Abstract of Volume 22(1M), 2010

On Adjacency Matrix and Connectedness of Three Optimal (4x4)/4 Semi-Latin Square Designs
P. E Chigbu¹ and A. Ekpo²
Abstract : We present new results regarding the adjacency matrices of three optimal (4 x 4)/4 semi-Latin squares. The most connected design for experimentation were discriminated among the three squares based on the number of "0's" and "1's" in the adjacency matrix of each of the designs.
Key words : Semi-Latin square, Variety-Concurrence graph, Automorphism group, Adjacency matrix, connected design.

On |A, p_n, d|_k Summability Factors of Fourier Hermite Series
V.N. Tripathi and R.K. Shukla
Abstract : Bor² has proved a theorem on summability factors of an infinite series. Özarslan and Ögdük⁴ have generalized the theorem due to Bor² by discussing |A, p_n|_k summability factors of the infinite series. Here, in the present paper, we have studied |A,p_n, d|_k summability factors of Fourier Hermite series which is an extension of the above results into another direction.
Key word: summability, summability factor, Fourier Hermite series, MS classification: 40F

On An Almost Unified Para-Norden Contact Metric Manifold
Shashi Prakash and S.D.Singh
Abstract :In this paper, we have considered an almost unified para-norden contact metric manifold. The Eigen values of the tensor of the type (1, 1) occurring in this manifold have been obtained. Also other theorems have been derived which are of great geometrical importance.
Key words: -manifold, almost Para contact metric manifold, almost norden contact metric manifold, almost unified para-norden contact metric manifold.
Mathematics Subject Classification No: 53

Some Boundary Value Problems of Mathematical Physics
V. Dharmaiah¹ and B. Surender Reddy²
Abstract :In this paper, the boundary value problems of Mathematical physics are considered and associated with operator polynomials to study the spectral results of boundary value problems in a Hilbert space setting.
Key words : Laminar flow, density of the fluid, specific heat, thermal conductivity, coefficient of viscosity, Lateral Buckling of a Beam, Transmission Line.
AMS Subject Classification No : 47

Steady MHD convergent channel flow of a non-Newtonian electrically conducting fluid
SHAMPA CHOUDHURY¹ and DEVAJYOTI BISWAS²
Abstract : The two-dimensional steady boundary layer flow through a convergent channel of a non-Newtonian electrically conducting fluid in presence of a transverse magnetic field has been studied. Similarity solutions are obtained by considering a special form of magnetic field. Expressions for velocity and approximate skin friction at the wall have been obtained and numerically worked out for different values of the flow parameters involved in the solution. The non-Newtonian effects on the velocity and the approximate skin friction have been shown graphically with the combination of other flow parameters.
Key words: Non-Newtonian, MHD, Boundary layer, Similarity solution, Skin-friction.
2000 Mathematics Subject Classification: 76A05, 76A10.

An architecture of a pentium microprocessor simulator
Salami, Hamza Onoruoiza¹ and Souley Boukari²
Abstract : In this paper, the main limitations of existing microprocessor simulators were identified. The limitations include lack of support for 32 - bit registers and instructions. A proposed model for the Pentium Simulator was developed using Unified Modeling Language diagrams.
Key words: register, assembly language, Pentium.

Renewal process with intuitionistic fuzzy random interarrival times
J. Earnest Lazarus Piriyakumar and J. Daniel
Abstract : In this paper, we discuss a renewal process using intuitionistic fuzzy random inter arrival times. Realistically the inter arrival times are perceived as non negative intuitionistic fuzzy random variables. With this new theoretical setting the rate of the intuitionistic fuzzy random renewal process is discussed. We have established elementary renewal theorem, and Blackwell's theorem for intuitionistic fuzzy random variables.

Key words: Intuitionistic fuzzy random variables, Inter arrival times, renewal process.

