I have to following code: \begin{align*} r^2  = \left[\frac  {23604,7 - \frac{1}{22} \cdot 253 \cdot 1942.5}  {\sqrt{[3795 - \frac{1}{22} \cdot 253^2]  [173348.4 - \frac{1}{22} \cdot 1942.5^2]  }} \right]^2 \\ \\  r^2  = \left[\frac{1265.95}{\sqrt{885.5 \cdot 1834.51}} \right]^2 \\ \\  r^2  = \left[\frac{1265.95}{\sqrt{1624458.2}} \right]^2 \\ \\  r^2  = \left[\frac{1265.95}{1274.54} \right]^2 \\ \\  r^2  = [0.99356]^2 = 0.9866 \end{align*}  and got the error:  ! Paragraph ended before \align* was complete. ! Missing $ inserted.  and a few more...can somebody spot the mistake? :&lt;
I wanted to align a set of equations to left. I found on the Internet that you can do it easily with align* environment.   I found it here:   So I did it:  \begin{align*}  f(b)-f(a)=&amp;f((b_1,b_2,\dots,b_k))-f((a_1,a_2,\dots,a_k))=\ &amp;=\sum_{i=1}^{k}[f((a_1,\dots,a_{i-1},b_i,\dots, b_k))-f((a_1,\dots,a_i,b_{i+1},\dots, b_k))  \end{align*}   Unfortunately, I got bunch of red errors saying that there are missing $s. Why? Doesn't that align* environment provide a math environment already?
The the title is self explanatory, I guess.  Why can two (or more) electric  never cross? is a dove a "she"? how to use "he" and "she" for animals? In the song &quot;Blowing in the Wind&quot; by Bob Dylan, there's a verse that reads:  Yes, and how many seas must a white dove sail Before she sleeps in the sand?  My question is, why he used &quot;she&quot; for a dove? What about other animals and other non-humans? Is there a general rule? After many unsuccessful trials based on almost everything about this topic on the Internet, I decided to ask this question again. There is almost  in this platform, but it did not work. That's why I am here.  I want to have Ubuntu 18.04 installed on my USB memory stick (SanDisk Cruzer Glide 32GB) with a persistent storage of more than 4GB (at least 23GB in my case).  I used MiniTool partition wizard to format the stick (NTFS) on Windows. Then, I used Universal USB Installer 1.9.8.2 to install Ubuntu 18.04 on the stick. Here, I tried to format the stick either fat32 or ntfs, but nothing changed. Later, I used another Ubuntu to delete the casper-rw file and create another partition with the same name by following the steps given in the link given above. Unfortunately, I couldn't make it working although I tried almost all combinations.  Can anyone give a thorough list of steps to follow in order to install it on the stick properly?  Edit: I gave ear to @c-s-cameron 's comment below and used YUMI to do that, and it worked. I believe all other answers would work, but I dont have time to give a try for all of them. Thanks all, again! I have been using the default Ubuntu 11.10 with Unity for some time now and decided to start customizing it.  I have already been able to make some changes with the gnome-tweak-tool. However, there are many themes that I get from gnome-look.org that don't appear in the gnome-tweak-tool even after putting them in the /usr/share/themes folder.  Any idea why this is happening? Thanks. Truncate a string to first n characters of a string and add three dots if any characters are removed How can I launch screensaver with a keyboard shortcut? Anthology for children; contains story about friendly Martian on postapocalyptic Earth I'm looking for the title of an anthology of children's science fiction stories from the 1950s. The best of the bunch involved a Martian who visited earth, and realized we'd blown ourselves up in a nuclear war and had fallen into savagery. The Martian is a vegetarian who subsists on biscuits made by a machine he brought with him, and communicates by using one of his tentacles to feed messages direction to/from the brain of the person he's talking to.  Inadvertently left behind by his expedition, he initially befriended some children, and eventually managed to rebuild civilization. Presently he dies, but when another expedition comes a generation later, they find the civilization he rebuilt.  there were other stories, but that was the best one.   