Let $X=\{x_1,...,x_n\}$ be the set of generators and $\Delta=\{s_1(x),...,s_r(x)\}$ be the set of relations. There is a homomorphism $G\to \langle t\rangle$, where $\langle t \rangle$ is the infinite cyclic group, that sends every generator into $t$. It is easy to prove. So, the set of all the nontrivial homomorphisms from $G$ to $\langle t\rangle$ is not empty. Let $\theta$ be one such homomorphism. Then $\theta$ sends $x_i$ into $t^{n_i}$ for some $n_i\in Z$. Now suppose $x_1^2x_3^{-1}=1$ is a relation in $G$. Then   $$\begin{align}t^{2n_1-n_3}&=t^{2n_1}t^{-n_3}\\ &=(x_1^2)\theta (x_3^{-1})\theta\\ &=(x_1^2x_3^{-1})\theta\\ &=1\theta\\ &=1. \end{align}$$  But $t$ has infinite order. So $2n_1-n_3=0$. More generally in this way I get a system of $r$ equations in $n$ unknowns with $r<n$. I know this system has a solution in the reals. I'll assume it has a solution in the integers. I'm not sure. If it has, then I have $L=\langle m_1,...,m_n: s_1(m),...,s_r(m)\rangle$. Here $L$ is generated by $n$ elements which satisfy the same relations as in $G$ and, by von Dyck's theorem, there is an epimorphism $\varphi:G\to L$. But $L$ is a subgroup of $Z$ the integers and, as such, it is infinite. Therefor $G$ is infinite.   There remains one thing to be proved. That a system of $r$ linear equations in $n$ unknowns and coefficients in $Z$ with $r<n$ has a solution in the integers. Honestly I do not know if this is even true. Assuming it is true, is the proof valid?  EDIT: I think the system has a solution in the rationals. Then I multiply each equation by the least common multiple of the denominators and I get a solution in the integers.

I some how feel that, any finitely presented group with less relations than generators has to be an infinite group.  In one of my questions, in an answer I have seen a group which is finitely presented but it is not finite.  $G=\langle a,b\mid a^2=b^2=1\rangle$ this group is infinite. I see that if there is at least one more relation in between $a$ & $b$ then the group is finite.     I claim that if there are fewer relations than generators of a finitely presented group, then the group has to be infinite.   I would like to see is it true in general??  Is any finitely presented group with fewer relations than generators an infinite Group?  Please suggest some idea to see if this is true/false?


Suppose $A(p, n)=(a_{ij}(p))_{i, j \leq n}$ is an $n\times n$ random matrix over $\mathbb{F_2}$, with  all its entries being i.i.d. and such that $P(a_{ij}(p) = 1) = p$, where $p$ is some real number from $[0; 1]$. What is the largest possible probability, that $A(p, n)$ is non-singular and with what $p$ is it reached?   Note, that $A(p, n)$ in non-singular iff $det(A(p, n)) = 1$.  Solution for $n=1$:  $det(A(p, 1)) = 1$ with probability $p$. The maximum of $det(A(p, 1))$ is $1$ and it is reached with $p = 1$.  Solution for $n = 2$:  $det(A(p, 2)) = 1$ with probability $2p^2(1 - p^2)$. The maximum of $P(det(A(p, 2))=1)$ is $\frac{1}{2}$ and it is reached with $p = \frac{1}{\sqrt{2}}$.  However, I would like to know some sort of general formula (or at least asymptotics).  EDIT:  After I failed to solve this problem using determinants, I tried to prove this using the fact that asquare matrix is non-singular iff its rows are linearly dependent. As there exists only one non-zero element in $\mathbb{F_2}$, we can write linear dependence of the vector system $\{v_i\}_{i \leq n}$ in $\mathbb{F}_2^n$ as $\forall S \subset \{1, ... , n\}$ such that $S \neq \emptyset$ we have $\sum_{i \in S} v_i \neq \overline{0}$. I know the probability that a given set of vectors with i.i.d. random entries Bernoulli distributed with parameter $p$ $\{v_i\}_{i \leq k}$ over $\mathbb{F}_2^n$ satisfy $\sum_{i = 1}^k v_i \neq \overline{0}$ is $(1 - \frac{p((1 - 2p)^k - 1)}{1 - 2p})$. However, I do not know how to proceed further in this direction.

Given a random square matrix of size $n\times n$ in the field $\mathbb F_2$, what is the probability that its determinant is $1$? (This is also the probability that the matrix is non-singular, since $\mathbb F_2$ only has the elements $0$ and $1$.)


How do I prove that $$ a^3+b^3+c^3−3abc = 1 $$ if   $ a = 1+\frac{x^3}{3!}+\frac{x^6}{6!}......$ , $b=x+\frac{x^4}{4!}+\frac{x^7}{7!}....$ , $c=\frac{x^2}{2!}+\frac{x^5}{5!}+\frac{x^8}{8!}......$ ?  I have tried the following :-  I discovered that $a+b+c=e^x$ and that $a=\frac{d(b)}{dx}$, $b=\frac{d(c)}{dx}$, $c=\frac{d(a)}{dx}$ . But I am unable to proceed further with these information.


Recently I came across a very strange issue (Oracle 12c), the LISTAGG works for the first alias column but not for the second one (both are almost identical) throwing ORA-00904: "PARAMDESC": invalid identifier. Here is the SQL:   SELECT s_sample.s_sampleid,    b.u_tarolotnumber,    p.productdesc,    s_sample.productid,    LISTAGG(wi.s_departmentid, '; ') WITHIN    GROUP(ORDER BY wi.s_departmentid) Department,     wi.workitemid,     s_sample.sampletypeid,     NVL((SELECT sa.aliasid            FROM sdialias sa          WHERE sa.sdcid = 'Workitem'            AND sa.keyid1 = wi.workitemid), wi.workitemdesc)workitemdesc,     NVL((SELECT sa.aliasid           FROM sdialias sa          WHERE sa.sdcid = 'ParamList'             AND sa.keyid1 = p.paramlistid), p.paramlistdesc) paramdesc   FROM s_sample  JOIN s_batch b ON s_sample.batchid = b.s_batchid             AND s_sample.classification = 'ReagentQuality'  JOIN s_product p ON s_sample.productid = p.s_productid  JOIN sdiworkitem sdi ON sdi.keyid1 = s_sample.s_sampleid                   AND sdi.sdcid = 'Sample'  JOIN workitem wi ON wi.workitemid = sdi.workitemid               AND wi.workitemversionid = sdi.workitemversionid  JOIN sdiworkitemitem sdiwi ON wi.workitemid = sdiwi.workitemid                         AND sdiwi.keyid1 = s_sample.s_sampleid                         AND sdiwi.sdcid = 'Sample'  JOIN paramlist p ON p.paramlistid = sdiwi.itemkeyid1               AND p.paramlistversionid = sdiwi.itemkeyid2               AND p.variantid = sdiwi.itemkeyid3  WHERE s_sample.s_sampleid IN ('S100')  AND 1 = 1  GROUP BY s_sample.s_sampleid,       b. u_tarolotnumber,       p.productdesc,       s_sample.productid,       s_sample.sampletypeid,       wi.workitemid,       workitemdesc,                 paramdesc;   Did lot of googling, but no luck! Any help would be highly appreciated.  Thanks in advance Suv

How to 'group by' a query using an alias, for example:  select count(*), (select * from....) as alias_column  from table  group by alias_column   I get 'alias_column' : INVALID_IDENTIFIER error message. Why? How to group this query?


So I've created a Mail Rule "Bin Spam Messages" that will delete messages from a sender. What I can't figure out is how to automate adding new sender addresses to the rule. I'm guessing I could do this with AppleScript but I'm also trying to do it without opening the message. The goal is to automatically delete spam messages from my inbox and junk mail folders. I thought this was what the Apply Rules menu option was for but apparently not. Any ideas?  Update: I have tried updating SyncedRules.plist using a Shell script (below) but (a) it doesn't show up in Mail preferences; and (b) SyncedRules is restored after relaunching Mail. Not sure where else Mail rules are stored.  #! /bin/zsh  # Generate 128-bit UUID CRITERION_UNIQUE_ID="$(uuidgen)"  # Define Shell input variables EXPRESSION="$1" HEADER="$2"  # Define SyncedRules.plist file FILENAME="/Users/tim/Library/Mail/V7/MailData/SyncedRules.plist"  # Run plutil plutil -insert 0.Criteria.0 -xml "<dict><key>CriterionUniqueId</key><string>$CRITERION_UNIQUE_ID</string><key>Expression</key><string>$EXPRESSION</string><key>Header</key><string>$HEADER</string></dict>" $FILENAME   This script inserts a dictionary into the first items Criteria array containing a 128-bit UUID, sender email address and email header, but my issue is persistence. If I run the command with sudo, I can update the SyncedRules.plist but Mail doesn't recognise the changes and the .plist is restored when Mail relaunches, anyway.  Getting warmer...  More Updates: So I doubled back and had a look at the Mail library in Script Editor.. then discovered this answer  - there's a block there that I'm particularly interested in... something like make new rule with properties {header:"", expression:thisItem, rule type:from header, qualifier:equal to value} condition - I think this is where I'm heading now.

I want to edit manually the following .plist file:  /Users/<myname>/Library/Mail/V5/MailData/SyncedRules.plist   Because I get a lot of spam and adding each spammer address to the rules using Mail is impraticable:    and there are many addres to be added. Since I know a bit bash scripting, sed and awk I'm thinking to write a script that automatically adds the addresses from selected email to the plist file above.      So, what is my question?  In conclusion, for each spammer addres the script should add a new dict entry with following fields:          <dict>             <key>CriterionUniqueId</key>             <string>CC4CB669-0D44-4A32-80B1-02D069718304</string> (*)             <key>Expression</key>             <string>spammer@address.spam</string>             <key>Header</key>             <string>From</string>         </dict>   How the string at (*) is generated? How can I fill it?


Stein‘s book “Complex Analysis” contains some outline of “pseudohyperbolic distance”：$$d(z,w)=\lvert \frac{z-w}{1-\overline{w}z}\rvert$$ My problem is that does it is a metric function. That is, does it satisfies the three axioms of metric? The difficulty is how to prove the triangle inequality? I have tried too many times, but I failed. Thank you for your attention.

For any $z, a$ in the open unit disk, we define$$d(z,a)=\left \vert \frac{z-a}{1-\overline{a}z} \right \vert$$  Show that $d$ is a metric on the open unit disk.     It is easy to show $d(z,a)=d(a,z)$ and $d(z,a)=0$ $\rm iff$ $z=a$. However, I am having trouble showing that it satisfies triangle inequality. Any help would be appreciated!


