相关论文: Mathematical definition of general systems based o…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…
A 'state property system' is the mathematical structure which models an arbitrary physical system by means of its set of states, its set of properties, and a relation of 'actuality of a certain property for a certain state'. We work out a…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
A foundation for closing the gap between biometrics in the narrower and the broader perspective is presented trough a conceptualization of biometric systems in both perspectives. A clear distinction between verification, identification and…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
Measures in the context of Category Theory lead to various relations, even differential relations, of categories that are independent of the mathematical structure forming objects of a category. Such relations, which are independent of…
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
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 provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
We consider two relations on a $\cap$-semigroup of partial functions of a given set: the inclusion of domains and the semiadjacencity (i.e., the inclusion of the image of the first function into the domain of the second), which…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…
Metaphysical interpretations of set theory are either inconsistent or incoherent. The uses of sets in mathematics actually involve three distinct kinds of collections (surveyable, definite, and heuristic), which are governed by three…