Related papers: A Short Course on Frame Theory
This is a very gentle introductory course on quantum mechanics aimed at the first years of the undergraduate level. The basic concepts are introduced, with many applications and illustrations. Contains 12 short chapters of equal length,…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower)…
These lectures are a brief introduction to supersymmetry.
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
We propose a framework for model-theoretic stability and simplicity in an approximate first-order setting and generalize some classical results.
In this paper, we first prove a theorem by a little modification on the Lax-Milgram theorem. Then, using $K$-frames, we obtain lower and upper bounds for the results obtained from this theorem. Also, we present some methods for the…
These are notes from a basic course in Several Complex Variables
This is a draft version of Part I of a three-part textbook on quantum field theory.
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
An overview of the recent developments in plurifine potential theory.
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
This is a written-up version of eight introductory lectures to the Hodge theory of projective manifolds. The table of contents should be self-explanatory. The only exception is section 8 where I discuss, in a simple example, a technique for…
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
An introduction and overview of constructive reverse mathematics.
We define a Frame of reference as a two ingredients concept: A meta-rigid motion, which is a generalization of a Born motion, and a chorodesic synchronization, which is an adapted foliation. At the end of the line we uncover a low-level…