I know that affine equalities such as  $$a_1 x_1 + a_2 x_2 + a_3 x_3 = b_3$$  are convex. I'm wondering whether there are nonlinear equality constraints, for instance something like  $$a_1 x_1 + a_2 x_2 + a_3 x_3 = b_3 + x^{2p},\quad p \in N$$  or even something like  $$x_1 = x_2^2$$  Are these kinds of equality constraint also convex? Can you give me any other example showing non-affine convex functions? Thanks!
In convex optimization, the feasible region is convex if equality constraints $h(x)$ are linear or affine, and inequality constraints $g(x) \leq 0$ are convex. Does this mean that if $h(x)$ is nonlinear, then the optimization problem is non-convex? Is there any special case where $h(x)$ is nonlinear and the feasible region is still convex?
/usr/bin vs /usr/local/bin on Linux My Father passed away - next test(s) on what remains of his DNA sample? I posted this general question over at the forum on FamilyTreeDNA. Though I received a reply, there is still no answer to my question, so I thought I'd try my luck at posting here.  Anyhow, in early 2009 I bought two kits for the Genographic Project and dutifully had my father do his cheek swabs: one kit for his Y-Chromosome, and one for his mtDNA. Once that was completed, I had his samples transferred to Family Tree DNA.  Then, late in 2009 I paid to have an mtFullSequence done on his mtDNA sample.  My father passed away in 2015. In early 2016, I phoned FTNDA to discuss. The first thing they did was arrange to merge his two original samples into one kit. Then, they suggested doing Family Finder. I did that and recently obtained the interesting results.  So, all told what I have done on my father is:   Y-12 (originally done for the Genographic Project) mtFullSequence Family Finder   My father's Y Haplogroup is R-M269 and I am being presented with the M343 SNP pack on FTNDA.  My question is, what now? My father is gone so the sample that remains with FTDNA is old and finite (their customer service says they still have "one container" of his DNA). His siblings have all passed away -- unfortunately, with no samples taken. What is the best way to make use of the sample of my father's DNA that is left?  Should I refine the Y-Chromosome to Y-111? That seems the most natural (though I'm a male and carry it too). Should any SNP tests best be done on his remaining sample as opposed to on me? Or, should I do nothing and just let his 2009 samples continue to sit at FTDNA?  By phone, FTDNA said that they should have enough left to do the Y-111 and a SNP pack which is great, but I'd love to know independent of their customer service if that is the wisest way to make use of the remaining DNA sample which they have?  Full disclosure: I did have my father do 23andMe in 2010 and I did have his blood drawn and sent to a DNA Bank. I hope to never touch his banked DNA (except maybe to do a full sequence someday), but at least it does exist. My question now is solely how to best make use of my father's remaining sample at Family Tree DNA? Filter to change the content of 404 page I have created custom rewrite rules. These rules now go to 404 page as expected. I can use action hook template_redirect to change the template matching query_var.  But I don't want to create separate template files as the page structure depend on the current theme in use. Rather I just want to change the content and title. I have tried change the content using the_content filter, but it seems the filter doesn't even get called for 404 page.  I also tried loading index.php template and then using the_content filter, but it also doesn't work.  Is there any way to achieve this? Is returning a pointer to a static local variable safe? I'm working with some code that widely uses the idiom of returning a pointer to a static local variable.  eg:  char* const GetString() {   static char sTest[5];   strcpy(sTest, "Test");   return sTest; }   Am I right in thinking that this is safe?  PS, I know that this would be a better way of doing the same thing:  char* const GetString() {   return "Test"; }   Edit: Apologies, the function signature should of course be:  const char* GetString(); Are there any tools for merging CSS? I have a couple CSS files with overlapping CSS selectors that I'd like to programmatically merge (as in not just appending one file to the end of the other). Is there any tool to do this online? or a Firefox extension perhaps? Prove: $\gcd(a,b) = \gcd(a, b + at)$. I know that $\gcd(a,b)$ divides $a$ and $b$, and must also then divide $(a)(t)$ ($t$ being some integer).  This makes sense to me, but how do I prove it?  It seems that the addition of $(a)(t)$ is a continuation of the linear combination of $\gcd(a,b) = av + bu$ for some $v$, $u$ being elements of $\mathbb{Z}$.    