012204   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.

87 ref

012203   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.

10 ref

012202   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.

8 illus, 5 ref

012201   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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012200   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.

3 ref

012199   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.

17 ref

012198   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.

6 ref

012197   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.

17 ref

012196   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.

21 illus, 3 tables, 21 ref

012195   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.

19 ref

012194   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.

4 ref

012193   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

012192   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.

15 ref

012191   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.

9 ref

012190   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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012189   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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012188   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.

2 ref

012187   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.

11 ref

012186   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.

15 ref

012185   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.

11 ref

012184   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.

3 ref

012183   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.

4 illus, 1 table, 3 ref

012182   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.

2 tables, 5 ref

012181   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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012180   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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012179   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.

9 ref

012178   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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012177   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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012176   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.

5 ref

012175   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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012174   Choudhury D (Dep of Mathematical Sciences, Loyola College Baltimore, Maryland 21210, , U. S. A., Email: dsc@loyola.edu) : Decomposition of matrices. Far East J mathl Sci 2004, 14(3), 303-14.

In matrix analysis matrix factorization plays an important role. Schur's triangular factorization and singular value decomposition in the context of rectanormal sets and orthogonal matrices have been discussed.

9 ref

012173   Chen S D;Chen W Y;Huang S S (Dep of Mathematics, National Changhua University of Education, Changhua City 50058, Taiwan, Email: shuang@math.ncue.edu.tw) : A new construction of Ewell's octuple product identity. Indian J pure appl Math 2004, 35(11), 1241-53.

An octuple product identity motivated by the work of Carlitz and Subbarao in which they use Jacobi's triple product identity has been established only to prove the quintuple product identity and Winquist's identity. The work turns out to be a new construction of Ewell's octuple product identity. On the other hand, an alternative proof has been offered for the octuple product identity by appealing to functional equations satisfied by related infinife products.

012172   Chen C M;Chang T H (Department of Mathematics Education, National Hsinchu Teacher's College Hsinchu, Taiwan, R. O. C) : H-S-KKM theorem and its applications. Far East J mathl Sci 2004, 14(3), 315-24.

Some fixed point theorems, generalized H-S-KKM theorems and matching theorems has been obtained using the concept of H-convexity in generalizing the S-KKM property and S-KKM(X, Y, Z) family. The results generalize many earlier results.

9 ref

012171   Chandramouli A B;Anuj Kumar (P.G. Studies and Research in Mathematics Dep, M.S. College, Saharanpur-247 001) : Development of fuzzy theory in medical science in the decade 1970-1980. Acta Cienc Indica-Math 2004, 30(2), 411-8.

The usefulness of fuzzy theory in medical science has been dealt with.

53 ref

012170   Bhagat N;Bansal N;Agarwal S C (Mathematics Dep, Govt. P.G. College, Berinag (Pithoragarh), (Uttaranchal)) : Stability of Rivlin-Ericksen dusty flow between two rotating coaxial circular cylinders in a porous medium. Acta Cienc Indica-Math 2004, 30(2), 291-8.

The stability of Rivlin-Ericksen dusty flow in a porous medium between two rotating coaxial circular cylinders is examined. Recovery of Rayleigh's and Rachna's modified criteria for stability under some physical situations provide important contribution. Other results include the conditions for stability and instability for oscillatory modes and the non-existence of the marginal state.

21 ref

012169   Ali S;Ram Nivas (Applied Science Dep, Shri Ram Swaroop Memorial College of Engineering and Management, Lucknow-227 105) : On submanifold of a Riemannian manifold with quarter symmetric metric and non-metric connection. Acta Cienc Indica-Math 2004, 30(2), 285-90.

Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection have been studied by Imai and others. Nirmala and Chaffle defined the notion of semi-symmetric non-metric connection in a Riemannian manifold. Professors Mishra and Pandey studied quarter symmetric metric connections in a differential manifold. Submanifolds of codimensions r of a manifold admitting quarter symmetric metric and non-metric connection have been studied. Some interesting results have been established on such manifolds.

