Abstract of Volume 18(3m), 2007

Common fixed point theorem for four mappings and compatible mappings
V.H. BADSHAH* and SHWETA GAGRANI**
Abstract: In this paper we prove some common fixed point theorem in metric spaces which is extension of result given by B. Fisher, G. Jungck, M.S. Khan and M. Imdad.              
AMS Subject classification (2000) : 54H25
Key words : Common fixed point, Complete metric space, Compatible maps, Weakly commuting mappings.  

Small Set of Generators of PSL (3,p)
Chandra Chutia
Abstract: It is proved that PSL (3,p) can be generated by two elements a,b satisfying a1=bm=(ab)n=l where l=2, m=3, n=7 or l=3, m=4, n=6 or l=3, m = P, n = 2p according as p = 2 or p = 3 or p > 3.         
Keywords and phrases : generators, presentations, projective linear groups, Fuchsian groups, smooth quotients.

Herschel-Bulkley fluid model for blood flow through a stenosed artery
S.U.  SIDDIQUI  and  Km.  SAPNA
Abstract: This model is presented to study the influence of shape parameter (m) on resistance to flow (l) and apparent viscosity (mo/m) on blood flow through stenosed artery. Blood is modeled as Herschel-Bulkley fluid in a uniform circular tube with an axially non-symmetric but radially symmetric stenosis. The expressions for dimensionless resistance to flow and apparent viscosity have been obtained. The variation of resistance to flow (l) and apparent viscosity (mo/m) with shape parameter (m), shear stress (to), stenosis length (Lo/L), and stenosis size (d/Ro) has been shown graphically. It has been found that the resistance to flow decreases as shape parameter increases as well as stenosis size increases. It has also been observed that resistance to flow increases as stenosis length increases and decreasing as stenosis shape parameter increases. The apparent viscosity decreases as stenosis shape parameter increases and stenosis size increases respectively. It has been shown that apparent viscosity increases as yield stress increases and decreases as stenosis shape parameter increases. Further, we have seen the effect of yield stress on resistance to flow and stenosis length on stenosis shape parameter.  The significance of the present model over the existing models has been pointed out by  comparing  the  results  with  other  theories  both  analytically and numerically.               
Key words :  Stenosis;  Herschel-Bulkley  fluid;  Non-Newtonian  fluid flow.    

Pulsatile flow of blood with periodic body acceleration and magnetic field through an exponentially diverging vessel
V. P. Rathod* and Shakera Tanveer#
Abstract: Pulsatile flow of blood through vessels of exponential divergence under the influence of periodic body acceleration and magnetic field by considering blood as a couple stress fluid. With the help of Laplace and finite Hankel transforms, analytical expressions for axial velocity, flow rate and fluid acceleration has been obtained. The solutions for velocities are compared with small increasing rates of vessel divergence. It is of interest to note that as the magnetic effect is increased the velocity of the blood decreased. Thus, by deaccelerating the velocity certain cardiovascular diseases can be treated by the magnetic effect. The effects of magnetic field and body acceleration have been discussed.            
Key words: Blood flow, couples stress fluid, body acceleration, magnetic field, exponentially diverging vessel, blood borne diseases.             

The stress intensity factors for three collinear Griffith cracks located symmetrically in a stress-free elastic strip and opened by a symmetrical system of body forces
A.P. Dwivedi and *Tarannum Siddiqi
Abstract: Main object of the paper is to obtain the solution for the problem of determining the stress intensity factors for three Collinear Griffith cracks located symmetrically in a stress -free elastic strip and opened by a symmetrical system of body forces, by reducing it to Fredholm integral equations of the second kind. The solution of these integral equations is given by expanding the unknown function in terms of d–1 (d being half of the width of the strip). Numerical results for physical quantities like crack shape, normal component of stress at y=0 are also included and finally the partial closure of the crack is considered.             
Key words: Griffith crack, body force, stress, displacement field, stress tensor, displacement vector, stress intensity factor.          

