-down. Note that this is not just a case of changes of reputation from the main site being out of sync with the meta site, as the reputation is displayed correctly in other places (e.g., in my profile on the meta site).


What is the advantage of Dual-Band Wireless?

I've been looking around for a good wireless router, and I've been seeing a lot of dual-band routers, but everyone I've asked at the stores seems to give me a different answer as to what it actually does. So I'd like to ask the wireless gurus over here at SU, what are the advantages and disadvantages to using the cliche dual-band wireless routers?


prove or supply counter example about graph

Let $G = (V, E)$ be a cycle of length $4n$ and let $V = V_1 \cup V_2 \cup  ... \cup V_n$ be a partition of its $4n$ vertices into n pairwise disjoint subsets, each of cardinality 4. Is it true that there must be an independent set of $G$ containing precisely one vertex from each $V_i$? (Prove or supply a counter example.)  I think this is not right because just consider square with four vertices and four edges,but I have doubt that it is proper counter example.please help with your knowledge,thank you very much.    actually this is exercise 4 of chapter 5 from alon spencer probabilistic method.so I also tag this question as mentioned.


PuTTY or OTHER - Keep executing command even after exiting PuTTY

I have a couple of commands that I need to run. These commands needs to continually run even after I exit my interface. When I have access to the Linux GUI, I execute something like:  cd /home/testuser/Scripts* xterm -hold -T "Background_Script1" -e  "service1-start.sh" & sleep 10 xterm -hold -T "Background_Script2" -e "service2-start.sh" &   Any help will be much appreciated.


Most accurate Map of Arda before Beleriand was lost

I am making my own Lotr themed Risk game and I am having trouble finding a very accurate map of Arda before beleriand was lost. This map should include Valinor and Numenor as well.  The best I can find so far appears to be a map from David Day's "Tolkien Bestiary"  I hope this is not a bad question, I am new.


If $B$ is nilpotent and $AB=BA$ then $\det(A+B) = \det(A)$

The following stumps me:     Let $\mathbb K$ be a field. Let $A, B \in \mathbb K^{n \times n}$ where $B$ is nilpotent and commutes with $A$, i.e., $A B = B A$. Show that $$ \det(A+B)=\det(A) $$   I have no idea how to approach this I thought perhaps raise both sides to a power but nothing works. Thanks for all help.


Tempest Cleric: when does Wrath of the Storm trigger?

I had a question regarding this ability and what causes it to trigger. It says a 'hit' but does a hit necessarily include a damage roll or does this include when an attack is above the character's touch AC but not the character's total AC?   Here's the description of the ability.     Wrath of the Storm      Also at 1st level, you can thunderously rebuke attackers. When a creature within 5 feet of you that you can see hits you with an attack, you can use your reaction to cause the creature to make a Dexterity saving throw. The creature takes 2d8 lightning or thunder damage (your choice) on a failed saving throw, and half as much damage on a successful one.   You can use this feature a number of times equal to your Wisdom modifier (a minimum of once). You regain all expended uses when you finish a long rest.


"No such file or directory" as error for wrong architecture

I'm trying to run a  on my 64 bit Ubuntu. and it results in a following error:  $ ./arm-none-eabi-gcc bash: ./arm-none-eabi-gcc: No such file or directory   The file is here and contains some data:  $ ls -la arm-none-eabi-gcc -rwxr-xr-x 2 alan alan 776368 Sep 26 19:36 arm-none-eabi-gcc $ head -n 1 arm-none-eabi-gcc ELFا4�          4  (44�4�  TT�T���|�   ldd shows there are no dependencies required:  $ ldd arm-none-eabi-gcc not a dynamic executable   strace also provides no additional info:  $ strace ./arm-none-eabi-gcc execve("./arm-none-eabi-gcc", ["./arm-none-eabi-gcc"], [/* 80 vars */]) = -1 ENOENT (No such file or directory) write(2, "strace: exec: No such file or di"..., 40strace: exec: No such file or directory ) = 40 exit_group(1)                           = ? +++ exited with 1 +++   Finally I figure out that it's for a 32 bit system:  $ file arm-none-eabi-gcc arm-none-eabi-gcc: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), dynamically linked, interpreter /lib/ld-linux.so.2, for GNU/Linux 2.6.8, stripped   Question  If the architecture of the binary is wrong why is the error so ambiguous?  I would expect analogous to the below situation where I'm trying to execute a .JPG, where the binary execution makes no sense:  $ ./DSC_0140.JPG  bash: ./DSC_0140.JPG: cannot execute binary file: Exec format error


I have a method in an interface that I want to deprecate with portable C++. When I Googled for this all I got was a Microsoft specific solution;  and . A second prize solution would be to ifdef a MSVC and a GCC solution.


Visiting Istanbul for a few hours while on a layover with Turkish Airlines - how do I get a visa, if I need one?

I am an Indian passport holder. I am travelling to Greece via Istanbul (Turkish Airline) from 10th to 25th June. My return flight to New Delhi from Athens has an 8 hour layover and I am considering applying for a transit Visa to take a look around Istanbul for a couple of hours. However, my Schengen Visa application is already under process and I haven't declared on the Schengen Visa application form that I intend to apply for a Turkey transit Visa. Will it pose a problem? If not, can I apply for an e-Visa and get a transit Visa for Turkey online? What do I need to keep in mind? This is my first international travel and any advice is appreciated. Thanks! Sruti


Transit visa Nigeria and India via Germany

I'm an Indian citizen who is living in Lagos, Nigeria. I have an Indian passport and a Nigerian residence permit. I'm planning to go for the following trip. All my flights will be from Lufthansa and will have a stopover in Frankfurt or Munich.  Leg 1: Lagos, Nigeria -> (Frankfurt) -> London, UK (Possess single entry tourist visa for UK) Leg 2: London, UK -> (Munich) -> New Delhi, India Leg 3: New Delhi, India -> (Frankfurt) -> Lagos, Nigeria  Leg 1 seems fine because my destination is London and I hold a visa for it. I however unsure of whether I'll require a transit visa for leg 2 and leg 3. The lufthansa page tells me  Indian nationals can Transit without Visa via FRA or MUC if holding a valid visa for the destination and a valid Visa for any of the following countries. Bulgaria, Canada, Cyprus, Ireland, Japan, Liechtenstein, Romania, UK and USA (the approval notice I-797 is not valid document for visa free airport transit).  I do hold a multiple entry tourist visa to the US that is valid during this travel period. However, I'm unsure of whether it is sufficient as none of my legs have a US destination.


