Installing VirtualBox 5.0.10 on the latest version of Windows 10 (ver. 1511, 10586)
How to Install Virtualbox on Windows 10 host?
I know that the product of two Gaussians is a Gaussian, and I know that the convolution of two Gaussians is also a Gaussian. I guess I was just wondering if there's a proof out there to show that the convolution of two Gaussians is a Gaussian. Setting up LVM Snapshot as a backup/restore point in ubuntu Setting up LVM Snapshot as a backup/restore point in ubuntu. Why? Well, as I see it, with all the great usefulness of Linux, its biggest drawback is with its mixed up way of installing apps. All the dlls go to one directory. All the configuration files to another. And the binaries are also put in a bunch. Yes, Windows works the same way more or less, but with the nature of system/server software installed on Linux, being that most of the software installed is only about 95% mature at any given time, messing up your system twice a month is very probable.. Of course, we can backup the system before and after each installation, but that takes a million years. System backups (as oppose to just data/files backup) requires you to turn off you computer and use some form of bootable live CD and a backup media. And, if the drive is more than 15% full, it might take a long time to do the backup, even with modern hardware. So, how can this be done? I'm just getting started with Pinter's A Book of Abstract Algebra, please be kind. The book solution for Chapter 2, Problem 7 claims that the following operator is non-associative:  $$ x * y = \frac{xy}{x+y+1}$$  The book solution:  $$ (x * y) * z = \left(\frac{xy}{x+y+1}\right) * z = \frac{xyz(x+y+1)}{x+y+z+xy+yz+xz+1}$$  $$ x * (y * z) = x * \left(\frac{yz}{y+z+1}\right) = \frac{xyz(y+z+1)}{x+y+z+xy+yz+xz+1}$$  However the $(x+y+1)$ and $(y+z+1)$ terms appear to actually cancel out:  $$ (x * y) * z = \left(\frac{xy}{x+y+1}\right) * z = \frac{\left(\frac{xy}{x+y+1}\right)z}{\frac{xy}{x+y+1} + z + 1} $$  $$ x * (y * z) = x * \left(\frac{yz}{y+z+1}\right)  =\frac{x\left(\frac{yz}{y+z+1}\right)}{x+\frac{yz}{y+z+1} + 1} $$  So the denominators cancel out, the two groupings are equivalent, the operator is associative.  This result is duplicated in Mathematica, but I'd like to make sure I'm not missing something.  Sorry for bothering people with such a basic question. Reading over the Monk I saw that for Martial Arts:     When you use the Attack action with an unarmed strike or a monk weapon on your turn, you can make one unarmed strike as a bonus action.   This implies that non-monk weapons do not count towards being able to make this single unarmed strike. However, when looking over Flurry of Blows:     Immediately after you take the Attack action on your turn, you can spend 1 ki point to make two unarmed strikes as a bonus action.   The requirement doesn't seem to be there anymore, and I didn't see where this discrepancy was covered in . This  says that you can use flurry of blows as a bonus action on any form of attack.   So does the limitation really only exist on a single unarmed strike, but you can use whatever attack action you want to trigger Flurry of Blows? I am able to solve simple differential equations like :  $$\dfrac{dy}{dx} = 3x^2 + 2x$$  We simply bring $dx$ to other site and integrate.  But how do we find solutions of differential equations like :  $$\frac{d^2x}{dt^2} + \dfrac{kx}{m} = 0$$  ?  We have been told the solution is $x(t) = A\cos ( \omega t + \phi_o)$ where $\omega\ =\sqrt{\dfrac{k}{m}}$  but how do we actually find it? Why is plain-hash-then-encrypt not a secure MAC? It seems that even in MAC-then-encrypt systems like SSL, something like HMAC is used rather than a plain hash. Why?   Suppose we use some stream cipher; then why can't we use $Encrypt(m | H(m))$ as the MAC-then-encrypted version of the message? Assuming no bad relations between $Encrypt$ and $H$, what are the possible weaknesses? It seems that in this case we are encrypting the hash with part of a secretly keyed stream cipher keystream, and the hash is secure; does this not fulfil an approximation of the ideal MAC?  This must be somehow bad, since no secure protocol seems to use it. Why? Linux ACL behaviour: settings the mask changes 'ls' output, but not actual permissions I have 12.10 ubuntu and when I try to remove / install programs I get notification :      Software can't be installed or removed because the authentication service is not available.    (org.freedesktop.PolicyKit.Error.Failed: ('system-bus-name', {'name':  ':1.104'}): org.debian.apt.install-or-remove-packages   When I log in as root user (instead of user account that I regulary use) i have no problems. I have not idea how to approach this differential equation.   $$y'-\int_0^xy(t)dt=2$$.  