020181   Ostrovska S (Mathematics, Atilim Univ, 06836 Incek, Ankara, Turkey, Email: ostrovskasofiya@yahoo.com) : Positive linear operators generated by analytic functions. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 485-93.

Let ϕ be a power series with positive Taylor coefficients {a_k)^∞_k=0 and non-zero radius of convergence r ≤ ∞. Let ξ_x, 0 ≤ x <60> r be a random variable whose values α_k, k = 0, 1,..., are independent of x and taken with probabilities a_kx^k/ϕ(x), k = 0, 1, .... The positive linear operator (A_αf)(x) := E[f(ξ_x)] is studied. It is proved that ifE(ξ_x = x, E(ξ²_x) = qx^{2 + bx + c, q, b, c ∈ R, q <62> 0, then A_ϕ} reduces to the Szasz-Mirakyan operator in the case q = 1, to the limit q-Bernstein operator in the case 0 <60> q <60> 1, and to a modification of the Lupas operator in the case q <62> 1.

16 ref

020180   Narasimha Sastry N S;Shukla R P (Stat.-Math. Unit, Indian Statistical Institute, 8th Mile Mysore Road, R.V. College Post, Bangalore-560 059, Email: nsastry@isibang.ac.in; rps@mri.ernet.in) : Structure of a code related to Sp(4,q),q even. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 457-70.

Determine the socle and the radical series of the binary code associated with a finite regular generalized quadrangle of even order, considered as a module for the commutator of each of the orthogonal subgroups in the corresponding symplectic group.

20 ref

020179   Majumdar A A K (NO, APU, 1-1 Jumonjibaru, Beppu-shi 875-8577, Oita-ken, Japan, Email: majumdar@apu.ac.jp ) : Some pseduo Smarandache function related triangles. Scienta Magna 2008, 4(3), 95-105.

Two triangels T(a, b, c) and T(a', b', c') are said to be pseudo Smarandache related if Z(a) = Z(a'), Z(b) = Z(b') Z(c) = Z(c'), where Z(.) is the pseudo Smarandache fucntion, and T(a. b, c) denotes the triangle with sides a, b and c. Proves the existence of an infinite family of pairs of dissimilar Pythagorean triangles that are pseudo Smarandache related.

020178   Majumdar A A K (NO, Ritsumeikan Asia-Pacific University, APU, 1-1 Jumonjibaru, Beppu-shi 875-8577, Oita-ken, Japan, Email: majumdar@apu.ac.jp) : Smarandache bisymmetric determinant natural sequence. Scienta Magna 2008, 4(3), 81-5.

Murthy introduced the Smarandache Bisymmetric Determinant Natural Sequence. Derived the sum of the first n terms of the sequence.

020177   Majumdar A A K (NO, , APU, 1-1 Jumonjibaru, Beppu-shi 875-8577, Oita-ken, Japan, Email: majumdar@apu.ac.jp ) : Alternative approach to the LP problem with equality constraints. Scienta Magna 2008, 4(3), 89-94.

Gives an alterantive approach to the solution of the LP problem with equality constraints. In this scheme, the constraint system of linear equations is first solved by elementary row operations (if such a solution exists). In the second stage, the solution of the system of linear equations is directly plugged in the objective function and then it is minimized. This scheme thus avoids the use of the simplex method.

020176   Li W N;Sheng W (Mathematics Dep, Binzhou Univ, Shandong 256603, People's Republic of China, Email: wnli@263.net; wh-sheng@163.com) : Some nonlinear dynamic inequalities on time scales. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 545-54.

The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation.

15 ref

020175   Feng D;Li J (School of Mathematics and Computing Science, Guilin Univ. of Electronic Technology,, Guilin 53, Guangxi 541004, People's Republic of China, Email: dahefeng@hotmail.com ) : Dynamics and bifurcations of travelling wave solutions of R(m, n) equations. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 555-74.

By using the bifurcation theory and methods of planar dynamical systems to R(m, n) equations, the dynamical behavior of different physical structures like smooth and non-smooth solitary wave, kink wave, smooth and non-smooth periodic wave, and breaking wave is obtained. The qualitative change in the physical structures of these waves is shown to depend on the systemic parameters. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above waves are given. Moreover, some explicit exact parametric representations of travelling wave solutions are listed.