If I can't find the name of the book it was in, I'd be happy to settle for the name of the author and the title of the story. Image of Jacobson Radical is the Jacobson Radical I'm stuck on the following problem:      Let $R$ be a commutative ring with $1$, and suppose $R$ is semilocal with maximal ideals $\mathfrak m_1, ... , \mathfrak m_s$.  Let $\mathfrak a$ be an ideal of $R$. The problem is to show that under the usual surjection $\pi:R \rightarrow R/\mathfrak a$, the Jacobson radical of $R$ is sent to the Jacobson radical of $R/\mathfrak a$.   My attempt: suppose that $\mathfrak m_1, ... , \mathfrak m_t$ contain $\mathfrak a$, but $\mathfrak m_{t+1}, ... , \mathfrak m_s$ do not.  Then $Jac(R/\mathfrak a) = (\mathfrak m_1/ \mathfrak a) \cap \cdots \cap (\mathfrak m_t/ \mathfrak a)$.  Obviously $\pi Jac(R) \subseteq Jac(R/ \mathfrak a)$, and the converse inclusion is equivalent to the following claim: if $x \in \mathfrak m_1 \cap \cdots \cap \mathfrak m_t$, then there exists a $y \in \mathfrak m_1 \cap \cdots \cap \mathfrak m_s$ such that $x - y \in \mathfrak a$.    This should be some application of the Chinese remainder theorem, but I'm not seeing it.  All I have to go on is that there exist $m_i \in \mathfrak m_i$ ($t+1 \leq i \leq s$) with $m_i \not\in I$.  I also haven't found out a way to use the fact that $\mathfrak m_1 ,... , \mathfrak m_s$ are all the maximal ideals of $R$.  I was also thinking about looking at some explicit maps.  If we let $\Gamma$ be the composition $$\frac{(R/\mathfrak a)}{Jac(R/ \mathfrak a)} \xrightarrow{\cong} \frac{(R/\mathfrak a)}{(\mathfrak m_1/\mathfrak a)} \oplus \cdots \oplus \frac{(R/\mathfrak a)}{(\mathfrak m_t/\mathfrak a)} \xrightarrow{\cong} R/\mathfrak m_1 \oplus \cdots \oplus R/\mathfrak m_t$$ then we have a commutative diagram $$\begin{matrix} R/Jac(R) &amp;  \rightarrow &amp; \frac{(R/\mathfrak a)}{Jac(R/\mathfrak a)} \\ \downarrow &amp; &amp; \downarrow \Gamma \\ R/\mathfrak m_1 \oplus \cdots R/\mathfrak m_s &amp; \rightarrow &amp; R/\mathfrak m_1 \oplus \cdots \oplus R/\mathfrak m_t \end{matrix}$$ where the vertical arrows are isomorphisms, and the horizontal arrows are surjections. Is it necessary to dispose System.Timers.Timer if you use one in your application? I am using System.Timers.Timer class in one of the classes in my application. I know that Timer class has Dispose method inherited from the parent Component class that implements IDisposable interface. Instances of the class below are created many times during my application lifecycle; each of them has an instance of Timer class that generates Elapsed events continuously during the class's lifecycle. Should I implement IDisposable interface in the class that uses Timer class to dispose the timer object? (I have seen code that doesn't do this at all). I am afraid that some unmanaged resources will not be freed if I use the class below like this:  SomeClass someClass = new SomeClass(); someClass.DoSomething(); someClass = null;   The class:  using System.Timers;  public class SomeClass {     private Timer m_timer;      public SomeClass()     {                    m_timer = new Timer();         m_timer.Interval = 1000;         m_timer.Elapsed += new ElapsedEventHandler(m_timer_Elapsed);         m_timer.AutoReset = false;         m_timer.Start();                            }      public void DoSomething()     {      }      private void m_timer_Elapsed(object sender, ElapsedEventArgs e)     {         try         {             //Do some task         }         catch (Exception ex)         {             //Ignore         }         finally         {             if (m_timer != null)             {                 //Restart the timer                 m_timer.Enabled = true;             }         }     } } Why did they make another prequel? Star Trek: Discovery, the first new Star Trek television series in 12 years, debuted last week.  As with a number of recent Star Trek efforts, this is a prequel to the Original Series, occurring roughly one decade prior chronologically.    The Original Series, the Next Generation, Deep Space Nine, and Voyager occur in a chronological sequence that, generally speaking, moves forward (although TNG, DS9, and Voyager overlap to various degrees).  