Simulation of a rotating strong gravity that reverses time

In this research we simulated how time can be reversed with a rotating strong gravity. At first, we assumed that the time and the space can be distorted with the presence of a strong gravity, and then we calculated the angular momentum density of the rotating gravitational field. For this simulation we used Einstein’s field equation with spherical polar coordinates and the Euler’s transformation matrix to simulate the rotation. We also assumed that the stress-energy tensor that is placed at the end of the strong gravitational field reflects the intensities of the angular momentum, which is the normal (perpendicular) vector to the rotating axis. The result of the simulation shows that the angular momentum of the rotating strong gravity changes its directions from plus (the future) to minus (the past) and from minus (the past) to plus (the future), depending on the frequency of the rotation.

Methods and algorithm for calculating the focal parameters of a hollow conical electron beam in high-voltage glow discharge electron guns with a focusing magnetic lens

The algorithm is considered for calculating the focal distance of a hollow conical electron beam generated by high-voltage glow discharge electron guns with magnetic focusing of the beam in the drift region, as well as a method for calculating the diameter of the focal ring and its thickness for such a beam. The proposed algorithm is based on the theory of electron drift in the field of a focusing magnetic lens and is designed using the methods of discrete mathematics and the minimax analysis. The obtained simulation results made it possible to establish the influence of the magnetic lens current on the focal diameter of a hollow conical electron beam and on its focal ring thickness. It is shown that the change in the focal parameters of a hollow conical electron beam can be effectively provided through the regulation of the magnetic lens current.

Fuzzy logical conclusions and conclusions in expert systems of medical diagnostics

The main problems in making a correct diagnosis are: subjectivity and insufficient qualifications of the doctor, difficulties in correctly assessing the patient’s complaints, signs and symptoms of the disease observed in the patient, as well as individual manifestations of the symptoms of the disease. In publications on the use of expert systems for medical diagnostics using fuzzy logic, the main attention was paid to the medical features of the problem. In this work, for the first time, general methodological aspects of building such systems, creating databases, representing by fuzzy sets of real numbers, digital scales, linguistic and Boolean data of symptom values are formulated. The types of membership functions that are advisable to use to represent the symptoms of diseases are proposed. In fuzzy-logical conclusions, not only the values of the characteristic functions of the logical terms of individual symptoms, but also complex arithmetic functions of their values are used.

Analysis and review on fuzzy evaluation of the performance

In modern conditions a comprehensive analysis of development trends and their effectiveness in various areas of human activity increasingly requires the analysis of data accumulated in numerous documents stored on the global network. Such an analysis is based on annual results in many areas of research, time trends and keywords. This analysis has certain peculiarities: it requires an analysis of not always accurate numerical information, comparison of qualitative indicators, obtaining both qualitative and quantitative characteristics, as well as the use of reference information for researchers and decision makers in related fields. In this regard, in recent years, a fuzzy assessment based on fuzzy mathematics is increasingly used in all types of assessing the effectiveness of various activities. The paper deals with conducting a bibliometric study based on the Extended Science Citation Index (SCI-E) and fuzzy performance measures to understand research trends and areas of focus. This paper takes the relevant scientific papers in Web of Science database as the research object, and analyzes the research trends with the help of bibliometrics. The results show that the number of papers published in the world is on the rise. The number of papers published in China and Iran is higher than that in other countries and regions. However, the number of papers cited in the United States and Turkey is higher than that in other countries or regions. Islamic Azad University is the largest. The research topics focus on fuzzy sets, fuzzy logic, genetic algorithms and performance evaluation. The research hotspots before 2011 included expert systems, neuro-fuzzy systems, and pattern recognition. After 2011, the research hotspots became neural networks, fuzzy sets, and machine learning.

Credibilistic fuzzy clustering based on evolutionary method of crazy cats

The problem of fuzzy clustering of large datasets that are sent for processing in both batch and online modes, based on a credibilistic approach, is considered. To find the global extremum of the credibilistic fuzzy clustering goal function, the modification of the swarm algorithm of crazy cats swarms was introduced, that combined the advantages of evolutionary algorithms and a global random search. It is shown that different search modes are generated by a unified mathematical procedure, some cases of which are known algorithms for both local and global optimizations. The proposed approach is easy to implement and is characterized by the high speed and reliability in problems of multi-extreme fuzzy clustering.

