How can you set multiple layers equal distance between them in Photoshop in a given distance?   I know you can do the math and manually set the x axis value for each of them, but I am looking for a simpler solution and, more importantly, faster.  Example:   Input - 5 rectangles 150x150 px size; distance between the grids 1000 px:      Do something set equal distance between rectangles 1, 2, 3, 4 and 5. Result:

I try to do it mostly with words but sometimes have to do it with other things too. How do you equally space out things automatically, I Know how to evenly distribute from the center of every layer/object but not how to have even actual space between those to objects.   This is really not a problem when all the things are of the same width (or height) but as you know words are hardly ever that. So what i do is is make a rectangle of size that i want space to be empty and once done typing i manually drag out that box to the end of the first word, then adjust the 2nd one decrease/increase the space to match the edges of the rectangle and so on for the texts after 2nd..like 3rd,4th...Usually it's Home, About, Products, Contact, etc...


So, my game is being developed in pure C++, with very limited dependencies (Mostly just pocoproject). The main goal here is portability, not performance. The code runs on multi-platform clients, as well as the server itself.  This is all headless, not graphics whatsoever. Everything is implemented, though. Menus, navigation, the game itself, online, single player, ... etc. You can essentially play the whole game with this C++ library. I added simple console bindings, so I can visually test and play the game, but haven't hooked it with a game engine yet.  I would really like to use Unity3D for the graphical part, as it kicks ass when it comes to rapidly developing graphics, but it was a hellish experience to try and marry Mono with C++, even when using SWIG. (Basically, Mono has limited C++ compatibility, but it is really annoying to work with).  Here is the problem, I am stuck between these two islands; C++ program and Unity3D. I am not very good with OS concepts, so I don't know if it's possible to fork the main process and run a local C++ server, and have the Unity game communicate using RPCs or even REST API. Performance isn't an issue, the only issue is maintainability. I need a robust and simple system that I can wrap my head around easily.  Other solutions welcome!

The title kind of says it all. Is it possible to replace C# with C++ on a game using Unity?


"Role Model" is used in a positive light, and thus doesn't fit the sentence below.  Bob saw his incriminated elder brother, and made a ____ out of him.

Example of bad/negative role model: someone whose action (and its consequence) one should learn to avoid instead of emulating such as a gambler or robber.


There is a pretty high-level of guarantee that we can have continued possession of  a chosen domain name as long as we renew it from our registrar (and provided that our registrar is not corrupted/incompetent).  For example, if we purchase a domain name my-domain-name.com and pay our annual renewal fees on time, it's unlikely that we will lose ownership of the domain name in the future.  Is there such a guarantee for continued possession of IP addresses?  For example,  has publicly stated that the specific IP addresses  8.8.8.8 and 8.8.4.4 belongs to him. Then, what are the necessary steps he must take to ensure that these addresses continue to belong to him in the future?  How much "guarantee" does future IP address ownership has?

How can I own an IP address like I do with domains?  I have done some research and it seems that you can't buy a single IP, but rather you have to purchase a range of IP addresses.  Update : Important Note I want this IP to use it with my servers. for example I had a VPS, it went bad, I want to be able to use the same IP on another VPS from another company.


Experiments using a computer show that the following binomial inequality (which is, to my mind, quite symmetric and natural) seems to be true for all $ a, t \in \mathbb{Z}_{\geq 0} $: $$ \binom{2t}{2a} \geq \binom{t}{a}^2 $$ Further, it seems that equality holds iff $ a = 0 $ or $ a = t $. I have tried all the simple methods of proof I can think of:  looking for a simple combinatorial argument of the form "every method of picking $a$ items from $t$ twice independently can be matched (via some method) injectively with a method of picking $2a$ from $2t$; expanding out the subtraction and quotient of both sides in terms of factorials and simplifying (by hand and with Mathematica); trying to use induction on $ a $; using Google and MSE to find a proof.  Unfortunately I am not that well versed in any inequality methods from enumerative combinatorics, so it is entirely possible one of these methods does work.  How would one prove this inequality (or is there some counterexample I have yet to find)? I would especially like a purely combinatorial proof, if possible.

I need to prove the inequality ${M}\choose{N_1}$ ${M}\choose{N_2}$ $\leq$ ${2M}\choose{N_1+N_2}$ for $M, N_1, N_2 \in \mathbb{N},\,M\geq N_1,N_2$. I wanted to prove it by induction. But since we are given 3 variables running, I was confused if the natural induction, as I know it, can be used in this case. Can you tell me if proving by induction is possible and necessary in this example ? We get $N_1, N_2, N_1+N_2$ fractions from ${M}\choose{N_1}$,${M}\choose{N_2}$, and ${2M}\choose{M_1+M_2}$, respectively. Without loss of generality, we assume $N_1\geq N_2.\,$An appropriate approximation of all fractions from left to right leads to: $$ \frac{M}{N_1}\frac{M-1}{N_1 -1}\frac{M-2}{N_1-2}\cdots \frac{M-(N_1-1)}{1} \cdot\frac{M}{N_2}\frac{M-1}{N_2 -1}\frac{M-2}{N_2-2}\cdots \frac{M-(N_2-1)}{1}\leq \frac{2M}{N_1+N_2}\cdots $$ For the second fraction from the left I get: $\frac{M-1}{N_1 -1}=\frac{2M-2}{2N_1-2}\geq\frac{2M-1}{2N_1-1}\leq\frac{2M-1}{N_1+N_2-1}.$ The last term in the last inequality is not the convenient approximation for $\frac{M-1}{N_1 -1}$ unless we got $\leq$ instead of $\geq$ sign in the last inequality. Can somebody provide some hint how to go further ? Thanks.


A: Where would you have the perfect date? B: In a place without people. Just him and me.  Is this written correctly?

I want to know the correct form:     He and I will go there   or   He and me will go there.   Which is correct?


For $x\in (0,\pi)$, how many solutions does the equation $\sin x+2\sin2x-\sin3x=3$ have?  My attempt is as follows:  One can see that if $\sin3x$ is positive, then it is not possible to have any solution, so $\sin3x$ should be negative.  $$\sin3x<=0$$ If $x\in (0,\pi)$, then $3x \in(0,3\pi)$  So $\sin3x\in[-1,0]$  We can also see that $\sin x$ and $\sin 2x$ should be positive in order to have the solution.  $$\sin x>0 \text { and } \sin2x>0$$ As $x \in (0,\pi)$, so $\sin x\in(0,1]$  But $\sin2x>0$, so it means $x$ has to be acute (less than $\dfrac{\pi}{2}$)  So $x$ will be in first quadrant, $2x$ will be in second quadrant, $3x$ will be in second quadrant.  We can also see that if $\sin x$ is high then $\sin2x$ will be low because graph of $\sin x$ is increasing in first quadrant and decreasing in second quadrant.  But $\sin 2x$ has higher coefficient, so if $\sin 2x$ is $1$, then $\sin x$ will be $\dfrac{1}{\sqrt{2}}$, but then $3x$ lies in second quadrant which should not be the case.  So $x$ should be at least $\dfrac{\pi}{3}$ so that $3x$ lies in the third quadrant.  So let's check at $x=\dfrac{\pi}{3}$, we get $\sin x$ as $\dfrac{\sqrt{3}}{2}$, $\sin2x$ as $\dfrac{\sqrt{3}}{2}$, $\sin3x$ will be $0$, so if we put these values into the original equation , it would be   $$\dfrac{\sqrt{3}}{2}+\sqrt{3}-0=\frac{3\sqrt{3}}{2}$$  It seems the equation has no solution, is there any better way to solve this problem. I also tried reducing the equation, but it is not getting reduced too much. Is there any better approach to this?

In $(0 \:\:\pi)$Find the number of solutions of $$\sin x+2 \sin 2x- \sin 3x=3$$  The equation can be written as  $$\sin x+4 \sin x \cos x=3+\sin 3x$$ i.e.  $$\sin x(1+4\cos x)=3+\sin 3x$$ i.e.,  $$\sin x(1+4\cos x)=3+\sin x(3-4\sin^2 x)=3+\sin x(4\cos ^2x-1)$$  so  $$\sin x(4\cos^2 x-4\cos x-2)=-3$$ Any hint from here?


After a lot of searching, I finally was able to create a SQL Query to retrive Wordpress User Meta Data. Now the problem is, the performance is so bad it doesn't even show me a result after 30 min.   Wordpress stores data in 3 columns: user_id, meta_key, meta_value.  So each entry gets one row.  What I need is one row per user, with each meta_key as its own column.   In other words, I have this:   user_id | meta_key | meta_value        1|Name      |David        1|Lastname  |Brown   But I need this:   user_id|Name |Lastname       1|David|Brown   My approch on this is:  select m1.user_id, m1.meta_value as Vorname_M, m2.meta_value as Nachname_M,m3.meta_value as Adresse_M from wp_usermeta m1 join wp_usermeta m2 on (m1.user_id = m2.user_id and m2.meta_key =  'nachname') join wp_usermeta m3 on (m2.user_id = m3.user_id and m3.meta_key = 'adress') where m1.meta_key = 'vorname'   With 5 joins it still works, but takes already 4 sec. All in all there are actually 17 joins, and at this point it doesnt show me anything.   I am running the query in phpMyAdmin, and would like to create a VIEW out of the result.   Now the actual question is: How can I increase the perfomance on my query, or how to rewrite it? I am givng my best, but I am actually a starter in SQL.   MySql version: 5.5

Been looking to pivot rows (progress_check) into columns check 1, check 2 etc... No sum or totals required, just to display the results hopefully... Can anyone help, Thanks Ad


I found a strange problem in my tikz picture. I use calc library to draw a line, and rotate this line with some angle, but I find I cannot specify its rotate center point. In other words, the rotation seems has no relationships with the center point I specified.  A minimal example is as follows:  \documentclass{standalone} \usepackage{tikz} \usetikzlibrary{calc} \begin{document} \begin{tikzpicture}   \draw [step=.5,help lines] (-3,-3) grid (3,3);   \node [fill=black, circle, minimum size=0.05, label=-30:$O$] at (0,0 {};   \coordinate (r5) at (1,1);   \draw [fill=yellow] ($(r5)+(1,0)$) circle (0.05);   \draw [fill=yellow] ($(r5)+(1,2)$) circle (0.05);   \draw [fill=yellow] ($(r5)+(1,1)$) circle (0.05);   \draw [rotate around={90:($(r5)+(1,1)$)}, red, thick] ($(r5)+(1,0)$) -- ($(r5)+(1,2)$); \end{tikzpicture} \end{document}   As my understanding, the code rotate a line with its center point. In other words, the line constructed with the three yellow point should rotate around the middle point. But actually the effect is as follows:   So, can you give me some help? Thanks for advance!

\begin{tikzpicture} \node [draw=black, anchor=south west] (label) at (0,0){\includegraphics[width=300mm]{th.jpg}}; \coordinate (ZX) at (157mm,104mm); \coordinate (YB) at (249mm,39mm); \coordinate (YY) at ($(ZX)!1.5!(YB)$); \coordinate (ZZ) at ($(YB)!2.5!(ZX)$); \draw[blue!20,very thick] (ZZ)--(YY); \draw[red!20,very thick, rotate around={90:(ZX)}] (157mm,104mm)--(249mm,39mm);%It works \draw[red!20,very thick, rotate around={-90:(ZX)}] (ZX)--(YB);%It doesn't work \filldraw[white] (ZX) circle (2mm); \filldraw[white] (YB) circle (2mm); \end{tikzpicture}   a working example       \documentclass{minimal} \usepackage{tikz,tikz-3dplot}  \begin{document}    \tdplotsetmaincoords{70}{115}    \begin{tikzpicture}[scale=4,tdplot_main_coords] \pgfmathsetmacro{\rvec}{.8} \pgfmathsetmacro{\thetavec}{30} \pgfmathsetmacro{\phivec}{60}  \tdplotsetrotatedcoords{\phivec}{\thetavec}{0}   \coordinate (O) at (1,1,1);   %these 2 lines overlap \draw[thick,->] (O) -- (0,.5,0); \draw[thick,tdplot_rotated_coords,->] (O) -- (0,.5,0);   %these 2 lines dont overlap \draw[thick,->] (1,1,1) -- (0,.5,0); \draw[thick,tdplot_rotated_coords,->] (1,1,1) -- (0,.5,0); \end{tikzpicture} \end{document}


If imaginary numbers bisect real numbers at zero, am I correct in thinking $0i = 0$?  And if so, does that mean $i = 0/0$?  EDIT:  I’ve just realised my careless error in my thought process.  I immediately just “removed” the $0$ from both sides without thinking about the fact that I was actually simplifying $\frac{0i}{0}=\frac{0}{0}$ to $i=\frac{0}{0}$ despite $\frac{0}{0}\neq1$, meaning $\frac{0}{0}i \neq i$

Why does $x$ divided by zero not equal $x$? After all, $x$ is not being divided by anything.


