Showing papers in "WSEAS Transactions on Mathematics archive in 2021"

Reduction of the Self-dual Yang-Mills Equations to Sinh-Poisson Equation and Exact Solutions

Abstract: The geometric properties of differential systems are used to demonstrate how the sinh-poisson equation describes a surface with a constant negative curvature in this paper. The canonical reduction of 4-dimensional self dual Yang Mills theorem is the sinh-poisson equation, which explains pseudo spherical surfaces. We derive the B¨acklund transformations and the travelling wave solution for the sinh-poisson equation in specific. As a result, we discover exact solutions to the self-dual Yang-Mills equations.

Application Local Polynomial and Non-polynomial Splines of the Third Order of Approximation for the Construction of the Numerical Solution of the Volterra Integral Equation of the Second Kind

Abstract: The present paper is devoted to the application of local polynomial and non-polynomial interpolation splines of the third order of approximation for the numerical solution of the Volterra integral equation of the second kind. Computational schemes based on the use of the splines include the ability to calculate the integrals over the kernel multiplied by the basis function which are present in the computational methods. The application of polynomial and nonpolynomial splines to the solution of nonlinear Volterra integral equations is also discussed. The results of the numerical experiments are presented.

Criterions of Supersinguliarity and Groups of Montgomery and Edwards Curves in Cryptography

Abstract: We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves. The criterions of the supersingularity of Montgomery and Edwards curves are found. In this paper, we extend our previous research into those Edwards algebraic curves over a finite field and we construct birational isomorphism of them with cubic in Weierstrass normal form. One class of twisted Edwards is researched too. We propose a novel effective method of point counting for both Edwards and elliptic curves. In addition to finding a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, we also find a general formula by which one can determine whether or not a curve Ed[Fp] is supersingular over this field. The method proposed has complexity O( p log2 2 p ) . This is an improvement over both Schoof’s basic algorithm and the variant which makes use of fast arithmetic (suitable for only the Elkis or Atkin primes numbers) with complexities O(log8 2 pn) and O(log4 2 pn) respectively. The embedding degree of the supersingular curve of Edwards over Fpn in a finite field is additionally investigated. Singular points of twisted Edwards curve are completely described. Due existing the birational isomorphism between twisted Edwards curve and elliptic curve in Weierstrass normal form the result about order of this curve over finite field is extended on cubic in Weierstrass normal form. Also it is considered minimum degree of an isogeny (distance) between curves of this two classes when such isogeny exists. We extend the existing isogenous of elliptic curves.

On the Solution of Fredholm Integral Equations of the First Kind

Abstract: As it is well known the problem of solving the Fredholm integral equation of the first kind belongs to the class of ill-posed problems. The Tikhonov regularization method is well known. This method is usually applied to an integral equation and a system of linear algebraic equations. The authors firstly propose to reduce the integral equation of the first kind to a system of linear algebraic equations. This system is usually extremely ill-posed. Therefore, it is necessary to carry out the Tikhonov regularization for the system of equations. In this paper, to form a system of linear algebraic equations, local polynomial and non-polynomial spline approximations of the second order of approximation are used. The results of numerical experiments are presented.

Classification of Evolutoids and Pedaloids in Minkowski Space-time Plane

Abstract: n this paper, we study the families of relatives of pedals and evolutes in the Minkowski spacetime plane R21. We obtain some relationships between these families which turn out to be different from Euclidean plane. Also, we classify and generalize these notions to the category of frontal curves in R21. Finally, some computational examples in support of our main results are given and plotted.

Fractional Fourier Series with Separation of Variables Technique and Its Application on Fractional differential Equations

Abstract: When using some classical methods, such us separation of variables; it is impossible to find a general solution for some differential equations. Therefore, we suggest adding conformable fractional Fourier series to get a new technique to solve fractional Benjamin Bana Mahony and Heat Equations. Furtheremore, we give new numerical approximation for functions using mathematica coding called conformable fractional Fourier series approximation

The Moment Properties of Order, Reversed Order and Upper Record Statistics for the Power Ailamujia Distribution

Abstract: The power Ailamujia distribution has been successfully developed in statistics, both theoretically and practically, performing well in the fitting of various types of data. This paper investigates the moment properties of the associated order, reversed order and upper record statistics, which are indeed unexplored aspects of this distribution. In particular, the exact expressions for the single moments of the order and reversed order statistics are provided. Some recurrence relationships for both single and product moments for the order and upper record statistics are proved. For additional goals, certain joint distributions are also given.

Soft Topological Spaces Induced Via Soft Relations

Abstract: Soft relation is a basic mathematical model that can be related to several real-life data. Throughout many fields, soft relations are used to build soft topological structures. In addition, soft topological constructs are generalized methods to calculate similarity and dissimilarity of objects. Within this article, we present a new approach for directly producing a soft topology by soft relation without using base or subbase. This process is important technique for applications of soft topology. There is investigations into the relationship between soft set topologies and different relations and some of their properties are obtained.

