On efficient domination number and chromatic
number of A graph-I
G.Mahadevan*1, A. Selvam
Avadayappan2 and M.Hajmeeral3
Abstract : Let ge (G) and
c(G) denote the efficient domination number and chromatic number of a connected graph G of order n. A dominating set S is
said to be an efficient dominating set if every vertex v
Î V-S is adjacent to exactly one vertex in S. The chromatic number
c(G) is defined to be the minimum number of colours required to colour all the vertices such that adjacent vertices do
not receive the same colour. In this paper we find an upper bound for the sum of
the efficient domination number and the chromatic number and characterize
the corresponding extremal graphs.
Key words : Efficient domination number, chromatic number. AMS Subject Classification 05C
K. Thiagarajan1, V. Lakshmi2 and B. Harish3
Abstract : In this paper we define (i, j) - Distance Coloring for the connected graph G. We get after studying the (i, j) - Distance graphs for the continuous joining of BANANA TREE, we observe new results under (i, j) - Distance coloring scheme for the above mentioned graphs (which are available in figures 1,2 respectively).
Key words : (i, j) - Distance Graph, (i, j) - Distance Coloring, Bi-partite
Pankaj Agarwal and V. K. Sharma
Abstract : In this paper an attempt has been made to incorporate the effect of deterioration assuming the demand rate at any instant of time to be a linear function of the on-hand inventory, at those instant, allowing shortages, which are completely backlogged, for both infinite and finite time-horizons.
1M. Ananthanarayanan and 2R. Sattanathan
Abstract : In this paper an Algorithm is presented to perform critical path analysis in a fuzzy environment. The Trapezoidal fuzzy numbers given by decision makers or characterized by historical data are utilized to assess the activity times in a project network .The fuzzy critical path thus obtained is compared with conventional method.
Key words : Fuzzy set theory, Trapezoidal fuzzy numbers Fuzzy critical path analysis.
Srinivas, T.* and Abdul Majeed**
Abstract : The papers of Frucht R.3, Izbicki H.6, and Sabidussi G.9 have dealt with the construction of finite graphs X whose automorphism group G(X) is isomorphic to a given finite group G. Examination of the graphs constructed in their results show the following two facts: (1) The graphs X have the property that for any two vertices x and y of X there is at most one f Î G(X) which sends1 x into y (is precisely the fact which is used in Frucht R.3 to prove that G(X) actually is isomorphic to G). (2) The graphs X are modifications of Cayley color-groups of the given group G with respect to some set H of generators of G (cf. Definition 2 below) in the sense that the vertices and edges of the color-group are replaced by certain graphs (cf. Definition 3). The purpose of the present work is to show that (1) implies (2), (Theorem 3).
Key words: Automorphism, Chromatic index, Fixed-point-free, Perfect graphs. Subject Classification: AMS-MS06C; 37EG22.
S. Chelian* and P. Santhi**
Abstract : Two pairs of integers (a, b), and (c, d) are said to be copairs if a + b + ab = c + d + cd. In this paper, we obtain a formula to generate infinite number of copairs.
Key words : Types of numbers, types of pairs of numbers, copairs. AMS Subject Classification Code: 11A (Primary)
P. SREEHARIREDDY1, A.S. NAGARAJAN2 and M. SIVAIAH3
Abstract : Transient MHD free convection flow of an incompressible fluid past an isothermal plate with temperature gradient dependent heat source and the influence of magnetic parameter are studied. Implicit finite difference scheme which is unconditionally stable has been used to solve governing partial differential equations of the flow. Transient Temperature profiles and velocity profiles are plotted to show the effect of heat source parameter and magnetic parameter.
Key words : Transient MHD free convection flow; Incompressible fluid; implicit finite difference scheme; Crank - Nicolson method.
P. Thangavelu1 and M. Anitha2
Abstract : Baker introduced approximately closed and approximately continuous functions in 1996 to characterize T½ spaces. Jin Han Park et al. introduced regular approximately closed and regular approximately continuous functions and characterize spaces. In this paper we introduce approximately homeomorphism and regular approximately homeomorphism and characterize them.
Key words and phrases
: a- closed, a-continuous, ar- closed, ar-continuous, regular closed, rg-closed, g-closed, a-
homeomorphism and ar- homeomorphism.
