Abstract of Volume 21(2m), 2009

Heat and mass transfer effects on MHD free convection flow of dissipative fluid past an infinite vertical porous isothermal plate
K. CHENNA KESAVULU* A.S. NAGARAJAN** and S. RAMAKRISHNA***
Abstract : A numerical study is performed to analyze the effect of mass transfer on unsteady MHD free convection flow of dissipative fluid past an infinite vertical porous isothermal plate taking into account viscous dissipative heat under the influence of transverse magnetic field. The governing equations are solved numerically by applying finite difference method. The velocity, the temperature and the concentration are studied for different parameters like magnetic field parameter M, suction parameter g, Schmidt number Sc, Eckert number E, Grashof number Gr and modified Grashof number Gm. The numerical results are presented graphically for different parameters. The numerical values of Skin-frictions are presented in tabular form.

Key words: Transient MHD free convection flow, Dissipative fluid, infinite vertical Porous isothermal plate, Non-linear Systems.

Influence of gravity in a rotating generalized thermoelastic medium with two temperature subjected to ramp type heating and loading
Praveen Ailawalia¹, Sunit Kumar¹ and Devinder Pathania²
Abstract : In the present problem we study the deformation of a rotating generalized thermoelastic medium with two temperature under the influence of gravity subjected to ramp type heating and loading. The components of displacement, force stress, conductive temperature and temperature distribution are obtained in Laplace and Fourier domain by applying integral transforms. These components are then obtained in the physical domain by applying a numerical inversion method. Some particular cases are also discussed in context of the problem. The results are also presented graphically to show the effect of rotation and gravity.

Key words: Rotation, gravity, ramp type heating, Generalized thermoelasticity, Laplace and Fourier transforms, conductive temperature, temperature distribution.

Radiation and mass transfer effects on unsteady mhd free natural convection flow past an inclined surface-A numerical study
K. CHENNA KESAVULU * A.S. NAGARAJAN** and S. RAMAKRISHNA***
Abstract : A study is performed to analyze the radiation effects on MHD unsteady natural free convection flow past an inclined surface with variable surface temperature in the presence of transversal uniform magnetic field. The governing equations are transformed into a linear algebraic system and the solution is obtained by employing implicit finite-difference scheme of Crank-Nicolson type. A parametric study is performed to illustrate the influence of radiation parameter, magnetic parameter, Prandtl number and Schmidt number on velocity profile, temperature profile and concentration profiles. The numerical results reveal that the radiation has significant influences on the velocity and temperature profiles. The profiles of the dimensionless velocity, temperature and concentration distributions are shown graphically for various values of the parameters entering into the problem.

Key words : MHD, Radiation, Heat and Mass transfer, Inclined surface, Natural convection.

On randomly K_n-packable graphs
S. SOMASUNDARAM¹ A. NAGARAJAN² and G. MAHADEVAN³
Abstract : A graph G is said to be packable by the graph F if its edges can be partitioned into copies of F. It is randomly packable if what remains of deletion of edges of a proper subgraph that is F packable is also F-packable. In this paper we investigate the properties of W (Y) where Y is a unique K_n - packing of a graph.

Some fixed point theorems for asymptotically regular maps in Hilbert space
Neeraj Malviya*, Devkrishana Magarde** and Pankaj Kumar Jhade***
Abstract : The aim of this paper is to prove fixed-point theorems for asymptotically T-regular sequences and asymptotically regular maps using parallelogram law in Hilbert space, which give proper generalization of recent results due to Engle Browder and Petryshyn, Hardy and Rogers. Mathematics Subject Classification - 47H10, 54H25

Key word: asymptotically T- regular sequence, asymptotically regular map, Hilbert Space, Fixed point.

Pseudo quasi metrics on fuzzy sets
Md. Arshaduzzaman* and Amrendra Kumar** Email.ID - shyan.zaman@gmail.com
Abstract : The paper is addressed to the introduction of a pseudo-quasi metric on fuzzy sets as a distance function between fuzzy subsets which enables us to have a fuzzy pseudo metric satisfying the normality condition.