I just downloaded ubuntu 18.04.3 LTS.   The web site suggests running a given command on the terminal, whereupon the following answer should emerge:  ubuntu-18.04.3-desktop-amd64.iso: OK   However, the answer I get (without any chance or clue as to what to do) is:  shasum: ubuntu-18.04.3-desktop-amd64.iso:  ubuntu-18.04.3-desktop-amd64.iso: FAILED open or read shasum: WARNING: 1 listed file could not be read.   Incidentally, when I tried to install ubuntu 18.04.3 it all went fine until, just before finishing, a message popped up:      "it is not possible to install the bootloader; choose a different   device to install the bootloader on".   No matter which option I chosed (I also tinkered with the boot sequence to no avail), when re-starting my computer, it went to the already installed Windows 10. This OS is on a 256GB SSD drive, while I was recommended (not know the rationale behind it, though) to rather install Ubuntu on the 500GB HDD. Thank you.

I've just downloaded a CD image of Ubuntu. I know the installer has a check CD option, but how can I check that the image is good before burning it to CD?


           <meta name="viewport" content="width=device-width, initial-scale=1">
How To Create A Loader

        I am not able to align the loader at the center of the screen. I have tried putting align:center in the loader class but that did not work.

How can I horizontally center a
 within another
 using CSS?

Foo foo


I should create some kind of a checklist.  If the user clicks on some task (in this case a <li>) the task should disappear and get strike-through. I solved this with toggling jQuery class:  $('li').click(function() {    $(this).toggleClass("checked unchecked"); });   Everything works fine. If the user clicks on a list item, the class changes from "unchecked" to "checked".  But there is an option to add new tasks (the little plus icon above). If you add an new list item, the class changer does not work for this. If you click on it, nothing happens.  I hope you guys understand me, my english is not so great :-)  Have a look: .

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


Today is not the first time I have seen a 1 icon in the remaining review count, but when I click on it, message says that there are no items in the queues.   Sorry for non-English site on the screenshot (I only have enough rep on ruSO).        I know that can be due to caching, and most times if I do refresh the page, the 1 icon disappears. But when I myself make a suggested edit to a tag's description I will see such 1 even when I do refresh a page many times. It can disappear and appear again, but it completely goes only when my suggested edit is approved or rejected.  So my thought here is some sort of weird bug. Need to dig more, though.

The suggested edits count at top is incorrect. Multiple browser refreshes did not clear it. Approving/Rejecting review decreases the count, but as you can see the count is incorrect.


A tutorial shows cp -r   but   only shows -R.

cp -r is meant to copy files recursively, and cp -R for copying directories recursively. But I've checked, and both appear to copy both files and directories, the same thing. So, what's the difference actually?


I am a high school student studying about gravitational waves. I hope they are similar to other waves like sound waves, etc. So I what to know exactly what oscillates in a gravitational wave. Like in sound waves, density of a medium oscillates over its maximum and minimum value. I wonder what could be oscillating?

Two kinds of wave transmission are:   Light waves, where a substance (photon) travels as a wave. An attached rope, like at the gym, that is "waved" up and down. Here, no substance travels to a new spot, but adjacent parts transmit the energy to others.   QUESTION: Which method do gravitational waves propagate by?


The  in the notification inbox has recently started occurring for me.   This is what I see now:    The circled comments links to: , But there is no such comment on the question, or any of the answers.  There is also this  which just gives the cause of the bug, but doesn't go into whether the bug is solved or not.

I realise that there is other questions out there about the  (First open one I found is ), but this is marked .  I often get the below issue where it will notify me about comments on my  (in this case what appears to be the user re-writing after deleting their comment) that no longer exist.  Also, occasionally, I see comment snippets with text that doesn't match what is on the page when I view it.  Let me know if I should be trying to edit that one to remove the tag indicating that it has been fixed, and add the above as another answer.


How can define variable like \var{arg1: Name}{arg2: Family} and in text use that like      My name is \var$arg1 and my family is \var$arg2   arg1 and arg2 are lables of arguments.

I'm fairly new to LaTeX and I'm struggling with something apparently simple, but for which I can't find a fair solution. The problem (simplified) is as follows (please take care terms used may not have the traditional meaning in LaTeX):  I need to references to files (many) throughout a text. As example, the files:  "C:/Work/this_file1.c", "C:/MoreWork/this_file1.c" and "D:/MoreWork/another_file2.h".  So, now I would like to create an "alias" to each directory and each name file so I can reference them. A "pseudocode" could be:  % Definition \alias \c_dir = C:/Work/ \alias \d_dir = D:/MoreWork/ \alias \file1 = this_file1.c \alias \file2 = another_file2.h  % Reference in text \c_dir\file1    % For referencing C:/Work/this_file1.c \d_dir\file1    % For referencing D:/MoreWork/this_file1.c \c_dir\file2    % For referencing C:/Work/another_file2.h   My first approach was using \newcommand, but that caused numerous problems due to naming limitations. (I also tried other methods like pgfkeys, but it always gets stuck somewhere!)  Can you suggest a method?


Is there an easy way to get the coordinates of a specific player using command blocks? I was trying to find a way to do this but I could not find any info about it.

Is there a way to find where other players are in the Minecraft world without asking them for their coordinates? I play with friends. We've sort of aligned ourselves in a 2 vs 2 match-up, and since we wanna PvP with them, we need to find them first.


Is it possible to represent the following series in term of a non-infinite function: $$ \sum_{n=1}^{\infty} n^2 x^{n-1} $$

I do have somewhat of a reasoning for this.   $$S = 1 + x + x^{2} + x^{3} +.. + x^{n} $$   Denoting the derivative of $S$ as $T$   $$T = 1 + 2x + 3x^{2} + 4x^{3} +... + nx^{n-1}$$  $$xT = x + 2x^{2} + 3x^{3} +... + nx^{n}$$  Writing the derivative of this series as $V$  $$V = 1 + 2^{2}x + 3^{2}x^{2} +... + n^{2}x^{n-1}$$  $$xV = x + 2^{2}x^{2} + 3^{2}x^{2} +... + n^{2}x^{n}$$  Which is ${\sum{n^{2}x^{n}}}$  However, I am unable to start from $\sum{n^{2}}$and finish where I started. Can someone give me systematic steps on how to manipulate ${\sum{n^{2}x^{n}}}$into a generating function?   The answers are a little different from what I expected.  Let me explain with $\sum nx^{n}$. This function is not the series of any known function but with one slight manipulation, we can change it.  $$\sum x\frac {d x^{n}}{dx}$$ $$=x \frac{d}{dx} {\sum x^{n}} = x\frac {d}{dx} \frac{1}{1-x}$$ $$=\frac {x}{ (1-x)^2 }$$  I wanted a similar trick for evaluating $\sum n^{2}x^{n}$ $$=\sum nx \frac{d}{dx} x^{n}$$ And, then what ? How can I finish this ? I know how to start at $S$ and finish here, but I'm having trouble doing the algebra of starting with this sum and finishing where I started.


In class, my professor just mentioned that some finite-amplitude water waves were satisfied by the KdV equation. Is there some reference which shows how to derive this from $1st$ principles, and also discusses other non-linear water waves?

What textbook would you recommend for a bachelor in theoretical physics to study ? I don't want to focus too much on chaos, just having a broad view of every interesting characteristic is enough. Physical meaning behinds equations should be explained.  Some related resources:   , but obviously those are math-y.  While there are some overlaps, the evolution of a simple oscillator can evoke interesting dynamics characteristics. , but I'm not sure if studying only fluid dynamics is too narrow for me.


I am working on a online sharepoint site collection, and i have attached files to custom list items, as follow:-    But i have the following questions:-   can i link the attachment with cusotm columns? so for example when users upload an attachment file, to select its type from a drop-down site column? when i search for the list items' attachments, then inside the search result i will get the item's dispform.aspx and not the actual attachment file. so is there a way to force the search to show the attached file instead of showing the item's dispform.aspx?

I have a list with a bunch of attachments. A recent request came through to make these attachments searchable. Is the an attachment type that is searchable?


Searching for a solution to my problem, I have found many fixes for something similar, but not identical. However, since I would categorize myself as a javascript beginner, I can't figure out how to use those fixes for my own solution. Hence, I am asking you.  I am working on a chat. On one page there is a list of conversations. Each conversation look like this:

" + participantsStringified + "

Me: "+obj.newest_message+"

;  As you can see, the  inside
 has an ID of obj.newest_message_time, which is a number that is programmatically added when the conversations is created.  So imaginging there are multiple
's, how can I sort them by using the id?

If I have a list like this:

text 1

text 2

text 3

text 4

   What's the easiest way to re-arrange the DOM nodes to my preference? (This needs to happen automatically when the page loads, the list-order preference is gained from a cookie)  E.g.

text 3

text 4

text 2

text 1


I just began a reread and it seems odd that Prof. McGonagall was at Privet Drive--all day watching the Dursleys--yet did not seem to know that Dumbledore planned to leave Harry with the Dursleys. Indeed, she seems almost shocked when Dumbledore suggests he is leaving Harry there. If she was surprised at this, why would she be at 4 Privet Drive in the first place? Did someone tell her to be at that particular place? Did she know Petunia? Is there any canon-based explanation for this, and if not, any other explanations?  Thanks.

Dumbledore gave her the news about the death of the Potters while they were sitting outside the Dursley's house. She had been watching the house all the previous day & into the night. So when she started, they didn't need a safe house for Harry, did they?


Similar (but different, please read on) questions have been asked dozens of times, so I'll try to be concise about this one.  The wording on protected questions "posting an answer now requires 10 reputation on this site" is incorrect. I have 60 reputation on the Physics SE site, but when I tried to post an answer on  I was greeted with the protected message warning:     Thank you for your interest in this question. Because it has attracted   low-quality answers, posting an answer now requires 10 reputation on   this site.   This is buggy documentation. I do have more than 10 reputation. If the origin of those points affects whether or not they're counted this should be clarified in the message (in this case the association bonus is not included, so the word earned might be appropriate, although still subjective). Previous gripes with this message were posted in these questions:      There are probably more. In these posts, the questioners were asking to improve the wording to clarify that the association bonus is not included. Since then, the word earned has been removed, so now the wording is not just confusing (as pointed out in those questions), it's simply wrong.  A previous question with the same message was posted, but this question is not a duplicate because it requests to change the feature, I'm asking for it to be correctly documented:    I posted a physics meta question about this here:    Unfortunately it was closed as duplicate, which I do not believe to be warranted. A commmenter suggested I post it on Meta SE.

I recently started an account on , and went to add an answer to a question which was protected. I have enough rep on other sites that I have the "Association Bonus", so I was confused as to why I wasn't being allowed to answer the question.     This question is protected to prevent "thanks!", "me too!", or spam answers by new users. To answer it, you must have earned at least 10 reputation on this site.   After re-reading the message and reviewing , I realized that the bonus didn't count as points earned toward that site.  This is a really minor issue, but I think it's worth fixing (not sure if bug or feature).  I believe that users who have enough rep to receive the association bonus should generally already know not to post "thanks!" and "me too!" style answers, so if the message is accurate, users who receive the association bonus should be able to answer protected questions.  If there's another reason to keep users from answering protected questions, such as  claim that:     For protected questions, you are expected to have experience on the target site itself. Experience at other sites is not enough.   then the message should be updated to reflect this.  Option 1:  make protected questions open to anyone who has >10 rep on that site and update the message to read:     This question is protected to prevent "thanks!", "me too!", or spam answers by new users. To answer it, you must have at least 10 reputation on this site.   Option 2:  leave protected questions the way they are, but update the message to read:     This question is protected to prevent "thanks!", "me too!", or spam answers by new users. To answer it, you must have earned at least 10 reputation on this site to show that you have experience on this topic; experience on other StackExchange sites is not enough.   Option 3:  Answer with your own suggestions/improvements to these ideas.


