Scattering of Rayleigh Wave by a Rigid Plane Strip at the Bottom of a Shallow Ocean
Jagdish Singh* and Manju Deshwal
Abstract: The problem of Rayleigh wave scattering due to a rigid plane strip at the bottom of a shallow ocean has been discussed. A thin rigid plane strip is fixed at the bottom (z=0, x£0) of an oceanic layer (- H£z£0) overlying a solid half-space (z³0). Fourier transformation and Wiener-Hopf technique are used to solve the problem. The results are derived in terms of integrals whose evaluation along suitable contours in the complex plane gives the reflected, transmitted and the scattered waves. The scattered wave behaves as a decaying cylindrical wave at distant points. The numerical calculations for the scattered waves show that their amplitude decreases rapidly for a small increase in the value of the wave number. 
Keywords : Seismic waves, Rayleigh waves, scattering, isotropic Medium, Fourier Transform, Wiener-Hopf technique. 

Fuzzy Multilevel Methodology for Reduction of Complexity of Software Reliability and Utility Equations 
Raghuraj Singh, Yogesh Singh,* Upmanyu Misra** and Ushhan D. Gundevia**
Abstract:Most of the existing models for assessment and allocation of soflware reliability have been fashioned after the hardware reliability models, with modifications accommodating the difference between the two. Formulation of most of the reliability allocation models has a form of the non-linear optimization with specified objective function. In this paper, we have approached to develop a reliability model, in a manner that reduces its complexity by replacing the non-linear constraints with linear ones. The model determines how reliable the software modules and program must be to maximize the user’s utility, while taking into account the financial and technical constraints of the system. We have used a model, which provides a unified approach in which the user’s requirements and preferences are formally integrated with the technical structure of the software and its module and program reliabilities. The proposed model determines reliability goals at the planning and design stages of the software project, hence making reliability a singular measure for performance evaluation and project control. 

MHD effects on the free convection and mass transfer flow through porous medium between a long vertical wavy wall and a parallel flat wall
S. Ahmed and N. Ahmed*
Abstract: This paper analysed the effects of magnetic field on the two dimensional free convective and mass transfer flow of a viscous incompressible fluid through a porous medium bounded by a vertical wavy wall and a parallel flat wall. The equations governing the fluid flow and heat transfer have been solved subject to a set of appropriate boundary conditions. The solution consists of two parts : a mean part and a perturbed part. To solve the perturbed part, long wave approximation has been applied. To obtain the solution of mean part, the well known approximation used by Ostrach1 has been utilized.
The zeroth order and first order velocity profile, temperature profile and the skin friction, heat transfer at the walls are demonstrated graphically for different values of the parameters involved. 
Key words and phrases : Magnetic field, Porous medium, Free convection and Mass transfer.

Maximize the production of cement industries by the maximum satisfaction of employees using fuzzy matrix
W. B. Vasantha, N. R. Neelakantan* and S. Ramathilagam
Abstract:In this paper we try to maximize the production of cement industries with maximum satisfaction to employees using fuzzy matrix. Using experts opinion we convert this problem into a relational map. This relational map relates both ways the attributes of the employee and the employer, which is described by the directed graph. Now this directed graph is given a relational matrix representation. As the next stage of the problem we define an average matrix for this relational matrix. This average matrix is converted into a fuzzy matrix by the method of membership functions. Finally using various a - cut values we give the graphical representation to the fuzzy matrices. We get the combined effects of the a - cuts and derive our conclusions. 

A correlation coefficient based on M-estimator
Mustafa Bin Mamat, Muhamad Safiih Bin Lola and Sabri Bin Ahmad
Abstract: This project paper is mainly emphasized on the assessment of the performance of the M-based correlation coefficient compared to the well-known classical correlation coefficient, namely the Pearson’s product moment correlation coefficient. The later is a popular measurement among the researchers and commonly used for estimating r, the population correlation coefficient between two random variables. Unfortunately, the computation of the Pearson’s correlation coefficient is based on the sample means and respectively, which are known to be very sensitive to the presence of outliers in the data set. In this paper, we proposed an alternative approach to compute the correlation coefficient estimate. The proposed method is employed based on M-estimator by incorporating the Huber weight function. A numerical example and simulation study are presented to evaluate the performance of the sample Pearson’s correlation coefficient and the correlation coefficient based on M-estimator. Empirical evidence shows that the performance of both the classical (Pearson’s product moment correlation coefficient) and the robust correlation coefficient (correlation coefficient based on M estimator) are equally good when there is no contamination in the data. However, the M-based correlation coefficient is found to be more efficient than the Pearson’s correlation coefficient when contamination occurs in the data. 
Key words : Pearson’s Correlation Coefficient, M-estimator, outliers, Re-weighted Least Square, scale estimator

Analysis of a nonlinear aids epidemic model with standard incidence
Ram Naresh and Sandip Omar
Abstract: In this paper, a simple nonlinear mathematical model is proposed and analyzed to study the spread of HIV/AIDS in a population with varying size. The population, under consideration, is divided into four subclasses. The dynamics of these classes is assumed to be governed by ordinary differential equations with immigration, nonlinear interaction and natural death terms. The interaction between susceptible and infective is taken to be of standard mass action type. The model has been studied qualitatively using stability theory of differential equations and some inference have been drawn regarding the spread of the disease by establishing local and global stability results. It is shown that the positive non-trivial equilibrium is always locally stable and it may become globally stable under certain conditions showing that the disease becomes endemic due to constant migration of the population into the community.

