Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$

This is the problem I am currently having trouble with:  If $\lambda_1$ and $\lambda_2$ are eigenvalues of matrix  $$         \begin{bmatrix}         a & b\\         c & d\\         \end{bmatrix}$$prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$.     $$A=\begin{bmatrix}     a^2 & ab & b^2\\     2ac & ad+bc &2bd\\     c^2 & cd &d^2\\     \end{bmatrix}$$  What have I considered so far:   I tried to find characteristic polynomial of first matrix and then find the roots which would be $\lambda_1$ and $\lambda_2$. I was hoping I can make a connection with characteristic polynomial of matrix $A$, but it got too complicated and did not seem like the right idea. Since there are two eigenvalues for first matrix, there are two eigenvectors. I thought about somehow using $A\vec v_i=\lambda_i\vec v_i$, where $i=1,2$  Also, I thought about finding a connection between these two matrices. What I see is that the sum of elements of first and second column, of first matrix, are $(a+c)$ and $(b+d)$, respectively.  Sum of first, second and third column of matrix $A$ are $(a+c)^2, (a+c)(b+d)$ and $(b+d)^2$. Now, if I could assign $\lambda_1$ and $\lambda_2$ to $(a+c)$ and $(b+d)$, then I would get that sum of first, second and third column of matrix $A$ are $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$, but what would be next?   I thought it would be good to combine 2. and 3rd idea, but I am not making any progress.  I appreciate any help.


Is it possible to block one cookie on a domain, without blocking all cookies on that domain? (I want to block the tracking cookies, without blocking the cookies that are required for functionality.) I'm using Chrome on Windows.  I'm aware of  but the answers given don't directly address the question.


How to format & print floating point numbers in Java with leading zeros?

For example: 23.7748884 and 344.456445 are the numbers I am working with. I am looking for the output with the format "000.0000". The desired result would be 023.7749 and 344.4564. I tried:  String.format("%.4f", 23.7748884) // Output: 23.7749, NOT OK! Desired: 023.7749 String.format("%.4f", 344.456445) // Output 344.4564, OK!


What does "A realization of independent copies"?

I read in statistic, "a realization of independent copies" from "Elements of copula modelling with R", and do not understand the meaning. I search and found that it means, the two random variables have the same distribution, but they are independent . I also found that the copies themself cannot be independent. That is, they are identical but not independent. So, I still do not understand what does "a realization of independent copies" and why they are not independent?


Redirect std::cout to newly created console

When you create a C++ console application under Windows you automatically get the console window created for you and std::cout outputs to the console window.  I have a GUI application for which I also want to create a console window. I can create the console window using the  AllocConsole() function, but how do I redirect / attach std::cout to the console so that the output appears in the console window?


Is there a difference here:        It happened that he did not go to work today.   As it happened, he did not go to work today.      Do "it happened that" and "as it happened" have different meanings?


Activating iPod that is linked to another Apple ID — previous owner not available

I bought an iPod off of ebay, and went to activate it. However, it was linked to another person's Apple ID and I have no contact with them. The ebay seller does not have the Apple ID either. Is there anyway around activating this iPod without contact with the original owner whose Apple ID this iPod is linked to?


I've been wondering how to do this for a while but I couldn't find anything that gave me answers. I'm trying to make a realistic-ish model but I don't know how to round the edges.


I have the following code:   Iterator<ggItem> iter = ggItemTimestampMap.keySet().iterator();  ggItem gg;  while (iter.hasNext()) {         gg = iter.next();         if (DateTime.now().isAfter(ggItemTimestampMap.get(gg).plusSeconds(10))) {              Log.v("ggItem 10 second limit:", gg.toString());              //If it hasn't been seen 10 seconds after its last timestamp. Remove it from the ArrayList and remove it from the ggItemTimeStampMap HashMap.              ggItemTimestampMap.remove(gg); //TODO probable problem causer.              removeggItemFromList(gg);          }  }   I get a ConcurrentModificationException error on the iter.next(); call and am uncertain why?  I realize you cannot both access a hashmap of object keys and timestamp values and modify it at the same time, but doesn't the iterator counteract that?


How to plot a graph from its adjacency matrix and coordinates of vertices?


Check if this proof about real numbers with an irrational product is correct.

Can anyone confirm if my proof is correct, please?  Claim:- “If $x$ and $y$ are real numbers and their product is irrational, then either $x$ or $y$ must be irrational.”  Proof:-   Assume that both $x$ and $y$ are rational. Now, let $x = \dfrac pq$ and $y = \dfrac mn$ since both of them are rational. $xy =\dfrac pq * \dfrac mn = \dfrac{pm}{qn}$ Thus, if the product $xy$ can be written as a fraction, it's not a irrational number. Therefore if one of $x$ and $y$ is not irrational, then the product is not irrational.  By the principle of proof by contraposition, If $x$ and $y$ are real numbers and their product is irrational, then either $x$ or $y$ must be irrational.


"reshaping" a list to a list of sub-lists

I want to break a list into sub-lists of n elements. I could convert the list (after adding appropriate padding) to a numpy array, e.g.:  n = 20 L = [x for x in range(93)] Lnp = np.array(L+[0]*7).reshape(-1,n) Lgrouped = [g for g in Lnp]     but this is sub-optimal. What would be a good way to do this without numpy? (itertools comes to mind, but didn't seem to find a straightforward function...)


Let $A$ be a ring. Let $x$ nilpotent and $u$ $\in$ unit of $A$ then $(x + u)$ $\in$ unity of $A$.

We have that, $x^{n}=0$ for some $n$ $\in$ $\mathbb{Z}_{+}^{*}$.  I want to find some $y$ $\in$ $A$, such that, $(x+u)y=1$,  so that $(x+u)$ is unity of $A$.  Could you help me determine $y$ or show a better demonstration?


Python Access Variable from Function to function

Hi I have question in Python, If my question is duplicate. Please link to the solution that have the similarity between mine I have this function which set idinput from input() however, the value don't change and from another function it read it as 0, and AddStudents() Function doesn't change it value. It append to the list correctly but in another function it read it as initial 0 materials = {} student = {} sidlist = [] idinput = 0    # Add Students def AddStudent():  idinput = int(input("ID: "))  name = input("Name: ")  lastname = input("LName:")  student.update({idinput: {name: lastname}})  # Append ID To ID List  sidlist.append(int(idinput))  AddMaterial()   def AddMaterial():  materialinp = input("MAT:")  degreeinp = int(input("DEGREE:"))  sidlist.append(idinput)  materials.update({idinput: {materialinp: degreeinp}})   askUserToContinue = input("Do you like to add more materials?: y/n")  if askUserToContinue.lower() == "y":   AddMaterial()  else:   print("Do you like to add more student or do search y/n")   askUserChoice = input(": ")   if askUserChoice.lower() == "y":    AddStudent()   else:    GetInfo()   and Thank you.


How should I inform my advisor about struggles with Aspergers syndrome?

Although similar questions have been asked before, I hope this is not a duplicate as I'm not asking about whether I should inform my advisor (that's already decided), but how and when to do it.   My situation is a little different than most in that I'm a biology major, and hoping to study autistic spectrum disorders for grad school. Aspergers almost became my "special interest" in a way, and so I'm trying to incorporate that into my work. Under these circumstances, I would expect my advisor to be a little more sympathetic to my condition. However, because I'm not officially her grad student yet (doing a summer project before lab rotations in her lab, with the possibility to become a permanent student made clear), I'm not sure exactly when to tell her. Specifically, should I do it before or after officially joining the lab? I'm leaning towards before since if any problems arise because of this, I'd like to know beforehand and seek out other advisors. But I'm wondering if this could also create an awkward situation since she can't legally discriminate me?  Also, how much should I disclose about my struggles? Should I be matter of fact and just state that I have this disorder (assuming she understands the implications), or actually outline some of my challenges.


What exactly does $\langle a,b \rangle$ mean? Where a and b are elements of a group G?

Does it mean either a or b will generate the whole of $\langle a,b \rangle$ or does it mean that some of the elements will be generated by a, some by b, and some by $a^rb^q$? The book I'm reading doesn't really make it very clear.


sql injection protection by restricting common symbols

Just a quick question about sql injections. I know that in order to do one you must enter some mysql code and enter it into a form textbox or somewhere and it would give you back the data. With my website, to protect the data i made it impossible to send the form to the database if the user uses an any '@', ';', or '/' symbols in the textbox, because those are some common symbols used to retrieve the info through injection. Do you think that i'm protected?


I have a Mac OS X and VMware Fusion.  I did a fresh install of 12.04.  I do not have VMware Tools installed.    I read that I do not have to log in at the command window, that I have to wait for VMware Tools to get installed. It seems like something is wrong.


What is more likely to boost my gaming performance: a new GPU or more RAM?

I would like to be able play GTA:4 on my PC, however my computer's specs are not the best.  I have an Intel Pentium R Dual Core e5200 2.50 ghz (Overclocked to 3.41 GHz) with:   ATI Radeon HD 4300 512 MB 2GB DDR2 RAM.    But it still cant support higher resolutions in some games. Which should I upgrade first, the GPU or RAM (I.e. which upgrade will give me the most benefit at this stage?) I think my CPU is OK to play games with.


Reading information from .bib file with lua?

I'm wondering if it's possible to access the information in a .bib file using Lua code in LuaTeX. Basically, I have a function where I'd like to be able to add idiosyncratic custom citation styles for certain works that rely on information other than the standard author/title/year available in most citation packages. I'm also open to a non-Lua way of doing this, but I haven't found any clear answers yet. The goal is to be as parsimonious as possible in terms of not having to duplicate information in multiple .lua/.bib/.tex files. Edit: Upon request, a MWE: We have a .bib that contains the following two entries: @book{yassawi1904,   author={Yassawī, Xoca Aḥmad bin Ibrāḥīm bin Muḥammad bin Iftiḥār},   title={Dīwān-i Ḥikmat},   publisher={Imperatorskaja Universitet},   editor={(anon.)},   address={Kazan},   year={1904} }  @book{yassawi2013,   author={Yassawī, Xoca Aḥmad bin Ibrāḥīm bin Muḥammad bin Iftiḥār},   title={Diwani Hikmet},   publisher={Living Zen Books},   editor={Johnathan Trapman},   address={Glastonbury},   year={2013} }  We want to be able to produce a citation that looks something like this:  This word appears as blah in ed. Kazan (1904), but this seems to be an error for bleh, as reflected in ed. Trapman (2013).  where the first would be based on a function that uses the address, and the latter the name of the editor. Edit: To be clear, I'm not having trouble writing the Lua; just asking if its possible in any way (Lua or not) to write a function that access bib information like this.


