011228   Varma S K;Sharma T C (Mathematics Dep, Govt. Science P.G. College, Bilaspur-495 001) : On hyperbolic measure of entropy. Acta Cienc Indica-Math 2004, 30(2), 393-6.

Some properties of measure of hyperbolic entropy introduced by Kapur Are studied. Its directed divergence measure of inaccuracy, normalised measure of entropy etc. are discussed in detail.

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011227   Varadhan S R S (Dep of Mathematics, Courant Institute of Mathematical Sciences, New York University, NY-10012, USA, Email: varadhan@cims.nyu.edu) : Random walks in a random environment*. Proc Indian Acad Sci-Mathl Sci 2004, 114(4), 309-18.

Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the 'quenched' and the 'averaged' case.

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011226   Thiyagarajan M;Sairam N (NO, School of Humanities & Sciences, Sastra Deemed University, Tirumalaisamudram, Thanjavur-613 402) : Power of foldr in functional programming. Acta Cienc Indica-Math 2004, 30(2), 387-92.

In functional programming, fold family allows one to write functions that capture a common pattern of computation. The universal property of fold has been discussed as proof principle, as rules far program odptimization and the necessary and sufficient conditions for a function to be fold.

1 table, 9 ref

011225   Tada T;Saitoh S (NO, , ) : A method by transforms of variables for the first order nonlinear ordinary differential equations. Far East J mathl Sci 2004, 14(3), 393-403.

It has been shown that there exist many kinds of nonlinear ordinary differential equations of the first order with variable coefficients that can be solved analytically, by variable transforms and by reducing the equations to separated forms of the variables.

3 ref

011224   Sudo T (Dep of Mathematics, Faculty of Science, University of the Ryukyus, Nishihara, Okinawa 903-0213, Japan, Email: sudo@math.u-ryukyu.ac.jp) : A topological rank for c* -algebras. Far East J mathl Sci 2004, 15(1), 71-86.

A topological rank theory for C* -algebras has been studied. From required axioms, a notion of topological rank for C* -algebras has been considered.

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011223   Srivastava M;Ghosh S C (Mathematics Dep, D.A.V. College, Kanpur) : Some properties on fixed point theorem in metric spaces. Acta Cienc Indica-Math 2004, 30(2), 317-24.

Some properties on fixed point theorem in metric space with more than one function have been studied.

9 ref

011222   Sreenadh S;Ramana Murthy M V;Prasad C N; Ismail S (Mathematics Dep, S.V. University, Tirupati) : Peristaltic transport of a conducting fluid in a channel with permeable walls. Acta Cienc Indica-Math 2004, 30(2), 349-54.

Peristaltic transport of a conducting viscous fluid in a channel bounded by permeable walls is studied under long wavelength and low Reynolds number assumptions. The expressions for the pressure rise (drop) over one cycle of the wave and the mechanical efficiency of pumping are obtained, It is found that the pressure difference increases with the increment in Hartmann number M and it decreases with the increase in the permeability parameter for a given flux.

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011221   Sreedhara Rao G;Ramakrishna S;Krishna D V (Mathematics Dep, Sri Venkateswara University, Tirupati) : Flow of immiscible fluids through a channel bounded by porous beds. Acta Cienc Indica-Math 2004, 30(2), 359-74.

An adjacent flow of two immiscible fluids between porous beds is investigated using finite element method. The finite element solution is obtained at an arbitrary cross section using linear and quadratic polynomial approximations. The velocity, shear stress and the mass flow rate are evaluated and their behaviour is disccussed for different values of the governing parameters.

28 illus, 2 tables, 18 ref

011220   Shrivastava P K (Mathematics Dep, Govt. Model Science College, Rewa-486 001) : On the limit of aλ mean of Legendre series. Acta Cienc Indica-Math 2004, 30(2), 383-6.

Borwein introduced an Abel type (A_λ) summability of an infinite series. Huzoor, H. Khan has given necessary and sufficient conditions regarding (A_λ) summability of Fourier series of a 2π-periodic function. A result related to (A_λ) mean, of Legendre series has been given.

