Abstract of Volume 21(3M), 2009

A Density Dependent Demographic Prey-Predator Model with Harvesting and Disease Related Deaths
Bijendra Singh, Rachana Khandelwal and Nitu Trivedi
Abstract : A prey-predator SIS model with logistic growth has been considered with parasitic infection in prey and more vulnerability of infected prey to predation. The combined harvesting of both species along with disease related death of prey has also been taken into account. It has been observed that the parameter concerned with disease related death affects the endemic state. Threshold numbers along with stability are also discussed. The contributions of Hethcote et. al.⁷ and Trivedi et. al.¹² follows as corollary.

Key words: Prey-Predator model, Epidemiological model, Stability.

On Sums of Conjugate k-EP Matrices
A.R. Meenakshi*, S. Krishnamoorthy** and B. Vasudevan***
Abstract : Necessary and sufficient conditions for the sums of Conjugate k-EP (Con-k-EP) matrices to be Con-k-EP are discussed. As an application it is shown that sum and parallel sum of parallel summable Con-k-EP matrices are Con-k-EP.

AMS Classification : 15A57, 15A15, 15A09

Key words : Conjugate k-EP matrix, parallel summable matrices.

Holomorphic sectional curvature on an integrated contact metric structure manifold
Shalini Singh
Abstract : In the present paper, after defining an integrated contact metric structure manifold I have studied holomorphic sectional curvature and some properties which are of great geometrical importance.

Key words : C^¥-manifold ,integrated contact structure manifold, integrated contact metric structure manifold, Riemannian metric, vector field, curvature tensor, holomorphic sectional curvature.

Modified sis prey - predator model with mass incidence
Bijendra Singh*, Suman Jain** and Atul Johri***
Abstract : Prey-Predator SIS model with Mass incidence and modified deaths has been analyzed. New threshold R₁ is identified. The stability criteria with different combinations are studied.

Key words : Prey, Predator, Infectious, Thresholds, Stability.

A compact fuzzy topological space
Md. Arshaduzzaman
Abstract : In this paper, a new notion of compactness has been developed in fuzzy topology generated by fuzzy metrics with a continuity based approach basis. The results provide an idea that fuzzy compactness is a good extension of ordinary compactness.

Key words : L-fuzzy real line. Fuzzy metric. Fuzzy topology generated fuzzy metric. Fuzzy continuity. Fuzzy compactness.

Damped Vibrations of Parabolic Tapered Exponentially Non-Homogeneous Isotropic Elastic Infinite Plate Resting On Elastic Foundation
Manu Gupta¹ and Babita Rani²
Abstract : The damped vibrations of non-homogeneous isotropic elastic infinite plate resting on elastic foundation are studied. The thickness variation is considered parabolically and non-homogeneity variation is taken as exponentially. In this paper a generalized eigenvalue problem is obtained by applying Frobenious method and suitable boundary conditions from which the values of a frequency parameter, deflection function and the corresponding mode shapes of vibration, for specific values of other parameters, are obtained.

Key words : Damped Vibrations; Non-Homogeneity; Isotropic; Elastic Foundation.

A remark of submanifolds in conformal and pseudoconformal spaces
K.C. Petwal and Vineeta Negi
Abstract : S. Sasaki¹ has studied the conformal connections on submanifolds and devoted the theory of conformal structure. In the present paper we consider the conformal structure of real manifold, in particular we introduce polyspherical coordinate and develop the method of moving frames and then study the submanifolds in conformal and pseudoconformal spaces. For this we construct an invariant normalization and find out its geometric characterization. We also define the fundamental geometric object, central hyperspheres and m-sphere of submanifolds and then investigate some theorems regarding them.

Index terms: Conformal, Pseudoconformal, Hypersphere, Holonomic, Polyspherical

MSC 2000: 53B15; 53A30; 53A55

Integral formulas and inequalities in Kaehlerian manifolds and their applications
S.S. Pujar and S.G. Purane*
Abstract : In this paper, we consider a Kaehlerian manifold M of complex dimension n admitting a holomorphically projective vector field ^1,2,5. The purpose of the paper is to obtain the integral formulas and inequalities in a simply connected, compact Kaehlerian manifold without putting restriction on the scalar curvature of M such as the constancy of scalar curvature K on M and to generalize some of the integral formulas, inequalities and some of the propositions of K.Yano and H. Hiramatu⁷. In section 4 , we introduce GH-projective vector field and study its properties and further generalize a Theorem of S.Tanno^9,10 and a Theorem of T Nagano¹¹.