Color intersection between curves using fillbetween

I have two Guassian distribution curves, as shown here and I am attempting to color the areas under the curves as well as the intersection between them, like here:    I assumed fillbetween would be the appropriate tool here, but that produced some strange results. Below is the code  \begin{tikzpicture}     \begin{axis}[     axis lines=left,     domain=0:10,      samples=100,     ymin=0,     xtick=\empty,     ytick=\empty,     enlargelimits=false,      clip=false,     ]      \addplot [thick, orange, name path=cat] {gauss(x, 3, 1)} node[pos=0.3, above]{cat};     \addplot [thick, purple!70!black, name path=puma] {gauss(x, 5, 0.5)} node[pos=0.5, above right] {puma};      \path[name path=axis] (axis cs:0,0) -- (axis cs:10,0);      \addplot[         thick,         color=orange,         fill=yellow,         fill opacity=0.25     ]     fill between[         of=cat and axis     ];      \addplot[         thick,         color=purple!70!black,         fill=purple!70!black,         fill opacity=0.25     ]     fill between[         of=puma and axis     ];      \addplot[         thick,         color=white,         fill=blue,         fill opacity=0.25     ]     fill between[         of=cat and puma     ];     \end{axis} \end{tikzpicture}   which produces this:    Every other answer I've found either miraculously makes fillbetween work or avoids it entirely (usually in ways that seem more complicated than is necessary for a simple task such as this).   Can anyone explain to me what is missing to make fillbetween achieve the desired results or recommend a clean alternative? Thanks in advance.


Suppose $f \in L^{p_0} \cap L^{\infty}$ for some $p_0 < \infty$.   Prove that:  $\lim_{p \rightarrow \infty} \|f\|_p=\|f\|_{\infty}$  My attempt:  So the first step seems to be showing that the limit exists at all. I'm having trouble showing this, I feel like I'm getting a massive case of tunnel vision.  I know that we have an upper bound of $\|f\|_{\infty}$, but the function isn't monotone so that alone doesn't ensure the limit exists. I've been toying around with trying to find a convergent subsequence, and I think I've cooked something up, but then that didn't really do much for me. Could use some help on this one. Thanks!


I'm creating a large ocean with the Ocean Modifier for a still render. I need the ocean to be fairly choppy but find that the only way I can get it fairly choppy is if I repeat the texture 5 time in both X and Y direction as per image below.    This makes the texture look very repetitive. Is there a way that I can create a large size ocean with lots of choppy waves that are not an exact repeat?


What is the difference between "off" and " off of"?

I heard somebody say that you get her off of me. I thought that "you get her off me" is right. So what is the difference between "off" and "off of"?


What is the difference between electric spark and electric arc?

In my student book they separate these two and indicate that sparks need high voltage to occur while arcs need low voltage with normal or low pressure and electric arcs CAN come with heat and bright light. But when I search on the web many people said that arc is just a hotter version of spark. So what is the difference between them?


Java: Why can I return a Set(Interface)?

I know that we cannot instantiate an interface.  HashMap method, keySet(), its return type is Set.  public class aMap{     public static void main(String args[]) {         HashMap newmap = new HashMap();         newmap.put(1, "please");         newmap.put(2, "help");         newmap.put(3, "me");         System.out.println("Key set values are: " +                 aMap.keySet());     }     }   Output: Key set values are: [please, help, ma]  -Why can the method return a Set, which is a interface?(if Set cannot instantiate)  -Suppose Set interface can only have static final attributes and empty methods, why can it (stores) Strings into a Set?


Finite Cartesian Product of Countable sets is countable?

Is the finite Cartesian Product of Countable sets countable?  If possible, could you give a bijection that would work for any example?  Any help would be appreciated.


All the textbooks I have ever come across during the course of my studying English emphasize that future tense should not be used in conditional clauses. For example,  If it rains in the evening, we will not go for a walk. (if it will rain in the evening...) We decided to go for a walk if it didn't rain in the evening. (...if it wouldn't rain in the evening)  However, in the following sentence I'm really inclined to use the future tense.  Don't implement this feature if it will significantly increase the complexity of the user interface.  According to all the rules I know of, the future tense is illegal here. However, my gut feeling tells me that the sentence is correct. If I am wrong, the question ends here. Otherwise please read on. I find the last example different from my first two because:  In the first examples we must wait and see if the condition is true, and then make a decision accordingly, whereas in the last example, we must actually analyze/predict/forecast the future in order to make the decision in the present. (might be irrelevant) In my first language - Armenian - where we have a special mood for conditions, the translation of the third sentence actually uses indicative, whereas the first two use that special mood (the conditional mood, as it were).  Since the second would-be principle is easier for me to experiment with, I noticed that every time a condition uses the indicative mood in my language, I'm inclined to use the future tense in English. As another example:  I will give you the money if it will make you happier.  Am I imagining things or are my examples of the future tense in the conditional clause valid? If they are valid, what rule would you suggest to distinguish the cases when it's OK?  (I do realize that translating a sentence to another language and analyzing the translation doesn't really count as a rule).


Is the title of a US President permanent?

Ultimately I'm wondering whether the descriptive in "former President [Name]" is superfluous or necessary in everyday usage, such as when talking to an audience who knows who the current president is.


How to remove file/directory that "doesn't exist"?

I recently saw that I had two strangely named directories in my home folder. I tried to remove them but was unsuccessful. Here is a look at what I tried:  theo@locker:~$ lh ls: cannot access ',jexcGMEs2uoH,6vFPgl5r3Y': No such file or directory ls: cannot access 'IFslbdRBIjiaEYdbO83xWAed': No such file or directory total 44K drwxrwxr-x 2 theo theo 4,0K Feb 10 15:37 Archives drwxr-xr-x 2 theo theo 4,0K Feb 10 14:38 Desktop drwxr-xr-x 5 theo theo 4,0K Feb 10 15:41 Documents drwxr-xr-x 2 theo theo 4,0K Feb 16 18:20 Downloads d????????? ? ?    ?       ?            ? IFslbdRBIjiaEYdbO83xWAed d????????? ? ?    ?       ?            ? ,jexcGMEs2uoH,6vFPgl5r3Y drwxr-xr-x 2 theo theo 4,0K Feb 10 14:38 Music drwxr-xr-x 3 theo theo 4,0K Feb 10 15:47 Pictures drwxrwxr-x 2 theo theo 4,0K Feb 21 19:37 Private drwxrwxr-x 6 theo theo 4,0K Feb 17 13:18 Projects drwxr-xr-x 2 theo theo 4,0K Feb 10 14:38 Public drwxr-xr-x 2 theo theo 4,0K Feb 10 14:38 Templates drwxr-xr-x 3 theo theo 4,0K Feb 10 15:39 Videos theo@locker:~$ rm -r IFslbdRBIjiaEYdbO83xWAed  rm: cannot remove 'IFslbdRBIjiaEYdbO83xWAed': No such file or directory   I had no better luck with rm -f or sudo. I'm not sure where these files come from either. Does anybody have any ideas?


For any $n$ there's a power of $2$ which contains $n$

So I saw this problem in an Olympiad book,  "Prove that for any natural number $n$, there exists a power of $2$ which contains $n$ in it. "  For example, $n=19$ is in $2^{13}=8192$, $n=24$ is in $2^{10}=1024$.  I tried solving it by Pigeonhole principle, but haven't made any progress. Any ideas?


Cardinality of subsets with fixed cardinal of a set

Let $\lambda\leq\kappa$ be infinite cardinals. Then $| \{X\subset \kappa | |X|=\lambda \} | = \kappa^{\lambda} $  $\leq$ part is trivial, but I don't know how to prove the other part. I used transfinite induction on $\lambda$ but it didn't work to me. Can I have any hint for this?  Thanks in advance


How can I create a curve by providing the coordinates of points 1-4.


I want to join the foll:  col = ('NS', 2013L)   to get:  'NS_2013'   I am doing this:  '_'.join(str(col)), and I get this: "(_'_N_S_'_,_ _2_0_1_3_L_)"


As a unit admin I’m often typing award certificates. The last line of the award citation usually goes something like this:     Private Joan Smith actions reflect great credit upon herself, the 120th Jumping Jacks Company, the 13th fighter Battalion and the United States Army.    It was recently pointed out to me that this is correct:      Private Joan Smith actions reflect great credit upon her, the 120th Jumping Jacks Company, the 13th fighter Battalion and the United States Army.   The first way is what I’m used to seeing and it looks right to me, but has always sounded awkward when reciting it. When I say the other way out loud it sounds better, but both seem to work. Which is correct?


Wine Installation problem after apt-get update

Since a sudo apt-get update, wine is no longer recognized by Ubuntu (as if I removed the package).  I decided to clean it completely and tried to install Wine again without success. OS : Ubuntu 13.10 64 bits  Output of sudo apt-get install wine  The following information may help to resolve the situation:     The following packages have unmet dependencies:      wine : Depends: wine1.6 but it is not going to be installed or                      wine1.7 but it is not going to be installed   Output of : sudo apt-get install wine1.6  The following information may help to resolve the situation:  The following packages have unmet dependencies:  wine1.6 : Depends: wine1.6-i386 (= 1:1.6.1-0ubuntu1~ppa1) E: Unable to correct problems, you have held broken packages   . I found many different potential solutions on AskUbuntu, but no one works :(  Thanks in advance  EDIT : output of sudo apt-cache policy wine  wine:   Installed: (none)   Candidate: 1:1.7.18-0ubuntu1~saucy1   Version table:      1:1.7.18-0ubuntu1~saucy1 0         500 http://ppa.launchpad.net/ubuntu-wine/ppa/ubuntu/ saucy/main amd64 Packages      1.4.1-0ubuntu7 0         500 http://archive.ubuntu.com/ubuntu/ saucy/universe amd64 Packages


Can Poincare representations be embedded in non-standard Lorentz representations?

My impression for how Poincare and Lorentz representations are linked in $3+1$ dimensions is:   Assuming positive mass for simplicity, irreducible representations of the Poincare group are indexed by their mass $M$ and spin $s$. Irreducible representations of the Lorentz group are indexed by two numbers $(s_1, s_2)$ and when restricted to the rotation subgroup contains spins from $|s_1 - s_2|$ up to $s_1 + s_2$ in integer steps. Particles transform in representations of the Poincare group, while fields transform in representations of the Lorentz group. They are related by defining $$|\mathbf{p}, \lambda \rangle = a^\dagger(\mathbf{p}, \lambda) |0 \rangle$$ where $\lambda$ is the helicity, and the field is defined in terms of the creation and annihilation operators in the usual way. The only requirement is that the Lorentz representation used for the field contains the spin $s$ used in the Poincare irrep. A relativistic wave equation is imposed to eliminate the unwanted degrees of freedom.   For example, a massive spin $1$ particle may be embedded in a vector field, which is in the $(1/2, 1/2)$ irrep of the Lorentz group. This vector field has one extra degree of freedom that is eliminated by the equation $\partial_\mu A^\mu = 0$.  Assuming this is right, I'm wondering why I've never heard of "alternative" embeddings. For instance, why can't one embed a spin $1$ particle inside the $(1, 0)$ irrep, which doesn't have any extra degrees of freedom at all, or inside the $(1, 1)$ irrep? For massive particles, I've only ever seen spin $0$ in $(0, 0)$, spin $1/2$ in $(1/2, 0) + (0, 1/2)$, and spin $1$ in $(1/2, 1/2)$. Are other embeddings very clunky, or not allowed, or are they actually used somewhere?


How to fix "Could not open lock file" because "Permission denied"?

