I tried following the instructions from &quot;How to compile FFmpeg for Ubuntu&quot; at . These are: sudo apt-get update -qq &amp;&amp; sudo apt-get -y install \   autoconf \   automake \   build-essential \   cmake \   git-core \   libass-dev \   libfreetype6-dev \   libgnutls28-dev \   libsdl2-dev \   libtool \   libva-dev \   libvdpau-dev \   libvorbis-dev \   libxcb1-dev \   libxcb-shm0-dev \   libxcb-xfixes0-dev \   pkg-config \   texinfo \   wget \   yasm \   zlib1g-dev  However, I get: The following packages have unmet dependencies.  libsdl2-dev : Depends: libsdl2-2.0-0 (= 2.0.8+dfsg1-1ubuntu1.18.04.4) but 2.0.9+dfsg1-1ubuntu1 is to be installed E: Unable to correct problems, you have held broken packages.
After upgrading from 10.04 to 12.04 I am trying to install different packages.  For instance ia32-libs and skype (4.0).  When trying to install these, I am getting the 'Unable to correct problems, you have held broken packages' error message.   Output of commands:  sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   After running this:  sudo dpkg --configure -a foo@foo:~$ sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
Jensen's Inequality implies convexity? Suppose $\phi$ is a real function on $\mathbb{R}$ such that $$\phi \Bigl(\int_0^1f(x)\,dx\Bigr)\leq \int_0^1 \phi(f)\,dx$$ for every real bounded measurable function $f$. Prove that $\phi$ is then convex.    This one is in Rudin's Real and Complex Analysis, page 74, and, to be quite honest, I am unsure what my first step to solve this problem should even be. To help think of a general methodology, I attempted this similar question, from page 71 of the same book:      Assume $\phi$ is a continuous real valued function on $(a,b)$ such that $$\phi\Bigl(\frac{x+y}{2}\Bigr)\leq\frac{\phi(x)+\phi(y)}{2}$$ for all $x, y\in (a,b).$ Prove that $\phi$ is then convex (the conclusion does not follow if continuity is omitted from the hypothesis).   I take it that the latter question is just a special case of the former (assuming $\phi$ is bounded on $(a,b)$), so I attempted to solve the latter problem first. My attempt was to note that \begin{align*} \phi\big(\lambda x + (1-\lambda)y\big) &amp;\leq \phi\Bigl(\frac{2\lambda x + 2(1-\lambda)y}{2}\Bigr) \\ &amp;\leq \frac{1}{2}\Bigl(\phi\bigl(2\lambda x\bigr)+\phi \bigl(2(1-\lambda)y\bigr)\Bigr) \\ &amp; \leq \phi\bigl(\lambda x\bigr)+\phi\bigl((1-\lambda)y\bigr) \end{align*} with the latter inequality justified simply by applying the hypothesis again twice to the previous expression.   From here, however, I am stuck; I cannot justify "popping out" the $\lambda$ and the $(1-\lambda)$ in the last inequality via some bound afforded by the hypothesis and/or the continuity of $\phi$. How can I verify a Google authentication access token?  I need to somehow query Google and ask: Is [given access token] valid for the [example@example.com] Google account?  Short version: It's clear how an access token supplied through the  can be used to then request data from a range of Google services. It is not clear how to check if a given access token is valid for a given Google account. I'd like to know how.  Long version: I'm developing an API that uses token-based authentication. A token will be returned upon provision of a valid username+password or upon provision of a third-party token from any one of N verifiable services.  One of the third-party services will be Google, allowing a user to authenticate against my service using their Google account. This will later be extended to include Yahoo accounts, trusted OpenID providers and so on.  Schematic example of Google-based access:    The 'API' entity is under my full control. The 'public interface' entity is any web- or desktop-based app. Some public interfaces are under my control, others will not be and others still I may never even know about.  Therefore I cannot trust the token supplied to the API in step 3. This will be supplied along with the corresponding Google account email address.  I need to somehow query Google and ask: Is this access token valid for example@example.com?  In this case, example@example.com is the Google account unique identifier - the email address someone uses to log in to their Google account. This cannot be assumed to be a Gmail address - someone can have a Google account without having a Gmail account.  The Google documentation clearly states how, with an access token, data can be retrieved from a number of Google services. Nothing seems to state how you can check if a given access token is valid in the first place.  Update The token is valid for N Google services. I can't try a token against a Google service as means of verifying it as I won't know which subset of all Google's services a given user actually uses.  Furthermore, I'll never be using the Google authentication access token to access any Google services, merely as a means of verifying a supposed Google user actually is who they say they are. 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I'm really outgrowing the two-screen setup, and am strongly considering bringing in my home monitor (which is almost never used) to bolster my usable space. If I can't, then my alternative is to replace one of these Dells with that Samsung, to give me at least a "little" more space.  (Before you ask, there's probably no chance I can get my company to spring for a second video card and third monitor. Even if I could, it would not be politically expedient, as a number of my other coworkers are already pretty jealous at my setup.) I have some Python code that makes Raster Attribute Tables for GeoTiffs using GDAL.    In ArcGIS I can see these attribute tables fine and they behave how I like (as classifications) but in QGIS the whole concept of an attribute table seems to be missing.    Is there any way to access a RAT in QGIS? How can you prove that a function has no closed form integral? How do I escape a backtick ` within in-line code in Markdown? 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I rebooted the phone, the video was there, but I couldn't play it from any media player on Android. It's in mp4 format.    So I tried to open it on PC and Mac with different video player, like VLC, quick Time, Windows Media Player etc., but none of them can play it. I know that the video is corrupted, but I believe it's repairable, since it got more than a GB in size. Is there anything that I can try  to repair the video file? The video is really important. Sorry to start a subjective question, but want to understand "own.sty" file.  Other than all \usepackage{} what sort of other commands can be added to the makeyourown.sty file.  Can you include \let command, and \newcommands in it.   What sort of precaution / structure newbies should follow. How can I mass rename files? I've got a bunch of files named with a the pattern 99 - DescriptiveName.txt and I'd like to remove the number from the front so I just have DescriptiveName.txt.  How can I do this? 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