I finished the mesh but went i try to smooth it i got a rare black shadow :  3D viewport - no smooth    3D viewport -  smooth    Render - smooth    Render - no smooth
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?
Should I use an offset for my Poisson GLM? I am carrying out research to look at differences in fish density and fish species richness when using two different underwater visual census methods. My data was originally count data but then typically this is changed to fish density but I have still decided to use a Poisson GLM, which I hope is right.   model1 &lt;- glm(g_den ~ method + site + depth, poisson)   My 3 predictor variables are method, site and depth which I ordered as factors when I input them.   My response variables are grouper species richness, grouper density and the same for other fish groups. I am aware that density is not an integer and it is numerical data e.g 1.34849. I am now however getting this error:      In dpois(y, mu, log = TRUE) : non-integer x = 0.037500   I've been reading up and many people suggest using an offset, is this the most advisable thing to do? If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square. Problem is as stated in the title. Source is Larson's 'Problem Solving through Problems'. I've tried all kinds of factorizations with this trying to get it to the form $$k^2l^2$$ but nothing's clicking. I tried Bézout but the same expression can be written as $$a^2 + (a^2 + 1)(a+1)^2$$ which would imply that there is no real root.  Would really appreciate some help, thanks. This is what my GRUB 2 menu looks like so far:  I want to do a few things here:  I want to rename &quot;Windows Boot Manager (on /dev/sda1)&quot; to just &quot;Windows 8.1&quot;. I'd like to rename &quot;Ubuntu&quot; to &quot;Lubuntu 14.04.1&quot;. I'd also like to switch the order of the options to this:  Windows 8.1 Lubuntu 14.04.1 Advanced options for Lubuntu    (Windows will be the default OS) If it helps in any way, I'll explain the steps I took prior to this, since I am very new to Linux and don't know what information is required.  I bought a laptop on Amazon (ASUS X551MAV-EB01-B) pre-installed with Windows 8.1 64-bit I downloaded the proper Lubuntu .iso file for my system (Lubuntu 14.04.1 amd64) and put it on my flash drive (via UNetBootin) I went to Disk Management, and shrunk the C:/ drive down 32Gb so that 32Gb will be free for Lubuntu I used my flash drive (32Gb Sandisk Cruzer) as a LiveUSB for Lubuntu 14.04.1 I went through the install process. It didn't recognize Windows 8.1 so I had to do the &quot;Something Else&quot; option. I highlighted the free space, and pressed the + button I created a 10,000mb ext4 partition and mount point is / (is now dev/sda7) I created a 4,000mb swap area partition (is now dev/sda8) I created an ext4 partition using the rest of the free space and the mount point is /home (is now dev/sda9) I selected dev/sda7 to install Lubuntu and selected dev/sda7 for the bootloader installation It installed just fine, booted up just fine, and I'm happy to know the GRUB menu works. Is $29$ the only prime of the form $p^p+2$? Javascript to sort contents of select element is there a quick way to sort the items of a select element? Or I have to resort to writing javascript?  Please any ideas.  &lt;select size="4" name="lstALL" multiple="multiple" id="lstALL" tabindex="12" style="font-size:XX-Small;height:95%;width:100%;"&gt; &lt;option value="0"&gt; XXX&lt;/option&gt; &lt;option value="1203"&gt;ABC&lt;/option&gt; &lt;option value="1013"&gt;MMM&lt;/option&gt; &lt;/select&gt; Here is what I tried doing:  #!/bin/sh res=`df | awk 'FNR == 2 { print $5 }'` res2=$((res+0))   Here is my error:     -bash: 53%: syntax error: operand expected (error token is "%")   I Googled 'string to int bash' which showed me $((res+0)) but it doesn't work due to the % in the string (53%). How do I convert it in such a way I can do an if statement such as the one below (but that works)?  if [ "$res2" -ge 50 ] then     echo "Your disk &gt;=50% full!" fi Is there a rule for pronouncing “th” at the beginning of a word? Consider the th in thistle versus the th in this: the former is unvoiced, while the latter is voiced.  Is there a rule or reason for the differences? for (i=0 ; i&lt;=10; i++) {     ..     .. }  i=0; while(i&lt;=10) {     ..     ..     i++; }   In for and while loop, which one is better, performance wise? If refraction slows down light, isn't it possible to hold light still? I have a quick question about the refraction of light, and I'm sorry if it seems a bit simplistic or even stupid, but I'm still learning.  