Wasted screen space due to multiple horizontal bars at the top when an application is open in GNOME desktop

Just moved from Unity to GNOME with the update to Ubuntu 17.10. There is a HUGE amount of wasted space at the top of the screen, when an application is open.  Evolution and Firefox both have four "bars" with 90% of each empty. Unity, to its credit was able to blend / mix these horizontal bars so there was only one / two.      Four is way too much. If this is GNOME I may carry on with Unity for the next six months.  Can anybody suggest a tweak/change/fix for this?


Java Constructor with object array NullPointerException

I've tried to implement a hash table myself without data structures provided by JDK. (such as Linkedlist...) So I tried to implement a hash table by implementing an array of linked lists. However, it returns NullPointerExcetion.  This is main code.  public static void main(String[] args) {     HTable test = new HTable(500000);     for(int i = 0; i < 50000; i++) {         BigInteger s = BigInteger.ONE;         for(int j = 0; j <= 0; j++) {             s = s.multiply(BigInteger.valueOf(37));         }         if(test.insert(s, String.valueOf(s))) {}     } }   and HTable is below.  class HTable { static int length; Linkedlist[] HT; HTable(int size) {     ...     Linkedlist[] HT = new Linkedlist[sample];     for(int j = 0; j < sample; j++) {         HT[j] = new Linkedlist();     }     length = sample; } public boolean insert(BigInteger i, String s) {     int sum = 0;     String[] i_toString = (i.toString()).split("");     System.out.println(i_toString[0]);     int[] data = new int[i_toString.length];     int[] multiple = new int[i_toString.length];     data[0] = Integer.parseInt(i_toString[0]);     multiple[0] = (int) Math.pow(data[0], (int)Math.log10(length));     ...     int index = sum % length;     if(HT[index].isEmpty()) {         HT[index].insertAtFront(i, s);         return true;     }     for(Iterator v = HT[index].getIterator(); !v.atEnd(); v.next()) {         if(v.getdata() == i) {             return false;         }     }     HT[index].insertAtFront(i, s);     return true; }   and finally, this is Linkedlist code.  class Linkedlist { public Node first;  public Linkedlist() {     first = null; }  public boolean isEmpty() {     return (first == null); }  public void insertAtFront(BigInteger x, String y) {     Node newnode = new Node();     newnode.data = x;     newnode.payload = y;     newnode.next = first;     first.prev = newnode;     first = newnode; }   I have been struggling to identify the problem, but I could not find a clear solution. However, I found that in inner constructor, HF[index] can be used, but in HTable.insert can't.  Why is that?


Why is travelling around the speed of light a problem?

I don't fully understand what would happen if we could travel at the speed of light. But I saw somewhere here that it would mean events happen out of order. But why is this a problem. It is said that cause has to happen before the effect, but why does this have to be linear?   And why is it that the speed of light is the maximum? I take it that light (photons?) are massless, so why can't they travel faster?


I have a whole bunch of people I would love to follow or at least check out on Stack Overflow. I know them from places like Github as well as personal friends. However I am having a really hard time finding them even though I know e.g. their Gmail address and that they use OpenID via Gmail to login and their full name.   How come this is so painful? Note that I don't want to have to fuzz around with the data explorer just to find a friend of mine on Stack Overflow. What am I missing? Is it just not there or just not working properly?


So I was assigned this homework problem: $$\ {s \choose s} + {s+1 \choose s} +...+ {n \choose s} = {n+1 \choose s+1}$$ for all s and all $n \geq s$ I've tried to email both my professor and my TA and their explanations seem contradictory. My professor responded saying the statement I need to prove is "The formula is correct for $0 \leq s \leq n$." Whereas my TA told me I need to use induction on both variables and I'm not sure how to do that. Any help is appreciated!


After update screen boots to black screen with login/password

I installed a large update and haldway through it crashed. After leaving it for an hour I reset the machine and now it boots to a black screen stating the following:  Ubuntu 16.04.1 LTS Stephen-NM70-M tty2 Stephen-NM70-M login:  No idea how to recover from this. Please help.  Thanks,


Derivation of the density function of student t-distribution from this big integral.

My lecturer posed a question where we derive the density function of the student t-distribution from the Chi-square and Standard normal distribution. I worked on this question for days, and I am pretty sure the below integral is correct (Verified by others)  $$f_T(t)=\int_{-\infty}^\infty|x|2nx\times \frac{\frac{1}{2}^{\frac{n}{2}}}{\Gamma\left(\frac{n}{2}\right)}(x^2n)^{\frac{n}{2}-1}e^{-\frac{1}{2}x^2n}\frac{1}{\sqrt{2\pi}}e^{-\frac{(xt)^2}{2}}dx$$ where n is the degree of freedom of the t-distribution and $\Gamma$ is the gamma function from the Gamma distribution. My goal is $$f_T(t)=\frac{\Gamma[(n+1)/2]}{\sqrt{n\pi}\Gamma(n/2)}\left(1+\frac{t^2}{n}\right)^{-(n+1)/2}$$  I was given 2 hints. To proceed, I need to do integration by parts first, then I should use the fact that the Gamma d.f integrates to 1. From this point on, I am unsure, but I shall show you my steps.  We know that the d.f of the Gamma density with parameters $\alpha=\frac{n+1}{2} \lambda=\frac{1}{2}$ integrates to $1$, that is $\int_{0}^{\infty}g(t)dt= \int_{0}^{\infty}\frac{\frac{1}{2}^{\frac{n+1}{2}}}{\Gamma\left(\frac{n+1}{2}\right)}t^{\frac{n+1}{2}-1}e^{-\frac{1}{2}t}dt=1$ Let $t=x^2n$.  Therefore,      $dt=2xn\,dx$ We have $\int_{0}^{\infty}g(t)dt=\int_{0}^{\infty}g(x^2n)2xn\,dx=\int_{0}^{\infty}\frac{\frac{1}{2}^{\frac{n+1}{2}}}{\Gamma\left(\frac{n+1}{2}\right)}(x^2n)^{\frac{n+1}{2}-1}e^{-\frac{1}{2}(x^2n)}2xn\,dx=1$ This should be useful because I noticed the $\Gamma[(n+1)/2]$ in the end result.  Working on the big integral now... $f_T(t)=\int_{-\infty}^\infty|x|2nx\times \frac{\frac{1}{2}^{\frac{n}{2}}}{\Gamma\left(\frac{n}{2}\right)}(x^2n)^{\frac{n}{2}-1}e^{-\frac{1}{2}x^2n}\frac{1}{\sqrt{2\pi}}e^{-\frac{(xt)^2}{2}}$ $=\frac{\Gamma[(n+1]/2)]}{\sqrt{n\pi}\Gamma(n/2)}\int_{-\infty}^\infty \frac{\sqrt{n\pi}\Gamma(n/2)}{\Gamma[(n+1]/2)]}|x|2nx\times \frac{\frac{1}{2}^{\frac{n}{2}}}{\Gamma\left(\frac{n}{2}\right)}(x^2n)^{\frac{n}{2}-1}e^{-\frac{1}{2}x^2n}\frac{1}{\sqrt{2\pi}}e^{-\frac{(xt)^2}{2}}dx$ After a load of manipulation, $=\frac{\Gamma[(n+1]/2)]}{\sqrt{n\pi}\Gamma(n/2)}\int_{-\infty}^\infty 2nx \frac{(\frac{1}{2})^{\frac{n+1}{2}}}{\Gamma [(n+1)/2)] }(x^2n)^{\frac{n-1}{2}}e^{-\frac{1}{2}(x^2n)}\times2n|x|e^{-\frac{(xt)^2}{2}}dx$ Note that the first half is integrate to 1. Hence I do by parts.  But I still cannot get to my goal. I had tried this question for at least 6 times already now. Can I get some help? I tried to type these out as neatly as I knew how.