On almost (N,p,q) summability of Derived Fourier series
Shyam Lal and Hare Krishna Nigam*
Abstract: In this paper a new theorem on almost (N,p,q) summability of derived Fourier series of Fourier series has been established under a very general condition.               
Key words & Phrases : Almost (N,p,q) summability, Fourier series, Derived Fourier series, almost convergence, bounded sequence & second mean value theorem. 

Steady two layered flow with periodic body acceleration
V. P. Rathod* and Habeeb Ahmed
Abstract: A mathematical model has been formulated to study the steady two-layer blood flow with periodic body acceleration. The effect of periodic body acceleration on the blood flowing through a uniform cylindrical tube has been analyzed. Blood is considered as a couple stress fluid. Analytic expressions for axial velocity, core region, peripheral layer and flow rate have been obtained by applying finite Hankel transform technique. The velocity variation for different parameters have been discussed and presented in the form of graphs. The result has been compared with existing theoretical models and is found in good agreement with the other results.         
Key words: Blood flow, Couple stress fluid, Body acceleration, Two-layer.

Pulsatile MHD flow and heat transfer between parallel porous plates with ohmic dissipation and heat source
P.R. Sharma1  and  Bhawana  Agarwal2
Abstract: Aim of the paper is to investigate pulsatile flow of a viscous incompressible electrically  conducting fluid and heat transfer through parallel porous non-conducting plates in the presence of pulsatile pressure gradient, Ohmic dissipation, heat source and transverse magnetic field. The fluid is injected through the lower plate at a constant rate and sucked at the same rate through the upper plate.  The plates are maintained at uniform temperatures. The governing equations of motion and energy are solved by the variable separable and regular perturbation techniques. The velocity and temperature distributions are derived, discussed numerically and shown through graphs. The expressions of skin-friction coefficient and the Nusselt number at the plates are derived, discussed numerically and their numerical values for various values of physical parameters are presented through Tables.      
Key words : Pulsatile, MHD, heat transfer, cross-flow, skin-friction, Nusselt number.                    

On Riemannian manifolds admitting a nonhomothetic infinitesimal conformal tramsformation group
S.S. Pujar and S.M. Bhati
Abstract: In this paper, we consider the n-dimensional (n > 2) compact and orientable Riemannian manifold M admitting a conformal transformation X in M satisfying (2.1). The main purpose of the paper is to obtained the integral formulas in Riemannian manifold and use them as powerful tool to describe the global results.In fact, we obtained some conditions in terms of integral formula for M to be isometric to a sphere without putting restrictions on the scalar curvature of M. Finally generalise some of the results of earlier authors and some of those of S.S. Pujar and S.M. Bhati.       
Key words: Riemannian manifolds, Lie derivative, conformal transformation, and scalar curvature,   

Unsteady Flow of A Visco-Elastic Maxwell Fluid Through A Rectilinear Inclined Pipe
V.P. Rathod  and T. Roni
Abstract: The unsteady flow of Visco-Elastic Maxwell fluid through a rectilinear inclined pipe having its cross section as a parallelogram with transient pressure gradient has been discussed .To solve this problem Variable Separable method has been used. The solution of two particular cases have also been obtained.
Key words: Variable Separable method / Visco-Elastic Maxwell fluid / rectilinear inclined pipe.                         

MHD free connective flow and mass transfer through porous medium bounded by a vertical plate
R. N. Jat and Anuj K. Jhankal*
Abstract: The problem of unsteady free convection flow and mass transfer through a porous medium for a rotating fluid bounded by an infinite vertical plate in the presence of uniform transverse magnetic field with a constant suction and constant heat flux is discussed. The analytical expressions for the velocity, mass concentration and temperature are obtained. 
Key words: Free Convection, Porous Wall, Boundary Layer Flow,  Transverse Magnetic Field.       

