How to make printed paper depth-of-field effect?
How to get this blur texture effect in photoshop?
how can I find sum of series $ \sum_{n=1}^{\infty} (n\cdot \ln \frac{2n+1}{2n-1} - 1) $? It is so weird for me because I put this to Mathematica and it tells me that sum does not converge...  Let consider sum no to infinity, but to n  $$ \sum_{k=1}^{n} (k\cdot \ln \frac{2k+1}{2k-1} - 1) =$$ $$ ln \frac{3}{1}\cdot \left(\frac{5}{3}\right)^2 \cdot...\cdot \left(\frac{2n+1}{2n-1}\right)^n - n = ln \frac{1}{1}\cdot \frac{1}{3}\cdot \frac{1}{5}\cdot ... \frac{1}{2n-1} - n $$ but $$ n = ln e^n $$ so it will be $$ln\frac{1}{e^n} \cdot \frac{1}{1}\cdot \frac{1}{3}\cdot \frac{1}{5}\cdot ... \frac{1}{2n-1}$$  So the limit of it is $-\infty$ Have I done this well or I missed sth? Stop suggesting Microsoft Edge browser in start menu when typing "internet" I use Chrome as my primary browser but must use Internet Explorer to be able to remote in to my work via Remote Desktop web client (since it uses ActiveX plugins). To start an app, I would often type out the name from the start menu unless I had a pinned link or shortcut handy. But if I type &quot;internet&quot; as if I were trying to start Internet Explorer, I will always be recommended Edge and have it highlighted by default.  I will never be able to use Edge here so stop recommending it... can this behavior be disabled somehow? Not even pinning the Internet Explorer link to the start menu prevents this. If I had any other shortcuts that started with the word &quot;internet,&quot; it still offers Edge and is preselected. At least if I type in &quot;chrome,&quot; Chrome is selected first. Windows 10 Pro 1909 (18363.900) Add and remove update channels in an easy terminal way I know there is a GUI in Ubuntu Software &amp; Updates to enable the update channels   updates proposed backports security   as shown in this screenshot:    I am looking for an easy way to do this from within a terminal using commands such as    sudo apt-add-update enable updates sudo apt-add-update enable proposed sudo apt-add-update enable backports sudo apt-add-update enable security  sudo apt-add-update disable updates sudo apt-add-update disable proposed sudo apt-add-update disable backports sudo apt-add-update disable security   and an additional thing  sudo apt-add-update enable default  sudo apt-add-update disable default     Some examples for a better understanding   An empty sources.list   cat /etc/apt/sources.list  &lt;empty&gt;  sudo apt-add-update enable security  &lt;empty&gt;   One enabled repository (main)   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main deb http://archive.ubuntu.com/ubuntu wily-security main   Two or more enabled repositories in one or two lines   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main universe   or   deb http://archive.ubuntu.com/ubuntu wily main deb http://archive.ubuntu.com/ubuntu wily universe  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu wily-security main universe   or  deb http://archive.ubuntu.com/ubuntu wily main deb http://archive.ubuntu.com/ubuntu wily-security main deb http://archive.ubuntu.com/ubuntu wily universe deb http://archive.ubuntu.com/ubuntu wily-security universe   With deb-src entries   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main universe deb-src http://archive.ubuntu.com/ubuntu wily main universe  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main universe deb-src http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu wily-security main universe deb-src http://archive.ubuntu.com/ubuntu wily-security main universe   With inactive deb-src entries   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main universe # deb-src http://archive.ubuntu.com/ubuntu wily main universe  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main universe # deb-src http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu wily-security main universe   The default thing    cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily-security universe  sudo apt-add-update enable default  deb http://archive.ubuntu.com/ubuntu wily universe deb http://archive.ubuntu.com/ubuntu wily-security universe   Only one entry and the disable action   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily-security universe  sudo apt-add-update disable security  &lt;empty&gt;   Different or the same servers for different or the samerepositories, respect each server   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily universe deb http://us.archive.ubuntu.com/ubuntu wily main  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily universe deb http://us.archive.ubuntu.com/ubuntu wily main deb http://archive.ubuntu.com/ubuntu wily-security universe deb http://us.archive.ubuntu.com/ubuntu wily-security main   Different Ubuntu releases for different repositories, respect each release   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu trusty main  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu trusty main deb http://archive.ubuntu.com/ubuntu wily-security main universe deb http://archive.ubuntu.com/ubuntu trusty-security main   PPAs or other package sources (not-Canonical)  in the sources.list?  