List of Plain TeX macros
Is there a printable version of a reference manual for all TeX primitives?
Why doesn't Volumetric follow the shape of Mesh in Eevee? So I was in the middle of making a ball-shaped smoke, but the volumetric effect didn't work following the basic shape. It remains cube in Eevee Blender 2.8; while in Cycle it works, but in Cycle it takes thousands of years for Render. Suppose that $y_1(x)$ and $y_2(x)$ are solutions of the differential equation $y''+py'+qy=0$ on $I$. How can I show that if $y_1$ and $y_2$ vanish at the same point then they are not linearly independent?   Here is my attempt to prove the problem. Since $y_1(x)$ and $y_2(x)$ are solutions of the differential equation $y''+py'+qy=0$ on $I$, it is enough for me to show that the Wronskian of $y_1$ and $y_2$ denoted by $W(y_1,y_2)$ is zero. Now since $y_1$ and $y_2$ vanish at the same point say $p$ we have $y_1(p)=0$ and also $y_2(p)=0$.   Solving for $W(y_1,y_2)(p)$ we have: $y_1(p)y_2'(p)-y_2(p)y_1'(p)=0$ since $y_1(p)=0$ and also $y_2(p)=0$.   Am I correct? Thanks I don't know if this is appropriate for math.stackexchange, or whether philosophy.stackexchange would have been a better bet, but I'll post it here because the content is somewhat technical.  In ZFC, we can prove that the (second-order) Peano axioms have a model, call it $\mathbb{N} = (N,0,S)$. Furthermore, $\mathbb{N}$ is unique up to isomorphism. Thus, it would seem that we've pinned down $\mathbb{N}$.  However, if ZFC is consistent, then it has some very peculiar models. In particular, it has a model $(V_0,\in_0)$ whose "native" $\mathbb{N}$, let call it $\mathbb{N}_0$, is a model for the sentence "ZFC is consistent," and another model $(V_1,\in_1)$ whose "native" $\mathbb{N}$, lets call it $\mathbb{N}_1$, is a model for the sentence "ZFC is inconsistent."  But in reality, in other words, for the "real" $\mathbb{N}$, only one of these can be sentences can be true. Furthermore, the objects $\mathbb{N}_0$ and $\mathbb{N}_1$ aren't isomorphic, since the set of sentences they satisfy are different.  So it seems to me that $\mathbb{N}$ cannot truly be pinned down. Furthermore, its categoricity is, in some sense, illusory. Is this correct, or am I missing something? Why are my quotation marks causing an “unexpected token” error with this command? I need help with a specific command that I am using in a new game that I am creating inside of Minecraft. The command is:  /give @p sign 1 0 {BlockEntityTag:{Text1:"{"text":" [MF2]","color":"gold","clickEvent": {"action":"run_command","value":"tellraw @a [""{"text":"[MF2]  ","color":"gold"},{"selector":"@p","color":"dark_aqua"},{"text":" is now an admin of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"},display: {Name:"Custom Sign"}}   If I take out the /tellraw command then the command works fine, but I need the command in there to announce to the game that a new admin has joined.  With the tellraw command, the error message is the following:  Data tag parsing failed: Unexpected token 't' at: text":" [MF2]","color":"gold","clickEvent":{"action":"run_command","value":"tellraw @a [""{"text":"[MF2] ","color":"gold"}, {"selector":"@p","color":"dark_aqua"},{"text":" is now an admin  of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"   If anyone knows how to fix this, please let me know. What is the best way to flatten a linked list with lists as values? Is "can not" unambiguous? I always try to remember to use "cannot" when applicable as in "I cannot take an umbrella" (because I do not have one).  I also thought that the problem with "I can not take an umbrella" was that it was ambiguous: it could also mean that I could decide not to take an umbrella. Trying to write unambiguously most of the time, I would therefore never use it.  Now I see it claimed that it is in fact not ambiguous, and only carries the second meaning. Usually I would accept such advice at face value and start using "can not" when the second meaning is unambiguously meant, but this comes from a style guide I have other reasons not to respect very much.  Does "can not" have a single unambiguous meaning?  (I have read  but my question is more about current usage. The length of the answer to that question does confirm my prejudice a bit, though) Accessing class members on a NULL pointer I was experimenting with C++ and found the below code as very strange.   class Foo{ public:     virtual void say_virtual_hi(){         std::cout &lt;&lt; "Virtual Hi";     }      void say_hi()     {         std::cout &lt;&lt; "Hi";     } };  int main(int argc, char** argv) {     Foo* foo = 0;     foo-&gt;say_hi(); // works well     foo-&gt;say_virtual_hi(); // will crash the app     return 0; }   I know that the virtual method call crashes because it requires a vtable lookup and can only work with valid objects.   I have the following questions    How does the non virtual method say_hi work on a NULL pointer? Where does the object foo get allocated?   Any thoughts? convergence of $\sum_{n=1}^{\infty }\frac{(-1)^{[\sqrt{n}]}}{n}$ where $[a]$ means floor function of $a$ I have a problem with solving the convergence of $\sum_{n=1}^{\infty }\frac{(-1)^{[\sqrt{n}]}}{n}$ where $[a]$ means floor function of $a$. I've already made the first thep and rewrote it with the $\sum_{n=1}^{\infty }(-1)^{n}\sum_{k=n^2}^{(n+1)^2-1}\frac{1}{k}$, which converges if and only if the previous one converges. Now I want to use Leibniz criterion, but I cannot prove that the second sum in the previous expression is monotonic. Does anyone know how to do it? (I cannot use Riemann integral, we haven't defined it yet) Reading/writing an INI file Is there any class in the .NET framework that can read/write standard .ini files:  [Section] &lt;keyname&gt;=&lt;value&gt; ...   