019558   Tripathy B C (Math Sci Div, Inst of Advd Study in Sci and Technol, Khanapara, Guwahati-781 022, Email: tripathy@yahoo.com) : On normal sequence spaces and domain of matrix maps. J Indian Acad Math 2005, 27(1), 63-7.

Conditions on the elements of the matrix for which the domain of the matrices trasforming one sequence space into another sequence space will be a normal space have been found. The matrices have elements which map a Banach space into the field C of complex numbers. The article concludes with some remarks as well examples justifying the reason for restricting the study to diagonal matrices.

5 ref

019557   Tak S S;Sisodia G S (Math and Statist Dep, JNV Univ, Jodhpur-342 001, Email: takssjnvu@sify.com) : Viscous heating in initial MHD free convection flow along uniformly moving vertical plate. J Indian Acad Math 2005, 27(1), 25-32.

The effects of viscous heating on a free convection along an infinite vertical porous plate suddenly set in uniform motion in an infinite mass of fluid at rest, in presence of transverse magnetic field fixed to fluid has been investigated. The plate is subjected to variable heat flux and suction. The momentum and energy boundry layer equations have been solved by taking series expansions of velocity and temperature functions in powers of product of magnetic field and time (mt). The analytical solutions of some of the resulting ordinary differential equations have been obtained in terms of complementary error function and rests of the differential equations have been solved numerically on computer. The numerical values of plate temperature function and skin-friction coefficient function, for different values of Brinkman number, magnetic field parameter and suction velocity parameter have been tabulated and discussed in detail. Also, the velocity and temperature profiles at a fixed time, for different values of the parameters, mentioned above, are drawn and discussed.

3 illus, 1 table, 22 ref

019556   Suresh Kumar R;Gopal G (Statist Dep, Univ of Madras, Chennai-600 005, Email: rsrsk@hotmail.com) : Stochastic model for the expected time to recruitment in a two grade hierarchy manpower system. J Indian Acad Math 2005, 27(1), 181-92.

In marketing organisations announcement of policy revisions (regarding wages, incentives and targets) results in the loss of manpower and frequent recruitments are not recommended in view of the various costs involved. A two grade organisation is considered. Of the two grades, grade II is sustained with the cumulative loss of manpower at several decision epochs and loss in grade I is compensated by means of transfer of personnel from grade II. This kind of mobility of persons avoids frequent recruitment Programmes, which is cost effective. For the organisation which has hierarchy of two grades, the expected time to recruitment and its variance are obtained using shock model approach.

5 ref

019555   Sundaram P (NO, Kandaswami Kandar's Coll, P. Velur-638 182) : Classification of non-oscillatory solutions of neutral difference equation. J Indian Acad Math 2005, 27(1), 95-108.

Consider the neutral difference equation Δ^m [x(n)-p(n)x(n-k)]+δ q (n)f(x(g(n))) = 0. n ∈ W (^*) where m ≥ 2, δ = ± 1, {p(n)} and {q(h)} are real sequences and {g(n)} is a sequence of integers such that g(n) ≤ and lim_n∞ g(n) = ∞. First the relation between the sequences {x(n)} and {x(n) - p(n) x (n-k) has been discussed. The results, thus obtained have been used to classify the nonoscillatory solution of (^*) into several classes according to the asymptotic behaviour as n → ∞.

8 ref

019554   Sundar S (Math Dep, Indian Inst of Technol Madras, Chennai-600 036, Email: slnt@iitm.ac.in) : Recursive packed alagorithm for Cholesky factorization of tridiagonal and pentadiagonal matrix. J Indian Acad Math 2005, 27(1), 193-200.

A new compact way to store a symmetric or triangular matrix called Recursive Packed Format (RPF) and a new algorithm Recursive Packed Cholesky Algorithm (RPC) is explained in the works done by Anderson and Wasniewski. RPF and RPC have been extended for the tridiagonal and pentadiagonal matrices. The extension is done with utmost care that it preserves the matrix shape for each block as in RPF thereby allowing the use of Level-3 BLAS which increases the speed of the extended RPC algorithm.

6 illus, 5 ref

019553   Sulochana C;Prasada Rao D R V;Krishna D V (Math Dep, Gulbarga Univ, Gulbarga, Karnataka) : Finite element analysis of convective heat and mass transfer through a porous medium in a horizontal channel. J Indian Acad Math 2005, 27(1), 69-94.