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011219   Shrivastava P K (Mathematics Dep, Govt. Medical Science College, Rewa-486 001) : Degree of approximation of functions by Legendre polynomials. Acta Cienc Indica-Math 2004, 30(2), 255-60.

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011218   Sheu T S;Liu P C;Chen J W (NO, , ) : Globally uniformly bounded stability of uncertain nonlinear dynamical systems described by differential inclusions. Far East J mathl Sci 2004, 15(1), 113-28.

The globally uniformly bounded stability of an uncertain nonlinear dynamical system described by differential inclusions is studied. The goal is to construct a feedback control such that all trajectories of the system are globally uniformly bounded stable with an exponential convergence rate to zero after a finite time T. An estimate of the time T of all trajectories attaining zero is given. An illustrative example has been provided to demonstrate the use of the main results.

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011217   Sharma V (Mathematics Dep, N.A.S. (P.G.), College, Meerut, Uttar Pradesh) : Availability analysis of a two-unit standby system with delayed replacement under perfect switching. Acta Cienc Indica-Math 2004, 30(2), 249-54.

Study has been made of system availability consisting of two identical cold standby units with constant failure rates. Initially, one unit is operative while other remains as standby. Each of the units of the system has three modes, i.e., normal, degraded and total failure. The system fails when both the units fail totally and may also fail due to common cause failure. The time taken in replacement of a failed unit by a standby unit is not negligible but is a random variable.

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011216   Sahleh H (Dep of Mathematics, Guilan University, P.O. Box 1914, Rast, Iran, Email: sahleh@cd.gu.ac.ir) : A covering of topological groups and the Schur multiplier. Far East J mathl Sci 2004, 14(3), 325-32.

For topological groups A, B, a covering of the direct product A x B via has been constructed ??? the 2nd nilpotent product. In particular, it has been shows that the 2nd nilpotent of two topological groups can be represented as an exact sequence whose kernel is isomorphic to the direct product of A ⊗ B and the Schur multipliers M(A), M(B).

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011215   Rathore C J;Srivastava U K (Mathematics Dep, Government Girls P.G. College, Bilaspur-495 001) : On degree of approximation of functions in the holder metric. Acta Cienc Indica-Math 2004, 30(2), 375-82.

The degree of approximation in the Holder metric by (f, dn) mean has been studied.

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011214   Rathod V P;Sheeba Rani I;Tanveer S;Rajput G G (Studies and Research in Mathematics Dep, Gulbarga University, Gulbarga-585 106) : Steady blood flow with periodic body acceleration. Acta Cienc Indica-Math 2004, 30(2), 405-10.

In normal life the human body is quite often subjected to acceleration. Prolonged exposure to such accelerations can generate significant effects on the blood circulation and its rheological behaviour depending on the configuration and geometry of the blood vessels. A mathematical model for steady blood flow subjected to externally imposed periodic body acceleration has been given. With the help of finite Hankel transforms, an exact solution for the steady flow of blood as an incompressible, couple stress fluid has been obtained. The distributions of velocities are portrayed graphically. The results have been compared with other existing models. Finally, some biological applications of this theory have been briefly discussed.

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011213   Ramakrishna Prasad A;Rao K L N (Mathematics Dep, JNTU College of Engg., Hyderabad-500 072) : Neural network for the availability analysis of series-parallel systems. Acta Cienc Indica-Math 2004, 30(2), 343-8.

Artificial neural networks can achieve high computation rates by employing a massive number of simple processing elements with a high degree of connectivity between the elements. Neural networks with feedback connections provide a computing model capable of exploiting finegrained parallelism to solve a rich class of complex problems. Network parameters are explicitly computed, based upon problem specifications, to cause the networks to converge to an equilibrium that represents a solution. Mahmoud and Suliman have introduced Neural Network approach to the reliability analysis. A systematic approach to the availability analysis of a three unit series parallel system with repair is used to illustrate the Neural Network approach. The discrete-time Markov model of Series-Parallel system is realized using Feed-Forward recursive neural network, The energy junction and update equations for the weignts of the neural network are established. The failure rate and repair rate, satisfying the desired availability, are extracted from the neural weights at convergence. The obtained results are verified with the continuous-time solutions of the markove model and digital simulation.