Axisymmetric Boussinesq problem for a heated punch of arbitrary profile in an elastic half space
P.K. Mathur and Madhvi Gupta
Abstract : A solution of axisymmetric Boussinesq-type problem is derived for transient thermal stresses in a half-space under heating by using the Laplace and Hankel transforms. An analytical method is developed to predict the temperature field that satisfies the prescribed mechanical conditions. Several simple shapes of punches of arbitrary profile are considered and an expression for the total load is derived to achieve penetration. The numerical results for the temperature and the total load on the punch are shown graphically.
Key words : 44-XX Integral Transform, Operational Calculus (for fractional derivatives & integrals), 45-XX Integral Equations, 47-XX Operator theory, 44A₁₀ Laplace Transform, 45B₀₅ Fredholm Integral Equation, 45F₁₀ Dual, Triple etc. Integral & Series Equations, 74B₀₅ Classical Linear Elasticity.

Power of - Charts Under Measurement Error
J. R. Singh¹ and R. Sankle²
Abstract : The expression for the power of the - chart are derived under measurement error. The power of a control chart under measurement error is examined for the case where both the process average and true variance can change. True and error measurements are additive in nature.
Key words : Measurement error, Power Function , Testing of Hypothesis, - chart

A pentium simulator
Souley Boukari¹ and Salami, Hamza Onoruoiza²
Abstract : In this paper, a simulator for the Pentium microprocessor (PENTISIM) was developed. The PENTISIM extended some of the features of existing microprocessor simulators such as number of registers and instructions implemented. This tool is strongly recommended for students and researchers learning to know more about microprocessors and assembly language programming.
Key words: register, assembly language.

Domination in bipartite graphs
V. Swaminathan¹ and Y.B. Venkatakrishnan²
Abstract : Let be a bipartite graph. A subset D of X is an X-dominating set if every is X-adjacent to at least one vertex . The cardinality of a minimum X-dominating set is called the X-domination number and is denoted by . A minimum cardinality subset which dominates all vertices in Y, such a set is called Y-dominating set. The Y-domination number is denoted by We characterize graphs for which , and also prove .
Key words: Bipartite graphs, X-dominating sets, Y-dominating sets, Hyper Y-dominating sets.
AMS Classification : 05C69.

Hall effects on unsteady hydro magnetic flow of an incompressible viscous fluid in a rotating parallel plate channel with porous lining
M. Veera Krishna¹ , S.V. Suneetha¹ and R. Siva Prasad²
Abstract : In this paper we make an initial value investigation of the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the lower plate. The flow in the clean fluid region is governed by Navier-Stoke's equations while in the porous bed the equations are based on Brinkman's model. The exact solutions of the velocity in the clean fluid and the porous medium consist of steady state and transient state. The time required for the transient state to decay is evaluated in detail and ultimate quasi-steady state solution has been derived analytically, its behaviour is computationally discussed with reference to the various governing parameters. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed.
Key words : Hall effects, unsteady flows, parallel plate channels, incompressible viscous fluids, Brinkman's model.

Analysis of a Nonlinear Model to Study the Removal of Gaseous Pollutants by Precipitation
Shyam Sundar and Atul Chaturvedi
Abstract : In this paper, a nonlinear mathematical model is proposed and analyzed to study the removal of gaseous pollutants from the atmosphere of a city by precipitation. In the atmosphere, during precipitation, the removal of gaseous pollutants takes due to absorption/impaction process. The proposed model is analyzed by stability theory of differential equations. It is shown that the concentration of pollutants decrease due to rain and its equilibrium level depends upon the rate of formation of raindrops, emission rate of pollutants, the rate of falling absorbed phase on the ground, etc. If the rate of rainfall is very high, all the pollutants may be removed completely from the atmosphere.
Key words: Nonlinear model, precipitation, stability, gaseous pollutants, phases.