Key word: Lattice, Fuzzy topological spa, pseudo-quarimetric, normal

A Model for TOPSIS method based on Intuitionistic Fuzzy Sets
Sreeda K.N.¹ and R. Sattanathan²
Abstract : Multicriteria decision making (MCDM) analysis may involve problems dealing with incomplete information. In such instances, the performance ratings of the criteria may be expressed in terms of Intuitionistic fuzzy values. These intuitionistic fuzzy values may then be utilized along with the traditional Technique for Order Performance by Similarity to Ideal Solution [TOPSIS] method so as to arrive at the decision where incomplete weight information are given. Using this method, the ranking of order of all alternatives are obtained by calculating the distances to both Intuitionistic fuzzy positive ideal solution (IFPIS) and the Intuitionistic fuzzy negative ideal solution (IFNIS) simultaneously. In this paper, we have discussed the use of Intuitionistic fuzzy sets (IFS) in multicriteria decision making (MCDM) analysis and its application to a practical problem in combination with the TOPSIS method.

Key words: Intuitionistic Fuzzy sets (IFS), Technique for Order Performance by Similarity to Ideal Solution [TOPSIS], Intuitionistic fuzzy positive ideal solution (IFPIS) and the Intuitionistic fuzzy negative ideal solution (IFNIS).

On secondary range Hermitian Matrices
A.R. Meenakshi, S. Krishnamoorthy* and K. Gunasekaran*
Abstract : The concept of secondary range Hermitian ( s-EP ) matrices is introduced as a generalization of s-Hermitian and EP matrices. Necessary and sufficient conditions are determined for a matrix to be s-EP_r( s-EP and rank r ) Equivalent characterizations of a s-EP matrix are discussed. As an application, it is shown that the class of all EP matrices having the same range space form a group under multiplication.

Key words: Matrix, Hermitian, Secondary hermitian, s-hermitian and Permutation matrix.
AMS: 15A09, 15A15,15A57.

Predicting the growth of manpower for the Tamilnadu software industry (India)
E. Susiganeshkumar and R. Elangovan
Abstract : Manpower is a term which means a group of persons who have acquired some particular skill or expertisation to undertake a particular type of job. There are various milestones one has to cross to adopt a particular skill or background to perform a job. Tamilnadu software industry has undergone a substantial expansion over the past few years. This has necessitated a corresponding increase in output of suitably qualified graduates from the appropriate training institutions. It is therefore desirable to determine the current and projected size of the industry and to establish whether the projected supply of qualified manpower is sufficient to maintain the current rate of growth. In this paper, a detailed survey of a representative sample of these firms is then carried out and used to estimate recruitment, transfer, promotion and leaving rates.

Key words: Manpower, Recruitment, Promotion, Growth Rate.

On fuzzy metric space
Bijendra Singh, R.K. Sharma*, Arihant Jain and Mohit Sharma
Abstract : The aim of this paper is to prove a common fixed point theorem for six self maps on Fuzzy metric space. Our result generalizes the result of Cho¹.

Key words : Common fixed points, Fuzzy metric space, weak compatible maps, compatible maps.
AMS Subject Classification : Primary 47H10, Secondary 54H25.

On Conjugate k-EP Matrices
A.R. Meenakshi*, S.Krishnamoorthy** and B. Vasudevan***
Abstract : The concept of Conjugate k-EP (Con-k-EP) matrix is introduced. Relations between Con-k-EP, Con-EP, k-EP and EP matrices are discussed.
2000 Mathematics Subject Classification: 15A57, 15A15, 15A09

Key words: EP matrices, Con-EP, k-EP matrices.