Ignore! Don't change the protocols, e.g. https, http, tor, ... Trouble trying to use Windows Search to search for file with a question mark in the content It seems that Windows Search is having trouble when I specify a question mark character as the content that I'm searching for within my files.  I've tried:   content:? content:"?" content:"\?" content:\? content:%3f content:"%3f" content:\3f content:"\3f" content:\00\00\00\3F   but each of these yield no results when I do indeed have files that contain ? within the scope of the search. If I instead search for something like content:happy it will indeed find all files with the phrase "happy" within those same files.  My assumption is that Windows Search is treating some characters such as the question mark as a special character likely for the purpose of wild card expressions. To test this theory I've also searched for files containing an asterisk * and indeed I have the same issue as when searching for content of question mark. What I'm wondering is whether there is any way to get a search to work where I can search for a literal expression without any type of wildcard matching or at least a way to escape the special characters within the expression.  By the way I'm using Windows 7 Enterprise. I know they have their adherents, but do more or less esoteric branches of mathematics such as Category Theory and/or Quantum Logic provide powerful tools for new theory development or are they just occasionally-useful presentational frameworks?  More particularly, is it worth investing the time to study these formalisms? For symmetric stable distributions, why is $\alpha \le 2$? Infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log (n)}$ Recently, I encountered a problem about infinite series. So my question is how to know whether the infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log (n)}$ is convergent? Reading the extension of files in a directory with Java? Mid 2012 MBP shuts down claiming no power with charge at 30% or 40% or more I have two mid 2012 MBPs. Sometime last year they both started randomly shutting down and showing the 'please plug me in to power' image when trying to start them up. That would be fine if the batter was at 1% or less but this happens when the battery is at anywhere from 30% to as high as 48% full. The power cycle info says 500 cycles or so. Both of them do this. They are both patched current, always. I asked Apple they suggested NVRAM PRAM and SMC reset, as expected, which had no effect. Any ideas? I have been reading Geoff Cumming's 2008 paper  [~200 citations in Google Scholar] -- and  am confused by one of its central claims. This is one in the series of papers where Cumming argues against $p$-values and in favour of confidence intervals; my question, however, is not about this debate and only concerns one specific claim about $p$-values.   Let me quote from the abstract:     This article shows that, if an initial   experiment results in two-tailed $p= .05$, there is an $80\%$   chance the one-tailed $p$-value from a replication will fall in   the interval $(.00008, .44)$, a $10\%$ chance that $p &lt; .00008$,   and fully a $10\%$ chance that $p &gt; .44$. Remarkably, the   interval—termed a $p$ interval—is this wide however large   the sample size.   Cumming claims that this "$p$ interval", and in fact the whole distribution of $p$-values that one would obtain when replicating the original experiment (with the same fixed sample size), depend only on the original $p$-value $p_\mathrm{obt}$ and do not depend on the true effect size, power, sample size, or anything else:     [...] the probability distribution of $p$ can be derived without   knowing or assuming a value for $\delta$ (or power). [...] We do not assume any prior knowledge   about $\delta$, and we use only the information $M_\mathrm{diff}$ [observed between-group difference] gives about $\delta$ as   the basis for the calculation for a given $p_\mathrm{obt}$ of the distribution of   $p$ and of $p$ intervals.      $\quad\quad\quad$    I am confused by this because to me it seems that the distribution of $p$-values strongly depends on power, whereas the original $p_\mathrm{obt}$ on its own does not give any information about it. It might be that the true effect size is $\delta=0$ and then the distribution is uniform; or maybe the true effect size is huge and then we should expect mostly very small $p$-values. Of course one can start with assuming some prior over possible effect sizes and integrate over it, but Cumming seems to claim that this is not what he is doing.  Question: What exactly is going on here?    Note that this topic is related to this question:  with an excellent answer by @whuber. Cumming has a paper on this topic to:  -- but that one is clear and unproblematic.  I also note that Cumming's claim is repeated several times in the 2015 Nature Methods paper  that some of you might have come across (it already has ~100 citations in Google Scholar):     [...] there will be substantial variation in the $P$ value of repeated experiments. In reality, experiments are rarely repeated; we do not know how different the next $P$ might be. But it is likely that it could be very different. For example, regardless of the statistical power of an experiment, if a single replicate returns a $P$ value of $0.05$, there is an $80\%$ chance that a repeat experiment would return a $P$ value between $0$ and $0.44$ (and a $20\%$ change [sic] that $P$ would be even larger).   (Note, by the way, how, irrespective of whether Cumming's statement is correct or not, Nature Methods paper quotes it inaccurately: according to Cumming, it's only $10\%$ probability above $0.44$. And yes, the paper does say "20% change". Pfff.) Plotting in the Complex Plane Particle energy in general relativity? Assume that a particle is moving with four-velocity $u^\mu$ through a spacetime with metric $g_{\mu\nu}$ ($-+++$ signature).  Let us also assume that there exists a time-like vector field $t^\mu=(1,0,0,0)$.  Is it generally true that the energy $E$ of a particle is given by the following expression:  \begin{eqnarray*} E &amp;=&amp; -mt_\mu u^\mu\\ &amp;=&amp; -mg_{\mu\nu} t^\nu u^\mu\\ &amp;=&amp; -mg_{00}u^0\\ &amp;=&amp; -mg_{00}\frac{dt}{d\tau}? \end{eqnarray*}  In the special case that $t^\mu$ is a Killing vector and $u^\mu$ is tangent to a geodesic then $E$ is a constant of motion of the particle. But the energy of a particle need not remain constant in the general case - is that true?  If $E=-mt_\mu u^\mu$ is indeed the particle mass/energy then does it act as a source of spacetime curvature given that it depends on the $00$-component of the spacetime metric ifself? I suppose that is not a problem. Is there a way to truly delete all deleted files? I know that on the windows operating system, when you delete a file it's still recoverable.  I'd like to avoid simply paving the harddrive with zeros as I would like to keep my OS installation as is, but is there a way to truly delete files that have been previously deleted? Strange, unexpected behavior (disappearing/changing values) when using Hash default value, e.g. Hash.new([]) How to reconcile the cashless human/Federation society with human traders and merchants From a variety of sources, including , we know that the Federation (or at least the humans) don't use money. This raises the problem that humans frequently visit worlds where there is currency, and, in the case of DS9, operate a station that has currency frequently in use (for example, Federation personnel frequently attend Quark's bar). Additionally, we see human traders.   My question is, how do humans get "money" (credits, latinum, etc.)? How would a human even get the resources to purchase their own merchant ship or the resources to fill its cargo holds with merchandise? If Federation personnel can simply be given money for the asking, why haven't they poured so much money down Quark's throat that he chokes on it? JavaFX accordion with multiple open panes Finding Maximum value of consecutive positive integers with constraints Let, $x,y,z$ be consecutive positive integers such that $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} &gt; \frac{1}{10}$ I need to find the maximum value of $x+y+z$ ?  My attempt:  I tried guessing first, To maximise $x+y+z$ it is necessary to have high value for $x$, But not too high which will contradict the constrain of the problem. As we can roughly split the $0.1$ into three parts so I started with numbers closer to $30$ with trial an error I got that for $x=29$ we get the optimum and final result would be 90 (=max. value of $x+y+z$).   Is there any way to arrive at this conclusion with using inequalities? Any hints will be appreciated... Projection of a point onto a simple convex polytope I have a convex polytope described by the intersection of a hypercube and two parallel lower and upper hyperplanes cutting through the hypercube. I want to find the projection of a point onto the polytope. I read the question  and see that the general problem of finding a projection onto a convex polytope can be solved with quadratic programming. However, taken alone, projection onto a hypercube or a hyperplane is trivial. For the hypercube, each dimension is defined by a lower+upper bounds and we just pull each dimension within those bounds, which take $O(n)$ time in $n$ dimensions. For the hyperplane just find the projection onto it. So I'm wondering whether there is simpler method for finding such a projection, maybe somehow combining the two independent projections. How to scale dimensions proportionally to a specific size? I modeled a man and would like to scale him down to be exactly 6' tall (Z dimension), however I cannot find a way to do that. I know I can go to front ortho view and and use the normal scale S  key to scale it, however that requires some pretty specific fine tuning in order to get it to the right dimensions.  I'd like to be able to essentially type "6" into the Z dimension (don't worry I have it setup in imperial) and have it scale the X and Y dimensions proportionally. I am thinking of moving my extensive eBook library to iBooks or Kindle. Has anyone done this, and what does it take?  I just don't want book libraries in multiple proprietary formats, and have to look for content across apps.