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012168   Ali R M;Ravichandran V;Hussain Khan M; Subramanian K G (NO, School of Mathematical Sciences, University Sains Malaysia, 11800 USM Penang, Malaysia, Email: rosihan@cs.usm.my) : Differential sandwich theorems for certain analytic functions. Far East J mathl Sci 2004, 15(1), 87-94.

If q₁ q₂ be univalent in Δ := {z : |z| <60> 1} some applications of first order differential superordinations to obtain sufficient conditions for normalized analytic functions f(z) to satisfy q₁(z) <60> zf'(z)/f(z) <60> q₂(z) have been given.

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012167   Alaca S;Spearman B K;Williams K S (School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6, Email: salaca@math.carleton.ca) : The factorization of 2 in cubic fields with index 2. Far East J mathl Sci 2004, 14(3), 273-82.

The explicit factorization of the principal ideal <60>2<62> has been given in cubic fields with index 2.

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011240   Yu H;Haiyan L;Liu Y (Dep of Mathematics, Shandong Normal University, Jinan 250 014, People's Republic of China, Email: ysliu6668@sohu.com) : Multiple positive solutions to third-order three-point singular semipositone boundary value problem. Proc Indian Acad Sci-Mathl Sci 2004, 114(4), 409-22.

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011239   Yildirim H;Sarikaya M Z;Ozturk S (Dep of Mathematics, Faculty of Science and Arts, Kocatepe University, Afyon, Turkey, Email: hyildir@aku.edu.tr) : The solutions of the n-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution. Proc Indian Acad Sci-Mathl Sci 2004, 114(4), 375-87.

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011238   Yanjun D;Hongya G (NO, , ) : On the regularity of very weak p-harmonic functions. Far East J mathl Sci 2004, 15(1), 129-36.

The <65>-harmonic equation div[<62>G(x)∇u(x), ∇u(x)<60>^(p-2)/2G(x)<177>u(x)] = 0, where 2 ≤ p < ∞ and G is an n x n matrix has been considered. Its G-coefficients K_G have been used to show that for every r <62> 1, very weak solutions of class W^1,r_loc(Ω) actually belong to W^1,p_loc(Ω) and are solutions in the distributional sense, provided p is sufficiently close to 2 and K_G - 1 is sufficiently small.

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011237   Yang X M;Yang X Q;Teo K L (Dep of Mathematics, Chongqing Normal University, Chongqing-400 047, People's Republic of China) : Two properties of semistrictly preinvex functions*. Indian J pure appl Math 2004, 35(11), 1285-92.

The class of semistrictly preinvex functions introduced by Yang and Li has been considered. Two properties of semistrictly preinvex functions are given. These properties include a gradient criterion of semistrictly preinvex functions and a criterion of semistrictly preinvex functions in terms of intermediate-point semistrict and prequasiinvexity. In particular, one of them improves Yang and Li's an interesting result.

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011236   Yadav R K;Singh B (Mathematics and Statistics Dep, J.N.V. University, Jodhpur-342 005) : Generating functions for the q-bedient's polynomials. Acta Cienc Indica-Math 2004, 30(2), 355-8.

By making use of the series rearrangment technique, generating functions for the q-Bedient's polynomials R_r(α, β; q, x) and G_r(α, β; q, x) have been established. The results obtained are q-Extensions of the results given earlier by Shah, some interesting special cases have also been deduced.

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011235   Warade R W;Deshmukh K C (Mathematics Dep, G.S. College, Khamgaon Dist : Buldana-444 303) : Analysis of thermoelastic deformation of a circular plate due to a partially distributed heat supply. Acta Cienc Indica-Math 2004, 30(2), 419-27.