Key words and Phrases: Kaehlerian manifold, H-Projective space and contravariant analytic vector fields.

A Matrix Identity on the Secondary Schur Complement
G. BHUVANESWARI
Abstract : This article presents a matrix identity on the Secondary Schur Complement along with various applications.

Key words: Schur Complement - Secondary Schur Complement - LDU Factorization.

Fuzzy Entire Double Sequence Spaces
K. Chandrasekhara Rao*, V. Karunakaran** and K. Vairamanickam**
Abstract : Let denote the space of all fuzzy double entire sequence. Let denote the space of all fuzzy double analytic sequence. In this paper we study general properties of the spaces like completeness, linear, etc.

Key words: Sequence Spaces, Double Sequence, Entire sequence, Analytic Sequence.

2000 mathematics subject classification: 46A45

Weak** commuting mappings and common fixed point theorem in fuzzy metric space using implicit relation
Suman Jain* and Sangita Aske**
Abstract : In this paper we present a fixed point theorem in Fuzzy metric space using weak** commuting property for four self mappings satisfying an implicit relation.

Key words : Fuzzy metric space, weak** commutative mapping, common fixed point, implicit relation.

Fuzzy shortest path problem based on triangular density function
L. Sujatha¹ and R. Sattanathan²
Abstract : The Shortest Path Problem is a classical and important network optimization problem which plays a major role in many applications. It has been proposed to find the Fuzzy Shortest Path using Similarity Degree where Triangular Density Function is used.

Key words: Fuzzy Shortest Path, Network, Triangular Fuzzy Number, Triangular Density Function, Similarity Degree.

Unsteady MHD flow of a dusty fluid through a circular pipe
K. Elangovan and Nirmala P. Ratchagar
Abstract : In this paper, the unsteady flow of a dusty viscous incom-pressible electrically conducting fluid through a circular pipe is investigated. A constant pressure gradient in the axial direction and a uniform magnetic field directly perpendicular to the flow direction is applied. The effect of dust is described by two parameters f and t, the mass concentration parameter 'f' is a measure of the concentration of dust particles and interaction parameter is a measure of the rate at which the velocity of dust particles adjusts to changes in the fluid velocity and depends upon the size of the individual particles possible limiting cases for t<<1 and t >>1 which corresponds to the case of fine dust and coarse dust respectively. The flow analysis is carried out using differential geometry techniques and analytical solutions of the problem are obtained, with the help of Laplace transform technique. The effect of the magnetic field parameter M, the size of dust particles and the time on velocity, volumetric flow rates and skin friction are determined and discussed with the help of graphs.

Key word : Pipe, Hydromagnetic flow, dusty fluid.

Pulsatile flow of blood through a stenosid tube in two layer model with effect of volume fraction of micro-organisms
V.P. RATHOD and SRINIVAS K.
Abstract : The flow of a Couple stress fluids, representing blood through an artery with mild stenosis is investigated under various approximations. The Blood flow consisting of a core region of suspension of erythrocytes assumed to be a couple stress fluid (Non-Newtonian) & a peripheral layer of plasma (Newtonian fluid) with dusty particles as micro-organisms. Analytical expressions for both blood and microorganisms have been formulated for blood taking the volume fraction of the microorganisms into account. A detailed study will be made as regards the couple stress parameter, pulsatile Reynolds number, volume fraction of microorganisms and stenosis with other parameters in this investigation. The velocity distribution, the relative apparent viscosity and flux for blood and micro-organisms are calculated as function of couple-stress parameter, pulsatile Reynold's number at different phase angles. The velocity is maximum in the core region. The expressions for velocity of blood and microorganisms, flow rate, apparent viscosity, phase-lag between flow rate and pressure gradient will be derived.

Keywords: Stenosis, Couple stress fluid.

On k-Unitary Matrices
R. KAVITHA
Abstract : The Concept of k-unitary matrices introduced. Characterization of k-unitary matrices are discussed.

Key words : unitary, k-unitary and Moore-Penrose inverse.

