I have the following expression   $$\left\{\varphi\in\text{End}\left({\widetilde{E}/\overline{\F}_{\Pf}}\right)\mid \varphi\text{Frob}_{\Pf}=\text{Frob}_{\Pf}\varphi\right\}$$   and would like to know how to match the length of \mid to the length of \left\{ and \right\}. Thanks!
I am looking for a pipe symbol that can be made to vary in height automatically.  One of the common ways of writing "such that" in mathematics is with the pipe symbol (|). The pipe can be represented in LaTeX directly as the character | or as \vert, but neither of these expands vertically in math presentation mode. I can adjust it manually this way:  \[\mathcal{H}=\left\lbrace h(x)=\sum_{i=0}^{k-1}a_{i}x_{i}\mod m\ \Bigg\vert      \ a_{i}\in\mathbb{Z}_{m^{k}}\right\rbrace\]     but I am looking for a true variable-sized option, parallel to \lbrace etc.  The amsmath package provides \lvert and \rvert, but I do not find them expanding as expected, and the amsmath documentation specifies that they should be used as binary delimiters (one on each side of something else), rather than alone.
Helllo!  For a project that I am doing, I need to render the my model to a sprite sheet. This is all fine, except that the model has a cloak, which uses a cloth animation. I need to smoothly transition from the end of the cloth simulation to the start, so it doesn't just jerk back, but I can't find any way of doing this.  Thanks in advance. Prove $p_n(x) \rightarrow \sqrt{x}$ uniformly as $n \rightarrow \infty$ Define $(p_n)_n$ recursively by $p_0(x) = 0$ and $p_{n+1}(x) = p_n(x) + \frac{1}{2}(x - p_n(x)^2)$.  Prove that $p_n(x) \rightarrow \sqrt{x}$ uniformly for $0 \leq x \leq 1$ as $n \rightarrow \infty$.  I'm not sure where to go with this.  I can show inductively that $\forall n,\  0 \leq p_n(x) \leq 1$ for $0 \leq x \leq 1$, and I think that $p_n(x)$ is increasing with $n$, but I have no idea whether this helps me.  I know that I need to show that $\forall \epsilon&gt;0: \exists N \in \mathbb{N}: \forall n \geq N: \forall x\in [0,1]: \big|p_n(x) - \sqrt{x}\big| &lt; \epsilon$ Edit:  I just had a thought.  I'm given a version of Dini's theorem that reads  Let $X$ be a compact metric space, $(f_n)_n$ a sequence of real-valued continuous functions on $X$, $f$ a continuous function on $X$ such that: (i) $f_n \rightarrow f$ pointwise on $X$, and (ii) $f_n(x) \geq f_{n+1}(x) $ for all $x \in X, n \in \mathbb{N}$. Then: $f_n \rightarrow f$ uniformly on $X$.  Obviously, (ii) is not true for my sequence, but what if I took $f_n(x) = -p_n(x)$ and $f(x) = - \sqrt{x}$?  Then I could prove (ii) to be true, I know that $[0,1]$ is compact, and $f_n(x)$ is real-valued.  The only part I would need to prove is (i), which is where I get confused.  Correct me if I'm wrong, but after that I could say that since $(-p_n)_n \rightarrow -\sqrt{x}$, then $(p_n)_n \rightarrow \sqrt{x}$.  Any advice? Does adding two linear equations will result in a line which will pass through an intersection of the linear equations? I was wondering why it is almost impossible to find a geometrical explanation of why adding two linear equations helps us to find a solution of a system of linear equations? Am I right that adding two linear equations will result in an equation of a line which will pass through a point where two linear equations intersect?  If it is right then I completely don't understand why such a crucial point in understanding how to solve systems of equations is never properly taught even at a university level. Extracting embedded images from a PDF How can I find out if Ubuntu supports a particular hardware component, that is, if it works in Ubuntu?  I am going to put together a computer and I am choosing components.   How do I know if Ubuntu supports this or that motherboard, or this or that sound card, or this or that graphics card, etc? How do I know that there is no conflict in Ubuntu between this and that hardware component?   What resources are there to help with such situations?  I know that there are computers with Ubuntu pre-installed and that there are  for whole computers but this is not what I'm looking for. I'm looking for resources to find out support for particular hardware components and conflicts among particular hardware components. Extracting numbers from vectors of strings Plot electric potential and field iPhone screen randomly turns on After installing iOS 10, I found that the screen on my iPhone 6s turned on at seemingly random times, and it slightly annoyed me. I now know that this feature does what it is supposed to (turn the screen on when the phone enters certain positions), but I want to disable it.  