We know that when light passes through a denser medium, it slows down. However, is there a limit to that slowing down? If no, wouldn't it be possible, with some type of medium we make ourselves (like a crystal), to decrease the light's speed down to a point where we would be able to "see the photons moving forwards"?  I know it is way more complicated than that and that you can't see light unless some other light bounces off it, what I mean is slowing down light to an extreme and unusual speed). That sounds completely absurd but I can't seem to find what is wrong. Can anyone can explain it to me? :) How do I show that the equation $x^3+10x^2-100x+1729$$=0$ has at least one complex root $a$ such that $|a|$$&gt;$$12$. What are the powers shown by the Rings of Power? Money transfer from India to USA My daughter is a US Citizen. We (parents)are also planning to permanently settle in US. We will go their as Permanent Resident,as per US Law. We have a house here in India worth Rs.2 Crores.  We want to sell it and take money with us. We have ordinary savings Bank account here in India.  My US Citizen Daughter is a Income Tax payer.  Now your advises are required as under:   What are the routes to take money from India to US and our tax liabilities Can I gift this whole amount to my US Citizen Daughter or what is the maximum limit of Gift amount.  What will be the tax liability on me and on my Daughter in case of Gift   Whether I have to show it in my Income Tax Return or in my Daughter's Tax Return. What US Income Tax Laws says. What will be the procedure to send money as Gift to my Daughter. Will the money will go directly from my Bank Act.to my Daughter's Bank Account. Will there will be wire transfer from bank to bank Can I send money through other money sender Certified Companies also.    Please advise. If there is something more on the subject to make me understand, please advise. Thanks, What's the difference between postfix/smtp and postfix/smtpd A bit confused when reading through the logs of my smtp/mail server, I'm turning this questions to you guys.   In the maillog files I'm seeing entries for postfix/smtp as well as postfix/smtpd. I can also see that there are possible settings for smtp as well as smtpd in the file main.cf  Trying to find some reasonable explanation through google search seemed to be impossible, so here is my question to you guys.  My server was kind of compromised and the spam mails where going through postfix/smtp and not smtpd. Please help me to understand. Thanks in advance! How do I check where devices are mounted? What is the command that lets me see what and where devices are mounted?  I'm having trouble changing songs on my old iPod, and I have a feeling it's because of the mount point. I am trying to find out how to approach a relief type project. I have a background image and a flat plane mesh to sculpt on, but I actually don´t see any changes looking straight on top. When I tilt the perspective a bit the image disappears.  Is there a way to make the image appear at all perspectives? Are PPAs safe to add to my system and what are some "red flags" to watch out for? "Questions like this" or "questions like these" Proof if $a \vec v = 0$ then $a = 0$ or $\vec v = 0$ I'm kicking myself over this one, but I just can't seem to make the argument rigorous. From Axler's Linear Algebra Done Right:  for a vector space $V$ with an underlying field $F$:  Take an element $a$ from $F$ and $\vec{v}$ from $V$. $a\vec{v}=\vec{0}\implies a=0 $ or $ \vec{v}=\vec{0}$  After only being able to come up with half of a direct proof, I tried doing this by proving the contrapositive $a\neq 0 \wedge \vec{v} \neq \vec{0} \implies a\vec{v}\neq \vec{0}$  Say $a\vec{v}=\vec{u}$. Since $a$ is non-zero, we can divide both sides by $a$.  $$\vec{v}=\frac 1 a \vec{u}$$  If $\vec{u}$ were $\vec{0}$ then by  $$\frac 1 a \vec{0}=\frac 1 a (\vec{0}+\vec{0})\implies\frac 1 a \vec{0}=\vec{0}$$ $v$ would be $0$ as well. Since it isn't by assumption, $\frac 1 a \vec{u}$ cannot be zero and so $\vec{u}$ cannot be as well.   Is this fully rigorous? It seems like a very simple question, but I'm not sure about it. Namely, the last step of $\frac 1 a \vec{u}\neq 0 \implies \vec{u}\neq 0$ doesn't seem obvious. I think I need to use the $1\vec{v}=\vec{v}$ axiom, but I'm not sure how.  Is there a more direct proof? This whole contrapositive business seems a bit clunky for something so simple. How to prepare files for rsync on a case insensitive filesystem? I'm trying to remember a film I saw years ago (1980's?).  The only part I clearly remember is a man and girl being bricked up alive (in a tower?) and escaping by turning his (magically large) coat or cloak into a rudimentary hang glider.  The film had a medieval sword/sorcery setting.