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011212   Rajput U S;Varshney N K;Rajput D (Mathematics Dep, S.V. College, Aligarh, U.P.) : Thermal-diffusion and transpiration effects on MHD free convection flow of viscous stratified fluid past a vertical moving plate. Acta Cienc Indica-Math 2004, 30(2), 233-40.

An unsteady free convection MHD flow of a viscous stratified fluid past a vertical moving plate in the rotating system with mass transfer, depending on vertical co-ordiante has been considered. The effects of thermal diffusion and transpiration have been observed. Analytical solutions for the velocity, temperatrue and concentration fields are obtained. The effects of various parameters (e.g., Magnetic parameter (M), Schimdt number (Sc), Soret effect (S₀), Grashof number (Gr), modified Grashof number (Gm) and stratification parameter (b)) on the velocity fields and skin-friction components have been discussed with the help of graphs and tables.

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011211   Rajput A;Malhotra S K;Shrivastava R (Mathematics Dep, Sadhu Vaswani College, Sant Hirdaram Nagar, Bhopal-462 030) : A fixed point theorem for a multivalued non-self mapping. Acta Cienc Indica-Math 2004, 30(2), 485-7.

A fixed point theorem for a multivalued non-self mapping in a metrically convex complete metric space has been proved.

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011210   Rajeswara Rao U;Sivaprasad R;Prasada Rao D R V (Mathematics Dep, S.K. University, Ananatapur) : Combined free and forced MHD convection flow in a wavy channel. Acta Cienc Indica-Math 2004, 30(2), 299-310.

An attempt has been made to analyse the effect of heat sources on the free convective flow of an incompressible, viscous, electrically conducting fluid confined between two horizontal wavy walls. The non-linear equations governing the fluid flow and heat transfer have been solved subject to the relevant boundary conditions by assuming that the solution consists of two parts, a mean solution and perturbed solution. To obtain perturbed part of the solution use has been made of the long wave approximation. The mean part corresponds to the fully developed flow and the perturbed part arises from the waviness of the wall. These mean and the perturbed solutions are evaluated and their behaviour is discussed numerically for variations in the governing parameters.

8 illus, 4 tables, 21 ref

011209   Rajamani M;Inthumathi V (Post Graduate Department of Mathematics, NGM College (Autonomous), Pollachi-642 001) : On sp-normal spaces and some functions. Acta Cienc Indica-Math 2004, 30(2), 261-70.

The concept of sp-normality which is weaker than s-normality has been introduced. It is shown that sp-normality is a topological property. Some characterization of sp-normal spaces are obtained. Some functions preserving sp-normality are also investigated.

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011208   Raghunathan M S (NO, School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai-400 005, Email: msr@math.tifr.res.in) : The congruence subgroup problem*. Proc Indian Acad Sci-Mathl Sci 2004, 114(4), 299-308.

This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.

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011207   Parthasarathy K R (NO, Indian Statistical Institute, Delhi Centre, 7, S.J.S. Sansanwal Marg, New Delhi-110 016, Email: krp@isid.ac.in) : On the maximal dimension of a completely entangled subspace for finite level quantum systems. Proc Indian Acad Sci-Mathl Sci 2004, 114(4), 365-74.

Let <72>_i be a finite dimensional complex Hilbert space of dimension d_i associated with a finite level quantum system A_i for i = 1, 2, ..., k. A subspace S ⊂ <72> = <72>_A1A2...Ak = <72>₁ ⊗ <72>₂ ⊗ . . . ⊗ <72>_k is said to be completely entangled if it has no non-zero product vector of the form u₁ ⊗ u₂ ⊗ . . . ⊗ u_k with u_i in <72>_i for each i. Using the methods of elementary linear algebra and the intersection theorem for projective varieties in basic algebraic geometry, it has been proved that max dim S = d₁d₂ ... d_k - (d₁ + ... + d_k) + k - 1, where ε is the collection of all completely entangled subspaces. When <72>₁ = <72>₂ and k = 2 an explicit orthonormal basis of a maximal completely entangled subspace of <72>₁ ⊗ <72>₂ is given. A more delicate notion of a perfectly entangled subspace for a multipartite quantum system has been introduced and, an example using the theory of stabilizer quantum codes has been constructed and a problem has been posed.