Mixed convective flow over a non-isothermal radiative Vertical surface embedded in a porous medium with Applied magnetic field
¹K. Rama Krishna, ²V.V. Sobha and ³R.K. Kondragunta*
Abstract: The present paper deals with magneto hydrodynamic mixed convection heat transfer analysis over a vertical surface embedded in saturated porous medium with variable wall temperature. The effects of transverse magnetic field, radiation heat transfer and dissipation are examined. The plate temperature in excess of constant temperature of the ambient fluid is assumed to be proportional to x^l. The ratio of Rayleigh to Peclet number is taken as mixed convective parameter

(�) and the effect of �>0 and �<0 on the boundary layer solution is studied and presented in the graphical form. The boundary layer solutions are obtained by using similarity variables for �>0 and �<0. It is found that with the increase in l value and radiation parameter (F), the rate of heat transfer increases through medium. Different velocity and temperature profiles and Nusselt number variation for both buoyancy aiding flow and opposing flow are also presented.

Key words : Mixed convection, Porous medium, Radiation, Variable Temperature, dissipation, MHD.

Some new relations of generalized voigt-function involving partial derivatives
Atul Garg
Abstract : Aim of this paper is to present multivariable and multiindices study of the generalized Voigt- function which plays an important role in the several diverse fields of physics such as astrophysical spectroscopy and the theory of neutron reactions. Derivative of Voigt function is introduced first time here. Some important recurrence relations involving derivative are also given in terms of generalized Voigt function.

Key words: Voigt function, Bessel function, Derivative, Recurrence relation.
AMS Subject Classification: 33E20, 85A99

Solution of certain simultaneous quadruple series equations involving generalized Bateman-k functions
Mukti Richhariya¹, P.K. Mathur² and Kuldeep Narain³
Abstract : In this paper, a closed form solution is obtained for the simultaneous quadruple series equations using generalized Bateman-k functions by multiplying factor method.

Effect of thermal dispersion and viscous dissipation on MHD radiative non-Darcy mixed convection in a fluid saturated porous medium
¹V.V. Sobha, ²K. Rama Krishna and ³R.K. Kondragunta*
Abstract : The present paper is aimed at analyzing magneto hydrodynamic mixed convective flow and heat transfer about a non-isothermal vertical wall embedded in a porous medium. The Frochheimer extension is considered and the effects of thermal dispersion, Radiation and viscous dissipation in aiding and opposing flow conditions are examined. The wall temperature in excess of constant temperature of the ambient fluid is assumed to be proportional to . The effects of thermal dispersion and viscous dissipation on heat transfer rate are examined under the above-specified conditions and are presented in graphical form. The observations revealed that both thermal dispersion and viscous dissipation enhances the heat transfer rate. However under high magnetic fields their effect is found negligible. Velocity, temperature profiles and Nusselt number variation under different conditions are also presented.

Key words : Thermal dispersion, viscous dissipation, MHD, Mixed convection, Porous medium, Radiation.

A stochastic model for estimation of expected time to recruitment under correlated wastage
A. Muthaiyan¹ and R. Sathiyamoorthi²,
Abstract : In Business and Industrial organization the leaving of personnel is a common phenomenon. This is called wastage. The estimate of the size of wastage and the likely important aspect of study in manpower planning models. The wastage on successive occasions of policy decision regarding, promotion pay, perquisites and targets, are allowed to cumulate since recruitment can not be done after every decision epoch. In this paper an estimate of the expected time to recruitment, is discussed, taking the time to recruitment as a random, variable. Its variance is also obtained and Numerical illustration provided.

Common Fixed Point Theorems in Hilbert Spaces
O. P. Gupta and V. H. Badshah*
Abstract : In this paper we prove a unique common fixed point theorem on a closed subset of a Hilbert space. The result presented in this paper is generalize and extended some previously know result.
Subject Classification. Primary 54H25,Secondary 47H10.

Key words: Fixed point, Hilbert space, Banach space and Closed subset.

Numerical Solution of Transient Free Convective Flow Past a Vertical Porous Plate with Viscous Dissipation and Radiation
S. S. TAK* and RAJEEV MATHUR**
Abstract : The combined effect of viscous dissipation and radiation on transient free convection flow past an infinite vertical porous plate has been studied numerically using Crank Nicolson finite difference scheme. It is found that the steady-state solution is reached after time t_s = 8.5. It is also observed that due to greater viscous dissipative heat or the presence of radiation, there is a rise in the skin friction and a fall in the Nusselt number.