Whenever trying to install any software and update manger,  I get an error stating    Package operation failed The installation or removal of a software package failed   When I run sudo apt-get update I got this result:   conan51xd@conan51xd-Lenovo-B470:~$ sudo apt-get -f install [sudo] password for conan51xd:  Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. conan51xd@conan51xd-Lenovo-B470:~$ apt-get update E: Could not open lock file /var/lib/apt/lists/lock - open (13: Permission denied) E: Unable to lock directory /var/lib/apt/lists/ E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?


Importing GPX files into ArcGIS 10.3 for Desktop Basic?

I want to import GPX files into ArcMap. There is a good answer  for version 10.1 using the GPX to Features tool but that is not available in 10.3. I think it has been superceded by Smart Mapping in 10.3, which is not in ArcGIS 10.3 for Desktop, Basic.  Currently I am using QGIS and the GPS plug-in


As a new user without much rep, what should I do if someone else has already asked a question I have, but it has no answers?

Suppose you had a question, and you really want a good answer that would solve your problem, but noticed it was already asked by someone else. However, no one has posted any answers. The question is technically considered "unanswered", but a lot of users who would otherwise bother to give a correct answer probably skip the question completely for some reason.  What should I do in this case?  One idea is to ask a new, completely identical question, in the hope users will notice the new question and post an answer there. But would that go against SE policy?     Note: This is adapted from , but that doesn't cover the case where the original question is unanswered. Also, it is not a duplicate of , as that question asks about getting attention for one's own questions, while this one and the one linked above ask about getting an answer if someone else has already posted the same thing.


Show that $\frac{1}{(n+1)!}(1+\frac{1}{(n+1)}+\frac{1}{(n+1)^2}+\frac{1}{(n+1)^3}+\cdots)=\frac{1}{n!n}$, (here $n$ is a natural number) Maybe easy, but I cannot see it. Thanks in advance! Alexander


A question on periodicity of complex functions

Show that if $f(z)$ is an entire function such that it takes real values on the lines $Im(z)=0$ and $Im(z)=a$ (for some $a \in \mathbb{R}_{\neq 0})$, then $f$ is periodic with period $2 i a$.    So here is my thought process: First of all by reflection principle $f(\bar{z})=\overline{f(z)}$ so if our function $f$ is given in the strip $0 \leq Im(z) \leq a$, then its values on $-a \leq Im(z) \leq a$ follow by reflection principle. Then by imposing $f(z)=f(z+2 ia)$ we can intuitively see that this will define an entire function by looking at how the strips $na \leq Im(z) \leq 2na$ seamlessly stack on top of each other. Is this logical? And how would one prove this analytically?


How many solutions are $ a+b+c+d = 30 ,(a\leq b\leq c\leq d) $?

I would appreciate if somebody could help me with the following problem:   Q: How many solutions are  there to the equation  $$ a+b+c+d = 30 ,(a\leq b\leq c\leq d) $$ where $a,b,c,d\in \{1,2,\cdots,30\}$


I would like to create a variable called acc and to select a full account that is inside my accounts:  Something like :  Account acc = [select account from account where name='p2'];   That would save the full account where the name is equal to p2 inside the variable acc


Protected constructor accessible in sibling-class

I have 1 abstract class: Model<E> with 2 implementations: ItemModel and ItemLogModel. The constructor of ItemLogModel is protected, but it is still accessible from ItemModel. I expect the protected constructor to only be accessible by subclasses of ItemLogModel. Can someone explain to me why this is possible?  Code:  public abstract class Model<E> implements IModel {     private final Repository<? extends IModel, E> _repository;     protected E _entity;      protected Model(Repository<? extends IModel, E> repository, E entity)          this._repository = repository;         this._entity = entity;     }             ... }  public class ItemModel extends Model<Item> implements IItem {     ...      @Override     public void setStatus(Status status, String logMessage) throws Exception {         super._entity.setStatus(status.toString());         super.update();          // CALLING protected constructor here!         new ItemLogModel(this, logMessage);     } }  public class ItemLogModel extends Model<ItemLog> implements IItemLog {      protected ItemLogModel(ItemModel itemModel, String message) throws Exception {         super(REPOSITORY, new ItemLog());         super._entity.setAccessPointBean(itemModel.getEntity());         super._entity.setStatus(itemModel.getStatus().toString());         super._entity.setMessage(message);         super.save();     }  }


I want to write a simplest program that gives me an opportunity to use sockets and serialization.  The basic idea is to transfer data to server side with the function name and data to process. And after that deserialize this data sent on server side, to call function and perform something. Then send back the response.  Right now data that is sent to server - func name that I need to call, data that I need to process with using that func.  Im using pickle.loads to unpack data and now I have a func name as a str and dictionary to process. If I will hardcode it - it will work.  The func name that I need to call - func. But I want be able to cal any func that will be sent from client side.  I understand that I need to use getattr to be able to do that. But how? I have read couple of questions here and on other websites but still can't figure out what do I need to do.


I try to use the following code for citation but it is not working .  \documentclass[10pt,a4paper]{article} \usepackage{apacite}  \usepackage{cite} \begin{document} ~\cite{Abuelyaman2008} ~\cite{Abuelyaman2008}  ssssssssss\citep{Agrawal2002}   \bibliographystyle{apacite} \bibliography{VSM_references}  \end{document}   I want to show author name and year if there is just one author but if there are three authors just show the first author and et al.  This is one of the .bib entries:   @ARTICLE{Abuelyaman2008,   author = {Eltayeb Salih Abuelyaman},   title = {An Optimized Scheme for Vertical Partitioning of a Distributed Database},   journal = {IJCSNS International Journal of Computer Science and Network Security},   year = {2008},   volume = {VOL.8 No.1},   pages = {310-316},   owner = {DELL2},   timestamp = {2013.03.31} }   And this is the other one:  @ARTICLE{Agrawal2002,   author = {Sanjay Agrawal, Surajit Chaudhuri, Gautam Das},   title = {DBXplorer: A System for Keyword-Based Search over Relational Databases},   journal = {Data Engineering, 2002. Proceedings. 18th International Conference     on. IEEE},   year = {2002},   owner = {Dell2},   timestamp = {2013.03.30} }   many thanks in advance Ayham


"I have written a book" or "I wrote a book" in this sentence?

Past perfect vs Past simple problems always baffle me..  When I want to talk about my experience of writing a book and getting a revision on it in the past, should I use past perfect? or simple past?     I have written a book and had someone look at it after.      I wrote a book and had someone look at it after.   I want to know the difference between the two sentence or which one is correct.  Thank you!


If cardinality of every minimal cut is even then graph is Eulerian.

So I have a connected graph $G$, whose every minimal edge cut contains even number of edges. How to prove from this that the graph is Eulerian?  If I knew from this, that every vertex has even degree I would be fine, but how do I deduce this?   EDIT: I realise this question has been asked before, but why is the degree of every vertex even? The original answer doesn't elaborate on that.


Proof- difference of absolute values and absolute value difference

prove that for all $a,b \in \mathbb{R}$, $ | |a|-|b|| ≤ |a-b|$  so what I have thought of so fat is I tried to use the definition of absolute value then getting $b-a ≤ |a|-|b| ≤ a-b.$ from there I'm getting $2b≤|a|-|b|≤2a$. Here is where I encountered the problem of where to proceed. How could I use the fact to keep going to proof the statement


Mysql replication no error and not replicating

I am getting no errors yet replication is not working. I wonder where I am going wrong?  My master status is                File: mysql-bin.000002         Position: 2006432     Binlog_Do_DB: site3,site2 Binlog_Ignore_DB:    My Slave Status is   *************************** 1. row ***************************                Slave_IO_State: Waiting for master to send event                   Master_Host: 104.131.119.241                   Master_User: drupal                   Master_Port: 3306                 Connect_Retry: 60               Master_Log_File: mysql-bin.000002           Read_Master_Log_Pos: 2006432                Relay_Log_File: mysqld-relay-bin.000003                 Relay_Log_Pos: 2006577         Relay_Master_Log_File: mysql-bin.000002              Slave_IO_Running: Yes             Slave_SQL_Running: Yes               Replicate_Do_DB: site3,site2           Replicate_Ignore_DB:             Replicate_Do_Table:         Replicate_Ignore_Table:        Replicate_Wild_Do_Table:    Replicate_Wild_Ignore_Table:                     Last_Errno: 0                    Last_Error:                   Skip_Counter: 0           Exec_Master_Log_Pos: 2006432               Relay_Log_Space: 2006879               Until_Condition: None                Until_Log_File:                  Until_Log_Pos: 0            Master_SSL_Allowed: No            Master_SSL_CA_File:             Master_SSL_CA_Path:                Master_SSL_Cert:              Master_SSL_Cipher:                 Master_SSL_Key:          Seconds_Behind_Master: 0 Master_SSL_Verify_Server_Cert: No                 Last_IO_Errno: 0                 Last_IO_Error:                 Last_SQL_Errno: 0                Last_SQL_Error:  1 row in set (0.00 sec)


Deleting comment removes "Add comment" link on Mobile

If I delete a comment on the mobile version of the site (at least if it's the only comment on an answer), the "Add comment" link will vanish along with the comment, so I have to reload to leave another comment.     but got declined as , which is why I'm reposting this (as it may well be a new bug with the same symptoms).  I'm using Firefox 32.0.3 on Android.


I was trying the study a new subject in groups (from a book I have). I came acorss with the following question:  Consider:  $X=S_4$  $Y=\{e,(12)(34),(13)(24),(14)(23)\}$  How can I prove that:  $$\{gY:g\in X\}=\{Yg:g\in X\}$$


What is release date for next long term release?

I'm getting tired of reloading new systems on my ancient laptop. I started with Mint, then went to Ubuntu 15.04. Will I be able to go directly to the next long term release (and rest a little)?


I am living with Irish citizen and Irish born child.we are planning to travel to Schengen zone. I have currently Russian citizenship and Georgian citizenship. I arrived to Ireland with Russian passport and renewed Georgian  passport 3 months ago.Russians do need visas to Schengen area,but Georgians are free of Visa.The Question is, can I travel with Georgian passport to Schengen zone and returned back with Russian passport.Thank you


How to check debug logs for trigger when executed from the front end?

How can I check the debug logs for my trigger when some goes to my website and clicks a button that inserts records on salesforce?


Probability of $\limsup$ of a sequence of sets (Borel-Cantelli lemma)

Let $(E_n)$ be a sequence of events in a probability space such that $$\lim_{n\to\infty}\mathbb P(E_n)=0.$$ I am trying to prove that if $$\sum_{n=1}^\infty\mathbb P (E_n\setminus E_{n+1}) <\infty$$ then $$\mathbb P\left(\limsup_{n\to\infty} E_n\right)=0.$$  For an example I am using the sequence of intervals $[0, 1/n]$ which goes to $0$ as $n$ increases to infinity. Then I can see how the probability of infinite sum of the intersection of the $E_n$ and the complement of $E_{n+1}$  is less than infinity and the probability of $\limsup_{n\to\infty} E_n$ equals zero.   Can anyone help me figure out how to prove this in general using any sequence? Especially to show how $\mathbb P\left(\limsup_{n\to\infty} E_n\right)=0$?  Thank you in advance for your thoughts.


Buy a roundtrip ticket for two people, but second person only travels on return - is that possible

If I buy airline tickets for a roundtrip for two people, and the second person does not show up for the first part of the roundtrip, do airlines cancel the return ticket for that person, or can that person fly the return trip only?


