Mac Pro 2019 with Blender? I've planned to buy the new basic 2019 Mac Pro, essentially for use with blender. Is that a good idea? I own a mid2010 Mac Pro for now but it's a little bit slow as soon as there are a few textures in my projects. ...or should I switch on a Windows solution? Thanks
Which Mac is suitable for Blender 2.8? I am considering purchasing a Mac for my godson who will be using it to run Blender 2.8.  I know very little about this program.  All I can find are requirements for a Mac that will run earlier versions of Blender.  Would someone please recommend a list of requirements for a Mac (or a link to a list of requirements) that I could use to find a model that can run 2.8?  Thank you in advance for all your help! Sincerely, M. Lap
Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$ Prove that $\left (\dfrac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} &gt; a^a b^b c^c$ if $a$, $b$ and $c$ are distinct natural numbers.  Is it possible using induction? How to connect to a MS Access file (mdb) using C#? A book suggests that we should not interchange "so" and "so that". "So" means "therefore", and "so that" means "in order that". However, it seems to me that in many cases they don't actually have a difference. For example:     Alice got up at 5:00 A.M., so that she could drive her son to school.   If I substitute "so that" with "so", this sentence presents the exact same causal relation to me:     Alice got up at 5:00 A.M., so she could drive her son to school.   I must have missed something here, since English is my second language. Could somebody explain the difference? Rewriting Triple Integral in different order How can I rewrite, say: $$\int^1_0\int^{z^2}_0\int^y_0{f}dxdydz$$ In the orders $dzdxdy$ and $dydzdx$?  Would I have to solve this triple integral all the way or is there a simple way to do this? It seems that we are . This is the speed of our galaxy relative to the cosmic microwave background. Where does this rest frame come from? Is this special in any way (i.e., an absolute frame)? EDIT: I think the more important question is &quot;where does the CMB rest frame come from?&quot;. I need to cite the journal "Sankhyā: The Indian Journal of Statistics" in a paper.  I would like to draw the ā character properly (i.e., I'd prefer, if possible, to avoid using some hack, such as \bar or \overline).  Question: How do I properly write ā in LaTeX?  I didn't have luck with  (after several attempts in both in capital and lowercase) nor The Comprehensive LATEX Symbol List (searching the file for "ā" and "india" revealed no hits). Is there a way to access wifi in Zurich airport without a phone service? I am traveling through Zurich and have a phone without any roaming there; I'm planning on picking up a SIM once I get to my final destination. Last time I was there, I couldn't access the airport wifi because it required a code sent via SMS.    In the event I need to contact someone or coordinate about flight delays, is there some alternate way to get wifi access? How do I remove Windows 7 from my dual boot system with Ubuntu? Hello can someone give me short tutorial how to:   Remove Windows 7 from my dual boot system (Ubuntu/Windows7) Let me use free space as new partition for data (so I don't need to extend Ubuntu itself here) Remove windows 7 option from boot screen   Update:  Thanks to Lekensteyn answer I successfully deleted windows. Now I created new partition (formatted to ext4), but I can not use it. I cannot copy files there, only as root.  Also when booting, Ubuntu complains it didn't find /windows partition (of course it didn't, I removed it). I feel like I should update some tables or what, any ideas? My question is pretty simple.  Since $n! \gt n!!$, it's clear by the comparison test that $\sum_{n=0}^\infty \frac {1}{n!!}$ converges.      But what value does the sum converge to? How does one go about determining its value (if possible)? Are there perfect elastic collisions in Nature? Understanding dummy (manual or automated) variable creation in GLM If a factor variable (e.g. gender with levels M and F) is used in the glm formula, dummy variable(s) are created, and can be found in the glm model summary along with their associated coefficients (e.g. genderM)  If, instead of relying on R to split up the factor in this way, the factor is encoded in a series of numeric 0/1 variables (e.g. genderM (1 for M, 0 for F), genderF (1 for F, 0 for M) and these variables are then used as numeric variables in the glm formula, would the coefficient result be any different?  