16 ref

020174   Chen L;Cui Y (Mathematics Dep, Harbin Univ of Science and Technology, Harbin, Heilongjiang 150080, People's Republic of China, Email: chenlili0819@yahoo.com.cn; cuiya@hrbust.com.cn) : On the compactly locally uniformly rotund points of Orlicz spaces. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 471-83.

Locally uniformly rotund points and compactly locally uniformly rotund points are introduced. Moreover, criteria for compactly locally uniformly rotund points in Orlicz spaces are given.

10 ref

020173   Becker-Kern P (Fachbereich Mathematik, Universitat Dortmund, 44221 Dortumund, Germany, Email: pbk@math.uni-dortmund.de) : Explicit representation of roots on p-adic solenoids and non-uniqueness of embeddability into rational one-parameter subgroups. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 443-55.

This note generalizes known results concerning the existence of roots and embedding one-parameter subgroups on p-adic solenoids. An explicit representation of the roots leads to the construction of two distinct rational embedding one-parameter subgroups. The results contribute to enlighten the group structure of solenoids and to point out difficulties arising in the context of the embedding problem in probability theory. As a consequence, the uniqueness of embedding of infinitely divisible probability measures on p-adic solenoids is solved under a certain natural condition.

3 tables, 24 ref

020172   Basak G K;Dasgupta A (Stat-Math Unit, Indian Statistical Institute, 203 B.T. Road Kolkata 700 108, Email: gkb@isical.ac.in) : Central limit theorems for a class of irreducible multicolor URN models. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 517-43.

Take a unified approach to central limit theorems for a class of irreducible multicolor urn models with constant replacement matrix. Depending on the eigenvalue, authors consider appropriate linear combinations of the number of balls of different colors. Then under appropriate norming the multivariate distribution of the weak limits of these linear combinations is obtained and independence and dependence issues are investigated. Our approach consists of looking at the problem from the viewpoint of recursive equations.

11 ref

019280   Wan Muhamad;Ahmad A W;Naing N N;Hussein M T A R (Mathematics Dep, Science and Technology Faculty, Malaysia Univ, Terengganu UNT, 210 30 Kuala Terengganu, Terengganu (Malaysia)) : How to determine the sample size. Ultra Scient phys Sci 2007, 19(3)M, 517-20.

Determining sample size is a very important issue because samples that are too large may waste time, resources and money, while samples that are too small may lead to inaccurate results. The sample size is very simply the size of the sample. If there is only one sample, the letter "TV" is used to designate the sample size. If samples are taken from each of "a" populations, then the small letter "n" is used to designate size of the sample from each population. When there are samples from more than one population, N is used to indicate the total number of subjects sampled. If the sample sizes from the various populations are different, then would indicate the sample size from the first population, n₂ from the second, etc. The total number of subjects sampled would still be indicated by N. Illustrate how to determine the sample size for an experiment in a study.

1 illus, 5 ref

019279   Thiagarajan K;Pushpalatha L;Natarajan P (Mathematics Dep, Mysore Univ, Manasagangothri, Mysore) : Special study in (1,2)-distance coloring and (1,2)-distance graphs. Ultra Scient phys Sci 2007, 19(3)M, 731-3.

(1, 2)-Distance Graph has been defined and (1, 2)-Distance Coloring for the connected graph G. Also get after studying the (1,2)-Distance graphs for paths and cycles, we observe new results under (1,2)-Distance coloring scheme for paths and cycles.

3 illus, 3 ref

019278   Thiagarajan K;Natarajan P (Mathematics Dep, Rajalakshmi Engineering College, Thandalam, Chennai, Tamil Nadu, Email: vidhyamannan@yahoo.com) : Special study in (2,2)-distance coloring and (2,2)-distance graphs(for Paths & Cycles). Ultra Scient phys Sci 2007, 19(3)M, 734-6.

In this paper we define (2, 2)-Distance Graph and (2, 2)-Distance Coloring for the connected graph G. We get some beautiful grapgs under (2.2)-Distance graph scheme for paths and cycles. Also we observe new results under (2,2)-Distance coloring scheme for paths and cycles.

3 illus, 3 ref

019277   Srinivasa Rao K N;Gayathri Devi B (Mathematics Dep, Garden City College, 16th K.M. Old Madras Road, Bangalore-560 049, Email: vishwa_devi@hotmail.com) : Elementary functions in the quaternion and other algebras of the Cayley-Dickson series. Ultra Scient phys Sci 2007, 19(3)M, 729-30.

