相关论文: Idempotent mathematics and interval analysis

Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.

Skew idempotent functionals of ordered semirings are studied. Different associative and non-associative semirings are considered. Theorems about properties of skew idempotent functionals are proved. Examples are given.

This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…

The empirical likelihood is a powerful nonparametric tool, that emulates its parametric counterpart -- the parametric likelihood -- preserving many of its large-sample properties. This article tackles the problem of assessing the…

Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…

We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…

An introduction to Hyperbolic Analysis is presented.

In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.

An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various…

In the framework of idempotent mathematics, analogs of the classical kernel theorems of L. Schwartz and A. Grothendieck are studied. Idempotent versions of nuclear spaces (in the sense of A. Grothendieck) are discussed. The so-called…

This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…

Short introduction in NPD with several applications to (in)finite dimensional problems of mechanics, hydrodynamics, M-theory and quanputing is given.

Preliminary version of a book on univariate real analysis, with 14 chapters and 2 appendices. 1. Real numbers; 2. Limits of real sequences; 3. Series; 4. Limits of real functions. 5. Elementary functions; 6. Continuous functions; 7.…

We recently introduced the notion of an idempotent system. This linear algebraic object is motivated by the structure of an association scheme. There is a type of idempotent system, said to be symmetric. In the present paper we classify up…

The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.

In this work, we propose a convenient framework for infinite-dimensional analysis (including both real and complex analysis in infinite dimensions), in which differentiation (in some weak sense) and integration operations can be easily…

The paper discusses the question of why intervals, which are the main object of Interval Analysis, have exactly the form that we know well and habitually use, and not some other. In particular, we investigate why traditional intervals are…

Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…

We study the concept of idempotence for relative monads, which exhibits several subtleties not present for non-relative monads. In particular, there is a bifurcation of notions of idempotence in the relative setting, which are…

This is the first volume of a textbook for a two-semester course in mathematical analysis. This first volume is about analysis of functions of a single variable. The topics covered include completeness axiom, Archimedean property,…