2000 Mathematics Subject
Classification: 54A05, 54C05, 54C10.
S.K. Sahoo* and S. Gountia**
Abstract : Minimum ratio spanning tree problem concerns with finding a spanning tree from a connected doubly weighted graph which minimizes the ratio of the weights of the spanning tree. Here a study has been made for the problem in a-cut fuzzy graph using a geometric approach.
Key words: Fuzzy logic, Fuzzy graph, spanning tree, Forest in a fuzzy graph. AMS Classification number (2000)-68T 27/W31352
V.P. RATHOD and SEEMA JABEEN
Abstract : In this paper the pulsatile flow of blood with volume fraction of microorganisms and gravity effect has been planned to study by assuming blood as couple stress fluid and dusty particles as microorganisms. The velocity expressions for both blood and microorganisms have been obtained in Bessel-Fourier series form. By the proper substitution the velocity expressions for blood can be reduced to pulsatile and steady flow of couple-stress and Newtonian fluid in the presence/absence of microorganisms. Further from the present analysis the expressions for flow rate, apparent viscosity, phase-lag between flow rate and pressure gradient have been derived. The results obtained in this model will be compared with the existing experimental results and theoretical models.
Key words: blood flow, dusty flow, dusty fluid flow.
H.T. Rathoda*, R.D. Sathishb and A.S. Hariprasadc
Abstract : Extended Gauss Lobatto quadrature rules of the type, first conceived and computed by Kronrod are investigated using the highly stable and efficient algorithm developed by Piessens and Brandeers. We have further proposed and investigated the existence of the generalized form of Gauss - Lobatto - Kronrod quadrature rule such that the new abscissas are reals, lie in the interval of integration, ie [-1,1] and the associated weight coefficients are all positive. Some sample output of the MATLAB programs for these extended quadrature rules are displayed with 32-digit accuracy, We have also appended MATLAB code which fully use the symbolic maths variables for ready reference, verification and further development in case of the need for applications.
Key words : Gauss Lobatto Quadrature, Gauss - Lobatto - Kronrod Quadrature, Numerical integration.
V.P. Rathod and Asha S.K.
Abstract : The Problem of peristaltic transport of a fluid with couple stress fluid through the gap between coaxial tubes where the outer tube is non uniform and the inner tube is rigid. The relation between the pressure gradient, friction force on the inner and outer tube are obtained in terms of couple stress parameter. The numerical solution of pressure gradient, outer friction and inner friction force and flow rate are shown graphically.
Key words : Peristaltic transport, couple stress parameter, and flow rate.
1J. Earnest Lazarus Piriyakumar and 2D. Rajan
Abstract : In this paper the notions of likelihood ratio ordering and hazard rate ordering are extended to the realm of fuzzy random variables. Since a-level set of a fuzzy set plays a decisive role this paper wholly depends upon the a-cuts but with the support of strong measurability conditions. The interplay between the likelihood ratio orderings, hazard rate orderings and stochastic orderings are identified and related results are established in this paper.
Key words : Fuzzy random variables, Fuzzy valued functions, Fuzzy Numbers, Likelihood ratio ordering and hazard rate ordering.
Anita Biswas* and Smita Verma*
Abstract : In statistics, exponential smoothing refers to a particular type of moving average technique applied to time series data, either to produce smoothed data for presentation, or to make forecasts. The time series data themselves are a sequence of observations. The observed phenomenon may be an essentially random process, or it may be an orderly, but noisy, process. Exponential smoothing is commonly applied to financial market and economic data, but it can be used with any discrete set of repeated measurements. In this paper different exponential methods are discussed, starting from simple exponential method, ARRSES, double exponential and triple exponential methods and then a comparison between them has been done
R. N. JAT* and SANTOSH CHAUDHARY**
Abstract : A general analysis has been developed to study the two-dimensional stagnation point flow of a non-Newtonian Walters 'B' fluid with slip in the presence of a magnetic field. The fluid impinges on the wall either orthogonally or obliquely. The effects of the parameters such as Weissenberg number, magnetic parameter and slip factor are discussed graphically on velocity profiles.