A note on fuzzy algebraic structures
Manoranjan  Kr. Singh
Abstract: Since the inception of the theory of fuzzy subsets in the realm of mathematics, researchers in several disciplines of mathematics are trying to extend their notions to the more general framework of fuzzy setting .For instance, in algebra the notions of subgroupoids, subgroups, ring, field, vector space, ideals, bi-ideals, etc have been extended. Rosenfeld, Wang Jin Liu, Nanda, Biswas, Katsaras, Kuroki and Mukherjee are pursuing these studies among others.    
       Zadeh named fuzzy sets as those sets whose boundary is not clear. Rosenfeld2 firstly used this concept to develop the theory of fuzzy subgroups. He also demonstrated the way by which we can extend many concepts of group theory in an elementary way to develop the theory of fuzzy subgroups. Similarly Nanda3 and Biswas4 proposed the notion of fuzzy ring and fuzzy field.             
        In this paper our aim is to investigate and analyze the notions of fuzzy subgroups, fuzzy normal subgroups, fuzzy ring and fuzzy field. Here we have also proposed the redefine version of these algebraic structures and have shown that every fuzzy algebraic structures in the sense of Rosenfeld, Nanda and Biswas is also a fuzzy algebraic structure in our sense but not conversely.  
Key words: Fuzzy subgroupoid, fuzzy subgroup, fuzzy normal subgroup, fuzzy ring, fuzzy field, fuzzy algebraic structure etc.  

Analysis of three dimensional couette flow and heat transfer in porous medium between two permeable plates with sinusoidal temperature
S.S. Tak* and M.K. Vyas**
Abstract: A three dimensional Couette flow and heat transfer through a porous medium between two parallel infinite porous plates is considered. The stationery plate is subjected to a slightly sinusoidal surface temperature with transverse sinusoidal suction velocity while the moving plate is isothermal with uniform injection velocity. The expressions for components of skin friction and rate of heat transfer at the stationery plate and recovery factor at the insulated plate are obtained. These parameters are plotted against Reynolds numbers for various values of other parameters and discussed in detail.      

Unsteady MHD flow of viscous incompressible immiscible fluids in a rotating channel bounded by permeable beds
S.V.K. VARMA1,  M. SYAM BABU2, D. SUBRAMANYAM3 and N. PRABHAKAR REDDY4
Abstract: The unsteady laminar flow of two electrically conducting, viscous incompressible and immiscible fluids in a rotating channel bounded by permeable media of different permeabilities under the influence of a uniform transverse magnetic field is studied by taking the pressure gradient to vary exponentially with respect to time.  Analytical solutions of the equations of motion are obtained for velocities and mass flow rates.  The effects of magnetic parameter M, Reynolds number Re, permeability parameters s1 and s2 and height h2 of the upper fluid on velocities and mass flow rates are studied through graphs.  

On nonhomothetic conformal changes of Riemannian metrics
S.S. Pujar and S.M. Bhati
Abstract: In this paper, a compact orientable Riemannian manifold M of dimension n > 2 with the metric g is considered and obtained the integral formulas. Applications of these integral formulas are studied to establish some of global results. In fact, the conformality and isometry of Riemannian manifolds are studied. Some Corollaries are studied as special cases of these results.  
Key words: Conformal changes of Riemannian metrics in Riemannian manifolds,nonhomothetic conformal transformations.            

Oscillatory mean for several positive arguments
V. LOKESHA1, ZH.-H.ZHANG2 and  K. M. NAGARAJA3
Abstract: In this paper, we define rth oscillatory mean and its dual. Using this we obtain some important relations between various important means. 
Key words and phrases: Oscillatory mean, Inequality, Monotonicities Logarithmic mean, Heron mean and Identric mean.              

