How can we break formula mentioned below into into two lines?   $\displaystyle \boldsymbol{{\left( {x\log x} \right)^{\log \log x}}\left\{ {\frac{1} {{x\log x}}\left( {\log x + \log \log x} \right) + \left( {\log \log x} \right)\left( {\frac{1}{x} + \frac{1}{{x\log x}}} \right)} \right\} }$   FYI: I'm using two column layout and this symbol is getting overlapped over next column.   EDIT: Added sample tex file having issue mentioned above:   \documentclass[addpoints,answers,10pt]{exam} \usepackage[margin=0.7in,headheight=3.5\baselineskip,headsep=1\baselineskip,includehead]{geometry} \usepackage{multicol} \usepackage[T1]{fontenc} \usepackage{graphicx} \usepackage{tabularx} \usepackage{nonfloat} \usepackage{caption} \usepackage{amsmath,amssymb} \usepackage{lmodern} \usepackage{textcomp} \usepackage{ifpdf} \usepackage{chemfig} \usepackage[export]{adjustbox} \begin{document}   \begin{multicols}{2} \begin{questions} \question[4] Ref: (111)\\If\ $\displaystyle \boldsymbol{y = {\left( {x\log x} \right)^{\log \log x}} }$ , then\ $\displaystyle \boldsymbol{\frac{{dy}} {{dx}} =  }$ \begin{choices} \choice $\displaystyle \boldsymbol{{\left( {x\log x} \right)^{\log \log x}}\left\{ {\frac{1} {{x\log x}}\left( {\log x + \log \log x} \right) + \left( {\log \log x} \right)\left( {\frac{1} {x} + \frac{1} {{x\log x}}} \right)} \right\} }$ \choice $\displaystyle \boldsymbol{{\left( {x\log x} \right)^{x\log x}}\log \log x\left[ {\frac{2} {{\log x}} + \frac{1} {x}} \right] }$ \choice $\displaystyle \boldsymbol{{\left( {x\log x} \right)^{x\log x}}\frac{{\log \log x}} {x}\left[ {\frac{1} {{\log x}} + 1} \right] }$ \choice none of these  \end{choices} \end{questions} \end{multicols} \end{document}
I am having the following equation:  \begin{equation}   Q(\lambda,\hat{\lambda}) = -\frac{1}{2} P(O \mid \lambda ) \sum_s \sum_m \sum_t \gamma_m^{(s)} (t) \left( n \log(2 \pi ) + \log \left| C_m^{(s)} \right| + \left( \mathbf{o}_t - \hat{\mu}_m^{(s)} \right) ^T C_m^{(s)-1} \left(\mathbf{o}_t - \hat{\mu}_m^{(s)}\right) \right) \end{equation}   which does not very well fit on one line. How can I split this over two lines? What I have in mind is that I specify the splitting place, and that the first line is left aligned and the second line right aligned to make clear that it is still the same equation.  The linebreak \\ does not work.
How to install Android Studio on Ubuntu? Ubuntu installation does not recognize drive partitioning I have a 1TB drive and installed Windows 7 on a 128GB partition.  When I now try to install Ubuntu 11.04 it does not recognize the Windows partition but offers the complete 1TB drive to install Ubuntu on instead. It displays:    However, in the Ubuntu Disk Utility the Windows partitions are recognized.    What do I need to do in order for Ubuntu to recognize the Windows 7 partition and install Ubuntu as a dual boot?   Response to comments  The following commands were executed and the results are shown below:  fdisk -l  WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk  doesn't support GPT. Use GNU Parted.  Disk /dev/sda: 1000.2 GB, 1000204886016 bytes 255 heads, 63 sectors/track, 121601 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x34a38165     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *           1          13      102400    7  HPFS/NTFS Partition 1 does not end on cylinder boundary. /dev/sda2              13       16318   130969600    7  HPFS/NTFS  Disk /dev/sdb: 500.1 GB, 500107862016 bytes 255 heads, 63 sectors/track, 60801 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x14a714a6     Device Boot      Start         End      Blocks   Id  System /dev/sdb1               1       60801   488384001   83  Linux   parted -l  Warning: Unable to open /dev/sr0 read-write (Read-only file system).  /dev/sr0 has been opened read-only. Error: /dev/sr0: unrecognised disk label is a light side power that many Jedi, including  are capable of. In Episode I, Qui-Gon uses it twice (once to outrun droids and once on Jar Jar's tongue), Obi-Wan uses it once and Anakin uses high speed reflexes for the entire duration of the pod race with no formal training.  According to  the power has a high drain and requires a longer recovery period than other powers. And then of course there are hilarious drawbacks such as .  But why wasn't this power used in the following scenarios (and many, many others):   The Redshirt Jedi who accompanied Windu to arrest Palpatine, before they were summarily dispatched to the Nether. Qui-Gonn, to avoid a lightsaber through his gut. Yoda, to avoid flying senate seats. By Windu, who is supposedly a notable practitioner. How do I get my PCs to not be a bunch of murderous cretins? Most RPGs teach you that casual violence is the best solution to all your in-game problems. This is so well established a part of the vast majority of RPGs that there are entire satire RPGs like Greg Costikyan's  and John Tynes'  dedicated to showcasing the issue. Even now that the '80's anti-RPG hysteria is past, you see more sober critiques of endemic violence in RPGs in places like . In most RPGs, PCs become inured to murder and other antisocial activities very quickly, and enter the depths of depravity that wouldn't be appropriate in the worst parts of the world. Armed robbery, mass murder, and genocide become routine parts of an adventurer's day, something only stick-in-the-mud characters with the most extremely stated ethics object to. , even though it is not properly applied to just any conflict, is a PC's friend and they generally escalate any conflict in that direction. The sophistication of the gamer mindset towards introspection on this issue can be demonstrated in that the most meaningful question usually debated about in-game violence is some variant on &quot;but should we kill the noncombatant children&quot; or &quot;can we just murder people out of hand as long as they're from a typically evil race?