I am trying to get bitmap form imageview in MainActivity.java .The image is on the cards displayed from Item.xml with the help of an array adapter. Here is MainActivity.java      private ImageView mimage;     mimage = (ImageView) findViewById(R.id.image);  flingContainer.setOnItemClickListener(new SwipeFlingAdapterView.OnItemClickListener() {             @Override             public void onItemClicked(int itemPosition, Object dataObject) {                  cards obj = (cards) dataObject;                 String name = obj.getName();                 String info = obj.getInfo();                  BitmapDrawable drawable = (BitmapDrawable) mimage.getDrawable(); //this is line 117                 final Bitmap bitmap = drawable.getBitmap();                   Intent intent = new Intent(MainActivity.this, ProfileActivity.class);                 intent.putExtra("Name",name);                 intent.putExtra("Info",info);                 intent.putExtra("bitmap",bitmap);                  startActivity(intent);                 finish();                 return;             }         });      }   and here is the error  `java.lang.NullPointerException: Attempt to invoke virtual method android.graphics.drawable.Drawable android.widget.ImageView.getDrawable()' on a null object reference``at com.example.android.tindercone.MainActivity$2.onItemClicked(MainActivity.java:117)`

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


I have made a paper plane by folding a flat mesh plain with a mirror modifier. I would like to animate the folding from start to finish. Is there a quick simple way to do this?

Imagine a piece of paper and you fold it in half and then fold it again. that's what I am trying to do and cant. If I use bones the influence of the bones won't allow me to because I need 2 bones to control the same area. If I try shape keys it just deforms the mesh if I try to make it in multiple steps or does the wrong animation because it draws the shortest path instead of rotating from a point like a piece of paper would.


I am studying from home and I'd like to learn linear algebra on my own.  Is there a good book I should buy?  Thanks in advance!

I'm looking for a book to learn Algebra. The programme is the following. The units marked with a $\star$ are the ones I'm most interested in (in the sense I know nothing about) and those with a $\circ$ are those which I'm mildly comfortable with. The ones that aren't marked shouldn't be of importance. Any important topic inside a unite will be boldfaced.  U1: Vector Algebra. Points in the $n$-dimensional space. Vectors. Scalar product. Norm. Lines and planes. Vectorial product.  $\circ$ U2: Vector Spaces. Definition. Subspaces. Linear independence. Linear combination. Generating systems. Basis. Dimesion. Sum and intersection of subspaces. Direct sum. Spaces with inner products.  $\circ$  U3: Matrices and determinants. Matrix Spaces. Sum and product of matrices. Linear ecuations. Gauss-Jordan elimination. Range. Roché Frobenius Theorem. Determinants. Properties. Determinant of a product. Determinants and inverses.  $\star$ U4: Linear transformations. Definition. Nucleus and image. Monomorphisms, epimorphisms and isomorphisms. Composition of linear transformations. Inverse linear tranforms.  U5: Complex numbers and polynomials. Complex numbers. Operations. Binomial and trigonometric form. De Möivre's Theorem.  Solving equations. Polynomials. Degree. Operations. Roots. Remainder theorem. Factorial decomposition. FTA. Lagrange interpolation.  $\star$ U6: Linear transformations and matrices. Matrix of a linear transformation. Matrix of the composition. Matrix of the inverse. Base changes.   $\star$ U7: Eigen values and eigen vectors Eigen values and eigen vectors. Characteristc polynomial. Aplications. Invariant subspaces. Diagonalization.   To let you know, I own a copy of Apostol's Calculus $\mathrm I $ which has some of those topics, precisely:   Linear Spaces Linear Transformations and Matrices.   I also have a copy of Apostol's second book of Calc $\mathrm II$which continues with   Determinants Eigenvalues and eigenvectors Eigenvalues of operators in Euclidean spaces.   I was reccommended Linear Algebra by Armando Rojo and have Linear Algebra by , which seems quite a good text.   What do you reccomend?


I do have an overlapping polygon shapefile of different radius. I want to clip a polyline for each fid individually. How is that possible in ArcGIS?

I want to clip a polyline feature class by a polygon feature class (buffers created from points). Several polygons overlap, so I want to get each polygon feature clipped with each polyline feature.  Using the Clip_analysis tool, I get the orange lines:   whereas I want the following red lines:    In a python script, I tried the following code to clip every polyline with each polygon:          temp = arcpy.ValidateTableName("clip_temp")     bufferCursor = arcpy.SearchCursor(buffer)     n = 0     for pRow in bufferCursor:         arcpy.AddMessage(n)         feat = pRow.Shape         arcpy.Clip_analysis(inputPolylineLayer, feat, temp, "#")         if n == 0:             arcpy.Copy_management(temp, clip)         else:             arcpy.Append_management(temp, clip)         n=n+1   But the execution is very very slow and it crashes before finishing.  I also tried the Intersect_analysis tool but I didn't get the right geometries:   Do you have any idea of a better methods to do it?


I have a JTextField in my form which i use for book name input. Based on this book's name, I'm trying to pass author's and publisher's values to new JFrame (NewPage) JTextFields (authortxtfield and publishertxtfield). Each time when i execute this code, i get java.lang.NullPointerException. authortxtfield and publishertxtfield are both public. Am i doing something wrong?  public void getBook(){     try {         ps = conn.prepareStatement("SELECT author, publisher FROM books WHERE txtfld_bookname=?");         ps.setString(1, txtfld_bookname.getText());            rs = ps.executeQuery();         while(rs.next())         {                                            NewPage.authortxtfield.setText(rs.getString("author"));             NewPage.publishertxtfield.setText(rs.getString("publisher"));         }       } catch(Exception e){         JOptionPane.showMessageDialog(null,e);     } }    I would also like to know if there's a way to concatenate author and publisher into one JTextField so i wouldn't have to use 2.


I need to upload and compile stuff on a remote machine that is only reachable inside a specific network that I can access over SSH.  So for example I perform the following steps:  me@mymachine$ ssh user@network_gateway user@network_gateway$ ssh seconduser@targetmachine seconduser@targetmachine$ #do stuff   Is there a way to make my local machine aware of the tunneling without undergoing the trouble of connecting to the network gateway every time?

Local Computer (Fedora)  --SSH-->  Server1  --SSH-->  Server2   In some environments I work in, we have to use "jump boxes" where you ssh to one server in order to get to another server. Is there a quick way to do this, perhaps by editing ~/.ssh/config, such that whenever I ssh to Server2 from my local computer, it automatically creates the necessary connection to Server1? I can setup keys so that I'm not prompted for a password to Server1 if necessary.


I am trying to write an ELSEIF conditional statement in QGIS Field Calculator (version 1.8.0). I have used an example I found online:  CASE WHEN val < 0 THEN 'negative'   WHEN val = 0 THEN "neutral'   ELSE 'positive' END   I modified the statement as follows:  CASE WHEN  "GRID_ID"  = 1 THEN 'complete'   ELSEIF  "GRID_ID"  = 2 THEN "in progress'   ELSE 'not started' END   This statement would not run, the Output preview stated Expression is invalid.  The more info stated: Parser Error: syntax error, unexpected COLUMN_REF, expecting WHEN or ELSE or END  If anyone has had this error, what did you do to fix it?


So let's assume that A and B are both nxn matrices, and that u is an eigenvector for both A corresponding to lambda one and B corresponding to lambda 2. I need to prove that u is also the eigenvector for the product AB.  Initial Thoughts: Au=x'=Bu Au=Bu  I'm really not quite sure about where to go with this one, unfortunately for me my teacher has an affinity for proofs.

I have never learned how to prove things, so I don't know how or when a proof is finished. If you prove this, it may help me understand a bit how things are done:  The vector $e$ is an eigenvector of each of the $n\times n$ matrices $A$ and $B$, with the corresponding eigenvalues $\lambda$ and $\mu$, respectively. Prove that $e$ is an eigenvector of the matrix $AB$ with the eigenvalue $\lambda\mu$.


I am still very new to blender. I am trying to make one connected bit of teeth, but the two faces/edges will not merge at the center of the mirror and I don't know why. the edges seem to connect when I turn off one of the modifiers, but won't once I turn it on again. Please help

I'm trying to model a spaceship and I ran into this weird predicament. I'm using a mirror modifier as can be seen and I get this annoying crease:   If I enter edit mode, you can see that the verticies are connected:   And adding mean crease doesn't fix much:   What's a good way to fix it?


Is the following statement correct?   "The absolute value of supremum of a set is smaller than or equal to the supremum of the absolute values of the first set"  It would be helpful to proof that the absolute value of the integral of a function is smaller than or equal the integral of the absolute value.

Can someone prove that |sup(A)|=sup|A| ? Please and thanks.


When a die is rolled, one of the first six positive integers is obtained. Suppose that the die is rolled five times and the sum of the five integers thus obtained is added. The five throws constitute a trial. Find the number of possible trials such that the sum is at most $12$. This can be written as $x_1+x_2+x_3+x_4+x_5\leq 12$ where $1\leq x_i\leq6$ for $i=1,2,...,5$. However, this restriction is making this problem difficult for me. I know that I can figure out the solution by considering the generating function $G(x)=(x+x^2+x^3+x^4+x^5+x^6)^5$ and take the sum of all the coefficients that are less than or equal to $12$, but I want to know how to do this with the stars and bars technique. I know that I can rewrite the linear inequality as $x_1'+x_2'+x_3'+x_4'+x_5'\leq 7$ so we can count the number of positive integral solutions, but then we have still over counted and we need to use the restriction $x_i\leq 6$. I do not know how to do this. Any solutions or hints are greatly appreciated.

Let $x_1, x_2, x_3, x_4$ be  nonnegative  integers.      (a) Find the number of solutions to the following equation:                $$ x_1 + x_2 + x_3 + x_4 = 14 $$   I got $17 \choose 3$ for this. Is that correct?     (b) Find the number of solutions if we add the restriction that $x_i \le 6$ for        $1 \le i \le 4$


We are shifting our MS windows lab to Linux.  I want to set up a custom ISO with our required software and remove unwanted software from ISO. This may help us in saving internet bandwidth and time in setting the same software for our lab PCs.  Ansible can install all required software but it is using the internet,   thanks

I would like to customize Ubuntu live CD by installing some additional packages. I have followed   but it doesn't seems to work. Can anyone provide clear instructions?   Note: I do not prefer Remastersys, manual way will be appreciated.  Customization  Packages that I want to install:   Thunderbird    Samba    SSH       Changes that I need:   Remove Games menu from the Application menu Firefox shortcut on Desktop Radiance as the default Theme Different default Ubuntu Wallpaper   Configuration file changes   I want the panel to be placed at the bottom I want to paste my Samba configuration file instead of default Samba configuration I have few Firefox shortcuts and folders I would like to show that in Desktop Also it will be nice if you say me how to change the icon sets   Recent Updates   I have customized Ubuntu 10.10 with Firefox shortcuts and few folders on desktops. Everything went smooth. But the installer gets crashes after choosing the timezone. How do i fix this issue? Also setting wallpaper affects the login screen. The wallpaper which i set is displayed on the login screen also. I just want the default one for the login screen.


