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.
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 R0 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.
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.
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.
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.