Applied Mathematics

The problem of generating bivariate normal distributions is drawing the attention of the reliability analyst. Amongst those approaches, the characterization approach and the modelling approach are very appealing. In fact characterization approach is of interest to both theoreticians and applied workers. Here we have used a bivariate normal distribution for application from Mutivariate normal distribution through characterization approach. In our application we have considered days of Menstrual Cycle with Melatonin hormone as variable combined with LH, Estradiol and Progesterone hormones as variables as women stress effects. In many applications involving functions of random variables one may be interested in only the mean & variance of these functions. Furthermore, one may have available data from which the mean, variance and perhaps correlation coefficients among the variables can be calculated. Here we express the statistics of a function of a several random variables as a function of statistics on its component. In the discussion which follows the joint density is assumed to be a multivariate normal. The mean and variance of four variales have been utilized in the application part. From the clinical point of view menstrual changes due to secretion of hormones Melatonin, LH, Progesterone, Estradiol which are first sign of ovarian function. The curve for moment generating function of the above four variables are obtained here and explained by using a figure in the mathematical results. Keywords: Melatonin, LH, Progesterone, Estradiol

In this paper, we introduced Samarandache-2-algebraic structure of Soft Neutrosophic Near-ring namely Smarandache –Soft Neutrosophic Near-ring. A Samarandache-2-algebraic structure on a set N means a weak algebraic structure S1 on N such that there exist a proper subset M of N, Which is embedded with a stronger algebraic structure S2 ,stronger algebraic structure means satisfying more axioms, that is S1 << S2 ,by proper subset one can understand a subset different from the empty set, from the unit element if any , from the Whole set. We define Smarandache - Soft Neutrosophic Near-ring and obtain the some of its characterization through Generalized soft neutrosophic near-field and Generalized soft neutrosophic (r,m) bi-ideals.For basic concept of near-ring we refer to G.Pilz ,for generalized near-field we refer T.Tamilchelvam and for soft neutrosophic algebraic structure we refer to Muhammed Shabir ,Mumtaz Ali,Munazza Naz, and Florentin Smarandache.

Wireless Sensor networks are dense wireless networks of small, inexpensive, low-power, distributed autonomous sensors which accumulate and propagate environmental data to facilitate monitoring and controlling of physical environments from remote locations with better accuracy. With the advent of new technology and low production costs, wireless sensor networks (WSN) prove to be useful in myriad of diversified applications, although its original development was motivated by military applications, such as battlefield surveillance. This paper describes the software architecture of an intelligent autonomous gateway, designed to provide the necessary middleware between locally deployed sensor networks based on mobile node and a remote location. The gateway provides hierarchical networking, auto management of the mobile wsn (MWSN), alarm notification and SMS/Internet access capabilities with user authentication. The main concern of QoS-based quadratic assignment technique is to increase reliability of network along with lifetime of the network. Several factors such as energy lifetime, throughput, end to end delay, packet delivery ratio and network security have been taken into consideration. Simulation results shows that the protocol offers a better performance in terms of network lifetime and energy consumption.

In this paper, we apply our generalized theorem on summability to derive some approximation formulae of the series involving quadruple hypergeometric function K12. This work may be useful in the field for computation of the solution of hydrodynamical problems. 2000 AMS Classification: 32A05, 33C47, 33C70, 33C90, 40A05, 40A25, 40D05.

In recent times the production sectors (PS) have started to concentrate not only on product production but also on an additional perspective that is research and product analysis in multidimensional aspects. The PS before commencing the production process have now started to find the ways and means of enhancing the product’s features and also they have began to analyze the propagation extent of the product that is the level of the reach of the product. The main notion of carrying out such activities is to produce novelty products. To achieve this PS seek the assistance of many consultancies or they establish research centre in their production environment. Conventional Inventory models do not satisfy the present needs of PS therefore inventive inventory model considering associated costs of research and product analysis have to be formulated. To fulfill this, inventory model is formulated with Decagonal Fuzzy Numbers to overcome the existing uncertainty. In this paper a new approach of Pascal’s Triangle Graded mean Approach is used for Decagonal Fuzzy number. Also Decagonal fuzzy number gives a better optimal value than all other types of fuzzy number.

The duct model used here is that Kahan and Eckart [1950]. The source of the electromagnetic field is taken to a vertical magnetic dipole in the upper surface layer, with an arbitrary time – varying moment , we can determine the transient behaviour of the electric field strength at any distance above the duct .The paper presents a method which allows the calculation of the atmospheric distortion of radar pulse , provided that the influence of the atmosphere is to transfer the transmitted signal through a duct .the polarization of the primary source whose moment varies arbitrarily in time, is chosen in such a way that it allows the exact determination of the electric field strength at some field point above the duct layer .From the physical point of view. Cahniard s idea is applicable as it is based on evaluating the field in a series of image sources of the primary source. The step – function solution of the problem can then be determined as an infinite integrals over finite integrals. Two cases would be distinguished on the basis of the distance between the receiving and transmitting ends and whether it is greater or lesser than the total reflection distance.

In this paper, we study the Q-homomorphism in Q-fuzzy subgroup and prove some results on these.

Soret effect on unsteady MHD flow past an impulsively started inclined oscillating plate with variable temperature and mass diffusion is studied here. The fluid taken is electrically conducting. The Governing equations involved in the present analysis are solved by the Laplace-transform technique. The velocity and concentration profile is discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof Number, Prandtl number, soret parameter, phase angle, the magnetic field parameter and Schmidt number.

A parametric mean length is defined as the quantity , Where This being the useful mean length of codewords weighted by utilities,  Lower and upper bounds for are derived in terms of ‘useful’ information measure.

Chemical reaction effect on unsteady MHD flow through porous medium past an impulsively started inclined plate with variable temperature and mass diffusion in the presence of Hall current is studied here. The fluid taken is electrically conducting. The Governing equations involved in the present analysis are solved by the Laplace-transform technique. The velocity profile is discussed with the help of graphs drawn for different parameters like thermal and mass Grashof Number, Prandtl number, chemical parameter, Hall parameter, permeability parameter, magnetic field parameter and Schmidt number, and the numerical values of skin-friction and sherwood number have been tabulated.