AMS Classifications: 15A09, 15A57

An Inventory Model with Linear Demand Rate, Finite Rate of Production with Shortage and Complete Backlogging
C. K. TRIPATHY*, U. MISHRA** and C.K. SAHOO***
Abstract : This paper deals with in developing inventory model with linear demand rate allowing shortages in the inventory. These shortages are considered to be completely backlogged. We have assumed that the production rate is finite and proportional to the demand rate. The analytical solution of the model has been done to obtain the optimal solution of the problem. Suitable numerical example has been discussed have to understand the problem. This model is suitable in case of steady increase or decrease in the demand in the market for some product.

Key words: Inventory; Economic order quantity; demand; Shortage

On k - Normal matrices
C. INDUMATHI
Abstract : The concept of k-normal matrices is introduced. Charac-terizations of k-normal matrices are discussed.

AMS Classifications : 15A09, 15A57

Key words : Normal, k-normal and Moore penrose inverse.

A common fixed point theorem for six weakly compatible mappings satisfying an implicit relation in fuzzy metric space
M.S. Chauhan*, V.H. Badshah** and Neetu Vishwakarma**
Abstract : The paper is based on a common fixed point theorem for six self maps on a fuzzy metric space using semi compatibilty, weak compatibility and an implicit relation. In this paper we further generalized the result of Patriciu⁶.

Key words: Fuzzy metric space, compatible mappings, Semi compatible mappings, weak compatible mappings, common fixed point, implicit relation.

Mathematics Subject Classification : Primary 47H10, Secondary 54H25.

Fixed Point theorem using semi-Compatibility in Menger probabilistic metric space
Ramdeen Ahirwar**¹, Arihant Jain*² and R. K. Gangele**³
Abstract : The object of this paper is to establish fixed point theorem for six self maps using the concept of semi-compatible self maps in a Menger PM-space. Our result generalizes the result of Singh and Sharma¹⁰.

Key words : Common fixed points, Compatible maps, Semi-compatible maps, t-norm.

AMS Subject Classification (2000) : Primary 47H10, Secondary 54H25.

Estimation of cobb-Douglas frontier production function using varying parameter models
K. Sreenivasulu¹ and C.S. Reddy²
Abstract : In this paper we propose Varying Parameter Models to estimate the measure of Technical Efficiency of Cobb-Douglas Frontier Production Function, in which the parameters are stochastic and estimated using Generalized Lease Squares method.

Key words: Technical Efficiency, Decision Making Unit, Cobb-Douglas Frontier production function, Varying Parameters, Stochastic Parameters, GLS method.

Tensor of the type (0, 4) in a manifold equipped with an integrated contact metric structure
SHALINI SINGH
Abstract : In the present paper, after defining an integrated contact metric structure manifold I have defined . Several useful theorems on these manifold have also been derived.

Key words : -manifold, integrated contact structure, integrated contact metric structure, Riemannian metric, Riemannian connexion, bilinear function, torsion tensor etc.

AMS subject classification Number: 53

Some Studies on Multi-Objective Fuzzy Game Theory
S.K. Sahoo^† and P.K. Parida^‡
Abstract : In this paper, theory of games dealing with decision making process in competitive situation considering the ambiguity of decisions with uncertainty and imprecision of information has been studied. Fuzzy game theory has been established in near past. Studies will be made on different results on multi-objective fuzzy game.

Key words and Phrases: Zero-sum game; mixed strategy; expected payoff; fuzzy goal; fuzzy decision; fuzzy mixed strategy; fuzzy two-person zero-sum game; single-objective game; multi-objective game; minimax theorem; maximin theorem; linear programming problem (L.P.P).

MHD oscillatory flow of a Micropolar fluid through a porous medium over a vertical porous plate
B. REDDAPPA^a, M. V. SUBBA REDDY^b and K. RAMAKRISHANA PRASAD^a
Abstract : In this paper, we studied the MHD oscillatory flow of a micropolar fluid through a porous medium over a vertical porous plate. The expressions for the velocity field, angular velocity and temperature filed are obtained analytically. The effects of time t, Hartmann number M, Darcy number Da, Grashof number Gr, viscosity ratio b and micro-gyration vector on the velocity field, angular velocity and temperature filed studied in detail.

Key words : MHD, micropolar fluid, porous medium, Grashof number

The strong cobondage number of a graph
Karam Ebadi* and L. Pushpa Latha**
Abstract : For a graph G = (V,E), a set D Í V is a strong dominating set if every vertex v in V - D has a neighbour u in D such that the degree of u is not smaller than the degree of v. The minimum cardinality of a strong dominating set of G is the strong domination number, g_s(G). The strong bondage number b_s(G) of a nonempty graph G is the minimum cardinality among all sets of edges E' Í E for which g_s(G - E') > g_s(G). In this paper we study the strong cobondage number b_sc(G) of a nonempty graph G to be the minimum cardinality among the sets of edges E' Í E () for which

g_s(G+E ₀) < g_s(G). Sharp bounds are obtained for b_sc(G). And the exact values are determined for several classes of graphs.