On 3 - inverses of GM matrix
Krishnamoorthy S., Gunasekaran.K** and Muthugobal.BKN*
Abstract : We initiate to fine the 3 - inverse of GM matrix on a set of two distinct positive integers. The eigen value and eigen vectors are determined for the GM matrix.

Key words: Matrix - GM matrix - Positive in integers - LCM - GCB - generalized inverse.
AMS Classification: 15A09, 15A15.

E-convex programmings
P. THANGAVELU and J. SHEIBA GRACE
Abstract : Youness introduced the concepts of E-convex sets and E-convex functions and studied their properties. Following this Xiusu Chen and Suneja, Lalitha and Govil studied the applications of E-convex functions. In this paper we show that Theorem 3.1 of Youness [J. Optim. Theory Appl. 102(2)(1999), 439-450] is incorrect by giving some counter examples. We modify Theorem 3.1 of Youness and apply this to solve an E-convex programming problem.

Key words and phrases : E-convex sets, E-convex functions, E-epigraph, counter examples, E-convex functions.
2000 MSC: 26A51, 26B25,32F, 32T, 46A03, 46A55, 52A.

Fixed point theorems on Hausdorff spaces
Zaheer K Ansari^#, Rajesh Shrivastava^*, Arun Garg and Manish Sharma^**
Abstract : In present paper, some fixed point theorems in Hausdorff spaces have been proved, which generalize the theorem of YEH, C.C. ². Let (X, d) be metric space. A mapping T of X into itself is said to be contractive if, d (Tx, Ty) < d (x, y) ; " x , y Î X.

Key words and phrases: Results on Hausdorff spaces, fixed point theorem.
MSC (2000): 54H25, 28A78.

On 4 - inverses of GM matrix
Krishnamoorthy S. and Gunasekaran K.** and Muthugobal BKN***
Abstract : We initiate to fine the 4 - inverse of GM matrix on a set of two distinct positive integers. The eigen value and eigen vectors are determined for the GM matrix.

Key words: Matrix - GM matrix - Positive in integers - LCM - GCB - generalized inverse.
AMS Classification: 15A09, 15A15.

Analytic Vector field on an almost hyperbolic Hermitian manifold
Sushil Shukla
Abstract : Y. Matsushima proved that in a compact Kähler-Einstein space, any contravariant analytic vector field is uniquely decomposed in the form of Killing vector fields. A. Lichnerowicz generalised this result for a compact Kähler manifold with constant scalar curvature. S. Sawaki generalised the same result for a compact almost Tachibana-Einstein manifold. In 1959, Tachibana introduced the concept of an almost analytic vector field in the almost complex spaces.

The aim of the paper is to discuss an analytic vector field on an almost hyperbolic Hermitian manifold and to obtain certain expressions of the curvature tensor on an almost hyperbolic Hermitian manifold admitting semi-symmetric metric connection assuming analytic vector field to be killing and affine.

Fuzzy Mathematical Solution's of Customer Relationship Management (Financial Sector for current Economic Era)
*Manoj Kumar Jain, **A. K. Dalela and ***Sandeep Kumar Tiwari
Abstract : Today, many businesses such as banks, insurance companies, and other service providers realize the importance of Customer Relationship Management (CRM) and its potential to help them acquire new customers retain existing ones and maximize their lifetime value. At this point, close relationship with customers will require a strong coordination between IT and marketing departments to provide a long-term retention of selected customers.

Drastic changes in communication technology are changing the way that traditional banking is done in current economic era. It has been given new shape of traditional banking. The resulting changes will have a great impact on financial sector. Firstly on the reset up of a financial sector network according to the focus of the market, secondly on the design of new products and on the development and the use of alternative distribution channels and finally on the customers' switching behavior^3,7,9,13.

