regression with multiple response variable in R
How to do a generalized linear model with multiple dependent variables in R?
How to make `sudo` preserve $PATH? For example, if the ex-dividend date is next Monday, and I buy the stock on next Monday, would I get the dividend? Or would the person who sold the stock to me get the dividend? Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$ tput: No value for $TERM and no -T specified I am trying to run a bash script I have via cron, and I am getting the following error at the beginning of the execution:  tput: No value for $TERM and no -T specified   Here is what is in my crontab:  0 8 * * 1-5 cd /var/www/inv/ &amp;&amp; /var/www/inv/unitTest run all 2&gt;&amp;1| mail -r "user@example.com" -s "Daily Inventory Unit Test Results" user@example.com In the last 30 years, human technology has developed massively.  Every year a new smartphone is released with a faster processor, more memory, better features.  Why hasn't the same level of progress happened in the Star Wars universe?  In The Phantom Menace, we see a number of droids - R2 units, C-3PO, Pit Droids, etc.  In Return of the Jedi - the droids we see pretty much have the same capabilities.  I would have thought that technology would still be progressing in the Star Wars universe - but it appears to have stopped.  During wars on Earth, our technology capabilities grow - so it can't just be the effect of a massive war which is causing the stagnation of development.  So, what gives? $G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$ I am trying to prove the following statement:     Let $G$ be a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K =  \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$.   From this, we get that $HK \cong H \times K$. Naturally, it would be ideal if I could prove that $HK \cong G$. One issue that I am facing here is the meaning of $G = \langle H, K \rangle$. How is this defined (I mean, more explicitly)? Is my strategy correct or When trying to install CrossOver deb I get "Error: Dependency is not satisfiable libpng12-0" I have tried to install libpng12-0 but it still doesn't work.  Here:    How do I fix this? Difference estimate & confidence intervals for $\chi^2$ test between 2 proportions I am using a chi-sq test between two proportions (). I am using this over the z-test for proportions because I do not think my data is normal.   My question is how do I get the difference (shift) estimate &amp; confidence intervals for this test.   For example,     Data1: 193/252=.77   Data2: 154/227=.68   P-value=.032 (I used the formula in the link above. I will also add my exact code below)  Shift Estimate: I assume its the difference between proportions, ie .77-.68=.09. Is this correct?   Confidence Interval: ??????????????????  Code for generating P-value (matlab):   % Pooled estimate of proportion  p0 = (n1+n2) / (N1+N2); % Expected counts under H0 (null hypothesis)  n10 = N1 * p0;  n20 = N2 * p0; % Chi-square test, by hand  observed = [n1 N1-n1 n2 N2-n2];  expected = [n10 N1-n10 n20 N2-n20];  chi2stat = sum((observed-expected).^2 ./ expected);  p = 1 - chi2cdf(chi2stat,1);  H=0; if(p&lt;.05), H=1; end Search and download audio-only from youtube Is there a way to search and then download from YouTube, with the situation that I only need to download the audio only, not the video. Is there a bijection of the natural numbers which swaps $\frac{1}{n}$-summable subsets with $\frac{1}{\sqrt{n}}$-summable subsets? Let me start with a precise statement of the question.  For a subset $A\subseteq \mathbb{N}$ and a series of positive real numbers $\sum_{n=0}^\infty a_n$, I'll use the notation $\sum_A a_n$ as a shorthand for $\sum_{n\in A} a_n$.  Is there a bijection $f:\mathbb{N}\rightarrow \mathbb{N}$ with the property that for every $A\subseteq \mathbb{N}$, $\sum_A \frac{1}{n}$ converges iff $\sum_{f(A)} \frac{1}{\sqrt{n}}$ converges?  Background: Fix a series of positive terms $\sum_{n=0}^\infty a_n$.  Given a subset $A\subseteq \mathbb{N}$, call it $a_n$-small if $\sum_A a_n$ converges.  The following proposition is easy to prove:  Proposition:  The set $\{A\subseteq \mathbb{N}: A\text{ is } a_n\text{-small}\}\cup \{\mathbb{N}\}$ is a topology of closed sets on $\mathbb{N}$.  I will use the notation $(\mathbb{N},a_n)$ to refer to this topology.  Then one can ask how topological properties of $(\mathbb{N},a_n)$ are related to series properties of $\sum a_n$.  For example, I can show:  Proposition:  The following are equivalent.  $\sum a_n$ converges.  $(\mathbb{N},a_n)$ is discrete.  $(\mathbb{N},a_n)$ is disconnected.  $(\mathbb{N},a_n)$ is Hausdorff    And there are other nice things.  For example, $(\mathbb{N},a_n)$ is compact iff $(\mathbb{N},a_n)$ is cofinite iff $\liminf a_n &gt; 0$. With this language, my question can be reformulated as...  Are $\left(\mathbb{N}, \frac{1}{n}\right)$ and $\left(\mathbb{N}, \frac{1}{\sqrt{n}}\right)$ homeomorphic?  