in the Piltz divisor problem__Speaker_ Cruz Casti 43:45 Generalized valuations and idempotization of schemes 57:55 Exceptional Chebyshev's bias over finite fields 56:34 Kummer Theory for Number Fields 45:06 A walk on Legendre paths 1:05:13 Zeros of linear combinations of L-functions near ...
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 ...
In Lagaris et al [89], the solution of a differential equation is expressed as a constant term and an adjustable term with unknown parameters, the best parameter values are determined via a neural network. However, their method only works for problems with regular borders. Lagaris et al [90...
This post is an unofficial sequel to one of my first blog posts from 2007, which was entitled “Quantum mechanics and Tomb Raider“. One of the oldest and most famous allegories is Plato’s allegory of the cave. This allegory centers around a group of people chained to a wall in a ca...
prismatic cohomology in coordinates can be computed using a “-derivative” operator that for instance applies to monomials by the formula where is the “-analogue” of (a polynomial in that equals in the limit ). (The -analogues become more complicated for more general forms than these.) In...
What is classical algebra? The History of Algebra: Mathematics involves studying several different subjects and concepts. Because of this, we have different branches of mathematics, and we can further classify those branches based on specific topics within each branch. Algebra is one branch that has...
Although it is defined as an internal angular momentum much of our understanding of it is bound up with the mathematics of group theory. This paper traces the development of the concept of spin paying particular attention to the way that quantum mechanics has influenced its interpretation in both...
In the Quantum Mechanics problem at hands, however, it is. So give now the operator an explicit representation as a linear vectorial differential operator (we use the inert form %Nabla, , to be able to proceed with full control one step at a time) > (20) The expression (19) becomes...
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal r
and the momentum operator , defined by (The terminology comes from quantum mechanics, where it is customary to also insert a small constant on the right-hand side of (1) in accordance with de Broglie’s law. Such a normalisation is also used in several branches of mathematics, most notabl...