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


Concatenation of lists inside lists with other lists inside lists

I want to concatenate every list in a list with the other list in list. This is what I want: given lists A and B that each have 2 lists inside it, I want to concatenate A[0]+B[0], A[0]+B[1], A[1]+B[0], A[1]+B[1]. I have written a simple code below:  def concatenate(seq1, seq2):     for i in range(len(seq1)):         for j in range(len(seq2)):             return seq1[i] + seq2[j]   When I put [[1,2],[3,4]],[[2,3],[4,5]] as an argument, I want [[1,2,2,3], [1,2,4,5], [3,4,2,3], [3,4,4,5]] as a result but I'm only getting [1,2,2,3] at the moment. Is there a method to fix this?


Enabling basic authentication and preventing the browser from prompting for authentication

First of all, I'm not 100% sure what I'm asking is a right thing to do or not. So please free feel to correct me if I'm wrong.  Using Spring Security, I've developed a REST API backend which users can log in using some custom entry. If my users authenticate themselves using my custom API, there will be a session created for them and the rest of API entries will be accessible to them, considering their role and ACL.  At the same time, these APIs are designed so they can provide services to other software. So I thought it makes sense to enable some HTTP Basic Authentication as well. Later on, I might be working on digest as well. And if some request is authenticated using one of these methods, there will be no session created for them. And they'll need re-authenticate for every single request. It's a stateless API.  So far everything is great. The users and other systems can make use of the same sets of APIs. But the problem is when a user's session is expired. Or when some user starts using the backend services before he logs in. In such cases, the right strategy is to redirect the user to a login page and ask them to authenticate themselves. But since I've enabled the HTTP Basic Authentication, calling a REST API which needs authentication (while the user is not authenticated) leads to a browser popup asking for the username and password.  Of course, the user can enter the credentials and keep using the system. But I don't like this way of authentication for my users. First of all, the authentication credentials will stick and I consider it a security risk. They are easily be saved into the browser without informing the user they are. And it's hard to get rid of the saved credentials. The user can leave the computer without even knowing that his username and password are saved.  So my question is, is it possible to have Basic Authentication enabled but at the same time, prevent the browser from knowing it? Or even better, acting on it?  I suspect that if I prevent the WWW-Authenticate response header on the way back, I might be able to do so. But then, I'm not sure of the ramifications of such a decision. Also, I don't know how to remove that header from the response for all of the APIs.


Bank balance query for UK visa from India

My wife and I have booked air tickets for London. Both of us work in a multi-national corporation.    How much bank balance will be considered as appropriate for our visas to not get rejected?    I am little worried reading about all the visa applications that are rejected. We will also have pay slips and company letters declaring when we are scheduled to get back to our office.  Itinerary: Bangalore -> London (stay for 4 nights) -> London to Paris (by Eurostar) -> Paris (stay for 4 nights) -> Fly to Bangalore.  All air tickets and train tickets are confirmed.


i'm trying to produce a few mockup pictures of a person using a tablet around the house. These are the conditions:   Camera Nikon D90, Lens 18-55 The pictures were taken in the morning Indoors but the room has a lot of natural light I didn't use zoom, the 'subject' was around half meter away from the camera Shooting Mode 'A', Image quality is RAW Fine, ISO 200 - 2000, F5.6v   The result was not good, the pictures have a lot of noise and grain.     How can i take crystal clear pictures without grain?  Thank you


How do I create a stored procedure that will optionally search columns?

I'm working on an application for work that is going to query our employee database. The end users want the ability to search based on the standard name/department criteria, but they also want the flexibility to query for all people with the first name of "James" that works in the Health Department. The one thing I want to avoid is to simply have the stored procedure take a list of parameters and generate a SQL statement to execute, since that would open doors to SQL injection at an internal level.  Can this be done?


I am working on the BusinessHours and I am getting the below error. I just want to calculate the no. of hours difference between MondayStartTime and MondayEndTime  Method does not exist or incorrect signature: [BusinessHours].diff(Id, Time, Time)   The code which I used  BusinessHours bh = [SELECT FridayEndTime,FridayStartTime,Id,IsActive,IsDefault,LastModifiedById,                               LastModifiedDate,MondayEndTime,MondayStartTime,Name,SaturdayEndTime,                               SaturdayStartTime,SundayEndTime,SundayStartTime,SystemModstamp,ThursdayEndTime,                               ThursdayStartTime,TimeZoneSidKey,TuesdayEndTime,TuesdayStartTime,                               WednesdayEndTime,WednesdayStartTime FROM BusinessHours where Name='XXX Hours'                                LIMIT 1];         System.debug('bh.MondayStartTime :: '+bh.MondayStartTime);         System.debug('bh.MondayEndTime  :: '+bh.MondayEndTime);         System.debug('-------------------------------------------------------------');         Datetime MondayStartDT = Datetime.newInstance(Date.Today(), bh.MondayStartTime);         System.debug('MondayStartDT :: '+MondayStartDT);         Datetime MondayEndDT = Datetime.newInstance(Date.Today(), bh.MondayEndTime);         System.debug('MondayEndDT :: '+MondayEndDT);         Long diff = BusinessHours.diff(bh.Id, MondayStartDT, MondayEndDT);         System.debug('diff  :: '+diff);   Edit: As per thatherahere code I am getting following output I dont see its calculating the diff correctly.    Now Updated


If i book a flight that goes for example  London -> Paris -> New York  Is that ok if I miss the London -> Paris flight but get in from Paris? and on return I skip the Paris -> London flight.  I thought it should not be a problem but I remember reading somewhere that airlines do not allow that. Is that true?


Two simple questions  1) Can users go onto another users page and down vote all their posts?  2) If so would they get banned?  Lately I have been receiving slow increments of downvotes, I am not sure if I offended any one but the thought that came in mind is that a particular user could be grinding my gears


Activity reputation pane shows a tag is completed when it's not

The reputation pane in the new activity tab shows I have achieved a gold badge for the  tag:    However, my score isn't high enough and the badges section doesn't show that badge.


What is the fastest way to add vertices to a curve at a specific point?

For example, in inkscape you can double click to add a new control vertex:    Is there a way to do that in Blender?  The closest thing I have found so far is CtrlLMB, but it just adds an unconnected vertex under the cursor.  Is there a way to add a connected vertex at a specific point along the curve, preferably without deforming the curve?


Is Zorn's lemma necessary to show discontinuous $f\colon {\mathbb R} \to {\mathbb R}$ satisfying $f(x+y) = f(x) + f(y)$?

A UC Berkeley prelim exam problem asked whether an additive function $f\colon {\mathbb R} \to {\mathbb R}$, i.e. satisfying $f(x + y) = f(x) + f(y)$ must be continuous. The counterexample involved taking a positive-valued Hamel basis $X$ of $\mathbb{R}$ as a vector space over ${\mathbb Q}$, and then letting $f(x_1) =1$ and $f(x_2)=-1$ for two different $x_1,x_2 \in X$, and letting $f(x)$ be arbitrary for other $x \in X$, and then extending the function to all of ${\mathbb R}$ using the property of additivity. Then a sequence $a_n = {p_nx_1 + q_nx_2}$ could be found with rational $p_n,q_n$ such that $a_n \to 0$ but $\lim \limits_{n\to \infty} f(a_n) \neq 0$, showing discontinuity. But is Zorn's Lemma necessary to produce such an example? In other words, is Zorn's Lemma saying we can find a Hamel basis of ${\mathbb R}$ over ${\mathbb Q}$ equivalent to being able to construct a discontinuous additive function $f\colon {\mathbb R} \to {\mathbb R}$?


When I want to talk about a successful student, can I describe him/her as follows?   She's very good in school. (or at school?) She's good at her lessons (or she's good in her studies?) She's good in her classes.   I appreciate your answers.


I want to create this table in LaTeX:    and receive this error:     Error: ! Missing $ inserted.   I can't change much of the tabularx stuff as it's in the template. How do I solve this error? My code:  <inserted text>                  $ l.120 \end{tabularx}  \begin{table}[h]  \tbl{Mechanical properties of cortical bone obtained from tensile testing and small punch test}  \small\addtolength{\tabcolsep}{5pt}  \begin{tabularx}{\textwidth}{@{}lll@{}}  \hline\noalign{\smallskip}  Location & Elastic modulus (\textit{E})  & Stiffness (\textit{k})  \\ & GPa & N/mm\\  \noalign{\smallskip}\hline\noalign{\smallskip}  Upper & 12.47 \pm $0.79^{b}$ & 309.27\pm $19.266^{b}$\\  Middle & 15.54\pm $1.45^{a,b}$ & 517.76\pm$22.241^{a,b}$\\  Lower & 9.48 $\pm$ 0.63 & 235.84\pm17.477\\  Overall & 12.49\pm 2.67  & 356.91\pm123.91\\  ANOVA & p \textless 0.05 & p \textless 0.05\\  \noalign{\smallskip}\hline  \end{tabularx} %line 120.  $^a$Indicates a statistically significant difference compared with upper location of  bovine femur (p \textless 0.05).\\  $^b$Indicates a statistically significant difference compared with lower  location of bovine  femur (p \textless 0.05).  \end{table}


I searched the internet but I cant find a solution for my problem. I want a numbered and labelled equation inside the text.Something like:  The equation a+1=b (2.1) does ...   The equation a+1=b shouldn't be in a new line like usual  The equation a+1=b (2.2) does...


I'm a maths student who would also like to know a bit about quantum physics. I keep reading that possible states of a system are represented by elements of a certain Hilbert space $\mathcal{H}$. This question is about which Hilbert space $\mathcal{H}$ is supposed to be.  From a few brief conversations I have had with people smarter than me, I've gathered that $\mathcal{H}$ is supposed to be $L^2(X)$ for some measure space $X$. But this just raises further questions. First of all, and most importantly, why have I never come across this information officially? In textbooks, lecture notes and some information that I have found online, they just tell us that quantum physics takes place on $\mathcal{H}$, which is some Hilbert space, not $L^2$ specifically. Is this because the details of $L^2$ are irrelevant to the physics? This surprises me, since in Terence Tao's An Epsilon of Room Part I, exercise 1.12.36 is to prove Heisenberg's Uncertainty Principle using just facts from Fourier analysis about $L^2$!  Supposing that we do indeed have $\mathcal{H}=L^2(X)$, what on earth is $X$ supposed to be? If $\psi\in L^2(X)$ with $||\psi||_{L^2(X)}=1$ is supposed to be a wavefunction, then it makes sense to me that for a single particle we would have $X=\mathbf{R}^3$, because then $|\psi|^2$ would be just a probability density for the position of the particle. The problem would then be if there were a lot of particles in the system of interest. What happens, for instance, if there are countably many particles?  Another problem with this hypothesis that $\mathcal{H}=L^2$ is that restricting our attention to only those $\psi\in L^2$ with $||\psi||=1$ seems to get rid of the point of working in a vector space. It no longer makes sense to add and subtract the elements because then they will no longer be wavefunctions. Moreover, we will only be working with the very specific class of linear operators that preserve norms. Even worse is the apparent restriction that $\psi$ be smooth, as in the Heisenberg and Schrodinger equations. Maybe this means that we have to restrict our attention to those $\psi\in \mathcal{S}\subseteq L^2$ like in Tao's question 1.12.36 (not forgetting that $||\psi||=1$). This seems even more restrictive.  I suppose there are other Hilbert spaces of interest, such as certain Sobolev spaces. I don't know a huge amount about these except for that they are pretty similar to $L^p$ spaces but with differentiation. Using these solve the conundrum about the Heisenberg/Schrodinger equations, but would just make me more confused as (a) it would no longer make sense for $\psi\in H$ to be like analogous to a probability density and (b) Tao's question 1.12.36 would no longer make as much sense.  This is a pretty wordy question which might be answered in just a single sentence or two, but I certainly would appreciate the help.  Edit: I think this question is appreciably different to the one Daniel asked. My question is on a lower level of understanding for one. Another difference is that Daniel's question is specifically about replacing $L^2$ with Sobolev space rather than asking about the general use of Hilbert spaces in quantum physics.


