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PHP MySQLi doesn't recognize login info 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 :\ Is a continuous function on a bounded set bounded itself? If $f\colon A\to\mathbb R$ is continuous and $A$ is a bounded set, does it necessarily follow that $f$ is bounded? What regular expression will match valid international phone numbers? Custom action to set emblem in thunar I have seen some comments and speculations about the robot having an off switch or whatever. But I want to know if there is any source material or comment from the author on how they managed to pass the exam.  I have only seen the actual author's comment on Mineta:     But I was wondering if there are author notes for the other characters. How do I disable Aero Shake in Windows 7? I'm always accidentally minimizing most of my windows. This is really annoying. How do I disable Aero Shake? The effect of gravitational & Coulomb forces on free electrons in a conductor In a metal, why don’t the free electrons fall to the bottom of the metal due to gravity?  Also, charges in a conductor are supposed to reside on the surface so why don’t the free electrons all go to the surface?   Regarding the first question, my hunch is that it is due to the electric force which is greater than the gravitational force and electric force act along the length of the conductor.  I don't have any intuition for the second. Email Deliverbility How can I enable permissions to edit Email Deliverability access level? Currently it is not editable and in system mode. I need to edit it and set it to "All Email so I can test Approval and workflow functionality. Integration of secant $$\begin{align} \int \sec x \, dx  &amp;= \int \cos x \left(  \frac{1}{\cos^2x} \right)  \, dx \\ &amp;= \int \cos x \left(  \frac{1}{1-\sin^2x} \right) \, dx \\ &amp; = \int\cos x\cdot\frac{1}{1-\frac{1-\cos2x}{2}} \, dx \\ &amp;= \int \cos x \cdot\frac{2}{1+\cos2x} \, dx  \end{align}$$  I am stuck in here. Any help to integrate secant? Should we have another site for frameworks (and alike) recommendations? There is . Is the site appropriate for stuff related to requesting frameworks and libraries? Or should we have another site for that (e.g. name it Frameworks Recommendations or stuff alike)?  I can ask stuff there like: I need a software satisfying W, X, Y, and Z, but I'd like -some day- ask like: I need a Python library satisfying W, X, Y, and Z. The audience may be (and perhaps will be) different.    Is that website on-topic for stuff like that? Or should we open another proposal for that?  No: It's not about asking for a giga-dump for subjectivish questions. The linked-to-dupe question was written and answered with an old mindset and without Software Recommendations in mind. Also it does not consider this specific kind of questions but all the crap in one place. So, no,  is not an appropriate dupe mark for this question. This is inspired by some discussions in .  In the Harry Potter universe, how are Dementors born?  Or are they artificially created by some magical means? Failed to start TSQL debugger I want to debug in TSQL.When I start the debug the following message box popup. In SSMS v17.2    Then I see this message:    In Microsoft Visual Studio 2015 Server Explorer same Error:    Then I see this message:    Thank You! Does the full quarantine period have to be observed for short trips of less than 14 days to England? I am planning to go to England for 2 days in preparation of moving (I already have a place rented and would be staying there) a few weeks later. I am coming from a country where I would need to do a 14 day quarantine as soon as I enter England. Does this mean that I have to stay in England for 14 days or can I leave the country before the end of the 14 day quarantine without facing a penatly? I have found no information about what the rules are for planned stays of less than 14 days on the , while  seems to say that short trips are OK. Official sources would be appreciated. Evaluating the double limit $\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2m}(n! \pi x)$ I have to find out the following limit $$\lim_{m\to\infty}\lim_{n\to\infty}[\cos(n!πx)^{2m}]$$ for $x$ rational and irrational. for $x$ rational $x$ can be written as $\frac{p}{q}$ and as $n!$ will have $q$ as its factor the limit should be equal to 1. the second part of irrational is giving me problems. I first thought that limit should be zero as absolute value of cosine term is less than 1 and power it to infinity you should get $0$. But then I realised that it was wrong. I brought the limit down to this form. $$e^{-\sin^2(n!πx)m}$$ after this I find the question quite ambiguous as they have just said $x$ is irrational. If I take $x$ as $\frac{1}{n!π\sqrt{m}}$ I get the limit as $\frac{1}{e}$ but if I take  $x$ as $\frac{2}{n!π\sqrt{m}}$ I get the limit as $\frac{1}{e^4}$. please help me and tell me where have I gone wrong? Probably dumb question, but I would like to ask it anyway.  I was to solve this equation:  $z^4 = -16$  At first glance, the way to solve it would be (as any other equation):  $z^2 = \sqrt{-1} * 4 \lor z^2 = -\sqrt{-1} * 4$  $z^2 = 4i \lor z^2 = -4i$  $z = 2\sqrt{i} \lor z = -2\sqrt{i} \lor z = 2i\sqrt{i} \lor z = -2i\sqrt{i}$  However, in suggested answers, there are $z_1, z_2, z_3$ and $z_4$ found using trigonometric formulas. Is there something particulary wrong in my solution and the only proper one uses trigonometric form of complex number? Take the manifold: The graph of $|x|$ on $(-1,1)$, with the induced topology from $\mathbb{R}^2$. This is a topological manifold, which is homeomorphic to $(-1,1)$ by projection. Is it a differentiable manifold? I believe it is, because we can take an atlas with only the projection, and then we will have only one transition map which is the identity, and therefore differentiable. But I'm not sure I get the definition of a differentiable manifold right...  Thanks! "named" vs "that is named" Add space between headings and body in the home of the iPad app It's a pain in the ass for me to quit the app, draw a red circle in another app and return to the app, so...    If you notice the three questions in the bottom, you will notice that the emboldened headings (New Answer, Comment) are stick to the next character. Imperfect.    App Version: 1.4.0.249 Device: iPad 2 (GSM) OS Version: Version 9.1 (Build 13B143) Is there any substantial disadvantage to booking two one-way tickets, versus a round trip ticket?  Booking vacation travel with family of four for winter, from Northeast US to Mexico.  Round trip is pricy and no preferred travel times.  Two one ways is slightly cheaper with much preferred timing.      Different airlines there and back, both reputable national US carriers.