"As though" PLUS "if"
Two "if"s in a row
Let $x,y,z&gt;0$. Show that $$\sum_{cyc}(1-x)^2\ge \sum_{cyc}\dfrac{z^2(1-x^2)(1-y^2)}{(xy+z)^2}.$$ Here's what I have done. The expression $$\sum_{cyc}(1-x)\left((1-x)-\dfrac{z^2(1+x)(1-y^2)}{(xy+z)^2}\right)\ge 0$$ or $$\sum_{cyc}(1-x)\cdot\dfrac{x^2y^2+y^2z^2+xy^2z^2+2xyz-2xz^2-2x^2yz-x^3y^2}{(xy+z)^2}\ge 0.$$ But this way does not help for the starting inequality. make tail -f exit on a broken pipe I want to watch a file until a bit of text appears  I found this answer:   but when I tried it on ubuntu, it doesn't exit:  $ echo one &gt; test.txt $ echo two &gt;&gt; test.txt $ echo three &gt;&gt; test.txt $ echo four &gt;&gt; test.txt $ cat test.txt | sed '/w/ q' one two $   works as expected.  however when I try to tail the file  $ tail -f test.txt | sed '/w/ q' one two   it never exits.  tail does not stop even though the pipe is broken.  Does anybody know how to make tail exit when sed exits? Find the Galois group of $x^3-5$ over $\mathbb{Q}$. In this case, the roots of $x^3-5$ are $\{\sqrt[3]{5},\omega\sqrt[3]{5},\omega^2\sqrt[3]{5}\}.$ I think $\mathbb{Q}(\sqrt[3]{5},\omega\sqrt[3]{5})$ is the splitting field of $x^3-5.$ Then, $[\mathbb{Q}(\sqrt[3]{5},\omega\sqrt[3]{5}):\mathbb{Q}]=3,$ I think the automorphisms are: $$id$$ $$\sigma:\sigma(\sqrt[3]{5})=-\sqrt[3]{5}$$ $$\tau:\tau(\omega\sqrt[3]{5})=-\omega\sqrt[3]{5}$$ I'm not sure about what I have done. But how to determine the Galois group based on this? And how to determine the solvability of this polynomial? Urdu language not listed in my ubuntu 16.04 LTS I am a new user of Ubuntu 16.04 LTS. To my surprise it does not have Urdu Language in language support widow. Kindly help.   The given answer to  is not helping me. Why can't humans throw objects at bullet speed when the force involved seems so small? The force that propels a bullet should at least be similar in intensity to the force experienced as recoil and the force exerted on the target. But these forces seem really low (the equivalent of a shove).  If all it takes to make a small object achieve bullet speed is the equivalent of a shove, why can't humans throw objects at these speeds? I'm trying to install drivers for my Wifi on my HP All-in-one desktop. I've been told to show the output of the command "sudo lshw -C network" so here it is:  *-network description: Ethernet interface product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller vendor: Realtek Semiconductor Co., Ltd physical id: 0 bus info: pci@0000:01:00.0 logical name: enp1s0 version: 15 serial: 48:ba:4e:5c:06:5f size: 100Mbit/s capacity: 1Gbit/s width: 64 bits clock: 33MHz capabilities: pm msi pciexpress msix bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168h-2_0.0.2 02/26/15 ip=192.168.1.21 latency=0 link=yes multicast=yes port=MII speed=100Mbit/s resources: ire:31 import:e000(size=256) memory: fea04000-fea04fff memory:fea00000-fea03fff  *-network UNCLAIMED description: Network controller product: Realtek Semiconductor Co., Ltd. vendor: Realtek Semiconductor Co., Ltd. physical id: 0 bus info: pci@0000:02:00.0 version: 00 width: 64 bits clock: 33MHz capabilities: pm msi pciexpress cap_list configuration: latency=0 resources: import:d000(size=256) memory:fe900000-fe90ffff   Output from "lspci -nnk | grep -A2 0280":  02:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821CE 802.11ac PCIe Wireless Network Adapter [10ec:c821] Subsystem: Hewlett-Packard Company RTL8821CE 802.11ac PCIe Wireless Network Adapter [103c:831a] 03:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS5229 PCI Express Card Reader [10ec:5229] (rev 01) I'm stuck in full screen in the node editor. Escape isn't working, and I have no menus and no idea how to leave except to quit Blender and reopen the program. How to add coloured line before caption? .NET OpenSource projects and strong named assemblies? I have Ubuntu 14.04 and two monitors. When I open applications I need some of them to be on the primary monitor and others On the secondary. At the moment, apps always open in the primary monitor.   I have dash icons only on one (left) display, so I can't launch apps using the cursor or active window setting from Compiz. Was Elrond, in Tolkien's opinion, more inherently powerful than Galadriel? I always thought it was the other way around, but then I read this (Letter 246):     "Of the others only Gandalf might be expected to master him – being an emissary of the Powers and a creature of the same order, an immortal spirit taking a visible physical form. In the 'Mirror of Galadriel', 1381, it appears that Galadriel conceived of herself as capable of wielding the Ring and supplanting the Dark Lord. If so, so also were the other guardians of the Three, especially Elrond. But this is another matter. It was part of the essential deceit of the Ring to fill minds with imaginations of supreme power."   This "especially Elrond" confuses me. I don´t think that Elrond is inherently more powerful than Galadriel, who is described as the greatest of the Noldor, except for Fëanor (and possibly even his equal).  A quote from Unfinished Tales says:     "...In this he (Tolkien) emphasized the commanding stature of   Galadriel already in Valinor, the equal if unlike endowments of   Fëanor; and it is said here that so far from joining in Fëanor's   revolt she was in every way opposed to him."   Furthermore,      "A queen she was of the woodland Elves, the wife of Celeborn of   Doriath, yet she herself was of the Noldor and remember the Day before   days in Valinor, and she was the mightiest and fairest (so even   fairer than Arwen I would guess) of all the Elves that remained in   Middle-earth."   (The Silmarillion, of the Rings of Power)  And again...     "Galadriel was the greatest of the Noldor, except Fëanor maybe, though   she was wiser than he, and her wisdom increased with the long years."   (the Shibboleth of Fëanor)  Restating it:     "These two kinsfolk (Fëanor and Galadriel), the greatest of the   Eldar in Valinor, were unfriends for ever." "Who together with the   greatest of all the Eldar, Luthien Tinuviel, daughter of Elu Thingol,   are the chief matter of the legends and histories of the Elves."   (Unfinished Tales)  The latter means that Luthien, Fëanor and Galadriel are the chief matter of the history and legends. It seems to me that Tolkien thought of those three as the creme de la creme of the elven crop.  Reading all that I have serious problems believing that Elrond could be superior to her. As great as Elrond is, descending from Melian, he is no equal of Fëanor, who is said to be the mightiest of all elves, and if Galadriel is his equal, then there is no way that Elrond would be mightier than her.  Maybe I just read this "especially Elrond" wrong; it could as well mean that especially Elrond was deceived into thinking that he could master the ring, because that was the deceit of the ring. And Tolkien said explicitly that only Gandalf could possibly master it.  So, what do you think? The proof of shrinking coefficients using ridge regression through "spectral decomposition" I have understood how ridge regression shrinks coefficients towards zero geometrically. Moreover I know how to prove that in the special "Orthonormal Case," but I am confused how that works in the general case via "Spectral decomposition." How does one restrict number of allowed types in Java generic type Installing MinionPro fonts on Ubuntu 10.04 running TexLive 2012 I followed the instructions to install MinionPro fonts from this website.   However, when I tried to run the tex file at the bottom, I have this error message:  ! LaTeX Error: File `MinionPro.sty' not found.   Running the command kpsewhich MinionPro.sty gives the following output:  /usr/local/share/texmf/tex/latex/MinionPro/MinionPro.sty   So the system knows where MinionPro.sty is, so why can't the file compile? Grant admin rights on an application I'm want to grant a user administrative rights to one application on Windows 7. I don't want them to be able to have full admin rights, but admin rights are required for one of the applications they need to use.   Is there a way to set up a batch script or something where the user won't know it's being run as admin?  Or is there another way?  How can I accomplish this? A two column loop with one lead post I got a loop from internet (I forgot the site) for two column post view. It has a nice CSS for it too. But skipping that for the question now.  &lt;?php $counter = 1; ?&gt;                  &lt;?php query_posts( 'cat=3&amp;showposts=6' ); //Find whether the catID is 3 ?&gt;             &lt;?php while ( have_posts() ) : the_post() ?&gt;                   &lt;?php /* Two Column Support get class */ ?&gt;              &lt;?php $class = ( $counter % 2  ? ' one' : '' ) ?&gt;                  &lt;?php /* Two Column output open the div class */ ?&gt;              &lt;div class="column&lt;?php echo $class;// echo $first; ?&gt;"&gt;              &lt;?php news_format(); ?&gt;             &lt;/div&gt; &lt;!-- End Two Column Support close div class --&gt; &lt;?php $counter++; //Update counter ?&gt;   It printed my posts into 2 columns like:  ========= | 1 | 2 | --------- | 3 | 4 | --------- | 5 | 6 | =========  It's fine. But I want to print it like this:  ========= |   1   | --------- | 2 | 3 | --------- | 4 | 5 | --------- | 6 | 7 | =========  What the modification I need to do? I can't pass any custom limit into the WordPress' custom loop &lt;?php while ( have_posts() ) : the_post() ?&gt;. It's for a custom theme. I did it, but the problem is, it's showing like:  ========= |   1   | --------- | 1 | 2 | --------- | 3 | 4 | --------- | 5 | 6 | =========   is my whole bunch of code. This song by The Rolling Stones, "(I Can't Get No) Satisfaction". As a non-native speaker, I always wondered what's the exact meaning of this phrase?   Is it "I'm not getting any satisfaction" (this seems to be the most widely met translation; double negation used where single negation should have been used). Or is it "I want my satisfaction, I cannot leave without getting some" (makes much more sense to me).   Or is it something else? I've always had troubles understanding double negation as applied to English. First I was taught it's a mistake to use double negation at all, and then I see it everywhere. Mathematical induction for inequalities: $\frac1{n+1} + \frac1{n+2} + \cdots +\frac1{3n+1} > 1$ How to run firefox and firefox ESR simultaneously The main reason I want to use firefox ESR is to use a proprietary database tool for work that only allows oracle-java based web logins for linux (or a windows only thin client). I also want to use the full version of the outlook web application which only works in firefox. I don't want to run the NPAPI plugins for normal web browsing and email.   I have the repo version of firefox installed and firefox ESR installed in /opt/firefox and linked to /usr/local/firefox-esr  When I run firefox any attempt to run firefox-esr either brings up a window without the NPAPI plugins.   If I try running with the --new-instance or --no-remote options I receive the following error:  Firefox is already running, but is not responding. To open a new window, you must first close the existing Firefox process, or restart your system.   Regardless which one I start first, I can only open that one, and get the above error if I attempt to sidestep.  What makes this an especially annoying problem is that I often have to respond to emails that I need to access the database to deal with. So either I close and open many windows. Is there a statement whose undecidability is undecidable? We know there are statements that are undecidable/independent of ZFC. Can there be a statement S, such that (ZFC $\not\vdash$ S and ZFC $\not\vdash$ ~S) is undecidable?