"Logic is a powerful weapon"
D.S. Solanki
Abstract : Author investigates a statement problem and tries to solve it by logic and Boolean algebra. A very famous German statement problem is pursued here. Historically it was solved with one condition but I have solved three cases/ aspects with the same limitations and found full solutions. In the solution twenty four prime positions for all three cases (I, II, III) can be described and diagrams prepared with the help of those positions and with their help one can easily reach the desired conclusion. As is well known there is a plethora of proof of problems in logic. Elegant as it is, Logic often gives the easiest solution.
M.S. Chauhan*, V. H. Badshah**, Arihant Jain** and Virendra Singh Chouhan***
Abstract : Som10 establishes a common fixed point theorem for R-weakly commuting mappings in a Fuzzy metric space. The object of this paper is to prove some fixed point theorems for compatible and weakly compatible mappings by improving the condition of Som10.
Key words : Common fixed point, Fuzzy metric space,
compatible maps and weak compatible maps.
AMS Subject Classification :
Primary 47H10, Secondary 54H25.
Shakeel Ahmed1, Sandeep Sharma2 and Alka Gupta
Abstract : The concepts of Covering Dimension and Finitisticness of general Bitopological Spaces have been introduced by Shakeel11. In this paper we have introduced the concept of I-Covering Dimension of Bitopological and Fuzzy Bitopological Spaces and studied their some of the basic properties.
Key words: I-Covering Dimension, Bitopological spaces,
Fuzzy Bitopological Spaces, Ideals, L-fuzzy Ideals.
AMS 2000 Mathematics Subject Classification:
54A40, 04A72.
R.S. CHANDEL*, K.K. KUMBHARE** and RAJESH SHRIVASTAV***
Abstract : This paper introduces the notion of semi-compatible self-maps in 2-metric spaces and establishes a fixed-point theorem for four self-maps, satisfying an implicit relation through semi-compatibility of pair of self-maps. This result in another fixed point theorem for five self-maps, which generalizes and improves many result of B. Singh and S. Jain10 With an application.
Key words : 2-metric space, fixed-point, semi-compatible and
weak-compatible mapping. 2000 Mathematics Subject Classification .47H25, 47H10.
In10 B. Singh and S. Jain proved the following result.
K.K. Dixit and S.K. Dubey
Abstract : In this paper, we introduce a new class Tj(n,a,r) of certain uniformly convex functions with negative coefficients defined by Salagean operator. Several properties like, the coefficient bounds, growth and distortion theorems, radii of close-to-convexity, starlikeness and convexity for the functions belonging to the class Tj(n,a,r) are thoroughly investigated. Many other interesting properties and consequences of our main results are also pointed out.
Key words and
Phrases: Analytic Functions, Convex functions, Close-to-convex functions, Starlike functions, Salagean operator .
2000 Mathematics subject classification, Primary 30 C 45.
PARIJAT SINHA
Abstract : In this paper we have introduced the concept of weak sequential drop property, which is weaker than weak drop property introduced by J.R. Giles, Brailey Sims and A.C. Yorke.
Key words : Locally convex spaces, Duality Mapping,
Stream, Reflexive spaces.
AMS (1991) classification number - 46
(B).
V. RAJESH* and S. VIJAYA KUMAR VARMA**
Abstract : The effect of thermal radiation on MHD flow past an impulsively started infinite vertical plate in the presence of heat generation has been discussed. The fluid is assumed to be gray, emitting/absorbing but non-scattering medium and the optically thick radiation limit is considered. The dimensionless governing equations are solved using Laplace Transform technique. Results for velocity and temperature are shown graphically whereas the numerical values of the skin-friction and the rate of heat transfer are entered in the table. The results are discussed in terms of the parameters M (the magnetic field parameter), F (the radiation parameter), H (the heat source parameter) and Pr (the prandtl number)
Key words : radiation, MHD flow, vertical plate, heat generation.
*Kiran Shrivastava and ** Sushma Duraphe
Abstract : In this paper we define i- separation and i- connectedness relative to a given topology on a set and several results on it are established.
Subject Classification : AMS(2000): 54 A 99
*E.K.R. Nagarajan and **R. Rathajeyalakshmi
Abstract : G. Gratzer2 has posed the problem, "Does every modular lattice have a proper, modular, congruence-preserving extension?" In this paper, we give an affirmative answer to the above problem for finite lattices.
Key words: Congruence, Congruence lattice,
Congruence-preserving extension, Gluing of lattices.
