This paper is connected with the theory of a-nonexpansive mappings, which were introduced by K. Goebel and M. A. J. Pineda in 2007. These mappings are a natural generalisation of nonexpansive mappings from the point of view of the fixed point theory. In particular, they proved that in Banach spaces all α = (α₁,..., α_n) -nonexpansive mappings with α₁ big enough, namely α₁≥2 (1/1-n), have minimal displacement equal to zero. This paper introduces some new results connected with this problem.

This paper presents some results concerning the Generalized Banach Contraction Principle: In a complete metric space X if for some N ≥ 1 and 0 < M < 1 the mapping T : X → X satisfies min{d(T^j x,T^j y), 1 ≤ j ≤ N} ≤ Md(x, y) for any x, y ∈ X , then T has a unique fixed point. In some special cases, the above constant M can be replaced by a continuous, non- -increasing function 0 ≤ φ (d(x, y)) ≤ 1 such that φ (t) =1 if, and only if, t = 0.

The aim of this paper is to generalize the Chirka-Sadullaev theorem, fundamental in the theory of extension of separately holomorphic functions with singularities, to the case of a s-compact Josefson manifold.

The paper presents a general theorem on fibers of singular sets: Let D₁ be a connected
σ-compact Josefson manifold and let D₂ be a σ-compact complex manifold. Let Ω⊂D₁×D₂ be
a domain and let Ω⊂M be a singular set with respect to the family Ƒ⊂

This paper presents general formulas for the kinetic properties of semiconductor crystals expressed in terms of the Fermi integrals. The formulas provide algorithms for the calculation or identification of the kinetic properties and constitute (together with the results of theoretical analysis and other presented relationships) the mathematical model of the charge carrier transport phenomena in semiconductor crystals.

This article relates to a synthesising output feedback that is used to control a network of discrete events. The feedback stabilises the system without reducing its initial throughput and its synthesis is mainly based on the theory of residues and the Kleene operator. This article suggests some theoretical results and mathematical foundations of max-plus algebra theory, and in particularly, discusses various other aspects of controlling discrete processes and their modelling in the context of a linear max-plus system.

In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.

The approach of evolutionary games like prisoner’s dilemma, among others, is based on a consistent strategy. We propose an experimentally verified system where cooperation can arise out of two simple factors: mutation and inheritance. This system has a social dilemma property and allows each agent to set its own desired number of participants. There are two essential mechanisms: fluctuation through which mutation leads to cooperation, and natural selection which tends to promote cheaters and therefore disrupts the cooperation. It is shown in numerical simulations that the interplay between both mechanisms leads to an equilibrium and that no intentional strategies are necessary to establish and sustain cooperation. Thus, starting from a population of non-cooperating agents, natural evolution can end with a population composed of cooperating groups with the mean group size determined by the fluctuation rate and the pay-off function. A thorough analytical explanation of numerical results is provided.

In the present paper, the case of a database of scientific articles is described. There can be observed the quantitative effects of the increasing strength of cooperation between scholars. It is manifested in time-related features changes of the numbers distribution of a single co-authors’ article. The distribution of the number of co-authors of an article recorded in the database evolves with time from a profile with no more than one author to a profile with several authors. A social dilemma model is proposed to explain the dynamics of changes in the distribution of the number of co-authors. The most successful strategy of the three considered alternative strategies of cooperation is selected.

This paper introduces an implementation of the Context-Driven Meta-Modeling Paradigm (CDMM-P). This implementation is the proof of concept for the CDMM-P as it shows that the idea of the CDMM-P is feasible. The software system presented here takes the form of the Context-Driven Meta-Modeling Framework (CDMM-F). This framework plays the key role in the Context-Driven Meta-Modeling Technology (CDMM-T) dedicated to generating software system artifacts in a model-driven manner. In contrast to all contemporary approaches to meta-modeling, the meta-model is dynamically loaded from the application context file. In result, the framework has a self-organizing structure and the modeling language does not have a fixed hardcoded predefined structure. This structure, as well as the set of meta-model elements, plays the role of the parameter for the general modeling tool, a part of which is presented in this paper.

The novel and crucial point of this paper is the illustration of the application of close ontology based meta-modeling to defining the open ontology based construction of modeling languages (meta-models). This approach is a generalization of Object Management Group (OMG) standards related to Model Driven Architecture (MDA). The existing modeling tools supporting the traditional approach can be reused when open ontology based meta-modeling tools are implemented. This paper describes Context-Driven Meta-Modeling Meta-Modeler (CDMM-Meta-Modeler) ‒ the Eclipse Plugin that constitutes such an open ontology based meta-modeling tool. The tool constitutes an implementation of the diagramming aspect for the Context-Driven Meta-Modeling Framework (CDMM-F), which is one of several possible implementations of the Context-Driven Meta-Modeling Paradigm (CDMM-P).