Transtent thermo-elastic problem of a thin circular plate due to partially distributed heat supply for the heating and cooling medium on the upper surface of the plate has been discussed by applying the generalized integral transform technique and also determined the expressions for force component and thermal deflection of the circular plate defined as : 0≤r≤a, - b/2≤r≤b/2. The results are obtained in a series form in terms of Bessel functions and illustrated graphically.

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011234   Waphare B B (Mathematics Dep, Maharashtra Academy of Engineering, Alandi(D), Khed, Pune-412 105) : Applications of vector differential operator ∇. Acta Cienc Indica-Math 2004, 30(2), 401-4.

Formulae for (curl)ⁿ F → have been obtained for even and odd positive integer n. Finally, some integral theorems have been proved.

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011233   Wang G;Yan J (Dep of Computer Science, Guangdong Polytechnical Normal University, Guangzhou, Guangdong-510 665, People's Republic of China) : Periodic solutions of delay different1al equations with piecewise continuous arguments. Indian J pure appl Math 2004, 35(11), 1293-1304.

The set of ω-periodic solutions is found for delay differential equations with piecewise continuous arguments.

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011232   Verma V K;Singh M P;Katiyar V K (Mathematics Dep, Gurukul Kangri University, Haridwar, Uttaranchal) : Analytical study of blood flow through an artery with mild stenosis. Acta Cienc Indica-Math 2004, 30(2), 281-4.

The shape of stenosis to blood flow through an artery with mild stenosis has been studied. As these growths project into the lumen of in artery, the flow is disturbed and there develops a potential coupling between the growth and blood flow through the artery. The growth of stenosis with stenosis height and impedance ratio have been evaluated and compared with D.F. young (1968) and K. Haider (1985).

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011231   Varshney N K;Shilendra Kumar (Mathematics Dep, S.V. College, Aligarh) : Effect of thermal diffusion on steady laminar free convective flow along a moving porous hot vertical plate in the presence of heat source with mass transfer. Acta Cienc Indica-Math 2004, 30(2), 489-95.

The effect of thermal diffusion on steady laminar free convective flow through porous medium through a moving porous hot vertical plate in the presence of heat source with mass transfer has been studied. The governing equations of motions are solved by a regular perturbation technique. The temperature profile, concentration profile and skin friction are discussed with the help of tables and graphs. The velocity profiles are shown graphically taking into cases viz.,

3 illus, 4 tables, 14 ref

011230   Varshney N K;Ram Prakash (Mathematics Dep, S.V. College, Aligarh) : MHD free convective flow of a visco-elastic (Kuvshiniski type) dusty gas through a porous medium induced by the motion of a semi-infinite flat plate moving with velocity decreasing exponentially with time. Acta Cienc Indica-Math 2004, 30(2), 467-73.

MHD free convective flow of a visco-elastic (Kuvshiniski type) dusty gas through a porous medium induced by the motion of a semi-infinite flat plate moving with velocity decreasing exponentially with time has been dealt with. The expressions for velocity distribution of the dusty gas, dust particles and temperature distribution are obtained. The effect of Visco-elastic parameter (α₁) Magnetic parameter (M), Permeability parameter (K₁) and Prandtl number (P_r) on velocity distribution of dusty gas, dust particles and temperature distribution are discussed graphically with the help of the tables.

3 illus, 3 tables, 17 ref

011229   Varshney N K;Dwivedi R K (Mathematics Dep, S.V. College, Aligarh, Uttar Pradesh) : Unsteady effect on MHD free convection and mass transfer flow of Kuvshinshki fluid through porous medium with constant suction and constant heat and mass flux. Acta Cienc Indica-Math 2004, 30(2), 271-80.

An analysis of unsteady two-dimensional free convection and mass transfer flow of a Kuvshinshki fluid through a porous medium bounded by a vertical infinite surface with constant suction velocity and constant heat flux in the presence of a uniform magnetic field is presented. The effects of G_r and λ₁ with the time on the velocity, temperature, concentration distribution and skin friction are discussed with the help of tables and graphs.

6 illus, 6 tables, 11 ref