Perceptional views of students on quality in engineering education-A case study
G. Tirupathi Reddy*, J. Kandasamy* and K.S. Rao+
Abstract: In the present scenario of Liberalization, Privatization and Globalization, Quality is buzz word of 80s, common parlance during 90s and a thing of everyone’s thought in 2000s. The paradigm shift of quality consciousness  from product quality to process quality initialized the research work on process industries. Educational institutions being the country’s backbone of providing human resource for industrial needs particularly from Engineering institutions. Hence, there is a necessity of reviewing quality aspect in the context of Engineering Institutions. The present research work has been conducted by adopting a survey among 25 Engineering institutions in Andhra Pradesh among the students; Faculty, Course Work and Facilities were given prime importance. This study is a two folded study viz.; the first fold is focused on the assessment of the reliability of the data collected using Cronbach’s Alpha model and the second fold is to asses the significance difference among the Engineering  institutions with respect to perceptional views of the student community of various colleges under study.         

Current approaches to handling uncertain and vague information in databases: a survey
 Karan Singh1 and Shailendra S. Thakur2
Abstract: This paper surveys and describes the methods for representing and modeling the uncertain and vague information. The attempt has been made to classify the different types of uncertainty that may occur in data, and a discussion of the sources of such uncertain and vague information. The work that is surveyed is drawn from the field of databases. The databases have long been concerned with the problems caused by uncertain and vague information, and this paper stresses the relationships between the approaches developed for handling uncertain and vague information. Some important open questions and unexplored areas of research in this domain are also discussed.            
Key words : uncertain information, vague information and databases.

Environmental pollution by dyeing industries: a fam analysis
W. B. Vasantha Kandasamy and Karuppusamy
Abstract: In this paper we analysis the environmental pollution by dyeing industries using Fuzzy Associative Memories. This paper is divided into three sections. In section one we give short description of the problem. Fuzzy Associative Memories are dealt with in section two. Section three uses FAM model to analyse the environmental pollution caused by dyeing industries and gives the conclusions based on our study.               
Key words: FAM-model, Fit vector, Dyeing industries.                      

Fixed point theorems for three mappings under weak commutativity condition
R. K. Jain1 and B. K. Nayak
Abstract: In this paper we replace commutativity condition by weak commutativity and using only orbital continuity in place of continuity.           

Semi-invariant submanifolds of a certain class of hyperbolic contact manifolds
Mobin Ahmad
Abstract:  Semi-invariant submanifolds of a certain class of hyperbolic contact manifolds are studied and Nijenhuis tensor is calculated. The integrability conditions for certain distributions on a semi-invariant submanifolds of a certain class of hyperbolic contact manifolds are investigated. Totally contact umbilical and totally contact geodesic submanifolds are also studied.  
Key words and phrses: hyperbolic contact manifold, semi-invariant submanifold, distribution.                         

Heat and mass transfer flow of a viscous fluid past an infinite porous plate with time dependent suction and heat flux
N. P. Singh*, Ajay Kumar Singh#, Arvind Kumar** and Atul Kumar Singh**
Abstract: A theoretical analysis of unsteady free convection flow of a viscous fluid past an infinite porous vertical plate in non-homogeneous porous medium taking time dependent suction velocity and constant heat source into account. The permeability of the porous medium and the suction velocity at the plate decreases exponentially with time. Approximate solutions are obtained for velocity and temperature fields. The expressions for skin-friction and rate of heat transfer are also derived. The effects of various physical parameters, encountered into the problem, on the velocity field and temperature field are numerically shown through graphs while the effects on skin-friction and rate of heat transfer are numerically discussed through tables.                    

Heat transfer flow of stratified viscous fluid past a porous vertical plate
N. P. Singh*, Ajay Kumar Singh#, Arvind Kumar** and Atul Kumar Singh**
Abstract: In the present paper unsteady free convection flow of an incompressible, electrically conducting, viscous, stratified fluid through a porous medium past a vertical, porous, infinite plate with time dependent suction velocity in presence of transversely applied uniform magnetic field is studied. The plate is maintained at a constant temperature, which decays exponentially with time. Perturbation technique is annlied as suggested by Lighthill1. Solutions for the fluid velocity and temperature field are obtained. The expressions for skin-friction coefficient and rate of heat transfer are also derived. The velocity field is discussed for different values of Prandtl number. Stratification factor, Grashof  number, Hartmann number, heat source parameter and permeability parameter with the help of graphs. The temperature distribution for various values of Prandtl number and heat source parameter is also discussed. The effects of various parameters on skin-friction and rate of heat transfer are presented in tables numerically and discussed.       