In this paper, we are exploring issues that put in the fundamentals of CRM for franchise's network optimization and discuss mathematical solution for that. Financial Institution's management team could use the findings of this study, in order to determine specific component in designing financial services and products, which would add in customers' satisfaction and reliability. The proposed approach could have significant implications for enlarging the duration of the relationship among customer and financial institution and for maximizing their franchise performance^6,9,12.

There are different issues relating to the reorganization of financial industry are examined. Specifically the performance of a franchise network, the online service's as an alternative distribution channel and the duration of the relationship among customers (individuals or enterprises) are the three interrelated parties. Fuzzy optimization techniques and generalized linear models are used in order to determine financial products and services which are offered to financial clients through traditional and Internet channels, forecasting customers' attitudes (adoption or rejection) to the new products and the time horizon of their cooperation with their sector^1,4,7.

Key words: CRM: Customer Relationship Management IT: Information Technology.

On Kenmotsu Manifold
Sushil Shukla
Abstract : In 1926, H. Levy proved that a second order symmetric parallel non singular tensor on a space of constant curvature is a constant multiple of the metric tensor. R. Sharma generalized Levy's result and studied second order parallel tensor on a Kähler space of constant holomorphic sectional curvature as well as on a compact K-contact manifold without boundary. U.C. De and Debasish Tarafdar showed that for a P-Sasakian manifold M with a symmetric parallel tensor of type (0,2) is also a constant multiple of the metric tensor and there is no parallel 2-form on M.

In this paper, We have studied symmetric and skew-symmetric second order parallel tensor on a Kenmotsu manifold.

New Characterizations of Semi-T₂, Semi-T₁, and Semi-T₀ Spaces
Charles Dorsett
Abstract : In this paper it is shown that semi-T_i reduces to T_i, i = 0, 1, 2, when an appropriate change of topology is invoked.

Mathematics Subject Classification: 54A10, 54D10.

A note on neo-curvature tensor filed in recurrent finsler manifolds
Sandeep K. Bahuguna^a and Kailash C. Petwal^b
Abstract : Takano¹⁴ has studied the decomposition of the curvature tensor field in a recurrent Riemannian space and various significant outcomes of such decomposition in recurrent Riemannian space have been drawn. The innovations of Neo-curvature tensor field in Finsler subspaces have been initiated by Chandra⁴. Moreover, he has defined and studied "Neo-covariant derivatives and its applications" and several interesting theorems concerning to this delighting research article have been derived. Singh¹¹ has defined and studied decomposition of Neo-curvature tensor filed of first order and has discussed various properties of such decomposition.

The present paper is intended to study "A note on decomposition of Neo-curvature tensor filed in recurrent Finsler manifolds", wherein the decomposition of Neo-curvature tensor field will be the composition of one vector and one tensor fields. Also, some theorems on such decomposition will be investigated.

Index Terms: Finsler, Neo-curvature, recurrence tensor, domain, Riemann, Reference frame

Common fixed point for multivalued and compatible maps
Durdana Lateef*^a, Shoyeb Ali Sayyed^b and A. Bhattacharyya^a
Abstract : A generalization of multivalued hybrid contraction and Meir - Keeler type multivalued maps are obtained in a metric space. Our result is a generalize concept of commuting and compatible mappings under some conditions and corresponding results of ^{1,2,3,4,5,6,7,8,9,10,11,12,} and many others.

Keywords and Phrases: Hausdorff metric, Multivalued mappings, Compatible mappings, Complete metric space.

The investigation of the process of working on Bieberbach conjecture
Ghorban Rajabikafshgar and S. Latha*
Abstract : The study of complex functions theory is one of the most fascinating subjects in complex analysis. The most interesting shape of this theory is the interplay of analysis and geometric. The theory of univalent functions is concerned primarily with such relations between analytic structure and geometric behavior, born around the turn of the century. The serious study of univalent functions theory began in 1907. This theory was given a powerful impetus by the conjecture of Bieberbach. In this article we investigate the process of studying this conjecture during approximately seven decades and attempts to prove of it.

