Why following code printing False?
How do I compare strings in Java?
Similar Matrices and Linear Transformations Why doesn't ZIP Compression compress anything? A 398MB directory was only compressed to 393MB using 7Z and Normal ZIP compression. Is this normal? If so, why do people continue to use ZIP on Windows? Show that for $\eta > 0$, $\alpha_\eta=-\infty$ and for the Cauchy problem $z'=x-z^2,z(0)=\eta$ the saturated solution is defined up to $+\infty$. We consider the differential equation $y'=x+y^2$ and for any $\eta \geq 0$ we denote by $\phi_\eta:(\alpha_\eta,\beta_\eta)\rightarrow\mathbb{R}$ the unique saturated solution of the Cauchy Problem $y'=x+y^2$, $y(0)=\eta$. I am required to do the change of variable $z(x)=y(-x)$ and I succeded here, obtaining $y'(-x)=y^2(-x)-x$ and so $z'(x)=x-z^2(x)$, then I was required to represent the $0-isocline$ and it was also simple as I obtained a parabolla and also I was required to write the equation of the tangent in the point $(0,\eta)$ which was also pretty simple as I obtained $\phi'_\eta(0)=\eta^2$ and the equation of the tangent is $y=\eta+\eta^{2}x$. Now, I am required to find $\phi^{(5)}_0(0)$( that $5$ indicates the number of differentiations), which puzzles me as I don't know the form of the solution and if it can be found out and also I am told to show that $\frac{1}{\eta}\geq\beta_\eta$ What I did not prove after the first edit : and that for $\eta &gt; 0$, $\alpha_\eta=-\infty$ and for the Cauchy problem $z'=x-z^2,z(0)=\eta$ the saturated solution is defined up to $+\infty$. At this last ones I am lost. Any help, please? Edit: I have passed beyond finding $\phi^{(5)}_0(0)$ and I think I did show that $\frac{1}{\eta}\geq\beta_\eta$, now it remains to prove the last questions. Are you allowed to use numbers as table names in MySQL? I'm thinking of having a program that dynamically creates new tables as the need arises. Can I have tables named with just numbers in MySQL? I have a production server running with the following flag: -XX:+HeapDumpOnOutOfMemoryError  Last night it generated a java-38942.hprof file when our server encountered a heap error. It turns out that the developers of the system knew of the flag but no way to get any useful information from it.  Any ideas? What is the method to make files in a USB Flash Drive undeletable? Does these method work with USB 3.0 interface?  (I have surveyed some Flash Drive manufacturers, and I only see undeletable files for USB 2.0 drives, and not 3.0 drives. One manufacturer claimed that USB 3.0 cannot do undeletable file, so I am curious whether the claim is correct...) I'm creating a model for a 3D game that will eventually be exported using a custom Python script. This model makes heavy use of UV textures.  However, the project now references a bunch of images that are not used by any objects in the project. Example:    I don't want the first two, or the red_bubble.png image. However, I have no idea how to remove them from the project. Selecting one of them reveals that there are "2 users of the data" although I am not using it anywhere.  How can I get rid of these excess images? I'm looking to view and archive all my old DMs in Twitter, since I would like to revive conversations that took place 1 year ago.  Acording to Twitter they don't delete old messages, they simply archive them in their database.  Is there a way to view and download all of these messages, just like you can view all your old public tweets with third party apps?  UPDATE: I found  but apparently it's not working for DMs now On the number divisors of a number Let $d(n)$ be the number divisors of a natural number $n$. Now let $m$ be a natural number. Find least natural number $n$ such that $d(n)=m$.  Thank you Do an action and its Euler-Lagrange equations have the same symmetries? Assume a certain action $S$ with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations.  