How can I print intermediate results from a pipeline to the screen?
How can I gzip standard in to a file and also print standard in to standard out?
Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$. Let A be a commutative ring with unity ring, M be a maximal ideal and $b\notin M$ . Show that there exists $q \in M, s\in A$ such that for every $a \in A$ we have $a=sba+qa$. Show that this is true only when $M$ is a maximal ideal.   Suppose if we take $A=2\mathbb Z$ and $M=4\mathbb Z$, $a=6.$ Then by the given statement $\exists$ $s\in A$, $q\in M$ s.t. $6=6(2s+q)$ $\implies$$s=\frac{1-q}{2}\implies q \text { is odd}$. But $q \in 4\mathbb Z.$  Please someone give some hints. how can solve this.  Thank you.. Can HTML checkboxes be set to readonly? How to change Status Bar text color in iOS Changing timezone in PHP Alright, quick question.  A server is running in Eastern Time. PHP program needs to make date calculations using Central time.  At the moment, I am putting this line at the very top of my script:  putenv("TZ=US/Central");   Is that the best way to go about that or is there some PHP trick I'm not aware of?  Cheers. Grammar of "supposed to": part of speech / word class, active or passive? If I say     I'm supposed to go.   Is supposed to here an adjective in a passive construction? Using the same variable as a fixed and random effect in Mixed Effect Models I use VirtualBox on my MBP and often need to mount my USB flash drive inside the guest.  The problem I'm running into is that the host OS (OS X Mavericks) immediately mounts the USB flash drive when I insert it.  When I try to unmount it (gracefully, through Finder), OS X complains that the device is in use.  Further research into lsof reveals that Spotlight and AVG are doing their thing with the flash drive.  Rather than fiddling with individual app settings, I'd like to just modify the host OS behavior so that the USB device doesn't auto-mount.  Any suggestions? Mask and convert color in photo/video I am very new to blender still.  I want to simply change the color of an object in the video.  I want to know if there is good way to do this.  I am including what I have to test. mysql_fetch_array, mysql_fetch_assoc, mysql_fetch_object How do you round a number to two decimal places in C#? Space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable Let's consider the space $\mathcal{L}^p(X, \Sigma, \mu)$ of all functions $f\colon X \to \mathbb{R}$ (or $\mathbb{C}$) for which: $$ \int\limits_X|f|^p \mu(dx) &lt; \infty. $$ Here $X$ is a metric space, $\Sigma\subset 2^X$ — sigma-algebra on $X$ and $\mu$ — is the measure on $\Sigma$. As usual, functions that are equal almost everywhere considered to be equivalent, so technically we are dealing with classes $$[f]=\{g\in \mathcal{L}^\infty(X,\Sigma, \mu) \colon \mu \{x\in X\colon f(x)\neq g(x)\}=0\}.$$ This space is endowed with integral metric $$\rho_p(f,g)=\left(\int\limits_X|f-g|^p \mu(dx)\right)^{1/p}$$  The statement is that space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable, where $\forall A,B\in\Sigma$ $$\rho_\Delta(A,B)=\mu(A\Delta B)$$ Here, again, we consider $A\in \Sigma$ as a class $[A]=\{A'\in\Sigma\colon \mu(A\Delta A')=0\}$ to have the identity of indiscernibles.  How do one prove the statement? Bounding lines around tax nodes I am trying to draw lines around a number of nodes. I very much like the definition of \convexpath definition given , but it is not working well on my setup (MacTex 2014 with all available updates).   I tried to compile , but what I get is the following, which is clearly not what I should be getting. Any ideas would be much appreciated. Convert from LyX/Latex to wordpress post I have some documents in LyX/Latex and I want them as a wordpress post. I have tried converting latex to HTML (with latex2html) and afterwards, pasting that code in the wordpress editor but everything looks ugly. Do you know a better approach? How to get parent process in .NET in managed way I was looking a lot for method to get parent process in .NET, but found only P/Invoke way. What is the difference between these two:     Suzuki was nearly close to go out of business just after the World War period.   Vs.     Suzuki was nearly close to going out of business just after the World War period.(from a video)   When talking about the past, do these two sentences different from each other? Like, if you use verbing(going) with infinitive(to) in the past, does it mean that there is another event happening? Or none. How to call a space in which every G$_\kappa$-set is open Recall that in a topological space $X$, we say that a subset $A\subset X$ is a G$_\delta$-set if $A$ is the intersection of countably many open sets of $X$. Also, we say that $X$ is a  if G$_\delta$-sets are open.  Now, call as G$_\kappa$-set the intersection of $\kappa$ many open sets, where $\kappa\geq\aleph_0$ is a cardinal. I would like to know if there is some standard name for those spaces in which G$_\kappa$-sets are open, for a fixed cardinal $\kappa\geq \aleph_0.$  Motivation: this kind of space arose in my PhD thesis, but I do not know any references in which they appear. I'm temporary calling them as $P_\kappa$-spaces. I have CSV data loaded into a multidimensional array. In this way each "row" is a record and each "column" contains the same type of data.  I am using the function below to load my CSV file.  function f_parse_csv($file, $longest, $delimiter) {   $mdarray = array();   $file    = fopen($file, "r");   while ($line = fgetcsv($file, $longest, $delimiter))   {     array_push($mdarray, $line);   }   fclose($file);   return $mdarray; }   I need to be able to specify a column to sort so that it rearranges the rows.  One of the columns contains date information in the format of Y-m-d H:i:s and I would like to be able to sort with the most recent date being the first row. The momentum-space fermion propagator in the free Dirac theory is given by       The arrow on the fermion propagator is said to represent the flow of charge.  How can we derive this statement quantitatively from the Dirac Lagrangian?  What is the quantitative form of the charge being referred to here? Why is it not true that if $\Phi \models \exists x \phi$ then there is a term $t$ with $\Phi \models \phi \frac{t}{x}$? How does QGIS Zonal Statistics handle partially overlapping pixels?