相关论文: Some notes about matrices, 2

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.

Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…

These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.

The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces,…

The slice condition and the more general weak slice conditions are geometric conditions on Euclidean space domains which have evolved over the last several years as a tool in various areas of analysis. This paper examines some of their…

We present some illustrations for the claim that already by looking at the ground states of classical lattice models, one may meet some interesting and non-trivial structures.

Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental…

We develop the theory of residuated lattices by introducing and studying several new types of filters and related concepts, including semi-simple filters, essential filters, the socle of a filter, and independent families of filters. Our…

In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on…

This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…

The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is…

This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of $\pi$. We shall study how many such angles may appear in a given lattice and in which positions, allowing the…

This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…

We study the structure of cubic matrix mechanics based on three-index objects. It is shown that there exists a counterpart of canonical structure in classical mechanics.

We describe some Cartesian products of metric spaces and find conditions under which products of ultrametric spaces are ultrametric.

These are the notes of lectures delivered at Grenoble's summer school on \emph{Arakelov Geo\-me\-try and Diophantine Applications}, in June 2017. They constitute an introduction to the study of Euclidean lattices and of their invariants…

These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.

Some special solutions to the reflection equation are considered. These boundary matrices are defined on the common quantum space with the other operators in the chain. The relations with the Drinfeld twist are discussed.

We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.

We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.