Sometimes the stress-energy tensor $T_1^{\mu\nu}$ is defined as $$T_1^{\mu\nu}=\frac{\partial \mathcal{L}}{\partial(\partial_\mu\phi)}(\partial^\nu\phi)-\eta^{\mu\nu}\mathcal{L}$$ which for translational symmetries of spacetime satisfies $\partial_\mu T_1^{\mu\nu}=0.$ It is not always symmetric. In general relativity, stress-energy tensor is defined as $$T_2^{\mu\nu}=\frac{\delta S}{\delta g_{\mu\nu}}$$ where $S=\int d^4x\sqrt{-g}\mathcal{L}(\phi,\partial_\mu\phi)$ is the action of the theory. It is always symmetric because the metric tensor $g_{\mu\nu}$ is always symmetric.   Can we say that the second definition is more general? If so, can we derive the $T_1^{\mu\nu}$ starting from the second expression $T_2^{\mu\nu}$ in the flat spacetime limit?   Please keep the discussion elementary.

What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu f_i - \eta^{\mu\nu}\mathcal{L}$$ (the four conserved Noether currents corresponding to four possible spacetime translations)  where $\{f_i\}_{i=1}^N$ are the $N$ matter fields in the theory, and we assume $f_i\mapsto\alpha^\nu\partial_\nu f_i$ for translations,  and stress-energy tensor from the Einstein-Hilbert action, which is: $$ T_{\mu\nu}\equiv-\frac{2}{\sqrt{-g}}\frac{\delta\mathcal{L}_{Matter}}{\delta g^{\mu\nu}} $$   In particular, how do you get that the two are equal (are they?) for Minkowski space, for which there is no variation in the metric?


i'm using biblatex with apa style. I have some authors that have too many middle names. It give me something like this :     Licht, C. M. M., de Geus, E. J. C., van Dyck, R., & Penninx, B. W. J. H. (2009). Association be- tween anxiety disorders and heart rate variability in The Netherlands Study of Depression and Anxiety (NESDA). Psychosomatic medicine, 71(5), 508–518   instead I would like to have something like this with a maximum of two middle name :     Licht, C. M., de Geus, E. J., van Dyck, R., & Penninx, B. W. (2009). etc...   I can't find any nice way of doing that (without deleting the additional names from my bib entry). Hope you can help me.  This is the MWE :  \documentclass{article} \usepackage{filecontents}  \begin{filecontents*}{demo.bib} @article{Licht2009, abstract = {}, author = {Licht, Carmilla M M and de Geus, Eco J C and van Dyck, Richard and Penninx, Brenda W J H}, doi = {10.1097/PSY.0b013e3181a292a6}, issn = {1534-7796}, journal = {Psychosomatic medicine}, number = {5}, pages = {508--518}, pmid = {19414616}, title = {{Association between anxiety disorders and heart rate variability in The Netherlands Study of Depression and Anxiety (NESDA).}}, url = {http://www.ncbi.nlm.nih.gov/pubmed/19414616}, volume = {71}, year = {2009} } \end{filecontents*}  \usepackage[backend=biber,style=apa,citestyle=authoryear,natbib=true,uniquelist=minyear,doi=false]{biblatex} \bibliography{demo}  \begin{document}     A reference to : \cite{Licht2009}  \printbibliography \end{document}   Thanks. br.

I am looking for a way to force biblatex to strip all first names except the very first one. I am actually using only initials, but even that gets messy when the author has 3-4 first names in a row and is known only by the first one.  Say I am citing this guy:  John Paul Peter Julian Doe   the output will be:  J. P. D. J. Doe   which is already quite long. Removing the dots and thin-spaces is not really an option. I would like it to just end up being J. Doe for the in-text (cbx) part of the reference.  Based on , I suppose it is possible with biblatex+biber and it is the solution I would favour.


Is it possible to place the caption a bit around includegraphics within the figure (to save some space?). As it may be misunderstood what I want, I try to explain it exemplary:   Currently the minimal example looks like this and uses minipage. I didn't know how to align without the ugly \vspace:  \documentclass{article} \usepackage[caption=false]{subfig} \usepackage{lipsum}  \begin{document} \begin{figure}   \centering   \subfloat[][]{\rule{0.49\textwidth}{5cm}}\hfill   \subfloat[][]{\rule{0.49\textwidth}{5cm}}\\   \begin{minipage}{0.49\textwidth}     \vspace{-7.70cm}     \subfloat[][]{\rule{0.49\textwidth}{2cm}}\hfill     \subfloat[][]{\rule{0.49\textwidth}{2cm}}   \end{minipage}\hfill\subfloat[][]{\rule{0.49\textwidth}{5cm}}   \caption{\protect\lipsum*[2]} \end{figure} \end{document}   Which is rendered to:

I have a TikZ figure that appears as follows. The figure also has a caption.  I'd like the caption to fill up that blank space in the bottom-right and bleed over into the space it current occupies.  Is there a way to do this?  Thanks!


I started by induction on $k$   For $k=1$ then : $1\in \mathbb{N}$  For $k=2$ then : $\frac{(p-1)}{2!} \in \mathbb{N}$ , indeed for all $p>{2}$, $p-1$ is even. (We still have $k<p$ it's important).  Suppose that $\frac{(p-1)...(p-k+1)}{k!} \in \mathbb{N}$ for a specific $k \in \{1,..,p-1\}$   Now try to prove that : $\frac{(p-1)...(p-k)}{(k+1)!} \in \mathbb{N}$.  By the recursive formula we have directly :  $\frac{\binom{p}{k+1}}{p} = \frac{[\binom{p+1}{k+1} - \binom{p}{k}]}{p}$ $\Leftrightarrow$ $\frac{(p-1)...(p-k)}{(k+1)!} = \frac{(p+1)(p-1)...(p-k+1)}{(k+1)!} - \frac{(p-1)...(p-k+1)}{k!}$  By hypothesis we know that $\frac{(p-1)...(p-k+1)}{k!} \in \mathbb{N}$  Now, the key is to see that a product of $k$ consecutive terms is divided by $k!$ (a little induction can solve this).  Then the induction is complete.

Question : If $p$ is prime, and $0< k< p$ show that $ p \mid {p \choose k}$  ${p \choose k}$ can be rewritten as:  $${p(p-1)(p-2)\dots(p-(k-1))(p-k)! \over (p-k)!\cdot k(k-1)(k-2)\dots3\cdot2\cdot1}$$  Now the $(p-k)!$ cancels out. Since in the numerator we have k consecutive  integers, k divides one of them (not p as p is prime and $k <p$). Then k-1 divides another one or two terms in the k consecutive terms (again not p). This reasoning continues until  3 and 2.   This means that ${p \choose k}$ can be rewritten as pq implying $p | {p \choose k}$  What if any of this proof is wrong. I am worried about any 'overlaps', i.e. say k-6 divides terms that k-3 divides invalidating the argument.  P.S. I hope the above is legible as I am new to this site. Thank you!


I have Ubuntu 15.10 (64 bit) installed on my laptop and I can't get rid of it. Tried making a bootable usb of windows 10, permission error. Tried looking for a solid answer to making a partition of windows ... no clear answer exists.  I'm very new to Linux and looking to get back into windows. If a solution deletes Ubuntu 15.10, that's fine.

I have Ubuntu on my laptop. Now I want install Windows 7 in a dual-boot. How can I do this? I can't lose my Ubuntu files, and I'm afraid that I might break . Go  for UEFI only!


I encounter java out of memory: perm gen exception. I tried to resolve it by expanding the java heap size, but unable to solve it. How can I increase the memory?

Recently I ran into this error in my web application:     java.lang.OutOfMemoryError: PermGen space   It's a typical Hibernate/JPA + IceFaces/JSF application running on Tomcat 6 and JDK 1.6. Apparently this can occur after redeploying an application a few times.  What causes it and what can be done to avoid it? How do I fix the problem?


I done a binary regression,it's possible that the the plot of residual vs Predict has two different line? I never see before one like this

Can anyone tell me how to interpret the 'residuals vs fitted', 'normal q-q', 'scale-location', and  'residuals vs leverage' plots?  I am fitting a binomial GLM, saving it and then plotting it.


I am looking for a way in Outlook 2010 to save attachments for selected messages. How can I do that?

Someone sent me 200 emails overnight, with one file attachment apiece. sigh  I'm expecting another 200 each night for the next three nights (the emails come from a server, so asking them to batch them isn't possible).  The file attachments have unique filenames, so is there a straightforward way to save the attachments from the entire group of emails at once?  I'd hate to have to open each email individually, right click, save, rinse, repeat...  I'm fluent in VBA, very comfortable creating Excel macros, so I can imagine it should be relatively easy to traverse a given folder for all messages and save attachments for each, but I haven't written an Outlook macro before, not familiar with the object hierarchy.


I was denied UK visa based on the followings:   You have stated that you will visit the UK for 6 days. I note that you were refused a visa for this purpose on 23 March,2019. At that time the Entry clearance officer had not been satisfied that you had sufficiently demonstrated your studies in resident country(Asia). You have not addressed this , nor have provided any evidence that you are currently pursuing a course of study there. I note that you have you have temporary residence in the (Country in Asia). The documents you submit do not demonstrate your long term intention on completion of any studies.   Note : I have been to UK on 6 months tourist visa,even Schengen country and Singapore( didnt over stayed nor abuse the visa stipulations ). I applied for 2 years tourist visa,and submitted back documents from my University ,showing am a bona fide full time PhD Student,with  8 months resident visa of my current resident country to show.   You have submitted a bank statement  in your name for the (Bank Name). I note that there are several cash deposit over the reporting period. The source of these fund is not clear and they dont reflect your stated annual income of 12,200GPS.   Note: I provided the name of sponsor(mom) with her payment payments slips,and other back others documents from my local bank to support the source of it.   I consider that you have not shown sufficiently strong family ,social or economics ties outside the UK or reason to return to your home country at the end of the trip.   Note: I secured my first UK tourist visa(6 months) with two landed properties in my city, resubmit additional landed property with stock shares (3 landed properties of mine ) ,and a letter from my parents stating am the sole heir of their  3 residential properties in the heart of my city. I dont have kids nor married

Over the course of time here on TSE, I have observed individuals whose pattern of visa applications is best described as ''...     serial refusals - Two or more consecutive visa refusals issued by the same regime to the same person. Commonly for the same, or nearly the same, reasons. In some visa regimes Serial refusals can have a cumulative effect wherein the applicant's credibility is increasingly eroded, especially when the application pattern suggests a secondary agenda.   A common thread appears to be the need to visit the destination country (especially Schengen, the USA, or the UK) with a special sense of urgency. Also common in these cases are the following types of questions...   Should I just reapply once again? What are my chances? What can I do to improve my odds in the future? Can I somehow address the previous refusals to avoid them being a burden on all future applications? How can I break the pattern?      NB: This question is intended as a canonical about serial refusals. I have never been personally denied a visa.


