Abstract of Volume 17 (2m) 2005
 

 A fixed point theorem for intimate mappings satisfying rational inequality
Arihant Jain and Bijendra Singh
Abstract : The aim of this paper is to prove common fixed point theorems for intimate mappings on complete metric space satisfying rational inequality and cited an example in support of our result. Our result generalizes the result of Savita12.
Key words : Compatible mappings, Compatible mappings of type (A).
AMS Subject Classification : Primary 47H10, Secondary 54H25.

Digital Certificate for Secure Transactions in E-Banking
S. Karforma* and S. Mukhopadhyay
Abstract : Transaction processing in a E-Banking system requires some technique for identification, authentication and non-repudiation of the customer. Digital certificate, using cryptographic technique, implements above three elements of security needed for E-banking. In this paper we have discussed how digital certificate can be used for secure transactions in E-banking.
Key words: Digital Certificate, PKI, Security, E-Banking.

Total error synthesis of saptial-slider crank mechanism via binary coding concept
Manoj Singh* Anil Rajput** and S.R. Madan***
erating mechanisms structural and mechanical error should be considered together, Although, it is desired that the total error should be small as for as possible in the entire range of function / path generation. And it is often required to control the total error in a certain region of function / path generation with the desired probability scheme. In other words the accuracy desired in this region is greater then the least squares accuracy. If the accuracy greater then least square is desired in a specified region of the operating rang of the mechanism with given probability scheme , then the weighted least squares method seems to be tailor-made for such problems. However no rational procedure is available in the literature which enables the selection of most proper 'weights' connected with desired probability. In this paper 'encoding concept' of information theory is used to develop a weighted least squares method for the total errors synthesis of a spatial-slider crank mechanism in which the error is required to be specifically controlled in the prescribed region of the range of function generation. The application of approach is illustrated by numerical example.

Generating Function for Charlier Polynomials Using Lie Group Theory
P.G. Andhare1 and M.S. Chaudhary2
Abstract : In this paper we determine generating function for Charlier polynomials using Weisner5 method of Lie group.
Mathematics Subject Classification : 33C45, 33C50,33C65.
Key Words and Phrases : Generating relations, Weisner method, Lie groups, Charlier Polynommials.

On certain classes of koebe type functions
S. M. Khairnar* and N. H. More*
Abstract : This paper deals with the n-fold Koebe type symmetric function

and we have obtained some properties and radial for univalence, strlikeness and convexity of the function fb(z) on the lines of Miller, Mocanu and Reade1 and Mocanu2.
Key Words : Univalence, Starlikeness, Convexity, Koebe function. 2000 Mathematics Subject Classification : 30 C 45.

Five series equations involving series of Jacobi Polynomials
A.P. Dwivedi and *Tarannum Siddiqi
Abstract : An exact solution of five series equations involving series of Jacobi polynomials is obtained by reducing them to Freholm integral equations of the second kind in one independent variable. These series equations can be change into the series involving ultraspherical polynomials as wel as Fourier cosine series which arise in mixed boundary value problems, when the distribution of stresses is considered in the interior of an infinitely long strips containing three Griffith cracks situated on a line perpendicular to the boundary lines of the strip2,8.
Key Words : Integral transform, Series Equations, Integral Equations, Mixed boundary value Problem, Series of Jacobi Polynomials.
AMS Classification of Subject : (2000), 65R10.

Fixed Point Theorem of Compatible and Multivalue Maps
Devendra Singh Solanki
Abstract : Aim of the present paper is to derive few results of common fixed point theorem of compatible and multivalued mappings. This paper is divided in three sections. In section 1.1 some useful definition and results are given. In section 1.2 we established a common fixed point theorem for three pairs of compatible mappings which improve the theorem5 2.2. After that this theorem is followed by two corollaries and in third section multivalued maps of d-Compatible and H-Compatible mappings.
Key Words : Compatible mapping, Common fixed point theorem, Complete metric space, Compact metric space, d and H-Compatible condition.
AMS subject classification 47H10.

