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.

Main Page

Submit a paper | Submission terms | Paper format


Volume 13, 2019

Title of the Paper: Subsonic to Supersonic Transition through a Vertical Pipe Bend


Author: Etsuo Morishita

Pages: 70-76

Abstract: It is theoretically possible to accelerate the one- dimensional compressible pipe flow from subsonic to supersonic by the gravity effect through a vertical pipe bend. A viscous one-dimensional compressible pipe flow under gravity effect is first studied analytically. The compressible one-dimensional pipe flow with friction is called Fanno flow and the solution is given by analytical formula. In gas dynamics, the gravity effect is minimal and it is not included in the equations. However, it was shown by the present author that the elevation of a pipe could change the flow conditions in a one-dimensional compressible potential flow under gravity. The sonic condition is reached at the maximum height for an inviscid pipe flow. In this paper, the gravity effect is extended to the viscous one-dimensional pipe flow. Subsonic–supersonic transition is also possible by up and down of a pipe, i.e. through a vertical pipe bend for viscous flows, and it is found that the sonic condition deviates from the peak position of the pipe. The analytical solutions are obtained for the prescribed Mach number distribution. For the given pipe geometry, numerical approach is necessary, and the classical method of characteristics is applied to the problem and compared to the exact analytical solutions.

Title of the Paper: Modeling Systems’ Interactions Type “Stochastic - Determined”


Authors: Stepan V. Mednikov, Vladimir I. Mednikov

Pages: 64-69

Abstract: Publications analysis revealed some disadvantages in enterprises’ interactions modeling. The article is “filling the gap” in modeling of inter-system interaction type “stochastic – determined” by using earlier devised enterprise math model. Main features of catastrophe theory were compared with developed protection theory. Previously unknown dependence of the kinetic energy on the substance viscosity in any of the environment, where force majeure exists, is given. Previously unknown fundamental relationships between the turbulence propensities of this substance and the probability density of the force majeure kinetic energy on these substances’ viscosity. Enterprise resource damage calculation was given; math model of rivalry in commodity market and pertinent indicators of enterprise activity were showed.

Title of the Paper: High Precision Stochastic Solvers for Large Autonomous Systems of Differential Equations


Author: Flavius Guias

Pages: 60-63

Title of the Paper: Group Consensus Analysis for First Order Collective Model with Spatial Coordinates Coupling


Authors: Fen Nie, Xiaojun Duan, Yicheng Liu

Pages: 52-59

Abstract: In this paper, we studied some consensus and group consensus algorithms for the collective rotating motions of a team of agents, which has been widely studied in different disciplines ranging from physics, networks and engineering. discrete group consensus algorithm when delay are free and consensus algorithm with processing delays are investigated. Based on algebraic matrix theories, graph theories and the properties of Kronecker product, some necessary and sufficient criteria for the consensus and group consensus are derived, where we show that both the eigenvalue distribution of the Laplacian matrix and the Euler angle of the rotation matrix play an important role in achieving group consensus and consensus. Finally, simulation examples are presented to validate the effectiveness of the theoretical results.

Title of the Paper: Comparing Partitions: Shortest Path Length Metrics and Submodularity


Authors: Jyrko Correa-Morris

Pages: 45-51

Abstract: With the recent impetus in the development of generic properties and formal frameworks for understanding and organizing the different clustering methods at a technical level, the interest in measures to compare partitions has risen, specially motivated by the applications these have to averagebased consensus methods, and the various notions of clusterability. In this regard, Shortest Path Length metrics (also known as Minimum Number of Structural Transformations metrics) have been established as one of the great paradigms for the comparison of not only partitions, but of structured data in general. It has been proven that these metrics can encode many of the properties of the primary notion of proximity that the refinement relation endows the lattice of partitions with. On the other hand, another property that has naturally emerges in many mathematical model in combinatorial optimization, economics, machine learning, among others, is submodularity, which has proven to be quite useful from the algorithmic and computational point of view. Motivated by these facts, a question arose: Are there Shortest Path Length metric which are submodular in any of its arguments? In this paper, we prove that there is no shortest path length metric on the lattice of partitions which is submodular in any of their arguments, thus demonstrating that measures such as Mirkin metric and Variation of Information fail to meet this property. We also prove that there are dissimilarity measures that are nonnegative; symmetric; satisfy the triangle inequality; for a chain of partitions, respects the nearness among partitions in the chain (which basically represent the aforementioned primary notion of proximity); and, in addition, are submodular in each of their arguments. These constitute a novel family of measure for comparing partitions with promising attributes.

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.