I am trying to typeset song lyrics in Hindi, where I want a bar over an "a" and an "i". I found \={} and \macron{} which both produce a nice bar over an "a", but the bar over an "i" (without the dot) is too long for my taste, because the bars appear connected when an "i" follows an "a" as in S\={a}\={\i} S\macron{a}\macron{\i}:    Is there a way I can make the bar over an "i" shorter?
Macrons appear really wide on all characters, but especially so on the i. Is it possible to make them less wide?  \documentclass{article} \begin{document} Tac\=e, M\=arc\=o, \=unus, f\=\i li\=\i? \end{document}
How much to store luggage at SFO for 24 hours? I want to install Ubuntu on the C: partition where my Windows 7 is, simply to replace the systems. I've also tried to install it on another partition (without formating it), which failed!  All I get is:      No root file system is defined. Please correct this from the partitioning menu.   I want to install Ubuntu without formatting any of my partitions. Is that possible? Proving $\sup B=\inf A$ Let $A$ be a nonempty and bounded below, and define $B= \{b\in \mathbb{R}: b$ is a lower bound for $A\}$. Show sup$B$ = inf$A$.   So far I have: Let $A$ be nonempty and bounded below. This implies $\exists l \in A, \forall a \in A, l\leq a$ and $l =$ inf$A$. Let $B = \{b\in \mathbb{R}: b$ is a lower bound for $A\}$ and let $M=$ sup$B$. This implies $\exists b\in B, \forall b \in B, b\leq M$. By definition of $B$, we know inf$A \in B$. Since $b\leq$ sup$B$, with sup$B$ the largest element in $B$, we have inf$A \leq M =$ sup$B$, so inf$A \leq$ sup$B$.  I realize I have to prove that sup$B \leq$ inf$A$ to get that sup$B$=inf$A$. I am having trouble doing so.   Part B: Use (a) to explain why there is no need to assert that greatest lower bounds exist as part of the Axiom of Completeness. System.FinalException: Record is read-only: Trigger.updateCompetitors: line 24 $(\Bbb R,+)$ is a topological group. Is there any other group structure on $\Bbb R$ such that it is still a topological group and this group is not isomorphic to $(\Bbb R,+)$ ?  Refer to  for the general problem. In that problem I have conjectured that there is no such group however I couldn't prove it. What does \s! do? Break a previous commit into multiple commits So I am running on Windows 7 (64-bit) Home Premium with 12 GB RAM (Intel Core i7 920).  I have restricted the Page File to 400MB since it was eating up a lot of space om my SSD (that is 80GB).   After that I sometimes get the "low memory"-warning, like this, except for the behold-comment:   When I get those warning I have usually a lot of RAM available; when I check Resource Manager I have over 2GB "Free" and over 2GB "Available" - usually more than that.  The diskspace on all my drives have over 10GB free.  So the question is - why does Windows complain? It actually restarted by computer (hard boot) when it happened, and as I said - lots or RAM available. Are there any distinct finite simple groups with the same order? In finite group theory, it's often quite easy to show that there are no simple groups of a given order $n$.  My question is different: is there some natural number $n$ such that there are two non-isomorphic simple groups of order $n$?  The two easiest families of finite simple groups - $\mathbb{Z}_p$ for $p$ a prime and $A_n$ for $n\ge5$ - clearly don't yield any examples.    It should be possible to check this using the , but I don't know enough about the fabled 'sixteen infinite families of groups of Lie type' to do the check myself.  Also, if the answer is 'no', I'd be much more interested to see an elementary(ish) proof than I would be to see a proof that relies on over 3,000 pages of non-stop hard group theory. Wrapped hexagon topology When a square is wrapped at the edges, obtains a torus. Is it possible to do the same for a hexagon?  What is the shape/topology of wrapping a hexagon?     Note: I was just reading this  and came up with this question. I'm a physicist. Why did the Nazgûl not attack a second time at Weathertop? I want to prove with mathematical induction that:  $$\sum_{i=1}^n i \cdot i! = (n+1)! - 1$$  So in the first step we define $n = 1$:  $$\sum_{i=1}^1 i \cdot i! = 1 \cdot 1! = 1 = 2! - 1$$  In the second step we define $n = n + 1$:  $$\sum_{i=1}^{n+1} i \cdot i! = \sum_{i=1}^n i \cdot i! + (n+1)(n+1)!