Wubi with 14.10 doesn't work - failed to partition the selected disk

I tried to install Ubuntu 14.10 on my computer with Wubi. The installation appeared to work in Windows, and told me to reboot.   After rebooting the Ubuntu installer continued the installation, until it stopped with an error message: Failed to partition the selected disk with the detail This probably happened because are too many primary partitions in the partition table.


Is the use of the introductory word first awkward or confusing in the following paragraph if I don't include another sentence starting with secondly?     In the process of learning them, I deeply felt that there were many more obstacles to overcome for girls than for boys in order to learn technology. First, generally speaking, girls are not as good at logical thinking or as familiar with various softwares as boys are. Another related fact is that professors tend to hire boys as their research assistants, which means that boys are given more opportunities to practice their technologies.    I do not use secondly to follow the adverb first. Do you think this makes my writing less clear? I myself sometimes find the use of "first, second" awkward.


Why is there a Swedish English keyboard Windows 10?

I have a Swedish Windows 10 computer and I made it to have 3 keyboards: Swedish, American English and French. But in the keyboard list, there is a fourth language, Swedish English, as you can see in the screenshot:    I went into language settings (by clicking on the språkinställningar button in the screenshot) and I could only see the three languages that I want: Swedish, American English and French. I clicked on each of these three languages and on the button Options and in each case, there was only one keyboard, the one for the language. To make this more clear, here is a screenshot of the options for American English:    It's the same for all other languages except that the only keyboard in the keyboard list is Swedish for Swedish and French for French.  I also tried deleting the Swedish and English keyboards and leaving only the French one (which is the only one that has nothing to do with Swedish English) and the Swedish English keyboard is still there.  The Swedish English doesn't seem to be anywhere in the settings, but it still shows up. Why is this? How can I take it away?


Historical stock prices: Where to find free / low cost data for offline analysis?

I am looking for a free way to get a large amount of data on the prices of stocks.  I am not a trader or anything like that so it wouldn't be worth it to pay for a service to give me stock prices. I have a mathematics background and I would like to make my own determinations of what stocks to invest in. To do this, I need some data.  Is there any free place online to download data on various stock prices over the last few years?  I would probably like to do this for a few stocks so it would be good if it could somehow be in a text file or a csv rather than having to type it out myself.  I know there are websites that crunch the numbers for you but I would prefer to do it myself.  EDIT: If there aren't any free services, where should I look for cheap ways to get the data I need?


How to Calculate the Sum of Coefficients in a Polynomial with known Integer Roots

I have this problem: given $N$,  $1 \leq N\leq 100$ integers which are roots from a polynomial, calculate the sum of coefficients from that polynomial  for example: given $3$ integers $2$, $2$ and $3$, I can calculate the polynomial $$x^3 - 7x^2 +16x -12,$$ so the sum of coefficients is $-2$  but if I have $100$ integers, I think calculating the polynomial will be enormous, so is there some way to find this sum of coefficients?


The set of algebraic numbers is a field.

I need help proving  this stunning result.  Let me state it this way.  Let  $\mathbb L$ be a field and $\mathbb K$ be a field with $\mathbb K \subset \mathbb L$  Let $A$ be the set of algebraic numbers ie $A=\{a \in \mathbb L, \exists P \in \mathbb K [X], P(a)=0 \}$  I managed to prove that $A$ is a ring with the following reasoning:  If $a,b \in A$ then $ \mathbb K[a]$ is a ring.  And $ \mathbb K \subset \mathbb K[a] \subset \mathbb K[a][b] $  Some finite-dimension argument(ask details if needed) proves that $\mathbb K[a][b]$ has finite dimension as a vector space over the field $\mathbb K$  Reminding that $\mathbb K[a+b] \subset \mathbb K[a][b]$ and $\mathbb K[ab] \subset \mathbb K[a][b]$ proves that they both have finite dimension, hence $a$ and $b$ algebraic.  How should I proceed with inverses ?


I have no idea what to do. How do i fix this eye sore?        Answer: The Problem was my start clipping distance was at the lowest setting. Increase the setting and everything will be good.


Prove if d | a, then d | ca for any integer c. Correction

I am frustrated because this is literally exercise 3 from my textbook and I still can not get it. I already failed my first midterm. I am wondering why I am bad with discrete mathematics, but love calculus?  Anyway, how do I solve this? I have tried looking for the same problem but to no avail.  Please help thanks.


Is sour cream in olde recipes the same as sour cream today?

I have a really old cookbook (about 1890) that calls for soured cream or sour cream in some recipes. Is this the same as the stuff you get in a tub at the store or is it like sour milk where you put vinegar in say, heavy cream??


I want to use the align environment inside a list but the equation shouldn't be centered with respect to the pagewidth but with respect to the intented block of the list.   A minimal example:  \documentclass[12pt,a4paper]{amsart} \usepackage[utf8]{inputenc} \begin{document} Some text.. \begin{itemize}     \item Very import point:     \begin{enumerate}         \item Yet another very important point substantiated by a long equation         \begin{align*}             x^2+y^2+5\int_{10003}^{10033455}\sin x\;dx+\tan^2(74638263x^2)=1.         \end{align*}      \end{enumerate} \end{itemize} \end{document}   I want to have the long equation centered under point (1).


How do Time Lords prove to others that they are the same person as their past regenerations?