Mathematical modeling of contact interaction of two electroelastic half-spaces (without electrode coating of surfaces) in the presence of a hard disk-like inclusion between them and pressure in the area of separation

Based on the use of a rigorous mathematical model that takes into account the connectivity of force and electric fields in electroelastic bodies, the contact interaction of two piezoelectric transversely isotropic half-spaces with different properties under compression (in the presence of a hard disk-shaped inclusion between them and pressure in the material separation region) was studied. The solution to the problem is obtained by representing the general solution of the static equations of the electroelasticity for a transversely isotropic body in terms of harmonic functions, followed by the construction of the boundary value problem of the electroelasticity to the consideration of the integral equation and the expansion of the desired function in a small parameter. As a special case from the constructed analytical expressions, the main parameters of the contact for two elastic transversely isotropic and isotropic half-spaces (with the inclusion between them and pressure in the separation region) are implied. Numerical results were obtained. The influence was studied of the electroelastic properties of half-spaces, the geometric dimensions of the inclusion, and loads on the parameters of the contact interaction of electroelastic bodies.

Technology progress implementation based on a modified version of R.M. Solow economic growth model: with production s-curve consisting of n-steps

The comparative analysis of the neoclassical Solow’s model and the modified Solow’s model in the implementation of technological progress has shown undeniable advantages of the modified Solow’s model. A modified version of the Solow’s economic growth model, based on an n-step production function in the form of n S-shaped functions for the implementation of technological progress, ensures the growth of the economy on a sufficiently large time interval comparable to the duration of the life cycle of the economy under study. In this interval, referred to as the “technology gap”, intensive output y (t) can be carried out according to the following options: monotonic decrease (stable 1-cycle) of the considered model; oscillations (stable n-cycles, n=2,4,16,…), “the economy marks time”; chaotic fluctuations. This result for the models of economic growth has not been described in the literature.

Cognitive modeling of informatization influence on socio-economic indicators of the region

The article discusses topical issues of the influence of informatization on the development of the country’s regions in the conditions of the modern unstable world. The nature of the development of a region can be reflected and understood on the basis of qualitative and quantitative information about its socio-economic indicators, about their relationship and trends in their changes under the influence of internal and external factors. At the same time, information can most often be incomplete, difficult to access, untimely, contradictory, etc. Therefore, in this paper, it is proposed to use a cognitive approach and cognitive modeling of complex systems to overcome the problems of information deficiency by imitating cognitive modeling of the structure and behavior of a complex regional system. The simulation was carried out using the author’s CMCS (Cognitive Modeling Complex System) software system. The results of multi-stage cognitive modeling, consisting in the development of cognitive maps “Influence of ICT on the state of the region” and “Digitalization of the republic” (according to the socio-economic state of the Republic of Dagestan), analysis of structural properties and modeling scenarios for the development of situations on the model are presented. Scenarios make it possible to foresee the ways of possible development of the system under the influence of various factors, including the factor of informatization.

Solving the problem of mathematical models overparameterization for some nonlinear oscillating systems

This study proposes a numerical-analytical method that allows us to simplify the model, which is obtained on the basis of the single observable variable of an object under the study, and which may be overparameterized. As a model, we consider a system of ordinary differential equations with polynomial right-hand sides. To solve this problem, the so-called differential model is used, that is, a system in which unknown variables are replaced by derivatives of the observed variable, and which is derived on the basis of a system under the study so that the observed variables of these systems coincide. The method of simplification of a system under the study is based on the fact that using a numerical method, a simpler differential model can be obtained. Next, an analytical transition from a simplified differential model to a simplified original system is performed. In this case, the time series error remains within given limits even for systems with deterministic chaos, despite their high sensitivity to the initial conditions.

Comparison of using Apache OpenWhisk and Google Cloud Functions for development of serverless applications on Google Cloud Platform

A comparison of using proprietary cloud platform Google Cloud Functions and open source platform Apache OpenWhisk for writing serverless applications based on the Google Cloud Platform was made. The following criteria were chosen for comparison: supported programming languages, convenience and speed of development and deployment of functions, possible ways to pass parameters to functions, options for monitoring the status of functions, speed of the cold start. As a result, main advantages and disadvantages of each platform were identified. Recommendations for use cases are given based on the features of the platforms. The results of the study can be used for further studies in the field of FaaS technologies, as there are a lot of solutions in this area that also need to be compared.