000956   Datta S K (NO, , 25, School Road, Kalianibash, Barackpore, P.O. Nonachandanpukur, Dist. 24 Parganas (North). P.S.Titagarh-743 102, West B) : Some results on the growth properties of composition of entire and meromorphic functions. Bull Calcutta Mathl Soc 2004, 96(5), 351-60.

Some theorems on the growth properties of composite function of entire and meromorphic functions have been established. Some examples are also provided to show that the conditions in the theorems are essential.

8 ref

000955   Dagadur I (Mersin Univ, Fac Arts & Sci, Math Dep, 33342 Ciftlikkoyu Campus, Mersin/Turkey) : Conullity and replaceability of matrices on rate spaces. Indian J pure appl Math 2004, 35(5), 563-71.

6 ref

000954   Choudhary R;Sarma H;Das A (Dep of Mathematics, Guwahati Univ, Guwahati 781 014) : Free convection of an elastico viscous fluid confined between two vertical wavy walls. Ultra Scient phys Sci 2004, 16(2), 179-88.

The flow of an elastico-viscous fluid in porous medium confined between two long vertical wavy walls has been studied. The wave length of the wavy walls is assumed to be large with amplitudes of two wavy wall being different. Regular perturbation technique is used to solve the problem where perturbation parameter is inversely proportional to the wave length. The analytic expression for dimensionless shearing stress at both the walls has been obtained and numerically worked out for different values of the parameters involved in the solution.

3 tables, 12 ref

000953   Bujurke N M;Pai N P;Katagi N N;Awati V B (Dep of Mathematics, Karnataka Univ, Dharwad 580 003) : Analytic continuation of series solution representing flow between plates. Indian J pure appl Math 2004, 35(5), 587-98.

The flow of an incompressible fluid between two rectangular and circular plates is reinvestigated. The problem admits similarity solutions there by reducing unsteady Navier-Stokes equations to non-linear ordinary differential equation of order four involving a small paramter α=h(t)h(t)—v. The proposed new semi-analytic semi-numerical scheme is convenient in obtaining analytic continuation of series solution. The series so generated yields expression for pressure gradient and it is analyzed using Pade' approximants and other useful techniuqes of series analysis.

3 illus, 3 tables, 12 ref

000952   Bhosle U N (Tata Institue of Fundamnetal Research, , Homi Bhabha Road, Mumbai 400 005) : Picard groups of the moduli spaces of semistable sheaves I. Proc Indian Acad Sci-Mathl Sci 2004, 114(2), 107-22.

Picard group of the moduli space U' of semistable vector bundles of rank n and degree d on an irreducible nodal curve Y has been computed and it has been shown that U' is locally factorial. The canonical line bundles of U' and U_L, the subvariety consisting of vector bundles with a fixed diterminant has been determined. For rank 2, the Picard group of other strata in the compactification of U' have been computed.

13 ref

000951   Bhatt L;Dube K K (Dep of Mathematics, Statistics and Computer Sciences, G.B. Pant Univ of Agriculture and Technology, Pantnagar 263 145) : On almost contact hyperbolic structures. Ultra Scient phys Sci 2004, 16(2), 127-32.

Hyperbolic Kaehlerian space has been studied by Prvanovic. Rasevaski was the first to consider such spaces. Almost hyperbolic Hermitian manifolds studied by Dube. Upadhyay and Dube studied almost contact hyperbolic structure. Almost r-contact hyperbolic structure have been studied by Dube and Niwas. Hyperbolic Coysmplectic, nearly hyperbolic Cosymplectic, almost hyperbolic Sasakian, quasi hyperbolic Sasakian, nearly hyperbolic Sasakian, K-contact hyperbolic Riemannian manifold, almost contact hyperbolic normal metric manifold, almost contact hyperbolic pseudo normal metric manifold, almost contact nearly hyperbolic normal metric manifold, quasi hyperbolic normal manifold, generalized hyperbolic Cosymplectic generalized nearly hyperbolic Cosymplectic manifold and generalized quasi hyperbolic Sasakian manifold have been defined.

5 tables, 6 ref

000950   Behravesh H (Math Dep, Urmia Univ, Urmia, Iran) : Characters and quasi-permutation representations of wreathed 2-group. Far East J mathl Sci 2004, 13(3), 285-90.

It is known that wreathed 2-group can be presented by the following presentation: G=(x,y,z:x^2m = y^2m = z2 = 1, xy,yx,zxz + y), m≥ 2. The irreducible characters of G have been calculated. c(G), q(G) and p(G) are defined. Here it has been shown that c(G) = q(G) = p(G) = 2^m+1.

