##### A Refinement of the Asymptotic Growth Bounds for the Vlasov Poisson System with a Point Charge

Athraa Neamah ALbukhuttar

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/23501

In  proved that global existence and uniqueness of a classical solution to the three dimensional Vlasov-Poisson system in presence of point charges in case of repulsive interaction. Authors in  were the first to establish a growth bound on the size of the velocity support of the phase space density. This paper improves it further.

##### Mathematical Analysis of a Swine Flu Model with Mixed Transmission

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2016/23142

In this paper, we proposed and analyzed an SEIR compartment model of Swine flu with mixing transmission. The stability of the disease-free equilibrium and the endemic equilibrium is obtained by Routh-Hurwitz criteria. The Basic Reproduction number R has also been discussed, when R0 < 1 , the disease free equilibrium point is stable. In case R0 > 1 , there exists endemic equilibrium. Numerical simulations are carried out for different values of contact rate to understand the transmission behavior of the disease.

##### Approximations of the Number π Using Onscribed Regular Polygons

Mieczysław Szyszkowicz

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2016/23947

Circa 255 B.C., Archimedes invented a method for approximating the value of the number π. He used the perimeters of the inscribed and circumscribed regular polygons to approximate the perimeter of a circle. Starting with two regular hexagons, he doubled the number of their sides up to 96. This approach allowed him to obtain lower and upper estimations of π. He showed that its value lies in the interval [3 + 10/71, 3 + 1/7]. Here the use of onscribed regular polygons is proposed for a similar purpose. The onscribed regular polygons are placed between the two polygons used in Archimedes’ method. Their location is unique and well defined by applying a criterion to minimize distances. The sequences of areas and perimeters produced by these regular polygons, and their linear combinations, generate values which better approximate π than many other geometrical methods.

##### A Computational Method for the Solution of Nonlinear Burgers’ Equation Arising in Longitudinal Dispersion Phenomena in Fluid Flow through Porous Media

M. O. Olayiwola

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2016/23856

This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed the procedure provides rapidly convergent approximation with less computational efforts.The result shows that the concentration C(x,t) of the contaminated water decreases as distance x  increases for the given time t.

##### Optimization Models of Components of Educational Process

Antonina Valerianovna Ganicheva

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/23900

Research objects are components of educational process: a macrosystem of educational process for formation of competence of a pupil (of an educational group), systems representing mathematical models of competencys, ontologies, textbooks. Research objectives: to construct mathematical models of components of educational process, to investigate a question of stability of these systems and their possible classifications, to consider research methods of models (quadratic forms) on convexity – concavity, on positive and negative definiteness.

##### Hyers-Ulam Stability of a Quadratic Functional Equation in Banach Algebras: A Fixed Point Approach

K. Ravi, P. Narasimman, A. Edwin Raj

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/BJMCS/2016/24013

In this paper, we obtain the general solution of a quadratic functional equation and study the Hyers-Ulam stability of generalized derivations in Banach algebras using a fixed point approach.

##### A Common Fixed Point Theorem with Three Pairs of Self Mapping in Fuzzy Metric Space Using Property (E.A.) and Implicit Relation

G. P. Pandey, Sanjay Sharma

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/19949

The proposed method generalises the implicit relation in fuzzy metric space by applying three pairs of self mapping to satisfy the property (E.A.) and the implicit relation.