How to write conditional equations within equation tags I used following tags to create equations in my document. But when I tried to add conditional equation within this tag, it didn't work properly. Is there any way to add conditional statement within equation tags?    \begin{equation}     \begin{cases}          xxxxx, &amp; \text{xxx}\\          xxxxx, &amp; \text{xxx}      \end{cases}   \end{equation}
How to write conditional equations with one-sided curly brackets I want to write a conditional expression such as the following.    What is the best way to express such conditional expressions in Latex?
How do I create an .exe for a Java program? What do you call someone who pretends to be your friend but is actually your enemy?  A friend suggested spy for me, but that does not nearly describe the word I need for an English project. The character is very good at manipulating how people see him. He's a good liar. And pretends to be your friend but actually is your enemy. Which is the preferred way to convert an Enum to a String in .NET 3.5?   Enum.GetName Enum.Format ToString   Why should I prefer one of these over the others? Does one perform better? This is an exercise in real analysis:     Let $E\subset{\Bbb R}^d$ be Lebesgue measurable. Show that    $$ m(E)=\sup\{m(K):K\subset E, K \text{compact}\}. $$   When $E$ is bounded, this can be done by the following proposition:       $E\subset{\Bbb R}^d$ is Lebesgue measurable if and only if for every $\varepsilon&gt;0$, one can find a closed set $F$ contained in $E$ with $m^*(E\setminus F)\leq\varepsilon$.    How can I deal with the case that $E$ is unbounded? Don't worry, I have written your name on the attendance sheet.   Or     Don't worry, I wrote your name on the attendance sheet. Can a Raspberry Pi run Ubuntu? I was thinking about buying a , and running Ubuntu on it. I have looked around the web, and a lot of stuff says that it's difficult for it to work on ARM processors. Has anyone figured out how to get a Raspberry pi to run Ubuntu? How to align two images side by side if one label has more lines I have two same sized images and want them side by side with a caption under them.  My code looks like this:   \begin{figure}[H] \centering \begin{minipage}{.5\textwidth}   \centering     \includegraphics[width=\textwidth]{3}     \caption{label1}   \label{fig:test1} \end{minipage}% \begin{minipage}{.5\textwidth}   \centering     \includegraphics[width=\textwidth]{4}     \caption{label2}   \label{fig:test2} \end{minipage} \end{figure}   which works fine until one of the labels has 2 lines, than it looks like this:    and I woud like to prevent it to look something like this:    How can it be done?  Thanks Question is :  Suppose $X$ is a topological space of infinite cardinality which is homeomorphic to $X\times X$. Then which of the following is true:   $X$ is not connected. $X$ is not compact $X$ is not homeomorphic to a subset of $\mathbb{R}$ None of the above.   I guess first two options are false.  We do have possibility that product of two connected spaces is connected.  So, $X\times X$ is connected if $X$ is connected. So I guess there is no problem.  We do have possibility that product of two compact spaces is compact.  So, $X\times X$ is compact if $X$ is compact. So I guess there is no problem.  I understand that this is not the proof to exclude first two options but I guess the chance is more for them to be false.  So, only thing I have problem with is third option.  I could do nothing for that third option..  I would be thankful if some one can help me out to clear this.  Thank you :) Is there an easy way to show which spheres can be Lie groups? How does QGIS Zonal Statistics handle partially overlapping pixels? Output two sided, but only on recto page -- occasional images on verso I am preparing a thesis. In order to reduce the number of physical sheets of paper, I need to print certain figures/tables on the verso side. However the university regs state that, while figs/tables may appear on the verso, the body text must appear on the recto side.  I would like to therefore output the vast bulk of the work on the recto page, but with occasional verso pages. Ideally they would be numbered as a "subpage" of the preceeding recto page (e.g. 131, 131a, 132...) or similar.  The approach which I will tentatively adopt is to use a "twoside" flag, then have "empty" and non-numbered verso pages until a page with content is required.   I'm sure I'm not the first person to have had a similar issue, but am unable to imagine other ways of posing the question. How can I use JavaScript on the client side to detect if the page was encrypted? Is it possible to detect, on the client side, whether the user is using an encrypted page or not?  Put another way -- I want to know if the URL of the current page starts with http or https. Please give me the proof for the following: Let $a_1,\,a_2,\,\dots\,a_n$ be $n$ positive real numbers whose product is equal to $1$. Prove that $$a_1+\cdots+a_n \geq n$$ and that the equality sign holds only if every $a_k$ is  equal to $1$. I would like to know if there is any way to add custom behaviour to the auto property get/set methods.  An obvious case I can think of is wanting every set property method to call on any PropertyChanged event handlers as part of a System.ComponentModel.INotifyPropertyChanged implementation.  