All Questions

As part of a different problem, I came across the following simplified question, for which I cannot exhibit a proof nor a counterexample. Note that the assumptions of smoothness and strict positivity ...

Consider a sequence of real number $\{s_i\}_{i\leq n}$. Now consider the real numbers $F$, $G$ and $\alpha$ defined below $$F= \sqrt{ \left( \sum ~\rho_{ij} ~\Psi_{ij}~ s_i ~s_j \right)^+}, $$ $$G = ...

Suppose you are given a set of functions $f_1, \ldots, f_n$. Every function is defined as follows $$f_i(x) = \sqrt{1+C^2_i-2C_i\cos (x-D_i)}$$ where $0<C_i<1$ and $0\leq D_i<2\pi$ are real-...

I am currently trying to show that a sequence of homeomorphisms converges to some limiting homeomorphism using Anderson's the inductive convergence criterion. However I can't explicitly compute the ...

I am having some trouble with this (undergrad) problem. The Twitter account I found this from was deleted so I unfortunately have not found an answer. I have tried decomposing into Riemann sum and ...