The exponential and the other elementary functions of an arbitrary element ω in any of the 2^m-dimensional (m = 1, 2, ...) algebras like the quaternion (m = 2) and the octonion (m = 3) algebras obtained by the Cayley-Dickson construction are shown to be well defined and explicit expressions for these functions in terms of the components of ω are obtained. It turns out that these functions satisfy almost all the identities satisfied by the corresponding functions of a complex variable.

6 ref

019276   Singh A K;Singh N P;Raghav S;Singh A K (Mathematics Dep, C.L. Jain (P.G.) College, Firozabad-283 203) : Effect of heat source on hydromagnetic convective flow through a vertical channel. Ultra Scient phys Sci 2007, 19(3)M, 623-8.

Hydromagnetic unsteady convective flow of an incompressible homogeneous, electrical conducting, viscous fluid through a porous medium in a vertical channel consisting of semi-infinite parallel walls is studied in the presence of constant heat source. The magnetic field is applied normal to the flow. Using Laplace transform technique the solutions for velocity and temperature fields are obtained. Expressions for skin-friction and rate of heat transfer are also derived. The effects of magnetic parameter, heat source parameter. Grashof number and Prandtl number on the velocity field, skin-friction and rate of heat transfer are discussed for symmetrical cooling of channel walls. It is observed that the influence of heat source parameter increases the velocity field but decreases the skin-friction and rate of heat transfer.

1 illus, 1 table, 18 ref

019275   Singh A K;Kumar A;Singh N P;Singh A K (Mathematics Dep, V.S.S.D. College, Kanpur-208 002) : Hydromagnetic free convection flow past an infinite porous vertical plate with time dependent suction velociy and heat source. Ultra Scient phys Sci 2007, 19(3)M, 609-16.

Unsteady, laminar, hydromagnetic, free conveetion flow of a viscous, incompressible, electrically conducting fluid past a porous vertical plate embedded with porous medium is studied. The plate is subjected to a periodic suction velocity. The flow field is considered in the presence of a uniform magnetic field applied normal to the flow. Purturbation technique is used to obtain velocity and temperature fields. Expressions for skin-friction and rate of heat transfer are also derived. The results obtained are discussed.

6 illus, 2 tables, 10 ref

019274   Shukla S S;Chaubey P K (Mathematics Dep, Allahabad Univ, Allahabad-211 002, Email: ssshukla_au@rediffmail.com) : On totally real warped products in locally conformal almost cosymplectic manifolds. Ultra Scient phys Sci 2007, 19(3)M, 617-22.

Establishs the inequality between the warping function of a warped product submanifold isometrically immersed in a locally conformal almost cosymplectic manifold of pointwise constant 0-sectional curvature and the squared mean curvature. Some applications are derived.

9 ref

019273   Shrivastava U K;Rathore C J (Govt., Girls P.G. College, Bilaspur(C.G.)) : On uniform [F, dn] summability of fourier series. Ultra Scient phys Sci 2007, 19(3)M, 713-16.

The concept of uniform summability has been introduced by Saxena. Saxena has applied summability concept for Fourier series by harmonic mean and proved two theorems on uniform Norlund summability. The object of the present paper is to prove a theorem on uniform [F, d_n] means.

9 ref

019272   Sharma R K;Vindhyachal Lal (Post Graduate Department of Mathematics, D.A.V.P.G. College, Azamgarh-276 001) : Mathematical model for population growth of hemiptera under starvation. Ultra Scient phys Sci 2007, 19(3)M, 489-92.

The population growth of hemiptera like aphides and mazus percisae is discussed. Hemiptera discharges a type of lethal mucilaginous material called saliva that smeared over the surface of the leaf preventing the individuals from further sucking and movements and so causing deaths due to starvation. Integro-differential equation of growth is studied assuming linear dependence between mortality rate and the integral density ƒ^t₀ n(s)ds, the area covered by saliva at time t.

10 ref

019271   Sehik Uduman P S;Sulaiman A;Sathiyamoorthy R (Mathematics Dep, B.S.A. Crescent Engineering Collgege, Vandalur, Chennai) : Determination optimal reserve inventory between two machines in series using order statistics. Ultra Scient phys Sci 2007, 19(3)M, 497-502.