Some applications of graceful labelling
R. Vikrama Prasad¹, and R. Sattanathan²
Abstract : A simple graph G is a graceful graph if there exists a graceful labeling of the vertices of G. A graph G with e edges has a graceful labeling if there exists an injective function l : V (G) ® {0, 1, …, e} such that |l (x) - l (y)| is distinct and nonzero for all xy Î E (G). If we cannot gracefully label the vertices of G, then G is a non-graceful graph. Graceful labeling is one of the best known labeling methods of graphs. In this work, We will try to give some of the Applications of graceful labeling in balanced graphs.
Key words: graceful labeling, graceful graph, balanced graph.
2000 Mathematics Subject Classification:

L(2,1) labeling of join of paths and cycles
Jaya Ambigavathi Ragavan¹ and R.Sattanathan²
Abstract : An L(2,1)-labeling of a graph G is an assignment of labels from {0,1,…,n} to the vertices of G such that vertices at distance two get different labels and adjacent vertices get labels that are at least two apart. The minimum span (difference between largest and smallest labels) taken over all L(2,1)-labeling of G is the l-number of G. The aim of this paper is to determine the l-number of the join of two graphs, C_m and P_n.
Key words: L(2,1)-labeling, l-number, join of two graphs.

Double Sampling Plan Under Inspection Error
J.R. Singh¹ and N. Singh²
Abstract :The effects of inspection errors on acceptance sampling when one is inspecting for the number of nonconformities per item is considered , two types of inspections are defined. Formulas are derived for the OC and ASN for situations when these inspection error are present for double sampling plan . An example illustrates the effects of these inspection errors on both the OC and ASN curves.
Key words: Inspection error, Double sampling plan, Poisson process, OC and ASN function.

Hall current effects on unsteady MHD flow of rotating maxwell fluid through a porous medium
M. Veera Krishna¹ , S.V. Suneetha¹ and R. Siva Prasad²
Abstract : In this paper we discuss analytical solution for the unsteady magneto hydro dynamic flow is constructed in a rotating non-Newtonian fluid through a porous medium taking hall current into account. The constitutive equations for a Maxwell fluid have been taken into consideration. The hydro magnetic flow in the uniformly rotating fluid is generated by a suddenly moved infinite plate in its own plane. The analytical solution of the governing flow problem is obtained by means of Fourier sine transform. It is shown that the obtained solution satisfies both associate partial differential equation and the initial and boundary conditions. The solution for a Navier-Stokes fluid is recovered if . The steady state solution is also obtained for.
Key words: Hall effects, unsteady flows, parallel plate channels, Maxwell fluids, porous medium.

Common fixed point theorems for weakly compatible mappings in non-Archimedean Menger pm-spaces
Sushma Chandel¹, N.K. Gautam² and Akhilesh Jain³
Abstract : In this Paper, we prove common fixed point theorems for weakly compatible mappings without using condition of continuity. We improve results of Cho,Ha and Chang²². For terminologies, notations and properties of probabilistic metric spaces^23,24,25,26.
Key words : Fuzzy metric spaces, expansion type maps, non-Archimedean Menger PM-space, Common fixed point. t-norm , weakly compatible mapping.
AMS Mathematics Subject Classification (2000): 54H25, 54A40, 47H10

Some theorems on almost product and almost decomposable manifold
U.S. Negi and Ashish Semwal
Abstract : Sinha² has studied H-projective curvature tensor in an almost decomposable manifold. Singh⁴ has studied some theorem on Kaehlerian spaces with recurrent H-curvature tensors.Further; Negi⁸ has studied some investigations in Kaehlerian spaces with recurrent H-curvature tensors. In the present paper; we have defined and studied almost product and almost decomposable manifold and several theorems have been derived.
INDEX TERMS: Kaehlerian, H-projective, Weyl, Conformal (Bochner), Concircular, Conharmonic, curvature tensors, recurrent.

Some properties of Kenmotsu manifolds
S.S. PUJAR¹ and S.S. NAIK²
Abstract : The purpose of the paper is to study some properties of W₂-Semisymmetric, Kenmotsu manifolds, Projectively flat Einstein Kenmotsu manifolds and Conharmonically flat Einstein Kenmotsu manifolds.

A Note on the Applications of Tensors in Physics, Mathematics & Medical Science
K.C. Petwal, S. Kumar and Shikha Uniyal
Abstract : The analysis of different physical systems and mathematical devices depends on the utilization of various types of algebraic quantities involved in the description of geometrical aspects of the phenomena and states which occur. Certain types of quantities are commonly identified as scalars, vectors and tensors. Among these, the tensors are quite complicated geometric structures as they involve not only magnitude and direction, but also have a dependence on orientation. The most familiar tensors in physical importance are internal stress in a solid and viscous stress in fluid. In both cases, the magnitude and direction of stress as a force per unit area depend on the orientation of the area on which it is acting.

