Applied Mathematics

Nestle is one of the world’s largest and most prominent food companies. Headquartered in Vevey, Switzerland, it was established in 1866 by Henri Nestle. In this article the authors attempted to identify the various problems encountered by the Nestle dealer and to ascertain the group of (based on product variants) worst affected by such problems.

Let G = (V,E) be any simple finite graph. A subset D of V (G) is said to be Split Majority Dominating set of G if and the induced subgraph is disconnected. A split majority dominating set D is said to be minimal if there exists a vertex v of V such that D-{v} is not a split majority dominating set of G. The Split Majority Domatic Number denoted by is the maximum number of disjoint minimal split majority dominating sets obtained for a graph G. In this article, we have initiated the study of this concept.

In this works, Human Immunodeficiency Virus (HIV) epidemic model including an eclipse stage of infected cells with latently infected cells was considered. The local and global stability of the system were established using the associated basic reproduction number .Bifurcation analysis was used to establish conditions for the local stability of the endemic equilibrium using the centre manifold theorem. The result shows that the disease free equilibrium is locally and globally asymptotically stable, when the associated disease threshold parameter is less than unity, and the system exhibit backward bifurcation. Numerical Simulations carried out for the analytical result suggest that the attack to the latently infected cells cannot be ignored because some quicker cells from this stage will move with time to productively infected class/cells. Keywords: HIV model; Basic reproduction number; sensitivity analysis; backward bifurcation;

Yilmag and Cahit defined Ek – cordial labelling of graphs by combining k-equitable labelling and edge-graceful labelling of graphs. In this paper, we investigate the Ek - Cordial labeling of the graphs.

Lo[14 ] introduced the notion of edge-graceful graphs. In this paper, we extend this to bi-edge and global edge-graceful graphs. Here, we completely characterized the global edge-graceful graphs.

Let f be an element and S a subset of a normed linear space x. A basic Problem of approximation theory is to find an element of S, which is as close as possible to f, i.e. seek an element S* of S such that ? f - S*? ? ?f - s? for all S* in S. This work seeks to use the fourier approximation method using the Inner product space to obtain a best approximation of functions. The fourier approximation in calculus is shown to be a special least square approximation. Define an inner product and norm on c[ -?, ?] by the equation. f.g =?_(-?)^??f(x) g(x)dx and ? f ?= [?_(-?)^??f^2 (x)dx]^(1/2) L Let Jn be the set of all trigonometric polynomial of degree at most n. We seek S* of Jn such that the integral ?_(-?)^?[f (x) - S* (x)] 2dx is minimum. The inner product space, or orthogonal projections, least square approximations and Fourier approximations are defined. The inner product space and orthogonal projection are applied to the least square approximation and subsequently to Fourier approximation in calculus.

Fuzzy cognitive maps (FCMS) are fuzzy graph structures representing casual reasoning. FCM was introduced by Bart Kosko in 1986 .A detailed report on the harmful effect faced by the people with the usage of pesticide in India was telecasted in star T.V.dated June 24, 2012 “SATYAMEVA JAYATHE” anchored by filim star Amir Khan. In this paper we study to identify the cause of using Endosulfan which leads to most dangerous side effects in human beings and animals. FCMs are more applicable when the data is an unsupervised one. As this problem involves more uncertainties FCM is one of the best tools to study the problem.

In this paper, we study some of the properties of interval valued fuzzy subhemiring of a hemiring and prove some results on these.

This paper investigate the effects of radiation and first order homogeneous chemical reaction on MHD boundary layer flow of a viscous incompressible radiating fluid towards a porous exponential stretching sheet in the presence of heat generation and viscous dissipation. The governing non linear partial differential equations are transformed into ordinary differential equations by using similarity variables. The resultant system of equations is solved numerically by using Runge-Kutta method along with shooting technique. The effects of governing parameters on the dimensionless velocity, temperature and concentration are discussed graphically while the skin friction coefficient, Nusselt number, Sherwood number are presented in tables. Moreover, the results thus obtained are also compared with the existing literature and were found to be in good agreement for special cases of previous literature

In this chapter, a Mathematical model is proposed to the study of depletion of a uniformly distributed forest biomass caused by different levels of industrialization and population in two adjoining regions of the habitat. Industrialization dependent, constant, instantaneous, and periodic emissions of pollutant into the environment are taken into consideration. Criteria for local stability, instability, and global stability of non-negative equilibrium are obtained in the absence of diffusion and in presence of diffusion. A model of a single species population living in two patch habitats with migration between them across a barrier was proposed by Freedman and Waltman [5]. The model was extended in [17,19] to include the case where animal species leaving one habitat does not necessarily reach the other habitat, the existence of a positive equilibrium as a function of barrier strengths was examined. Also Freedman [7] studied a single species diffusion model by assuming that the habitat consists of two patches and has shown that there exists a positive, monotonic, continuous non uniform steady state solution that is linearly asymptotically stable under both reservoir and no-flux boundary conditions.