Applied Mathematics

In this paper we formulate a new local function called ?-closure local function and we construct ?-closure compatible spaces using ?-open sets. Further we introduce an operator ?_?(A) for each A ? P(X) by utilizing ?(A). Moreover we characterize the properties of ?-closure local function and investigate their relationship with other types of similar functions.

In this paper, the author has studied performance of a three unit redundant system with the impact of switch and human failure. A system with three identical unit has been considered for assessment of performance under 2-out –of -3: G; policy. In the system, a switch is used to transfer load from one unit to another unit. All three units of system are connected in parallel configuration and working under 2-out-of-3: G; policy. The system can have two types of failure partial failure and complete failure. Partial failure degrades the efficiency of system but the complete failure breakdown the system and stop functioning of the system. Switch failure and human failure are considered as complete failure. The system has two types of failure and two types of repair. General repair is employed to the partially failed system and Gumbel-Hougaard family copula distribution complete failed system. The system is studied by supplementary variable technique and various measures of reliability, such as availability, reliability, MTTF and profit functions have been discussed. Some particular cases have been discussed by taking different failure rates.

In this analysis we investigate the effect of chemical reaction, thermo diffusion and diffusion thermo on the convective heat and mass transfer flow of a viscous electrically conducting fluid through a porous medium bounded by a semi-infinite vertical plate at with thermophoresis. The equations governing the flow heat and mass transfer are solved by employing Galerkine-finite element analysis with three nodded line segments.

Let G be a simple connected graph of order n. Let Dct(G, i) be the family of connected total dominating sets of G with cardinality i. The polynomial Dct (G, x) = dct (G, i) xi is called the connected total domination polynomial of G. In this paper, we study some properties of connected total domination polynomials of the Extended grid graph Gn. We obtain a recursive formula for dct (Gn, i). Using this recursive formula, we construct the connected total domination polynomial Dct (Gn, x) = dct(Gn, i) xi , of Gn, where dct(Gn, i) is the number of connected total dominating sets of Gn with cardinality i and some properties of this polynomial have been studied.

Legendre and Chebyshev collocation methods are presented to solve numerically the voltterra-fredholm integral equations with exponential kernel. We transform the Volterra Fredholm integral equations to a system of Fredholm integral equations of the second kind,a system Fredholm integral equation with exponential kernel is obtained and will be solved using Legendre and Chebyshev polynomials.This lead to a system of algebraic equations with Legendre or Chebychev coeffcients. Thus,by solving the matrix equation,Legendre and Chebychev coeffcients are obtained.A numerical example is included to certify the validity and applicability of the proposed technique.

Game Theory may be applied in situations in which a Decision Maker (DM) must take into account the reasoning of other Decision Makers. It has proved to be an enormously fruitful approach to the analysis of a wide range of problems. Any situation in which rivals make strategic choices, to which competitors will respond, can be assessed using game theory analysis. An Oligopoly is a market dominated by a few large suppliers. The degree of market concentration is very high (i.e. a large % of the market is taken up by the leading firms). Firms within an oligopoly produce branded products (advertising and marketing is an important feature of competition within such markets) and there are also barriers to entry. Another important characteristic of an oligopoly is interdependence between firms. This means that each firm must take into account the likely reactions of other firms in the market when making pricing and investment decisions. This creates uncertainty in such markets - which we seek to model through the use of game theory. The purpose of this paper is to develop a purely mathematical approach to determine a Payoff for oligopoly market. The model developed allows the researcher to derive Payoff Matrix in an oligopoly market using only assumption about each firm.

The purpose of this paper is to utilize several classes of bivariate distributions whose conditionals belong to the two and three parameter lognormal distribution, and to some of their extensions. In this paper, the most general bivariate distribution with lognormal conditionals is fully characterized. The new distribution is very general, and contains as a particular case the classical bivariate lognormal distribution. We present quantum chemical computational method based on the conditional specification. In the application part, we have found the values for salivary cortisol of shy and non-shy adults by using the lognormal distribution and the corresponding mathematical figures are obtained in section 3. From these curves, computational results have been analysed and compared with medical conclusion.

This paper introduces a new type of labeling called separation cordial labeling. A separation cordial labeling of graph G is a bijection f from V to {1,2,… ,|V|} such that each edge uv is assigned the label 1 if f(u) + f(v) is an odd number and label 0 if f(u) + f(v) is an even number. Then the number of edges labeled 0 and the number of edges labeled 1 differ by at most 1. If a graph has a separation cordial labeling, then it is called separation cordial graph. Here, the class? Pl?_n ( n ? 5), ?Pl?_(m,n) (m,n ? 3) of planar graphs, full binary tree, the star graph? K?_(1,q), the complete bipartite graph K_(m ,n), path P_n, the cycle? C?_n, are discussed and found to be separation cordial. Also, found that complete graph K_n is not separation cordial for, n ? 4.

ABSTRACT Batch arrival retrial queue with positive and negative customers is considered. Positive customers arrive in batches according to Poisson process. If the server is idle upon the arrival of a batch, one of the customers in the batch receives service immediately and others join the orbit. If the server is busy, the arriving batch joins the orbit or collides with the customer in service resulting in all being shifted to the orbit or one of the customers in the batch interrupts the customer in service to get his own service. The arrival of a negative customer brings the server down and makes the interrupted customer to leave the system. The repair of the failed server starts after a random amount of time. During the repair time and delay time, customers may balk the system. After each service completion, the server searches for customers in the orbit with certain probability. Using supplementary variable technique various performance measures are derived. Stochastic decomposition property is established. Special cases are discussed and numerical results are presented.

In this paper, the south east corner [ SEM ] procedure is successfully coded and tested via many randomly generated problem instances . Based on the results we can conclude that the correctness of the newly coded SEM is promising as compared with the previously coded one.