Statistical models for wet-spell analysis
D. Venkatesan* and K. Sita Devi**
Abstract : Wet-spell analysis is an important part of rainfall analysis. The distribution of the length of wet-spells provides useful information on the temporal distribution of rainfall. This distribution has traditionally been modelled through different probability distributions. In this paper, we compare three such models, namely, truncated poisson distribution, truncated negative binomial distribution and logarithmic series distribution.
Key words : Bernoulli trials, Logarithmic series distribution, Negative binomial distribution, poisson distribution, Truncated distribution, wetspell, Run length.

"Analytical Hierarchy Process" A new paradigm in decision theory with a case study
Ashok Ganguly and Satish Talreja
Abstract : In this paper, we have presented the subject matter and mathematical technique of ‘Analytical Hierarchy Process' (AHP) and displayed its application with a case study i.e., selection of the best team in the group of four cricket teams with different criteria.
Our Evaluation comes closer to that of Wisden’s Cricket Rating.

Fuzzy almost semi d-pre continuous mappings
S.S. Thakur and R.K. Khare
Abstract : In this paper the concept of fuzzy almost semi d- pre continuous mappings have been introduced and some of its properties are studied.

Common fixed points of five maps in a seperated d-complete L-space
Sweetee Dubey
Abstract : In this paper the concept of common fixed points of commuting, continuous, self mapping in L-space has been extended and generalized for five mappings.
Key words : Seperated L-space, d-completeness.

Iterative algorithm of fixed point for finding approximate solutions to completely generalized strongly quasivariational inequalities for fuzzy mappings
Anil Rajput* S.K. Malhotra,** A.K. Yadav*** and D. S. Solanki****
Abstract : In this paper we construct iterative algorithm, which includes many known algorithms as special cases to solve variational inequalities and quasivariational inequalities for fuzzy mappings. We prove the convergence of the iterative sequences generated by this algorithm. Our main results extend and improve the results of Noor7, Park and Jeong8, Park and Jeong9.
Key words and Phrases: Fixed point, variational inequalities, Iterative algorithm, fuzzy mapping.
AMS (2000) MATHEMATICS SUBJECT CLASSIFICATION: 47H10, 54H25.

Multi FAM model and its Applications to analyze Habits and its Consequences in HIV/AIDS patients
W.B. Vasantha Kandasamy and T. Johnson
Abstract : In this paper we consider some m-number of experts’ opinion and we apply the idea of multi-person decision making to find the combined effect of all the experts’ opinion for a given input vector A. In this paper for the first time we introduce the new model which is a model analogous to FAM, called Multi Fuzzy Associative Memories (MFAM) which can at a time work with more than one expert say p expert’s p ³ l.

On strong (E,q) (C,1) summability of fourier series and its derived series
V.N. Tripathi and A.K.Pandey
Abstract : The present paper deals with one theorem on strong (E,q)(C,l) summability of Fourier series and another that of its derived series under very general condition. It generalizes a well known result on strong (E,1)(C,1) summability of Fourier series under certain condition due to Bhatia and Sachan1.

Fixed points of expansive mappings in probabilistic D-metric spaces
Renu Chugh and Savita Rathi
Abstract : The purpose of this paper is two fold. First we observe that under suitable conditions an expansive mapping can be viewed as a Banach contraction mapping in probabilistic D-metric space. Secondly, we prove some common fixed point theorems for expansive mapping in probabilistic D-metric spaces, which are probabilistic analogue of the result of Ahmad, Ashraf and Rhoades1 in D-metric space. In this paper it is shown that the class of probabilistic D-metric spaces is metrizable. The metric D (as defined by Dhage in5) is related to the distribution function F by D(x,y,z) < t if and only if F(x,y,z;t) > 1-t.
Running Title: Expansive mapping.
1991 AMS Subject classification 47H10,54H25.
Key word and Phrases: Probabilistic D-metric Space, Expansive mapping.

Decision of critical path under multiple criteria through 'Analytical Hierarchy Process'
Ashok Ganguly and Satish Talreja
Abstract : In the paper, we solve the shortest path problem under multi criteria situation through 'Analytic Hierarchy Process'

Self similar isothermal expansion of magneto-hydrodynamic gas behind a spherical shock wave with self gravitation
Pankaj Sharma
Abstract : Self -similar power driven isothermal flow behind a spherical Shock has been discussed in a heterogeneous, magnetic, self- gravitating medium. The Shock radius, the density distribution and the internal heat generation are assumed to vary with some power of time. The variation of flow variables behind the shock with respect to distance have been displayed graphically and comparison has been made for the cases of presence and absence of magnetic field.