Global and Sensitivity Analyses of Unconcerned COVID-19 Cases in Nigeria: A Mathematical Modeling Approach

Abstract: Covid-19 is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Many measures have been made by World Health Organization (WHO), but these may be threatened by unconcerned infectious individuals (some infectious individuals who do not take the disease serious, by ignoring non-pharmaceutical intervention). A system of nonlinear ordinary differential equations that absorbs a class of unconcerned infectious individuals, is developed. An invasion threshold parameter, Rc, is derived using the next generation matrix approach. This is used to establish the global stability of COVID-19-free equilibrium points. The global asymptotic stability of COVID-19 persistence equilibrium solution is studied through the use of suitable LaSalle’s Invariance Principle with a Lyapunov function of Goh-Volterra type. The intervention of the model key parameters is assessed through sensitivity analysis. Our results indicate that increase in the rate of hospitalization of the asymptomatic infectious and unconcerned infectious individuals after a compulsory national testing, could bring Rc below one. Our results suggest that there should be compulsory national testing and continuous enhancement, the awareness through effective risk communication concerning COVID-19 to the general public. Numerical simulations are carried out to validate the analytical results.

Heat Transfer Process with Solid-solid Interface: Analytical and Numerical Solutions

Abstract: This work is aimed at the study and analysis of the heat transport on a metal bar of length L with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials. Analytical and numerical solutions are obtained under continuity conditions at the interface, that is a perfect assembly. The lateral side is assumed to be isolated and a constant thermal source is located at the left-boundary while the right-end stays free allowing the heat to transfer to the surrounding fluid by a convective process. The differences between the analytic solution and temperature measurements at any point on the right would indicate the presence of discontinuities. The greater these differences, the greater the discontinuity in the interface due to thermal resistances, providing a measure of its propagation from the interface and they could be modeled as temperature perturbations. The problem of interest may be described by a parabolic equation with initial, interface and boundary conditions, where the thermal properties, the conductivity and diffusivity coefficients, are piecewise constant functions. The analytic solution is derived by using Fourier methods. Special attention is given to the Sturm-Liouville problem that arises when deriving the solution, since a complicated eigenvalue equation must to be solved. Numerical simulations are conducted by using finite difference schemes where its convergence and stability properties are discussed along with physical interpretations of the results.

Generating Fuzzy Sets and Fuzzy Relations based on Information

Abstract: Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced.

Approximation on Manifold

Abstract: The purpose of this work is to obtain an effective evaluation of the speed of convergence for multidimensional approximations of the functions define on the differential manifold. Two approaches to approximation of functions, which are given on the manifold, are considered. The firs approach is the direct use of the approximation relations for the discussed manifold. The second approach is related to using the atlas of the manifold to utilise a well-designed approximation apparatus on the plane (finit element approximation, etc.). The firs approach is characterized by the independent construction and direct solution of the approximation relations. In this case the approximation relations are considered as a system of linear algebraic equations (with respect to the unknowns basic functions ωj (ζ)). This approach is called direct approximation construction. In the second approach, an approximation on a manifold is induced by the approximations in tangent spaces, for example, the Courant or the Zlamal or the Argyris fla approximations. Here we discuss the Courant fla approximations. In complex cases (in the multidimensional case or for increased requirements of smoothness) the second approach is more convenient. Both approaches require no processes cutting the manifold into a finit number of parts and then gluing the approximations obtained on each of the mentioned parts. This paper contains two examples of Courant type approximations. These approximations illustrate the both approaches mentioned above.

Option Pricing under GARCH Models Applied to the SET50 Index of Thailand

Abstract: Variance changes over time and depends on historical data and previous variances; as a result, it is useful to use a GARCH process to model it In this paper, we use the notion of Conditional Esscher transform to GARCH models to find the GARCH, EGARCH and GJR risk-neutral models Subsequently, we apply these three models to obtain option prices for the Stock Exchange of Thailand and compare to the well-known Black-Scholes model Findings suggest that most of the pricing options under GARCH model are the nearest to the actual prices for SET50 option contracts with both times to maturity of 30 days and 60 days

Contra-continuous Functions Defined Through Λ1-closed Sets

Abstract: We introduce some variants of contra-continuity in terms of ΛI -closed sets, namely contra-ΛI - continuous, contra quasi-ΛI -continuous and contra ΛI -irresolute functions. The relationships between these functions are investigated and their respective characterizations are established. Moreover, we study their behavior of several topological notions under the direct and inverse images of these functions.