Key words : Univalent functions, area theorem, Bieberbach conjecture, Milin conjecture, Robertson conjecture, Littlewood conjecture, Loewner theorem, Koebe distortion theorem, Garabedian-Schiffer method, Charzynski-Schiffer method, Grunsky inequalities, logarithmic coefficient, Louis de Branges Proof of the Bieberbach conjecture.

An EOQ model with two-parameter constant deterioration and price dependent demand
N.K. Sahoo¹, C.K. Sahoo² and S.K. Sahoo^{2 1}Maharaja Institute of Technology (M.I.T), Khurda, Bhubaneswar-752055 (INDIA)
Abstract : In this paper, inventory replenishment policy is developed for constant deteriorating item and price-dependent demand. The rate of deterioration is taken to be time proportional. A power law form of the price dependence of demand is considered and the numerical example is taken up to illustrate the solution procedure and sensitivity analysis is also carried out.

Key words : Inventory, deterioration, price-dependent demand.

Optimization of fuzzy expert systems using neural network in decision-making in competitive situation
P.K. Parida¹ and S.K. Sahoo²
Abstract : Many decision making problems may be solved with Heuristic search algorithms. Expert systems taking decisions in competitive situation in uncertain environment/fuzzy environment may take a graph-search algorithm to tackle the situation. To improve the performance of the overall system, a set of important parameters of the decision making system is identified. Optimization methods such as Neural Network (N.N.) is used for the learning of the optimum parameters and also for an improvement of the performance.

Key words and Phrases: Fuzzy logic, Defuzzification, Neural Network (N.N.). M.S. Classification Number (2000): 68T37

A weaker version of zeeman's conjecture on space topology
Ujagar Patel and Somanath Choudhury
Abstract : Zeeman, in his paper 'Topology of Minkowski Space' made two conjectures :

(1) the topology in Minkowski Space that induces the 3-dimensional Euclidean topology on every space- like hyperplane (S-topology) has G as its group of homeomorphisms, where G is the smallest group generated by the inhomogeneous Lorentz group and dilatation (multiplication by +ve scalars);

(2) the topology on Minkowski space that induces the one-dimensional Euclidean topology on every time-like line (T-topology) also has G as its homeomorphism group.

Since it is known that G is precisely the set of < - automorphism (where < is the causality relation on Minkowski space), we have made an alternative formulation of the second conjecture as follows : every homeomorphism of the T-topology is a < - automorphism.

Here we have dealt with a weaker version of Zecman's conjecture on space topology.

Some Conharmonically Flat Manifold
Rajendra Prasad* and Satya Prakash Yadav**
Abstract : In the present paper we carry on a systematic study of conharmonically flat generalized Sasakian space form and conharmonically flat (k,µ)- manifold. We have find the eigenvalues and eigenvectors of Ricci-operator Q. Further, we have established the relations between f₁, f₂ and f₃ for three dimensional conharmonically flat generalized Sasakian space form and proved that curvature tensor of three dimensional conharmonically flat generalized Sasakian space form is zero. We have find the condition that a (k,µ)- manifold becomes an h-Einstein manifold and Einstein manifold. It is also proved that only three dimensional (k,µ)- manifold may be Einstein manifold iff k = 0.

Mathematics Subject Classification: 53D10, 54D10, 45C05
Key words and phrases: Kenmotsu manifold,Contact manifold, Eigenvalue, Eigenvector.

On Unifrom T(C,I) Summability of Legendre Series
V.N. Tripathi and Sonia pal
Abstract : The present paper deals with a thereom on uniform T(C, l) Summability of Legendre series under very general condition. It generalizes a very recently known result due to Tripati and Yadav³ on uniform (Np,q) (C,l) Summability of Legendre series under similar condition. It may be noted that the (Np,q) Summability is a particular T-Summability method.

On generalised m-entropy and its directed divergence
K. Awasthi* and S.K. Varma**
Abstract : In the present paper we have generalised M entropy defined by Kapur and Sharma⁵ and studied some of its properties.

