Open Access Original Research Article

On a Hybrid Clayton-Gumbel and Gumbel-Frank Bivariate Copulas with Application to Stock Indices

Maxwell Akwasi Boateng, Akoto Yaw Omari-Sasu, Nana Kena Frempong, Richard Kodzo Avuglah

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/JAMCS/2019/45668

The study proposes two convex convolution based bivariate Archimedean copulas with their joint distribution functions and conditional distribution functions. Several simulations were performed using sample sizes 100,1000, 10000 and 1000000 for combinations of distributions: Gamma and exponential, Normal and exponential, Gamma and normal, Chi-square and Poisson as well as Skew normal and skew normal for the pairs of random variables to assess the performance of the models under different pairs of distributions. Using the method of maximum likelihood estimation, estimates were obtained for the likelihood function and used in obtaining Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for comparison of the proposed copula models with existing copula models. The models were applied to two listed stocks on the Ghana Stock Exchange. In all, the proposed models, Clayton-Gumbel and Gumbel-Frank outperformed the existing models.

Open Access Original Research Article

Decomposition of Riemannian Curvature Tensor Field and Its Properties

James Gathungu Gicheru, Cyrus Gitonga Ngari

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/JAMCS/2019/43211

Decomposition of recurrent curvature tensor fields of R-th order in Finsler manifolds has been studied by B. B. Sinha and G. Singh [1] in the publications del’ institute mathematique, nouvelleserie, tome 33 (47), 1983 pg 217-220. Also Surendra Pratap Singh [2] in Kyungpook Math. J. volume 15, number 2 December, 1975 studied decomposition of recurrent curvature tensor fields in generalised Finsler spaces. Sinha and Singh [3] studied decomposition of recurrent curvature tensor fields in a Finsler space.

In this paper we study the Riemannian Curvature tensor with its properties its decomposition of the Riemannian curvature tensor and its properties. This raises important question: in Riemannian manifold , is it possible to decompose Riemannian curvature tensor  of rank four,  get another tensor of rank two and study its properties?

Open Access Original Research Article

Effect of Electric Field on MHD Flow and Heat Transfer Characteristics of Williamson Nanofluid over a Heated Surface with Variable Thickness. OHAM Solution

Gossaye Aliy, Naikoti Kishan

Journal of Advances in Mathematics and Computer Science, Page 1-23
DOI: 10.9734/JAMCS/2019/45297

The magneto-hydrodynamic flow with heat and mass transfer of Williamson nanofluid over a heated surface with a variable thickness under the effect of an electric field is examined. It is assumed that the sheet is non-flat. The arising flow governing equations are simplified under the usual boundary layer suppositions. The solution of highly nonlinear transformed simultaneous differential equations is computed by an efficient analytic method called optimal homotopy asymptotic method (OHAM). Consequently, the effects of the governing parameters of the velocity, temperature and concentration profiles are presented graphically and discussed. It is seen that the effect of an electric field has a direct impact on the behavior of the magnetic field in the velocity profile and an increment of Biot number  implies stronger convection at the surface. Comparison of results has been made with the existing literature, and a very good covenant has been observed.

Open Access Original Research Article

Viscous Dissipation Effect on Steady Natural Convection Couette Flow of Heat Generating Fluid in a Vertical Channel

Abiodun O. Ajibade, Tafida M. Kabir

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2019/45020

This article investigates the viscous dissipation effect on steady natural convection Couette flow of heat generating fluid in vertical channel formed by two vertical parallel plates. The dimensionless governing equations are solved analytically using the Homotopy perturbation method (HPM). The temperature and velocity profiles are presented graphically for various values of physical parameters. During the course of investigation, it is found that fluid temperature and velocity increase with the increase in viscous dissipation. However, heat absorption leads to increase in the heat transfer on the heated plate while it decreases on the cold plate. Finally, it is concluded that viscous dissipation is very significant in natural convection problems and should not be ignored in future investigations.

Open Access Original Research Article

Compounding Commuting Matrices

Ronald P. Nordgren

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/JAMCS/2019/45969

We formulate a method of constructing families of commuting matrices of increasing order by sequential compounding. Formulas are derived for sequentially constructing their Jordan forms and singular-value decompositions. Examples are given to illustrate our methods including construction of commuting Latin squares.