The purpose of the present manuscript is to discuss a nice and lucid characterization of tensor and their basic features. Moreover, the manuscript is intended to serve the purpose of familiarity with recent developments in the tensor theory and its applications in various fields of sciences and Bio-sciences. We have just reviewed and combined the results on applications of tensors, which we feel useful in the recent developments. The manuscript begins with tensor primer and consists of few applications in elasticity including illustrations of stress and deformation tensors of elastic bodies, electro-dynamics with Maxwell's tensor and finally includes brief notions of diffusion tensors used in MRI and strain Green's tensors applied in the study of seismology.

Key words: Elastic; Maxwell; Strain Green; Diffusion tensor; MRI
AMS Subject Classification: 15A72; 83C22; 60J60

a - Domination in Fuzzy graphs
S.K. Ayyasamy and C. Natarajan*
Abstract : In this paper we introduce the concept of a- domination in fuzzy graphs. We determine the a- fuzzy domination number for fuzzy graphs and obtain bounds for the same. This paper also contains many counter examples especially to show that Nordhaus Gaddum type result need not be true not only for fuzzy graphs but also for crisp graphs.
Key words : Fuzzy graphs , fuzzy domination , a - domination , a - fuzzy dominating set .

AMS MSC classification : 05C69

Fixed Point Theorems on Expansion Type Maps in Intuitionistic Fuzzy Metric Spaces
R.S. Chandel¹, Rakesh Verma² , Akhilesh Jain³ and Susma Chandel⁴
Abstract : In this paper, we introduce the concepts of commutativity and give the relationship between the concepts of commutativity and compatibility in intuitionistic fuzzy metric spaces. Thereafter, we prove two common fixed point theorems for the concept of compatibility in intuitionistic fuzzy metric spaces.
Key words: Intuitionistic fuzzy metric space, Triangular norm, Triangular co-norm, Commutative mappings, Compatible mappings, fixed point.
AMS Mathematics Subject Classification (2000): 54H25, 54A40, 47H10.

Distance Graphs on Constant Weight Metric Spaces with Rosenbloom -Tsfasman Metric
W.B. Vasantha and R. Rajkumar
Abstract : Rosenbloom and Tsfasman introduced a new metric (RT metric) which turned out to be a generalization of the Hamming metric. In this paper, we study the distance graphs of constant weight subspaces of the spaces and with RT metric.
Key words : Distance graphs, Metric spaces, Rosenbloom- Tsfasman metric, constant weight, Symmetric groups.
AMS Subject Classification (2000): 05C12, 20B30

Integral formulas and inequalities in Kaehlerian manifolds and their applications-II
S.S. Pujar¹ and S.G. Purane²
Abstract : In this paper, we consider a Kaehlerian manifold M of complex dimension n>1 admitting a holomorphically projective vector field^{1,2 ,5}. The purpose of the paper is to obtain the integral formulas and inequa-lities in a simply connected, compact Kaehlerian manifold with constant scalar curvature of M and to generalize some of the propositions of H. Hiramatu¹.
Key words and Phrases: Kaehlerian manifold, H-Projective space and contravariant analytic vector fields.

On the least absolute error estimation of linear regression models with auto-correlated errors
S. Eakambaram^* and R. Elangovan
Abstract : There is considerable evidence that many econometric models make use of variables which give rise to error term distributions characterized by fat-tails or infinite variance. Usually linear models are estimated by the Ordinary Least Squares (OLS) or Maximum Likelihood Estimator, (MLE) by assuming normality. When estimating linear models, where fat-tailed and serially dependent residuals appear, it is important to find robust alternatives to these estimators. This is especially true in the case of small sample estimation. An alternative to the OLS estimator is Least Absolute Error (LAE). In this Paper Least Absolute Error Estimation of Linear Regression Models with Auto Correlated errors are discussed and observed that least squares based on absolute errors are preferable over the methods, when the errors are normally distributed.