Not sure if this is addressed in the old series:  Suppose that there is this famous Time Lord that invented chess, and one morning he regenerates and no one witnesses it.  How do Time Lords prove to others that they are the same person?  Since the regeneration thing is managed by those High Council guys, I suppose that they are able to verify it somehow. But what about the rest of the community? How can they tell, trivially, if this new face is truly the inventor of chess, and not somebody impersonating him?  I'd imagine that a TARDIS, which is apparently linked to its owner, can serve as credentials. But I doubt everybody has a TARDIS - besides, that's probably not the most convenient way to show people who you are.  And finally, I'm not sure, but it looks like most Time Lords have some sort of tool (like the Doctor's screwdriver, or the Master's deathstick), which I guess is good for credentials - but heck, the impostor could've just stolen it.


Higher-order Weyl dependence of geodesic distance

This is a screenshot from Polchinski String Theory Vol 1. Can anyone please explain how to derive these identities ?


How can/should I include annotated images?

It's often the case that I'd like to include some graphic in a LaTeX document and overlay it with some text or other annotation, maybe including arrows or other simple graphics. The annotations can be easily handled using TikZ, so obviously if I create the graphic itself in TikZ, I'm all set. But sometimes the graphic is very complex and it's not practical to recreate it with TikZ commands. In these cases, I would like to include the graphic file directly, but still be able to layer my annotations over it. Editing the image to include the annotation is a possibility, but I'd really like to avoid that because the annotations then wouldn't reflect the document's font style and size, and also because it'd be harder to change them.  Is there a preferred way to include an external image and then layer additional content over it? A solution that lets me continue to use TikZ for the annotations is preferred, but not required.  EDIT: All three answers (overpic, a TikZ node, and \pgftext) work fine, but unfortunately I can only accept one, so I'm going with the one recommended in the "official source," the TikZ manual.


How to show the angle is $\frac{\pi}{2}$ which between tangent of an ellipse and its chord that through the focus?

The proposition is told to me without proof, may it is true but I cannot to believe it with my heart before I get the proof of it or the lights. I got some problems, however, after I try to proof it.   Let there is an ellipse $E(a,b)$ $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ then its auxiliary circle is $x^2 + y^2 = a^2$ and tangent of $(x_0,y_0)$ of the ellipse is $$\frac{x_0x}{a^2} + \frac{y_0y}{b^2} = 1.$$  Let $P$ is on both the auxiliary circle and the tangent, and $F = (-c,0)$ is the focus and $P_0 = (x_0,y_0)$, how to show $\overrightarrow{FP} \cdot \overrightarrow{P_0P} = 0$ ?   May one can show it by find out the point $P$. Let $m = \frac{x_0}{a^2}$ and $b = \frac{y_0}{b^2}$ thereby the equation become $mx + ny = 1$. Put it into the circle then $$\begin{aligned} (na)^2 &= (nx)^2 + (ny)^2 = (nx)^2 + (mx - 1)^2 \\ &= (n^2 + m^2)x^2 - 2mx + 1\end{aligned}$$  or $(n^2 + m^2)x^2 - 2mx + 1 - (na)^2 = 0$. Thereby the roots are $$x = \frac{2m \pm \sqrt{D}}{2(m^2 + n^2)} = \frac{m \pm \sqrt{n^2((m^2 + n^2)a^2 - 1)}}{m^2 + n^2}$$ where $$\begin{aligned} D &= 4m^2 - 4(m^2 + n^2)(1 - (na)^2) = 4(mna)^2 + 4n^2((na)^2 - 1)\\ &= 4n^2((m^2 + n^2)a^2 - 1) \end{aligned}$$  If bring the $\frac{x_0}{a^2}$ and $\frac{y_0}{b^2}$ back into the equation of the roots, how can one easily look out $\overrightarrow{FP} \cdot \overrightarrow{P_0P} = 0$ ?   Or, to find out the solutions of equation $\overrightarrow{FP} \cdot \overrightarrow{P_0P} = 0$ first, $(x - x_0, y - y_0) \cdot (x + c,y) = 0$ it is. Thereby $(x + c)(x - x_0) + y(y - y_0) = x^2 + y^2 + (c - x_0)x - y_0y - cx_0 = 0$. I would like to see $a^2 = (x_0 - x)x + y_0y + cx_0 $ but the $x$ and $y$ are variables such that look like impossible.   Let $E(a,b)$ is set of points of the ellipse such that $p  \in E(a,b)$ have form $(a\cos \theta, b\sin \theta)$. And let there is a matrix such that $C(r) := E(r,r) \cong E(a,b)$ which $$A = \begin{bmatrix} \alpha & 0 \\ 0 & \beta \end{bmatrix}.$$ Thereby $$\alpha = \frac{a}{r},\ \beta = \frac{b}{r} \ \mathrm{and}\ A^{-1} = \begin{bmatrix} \alpha^{-1} & 0 \\ 0 & \beta^{-1} \end{bmatrix}. $$  Therefore $Ap' = (-a\dot{\theta}\sin \theta, b\dot{\theta}\cos \theta) = (Ap)'$ where $p \in C(r)$. Can it be used to bring the question into problem of circle and its tangent, then carry the solution back to the question of ellipse and its tangent ?


Multiple authors in one row with refmark, multiple affiliations in separated columns in another row

I wonder how we can list author names in the following format in LaTeX.   I have 5 authors with 3 different affiliations. I am trying to list all author names with refmark in one row, and 3 affiliations with refmark in another row, but each in one separated column. It should look like this:          author1{1} author2{2} author3{1} author4{2} author5{3}            {1}department      {2}department        {3}department               school              school              school               email                email              email   I did saw some papers that have the above format, but cannot search for any guideline. IEEE guideline suggests another way to list authors, but sadly it does not look that neat          author1{1} author2{2} author3{1} author4{2} author5{3}                         {1} department, school                               email                         {2} department, school                               email                         {3} department, school                               email


I've been scouring the internet for this and I'm pretty sure it's an /ɛ/ or /ei/ but I've also seen it pronounced as a long /i/ (as in beat) or as a weird /aeo/.


Can we get rid of the 'Comments are not for extended discussion; this conversation has been moved to chat.' "feature"?

