Faculty of Mathematics Annamalai University Annamalai Nagar Tamil Nadu India
In the study of HIV infection and AIDS, the estimation of expected time to Seroconversion and its variance is an important aspect. As and when the total antigenic diversity crosses a threshold level, the Seroconversion takes place. In this paper, assuming the threshold level undergoes a change in the form of distribution after a truncation point where the truncation point is taken to be a random variable. The distribution function for the threshold level is obtained by taking exponential distribution and Erlang 2 distribution as the threshold levels before and after the truncation point respectively. Using this distribution function for the threshold level, the expected time to Seroconversion and its variance are derived.
Deparment of Mathematics ,MJP Rohilkhand University Bareilly UP India
1Deparment of Mathematics ,Bareilly College Bareilly UPIndia
In this paper, we propose and analyze production form solutions open and closed networks of queues. Simple analytical results are usually only possible for Markovian queueing networks. We will start by establishing the product form solution for the equilibrium state probabilities for such network. The existence of the product form solution basically nears that the joint state probability can be expressed as a simple product of function associated with a networks individual queues. We generalized the families of queueing network known to have the product form solution.
1,2PG and Research Department of Mathematics Jamal Mohamed College Tiruchirappalli India
In this paper, we define a strong arc in an intuitionistic fuzzy graph and strong intuitionistic fuzzy graphs. This paper discusses the connectedness of isomorphic intuitionistic fuzzy graphs. Some properties and image of a strong arc under isomorphism and co-weak isomorphism are studied. The image of a strong intuitionistic fuzzy graph under isomorphism, co-weak isomorphism and weak isomorphism is also studied.
Department of Mathematics, Laxmin Narain College of Technology Bhopal MP India
*Department of Mathematics, Saifia P.G. College of Science & Education Bhopal MP India
In the present paper a problem for an infinite thermoelastic solid weakened by an internal penny-shaped crack has been solved. The solid that is assumed to be homogeneous and isotropic is subjected to temperature and stress distributions. A cylindrical system of coordinates is used, in which the plane z = 0 is that of the crack and the z-axis is normal to it at the centre. In addition, the crack occupies the region Z = o, 0 £ r £ a that is subjected to prescribed temperature and stress distributions which vary with the radial distance r. The boundary conditions of the problem give a set of two dual integral equations, which we have solved analytically. The problem is solved using the Hankel transform. The inversion of the transform is then obtained analytically. Numerical results for the temperature, stress and displacements distributions are shown graphically and then discussed. All the definite integrals involved were calculated using Romberg technique of numerical integration with the aid of a Fortran program compiled with Visual Fortran v.6.1 on a Pentium-IV pc with processor speed 2.0 GHz.
*Department of Mathematics, University of Rajasthan Jaipur India
Bianchi Type V bulk viscous cosmological model for barotropic fluid distribution (p = gr, 0 £ g £ 1, p being the isotropic pressure, r the matter density) with time dependent displacement vector in the frame work of Lyra geometry is investigated. To get the deterministic solution, we have also assumed zq = constant where z the coefficient of bulk viscosity and q the expansion in the model. For g = 0 (dust distribution), we get the same model as obtained by Bali and Chandnani5. The physical and geometrical aspects of the model are also discussed.
The aim of this paper is to present a common fixed point theorem in E chainable fuzzy metric space for six maps.
Department of Mathematics Malaviya National Institute of Technology Jaipur India
In this paper, we establish two new theorems involving the H-function, Gauss hypergeometric function and incomplete elliptic integrals with the application of interesting theorems given by Orr and Bailey. Some new and interesting integrals involving multi-index Mittag-Leffler function, generalized Wright Bessel function and other simple functions which follow as special cases of our main findings have also been presented.
P.G. & Research Depatment of Mathematics, Jamal Mohamed College Trichy Tamil Nadu India
Intuitionistic fuzzy numbers each of which is characterized by the degree of membership and the degree of non-membership of an element are a very useful means to depict the decision information in the process of decision making. In this article, by compromise ratio method, we investigate the group decision making problems in which all the information provided by the decision makers is expressed as intuitionistic fuzzy decision matrices where each of the elements is characterized by intuitionistic fuzzy number, and the information about attribute weights are known. The compromise ratio method for intuitionistic fuzzy multi-person multi-attribute decision making has been considered here by taking the ranking index based on the concept that the chosen alternative should be as close as possible to the positive ideal solution and as far away as possible from the negative ideal solution simultaneously. The ranking method is used to find the best alternative. The compromise ratio method for intuitionistic fuzzy environment is proposed. Finally the illustrated example is given.
*Department of Mathematics, University of Rajasthan Jaipur India
Bianchi Type II dust filled universe with time dependent cosmological term (L) in presence of C-field (Creation field cosmology) is investigated. To get the deterministic solution, we have also assumed that s a q where s is shear and q the expansion in the model. This leads to A = Bn where A and B are metric potentials and n is a constant. To find the solution in terms of cosmic time t, we have assumed n = 1/2. The solution so obtained satisfies conservation equation (8pi GTji + /gji ) =0which leads to C = t. Thus C increases with time, which agrees with creation field cosmology. The deceleration parameter q > 0 represents decelerating phase. It gives the significance to study early universe. The cosmological constant (L) decays with time which agrees with the present day observations of the universe. The other physical aspects of the model are also discussed.
1Department of Mathematics Government Engineering College Ajmer India
2Department of Mathematics Government College Jalore India
We study a space time of a spherical ball having cosmological constant filled with perfect fluid, where in weak energy conditions, the interior region undergoes gravitational collapse. For negative radial pressure, we show that the singularity will be naked if the ratio of pressure to the density is equal to -1/3 and covered with horizon if this ratio is,-1/3. Also, this model is a generalization of the model given by D Garfinkle and C Vuille.