Basically, I did,  $$F''(t)-F(x)+F(0)=2 \;\;\;\;\;\;\; F'=y$$  I am stuck.  Thank You. Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$ Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$.  I started off by putting $\gcd(a+b, a-b) = d$. This implies that there are two relatively prime integers $x_1, x_2$, such that   $dx_1 = a+b$   $dx_2 = a -b$  Adding the first equation to the second gives us: $d(x_1 + x_2) = 2a$, and subtracting the second from the first gives us $d(x_1 - x_2) = 2b$. This implies that $d\mid2a, d\mid2b \implies \gcd(2a, 2b) = d \implies d = 2\cdot \gcd(a,b) \implies d = 2$.   This is based on the fact that $\gcd(x_1 + x_2, x_1 - x_2) = 1$, which is in fact the statement of the problem. How do I prove this? Can I somehow use the Euclidean Algorithm for this. Finding UMVUE of $\theta$ when the underlying distribution is exponential distribution Hi I'm solving some exercise problems in my text : "A Course in Mathematical Statistics".  I'm in the chapter "Point estimation" now, and I want to find a UMVUE of $\theta$ where $X_1 ,...,X_n$ are i.i.d random variables with the p.d.f $f(x; \theta)=\theta e^{-\theta x}, x\gt0$.   I know that $E(X_i)=1/\theta,$ for each $i$, and also have that $\bar{X}$ (or equivalently $\sum_1^n X_i$) is a complete sufficient statistic for $\theta$. But I cannot go any further here. Somebody can help me? Is it safe to use the hash of the data as the key to encrypt them? Is it safe to use the hash of the data as the key to encrypt them?  That is, if I give one some encrypted data and tell them that the key that was used to encrypt them was the hash digest of the data before encrypting, will it be easier for them to decrypt them?  Edit as I can not reply to comments: The recipient will have the keys, that is no problem. Trash icon and files have disappeared from the desktop after upgrade to Ubuntu 19.04 Blender is rendering an older version my project Blender is rendering an older version of my project, not the most recent one. I have made it using the Blender Render but it does not want to render in cycles either. A black and grey screen is rendered as if everything is transparent. Checked general camera, lighting and compute devises in case I messed something up but I can't find anything. All my textures and objects look normal, does anybody know what is wrong or what to check?  Ok added link: Subdivision Surface on curved mesh I'm trying to delete those ugly lines visible in the cylindrical shape of the lens. What is causing them is the added edge loops I made for the protruding detail with the switch. The problem is that if I delete those edges, it'll look even worse because of the n-gons. Any ideas? Value of $\frac{x^n -a^n}{ x-a}$? Let $S=\{\{x\}\mid x \in \mathbb{R}\}$. Is $\sigma(S)$ included in the Borel $\sigma$-algebra on $\mathbb{R}$? Is $\sigma(S)$ equivalent to the Borel $\sigma$-algbrea on $\mathbb{R}$?    I think the answer to the first question is yes. Because the Borel sets include singletons, the Borel $\sigma$-algebra must contain the smallest sigma-algebra of the set of all singletons.   Here's my attempt at the second question: my answer would be no. Countable unions (or intersections) of countable sets are countable, so that any $X \in \sigma(S)$ is either countable or a compliment of a countable set. Therefore, the interval $(0,1) \not \in \sigma (S)$ but it is included in the Borel $\sigma$-algebra. My issue here is that I don't know how to formalize this statement, if it is even correct. I will soon be attending a Ph.D program in mathematics. I do not know how common this practice is, but the department has a requirement that graduate students must learn a foreign language and be able to read and write mathematics in that language. The three choices are French, German, or Russian. I personally have no preference on which to learn, but I was wondering if there were other reasons that would make one language more advantageous over the others in terms of a general mathematical career. Thanks in advance in any response. I recently had somebody tell me that a mutual friend of ours who is  prefers that people refer to him/her using the gender-indefinite pronoun they.   In some cases, this almost seems okay:   Kris left their umbrella at our house.  On the other hand, if Kris is sitting right next to you, it feels very odd to say       They (meaning just Kris) would like more cake.   Or even odder,      Kris would like some more cake, can you please pass it to they/them?"   Are these usages grammatically correct? Are they in the process of becoming grammatically correct? Are there more correct alternatives? When i put the code $(f_{\mathcal{X}},f_{\mathcal{X}}^{\partial})$ I get the following:  But I want the subscripts to be aligned. How can I do this?