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011206   Paramasamy K (NO, Chennai Mathematical Institute, Chennai-600 017, Email: paramas@cmi.ac.in) : Cohomology of line bundles on Schubert varieties: The rank two case. Proc Indian Acad Sci-Mathl Sci 2004, 114(4), 345-63.

Vanishing and non-vanishing of cohomology of 'most' line bundles have been described over Schubert subvarieties of flag varieties for rank 2 semisimple algebraic groups.

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011205   Pagey S S;Vyas U (NO, Institute for excellence in higher education, Kaliysot Dam, Kolar Road, Bhopal-462 016) : Set valued mapping on metric space. Acta Cienc Indica-Math 2004, 30(2), 481-3.

A mapping F of a complete metric space (X, d) into the class B (X) of non empty and bounded subsets of X has been considered.

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011204   Navada K G (Dep of Mathematics, University College, Mangalore University, Hampanakatta-575 001, Email: gnavada@yahoo.com) : Some remarks on good sets. Proc Indian Acad Sci-Mathl Sci 2004, 114(4), 389-97.

It is shown that if a good set has finitely many related components, then they are full, loops correspond one-to-one to extreme points of a convex set. Some other properties of good sets are discussed.

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011203   Manhas J S (Dep of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, P.C. 123 Al-Khodm Sultanate of Oman, Email: manhas@squ.edu.om) : Non-singular and singular operators in the locally convex framework. Far East J mathl Sci 2004, 15(1), 21-40.

Let CL(E, F) be the locally convex algebra of continuous linear operators from the locally convex Hausdorff space E to the locally convex Hausdorff space F and let Fa(X, E)(F_*(X, E)) be the locally convex spaces of functions from the bornological space X into E, where a ∈ {1, 2, ∞} and * ∈ {00, 0, c}. Then using the generalized concepts of bounded below operators, open and almost open operators and topological divisors of zero on general locally convex spaces and locally convex algebras, an attempt is made to establish a study of these non-singular and singular operators on the spaces CL(E, F) and Fa(X, E)(F*(X, E)) generalizing the results of Harte and Wilansky proved for normed linear spaces.

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011202   Mahmood R M S (College of Education and Basic Science, Ajman University of Science and Technology Abu Dhabi, United Arab Emirates, Email: rasheedmsm@yahoo.com) : On bounded subgroups of quasi HNN Groups. Far East J mathl Sci 2004, 14(3), 371-84.

It has been shown that if G is a group acting on a tree X with inversions such that G has a bounded tree of representatives and G does not fix any element of X, and if H is a bounded subgroup of G (there is a bound on the lengths of the elements of H), then H is not in any vertex stabilizer of G if H contains an element which transfers an edge of X into its inverse, otherwise H is in a vertex stabilizer of G. Such results has been applied to a new class of groups called quasi HNN groups.

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011201   Li J;Shen J (Dep of Mathematics, Hunan Normal University, Changsha, Hunan-410 081, People's Republic of China) : Periodic boundary value problems for impulsive differential-difference equations. Indian J pure appl Math 2004, 35(11), 1265-77.

By means of comparison principle and monotone iterative techniques, a new theorem about the existence of solutions for impulsive differential-difference equations has been obtained.

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011200   Leelaratnam A;Sarojamma G;Neeraja G (Mathematics Dep, Sri Padmavathi Mahila Visva Vidyalayam, Tirupati) : Transient convection flow through a porous medium in a horizontal channel with prescribed discharge. Acta Cienc Indica-Math 2004, 30(2), 441-57.

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011199   Lansky J;Raghuram A (Dep of Mathematics, American University, Washington DC-20910, USA, Email: lansky@american.edu ) : Conductors and newforms for U(1,1). Proc Indian Acad Sci-Mathl Sci 2004, 114(4), 319-43.