Convective heat and mass transfer flow through a porous medium in a horizontal channel have been analysed. The Galerkine finite element analysis is used to discuss the flow, heat and mass transfer through the porous medium using serendipity elements. The velocity, the temperature and the concentration and the rate of heat transfer are analysed for variations in the governing parameters.

2 illus, 4 tables, 17 ref

019552   Somasundaram R;Rajasekar M (Math Sect Fac of Engng Technol, Annamalai Univ, Annamalainagar-608 002) : Synchronization in a fuzzy automata. Bull pure appl Sci-Sect E 2005, 24(1), 117-21.

Gamma-synchronization of a word has been defined in a Fuzzy Automata and a γ-synchronization word has been computed for a gien fuzzy automata.

5 illus, 2 ref

019551   Sivakumar K C;Mercy swarna J (NO, Indian Inst of Technol Madras, Chennai-600 036) : Explicit solvability of dual pairs of infinite linear programs. Opsearch 2005, 42(3), 288-96.

Obtains explicit slutions of a pair of infinite linear programs in terms of generalized inverses. This is done by reducing one of the problems to an interval linear program. The main result is posed in the setting of a class of dual pairs of real Banach spaces and is illustrated with an example.

15 ref

019550   Sharma K K;Sharma S;Goel J (Statist Dep, C.C.S. Univ, Meerut-250 005) : On the robustness of plans for variables in view of quality variations. Bull pure appl Sci-Sect E 2005, 24(1), 207-15.

In classical acceptance plans (ASP) for variables, the product quality is considered as constant. However, this assumption is unduly restrictive and unrealistic as a strong prior information representing variations in product quality is available as statistical quality control (S.Q.C.) is a continuous valuation process. The study deals with the robust character of plans for variables in respect of producer's and consumer's risk when product quality varies randomly.

1 illus, 1 table, 6 ref

019549   Shanmugam T N;Gangadharan A (Math Dep, Coll of Engng Anna Univ, Chennai-25, Email: shan@annauniv.edu) : On a class of univalent functions. J Indian Acad Math 2005, 27(1), 201-11.

The class T (A, B) of functions ƒ (z) which are analytic in the open unit disc U = {z : <124> z <124> <60> 1} with a normalisation ƒ(0) = 0 = ƒ^' (0) - 1 and satisfying the condition x²ƒ1(z)/ƒ²(z) - 1 + Az/1 + Bz, where - 1 ≤ B <60> A ƒ 1. have been considered. Among other results, the university of the class T (A, B) and certain radius problems have been discussed. Also certain properties of the sub-class T₂ (A, B) of T(A, B) for which ƒ" (0) have been studied.

5 ref

019548   Shams S;Kulkarni S R (Math Dep, Fergusson Coll, Pune-411 004, Email: kulkarni_ferg@yahoo.com) : On a certain subclass of univalent functions defined by Ruscheweyh derivative and subordination (I). J Indian Acad Math 2005, 27(1), 39-52.

A certain subclass of of univalent functions with negative coefficients have been introduced by making use of Ruscheweyh derivative and subordination notation. Some properties of this class have been investigated.

6 ref

019547   Saxena R K;Ram J;Chandak S (Math and Statist Dep, Jai Narain Vyas Univ, Jodhpur-342 005) : On two-dimensional generalized Saigo fractional calculus associated with two-dimensional generalized H-trasnforms. J Indian Acad Math 2005, 27(1), 167-80.

A relation between the two-dimensional generalized H-transofrm and the Weyl type two-dimensional Saigo-Maeda operator of fractional integration is established.

27 ref

019546   Santhakumaran A p (Math Dep, St. Xavier's Coll (Autonomous), Palayamkottai-627 002) : Unique vertex-to-clique eccentric clique graphs. Bull pure appl Sci-Sect E 2005, 24(1), 167-72.

The concepts of unique (V,ζ) - eccentric clique graphs and self (V, ζ) - centered graphs in a connected graph G are introduced, their properties are investigated and certain classes of such graphs are determined Also unique (V,ζ)- Centered trees and self (V,ζ) - centered trees are characterized.