Mathematics Subject classification: Primary: 06B10, Secondary: 06D05
Awadhesh Kr Pandey and Kamal Wadhwa
Abstract : In this paper, we determine the basic definition of generalized hyper-geometric function with their conditions, convergence or divergence conditions of generalized hypergeometric function generalized hypergeometric function generalized hypergeometric function. The exponential and binomial transfor-mation of generalized hypergeometric function. This gives to find the solution of Bessel's function, exponential function, and binomial function etc.
Key words: 0F0,1F0, 0F1,Bessel' function, exponential.
Raj Bali* and Radhika Goyal**
Abstract : Bianchi Type IX inflationary cosmological models for perfect fluid distribution in General Relativity are investigated. To get the deterministic model, we have assumed the conditions (i) s a q which leads to a = g bm where a and b are metric potentials, m and g are constants, s the shear and q the expansion in the model, (ii) V a fn where V is the potential and f the Higg's field. The inflationary scenarios for m = 2 and n = 1 are discussed in detail. The other physical aspects of the model are also discussed.
Key words: Bianchi IX, Inflationary, perfect fluid, Cosmological. PACS No.: 04.20.-q, 04.20.Jb; 04.20.Dv; 04.20.Ex.
A. MAITY1 and A.K. CHONGDAR2
Abstract : In this note, we have obtained an extension of the result on quasi-bilateral generating function involving modified Laguerre polynomials from the existence of a partial quasi-bilateral generating function of the polynomial under conside-ration. Some particular cases of interest are also discussed.
AMS Subject classification code : 33A47
1Nirmala. P. Ratchagar, 2S. Vijaya and 3R. Sathiyamoorthy
Abstract : In the study of HIV infection and AIDS, the estimation of expected time to seroconversion and its variance is an important aspect. In doing so, the concept of antigenic diversity threshold is of prime interest. Many authors have obtained the estimate of expected time to seroconversion and its variance under the assumption that the amount of antigenic diversity contribution due to successive contacts are independent random variables as well as the interarrival times between successive contacts are identically independent random variables. In this paper, the expression for E(T) and its variance are derived under the assumption that the contribution to antigenic diversity in successive contacts are correlated r.v's as well as sequence of interarrival times between successive contacts form an order statistics.
Key words: HIV infection, seroconversion, antigenic diversity, threshold. The AMS classification number is 92C60.
Rizwana Jamal
Abstract : Through this paper the author obtained Unique common Fixed point theorem for two and three mappings for 2-Banach space. The author also generalizes the proved theorem of Sharma and Bajaj1 for Banach space.
Sushil Shukla
Abstract : R.S.Mishra and Ram Hit1, K.L. Duggal2, K. Kodaira and K. Nomizu3 have studied differentiable structures defined by algebraic equations. A.Nijenhuis4 studied Xn-1 forming set of eigen vectors. K. Yano5 gives some geometrical meaning of vanishing of Nijenhuis tensor in a X2n with an almost complex manifold. In the present paper, we have studied Nijenhuis tensor and its associated on almost hyperbolic Hermitian manifold and some of their properties have been discussed.
Atul Garg1 and Yashwant Singh2
Abstract : This paper deals with a special class of functions called generalized voigt function Vµ,v (x, y). It plays an important role in the several diverse fields of physics such as plasma spectroscopy, astrophysics, nuclear magnetic resonance and the theory of neutron reactions etc. Some new properties of generalized voigt-function are introduced here to facilitate the computation of Vµ,v (x, y) when parameters or arguments take different values.
AMS Subject Classification: 33E20, 85A99 Key words: Voigt function, Bessel function
V.N. Tripathi and Abhaya Kumar Pandey
Abstract : The present paper deals with a theorem on uniform Kl (C, 1) summability of Legendre series under very general condition.
D.V. Krishna1, P. Narasimha Rao2 and S.G. Malashetty
Abstract : The problems related to the dynamics of fluid flow either through porous medium or through channels bounded partially or fully by permeable walls has wide applications in Petroleum Engineering, Geothermal Engineering, Soil Mechanics and Biomechanics. In the field of Biomechanics the study of flow past a permeable bed is applicable in understanding the circulation of blood in the lungs between the opposing layers of capillary endothe1ium, held apart by endothelium covered 'Posts' of septal tissue. This capi1lary endothelium is covered inturn by a thin layer lining the alveoli. The blood space in the lung is idealized into a two-dimensional channel and the interstitial tissue space into a porous medium. As the endothelial layer between the two regions is permeable to water and certain other solutes it can be considered as a permeable membrane of neg1igible thickness. The epithelial tissues between the air and vascular spaces are less permeable and can thus be treated as impermeable membrane. The irregular posts which keep apart the endothelial walls can be ignored.
