Applied Mathematics

The aim of this paper is to establish the concept of vague congruence relation on a residuated Lattice. We discuss the relationship between vague Filters and vague congruence relations. Further we define the vague congruence relation corresponding to a given vague filter and some of its properties are obtain. Finally, we determine the quotient algebra induced by this relation and discuss some properties.

The present study is carried out to examine the effects of rotation and Hall current on unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively started vertical plate in a porous medium under the influence of transversely applied uniform magnetic field. Exact solution of energy equation is obtained in closed form by Laplace transform technique, and solution of momentum equation is obtained by defining a complex variable. The expression for the shear stress at the plate due to the primary and secondary flows is obtained. The results obtained are shown by graphs and table.

Graph theory is a branch of Mathematics deals with the study how networks can be encoded and their properties can be measured. Graph theory is becoming most significant as it is most frequently used too many other areas of Mathematics, science and Engineering etc. It is being actively used in varies fields such as biochemistry, Communication networks and Coding theory), Algorithms and Computation and operations research etc. The powerful combinatorial methods found in graph theory have also been used to prove fundamental results in other areas of pure mathematics. This paper, besides giving a general outlook of these facts, includes new graph theoretical proofs of Fermat’s Little Theorem. In this paper we also discussed the timetabling problem and the assignment of frequencies in GSM mobile phone networks.

The aim of this paper is to study the flow of visco-elastic fluid of Rivlin-Ericksen and Walters type through a porous media bounded by a rectilinear pipe of uniform cross section in the presence of a transverse magnetic field. The flow takes place under the action of transient and periodic pressure gradients. Using integral transform technique, the exact solution for velocities have been obtained in case of visco-elastic Rivlin-Ericksen fluid and Walters fluid. Finally various cases of permeability of the porous media have been discussed for both the fluids.

We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we present a necessary condition for similarity of indefinite Sturm-Liouville operators to self-adjoint operators. Using this result, we construct two examples and prove that none of them is similar to a self-adjoint operator.

In this paper we will discuss the algorithm for new type of graph which vertices are different. The algorithm for each type of this graph also will be illustrated. Then we will illustrate different examples for each type.

Chang et al proposed an integrated inventory model with an order-size-dependent trade credit. However, quality issues were not discussed in their model. It is unrealistic for a production system to produce 100 percent good products. This paper extends Chang et al. model and studies an integrated supplier-retailer inventory model where trade credit and defective items are considered. Therefore, to incorporate the concept of supplier – retailer integration and order-size-dependent trade credit, we present a stylized model to determine the optimal strategy for an integrated supplier -retailer inventory system under the condition of trade credit linked to the order quantity, where the demand rate is considered to be a decreasing function of the retail price. In this paper, we propose an integrated supplier–retailer inventory model in which both supplier and retailer have adopted trade credit policies, and the retailer receives an arriving lot containing some defective items. An attempt is made to characterize the preservation technology for deteriorating items to reduce the deterioration rate. Moreover, we consider the capital investment in quality improvement. The objective of our analysis is to determine the optimal ordering, shipping, and quality improvement policies to maximize joint total profit per unit time. Results have been validated with relevant examples.

We study the Jordan Canonical Forms of complex s-orthogonal and s-symmetric matrices, and consider some related results.

The main purpose of the paper exerts the relation between lineage and directed line segments of vector. This approach is an analogical analysis with directed straight line vectors. Every Sib or Lineage consists with Initial and Terminal position which indicates a straight line. The straight line is characterized with its magnitude and having direction. Length, sense and line support are important properties of vectors have not been noticed in this research. Apical ancestor and its latest generation make the straight line due to transmission of a clan and taboos on genealogy. Every lineage means maximum to minimal parental stalk is carried out on a substantial number of directed line segments. These directed line segments are proved by the triangle and parallelogram and P-system graph theory and manifested in that these several line segments propose the theory of structural continuity. Thus it has been examined that the unique direction of lineage is common from apical to latest parental stalk. This paper exercises the overview of male and female line inheritance which can be analyzed with analogical application of Directed line segments of vector and scalar quantities.

In mathematics or its applications, a functional equation is an equation in terms of independent variables, and also unknown functions, which are to be solved for. Many properties of functions can be determined by studying the types of functional equations they satisfy. Usually the term functional equation is reserved for equations that are not in some simple sense reducible to algebraic equations, often because two or more known functions of the variables are substituted as arguments into an unknown function to be solved for. For example: The commutative and associative laws are functional equations. When the associative law is expressed in its familiar form, one lets some symbol between two variables represent a binary operation, thus: (a * b) * c = a * (b * c) But if we write f (a, b) instead of a * b, then the associative law looks more like what one conventionally thinks of as a functional equation: f (f(a, b), c) = f(a, f(b, c))We study generalized quadratic functional equations on quasigroups. These are equations s = t, where each variable appears exactly twice in s = t and each Operational symbol is assumed to be a quasigroup operation on a (fixed) set. A fundamental problem in this class of equations is to investigate their structure and classify them accordingly.