Inventory systems may be under the category of parallel systems, or series systems. A system in which two machines M₁ and M₂, which are in series is considered. The output of M₁ happens to be the raw material for M₂. The shortage cost arises due to the idle time of M₂, caused by a breakdown of M₁. Hence a reserve in between M₁ and M₂ is cost effective. The optimal size of the reserve inventory in between M₁ and M₂ considering the interarrival times between the successive breakdowns of M₁ as i.i.d random variables has been considered by some authors. An expression for the optimal reserve inventory is obtained taking the interarrival times as order statistics. Numerical Illustrations are provided.

3 illus, 3 ref

019270   Satish Chandra;Chaudhary G (Mathematics Dep, S.M. Post-Graduate College, Chandausi-202 412) : On (H, μ_n) summability of the factored fourier series. Ultra Scient phys Sci 2007, 19(3)M, 679-84.

Authors have proved a theorem on (H, μ_n) summability of the factored Fourier series, which generalize various known results.

15 ref

019269   Rangarajan R;Baishya C (DOS in Mathematics, Mysore Univ, Manasagangotri, Mysore, Mysore-570 006, Email: rajra63@yahoo.com) : Regular pertubation method for fisher kolmogorov type PDES. Ultra Scient phys Sci 2007, 19(3)M, 503-10.

u_txx = u(1 - u) is a well known equation by name, Fisher-Kolmogorov equation in the literature. It is one of the standard models used in population dynamics. The term u(1-u) is the reaction term with logistic distribution. In the present paper, we have worked out a perturbation series solution for models which resembles Fisher-Kolmogorov equation.

5 illus, 5 ref

019268   Natarajan P;Thiagarajan K;Nanditta S (Research & Development, Rajalakshmi Engineering College Thandalam, Chennai) : Isomorphical 0-1 labeling for network characterization. Ultra Scient phys Sci 2007, 19(3)M, 493-6.

Deals with iteration of links with nodes in combinations with Binary digit labeling thereby observing the isomorphism of 2 different network topology one of which having a cycle network. This method helps to access a given network, under set of constraints, hence having traffic growth with regards to network characterization, without having to consider the extension to the general case with more than one interior or exterior nodes.

4 illus, 2 tables, 4 ref

019267   Mustafa Bin Mamat;Fong W T;Ismail Bin Mohd; Yosza Bin Dasril (Mathematics Dep, Faculty of Sciences and Technology, Malaysia Univ, Teregganu, Malaysia) : New search direction for modifying BFGS method. Ultra Scient phys Sci 2007, 19(3)M, 673-8.

This paper discussed about modified BFGS methods in solving unconstrained optimization problems. This method is efficient in solving unconstrained optimization problems. By using the modified BFGS (mBFGS) method, the objective function has to be differentiating in solving unconstrained optimization problems. The numerical results will show that the hybrid modified BFGS (hmBFGS) method at least as competitive as the modified BFGS method which is recommended by Liao. Hybrid modified BFGS method is giving another alternative in solving the unconstrained optimization problems.

1 table, 4 ref

019266   Meena B L (Mathematics Dep, Rajasthan Univ, Jaipur-302 004) : Bianchi type tilted cosmological model with perfect fluid dust distribution in general relativity. Ultra Scient phys Sci 2007, 19(3)M, 707-12.

Bianchi Type I tilted cosmological model for perfect fluid dust distribution is investigated. To get the determinate model, we have assumed the condition that the component (σ|) of shear tensor (σ_i^j) is proportional to the expansion (θ) in themodel. This leads to A=(BC)ⁿ where n is the constant. The physical and geometrical aspects of the model are also discussed.

18 ref

019265   Mahyoub Q M;Soner N D (Mathematics Dep, Mysore Univ, Manasagangorti, Mysore-570 006, Email: Mahioub70@yahoo.com) : Fuzzy covering and Fuzzy neighborhood set in Fuzzy graphs. Ultra Scient phys Sci 2007, 19(3)M, 601-08.

Presents a concepts of adjacency, incident in a fuzzy graphs and we extend the notions of a covering number and independence number in a crisp graphs to a fuzzy covering number and fuzzy independence number in fuzzy graphs. Also discuss the relationship between these parameters. This study gives the notion of fuzzy neighborhood set of a fuzzy vertex, a fuzzy adjacency matrix of them and its properties, then give the concept of a fuzzy neighborhood number of a fuzzy graphs. Also many other results are given.