It is clear that the pressure equations have to be solved first and making use of the equations relating the pressure to the velocity components, the expressions for the velocity components have to be obtained to different orders under perturbation scheme. For computional purpose, we have assumed the non-dimensional inlet and outlet pressure Pin = 5 and Pout = 15. Also the geometry of the tube is considered to be f = exp (-az). Figs. (1-10) indicate the axial and radial velocity profiles for variations in the governing parameters R, a, G, K0, Z. For fixed a, G, K0, we observe from Fig. (1) and (6) the axial and radial velocity components reduce in its magnitude for an increase in R at all points in the flow region. For all other variations Fig. (2) - (5) and (7) - (10) we observe that w increases and u decreases from its maximum on the wall to zero on the axis.
*Sushma Duraphe **Kiran Shrivastava and ***Vijeta Iyer
Abstract : The work in this paper is in continuation to our previous work7. Several results on i-connectedness relative to a topology on a given set are obtained in the paper. The following definitions and theorems are taken from 7 our work and hence the proofs of these theorems are omitted.
Wan Muhamad Amir W. Ahmad1, Nyi Nyi Naing2 and Tengku Mohamad Ariff Raja Hussein3
Abstract : The choice of a transformation has often been made in an ad hoc trial-and-error fashion but in this research paper we deals with the new solution of transformation which is covering all the real numbers. The assumption of normality that gained from the optimization method is much better improved compared to Box-Cox transformation through the statistical P value. The biggest values of the statistical P value (>0.05) reflect the goodness of the normality achievement. In order to obtain the efficiency status, we will illustrate the application of transformation method with the data that are getting from Hospital University Science Malaysia (HUSM).
Key words: Box-Cox Formula, Alternative Formula, parameter l and P- values.
S.U. SIDDIQUI, N.K.VERMA* SHAILESH MISHRA and R.S.Gupta1
Abstract : It is well known that the fluid dynamics of arterial blood flow plays an important role in arterial diseases. A mathematical model for the pulsatile flow of blood in a small vessel in the cardiovascular system with a mild stenosis is analyzed. Blood is modelled as a couple stress fluid and the effects of time dependent axisymmetrical developing stenosis on blood flow have been investigated. Expressions for the velocity profile, flow rate, and the wall shearing stress have been determined by energy integral method. The velocity and wall shearing stress increase with the developing stenosis. In small diameter vessels, the time dependent stenosis increases the axial velocity. Particularly it is true in the case of slowly varying radius with time. Slow time dependent stenosis does not introduce a radial component in simple laminar flows but accelerates the axial velocity. The effect of pulsatility further increases the velocity in the axial direction.
Key words: Couple stress, Pulsatile, Stenosis, Energy integral method, Wall shearing stress.
R.S. Chandel1, Yasmeen Bano2 and Akhilesh Jain3
Abstract : The concept of semi compatibility is given in probabilistic metric space and it has been applied to prove the existence of unique common fixed point of six self-maps with weak compatibility satisfying an implicit relation.
R. N. JAT* and SANTOSH CHAUDHARY**
Abstract : This paper deals with the two-dimensional laminar boundary layer flow of an incompressible viscous electrically conducting fluid at a stagnation point towards a permeable surface in the presence of a uniform magnetic field. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity variables. The solutions of momentum and energy equations have been obtained independently by a perturbation technique for a small magnetic parameter. The effects of the various parameters such as suction parameter, Hartmann number, Prandtl number and Eckert number for velocity and temperature distributions have been discussed in detail through graphical representation.
K.K. Dixit and Vikas Chandra
Abstract : We introduce a subclass Tk,p (A, B, l, a) of the class Sk,p of analytic and multivalent functions in the unit disc E. The object of the present paper is to determine sharp coefficient estimate, distortion theorems, radius of convexity and closure theorems for this class defined by fractional integral. Finally, we have investigated some results involving modified Hadamard product of two functions belonging to the class Tk,p(A, B, l, a).