Some stupid meme my sister showed me went along the lines of "will my laptop get heavier if I put more files in it?", but it was sufficient to get me thinking--is there an energy change & associated mass change when a file is written to a solid state drive? I don't know enough about how a solid state drive works to know for sure... but my intuition says that for highly compressed files, the informational entropy is probably the same as an unwritten (sector? Again, I don't know that much about SSDs). However, I wonder if highly organized/low entropy files, such as uncompressed text files or bitmaps, would affect a change in the mass of the drive, one way or another.

Browsing Quora, I saw the following  with contradicting answers.  For the :     The bits are represented by certain orientations of magnetic fields   which shouldn't have any effect on gravitational mass.   But,  contradicts that one:     Most importantly, higher information content correlates with a more   energetic configuration and this is true regardless of the particular   type of storage... Now, as per Einstein's most famous formula, energy   is equivalent to mass.   Which answer is correct?


When I work in a tty (ALT 1-6), is annoy not see previous comands output. In tty is posible scroll up, with a keyboard shorcut?

I know there is a simple unix command that allows you to view things from the top and/or allows you to scroll indefinitely toward the top. Not sure what to call it, so it's difficult to google. Thanks to anyone who can explain how to do either one for me


Suppose $\ f  \colon X \to X $ is a continuous function from a compact,Hausdorff space to itself. Prove that there exists a subspace $A$ such that $f(A) =A$.  I came up with an answer based on nets (see the answer below). But i am not very much familiar with nets. So please point out,if there is any error in argument.  Let $Y=f(X)$ then $X= \mathop{\cup}_{y  \in Y} f^{-1}(y)$ where the union is over disjoint sets. Since each of the pullback is a closed set. Being in a normal space, $\forall \ f^{-1}(y), \  \exists \  U_{y}$ open in $X$ such that  $f^{-1}(y) \subset U_{y} \subset \overline{U_{y}} \subset X$ .  Hence $X = \bigcup_{y \in Y} U_{y} $.  This open cover has a finite subcover. $X=U_{1} \cup U_{2} \cup \ldots \cup U_{n} $. Let $\Sigma = \lbrace A \  \ \vert A \subset X \rbrace$, suppose $\nexists$ any $A \in \Sigma$ st $f(A) =A$ then $\forall A \in \Sigma , \ \exists \ f (x)_{A} $ st $f (x)_{A} \notin A$.  define partial order on $\Sigma$ by set inclusion so that it becomes a directed set.   Let $\ell \colon \Sigma \to X$ be a net such that $\ell(A) = f(x)_{A} $. For simplicity let us represent it the net by $(f(x)_{A})$.  Since $X$ is compact,every net has a cluster point,call the cluster point of the above net as $p$.  Since $p \in X=U_{1} \cup \ldots \cup U_{n} $, we may assume $p \in U_{1} $.  Let $U_{1}$ be the neighbourhood of $p$ and $A=   U_{1}$ then $\exists  \ B \in \Sigma $  such that $ A \subset B $ and $f(x)_{B} \in U_{1}$. But $f(x)_{B} \notin B \Rightarrow f(x)_{B} \notin A=U_{1}$.   This is a contradiction. $\square$

I am trying to solve the following problem.     Let $X$ be a compact Hausdorff space and let $f:X\to X$ be continuous.   Show that there exists a non-empty set $A\subset X$ such that   $f(A)=A$.   There is a hint to define $A=\cap_{n\ge 0} A_n$ with $A_{n+1}=f(A_n)$ and $A_0=X$.  Then $x\in A_{n+1}$ implies that $f^{-1}(x)\cap A_n\ne\emptyset$. Right? So if $f^{-1}(x)\cap A_n=\emptyset$ then $x\notin A_{n+1}$. Is this correct?  First I need to show that for $A$ defined in the hint it holds $f(A)=A$. For this to happen it is enough to have $f(A)=\cap_{n\ge 0} f(A_n)$ Because then $f(A)=\cap_{n\ge 1} A_n=\cap_{n\ge 1} A_n\cap X=A$. But got stuck proving the equality.  What I did for that is to assume that there exists $x\in A$. This means that $\exists y_n\in A_n$ such that $f(y_n)=x$ for all $n$. Is this enough to deduct that $f(x)\in A$?  Then I need to show that $A$ is not empty. For this I think it is enough to show that $A_{n+1}\subset A_n$, because $A_n$ are compact and then their intersection is not empty. However I am stuck there too. I tried by contradiction assuming $\exists x\notin A_n$ with $f(x)\in A_{n}$, but I cannot work from there.  Initially I thought of something else. Choose $x_n\in A_n$ and create the sequence $\{x_n\}$. This has a convergent subsequence $\{x_{n_k}\}$. Then I create a sequence $\{x'_m\}$ by defining $x'_m=x_{n_k}$ with $n_k=\max\{j\in\{n_k\}|j\le m\}$. So basically i repeat the terms of the subsequence to get a convergent sequence. However this again requires that $A_{n+1}\subset A_n$ so I have $x'_m\in A_m$. Then I think that the limit $x'_m\to x$ is in $A$ but I was not able to show that also.  Thanks in advance.


Can I install CentOS on the same hard disk on which Ubuntu is already installed without overwriting Ubuntu?  Will grub give me the choice to select between OSs at boot time? P.S.: i have 500GB on the hard disk and Ubuntu only locate 8%*

I want make dual boot with feodra 15 and ubuntu 11.04 for testing features,please guide me the same.          i had done dual boot with windows and linux but not linux linux.


I know from L'Hopital's Rule that  $$\lim_{t \to 0} \frac{t^2} {\sin^2(t)}=1$$ But I'm also trying to verify this using the Squeeze Theorem. My first thought is to use the upper and lower bounds of possible outputs (range) of $\sin^2(t)$ as the functions which $\sin^2(t)$ would be between: $$ 0 \leq \sin^2(t) \leq 1 $$ We want the function in the middle of the inequality to resemble the function we are taking the limit of, so dividing the whole inequality by $t^2$ $$0 \leq \frac{\sin^2(t)}{t^2} \leq \frac{1}{t^2}$$ Then taking the reciprocal of each term $$0 \geq \frac{t^2}{\sin^2(t)} \geq t^2$$ Now taking the limit of each term of the inequality as $t \to 0$ $$\lim_{t \to 0} 0 \geq \lim_{t \to 0} \frac{t^2}{\sin^2(t)} \geq \lim_{t \to 0} t^2$$ $$ 0 \geq \lim_{t \to 0} \frac{t^2}{\sin^2(t)} \geq 0$$ Thus, by the Squeeze Theorem $$\lim_{t \to 0} \frac{t^2}{\sin^2(t)} = 0$$ But I know this is incorrect and the limit should evaluate to $1$ just like the answer I got using L'Hopital's Rule. (And this can also be verified looking at the graph of  $\frac{t^2}{\sin^2(t)}$ as $t \to 0$). I'm not sure what step I did incorrectly or perhaps the functions I initially chose as the boundaries are incorrect. So my questions are how would I evaluate this using the Squeeze Theorem and what part of my thought process is wrong?

$$\lim_{x\to 0}\frac{\sin^2x}{x^2}$$  I'm trying to evaluate this limit using Squeeze Theorem. However, looking at the graph I know it approaches $1$, but I am getting $0$ using the Squeeze Theorem.  $$-\frac{1}{x^2} < \frac{\sin^2x}{x^2} < \frac{1}{x^2}$$  when I sub in $0$ it's just $0$. What am I doing wrong?  Edit: Wait, it's not zero! The upper and lower bounds are indeterminate. So I can't use squeeze theorem, correct?


I have 3 references in my report, below is my bibtex file. The problem is when I do \cite{article1} in my first citation, it showed [2]. And the second \cite{article2} showed [3] and the last showed [1].   @article{ article1, Author = {Jie, Ding and Ning, Li.}, Title = {A Distributed Adaptation Management Framework in Content Delivery Networks}, Journal = {Wireless Communications, Networking and Mobile Computing (WiCOM)}, Pages = {23-25}, Year = {2011} }  @article{ article2, Author = {Molina, B. and Ruiz, V. and Alonso, I. and Palau, C.E. and Guerri, J.C. and Esteve, M.}, Title = {A closer look at a content delivery network implementation}, Journal = {Electrotechnical Conference}, Pages = {685-688}, Year = {2004} }  @article{ article3, Author = {Chen, Y. and Katz, R.H. and Kubiatowicz, J.D.}, Title = {Dynamic Replica Placement for Scalable Content Delivery}, Journal = {Intel workshop on Peer-to-Peer Systems}, Pages = {306-318}, Year = {2002} }

By default (using the plain style) BibTeX orders citations alphabetically.   How to order the citations by order of appearance in the document?


I want to install Ubuntu in a PC (having Gigabyte GA-J1800M-D2P-IN (Intel Celeron J1800 2.4Ghz processor) with maximum 4GB DDR3 RAM & 80GB Seagate Barracuda HDD) after removing Windows 7. Please tell how can I install Ubuntu OS in this PC without losing any data except Windows 7? Urgently waiting for your valuable reply.  Thankfully yours  Arpan Purakait

I need my pre-installed version of Windows 7 (or any other version of Windows), how could I install Ubuntu without erasing it?