5 illus, 7 ref

019264   Kobayashi K;Sadasivan Pillai K;Sakuratani Y; Suzuki M;Jie W (National Institute of Technology and Evaluation (NITE), 2-49-10 Nishihara, Shibuya-ku, Tokyo, 151-0066, Japan, Email: kobayashi-katsumi@nite.go.jp) : Do we need to examine the quantitative data obtained from toxicity studies for both normality and homogeneity of variance. J envir Biol 2007, 29(1), 47-52.

Most of the statistical techniques used to evaluate the data obtained from toxicity studies are based on the assumption that the data show a normal distribution and homogeneity of variance. Literature review on toxicity studies on laboratory animals reveals that in most of the cases homogeneity of variance alone is examined for the data obtained from these studies. But the data that show homogeneity of variance need not always show a normal distribution. In fact, most of the data derived from toxicity studies, including hematological and biochemical parameters show a non-normal distribution. On examining normality of data obtained from various toxicity studies using different normality tests, observes that Shapiro-Wilk test is more appropriate than Kolmogorov-Smirnov test, Lilliefors test, the normal probability paper analysis and Chi square test. But there are situations, especially in the long-term toxicity studies, where normality is not shown by one or more than one of the dosage groups. In this situation, proposes that the data may be analyzed using Dunnett multiple comparison test after excluding the data of the groups that do not show normality. However, the biological relevance of the excluded data has to be carefully scrutinized. Also observes that the tendency of the data to show a normal distribution seems to be related to the age of the animals. Describes various tests commonly used to test normality and their power, and also emphasizes the need of subjecting the data obtained from toxicity studies to both normality and homogeneity tests. A flow chart suggesting the statistical techniques that may be used for both the types of data showing a normal or non-normal distribution is also proposed.

4 illus, 10 tables, 24 ref

019263   Kalpana;Srivastava P (Mathematics Dep, Banaras Hindu Univ, Varanasi-221 005) : On a D-conformal transformation in an SP-Sasakian manifold. Ultra Scient phys Sci 2007, 19(3)M, 581-4.

Established some invariants of a D-conformal transformation of a semi-symmetric metric connexion in an SP-Sasakian manifold.

4 ref

019262   Garg M;Agarwal S;Goel S;Goel C K (Mathematics Dep, Nehru P.G. College, Chhibramau, Kannauj, Email: garg_manoj1972@ahoo.co.in) : On g-Homeomorphism in topological spaces. Ultra Scient phys Sci 2007, 19(3)M, 697-706.

New class of closed maps namely g-closed maps has been introduced which settled in between the class of closed maps and the class of Ψ-closed maps. Authors also introduce and study new class of homeomorphisms called g-homeomorphisms and g c-homeomorphisms. Further we show that the set of all g c-homeomorphisms form a group under the operation composition of maps.

1 illus, 21 ref

019261   Eyo A E (Maths/Stat/Comp Dep, Science Univ of Uyo, Uyo) : Determination of vorticity in a hydraulic jump and the use of a general velocity profile. Ultra Scient phys Sci 2007, 19(3)M, 685-92.

The sole aim of this study is to obtain a new general expression for the mean vorticity downstrean of hydraulic jump in terms of the Froude number. In doing this a new form of momentum equation for the determination of the mean vorticity downstream of a hydraulic jump is derived using substitution method. The new momentum differs from that of Hornung et al in the sense that it contains additional term which is the vertical acceleration term. A general linear velocity profile is proposed and incorporated into the new momentum equation and the new torque, different from ', exerted by the excess bottom pressure on the fluid is obtained. Incorporating this torque into the angular momentum balance leads to a general expression for the mean vorticity in terms of the Froude number. The present work generalizes since it extends the model to include a general linear velocity profile.

1 illus, 9 ref

019260   Elangovan R;Ramachandran V;Ramalakshmi S (NO, Annamalai Univ, Annamalai Nagar-608 002, Email: srelagovan@rediffmail.com) : Appraisal of least absolute value analysis of variance. Ultra Scient phys Sci 2007, 19(3)M, 547-58.

