International Journal of Mathematical Models and Methods in Applied Sciences

ISSN: 1998-0140
Volume 14, 2020

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 14, 2020

Title of the Paper: Minimum-projection in the Integer Lattice


Author: Tomaz Dobravec

Pages: 102-109

Abstract: According to the l1 norm, the minimum-projection Pi(x, v) is the smallest element of the intersection of the discrete straight line t(x, v) = {x + t * v, t ∈ Z} and the half-plane Zi2= {x &isin ZxZ sign(i) * x|i| ⋜ 0}. The minimum- projection is, among other things, also used to execute effective routing algo- rithms in circulant graphs. This arti- cle presents an algorithm for calculat- ing the minimum-projections and an al- gorithm for calculating the smallest ele- ment of the discrete straight line t(x, v) in the whole plane ZxZ. Both algorithms have the time complexity O(1). The arti- cle also discusses the k-dimensional gen- eralization of the above-mentioned algo- rithms.

Title of the Paper: The Centroid Solid Angle and Probability Models of Square Prism Dice Rolls


Author: Paul R. Hurst, Vanessa Tandiman

Pages: 95-101

Abstract: Past studies have indicated that the centroid solid angle is related to probabilities of square prism dice rolls. We explain how it is relevant to these probabilities and how to use the spherical projection to calculate the centroid solid angles for the faces on a square prism. These values are then used in a statistical analysis in the quest of constructing a mathematical prob- ability model. The proposed model is based on the principle that the probability of ending up on a particular resting aspect is proportional to the centroid solid angle of that aspect and in- versely proportional to a power of the centroid height in that aspect. Using a power of 2.427, this proposed model ts our data of over 60,000 non-symmetrical square prism dice rolls of vari- ous sizes (unequal heights and widths) with the largest magnitude Z-score of 1.01. Di erent pow- ers can potentially describe other situations; e.g. di erent surfaces, larger dice, heavier dice, etc.

Title of the Paper: Higher-Genus Contributions to an Induced Supergravity Action


Author: Simon Davis

Pages: 81-94

Abstract: The higher-genus contributions to a supergravity action induced by the evaluation of the superstring path integral are considered. Three extra terms are found in the BRST transformation that would arise in the supergravity action. The supersymmetric BRST contour integral over the ideal boundary of an in.nite-genus surface is found to be vanishing if the harmonic measure is zero. The e.ect of a conformal transformation is demonstrated to be consistent with the vanishing of the BRST superspace contour integral. Since the commutator of BRST and conformal Since the BRST symmetry and conformal transformations transofrmations is proportional to the .rst current in four-dimensional gravity, and the vacuum is invariant under both transformations, conditions on the worldsheet .elds result from the dynamics in the embedding space. A connection between conformal models on the two-dimensional worldsheet and the quantum action of the gravitational theory in four dimensions is established through the ghost sector. The number of degrees of freedom in the gravity theory must be reduced to achieve this result. The introduction of new variables related to the embedding of two-dimensional surfaces in three-geometries and then fourmanifolds is then required to satisfy the condition of quantum consistency characteristic of conformal .eld theories.

Title of the Paper: Arbitrage Pricing Model Based on Factor Analysis-Random Forest Regression and its application


Author: Xiaoyang Zheng, Guyue Tian, Fengsi Yu

Pages: 76-80


Abstract: Firstly, this paper establishes K-factor linear model and arbitrage pricing model (ATP) according to ‘the Asset Pricing Model-Arbitrage Pricing Theory’, Then from 2001 to 2017, the Statistical Yearbook of the National Bureau of Statistics collected 10 factors as the original factors such as gross national product, gross industrial product and gross tertiary industry product. After synthesis and simplification, three common factors are extracted to replace ten original factors.The first common factor variable is used to reflect the overall economic level of the country;The second common factor variable reflects a country's inflation rate;The third public factor variable reflects the total annual net export trade situation of the country. After the common factor is determined, the value of the common factor is calculated from the original data.Collect the annual return of 10 stocks for 17 years and do twice random forest regression,we get the arbitrage pricing model. Then, based on the same common factor data, another arbitrage pricing model is obtained by imitating the linear regression method of previous similar papers. By comparing the pricing error, we can find the pricing effect of the model obtained by random forest regression is better than that of the model obtained by linear regression.

Title of the Paper: Three Species Epidemiological Model with Holling Type Functional Responses


Author: S. Hariprasad, M. A. S. Srinivas, N. Phani Kumar

Pages: 62-75


Abstract: In the analytical and numerical study, the interaction between three species is modeled, where in the three species are identified as a prey , which is susceptible, the infected prey and the predator with type-II and type-Iv functional responses, which represents a mathematical model of eco-epidemiology. This study is carried out in both analytically and numerically. The boundedness of the model is studied and the stability analysis of the model is carried out at the positive equilibrium point in terms of locally and globally. The conditions for the occurrence of Hopf bifurcation with fixed biological parameter values are investigated and also it is noticed that the bifurcation occurs by sensitive changes in the parameter values of 3 0 l ,l , and  which represents the growth rate of a predator, transmission rate from infected prey to susceptible prey and half-saturation constant of predator respectively. Further, the stochastic nature of the model is analyzed both analytically and numerically. It is observed that the system exhibits chaotic behavior with the sensitive parameter values which causes large environmental fluctuations.