I live in Poland. I am a citizen of Turkey, so I am a non-EU citizen. Few days ago i lost my residence card and in 7-8 days i will go to Italy for a nice trip.   I know it's a domestic flight from Poland to Italy, however someone told me that some flight companies are checking validity of your documents. I have a ticket from RyanAir. How screwed up am I?

I'm a non-EU citizen, and I'm studying in Italy.  I traveled to Hungary last week with Ryanair from Italy. I showed them my passport, residence permit and Italian identity card. Everything was OK. But after a week when I wanted to come back to Italy I found that I lost my residence permit. But still I have the passport and identity card (paper).  Now I'm afraid they don't let me get back to Italy at the Hungarian airport. What should I do now?  I have a picture from my residence permit (Permesso di soggiorno).     UPDATE: Fortunately, I found my card in the house, YaaaaY.


Find all postive integers $(a,b,c)$ ,  such that$a^2b-c,b^2c-a,c^2a-b$ are all powers of  2  someone can take a example such this condition

This is a 2015 IMO problem.  It seems difficult to solve.     Find all triples of positive integers $(a, b, c)$ such that each of the numbers $ab-c$, $bc-a$, and $ca-b$ is a power of $2$.   Four such triples are $(a,b,c)=(2,2,2),(2,3,2),(3,5,7),(2,6,11)$.


Consider the below figure and the caption.  Now I want to display only part of the caption in the list of figures instead of the entire caption. For example, here I would like to display "Figure 1.3: Burke-Schumann flame structure in mixture fraction space", only in the list of figures. Is there a way to do this?

When I use \listoftables and \listoffigures I get in the list long captions that appear next to the tables/figures.  I would like to use short captions for this list which summarize these captions. Is that common to do? If so, what is one way to do it?


I am trying to understand the proof provided on  that there is no Lebesgue measure on infinite-dimensional, separable Banach spaces. This proof starts by saying that if $(X,\|\cdot\|)$ is such a Banach space, and $\delta > 0$, and $B$ is an open ball of radius $\delta$, then there is a sequence $(B_n)^\infty_{n=1}$ in $B$ of pairwise disjoint open balls of radius $\delta/4$. Why is that?  For convenience, suppose that $B$ is centered around $0$. I understand that if $X$ is the Hilbert space $\ell^2$ of square summable sequences, then it has a basis $(e_n)^\infty_{n=1}$ defined by \begin{equation*} \begin{aligned} e_1&=(1,0,0,0,\ldots)\\ e_2&=(0,1,0,0,\ldots)\\ e_3&=(0,0,1,0,\ldots)\\ \text{etc.} \end{aligned} \end{equation*} and one can obtain a sequence $(B_n)^\infty_{n=1}$ of pairwise disjoint open balls in $B$, each of the same strictly positive radius, by centering each $B_n$ around a certain multiple of $e_n$.  But how to show this for general infinite-dimensional, separable Banach spaces?

Given an infinite dimensional normed linear space, how would one show that it is possible to fit an infinite collection of non-overlapping balls of radius $\frac{1}{4}$ in the unit ball?  I guess one can immediately reduce the problem to a normed linear space of countably infinite dimensions. The solution seems clear if the concept of orthogonality exists, but not every normed linear space has an inner product so it's not possible to apply something like Gram-Schmidt to produce an orthogonal basis. Is there any way around this, or there another approach that can be used?


While converting from one geosystem to another polygons crossed by 180 meridian left got split into eastern and western parts. Tool used - ogr2ogr library.  Initial geosystem - WGS84, target - Albers-Siberia. Desired projection is shifted from Greenwich to the center of Siberia. So splitting each Chukotka region polygons (the far eastern ones in Eurasia) by two is needless. But conversion doesn't eliminate this artifact.  Is there a way to fix the problem?

I am having the issue where the International Dateline is splitting a polygon I am working with.  I have a layer of the "Federal Districts" of Russia, and the eastern most federal district is being "cut" by the international dateline.   I currently have the data frame's coordinate system set to Asia Lambert Conformal Conic and this places the two "cut" polygons next to each other (how they should be).  I really need the polygon to not be cut and show as a continuous polygon.   I've researched up and down, tried changing the projection/coordinate system, but with no luck.  I've attached a screenshot of the one multi-part polygon that is being split by the international dateline.  I would like it so that there is no cutting of the polygon, and therefore no boundary line going through the polygon.  I've even tried transforming this multi-part polygon into separate, single-part polygons, then merge them back together, but anytime any part of any polygon crosses this line, it gets cut.  Layout View:    Data View:


I have the intension of buying a Drill, At shops, I see the corded and cordless Types, Although the cordless drill is more handy and portable, I always have a little doubt about that it's effectiveness and efficiency might not be as the corded type.....Is it true and also is choosing a cheaper manufacturer going because they are cheaper going to affect the quality of the Drill?

I am planning to build a new Computer table and a book shelf by myself. I will require a drill machine that can drill a hole into wood and that can also drive a screw into this hole (using the drill, not manually). Would I require an Impact drill / Hammer drill / any other type of drill machine?  I would also occasionally use it for drilling into brick (not concrete). I have created a filter based on budget and Brand in the shop where I would be buying. A suggestion of the product here would be even more helpful:


I have some golden syrup in a plastic bottle, all looks normal. It has a best before date Feb 2010. Is it still ok to feed to kids on pancake day February 2015??

I had a tin of golden syrup for a long time - longer than I care to admit. When I opened it up yesterday (to sweeten up some mulled wine), it was granular (a bit like honey can be), and black around the edges.   Is this 'bad', or just different?   Is the blackness the result of some chemical reaction with the tin?  And in general, does it eventually go off, or does it last indefinitely?


In on 18.04, I've updated to linux kernel 5 using sudo apt install --install-recommends linux-generic-hwe-18.04 xserver-xorg-hwe-18.04  Now, when do a apt-get dist-upgrade It downloads both kernel 4.15.0-X & 5.0.0-X but ends up using 5.0.0-X. Now how do I prevent dist-upgrade to download 4.15.0-x? is it even required?

I ran the following a week ago to upgrade from 16.04.1 to 16.04.2 with HWE:  sudo apt install --install-recommends xserver-xorg-hwe-16.04   It installed a 4.8 kernel which I'm running now. Just now, I ran the following:  sudo apt update && sudo apt dist-upgrade   This installed the 4.4.0-62-generic kernel and made that the kernel that will be booted into, I think, because it's pointed to by /initrd.img and /vmlinuz. How do I stop future updates of the 4.4 kernel series and set the kernel that will be booted into next time back to the 4.8 kernel series?


I'm a philosophy student whose knowledge of physics is fairly piecemeal - I've read a few books (prominently Rovelli's Reality Is Not What It Seems) but want to know more. I don't currently have the time (or the means) to enrol in an actual physics course or to devote all of my time to the study of physics, but I want to develop an understanding that I can build upon at a later date. Many of the books I've looked at thus far have either been too immediately technical or assume more familiarity with maths than I'm comfortable with.   Does anyone have any recommendations of introductory books, lectures, podcasts, etc. that will help me to reach a stage of proficiency so that I can navigate more complex terrain unaided? Introductions to classical physics and the history of physics are appreciated, as are exercise books or introductions to the mathematics required. Please assume as little prior knowledge as possible - I have some formal maths training, but it's somewhat hazy, and my grasp of algebraic equations and so on is very loose indeed!

Every once in a while, we get a question asking for a book or other educational reference on a particular topic at a particular level. This is a meta-question that collects all those links together. If you're looking for book recommendations, this is probably the place to start.  All the questions linked below, as well as others which deal with more specialized books, can be found under the tag  (formerly ).  If you have a question to add, please edit it in. However, make sure of a few things first:   The question should be tagged  It should be of the form "What are good books to learn/study [subject] at [level]?" It shouldn't duplicate a topic and level that's already on the list   Related Meta:


How do you prove the space of smooth functions with compact support in an interval $[a,b] \subset \mathbb{R}$, with the metric $\rho(\varphi_{1},\varphi_{2})= \sum_{n=0}^{\infty}2^{-n}\frac{\left \| \varphi_{1} - \varphi_{2} \right \|_{n}}{1 + \left \| \varphi_{1} - \varphi_{2} \right \|_{n}}$ where $\left \| \varphi\right \|_{n} = \sum_{j=0}^{n}\sup_{x \in [a,b]}|\varphi^{(j)}(x)|$ is complete? I've tried to consider the pointwise limit and use the fact that $\mathbb{R}$ is complete but as yet have been unsuccessful. Apparently the proof uses the following fact repeatedly: if $f_{n} \to f$ uniformly and $f_{n}' \to g$ uniformly, then f is differentiable and $g= f'$

Is the space of smooth functions with compact support in an interval $[a,b] \subset \mathbb{R}$, with the metric $\rho(\varphi_{1},\varphi_{2})= \sum_{n=0}^{\infty}2^{-n}\frac{\left \| \varphi_{1} - \varphi_{2} \right \|_{n}}{1 + \left \| \varphi_{1} - \varphi_{2} \right \|_{n}}$ where $\left \| \varphi\right \|_{n} = \sum_{j=0}^{n}\sup_{x \in [a,b]}|\varphi^{(j)}(x)|$ complete?


So given a fair unbaised coin and the objective of choosing one of the three given objects with equal probability. How would you go about the task.  I would toss the coin two times and repeat it if I get two tails. I think that way I would be having 33.3333% choices of selecting one of the three objects.

It is possible to choose between three equally desirable outcomes by tossing a fair coin as follows:  Choose option 1 if the first head appears on an even toss  Choose option 2 if the first tail appears on an even toss  Choose option 3 if the first head and the first tail both appear on an odd toss  Note that option 1 and option 2 are mutually exclusive, because we must have a head or a tail on the first toss.  This works because the binary expansion $$\frac 13 =0.010101010101 \dots$$ has a $1$ in all the even places. Or equivalently because $$\frac 13=\frac 14+\frac1{16}+ \dots +\frac 1{4^n}+\dots$$  This is quite a simple procedure (though perhaps not as well known as it might be). I was pondering in the bath what might be the most convenient set of options if there were five or seven possibilities.  For example I can pick off two fifths using the binary expansion of $\frac 15$ with heads and tails, and use my procedure for thirds to do the remaining three fifths - so it is possible. But can one do fifths or sevenths without resort to this kind of recursive procedure?


It's well known that by application of biot-savart law, the magnetic field at the center of a loop of current is $\frac{\mu_0 I}{2r}$.  Now when we consider a solenoid, isn't the resulting magnetic field at the center inside essentially just formed from a superposition of many current loops?  The magnetic field at the center of a solenoid is $\mu_0 N I$ where N is the number of turns per unit length. If we consider the case where there is only 1 turn, however, this doesn't seem to give the same result that manual integration via biot-savart did.  Similarly, a toroid with only 1 loop should be equivalent to a current loop, but we don't get the same result then either.  Why is it wrong to find the magnetic field at the center of a current loop in this way?