In linear model analysis, a wide variety of statistical tools are applied to obtain valid inferences. The prime among them is the Least Square approach. This has been developed in all its details and is universally used. But in many situations the use of this method is less reliable. As an alternative to Least Square technique, Least Absolute Value method has been suggested. This present work is based on Least Absolute Value method and verification of results empirically using simulation studies with special reference to Analysis of Variance. In this paper an empirical behavior of the classical linear model approach and the method of Least Absolute values for estimation, when the error distribution with log normal, is attempted for one way classification model, and verification of results empirically using simulation studies. It is to be noted that this procedure gave correct decision in more than 90% of the cases.

1 illus, 1 table, 12 ref

019259   Chandra Sekhar A;Sudha K R;Prasad Reddy P V G D (Engineering Mathematics Dep, GITAM, Visakhapatnam, Email: acs@gitam.edu) : Algebraic curves in public key cryptosystems. Ultra Scient phys Sci 2007, 19(3)M, 533-40.

Cryptography falls under the umbrella of Cryptology, the science of making and breaking secret communications. Information security manifests itself in many ways according to the situation and requirements. Regardless of who is involved, to one degree or another, all parties to a transaction must have confidence that certain objectives associated with information security have been met. This paper provides the main trends and process of asymmetric key cryptosystems, Public Key Cryptosystems (PKC) using Algebraic Curve Cryptosystems (ACC).

2 illus, 21 ref

019258   Biswas D (Mathematics Dep, Indian Institute of Technology, Kharagpur-721 302, Email: d_priya05@yahoo.co.in) : Cayley transform and the unit cycle in elliptic and hyperbolic cases. Ultra Scient phys Sci 2007, 19(3)M, 559-70.

Cayley transform and the unit cycle in the elliptic and hyperbolic (EH) cases have been studied. We first study the Cayley transform for the elliptic and hyperbolic cases. We give a result that for both elliptic and hyperbolic cases the "real" axis u is transformed to the unit cycle but only the upper half plane in the elliptic case, is transformed to the unit disk. Authors have also defined the elliptic and hyperbolic alternative Cayley transforms.

7 illus, 11 ref

019257   Bhagwat Prasad;Gupta S P (Mathematics Dep, S.M.M. Town (P.G.) College, Ballia-277 001, Email: bp_kushwaha@sify.com) : Generalized co-symplectic manifold of second class. Ultra Scient phys Sci 2007, 19(3)M, 591-6.

Discuss the integrabiiity condition of this manifold. Some inclusions relations have been also investigated. Also affine connection of generalized co- symplectic manifold of second class has been studied.

5 ref

019256   Awasthy M (Mathematics Dep, Govt. P.G.College, Damoh) : Some theorems on fixed point in two-L spaces. Ultra Scient phys Sci 2007, 19(3)M, 483-8.

Some related fixed point theorems of Two L-Spaces are obtained.

3 ref

019255   Ajil S B M;Ismail Bin Mohd;Dasril Y B (Mathematics Dep, Faculty of Science and Technology, Univ Malaysia Terengganu, Mengabang Telipot, 210 30 Kuala Terengganu (MALAYSIA), Email: sma6316@yahoo.com.my) : Several points modified explicit group iterative method for fast solution of poisson equation. Ultra Scient phys Sci 2007, 19(3)M, 653-64.

Modified explicit group iterative methods that use several points per group for fast solution of Poisson equation. The main concern of this paper is to construct new groupings of the mesh points of the network into two and six points using the second order accurate five-point finite difference equations and to investigate their advantages when compared to the four points group explicit iterative methods. This work indicates that the six points modified explicit group method can also be another alternative method in this class of algorithm besides the existing four points modified explicit group Poisson solver which was given3. In order to confirm our recommendation, we provide some numerical results of the test problem.

6 illus, 3 tables, 7 ref

019254   Ahmed S (Mathematics Dep, Govt. Degree College, Thanna Mandi-185 212, Email: shakeelar2002@yahoo.co.in) : On B-finitistic fuzzy bitopological spaces and P-finitistic fuzzy bitopological spaces. Ultra Scient phys Sci 2007, 19(3)M, 665-72.

Concept of Covering Dimension and Finitisticness of general Bitopologicai Spaces has been introduced and studied some basic properties of these concepts their. Also introduced two concepts B- Finitistic Fuzzy Bitopological Spaces and P-Finitistic Fuzzy Bitopological Spaces and studying their some of the basic properties.