Key words : M- Entropy /Directed Divergence/ Shannon Measure/ Havrda CharvatMeasure/Generating function/Measure of Information Improvement/Measure of Generalised Information Improvement /Measure of Inaccuracy/ Normalised Measure of Entropy.

Optimal flow time in open shop scheduling including weights and transportation time
Indira Vij*, S.K. Mittal** and T.P. Singh***
Abstract : The paper deals with n´2 open shop scheduling problem in which the processing time of jobs on machines, transportation time of each job from one machine to another and weightage to jobs is considered. The objective of the study is to find an optimal sequence of jobs which minimizes total weighted mean production time. The algorithm is derived to find out the optimal sequence and is demonstrated with numerical illustration.

Key words: Open shop, make span, weighted mean production time etc.

Unsteady flow of Rivlin-Ericksen visco-elastic fluid through porous medium in a confocal elliptical duct
Ravindra Kumar¹, K.K. Singh² and A.K. Sharma³
Abstract : The purpose of the present paper is to study the unsteady flow of visco-elastic Rivlin-Ericksen type fluid through porous medium in a long uniform confocal elliptical duct under the influence of an arbitrary time dependent pressure gradient. Mathieu functions have been used to obtain the exact solution of flow problem. Some particular cases for different pressure gradients have also been discussed in detail. We have used the notations of Mc Lachlan⁷ as regard to Mathieu functions.

An Algorithm to determine the chromatic number of a graph
Shantharaju C. V.¹ and Veena Mathad²
Abstract : A coloring of a graph is an assignment of colors to its vertices so that no two adjacent vertices receive the same color. An n-coloring of a graph G uses n colors. The chromatic number c(G) of a graph G is the minimum n for which G has an n-coloring. In this paper, we give an algorithm to determine the chromatic number of a graph.

Key words: Chromatic number, color class.
2000 AMS subject Classification 05C15

Triple series equations involving the product of 'r' generalized Bateman-k functions
PRADEEP KUMAR MATHUR* and MADHVI GUPTA**
Abstract : In the present paper the solution for the series equations is obtained by using the multiplying factor technique.

Circular chromatic number of lexicographic products
R. Ganapathy Raman* and R. Sattanathan**
Abstract : Of interest in this theory is the question of determining the circular chromatic number of product graphs. There are four kinds of graph products: (i) Cartesian Product (G � H), (ii) Categorical Product (G � H), (iii) Lexicographic Product (G . H) and (iv) Strong product (G� H). We discuss some theorems on circular chromatic number of lexicographic products.

Estimation of the reliability characteristics of a plate mill system of an integrated steel plant
Satyendra Prasad Singh*, Pragnyaban Mishra** and S. K. Singh***
Abstract : This paper discusses the estimation of reliability characteristics of a plate mill system of Bhilai Steel Plant. The whole system consists of one reheating furnace two slab pushers, one horizontal stand and one finishing stands. Reheating furnace is used to reheat the slabs in order to convert them into specific sizes of plates with the help of slab pushers, horizontal stand and finishing stand. Slab pusher is used to push the red hot slabs towards the horizontal stand. Horizontal stand is used to cut the end of the red hot slabs and is used in expanding the length of slabs horizontally according to required length. Finishing stand gives final shape to red hot slabs. All the failure time distribution along with preparation time of reheating furnace and repair time of slab pusher where as all the other repair time distribution are taken as arbitrarily distributed. Using regenerative point technique, various reliability characteristics of interest to the system designers as well as for operation managers have been evaluated. Finally, some graphs are also plotted in order to highlight the important results.

Key words : Regenerative point technique, Transition Probability, Mean Sojourn Time, MTSF, Availability and Busy Period Analysis.

A Comparative Study of Traditional Search Engines with The Metasearch Engines
*Satinder Bal and **Rajender Nath
Abstract : The exponential growth of information source on the web and in turn continuing technological progress of searching the information by using tools like Search Engines gives rise to many problems for the user to know which tool is best for their query and which tool is not. To overcome this problem, Metasearch Engines are developed, which dispatch the user's query to multiple search engines automatically and refine the results obtained from the underlying search engines to give the best out of the best to the user. This paper gives the overview of the architecture of a typical metasearch engine and identifies various technical and non-technical parameters. On the basis of these parameters, a comparative study between traditional search engines and metasearch engines has been carried out and reported.