Let F be a non-Archimedean local field whose residue characteristic is odd. A theory of newforms for U(1, 1)(F) has been developed, building on previous work on SL₂(F). This theory is analogous to the results of Casselman for GL₂(F) and Jacquet, Piatetski-Shapiro, and Shalika for GL_n(F). To a representation π of U(1, 1)(F), an integer C(π) called the conductor of π has been attached, which depends only on the L-packet Π containing π. A newform is a vector in π which is essentially fixed by a congruence subgroup of level c(π). It has been shown that the newforms are always test vectors for some standard Whittaker functionals, and, in doing so, various explicit formulae for newforms have been given.

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011198   Kwon Y I (Dep of Mathematics Education, Gyeongsang National University Jinju-660 701, Korea, Email: yikwon@nongae.gsnu.ac.kr) : On minimal quasi-ideal elements in poe-Γ-semigroups. Far East J mathl Sci 2004, 14(3), 385-92.

Two basic theorems which characterize the minimal quasi-ideal element has been given and it has been shown that the minimal quasi-ideal element is the intersection of a minimal right and a minimal left ideal element.

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011197   Krishna D V;Sivaprasad R;Rajeswara Rao U (Mathematics Dep, S.K. University, Anantapur-515 003) : MHD convection in a cylinder maintained at non-uniform temperature. Acta Cienc Indica-Math 2004, 30(2), 429-39.

Free and forced convection flow in a vertical circular cylinder maintained at non-uniform temperature under magnetic field has been analysed. The axial dependence of the flow variables has been taken in accordance to the prescribed non-uniform temperature on the boundary (ii) the analysis is valid for all finite values of the parameters governing the flow viz. the Reynolds number, the Grashoff number and the Peclet number. The governing non-linear equations are reduced to a single equations in terms of the Stoke's stream function, on eliminating pressure and using the equation of continuity. The temperature on the boundary is assumed to vary slowly in the axial direction with slope δ(<<1). The streamlines, the isothermal lines, the velocity and temperature profiles are plotted for different sets of the governing non-dimensional parameters and their behaviour is discussed in detail.

8 illus, 3 tables, 9 ref

011196   Kim S Y;Kwun Y C;Park J S (Dep of Mathematics Education, Chinju National University of Education, Jinju, 660-756, Korea, Email: sykim@cue.ac.kr;parkjs@cue.ac.kr) : Complete t-controllability of nonlinear delay parabolic equations under boundary control. Far East J mathl Sci 2004, 15(1), 53-69.

The complete T-controllability conditions of nonlinear delay parabolic equations have been found under boundary control by using Nussbaum's fixed point theory.

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011195   Kim B J (Dep of Mathematics, Daejin University, Pocheon, 487-711, Korea, Email: bjkim@daejin.ac.kr) : Integral transforms and convolution products of functionals involving double integrals. Far East J mathl Sci 2004, 15(1), 9-20.

The integral transform and the convolution product for a class of functionals of the form F(y) = exp{???^T₀ ???^T₀ f(s, t, y(s), y(t))dsdt} defined on K[0, T], the space of comolex-valued continuous functions on [0, T] which vanish at zero have been developed. It has then been shown that the transform of the convolution product is a product of the integral transforms.

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011194   Khairnar S M (Mathematics Dep, Anuradha College of Engineering, Chikhli-443 201) : A class of convex functions in the unit disk. Acta Cienc Indica-Math 2004, 30(2), 311-6.

Deals with a new class; J(α, β); where α ∈ [0, 1]; β ∈ (1+2α)/4, β) of functions f(z) = z + a₂z² + a₃z³ + ... which are holomorphic in the unit disk E = {z; |x| <60> 1} and also investigated various properties of the class J(α, β).

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011193   Khabazian H (Dep of Mathematical Sciences, Isfahan University of Technology Isfahan-84154, Iran, , Email: khabaz@cc.iut.ac.ir) : Uniquely decomposition of a ring into the product of certain rings. Far East J mathl Sci 2004, 15(1), 41-51.

The conditions under which a ring can be decomposed uniquely into certain rings have been considered.

