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Both relativistic mechanics and Newtonian mechanics are based on principles that have ontological implications. We propose a series of formalisms that rigorously define the ontology underlying mechanical theories, in order to clarify and…
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…
This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…
An overview of the cosmological models with expansion, shear and rotation is presented. Problems of the rotating models are discussed, their general kinematic properties and dynamical realizations are described. A particular attention is…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
This paper examines a denumerable version of the nested-set theorem and derives from it a contradiction involving the formal consistency of the actual infinity assumed by the Axiom of Infinity.
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
The hypothesis of locality, its origin and consequences are discussed. This supposition is necessary for establishing the local spacetime frame of accelerated observers; in this connection, the measurement of length in a rotating system is…
The separately continuity topology is considered and some its properties are investigated. With help of these properties a generalization of Sierpinski theorem on determination of real separately continuous function by its values on an…
From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a…
We review some modern theories about the structure of space and time, in particular those related to discrete space and time. Following an epistemological method we start from theories which discuss discrete space and time as a mathematical…
The mathematical description of stable particle-like systems appearing in relativistic quantum field theory at large, respectively small scales or non-zero temperatures is discussed.
We offer a fresh perspective on the relational interpretation of quantum mechanics as a way of thinking about the world described by quantum theory based on quantifiable notions of information. This allows us to provide a definition of a…
We present here a note which synthesizes our previous ideas concerning some problems in cosmology, and the numerical correspondences between the physical constants that we could deduce.
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…