4 illus, 7 ref

019545   Saad O M (Math & Phys Dep, Coll of Arts & Sci Univ of Qatar, P.O. Box 2713, Doha, State of Qatar) : On the integer solutions of the generalized transportation problem under fuzzy environment. Opsearch 2005, 42(3), 238-51.

It is shown that a fuzzy generalized transportation problem can be converted into a nonfuzzy one which can be changed to an equivalent from for which there is an immediate basic solution by making use of a particular basic solution to the dual problem. The computation involved is minimal. For problems with integer coefficients, an all integer algorithm due to Greenberg can be initialized immediately to the equivalent problem to obtain the optimal integer solution to the original problem in a finite number of steps. The method appears to be efficient.

14 ref

019544   Ratnam L;Malleswari D (Appl Math Dep, Sri Padmavathi Mahila Visvavidyalayam, Tirupati-517 502) : Convection flow through a porous medium in a coaxial cylinder. Bull pure appl Sci-Sect E 2005, 24(1), 145-52.

Free and forced convection flow of a viscous fluid through a porous medium in a coaxial cylinder has been considered . The equations of motion and temperature are solved using perturbation method. The shear stress, Nusselt number at the boundary for different varations of the governing parameters are evaluated.

8 illus, 10 ref

019543   Rajamani M;Viswanathan K (Post Grad Dep of Math, N.G.M. Coll (Autonomous), Pollachi-642 001) : On α generalised semi closed sets in bitopological spaces. Bull pure appl Sci-Sect E 2005, 24(1), 39-53.

Fukutake introduced generalized closed sets in bitopological spaces. Recently Fukutake et. al introduced the concept of ω closed sets and ω open sets and ω continuity in bitopological spaces. αgs closed sets in bitopological spaces have been introduced as follows: Let, j ∈ {1,2} be fixed integers. In a bitopological space (X: τ₁, τ₂), a subset A is said to be (τ_i, τ_j) - αgs closed if τ_j-αcl(A) ⊆ U whenever A ⊆ U and U is semi open in (X, τ_i). Also introduce αgs continuous maps, (t_i, T_j)-T_αgs spaces, pair wise α generalized semi closure operator, pair wise αgs irresolute maps have been introduced in bitopological spaces. Some of their properties have been studied.

9 ref

019542   Parthasarathy S;Kannan R;Ravichandran M K (Fac in Mgmt, Multimedia Univ, Malaysia-68100) : Expected time to recruitment in a two grade organization - shock model approach. Bull pure appl Sci-Sect E 2005, 24(1), 185-93.

Recruitment is required to compensate the wastage of manpower planning. So in manpower recruitment of personnel is an important aspect. Sathyamoorthy and Parhasarathy (2002) have derived an expression for the expected time for recruitment in a two grade organization in which the movements of personnel from one grade to another is permited. The total loss of manpower put together is dropped and the expected time for recruitment in both the grades are found out using shock mode and cumulative damage process.

2 illus, 5 ref

019541   Ongun M Y (Math Dep, Suleyman Demirel Univ, Cunur Canpus, 32660, Isparta, Turkey, Email: myakit@fef.sdu.edu.tr) : On a dissipative Schrodinger problem with a spectral parameter in the boundary condition. Bull pure appl Sci-Sect E 2005, 24(1), 55-61.

Nonselfadjoint singular Schrodinger boundary value problems have been considered in the limit-circle case with spectral parameter in the equation and boundary conditions. The approach is based on the use of the maximal dissipative operator. The article is devoted to studying the basis properties of chain of eigenfunctions and associated functions of the boundary value problem (2.3)-(2.5) in L²(R₊).

13 ref

019540   Nematollahi A R;Suba Rao T (Statist Dep, Shiraz Univ, Shiraz 71454, Iran, Email: nematollahi@susc.ac.ir) : On the spectral density estimation of perioedically correlated (Cyclostationary) time series. Sankhya 2005, 67(3), 568-89.

The estimation of the spectral density matrix of a periiodically correlated (PG) time series (also known as cyclostationary time series) has been considered. The well known relation between the spectral density matrix of a periodically correlated time series and a stationary vector time series have been used (Gladyshev, 1961). The spectral matrix of the stationary vector time series is estimated using the eigenvalue decomposition of block Toeplitz matrices. The method of estimation is illustrated with simulated and real time series.