In the B field of the loop, if R is the radius and z is the distance along the axis perpendicular to the center of the loop, let z go to zero, and multiply by N loops. Starting with the B field of the loop axis:  $$B=\frac{\mu_0 i R^2}{2(R^2+z^2)^{3/2}}$$ Becomes: $B_{\text{N loops}}=\frac{\mu_0 i N}{2R}$ and not $B_{\text {solenoid}}=\mu_0 i n$. What is the difference?


Word "Fella" will indicate the gender "Male". Can anyone say the word like "fella" for the gender "female"?.

If sistren is the female equivalent of brethren, what is the female equivalent of fellow?  Words usually paired are: guy/gal; man/woman; boy/girl; lad/lass; brethren/sistren; fraternity/sorority; but I have seen nothing for fellow.


TL;DR The number of polygons has negligible impact on rendering time. I'm having a furniture designed part by part using FreeCAD and exported as Wavefront OBJ (following ). This furniture is then placed in a very simple approximation of my apartment (also modeled using FreeCAD). The problem is with rendering time. With 8K resolution and 2048 samples this is ~14 hours on (not built for this purpose) entry level 8 core 2nd generation Xeon Scalable Processor. With this amount of samples noise is still clearly visible, especially in shadows. Going down to Full HD reduces time to some 50 min. This amount of time is in odds with what I found on the internet, where (apparently) much more rich models tend to render in an order of minutes. This makes me think about one thing: my furniture model is probably much more detailed than average model of object used for rendering in blender. In particular there is plenty of polygons inside the object which are clearly not visible. Do these still slow down the rendering? If yes, is there some tool which could automatically simplify FreeCAD models for rendering removing invisible polygons? Just for the record: I don't have any GPU capable of rendering. EDIT: I made one more super simple experiment: I removed all the furniture leaving just an empty apartment, light and camera. It had negligible impact on total rendering time (Full HD, 32 samples). In retrospect I could have done more to answer this question myself.

Does decimate an object helps cycles rendering faster in blender?  If we decimate the object and use smooth shading, will it render faster specially in those scenes where lightning matters the most?


I rendered an intro template and I don't want to have to render it again. If I didn't select an output folder, where would the file end up?

I'm using the Blender Video Editor. I finished, rendered it, and went to open the file, but I do not know where my file saved to!  I want it to be saved as a video file and I would like to know where it is, but I do not. I've already tried to look through all my folders, but I don't know if I'm checking the right place.


The current software that is in use by more and more universities for the purpose of questions & answers in courses is Piazza. Unfortunately, this software has a broken search capability, and is otherwise clunky (such as not allowing multiple student answers).  I think the Stack Exchange system could work very well for courses, and I wonder if the company has any plans to move into the area of education.

Is the Stack Exchange engine that powers Stack Overflow available to download or install internally for an enterprise or company?  I think Stack Exchange's engine is very great and could be very cool to use for internal enterprise patterns and practices, like the engine of Wikipedia.


I am trying to convert a SHP to KML in QGIS and want to keep all the attribute fields. As far as I can tell when you do this operation, you can only choose 2 fields (DescriptionField and NameField). Is there a way to do the conversion and keep all attributes?

I want to convert a shapefile to a KML using QGIS. When I do it, the output I obtain is without attributes. And I want a similar product as it is provided by shape2kml of zonum solutions.


I'm trying to extract a part of a video with quite accurate time values. I tried following methods which were not a success.  ffmpeg -y -i <input_mp4> -ss 0.570 -f lavfi -i aevalsrc=0 -t 6.690000 -strict -2 -c:v libx264 -preset faster -crf 28 -acodec aac -map_metadata -1 -movflags faststart <output_mp4> ffmpeg -y -ss 0 -i <input_mp4> -ss 0.570 -f lavfi -i aevalsrc=0 -t 6.690000 -strict -2 -c:v libx264 -preset faster -crf 28 -acodec aac -map_metadata -1 -movflags faststart <output_mp4> ffmpeg -y -ss 0 -accurate_seek -i <input_mp4> -ss 0.570 -f lavfi -i aevalsrc=0 -t 6.690000 -strict -2 -c:v libx264 -preset faster -crf 28 -acodec aac -map_metadata -1 -movflags faststart <output_mp4>   In all of those commands I wanted to extract a video with duration of 6.690000 seconds, but actual resulted video was 6.712000 seconds long.  is the uncut FFmpeg output.  Following is the FFprobe command I used to get the duration of the output video.  ffprobe -i <extracted_video> -show_entries format=duration -v quiet -of csv="p=0"   I was referring to  document for FFmpeg. Is there anything wrong with above commands or is there any alternative way to extract the video with accurate time duration?   Input video framerate: 60 fps Input video bitrate: 25380 kbps

I want to extract segments of video with extremely precise start and end points. Unfortunately I'm only seeing accuracy to a hundredth of a second.  ffmpeg -i kayak.mp4 -ss 00:00:00 -t 2.86953 kayak_segment.mp4   Though I expect this segment to have a duration of 2.86953, analysis on the outputted segment shows 2.891.  ffprobe -i kayak_segment.mp4 -show_format -v quiet | sed -n 's/duration=//p'   (returns 2.891000)  How do I best ensure that the durations of extracted video segments are as close to what is specified as possible? I'm not concerned about audio.  Thanks!


I'm using Ubuntu Gnome 17.04 on Asus UX305.  I would like to enable automatic login after waking up from suspend (so I don't have to enter the password).  I have enabled "Automatic Login" in Settings->Users (I have only one user on this machine), but it doesn't work - after waking up from suspend (and restarting) I need to enter password to log in. Any ideas on how to debug/fix this?

On GNOME the screen locks when I suspend, and I find that a bit annoying (no one else in the house uses ubuntu anyway haha). What can I do to stop this?


This question is for 5e; I've posted a similar question for Pathfinder .   I'm designing a character for a campaign whose role is to be a recurring antagonist. When the characters first meet him, I want him to seem undeniably human. The idea is that the party will "kill" him and his body will be destroyed, only for him to be revived later and come back for revenge as Lich.  The party will be able to check him for magical effects when they first meet and I want it to be a surprise that he is a Lich. If they party detects Transmutation or Illusion magic on him or detect him as Undead it will give too much of a hint to his true nature. Disguise self could work, but the Lich's face will be seen by the characters and would require a massive skill to pull off.   Is there a way the Lich could retain a human form without magic?

I'm designing a character for a campaign whose role is to be a recurring antagonist. When the players first meet him, I want him to seem undeniably human. The idea is that the party will "kill" him and his body will be destroyed, only for him to be revived later and come back for revenge as Lich.  The party will be able to check him for magical effects when they first meet and I want it to be a surprise that he is a Lich. If they party detects Transmutation or Illusion magic on him or detect him as Undead it will give too much of a hint to his true nature.   Is there a way the Lich could retain a human form without magic?


So I am using a vm for ubuntu and i want to use my full 2GB of video memory from my graphics card, and i can boost the memory to 256MB but its nowhere near what i want. Is there a mod, driver, ANYTHING, that can allow me to get more than a useless 256MB of video memory?

I have just installed Ubuntu 14.04 on VirtualBox, including the guest additions.   However, the display is really slow. Looking at the display settings I can see that the video memory is only 12MB but I can't move the slider to increase it. The checkboxes for extended features are greyed-out too. See screenshot.  .  How do I increase the amount of memory?  TIA


Is it possible to install Lubuntu on iMac PowerPC G5 using a USB? I created an bootable USB with Lubuntu image using unetbootin, inserted to the iMac, restarted it holding down Option key but the USB image did not appear.

How do I install Ubuntu on my powerpc G5? which version do I download? where do I download it from? and how do I get it to install? I tried burning ubuntu powerpc 12.04 and booting from the cd and all I get is a DOS like setup prompt "boot:" I've tried 'live' and everything else listed when I push tab; but, every time I get a bunch of white text on black screen, then black text on white and then my monitor just goes black and nothing happens??? what am I doing wrong? any suggestions?


I'm trying to implement MVC pattern in C++. I follow the instructions in the file:    But when I compile program I gets this errors:  In file included from C:\Users\Lukasz\ClionProjects\CDDB\Controller.h:10:0,                  from C:\Users\Lukasz\ClionProjects\CDDB\Controller.cpp:5: C:\Users\Lukasz\ClionProjects\CDDB\View.h:17:5: error: 'Controller' does not name a type      Controller *myController;      ^ C:\Users\Lukasz\ClionProjects\CDDB\View.h:28:13: error: 'Controller' does not name a type      virtual Controller *makeController() {}              ^ C:\Users\Lukasz\ClionProjects\CDDB\View.h:33:5: error: 'Controller' does not name a type      Controller *getController() { return myController; }      ^ C:\Users\Lukasz\ClionProjects\CDDB\View.h: In constructor 'View::View(Model*)': C:\Users\Lukasz\ClionProjects\CDDB\View.h:19:34: error: class 'View' does not have any field named 'myController'      View(Model *m) : myModel(m), myController(0)                                   ^ In file included from C:\Users\Lukasz\ClionProjects\CDDB\View.h:10:0,                  from C:\Users\Lukasz\ClionProjects\CDDB\View.cpp:5: C:\Users\Lukasz\ClionProjects\CDDB\Controller.h:17:22: error: expected ')' before '*' token      Controller( View *v )  : myView(v){                       ^ C:\Users\Lukasz\ClionProjects\CDDB\Controller.h:27:5: error: 'View' does not name a type      View    *myView;      ^   My files:  View.h  #ifndef CDDB_VIEW_H #define CDDB_VIEW_H   #include "Observer.h" #include "Model.h" #include "Controller.h"  class View : public Observer {   public:     Model *myModel;     Controller *myController;      View(Model *m) : myModel(m), myController(0)     {         myModel->attach(this);     }     virtual ~View() {  }     virtual void update() { }      virtual void initialize() {}      virtual Controller *makeController() {}      virtual void draw();      Model *getModel() { return myModel; }     Controller *getController() { return myController; }  };  class BarChartView : public View {  public:     BarChartView(Model *m) : View(m) { }     virtual void draw(); };  #endif //CDDB_CONTROLLER_H   Model.h  #ifndef CDDB_MODEL_H #define CDDB_MODEL_H  #include <iostream> #include <cstdlib> #include <list> #include <set> #include <iterator> #include "Observer.h"  using namespace std;  class Model{      string cdName;  public:     Model(string cdName);      void addRecord();     void removeRecord();     void attach(Observer *s) { registry.insert(s); }     void detach(Observer *s) { registry.erase(s); }  protected:     virtual void notify();  private:     set<Observer*> registry; };  #endif //CDDB_CONTROLLER_H   Controller.h  #ifndef CDDB_CONTROLLER_H #define CDDB_CONTROLLER_H   #include "Observer.h" #include "View.h"  class Controller : public Observer {  public:     virtual void handleEvent() {}      Controller( View *v )  : myView(v){         myModel = myView->getModel();         myModel->attach(this);     }      virtual ~Controller() { }     virtual void update() { }  protected:     Model   *myModel;     View    *myView;  };   #endif //CDDB_CONTROLLER_H   Model.cpp, View.cpp, Controller.cpp are empty. I compile this code using cmake  cmake_minimum_required(VERSION 3.3) project(CDDB)  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")  set(SOURCE_FILES main.cpp Model.h Observer.h View.h controller.h Controller.cpp Controller.h Model.cpp View.cpp Observer.cpp) add_executable(CDDB ${SOURCE_FILES})   Any ideas?   EDIT:  Ok, I add class Model; class View; into Controller.h but I have new error 25: error: invalid use of incomplete type 'class View' myModel = myView->getModel();

