Is it possible to color some of my text in the post?  I have 2 columns in my question post. I want to show column one as red and column 2 as green.  Is this possible?
Stack Overflow provides good tools in the question editor, like "Links" and "Styling".  Another thing that for me would be nice is a color selector. Although an HTML editor is available, a direct click on tool would be good, and users can select different colors, as for marking errors in their program with red, and more important data with blue.
My application got crashed because of not initializing the view Minion Pro, TL2016 and LuaLaTeX Let $R$ be a commutative ring with identity. Assume that $R$ has exactly three distinct ideals: $\{0\},I, R.$      1) Show that if $a \in R-I$, then $a$ is a unit in $R$.      2) Let $a,b\ne0$ in $I$. Show that $ab=0$. I used this isomorphism today but now I'm having trouble justifying it. The norm function isn't additive so I can't come up with a ring isomorphism to prove the following:     For any $\,a+bi\in\Bbb Z[i],\,\gcd(a,b)=1$, we have a ring isomorphism   $$\Bbb Z[i]/\langle a+bi\rangle\,\cong\Bbb Z/(a^2+b^2)\Bbb Z=:\Bbb Z_{a^2+b^2}.$$   Could someone show me an isomorphism between these rings to prove this? Is it possible to password protect a zip file created by Windows itself (without external tools?) How can I list all user names and/or home directories? I want to list all the users dirs on the machine.Usually, I will do:  ls -l /home   But I use it in a script that will be deployed on others machines and maybe on that machines they don't call it home (e.g. myHome). So I want to generalize it to ls -l ~. But it just lists my users home dirs instead of all users home dirs name (basically I want to get a list of the users names on the machine). How can I generalize it? When to use Stateful session bean over Stateless session bean? Jutifying: irrational + rational = irrational I am not sure how to show this. This is what I tried.   Proposition: If x is rational number and y is an irrational number then x+y is an irrational number.  Logically speaking this is  P=x is rational  Q= Y is irrational  R= x+y is irrational  $P\wedge Q \rightarrow R$  Explanation: What I did  $x=\frac{p}{q}$ P and Q integer  Y cannot be written as the a rational by definition  So therefore  $x+y=\frac{p}{q}+y$  Will not be a rational number as there cannot be a common denominator. How to ignore accent in SQLite query (Android) Let $V$ be spherically symmetric and $W$ i.i.d. Gaussian. Then $E[V|V+W=t]=g(\|t\|)$ A random vector $V \in \mathbb{R}^n$ is said to be spherically symmetric. If for every orthogonal matrix  $A$   the distribution of $AV$ is the same as the distribution of $V$.   My question: Let $W$ be  i.i.d. zero mean Gaussian random variable.     Can we show that  for a spherically symmetric $V$ the conditional expectation  \begin{align} E[V|V+W=t]=   g(\|t\|).  \end{align}  That is the conditional expectation is only a function of the magnitude.   My attempt:  \begin{align} E[V|V+W=t]= \int  V  \frac{f_W(t-v)}{f_{V+W}(t)} dP_V(v)= \frac{\int  v  f_W(t-v) dP_V(v)}{f_{V+W}(t)}= \frac{E[ V  f_W(t-V) ]}{f_{V+W}(t)} \end{align}  Therefore, we can show that the two functions in the above ratio only depend on $\|t\|$.   Observe that we can write $t= \|t\| u_t$  where $u_t$ is a unit vector. Then, for any orthogonal matrix $A$ \begin{align} f_{V+W}(t)=f_{V+W}(\|t\|, u_t)&amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-AV  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|tA^{-1}-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t A^T-V  \|^2}{2}} ]\\ &amp;= f_{V+W}(tA^T)\\ &amp;= f_{V+W}(\|t\|,  u_t A^T) \end{align}  Since, $A$ was arbitrary  we have that $f_{V+W}(t)=h(\|t\|)$(i.e., only depends on the magnitute).  