Special semigroup set vector spaces
Ilanthenral. K.P.S.K
Abstract : In this paper for the first time we introduce the notion of special semigroup set vector spaces. This paper has two sections. First section just recalls some of the basic definitions³. Section two defines the notion of special semigroup set vector spaces and special semigroup set linear algebras and dicuss their properties.

Variational principle in Menger's spaces
MD. ARSHADUZZAMAN* and R.K.DAS**
Abstract : In this paper, a variational principle has been presented in fuzzy metric space and its applications in Menger's spaces have been discussed through a firxed point theorem.
Key words : -Level convergence, Fuzzy metric, Fixed point theorem, variational principle.

Approximation of randomized block designs to linear model
Wan Muhamad Amir W Ahmad¹, Nyi Nyi Naing², Zalila Ali³ and Mustafa Mamat⁴
Abstract : In this paperwork, we discussed the regression approach to randomized block designs which is involving qualitative predictor variables under consideration of linear regression. The idea from this research will be a useful thread for establishing a comprehensive connectivity between randomized block designs and regression.

Keywords and Phrases: Qualitative predictor variables, ANOVA and linear regression.

On the time to cross the Antigenic Diversity Threshold in hiv infection-a stochastic approach
R. Elangovan,¹ R. Jaisankar² and R. Sathiyamoorthy³
Abstract : It has been recognized worldwide that the dreaded HIV infection takes place mostly under homo or hetero sexual contacts. There is still significant debate about the details of how HIV eventually overwhelms the immune system. One possibility is suggested by the antigenic diversity threshold hypothesis⁴. This hypothesis suggests that HIV's rapid mutation rate allows the virus to churn out a constant stream of escape mutants. As more and more escape mutant strains appear, the immune system has to keep increasing the number of strain-specific antibody classes at the same time that its being systematically attacked by the virus. Eventually the virus builds up enough diversity. So that the immune system may find it harder and harder to mount responses against these newly emerging virus variants. Once the antigenic diversity of the virus population has increased above a threshold value, the immune system can no longer control of virus, which results in the development of AIDS. This paper aims at developing a mathematical model to find the time to get AIDS after the first infection, is made taking in to the consideration of antigenic diversity threshold.

Key words used : HIV Infection, Antigenic Diversity Threshold (ADT), Antigenic Diversity, Immune System, Acquired Immune Deficiency Syndrome.

On Weak - Symmetries of Kenmotsu Manifolds
S.S. Pujar and S.S. Naik
Abstract : The purpose of the paper is to introduce the weakly -Symmetric and weakly Ricci f-Symmetric Kenmotsu Manifolds. In this paper it is proved that there exists no weakly Ricci f-Symmetric Kenmotsu manifolds unless the sum of the one forms A, B and C is not vanishing everywhere and further it is proved that a Weakly f-Symmetric manifold is Einstein manifold.

Modified Ijarah Model
Nurfadhlina Abdul Halim ¹, Saiful Hafizah Jaaman@Sharman², Norizura Ismail³ and Rokiah@Rozita Ahmad⁴
Abstract : The purpose of this paper is to discuss on a modified ijarah (Islamic renting) modeling. The model constructed is within Shari'ah regulation for ijarah (lease) contract. The model proposed in this paper is considered pioneer in Islamic finance field as previous researchers only discuss on the philosophy of ijarah contract. None discuss on the mathematical perspective. The ijarah model we proposed a use the appreciation sharing ratio (ASR) and the existence of ASR in the model is based on musyarakah concept. It was introduced to eliminate impermissible element such as extra profit generated from financial leasing. This ensure that the model becomes legal from Islamic perspective.
Key words: modified ijarah model, appreciation sharing ratio, Shari'ah compliant.

On Quasi- Conformally Semi- Symmetric Kenmotsu Manifold
Rajendra Prasad¹, Shyam Kishor² and Satya Prakash Yadav³
Abstract : Quasi- conformal curvature tensor was introduced by Yano and Sawaki¹. Various properties of quasi- conformal curvature tensor on contact manifolds have been studied by Amur², De^3,4, Shaikh⁵ and other geometers. In the present paper, we study quasi- conformal semi symmetric Kenmotsu manifolds.
Key words : Kenmotsu Manifold, quasi- conformal curvature tensor, Ricci- curvature, Ricci-operator, scalar curvature.
MS Classification 2000: 53C25.