I often find myself in a situation where I am facing multiple compilation/linker errors in a C++ project due to some bad design decisions (made by someone else :) ) which lead to circular dependencies between C++ classes in different header files (can happen also in the same file). But fortunately(?) this doesn't happen often enough for me to remember the solution to this problem for the next time it happens again.  So for the purposes of easy recall in the future I am going to post a representative problem and a solution along with it. Better solutions are of-course welcome.     A.h  class B; class A {     int _val;     B *_b; public:      A(int val)         :_val(val)     {     }      void SetB(B *b)     {         _b = b;         _b->Print(); // COMPILER ERROR: C2027: use of undefined type 'B'     }      void Print()     {         cout<<"Type:A val="<<_val<<endl;     } };       B.h  #include "A.h" class B {     double _val;     A* _a; public:      B(double val)         :_val(val)     {     }      void SetA(A *a)     {         _a = a;         _a->Print();     }      void Print()     {         cout<<"Type:B val="<<_val<<endl;     } };       main.cpp  #include "B.h" #include <iostream>  int main(int argc, char* argv[]) {     A a(10);     B b(3.14);     a.Print();     a.SetB(&b);     b.Print();     b.SetA(&a);     return 0; }


String st="java is awesome";    char[] ch=st.toCharArray();     st="";     for(int i=0;i<ch.length;i++)     {         if(ch[i]!='a')             st=st+ch[i];         else if(ch[i]=='a')             st=st+ch[i]+'#';     }     System.out.println(st);   i have to perform character concatenation without using '+'.Is it possible?

Assuming String a and b:  a += b a = a.concat(b)   Under the hood, are they the same thing?  Here is concat decompiled as reference. I'd like to be able to decompile the + operator as well to see what that does.  public String concat(String s) {      int i = s.length();     if (i == 0) {         return this;     }     else {         char ac[] = new char[count + i];         getChars(0, count, ac, 0);         s.getChars(0, i, ac, count);         return new String(0, count + i, ac);     } }


During the orientation programme conducted for the resource persons in English in Hyderabad,one of the professors wrote a sentence on the board and it is given below     The board writes well.      She asked us to say whether the verb write is transitive or intransitive. We could not satisfactorily answer the question.because It did not look like either transitive. or intransitive she explained something which I forgot so I need explanation from the scholars  Another example  is        He walks the dog everyday   I found the sentence in a text for Tenth class students  The sentences are indifferent from the sentences like he writes well and the dog walks.   I would like to know the function of the verb and the subject in the sentences above,  I know that the two verbs are different   I would like to know whether the topic comes under semantics.  EDIT This is not a duplicate of the question  because I am not asking whether the sentences mentioned above are grammatically correct, my question is focused on their syntax and semantics.

You're standing in front of a ticket vending machine and it says "The ticket is printing". Is that correct or should it be "The ticket is being printed"?  EDIT:  If both are correct, which one should be preferred or is more common?


Prove that $\mathbb{R}_l$ is not a second countable. ($\mathbb{R}_l$ are the real ones with the topology of the lower limit)  I have tried to reason for the absurd and suppose that $\mathbb{R}_l$ has an countable basis but I can not find it, in that case any discrete subset of $\mathbb{R}_l$ would be countable, but I do not know how to find an countable base and if I find it I do not know how to find a discrete subset that is not countable.Could anyone help me, please? Thank you very much.

I am trying to prove that $\mathbb{R}$ with the lower limit topology is not second-countable.  To do this, I'm trying to form an uncountable union $A$ of disjoint, half-open intervals of the form $[a, b)$, $a < b$. Is this possible? I think this would imply the $A$ is open but no countable union of basis elements could coincide with $A$ therefore making the real numbers with the lower limit topology not second-countable.  I think there must exist something like $A$ described above but I am having trouble visualizing it and coming up with a formula to represent it.  Maybe there is some other way to show it is not second-countable.


So speckling might not be the best description, but I'm not sure what else to call it. Neither am I sure if this is the right place to ask this question, so if it isn't, please direct me to a better location.   The speckling can be seen best in the orange/yellow part at the top of the image, though you can really see it throughout. Notice the regular color dots; that's the speckling that I am referring to. I'm using a Mustek A3 1200S Large Format scanner, and nearly every image is speckled. (Maybe 1/50 doesn't have it). The level of speckling varies. Sometimes it isn't too noticeable, and sometimes it completely alters the image. I've noticed it seems more pronounced on oranges.   My question is two-fold: What is causing this, and can I fix it (without buying a new scanner)?   P.S. Again, I apologize if I'm in the wrong place. It was a toss-up between here and Graphic Design SE. Thank you for your time.

I have scanned this photo from a book that's printed with color ink, but the picture is a black and white one. When I scanned it with Vuescan as a color photograph I get vertical lines like    I think it's called a Moire pattern, but I haven't seen one like this one. How can i prevent them or how can I get rid of them in Photoshop or other software?


In other words, is $S^2$ unbiased for $\sigma^2$ for any distribution? I know how to prove this for the normal distribution, but is it possible for me to prove this generally? Thank you

The formula for computing variance has $(n-1)$ in the denominator:  $s^2 = \frac{\sum_{i=1}^N (x_i - \bar{x})^2}{n-1}$  I've always wondered why. However, reading and watching a few good videos about "why" it is, it seems, $(n-1)$ is a good unbiased estimator of the population variance. Whereas $n$ underestimates and $(n-2)$ overestimates the population variance.  What I'm curious to know, is that in the era of no computers how exactly was this choice made?  Is there an actual mathematical proof proving this or was this purely empirical and statisticians made A LOT of calculations by hand to come up with the "best explanation" at the time?   Just how did statisticians come up with this formula in the early 19th century with the aid of computers? Manual or there is more to it than meets the eye?


If $E$ and $F$ are disjoint closed subsets of a metric space $(X,d)$, then is $dist~(E,F) >0?$  My attempt:  Suppose $dist~(E,F)=0.$   Then $\exists~e \in E,f \in F$ such that $~\forall ~r>0,~d(e,f)<r.$  $\implies f$ is an accumulation for the set $E$ and $e$ is an accumulation point for $F$.  But, since, closed sets retain their accumulation points $\implies f \in E \bigcap F$ . But given that $E \bigcap F = \{\emptyset\}$ leading to a contradiction.   Hence, $dist~(E,F)>0.$  Could someone please have a look at my proof and point out flaws , if any.  Thank you very much for your help!

Let $A$ and $B$ be two sets of real numbers. Define the distance from $A$ to $B$ by $$\rho (A,B) = \inf \{ |a-b| : a \in A, b \in B\} \;.$$ Give an example to show that the distance between two closed sets can be $0$ even if the two sets are disjoint.


There are many ads when playing videos on the Youtube app, I have tried many things but nothing works. Is there a way to avoid all the ads?

Since ads are almost inevitable on official YouTube app on Android device, I was wondering if those can be skipped automatically?  This post is only about those ads which can be skipped, lets ignore ads which can not be skipped.  For example: When YouTube video starts, for some ads, there is an option to "Skip this ad in 5 sec".   Once "Skip ad" label is enabled, we can click on it to move to video. Of course this is all manual, and as a user you need to focus on EXACT timing to HIT the skip button. And it becomes worse if the video is having multiple Ads(few of which will be shown in future time), where when Ad plays, user need to again click manually to skip it.  Can this be AUTOMATED, meaning when there is an Ad which can be "Skipped", then just let the YouTube skip it without user's intervention.   This will be specially useful for those videos which has multiple Ads spanned across the video length and few of them can be skipped.  Looking for a solution on non-rooted device.  Update: It seems like Google is introducing new ad format called .  Bumpers, which are unskippable 6-second shorts placed in front of videos.      So, soon we may not see an ad which can be skipped, forget about   skipping it via automation!


Let : $$f(x)+f\left(\frac{1-x}{x} \right)=x$$ then: $$f(x)=?$$   My Try :  $x\to  \dfrac{1-x}{x}$  \begin{align}f\left(\dfrac{1-x}{x}\right)+f\left(\frac{1-\dfrac{1-x}{x}}{\dfrac{1-x}{x}} \right)&=\dfrac{1-x}{x}\\ f\left(\dfrac{1-x}{x}\right)+f\left(\dfrac{2x-1}{x^2} \right)&=\dfrac{1-x}{x}\end{align}  And $u=\dfrac{1-x}{x}$  $$f(u)+f\left(\dfrac{2x-1}{x^2} \right)=u$$  Now what ?

What function satisfies $ f(x)+f\left(\frac{1-x}x\right)=x$ ?


A man claims he wants to send me money to my credit card. He wants me to send him a picture of both the front and back side. He claims that he’s going to send it to his accountant and put me on a payroll. He also wants my login information. I’m not sure what to do , it’s not like I have a balance on it or he can take any money out of my savings, but with the picture it gives him all of the information to use it online.

A friend of mine is in another state wanting to pay my credit card. He says he needs my credit card number, name on card, username, password, and card limit. Is he trying to defraud me? Or does he really need all of this info to pay off my card?


Is there a way to automate the creation of a Network Dataset in Model Builder using a line shapefile as an input? (ArcGIS 10.4)  The only documentation I have been able to find on creating a network dataset involves right clicking on a feature dataset > New > Network Dataset.   I have tried using the "Build Network" stand-alone tool, but it will not accept either a polyline or polylineM as an input. It seems like the "Build Network" tool simply re-builds any pre-existing network dataset.

I am working on modeling a project that requires me to create a network dataset in ArcCatalog. To do this, you simply right click on the roads shapefile and choose, "Create Network Dataset". You then just follow the wizard. I was wondering how that can be modeled in ModelBuilder.   There is a "Build Network Dataset" tool, but that doesn't seem to be what I'm looking for.


Find smallest $\sigma$-algebra so that it contains sets $\{x\}$, where $x \in \mathbb{R}$.  I was thinking of putting  $ F = \{ A\subset \mathbb{R} : A \text{ is countable or } A^{c}  \text{ is countable}\} $, but while I was proving it, I figured out that maybe that isn't it.

Let $S=\{\{x\}\mid x \in \mathbb{R}\}$. Is $\sigma(S)$ included in the Borel $\sigma$-algebra on $\mathbb{R}$? Is $\sigma(S)$ equivalent to the Borel $\sigma$-algbrea on $\mathbb{R}$?    I think the answer to the first question is yes. Because the Borel sets include singletons, the Borel $\sigma$-algebra must contain the smallest sigma-algebra of the set of all singletons.   Here's my attempt at the second question: my answer would be no. Countable unions (or intersections) of countable sets are countable, so that any $X \in \sigma(S)$ is either countable or a compliment of a countable set. Therefore, the interval $(0,1) \not \in \sigma (S)$ but it is included in the Borel $\sigma$-algebra. My issue here is that I don't know how to formalize this statement, if it is even correct.


