Linear Algebra Matlab matrix loop?
Matlab Recursion Loop
Appositives with possessiveness? I would like to say something like     The boy, Adam's, favorite toy was a bike.   What is the proper way to say this? Find conditional expectation from a 3-dimensional random vector? How to Preload Tabs/Set Multiple Websites as Default in Firefox, IE, etc Any website can set as the homepage of Firefox which loads spontaneously. Is this for multiple tabs? Then BBC Health, CNN, Yahoo Health, msn.com would all extemporarily materialise (in four separate tabs); I then wouldn't have to open each website manually. Is there a way to programmatically change the screen resolution or enable/disable multiple monitors in Windows XP?  For example to change from 1024x768 with one monitor to 1280x104 on two monitors?  I would be most interested in a win32 function to do this but anything that can be tied to a windows shortcut would suffice. How can I encrypt and decrypt a string in C#? Proof involving absolute value and maximums Given the definition for any real numbers a and b, the max function is   $\max\{a, b\} =  \begin{cases}                                    a \text{ if } a \geq b \\                                    b \text{ if } a &lt; b \\   \end{cases} $  Lemma: for any two real numbers $a\text{ and }b, a \leq \max\{a,b\}$ and $ b \leq \max\{a,b\}$.  Prove that for real numbers, $a, b$, and $x$, if a $\leq x \leq$ b then $|x| \leq \max\{|a|,|b|\}$.  So far, I have  $x \geq 0$ or $x &lt; 0$ by the law of trichotomy  Case 1: $x\geq 0$  $|x| = x$ by the definition of absolute value  and I'm not sure where to go from there. Any hints? Is there a published way to take text that may have accent marks and remove the accent marks?  For example:  System.assertEquals('Hello', transform('Ḧéļḻṏ'));   I believe there is an equivalent method in Java, C# and JavaScript. I can't seem to find the Apex equivalent and I'm disturbed that I might have to do it on my own. In the 3d-view workspace, we can use a random color to give our separated object a distinct look.  What if I don't like the result and I want to randomize the color again?   Swapping the setting doesn't change the random seed in color.    (Blender 2.80.64.) "Where" exactly are complex numbers used "in the real world"? I've always enjoyed solving problems in the complex numbers during my undergrad. However, I've always wondered where are they used and for what? In my domain (computer science) I've rarely seen it be used/applied and hence am curious.  So what practical applications of complex numbers exist and what are the ways in which complex  transformation helps address the problem that wasn't immediately addressable?  Way back in undergrad when I asked my professor this he mentioned that "the folks in mechanical and aerospace engineering use it a lot" but for what? (Don't other domains use it too?). I'm well aware of its use in Fourier analysis but that's the farthest I got to a 'real world application'. I'm sure that's not it.  PS: I'm not looking for the ability to make one problem easier to solve, but a bigger picture where the result of the complex analysis is used for something meaningful in the real world. A naive analogy is deciding the height of tower based on trigonometry. That's going from paper to the real world. Similarly, what is it that is analyzed in the complex world and the result is used in the real world without imaginaries clouding the problem?  The question:  is nice but covers a more mathematical perspective on interim results that make solving a problem easier. It covers different ground IMHO. How to open a file manager of the current directory in the terminal? When I work in terminal, sometimes I want to open the current directory in a GUI file manager. And then to click the items in the window to run the application. How can I do this? What's the protocol for requesting a tag warning? On a particular site, RPG Stack Exchange, we've decided on our meta on a couple of tags that should have tag warnings, and on what those tag warnings should say. I am  on the site in question.  What should we do to get the tag warnings implemented? Do we do any/all of the following?:   start a [feature-request] on our meta for the tag warnings? raise a CM escalation? contact staff via the contact form? ping a staff member in the Teacher's Lounge? anything else? $L^p$ and $L^q$ space inclusion Let $(X, \mathcal B, m)$ be a measure space.  For $1 \leq p &lt; q \leq \infty$, under what condition is it true that $L^q(X, \mathcal B, m) \subset L^p(X, \mathcal B, m)$ and what is a counterexample in the case the condition is not satisfied? If $p$ is prime, then $(x+y)^p=x^p+y^p$ holds in any field of characteristic $p$. However all the proofs I have seen use induction and some relatively nasty algebra despite how fundamental this fact seems.  What is the nicest, "highest level proof" you know? Do tenses in a time clause never back-shift in reported speech? Do tenses in a time clause never back-shift in reported speech?  For example, does      "I went to Italy when I finished school."    become      She said she had gone to Spain when she finished school.   -or-   She said she had gone to Spain when she had finished school.   and does      "I will go to Italy when I finish school."    become     She said she would go to Italy when she finishes school.   -or-   She said she would go to Italy when she finished school. Determining likely relationship based upon autosomal DNA shared cM Transparent model when exporting fbx file to Unity So I have this shark model which I animated and ready to export it on fbx and transport it to Unity.  But When I put it on Unity, It looks transparent like this.    Many of the solutions online say that the problem is because of my faces, and they told me to recalculate it or something, but normals are just fine. Is there any other solution?  here's the blend file: Is $f(x,y) = |xy|$ differentiable in $(0,0)$? I have no idea how to approach this problem. Cannot change lock screen background on Ubuntu 18.04 For $n$ a positive integer, let us write $\zeta_n = e^\frac{2 \pi i}{n}$, a primitive $n$th root of unity. It is clear that, if $m$ divides $n$, then we have an inclusion of cyclotomic fields $$ \mathbb{Q}(\zeta_m) \subseteq \mathbb{Q}(\zeta_n).$$ On the other hand, these inclusions are not always strict. For example, since $\zeta_3  = \frac{1+i \sqrt{3}}{2}$ and $\zeta_6 = \frac{-1 + i \sqrt{3}}{2}$, we have $$\mathbb{Q}(\zeta_3) = \mathbb{Q}(\zeta_6) = \mathbb{Q}(i\sqrt{3}).$$ Does this sort of thing happen infinitely often, or are there just some coincidences among small numbers? If this continues, is there some way to know when a particular inclusion of cyclotomic fields is strict? Objects, shadows and reflections not rendering in EEVEE I started to work with EEVEE short time ago and I was amazed by the capabilities of this engine. However, I noticed something strange when I was rendering some tests. Some objects/reflections/shadows dissapear when they're off canvas. I imagine that maybe this is for save memory data, but it can be not suitable to some projects. To make my point graphical, I made a simple scene with simple objects. The main object is the sphere with a mirror-like shader. Out of focus there are different objects with different shaders. A yellow cone, a blue cylinder and a white cube light. But surprisingly, those objects dissapear when the composition is rendered. See the rendered animation below:  Notice that the blue cylinder is not even showing at all in the final render. And the blooming effect from the light cube also dies. I would like to improve this bahaviour and render the objects that are still out of canvas using EEVEE. Do I missing something like memory configuration or reflection/shadow tweaks? Is this caused by the EEVEE engine or by my GPU config (GTX1060)? Thank you in advance!