Apparently $\sqrt{ab}$ = $\sqrt{a}\sqrt{b}$ is only true if a and b are both positive or if a is negative and b is positive or if a is positive and b is negative. In other words, a and b can't both be negative.  Is it possible to algebraically prove this? Or is it just a result of the way the square root function is defined?   I know of 1 way to prove this radical property, but I'm still not sure why it won't work for negative numbers.  Let x = $\sqrt{ab}$.  Let y = $\sqrt{a}\sqrt{b}$  Square both sides for both equations.  $x^2 = (\sqrt{ab})^2 = ab$  $y^2 = (\sqrt{a}\sqrt{b})^2 = (\sqrt{a}\sqrt{b})(\sqrt{a}\sqrt{b}) = (\sqrt{a})^2(\sqrt{b})^2 = ab$  $\therefore x^2 = y^2$  $x^2-y^2=0$  $(x+y)(x-y)=0$  $\therefore x = y$ or $x = -y$  Or  $\therefore y = x$ or $y = -x$    A lot of people will go through this line of reasoning (shown below) in order to justify why a and b can't both be negative.   Considering that mathematicians define $i^2=-1$ or $i = \sqrt{-1}$  $1 = \sqrt{(-1)(-1)} = \sqrt{-1}\sqrt{-1} = (i)(i) = i^2 = -1  $  But this is only a specific instance where this property fails us. This isn't a  rigorous or at least satisfying proof of why $\sqrt{ab}$ = $\sqrt{a}\sqrt{b}$ can only be true if a and b are not both negative.  Note: I just started learning about complex and imaginary numbers and I am no means an expert in  mathematical proofs, so if you do know the answer to this question please try (if possible) your best to answer the question without using too much complex or high-order math that I won't be able to understand.

I know there must be something unmathematical in the following but I don't know where it is: \begin{align} \sqrt{-1} &= i \\\\\ \frac1{\sqrt{-1}} &= \frac1i \\\\  \frac{\sqrt1}{\sqrt{-1}} &= \frac1i \\\\  \sqrt{\frac1{-1}} &= \frac1i \\\\  \sqrt{\frac{-1}1} &= \frac1i \\\\  \sqrt{-1} &= \frac1i \\\\  i &= \frac1i \\\\  i^2 &= 1 \\\\  -1 &= 1 \quad !!? \end{align}


Let $f: \mathbb{R}^2 \to \mathbb{R}$ be defined by $f(x)=\begin{cases} \frac{x_1^2x_2}{x_1^2+x_2^2}, \quad x\neq 0 \\ 0 , \quad \quad \, \, \, \,  x=0\end {cases}$.  Show that all directional derivates in $0\in \mathbb{R}^2$ exist.  My attempt:  Let $a:=(0,0)$ and $v:=(x,y)$ with $x\neq y$, then:$$\partial _v f(0)=\lim\limits_{t\to 0}\frac{f(0+t(x,y))-f(0)}{t}=\lim\limits_{t\to 0}\frac{f(xt,yt)}{t}=\lim\limits_{t\to 0}\frac{\frac{(xt)^2(yt)}{(xt)^2+(yt)^2}}{t}=\lim\limits_{t\to 0}\frac{t^3x^2y}{t^3(x^2+y^2)}=\lim\limits_{t\to 0}\frac{x^2y}{x^2+y^2}=\frac{x^2y}{x^2+y^2}$$ But that is just valid iff $x\neq y$. Do I have to show $x=y$ seperately?

Let $f(x,y)=     \begin{cases}       \frac{2x^2y}{x^2+y^2} & if & (x,y) \neq (0,0) \\       0       & if & (x,y)=(0,0) .  \end{cases}$  (i) Prove the directional derivatives of $f$ exist in any direction at the point $(0,0)$.  (ii)¿Is $f$ continuous on (0,0)?  For (i) I took $u=(u_{1},u_{2}) \in \mathbb{R^{2}}$ such $\|u\|=1$ and $0=(0,0)$. So $$\lim_{t \to 0} \frac{f(0+ t u)-f(0)}{t}=\lim_{t \to 0}\frac{2(tu_{1})^2 (tu_{2})}{(tu_{1})^4+(tu_{2})^2}=\lim_{t \to 0}\frac{(t^2 u_{1}^2)(t^2 u_{1}^{2}) tu_{2}}{t^{4}u_{1}^{4}+t^{2} u_{2}^{2}}.$$ But I cannot find the limit when $t$ aproaches to $0$. Which by finding them I would prove the directional derivative exist at every direction right?  For (ii) I got the intuition $f$ is not continuous at $(0,0)$ so I took $\lbrace (\frac{1}{k},\frac{1}{k}) \rbrace_{k \in \mathbb{N}}$ and $\lbrace (\frac{1}{k},0) \rbrace_{k \in \mathbb{N}}$ which are two different sequences in $\mathbb{R}^{2}$ converging to $(0,0)$. However, $\lbrace f(\frac{1}{k},\frac{1}{k}) \rbrace_{k \in \mathbb{N}}=\lbrace \frac{1}{k^{2}} \rbrace_{n \in \mathbb{N}} \to 0$ and $\lbrace f(\frac{1}{k},0) \rbrace_{k \in \mathbb{N}} \to 0$. So maybe my intuition was not right? Can anyone help me end the proof of continuity or not continuity , please?


$n \in \mathbb{N}$, bigger than zero. My proof:(A Proof by Contradiction) Alert: There is a lot of variables. Suppose that: $n(n+1)(n+2)(n+3)=x^{2}$, with $x \in \mathbb{N}$ $$n(n+3)(n+2)(n+1)=x^{2}$$ $$(n^{2}+3n)(n^{2}+3n+2)=x^{2}$$ let $n^{2}+3n = a$. $$a(a+2)=x^{2} \iff a^{2} +2a=x^{2} \iff a^{2} +2a-x^{2}=0$$ And this is a quadratic equation in $a$, So: $$a=\frac{-2 \pm \sqrt{4+4x^{2}}}{2} \implies \sqrt{4+4x^{2}} \in \mathbb{N} \iff 4+4x^{2}=b^{2}$$ $$ 4(1+x^{2})=b^{2} \iff 4 \mid b^{2} \iff 2 \mid b \iff b=2c.$$ Now let's plug this result to this equation: $$4(1+x^{2})=(2c)^{2} \iff 4(1+x^{2})=4c^{2} \iff 1+x^{2}=c^{2} \iff (c-x)(c+x)=1$$ And $1=1 \cdot 1$, so :$(c-x)=1$ and $(c+x)=1$ $$c+x=c-x \iff x=-x \iff 2x=0 \iff x=0$$ By plugging this result into this equation : $a(a+2)=x^{2}.$ $a(a+2)=0 \iff a=0$ or $a=-2$ but $-2 \notin \mathbb{N}$ So : $x=0$ And finally: $$n(n+1)(n+2)(n+3)=0 \iff n=0$$ And the other values $\notin \mathbb{N}$ This proof is too huge for me so perhaps I've made some mistakes, And if you have an easier proof please post it.

$n$ is a natural number. I’ve tried to turn this problem to this: Prove that: $n(n+1)(n+2)(n+3)+1 $is always a perfect square. So: $$n(n+1)(n+2)(n+3)+1 =x^{2}$$ And i’ve expanded the whole equation but it didn’t help me a lot.


I am looking for a formula I can use in any cell that will return the column LETTER of the column the formula is in,  I can get the LETTER and ROW number using the below, but I cant get it without the ROW information  =ADDRESS(CELL("row"),CELL("col"))   I don't mind using vba to work it out if there isn't a formula that can achieve this.  NOT A DUPLICATE OF  I only want the COLUMN and not the line number !

What is the function to get the current line number and the current column name for a cell in Excel?


I am wanting to build a device with gyro, accellero, gauss (compass) sensors and barometric sensor.  This device will record all data from the sensors over a period of about 15 minutes where a person is in freefall (jumped from an airplane).  Fall velocity is easy, using the barometer, but I am not sure about the angle.  I want to know the absolute angle along all axises of the person. Due to the acceleration after the jump, decceleration after opening of parachute and (de/a)cceleration due to change in position in freefall and therefore air resistance all the accelerometer forces will constantly change among all axises.   How would I be able to calculate the absolute angle/rotation of the person in 3 dimensions (roll/pitch/yaw).  Right before the jump, the person is in an airplane and full of adrenaline. Because of this combined with tight space and high noise from the engines, I want to prevent having to use calibration on forehand where possible.

For whatever reason, I seem to have gotten myself twisted into quite a confusion on how to process data from my 3 axis gyro and 3 axis accelerometer to get gyro rotation values related to the earth's reference frame. i.e. Given my accelerometer measures gravity (we assume it's stable) along the sensors (x,y,z) reference frame, how do I adjust the values of my gyro, measured along the sensors same (x,y,z) reference frame such that I am actually measuring the rotating about the Earth's frame x (North), y (West), and z (downwards) direction?  I just can't seem to wrap my head around the use of the rotation matrix. Do I simply employ a 3d rotation matrix, and multiply the vector, \$[gyro_x, gyro_y, gyro_z]^T\$, by a rotation matrix, R? I then assume the rotation angles, are somehow derived from the filtered accelerometer outputs, but I'm having trouble deciding on what those should be.  I have yet to find a concise reference on how to move the rotation and acceleration values from the sensor reference frame into the earth global reference frame. Perhaps someone can help? Thanks


My aim was to display the meta description on this page to improve CTR - However, I was disappointed because the meta description is only shown in Google SERP on mobile not on Web. Please see the 2 images.  Please note : The meta description have the keywords search in Google bar.    Here, the below images is snapshot of web, which lack the meta description. Any one please help me get the meta description on web SERP as well?

I have unique meta descriptions on each of my pages, and when I search my site in google it will come up with no description.  Any idea what I might have done wrong?


I know that some songs in anime openings or endings come from popular J-Pop singers/albums (such as the Bleach opening Rolling Star by Yui). However, some opening songs seem to show up during the show, such as themes appearing during final battles. Are opening or ending themes generally written specifically for the show or are they taken from popular Japanese songs.

Are the opening/ending themes, insert songs, and background music created specifically for the series they represent, or are they just picked by the producers/production committee based on how well they would fit their series?   What typically happens? What exceptions are there? How much have things changed now compared to the past?


We just started playing D&D we are huge noobs and have problems with the wizard. I'm a level 2 Wizard with 3 level 1 Spellslots. Now the rulebook says:      You prepare the list of wizard spells that are available for you to   cast. To do so, choose a number of wizard spells from your spellbook   equal to your Intelligence modifier + your wizard level (minimum of   one spell).   Does that mean I can prepare for example Magic Missile 5 times? So I can cast it 5 times before the next rest? Or can I only cast it 3 times because I have only 3 level 1 spell slots??

I am a level 4 cleric with a 20 (+5) wisdom in D&D 5e. This means I have a total of 9 spells I can cast in 1 day. I only have 4 level 1 spell slots and 3 level 2. So if I were to use all those spell slots in one day what would happen to the extra 2 spells I can cast? Can I not use all 9 spells I have available for me to cast?


I am using 3 keyboard layouts (to be exact: English, , Russian). On Unity, when I pressed my "next layout" keybinding, layouts whould only be smitched in the order set in the settings window (English - Latex - Russian - English again...).  On Gnome, the story is completely different: it looks like it switches them in order of usage, like this:   Was on Russian, switched to English. Press keybinding -- back to Russian. Press again -- back to English. Press twice in a row -- Latex! Press once more -- English. Once more -- Latex! Twice -- Russian. Once more -- back to Latex.   If you have only two layouts you will never see a difference.  It's pretty obvious to me that these reorderings require some logic to be implemented, but I would like to turn that off and "freeze" the order. Is there a way, though?