This would allow a class to have numerous properties that can be observed, where each property is defined using auto property syntax.  Basically I'm wondering if there is anything similar to either a get/set template or post get/set hook with class scope.  (I know the same end functionality can easily be achieved in slightly more verbose ways - I just hate duplication of a pattern) Where, precisely, does feedback on Community ♦ generated flags go to die? For the most part, I treat "Community" like any other user when handling system raised flags. If they are useful, I mark them as such. If they are noise, I dismiss them as such. The Community user has a static flag weight, so our reaction to them is more or less feedback for developers.  Is this feedback from moderators network wide used in any way to help improve the accuracy of system raised flags? Or, would clicking either button suffice?  I'm asking because our reasoning behind declining a flag is now more precise. Does dismissing some as noise help improve the criteria that ultimately generates the flag?  Edit  Yes, thank you Skype, I realize that  asked a similar question . The official Checkpoint out command line tool from CheckPoint, for setting up a SSL Network Extender VPN is not longer working from the Linux command line. It is also no longer actively supported by CheckPoint.  However, there is a promising  project, that tries to replicate the Java applet for authentication, that talks with the snx command line utility, called snxconnect.   I was trying to put snxconnect text utility to work in Debian Buster, doing:  sudo pip install snxvpn   and  export PYTHONHTTPSVERIFY=0 snxconnect -H checkpoint.hostname -U USER    However, it was mostly dying either with an HTTP error of:   HTTP/1.1 301 Moved Permanently:   or:  Got HTTP response: HTTP/1.1 302 Found   or:  Unexpected response, try again.   What to do about it?  PS. The EndPoint Security VPN official client is working well both in a Mac High Sierra and Windows 10 Pro. What causes a "Java Hotspot 64-Bit Server VM Warning"? I get this warning:     Java HotSpot(TM) 64-Bit Server VM warning: Using incremental CMS is deprecated and will likely be removed in a future release   What does it mean? I launch a batch which call a lot of scheduled job. But I reach the governor limit :     Maximum number of Apex classes scheduled concurrently : 100   I'm wondering what happens when this limit is reached. The next scheduled jobs are waiting the number of scheduled jobs is lower than 100 for being executed or are they all cancelled ?  And is there to way to manage the number of scheduled jobs to avoir reaching this limit ? For example wait before schedule a new job if we are near the limit. Distance between points along polyline ArcGIS for Desktop? I'm using ArcGIS 10.3 (Desktop), and I'm trying to measure the distance between points following a path determined by a set of polylines.  Hand measurement is not a viable option-- there are ~7500 points, and my polyline set is the global coastline.  The ultimate goal is to get the spacing of these points along the polylines, so that I can analyze this with respect to a few other variables.   I can read python-- with a bit of effort-- but not write or edit it, so code-based solutions will not be particularly useful to me.  I have tried using the linear referencing tools-- I snapped the points to the lines, then transformed the polylines to routes and used 'locate features'-- but because my points are not (entirely) ordered along the path, using the difference between  linear reference locations of subsequent points yields some fairly unlikely answers.  In addition, spot checks of (hand-measured, using the built-in path length measuring tool) point-to-point along-polyline distance yield different answers than given by the corresponding linear references for the point pair. (Some of the answers were close enough that they could very well be measurement error on my part, but others were nearly 20%, despite my having zoomed in and snapped the measurement cursor to the polyline, proceeding vertex-to-vertex.)  Sorting first by linear distance seems to fix the first problem, but in light of the second one, I remain skeptical of this process.   I then tried simply splitting the polylines into segments ('split line at point') using the (snapped) points as the dividers, with the eventual goal of finding the segment length with the calculate geometry feature.  This produced gibberish. I'm not sure what criteria ArcGIS used to split the lines, but it wasn't the point set I provided.  Segments in the resulting shapefile ran right through tens of points, only to terminate at a place with no point. (Also, there were segments utterly empty of points...you get the gist.) I reiterate that the pointset was specifically snapped to the polylines, so this problem shouldn't be caused by excessive distance between the point and the polyline.  I'm at a bit of a loss, here: could someone point out where I might have gone astray and/or suggest a solution?  Or, failing that, a new method that I could try?  It seems like a fairly basic (not necessarily simple, but fundamental) analysis to do with geographic data, and I don't understand why it has presented so many difficulties. When to Garbage Collect