$$ $$\implies (n+1)! - 1 + (n+1)(n+1)!$$  This can now be simplified to $(n+2)(n+1)! - 1$ but I do not see how...  We could do $(n+1)!(-1 + (n+1)) = (n+1)! \cdot n$ but still this will not be the same as above.  What did I miss?  Bodo What are some scenarios where FTL information transfer would violate causality? I've always heard people saying, "Faster than light information transfer can't happen because it would violate causality!  Effects can precede their causes!"  However, I'm trying to think of a situation where this would happen.  I'm sure it has something to do with relativity or something like that.  I sort of understand that people going faster perceive time slower.  Can someone help illuminate this for me by showing a scenario where causality is clearly violated due to FTL information transfer? Maximum Likelihood Estimator for $\theta$ when $X_1,\dots, X_n \sim U(-\theta,\theta)$ Exercise :     Calculate a Maximum Likelihood Estimator for the model $X_1,\dots, X_n \; \sim U(-\theta,\theta)$.   Solution :  The distribution function $f(x)$ for the given Uniform model is :  $$f(x) = \begin{cases} 1/2\theta, \; \; -\theta \leq x \leq \theta \\ 0 \quad \; \; , \quad\text{elsewhere} \end{cases}$$  Thus, we can calculate the likelihood function as :  $$L(\theta)=\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n\mathbb I_{[-\theta,\theta]}(x_i)= \bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[0,\theta]}(|x_i|) $$  $$=$$  $$\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[-\infty,\theta]}(|x_i|)\prod_{i=1}^n \mathbb I_{[0, +\infty]}(|x_i|)$$  $$=$$  $$\boxed{\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[-\infty,\theta]}(\max|x_i|)}$$  Question : How does one derive the final expression in the box from the previous one ? I can't seem to comprehend how this is equal to the step before.  Other than that, to find the maximum likelihood estimator you need a $\theta$ sufficiently small but also $\max |x_i| \leq \theta$ which means that the MLE is : $\hat{\theta} = \max |x_i|$. On Knoppix-based distros, you get a nice Tux logo on the left of the screen during text boot. Is this possible to get on Ubuntu? Yesterday, I tried to dualboot Ubuntu 16.04 onto my hard drive, creating a new partition for Ubuntu alongside my existing Windows 8. First, I disabled the fast-boot option in Windows 8, and still GRUB did not load, and it went directly to Windows boot-up. Then I did some research and found this article:     Basically, I issued the BCDEdit command in Windows, and entered in the following code:  bcdedit /set {bootmgr} path \EFI\ubuntu\grubx64.efi   When I reboot, I get a basic GRUB2 terminal, and after I type in the exit command, then a second Shell prompt appears, and after typing the exit command again, the GRUB2 menu to select the OS to boot finally appears... with only Ubuntu and Ubuntu memory test as options, not Windows 8.  After booting into Ubuntu, I tried to run the Boot-repair Utility, but that shows this following error:   How do I approach this problem? The Pastebin log is here:   Thanks for the help! How do I access a field value for an entity (e.g. node) object? node_load((int) $nid) loads a fully-populated node entity. $node-&gt;title-&gt;value gets the title, but how do I access field values in Drupal 8? I'm using Ubuntu 11.04 and I want to free up some space in my root directory, which is overloaded. I especially want to change the path used for installing applications (they are getting installed directly to the root drive).  Another consideration is that I'm working on a MySQL database server. The server is installed in the root directory itself, so I don't want to  risk losing any data.  Please give me some tips to help sort out this problem. How do I list all available shell builtin commands? We know bash supports number of  buitin commands  like:  $ type type cd help command type is a shell builtin cd is a shell builtin help is a shell builtin command is a shell builtin   I want to get list of all available shell builtin commands. How do I do that by command-line? Greek numbering