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011192   Kasuga T;Sakai R (Dep of Mathematics, Kumamoto National College of Technology, Nishigohshi-machi, Kikuchi-gun, Kumamoto 861-1102, Japan, Email: qq6k6yv9@sage.ocn.ne.jp) : Orthonormal polynomials for Laguerre-type weights. Far East J mathl Sci 2004, 15(1), 95-105.

Orthonormal polynomials {p_n(W²_rR; x)}^∞_n=0 with Laguerre-type weights W²_rR(x) = x^2r exp(- 2R(x)) on R⁺ = [0, ∞), where the continuous function R(x) satisfies some conditions have been studied. Some interesting properties of p_n(W²_rR; x) have been obtained.

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011191   Jung S D;Kang D S (Dep of Mathematics, Cheju National University Jeju 690-756, Korea, Email: sdjung@cheju.ac.kr) : Eigenvalues of the basic Dirac operator and transversal twistor operator on Riemannian foliations. Far East J mathl Sci 2004, 14(3), 361-9.

The transversal twister operator has been introduces to get lower bound for the eigenvalues of the basic Dirac operator on a Riemannian foliation. Also the limiting case has been studying.

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011190   Ikawa O (Dep of General Education, Fukushima National College of Technology Iwaki, Fukushima, 970-8034, Japan, Email: ikawa@fukushima-nct.ac.jp) : Motion of charged particles in Bomogeneous Kahler and homogeneous Sasakian manifolds. Far East J mathl Sci 2004, 14(3), 283-302.

The motion of charged particles has been studied homogeneous Kahler manifolds with certain conditions and also in homogeneous Sasakian manifolds. By using a law of conservation proved it has been proved that if the motion intersects itself, then it is simply closed.

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011189   Han Z Q (Dep of Applied Mathematics, Dalian University of Technology, Dalian-116 023, Liaoning, People's Republic of China, Email: hanzhiq@dlut.edu.cn) : Fixed point index and solutions of differential equations in Banach spaces. Indian J pure appl Math 2004, 35(11), 1255-64.

In reflexive Banach spaces by constructing homotopies, Present a formula has been presented for the computation of the fixed point index for completely continuous operators by the solutions of the corresponding ordinary differential equations. The formula is then used to obtain fixed points for completely continuous operators defined on cones.

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011188   Gupta P P;Sharma D (Mathematics Dep, K.N. Modi Engineering College, Modinagar, Ghaziabad) : Reliability forecast under pre-emptive repeat resume repair policy. Acta Cienc Indica-Math 2004, 30(2), 475-9.

The analytical behaviour of a complex system which consisting of two subsystems namely A and B has been studied. The subsystem A consisting of N-units in series and B, M-units in parallel. The system can fail completely either due to failure of one unit of A or due to environment failure and causes to work in reduced efficiency state only when any unit of subsystem B fails. Pre-emptive repeat resume repair policy is adopted for all type of repairs.

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011187   Gupta P P;Ekata (Mathematics Dep, Dr. K.N. Modi Institute of Engg. and Tech., Modinagar, Ghaziabad) : Stochastic behaviour of compound redundant system under perfect switching. Acta Cienc Indica-Math 2004, 30(2), 459-60.

A system consisting two subsystems A and B, in series is considered with a single repair factlity incorporating the concept of compound redundancy. 'Compound' means subsystem A corporating with parallel redundancy while subsystem B with standby redundancy. Failure rates follow exponential distribution while repair rates are distributed quite generally. Various reliability parameters are computed with numerical calculation with the principle of supplementary variable technique.

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011186   Gupta A (Mathematics Dep, D.N. College, Meerut) : On the robustness of M/M/1 queue system in health care planning when variations in traffic intensity are suspected. Acta Cienc Indica-Math 2004, 30(2), 397-400.

Assumption regarding constant intensity of patients in a health care planning system seems to be unduly restrictive. Representing the system by a M/M/1 : (∞, FIFO) system, the robust character of the queue characteristics of a M/M/l : (∞, FIFO) has been analysed in respect of health care planning system when the traffic intensity is treated as a random variable.