I have made very little progress on this.  Of course, the identity function $i:(\mathbb{N}, \frac{1}{\sqrt{n}})\rightarrow (\mathbb{N}, \frac{1}{n})$ is a continuous bijection, but the inverse map is not continuous.  Also, if there is such a bijection, there there is such a bijection with agrees with $i$ on any preassigned finite set. Edit  I thought I add in a slightly suprising (to me, at least) example when things work out to be homeomorphic. Begin with a convergent series $\sum c_n$. and divergent series $\sum a_n$ with $\lim a_n = 0$.  Create a new series $b_n$ using all the terms of $c_n$ and $a_n$ (in whatever order you wish).  Then $(\mathbb{N}, a_n)$ and $(\mathbb{N}, b_n)$ are homeomorphic.  The idea is that since $\lim a_n = 0$, there is a convergent infinite subseries $\sum_A a_n$.  Then we use a bijection which with $A$ and $A\cup \{\text{indices of }c_n\}$ to &quot;squeeze&quot; the $c_n$ in without changing the topology.  Of course, I am glossing over many details, but I can include them if desired. Silencing "Your disk is almost full" notification Short way for upper triangularization Comaximal ideals in a commutative ring I use a very custom style (not mine) and very frequently I get a heading  on the bottom of a page and the next paragraph on the top of the next page. Sometimes this paragraph may be a list or similar. The same is true for listings and the listing description.   Is there a general way how I can adjust the "badness" of these events? Or can I adjust when a section heading would be on the last, say, 3cm of a page it should go to the next page? Or can I say, if a *listing description" is on the top 3cm of a page pull 5 more listing lines from the last page onto this page?   The style I use does not use standard structure tags and environments. But lets call them section, subsection, listing and I will try to migrate them to my lingo. Sharing alignment between equations in two different items In the following minimal example, I have two equations inside an itemize environment, with an item per equations. Each equation is defined in its own equation environment.    \documentclass{article} \usepackage{amstext}  \begin{document}  \begin{itemize}  \item Lorem ipsum dolor sit amet, consectetur adipiscing elit:   \begin{equation}     f(x) = \left\{     \begin{array}{l l}       1 &amp; \text{ nisl justo, hendrerit} \\       0 &amp; \text{ sagittis condimentum}\\     \end{array} \right.  \end{equation}   \item Duis magna nunc, ultrices at fringilla non, feugiat sed massa:   \begin{equation}     g(x) = \left\{     \begin{array}{l l}       -1 &amp; \text{ fermentum fringilla mauris eget} \\       0 &amp; \text{ gravida ipsum vitae}\\     \end{array} \right.  \end{equation} \end{itemize}  \end{document}   However, each equation has its own alignment, giving the following result:    It would be nice (I think) if both equations could be aligned in the same way, something like this:    Is this possible?   Note: it would be nice if the solution could be also applied to equations in different paragraphs.    UPDATE:   presented a very nice solution, which is currently the most upvoted, but it does not work quite well:  \documentclass{article} \usepackage{amsmath} \begin{document}  This is a list.  \begin{itemize}    \item First item.   \begin{align*}   f(x) &amp;= \begin{cases} 0 &amp; \text{now} \\ 1 &amp; \text{then} \end{cases}   \intertext{\item Second item.}   g(x) &amp;= \begin{cases} 0 &amp; \text{here and there}  \\ -1 &amp; \text{to and fro} \end{cases}   \end{align*}  \end{itemize}  After the list. \end{document}     Can you see? "now" and "then" are not aligned to "here and there" and "to and fro". Can we solve this? :) How to combine bold and "code sample" in Markdown? Application of Kolmogorov's Zero-One Law Most of the books I read, they only state some examples of tail events. One of them is  $[\sum_n X_n \ converges]$. My main problem is to show that this is indeed a tail event. Pre & post increment operator behavior in C, C++, Java, & C# Homework - set theory infinite union A question from my homework I'm having trouble understanding. We are given:  $A(1) = \{\varnothing\}$, $A(n+1) = A(n)\cup (A(n)\times A(n))$  $A=A(1)\cup A(2)\cup A(3)\cup \cdots \cup A(n)\cup A(n+1) \cup \cdots$ to infinity  The questions are:  1) show that $A\times A \subseteq A$  2) Is $A \times A = A$?  Thank you for your help.  I've tried writing $A(2)$ but it gets really complicated and I'm having trouble understanding what the sets are. Let alone solve the question. Advantages/Disadvantages of Partitioning a Drive I have a 100GB hard drive in my Win XP Pro desktop. I use an external 250GB drive for backups, and am wondering if there would be any advantages to partitioning my internal hard drive.   I understand that some people like to keep their OS and programs on one partition, and their data on another partion on the same hard drive.  I'd like people to list the advantages, or note any disadvantages.  Thanks.