On the degree of approximation to a function of the class Lip(a, p), 0 < a < 1 and p > 1
U.K. Shrivastava+, Manish Jaiswal++ and Amit Soni++
Abstract : We find that the order of approximation of a continuous 2p periodic, function f belonging to class Lip(a, p) by [S, an] mean is of Jackson order if a suitable integrability condition is imposed upon the function fx(t).

Three dimensional fluctuating free convective mhd flow and heat transfer through a porous medium bounded by an infinite vertical porous plate
U.N. DAS, A. AZIZ* and M. RAHMAN**
Abstract : The free convective unsteady MHD flow and heat transfer through a porous medium bounded by an infinite vertical porous plate is investigated when transverse sinusoidal suction velocity distribution fluctuating with time is applied. Due to this transverse velocity the flow of the fluid becomes three dimensional. A series expansion method is used to get the solution of the governing equations and expressions for the velocity and temperature fields are obtained. The skin friction and the rate of heat transfer at the surface are discussed in detail. The effects of various parameters entering in to the problem are discussed and shown graphically.
Key words and phrases : Free Convective, Fluctuating and MHD Flow, Porous Medium, Heat Transfer.
2000 American Subject Classification : 76W

Genera of compact Riemann surfaces with dihedral automorphism groups
Buddha Prasad Chetiya* and Chandra chutia**
Abstract : Let DPpq be the dihedral group of order 2pq where p and q are odd primes. Dpq can act as a group of automorphisms of Riemann surfaces of different genera. In this paper we obtain all possible genera ( ³ 2) of the Riemann surfaces on which Dpq acts as a group of automorphisms.
199l Mathematics subject classification : 20H10, 30F10
Keywords : Fuchsian group, Smooth quotient, Riemann surface automorphism group, Dihedral group.

Duality in multiobjective fractional programming problem involving r-convexity
Reddy, P.R.S.1 and Varalakshmi, G.2
Abstract : In this paper, we derive necessary and sufficient conditions for a multiobjective fractional programming with respect to r-generalized convexity. In addition, weak and strong duality results are proved in this context.
Key words : Multiobjective fractional programming problem, r-generalized convexity, duality.

A Squeeze Film Lubrication Model for Knee Joints
A. K. Shukla and S. K. Sharma*
Abstract : A theoretical analysis of squeeze film lubrication has been made for better understanding of the lubrication phenomenon of synovial joints. The appropriate mathematical model characterizing the biphasic nature of the articular cartilage as a immisible mixture of interacting continua: a linear elastic solid and viscous fluid and the non-Newtonion aspect (viscoeleastic fluid) of the lubricant is presented. The non linear momentum equations are linearize by the perturbation technique and obtained the approximate solution. Numerical results are obtained for fluid film pressure, load capacity, normal components of velocity and coefficient of friction. The load capacity is found to be higher in the present model compared with that of classical viscous lubrication. The influence of viscoelasticity is to increase the pressure distribution, load carrying capacity and coefficient of friction.
Key words : Viscoelastic fluid, Lubrication. Articular cartilage

On A Numerical Method For Solving Ordinary Differential Equations Arising From Flow In The Arteriorsclerotic Blood Vessel
*E.A. Ibijola1 and B.S. Aribisala2
Abstract : Bestman1 presented a detailed analysis that centers on the application of Mathematics to the systematic circulation of large mammals. Of great interest is the analysis of the flow in the arteriosclerotic blood vessel. In this paper, we present a numerical method that can be used to solve the Ordinary Differential Equations arising from flow in the arterisclerotic blood vessel.

On the stability of the diagonally additive mapping
Kiran Shrivastava* and Kavita Shrivastava**
Abstract : In this work the stability problem of the functional equation 22(x+y)-1 f(x+y,x+y) = 22x-1f(x,x) + 22y-1f(y,y) (*) shall be investigated where f : R+ x R+ ® E be a mapping and where E is a Banach space.
AMS (1991) subject - classification 39B22, 47H19. Primary 39B72.
Key words: stability of mapping, Hyers Ulam Rassias stability, Banach space.

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