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011185   Gorgi M E;Yazdanpanah T (Dep of Mathematics, Faculty of Sciences, Semnan University, Semnan, Iran, Email: madjideg@walla.com) : Derivations into duals of ideals of Banach algebras. Proc Indian Acad Sci-Mathl Sci 2004, 114(4), 399-408.

Two notions of amenability have been introduced for a Banach algebra <65>. For a closed two-sided ideal in <65>, <65> is I-weakly amenable if the first cohomology group of <65> with coefficients in the dual space I* is zero; i.e., H¹ (<65>, I*) = {0}, and, <65> is ideally amenable if <65> is I-weakly amenable for every closed two-sided ideal I in <65>. These concepts have been related to weak amenability of Banach algebras. It has also been shown that ideal amenability is different from amenability and weak amenability. I-weak amenability of a Banach algebra <65> for some special closed two-sided ideal I has been studied.

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011184   Gopalan M A;Mythili V (Mathematics Dep, National College, Trichy-620 001) : Note on three remarkable observations. Acta Cienc Indica-Math 2004, 30(2), 241-2.

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011183   Dwivedi A P;Siddiqui S U;Chandel J;Bajpai P (Mathematics Dep, Harcourt Bulter Technological Institute, Kanpur-280 002) : Six series equations involving Jacobi polynomials of different indices. Acta Cienc Indica-Math 2004, 30(2), 243-8.

The solution of six series equations involving Jacobi polynomials of different indices, by reducing them to simultaneous Fredholm integral equations of the second kind, have been obtained.

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011182   Djillali B (Dep of Mathematics, Faculty of Sciences and Science Engineering, University of Mostaganem, B. P. 227 Mostaganem-27000, Algeria, Email: bouagadadj@yahoo.fr) : Influence of the value of discretisation step on positivity of 2D linear continuous-discrete systems. Far East J mathl Sci 2004, 15(1), 107-12.

An analysis of the influence of the value of discretisation step on posittvity of general 2D discrete-time linear system obtained by discretisation from 2D continuous-discrete linear system has been presented.

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011181   Detalla A;Horiuchi T;Ando H (Dep of Mathematical Sciences, Ibaraki University, Mito Ibaraki, 310, Japan) : Missing terms in Hardy-Sobolev inequalities and its application. Far East J mathl Sci 2004, 14(3), 333-59.

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011180   Dedania H V (Dep of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388 120, Gujarat, Email: hvdedania@yahoo.com) : On standard ideals in weighted convolution algebras on subsemigroups of IR<. Indian J pure appl Math 2004, 35(11), 1279-84.

For a unital, dense, difference, subsemigroups of the positive real line, it is a well-known problem to ask whether there exists a local weight ω on S such that the convolution of Banach algebra l¹ (S, ω) has only standard closed ideals. Thomas proved that, if the weight ω satisfies some extra condition, then every primary element of l¹ (S, ω) generates a standard closed ideal. In this article, it has been proved that, if the weight ω satisfies some mild condition, then there do exist secondary elements in l¹ (S, ω) which generate standard closed ideals.

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011179   Darus M;Hong N C (NO, , ) : The Fekete-Szego problem for strongly close-to-convex functions with Hadamard product. Far East J mathl Sci 2004, 15(1), 1-7.

For 0 <60> α ≤ 1 and β ≥ 1, let MCC(Φ, Ψ; α, β) be the class of function defined in the open unit disk U by |arg(zf'(z)/g(z))| <60> (π/2α), where g(z) = z+b₂z² + b₃z³ +... is analytic function and satisfies |arg(g(z)*Φ(z)/g(z)*Ψ(z))| <60> (π/2β), z ∈ U, for some Φ(z) = z + Σ_n=2^∞ λ_nzⁿ and Ψ(z) = z + Σ_n+2^∞ γ_nzⁿ analytic in U such that g(z) * Ψ(z) ≠ 0, λ_n ≥ 0, γ_n ≥ 0 and λ_n <62> γ_n (n ≥ 2). For f ∈ MCC(Φ, Ψ; α, β) and given by f(z) = z + a₂z² + a₃z³ +... a sharp upper bound is obtained for |a₃ - μa₂z²| when μ ≥ 1.

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