##### On Convexity of Right-Closed Integral Sets

E. Salimi, R.S. Sreenivas

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2017/30348

Let N denote the set of non-negative integers. A set of non-negative, n-dimensional integral vectors, M⊂Nn, is said to be right-closed, if ((x ∈ M) ∧ (y ≥ x) ∧ (y ∈Nn)) ⇒ (y ∈ M). In this paper, we present a polynomial time algorithm for testing the convexity of a right-closed set of integral vectors, when the dimension n is xed. Right-closed set of integral vectors are innitely large, by denition. We compute the convex-hull of an appropriately-dened nite subset of this innite-set of vectors. We then check if a stylized Linear Program has a non-zero optimal value for a special collection of facets of this convex-hull. This result is to be viewed against the backdrop of the fact that checking the convexity of a real-valued, geometric set can only be accomplished in an approximate sense; and, the fact that most algorithms involving sets of real-valued vectors do not apply directly to their integral counterparts. This observation plays an important role in the ecient synthesis of Supervisory Policies that avoid Livelocks in Discrete-Event/Discrete-State Systems.

##### Existence and Stability of Equilibrium Points under Combined Effects of Oblateness and Triaxiality in the Restricted Problem of Four Bodies

J. Singh, A. E. Vincent

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/BJMCS/2017/30510

The restricted four-body problem consists of an infinitesimal body which is moving under the Newtonian gravitational attraction of three finite bodies m1,m2,m3 The three bodies (primaries) lie always at the vertices of an equilateral triangle, while each moves in circle about the centre of mass of the system fixed at the origin of the coordinate system. The fourth body does not affect the motion of the three bodies. We consider that the dominant primary body m1 and smaller primary m2 are respectively triaxial and oblate spheroidal bodies. We investigate the existence and locations of the equilibrium points and study their linear stability for the case of two equal masses. The result shows that the non-sphericity of the bodies plays an important role on the existence and evolution of the equilibrium points and influences in a very definitive way their position, as well as, their stability.

##### Convergence Results of Two Step Iteration Procedure with Errors for a Pair of Asymptotically Non-Expansive Mappings in the Intermediate Sense

Anju Panwar, Ravi Parkash Bhokal

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2017/30320

In this paper, we study strong and weak convergence results of a two step iterative process with errors for a pair of asymptotically non-expansive mapping in the intermediate sense.Our results generalize the corresponding results due to Hou and Du  by taking the class of asymptotically non-expansive mapping in the intermediate sense.We have also studied weak and strong convergence results under speci c conditions.

##### Empirical Performance of Internal Sorting Algorithm

Faki Ageebee Silas, Yusuf Musa, S. Akosu Joyce

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2017/29238

Internal Sorting Algorithms are used when the list of records is small enough to be maintained entirely in primary memory for the duration of the sort, while External Sorting Algorithms are used when the list of records is large enough to be maintained in physical memory hence a need for external/secondary storage for the duration of the sort. Almost all operations carried out by computing devices involve sorting and searching which employs Internal Sorting Algorithms. In this paper, we present an empirical analysis of Internal Sorting Algorithms (bubble, insertion, quick shaker, shell and selection) using sample comprising of list of randomly generated integer values between 100 to 50,000 samples. Using C++ time function, it was observed that insertion sort has the best performance on small sample say between 100 to 400. But when the sample size increases to 500, Shaker sort has better performance. Furthermore, when the sample grows above 500 samples, shell sort outperforms all the internal sorting algorithms considered in the study. Meanwhile, selection sort has displayed the worst performance on data samples of size 100 to 30,000. As the samples size grows to further to 50,000 and above, the performance of shaker sort and bubble sort depreciates even below that of selection sort. And when the sample size increases further from 1000 and above then shell sort should be considered first for sorting.

##### An Efficient Method for Solving Linear and Nonlinear System of Partial Differential Equations

Mohand M. Abdelrahim Mahgoub, Abdelilah K. Hassan Sedeeg

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2017/30259

In this paper, Aboodh transform which is based on the Adomian decomposition method (AADM) is introduced for the approximate solution of the linear and nonlinear systems of partial differential equations. This method is very powerful and efficient techniques for solving different kinds of linear and nonlinear System of PDEs. The result reveals that the proposed method is very efficient, simple and can be applied to linear and nonlinear problems.

##### Stability Analysis for Stochastic Differential Equations in Virology

Marouane Mahrouf, El Mehdi Lotfi, Mehdi Maziane, Khalid Hattaf, Noura Yousfi

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2017/30345

In this paper, we propose a viral infection model governed by three stochastic differential equations. The global existence and positivity of solutions is investigated. Further, we give sufficient conditions for the stability in probability of the endemic equilibrium by using the direct Lyapunov method. Moreover, an application and numerical simulations are given to illustrate our theoretical results.

##### Boundary Layer Analysis of Unsteady Forced Convection of a Newtonian Fluid with Variable Thermo-physical Properties in the Presence of Induced Magnetic Field

M. Choudhury, G. C. Hazarika

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/BJMCS/2017/30673

This paper attempts to effectively model the effects of variable viscosity and thermal conductivity on the unsteady hydromagnetic boundary layer flow past a semi-infinite plate when the oncoming free-stream is perturbed by an arbitrary function of time and applied magnetic field is far from and parallel to the plate. The two dimensional boundary layer equations are separated into those representing steady and unsteady parts of the flow. For, steady flow equation and unsteady flow equation, viscosity and thermal conductivity are considered as inverse linear functions of temperature. The basic steady flow governing partial differential equations are transformed into ordinary differential equations by means of similarity transformation which are solved numerically using shooting method and the resulting approximate solution have been used in the subsequent study of the unsteady flow. The unsteady flow equations are subject to the Laplace Transformation technique. In this case, solution for large time is obtained assuming velocity, temperature and Magnetic field as asymptotic expansion. The relevant flow and heat transfer characteristics that is the skin-friction coefficient, the plate temperature and the tangential magnetic field at the plate are derived and discussed numerically.