Can it happen that the equations of motion derived by this procedure have different kinds and/or numbers of symmetries than the action one has started with? And if yes, are there underlying principles that state why which kind of symmetries the action does not have can emerge in corresponding EOMs or which kind of symmetries of the action can potentially disappear in the EOMs derived from the Euler-Lagrange equations? How to find $\lim_{n\to\infty}\frac{1!+2!+\cdots+n!}{n!}$? Pretty much the problem asks if a function is continuous at the point $c$ and $f(c) &gt; 0$ then there exists a $d &gt; 0$ such that $\forall x$, $f(x) &gt; 0$ with $|x-c| &lt; d$.   I can understand what the problem means. That if a function is positive at a point then there is another point that's really close that'll also be positive. I can not prove this in a formal way though. I've tried using the intermediate value theorem and I do not know hot to implement it. Any ideas? Proving the given quadratic form is chi-squared $k$ Suppose $\underline{X}$ is an $m$-dimensional vector following multivariate Normal distribution i.e. $\underline{X}$~$N_m(\underline{\mu},\Sigma)$ where $\Sigma$ is positive definite. Let $B$ be a symmetric $m$ by $m$ matrix, having the following properties:  $B\Sigma B=B$  $\underline{\mu}'B\underline{\mu}=0$  $trace(B\Sigma)=k$, where $k&lt;m$   Prove that $\underline{X}'B\underline{X}$ follows chi-squared ($k$).  I proceeded a lot but got stuck in one last step where I think linear algebra is troubling me. Kindly have  a look at my &quot;solution&quot;.  The second condition can be written as $\underline{\mu}'B\Sigma B\underline{\mu}=0\implies B\underline{\mu}=\underline{0}$ as $\Sigma$ is Positive definite. Then after a little algebra and considering condition 2, we can write $\underline{X}'B\underline{X}=(\underline{X}-\underline{\mu})'B(\underline{X}-\underline{\mu})=(\underline{X}-\underline{\mu})'B\Sigma B(\underline{X}-\underline{\mu})$ But $\Sigma$ is positive definite hence we can have a symmetric matrix $\sqrt{\Sigma}$ defined such that $\sqrt{\Sigma}\sqrt{\Sigma}=\Sigma$. Using this, we can write $(\underline{X}-\underline{\mu})'B\Sigma B(\underline{X}-\underline{\mu})=(\sqrt{\Sigma}B(\underline{X}-\underline{\mu}))'(\sqrt{\Sigma}B(\underline{X}-\underline{\mu}))$ We want to show that this follows chi-squared ($k$). Now, it is obvious that as $(\underline{X}-\underline{\mu})$~$N(\underline{0},\Sigma)$, $\sqrt{\Sigma}B(\underline{X}-\underline{\mu})$~$N(\underline{0},\sqrt{\Sigma}B\Sigma B\sqrt{\Sigma})=N(\underline{0},\sqrt{\Sigma}B\sqrt{\Sigma})$ Now, $trace(\sqrt{\Sigma}B\sqrt{\Sigma})=trace(B\Sigma)=k$ and $\sqrt{\Sigma}B\sqrt{\Sigma}$ is idempotent (verified). So its eigenvalues are only $0$ or $1$. Since its trace is $k$, there are $k$ eigenvalues with value $1$ and other $m-k$ eigenvalues are $0$. Now here is the thing I want to prove: I want to show that$\sqrt{\Sigma}B\sqrt{\Sigma}$, which is the covariance matrix, is diagonal and has only $k$ $1$'s and remaining $m-k$ diagonal entries $0$. The reason is, then I will be able to say that $k$ components of $\sqrt{\Sigma}B(\underline{X}-\underline{\mu})$ are independent standard normals whose sum of squares is our quadratic form and thus it follows chi-squared ($k$). But I really could not show that $\sqrt{\Sigma}B\sqrt{\Sigma}$ has the desired property i.e. it is diagonal with rank $k$. But this is crucial, it is the finale. If this does not happen, then some components will be correlated with each other and we cannot say that our quadratic form has chi-squared ($k$). I would really appreciate if someone helped me to prove this final part. Decrease available inventory item on Cognito Form, removing it when zero I want to limit inventory quantities on a sales form, so that it can start at say 100 and count backwards as applicants submit orders and then shut down that particular option when it reaches 0.    