Related papers: Protometrics

Mathematical aspects of the theory of interfaces in statistical mechanics are discussed.

These notes aim to give an introduction to a few aspects of noncommutative geometry.

Characterizations of pseudoultrametric-preserving functions and semimetric-preserving functions are found. The structural properties of pseudoultrametrics which can be represented as a composition of an ultrametric and…

We study convex subsets of buildings, discuss some structural features and derive several characterizations of buildings.

We characterize the extendibility of the normal curvature on frontals and we give a representation formula of this type of frontals. Also we give representation formulas for wavefronts on all types of singularities and others sub classes of…

We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.

We give an elementary account of the notion of Y-frieze patterns, explain some of their properties, and reveal their connection with Coxeter's frieze patterns.

We introduce a new type of means. It is new in two ways: its domain consists of sets and its values are sets too. We investigate the properties and behavior of such generalization. We also present many naturally arisen examples for such…

This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…

A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.

Algebraic and combinatorial properties of a monomial ideal and its radical are compared.

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

We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…

We present some episodes from the history of interactions between geometry and physics over the past century.

In this paper we suggest to anticipate the introduction of concepts such as quantum state and the operators connected to their transformations well in advance of what is usually done.

Using a concept of filter we propose one generalization of Riemann integral, that is integration with respect to filter. We study this problem, demonstrate different properties and phenomena of filter integration.

A short review of phenomenological and experimental aspects of extra spatial dimensions at colliders is presented.

We change the definition of the vertex representations. As a result the vertex representations has one parameter.

We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.

A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…