5 illus, 1 table, 31 ref

019539   Neagu M G (Pure Math Dep, Univ of Waterloo, University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Email: mgneagu@math.uwaterloo.ca) : Asymptotic freeness of random permutation matrices from gaussian matrices. J Ramanujan Mathl Soc 2005, 20(3), 189-213.

It is shown that an independent family of uniformly distributed random permutation matrices is asymptotically *-free from an independent family of square complex Gaussian matrices and from an independent family of complex Wishart matrices, and that in both cases the convergence in *-distribution actually holds alomst surely. An immediate consequence is that, if the rows of a GUE matrix are randomly permuted, then the resulting (non self-adjoint) random matric has a *-distribution which is asymptotically circular; similarly, a random matrix which is asymptotically *-distributed like and R-diagonal element from free probability theory.

13 ref

019538   Nagaraja Rao I H;Ramana R V (NO, G.V.P. Coll for P.G. Courses, Rushikonda, Vishkhapaptnam-530 045) : Some relations involving the orders and types of two or more entire Dirichlet series. J Indian Acad Math 2005, 27(1), 17-24.

Entire functions represented by Dirichlet series have been considered. Some relationships involving orders and types of two or more entire Dirichlet series have been obtained.

3 ref

019537   Nadarajah S;Kotz S (Statist Dep, Univ of Nebraska, Lincoln, NE 68583) : Probability inequalities of the multivariate t distribution. Proc Natn Acad Sci India-Sect A 2005, 75(3), 193-8.

Results on probability inequalities of the multivariate t distribution are reviewed. Believes that this review will serve as an important reference and encourage further research activities in the area.

19 ref

019536   Misra U K;Sahoo N C;Mishra A K (Math Dep, Berhampur Univ, Berhampur-760 007) : Relation between two index summability methods. Bull pure appl Sci-Sect E 2005, 24(1), 99-106.

A relation between two summability methods X - <157> N^-, p_n<157>_k and Y - <157>N, q_n; δ<157>_k, k ≥ 1 is established.

5 ref

019535   Meintanis S;Bassiakos Y (Economics Dep, Natn and Kapodistrian Univ of Athens, 8 Pesmazoglou Street 105 59 Athens, Greece, Email: simosmei@econ.uoa.gr) : Goodness-of-fit tests for additively closed count models with an application to the generalized hermite distribution. Sankhya 2005, 67(3), 538-52.

A general metod is proposed for testing the fit to any member of the invariant under onvolutions family of count models, parameterized by mean and variance. The test statistics, which are of the weighted L2-type, exploit the specific structure of the corresponding probability generating function. Their asymptotic null distribution is obtained, and the consistency of the tests is studied. As an example, the generalized Hermite distribution, a specific member of this family, is analysed. In this case, two methods of estimation of the parameters are considered, for which limit statistics are obtained as the decay of the weight function tends to infinity. The performance of a parametric bootstrap version of the method is investigated via Monte Carlo.

2 tables, 16 ref

019534   Matei A;Tille Y (NO, Statist Inst Univ of Neuchatel, Espace De L'Europe 4, CP 805 2002 Neuchatel, Switzerland, Email: alina.matei@unine.ch) : Maximal and minimal sample co-ordination. Sankhya 2005, 67(3), 590-612.

Maximinzing/minimizing the expected overlap between two or more samples drawn in different time points have been the objective. For this it is necessary to compute the joint inclusion probability of two samples drawn in diferent time periods. A solution is given by using linear programming and more precisely by solving a transportation problem. This solution is not computationally fast. The conditions unded which the objective function associated with an optimal solution of the transportation problem is equal to the bound given by maximizing/minimizing the expected overlap. Using these conditions a new algorithm to optimize the co-ordination between two samples without using linear programming has been proposed. The algorithm is based on the iterative proportional fitting (IPE) procedure. Theoretical complexity is substantially lower than for transportation problem approach, because more than five iterations of IPF procedure are not required in practice.

19 tables, 26 ref

019533   Marchand E (Departement De Mathematiques Sherbrooke, Univ of New Brunswick and Universite de Sherbrooke, QC J1K 2R1, Canada, Email: eric.marchand@usherbrooke.ca) : Minimax estimation of a constrained binomial proportion p when <157>p - 1/2<157> is small. Sankhya 2005, 67(3), 526-37.

