Set -h as default for ls?
How do I create a permanent Bash alias?
Find the sum $\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\dots+\frac{1}{99\cdot 100}$ Please help me calculate the following sum     $$\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\dots+\frac{1}{99\cdot 100}$$ What can be considered as "Home ties" for a UK Standard Visitor visa (PLAB)? Option to hide rep/badges on the avatar block displayed of you Update on Ubuntu - coloured lines around everything Everyday I check for updates on Ubuntu 16.04 LTS. I updated to 4.4.0-65-generic today and now on everything I'm getting thick rainbow coloured lines around every dialog box in every program. My setup is pretty standard. Skylake i5-6500, Nvidia 950gtx. Does anyone know how to fix it? Failed to download repository information due to missing CDROM Nginx installation error in Ubuntu 16.04 :~$ sudo apt-get remove nginx* && sudo apt-get install nginx-full*  Reading package lists... Done Building dependency tree        Reading state information... Done  After this operation, 5,579 kB of additional disk space will be used. Do you want to continue? [Y/n] y Get:1 http://in.archive.ubuntu.com/ubuntu xenial-updates/universe amd64 nginx-full-dbg amd64 1.10.0-0ubuntu0.16.04.1 [3,789 kB] Fetched 3,789 kB in 33s (112 kB/s)                                              Selecting previously unselected package nginx-common. (Reading database ... 189767 files and directories currently installed.) Preparing to unpack .../nginx-common_1.10.0-0ubuntu0.16.04.1_all.deb ... Unpacking nginx-common (1.10.0-0ubuntu0.16.04.1) ... Selecting previously unselected package nginx-full. Preparing to unpack .../nginx-full_1.10.0-0ubuntu0.16.04.1_amd64.deb ... Unpacking nginx-full (1.10.0-0ubuntu0.16.04.1) ... Selecting previously unselected package nginx-full-dbg. Preparing to unpack .../nginx-full-dbg_1.10.0-0ubuntu0.16.04.1_amd64.deb ... Unpacking nginx-full-dbg (1.10.0-0ubuntu0.16.04.1) ... Processing triggers for ufw (0.35-0ubuntu1) ... Rules updated for profile 'Apache Full' Rules updated for profile 'Nginx HTTP'  Processing triggers for systemd (229-4ubuntu4) ... Processing triggers for ureadahead (0.100.0-19) ... Processing triggers for man-db (2.7.5-1) ... Setting up nginx-common (1.10.0-0ubuntu0.16.04.1) ... Setting up nginx-full (1.10.0-0ubuntu0.16.04.1) ... Job for nginx.service failed because the control process exited with error code. See "systemctl status nginx.service" and "journalctl -xe" for details.  invoke-rc.d: initscript nginx, action "start" failed.  dpkg: error processing package nginx-full (--configure):  subprocess installed post-installation script returned error exit status 1 dpkg: dependency problems prevent configuration of nginx-full-dbg:  nginx-full-dbg depends on nginx-full (= 1.10.0-0ubuntu0.16.04.1); however:   Package nginx-full is not configured yet.  dpkg: error processing package nginx-full-dbg (--configure):   dependency problems - leaving unconfigured No apport report written because the error message indicates its a followup error from a previous failure.                            Errors were encountered while processing:  nginx-full   nginx-full-dbg  E: Sub-process /usr/bin/dpkg returned an error code (1) Using terminal escape-sequences within GNU screen I have a ruby terminal script that I would like to print out hyperlinks. I achieve that like so:  puts("\e]8;;https://example.com\aThis is a link\e]8;;\a")   This works perfectly fine in a "normal" terminal (gnome-terminal btw) window.  But I need to run this script within GNU screen, where the escape-sequence simply has no effect. Other sequences (like colors for example) work fine, the hyperlink one (which according to the  might be a gnome-terminal-only thing) doesn't. (screen is running inside gnome-terminal)  How can I get screen to acknowledge my link sequence and display it properly? Conditional page breaking I have used LaTeX on and off for a number of years now for several large documents with evolving versions over long lifetimes. But every time it seems like, powerful and wonderful as LaTeX is, there arise cases where I want to tweak the pagination in ways that are impossible without using the \newpage or \clearpage sledgehammer.  The macro I think I want is something like  \ifnotremaining{&lt;length&gt;}{&lt;cmd&gt;}   that is, if less than  space remains on the page then perform . For example:  \ifnotremaining{5cm}{\newpage}   Note that &lt;length&gt; need not be perfect–if a little too big no problem, or a little small (perhaps because the "protected" text got bigger) then you just increase it a bit. FWIW, I am usually happy with \raggedbottom.  An alternative might be a \disablepagebreak and \enablepagebreak pair which could be used to forbid a page break in the given range of text. (This capability cannot be formulated as an environment because it cannot always nest wrt other environemnts.)  