Just installed Ubuntu 17.10 and it seems that the keyboard layout switching has changed its behavior.  In the previous version of Ubuntu (such as 16.04 Unity), if I have 3 different keyboard layouts (for example EN-TH-JA), hitting Super+Space would always cycle to the next layout in the same order (e.g. EN to TH to JA then back to EN).  However since Ubuntu 17.10, this is no longer the case. It cycles through the layout in the MRU (Most Recently Used) ordering. So suppose that the layout starts with EN, then I cycled to TH. Next time I hit Super+Space, it would give me EN instead of JA.   I tried to dig up and found that the culprit is the newly implemented DCONF settings inside org.gnome.desktop.input-sources and there seems to be no way to change this behavior.   So my question is: Is there a way to change this behavior to "static ordering" of keyboard layout switching?    (As a side-note, the new behavior is very bad when we have three or more layouts. Most of the time we as a user couldn't remember the MRU layouts, so layout switching is very inconvenient and much slower than already knowing what the next layout would be if static ordering is used.)  If there is no settings to change this behavior, where should I report this as a bug or a feature request?


Ok So i making this simple platformer with a ball. So basically i have A pickup / Collectible that is a Coin. I want the coin till it gets collected by the ball to keep rotating around it axis . Also I know I could do this by adding a Animation but I would prefer doing it Via A C# Script. So please if anybody knows how then Tell me. Thanks

I am attempting a simple script to swing a door open in Unity.  This requires a smooth rotation of 90 degrees around the Y axis.  I have seen that one way to do this is using Unity's Quanternion object.  I believed that this should work:  public class DoorOpenScript : MonoBehaviour  {      public float smooth = 20;      // Use this for initialization     void Start ()      {            SwingOpen ();     }      // Update is called once per frame     void Update ()      {      }      void SwingOpen()     {            Quaternion newRotation = new Quaternion(transform.rotation.x,transform.rotation.y,transform.rotation.z,transform.rotation.w);;         newRotation *= Quaternion.Euler(0, 90, 0); // this add a 90 degrees Y rotation         transform.rotation= Quaternion.Slerp(transform.rotation, newRotation,20 * Time.deltaTime);            }  }   However, this just opens the door completely. I have tried playing with the third parameter to Slerp but with no results. What am I doing incorrectly?


Are there any desktop environments designed to look exactly like a Windows machine? Not like Cinnamon or GNOME, but exactly the same?

I want to know is there any theme available make it Ubuntu look like Windows 7 ?


Completely ignoring the sexist aspect of the word, is using "he" as a gender neutral pronoun grammatically correct or incorrect? I'm well aware that using "he" may come off as sexist or politically incorrect and that it's better to use "they" but grammatically is it correct?

I know there are different opinions on this issue. My question: Is using "he" for a general, gender-neutral third person still in common use for formal writing? By common use I mean, can I expect my paper not to be penalised because I use "he" as pronoun for "a student", etc.?   I think "he/she" is too clumsy and I am not comfortable with singular they.


I'm just a photo enthusiast knowing just the basics so far. My dad used to work with a film SLR and taught me a few things. I currently own a Canon 60D with the 18-135mm kit lens. I originally wanted to invest in a 50mm f/1.4 prime lens (rec'd by Dad), but I don't think it'll be versatile enough for traveling.  I will be taking lots of family pictures/city views. And most search came up for a wide-angled lens, such as the 10-22mm. But it seems a bit too short on its own. Would it be a good combo with the kit-lens.  I want to get one versatile lens that I can combine with my 18-135mm, or invest in just one lens to travel. (lots of walking!)  18-135mm is great, but it's quite bulky, and the lens has a terrible droop.  However, I'm not sure if I'm ready to replace it yet (still learning).  I want to take 2-3 lens max. Budget is under $1500.   What combination would you recommend for my week trip to NYC with family?   Thank you!

On a crop sensor camera, e.g. Canon EOS 7D, what would be the best kit to travel with around Europe for a few weeks? My shooting style will focus on landscape, architecture, and general travel shots (of note would be my lack of interest for portraits).     Limit to around 1-3 lenses, and I prefer light ones.   Crop sensor camera chosen to save on weight over a full frame option. Question is open to all brands for general guidance, but I will be using a Canon body.   Cost is not a factor, I will rent the lenses I do not already own.   Quality is of paramount importance. I will not have a tripod.   I understand some may consider this subjective, but I do believe that for a crop sensor body, with weight as a consideration, and a limit to the amount of lenses, a true best kit can be determined.


What would be a better and more formal way out of the two below:  The capability was not catered for.   or   We did not cater for this capability.   Or perhaps these are fully interchangeable?

Like many others, I commonly find myself ending a sentence with a preposition.  Yes, it makes me cringe.  I usually rewrite the sentence, but sometimes (in emails) I just live with it.  To, with... you know who you are.  Should I keep fighting myself on this one, or is it okay in some circumstances?


Is it possible to declare an instance of a generic without knowing the type at design-time?  Example:  Int i = 1; List<typeof(i)> list = new List<typeof(i)>();   where the type of i could be anything, instead of having to do:  List<int> list = new List<int();

What's the best way to call a generic method when the type parameter isn't known at compile time, but instead is obtained dynamically at runtime?  Consider the following sample code - inside the Example() method, what's the most concise way to invoke GenericMethod<T>() using the Type stored in the myType variable?  public class Sample {     public void Example(string typeName)     {         Type myType = FindType(typeName);          // What goes here to call GenericMethod<T>()?         GenericMethod<myType>(); // This doesn't work          // What changes to call StaticMethod<T>()?         Sample.StaticMethod<myType>(); // This also doesn't work     }      public void GenericMethod<T>()     {         // ...     }      public static void StaticMethod<T>()     {         //...     } }


I need to subscribe to specific tags, for example:  If I need to subscribe to the [android] tag I just go through this tag and subscribe to it. What if I need to make it more specific, like [android][java] which will send me emails with the questions containing these tags only (meaning I won't receive separate emails for [android] only or [java] only)?  Is that possible or not?

Lately I've noticed that hovering over tags opens a mini info-window with tag related data and activities including email subscription option. Great!  But instead of subscribing to just a single tag I'd rather subscribe to a combination:     tagX and tagY and tagZ ...   giving me a much better selection of questions delivered to my email inbox.  Similar to viewing questions with a particular tag. You can always click on any of the related tags and you get a subset of questions that have both tags (the first one and the second one as well) and not either.  Is this kind of email subscription possible or are there any plans on developing it?  Edit  Tag sets on StackExchange (as suggested by @Barry) don't work, because they are combined by an OR operator instead of an AND. A tag set therefore widens the filter instead of narrowing it. Just so you know this question hasn't been sufficiently answered yet.


has an unusually large amount of answers where he seems to almost always point to WPF Application Framework (WAF) - http://waf.codeplex.com  The questions have around a long time so I'm curious if this sort of "advertising" is somehow different than what I have seen discouraged.   A number of examples (not even the tip of the iceberg):                  Essentially the website is a collection of samples. And the format for his answers is something to the tune of "see more samples here", or "go here to see examples". Maybe his answer is on-topic. But with a large database of samples it essentially allows for a "closing sentence" where you can promote your website without repercussions, since the samples are relevant to the question. My comment in Razlebe's answer attempts to make this more clear.  EDIT: Found a great thread dealing with this:      Pekka, I think your heart is in the right place, but... This should   not be necessary. You're effectively setting up guidelines for   targeted advertising on SO - and there's already a system in place for   that. One or two self-promoting answers out of 100 might be called a   misunderstanding; 400+ is a blatant attempt to get around paying for   your ads, and deserves neither sympathy nor "clarification".   –  Shog9♦

It's    that posting links to your own website is ok, but should there be a line drawn? There were several spam flags today for 's recent posts, presumably because they all link to his website. Initially I disagreed because his answers seem for the most part relevant to the question, but then I looked into it more and realized there's three things that set this apart from most of the related cases that have come up:   This isn't an occasional thing -- he's posted  in the last year This isn't a random blog he writes for a fun, it's a for-profit company he  and makes money promoting I'm not willing to go through all 412, but from the sample I checked, he generally doesn't mention that the products he's recommending are his own. The site is linked from his profile, but most people aren't going to check that   Is all this considered acceptable use, or are the spam flags accurate?


Alright, I'm having this huge ongoing debate with my friend about 'can't have' and 'couldn't have'. So I was talking to him a few days ago and, quite naturally, said, "No, she can't have passed the test!'' and he said that I meant 'couldn't have passed the test'. But 'can't have' sounds correct to me. Since then, we've been constantly arguing over 'can't have''s correctness. I say that both are right but he initially said that 'can't have' is totally incorrect, then switched to saying that it is correct, but MY context was wrong. Final question: would it be (in)correct for me to say, 'she can't have done that'. Please enlighten me.

I don't understand when and why to use can't have been. It seems so strange to me.


The whole class was working hard preparing for the exam.   The whole class was working hard to prepare for the exam.      What are the differences between these two sentences?

What is the difference in meaning when the catenative verb “like” is followed by an infinitive, or by a gerund? For example:      Do you like ski jumping?    vs.      Do you like to ski jump?   Also, what is the difference between:      My brother taught me to read and write.    vs.       My brother taught me reading and writing.


If my iOS device is in low power mode and I am charging it then at a certain percentage iOS automatically turns off low power mode (and it always tells me) but I'd like to keep low powered mode on all the time. How do I prevent iOS from turning off low power mode all the time? Note: This is the opposite of a similar question I asked a while back.

I would like Low Power Mode to be the default state of my device.  When I get to 80% battery it toggles itself off automatically.  How can I stop it turning itself off?  How can I always keep my phone in low power mode (or some other equivalent)?


The output of this program is 5. Why is that the case? Why isn't the output 6? How to write a method that will actually add value to x? Thanks. public static void main (String args []) {                  int x = 5;     example (x);     System.out.println(x);              }              public static void example (int x) {                      x = x + 1;                  }

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


Can two people on the same console play COD WW2, not in multiplayer or Nazi  zombie mode? Splitscreen?

How many players can play split-screen, and what game modes are (or aren't) available?   How many players can play local co-op? How many players can play local multiplayer? How many players can play online multiplayer from a single console?   These questions don't appear to be specifically addressed anywhere on , and I didn't see any mention in any of the reviews I've read. Even the packaging of the game itself (I haven't seen it, basing this claim off of the standard Xbox One game packaging details) only answers the first of these three questions.


I connected to mysql database and fetched two columns from mysql with python with       query  = ('select test_id, a_id from b.atc_id_TO_cID ')       cursor.execute(query)     rows = cursor.fetchall()        CountinmyDi = {}      for row in rows:              if not row[0] in CountinmyDi.keys():                     CountinmyDi[row[0]] = 1             else :                     CountinmyDi[row[0]] += 1     for key in CountinmyDi.keys():                     print str(key) + ":" ,CountinmyDi[key]   and created a dictionary CountinmyDi to count the unique items inside the dictionary. Now i have for example :   testA : 2 testB : 82 testC:102 test D : 3 test E:1 and so on .. about 220 items   I want to sort the items inside my dictionary for example increasing to decreasing order based upon their values for instance testC : 102, testB : 82 , testD :3 , test A :2 , test E : 1. I would like to get an idea how i could do that . Thank you and if you need further infos, i could gladly provide.