27 ref

019253   Ahmed S (Mathematics Dep, Goalpara College, Goalpara, Assam-783 101, Email: sahin_glp@yahoo.co.in) : Steady free convective MHD flow and heat transfer through a porous medium bounded by a uniformaly moving porous vertical plate. Ultra Scient phys Sci 2007, 19(3)M, 585-90.

The effects of permeability of porous medium on the two dimensional steady laminar free convective flow of an electrically conducting fluid along a porous uniformly moving hot vertical plate in presence of heat source/sink has been analysed. The governing equations of motion are solved by perturbations technique. The velocity profile, temperature profile, skin friction and the heat transfer coefficient are demonstrated graphically for different values of the parameters involved.

8 illus, 15 ref

018183   Yadav R K;Singh B (Mathematics and Statistics Dep, J.N. Vyas Univ, Jodhpur-342 005, Email: rkmdyadav@yahoo.co.in) : On certain properties of a general class of q-polynomials suggested by basic laguerre polynomials. Bull pure appl Math 2007, 1(1), 94-102.

Having defined a q-extension of the polynomial L^α,β_n (x), we investigate its fundamental properties such as q-generating relation, q-partial difference equation and recurrence relations. A generalized q-generating function for the said polynomial is also established. It has further been shown that the newly defined polynomial is closely related to the q-Laguerre polynomial L^β_n (x; q) . Certain interesting limiting cases in the form of the known results have also been discussed.

11 ref

018182   Xiao Z;Shao J;Xu R;Palta M (Statistics Dep, Univ of Wisconsin-Madison, 610 Walnut Street Madison, WI 53726, USA, Email: zhiguo@stat.wisc.edu) : Efficiency of GMM estimation in panel data models with measurement error. Sankhya 2007, 69(Pt 1), 101-18.

Wansbeek (2001) proposed a generalized method moment (GMM) frameªwork for analysing static panel data with measurement error in one regresªsor, without requiring external information such as a validation or replicate data set. We follow Wansbeek (2001) and provide a corrected formula for the asymptotically optimal second-stage GMM estimator. Furthermore, we show that, in some important special cases, the first-stage unweighted GMM estimator is actually asymptotically optimal. Some Monte Carlo results are presented to examine the finite sample performance of the first-stage and second-stage GMM estimators.

2 tables, 18 ref

018181   Wu Y D;Zhang Z H;Lokesha V (Xinchang High School, Xinchang City, , Zhejiang Province 312 500 P.R. China, Email: zjxcwyd@tom.com) : Sharpening on mircea's inequality. J Analysis Computn 2007, 3(2), 93-8.

By using one of Sh. L. Chen's theorems, combining the method of mathematical analysis and nonlinear algebraic equation system. Mircea's Inequality involving the area, circumradius and in radius of the triangle is sharpened.

12 ref

018180   Wahid S A (Mathematics and Computer Sciences Dep, The University of West Indies, St Augustine, Trinidad) : On matching polynomial of square corridor. Indian J Math 2007, 49(3), 315-22.

A recurrence relation is derived for the matching polynomial of the square corridor type graph. Explicit formulae are then given for the first seven and filial three coefficients.

1 illus, 1 table, 7 ref

018179   Waghamore H P (Mathematics Dep, Central Coll Campus, Bangalore Univ, Bangalore-560 001) : On nevanlinna characteristic function. J Analysis Computn 2007, 3(2), 135-9.

4 ref

018178   Trivedi N;Singh B (Sch of Stud in Mathematics, Vikram Univ, Ujjain, Madhya Pradesh) : Simple sir model for dengue/haemorrhagic fever. Bull pure appl Math 2007, 1(1), 22-7.

Using compartmental model host-vector transmission for dengue fever disease, in which a portion of new born hosts are vaccinated, has been analyzed. Two states of equilibrium are studied, one is trivial and other is endemic. For a particular case R ≤ ((I + p') /(1- P s)), only trivial solution exists and is stable. However, for R <62> ((1 + p') /(1- P s)), both the equilibriums exist. Stability criteria for them are also studied.

7 ref

018177   Tinsson W (Laboratoire de Mathematiques Appliquees CNRS UMR 5142, Univsite de Pau et Des Pays de L'Adour, BP 1155, 64013 PAU Cedex, France, Email: walter.tinsson@univ-pau.fr) : Note on small size augmented pair designs. Sankhya 2007, 69(Pt 1), 119-36.