The linear trajectory of Star Trek productions took a sudden shift with the television series Enterprise, which was set just over 100 years before TOS. This was followed by J.J. Abrams' 2009 film Star Trek, which created a new timeline and which followed the characters from TOS, but at a time that is also chronologically one decade before TOS.  Given that the last few interpretations of Star Trek were prequels in one sense or another, I was disappointed that Discovery was yet another prequel.  I'd like to know why the showrunners decided to take this direction.  I haven't been able to find any statements about the rationale.    That being said, I find it interesting that Star Trek (2009) was set in 2255-2258 and Discovery is currently set in 2256, even though they are ostensibly in different timelines &mdash; the former in the reboot timeline and the latter supposedly in the original timeline.  Also, one of the showrunners for Discovery, Alex Kurtzman, was one of the principal members of the creative team behind the Abrams films.  Why did the creative staff behind Discovery decide to make another prequel?  Does it have anything to do with the fact that Star Trek (2009) and Discovery are set in roughly the same years? I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "&lt;Regex for 'doesn't contain hede'&gt;" input   Desired output:  hoho hihi haha Windows 10 - disable reopening programs after restart/startup I have two directories that should contain the same files and have the same directory structure.  I think that something is missing in one of these directories.  Using the bash shell, is there a way to compare my directories and see if one of them is missing files that are present in the other? I tried to learn Dvorak keyboard layout a few years ago, and got reasonably good at it, but I couldn't get past the fact that command-key shortcuts were no longer in the right place.  In particular, Ctrl+Z (undo), Ctrl+X (cut), Ctrl+C (copy), and Ctrl+V (paste) are all chosen specifically because of the location of those keys on a Qwerty keyboard (well, maybe Ctrl+C makes sense).  Ctrl+A (select all) and Ctrl+S (save) are also very convenient because of their Qwerty keyboard location.  Is there any way (on Windows XP) to use Dvorak except when a control key (Ctrl, Alt, and/or WinLogo) is pressed?  (Preferably without having to install any third party app.) I need a list of integers from 1 to x where x is set by the user.  I could build it with a for loop eg assuming x is an integer set previously:  List&lt;int&gt; iList = new List&lt;int&gt;(); for (int i = 1; i &lt;= x; i++) {     iList.Add(i); }   This seems dumb, surely there's a more elegant way to do this, something like the One or more of the following things happened to me on a Stack Exchange site:   My post(s) were wrongly deleted or locked by a moderator A moderator posted a wrong comment on one of my posts I was suspended, but did not do anything wrong I asked a meta question, but the question was closed and/or deleted A moderator discredited me in public ...   I think a moderator has abused their power, but I feel powerless against them.  What recourse do I have now? What can I do when I feel that a moderator has abused their power, and has been repeatedly unfair in their dealings with me? Calculating grid convergence (True North to Grid North) I would like to know how to calculate the grid convergence angle between True North and Grid North for UTM maps. I am using ArcGIS 10.0 (ArcView licence). and have used the  tool from the Cartography toolbox. However, I would like to know how to calculate this angle myself (using Excel) to compare against the ArcGIS result? Georeferencing scanned map using ArcMap? A single word or phrase for something that necessarily causes both harm and benefit? What is a single word, or phrase, for something that necessarily causes both harm and benefit? For example, a coal-fired power plant will harm human health through air pollution, but will bring electricity and economic development to a poor area. I read this sentence in a book:     I just took part in a study over in the Psychology Department.   Why do we add over in front of in the here?