I have a dictionary of values read from two fields in a database: a string field and a numeric field. The string field is unique, so that is the key of the dictionary.  I can sort on the keys, but how can I sort based on the values?  Note: I have read Stack Overflow question here  and probably could change my code to have a list of dictionaries, but since I do not really need a list of dictionaries I wanted to know if there is a simpler solution to sort either in ascending or descending order.


This relates to the method userInput() and its if statements. The output for userInput() is 0 no matter what, why? I know the initial value of calculate = 0; but i want to change it so that each time the user enters "Paper" for example the value of calculate = 1; IVE TRIED EVERYTHING! now im stuck wondering whats wrong with my if statements. Please help. (sorry if i'm a noob)  import java.util.Scanner;  class RPS{      private static String[] userOption = new String[]{"Rock", "Paper","Scissors"}; public static void main(String[] args){      System.out.println("Enter: Rock, Paper Or Scissors");     System.out.println(userInput());         }      public static int userInput(){          int calculate = 99;           Scanner input = new Scanner(System.in);          String userChoice = input.nextLine();              if(userChoice == userOption[0]){                 calculate = 0;             } else if(userChoice == userOption[1]){                 calculate = 1;             } else if(userChoice == userOption[2]){                 calculate = 2;             }                         return calculate;         }    }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


Rename filename.JPG to filename .jpg recursively  I want all the files with .JPG extension to be changed as .jpg

Script to convert filenames to lowercase depending on extension


I want to get a PhD in psychology. I have a computer Science /minor in math with a 2.9. I worked two jobs while in school (as a software technician and a Calculus tutor) and I have one year experience as a SW engineer outside of school. I am currently 25 years old.   This question is not the same as being a weak student and getting in to a great program. Rather this is a complete shift from major and discipline; while also being semi-borderline.

When applying to a PhD program in the US, how does the admissions process work? If an applicant is weak in a particular area, is it possible to offset that by being strong in a different area?  Note that this question originated from this . Please feel free to edit the question to improve it.


When creating a new ASP.NET project in Visual Studio should I chose create: website or project?   I understand that web application project was the way to do it back in the day with VS 2003 but is it still applicable today? What are some of the caveats using one over the other?

When I start a new ASP.NET project in Visual Studio, I can create an ASP.NET Web Application or I can create an ASP.NET Web Site.  What is the difference between ASP.NET Web Application and ASP.NET Web Site? Why would I choose one over other?  Is the answer different based on which version of Visual Studio I am using?


What is $$\int_{0}^\infty \frac{dx}{(x^2+ax+b)^{\frac{3}{2}}}$$  Starting with a very non-trivial analysis question, this is what I have managed to boil it down to. I do not know the standard computation procedure, substitutions for this type of integrand. Thanks in advance for help!

Need the indefinite integral with $a,b$ constants. This is not a homework question. Need it for a physics problem.


If an object emitting light falls into a black hole, the conventional wisdom is that an observer (at infinity) will never actually see it fall in - they will see it moving slower and slower as it approaches the horizon and then eventually freeze at the horizon, making the time of "falling in" to be infinite for the outside observer.  During BH mergers we can actually see one BH "fall into" another one in a finite time. Why does the same thing not happen with gravitational waves?

I've read a lot of conflicting answers in these forums. However, today saw the awesome announcement of gravitational waves. Two black holes merged:   Not only that, they merged FAST. In 1/5th of a second revolving around each other 250 times a second. The entire event was quicker than a heartbeat. Moreover, we observed this happening as distant outsiders. So now we can say for sure:   Objects approaching the event horizon DO NOT appear to slow down Black holes CAN merge in a finite (and quick) amount of time And all this is wrt a frame of reference far, far away   To quote the NYTimes article:  One of them was 36 times as massive as the sun, the other 29. As they approached the end, at half the speed of light, they were circling each other 250 times a second.  And then the ringing stopped as the two holes coalesced into a single black hole, a trapdoor in space with the equivalent mass of 62 suns. All in a fifth of a second, Earth time.  However, everything I've read so far has let me to believe that an outside observer should never be able to measure the collision happening in a finite time. So what exactly is happening here? I must have read at lest 5 different versions of this so far everywhere in these forums over the past several years.


can somebody please explain how to construct free resolution of the $ℤ_{4} $ module $ℤ_{2}$??

If $m$ divides $n$, find a free resolution of $\mathbb{Z}/m$ as a $\mathbb{Z}/n$-module.   I have tried this one and got $0 \leftarrow \mathbb{Z}/m \leftarrow \mathbb{Z}/n \leftarrow \mathbb{Z}/n$.  The map $\mathbb{Z}/n \to \mathbb{Z}/n$ is multiplication by $m$, but I couldn't go further. Please help me.


I understand that the orbitals are a 3D contour inside of which there is a certain probability ( for example 90% ) to find the electron ( this is my understanding of it, so correct me if I am wrong ).  Now, I want to know the meaning of shapes like that of p-orbital. They are dumbbell-shaped ( sort of ) and are located on the x-, y- and z-axis. But aren't the axis completely arbitrary. Since the axis are arbitrary, we should expect only shapes that remain invariant upon any kind of rotations of the axis. The only thing that fits in that criterion is the spherical shape (or s-orbital).  So, what is the meaning of the non-spherical shapes of various orbitals, in the context I have mentioned above?

I know very little about quantum physics, but I just can't wrap my head around the fact that non-spherical orbitals appear to be "oriented", constituting a set of fixed "frame of reference axes".  Does it really work like that? Are there for a single atom given directions in which the orbitals "protrude"? And if so, what are they based on? If I understand it right, the nucleus is seemingly spherical - symmetrical with no unique axis of symmetry. What would then decide the orientation of the orbitals in space (with respect to the surroundings)?  Edit: I understand any orientation works to satisfy the wave equation. I was more curious why the atom would choose one direction, instead of any of the others. Is that fundamentally random? And is this setup retained further, or can it change at any time?


I made a button:  var btn = document.createElement("button"); var value = "text I want to copy"; btn.appendChild(document.createTextNode("copy")); btn.onclick = function(){ // this is something I want, demo code: copy(value); console.log("copy successful"); }; // and then when I ctrl + V (paste) to somewhere else, the output should be this: "text I want to copy"   I hope you get the idea, I hope someone can help me this.

What is the best way to copy text to the clipboard (multi-browser)? I have tried: function copyToClipboard(text) {     if (window.clipboardData) { // Internet Explorer         window.clipboardData.setData("Text", text);     } else {         unsafeWindow.netscape.security.PrivilegeManager.enablePrivilege("UniversalXPConnect");         const clipboardHelper = Components.classes["@mozilla.org/widget/clipboardhelper;1"].getService(Components.interfaces.nsIClipboardHelper);         clipboardHelper.copyString(text);     } }  But in Internet Explorer it gives a syntax error. In Firefox, it says unsafeWindow is not defined. A nice trick without using :


I have the following sed command: sed 's/\('\''\).*div>
/,/' which take everything between a single quote ' and div>
 and replaces it with a comma ,. Which works near enough perfectly to how I want it. However there are some lines that contains two div>
 and my command is taking the second one to be its stoppping point, where I'm trying to cut it off at the first. To try and provide more clarity, heres the line in the file that I am trying to extract data from: '>Person A

Teaching A

Unknown or external

Teaching B
 instead of the last?

I want to use sed to replace anything in a string between the first AB and the first occurrence of AC (inclusive) with XXX.  For example, I have this string (this string is for a test only):  ssABteAstACABnnACss   and I would like output similar to this: ssXXXABnnACss.    I did this with perl:  $ echo 'ssABteAstACABnnACss' | perl -pe 's/AB.*?AC/XXX/' ssXXXABnnACss     but I want to implement it with sed. The following (using the Perl-compatible regex) does not work:  $ echo 'ssABteAstACABnnACss' | sed -re 's/AB.*?AC/XXX/' ssXXXss


It seems rather silly to go through the whole effort of climbing a 700ft wall when they could simply use boats to go around it. I mean really, even Jon Snow did that when he came to try and rescue some of the wildlings before the got attacked. Are you telling me they couldn't figure out how to build rafts?

In the first series of the TV show several things apparently bypass  to reach Winterfell:   The Night's Watch member  captured near Winterfell and executed by Ned. The Direwolf & her pups found immediately after the execution  and the other Wildlings travelling with her   If The Wall is approximately the same along its length it would presumably be impassible. Is the only option for them to go around the western end (since it stops at the Shadow Tower)? Is this clarified in the book? Are other methods mentioned in subsequent books?


How to format  pen drive in ubuntu via command line with sudo.

Possible Duplicate:             How to format a pen drive in Ubuntu? I have this pen drive which I made bootable using some other system (OS). But I need to format it from my Ubuntu 12.04. Please guide me.


I'm using MiKTeX and TeXnicCenter to compile my projects. Is there a folder where I can store all your input files which I want to include in another document, so I don't have to put all the files in the specific folder where my current document is located?

I know how to define a package or a class, but how do I make it available (to myself) at all times?  Say I have the package file commonstuff.sty (or myprettyclass.cls), that I want to be able to include in any .tex file I create on my computer. Where do I put it? Do I need to run some installer on it, or is it enough to keep it in a certain folder?  Note: I know I can just place it in the same folder as the .tex file, but that's not what I'm after here. I'm looking for a way to "install" the package centrally on my computer.


I have a problem with outputstream, I have this Java Spring code:     @RequestMapping(value="/downloadZip", produces="application/zip") public void downloadZip(HttpSession session,HttpServletResponse response) throws IOException {     OutputStream out = response.getOutputStream();     FileInputStream in = new FileInputStream(FileManager.EXPORT_FOLDER + File.separator + FileManager.EXPORT_FILE);     byte[] buffer = new byte[4096];     int length;     while ((length = in.read(buffer)) > 0){         out.write(buffer, 0, length);     }     in.close();     out.flush();     response.flushBuffer(); }  The "file" that i'm exporting it's a ZIP file with other two files in it. The thing is that I call from the front this api to download the zip file, and it downloads ok, but with no extension and with other name that i don't have in anywhere of the application, it's like, the FileManager.EXPORT_FILE name is "FileToDownload.zip" and when i download the file it's called "file" and that "file" name i don't have it anywhere and when i uncompress that file it's good, but i need the extension, any clues? Thanks a lot!

Web applications that want to force a resource to be downloaded rather than directly rendered in a Web browser issue a Content-Disposition header in the HTTP response of the form:  Content-Disposition: attachment; filename=FILENAME  The filename parameter can be used to suggest a name for the file into which the resource is downloaded by the browser.  (Content-Disposition), however, states in  (The Filename Parameter) that the file name can only use US-ASCII characters:     Current [RFC 2045] grammar restricts   parameter values (and hence   Content-Disposition filenames) to   US-ASCII.  We recognize the great   desirability of allowing arbitrary   character sets in filenames, but it is   beyond the scope of this document to   define the necessary mechanisms.   There is empirical evidence, nevertheless, that most popular Web browsers today seem to permit non-US-ASCII characters yet (for the lack of a standard) disagree on the encoding scheme and character set specification of the file name. Question is then, what are the various schemes and encodings employed by the popular browsers if the file name “naïvefile” (without quotes and where the third letter is U+00EF) needed to be encoded into the Content-Disposition header?  For the purpose of this question, popular browsers being:   Firefox  Internet Explorer  Safari Google Chrome  Opera


I'm trying to figure out what's the difference between a master-slave flip flop and a jk flip flop with the clock negated.   Do they behave in the same manner?  can I just say that a master slave flipflop is a flip flop which output id giben in the falling edge but recorded in the rising edge?