How to print name of the variable which stores an array in php?

I want to print the array identifier name along with its content. In situations where a page contains many arrays, then there is a confusion - which elements belong to which array.  $user= array('id' => 1,'name' => "Tom");  //expectation user Array (     [id] => 1     [name] => Tom )


LaTeX - Assistance Publishing a Mathematical Theorem

I have a mathematical theorem written in pencil on paper. I am using a handheld device to use the internet.  On this webpage -  - are the high requirements of the modern world for the publication of a math paper. I have hundreds of handwritten pages of mathematical work, but what I need to publish should be only ten pages or so.  Proving Legendre's conjecture took a lot of work. Verifying the proof took a lot of work. Putting the proof into text will be a lot of work, for my handwritten papers have more numbers than words, and the drawings have to be explained. Publishing the proof of Legendre's conjecture in a refereed mathematics publication of worldwide repute would allow other mathematicians to read it at their convenience and verify it for themselves and, most importantly, make use of the other results which follow from the proof technique.  From the start, through the process, to the finish is the way to go. I need assistance getting started.


Static member undefined reference c++ without header file

I am new to C++, and i can't figure out what's wrong in this code. Will appreciate any help.  class ResourceLoader { protected:     static std::map<int, Texture> textureCollection; public:     static Texture getSingleTexture(GameTexture gameTexture) {         return ResourceLoader::textureCollection[gameTexture];     }      static void loadTexturesFromFiles() {         ResourceLoader::loadSingleTexture(GameTexture::Character);     }      static void loadSingleTexture(GameTexture gameTexture) {         Texture texture;         texture.loadFromFile("texture.png");         ResourceLoader::textureCollection[gameTexture] = texture;     } };   This results in:     undefined reference to `ResourceLoader::textureCollection'"   How is it undefined if textureCollection is declared in the protected section?  Also I don't user headers for class declaration. I know that this is not the best practice, but this speeds up the whole process..


It seems that I'm missing something fundamental in casting and I don't know what it is!  check this code:  int main(void) {      float current_i;     float floating_part;     int float_to_int_part;      current_i=13;      printf("----------------- current_i = %f ------------------\n",current_i);     current_i=current_i/10;     printf("new current_i = %f \n",current_i);      floating_part = (current_i-(int)current_i);     printf("floating_part = %f\n",floating_part);      float_to_int_part= (int)(floating_part * 10.0); //i have a problem unserstanding where i went wrong here     printf("float_to_int_part = %d\n",float_to_int_part);      return 0; }   the output here is  ----------------- current_i = 13.000000 ------------------ new current_i = 1.300000  floating_part = 0.300000 float_to_int_part = 2   I expected float_to_int_part to be 3 but the output is always 2 which is very confusing. the fact that I don't know why means I'm missing something very basic which could mean I'm missing more basic facts. if someone could tell me what is wrong with my code and suggest a book or a link (that you think will help) to fill this gap.  It's more important for me to know what caused the error. if all my variables are float then the output is correct and my module works.


Determine when Windows was installed on a computer

Is it possible to check the date when Windows was installed on a PC and if so how?


The 3D cursor can be moved by simply LMB  clicking anywhere in the viewport. Is there a faster and easier way to position the 3D cursor?


Prove or disprove: if $x$ and $y$ are real numbers with $y\ge 0$ and $y(y+1)\le (x+1)^2$, then $y(y-1)\le x^2$.  How should I approach this proof?  The solution starts with assuming $y\ge 0$ and $y\le 1$, but I'm not sure how to arrive at that second assumption or go from there.  Thank you in advance!


Verifying that a pdf is correctly displayed using new relic synthetics

I have created scripts in new relic synthetics that verify the web application is still behaving correctly.   This script does the following things:    go to the specific page click on a pdf link  verify that the pdf is correctly displayed   To do that, here is a snippet of my script:      .then(() => { // Here I click on my link             logger.log(10, "clickElement link=The link text");             return $browser.waitForAndFindElement(By.linkText("The link text"), DefaultTimeout)                 .then(function (el) {                     el.click();                 })         })     .then(() => { // I switch to the newly open pdf windows             // switchTo window [1] as the new window             logger.log(11, "switch window ");             return $browser.sleep(1000)                 .then(function() {                     return $browser.getAllWindowHandles()                 })                 .then(handles => {                     return $browser.switchTo().window(handles[1])                 })         })       .then(() => {  // I verify that the pdf is displayed by looking for the id "viewer"             logger.log(12, "waitForElementPresent");             return $browser.waitForAndFindElement(By.id("viewer"), DefaultTimeout)          })   The problem is, new relic doesn’t find the id “viewer” even though the screenshot shows that the pdf is correctly displayed. I also tried to us $browser.waitForAndFindElement(By.class("page"), DefaultTimeout) instead, but I have the same error.  Any thought?  (Please note that my way of verifying the pdf display works with selenium+java)


Have the comment reply autocomplete popup for more than one user

Suppose there are two users, say Bob and John who made comments on my post.  There is a situation I would like to address both of them in a single comment. However I can address them by @Bob and @John, but only typing the second person name (in this case John) manually, i.e. autocomplete will not popup.  The autocomplete will only show the first person name (in this case Bob) automatically but not the second person name.  Can the popup be displayed for the second user as well?


Unable to get list of updates: failed to get updates for refresh: Error: Malformed entry 51 in list file/etc/apt/sources.list(omponent)

i am Ambrose. I write from Nigeria. i tried to install acroread (Adobe reader) in ubuntu 18.04.2 LTS using a command i obtained from a You Tube video but something strange happened in the process. Presently, Sudo apt-get update does not work. if i do sudo apt-get update in the terminal, i get the the following; "E: malformed entry 51 in list file/etc/apt/sources.list(component)" "E: The list sources could not be read" Honestly, this is frustrating and this have hampered working with my machine and research.  Secondly, my machine (Laptop) can not detect Wifi in my place of work. Honestly, i bought the Laptop with Window 10 installed in it, but for the fact that my Ph.D research required me to use Ubuntu, the Window 10 was removed and Ubuntu 18.04.2LTS was installed and since then Wifi is not functional.  please, i need your assistance and help to solved the aforementioned problems. please, e-mail me to jerry410001@gmail.com  Thanks for your assistance.


At the end of Avengers: Endgame, Captain America is given the job to go back in time and restore the Stones to where they stole them originally. The question: what exactly happened?  Did he plan on restoring them to right after they were stolen to make it as if they were never taken, or before? And either way, according to their time travel rules -- changing the past doesn't change the future, only create a new alternate universe. So how could they possibly travel back into that same alternate universe, if every time a new alternate reality is created?


Old post apocalyptic cartoon where the main character has red hair and lives with a nomadic group

I am looking for an animated TV series which was probably made in the '80s or '90s.  The main character had red hair.  The cartoon is set in a post apocalyptic environment and the character lives with his mother and an old man —his mentor I guess— with a nomadic group.  In one early episode, one of the group is wounded in an ambush, he is taken back to the camp where the mentor performs surgery which is revealed he learned during the war. The wound is caused by a bullet, then the mentor is surprised saying that guns were lost and forgotten.  In another episode the main character is captured and sent to a prison. Then after he escapes with other prisoners, they look outside the gate and see grass and soil which they either didn't see in their lives or were in the prison for a long time.  The main character later finds a sword like Excalibur which can cause some sort of electrical disruptions.  I think his mother was kidnapped in the beginning.


What property of modular arithmetic lets us conclude than a^(2b) mod n is congruent to a^b mod n * a^b mod n?

After several years of absence, I seem to have lost track of the very basic of number theory. In my head, I know what I am allowed to do, but not why I am allowed to do it. I have been consulting , but I can't find any property that matches up to the following: What property of modular arithmetic lets us conclude that $a^{2b}\mod{n} \equiv a^{b}\mod{n} \cdot a^{b}\mod{n}$ for $a,b,n \in \mathbb{Z}$? I worry that I've confused the Computer Science style of "mod as in remainder upon division"  and the mathematics style of "mod as in congruence", but I was sure that this worked for both. For example, I am confident that $5^4\mod{3} = 5^{2}\mod{3} \cdot 5^{2}\mod{3}=(5^{2}\mod{3})^2=(5\mod{3})^4 =(2\mod{3})^4 =(2)^4\mod{3} = 16 \mod{3} = 1\mod{3}$ is completely valid.


Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$

For my matrix algebra class I need to prove the following:  If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$. So if A is nilpotent prove Rank(A) $\le \frac{n}{2}$  I know already how to solve this, but my initial way of solving is false. I am looking for the mistake, but cannot find one. I know there already exists a question where this is asked. I'm just curious about my particular mistake.  Proof:  $A=\begin{bmatrix}a_1&&a_2&& ...&&a_n\end{bmatrix}$ and $A=\begin{bmatrix}a^T_1\\a^T_2\\...\\a^T_n\end{bmatrix}$   $AA=\begin{bmatrix}a_1 && a_2 && ... && a_n\end{bmatrix}\begin{bmatrix}a^T_1\\a^T_2\\...\\a^T_n\end{bmatrix}$  $=\begin{bmatrix}a_1a^T_1&&...&&a1a^T_n\\...\\a_na^T_1 && ...&& a_na^T_n\end{bmatrix}$  $=\begin{bmatrix} a_1 \cdot a_1&&...&&a_1 \cdot a_n\\...\\a_n \cdot a_1 && ...&& a_n \cdot a_n\end{bmatrix}$  $=0_{nxn}$  So we know the diagonal is zero thus  $a_i \cdot a_i = 0$ this equals $\vert\vert{a_i}\vert\vert^2$ The square root of this equals the length, therefore the length is equal to 0. The only vector with this property is the zero vector. Herefore all vectors $a$ must be equal to the zero vector.   The last however is not the truth, is there anyone who can spot my mistake?


Place node a fixed length along a transparent bisector?

