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"Mixed declaration and code" warning, is it worth addressing? This problem is really proving to be a tricky one (and quite annoying).  In SQL Server Management Studio 2008, up until a few days ago my IntelliSense was working great.  Then all of a sudden it stopped.  The icon as it as enabled on the toolbar menu, and under Tools -> Options -> Text Editor -> T-SQL -> IntelliSense it says it is enabled there.  I have tried refeshing the IntelliSense cache with Ctrl-Shft-R but that doesn't work either.  Any ideas what happened to my IntelliSense and what I need to do to get it back? When will data.SE get updated data? promised that data.SE would &quot;soon&quot; get live data:     I realize it's a long weekend, but given that data.SE is now over 2 months out of date, it would be nice if this was finally rolled out. Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$ Compute the definite integral      $$ \int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx $$      where $n\in \mathbb{N}$.   My Attempt:  Using $\cos (x) = \frac{e^{ix}+e^{-ix}}{2}$, we get  $$ \begin{align} \int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx&amp;=\int_{0}^{\pi/2} \left(\frac{e^{ix}+e^{-ix}}{2}\right)^n\left(\frac{e^{inx}+e^{-inx}}{2}\right)\,dx\\ &amp;= \frac{1}{2^n}\mathrm{Re}\left\{\int_{0}^{\pi/2} \left(e^{ix}+e^{-ix}\right)^n\cdot e^{inx}\,dx\right\}\\ &amp;=\frac{1}{2^n}\mathrm{Re}\left\{\int_{0}^{\pi/2}\left(e^{2ix}+1\right)^n\,dx\right\} \end{align} $$  Letting $z=e^{4ix}$ gives us  $$ \begin{align} e^{4ix}dx &amp;= \frac{1}{4i}dz\\ dx &amp;= \frac{dz}{4iz} \end{align} $$  So the integral becomes  $$\frac{1}{4\cdot 2^n}\mathrm{Re}\left\{\int_{C}\left(\sqrt{z}+1\right)\cdot \frac{dz}{iz}\right\}$$  How can I complete the solution from here? The Android app crashes when trying to upload a picture from my phone How to space columns evenly in a table with multicolumns? How do I install GNOME Shell extensions?  Is it possible to update, remove and manage the extensions? Why can't photons have a mass? Could you explain this to me in a short and mathematical way? This post is an expansion of  For many graduated sites (eg Physics), moderators do not want to apply the unilateral close vote in all cases--it is better to let some community votes pile on first.  We only use the unilateral in obvious cases then. This renders the CV queue useless to us. If we &quot;skip&quot; something, we can't get back to it. If we say &quot;do not close&quot;, it's removed from the queue and our community can't see it. If we use &quot;close&quot;, we are using a unilateral mod vote--we don't want to do that. What I propose is a set of &quot;next/previous&quot; buttons, that let us navigate the queues, looking for closeable questions, and coming back to the others later. Thoughts? Update and bounty reason Due to the recent Great Flag Overhaul, mods no longer see close flags in the flag queue. Which means that the only way to get to them is via the review queue 1 Shog's solution is ideal in this case; let mods view the close queue as a list. (In fact, a list similar to the old flag queue -- which shows a list of mods who have seen the post and what mod actions have already been taken -- would be great) On Physics, the majority of the flags that we get are VTC flags. And the community isn't always able to close things on their own, so we have to step in. However, powering through the close queue isn't an option; because &quot;skip&quot;ing a post2 leads to it being dumped into the void (I can't get back to it unless I have a link). Extremely inconvenient. Could the workflow here be improved? 1. The /tools listing for posts with outstanding close votes doesn't work because it doesn't list posts which have been flagged but not VTCd 2. which I may want to take a closer look at later; gotta be careful with the binding votes. Relationship between Partial Harmonic Sum and Logarithm. How to get a JavaScript object's class? Friend was brainwashed by MLM-/ponzi investment scam. What can I do? Recently a friend of mine invited me to hear about “an interesting chance to simply earn money.” Basically we and other invited people drove to a meeting room where a speaker told us about a growing startup where you could invest money in a field where similar investments had an ROI of apparently 1000 times the investment in 6 years. Afterwards there was coffee and small talk together, during which they also indoctrinated people saying, they should avoid talking to people talking bad about the investment (or saying it is scam) because you can't gain money from them and they just want to destroy your business.  You earn money if you invest money and if you refer friends who invest money up to multiple levels. The more you invest yourself the greater percentage you earn for your referrals.  Since I had already seen other ponzi-/MLM-schemes and I am from the field it is based in, I recognized that there is no real product and it is a ponzi-/MLM-scheme. Later I found its name on the official scam warning list of multiple countries.  From what I understand, my friend has already invested multiple months or years worth of income; and is earning an amount of money through referrals that would mean scamming other people directly or indirectly through referrals for possibly several $100,000's per month to earn an additional bonus. He also wants to use his position as a respected member of multiple local youth groups and other community groups to get their members as referrals or in his words “…to give them the opportunity to also simply earn money.”  