I have simple WPF application, and I need to let user choose value from Calendar and then work with the day only. For example, user chooses date 06/08/2020, so I need to take the "06" value and assign it to double variable, then work with it in some mathematical equations. Unfortunately I did not find on the interner, how to exactly do it. When the user enters number into textbox, its quiet easy, you just state the variable and put the TextBox.Text as a value, like double x = double.Parse(TextBox1.Text); Can you guys help me on this?

I have no idea how to use the DateTimePicker control in WPF. It is not available in the Toolbox.


I have a confusion matrix,But I want to increase its scale along x-axis and y-axis for better reading. for plotting confusion matrix, I am using sklearn confusion matrix. Since the class labels are around 20, so I want to increase the size. These options not working  **AS THEY ONLY INCREASE THE SIZE OF THE FIGURE AND NOT THE PLOTTED CONFUSION MATRIX INSIDE IT  fig, ax = pplt.subplots()#pplt.subplot(111) fig.set_size_inches(25.5, 15, forward=True)

How do you change the size of figure drawn with Matplotlib?


I am trying to get Emacs-like Keybindings in GTK, Firefox, Chrome, etc.  I have followed the directions recommended  (and in lots of places) but to no effect.  In other words, I added gtk-key-theme-name = "Emacs" to my .gtkrc-2.0, and I also ran gconf-editor and set /desktop/gnome/interface/gtk_key_theme to "Emacs".  I even rebooted just for good measure.  I am using an ordinary 12.04 install, with Unity 3D as the desktop environment.

Can anyone tell me how to enable Emacs keybind on Chrome?  I found some links but they are either  so or  (I don't want external tools to be run for this purpose).


Should danger approach either its nest or the crocodile nest, the bird would emit warning cries.   A. What is the grammatical name for this expression? B. What is its function?

What is the meaning of should loss occur in the following text?     Backup and recovery procedures protect your database against data loss and reconstruct the data, should loss occur. The reconstructing of data is achieved through media recovery, which refers to the various operations involved in restoring, rolling forward, and rolling back a backup of database files. This chapter introduces concepts fundamental to designing a backup and recovery strategy.


I am having a bit of difficulty wading through the what seems to be multiple usages for Observables in Quantum Mechanics.  "" However it seems as if the observables are actually the eigenvalues of the operator:  as well as, according to wikipedia "a system observable is a measurable operator, or gauge, where the property of the system state can be determined by some sequence of physical operations" . But here is a prime example of where they are calling the operator $O$ an observable, but as it "operates" on some vector and there are eigenvectors and eigenvalues (the observables), associated, I don't understand why they are using observables for the operator as well . I can see that observables are associated to operators, but I don't see why they are called observables.  Any help is appreciated.

In Quantum mechanics, observables are represented by hermitian operator. But does every hermitian operator represent a observable? If not , how do we know that whether a hermitian operator represent observable or not? What is the precise definition of the term "observable"?


First let me show my launcher :-     I feel my launcher is made to look ugly by the 'square-tile-thing'(for the lack of a better word) thats behind the icon. I want the icons alone to be viewed(without the tile behind). So are there any ways to remove the 'square-tile-thing' ?  PS:- I am using Ubuntu 14.04 LTS with unity. By 'square-tile-thing' I mean the square that is around each icon. (See the picture above or see your own launcher!)

Is there a way to turn off the boxes around the icons in Unity?  Clarification: I do not mean the backlight color -- there are plenty of questions about turning that off. I want the icons, and just the icons, to appear in the Unity bar, without any lights and shadows and borders. Can this be done?


I am a college student considering applying to PhD programs both in the US and internationally. Currently I research in a lab affiliated with a top US university and run by my older brother, an instructor at that university. I really enjoy my research here and hope to continue with it; however, I worry about getting letters of recommendation for grad school. I will ask professors in project based classes at my university, but if I continue with this lab as I hope to, only my brother will be qualified to write one about my research abilities. Although the group has other affiliated instructors, my brother oversees the division I research in and my work. Will an admissions committee simply chalk a letter from him up to nepotism or, provided I demonstrate meaningful research, understand the circumstances?

My mother is a quite famous researcher (she has a PhD) on the field I want to do a PhD in. She works on the industry (not academia). I helped her on successful projects. She knows more about my work than my professors since we have worked much longer together.  Is it a good idea to ask for a recommendation letter from her? Since our personalities are very similar she can point out the high probability that I will be successful like her?


I added a new entry type to my book, article and incollection functions called abbreviation. This way, dictionaries appear in the bibliography as my publisher wants them to appear :      TLIO = Beltrami, Pietro G./Leonardi, Lino (dir.),Tesoro della Lingua Italiana delle Origini,Florence, CNR, 1998-., [URL = .   My problem now is that, in the bibliography, these entries are sorted alphabetically by the author, not by the abbreviation:      Casula Cant. Enn. = Antioco Casula,Boghes de Barbagia. Cantigos d’Ennargentu.ed.Giovanni Pirodda, Nuoro, Ilisso, 1999.      Ax, Wolfram,Zellmer, E., Die lateinischen Wörter auf -ura, Indogermanische Forschungen, 82(1977), 302-307.      TLIO = Beltrami, Pietro G./Leonardi, Lino (dir.),Tesoro della Lingua   Italiana delle Origini,Florence, CNR, 1998-., [URL =   .      Buchi, Éva,Where Caesar’s Latin does not belong : a comparative   grammar based ap-proach to Romance etymology   I need my bibliography to consider the abbreviation  for the alphabetic sorting instead of the author, each time there is such an entry for a reference, but I don't know how to modify my bibliographystyle so that it will do this.  Any help would be very welcome !   A simplified version of my code is:   \documentclass[openany,ngerman]{book} \usepackage[small]{dgruyter} \usepackage{microtype}  \usepackage{fontspec} \usepackage[main=french,italian, spanish, portuguese, latin, greek]{babel} \usepackage[round]{natbib} \usepackage{amsmath,amsfonts,amssymb} \usepackage{graphicx} \usepackage{lmodern}  \begin{document} Cf. \cite{DCECH}\\  \bibliographystyle{Bianca} \bibliography{bibliographie}  \end{document}   And you can find my bibliographystyle here :

I've got a bilingual bibliography (Russian and German). I want to sort the entries alphabetically. The Russian entries have to appear alphabetically as well. Unfortunately, since the authors names are written in Russian using the \cyr command (for cyrillic), the Russian entries are sorted by the first name of the author, not the second. Is there any possibility to change my .bst file? In plain.bst I deleted the sorting function. But now it sorts by the text citation order, which I don't need.  It would be best if there was a style (looking like plain style) which sorts after the source file, i.e. how the entries are made by hand in my myliterature.bib file.


Very simple question. I want to know the non-diagonal physical dimensions of the screen itself of a Nexus 7 (eg: 4" by 5" or whatever).  Every site I look it up on seems to just happily repeat that it's a 7" tablet with 1280x800px and so on.

I'm not asking the diagonal values, but the length and breadth ones of the Nexus 7. And only of the LCD screen, not the entire hardware.


Using the definition, that for every $\epsilon>0$, there exists a $N\in\mathbb{N}$, so that $d(v_i,L)$ for all $i\geq N$, where $v_i$ is the $i$th vector in the sequence. And $L$ is the limit.  I assumed that let there be two limits, $L$ and $M$.  Now I choose my epsilon to be $\frac13d(L,M)$, but after that, how do I proceed? Plain algebra doesn't help.  Note that $d(a,b)$ is the distance between vectors $a$ and $b$ in $\mathbb{R^n}$.

I'm reading through a proof in my lecture notes:     Every convergent sequence of a metric space has a unique limit.   Suppose $\lim_{n \to \infty} x_n = l$ and $\lim_{n \to \infty} x_n = m.$ Then for every $\epsilon > 0,$ there exists $N$ such that for every $n \geqslant N,$  $$d(l,m) \leqslant d(l,x_n) + d(x_n,m) < \epsilon + \epsilon = 2 \epsilon. $$  So $(\star) \hspace{1mm} 0 \leqslant \frac{d(l,m)}{2} < \epsilon \Longrightarrow \hspace{1mm} (\star^\prime) \hspace{1mm} \frac{d(l,m)}{2} =0 \Longrightarrow l = m.$  I can follow the proof up until the jump from $(\star)$ to $(\star^\prime)$. Why does $\frac{d(l,m)}{2}=0$?


html markup:  <input id="fileSelect" type="file" id="file" name="files[]" multiple="multiple" accept="image/*" />   I am uploading multiples files with php. I want to make an array of upload files and send to server with ajax. how to make an array of the multiple selected files?  JavaScript:  jQuery.ajax({     url: 'insertfiles.php',     type: "POST",     data: {       file: // array of selected files.     },     success: function(data){     },     error: function(data){       alert( 'Sorry.' );     } });

I would like to upload a file asynchronously with jQuery.     $(document).ready(function () {     $("#uploadbutton").click(function () {         var filename = $("#file").val();          $.ajax({             type: "POST",             url: "addFile.do",             enctype: 'multipart/form-data',             data: {                 file: filename             },             success: function () {                 alert("Data Uploaded: ");             }         });     }); });  File <input type="file" id="file" name="file" size="10"/> <input id="uploadbutton" type="button" value="Upload"/>     Instead of the file being uploaded, I am only getting the filename. What can I do to fix this problem?


Prof. Charles Pinter's "A Book of Abstract Algebra" provides this exercise:     Ch 7 (Groups of Permutations)    Part B #3 - Find a four-element abelian sub-group of $S_5$. Write its table.   Please provide guidance on how to answer this question.  I'm guessing that I need to come up with a permutation table:  $$\begin{matrix} 1& 2& 3& 4& 5&\\ ?& ?& ?& ?& ?&\\  \end{matrix} $$  Then, I need to compose $f$ (where f defines the initial table) 5x in order to get $S_5$. However, I'm unsure if that's correct, and how I'd proceed once I found $S_5$.

I have a homework question from my intro to group theory class.   Question:   Find a 4 element abelian subgroup of $S_5$.  Write it's table.  This is where I've gotten so far, but I don't even know if I'm on the right mental track.  We know $S_5 = \{1,2,3,4,5\}$. Abelian means the subgroup of $S_5$ is commutative.   I am having trouble figuring out how to start this.  Do I pick any 4 elements of $S_5$?  Or are there particular elements that must be chosen?  Do I perform permutations on the group first? Or do I chose my 4 elements, and then perform the permutations?  Thank you!


Is a Virtual Terminal the terminal that you get when you type Ctrl+Alt+F#, and which is represented by the file /dev/tty#.  While a Pseudo Terminal is a terminal that actually runs "inside" a tty, for example: gnome-terminal, xterm, etc. And which is represented by the file /dev/pts/#.  Am I correct?

I think these terms almost refer to the same thing, when used loosely:   terminal shell tty console   What exactly does each of these terms refer to?