Doing some hocus-pocus to mark the angle of a triangle a fixed length away from the point and I want to now place a node midway between the point and the arc so I can label the value of the angle.   I'm aware that the way I've constructed the arc means that there isn't a defined midpoint for that particular section that's showing (for reasons beyond the scope of the question \tkzMarkAngle and \tkzLabelAngle are not options), which is why I'm thinking the way to do this would be with a bisector, but I can't figure out how to place the node.   Open to any other suggestions also.   \usepackage{tkz-euclide} \usetkzobj{all} \begin{document} \begin{tikzpicture}   \coordinate (A) at (0,0);   \coordinate (B) at (4,6);   \coordinate (C) at (9,1);   \draw (A)--(B)--(C)--cycle;   \begin{scope}     \clip (A) -- (B) -- (C) -- cycle;     \path[draw,color=red,line width=1.5,opacity=0.5] (A) circle (1.5);     \tkzDrawBisector[opacity=0](B,A,C);   \end{scope} \end{tikzpicture} \end{document}


Quick proof that every finite integral domain is a field.    I'm not sure if I'm missing anything, but here is my attempt.  Let $R$ be a finite integral domain. So it is unital and commutative. Since $R$ is finite, it is of the form $R= \{a_1,a_2,...,a_n\}.$ Let $0\neq a\in R.$ Then if $aa_i = aa_j,$ we must have $a_i=a_j$ (because $R$ has no zero divisors). Since $R$ is closed under multiplication, $R= \{aa_1,aa_2,...,aa_n\}.$ Since $R$ is unital, there exists $a_i\in R$ such that $aa_i=1.$ Thus $R$ is a field.


Why does increasing the dpi of an image on export from Lightroom not increase the file size?

I have a Nikon D3300. RAW images are usually 25-28 MB at a resolution of 6000 x 4000. I exported from Lightroom at Quality: 100; DPI: 240. The exported JPEG turns out to be around 12 MB. I took the same RAW file and this time bumped up the DPI to 600. It turns out, both images are exactly the same file size.   I was anticipating that a higher DPI setting would mean larger files. Higher DPI = more dots per inch = more information = bigger files. Why is this not the case?


Is there a way to view passwords in plaintext?

I need to figure out a password, but I'm not supposed to change the password itself. Is there anyway, perhaps through the common-password file or a command to show the plaintext password of a user?


A generalisation of the fundamental theorem of algebra

We already know the following theorem by d'Alembert and Gauss, often called fundamental theorem of algebra.  Theorem Let $P$ be in $\mathbb C[X]$ of degree $1$ or greater. There exists $\alpha\in \mathbb C$ such that $P(\alpha)=0$.  Can we give the following generalisation for polynomials with several variables?  Generalisation Let $n$ be in $\mathbb N^*$ and $P$ be in $\mathbb C[X_1,\ldots,X_n]$ of degree $1$ or greater. There exists $\alpha\in \mathbb C^n$ such that $P(\alpha)=0$.  Any references, hints or solutions would be greatly appreciated.


how can you generate multiple random numbers in a changing range?

Noob here. I've tried using the other answers for random numbers, but they don't seem to accomplish what I'm trying to do.  So... I'm trying to make a method that catches a random fish in a pond. It will catch multiple fish in a row that are stored in an array, and I basically want it to avoid catching null, and still catch a fish every time it is run. Here's the method.  public String catchAFish(){    int x = (int)(numFish * Math.random());   pond[x] = pond[numFish+1];   pond[numFish+1] = null;   numFish--;   return ("You have caught "+pond[x]); }   The last fish in the array moves into the spot of the fish that was caught. I tried a function in a for loop before, and it accomplished the same thing. The problem is that the number of possible fish to catch changes whenever a fish is caught, so I can't just set a range of "0-10".


What is the intuition behind the unit normal vector being the derivative of the unit tangent vector?

I've seen the math, but... It just doesn't make sense to me. How is the slope going to point perpendicular to the vector that is clearly a straight line not going in that direction?


How can I get into computer science research as a high school student?

I am in High-School but want to pursue research in Computer Science, but as you know High-School usually does not offer any such options or tasks.   So I want to explore avenues where I can get these options and tasks as I am very very interested and really want to do it.   I would also like to say that I have good-strong knowledge of C++, C and assorted APIs from that (3 years programming for 5+ hours daily). So I wouldn't call my self too new to programming and think I can handle programming and so on.   Now, these are my questions:   How can I get involved in research? How can I contact academics to ask them for research position or even an intern position in research for that matter without coming across as a "waste of time"?


I'm playing a mono-Green infect Pauper deck that relies heavily on instant-speed pump spells in order to win. My opponent ruins my day pretty badly by playing a :  Fortunately, my deck also has  and .  It occurs to me that I might be able to play one of these spells on the Standard Bearer, rendering it an illegal target for that turn, then play my other spells on my own creatures as intended. But will this actually work? I'm not sure about the subtleties of interpreting these effects when the target creature and the spell have different controllers, and I didn't get a chance to try it before the match ended.


Visa for European countries for US passport holder

I'm a US passport holder. What documents do I need when I fly from the U.S. to Germany?  Assume I'm going for a few weeks of vacation.  Obviously I need my passport.  What about a "visa"?  Anything else?


How to install kde and totally remove unity on ubuntu 14.04 lts?

I did not like unity desktop.I want to install kde desktop enviorment.Please help!!!


I'm a Canadian traveling to the US next month. I haven't traveled internationally before and I'm not sure how money works. Am I able to use my credit card in the US? I have a $2000 limit, will USD transactions apply to that via the exchange rate or something else? Is my card able to be preauthorized by a US merchant? Can I withdraw from US ATMs using my debit card?


Until I went to army, I (had been / used to be / was ) a introverted person. - which one is right?

Until I went into the army, I (had been / used to be / was ) an introverted person. And after I I finished army service, I became more confident.   I think all of these are possible.  As for had been, I'm referring to the state of me being introverted before the accident that happened in the past. So, I think I can use had been.  And at the same time I feel I can use used to be and was.. If I don't want to emphasize the time gap between two accident, I feel I don't need to use past perfect. So I think this problem depends on how I'm going to say something.   which one is preferable? and what is the difference?


Long exact sequence of reduced homology groups

Here are two fragments out of Hatcher's book (see  for the full book).  Questions: (1) Does this mean we get a long exact sequence which has the form $$\dots \to\tilde{H}_n(A) \to \tilde{H}_n(X) \to H_n(X,A) \to \tilde{H}_{n-1}(A) \to \tilde{H}_{n-1} \to \dots$$ Or do I need to modify the $H_n(X,A)$ by $\tilde{H}_n(X,A)$ or something like that? (2) Can someone explain the second paragraph in the picture in some detail? I was not able to understand what Hatcher was trying to explain. Thanks in advance for any help.


I need to resize PNG, JPEG and GIF files. How can I do this using Java?


Free Shows:  free -m               total        used        free      shared  buff/cache   available Mem:          32130       22377        9553          48         200        9368 Swap:          8191         465        7726   But ps aux shows in the RSS Column(I didn't include 0's).  It only adds up to 6325.  Does free know something PS doesn't?  0.0859375 MB        /sbin/iscsid 0.550781 MB     /usr/sbin/watchdog-mux 0.617188 MB     (sd-pam) 0.667969 MB     sleep 0.777344 MB     sort 0.910156 MB     awk 1.52734 MB      /usr/bin/lxcfs 1.5625 MB       /sbin/agetty 1.67188 MB      /sbin/lvmetad 1.87891 MB      /usr/sbin/pvefw-logger 2.39062 MB      /bin/bash 2.48828 MB      /usr/sbin/rsyslogd 2.55469 MB      /usr/sbin/cron 2.57031 MB      /usr/bin/rrdcached 2.76562 MB      /lib/systemd/systemd-udevd 2.875 MB        /usr/lib/x86_64-linux-gnu/lxc/lxc-monitord 2.98047 MB      /sbin/rpcbind 3.16016 MB      pvedaemon 3.21094 MB      /usr/lib/postfix/sbin/master 3.23047 MB      pveproxy 3.28516 MB      ps 3.32422 MB      /usr/bin/dbus-daemon 3.53125 MB      /lib/systemd/systemd-timesyncd 3.58203 MB      /usr/sbin/smartd 3.85547 MB      /usr/sbin/rpc.mountd 4.32422 MB      /lib/systemd/systemd-logind 4.82422 MB      /sbin/iscsid 5.33203 MB      /usr/sbin/sshd 5.59375 MB      qmgr 5.60547 MB      /lib/systemd/systemd 5.9375 MB       /lib/systemd/systemd-journald 6.41406 MB      pickup 6.6875 MB       /sbin/init 6.70703 MB      sshd: 9.11328 MB      pve-ha-crm 13.3555 MB      pve-ha-lrm 16.6328 MB      -bash 17.0898 MB      /sbin/dmeventd 23.6094 MB      pve-firewall 28.7695 MB      task 32.1758 MB      pvestatd 35.6953 MB      pvedaemon 36.2188 MB      pvedaemon 37.9297 MB      pvedaemon 41.3477 MB      pveproxy 42.7656 MB      pveproxy 46.2617 MB      pveproxy 56.0391 MB      /usr/bin/pmxcfs 66.5078 MB      spiceproxy 71.3086 MB      spiceproxy 83.8711 MB      /usr/bin/perl 5586.38 MB      /usr/bin/kvm   EDIT:  I should note, not sure if it matters but the is Proxmox(A debian distro). You can see the largest memory user is a VM.  Also this usage spiked after a large rsync over NFS.  Could that have anything to do with it?


Let $f:V\times V\rightarrow F$ be a bilinear form in a finite inner product space V.  If $F=R$, how can I prove that there exists a single linear transformation $T:V \rightarrow V$ so that for each $v,u\in V$, $f(u,v) = (Tu, v)$ ?  Would that sill be the case if $F=C$?


to find memory occupied by individual application software in linux

to find memory occupied by individual application running  in linux.  actually i'm having a boot issue that is after installing an application Software so i want to see the memory occupied by that application. Ay one please help me


I have read at different times in different tutes instructions for creating a floor, backstop, or other "scenery" object in a rigid body world;  some say "create object, add rigid body physics, then turn off Dynamic,"  while other say "create object etc, then change Active to Passive."  I have tried both, and for a simple floor I've seen little difference.  BUT...  recently I was building the Wrecking Ball demo from blenderguru, and out of habit I made the floor by turning off Dynamic, which has worked for me before.  it all worked fine until I changed the floor (by extruding one edge into a backstop);  then all of a sudden, cubes started falling right through it.  I could not figure it out, could not figure it out, much headbanging, then finally changed it to Dynamic+Passive rather than !Dynamic+Active (in other words, followed BG's instructions properly!).  then everything worked perfectly.  so, can someone enlighten me as to the -- subtle? -- diff between an RB object that is Not Dynamic but Active, and one that is Dynamic but Passive?  I'm guessing that the latter is the correct way to make immovable scenery objects.


How would you handle a D&D 4e Total Party Kill without killing them?

I have a lot of story planned and it's just as lame for me as it is for them. I accidently threw a couple Mud Lashers that were too difficult after they had defeated the huge Mudbeast. This was honestly just a filler quest to waste their time but it just killed them. Sadly we're running a two person thieves guild campaign without a cleric so it's fairly difficult to scale for them so I feel like I'm to blame just as much as they are for not running away at low health.  I've thought of some solutions like removal of enchantments or skill penalties but they don't feel good enough. I was wondering what other DMs would do - how should I handle this situation?