Is there something I have overlooked that can fill this need? how do i change the color of typeface on photoshop? Compactness of $\operatorname{Spec}(A)$ In an exercise in Atiyah-Macdonald it asks to prove that the prime spectrum $\operatorname{Spec}(A)$ of a commutative ring $A$ as a topological space $X$ (with the Zariski Topology) is compact.   Now because the basic open sets $X_f = \{\mathfrak{p} \in \operatorname{Spec} (A) : \{f\} \not\subseteq \mathfrak{p} \}$ form a basis for the Zariski Topology it suffices to consider the case when   $$X = \bigcup_{i \in I} X_{f_i}$$   where $I$ is some index set. Then taking the complement on both sides we get that   $$\emptyset = \bigcap_{i \in I} X_{f_i}^c$$  so there is no prime ideal $\mathfrak{p}$ of $A$ such that all the $f_i$'s are in $\mathfrak{p}$. Now from here I am able to show that the ideal generated by the $f_i$'s is the whole ring as follows. Since there is no prime ideal $\mathfrak{p}$ such that all the $f_i \in \mathfrak{p}$, it is clear that there is no $\mathfrak{p}$ such that $(f_i) \subseteq \mathfrak{p}$ for all $i \in I.$ Taking a sum over all the $i$ then gives $$\sum_{i \in I} (f_i) = (1).$$  Now here's the problem:          How do I show from here that there is an equation of the form $1 = \sum_{i \in J} f_ig_i,$ where $g_i \in A$ and $J$ some finite subset of $I$?       This part has been giving me a headache. I am not sure if the finiteness bit has to do with algebra, topology or the fact that we are dealing with prime ideals.  This is not a homework problem but rather for self-study.  $\textbf{Edit:}$ I have posted my answer below after the discussion with Dylan and Pierre. Reasons why not to update an Ubuntu version to a newer/older kernel version Do PhD courses in engineering fields in European non-English speaking countries require knowledge of the native language? Can a Ph.D. student who only knows how to speak English study in a European non-English speaking country (e.g., Austria, Netherlands, Switzerland, Italy, etc.)  without any problems? Does applying to these universities require knowledge of that country's language? Can you stay in Turkey for over 90 days within the 180 day visa period but split over different visits? The Turkish e-visa is valid for a period of 180 days and allows you to stay for a maximum of 90 days. Am I allowed to stay for say 50 days, then another 50 days, over two different visits within the 180 day period?  I'm looking at the e-visa website  and it doesn't seem to be too clear on this. Suppose $X$ and $Y$ are independent positive random variables with probability density functions $f_X$ and $f_Y$ respectively. Show that $Z=X/Y$ is absolutely continuous and find its probability density function.   $\textbf{My Thought:}$ In order to show that $Z$ is absolutely continuous, I need to show that it has a commulative distribution function. Then I can also differentiate the latter to obtain the probability density function of $Z$. I have the following calculation \begin{align*} P(X/Y\leq z)&amp;=P(X\ge zY,Y&lt;0)+P(X\le zY,Y&gt;0)\\ &amp;=\int_{-\infty}^{0}\left(\int_{yz}^{\infty}f_{X}(x)dx\right)f_{Y}(y)dy+\int_{0}^{\infty}\left(\int_{-\infty}^{yz}f_{X}(x)dx\right)f_{Y}(y)dy\\ &amp;=\int_{0}^{\infty}\left(\int_{0}^{yz}f_{X}(x)dx\right)f_{Y}(y)dy. \end{align*} Also, if $z&lt;0$, then we have that $F_Z(z)=0,$ since $X,Y$ are positive random variables. Therefore the random variable $Z$ is continuous, and we can differentiate it to obtain the probability distribution function of $Z$. We have that $f_Z(z)=0$ if $z\leq 0,$ and otherwise we have $$f_Z(z)=\int_{0}^{\infty}yf_{X}(yz)f_Y(y)dy.$$    Is my reasoning above correct?  Any feedback is much appreciated.  Thank you for your time. The refraction through hot air around a candle flame Why the intensity of light is more around the region of hot air around the flame of candle in the shadow cast by the light from the collimated source ?    Most of the articles mention it is due to the refraction of light through hot air around the candle's flame. But I'm unable to understand how refraction make this happen. How can I calculate the R-squared of a regression with arima errors using R? If I have an arima object like a:  set.seed(100) x1 &lt;- cumsum(runif(100)) x2 &lt;- c(rnorm(25, 20), rep(0, 75)) x3 &lt;- x1 + x2  dummy = c(rep(1, 25), rep(0, 75))  a &lt;- arima(x3, order=c(0, 1, 0), xreg=dummy) print(a)   .  Series: x3  ARIMA(0,1,0)                      Call: arima(x = x3, order = c(0, 1, 0), xreg = dummy)   Coefficients:         dummy       17.7665 s.e.   1.1434  sigma^2 estimated as 1.307:  log likelihood = -153.74 AIC = 311.48   AICc = 311.6   BIC = 316.67   How do calculate the R squared of this regression? Solving an equation over the reals: $ x^3 + 1 = 2\sqrt[3]{{2x - 1}}$ Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$ Cannot get specific WMS to display in Leaflet or OpenLayers 3 How to zero out a drive?