International Journal of Mathematical Models and Methods in Applied Sciences

ISSN: 1998-0140
Volume 13, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of NAUN Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

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Volume 13, 2019

Title of the Paper: Modeling the Impact of Cyber Threats on an Organization's Information System in the Framework of Cyber-Risk Insurance


Authors: Lukáš Pavlík

Pages: 40-44

Abstract: Many organizations around the world are exposed to cyber risks every day. This has also begun in recent years to react to the insurance market. This paper presents possible approaches to modeling the impact of selected cyber threats on the organization and its information system. The proposed algorithm is divided into two parts. The first one is focused on the pricing of selected parameters. The second part focuses on identifying the most serious cyber threat scenario. The main results are then based on the interaction of cyber threats and predefined parameters and can be implemented in the process of determining insurance coverage. On the basis of the results found, it is possible in the next steps to estimate the amount of insurance cover for each organization. It is also described the possible development of this field in the future.

Title of the Paper: Modeling of Cardiac Arrhythmias and Blockades as the Unity of Fractal and Anti-Fractal Antonyms


Authors: Sergii K. Kulishov

Pages: 35-39

Abstract: Different technologies were used for mathematical modeling of biological rhythms. The purpose of our study is to simulate cardiac arrhythmia and blockade as a unity of opposites, pairs of fractal and anti-fractal antonyms. We proposed and tested algorithms for solving these problems. Our concept is presented in the form of a step-by-step analysis of myocardial electrical instability. The methodology of this analysis: the initiation of electrical instability of the myocardium in a particular case; definition of arrhythmic and blockade types; search for cardiac arrhythmias and conduction components as a unity of opposites, antonyms; selection of basic and additional pairs of antonyms, oxymorons; identification of these pairs; the conversion of these results into fractal and / or anti-fractal antonyms; representation of this data in the form of graphical models. Additional investigations were included the graph theory, topology, convex analysis. The proposed algorithms, graphical models contribute to the understanding of arrhythmogenesis, triggers and resonators of these processes; improving the quality of diagnosis as a prerequisite to correct treatment.

Title of the Paper: Career Determination using Information Theoretical Measure and It’s Comparison with Distances in IFS and PFS


Authors: A. Mandaliya, M. Sahni, R. Verma

Pages: 28-34

Abstract: In this paper, we have proposed a method to help students of High School to choose a career having multiple options available after High School. It is based on the student’s marks and their Teacher’s perception of their own marks using generalized intuitionistic fuzzy divergence measure. The method is also compared with distance measure using intuitionistic fuzzy sets (IFS) and pythagorean fuzzy sets (PFS). Tables are drawn using the results based on the feedback collected from the student’s perception and their teacher’s perception about their High School result and compared with the table of membership and non-membership values required in each subject versus career written arbitrarily.

Title of the Paper: Using Random Adaptive Grouping for Improving the Performance of Evolutionary Algorithms Solving LSGO Problems


Authors: A. Vakhnin, E. Sopov, E. Semenkin

Pages: 13-27

Abstract: In fact, many modern real-world optimization problems have the great number of variables (more than 1000), which values should be optimized. These problems have been titled as large-scale global optimization (LSGO) problems. Typical LSGO problems can be formulated as the global optimization of a continuous objective function presented by a computational model of «Black-Box» (BB) type. For the BB optimization problem one can request only input and output values. LSGO problems are the challenge for the majority of evolutionary and metaheuristic algorithms. In this paper, we have described details on a new DECC-RAG algorithm based on a random adaptive grouping (RAG) algorithm for the cooperative coevolution framework and the well-known SaNSDE algorithm. We have tuned the number of subcomponents for RAG algorithm and have demonstrated that the proposed DECC-RAG algorithm outperforms some state-of-the-art algorithms with benchmark problems taken from the IEEE CEC’2010 and CEC’2013 competitions on LSGO.

Title of the Paper: Ranking of Teachers based on Feedback from the Students using Multiple Subjects


Authors: M. Sahni, A. Mandaliya, R. Sahni

Pages: 7-12

Abstract: The purpose of this paper is to evaluate the teachers' performance by using the concept of metric. For the evaluation, we have prepared a questionnaire of fifteen questions divided in six categories. An aggregator operator is used to calculate the mean corresponding to different Teacher's and performance evaluation is done for multiple subjects. The overall evaluation is done for the teachers and the ranking is shown in the form of table.

Title of the Paper: Solution of Radiation and Scattering Electromagnetic Problems in Cartesian, Spherical and Cylindrical Coordinates by Green's Function Method


Authors: Sergey Knyazev, Boris Panchenko, Sergey Shabunin

Pages: 1-6

Abstract: The method of Green’s functions for layered magneto-dielectric structures with arbitrary extraneous electric and magnetic currents is described. Application peculiarities of the method for Cartesian, cylindrical and spherical coordinate system are under consideration. The equivalent circuit approach is applied for layered structures description. Transmitting matrices are used for wave propagation modelling in each layer and through boundaries between layers. It is shown that the boundary transmitting matrix for flat and spherical structures is equal to the unit matrix. Different kinds of loads are used for region boundaries modelling. Suggested method with transmitting matrices allows one to develop universal algorithms with common modules for wave propagation, antennas radiation and scattering problems associated with flat, cylindrical and spherical structures of any number of layers, arbitrary permittivity and permeability. As an example, the problem of minimizing the reflection from a perfectly conducting surface with a two-layer cover using the Green’s functions method is considered.