I truly loathe the 'Comments are not for extended discussion; this conversation has been moved to chat.' (air-quotes)"feature". Semantically, it does not even make sense: why move a conversation to chat? What makes a chat-room suitable for conversation?   I like the comments section. In fact, I've profited and learned more from the comments on answers (and often not the accepted answers) than from the answers themselves. Moving these fruitful and enlightening conversations kills them, perhaps even prematurely. The flow is broken, the context is lost, the conversation is dead.  Granted, my experience is mostly on StackOverflow. But take this question on Worldbuilding: . If ever there was a topic that invites extended discussion, surely this is it. I was going to comment on an answer in which a just-so story was presented as historical fact, but was blocked by 'Comments are not for extended discussion; this conversation has been moved to chat.'. I checked out this chat and it was dreadful. Only a few lines of the long answer were visible, and the context of the original question and the other answers was completely lost. It felt like a closet to which the undesirables had been banned, whiling away their exile in random shouting.  To me the whole concept seems flawed. Why would StackExchange discourage extended discussion? Why have a "chat" feature at all? The internet is replete with chatter -- why do we need to facilitate and encourage more chat? Why not encourage discussion?   I understand the need to curb idle, off-topic or overly personal chattiness, but then let's do that. Rename "Comments" to "Discussion" and flag the chatter, like we do offensive or aggressive comments. Gently chastise the chatterers with a cupcake, and reward those contributing to extended discussions in a meaningful way with a badge.


Scorpion Whip - how does it actually work?

The Scorpion whip says:   This whip has a series of razorsharp blades and fangs inset along its tip. Benefit: It deals lethal damage, even to creatures with armor bonuses. If you are proficient with whips, you can use a scorpion whip as a whip. Weapon Feature(s): performance (plus disarm, reach, and trip if you are proficient with whip.)  This seems very unclear though. Does it have 15' reach? Does it threaten? (At 5'? At 10'? At 15'?) Does it do nonlethal damage if used at 15'? I've found quite a bit of discussion online but mostly people arguing, nothing definitive.


There's all kinds of research on how to make something cut through the water with minimal resistance, but what if resistance was exactly what you wanted? What kinds of shapes create above-average resistance with water? Also, does the hydrophobicity of a material affect its fluid-resistance in water? Because hydrophobic materials are pretty jagged...but they also repel water. Note that this is different than drag as drag deals with aerodynamics.


I just bought new macbook pro, and opened up my terminal . it shows: (base) Jiui-MacBookPro:~ myname$ I want to change that "Jiui" part that is located in front of -MacBookPro. How can I do that? I know how to change that "myname" part but don't know in front of that macbookpro. Please save me :(


Prove if a function is uniformly continuous on open interval, it is continuous on closed.

Suppose $f: (a, b) \rightarrow \mathbb{R}$ is uniformly continuous. Prove that $f$ can be extended to a continuous function on $[a, b]$.


Many people say 4.10 was the first version of Ubuntu. However, a article i saw said that Ubuntu 4.10 was the first version open to the public, and that 4.04 was a development version not open to the public and 1.0 existed (and was quickly obsolete), too. Is this true?  Notes:   In your answer, you can also add why it wasn't true, or why it is true. This has nothing to do "What is the first version?". It's a question asking "Is 4.04 and 1.0 real?". This is not a duplicate.


Stack Exchange is intermittently failing at random areas. Some issues experienced by me and others:  I got logged out and couldn't log in Stack Overflow intermittently goes down saying it's unavailable Search is broken everywhere Posting was broken at some point/is still broken now


Google not indexing a recent WordPress post

Recently I've published my recent WordPress post on my blog. Normally whenever I post something on my blog It gets indexed almost instantly. But that didn't happen with my recent post.  I've asked from some of my colleagues about this incident and they told google can take up to 4 to 5 days to index new content. So I checked after 3 days by searching site:mydomain.com and I got my new post in results. In fact, it was ranking on the first page with targeted keywords.  But now after a week, It is again removed from the Google index. even its not coming by typing site:example.com.  I think this post appears to be suspicious to google bot because of this paragraph:     After implementing this technique I had reduced the response time from   1.5  seconds to under 170 milliseconds. So you can expect a 94% reduction in server response time if you also have a response time of   1.5 seconds or above.   Also, I've tried requesting google to index the new post from google webmaster.  Not this question is not only about Google not indexing a page. Google did index this page but now it has been removed from the index.  Update The content in the post is 100 % unique.


Stay in the Schengen area for two consecutive 180-day periods

Can I use a balance remaining from my first 180-day period and add 90 days from my second 180-day period, without leaving the Schengen area?


What is the difference between "use" and "utilize"? Which one is more common?      utilize : to use something in an effective way       "The vitamins come in a form that is easily utilized by the body."   It is also possible to use "use" in the example. Right?


How to UV map and what s the point of it?

hi, as you can see i ve made a shipping container model with many polygons, i d like now to apply textures on it, i d like to use Substance Painter to do that, I saw on youtube that you need to export the fbx file from blender and open it on substance painter. do i need to create a UV map to apply textures anyway?


how a microcontroller or microprocessor is called as 8 bit, 16 bit?

In what basis a micro controller or a microprocessor is classified as 8bit and 16bit?


I live in Norway. Is there a site where I can read Bleach online legally? I have tried to look, but I have not found a suitable site yet.


I tried to 3d camera track my footage in blender and my solve error was 1.1846 and I didn't think that was that bad. I set the lens to 14mm because that was the lens I was using with my Panasonic g7, I did the refine K1, K2 thing and I set three points as the floor and set one as the origin so I don't know what went wrong. I was using a Steadicam as well so I think it was pretty stable What it looked like:   I just started blender not long ago so it is probably something obvious lol


In Star Trek Discovery episode three, why let the tardigrade out?

In Star Trek Discovery episode 4, one of the crew members deliberately lets out the (seemingly) murderous and invincible . Unsurprisingly, this doesn't end well. Why would she do that when she must have known that a phaser would not stop it and that it would kill her and most likely her crew mate too?


Cannot switch keyboard layout at GDM login

I just put my drive with my existing Ubuntu 17.10 installation from my old into my new laptop which has a different keyboard layout and I noticed that the functionality to switch keyboards is missing. There is no icon in the menu bar and pressing super + space also does nothing. It works fine at the desktop and at the lockscreen, just not in GDM… it's working on Fedora though and I did nothing fancy there either.  I compared Fedora GDM config in /etc with Ubuntu, no luck.  Please tell me what's required to get it working.  I prefer to use Wayland, if your answer suggests configuring something related to X11 please explain why.  Edit:  Here is what I see in Region & Language, there is no Login Screen button as far as I can see.    Edit 2:  As requested by Gunnar Hjalmarsson:  $ cat /etc/default/keyboard  XKBLAYOUT=de,us,gb XKBVARIANT=,intl, BACKSPACE=guess


Java Generics: Generic type defined as return type only

I'm looking at some GXT code for GWT and I ran across this use of Generics that I can't find another example of in the Java tutorials. The class name is  if you want to look at all of the code.  Here are the important parts:  private RpcMap map;  public <X> X get(String property) {   if (allowNestedValues && NestedModelUtil.isNestedProperty(property)) {     return (X)NestedModelUtil.getNestedValue(this, property);   }   return map == null ? null : (X) map.get(property); }   X is defined nowhere else in the class or anywhere in the hierarchy, and when I hit "go to declaration" in eclipse it just goes to the <X> in the public method signature.  I've tried to call this method with the following two examples to see what happens:  public Date getExpiredate() {     return  get("expiredate"); }  public String getSubject() {     return  get("subject"); }   They compile and show no errors or warnings.  I would think at the very least I would have to do a cast to get this to work.  Does this mean that Generics allow a magic return value that can be anything and will just blow up at runtime?  This seems counter to what generics are supposed to do.  Can anyone explain this to me and possibly give me a link to some documentation that explains this a little better?  I've went through Sun's 23 page pdf on generics and every example of a return value is defined either at the class level or is in one of the parameters passed in.