Python random.shuffle() on a list of lists returns a list of identical lists

In my script I need to generate a simple list of [1,2,3,4] values and then shuffle each one of those lists inside this list individually. I used random.shuffle() function which works fine on single arrays, but when I try to use it in a for loop the output is a list of shuffled arrays, but all of them identical:     [3, 1, 2, 4]   [3, 1, 2, 4]   [3, 1, 2, 4]   etc...   I have tried running the script with different python versions (2.7, 3.6) but the problem persists.  Here is a simplified code that represents the issue:  import random  numbers_list = [1,2,3,4] #make a list of 10 numbers_list list_of_lists = [numbers_list]*10  #shuffle every list inside list_of_lists for i in list_of_lists:     random.shuffle(i)  #print every list from list_of_lists for a in list_of_lists:     print(a)   Running the script multiple times results in different lists, but they always consist of a repeated one array. What can I do to fix it? Is it an issue with random.shuffle() or my script? What am I doing wrong?


Properties of size function in a general Euclidean domain

In ring theory a given ring $R$ is called a Euclidean domain if there exists a function $\sigma:R -\{0\}\rightarrow \{0,1,2,3...\}   $ which satisfies the division algorithm i.e. $ $ if $a,b \in R$ then there exists $q,r \in R$ such that  $b=aq+r$ and either $r=0$ or $\sigma(r)\lt \sigma(a) $ Now I want to ask if we can prove, using just this definition that an element of larger degree won't divide an element of smaller degree. In specific rings such as (i) the integers we can say$$\sigma(a)=|a|$$ $$\sigma(ab)=\sigma(a)\sigma(b)$$ ii) polynomials where$$\sigma(f(x))=deg(f(x))$$$$\sigma(ab)=\sigma(a)+\sigma(b)$$ So in both the above cases the size of product of two elements will always be greater than or equal to the size of individual elements and hence the larger element can never divide the smaller element. But is this true in general for all Euclidean domains ? And how will we prove that


Would real Moody have taught 4th year students about Unforgiveable curses?

Would real Moody have taught 4th year students about Unforgiveable curses the way fake Barty Crouch Moody did?  In other words, did Barty teach about them (leaving aside his hands-on teaching approach) just to satisfy his Death Eater wishes, or did he teach them as part of his cover as Moody impersonator because Moody would have taught about them?


May I use Dropbox as hosting for website's static files?

I'm making a website on a free hosting that doesn't have much space or bandwidth. So I considered using Dropbox Public folder for static files, such as:   Javascript, CSS Images Downloads (each a few hundred kilobytes)   Does Dropbox allow such extensive usage, and what is the limit?


I want to resize the Unity launcher. Is that possible?


I tried to find a precise definition. I found clues on  and , but I cannot find more than an approximation like:     Equivalent of blockbuster movie in cinema, an AAA game is a game with highest development budgets and levels of promotion.   The definition seems imprecise. How can I be sure a game is AAA?   Let's imagine a small indie studio making games and growing up. They hire more and more people through the years and invest more and more money in their game. At which milestone would their game be considered as AAA?


What is the name of a small unluxurious restaurant?

Is there a name for this kind of restaurant? Searching Google, I can't find any synonym of restaurant. I've tried to search for images of unluxurious restaurant, small restaurant or mundane restaurant, with no satisfactory result. The restaurant I'm looking for is small, not so clean and definitely not a place that high class people go to eat.  It can be a house:    Or lie on a side of the street:


How do I create an expression tree to represent 'String.Contains("term")' in C#?

I am just getting started with expression trees so I hope this makes sense. I am trying to create an expression tree to represent:  t => t.SomeProperty.Contains("stringValue");   So far I have got:      private static Expression.Lambda<Func<string, bool>> GetContainsExpression<T>(string propertyName, string propertyValue)     {         var parameterExp = Expression.Parameter(typeof(T), "type");         var propertyExp = Expression.Property(parameter, propertyName);         var containsMethodExp = Expression.*SomeMemberReferenceFunction*("Contains", propertyExp) //this is where I got lost, obviously :)         ...         return Expression.Lambda<Func<string, bool>>(containsMethodExp, parameterExp); //then something like this     }   I just don't know how to reference the String.Contains() method.  Help appreciated.


For $(x,y)\in\mathbb R^2$, consider the series  $$ \lim_{n→\infty}\sum_{l,k=0}^n\frac{k^2x^ky^l}{l!}.  $$ Then the series converges for $(x,y)$ in   $(-1,1)\times(0,\infty)$ $\mathbb R\times(-1,1)$ $(-1,1)\times(-1,1)$ $\mathbb R\times\mathbb R$   *As the series contains $k^2\cdot x^k$ which diverges if $|x|\not\lt1$ while the other in powers of $y$ converges for all $y$. So (1) is true $\implies$ (3) is true. But what about other options due to partial behaviour in $x$ and $y$?


What are the differences between vector graphics and raster graphics?

I understand from prior knowledge that there are two different image format / composition options available for creating images; raster and vector.  I would like to understand more about them, such as what the defining characteristics of each are, and what typical, generic use-cases each might have.       What are raster graphics composed of?   When would I want to choose raster over vector?       What are vector graphics composed of?   When would I want to choose vector over raster?


$x+y=2$ implies $x^3y^3(x^3+y^3)≤2$, for positive $x$ and $y$.

Let $x$, $y$ are two positive real numbers such that $x+y=2$. Then show that $x^3y^3(x^3+y^3)≤2$.  I have tried a lot using $AP$ $GP$ inequality formulas but failed. Also  proceed like that, $x+y=2$ implies $(x+y)^3=8$ implies $x^3+y^3≤ 8$ since $x$ and $y$ are positive, but failed to prove. Please help me to prove this inequality.


I wondered what are your plans? & I wondered what your plans are

Are Both  "I wondered what are your plans?"  &  I wondered what your plans are."  Correct?  There is a little difference in the the existence of quotation mark.


Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC

I'm quite sure I'm missing something obvious, but I can't seem to work out the following problem (web search indicates that it has a solution, but I didn't manage to locate one -- hence the formulation):     Prove that there exists a surjection $2^{\aleph_0} \to \aleph_1$ without using the Axiom of Choice.   Of course, this surjection is very trivial using AC (well-order $2^{\aleph_0}$). I have been looking around a bit, but an obvious inroad like injecting $\aleph_1$ into $\Bbb R$ in an order-preserving way is impossible.  Hints and suggestions are appreciated.


Let H = ⟨R n ⟩. Show that H is normal in D2n.

Let n ∈ Z≥2, and let D2n be the symmetry group of a regular 2n-gon. Recall that D2n = {I, R, R^2, . . . , R^2n−1, F, RF, R^2F, . . . , R^(2n−1)F} and F R = R^(2n−1)F. Let H = ⟨Rn⟩. Show that H is normal in D2n.  Work: I know if I just plug in values its normal but I don't know how to show it arbitrarily in a proof.


Inequality related with $abcd=(1-a)(1-b)(1-c)(1-d)$

Given that $0<a,b,c,d<1$ satisfying $abcd=(1-a)(1-b)(1-c)(1-d)$. Prove that $$(a+b+c+d)-(a+c)(b+d)\geq 1.$$  First, I have already done a quite similar exercise as below: "Given that $a^2+b^2+c^2+d^2=1$. Prove that $(1-a)(1-b)(1-c)(1-d)\geq abcd$". The solution is to use the remark of $(a+b-1)^2\geq 0$, which leads to $2(1-a)(1-b) \geq 1-a^2-b^2 \geq 2cd$.  Then, I use the same method for this problem and I have showed that $a^2+b^2+c^2+d^2 \geq 1$. I don't know what to do next with $(a+b+c+d)-(a+c)(b+d)$.  Many thanks!


What are the best books to study Neural Networks from a purely mathematical perspective?

I am looking for a book that goes through the mathematical aspects of neural networks, from simple forward passage of multilayer perceptron in matrix form or differentiation of activation functions, to back propagation in CNN or RNN (to mention some of the topics).  Do you know any book that goes in depth into this theory? I've had a look at a couple (such as Pattern Recognition and Machine Learning by Bishop or Deep Learning by Goodfellow, Bengio and Courville) but still have not found a rigorous one (with exercises would be a plus). Do you have any suggestions?


Which partition to select for bootloader (UEFI, 2nd HDD)

So here is the picture of current situation ->  and I'm not sure which one to select for boot, since Windows is installed on sdb4. First time I installed I just left it on /dev/sda as it is in picture (default). Also I'm using UEFI and GPT if that means something? I tried to repair boot with boot-repair and it didn't work so I need to reinstall ubuntu again with correct place for bootloader. Thanks!


Use Stack Exchange icon for Stack Exchange blog posts in the Community Bulletin

is used to host global Stack Exchange blog posts and is using favicon of Stack Exchange itself. All good. However, when published in the bulletin, the Meta Stack Exchange icon is used for some reason:    Can it be changed please to using the "full" icon?


How can I truncate a double to only two decimal places in Java?

For example I have the variable 3.545555555, which I would want to truncate to just 3.54.


help to understand have/have been example

what is the difference between these examples and which one is correct.  1) I have this phone for years  2) I have been this phone for years


Derivative of $a^x$ from first principles

I've been trying to think for the past few days how one could differentiate $a^x$ based on the definition that $a^n$ is repeated multiplication, $a^{n/m}=(\sqrt[m]a)^n$, and $a^x$ is the completion of the above function by continuity.  With a bit of algebra, the problem quickly reduces to finding the derivative at $0$:  $$\lim_{h\to0}\frac{a^h-1}{h}\tag{1}$$  And that limit's really got me stumped. Since you'll obviously have to use the definition in some way, I thought I'd replace $h$ with $\frac{1}{n}$ and use the $n$-th root definition:  $$\lim_{n\to\infty}n(\sqrt[n]a-1)\tag{2}$$  Of course, just because $(2)$ exists doesn't automatically imply $(1)$ exists, but it might be a first step. Even $(2)$ has me stumped, though.


I would like to create something like a=array[1,2,15,6,18] and then a[0]=1, a[1]=2. Is it possible to create an array in LaTeX (with pgf or another package)?


Why this $\sigma \pi \sigma^{-1}$ keeps appearing in my group theory book? (cycle decomposition)

I'm studying cycle decomposition in group theory. The exercises on my book keep saying things like:   Find a permutation $\sigma$ such that $\sigma (123) \sigma^{-1} = (456)$ Prove that there is no permutation $\sigma$ such that $\sigma (1 2) \sigma^{-1} = (123)$ Show that $\pi(x_1 x_2 \cdots x_n)\pi^{-1} = (\pi(x_1)\cdots \pi(x_n))$   Why this  $\sigma \pi \sigma^{-1}$ appears every time in this book? Is this important for something? Could somebody give me a clear picture of how we arrive at this? Also, would be nice to know how to prove the third one, if somebody could help me.


How to fix "Could not open a connection to your authentication agent." error when trying to add ssh-key?