I tried to convince him that it is just a ponzi scam with my knowledge in this field but he answered with the indoctrinated speech “You don’t need to know the details if it makes you rich or use it. You also don't know how every detail of a smartphone works?”/“My sponsor already earned $x with this” or “If you don't believe in this, just stop talking about it to me and other people or do you want to ruin me, my business and my investments?.” So basically this means I can either make his investment worthless/let him lose everything (he also quit his job) or let him scam other people and motivate them to scam other people.  At the moment you can only withdraw small amounts of money out of it because the company invented some reason but you will be able to withdraw all of it “soon” (=most likely never).  What is the best way to resolve this situation (best meaning with lowest loss of money for everybody)?  Edit: The founders are known names in Ponzi schemes or convicted for crimes like fraudulent bankruptcy and many of their claims are technically impossible or proven to not exist with very high probability according to sites about ponzi schemes. But of course they say "Every bigger company has their scandals".  You can't trade the bought virtual coins outside the company and the only product you can buy can be bought anywhere else for less than 10% of the price without the logo.  When I met other friends they mentioned that they got invitations for the same meeting. I just stated to them that I already went to one and told them the name of the company (which was not stated on the invitation) and that I will not invest in it because there are official warnings that this is a scam. Is there a word or phrase for someone who works hard at night and does not sleep? All the words or phrases I know for people who stay up at night merely describe the habit of not sleeping (e.g.: a night owl or insomniac)  I am looking for a word or phrase with an emphasis on working hard at night. These people work are different from insomniacs because they have no problem sleeping but they refuse sleep to work. They are different from night owl because they wake up early in the morning.  To give more context, suppose a nurse with kids who has a normal day life like most people and takes care of the kids but also works most nights in a hospital. Derivative (or differential) of symmetric square root of a matrix Let A be a square, symmetric, positive-definite matrix.  Let S be its symmetric square root found by a singular value decomposition.  Let vech() be the half-vectorization operator.  Is there a convenient expression for the derivative (or differential) of vech(S) with respect to vech(A)?  I know the expression for an inverse, which is sort of like a matrix version of the power rule.  Would this approach work for a symmetric square root as well (i.e., (1/2)S^(-1/2))? Referring to correctly-styled algpseudocode procedure name in document Given an algorithm written in algpseudocode:  \documentclass{article} \usepackage{algorithm} \usepackage{algpseudocode} \begin{document} \begin{algorithm}   \caption{Part 1}   \begin{algorithmic}[1]     \Procedure {FooProc}{$G$}       \State ...     \EndProcedure   \end{algorithmic} \end{algorithm} \end{document}   How can I now refer to FooProc in my document (outside of the algorithm environment) such that it has the same typeset as in inside the algorithm environment? In high Reynolds numbers we have turbulent flow. This is because the inertial forces are much greater than the viscous forces. I understand inertial forces to be actually the fictional forces due to the momentum of the moving fluid. And viscous to be the forces that drag each layers together. But why when inertial forces are too high than the viscous forces, there is turbulence? Why don't the molecules just continue to move laminarly due to their momentum? I can assume the viscous forces are not very strong in high speeds (in high inertial forces) to keep them together to form a laminar flow? But again, why they result in irrational movement after the effect of viscous forces is not anymore considerable? As a mechanical analogue, if I have balls attached together and make them travel linearly, and remove their between them attachment, they can continue to travel linearly. But what happens in fluid molecules that turbulence is created? Can I deploy Juju on Eucalyptus? Please let me know if I can deploy juju on Eucalyptus, if yes please provide me the configuration details which i need to edit on environments.yaml file. Can I configure it to allow:   select right-click to copy right-click or ctrl-v to paste? Can somebody help me understanding the fouries series coefficients?  I know that if we have:  $$f(t) = \sum_{n=1}^N A_n \sin(2\pi nt + Ph_n) \tag{where $Ph_n$ = phase}$$  And because of the $\sin(a+b)$ formula: $$ f(t) = \sin(2\pi nt + Ph) = \sin(2\pi nt )\cos(Ph_n) + \cos(2\pi nt )\sin(Ph_n)$$ Then:  $$\sum_{n=1}^N A_n \sin(2\pi nt + Ph) = \sum_{n=1}^N (A_n\sin(2\pi nt )\cos(Ph_n) + A_n\cos(2\pi nt )\sin(Ph_n))$$ And by definition: $$a_n = A_n\cos(Ph_n)$$ $$b_n = A_n\sin(Ph_n)$$ Then:  $$f(t) = \sum_{n=1}^N A_n \sin(2\pi nt + Ph) = \sum_{n=1}^N (a_n\sin(2\pi nt ) + b_n\cos(2\pi nt ))$$ Where does the $A_n$ in the first formula come from? Could somebody explain me where does the $\frac{a_0}{2}$ in the formula below come from? $$f(x) = \frac{a_0}{2}+\sum_{n=1}^\infty (a_n \cos(nx) + b_n \sin(nx))$$  And the most important:  How can I proof the formulas for the $a_n$ and $b_n$ coefficients?  PLEASE, I'm searchinf for these answers for DAYS. Is it safe to put a clothes washer outdoors?