&quot; In the real world, we generally a priori regard anyone having to have this discussion as a monster already. (P.S. The &quot;wipe out a given evil race&quot; thing isn't the point of this question; it is only mentioned to indicate that it's only &quot;that far&quot; that usually causes ethical handwringing from players, when that is a really quite extreme case and we should be uncomfortable with casual violence a lot sooner. ) What I'd like to have is a more realistic in-game treatment of conflict.  People getting wounded and giving up, taking and ransoming of prisoners, not always escalating a fistfight to weapons, not always escalating weapon combat to killing, etc.  Heck, as I write this, I'm watching an episode of Adventure Time with my daughter and the protagonists snuck in and rescued a princess kidnapped by the Ice King and then exit right next to his sleeping form. I thought, &quot;If this were D&amp;D they'd all be carefully coordinating a coup de grace to kill him in his sleep on the grounds that he inconvenienced them.&quot;  The problem isn't limited to D&amp;D of course, sci-fi PCs are happy to neutron bomb planets for convenience too, for example. I'm not part of the &quot;D&amp;D is Satanic&quot; crowd obviously, but I frankly do have compunctions about continually playing in games where the taught behavior is uncomfortably equivalent to the worst examples of human behavior we see on the nightly news. How can I give my PCs a newfound respect for human life? When should I start the DLC? I'm late to the Borderlands 2 party, but I picked up the Season Pass for a steal.  I'm still only in the teens as far as my level is concerned.  However, there are now 3 DLC packs out and I've got them all installed.  Sometimes it's tempting to go away from the main quest and just jump into something new and potentially interesting.  In BL1, I played through the DLC between playthroughs of the game, treating the add-ons like continuations of the game post-final-boss.  I'm not sure if this is a good idea in BL2 (or even if it was smart in BL1, honestly...)  Is there a recommended level for starting the DLCs?  Will I encounter enemies that are too hard if I go early, or too easy if I go late?  Are there some weapons or quest rewards that I really can't get the most of until after I'm a certain level? When should I use velocity versus addForce when dealing with player objects? Using Rule of Three to obtain confidence interval for a binomial population I have a large population of data instances (say, 1000 instances) that are either of class1 or of class2. I would like to obtain a confidence interval for how many instances are of class1 without exhaustively checking all instances. I have randomly sampled 50 instances, and all 50 were of class1. I used the  to determine that a 95% confidence interval for the percentage that an instance is of class1 is  [0.94, 1].  From my sampling, I know that at least 50 instances are of class1. For the remaining 1000 – 50 = 950 instances whose classes are unknown, I assume I can apply the [0.94, 1] confidence interval found above. Therefore, can I conclude that, with a 95% confidence, there are at least 50 + (1000 – 50)(0.94) = 943 instances from the population of 1000 that are of class1?  If this conclusion isn’t statistically sound, how can I obtain a confidence interval for class1? Logical Volume, Physical Volume and Volume Groups Please can someone explain to me the meaning of Logical Volume, Physical Volume and Volume Groups? Of what importance and advantage are they in linux? I am creating a model of a glass and I would like to put a drawing on it (a png picture).  I know how to do it using Blender Render, but not with Cycles Render. Help :) Omitting article “the” in front of plural nouns I'm helping someone learn English (second language), and I'm having trouble explaining when to use the and when not to. For example:     Students learn better when teachers are passionate about teaching.   versus     The students learn better when the teachers are passionate about teaching.   There's a subtle difference. The first one is a general statement, whereas the second might imply a study where a group of students learned better than another.  Is the difference simply that, general v. specific? Ubuntu 14.04 has visual artifacts and freezes Convert date to another timezone in JavaScript Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective Let $f: A \rightarrow B$ be a function. How can we show that for all subsets $S$ of $A$, $S \subseteq f^{-1}(f(S))$? I think this is a pretty simple problem but I'm new to this so I'm confused.  