I'm using Ubuntu server 10.04.   ssh-add /foo/cert.pem gave the following output:     Could not open a connection to your   authentication agent.   These are my running processes:  ps -aux | grep ssh Warning: bad ps syntax, perhaps a bogus '-'? See http://procps.sf.net/faq.html root      1523  0.0  0.0  49260   632 ?        Ss   Dec25   0:00 /usr/sbin/sshd root     10023  0.0  0.3 141304  6012 ?        Ss   12:58   0:00 sshd: padmin [priv] padmin   10117  0.0  0.1 141304  2400 ?        S    12:58   0:00 sshd: padmin@pts/1 padmin   11867  0.0  0.0   7628   964 pts/1    S+   13:06   0:00 grep --color=auto ssh root     31041  0.0  0.3 141264  5884 ?        Ss   11:24   0:00 sshd: padmin [priv] padmin   31138  0.0  0.1 141264  2312 ?        S    11:25   0:00 sshd: padmin@pts/0 root     31382  0.0  0.3 139240  5844 ?        Ss   11:26   0:00 sshd: padmin [priv] padmin   31475  0.0  0.1 139372  2488 ?        S    11:27   0:00 sshd: padmin@notty padmin   31476  0.0  0.0  12468   964 ?        Ss   11:27   0:00 /usr/lib/openssh/sftp-server   These are my environment variables:  $ env | grep SSH SSH_CLIENT=192.168.1.13 42626 22 SSH_TTY=/dev/pts/1 SSH_CONNECTION=192.168.1.13 42626 192.168.1.2 22   What is wrong? Why can't I add any identities?


so i tried to make a grass and i wanted to change colour with colour ramp. it's a particle effect. when i change the colours and mix it only bottom base layer changes the colours. but the actual blades of "grass" stay the same one colours.


PHP regex content between tags with square brackets

I am trying to create a regex that will give me everything that appears between [start-flashcards] and [end-flashcards]  I am using \[start-flashcards\](.*?)\[end-flashcards\] but this doesn't match. I must be missing something?
[start-flashcards]

[London|This is the capital city of the United Kingdom]

[Paris|This is the capital city of France]

[Madrid|This is the capital city of Spain]

[Tokyo|This is the capital city of Japan]

[Moscow|This is the capital city of Russia]

[end-flashcards]


jQuery Pagination - Button doesn't work after first page

There's a list of people whose info should be fetched. I have made a simple pagination for that list. However, List looks fine, but the buttons does not work after the first page. Here is the HTML Code:
  <input type="text" class="search" style="width: 50%" placeholder="Search..." />

<button id="people_1" class="btn btnlink name">People 1</button>

<button id="people_1" class="btn btnlink name">People 1</button>

<button id="people_2" class="btn btnlink name">People 2</button>

<button id="people_3" class="btn btnlink name">People 3</button>

<button id="people_4" class="btn btnlink name">People 4</button>

<button id="people_5" class="btn btnlink name">People 5</button>

<button id="people_6" class="btn btnlink name">People 6</button>

<button id="people_7" class="btn btnlink name">People 7</button>

<button id="people_8" class="btn btnlink name">People 8</button>

<button id="people_9" class="btn btnlink name">People 9</button>

<button id="people_10" class="btn btnlink name">People 10</button>

  Library:      Here is The jQuery code: var monkeyList = new List('test-list', {   valueNames: ['name'],   page: 5,   pagination: true, });  for button click: $(document).ready(function() {                         $(".btnlink").on("click", function(){                                                   var id = $(this).attr('id');          alert(id); }); });  After first page, button click doesnt give alert, not working; i also tried event binding functions, but doesnt work also.


I'm trying to understand how System.out can invoke println(). All the searches  say System.out is an instance of PrintStream class therefore it can invoke a method in that class.  BUT...  When I try to duplicate this with the following a NullPointerException results.  public class Main {     public static void main(String[] args){         Tasker.calc.add(1, 2);     } }  class Tasker{     static Calc calc; }  class Calc {     public void add(int x, int y){         System.out.println(x+y);     } }   Isn't Tasker.calc a similar instance of Calc? How is System.out not a NullPointerException?  To be clear, this is not a question about NullPointerException... this is a question about why System.out doesn't require initialization.  Thanks a bunch!


this is very easy I think but I don't have much experience with geometric series. I need to find/simplify the sum  $x^k+x^{k+1}+\dots+x^{k+m}$   where $x\in\mathbb{R}, k\in\mathbb{Z},m\in\mathbb{N}$  So I'm thinking I just write this as  $x^k+x\times x^k+x^2\times x^k+\dots+x^m\times x^k$  Now isn't this a geometric series with $a=x^k$ and $r=x$? So it should have the sum  $$s=\frac{x^k(1-x^{k+m})}{1-x}=\frac{x^k-x^{2k+m}}{1-x}$$  Is this the correct answer?


If $ax^2+(b+c)x+d+e=0$ has roots greater than $1$, then show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root

Your are given an equation $$ ax^2+(b+c)x+d+e=0 $$ whose roots are real and  greater than $1,$ show that the equation $$ ax^4+bx^3+cx^2+dx+e $$ has at least one real root. Note that $a,b,c,d,e$ are all real numbers. I have tried to solve this question using the method of contradiction. However I was not able to make great progress. Is there any way I can solve it using the method of contradiction or any other proof strategy. I would also love to see an approach using predicate logic (only if it's possible).


$$\{(x,y)\,|\,Ax+By+Cz=0\} = L$$ \begin{flushright}\dag \end{flushright}[1]   I am trying to align the dagger so it is flushed to the right but on the same line as the equation. When i insert \begin{flushright}\dag \end{flushright}inside $$ I get a compiling error.


I have no calculations, I just converted, I need to send data in numeric type, but after conversion is not normal, why java python kotlin conversion is no problem, swift has a problem? I know the problem of computer storage accuracy, is there a way for swift to correctly convert string?   How can I make a string to a number without distortion?


I can't saturate my NPN transistor!  Here is my circuit:         – Schematic created using   The Vce is around 1.7 V, which is way above the saturation Vce of 0.3, meaning that I must be in linear mode right?  No matter what value resistor I try for Rb, the Vce doesn't change.  My LEDs are super-bright, 2.4v, 20 mA


Distribution of $(X_1-\mu)^T\Sigma^{-1}(X_1-\mu)$ is chi-squared?

If $(X_i)_{i=1}^{20}\sim N_6(\mu,\Sigma),$ then find the distribution of   $$ (X_1-\mu)^T\Sigma^{-1}(X_1-\mu)$$  The solution is $\chi^2_6,$ but could someone show why? I only know that the sum of standard normal variables is itself chi-squared but I'm not sure how to approach this.


Using the css content property, I am trying to make put an HTML entity after an element.  Here is my HTML:

   And my CSS:  table{     text-align:center;     font-size:2em;     font-weight:bold; } td.o:after{     content:"&#9675;";     font-weight:bold; } td.x:after{     content:"&#x2716;" }   Unfortunately, instead of getting the ○ character and the ✖ character, I get the entity names.    How can I fix this? Thanks!


Convert like raster cell values to a polygon?

I have a population density raster and would like to create 5 polygons from the 5 natural break (jenks) classification ranges. 1 polygon for each classification range. I'm using ArcMap10 and have all of the Extensions enabled in the ToolBox to my disposal.   Thanks!


How to install MySQL on OS X Mountain Lion?

I tried downloading the MySQL community server from the MySQL website, however, when I try to open the installer, I get a popup saying "You may only run executables from the Mac App Store". What kind of tyranny is this!?  So I go to store.apple.com and type in "MySQL" into the search bar but it brings up no results. How am I supposed to install MySQL on my laptop??


New software centre won't run after 16.04 upgrade

The new "software centre" won't run after my upgrade to 16.04 last night. Trying it from the unity bar - nothing happens.  I read that it should be running gnome's software manager.  Trying from the command line - if I got the command right, gives this result      $ gnome-software  (gnome-software:5748): Gs-WARNING **: failed to open plugin /usr/lib/gs-plugins-9/libgs_plugin_xdg_app_reviews.so: /usr/lib/gs-plugins-9/libgs_plugin_xdg_app_reviews.so: cannot open shared object file: No such file or directory Timeout was reached


Prove that if $G$ is a simple graph on n vertices such that $\delta(G) \geq \lfloor n/2\rfloor$, then $G$ is connected.

I need to prove that if G is a simple graph on n vertices such that $\delta(G) \ge \lfloor n/2\rfloor$, then $G$ is connected (Where $\delta(G)$ represents the minumum degrees in $G$).  To prove this I want to show that for every vertex $u,v \in V(G)$ (where V represents the vertex set of our graph $G$) there exists a $u,v$-path in $G$.  So far I have:  Let $u,v \in V(G)$. If $u$ and $v$ are adjacent, there exists a path from $u$ to $v$ consisting of a single edge.  How do I prove this for greater lengths? Any hints would be appreciated.


If I login on my Ubuntu 14.04, I get the following desktop:  This weird behavior appeared after I executed sudo apt-get update && sudo apt-get upgrade and restarted my computer. Don't know why though.  To my Ubuntu I have tried the following (nothing seems to work so far)  Fix any broken packages:  sudo apt-get update sudo apt-get autoclean sudo apt-get clean sudo apt-get autoremove   Locate any broken packages and reinstall them:  sudo apt-get install debsums sudo apt-get clean sudo debsums_init sudo debsums -cs sudo apt-get install --reinstall $(sudo dpkg -S $(sudo debsums -c) | cut -d : -f 1 | sort -u)   Removing some compiz files:  rm -r ~/.cache/compizconfig-1 rm -r ~/.compiz   Purging of NVIDIA and installing NVIDIA-prime:  sudo apt-get install --reinstall ubuntu-desktop sudo apt-get install unity sudo apt-get purge nvidia* bumblebee* sudo apt-get install nvidia-prime sudo shutdown -r now   Compizconfig Settings Manager:  sudo apt-get install compizconfig-settings-manager  export DISPLAY=:0 ccsm  // Back to UI and enablement of Unity Plugin   Unity replace, which stopped at a while and did nothing afterwards  unity --replace   Some dconf reset  dconf reset -f /org/compiz/ unity --reset-icons &disown   Actually dconf did not work and I got this error:  error: Cannot autolaunch D-Bus without X11 $DISPLAY   Can anybody help me on that?    This is my hardware (hope it helps in any way):   Intel® Core™ i7-3770 ASUS GTX660TI-DC2-OG-2GD5 () ASUS P8Z77-V LX Corsair DIMM 8 GB DDR3-1600 Kit Samsung 830series 2,5" 256 GB (Windows is installed here) Seagate ST31000524AS 1 TB (3/4 are reserved for files; 1/4 is for Ubuntu (16GB swap included))


Percentage progress on Automator application(.app) on Mac OS

I have used Automator Application to create application(.app which runs by double clicking). It runs commands which executes command one by one. Every command takes 2-3 minutes. What I want to achieve is show percentage progress after completion of every command.    In above image percentage is always zero. I want to explicitly set progress after completion of every command. I also know this is possible using AppleScript but I want to implement in bash script.


Notification on Unity after i3 desktop removal

I installed i3 desktop environment and then removed it via software manager since I didn't like it very much.   Now I started to use unity (default) back again. However, now I have a white over blue notifications on the upper left of my screen. I usually see them when wifi is connected or I received an email.  This notification also appears on the login screen and does not let me to write my password during the check of preferred wirelesses.  I need to remove this notification thing.


regex implementation to replace group with its lowercase version

Is there any implementation of regex that allow to replace group in regex with lowercase version of it?