The problem of estimating the parameter p of a Binomial (n,p) distribution when p lies in the symmetric interval about 1/2 of the form [a, 1 - a]. with a ∈ (0, 1/2) has been considered. For a class of loss functions, which includes the important cases of squared error and information-normalized losses, conditions are investigated for which the Bayes estimator, δ BU, with respect to a symmetric prior concentrated on the end points of the parameter space is minimax. The conditions are of the form 1 - 2a ≤ c(n) with c(n) = O (n^-1/2), and various analytical evaluations, lower and upper bounds, and numerical evaluations are given for c(n). For instance, the simple condition 1 - 2a ≤ 1/√2n guarantees, for all n ≥ 1, the minimaxity of BU under both squared error and information-normalized losses.

1 illus, 17 ref

019532   Mamta Rani;Vinod Kumar (Computer Sci Dep, Gurukula Kangri Univ, Hardwar-249 404, Email: vedicmri@sancharnet.in) : New experiment with the logistic function. J Indian Acad Math 2005, 27(1), 143-56.

Remarkably benign looking logistic transformations x_n+1=rx_n (1-x_n) for chosing x₀ between 0 and 1 and 0 <60> r ≤ 4 have found a celebrated place in chaos, fractals and discrete dynamics. The purpose of the study is to introduce the Mann interative procedure in the dynamics of logistic function. the numerical analysis, mainly experimental, embodied in the paper shows that many beautiful properties of the logistic function are extendable to a value of r as large as 21 and possibly beyond. This is a new beginning in the chaotic dynamic of the logistic function. The new algorithm based on the Mann iterations to implement the computer program extends and unifies the existing algorithm based on the function interations. Several figures are given to depict the dynamics of the Mann orbit.

5 illus, 6 tables, 17 ref

019531   Li R;Marron J S (Statist Dep, Pennsylvania St Univ, University Park, PA 16802-2111, USA, Email: rli@stat.psu.edu) : Local likelihood SiZer map. Sankhya 2005, 67(3), 476-98.

The SiZer Map, proposed by Chaudhuri and Marron (1999), is a statistical tool for finding which features in moisy data are strong enough to be distinguished from background noise. The local likelihood SiZer map is proposed. Some simulation examples illustrate that the newly proposed SiZer map is more efficient in distinguishing features than the original one, because of the inferential advantage of the local likelihood approach. Some computational problems are addressed, with the result that the computational cost in constructing the local likelihood SiZer map is close to that of the original one.

10 illus, 1 table, 23 ref

019530   Kubokawa T (Fac of Economics, Univ of Tokyo, 7-3-1, Hongo, Bunkyo-ku Tokyo 113-0033, Japan, Email: tatsuya@e.u-tokyo.ac.jp) : Estimation of a mean of a normal distribution with a bounded coefficient of variation. Sankhya 2005, 67(3), 499-525.

The estimation of a mean of a normal distribution with an unknown variance is addressed under the restriction that the coefficient of variation is within a bounded interval. Constructs a class of estimators improving upon the best location-scale equivariant estimator of the mean. It is demonstrated that the class includes three typical estimators: the generalized Bayes estimator based on the uniform prior over the restricted region, the generalized Bayes estimator based on the prior putting mass on the boundary, and a truncated estimator. The non-minimaxity of the best location-scale equivariant estimator is shown in the general location-scale family. When another type of restriction is considered, however, there is a different story that the best location-scale equivariant estimator remains minimax.

5 illus, 15 ref

019529   Krishna D V;Narasimha Rao P (Math Dep, S K Univerity, Anantapur-515 003) : Finite element analysis of viscous flow through a porous medium in a triangular duct. Bull pure appl Sci-Sect E 2005, 24(1), 1-16.

Galerkin finite element method is used to discuss the steady flow of an incompressible viscous fluid through a porous medium in a triangular duct, using triangular elements. The flow primarily takes place under a uniform pressure gradient. The velocities are evaluated at different levels for variations in the governing parameters.

13 illus, 15 ref

019528   Khalsa L;Jumale J K;Thengane K D (Math Dep, Mahatma Gandhi Coll, Armori, Dist. Chandrapur) : Solutions of field equations R_ij = 0 for [ 1/√2 (y + z) - t] - type and [t √2/(y + z] -type waves in six dimensional space-time. J Indian Acad Math 2005, 27(1), 109-21.