Title of the Paper: Optimization of Honey Bee Production


Author: Y. O. Aderinto, A. Azagbaekwue, O. M. Bamigbola, M. O. Oke, A. A. Obayomi, L. O. Salaudeen, T. O. Aliu

Pages: 54-61

Abstract: Beekeepers are faced with quite a number of challenges such as selection of fields and enhancement of honey production. In this paper crisp deterministic honey bee production model was formulated in an attempt to optimize the distribution of beehives in the apiary in order to maximize production of honey and minimize unhealthy competition among foraging bees which often arises as a result of overcrowding. The model was characterized using Weighted sum model (WSM) and Analytic Hierarchical Model (AHM). Finally the validity of the model was tested with the real life data and the results obtained shows that proper distribution of the bee hives in the apiary is important to maximize production and minimize unpleasant fields.

Title of the Paper: Numerical Solution of a Certain Class of Singular Fredholm Integral Equations of the First Kind via the Vandermonde Matrix


Author: E. S. Shoukralla, M. A. Markos

Pages: 48-53

Abstract: In this paper, a computational method is presented to solve potential-type Fredholm integral equations of the first kind, equations in which the unknown functions are singular at the endpoints of the integration domain, in addition to the weakly singular logarithmic kernels. This method provides a numerical solution based on the Newton interpolation technique via the Vandermonde matrix, which can accommodate an approximation of the unknown function, in such a manner that its singularity is easily removed, as well as the removal of kernel singularity. In addition, the Gauss–Legendre formula is adapted and applied for the computations of the obtained convergent integrals. Thus, the obtained numerical solution is equivalent to the solution of an algebraic equation in matrix form without applying the collocation method. The numerical solutions of the illustrated example are strongly converging to the exact solution for all values of 1 x  including the end-points 1 whereas the exact solution fails to find the functional values at these end-points; which ensures the powerful and high accuracy of the presented computational technique

Title of the Paper: Numerical Study of the Turbulent Natural Convection in a Trapezoidal Cavity: Influence of the Inclination of the Lateral Walls


Author: Dj. Taloub, A. Bouras, Z. Driss

Pages: 41-47

Abstract: In this paper, we study the heat transfer in turbulent natural convection in a two- dimensional cavity with a trapezoidal section and isoscales filled out of air with as height H =2.5 m. In these conditions, the side walls are differentially heated while the horizontal walls are adiabatic. The k-ε turbulence model with a small Reynolds number was integrated in our calculation code. The governing equations of the problem were solved numerically by the commercial CFD code Fluent; which is based on the finite volume method and the Boussinesq approximation. The elaborated model is validated from the experimental results in the case of the turbulent flow in a square cavity. Then, the study was related primarily to the influence of the slope of the side walls of the cavity on the dynamic behavior and the heat transfer within the cavity.

Title of the Paper: Nonsingular Gradient Solutions in Crack Mechanics and the Concept of Stress Concentration


Author: Valery Vasiliev, Sergey Lurie, Dmitrii Volkov-Bogorodskii

Pages: 38-40

Abstract: We consider the fracture mechanics problem for the finite and semi-infinite cracks in the gradient elasticity. Local stress fields that define the fracture the strength of materials are found as solutions of the inhomogeneous Helmholtz equations in which the inhomogeneity is determined by classical stresses. To construct solutions, the radial factors method and the Papkovich-Neuber representation are used. It is shown that, in problems of crack mechanics. We show that the local stresses in the vicinity of crack tips are non-singular, have the form characteristic of stress concentration, and depend only on the level of acting stresses and the scale parameter, which is found as a result of mechanical testing of material samples.

Title of the Paper: Application of Neural Network Technologies for Inflation Forecasting


Author: Dadyan E.G.

Pages: 34-37

Abstract: The paper considers the methodology of forecasting the level of inflation in Russia with the help of analytical platform Deductor Studio. In solving the problem, the mechanisms of data purification from noises and anomalies were applied, which ensured the quality of forecast model construction and receipt of forecast values for five months in advance. The principle of forecasting the time series was also demonstrated: import, seasonal detection, cleaning, smoothing, construction of forecast model, and forecasting the inflation rate for five months ahead.

Title of the Paper: On the Behavior of One Stochastic Automaton in a Random Environment


Author: Tariel Khvedelidze

Pages: 30-33

Abstract: A construction (behavior algorithm) of a finite stochastic automaton functioning in a stationary random environment with three classes of reactions (encouragement, punishment, indifference) is proposed. Using the methods of the theory of random walks, formulas are obtained for the generating function of the probability of changing the action and for calculating the probability characteristics of the behavior of an automaton. The convergence of sequences of finite automata (when the memory of the automaton n → ∞) to the corresponding infinite automaton (with a countable number of states) of a similar structure is established and given a classification of his possible behavior in this stationary random environment.