The divisibility of Mersenne Arithmetic mean by the Mersenne Meet matrices
S. Krishnamoorthy¹ and N. Elumalai²
Abstract : We define Mersenne Arithmetic Mean and Mersenne Meet matrices on a subset with of a lattice with respect to a complex valued function by where and where. In this paper, we assume that the elements of the matrices A and B are integers and find A/B of the matrices in terms of the usual divisibility in.
Key words: Lattice, Mersenne Arithmetic Mean Matrix, Mersenne Meet Matrix, Divisibility.
Mathematics Subject classifications: 15A57, 15A36, 11A05, 11C20, 11A25

A stochatic model for estimation of time to stop enrolement for recruitment
G. Arivazhagan, R. Elangovan and R. Sathiyamoorthi
Abstract : Certain organizations engaged in HRM activities, take up the process of registration of personnel for recruitment. They keep a reserve or inventory of manpower and supply the same to organizations which need manpower at random times points. The reserve of manpower cannot be beyond a certain limit called the threshold, because it would be expensive and also has impact on the goodwill of the recruiting organization. Hence they stop the registration for recruitment as and when the threshold is reached. An additional manpower stock is also maintained to meet the situations which arise due to the fact that some of the persons who have registered for recruitment may not turn up at the time of demand. Hence the threshold can be represented as a total of two components. Using the shock model and cumulative damage process concept the expected time to stop registration and its variance are derived in this paper. Numerical illustration is also provided.
Key words : Registration for Employment, Threshold Shock Model and Cumulative Damage Process.

A convergence problem of Hermite interpolation on unit circle
Ashwani Kr. Srivastava** and P. Mathur*
Abstract : The object of this paper is to study the regularity, explicit representation and convergence of Hermite interpolation polynomial, when function values and its first derivatives are prescribed on the non uniformly distributed points obtained by vertical projection of the zeros of Legendre polynomial together with {-1, 1} on unit circle.
Key words: Interpolation, Legendre polynomials, regularity.

Some metrical problems on symmetric groups with Rosenbloom-Tsfasman metric
W. B. VASANTHA¹ and R.RAJKUMAR²
Abstract : In this paper we study the properties of Rosenbloom-Tsfasman metric on the symmetric groups. The invariance properties of this metric on permutation groups are described. The volume of the spheres and balls in this metric space are discussed.
Key words: Rosenbloom-Tsfasman metric, symmetric groups.
2000 Mathematics Subject Classification: 20B30 (54E35).

Approximation of conjugate of a function class by (E,1)(C,1) product means of conjugate series of fourier series
Hare Krishna Nigam
Abstract : In this paper, a new theorem on degree of approximation of conjugate of a function using (E,1) (C,1) product summability means of conjugate series of Fourier series has been established.
Key words and phrases : Degree of approximation, class of function, (E,1) summability, (C,1) summability, (E,1)(C,1) product summability, Fourier series, conjugate series of Fourier series, Lebesgue integral.
2000 Mathematics Subject Classification: Primary 42B05, 42B08

On a new kind of numbers (1)
P. Rajkhowa and Ananta Kumar Bora
Abstract : In this paper we discuss some properties of "a new kind of numbers", originally defined by a.k. Agarwal¹.

A New Modification of the Homotopy Perturbation Method
¹S. Seddighi Chaharborj, ¹M. R. Abu Bakar, ¹A.H. Malik, ²M.A. Kamel Ariffin, and ^1,2I. Noor Akma
Abstract : In this paper, a new modification of the homotopy perturbation method (HPM) is presented and applied to linear ordinary differential equations and nonlinear differential equations. A comparative study between the new modified homotopy perturbation method (MHPM) and the classical homotopy perturbation method (HPM) is conducted. Several illustrative examples are given to demonstrate the effectiveness and reliability of MHPM. The numerical results obtained from the MHPM and HPM are compared with the fourth-order Runge-Kutta method (RKM).