Investigating six dimensional plane symmetric space-time, plane wave solutions of field equations, R_ij = 0 for [1/√2 (y + z) -1]-type and [ t√2/(y + z)] -type plane waves are obtained as P = (3m⁼/2m) - [(3m^-2)/4m²] - (3mB^-/2mB + B⁼/2B - (3B^-2/4B² = 0. Furthermore, an equivalent plane wave solutions are obtained by using the concept of curvature tensor and Ricci tensor for the same space-time.

6 ref

019527   Khadekar G S;Patki V (Math Dep, Nagpur Univ, Mahatma Jyotiba Phule Campus, Amravati Road, Nagpur-440 010, Email: gkhadekar@yahoo.com) : De-sitter type of cosmological model in n-dimensional space-time-mass theory of gravitation. J Indian Acad Math 2005, 27(1), 123-7.

An exact homogeneous, spatially isotropic cosmological solution are obtained in a matter free space with or without cosmological constant for a n-dimensional Kaluza Klein type of metric in the rest varying theory of gravitation proposed by Wesson. Some comments are given on the solution.

4 ref

019526   Kantawala P S (Appl Math Dep Fac of Technol and Engieering, M.S. Engng Coll, Vadodara-390 001) : On strong Norlund summability of orthonormal series. J Indian Acad Math 2005, 27(1), 53-62.

Sunouchi has discussed the strong (C, α)-summability of orthonormal series ∑^∞_n=0c_n<102>_n (x) under the conditions ∑^∞_n=0 c²_n <60> ∞ and (C, 1) summability of orthonormal series. Also obtained the very (C. α)-summability of orthonormal series under the condition ∑ c²_n (log log n)² <60> ∞. The author attempts to generalise these results under similar conditions for strong Norlund summability and very strong Norlund summability of orthonormal series.

9 ref

019525   Kalita B (Computer Applic Dep, Assam Engng Coll, Guwahati-781 013) : A new set of non-planar graphs. Bull pure appl Sci-Sect E 2005, 24(1), 29-38.

A new set of non-planer graphs have been developed from the TEEP graph H₁ (2m+2, 6m) for m ≥ 2. Some theoretical investigations relating to the existence of edge - disjoint Hamiltonian circuit, maximal clique, crossing number and isomorphic properties of the graphs of the set have been studied. The application of the members/elements of the set have been cited taking one general problem for better communication network.

5 illus, 23 ref

019524   Kadhao S R;Thengane K D (NO, , Dnyanesh Mahavidyalaya, Nawargaon-441 223) : Plane wave solutions of field equations R_ij + 0 in V₄ with two time axes. Bull pure appl Sci-Sect E 2005, 24(1), 63-7.

The plane wave solutions of the field equations R_ij = 0 in four dimensional space-times V₄ having two time axes for general relativeity are given by G_ij satisfying ρ₁ = g^-_li wⁱ = 0 and Nρ_αβ + Mσ_{αβ = 0, α, β = 2,3,4.}

1 ref

019523   Joshi D C;Doctor H D (Math Dep, South Guj Univ, Surat-395 007) : Numerical solution of boundary layer equation through quintic B-spline collocation. J Indian Acad Math 2005, 27(1), 1-16.

A collocation method has been introduced using a quintic B-spline to solve the third order linear boudnary value problem (BVP). The method is illustrated by solving a boundary layer equation, which involves a non-linear BVP of third order. Particularly, a well-known Falkner-Skan (F-S) problem with mass transfer taking place at the boundary is studied. The nonlinearity of the BVP is tackled by Quasilinearisation technique. Numerical results are obtained for different values of affecting parameters in the form of velocity profile and skin frictions. The results are compared with those values available in the literature. Comparison proves the reliability of the method. It is observed that the velocity and skin friction for the fluid vary directly with the wedge angle, and mass transfer parameter.

2 illus, 6 tables, 18 ref

019522   Jamwal D S;Ahmed S;Ashwani Kumar (Math Dep, Univ of Jammu, Jammu-180 006) : Group topology and finitistic spaces. Bull pure appl Sci-Sect E 2005, 24(1), 123-32.