Title of the Paper: On the Implementation of Lattice-Based Identification Schemes


Author: Azhar Murzaeva, Sedat Akleylek, Mesut Döngül, Erdal Kılıç

Pages: 24-29

Abstract: Identification is one of the important concerns of information security, that is widely used in our daily e-systems to approve authorised users. With the advent of quantum computers, development of quantum secure identification schemes is essential. In this paper, we give the implementation details of quantum secure Kawachi’s and Cayrel’s identification schemes performed in JavaScript. The hardness of these schemes is based on lattice-based problem SIS in post-quantum cryptography, which requires matrix-vector product operations for its execution. It’s important that for efficient implementation choosing an algorithm with low complexity needs more careful. Therefore, in identification schemes chosen for this study, we use algorithms specific to those schemes’ parameter properties. Then, we carry out matrix by sparse vector and sparse matrix by vector product operations.We provide experimental results of both standard and property-specific algorithms’ execution with their comparison. According to the experimental results, we receive improvements in the specific implementations.

Title of the Paper: Riesz Space Susing Modulus Function


Author: Abdul Hamid Ganie

Pages: 20-23

Abstract: The aim of this paper is to introduce the new techniques of modulus function involving the sequences of Riesz nature. Some of its basic properties has been established.

Title of the Paper: Dissipation of Energy of an AC Electric Field in a Semi-Infinite Electron Plasma with Diffusive Boundary Conditions


Author: Alexander Yushkanov, Sevda Suleimanova

Pages: 17-19

Abstract: Let us consider the electron plasma response with an arbitary degree of degeneracy to an external ac electric field. Surface absorption of the energy of an electric field is calculated.

Title of the Paper: Numerical Study of Intake Flow Optimization using Genetic Algorithm and Artificial Neural Networks


Author: Manimaran Renganathan, Thundil Karuppa Raj

Pages: 13-16

Abstract: An easy way to comply with the conference paper formatting requirements is to use this document as a template and simply type your text into it. The increase in the performance of internal combustion engines for diesel engines has driven to follow alternative ways in order to improve the flow characteristics. This paper presents the computational fluid dynamics (CFD) modeling to study the effect of intake flow condition on the swirl ratio and volumetirc efficiency of a direct injection (DI) diesel engine. A single cylinder direct injection diesel engine with two directed intake ports whose outlet is tangential to the wall of the cylinder has been considered. The numerical results from this geometry are validated with the experimental results and published in the literature. In order to enhance the swirl ratio, intake flow in different components are adjusted instead of modifying the intake manifold shape and profile. The experiments are designed by full factorial approach for 3 variables (three components of intake velocity) to study the turbulent flows in a computational way and accomplished using OpenFOAM software. The induced swirl and tumble at the end of compression stroke are also computed and visualized. Numerous computations have been performed in this work during maximum intake valve lift and closed exhaust valve positions. To estimate the reliable data for predicted results, machine learning techniques such as artificial neural network is employed. Information is gathered for different combinations of intake velocity on swirl ratio and volumetric efficiency. Genetic algorithm is applied to fund the fittest data-set for several generations thereby the best optimal flow components are determined. The results from design of experiments approach and neural network techniques are compared.

Title of the Paper: Discontinuous Galerkin Spectral Element Method for Solving Population Balance Differential Equations


Author: Mahmoud Lotfi

Pages: 8-12

Abstract: In this paper, we study the discontinuous Galerkin spectral element method for solving the population balance differential equation. We use the Legendre polynomials of order k as test functions on each element. Calculate the matrices used by Gauss Quadrature integration and then compare the numerical results with the other methods.

Title of the Paper: Some Approach to Key Exchange Protocol Based on Non-commutative Groups


Author: Ruslan Skuratovskii, Aled Williams

Pages: 5-7

Abstract: We consider non-commutative generalization of CDH problem [1,2] on base of metacyclic group G of type Millera Moreno (minimal non-abelian group). We show that conjugacy problem in this group are intractable. The algorithm of generating (desinging) of common key in non-commutative group with 2 mutually commuting subgroups are constructed by us.

Title of the Paper: An Improved User Authentication Scheme for Hierarchical Wireless Sensor Networks without Tamper-Proof Smart Card


Author: Min-Shiang Hwang, Eko Fajar Cahyadi, Yuen-Cheng Chou, Cheng-Ying Yang

Pages: 1-4

Abstract: Recently, Maitra et al. proposed an efficient and robust user authentication scheme for hierarchical wireless sensor networks. They claimed that their scheme does not need tamper-proof smart card and resisted different possible attacks include smart card stolen attack, impersonation attack, privileged insider attack, replay attack, off-line password guessing attack, theft attack, session key recovery attack, denial of service attack, and cluster head capture attack. However, we find some weaknesses of his scheme in this article. We show that their scheme is vulnerable to off-line password guessing with smart card stolen attack.