Key words: Analytic Function, Multivalent function,
Fractional integral Modified Hadamard product.
2000 Mathematics Subject classification : Primary 30C45:
secondary 26A33, 33B15.
Selvam Avadayappan* and R. Vasuki**
Abstract : Let G(V,E) be a graph with p vertices and q edges. For every assignment f :V(G) ®{0,1,2,...,q}, an induced edge labeling f*:E(G)® {1,2,...,q} is defined by
for every edge uv Î E(G). If f*(E) = {1,2,...,q}, then we say that f is a mean labeling of G. If a graph G admits a mean labeling, then G is called a mean graph. In this paper, we prove that the graph Cm ´ Pn, the caterpillar P(n,2,3), Q3´P2n, Carona of a H-graph, mC3, CnÈK1,m (n³3,1£m£4), mC3ÈK1,m (1 £ m £ 4), the dragon Pn(Cm) and some standard graphs are mean graphs. We also establish some general results on mean graphs. An assignment f:V(G) ®{0,1,2,...,p-1} is called an odd edge labeling, if for the edge labeling f+ on E defined by f+(uv) = f(u)+f(v) for any edge uv, f+(E) = {1,3,5,...,2p-3}. In this paper, we have studied the connection between odd edge labeling and mean labeling.
Key words: labeling, mean labeling, mean graphs, odd edge labeling. AMS Subject Classification code: 05C (Primary)
Sushil Shukla
Abstract : R.S. Mishra1, K.L. Duggal2 studied differentiable structures defined by algebraic equations. A.W. Adler3, D.C. Spencer4, B. Eckmann and A. Frolicher5 derived integrability conditions for almost complex structures. In this paper, the integrability conditions for hyperbolic almost complex structure have been derived. Certain results for hyperbolic almost complex manifold have also been obtained.
Charles Dorsett
Abstract : Within this paper, open images are further investigated and additional topological characterizations of nonempty finite sets are given.
Key words: finiteness, open images, separation axioms
2000 Mathematics Subject
Classification: 54A05, 54C10, 54D10, 54D15.
Anita Biswas* and Smita Verma**
Abstract : Most people view the world as consisting of large number of alternatives. Future research evolved as a way of examining the alternative futures and identifying the most probable. Forecasting is designed to help decision-making and planning in the present. Forecasting involves making projections about future performance on the basis of historical and current data. Forecasts empower people because their use implies that one can modify variables to alter the future. A prediction is an invitation to introduce change into a system. In this paper, two types of forecasting techniques discussed are quantitative technique and qualitative technique.
SATISH TALREJA
Abstract : The environmental pollution can significantly reduced by different condition monitoring techniques for various thermal systems like Boiler, Furnaces, Combustors etc. Huge benefits can be obtained from condition and health monitoring systems. These monitoring systems provide certain diagnostic and predictive information about developing fault conditions. Condition monitoring systems are particularly effective in detecting long term component degradation faults. Analytical Hierarchy Process (AHP) is a very strong mathematical tool for decision making. In this paper I have used this method in prioritizing the condition monitoring techniques which is proved satisfactory.
Ujagar Patel and S. Choudhury
Abstract : It is well known that a convex numerical function q on an open set u of Rn continuous. It has been also proved that under suitable conditions the result also holds for cone-convex functions. The object of this note is to show that under suitable conditions, such a result also holds for monotone functions.
Wan Muhamad Amir W. Ahmad1, Norazlida Aleng2, Nyi Nyi Naing3, and Tengku Mohamad Ariff Raja Hussein4
Abstract : This paper is discussed the applied of the poisson regression model. A poisson regression model is given by
, 
because the log of this function produces a linear combination of the predictors,
this model is said to have a log link function. In this paper, we will illustrate
the application of Poisson regression using S-PLUS Software. The source of
the data is from Polis Di Raja Malaysia (2008).
Key words : Poisson regression model.
Yogendra Yati and R.C. Jain1
Abstract : In this paper, we review the past work and discuss the future integration of Data Mining and Operation Research. We also discuss intersection between them.
Key words: Data Mining (DM), Operation Research (OR), integration, KDD, Optimization and Clustering.