The concept of Group Topology has been introduced and it's many properties have been discussed. With the help of this topology, many examples and counter examples can be constructed in General Topology. The paper has been divided into six sections just to arrange and study many properties of this topology systematically. All the results about this topology which are known have been stated but proofs have been given of only those results which are nontrivial,

7 ref

019521   Gupta N K;Abbas H;Hosseini M (Appl Maechanics Dep, Indian institute of Technol Delhi, Hauz Khas, New Delhi-110 016, Email: nkgupta@am.bitd.ernet.in) : Axi-symmetric crushing of thin walled frusta and tubes. Proc Indian Natn Sci Acad 2006, 72(1), 49-54.

An analytical straight fold model with partly inside and partly outside folding in axi-symmetric crushing of thin metallic frusta has been presented. Existing total outside fold model of a frusta and partly inside and partly outside fold models as well as total outside or total inside fold models of a tube can be derived from the present model. The relations for obtaining the inside and outside fold legnths in the case of tubes are derived. The difference in the values of yield stress of the material in compression and tension has been incorporated in the analysis. Variation of circumferential strain during the formation of a fold has been taken into account. The mean and the variation of crushing load have been computed. The results have been compared with experiments and good agreement has been observed. The results are of help in understanding the phenomenon of actual fold formation.

3 illus, 13 ref

019520   Gupta M K;Singh R P (Math Dep, Ch. Charan Singh Univ, Meerut-250 005, Email: mkguprta2002@hotmail.com) : On some generalizations of continuous functions in fuzzy bitopological spaces. Bull pure appl Sci-Sect E 2005, 24(1), 133-43.

The concepts of generalized fuzzy pairwise closed, generalized fuzzy pairwise α-closed and fuzzy pairwise α-generalizede closed sets in fuzzy bitopological spaces are introduced. Also the implications that exist between them have been studied. Also various generalizations of fuzzy pairwie continuous functions have been investigated.

5 ref

019519   Gopalan M A;Somanath M;Vanitha N (Math Dep, Natn Coll, Trichy) : Triple coincidence among R₂ numbers. Proc Natn Acad Sci India-Sect A 2005, 75(3), 199-200.

An elegant formulation to construct triple coincidence among R₂ numbers is presented together with generation of quadruple coincidences.

2 ref

019518   Gopalan M A;Devibala S (Math Dep, Natn Coll, Trichy) : On ternary quadratic homogeneous equation (x-y)(x-z) + y<. Bull pure appl Sci-Sect E 2005, 24(1), 25-28.

The ternary quadratic homogeneous diophantine equation of the form (x-y)(x-z) + y² = 0 is analyzed for its integral solutions at different angles and thier parametric representations are obtained. Given an integral solution, a process to generate a sequence of solutions is presented. Integral solutions of some higher degree equations are deduced.

1 table, 7 ref

019517   Gogulwar V S;Desmukh K C (Math Dep, Rajeev Gandhi Coll of Engng Res and Technol, Chandrapur-442 403, Email: rcert_maths@yahoo.co.in) : Thermal stresses in a thin circular plate with heat sources. J Indian Acad Math 2005, 27(1), 129-41.

A thin circular plate is considered and the thermal stresses due to partially distributed and axially symmetric heat supply on the outer curved surface are discussed with the help of integral transform technique. The results are obtained in the form of infinite series in terms of Bessel's functions and are illustrated numerically.

5 illus, 7 ref

019516   Gani A N;Rita W (PG and Res Math Dep, Jamal Mohamed Coll, Tiruchirappalli-620 020) : Analysis fuzzy queues usisng parametric programming. Bull pure appl Sci-Sect E 2005, 24(1), 17-23.

The paper tries to combine the ability of fuzzy set to represent more realistic situations with the well-established traditional queueing model problem. A fuzzification of M/M/1 queueing system with the capacity of the system is proposed. Limited to k and the calling population is infinite. Thus the characteristic and performance of this model is represented based on fuzzy queueing system. A pair of parametric propgrams is formulated to describe that of crisp queues via which the membership functions of the performance measures are derived. Fuzzy queues are much more realistic than the commonly used crisp queues in many prectical situations. A simple numerical example is also presented.

5 ref

019515   Eroglu A;Yilmaz S (Math Dep Fac of Sci, Gaziosmanpasa Univ, Tokat, Turkey) : The relation between (N,p,q) and (N<. Bull pure appl Sci-Sect E 2005, 24(1), 159-66.