Approximation Functionals and Their Application

Abstract: The purpose of this work is to obtain local estimates, and to calculate the constants of approximation of smooth functions. To achieve this goal, the trajectory of functionals, the concept of an approximation families of functionals, the tape of the trajectory of functionals and the width of the tape are considered. For this, the concepts of approximation functionals and their trajectories in the conjugate space are introduced, and the concepts of the trajectory tape and the tape width at a given point are discussed. The resulting overall evaluation of the approximation is applied to multidimensional cases, namely, to approximations by the Courant and Zlamal elements.

Continuity for Multifunctions in Ideal Topological Spaces

Abstract: This article presents the concept of ı ⋆ -continuous multifunctions in ideal topological spaces. Especially, several characterizations of ı ⋆ -continuous multifunctions are investigated. Moreover, the relationships between ı ⋆ -continuity and the other types of continuity for multifunctions are established.

Minimality of SRPT Networks with Resource Sharing

Abstract: A general multi-resource network with users requiring service from a number of shared resources simultaneously is considered. It is demonstrated that the Shortest Remaining Processing Time (SRPT) service protocol minimizes, in a suitable sense, the system resource idleness with respect to customers with residual service times not greater than any threshold value on every network route. Our arguments are pathwise, with no assumptions on the model stochastic primitives and the network topology.

Confidence Intervals for the Ratio of Means of Two Independent Log-Normal Distributions

Abstract: In this paper, we investigate confidence intervals for the ratio of means of two independent lognormal distributions. The normal approximation (NA) approach was proposed. We compared the proposed with another approaches, the ML, GCI, and MOVER. The performance of these approaches were evaluated in terms of coverage probabilities and interval widths. The Simulation studies and results showed that the GCI and MOVER approaches performed similar in terms of the coverage probability and interval width for all sample sizes. The ML and NA approaches provided the coverage probability close to nominal level for large sample sizes. However, our proposed method provided the interval width shorter than other methods. Overall, our proposed is conceptually simple method. We recommend that our proposed approach is appropriate for large sample sizes because it is consistently performs well in terms of the coverage probability and the interval width is typically shorter than the other approaches. Finally, the proposed approaches are illustrated using a real-life example.

On the Diophantine equation 3 x +p y =z 2 where p ≡ 2 (mod 3)

Abstract: Let p be a prime number where p ≡ 2 (mod 3). In this work, we give a non­negative integer solution for the Diophantine equation 3x+py=z2 . If y = 0, then (p, x, y, z) = (p, 1, 0, 2) is the only solution of the equation for each prime number p. If y is not divisible by 4, then the equation has a unique solution (p, x, y, z) = (2, 0, 3, 3). In case that y is a positive integer that is not divisible by 4, we give a necessary condition for an existence of a solution and give a computational result for p < 1017. We also give a necessary condition for an existence of a solution for qx + py=z2 when p and q are distinct prime numbers.

On the Diophantine Equation n^x + 13^y = z^2 where n = 2 (mod 39) and n + 1 is not a Square Number

Abstract: The purpose of the present article is to prove that the Diophantine equation nx + 13y = z2 has exactly one solution (n, x, y, z) = (2, 3, 0, 3) where x, y and z are non-negative integers and n is a positive integer with n ≡ 2 (mod 39) and n + 1 is not a square number. In particular, (3, 0, 3) is a unique solution (x, y, z) in non-negative integers of the Diophantine equation 2x + 13y = z2.

Pairwise Strongly Lindelöf, Pairwise Nearly, almost and Weakly Lindelöf Bitopological Spaces

Abstract: The main purposes of this article is to introduce new generalizations of the notion of pairwise Lindelof spaces in bitopological spaces where new notions: pairwise strongly Lindelof, pairwise nearly, pairwise almost and pairwise weakly strongly Lindelof bitopological spaces depend on the new notion pairwise preopen countable covers. These covers where we focused on their importance in topology consist of countable subfamilies whose closures cover the bitopological spaces and we clarified how pairwise preopen countable covers effect on pairwise strongly Lindelof spaces. The new concepts of pairwise strongly Lindelof, pairwise nearly, pairwise almost and pairwise weakly strongly Lindelof bitopological spaces are introduced and many definitions, propositions, characterizations and remarks concerning those notions are initiated, discussed and explored. Furthermore, the relationships between those bitopological spaces are examined and investigated. We illustrated the implications hold by these new bitopological spaces. We put some queries and claims, then we struggle to provide their proofs.

The Modified Sadik Decomposition Method to Solve a System of Nonlinear Fractional Volterra Integro-Differential Equations of Convolution type

Abstract: In this work, an incorporated form of Sadik transform and Adomian decomposition method which is called the Sadik decomposition method is presented. The method is applied to solve a system of nonlinear fractional Volterra integro-differential equations in the convolution form. To avoid collecting the noise terms that lead the method to fail for seeking the solution, the proposed method is modified by selecting a suitable initial solution. The obtained results are expressed in the explicit form of a power series with easily computable terms. In addition, illustrative examples are shown to demonstrate the effectiveness of the method.