Why is having a 2 stage flip-flop desirable? Are there advantages of having a master-slave compared to a one stage JK flip flop?


Proof by contradiction, Assume $2^{1/n}$ is rational so:  $$2^{1/n} = \frac ab $$ where a,b have no common factors.  $$2 = \frac{a^n}{b^n}$$  $2$ divides LHS, therefore $2$ divides RHS so $2$ divides $a^n$ or $2$ divides $b^n$ which implies $2$ divides $a$ or $2$ divides $b$.   Stuck on what to do next.

Is my proof beneath perfect and complete?  I wanted to prove that for any nth root of an integer, if it's not an integer, than it's irrational: $$\begin{cases} m,n\in \mathbb{N}\\\sqrt[n]{m}\notin \mathbb{N} \end{cases}\implies \sqrt[n]{m}\notin \mathbb{Q}.$$  I start by assuming that $m^{\frac 1n}$ is rational and non-integer. So there exist  co-prime integers $a,b$ so that $$\sqrt[n]{m}=\frac{a}{b}$$ $$\implies  m=\frac{a^n}{b^n}\in\mathbb{N}.$$ But since $a$ and $b$ have no common factor, $a^n$ and $b^n$ also have no common factor. So: $$\frac{a^n}{b^n}\notin\mathbb{N},$$ a contradiction.


I was looking at the rep leagues for Interpersonal skills from last year, when I noticed something odd. There are several users on the list whose total reputation is listed as being less than their reputation for the year. It's usually a small amount (less than 50). This makes me think that it's likely that the year rep doesn't take into account rep losses from down voting answers and posting bounties.  However, I came across one where the difference is quite substantial (~1400).    When I checked the user's profile, I saw that they posted 100 rep worth of bounties and voted less than 30 times, so that wouldn't explain a gap this large. What exactly is going on here?

When I went to the  to see my ranking in the reputation league, I saw this. Is this an error? My total reputation is less than my monthly reputation.


I'm trying to learn the archaic conjugation (for fun) and I wonder if the imperative verbs in the archaic form can be conjugated with -est for the second person singular (ex: Eatest thy vegetables).  Thank you in advance for your answers!

I was driving today, and I saw this billboard:     The tax man cometh.  Geteth the health insurance.   Is this spelling correct? I'm not used to -eth, so I am not sure. Should it be "getteth"?


What is the general way of finding the basis for intersection of two vector spaces in $\mathbb{R}^n$?  Suppose I'm given the bases of two vector spaces U and W: $$ \mathrm{Base}(U)= \left\{ \left(1,1,0,-1\right), \left(0,1,3,1\right) \right\} $$ $$ \mathrm{Base}(W) =\left\{ \left(0,-1,-2,1\right), \left(1,2,2,-2\right) \right\} $$  I already calculated $U+W$, and the dimension is $3$ meaning the dimension of $ U \cap W $ is $1$.  The answer is supposedly obvious, one vector is the basis of $ U \cap W $ but how do I calculate it?


I have some icons I'd like to purchase and use from iconfinder.com, but they are only available as .ico files. I want to use these as part of a user-interface on a website, so I need them as either bitmap or vector format that I can bring into Photoshop to produce transparent .png files.  Does anyone have any suggestions on how to get .ico files into Photoshop through some third-party application? If it matters, I am using a Windows computer.

in Photoshop has been around for a while, but I can't seem to make it work for CS6. According to , the plug-in works if installed in C:\Program Files\Adobe\Adobe Photoshop CS6 (64 Bit)\Required\Plug-Ins\File Formats but it's not doing anything. Do you know of any alternative plugins for CS6? I'm using win seven 64 bits.  EDIT: The plugin does work, just not for images that are bigger than 256px x 256px.


i install a new operating system Ubuntu in my computer.During the installation i choose to crush the last system.i forget to copy and save all my web project before install the new system     opt/lampp   please somebody can help me how to find my folder project.thank

Are there any tools, methods, incantations to recover recently deleted files on Ubuntu?  If it makes any difference, I want to recover a  2.x database file. But would be better to have a method/tool that works on any kind of file.


When using BibTeX, I am happy enough adding accents where appropriate. For example  @article{key, author="Th{\'e}venaz, Jacques", title={Permutation Representations Arising from Simplicial Complexes}, journal={Journal of Combinatorial Theory, Series A}, year={1987}, }   However, if the above is an entry in my bib file and I use the option   \bibliographystyle{alpha}   in a LaTeX file, then this creates an error, as BibTeX naturally creates the key [Th\87] for this entry. Obviously I can go back to my bbl file and change the key here, but are there more general ways of solving this problem?

How to write in bibliography (package natbib) letter "a" with two dots above? Specially, I mean the word Birkhäuser.  Is there a general rule or way how to write such umlauts or other accented letters in bibliographies?


I am using TeamViewer to 1. control my computers and 2. prank my friends. So how do I hide the little TeamViewer icon on my desktop? (On Windows 10, and I have the latest version of TeamViewer) And the icon I mean is an attachment.  - The Image

Is it possible to hide a quick panel of the TeamViewer in the right corner and other notifications and pop-ups to enable a "silent" remote session?  While using team viewer Host application in android phone(remote phone) and connected to that device , the host application is showing a permanent notification in remote phone as long as connection ends. How to disable that notification? (Not able to disable in settings>apps. Turn off notification is not found for teamviewer host app)


I have downloaded the iredmail tar file iRedMail-0.9.9.tar.bz2, and placed it ia a folder named iRedMail. Can some one give ma step-by-step instruction how I install it on Ubuntu 18.04? I will very much appreciate help from an expert.

I have downloaded tar.gz files. But I don't know how to install it. How do I install this kind of file?


I'm trying to use string substitution to combine an array. Output: a,b,c  The below works, but isn't there a way to do with without piping? #!/bin/bash  words=(a b c)  echo "${words[@]}" | sed 's/ /,/g'  I've tried this, which doesn't work. echo "${words[@]// /,/}"

I'm trying to use Bash string substitution to combine an array. Desired output: cat,dog,fish  This works, but isn't there a way to do with without piping? #!/bin/bash  words=(cat dog fish)  echo "${words[@]}" | sed 's/ /,/g'  I've been trying this, which doesn't work. echo "${words[@]// /,/}"


I don't understand the following statement: Let $X_N$ , N $=$ 1,2, ... random variables with hypergeometric distribution; Parameter ($N$,[P$N$],n).  Show that:  $$\lim_{N\to \infty} P(  X_N  = k ) =  \binom{n}{k} p^k (1-p)^{n-k}$$  Does this means that the hypergeometric distribution approaches binomial distribution for N $\rightarrow$ $\infty$ ?   Can somebody give me only the beginning of this proof?

I have this problem on a textbook that doesn't have a solution. It is:  Let $$f(x)=\frac{\binom{r}{x} \binom{N-r}{n-x}}{\binom{N}{n}}\;,$$ and keep $p=\dfrac{r}{N}$ fixed. Prove that $$\lim_{N \rightarrow \infty} f(x)=\binom{n}{x} p^x (1-p)^{n-x}\;.$$  Although I can find lots of examples using the binomial to approximate the hypergeometric for very large values of $N$, I couldn't find a full proof of this online.


I am in the process of customising my new Dell Inspiron 15 3581, which came installed with Ubuntu 18.04.  I am a bit uncertain/confused when it comes to the Ubuntu Software Installer. i.e. I look for Claws Mail and up comes claws-mail-moon127 (Snap Store, 84.3 MB, 3.17.2). But when I scroll down further, there is Claws Mail (ubuntu-bionic-universe, 1.4 MB, 3.16.0-1).  I probably haven't quite understood yet, what this snapcraft is about, and how it is related to the Ubuntu repositories.  I guess, my actual questions are:  a) If there are two versions available, like the Claws Mail example above, which one would be the preferable, and why?  b) Which one would be the more stable version?  c) Will there be a conflict if I install both versions?

This is not a duplicate of the following questions     because:  My question specifically states that I am interested in end-user experience, not ease or efficiency of development, which is what the other question largely refers to.  As has been noted, development/deployment affects end-user experience, but it is not all there is to it, and neither of the referenced questions address issues that directly impact an end-user's ability to use the application (e.g. trouble accessing data on other partitions, sluggishness, etc.) Maybe "compelling" wasn't the right word to use; my intent was to ask about real-world, experiential consequences, i.e., things that happen or  don't happen, as opposed to theoretical/architectural statements that, while presumably accurate, don't appear to be backed up with any real-world examples to support the statement. I should have stated more directly that my intention was to get answers that consider the balance of "advantages" to snaps against the real-world downsides experienced by end-users. The "duplicate" question is largely theoretical, and doesn't discuss end-user experience at all. The "duplicate" question makes no mention of anything remotely similar to the example I used here, i.e., that there is an end-user downside to snaps (in this case, lack of access to data on other partitions and snap app performance) that isn't discussed in any available documentation that I can find.   While I understand that snap has a big advantage in making apps more widely available, is there any compelling reason to choose snap over apt, if the app is available for my distro/version via an apt package? I am curious because I've been doing some reading about snaps, and all the excitement about the method seems to be about things that are advantageous for app developers, but I've seen virtually nothing on how this makes life easier for end users (aside from the obvious; that they may be able to install apps that aren't otherwise available on their distro/version). I installed snapd and installed a couple of snaps and was really frustrated and disappointed.  The snap apps are slow and it's difficult, if not impossible, to access files on other partitions from within the snap. While I've seen plenty of info that says snaps are "faster," "easier," "safer," etc., I haven't been able to find anything that explains why or how this is actually the case. Being very new to Linux, I am wondering if maybe I'm just missing something obvious? To be clear, I understand why the technology might be useful overall, but I can't find anything that explains whether/why it is a better option even when the app in question is available for install via a more traditional method, and all dependencies are met.