A Model for Weakness Measurement of Modular System
Pradeep Bhatia* Yogesh Singh** H. L. Verma*
Abstract: Measurement of program weakness is considered one of the important software product quality parameters. The proposed piece of research work is intended to produce an improvement in the framework for computing program weakness that includes the concept of coupling and cohesion together. The improved framework has introduced the low program weakness. The minimization of program weakness has been achieved by minimizing coupling and maximizing cohesion with in a program. Program weakness is an important software product quality criterion. Low program weakness is considered to be desirable quality. This will be helpful for providing guidelines related to quality of design. This paper proposes the quantitative measurement of program weakness in a modular system. It aims to provide guidelines to software designers and project managers. 
Key words: Average number of Live variable(LV), Average life of variable(g), Module(m), System(S), Modular system(MS), Slice, Token, Glue Token, Superglue Token, Adhesiveness of glue token. 

Fuzzy theory method in the problem of unknown flow-rates in chemical plant
S. R. Kannan
Abstract: Experimental study of chemical plants is time consuming expensive and need intensive labour, researchers and engineers prefer only theoretical approach, which is inexpensive and effective. Estimation of unknown flow-rates in splitter mixer unit of a chemical plant plays a vital role in describing the state of the plant. Researcher approached this problem theoretically using energy and material balance method and has given solution for some unknown flow rates of splitter-mixer unit. But they did not give solution to all unknown flow-rates and in their method, error occurred between the measured and the predicted value. In this paper, approach the flow-rates problem theoretically using new fuzzy relational neural network methods. Probably, so far no one has approached the flow-rates problem via a new fuzzy relational neural network method. This paper uses the new fuzzy relational neural network method in the estimation of unknown flow-rates of chemical plant; further the difference between the measured and predicted value is made very close to zero. Estimation of unknown flow-rates is carried out in two stages. In the first stage, this paper gives a fuzzy relational equation representation to the data. If solutions cannot be obtained by this method and errors occur between the measured and predicted values then the second stage a fuzzy neural network method is used to estimate the unknown flow-rates and this method guarantees a solution to all unknown flow-rates. Here if error exists between measured and predicted value then by varying the membership that is weightages the process in repeated a finite number of times until the difference between the measured and predicted value is made very close to zero. Also this paper describes a generalized result for a chemical plant with n-flow-rates.

Averaging operators on non commutative L^P-Spaces
A. A. Tijjani
Abstract: Theory of averaging operatrs on Haagerup L^P-spaces is considered and relations between averaging operators and conditional expectations are studied. 

A generalization of meir-keeler type fixed point theorem for four mappings
R.P. Pant and K. Jha*
Abstract: The object of this paper is to introduce a common fixed point principle which includes all the known contractive definitions as particular cases and employs a Lipschitz type analogue of known contractive definitions. 

Mean flow and Mean temperature of a non-newtonian fluid along a porous moving vertical plate in the presence of oscillating free stream
Y. N. Gaur*, P. R. Sharma** and R. P. Sharma***
Abstract: Free convection effect on mean velocity and mean temperature distributions of a non-Newtonian fluid flow along porous moving vertical plate in the presence of oscillating free stream, constant suction and constant heat flux is investigated. The governing equations of motion and energy are solved by the successive perturbation technique. The expressions of mean velocity and mean temperature are derived, shown through graphs and discussed numerically. The expression of skin-friction coefficient at the plate is derived and discussed numerically its numerical values presented through table. 

A Simple model for temperature regulation in synovial joint
Rekha Bali and A.K. Shukla
Abstract: The studies of the temperature regulation in synovial joint has been presented in this paper. Intra articular generation of heat is expected in any joint during its movement. The more heat is produced, the more wear occurs with the result of disorganisation of the joint and functional impairment. The articular cartilage minimises frictions and heat generation due to its poroviscoelastic and water locatable nature. Its has been observed experimentally that there is hardly any rise in temperature of synovial fluid in normal state but in diseased state, the variation in temperature of synovial fluid has been observed. Analytically the problem is formulated as a two region flow and diffusion model flow and diffusion in between the cartilage. The synovial fluid has been represented by visco-elastic fluid model, the parametric values for which already have been estimated for normal, old and diseased joints. The temperature distribution is obtained by solving energy equation in both the region using proper boundary and matching conditions and perturbation technique. 

Axisymmetric free convection flow of viscous incompressible fluid on a horizontal infinite plate
M. Syam Babu and B. Jayaraj 
Abstract: In this paper the axisymmetric free convection flow of viscous incompressible fluid on a horizontal infinite plate subjected to a mixed thermal boundary conditions under the influence of a uniform transverse
magnetic field is considered. Similarity analysis is used and the non-linear ordinary differential equations are solved by numerical integration using Range-Kutta Gill method with a systematic guessing of conditions
of the problem. The effect of magnetic field on velocity, temperature and pressure for different flow parameters is studied.

Integrals and Partial Derivatives of certain Dirichlet Average
P. K. BANERJI*, S. P. GOYAL** and YOGENDRA DEROA***
Abstract: In this paper we study the integral 

(1 - x)a (1 + x)b S(b, b';1, x)dx

and its partial derivatives with respect to a and b, where S(b, b ' ; x, y) is the Dirichlet average of the function e^x. 
Keywords : Dircihlet Average, Di-Gamma Function or Psi-function, Gauss hypergeometric function.

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