Modeling the Effect of Global Warming on the Sustainable Groundwater Management: A Case Study in Bangladesh

Abstract: The paper deals with a deterministic model for the declination of groundwater level due to deforestation and evaporation that is caused of global warming. The model is governed by three compartments by considering different level of water. The model is analyzed by finding the existence of equilibrium points and also derived the conditions of stability at the equilibrium points by using Jacobian matrix and Routh-Hurwitz criterion for the system of non-linear differential equation. We also observe the qualitative behavior by using phase portrait diagram. Finally, the numerical simulations have been performed to illustrate the effect of deforestation, poor storage of water and evaporation on the groundwater level in support of analytical findings briefly. Our study shows that, groundwater level decreases drastically due to deforestation and global warming.

Estimation of Multicomponent Reliability based on Progressively Type II Censored Data from Unit Weibull Distribution

Abstract: In this paper, inference upon stress-strength reliability is considered for unit-Weibull distributions with a common parameter under the assumption that data are observed using progressive type II censoring. We obtain di_erent estimators of system reliability using classical and Bayesian procedures. Asymptotic interval is constructed based on Fisher information matrix. Besides, boot-p and boot-t intervals are also obtained. We evaluate Bayes estimates using Lindley's technique and Metropolis-Hastings (MH) algorithm. The Bayes credible interval is evaluated using MH method. An unbiased estimator of this parametric function is also obtained under know common parameter case. Numerical simulations are performed to compare estimation methods. Finally, a data set is studied for illustration purposes.

A note on the stability of a modified Lotka-Volterra model using Hurwitz polynomials

Abstract: In the analysis of the dynamics of the solutions of ordinary differential equations we can observe whether or not small variations or perturbations in the initial conditions produce small changes in the future; this intuitive idea of stability was formalized and studied by Lyapunov, who presented methods for the stable analysis of differential equations. For linear or nonlinear systems, we can also analyze the stability using criteria to obtain Hurwitz type polynomials, which provide conditions for the analysis of the dynamics of the system, studying the location of the roots of the associated characteristic polynomial. In this paper we present a stability study of a Lotka-Volterra type model which has been modified considering the carrying capacity or support in the prey and time delay in the predator, this stable analysis is performed using stability criteria to obtain Hurwitz-type polynomials.

Splines of the Fourth Order Approximation and the Volterra Integral Equations

Abstract: This paper is a continuation of a series of papers devoted to the numerical solution of integral equations using local interpolation splines. The main focus is given to the use of splines of the fourth order of approximation. The features of the application of the polynomial and non-polynomial splines of the fourth order of approximation to the solution of Volterra integral equation of the second kind are discussed. In addition to local splines of the Lagrangian type, integro-differential splines are also used to construct computational schemes. The comparison of the solutions obtained by different methods is carried out. The results of the numerical experiments are presented.

Solutions of Certain Fractional Partial Differential Equations

Abstract: In this paper we find certain solutions of some fractional partial differential equations. Tensor product of Banach spaces is used where separation of variables does not work.

A Generalized of Nörlund Ideal Convergent Double Sequence Spaces

Abstract: In this paper, by using the Norlund mean Nt and the notion of ideal double convergence, we introduce new sequence spaces c0Ι2 (Nt), and l∞I2 (Nt). Besides, we study some topological and algebraic properties on these spaces. Furthermore, some inclusion concerning these spaces are proved.

An Efficient Information Hiding Mechanism Based on Confusion Component over Local Ring and Moore-Penrose Pseudo Inverse

Abstract: The basic requirement by adding confusion is to ensure the confidentiality of the secret information. In the present article, we have suggested new methodology for the construction of nonlinear confusion component. This confusion component is used for enciphering the secret information and hiding it in a cover medium by proposed scheme. The proposed scheme is based on ring structure instead of Galois field mechanism. To provide multi-layer security, secret information is first encrypted by using confusion component and then utilized three different substitution boxes (S-boxes) to hide into the cover medium

The Shock Reaction in a Simple Close Economy

Abstract: As the general objective of a representative government is to achieve in creating the economic conditions that support the wellbeing of citizen, it, thus, needs to design and implement its policies in an appropriated manner. Hence, to support the valuable information for designing and implementing such policies, this work is designed to gain that information by trying to identify the reactions of various variables to government policies. To meet this objective, this work proposed a simple close economy Dynamic stochastic general equilibrium (DSGE) model with the public goods in the household consumption bundle. Also, the usual shocks studied in the DSGE model were included in the reaction investigation process. The Bayesian technique is then employed to estimate the model parameters by using the quarterly detrended data of Thailand in the period of 2001 to 2019. The result showed the crowding-out effect driven by government spending. Also, the reactions of the major macroeconomic variables to each shock were consistent with some previous studies.