i always get the following error when running sudo apt-get update  Get:1 http://us.archive.ubuntu.com trusty InRelease [356 B] Get:2 http://security.ubuntu.com trusty-security InRelease [363 B] Ign http://us.archive.ubuntu.com trusty InRelease                         Splitting up /var/lib/apt/lists/partial/us.archive.ubuntu.com_ubuntu_dists_trusty_InRelease into data and signature failed E: GPG error: http://us.archive.ubuntu.com trusty InRelease: Clearsigned file isn't valid, got 'NODATA' (does the network require authentication?)   here is my resources file  # newer versions of the distribution. deb http://us.archive.ubuntu.com/ubuntu/ trusty main restricted deb-src http://us.archive.ubuntu.com/ubuntu/ trusty main restricted  ## Major bug fix updates produced after the final release of the ## distribution. deb http://us.archive.ubuntu.com/ubuntu/ trusty-updates main restricted deb-src http://us.archive.ubuntu.com/ubuntu/ trusty-updates main restricted  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu ## team. Also, please note that software in universe WILL NOT receive any ## review or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ trusty universe deb-src http://us.archive.ubuntu.com/ubuntu/ trusty universe deb http://us.archive.ubuntu.com/ubuntu/ trusty-updates universe deb-src http://us.archive.ubuntu.com/ubuntu/ trusty-updates universe  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu  ## team, and may not be under a free licence. Please satisfy yourself as to  ## your rights to use the software. Also, please note that software in  ## multiverse WILL NOT receive any review or updates from the Ubuntu ## security team. deb http://us.archive.ubuntu.com/ubuntu/ trusty multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ trusty multiverse deb http://us.archive.ubuntu.com/ubuntu/ trusty-updates multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ trusty-updates multiverse  ## N.B. software from this repository may not have been tested as ## extensively as that contained in the main release, although it includes ## newer versions of some applications which may provide useful features. ## Also, please note that software in backports WILL NOT receive any review ## or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ trusty-backports main restricted universe multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ trusty-backports main restricted universe multiverse  deb http://security.ubuntu.com/ubuntu trusty-security main restricted deb-src http://security.ubuntu.com/ubuntu trusty-security main restricted deb http://security.ubuntu.com/ubuntu trusty-security universe deb-src http://security.ubuntu.com/ubuntu trusty-security universe deb http://security.ubuntu.com/ubuntu trusty-security multiverse deb-src http://security.ubuntu.com/ubuntu trusty-security multiverse  ## Uncomment the following two lines to add software from Canonical's ## 'partner' repository. ## This software is not part of Ubuntu, but is offered by Canonical and the ## respective vendors as a service to Ubuntu users. # deb http://archive.canonical.com/ubuntu trusty partner # deb-src http://archive.canonical.com/ubuntu trusty partner  ## Uncomment the following two lines to add software from Ubuntu's ## 'extras' repository. ## This software is not part of Ubuntu, but is offered by third-party ## developers who want to ship their latest software. # deb http://extras.ubuntu.com/ubuntu trusty main # deb-src http://extras.ubuntu.com/ubuntu trusty main   i am pulling out my hair on what to do since i've tried almost all recommendations in this group  i can ping just fine to other websites

I can use my mobile broadband to access Internet with Firefox but when I want to install any package from terminal or make 'apt-get update' command I got the following error:  got 'NODATA' (does the network require authentication?)   apt-get update output:  Get:1 extras.ubuntu.com trusty InRelease [213 B] 98% [1 InRelease gpgv 213 B] [Connecting to archive.ubuntu.com] Splitting up /var/lib/apt/lists/partial/extras.ubuntu.com_ubuntu_dists_trusty_InRelease into data Ign extras.ubuntu.com trusty InRelease E: GPG error: extras.ubuntu.com trusty InRelease: Clearsigned file isn't valid, got 'NODATA' (does the network require authentication?)    output of `cat /var/lib/apt/lists/partial/extras.ubuntu.com_ubuntu_dists_trusty_InRelease  <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <html> <head> <title>404</title> <meta http-equiv="Cache-Control" content="no-cache"/> </head> <body> <p> Not Found </p> </body> </html>   output of wget:  wget -O - http://extras.ubuntu.com/ubuntu/dists/trusty/InRelease  --2014-06-01 09:23:35--  http://extras.ubuntu.com/ubuntu/dists/trusty/InRelease Resolving extras.ubuntu.com (extras.ubuntu.com)... 91.189.92.152 Connecting to extras.ubuntu.com (extras.ubuntu.com)|91.189.92.152|:80... connected. HTTP request sent, awaiting response... 200 OK Length: 213 [text/html] Saving to: ‘STDOUT’   0% [                                       ] 0           --.-K/s              <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <html> <head> <title>404</title> <meta http-equiv="Cache-Control" content="no-cache"/> </head> <body> <p> Not Found  </p> </body> </html>


What can I do to compare two variables of type float accurately in C++, one being initialized at the time of declaration and the other being computed through the program?   When I am comparing two variables having value either 0.5 or 0.25, the program is showing the desired output but when I am comparing two variables having value either 0.333333 or 0.666667, the program is not showing the desired output. Will you please tell me where I am going wrong? Please help me in writing the correct piece of code. I am a novice and it will be a great experience to learn from you. Thank you for your concern. Here is the code with some of the outputs:

What would be the most efficient way to compare two double or two float values?  Simply doing this is not correct:  bool CompareDoubles1 (double A, double B) {    return A == B; }   But something like:  bool CompareDoubles2 (double A, double B)  {    diff = A - B;    return (diff < EPSILON) && (-diff < EPSILON); }   Seems to waste processing.  Does anyone know a smarter float comparer?


Is there a symbol for the following set?  $$ \left\{ x \in \mathbb{R} : x > 0 \right\} $$

What is the "standard" way to denote all positive (or non-negative) real numbers? I'd think  $$ \mathbb R^+ $$  but I believe that that is usually used to denote "all real numbers including infinity".  So is there a standard way to denote the set  $$ \{x \in \mathbb R : x \geq 0\} \; ?$$


I use this query to get a value for a range of months. For example, January 1.10, February 2.37.  "SELECT SUM(DISTRIBUTED_AMOUNT / EXCHANGE_RATE) FROM royalties WHERE DATE BETWEEN '".$datemin."' AND '".$datemax."' GROUP BY DATE  ORDER BY DATE ASC"   Is there a way to return a value of 0 if there are no rows within a certain month?

I'm building a quick csv from a mysql table with a query like:  select DATE(date),count(date) from table group by DATE(date) order by date asc;   and just dumping them to a file in perl over a:  while(my($date,$sum) = $sth->fetchrow) {     print CSV "$date,$sum\n" }   There are date gaps in the data, though:  | 2008-08-05 |           4 |  | 2008-08-07 |          23 |    I would like to pad the data to fill in the missing days with zero-count entries to end up with:  | 2008-08-05 |           4 |  | 2008-08-06 |           0 |  | 2008-08-07 |          23 |    I slapped together a really awkward (and almost certainly buggy) workaround with an array of days-per-month and some math, but there has to be something more straightforward either on the mysql or perl side.   Any genius ideas/slaps in the face for why me am being so dumb?    I ended up going with a stored procedure which generated a temp table for the date range in question for a couple of reasons:   I know the date range I'll be looking for every time The server in question unfortunately was not one that I can install perl modules on atm, and the state of it was decrepit enough that it didn't have anything remotely Date::-y installed   The perl Date/DateTime-iterating answers were also very good, I wish I could select multiple answers!


Suppose, a tunnel is made along the diameter of Earth and we drop a ball inside it. How will the ball behave? Please help me understand.

...And you jumped in.  What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like it was up?


I had a question in   which in turn made me to change my project CRS from EPSG: 3857 to EPSG: 25832.  My project location is in the middle of Germany (Shown in the image with the green dot, that i added manually)  But then, i queried some data from Quick OSM, only for it to appear somewhere in south of France. (Shown as the red dot)    At first I realized that the OSMquery layer have a different CRS than my project. (EPSG: 4326), so in turn, I changed the layer CRS from the OSMquery to my Project CRS, which is EPSG: 25832, but then this happened:     The red dot (Representing the layer with changed CRS) appears on the sea near the African Continent!  Did I do something wrong? Is there a way to repair this? Is there any command I have to change in the QuickOSM? Or is this a problem with the CRS? Or I just missed a setting somewhere? (Note: I am very new to GIS software in general)

I'm using QGIS 3.4.1, and I'm trying to print 61km x 61km area map of somewhere South Korea. Then I need to send this map with west / east latitude and north / south longitude info to other person, who need to do some work on that map. Here's what I did.   First, I set project CRS to EPSG 32652, WGS84 - UTM zone 52N, because most of South Korea is in the zone 52N.   Second, I load maps from Quick Map Service plugin, ESRI map from ArcGIS Map Server layer, Openlayers plugin. I also downloaded SRTM data using SRTM downloader, and also from CGIAR-CSI for double check.   Third, I found out that all of layers that I loaded or downloaded have CRS of EPSG 3857, WGS84 - Pseudo Mercator. I intuitively thought that they should have the same CRS with project CRS. So I changed CRS of all layers to project CRS, which is EPSG 32652, WGS84 - UTM zone 52N.   Then I found out something gone wrong seriously. Distance is distorted, grids, scale bar, and ruler show unusually shorter distance than it should be. In addition, I found that lat long coordinate shown from Lat Long tools plugin is really really off from real Lat and Long coordinate. For example, typical Lat Long position of Seoul is around 37.55 N, 127.03 E. However, Lat Long position from map after map CRS conversion shows around 8.45 N, -151.53 E. Moreover, all SRTM data layer moved to really strange position.   Just in case, I repeated the same procedure from QGIS 2.18 with on-the-fly CRS transformation option on. But the same symptom occur.   I think major problem here is the CRS, project CRS and layer CRS. I think my "I intuitively thought that they should have the same CRS with project CRS. " this part is wrong, but I can't understand.   Why should I need to use WGS 84 Pseudo-Mercator CRS for layers, while using WGS 84 UTM 52N CRS for project?   And I don't know what to tell my coworker, which CRS I used for this 61km x 61km area  map.


So far I have  $${{\phi(n)^2} \over n} = n \prod_{i = 1}^k \left(1 - {1 \over p_i}\right)^2$$  We know that $$\left(1 - \frac{1}{p_i}\right) \geq \frac{1}{2}$$  So $$n \prod_{i = 1}^k \left(1 - {1 \over p_i}\right)^2 \geq \frac{n}{4^k} = \frac{n}{2^{2k}}$$  Want to show that $$\frac{n}{2^{2k}} \geq \frac{1}{2}$$  $n \geq  2^{2k - 1}$  Got stuck here. Any help to prove this?  EDIT: Ok so I looked at the answer in the thread provided and I don't understand how $\frac{\phi(n)^2}{n}= \prod_{p|n \ \text{prime}} \frac{(p^{a_p-1}(p-1))^2}{p^{a_p}}$  There's a factor of n missing since the $\phi$ function is being squared

So I'm trying to prove the following two inequalities: $$\frac{\sqrt{n}}{2} \leq \phi(n) \leq n.$$ The upper bound we get from simply noting that $\phi(n) = n \prod_{p | n}\left( 1 - \frac{1}{p}\right)$ and the fact that $(1 - \frac{1}{p}) \leq 1$. But how can we get the lower bound? I tried using the same expression for $\phi(n)$ but it seems to not really give me the inequality. Can you help?


The real duplicate is:   Say someone joins a site in Stack Exchange and posts an answer. That answer is not good enough, so it gets some comments to finally be deleted by a moderator. The user has not been active on the site during all of this, so no notifications arrived to him before the question got deleted.  After few days, the user enters the site again and his answer is gone. However, is he still able to see the comments that were written to him, as well as to see his initial post and update it? More importantly: does he get the notifications on the comments? (which is something not covered in any of the targeted duplicates).  This is relevant to me since in a site I mod we some times have the case of someone posting an answer that can be a hidden gem, but needs quite a lot of polishing. This is a common case in Spanish Stack Exchange: a very basic answer consisting in a mere translation, that could somehow get improved by the author by adding some references and examples. It is more a comment than an answer, so it does not deserve to be kept there, but if the author dares to do some extra work on it, it will be very useful. I do want the user to get our feedback in comments, so I wonder if it is lost if the post gets deleted.  It would be also interesting to know if such behaviour is the same for users with reputation 1 (brand new users) and reputation 101 (trusted users in other sites).