3 ref

000949   Atri N;Basu S;Chakravarti A K (Information Technology Dep, , New Delhi) : Spamming : a perspective. Elect Inf Plann 2002, 30(1-2), 44-55.

The use of the Internet has grown rapidly world-wide in last few years and it has now acquired the status of a purposeful tool. As Internet users gain experience online, they increasingly turn to the Internet to perform work-related tasks, to write e-mails with weighty and urgent content, to seek information that is improtant to their work and everyday lives, to make purchases and do other financial transactions. Such wide scope of Internet has created a significant need for the regulation and governance of activities on Internet, a requirement that lead to the creation and implementation of cyber laws across the globe. India became the 12th nation in the world to adopt a cyber law regime during year 2000. The country's cyber laws are contained in the Information Technology, Act 2000. Cyber lows are in different stages of evolution in various countries and have been able to reduce extent of cyber-crimes. However, certain new problems like spamming and cyberstalking etc. have found their way on the Internet. Who should be responsible for policing the Web? What laws are existing and what laws are required for enforcing discipline? Whether too many laws or restrictions will restrict the smooth growth process? What tools and technologies can be used? Dealing with such kind of problems comes under the purview of Internet Sanitization which requires code of conduct, self-regulation, good practices, ethics and awareness, along with technological measures and legislation.

1 illus, 18 ref

000948   Asadollahi J;Khashyarmanesh K;Salarian S (Shahre-Kord Univ, Sci Fac, P.O. Box 115, Shahre-Kord, Iran) : On primes dual to associated primes for cotorsion modules. Indian J pure appl Math 2004, 35(5), 621-7.

Using the theory of flat covers, a set of primes dual to the set of associated primes has been introduced. It turns out that this set has properties similar (or rather dual) to those of the set of associated primes. With the aid of this set of primes, a ncessary and sufficient condition for a cotorsion module M, over a ring whose injective hull is flat has been obtained to have nonzero injective cover.

15 ref

000947   Anwar Kamal M;Siddiqui A Z A (Math Dep, King Saud Univ, Riyadh, Saudi Arabia) : Numerical investigation of flow due to accelerated circular cylinder. Indian J pure appl Math 2004, 35(5), 679-97.

The non-steady flow due to an uniformly accelerated circular cylinder from rest in a stationary viscous incompressible fluid is considered where flow is assumed to remain symmetrical about the direction of motion of a cylinder. This numerical experiment is made for various values of Reynolds numbers in the range of 1 to 350. In this numerical attempt, the scheme which consists of two steps has been adopted. In the first step, the special finite-difference method is used to approximate the vorticity transport equatin. This method transforms the governing partial differential equation to a system of finite-difference equations, which are solved numerically by Successive Under Relaxation point iterative method. In the second step, the results obtained are further refined and upgraded by Richardon's extrapolation method. For the purpose of verification, the obtained results are compared on five different grid sizes as well as with those of Collins. The comparison is very well.

15 illus, 1 table, 13 ref

000946   Ansari-piri E (Dep of Math, Fac of Sci, Guilan Univ, P.O.Box 1914, Rasht, Iran) : Equivalent definitions for fundamental topological vector spaces. Far East J mathl Sci 2004, 13(3), 319-23.

A New class of topological algebras namely fundamental one, has already been introduced to generalize the famous Cohen factorization theorem. A characterization of the defenitions of fundamentality, and some results on dual spaces of fundamental topological vector spaces have been given.

6 ref

000945   Alimohammady M (Dep of Mathematics, Univ of Mazandran, Faculty of Basic Sciences, Babolsar Iran) : Containment of c_o and l₁ in Π₁(E,F). Proc Indian Acad Sci-Mathl Sci 2004, 114(2), 199-202.

If Π₁(E,F) be the space of all absolutely 1-summing operators between two Banach spaces E and F. and if F has a copy of c_o, then Π(E,F) will have a copy of c_o, and under some conditions if E has a copy of l₁ then Π₁(E,F) would have a complemented copy of l₁.

7 ref

000944   Ahmad I;Husain Z (Math Dep, Aligarh Muslim Univ, Aligarh 202 002) : On nondifferentiable second symmetric duality in mathematical programming. Indian J pure appl Math 2004, 35(5), 665-76.