Key words: Strong domination, bondage number, strong bondage number,strong cobondage number.

An Algorithm of BFGS^AMI Method for Unconstrained Optimization
Mustafa Mamat¹, Mohd Asrul Hery Bin Ibrahim² and Ismail Mohd³
Abstract : In quasi-Newton, there are several of updated approximation formulas and one of them is Broyden-Fletcher-Goldfard-Shanno (BFGS) method. The convergence of BFGS method are depends on the search direction, and step size, . To determine step size, many recent author uses only single type of step size and proved its super linear convergence but in this paper we propose a modification and combination on two step sizes in BFGS algorithm to solve unconstrained optimization problems. The numerical results based on the number of iteration and function evaluation will be provide at the end of this paper

Key words : exact line search, estimation for line search, step size, superlinearly convergence, BFGS^AMI.

Application of new fuzzy preference relation in car failure diagnosis system
Manoj Sharma¹and Rajesh Shrivastava²
Abstract : Decision making preferences to certain criteria usually focus on positive degrees without considering the negative degrees. However, in real life we came across more frequently with problems related to our Car, valuation of faults becomes more comprehensive if negative degrees are considered concurrently. Preference is expected to be more effective when considering both positive and negative degrees of preference to evaluate the best decision. Therefore, the aim of this paper is to propose the conflicting bi-fuzzy preference relations in decision making by utilization of a modified novel score function. The conflicting bi fuzzy preference relation is obtained by intuitionistic fuzzy preference relations. Releasing the intuitionistic condition by taking into account positive and negative degrees simultaneously and utilizing the novel score function are the main modifications to establish the proposed preference model. The proposed model is tested with a numerical example and proved to be simple and practical.

Key words: Fuzzy preference relations, score function, conflicting bi fuzzy, decision making.

On generalized Nörlund summability of infinite series
Satish Chandra and Vibhuti Goel
Abstract : In this paper we have proved a theorem on generalized Nörlund summability of infinite series, which generalizes various known results. However, our theorem is as follows.

Theorem : Let {p_n} be a positive non-increasing sequence, {e_n} is a positive non-decreasing sequence and {l_n} is a non-negative,

non-increasing such that

as n®¥

n Dl_n = O(l_n )

Sp_n l_n < ¥

and

then the series Sa_ne_nl_n is summable by G(N, p, l).

Key words and phrases: Generalized Nörlund summability, Infinite series.

Multiobjective fractional minimax problem involving locally Lipschitz functions V-r-invexity
Madhavi K.¹, Vara Lakshmi G² and Reddy P.R.S.³
Abstract : Sufficient optimality conditions and duality results for a class of minimax nonlinear parametric programming problems are obtained under V-r - Invexity.

Key words : V-r - Invexity, Multiobjective fractional programming problem, Minimax Parametric Problem and Duality.

n^th Power of GM Matrices
S. Krishnamoorthy*, K. Gunasekaran** and G. Manikandan***
Abstract : In this paper we find the n^th power of GM Matrix on a set of distinct positive integers in terms of the matrix and its power of trace.

Key words: GM Matrix-Eigen value- trace- positive integers.

Ams Classification: 15A09, 15A45, 15A49

Almost Hyperbolic Hermite manifolds
*SHANKAR LAL and ** MANOJ SEMALTY
Abstract : The aim of the present paper, we have studied almost hyperbolic Hermite manifolds and also obtain a few interesting results. Almost contact hyperbolic (f,g,h,x) structures have been defined by M.D. Upadhyay and K.K. Dube⁷ and others. Vanzara⁸ studied almost r-contact structures. The paper is organized as fallows. Section1, contains a brief introduction to hyperbolic Hermite and Nijenhuis tensor, while in section 2 some necessary details about some results of manifolds are presented. In section 3, we define affine connections of D in mⁿ and a vector valued bilinear function of torsion tensor.

Key words : Riemannian metric, hyperbolic Hermite manifold, Nijenhuis tensor, torsion tensor, affine connection.

