Advanced Mathematics

In this article, the homotopy perturbation method (HPM) and Kamal transform are introduced for obtaining the approximate analytical solution of the Linear and Nonlinear Schrodinger Equations. The proposed method is an elegant combination of the new integral transform “Kamal Transform” and the homotopy perturbation method.

In this paper, we study some of the properties of multi intuitionistic fuzzy rw-open mappings and multi intuitionistic fuzzy rw-closed mappings in multi intuitionistic fuzzy topological spaces and prove some results on these.

This paper contemplates a single vendor single buyer integrated production inventory problem with stochastic demand and transportation cost. Instead of constant lead time, it is assumed to be proportional to the size of vendor’s batch in each cycle. That is, lead time is composed of a lot size dependent run time and constant delay times such as moving, waiting and setup times. Transportation takes a crucial part in the manipulation of supply chain. The operation of transportation determines the efficiency of moving products. The problem is to find the number of shipments m, shipment size Q, safety factor k and the reorder point r. The objective is to minimize the joint total relevant cost incurred in the supply chain. A solution procedure is mentioned for solving the proposed model. Finally a numerical example is provided to illustrate the proposed model.

The purpose of this paper is to introduce a new class of sets called Nano pre-generalized locally closed set in Nano topological space and to discuss some of its properties.

The aim of this paper is to introduce a new class of sets called (1 ,2)*alpha* -closed sets in topological spaces and to study their properties. Further, we define and study (1,2)*T_alpha* space , (1,2)*_gT_alpha* -space and their properties. 

The purpose of this paper is to obtain common fixed point theorem in intuitionistic fuzzy metric spaces while proving this result we utilize the idea of occasionally weakly compatible maps due to AI Thagafi and N.Shahzad [14]. In this paper we have generalized the result of Kamel Wadhwa and Huriom Dubey [8] and occasionally weakly compatible maps by using intuitionistic fuzzy metric spaces.

In this paper, quasi T-flat, the xi T- flat, and phi T-flat trans-Sasakian manifolds are studied. It is proved that quasi T-flat, the xi T- flat, and phi T-flat trans-Sasakian manifolds are Einstein under the condition

In this paper, we study some of the properties of (?, ?)-level subsets of bipolar valued fuzzy subsemiring and prove some results on these.

Modern probability theory studies several processes for which the knowledge of previous outcomes influences predictions for future experiments. When we observe a sequence of chance experiments, all of the past outcomes could influence our predictions for the next experiment. In this work, our aim is to discuss the properties of the Markov Chain model applied to the data set which includes the details on smoking cessation of U.S.A. adults. In this set of data, the selected possible outcomes are, an adult being a non – smoker (A),a smoker who is interested in quitting (B),a smoker who is not interested in quitting (C). All the data was taken from CDC Morbidity and Mortality Weekly reports 2011 and 2009. Using the information given in the data set, the transition probabilities of matrix P were calculated and they are PAA = 0.951, PBA = 0.062, PCA= 0, PAB= 0, PBB = 0.524, PCB = 0.879, PAC = 0.049, PBC = 0.414, PCC = 0.121. Since column entries of matrix P add up to 1 this is a stochastic matrix (a Transition matrix). Then, the probability vector for this study was obtained and named as X0, X0 = [ 0.794 ; 0.0933; 0.1127]; which explains the probability of non- smokers in 2008 = 0.794, probability of smokers who are interested in quitting 2008 = 0.0933, probability of smokers who are not interested in quitting 2008 = 0.1127. Furthermore, the properties of P were analyzed and regularity was determined and the equilibrium approach was calculated. Using this method smoking behavior of US adults was predicted. Our choice of transition probabilities for each outcome, lead to a regular transition matrix P. Hence, after 92 steps, the system converged to a steady state vector V = [0.4508; 0.3562; 0.1929]. This can be seen after 184 years. Therefore, mandatory actions can be taken to prevent tobacco smoking. All the matrix calculations were implemented by MATLAB software.

In this paper, we define a set of polynomials and two dimensional gamma density function to obtain its expectation formula. Again, we derive the generalized Bosanquet and Kestleman convergence theorem and then use it to evaluate an approximation formula of the series involving this set of polynomials. Finally, we make an application of this approximation formula to derive the generating functions of various hypergeometric functions.