Prove that $\cos A + \cos B + \cos C \geq \frac{1}{4}(3 + \cos(A - B) + \cos(B - C) + \cos(C - A))$
Prove this inequality $\sum \cos{A}\ge\frac{1}{4}(3+\sum\cos{(A-B)})$
Parse JSON with R Real analysis - proof approach help How do the tens­es and as­pects in English cor­re­spond tem­po­ral­ly to one an­oth­er? Gedit has a transparent background since upgrade to 16.10 Since I upgraded to from 16.04 to 16.10, gedit has strange new "feature": its background is totally transparent.    Where can this come from ?  Notice I'm using Unity and don't have any specific gnome package installed besides what comes by default. Notice also that in 16.04 I used the Vivacious theme from ravefinity PPA, but I had to go back to Ambiance as Vivacious was broken in 16.10. Maybe it's related.  [EDIT] changing the 'Fonts and Colors' in gedit to any theme other than default (Kate, Solarized, Oblivion, etc..) solves the issue. So there must be a faulty gtksourview file in my home somewhare, but I can't find it... Attacks of the MAC construction $\mathcal{H}(m\mathbin\|k)$ for common hashes $\mathcal{H}$? I have ubuntu 12.04 (original) installed on a server.  How do I upgrade this to 12.04.03? Is there a way to search the latest version of every file in TFS for a specific string or regex? This is probably the only thing I miss from Visual Source Safe...    Currently I perform a Get Latest on the entire codebase and use Windows Search, but this gets quite painful with over 1GB of code in 75,000 files.    EDIT: Tried the powertools mentioned, but the "Wildcard Search" option appears to only search filenames and not contents.  UPDATE: We have implemented a customised search option in an existing MOSS (Search Server) installation. Is it okay to have a multi-language deck? I want to buy a few booster pack from a local shop that only gets them in French. Is it generally acceptable to show up to a tournament with cards in different languages? Best place to put bug reports? What websites or other resources do users of Blender have available to them to report bugs or problems with the program?  I would like to get this issue cleared in Q&amp;A format so that we can link new users with bug-report-style questions to this post. In an enumerate environment, I want a few (not all) of the items to have asterisks which appear before the number (I don't feel strongly about whether the number or the asterisk is horizontally aligned with the other numbers).  Is there a less crufty way to do this than, say, using multiple lists (or &mdash; horrors &mdash; numbering manually)?  I'm already using enumitem for an unrelated purpose, if that helps, although I didn't find a solution after a quick skim of its manual. I use both GNOME and KDE SC. In GNOME, I use Docky but I do not use it with KDE. So, I would like Docky to start up only when I login into GNOME not KDE. In KDE, there is an option to make a program autostart only in KDE. But I cannot find any such option in GNOME.    How can I do this?    Thanks in advance. Linked and Related sections contain duplicate links to questions Does causation imply correlation? GUI/Unity crashing in 16.04 LTS after updates 2018-01-04, compiz segfaults How to convert PDF to (La)TeX? I know that hardly any information is passed to the PDF when a .tex file is compiled.  But is there a tool that can convert a PDF document back to (La)TeX? How do you compile OpenSSL for x64? After following the instructions in INSTALL.W64 I have two problems:   The code is still written to the "out32" folder. I need to be able to link to both 32-bit and 64-bit versions of the library on my workstation, so I don't want the 64-bit versions to clobber the 32-bit libs. The output is still 32-bit! This means that I get "unresolved external symbol" errors when trying to link to the libraries from an x64 app. Comparing currency values as floats does not work How do I rollback a TFS check-in? I'd like to rollback a change I made recently in TFS. In Subversion, this was pretty straightforward.  However, it seems to be an incredible headache in TFS: Option 1: Get Prior Version  Manually get prior version of each file Check out for edit Fail - the checkout (in VS2008) forces me to get the latest version  Option 2: Get TFS Power Tools  Download Team Foundation Power Tools Issue rollback command from cmd line Fail - it won't work if there are any other pending changes  Option 3: Manually Undo Changes  manually undo my changes, then commit a new changeset  Question How do I rollback to a previous changeset in TFS? Scenario (Ubuntu 16.04):  I compile and run a C program (with -g, I get the traditional Segmentation Fault (core dumped), and then (of course) there is no mythical "core" file to be found. Some digging says to modify /proc/sys/kernel/core_pattern with a command to the effect of: echo '|tee /home/me/my_core_folder/my_core_file' | sudo tee /proc/sys/kernel/core_pattern, and after doing this, I stop getting (core dumped) and start only getting the plain Segmentation Fault. I try things like gdb ./program_object_file.out core.pid which obviously doesn't exist (I was getting desperate), and of course try the plain gdb ./a.out followed by (gdb) core core.pid and variants of the commands where I spam the tab key desperately trying to get auto-completion to get me to where I need to be.  Question:  Is there a generalized way I can get to core dumps? I recognize that every machine that I touch seems to have a Michael Bay's Transformers-esque ability to reconfigure hardware and software such that no device I own can be expected to work normally out-of-the-box. Is there a simple algorithm/recipe I can follow to locate core dumps on my own machine as well as on other peoples' machines? I always find myself tutoring friends on stuff like this after no small amount of  work to get things working for myself and it would be nice to be able to run a command or something to get core files dumped to the directory which the executable was run from... is there any way to do this that should work on most (I would settle for "some") Linux/Unix machines? Does League of Legends have a tournament that is recognized as the 'Most Important'?