CPU platform is changing after resizing the instance

I am using GCE for nested virtualization. I am aware of the specific CPU architecture to be used for nested-virtualization compatibility.  Everything is going smoothly and I am using this feature without any issues, however, if I apply the recommendation for instance resizing I noticed that this feature 'nesting virt.' is not available.  I know this by running command grep -cw vmx /proc/cpuinfo and lsmod.


Is it possible to display the text in a TextBlock vertically so that all letters are stacked upon each other (not rotated with LayoutTransform)?


Which is correct: "on foot" or "by foot"?

He went there on foot.   Or     He went there by foot.   Which one is correct, and on what basis?


Why did she implant this memory illegally?

In , there is a plot twist in which we find out that K's childhood memory, which turned out to be a real memory,      was actually Dr. Ana Stelline's memory, and so while K's memory wasn't a fake memory, it wasn't his, she had implanted it.   It's explained that using real memories to implant to androids is illegal. It's one thing that she may have broken the law, but my question is: why implant the memory into K/other androids? Did she have an alterior motive or some idea that it could eventually lead to that person finding her father?


OP getting me to do the work for them over time

I've answered this question for a new user that wasn't originally worded like a "do my work for me" type of question, but has since turned that way through discussion in the comments.   They have posted a link to their code and asked how they should tweak it, to which I responded with help.  Then they responded with something to the effect of "We're almost there. Just a few more tweaks. Try doing it with something like..."  They're very clearly trying to drag the complete solution out of me. How should I go about dealing with this OP?


How to redefine a command properly to avoid recursive call to itself?

I'm trying to renew a command in terms of its old definition... something similar to this:  \renewcommand{\vec}[1]{\vec{\mathbf{#1}}}   But this seems to send the interpreter in an infinite loop. How do I do this properly?


Why is the color of fire is yellow or blue sometimes?

If you light up any thing it burns in yellow and as well when you light up a gas stove it burns in blue color. What brings this color change?


QUESTION 1 I'm trying to figure out the seemingly subtle difference(s) between a sentence modified by a bare infinitive and one modified by a participle phrase. What do you get out of these:   I watched her run across the bridge --> verb of perception followed by bare infinitive I watched her running across the bridge --> participle phrase   I don't get why and when I should choose a bare infinitive over a participle phrase.   QUESTION 2 Also, 'watch' is a verb of perception, isn't it, similar to 'see'. - I'm not sure if that explained the differences between watch and see, though; I might or might not have missed it.


Alternative to AlwaysAppendSearchDomains on Yosemite?

Since Lion, I have used the AlwaysAppendSearchDomains trick on mDNSresponder to resolve names with dots in search domains.   In yosemite this doesn't work any more. In fact, mDNSresponder doesn't seem to be running:  $ ps ax | grep -i dns | grep -v grep $


Why does an conditionally convergent infinite series, when deranged, have a different limit?

$\sum u_n = 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\dots$ conditionally converges to $\log 2$; and, when deranged to $\sum u'_n = 1-\frac{1}{2}-\frac{1}{4}+\frac{1}{3}-\frac{1}{6}-\frac{1}{8}+\dots,$ converges to $\frac{1}{2}\log 2$. Why does a deranged conditionally convergent series have a different limit? First Course in Math Anal, p.93, by Burkill, explains that the sums $s_n, t_n$ of the first n terms of the two series are different functions of $n$. This reasoning is incomplete, because different functions of $n$ can converge to the same limit; for example, let $r_n$ be the first $2n$ terms of $\sum u_n$, then $s_n$ and $r_n$ are different functions; besides, by differently defining terms, i.e. clustering pieces of a series, e.g. \begin{align*} 1-\tfrac{1}{2}-\tfrac{1}{4}+\tfrac{1}{3}-\tfrac{1}{6}-\tfrac{1}{8}+\dots = \left(1-\tfrac{1}{2}-\tfrac{1}{4}\right)+\left(\tfrac{1}{3}-\tfrac{1}{6}-\tfrac{1}{8}\right)+\dots \\ = \left(1-\tfrac{1}{2}-\tfrac{1}{4}+\tfrac{1}{3}-\tfrac{1}{6}-\tfrac{1}{8}\right)+\dots,\\ 1-1+1-1+\dots = (1-1)+(1-1)+\dots \\ =(1-1+1-1)+\dots,\\ 1+1+1+1+\dots = (1+1)+(1+1)+\dots \\ = (1+1+1+1)+\dots, \end{align*} one gets the sum of first n terms as different functions, but the series's limit remains. One could view a changed limit from the perspective of the changed number of terms, Denote 'countably many', the size of natural number, as $\lvert\mathbb{N}\rvert$, then $\lvert\mathbb{N}\rvert = \lvert k\mathbb{N}\rvert = \lvert\mathbb{N}\times\mathbb{N}\rvert$. Then two series with different numbers (e.g. $\lvert \mathbb{N}\rvert$, $\lvert k\mathbb{N}\rvert$) of terms– and so having different limits– paradoxically have same number of terms–and so are possibly formed by the same terms. The paradox could be the fundamental reason. Are there other explanations? Is the use here of 'countably many' is proper?


Which textbook is good for introductory group theory?


My application requires me to drop voltage from 12v to 6v or any other lower voltage.  I have used resistors but they are not efficient for prolonged use as they tend to heat up and burn my fuse. I want to know whether there are any other IC or a simple circuit which 'll be small in size, inexpensive, efficient and does not heat up much to cause problem.