Is this possible with Cognito? How many rectangles or triangles. I have come across numerous questions where I am given the picture such as the above one been asked "how many rectangles are there?". I have even come across some slightly different images that instead of rectangles you are supposed to find the number of triangles. Well, I was thinking whether there is any formula or strategy that is used to solve these problems without having to manually count every shape.  Help would be appreciated.  Thank you :) Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$ Find all functions $f$ such that $f:\mathbb{N}\rightarrow\  \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$   Let us plug in $n=1$  $f(f(1))+f(2)=3$  Since the function is from $\mathbb{N}$ to $\mathbb{N}$, $f(2)$ can only take the values $1,2$. Now we divide the problem into cases.  Case-1: $f(f(1))=2,f(2)=1$  We can assume that $f(1)=c$ for the time being. Then plugging in $n=3$ and using $f(2)=1$ gives $$f(3)=4-c$$ and again since the range of the function is positive integers,then $4-c$ has to be positive and hence $c$ belongs to  {$1,2,3$}. Now, $$f(1)=c$$$$\implies f(f(1))=f(c)$$$$\implies 2=f(c)$$ by the assumption that $f(f(1))=2$ . Now,since $c$ can only take the values $1,2,3$,we start treating cases. If $c=1$,$$f(c)=2$$$$\implies f(1)=2$$ but we know from the deinition of $c$ that $f(1)=c=1$,a contradiction.If $c=2$,then $2=f(c)=f(2)$ but $f(2)=1$ by assumption. Finally,if $c=3$ $$2=f(c)=f(3)$$ but $$f(3)=4-c=4-3=1$$ which is once again a contradiction. Therefore there are no such functions in this case.  Case-2: $f(f(1))=1,f(2)=2$  Again assuming $f(1)=c$ and using $f(n)\le n$ along with plugging $n=c-1$ will give us that $f(1)=1$ and then it is easy to prove that such a function exists by recursion. I can only give a "sort of recursive" way to define the function. Here it goes $$f:\mathbb{N}\rightarrow \mathbb{N}$$$$f(1)=1$$$$f(n)=n+1-f(f(n-1))$$  But this case is harder to deal with.Some help will be appreciated. Is there a way for me to Export my Minecraft Realms World? I have played on my friend's Survival Realm for ~3 months and he was going to stop paying for the realm so I was wondering is there any way to get that world for my Personal Client. I use form to send POST request to a page and to login user with wp_signon() in order to authenticate user to my wordpress installation as described in WP documentation:  $creds = array(); $creds['user_login'] = $_POST["user-login"]; $creds['user_password'] = $_POST["user-password"]; $creds['remember'] = true;  $user = wp_signon( $creds, false );   After this little piece of code I'm checking if user was logged in:  if ( is_user_logged_in() ) { echo "SUCCESS"; } else { echo "FAIL!"; }   But I got FAIL! all the time. Then after sniffing around I found this little trick:  wp_set_current_user( $user ); if ( is_user_logged_in() ) { echo "SUCCESS"; } else { echo "FAIL!"; }   I've got SUCCESS on this one but when I leave this page I got FAIL again and again.  Can anyone explain me how to login user with wp_signon() without logging her out after page is changed or reloaded or whatever.    I've got desirable result when I go to /wp_admin and login with WP's default login form. I can navigate through every page of my WP site remaining logged-in all the time. But when I try to do this outside the default form I FAIL.  Guide me! PLEASE! How do I add PHP code/file to HTML(.html) files? How to make a multiboot USB key? I want to cut my 8 GB USB key into several partitions to use  for a Windows XP (maybe d before).   I also want to put the  remix pack into it such that it has the second bootable OS. I want to tweak and modify it a little because if I can I want to switch Ubuntu 9.04 to the  version.  How to do it easily?  IMP: in short I want to make a dual-boot USB key with Windows XP SP3 and Ubuntu 8.04.3 LTS.