Also, how can we show that $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective? Can you use twinned spell on the same target? So me and my DM have been arguing on how Twinned spell works. Twinned spell:  When you cast a spell that targets only one creature and  doesn't have a range of self, you can spend a number of  sorcery points equal to the spell's level to target a second  creature in range with the same spell (1 sorcery point if  the spell is a cantrip).  I argued that &quot;a second creature&quot; can be a the same target as it is not worded as &quot;another creature&quot; For this example counter spell with twinned spell.  A wizard casts fireball on me I use CounterSpell#1 with Twinned Spell Wizard casts CounterSpell on my CounterSpell#1 I use him as the same target for my twinned Spell CounterSpell#2  Result countered Is this possible? mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$ I stumbled across this problem  Find $\,10^{\large 5^{102}}$ modulo $35$, i.e. the remainder left after it is divided by $35$  Beginning, we try to find a simplification for $10$ to get: $$10 \equiv 3 \text{ mod } 7\\ 10^2 \equiv 2 \text{ mod } 7 \\ 10^3 \equiv 6 \text{ mod } 7$$ As these problems are meant to be done without a calculator, calculating this further is cumbersome. The solution, however, states that since $35 = 5 \cdot 7$, then we only need to find $10^{5^{102}} \text{ mod } 7$. I can see (not immediately) the logic behind this. Basically, since $10^k$ is always divisible by $5$ for any sensical $k$, then: $$10^k - r = 5(7)k$$ But then it's not immediately obvious how/why the fact that $5$ divides $10^k$ helps in this case. My question is, is in general, if we have some mod system with $a^k \equiv r \text{ mod } m$ where $m$ can be decomposed into a product of numbers $a \times b \times c \ \times ...$, we only need to find the mod of those numbers where $a, b, c.....$ doesn't divides $a$? (And if this is the case why?) If this is not the case, then why/how is the solution justified in this specific instance? How can I develop for iPhone using a Windows development machine? Is there any way to tinker with the iPhone SDK on a Windows machine? Are there plans for an iPhone SDK version for Windows?  The only other way I can think of doing this is to run a Mac VM image on a VMWare server running on Windows, although I'm not too sure how legal this is. biblatex: per-entry language switching According to biblatex manual (p.24), the hyphenation field in a bib-entry switches language on per-entry basis:     hyphenation field    The language of the bibliography entry. The identifier must be a language name   known to the babel package. This information may be used to switch hyphenation   patterns and localize strings in the bibliography.   This functionality seemed to not work. I just used an example of bib base that comes with biblatex documentation to print the entire bibliography.   \documentclass[a4paper]{article} \usepackage[T1]{fontenc} \usepackage[german,american]{babel} \usepackage{csquotes} \usepackage[style=numeric,backend=biber]{biblatex} \addbibresource{biblatex-examples.bib} \begin{document} \nocite{*} \printbibliography \end{document}   The bibliography contains few entries in German. However in the printed list of references they are formatted with english strings.     [8] Averroes. Drei Abhandlungen über die Conjunction des separaten Intellects   mit dem Menschen. Von Averroes (Vater und Sohn), aus dem   Arabischen übersetzt von Samuel Ibn Tibbon. Ed. and trans. by J. Hercz.   Berlin: S. Hermann, 1869.   Per-entry language switching is provided by the  bundle of bst style for BibTeX. Looking through biblatex internal code, I've got an impression that biblatex needs major re-implementation in order to provide similar functionality. Or am I wrong? What is the association bonus, and how does it work? I was just awarded +100 reputation on all of my Stack Exchange accounts.  What is this bonus for? It simply says "Association Bonus" on my reputation overview.  Also:   What privileges does the association bonus grant users? Can I lose the association bonus? Does it make my reputation 101 everywhere? Can I earn the association bonus on sites I haven't joined yet? Does it matter which site I earn the 200 reputation on? Will I get an association bonus every time my reputation on a site crosses 200 points? Does the association bonus allow me to answer protected questions? Does the association bonus count towards the reputation cap? Can I get the association bonus if I only have a profile on one site? What else is there to know about the association bonus? This is a  about how to handle email sent from your server being misclassified as spam.  For additional information you may find these similar questions helpful:                    Sometimes I want to send newsletters to my customers. The problem is, that some of the emails get caught as spam messages. Mostly by Outlook at the client (even in my own Outlook 2007).  Now I want to know what should be done to create "good" emails. I know about reverse lookup etc., but (for example), what about a unsubscribe link with an unique ID?  Does that increase a spam rating? Insert issue with arrays