I have a Scott Speedster 30 Aluminum bike 2016 with 10speed Shimano Tiagra Flat pedals stock wheels...  I seek advice What reasonable upgrades can I make and benefits  Thanks


Java translating error. I am trying to take user input and translate it to values in an array

I am making a translator that takes english and translates it into a made up language called Talhamr. To do this I take user input and make it into an array. Then I test it against a word bank array that contains english words with the corresponding Talhamr word next to it. If the english word works I want to replace it with the corresponding Talhamr word. Can any one help me code this? bellow is the code I have so far.  Main class:  import java.util.Scanner;  public class Translator {     public static String userInput = "";      public static String[] wordBank = {"a/an","Ai","about","circa" /*...*/};      public static void main(String[] args) {         /**          * getting input          */         Scanner scanner = new Scanner(System.in);         System.out.print("Write something to be translated into ancient language: ");         /**          * formatting input          */         userInput.toLowerCase();         userInput = scanner.nextLine();         String[] wordArray = userInput.split(" ");         /**          * Creating a, and preforming english to talhammir, translation          */         EtoT e2t = new EtoT();         e2t.translateToTalhamr(wordArray, wordBank);         System.out.println(wordArray[0]);         /**          * This is how I formatted the word bank. After I went to quizlet and changed all the spaces between rows and columns to "-"          * String makeNice = ...;          * System.out.println("\""+ makeNice.replace("-", "\",\""));          */      }//end of main method    }//end of Translator class   Second class containing translation method:  public class EtoT {     /**      * establishing word bank to loop through and translate      */     public String[] wordBank = {"a/an","Ai","about","circa" /*...*/};      public EtoT() {     }      public String translateToTalhamr(String[] wordArray, String[] wordBank) {         for (int i=0; i < wordArray.length; i++) {             System.out.print("'");             for (int j = 0; j < wordBank.length; j++) {                 System.out.print(".");                 if (wordBank[j] == wordArray[i]) {                     System.out.print(",");                     wordArray[i] = wordBank[j + 1];                 } else {                     wordArray[i] = wordArray[i] + "!";                 }             }//end of inner word bank         }//end of outer for loop         System.out.println("\n" + wordArray.toString());         return wordArray.toString();     }//end of translateToTalhamr      public static void main(String[] args) {     }//end of main method }//end of EtoT


I got stung by bees in animal crossing new leaf and None of the people have offered medicine. I don't know how to upgrade nookling junction. If anyone has gotten medicine from the following please tell me:  Walt, Bruce, Pietro, Alice, Derwin, Bluebear, Frobert, or Diana.  Where am I supposed to get the medicine for my bee stings?


javac is still not recognized, I tried everything

I am new to programming.  I want to set java environment, but it is not working even I set the path.  This is the directory, I put the first one on path C:\Program Files\Java\jre1.8.0_181\bin:   here is my path for java in system variable:   I tried to restart cmd and even my laptop, but it is still not working  Thank you for you help!


Migrating ubuntu; fetch manally installed packages to feed apt-get install

Description:  This is somehow simple; I am migrating to an other computer. I am going to take the opportunity to switch to the new 18.04 LTS from the 16.04 (on the old computer).  On the 16.04 I installed so many (!) libraries and packages manually using apt-get.   Question:  Is there a way to fetch these packages, in a text file for example, that I can copy and paste on the 18.04 to feed an apt-get command to install them back?


Why charges reside on the surface on conductor?

In a hollow conductor and in a spherical shell the charges reside on its surface and there is no electric field inside it.Please tell me the reason behind it.


Should I use `\ ` or `{}` after custom commands?

I often use custom commands or macro as we all do. But I'm not sure what to do about the space following the command. I've sometimes done \mycommand\ and sometimes I've done \mycommand{}. I'm not sure which is better or more correct. Perhaps there's an even better way to do this. Can someone please describe what is the "best" way to do this?


how to hide the url variable from url in pagereference?

i want to hide the url value from the url,here is my code  string st = lowesPortalTranscations[0].Store_Number__c;                         system.debug(st);                             PageReference pageRef = new PageReference('/StoreNumAssistance?str='+st);                             pageRef.getParameters().put('str',lowesPortalTranscations[0].Store_Number__c);                             pageRef.setRedirect(true);                             return pageRef;   i am getting the url like this  StoreNumAssistance?str=1440   i want to hide the value str=1440  i didn't understand how to do it,please help me?


When rendering an image the output is grey

I've tried rendering an image using the Cycles render engine. here is the output:(everything looks good)   I tried rendering the same image, but using Radeon ProRender engine. This is how it looks at samples 28/128(not ready yet, it looks fine):   And this is the output.. I don't understand why I get a grey image. Did I miss something ?  EDITHere are my blender preferences   I have also installed this from their official website //// i do not know what other settings so show here   My .blend file is this


Creating a method inside the arguments list of a java method

I came across this piece of code today : client.post(getApplicationContext(),url, entity,"application/json", new JsonHttpResponseHandler() {                 @Override                 public void onSuccess(int statusCode, Header[] headers, JSONObject response) {                   System.out.println(statusCode);                 }                 @Override                 public void onFailure(int statusCode, Header[] headers,String responseString, Throwable throwable) {                     // called when response HTTP status is "4XX" (eg. 401, 403, 404)                 }             })  What exactly is being attempted and is it even legal ? It does not throw any errors when compiling....


How to group SQL Server files for restoring database

I have a SQL Server database that is creating full backups once a week, differential backups once a day, and transaction log backups hourly. These are being FTP'd to another box, where I would like an automated system (which I am writing) to pick them up and restore them into a working database.  So basically every hour when a new transaction log file comes in, I want to find the appropriate full backup file, differential backup file, and other log txn files for that day use them to restore the database.  The issues is that this machine will have several weeks of backup files on it so I need a way to group them together appropriately. What is the best way to do this?  When you go into Management Studio and do a database restore, it gives you a listing off all the full, diffs, and logs grouped together so clearly it's storing this grouping data somewhere.  I've seen the  command, which seems to provide some information but I'm not 100% sure how to use it.  It looks like you could make the CheckpointLSN  of the full backup to the DatabaseBackupLSN of all the other files, but I'm not totally sure about that.  My log files to have date/time stamps in the name but I would rather not rely on parsing file names to group everything together.   does provide some insights but I would prefer some sanctioned documentation from Microsoft before I embark on a solution.


Solving Keplerian two-body problem numerically?

I'm trying to solve the two-body problem numerically, setting up G, m1 and m2 =1.0.  The masses are placed at the positions -10 and 10 respectively along the x-axis and gave them both 0 on the y-axis. I am having some real issue with the initial conditions fitting for a keplerian orbit with a given eccentricity (e=0.9)! Also how would the initial condition change for different mass ratios?


Why exactly did the Sorting Hat originally want to put Harry in Slytherin?