Small size experimental designs for response surfaces are presented. Our first purpose is to investigate the class of augmented pair designs obtained from an initial saturated simplex design with only two or three levels. Then we are looking in this new class of designs, for optimal configuration.

1 illus, 2 tables, 14 ref

018176   Thakur S S;Chaturvedi R (Appl Mathematics Dep, Govt. Engng Coll, Jabalpur-482 011, Email: samajh_singh@rediffmail.com) : rg-Continuous mappings in intuitionistic fuzzy topological spaces. J Indian Acad Math 2007, 29(2), 467-73.

Concept of intuitionistic fuzzy rg-continuous mappings have been introduced and some of its basic properties are studied.

16 ref

018175   Tejpal S;Narang T D (Mathematics Dep, Guru Nanak Dev univ, Amritsar-143 005, Email: shwetambry@gmail.com) : On closest and minimal points. Indian J Math 2007, 49(3), 343-53.

In this paper author discussed closest, minimal points and center of a set in metric spaces and proved that minimal and closest points are the same in strictly convex metric spaces. It is also shown that a set C in a metric space is optimal i.e. C = min(C) if and only if C is the fixed point set of a quasi non-expansive mapping.

12 ref

018174   Tak S S;H Kumar (Mathematics Statistics Dep, JNV Univ, Jodhpur, Email: takssjnvu@sify.com) : Heat transfer with radiation in MHD free convection flow confind between a vertical wavy wall and a flat wall. Bull pure appl Math 2007, 1(2), 126-40.

In the present problem, two-dimensional free convective MIID flow with radiation and heat transfer of a viscous incompressible fluid, in a vertical wavy channel with heat source, is studied. The non-linear equations governing the flow have been solved by assuming that the flow consists of a mean part and a perturbed part as one of the wall is pure sinusoidal wavy perturbation to the plane y = 1 . It is also assumed that both the walls are isothermal. The effects of the various parameters, entering into the problem, on the velocity field and temperature distribution are discussed. The Skin friction and Nusselt Number for both the walls are also tabulated for different values of parameters.

7 illus, 1 table, 20 ref

018173   Suryanarayana Murty G (NO, , 503, Sri Rama Towers 2-2-647/118, Central Excise Colony, Bagh Amberpet, Hyderabad-500 013, Email: gurajadamurty@yahoo.com) : Is there a kinematical model of space-time encompassing classical quantum and relativistic mechanics. J Indian Acad Math 2007, 29(2), 505-22.

Discusses a kinematical model of space-time in which the speed of light is not an absolute constant but can be an asymptotic property of space-time which is defined by 'Planck's length. As a result, one arrives at two first-order fifth-(or higher) degree inhomogeneous differential equations connecting space and time variables. Thus, the kinematical space-time structure is defined by two inhomogeneous differential equations but not by line element as in the field theories. One of these equations corresponds to 'space-like space-time', while the other corresponds to 'time-like space-time'. Both of them lead to nonlinear 'non-parametric' relations between space and time, which pass through the origin of space- time' but do not conform to the principle of Special Relativity. However, there are 'parametric' solutions, which do not pass through origin of space and time but agree with relativity principle asymptotically. The solution of the 'time-like space-time' equation allows only 'faster-than-light-speed' while the solution of the 'space-like space-time' equation has, in addition, two cusps and a branch point. At the branch point, space is independent of time as in classical physics. The conceptual problems and the physical implications of this model are discussed briefly. Some possible avenues of further research are pointed out. It is expected that the model would be useful not only for its pedagogic features but also provides scope for further mathematical study of space-time relationship.

5 illus, 14 ref

018172   Sulaiman W T (Coll Computer Sci and Math, Univ of Nosul, Nosul-Iraq, Email: waadsulaiman@hotmail.com) : On inclusion relations for absolute summability. Indian J Math 2007, 49(3), 303-13.

Obtained necessary and sufficient conditions for a series ∑ an summable <157>R, pn<157>k, 1 <60> k ≤ s <60> ∞, to imply that the series ∑ a_n λ_n is summable <157>T<157>_s where (R,pn) is a weighted mean matrix and T is a lower triangular matrix. Some other results are also deduced.

5 ref