Does symbolic logic count as discrete mathematics? What does the notation 2^\mathcal{S}, where \mathcal{S} is a set, denote? What does epsilon mean in math? What does e stand for in a Poisson formula? How to characterize in terms of set theory operations a sigma-algebra generated by...
Is complex analysis used in statistics? Is complex analysis proof based? What does a line over a complex number mean? What is intermediate real analysis? What is a harmonic conjugate in complex analysis? What is a compact set in real analysis?
Alleviating the almost century old confusion, the correct laws of statistics and logic pinpoint the true oddity of quantum objects: duality. As it is shown in the first part of this short essay, duality plus conservation laws allow the violation of Bell’s inequalities for any spatio-temporal ...
Studies byEpsilonshow that 80% of consumers are more likely to become repeat customers when offered personalized experiences. Furthermore, DTC proves to be financially viable. By eliminating distribution channel costs, companies can improve profit margins. It also allows greater control over pricing str...
We remark that\(\left\{ \chi _j(\textbf{r}; \textbf{R})\right\} _{j=0,\infty }\)and\(\left\{ \epsilon _j(\textbf{R})\right\} _{j=0,\infty }\)depend (parametrically, in the first case) on\(\textbf{R}\)because the electronic Hamiltonian does. One can expand\( \Psi ...
Me: What does trust mean to you? Angie: As an AI, I don’t have emotions or feelings. So I don’t have a personal understanding of trust. However, trust is generally defined as a belief or confidence in the reliability, honesty, and integrity of a person or entity. In the context ...
“A sharp square function estimate for the cone in “, by Larry Guth, Hong Wang, and Ruixiang Zhang. This paper establishes an optimal (up to epsilon losses) square function estimate for the three-dimensional light cone that was essentially conjectured by Mockenhaupt, Seeger, and Sogge, whic...
As it turns out, this type of control works well except in some rare cases in which the normal is “compressible” or otherwise highly structured; but epsilon-net arguments can be used to dispose of these cases. (This general strategy was first developed for the technically simpler singularity...
Oh dear, it could be there is something wrong in my "answer". I think I was supposed to prove D_{\alpha} (f\circ T(\alpha))(x,y) = (U(f\circ...
This often comes up in the context of regression, where we assume that the values of ϵiϵi in yi=βXi+ϵiyi=βXi+ϵi are independent and identically distributed. If the latter condition does not hold (e.g. the variance of epsilon depends on XiXi), the standard approach to ...