I ask partially in relation to , but also for my own use;  My question is, if I leave a comment on a question or answer that is subsequently deleted, does the (non-10k) poster get a notification, if they arrive on the site after the content has already been deleted? And if so, can they then view the content?  I often leave what I hope are helpful comments when I flag content for deletion, especially for borderline spam and for non-answers. Very often, the user won't return to the site before the content is deleted, though.  So, is this practice at all helpful to the OP?


I have a document where footnote numbers restart every page, when I use the paracol environment this seems to stop working. In my MWE the footnotes in each page are okay for normal text but the second paracol environment numbers the footnotes as 3 and 4 instead of 1 and 2 even though it is on a new page.  \documentclass[10pt,a4paper]{article} \usepackage[latin1]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx}  \usepackage{everypage} \AddEverypageHook{\setcounter{footnote}{0}} % resets footnote counter on every page  \usepackage{paracol}  \begin{document}     this is the first page\footnote{footnote 1 page 1}     \pagebreak%      second page\footnote{footnote 1 page2}     \pagebreak%      \begin{paracol}{2}         \setlength{\columnseprule}{0.4pt}         \setlength{\columnsep}{15pt}          left column              \switchcolumn%           right column\footnote{a footnote}\\%          \switchcolumn*%          left column again          \switchcolumn%               right column again\footnote{2nd footnote}\\%     \end{paracol}      \pagebreak%      another page with normal text\footnote{and a footnote}      \pagebreak%      \begin{paracol}{2}         \setlength{\columnseprule}{0.4pt}         \setlength{\columnsep}{15pt}          left column              \switchcolumn%           right column\footnote{a footnote}\\%          \switchcolumn*%          left column again          \switchcolumn%               right column again\footnote{2nd footnote}\\%     \end{paracol}   \end{document}

Is there a way to reset the footnote counter every page without getting errors and warnings?  If I use \usepackage[perpage]{footmisc} I get an error. If I use \usepackage{perpage} \MakePerPage{footnote} I get a warning.  MWE     \documentclass{article} \usepackage{paracol} \footnotelayout{m}  \usepackage{blindtext}  \begin{document}    \blindtext{1}    \begin{paracol}{2} % left column   \textbf{Hello, I'm column one.}\footnote{I'm a footnote.}   \blindtext{1}   \switchcolumn % right column   \textbf{Hello, I'm column two.}\footnote{I'm a footnote.}   \blindtext{1}   \end{paracol}    \blindtext{1}    \blindtext{1}    \begin{paracol}{2} % left column   \textbf{Hello, I'm column one.}\footnote{I'm a footnote.}   \blindtext{1}   \switchcolumn % right column   \textbf{Hello, I'm column two.}\footnote{I'm a footnote.}   \blindtext{1}   \end{paracol}  \end{document}


I want to automatically update the timezone on my Windows 7 laptop after traveling to a new locale.  Is there any method of doing this, perhaps by using an Internet location service?

I often move between 2 time zones, and expect my Windows 7 laptop to somehow automatically change the system time, being spoiled by the same feature on my cell phone. I always assumed that desktop O/Ses simply did not do this, but I was shocked yesterday when I noticed that OSX on the MacBook actually does this!  Does anybody know of any utilities that does this on Windows, specifically Windows 7? There has to be something out there?


Can someone please tell me how to logout and log back in again via the command line so that I can apply a new group's settings to a user. To put this in perspective, assume that I am currently logged in as testuseraccount, and then I  issue the commands below into the terminal.  su usermod -aG sudo testuseraccount   So I believe by typing su this logs me into root (but just within the shell). So how do I logout of root, then logout of testuseraccount & sign back in (in order to apply the sudo group to testusersaccount) via the terminal?

Assume I'm logged in with user takpar:  takpar@skyspace:/$   As root, I've added takpar as a member of group webdev using:  # usermod -a -G webdev takpar   But it seems it has not been applied, because for example I can't get into a webdev's directory that has read permission for group:  400169 drwxr-x--- 3 webdev webdev 4.0K 2011-08-15 22:34 public_html  takpar@skyspace:/home/webdev/$ cd public_html/ bash: cd: public_html/: Permission denied   But after a reboot I have access as I expect. As this kind of group changing is in my routine, is there any way to apply changes without needing a reboot?  Answer It seems there is no way to make the current session know the new group, for example the file manager won't work with new changes. But a re-login will do the job. The su command is also appropriate for temp commands in urrent session.


I downloaded Ubuntu 15.10 desktop software from its official website which was in a winrar file. I have been having problems to convert to a iso disc image file. Is there a link where i can download the iso file directly.

I would like to see a full how-to guide on how to install Ubuntu.


I am not able to open a lightning component using "e.force:navigateToComponent"  this is the error when i click on the button:   this is my 1st component:  <aura:component controller="RecruitmentClass" implements="force:appHostable" access="global"> <aura:attribute name="LoginName" type="String"/> <aura:attribute name="LoginPwd" type="String"/> <aura:attribute type="Interviewee__c" name="Candidate1"/>
     <lightning:card title="" >
Login

         <ui:inputText label="Enter your name " value="{!v.LoginName}"/>
         <ui:inputText label="Enter your password " value="{!v.LoginPwd}"/>
         <lightning:button  label='Login' onclick="{!c.myAction}"/>
     </lightning:card>
     this is my js controller:  ({ myAction : function(component, event, helper) {     var name=component.get('v.LoginName');     var pwd=component.get('v.LoginPwd');      var action=component.get("c.Login");     action.setParams({         n:name,         p:pwd     });     action.setCallback(this,function(response){         if(response.getState()==='SUCCESS'){             var c=response.getReturnValue();             component.set('v.Candidate1',c);              //this is where im facing problems             var evt = $A.get("e.force:navigateToComponent");             evt.setParams({                 componentDef : "c:RecruitmentApp2ParentComponent",                 componentAttributes: {    Candidate : c                                       }             });             alert('succesful'+evt+'candidate: '+c);             evt.fire();          }         else {             alert('error something happend');         }     });     $A.enqueueAction(action);  }   })

Can anyone help me? Trying to do very simple function to navigate from component to another. I copied the code from Developers guide, but for some reason it doesn't work for me.  My function to navigate to another component:  nav : function(component, event, helper) {             var evt = $A.get("e.force:navigateToComponent");             evt.setParams({                 componentDef : "c:navToComponentTest2",                 componentAttributes: {                     continent : component.get("v.continent")                 },                 isredirect : false             });             evt.fire();     }   And here's the error I get in my Lightning App   EDIT: Got it working in Lightning tab. Would it be somehow possible to get it working in communities as well? Or is there anyway to make same functionality?


When I buy new computers, I usually do a "burn-in" with 100% CPU load for, say, seven days, in a well ventilated place.  This is to    find out if the computer has problems before I invest time into setting it up for me let it "steam out" some of the "plastic/chemical gasses" before I use it in my home   But, now I'm wondering, am I creating hardware problems by doing this? Are modern notebooks built to withstand this?   I guess a server surely is, but is a notebook? I'm talking one from a "well" known brand as Apple, Lenovo, HP, ASUS, Dell, etc.  So I did a burn-in for a new notebook recently. It went fine and didn't crash the OS even once. The notebook is of a model that doesn't get that very hot.  But after some weeks the hardware seems to "give up", recently the  has started to act up.  So, can a seven days full 100% CPU load "burn-in" / "stress test" damage a modern notebook??  How would you do a "burn-in" of a notebook? I guess one could put a fan next to it, but then the temperature would not get that high, and huge part of the reason for burn-in would disappear.    Thank you all for answers!   But reading them, I really wonder where "computing" is today. Many say that this seven days 100% CPU load will be damaging (/wear out early) to the computer.   From my computing background (1990- ) this sounds really strange - though I'm not saying it is wrong.  What if you have some encoding work to do? Or some 3D-rendering work? Those can easily run for three days, 100% CPU load. Shouldn't notebooks be used for those things?   I can accept that some people are skeptical about my worries about "toxic fumes"; you want to see proof. OK. But really, if one can't use a new notebook at 100% CPU for some days, I really would like to see some disclaimers from computer manufacturers, or some kind of admissions from them, that this is the case.   "This notebook is not suitable for 3D rendering." LOL!!!    Added 22 Oct 2014: I took a look at the SSD using some diagnostics software. It had information on the temperatures:   Highest temperature recorded ever was around 42 °C Highest temperature recommended was circa 70 °C Shutdown temperature was circa 75 °C   Conclusion: My seven days 100% CPU burn-in did not create a high temperature in the SSD, and it kept very good margin to the given max. Remember that I had the notebook in a room that never had an air temperature over, say, 26 °C.

I often do 3D rendering in the background which consumes 100% of the CPU (I lower the priority of the process so that it does not hinder any tasks I am working on).  My concern/question is whether it is okay to run a computer/laptop with a 100% CPU load constantly.  Could this reduce the lifespan of the system?


I am trying to show:  $\text{erf}(x) \leq \sqrt{1-\exp{(-\frac{4}{\pi}x^2})}$  I tried applying a chernoff bound, but that doesnt give me a bound in terms of the squareroot.

This is a follow-up to  question. I came across a tighter potential bound and checked it numerically for $0\le x\le 5$. I think it holds for all positive $x$, can anyone see a proof?  $$1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$$  Note: using analysis for previous  you can show that $1-\exp(-k x^2)$ is an upper bound on $\text{erf}(x)^2$ for $k=2$ and a lower bound when $k=1$. The factor $k=4/\pi$ comes out when numerically searching for tightest upper bound. Not only does it seem to give an upper bound, but it also tracks $\text{erf}(x)^2$ very closely.  Dashed graph below is $\text{erf}(x)^2$, red is $1-\exp(-k x^2)$ for $k=4/\pi$, other two graphs are for $k=1$ and $k=2$


Yesterday (April 7th, 2018), my Grandmother from my Mom's side passed away. Later on that same day, less than 24 hours apart, my other Grandmother (Dad's Mom), passed away. My question is simple; what are the odds of this happening? I searched around but haven't found anything close to this.

I have been teaching statistics for many years at the university level - but this question is beyond my understanding - due to the variables involved.  Several years ago, I was entertaining a relocation to a different area and a different way of life. I was very unsure and skeptical - as the change would have followed my heart - but not the rational practicality of my head.  Then a sequence of events took place - none of which were of my own choosing. I want to know what the statistical probability is of these events occurring by chance alone. They are as follows:  1) The property I had wanted to buy was already under contract, yet came back on the market on the anniversary of my father's death.  2) My immediate offer to purchase was accepted by the sellers (two days later) on the anniversary of my grandmother's death.  3) My loan was approved by my bank on the anniversary of my late grandmother's birthday (7 days later)  4) Our closing date was set by the title company on the anniversary of my late, great-aunt's birthday.  5) The permit for our business (for which we brought the property) was approved and issued on my parent's anniversary.  Can the probability of these dates be statistically determined?


Is it possible to give an intuitive/elementary proof of the theorem that says that the row rank of a (finite-dimensional) square matrix matrix equals its column rank?

I am looking for an intuitive explanation as to why/how row rank of a matrix = column rank. I've read the proof at  and I understand the proof, but I don't "get it". Can someone help me out with this ?   I find it hard to wrap my head around the idea of how the column space and the row space is related at a fundamental level.


Is there a reason that Moose becomes Mooses instead of Meese (as in tooth/teeth and foot/feet)

Why is it that the plural of goose is geese but the plural of moose is moose? The same goes for mouse and house. Mouse becomes mice, yet house becomes houses.