Any help? How do I troubleshoot a Windows freeze or slowness? A machine is described as being "really slow" or "freezing". How can I troubleshoot/resolve this issue? What should be the first steps to take? What color would you see if you place 2 mirrors in opposit when one is a one way mirror Investment options for f1 visa students in USA Determining ethnicity according to ancestry? My sister, cousins, and other relatives speculate that my mom's grandmother was Jewish (for various reasons). I've heard people say at times things like, for example, "I'm 50% German" or "I'm 25% Swedish." This has to do with their ancestry. But, how exactly is this calculated? Say for example that my mother's paternal grandmother was indeed 100% Jewish, what would that make me and my siblings, and how is it calculated? A positive integer $n$ is called a balancing number if  $$1 + 2 + \cdots + (n − 1) = (n + 1) + (n + 2) + \cdots + (n + r) \tag{1}$$  for some positive integer $r$.     Problem: Find the general solution (closed-form expression) of equation $(1)$, in other words, find $f_1(m)=n, f_2(m)=r$ where $f_1, f_2$ are solution of $(1)$ for any integer $m \in \mathbb Z$.   I have asked a  with a constrain involving Pell's equation. I have damaged the screen on my phone, so much so, it will not allow me to get the data to transfer onto my laptop. On opening Samsung Kies, it is saying that the connected device is locked. Please enter password on the connected device. I can only assume its the pattern lock they are referring to as I have managed to unlock the sim.  As I am unable to do this due to the screen being cracked, I wondered whether there is any other way of doing this, before sending the same onto my insurance company, as they are saying that I will lose all the data! Cant see why seeing as its just the hardware that is damaged and not the software. Asserting that Atheism and Theism are both faith based positions I am recently testing an assertion that I have concluded namely that atheism is a faith based position just like theism is a faith based position.  The reason I arrived at this conclusion is that theists have no proof that God actually exists. It's purely a matter of faith. Yes, there maybe strong implicit proof that God exists in their opinion (scriptures, history, etc) but there is no concrete proof of God's existence. In my view, atheists also suffer from the same problem of providing a proof of their position. Specifically that they cannot prove that God is non-existent.  The typical rebuttal I get is that the burden of proof is on the theists. But I view this as a cop out and they hide behind the wall of burden of proof which is just a bias in the debate.  Given the above, I claim that both atheism and theism are positions based on faith. Would it be incorrect to claim that? $AB-BA=I$ having no solutions The following question is from Artin's Algebra.      If $A$ and $B$ are two square matrices with real entries, show that $AB-BA=I$ has no solutions.    I have no idea on how to tackle this question. I tried block multiplication, but it didn't appear to work. Maximum temperature laptop internals can handle? Cooling options? So I have a Compaq CQ50-215CA and my sister was using her laptop on her bed and I was just using it quickly to check my email. The surface of the laptop was really hot and I opened Speccy to see that the CPU and GPU temperature was 96 C. A couple months ago, my laptop was on the desk without a cooling pad and I was playing a game. Using GPU-Z back then, I had a reading of 104 C. Even with a cooling pad on a desk, running several processes/games keeps me around 88-90 C.  Is this normal for a laptop and what's the highest temperature the internals can handle? Besides a cooling pad, are there any other more effective ways of cooling a laptop? What is the C# equivalent of NaN or IsNumeric? What is the proper name for a "river plot" visualisation In a famous plot, Charles Minard visualised the losses of the French Army in the Russian campaign of Napoleon:    (another nice example is  xkcd plot)  Is there a canonical name for this type of visualisation? I'm actually looking for an R package to create such plots, but I don't even know how to look for it.  EDIT:  As I could not find a good package in R do do this type of plots, I have created my own, called "riverplot" -- you can download it . Here is a simplified version of the above diagram:    And an example of what other diagrams can be created with the package: What's wrong in taking the cat as an observer in Schrodinger's experiment? Plz kindly elaborate! And if possible also describe about possible logics if the question bears the answer No. A solid spherical cap of radius $R$ is the solid delimited by a sphere    of radius $R$ and a plane that intersects the sphere.   The height $h$ of the solid spherical cap is the largest distance from a point of the solid to the plane intersecting the sphere.   Show that the volume of a solid spherical cap is given by:  $$V = \frac{\pi h^2(3R-h)}{3}$$   It is enough to consider the solid spherical cap delimited by the sphere $x^2 + y^2 + z^2 = R^2$ and the plane $z = R-h$  use triple integrals by spherical or cylindrical coordinates. Give me a few min to try it out. Block network access of a process? Is it possible to block the (outgoing) network access of a single process?