Is there a setting can I use to do so? Smileys in LaTeX I would like to include smileys in my LaTeX document. Is there any package with lots of different smileys?  In mnsymbol and wasysym, I found some general symbols:  \documentclass{article} \usepackage{MnSymbol,wasysym} \begin{document} wasysym: \smiley{} \frownie{} \blacksmiley{}  MnSymbol: \(\smile{} \frown{}\) \end{document}     But I do not like the output. Actually, I am looking for smileys which look like "default smiles" in Google Talk, MSN, ... ;) &lt;- this one is my favourite. ;) I have a residence permit (permesso di soggiorno) for Italy. I am currently in the Netherlands for an exchange. My permit expired on the 30th of November and I applied for a new one but I will get the card in January. I have the documents supporting that I have applied for the renewal of the permit. In the middle I want to travel to Italy for Christmas and come back to the Netherlands.    Would this be a problem? Constants of integration in integration by parts I tend to use the terminal a lot,  So I wondering if there is a way I can make Ctrl+Alt+T focus the existing terminal if there is one, otherwise create a new terminal? Validation Error: Value is not valid I often see questions on Stack Exchange sites which I presume are written by non-native English speakers who use the word "doubt" in place of the word "question". Is this a case of misunderstanding the correct meaning or are people being taught that this is correct usage? How do i create a linestring from points sort by date in PostgreSQL?  I tried:  SELECT observations.id,    ST_MakeLine(observations.geom ORDER BY observations.date) AS newgeom    FROM   observations     GROUP BY    observations.id;   This is going wrong. It returns me a linestring with same coordinates.  So, instead of a line from a to b, it gives me a to a.    What am I doing wrong? found a 1994 uncashed profit sharing retirement plan check Intuition behind logistic regression Recently I began studying machine learning, however I failed to grasp the intuition behind .   The following are the facts about logistic regression that I understand.   As the basis for hypothesis we use . I do understand why it's a correct choice, however why it's the only choice I don't understand. Hypothesis represents the probability that the appropriate output is $1$, therefore the domain of our function should be $[0,1]$, this is the only property of sigmoid function I found useful and appropriate here, however many functions satisfy this property. In addition, sigmoid function has a derivative in this form $f(x)(1-f(x))$, but I don't see the utility of this special form in logistic regression.   Question: what so special about sigmoid function, and why we cannot use any other function with domain $[0,1]$? The cost function consists of two parameters ${\rm Cost}(h_{\theta}(x),y)=-\log(h_{\theta}(x))$ if $y=1, {\rm Cost}(h_{\theta}(x),y)=-\log(1-h_{\theta}(x))$ if $y=0$. In the same was as above, I do understand why it's correct, however why is it the only form? For example, why couldn't $|h_{\theta(x)}-y|$ be a good choice for the cost function?  Question: what is so special about the above form of cost function; why cannot we use another form?   I would appreciate if you could share your understanding of logistic regression. Explanation of Spikes in training loss vs. iterations with Adam Optimizer I am training a neural network using i) SGD and ii) Adam Optimizer. When using normal SGD, I get a smooth training loss vs. iteration curve as seen below (the red one). However, when I used the Adam Optimizer, the training loss curve has some spikes. What's the explanation of these spikes?   Model Details:  14 input nodes -> 2 hidden layers (100 -> 40 units) -> 4 output units  I am using default parameters for Adam beta_1 = 0.9, beta_2 = 0.999, epsilon = 1e-8 and a batch_size = 32.  i) With SGD  ii) With Adam How to detect if a function is called as constructor? Given a function:  function x(arg) { return 30; }   You can call it two ways:  result = x(4); result = new x(4);   The first returns 30, the second returns an object.  How can you detect which way the function was called inside the function itself?  Whatever your solution is, it must work with the following invocation as well:  var Z = new x();  Z.lolol = x;  Z.lolol();   All the solutions currently think the Z.lolol() is calling it as a constructor. How can I type a Unicode character (for example, em-dash —?) The title pretty much says it all: how can I type Unicode characters - specifically the em-dash —?