Tchebychef Polynomials and Lucas Numbers
Amitava Saraswati¹, Bijendra Singh² and C.L. Parihar³
Abstract : A relationship exists between the algebraic sum of the coefficients in the nth rising diagonals of the left justified Tchebychef polynomials and Lucas numbers.

Key words : Fibonacci polynomials / numbers, Tchebychef polynomials, Lucas polynomials/numbers,

SUBJECT CLASSIFICATION MSC(2000)11B39

A note on s-normal matrices
S. Krishnamoorthy* and R.Vijayakumar**
Abstract : In this short note, the concept of s-singular values of a given matrix is introduced. Also, we present two simple results on s-normal matrices.

Key words: Conjugate secondary transpose, s-normal matrix, eigen value.

Approximations of Fuzzy Systems
V. Suresh Kumar¹, P. Thangavelu² and K. Iyakutti³
Abstract : A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems with product inference, centroid defuzzification and Gaussian membership functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions.

Key words: Fuzzy systems, Stone Weierstrass Theorem, Universal Approximators.

Analysis of Intelligent Information Retrieval Techniques in a Digital Library Services
¹S. Sasidhar Babu, ²M. Vinaya Babu and ³N.V. Kalyankar
Abstract : This paper reviews the different information retrieval models that can be used to represent information from digital library. It also describes document retrieval from the digital library, followed by experimental analysis of various traditional IR models like Boolean model, Vector model, Probabilistic model on a sample corpus. We present the Private Digital Library (PDL) project that represents a service of the Corporate Digital Library (CDL) prototype. The main ideas underlying this project are the following. When a user is looking for documents that he already retrieved in the past, he has to repeat the search procedure and solve the same problems he encountered in the past access. On the contrary, consider the possibility for the user to store documents in a private library. In this case, he will have the chance to retrieve the documents of interest more easily and quickly. It may also be the case that the user has not a clear understanding of what he is looking for. Moreover, he might not know exactly the library content and organization. This paper also discusses way of representing index terms in form of indices so that they can be searched later. Thus, he needs for assistance to suggest him what to look for and how to query the system. A method to store and catalogue documents according to personal criteria might help to overcome these problems.

Key words : Cataloguer, Query Suggester, Information Retrieval.

Comparison of similarity measure for web document clustering
Gunjan Ansari
Abstract : With the rapid growth of the World Wide Web (www), it becomes a critical issue to design and organize the vast amounts of on-line documents on the web according to their topic. Even for the search engines it is very important to group similar documents in order to improve their performance when a query is submitted to the system. Clustering is useful for taxonomy design and similarity search of documents on such a domain.

Similarity or distance measures play important role in the performance of clustering algorithms. This paper compares three term based similarity measures for web document clustering. The similarity measures used are Euclidean distance, cosine measure and jaccard measure. The clustering algorithm used is the so-called k-means clustering to cluster web documents. These three different similarity measures are used to find the similarity between documents. The clusters are formed based on their similarity measure calculation using k-means clustering algorithm. Overall similarity measure is used to evaluate the clusters formed using different similarity measure. Tested with web data, we observe that the Euclidean measure outperforms the other similarity measures in clustering accuracy.

An Integrated DNA Support System for Crime Investigations: DNA Tracers
NOOR MAIZURA MOHAMMAD NOOR and RAZIF BIN
Abstract : DNA TRACERS is developed to assist in solving violent crime using forensics method. It is an experimental approach to aid the process of investigating crime by treating cases and subjects of the case as the nodes that might be linked to each other using DNA matching. The relation between the subjects of the cases and cases itself is defined by their DNA frequency and likelihood ratio. DNA TRACERS analyze each cases and subjects using non-linear method to further improve investigation by finding any possible relation between distinct cases, which is not implemented as an automated process in current practice. These relations are depicted in the form of graphical diagram which is easy to interpret by end-user. Statistical graph and score table for convicted offenders is calculated based on several criteria. It is provided in order to support the process of decision making. Mechanism procedure in DNA TRACERS made it possible to separate between forensics unit and investigative unit as different entities. Both entities are working together to solve cases with controlled access to their authorized database. DNA TRACERS support structured data format for casework, case subject and case analysis record. Built in security and strict data transfer control is implemented to ensure the integrity of the system and subsystems. Generated report automation with standardize format will become easier for different investigative unit do collaboration to solve crime investigations.

Key words : case chain, computer-aided investigation, DNA analysis, DNA TRACERS, forensic, investigation.

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