Quantitative Forecasting Techniques: An Overview
Smita Verma and Reema Joshi
Abstract: Good strategic planning focuses on successfully managing the future. To manage the  future,  we  need to project what is likely to occur in the future. Forecasting methods can be used to accomplish this goal. Forecasting methods can be classified as qualitative, quantitative, or as a combination of both methods. Quantitative methods involve the analysis of patterns inherent in historical data to predict future events. These methods are based on the assumption that tomorrow’s world will be similar to today’s, and that patterns observed in the past will continue into the future. If historical patterns can be expected to persist into the future, quantitative methods should produce relatively accurate forecast. On the other hand, if past patterns change for some reason, then these models may not provide accurate forecasts.            

On f-Bisectional curvature of a P-Sasakian manifold
 Kalpana and Sarita Singh
Abstract: In this paper a P-Sasakian manifold has been taken admitting an almost semi-invariant submanifold and its f-bisectional curvature has been obtained by using the integrability conditions of the various distributions.         

MHD three dimensional couette flow with transpiration cooling between two horizontal parallel porous plates
R. C. CHAUDHARY1 and UMESH GUPTA
Abstract: The Couette flow between two horizontal parallel porous flat plates with transverse sinusoidal injection of the electrically conducting viscous incompressible fluid, at the lower plate and its corresponding removal by constant suction through the upper plate has been analyzed when both plates are at constant distance and in motion. Due to this type of injection velocity, the flow becomes three-dimensional. A magnetic field of uniform strength is applied normal to the plates of the plates. To obtain the expression for the velocity and temperature fields, the method of solution for a small perturbation approximation is used. The effect of injection / suction velocity on the flow field, skin friction and heat transfer are reported and discussed with the help of graphs.   
Key words: Three dimensional; Couette flow; Transverse sinusoidal injection/suction; Heat transfer.

Slow Flow Past a Slightly Deformed Porous Sphere
SATYA DEO and SUNIL DATTA*
Abstract: The problem of symmetrical flow past a porous spheroid whose shape deviates slightly from that of a sphere is investigated. The Brinkman’s equation for the flow inside the porous region and the Stokes equation for the free-flow region in their stream functions are used. As boundary conditions, continuity of velocity and surface stress across the porous surface are employed. Explicit expressions are obtained for both the inside and outside flow fields to the first order in small parameter characterizing the deformation. As a particular case, the flow past a porous oblate spheroidal particle is considered and the drag experienced by it is evaluated through a simple analytical formula. The dependence of drag coefficient on permeability for porous oblate spheroid is presented graphically and discussed. The earlier results reported for a perfect porous sphere and for a rigid oblate spheroid, are then deduced from the present analysis.       
Key words : Stokes Flow; Brinkman model; Gegenbauer Functions; Modified Bessel Functions.      

An expansion mapping theorem in metric spaces
Sanjay Kumar
Abstract: In this paper we replace the necessary condition of commutativity of Rhoades paper7 with weak compatibility (weakly compatible), which are not necessarily continuous.          
Key words: Fixed- point, Expansion mappings, Weak compatibility maps Subject classification: (2001) 47H10, 54H 25

Planarity of the point-block graph of a graph
V. R. KULLI and M.S. BIRADAR
Abstract In this paper, we present characterization of graphs whose point-block graphs are planar outerplanar and minimally nonouterplanar. In general, we also characterize graphs whose point-block graphs are k-minimally nonouterplanar ( k ³ 2 ).