Delphi has the TIniFile component and I want to know if there is anything similar for C#? I'm struggling to understand the core reason to invest in stocks as a minority shareholder. Majority shareholding makes more sense as you effectively control the company, so you can pay yourself dividends or even sell the entire company at will. You can guarantee your own payback.  However, as a minority shareholder, you don't get to make any of these decisions. You're basically just hoping to eventually, some day get paid, if the majority holders decide so.  Why do so many investors agree to pay now huge sums of money (trillions in total) for something that may eventually pay dividends, and even in the best case, these dividends are only a fraction of the price you paid to acquire these stocks?  The average annual dividend rate for the US stock market is 2%. That means if you bought 100 million worth of shares, you'd have to wait 50 years to recover your investment.  Of course, the most probable way you'd eventually get liquidity for these shares is by selling them to some other starry-eyed investor - which makes the whole thing seem like a giant Ponzi scheme.  Given all that, it's unclear to me why the public is willing to spend so much money to acquire minority shares in companies. Can not switch Node.js to a default version of my choice Bash is not finding a program even though it's on my path I have a program on my path.  The program runs when executed with a full path specified.  But the program cannot be found when I run it with just its name.    Essentially, I want to understand how the below output is possible, and how to fix it so that my program can actually be found without a full path specified:  root:/usr/local/bin# ./siege **************************************************** siege: could not open /usr/local/bin/etc/siegerc run 'siege.config' to generate a new .siegerc file **************************************************** root:/usr/local/bin# echo $PATH /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games root:/usr/local/bin# siege bash: /usr/bin/siege: No such file or directory root:/usr/local/bin# wtf!?!?   I'm on Ubuntu 12.04 using bash.  Also please note the warning output from siege is not relevant for the purposes of this question, as I am only interested in whether or not the program can be found and invoked. How to tell the difference between linear and non-linear regression models? I was reading the following link on non linear regression . My understanding from reading the first section "Nonlinear Regression vs. Linear Regression" was that the equation below is actually a linear regression, is that correct? If so why?  $$y = b_1x^3 + b_2x^2 + b_3x + c$$  Am I also to understand that in non linear regression multicollinearity isn't an issue? I know that multicollinearity can be an issue in linear regression so surely if the model above is in fact a linear regression there would be multicollinearity? The "Hurry up, it's raid night" achievement in Starcraft 2 involves "beating Wings of Liberty, on normal, in 8 hours or less."  Is there a recommended mission path to take? Which mission should I take for the branching paths? Does it count time spent on the Hyperion in between missions, or is it exclusively time elapsed on missions. Does replaying a mission affect the time? General tips / hints from those who've unlocked the achievement?  Edit: Just got this achievement tonight, finally! The answer was perfect. One of the ways I quickly rename files in Windows is   F2 &gt; Rename &gt; Tab (to next file) &gt; Rename ...   But in Ubuntu/Nautilus, I can't tab to next file. But being on Linux, I think there must be a command line alternative.  However, sometimes, I may want more control over how to rename specific files. In that case, perhaps its better to be able to tab to the next file Irreducible polynomials and affine variety Let $k$ be any field, and let $f,g\in k[x,y]$ be two irreducible polynomials such that $g$ is not divisible by $f$. Prove that $V(f,g)\subseteq A_k^2$ is finite. Will free-fall object into black hole exceed speed of light $c$ before hitting black hole surface? In Newtonian mechanics, if we throw an object in against direction of gravity with speed $v$ and it achieve max height of $h$. Now if we allow object to fall from that height $h$, it will eventually attain speed $v$ when it reach position where we launch it.   Now applying same idea to a black hole in general relativity. Speed require to escape black hole gravity is greater than $c$, so if we throw something into black hole with almost the speed of light, the object speed will exceed speed of light $c$ before hitting black hole surface! How relativity explain this? Can space-time curvature reduce speed of this freely falling object from attaining speed of light? How can I revert a config file back to the originally installed version after I have edited it? I want to revert a file in /etc/ back to its originally-installed form. I have edited the file since it was installed. How can I revert this config file? Apt is smart enough not to overwrite edited config files, so how do I tell it that I want it to do so?  For argument's sake, let's say that I want to revert the file /etc/foo.conf from the package foo. Proving that the map from a topological space to a fiber bundle is open. What method in the String class returns only the first N characters?