相关论文: Potpourri

Lecture notes on selected topics in the theory of gravitation.

Some speculative preliminary ideas relating matrix theory and cosmology are discussed.

The mathematics of linear fits is presented in covariant form. Topics include: correlated data, covariance matrices, joint fits to multiple data sets, constraints, and extension of the formalism to non-linear fits. A brief summary at the…

This short note is an "elementary'' introduction to the conjectural theory of motives.

Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.

These are lecture notes for the course "Analysis and X-ray tomography". The course is a broad overview of various tools in analysis that can be used to study X-ray tomography. The focus is on tools and ideas, not so much on technical…

One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.

These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.

In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the…

This note develops some fundamental properties of resultants and related notions. It represents my own personal exploration of this domain, which I found more instructive than seeking answers in the standard literature. Consequently,…

An expository hitchhikers guide to some theorems in mathematics.

This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…

New cases of the multiplicity conjecture are considered.

This thesis is basically devoted to matroids -- fundamental structure of combinatorial optimization -- though some of our results concern simplicial complexes, or Euclidean spaces. We study old and new problems for these structures, with…

We present an overview of selected topics in random permutations and random partitions highlighting analogies with random matrix theory.

These notes provide a quick introduction to the Coq system and show how it can be used to define logical concepts and functions and reason about them. It is designed as a tutorial, so that readers can quickly start their own experiments,…

The first-order model theory of modules has been studied for decades. More recently, the model theoretic study of nonelementary classes of modules--especially Abstract Elementary Classes of modules--has produced interesting results. This…

This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.

I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.

These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…