Now I am not sure how to show that $E[ V  f_W(t-V) ]$ only depends on $\|t\|$? There's a fairly standard two or three-semester curriculum for introductory quantum field theory, which covers topics such as:   classical field theory background canonical quantization, path integrals the Dirac field quantum electrodynamics computing $S$-matrix elements in perturbation theory, decay rates, cross sections renormalization at one loop Yang-Mills theory spontaneous symmetry breaking the Standard Model   What is a good, complete and comprehensive book that covers topics such as these? ASP.NET MVC 3 localization with DisplayAttribute and custom resource provider As I have seen in other posts, i.stack.imgur.com is blocked by numerous companies' firewalls including my own. I have started the process to get the restriction lifted but to increase the likelihood of it being granted, have only requested that i.stack.imgur.com be unblocked.  Staying within the context of SO, imgur and the hosting arrangement SO has with them, are there any other sub-domains/domains that I should be requesting be unblocked? i.e. p.stack.imgur.com or *.stack.imgur.com?  I'm not sure if images can still be embedded/hotlinked in posts from other image hosts or not but if they can I'm not interested in unblocking those hosts, just the addresses used by SO for imgur.  Cheers :) No module named numpy I am trying to run Jupyter notebook from my Ubuntu subsystem in Windows 10. I've installed numpy, scipy, and pandas using the following commands:  pip install scipy numpy pip install pandas   When I load python in Ubuntu, there is no issue importing numpy in Ubuntu cmd.   But, when I run my Jupyter Notebook from Ubuntu terminal, and try to import numpy as np, or import pandas as pd, they report  ModuleNotFoundError                       Traceback (most recent call last) &lt;ipython-input-1-a9340201ed9f&gt; in &lt;module&gt;       5 import dash_html_components as html       6 import plotly.graph_objs as go ----&gt; 7 import numpy as np       8 from dash.dependencies import Input, Output       9   ModuleNotFoundError: No module named 'numpy'   Is there anyway to solve this issue? Thanks a lot. I'm looking to have cell borders automatically applied when a cell is not empty. I thought I could use conditional formatting for this, but it doesn't seem to be an option. Let $a_k:=(-1)^k$ where $k\in\mathbb{N}$. $\mathbb{N}$ is the set of all non-negative integer.  And we define the partial sum $S_n:=\sum \limits_{k=0}^{n}a_k$. Notice that the sequence $\{S_k\}$ diverges which also implies that the infinite series $\sum \limits_{k=0}^{\infty}a_k$ cannot be defined.  If I consider the infinite sum $1-1+1-1+1-1+\cdots$, then this statement is equivalent that I just defined the infinite series $\sum \limits_{k=0}^{\infty}a_k$, which is contradiction.  But, suppose that the sum $1-1+1-1+1-1+\cdots$ exists and let the value of the sum be $S$. Then, we can easily observe that $S=1-S$, therefore $S=1/2$. The supposition of this proposition already proved as false, but if I ignore the definition of infinite series, it holds.  Which one is right? Or are these propositions depends on what we define? My QGIS project has two layers, one layer is retrieved by Google layer plugin which fetches the static Google map image whose CRS is +proj=merc +lon_0=0 +lat_ts=0 +x_0=0 +y_0=0 +a=6378137 +b=6378137 +units=m +no_defs and another vector layer is a postgis layer whose CRS is +proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs.  I digitalized some polygon features from Google Layers and added it to the vector layer. However, QGIS seems do not make the automatic CRS transformation. How can I change its projection?   Thanks My keyboard has no "media" keys; can I control media without them? My USB keyboard does not have "media" keys -- that is, dedicated keys for play, stop, next, prev, volume up/down, etcetera.    For the sake of this question, I would prefer not to install additional software if I can avoid it.  Is it possible to issue some standard key sequence on a generic USB keyboard that emulates these play, stop, etc. multimedia keys?  Like Ctrl+Alt+Shift+F12 or something obscure like that? How do I run an executable file with a double click? I'm trying to run an executable (testdisk) but double click doesn't work. The only way is to run:  sudo ./testdisk   from terminal. But I'd like to open executables with double click in future. How can I do this? Construct a fourth circle tangent to 3 circles forming a tangency chain