On H-curvature tensors in Kaehlerian recurrent space
U.S. Negi and Kailash Gairola
Abstract : Singh² has studied Kaehlerian spaces with recurrent Bochner curvature; Sinha¹ has studied H-curvature tensors in Kaehler manifold. Further, Singh³ has studied some theorem on Kaehlerian spaces with recurrent H-curvature tensors. In the present paper, we have defined and studied Kaehlerian conharmonic* recurrent spaces. The necessary and sufficient condition for a Kaehlerian conharmonic* recurrent space to be Kaehlerian recurrent has been established. Several other theorems have also been derived on H-curvature tensors in Kaehlerian recurrent space.
Index terms : Kaehlerian, H-projective, Conformal (Bochner), Concircular, Conharmonic, Conharmonic*, curvature tensors, recurrent.

On -closed sets in bitopological spaces
¹MRADUL DIXIT, ²MANOJ GARG and ³P.K. TRIPATHI
Abstract : In this paper we introduce -closed sets¹⁹ in bitopological spaces. Properties of these sets are investigated and we introduce two new bitopological spaces (i, j)- spaces and (i, j)-spaces as applications. Further we introduce and study -continuous maps¹⁹ and -irresolute maps¹⁹ in bitopological spaces.
Key words : (i, j)--closed sets; (i, j)- spaces; (i, j)- -spaces; -continuity; -irresoluteness

Sufficient conditions for Dziok-Srivastava type functions of order b
S. Latha and D.S. Raju
Abstract : Let A_n denote the family of functions f (z) = z + a_n+1z^{n +1} +..., which are analytic in U, normalized by f (0) = 0 and (0) = 1. We define Dziok-Srivastava type functions of order b denoted by K(b) to be in the class of functions obeying , where 0 £ b < 1 and Hf(z) is the Dziok-Srivastava type functions of f (z), a₁ > -1. Certain sufficient conditions for functions in A_n to belong to K(b) are derived.
Key words and phrases. Dziok-Srivastava operator, Hypergeometric function.
2000 Mathematics Subject Classification. 30C45.

Common fixed point theorem in fuzzy metric spaces
Sanjay choudhari*, Kamal Wadhwa*, Lalit Sharma*
Abstract : In this paper we establish a common fixed point theorem for four maps in two fuzzy metric spaces. Our theorem is an extension of result of Fisher and Murthy¹ to fuzzy metric spaces.
Key words : Fuzzy metric spaces, sequence, common fixed point, complete metric space, continuous map.

The solution of one dimensional vertical ground water recharge through porous media by Laplace transformation technique
K. A. Patel¹ and R.S. PATEL²
Abstract : In this present paper we have obtain a classical solution of one dimensional vertical ground water recharge by using Laplace transformation technique. Here we have use average diffusivity co-efficient over the whole range of moisture content is regarded as constant and a parabolic variation of permeability is assumed. The scope of the present investigation lies in an everincreasing importance of the hydrodynamics of polyphase fluids through porous media.

Graph Coloring Based on Prim's and Kruskal's Strategies
U.S. Rajput¹ and Nirmal Srivastava²
Abstract : Since the development of graph theory, its applications are gaining a lot of importance among the researchers. Coloring of graphs is one of those applications used for creating maps and networks. Coloring involves use of different colors to print the regions of the graphs. A number of algorithms^1-3 have been developed for coloring the graphs. In this paper we are presenting two algorithms for coloring the vertices and finding the chromatic number of the planer graphs.
Key words : Vertex coloring, Chromatic number.

By adjacency matrix algorithm for the chromatic number of a graph
Shantharaju. C. V. ¹ and Veena Mathad ²
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 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 using adjacency matrix.
Key words: Chromatic number, color class.
2000 AMS subject Classification 05C15

Application of H-function in the problem related to Ornstein-Uhlenbeck diffusion process
Pratibha ghughuskar* Darshna Jain** and K. Qureshi***
Abstract : In this paper we will obtain the general solution of the backward equation occurring in the Ornstein- Uhlenbeck Diffusion process involving H-function of one variable.
Key words : H-Function, backward equation, Hermite equation, Differential equation, Ornsteie-Uhlenbeck diffusion process

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