"Can you send me Fred and your flight information?"
Compound possessives and yours
Is there really a way to make a true toon shader material in Cycles? Find when three numbers have the same remainder when divided by the same number If three numbers 112, 232, and 400 are each divided by the number D, each of their quotients will have the same remainder R. Find R where R>1  How should I approach this? Prove that $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$   My proof is below. I am interested in other proofs.    My proof  Let   $$f (\mathrm X) := \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B)$$  Hence,  $$\begin{array}{rl} f (\mathrm X + h \mathrm V) &amp;= \mbox{tr} (\mathrm A (\mathrm X + h \mathrm V)^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A (\mathrm X ( \mathrm I + h \mathrm X^{-1} \mathrm V))^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I + h \mathrm X^{-1} \mathrm V)^{-1} \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I - h \mathrm X^{-1} \mathrm V + O (h^2)) \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) - h \, \mbox{tr} ( \mathrm A \mathrm X^{-1} \mathrm V \mathrm X^{-1} \mathrm B) + O (h^2)\\ &amp;= f (\mathrm X) - h \, \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) + O (h^2)\end{array}$$  Thus, the directional derivative of $f$ in the direction of $\mathrm V$ at $\mathrm X$ is  $$D_{\mathrm V} f (\mathrm X) = - \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) = - \mbox{tr} ( (\mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top})^\top \mathrm V ) = - \langle \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}, \mathrm V \rangle$$  and, lastly,  $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$ I'm trying to write a shell script that, when run, will set some environment variables that will stay set in the caller's shell.  setenv FOO foo   in csh/tcsh, or  export FOO=foo   in sh/bash only set it during the script's execution.  I already know that   source myscript   will run the commands of the script rather than launching a new shell, and that can result in setting the "caller's" environment.  But here's the rub:  I want this script to be callable from either bash or csh.  In other words, I want users of either shell to be able to run my script and have their shell's environment changed.  So 'source' won't work for me, since a user running csh can't source a bash script, and a user running bash can't source a csh script.  Is there any reasonable solution that doesn't involve having to write and maintain TWO versions on the script? Get the size of the screen, current web page and browser window How do you fix a bad merge, and replay your good commits onto a fixed merge? I accidentally committed an unwanted file (filename.orig while resolving a merge) to my repository several commits ago, without me noticing it until now. I want to completely delete the file from the repository history.   Is it possible to rewrite the change history such that filename.orig was never added to the repository in the first place? What causes the portraits of Wizards to behave interactively? Does J.K. Rowling address how the interactive portraits work? Would a portrait painted after a Wizard/Witch died become interactive, or does the painting of the portrait have to take place during the Wizard/Witches lifetime? How can I efficiently generate a Set from a List structure? I have a bit of code where I've written a SOQL query that returns a list of SObject records, however I need a Set&lt;Id&gt; structure to pass to another method that I don't have control of (and thus can't change the method signature of).  How can I turn my returned List&lt;SObject&gt; into a Set&lt;Id&gt;? Is the best option just a for loop? Where are packages stored installed with APT in Ubuntu 16.04? A gerund or use a regular noun? Which of these is correct or more natural?        One of my greatest strengths is critically analyzing.      One of my greatest strengths is critical analyzing.     One of my greatest strengths is critical analysis. I would like to show that   $$ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $$  What annoys me is that $ x-1 $ is the numerator so the geometric power series is useless.  Any idea? Frequent Write to Non-volatile Memory I am designing a device that automatically adjusts it's physical position as temperature changes. If the device it shut off or power is disconnected the device needs to remember it's last temperature and position. I have the ability to store these values in EEPROM but the problem is the position and temperature could be changing very rapidly. If I were to write the temp and pos to EEPROM after every time they changed that would (1) slow down the firmware a bit, and (2) likely kill the EEPROM after a year or two. So as I see it my options are as follows...  1) use a capacitor/battery to keep the device powered for a short time after power is lost so that I can write the values to EEPROM at that time only. I don't like this because the board is kinda power hungry and this would require a big cap. And I don't have a ton of free space. And I don't want the added cost of a battery and battery holder / or a big cap.  2) use F-RAM instead of EEPROM so that I can write to it trillions of times without wearing it out. I don't like this option because FRAM is quite a bit more expensive than EEPROM and this is for a production product (not just one).  3) Only write the position and temperature every 5 minutes or so. That way I always have a fairly recent position/temp recorded but I am not writing every second so my program is not slowed down and the EEPROM won't die as fast. This seems like my best option.  Does anyone else have any suggestions that I'm not thinking of? I am having a serious trouble finding an agreement between the two facts in Special Relativity:  (1) given two events $A$ and $B$ in spacetime separeted by a spacelike interval $s$, the distance in space between the two events will be the shortest in the reference frame which the two events occur simultaneously:   The invariance of the interval says $s^2=(\Delta x)^2-(c\Delta t)^2$ and $\Delta x$ is minimum when $\Delta t=0$  (2) the length contraction says $L=\dfrac{L_0}{\gamma}$ where $\gamma=(1-(v/c)^2)^{-1/2}$ , $L_0$ is the proper length of an object in a reference frame which the object is at rest and $L$ is the length of the object in a reference frame which the object moves with speed $v$ in the $x$ direction.  This says that the lenght of the object in the $x$ direction is the largest in the comoving reference frame of this object.  The question is: According to (1), the reference frame in which two events $A$ and $B$ occur simultaneously is the reference frame that gives the shortest distance in space between the two events. Let $A$ and $B$ be the two end points of a meter stick in a reference frame in which the stick is at rest and at time $t=0$. This two events occur simultaneously, so the distance in space between the two is the shortest acording to (1). But according to (2) shouldn't this distance be the largest?  What is wrong? Could I have a hint for testing the convergence of the following series please?  $$\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$$  I am very appreciative for your help. Any time I am inserting new point feature in QGIS, the Feature Attribute dialog box is popping up. Is there a way to prevent it? (I am willing to insert many points at once and this pop up box slows down the process). Parsing JSON with Unix tools Multiplying Binomial Terms What should be done when no more Pokemon can be caught? (when full storage) Connect to Linux by name rather than IP I'd like to create a Categorized style in QGIS, classify with it data in a shapefile and then save the shapefile with the new categorized style. Is it possible?