Applied Mathematics

In this paper the Orlicz space of Hahn sequence of fuzzy numbers is introduced. Some properties of this sequence space like solidness, symmetricity, convergence free are studied. Some inclusive relations involving this sequence space are also obtained.

A groupoid is medial if it satis_es the identity wx • yz = wy • xz. A groupoid is trimedial if every subgroupoid generated by 3 elements is medial. Medial groupoids and quasigroups have also been called abelian, entropic, and other names, while trimedial quasigroups have also been called triabelian, terentropic, etc. (See [5], especially p. 120, for further background). The notion of variety of algebras having the property (k, n) was given in [6] and equationally defined classes of cancellative groupoids having the property (2, 4) and (2, 5) were considered there. This notion was qeneralized in [7], where it was shown that the condition of the cancellativity is superfluous, that is, any variety of groupoids with the property (2, n) is a variety of quasigroups. Let k and n be two positive integers and k n. An algebra A is said to have the property (k, n) if every subalgebra of A generated by k distinct elements has exactly n elements. We also say that A is a (k, n)-algebra. A class K of algebras is said to be a (k, n)-class if every algebra in K is a (k, n)-algebra. A variety is called a (k, n)-variety if it is a (k, n)-class of algebras. Trivially, the variety of Steiner quasigroups (xx = x, xy = yx, x•xy = y) is a (2, 3)-variety. It is the unique variety of groupoids with the stated property, and the same holds for the (2, 4)-variety (x•xy = yx, xy•yx = x) given by Padmanabhan in [6]. He has also constructed two (2, 5)-varieties. One of them is commutative (xy = yx, x(y•xy) = y, x(x•xy) = y•xy), while the other one (x•xy = y, xy•y = yx) consists of anticommutative quasigroups. It is an verify the existence of (2, n)-varieties for n?10

The purpose of this study to show the effects of Hematocrit (Red blood cells), height of stenosis, porous parameter and velocity of blood on wall shear stress of the flow of blood through tapered artery. The study reveals that wall shear stress reduces for increasing Hematocrit percentage. It is also observed that wall shear stress increases as stenosis height and porous parameter increase whereas it decreases with the increasing values of velocity of blood and slope of tapered artery.

In this paper we paper we define smooth graceful labeling and semi smooth graceful labeling for a graph. We also prove that a grid graph PnXPm is smooth graceful graph and a star K1,n is semi smooth graceful graph. Using this we proved that star of a star, star of smooth graceful tree and path union of a smooth graceful tree are graceful trees. We also get graceful labeling for comb graph and simple lobster graph.

The vehicle routing problem is to determine K vehicle routes, where a route is a tour that begins at the depot, traverses a subset of the customers in a specified sequence and returns to the depot. Each customer must be assigned to exactly one of the K vehicle routes and total size of deliveries for customers assigned to each vehicle must not exceed the vehicle capacity. The routes should be chosen to minimize total travel cost. This paper gives a solution to find an optimum route for vehicle routing problem using Hybrid Encoding Genetic Algorithm (HEGA) technique. The objective is to find routes for the vehicles to service all the customers at a minimal cost without violating the capacity, travel time constraints and time window constraints

In this paper we are study on time minimizing transportation problem for Albert David Company. The object of this problem is minimizing the transportation time of goods which supply from one source to another source. In this paper we are using zero point method [6,7] to solving time minimizing transportation problem and compare the obtained results with the regulars with the regular methods, which is solve by tora software to get feasible solution and we find that zero point method is best from another method.

In this study, we consider natural convection in a cubic enclosure with the heater and window placed on opposite ends of adjacent vertical walls. For analysis a complete set of non-dimensional equations governing a Newtonian fluid and boundary conditions are recast into velocity or vector potential to eliminate the need for solving the continuity equation. The governing equation with the boundary equations are then descritized using three point central and forward difference approximation for non-uniform mesh. The resulting finite difference equations are then solved using Matlab computer software. The solutions shall be presented at the Reynolds number 2,000 with Prandtl number 0.71. The results are discussed and presented in graphical forms. The room is divided into two regions with those near the heater having high temperatures as those near the window have low temperatures. Mixing of hot and cold fluid and turbulence makes the other areas warm.

In this paper we use a tool called Neutrosophic Cognitive Maps (NCMs) defined by W.B.Vasantha Kandaswamy and Florentine Smarandache in the year 2003.In this paper we study to identify the cause of using Endosulfan in agriculture using NCMs which leads to most dangerous side effects in human beings faced by the peoples of South Indian state of Kerala (Kasargod and Palakkad Dt.). A detailed report on the harmful effects faced by the people with the usage of pesticide in India was telecasted in Star T.V. dated June 24, 2012 “SatyamevaJayathe” anchered by filim star Amir Khan.

In this paper, existence and uniqueness of solutions to three-point boundary value problems associated with a system of first order rectangular matrix differential equation involving kronecker products by using variation of parameters formula are derived. These generalize the results obtained for three-point boundary value problems involving kronecker products.

An Hepatitis B epidemic model with treatment is investigated. The model allows for the some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. The model exhibits two equilibria, namely, the disease-free equilibrium (DFE) and the endemic equilibrium. The stability of these two equilibria is controlled by the basic reproduction number It is shown that if is less than one, the disease-free equilibrium is locally asymptotically stable and is greater than one, the unique endemic equilibrium is locally asymptotically stable. By computer simulation it is found that if the growth rate of pharmacological effect of the lamivadine to the free virus increases, the symptomatic phase decreases. Numerical simulations are also carried out to investigate the influence of certain parameters on the spread of disease, to support the analytical results. Also, sensitivity analysis of the endemic equilibrium point is carried out.