I know that the Sorting Hat wanted to for other reasons, but if he made the right decision then why did he ever want to? The Sorting Hat made it very clear that he chose the right house, then why did he ever consider putting Harry in Slytherin?


Creating graduated legend for rasters using QGIS?

I have see a few posts about the difficulties of generating nice looking legends for rasters but they all seem to relate to older versions of QGIS (Las Palmas and older). I'm on 3.4.4 and want to know what is the best way to create a legend entry for a graduated raster with many values such as a DEM.  Are there any plug-ins designed for this that work with 3.4.4?


Java exhibiting pass-by-reference behavior

Writing code to reverse the elements in an array. Both method1 and method2 perform the same operations, but are changing the values of the array in main, despite scope and no assignment.  import java.util.Arrays; public class ReversingMatrix {     public static void main(String[] args) {         int values[] = {1, 2, 3, 4, 5, 6, 7};         method1(values, 0, values.length - 1);             // Values array is now : {7, 6 ... 1} --> why?         method2(values);     }     public static void method1(int[] arr, int lPos, int rPos) {         if(lPos >= rPos) System.out.println("1D Recursion Reverse: " + Arrays.toString(arr));         else {             int temp = arr[lPos];             arr[lPos] = arr[rPos];             arr[rPos] = temp;             method1(arr, lPos + 1, rPos - 1);         }     }     public static void method2(int[] arr) {         int temp;         for(int a = 0; a < arr.length / 2; a++) {             temp = arr[a];             arr[a] = arr[arr.length - (1+a)];             arr[arr.length - (1+a)] = temp;         }         System.out.println("1D For Loop Reverse: " + Arrays.toString(arr));     } }   Why doesn't values array remain {1, 2, 3, 4, 5, 6, 7}, so I can use it multiple times?


Do oceans produce the cosmic microwave background?

A guy who has a career in medical physics named Pierre-Marie Robitaille argues in two recently published papers in “Progress in Physics”, that the CMB is not from the big bang but from the oceans.   The first paper is entitled WMAP: A Radiological Analysis. This work analyzes the WMAP images based on accepted standards for image acquisition and processing.  It demonstrates that it is not appropriate to evaluate cosmological parameters based on  measurements from either WMAP or COBE.  In the second paper, evidence is presented for the reassigment of the CMB to the oceans of the Earth.  This work demonstrates that the Earth cannot be modeled as a 285K source as the COBE team assumes.  This is postulated by a third paper authored by Dmitri Rabounski, a Russian theoretical physicist in "The Relativistic Effect of the Deviation between the CMB Temperatures Obtained by the COBE Satellite".   Robitaille  and this  is of him claiming that Penzias and Wilson measured water on Earth.  These people also base their case on 2 questions: (1) When you put a glass of water inside a microwave oven and turn it on does the water in the glass reflect the microwaves or does it absorb them? (2) Is a powerful absorber of microwaves also a powerful emitter thereof?  Can anyone debunk and address these claims?


Show that there is no $(6,9,3)$ binary code.  I'm pretty sure the way to tackle this problem is to deal with it's generator matrix and then get a condradiction.  However I seem to be getting no contradiction and I'm unsure if this is even the right approach.  Any help would be appreciated.


I downloaded Ubuntu 13.10 iso file. I mounted it and it asked for reboot. After reboot windows started normally. Every time its just asks for reboot and does nothing.


How to INSERT a row INTO a table that has an 'order' column without cursor

I have a SQL Server 2016 table with an order/position column.  This column is an INT that indicates the preferred order/position of the rows in table for presentation purposes.   How do I INSERT a row in position 1 without using a cursor?  (i.e. new row has position 1, existing rows - assumed to be in correct order before insert - must be "moved down")   The order/position column is NOT NULL and enforced to be UNIQUE. I would also prefer not to use "blunt force" technique like set all rows' order/position value to some "never used" values and then just perform reorder on all rows.


CDF, PDF, and integral with respect to a function

In a certain textbook, I see the Cumulative Distribution Function (CDF) of a continuous random variable X defined as $$\int_{-\infty}^{x'} dp(x)$$ where p(x) is the Probability Density Function of X.  Usually, I see the CDF defined thus: $$\int_{-\infty}^{x'} p(x)dx$$ I have only ever seen and solved integrals with respect to a variable, not with respect to a function of a variable, so I don't know if those two are equivalent. Are they? Or is the first expression wrong?


I have a shapefile with contours and their heights.   Is it possible to make a DEM from contours in QGIS without using GRASS?   I found  but the answer is for ArcGIS Desktop.


I am very new to Linux and Ubuntu. I use Ubuntu 11.10.  I was trying to exit the X server (in order to install some Nvidia drivers) and I typed in the terminal:  sudo service lightdm stop   How can I return to the Ubuntu interface?


Löwenheim-Skolem and proper class models of ZFC.

Let $N$ be a proper class model of ZFC and $x \subset N$ a set. Show that  there is a set $y \in N$ such that $x \subset y$.   If $x \subset N$, I think that by the downward's part of Löwenheim-Skolem, we can find an elementary submodel $y$ of $N$ such that $x \subset y$. But how would I conclude that $y \in N$? It seems like I'm missing something trivial but I can't figure out what exactly.   Note: A hint to point me to the right direction would be more appreciated than a complete answer.


What is the policy on signatures and links in answers?

This is a general policy/netiquette question for the sites?   Some people like to include 'signatures' in their answers But signatures are redundant, since the poster's gravatar is already on each answer. Some signatures have links, which I think are appropriate for articles but not for answers, since the link should already be part of your profile for those that are interested. Most answers have neither signatures nor links. Links in signatures won't actually increase the search-engine ranking of the linked-to web site, since they're automatically marked rel=nofollow Links in answers tends to 'clutter' the thread   So what is the policy, official or otherwise?  This post is a community wiki, with some stock answers for up/down votes (note there is no penalty for downvoting a wiki post). Salient points/opinions should be added as wiki posts also please.  If a consensus is reached, perhaps it should be added to the FAQ. If link-farming is deemed OK, my site could use the exposure as much as anyone else's ;-)  EDIT: Why should we care? Other than the cluttering and he/she-does-it-so-I-want-to-also issues, if signatures and links are OK then they should be respected when editing and/or consolidating answers. If not then it is OK to edit an answer to remove the signature/link clutter.


What do the buttons on Darth Vader's suit do?

In all three of the original trilogy not once does anyone interact with (or even discuss) those damn buttons on his chest plate.  Do they do anything?  Is there a reference to them in the extended universe of what they do?  UPDATE: This has been answered here ()