Basically the question is: does R use a different coefficient calculation when working with factor variables versus numeric variables?  Follow-up question (possibly answered by the above): besides just the efficiency of letting R create dummy variables, is there any problem with re-coding factors as a series of numeric 0,1 variables and using those in the model instead? I've noticed something while trying to prove the properties of parallel lines, and the properties that a triangle has 180 degrees. To prove the properties of parallel lines, such as alternate angles, you need to use the property that a triangle has 180 degrees. To prove a triangle has 180 degrees however, you need to use the properties of parallel lines. This really bothers me because of how circular it is. They are both reliant on each other to be true, and do not logically show, without being reliant on each other, why triangles have 180 degrees, and why parallel line properties are true.   So what I hoping for here is a way to prove parallel line properties without using the fact that a triangle has 180 degrees, or a way to prove triangles have 180 degrees without using parallel line properties. This way, things will be logical to me, and make sense.   Thanks in advance. Consider the IVP $$y'(t)=f(y(t)), \ \ \ \ y(0)=a \in \mathbb{R}$$ $$f : \mathbb{R} \rightarrow \mathbb{R}$$ Which of the following is/are true $(A)$  There exists a continuous function $f : \mathbb{R} \rightarrow \mathbb{R}$ and $a \in \mathbb{R}$ such that the above problem does not have a solution in any nbd of $0$. $(B)$  The problem has unique solution for every $a \in \mathbb{R}$ when $f$ is Lipschitz continuous $(C)$ When $f$ is twice continuously differentiable the maximal interval of existence for the above IVP is $\mathbb{R}$ $(D)$ The maximum interval of existence  for the IVP is $\mathbb{R}$ when $f$ is bounded and continuously differentiable.  It is obvious to me that $A \ \&amp; \ B$ are false from traditional existance and uniqueness theorems (viz Picards Theorem). I am not sure about $C \ \&amp; \ D$ and this is really bugging me. Please could anyone shed light on this. PS: Multiple correct options are allowed. What is the noun for someone who receives a referral? When a referrer (noun) gives a referral (noun) to another person, what is the term (noun) used for the recipient of the referral? "The referred" may work, but am I missing another term? "Referred" indicates past-tense, but I intend to use the term in future and present tense as well. How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$ How to solve the following functional equation:  Find all $f:\mathbb{R}\to\mathbb{R} $ such that: $$ f\left(x^2+f(y)\right)=y+f(x)^2 $$ Holds for every $x,y\in\mathbb{R}$.  A friend gave it to me, probably its an olympiad question.  I started with the equation $f(f(y))=y+f(0)^2$ which seems to be quite helpful, but I couldn't do it effectively. How to solve it properly? Moving all files to a new computer, my concern is links only display df lines that have more fs usage than 80% Recursively rename files and directories Every Artinian ring is isomorphic to a direct product of Artinian local rings Proposition. Let $R$ be commutative ring with $1_R$. We assume that $R$ is an Artinian ring and $M_1,\dots,M_n$ its maximal ideals. Then         $R/\mathrm{Jac}(R)\cong (R/M_1)\times \dotsb \times (R/M_n)$.   The ring $R$ is isomorphic to the direct product of a finite number of Artinian local rings.      Proof. 1. It's obvious that $M_i+M_j=R,\ \forall 1\leq i \neq j \leq n$. So, from Chinese Remainder Theorem, we have  $$R/\bigcap_{i=1}^{n}M_i = R/\mathrm{Jac}(R) \cong (R/M_1)\times \dotsb \times (R/M_n),$$ as we wanted.    Since $R$ is an Artinian ring, we have $\mathrm{Jac}(R)^m=\{0_R\}$, for some $m\in \Bbb Z^+$. But,  $$\{0_R\}\subseteq M_1^m\dotsb M_n^m=(M_1\dotsb M_n)^m\subseteq (\bigcap_{i=1}^{n}M_i=\mathrm{Jac}(R))^m=\{0_R\}.$$ So, if we apply CRT we will take  $$R\cong R/\{0_R\}\cong R/M_1^m\dotsb M_n^m\cong (R/M_1^m)\times \dots \times (R/M_n^m).$$   Questions.   1) Are these thoughts complete and correct?  2) Why $R/M_i^m$ are artinian local rings?  3) Could you please elaborate some examples as an application? When should I use the Visitor Design Pattern?