Key words : Database, Web Crawler, Metasearch Engine, Search Engine, Query.

ICT: An Effective Retrofit Tool For Cyber Terrorism
S.N Panda* and Narinder Singh Rana**
Abstract : The tremendous growth and utilization of Information and Communication Technology's (ICT) influence on our society has lead to increased risk of its exploitation by the criminals and terrorist groups. In this age of information superhighways, the traditional paradigm of terrorism is evolving beyond traditional physical violence, hijack, and bombing. Today, a terrorist does not need to travel thousands of miles to attack a target, rather it uses the networked critical ICT infrastructure to target the nation's sensitive installations. This paper explores emerging security threats, tremendously increasing rate of vulnerabilities and multiple types of incidents and its impact.

Key words : Cyber terrorism, ICT, Vulnerabilities.

Fuzzy Decision system for Student Evaluation
Suvobrata Sarkar
Abstract : The main aim of this paper is to generalize fuzzy decision system for the Assessment of Students in an Engineering colleges or Universities. Roughly speaking, the student's category can be classified into three major classes: so- called Good, Average and Poor. The Teachers who are involved in the course & regularly delivering the lecture Classes, interacting with the students are the best persons to judge or assess a student. The various factors that are taken into consideration for the Student's Assessment are Appearance, Communication skills, IQ, Class Attendance, Punctuality, Alertness, Class Performance and Extra-curricular Activities. Periodically, the University Director is interested in studying the performance Assessment of the Students. Generally, meetings are held where the Teachers involved in the course give their opinion linguistically to the respective Students depending upon the various factors that are taken into consideration for Student's Assessment Process. Then a decision is taken to find out the best Student in the University. A requirement fuzzy subset has been formulated. A relationship is formed between the respective students and the teacher's opinion using the fuzzy subset representation. It is proposed to construct fuzzy decision set which includes the relative merits of all Students in the University. The Index of fuzziness of various Teacher involved in the course are measured and compared. A decision system has been developed using fuzzy distance approach to select the best Student.

Image restoration using wavelet transformation
Pradeep Kumar Jaswal^*, ¹D.S. Pathania, ²H. K.Grewal and ³Sandeep Kumar Singla
Abstract : Image de-noising and restoration represent basic problems in image processing with many different applications including engineering, reconstruction of missing data during their transmission and enhancement of biomedical structures as well. This problem occurs also in filling-in blocks of missing or corrupted data. The paper presents the use of Wavelet transform in this area including its application for image decomposition and rejection of its components at first. The main part of the paper is then devoted to methods of restoration of missing image blocks by the search of similar structures of a given image in the Wavelet domain space and comparison of this approach with iterated Wavelet interpolation and predictive image modeling. Proposed methods are verified for simulated images and then applied for processing of magnetic resonance images.

Key words : Wavelet transform, image de-noising, restoration, interpolation, biomedical image processing.

A Novel Approach for Message Security Using Steganography
Madan Lal* and Jagtar Singh**
Abstract : Establishing hidden communication is an important subject of discussion that has gained increasing importance nowadays. There has been many secret communication techniques proposed in the last few years. The focus was given to steganography to build such techniques .Utilizing stego-keys to hide secret messages into images strengthen the security of these techniques. Informally, steganography refers to the practice of hiding secret messages in communications over a public channel so that an eavesdropper (who listens to all communications) cannot even tell that a secret message is being sent. In contrast to the common LSB method used for hiding information in images we have generated a better algorithm for steganography along with its implementation with better security. In this work we have illustrated the fact that next to LSB method with minimum noise of steganography gives less chance for the hacker to hack the information in the network as compared to LSB method.

Key words: hidden communication, Stego-keys, Image steganography, and LSB steganography.

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