The relation between the Riesz transformation (N^-, p) and the generalized Norlund transformation (N, p, q) have been established.

5 ref

019514   El Shafei (Math Dep Fac of Sci, Helwan Univ, Ain Helwan, Cairo, Egypt) : Pareto-minimal solutions for large scale continuous static games (LSCSG). Opsearch 2005, 42(3), 228-37.

Presents a new problem formulation of special class of large scale continuous static games (LSCSC) and how to solve this problem by using the concept of pareto- minimal solutions. A method to solve (LSCSG) is presented have been presented. A. numerical example is given to clarify this method.

1 table, 7 ref

019513   Dummigan N (Pure Math Dep, Univ of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, U.K., Email: n.p. dummigan@shef.ac.uk) : Values of a hilbert modular symmetric square L-function and the bloch-kato conjecture. J Ramanujan Mathl Soc 2005, 20(3), 167-87.

Let F be a totally real field, of narrow class number one and odd degree over Q, and let ƒ be a Hilbert modular eigenform over F, cuspidal and of level one and scalar weight k such that k/2 is odd. Analogy with earlier calculations in the case F = Q leads us to expect large primes dividing ξF (1-k) to appear in a certain critical valaue of the symmetric square L-function. This is verified by direct computation in what appears to be the only tractable example such that F ≠ Q, namely F is the totally real cubic field of discriminant 49, and ƒ is of weight six. Attempt an explanation via the Bloch-kato conjecture on special values of L-functions, and a contruction of elements in a generalised Shafarevich-Tate group.

32 ref

019512   Dahiya K;Verma V (Cent for Advd Stud in Math, Panjab Univ, Chandigarh-160 014) : Ranking in Integer programming with bounded variables. Opsearch 2005, 42(3), 252-79.

An algorithm is developed which ranks the feasibel solutions of an integer linear and linear fractional programming problems with bounded variables in decreasing order of objective values. Numerical illustration is also included.

8 ref

019511   Choudhury R;Das A (Math Dep, Gauhati Univ, Guwahati-781 014) : Elastico-viscous flow between eccentric disks rotating about different axes at different speeds. Bull pure appl Sci-Sect E 2005, 24(1), 107-15.

The flow of a visco-elastic fluid contained between two infinite disks that are rotating with different angular velocities about different axes of rotation is considered. The solution is obtained by expanding the velocity components in terms of a suitable small parameter when the inertia effects are also assumed to be small. The force on one of the disks has been calculated and it is observed that the two component of the force can be used to determine the visco-elastic parameter of the fluid.

4 illus, 16 ref

019510   Chirde V R;Metkar A M;Deshmukh A G (NO, , ) : Plane gravitational waves g_ij(Z) of the Einstein's field equation for Z = (x+y+z)/√3 - t. Bull pure appl Sci-Sect E 2005, 24(1), 217-20.

It is investigated that g_ij(Z), where Z = (x+y+z)/√3 - t be the solution of the field equation P ≡ Cu/3m - Cv/n = 0 : obtained by using curvature and Ricci tensor, where i, j = 1, 2, 3, 4. m=(1/9) (EC+C²):n=-(1/3)(EC+C²), u = (E^dd-C^dd)/18 - C(E^d-C^d)²)/324m - (C^dE^d-C^d2)/18C and v = E^dd+C^dd/18 + C(E^d+C^d)²)/180m + (CE^-+C^d2)/18C d denote derivative with respect to Z. Further more it is shown that the above field equation is equivalent to the field equation obtained by Chirde et al.

4 ref

019509   Cheng F (Math Dep, Illinois St Univ, Normal, IL 61790-4520, USA, Email: fchen@ilstu.edu) : Asymptotic distributions of error density estimators in first-order autoregressive models. Sankhya 2005, 67(3), 553-67.

Considers the asymptotic distributions of the error density estimators in first-order autoregressive models. At a fixed point, the distribution of the error density estimator is shown to be normal. Globally, the asymptotic distribution of the maximum of a suitably normalized deviation of the density estimator from the expectation of the kernel error density (based on the true error) is the same as in the case of the one sample set up, which is given in Bickel and Rosenblatt (1973).

17 ref