around the eyes it just goes dark and i do not know how to fix it
While rendering a mesh with smooth shading on, I get a dark region/shadow on certain faces. The effect is more evident when smooth shading is applied to a mesh containing ngons, with the ngons turning black when rendered.   The blackening effect is visible in the viewport too.  How can I solve this problem?
Did I "get" (or "take") my degree "from" (or "in") the University of Somewhere? I would like to know what is the preferred way to indicate that I took a degree in some subject while also naming the place where I obtained the degree from:   I got my master's degree from the University of Somewhere; I got my master's degree in the University of Somewhere; I took my master's degree in the University of Somewhere.   I would say that "in" is more suitable to mention the particular subject (a degree in maths, for instance) than to indicate the place, but I still have doubts.  By the way, is it a "master's degree" or a "Master's degree"? I have the following equation, where there is a lot of stuff under the sum symbol:  \begin{equation} d(\vec{x},\vec{y})=   \sum_{Z_{xy}\in\vec{Z}_{xy},\forall x\in\vec{x},\forall y\in\vec{y}}      f(Z_{xy}) \end{equation}   In the resulting document, I find it kind of hard to read. Is there a way to write the equation to make the result more readable, e.g. putting the stuff under the sum symbol on different lines? Do subdomains help/hurt SEO? How to shift EXIF date/time created by time in days, hours, minutes? Let $a\ge1$ and define the sequence $(x_n)$ recursively by: $$x_1 = \sqrt{a}$$ $$x_{n+1}= \sqrt{a+x_n}$$  Here's what I did:  Plugging in some values makes it seem as if the sequence is increasing. I first solve the equation $t=\sqrt{a+t}$, equivalently $t^2 -t -a =0$, to get an idea what's going on. The roots are $$t_{1,2}= \frac{1 \pm \sqrt{1+4a} }{2}.$$ Therefore, between the roots, that is for $$t\in \left( \frac{1 - \sqrt{1+4a} }{2}, \frac{1 + \sqrt{1+4a} }{2}\right)$$  we have $t^2-t-a \le 0 \iff t \le \sqrt{a+t}$. Here's my attempt at showing inductively that $$\forall n\in \mathbb{N}, \ x_n \le \frac{1 + \sqrt{1+4a} }{2}$$  For $n=1$, the statement is true (simple arithmetic). Suppose it's true for $n$. Consider  $$x_{n+1}= \sqrt{a+x_n}\le \sqrt{a+\frac{1 + \sqrt{1+4a} }{2}}=\frac{1 + \sqrt{1+4a} }{2},$$  because $\frac{1 + \sqrt{1+4a} }{2}$ satisfies $x=\sqrt{x+a}$.  So this establishes the sequence $(x_n)$ is bounded. Now, by induction again, I try to show it's monotonically increasing. The base case $x_1\le x_2$ is obvious. Assume (strong induction) $x_{n-1}\le x_n$ for all $n&gt;1$. But since we have $$x_1\le x_n \le \frac{1 + \sqrt{1+4a} }{2}, $$   then $x_n$ lies in the appropriate interval, so $x_n \le \sqrt{a+x_n}=x_{n+1}.$  Is this proof correct? Can the condition on $a$ be relaxed to $a&gt;0$? Maybe even small negative $a$? And could someone provide me with another proof of convergence of $x_n$? I absolutely hate this one! How to execute a Matlab script from C++ $$\int x^3\sqrt{4-x^2}dx$$ I tried changing the expression like this: $$\int x^3\sqrt{2^2-x^2}dx=\int x^3\sqrt{(2-x)(2+x)}dx$$ And that's where I got stuck. I tried integration by parts but it doesn't simplify the expression. Can truesight see through a druid's Wild Shape? The rules for truesight state:     A creature with truesight can (..) perceive the original form of a shapechanger or a creature that is transformed by magic   A druid player argued that since the druid is still a "humanoid" (not a "shapechanger"), and since , a creature with truesight should not see through it.  As the DM, I ruled against it because I believed the intent of truesight is to see through all kinds of shapechanging effects but I was still left wondering if I missed anything. I couldn't find anything about this in the errata either.  So, going by strict RAW, should a creature with truesight be able to see the druid's true form while a druid is using wild shape? I know that an easy to handle formula for the CDF of a normal distribution is somewhat missing, due to the complicated error function in it.  However, I wonder if there is a a nice formula for $N(c_{-} \leq x &lt; c_{+}| \mu, \sigma^2)$. Or what the "state of the art" approximation for this problem might be. Possible to get type of an aliased type in c#? Type.GetType("System.String")   Is there a lookup for the aliases available somewhere?  Type.GetType("string")   returns null. I am using Ubuntu 16.04 with GTX 1080. On my first boot, the screen turn black after I selected Ubuntu in grub. After I added nomodeset, the black screen gone however it only shows the Ubuntu default background image. It can't reach the login screen. How do I completely uninstall Google Chrome and Chromium? I'm having a problem with Chrome and one of its extensions, so I want to completely uninstall everything. I've uninstalled Chrome through the Software Center, but when I reinstall it, all of my extensions and preferences are still there.   If I want to start over from scratch, what do I need to do? Trouble creating 3TB ext4 partition due to msdos-partition-table-imposed error What was the origin of Star Trek's Borg? What is the difference between range and xrange functions in Python 2.X? I wanted to upgrade to 14.04.2 point release from 14.04.  What I did was:  sudo apt-get update &amp;&amp; sudo apt-get upgrade &amp;&amp;  sudo apt-get dist-upgrade -y   Then I wanted to upgrade to 3.16 kernel, since it wasn't done with the the above command, so what I did was:  sudo apt-get install linux-generic-lts-utopic xserver-xorg-lts-utopic libegl1-mesa-drivers-lts-utopic xserver-xorg-video-all-lts-utopic xserver-xorg-input-all-lts-utopic sudo apt-get install linux-signed-generic-lts-utopic   Now when I do:   uname -a I get   Linux Y500 3.16.0-33-generic #44~14.04.1-Ubuntu SMP Fri Mar 13 10:33:29 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux  cat /etc/os-release | grep VERSION= I get  VERSION="14.04.2 LTS, Trusty Tahr"   And when I do lsb_release -a I get  Distributor ID: Ubuntu Description:    Ubuntu 14.04.2 LTS Release:    14.04 Codename:   trusty   I know that uname -a and lsb_release -a both refer to different info, but why does  cat /etc/os-release | grep VERSION= show different version? How do I rollback a TFS check-in? I'd like to rollback a change I made recently in TFS. In Subversion, this was pretty straightforward.  However, it seems to be an incredible headache in TFS: Option 1: Get Prior Version  Manually get prior version of each file Check out for edit Fail - the checkout (in VS2008) forces me to get the latest version  Option 2: Get TFS Power Tools  Download Team Foundation Power Tools Issue rollback command from cmd line Fail - it won't work if there are any other pending changes  Option 3: Manually Undo Changes  manually undo my changes, then commit a new changeset  Question How do I rollback to a previous changeset in TFS? HSA - Continue to Invest? Lyman and Balmer series Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$