I have seen it conjectured several times that Artin groups are torsion-free. This is a very basic question one could ask about these groups. Intuitively, to me it seems like it must be true however it seems impossible to prove. I am curious if anyone is actually working on this / what kind of met...

I had an annoying bug, where I forgot to write do in a do...while loop. int main() { /*do*/ { int status = foo(); } while (status); } Why does this still compile and run? It seems to me that the compiler should reject this as nonsensical or at least raise a warning (I have -Wall in my co...

// short update at the bottom So, at first I had this idea: Find a virtual driver to set up and use software raid on windows. Result: Failed even with support from developer. The next idea then came into my mind after watching a YouTube video about virtualization: Put in a 2nd rather cheap gpu fo...

I'm looking for a good quotation and comprehensive explaination of the theorem of Chow-Rashewski. I'm writing my thesis on sub-Riemannian Geometry and a special control problem. Therefore I want to state the theorem of Chow–Rashewski in its sub-Riemannian version and prove it: Let $M$ be a connec...

I don't understand why the following does not compile (e.g. in gcc 9.10 or MS VS C++ 2019): class X { public: friend bool operator==(int, X const &); }; int main() { 2 == X(); // ok... static_cast<bool (*)(int, X const &)>(&operator==); // Error: 'operator==' not defined return 0; ...

Today while coding, visual studio notified me that my switch case could be optimized. But the code that I had vs the code that visual studio generated from my switch case does not result in the same outcome. The Enum I Used: public enum State { ExampleA, ExampleB, ExampleC }; After t...

Question: What are (some of) the stacks (occurring in algebraic/differential geometry) that are fibered in arbitrary categories and not necessarily in groupoids? In the notes Notes on Grothendieck topologies,fibered categories and descent theory Angelo Vistoli introduce the notion of a stack ov...

My initial dataframe is: Name Info1 Info2 0 Name1 Name1-Info1 Name1-Info2 1 Name1 Name1-Info1 Name1-Info2 2 Name1 Name1-Info1 Name1-Info2 3 Name2 Name2-Info1 Name2-Info2 4 Name2 Name2-Info1 Name2-Info2 and i would like to return the number of repetitions of each ...

I am using Excel that comes with Office 365. And this version of Excel does something annoying that's breaking all my macros. I want to import a CSV file into a sheet WITHOUT any table formatting and such. This was the default behaviour in older versions of excel. But now that the table formatt...

The navier stokes equations are as follows, with $u$ the velocity field, $\nu$ the viscosity, and of course $p$ the pressure $$\dot{u}+(u\cdot \nabla ) u +\nu \nabla^2 u =\nabla p$$ Some elementary manipulations shows that if you zoom in by a factor of $\lambda$, then you expect viscosity to scal...

I was in the process of moving repeated arithmetic code into reusable chunks using funcs but when I ran a simple test to benchmark if it will be any slower, I was surprised that it is twice as slow. Why is evaluating the expression twice as slow using System; using System.Runtime.CompilerServices...

In a context where I try to estimate some combinatorial sums, I'm faced with vector random variables $(x_1,...,x_n)$ uniformly distributed with $n \rightarrow \infty$. I want to know if the components have to behave in a wellknown fashion. I recently read the following. (Sourav Chatterjee math su...