I have created an object but when called ,it says not defined (JavaScript)
What is the scope of variables in JavaScript?
How to obtain Hamiltonian formalism and phase space for Lagrangian with second-derivatives? I am trying to prove that all vector spaces can be written as the direct sum of two subspaces.  My attempt: If each vector in vector space V can be uniquely written as the sum of two other vectors in V, the two vectors can be categorized into subspaces and thus V can be written as the direct sum of these subspaces. I am not sure how to show that this is true for all cases though. Edit Sorry for the confusion,to clarify I meantGiven a vector space V with a subspace W, prove that there exists a subspace W' such that the direct sum of W and W' is V.I am not sure about my proof method at all. Thank you. I know that if you held an infrared remote in front of a digital camera, it'll flash a blue/purplish light when you press the buttons. Why?    (Image by  .) SEDE logs me out more often than it used to do I'm pretty sure that since a month or so,  seems much more eager to get rid of my session and log me out in that process. I don't mind logging in a couple of times per day, if that helps to reduce resource consumption, but the user experience isn't all that great when it happens. Here is why: I'm most often in the middle of writing a query for an MSE question, for example . So I have the edit window open and am creating a new revision of my query. When I click &quot;run,&quot; I do notice the button gets grayed-out, as it normally does, but I never get any result back. There is also no error message. To recover from this I have to copy the SQL text I have typed, open a new tab and load SEDE, log in, switch back to the stalled tab, refresh, paste the SQL text, run query. Repeat the process after 10 minutes. If the intended behavior is to log users out of their session on such short notice (I recall sessions lived for 24 hours), can there then be a slightly better handling in the browser of that state, so it is clear you're logged out once you click the run button? I prefer, however, to have the longer allowed sessions back. I'm experiencing this behavior mostly in Chrome on Win 10. How to see data from .RData file? If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$ Let $1\leq p &lt; \infty$. Suppose that    $\{f_k\} \subset L^p$ (the domain here does not necessarily have to be finite),  $f_k \to f$ almost everywhere, and  $\|f_k\|_{L^p} \to \|f\|_{L^p}$.    Why is it the case that $$\|f_k - f\|_{L^p} \to 0?$$   A statement in the other direction (i.e. $\|f_k - f\|_{L^p} \to 0 \Rightarrow \|f_k\|_{L^p} \to \|f\|_{L^p}$ ) follows pretty easily and is the one that I've seen most of the time. I'm not how to show the result above though. how is this possible? I know there is some trick, should someone please explain?! Change location of macOS Notification Center alerts? Is it possible to change where macOS Notification Center alerts appear on the screen?  They currently appear at the top right of the screen with the menu bar:    Alerts appearing in the top right tend to cover up work I'm doing more often than not. They cover up browser tabs, toolbar icons, and window titles.  I would prefer, say, the bottom right corner of the screen.  If moving the alerts is not possible, is it possible to change the screen on which they appear? Plotting graphs using bash Most efficient method to break Ubuntu Limit of derivative is zero. Does it imply a limit for f(x)? How to show this property of $\mathbb{RP}^{n}$. To prove that: The $n$-dimensional projective space can be presented as:  $\mathbb{RP}^n=\bigcup_{i=0}^{n} A^{i}$.  (The intersection of each two $A^{i}$ is empty)، $A^{i}$ is isomorphic to $\mathbb R^{i}$ ($A^{0}$ includes only one point). The definition of $\mathbb{RP}^n$ is: $\mathbb{RP}^n= (\mathbb R^{n+1} \setminus \{0\})/ \sim$ , $\sim$ is defined as: $x \sim \lambda x$for all $\lambda\in \mathbb R^\times$ and $x\in \mathbb R^{n+1} \setminus \{0\}$. $\mathbb R^\times $ is the productive group of scalars $\ne0$ in the field $\mathbb R$. I'm just a beginner in this field so any help would be appreciated. What's the bad magic number error? Name finding problem with comment notification feature I just received the following in my Response pane (from ), but you can see it was meant for another user.  The @Robert line seems to have found 'Robert' in my name first, instead of Robert C. Cartaino.  I think the comment notification feature should match based on the closest match from the first character in a name (in posting order), and not just the first match found in posting order. Equivalent definition of metric compatibility for a connection: what does $\nabla g$ mean? So the definition I know for metric compatibility is:  $$Xg(Y,Z)=g(\nabla_XY,Z)+g(Y,\nabla_XZ),$$   which make sense, as $g(Y,Z)$ is a smooth function from the manifold to reals and we think of $X$ as a derivation. So now I read this apparent equivalent definition that says $\nabla g=0$. Can someone explain what this means? How can I do $\nabla$ of $g$ I thought $g_p$ is an element of $T_p^*M\otimes T_p^*M$ at every point. Furthermore after you explain the meaning of this can you show me that these two definitions are indeed equivalent? Induction proof: $S$ contains powers of 2 and predecessors implies $S={\bf N}$ Let $S$ be a subset of $\mathbb{N}$ such that $$2^k\in S\quad\forall\ k\in\mathbb N$$ and, $$k\in S\Rightarrow k-1\in S\quad\forall\ k\ge2,k\in\mathbb N$$  Show by induction that $S=\mathbb N$. Why is "chmod -R 777 /" destructive? This is a  about File Permission and Why 777 is "destructive".   I'm not asking how to fix this problem, as there are a ton of references of that already on Server Fault (reinstall OS). Why does it do anything destructive at all?  If you've ever ran this command you pretty much immediately destroy your operating system. I'm not clear why removing restrictions has any impact on existing processes. For example, if I don't have read access to something and after a quick mistype in the terminal suddenly I now have access well... why does that cause Linux to break? I am solving a series of ODE, such that each DE is equal to some degree of term that I'm expanding to. For instance, one DE is this:  $\xi^r\partial_r g_{rr}+2g_{tt}\partial_t\xi^t=\mathcal{O}(r)$  $g_{ii}$ are given, from metric, but that's not important. I need to assume that the solution (since I'm looking for components of $\xi^\mu$, which is a vector with components $\xi^t,\xi^r,\xi^\phi$) is given with power series of the form:  $\xi^\mu=\sum\limits_{n}\xi^\mu_n(t,\phi)r^n$, and this is to be seen as expansion around $1/r$ (expansion around $r=\infty$).  Now when I plug this in the ODE I get this  $\frac{2}{l^2}\sum_n\xi^r_nr^{n+1}+2\sum_n\xi^t_{n,t} r^n+\frac{2}{l^2}\sum_n\xi^t_{n,t}r^{n+2}=\mathcal{O}(r)$, where   $\xi^\mu_{n,i}$   is the derivative with the respect to i-th component.   What troubles me is, how to expand this? Do I set n=0,-1,-2,... until my $\mathcal{O}(r)$ terms cancel each other out? Or?  I'm kinda stuck :\ Basically the problem is that each time the assembly version changes (i.e. the user installs a new version of the application) all their settings are reset the the defaults (or more accurately a new user.config file is created in a folder with a different version number as the name)  How can I keep the same settings when upgrading versions, since using ini files or the registry seem to be discouraged?  When we used Clickonce it seemed to be able to handle this, so it seems like it should be able to be done, but I'm not sure how. Are there any areas that should be avoided and are there any steps I should take to protect myself from radiation?