Separate labels in dcases lines and then reference to them
Separate labels in cases
When is logistic regression solved in closed form? Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$ $T(0)=1 \\ T(n) = 1 + \sum_{j=0}^{n-1}T(j) \\ $  Show that $T(n) = 2^n$.  I know how to prove this by induction, but I would like to know how to show this using first principles.  Edit: The way I want to solve this problem is manipulate $T(n)$ in such a way that it ends up as $2^n$. A function that is continuous at the origin but not differentiable there Show that $f(x,y)=\dfrac{xy^2}{x^2+y^2}$ (with $(x,y)\not=(0,0)$ and $f(0,0)=0$) is continuous but not differentiable at $(0,0)$.  I tried to show continuity with an $\epsilon -\delta$ argument but I don't know how to factorize the expression so that I can have something useful.   For differentiability I think I should show that the partials are not continuous at $(0,0)$. But finding the partials is also painful. "He was neither seer nor prophet" How would you explain the absence of an article? Here's a fragment from Jack London's Star Rover:     Wordsworth knew. He was neither seer nor prophet, but just ordinary man like you or any man. What he knew you know, any man knows. But he most aptly stated it in his passage that begins "Not in utter nakedness, not in entire forgetfulness.   To the best of my — admittedly sketchy — knowledge of grammar, the second sentence should read neither a seer nor (a) prophet, but just an ordinary man. Even if we accept the seer and the prophet as "poetic entities" ("father and son," "robber and robbed," "man to man," or whatever), logic would still dictate that ordinary man should be preceded by an an.  It is a well-known fact that Jack London's usage wasn't always up to par; his grammar, on the other hand, was always top-notch.  Logically, the sentence is grammatically incorrect (correct me if I'm wrong: no pun intended).  Illogically, it reads smoothly: intuitively, a native speaker understands that there's nothing wrong here.  However, those to whom English is not the first language cannot be expected to be intuitive in this case and would want an explanation. Any suggestions? To what extent is WhatsApp's statement on secure messaging realistic? Beamer: \nonumber equivalent for slides? Is there an equivalent command to \nonumber when one doesn't want to include certain slides in the numbering? I would like to leave outline and title slides out of my numbering, and instead just number slides with actual content. Other workarounds would be nice to know about as well.  Edit: Since a MWE example was requested, here is one. Suppose I have a title page and two other slides. The code below gives a slide counter that goes up to 3, and the title slide is slide 1. I would prefer to have the title slide not be numbered, the counter go up to 2, and the the numbering start at the slide after the title. Here is some code.  \documentclass{beamer}  \mode&lt;presentation&gt;  {    \usetheme{Dresden}  }   \setbeamertemplate  {footline}{\quad\hfill\insertframenumber/\inserttotalframenumber\strut\quad}    \begin{document}  \begin{frame}  \titlepage \end{frame}  \begin{frame} Some actual content here \end{frame}  \begin{frame} Some more actual content here \end{frame}  \end{document} How to apply multiple format to a list Why are conference papers so important in computer science (CS)? From my understanding many CS conferences are highly selective and the papers are peer-reviewed. The CS field also seems to publish traditional journal articles. I do not understand the difference between the two and in particular I am curious about the advantages of having two different publication streams. The type of things I am curious about are:   What is the difference between a paper published in a top CS conference and a top specialist journal? Is one more prestigious than another and if so how do they line up? Why not just publish conference papers as a special issues of a journal? Integrating a function of tan inverse How would I carry out the following integration? $$\int_0^12\arctan x^2$$  I tried to substitute $x^2 = \tan\theta$ From there I wrote the integral as: $$\int_0^{\pi/4}\theta\cdot \frac{\sec^2\theta}{\sqrt{\tan\theta}}\ d\theta$$  Now, is my only option to use integration by parts? Or is there a better method to solve this integral? Filter questions with no accepted answer I have some questions with answers, but none of the answers are acceptable (just wrong).  I'm sure there are a lot more people with the same problem.  Can you add a button to filter questions with answers but no accepted answer?  This way, people will see those questions and maybe try to offer a new perspective. How to make a persistent live Ubuntu USB with more than 4GB I want to make a persistent live Ubuntu USB drive with more than 4GB of storage.   I know there is an option of installing directly on the drive but I don't want to do this as it will restrict the drive from working on different computers.   One option is to make an additional partition with extra space but if I do this how can I get newly installed software to be stored on this partition? Moving from SQL 2005 [SQL_Latin1_General_CP1_CI_AS] to 2008 - will I lose any features by using 'backwards compatibility' "Timed Out" error when trying to join server What would be a good way to go about attacking a Quagmire 3 cipher?  I understand that it is polyalphabetic with a key and an indicator. I have started by taking the cipher text, taking every n-th letter and putting that in a string, computing the index of coincidence for the n strings I get and then averaging that. I would assume that whatever n value corresponds with the closest average index of coincident to English (0.066) would be the number of alphabets, i.e. the length of the indicator.  Where do I go from there? Or is my approach incorrect? How to style text in hyperref \url? I want to set color, font and similar style attributes for the text in a \url from the hyperref package. How do I go about doing it? All I have found are . I want to because I am using ttf fonts for my texts and I want my urls to be in that ttf and not the default (typewriter font?) that the hyperref package gives me. I started with just trying to get it in italics but didn't even succeed with that:  \documentclass{memoir} \usepackage{hyperref} \begin{document} Lala \url{\itshape www.example.com}. \end{document}     I am guessing there is some hook or something but I just can't find it. Maybe I have gone blind? Macro for figure position? Why is the following minimal example not working?  I.e., what do I need to do, in order to define the float placement specifier of a figure within a macro? (I know that I should use \newcommand, but in the "full" example the error is part of an involved "superfigure" command. \newcommand is not working too btw.)  \documentclass{scrreprt} \usepackage{blindtext}  \def\PosNotWorking{h} \def\FramboxNotWorking{5cm} \def\CaptionWorking{Caption is working.}  \begin{document}  \Blindtext[1]  \begin{figure}[\PosNotWorking]   \centering     \framebox[5cm]{My special figure. (Pos: \PosNotWorking)}             \caption{\CaptionWorking} \end{figure}  \Blindtext[1]  \end{document}   If I compile this, the figure is at the top (default behaviour). If I enter \figure[h] instead of \figure[\PosNotWorking], the figure is of course between the two paragraphs. Can a ultracentrifuge be used to test general relativity? With today's ultracentrifuge technology, they can spin so fast that the sample can be subjected to  accelerations of up to 2 millions Gs. That is equivalent to two solar masses. Has someone tried to measure the time dilation in a radioactive sample? How calculate that time dilation respect to the time outside the ultracentrifuge, for example one week. I think that that time dilation will be significant enough to be measured. Evolving Pokemon based on CP vs Moves Many people are evolving their pokemons based on the CP. However, there's a growing number of people evolving based on Moves instead of CP. In other words, choosing pokemons that have the highest Moves to keep, even if it isn't necessarily the highest CP. I am new to pokemon and don't quite understand the difference between the two. Thus, which strategy is better? show that Cov(X+ Y, X-Y)= Var(X) - Var(Y) Can I completely disable Cortana on Windows 10?