Open Access Original Research Article

A New Projection Type Algorithm for Compressive Sensing

Bohan Zhang, Hongchun Sun

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2019/45973

Compressive sensing (CS) is to recover a sparse signal from an undetermined linear system, which has received considerable interest, and some customized iterative methods for solving CS have been proposed in recent years. In this paper, we further consider an algorithm for solving the CS. To this end, a new projection-type algorithm (PTA) is proposed to solve CS based on a new formulation of the problem, which needs only one projection onto the nonnegative quadrant and only one value of the mapping per iteration. Global convergence results of the new algorithm is established. Furthermore, we illustrate the efficiency of given algorithm through some numerical examples on sparse signal recovery.

Open Access Original Research Article

Derivation of a Scalable Solution for the Problem of Factoring an n-bit Integer

Ali Muhammad Rushdi, Sultan Sameer Zagzoog, Ahmed Said Balamesh

Journal of Advances in Mathematics and Computer Science, Page 1-22
DOI: 10.9734/JAMCS/2019/45009

The problem of integer factorization is ubiquitous in scientific and engineering applications including the challenging task of cryptanalysis. This problem is intractable but might admit real-time hardware solutions for small bit sizes. This paper suggests manual and automated scalable solutions for integer factorization based on equation solving over big Boolean algebras. The manual solution is illustrated over a form of 8-variable Karnaugh maps that is highly regular and modular. This solution covers the problem of 6 bits, which includes the problems of 5, 4, and 3 bits as special cases. Moreover, the automated solution is implemented, and subsequently its results are presented and discussed briefly. These results show the notorious evolution of the temporal and spatial complexities as the number of input bits increases. Based on the automated solution, the largest possible hardware circuit obtained via the automated solution is to be constructed, verified and tested. Such a hardware implementation (e.g., FPGA implementation) could serve as a ready real-time look-up solution not only of the pertinent problem but also of all smaller problems.

Open Access Original Research Article

Mathematical and Numerical Analysis for Neumann Boundary Value Problem of the Poisson Equation

Germain Nguimbi, Diogène Vianney Pongui Ngoma, Vital Delmas Mabonzo, Bienaime Bervi Bamvi Madzou, Grâce Lionel Ngoma Bouanga

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/JAMCS/2019/45069

This paper falls within the framework of mathematical modelling and that of numerical analysis. The analysis to be developed through this paper deals with three Neumann boundary value problmes: one pure, one modified and the other with conduction term for the Poisson equation. We introduced Dirichlet and Neumann problems with conduction valuables to prove the continuity in comparison with conduction term of the Neumann problem. We demonstrated the existence and uniqueness of the modified Neumann problem. For simplicity and concreteness, it was appropriate to choose the finite element and classical methods to find the numerical and the explicit solutions, respectively so that numerical simulations were implemented in Scilab.

Open Access Original Research Article

Solution to the Dirichlet Problem on Irregular Domains Using Wavelet-Based Approach

Francis Ohene Boateng, Joseph Ackora-Prah, Anthony Y. Aidoo

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2019/45965

We present a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) with penalty for solving two dimensional (2D) Dirichlet problem for linear elliptic PDE on irregular geometric domains. In this method, the 2-D Dirichlet problem is discretized along one of the spatial variables, reducing it to a 1-D problem. The problem and the boundaries of the irregular domain are approximated using compactly supported wavelets. Results from the numerical analysis indicate that, our method performs better in terms of accuracy and convergence of the approximate solution compared with finite element method.

Open Access Original Research Article

Modeling with the Power Variance form of the Gamma Distribution

Katherine E. Irimata, N. David Yanez, Ibrahim A. Aljasser, Jeffrey R. Wilson

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/JAMCS/2019/45962

It is not uncommon to encounter data where the distribution of the responses is not known to completely follow any of the common probability models. While there are general classes of models, such as the Tweedie distribution, which can be adopted in such cases, many approximations have been proposed based on the fact that they are often easier to obtain. We bring to the discussion a three-parameter power variance representation of the gamma distribution Γ(α, β) that has a general mean-variance relationship , where μ = E(Y) is the mean or expected value of Y,  is a scale parameter, and  is the degree of power of the expression. This power variance formulation is a flexible extension of the gamma distribution, and are used to approximate various models and determine significant predictors even when the distribution is not fully realized. We present a comparison of the power variance model to several known distributions which have similar mean-variance. In addition, we provide a more general representation of the relation , where  is the variance function indexed by the parameter . We demonstrate the performance of the power variance modeling approach through a simulation and evaluate two numerical examples, including high school absenteeism and concrete compression strength.