Usual duality results are established for a pair of Wolfe type non-differntiable second order symmetric dual nonlinear programs. Then these are used to investigate symmetric duality for minimax version of nondifferentiable second order symmetric dual models wherein some of the primal and dual variables are constained to belong to some arbitary sets e.g., the sets of integers. Also self duality for this pair has been discussed.

16 ref

000016   Daoud (Dep of Mathematics, Faculty of Sciences, Zagazig Univ, Zagazig Egypt) : Average number of photons present in a single-mode squeezed vacuum state as function of the mean free path. Indian J Phys-Pt B 2003, 77(6), 663-8.

Devotes this research paper to construct a relationship between the average of the total number of quanta in a single-mode squeezed vacuum state and the mean free path of atoms of a material through which the natural light passes. This relationship provides a method to measure experimentally the mean number of photons present in this mode of the quantum radiation field.

18 ref

014431   Zhangjia H (College of Mathematics, Chengdu Information Technology Univ, Sichuan 610225, People's Republic of China, Email: hzjmm11@yahoo.com.cn) : On s-semipermutable subgroups of finite groups and p-nilpotency. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 141-8.

A subgroup H of a group is said to be s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. Using the concept of s-semipermutable subgroups, some new characterizations of p-nilpotent groups are obtained and several results are generalized.

14 ref

014430   Yi Y (Research Centre for Basic Science, Xi'an Jiaotong Univ, Xi'an, Shaanxi 710049, People's Republic of China, Email: yuanyi@mail.xjtu.edu.cn) : On the general dedekind sums and its reciprocity formula. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 1-6.

In this paper, authors prove an interesting reciprocity formula for a certain case of a general Dedekind sums using analytic methods and the Fourier expansion of the Bernoulli polynomials.

4 ref

014429   Yao H (School of Science, Nanjing Univ of Sci & Tech, Nanjing 210014, People's Republic of China) : AT-algebras and extensions of AT-algebras. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 199-207.

Lin and Su classified AT-algebras of real rank zero. This class includes all AT-algebras of real rank zero as well as many C*-algebras which are not stably finite. An AT-algebra often becomes an extension of an AT-algebra by an AF-algebra. In this paper, we show that there is an essential extension of an AT-algebra by an AF-algebra which is not an AT-algebra. We describe a characterization of an extension E of an AT-algebra by an AF-algebra if E is an AT-algebra.

7 ref

014428   Yajun M A;Zhang Y U;Sun J (Mathematics Dep, Tongji Univ, Shanghai 200092, China, Email: sunjt@sh163.net) : On qualitative analysis of delay systems and x<. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 249-58.

Solved two problems presented in paper [9] (C C Tisdell and A Zaidi, Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling, Nonlinear Anal. 68 (2008) 3504-3524). We study existence and uniqueness of solutions for delay systems and first-order dynamic equations of the form x^Δ = f(t, x, xσ) on time scales by using the Banach's fixed-point theorem. Some examples are presented to illustrate the efficiency of the proposed results.

13 ref

014427   Xiao Y;Qiu W (Mathemaitcs and Economics College, Hunan Univ, Changsha 410082,China) : Rational maps Fλ(z) = z<. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 403-7.

It is proved that the rational maps in the family {z → z^m+λ/z^d:λ ∈ C{0}} for integers m, d ≥ 2 have no Herman rings.

134 ref

014426   Xiang Y (Mathematics and Computer Science School, Hunan Normal Univ, Changsha-410006, China, Email: xymls999@126.com) : FGT-injective dimensions of II-coherent rings and almost excellent extension. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 149-61.

Studied, in this article, the FGT-injective dimensions of ∏-coherent rings. If R is right n-coherent, and TI (resp. TF) stands for the class of FGT-injective (resp. FGT-flat) R-modules (n ≥ 0), Authours show that the following are equivalent: (1) FGT-Id_R(R) ≤n; (2) If 0 → M → F° → F¹ → ... is a right TF-resolution of left R-module M, then the sequence is exact at F^k for k ≥ n - 1; (3) For every flat right R -module F, there is an exact sequence 0 → F → A⁰ → A¹ → ... → Aⁿ → 0 with each Aⁱ ∈ TI; (4) For every injective left ft-module A, there is an exact sequence 0 → F_n → ...→ F1 → F₀ → A → 0 with each F_i ∈ TF; (5) If ... → I₁ → I₀ → M → 0 is a minimal left TI-resolution of a right R-module M, then the sequence is exact at I_k for k ≥ n - 1. Further, we characterize such homological dimension in terms of TI-syzygy and TF-cosyzygy of modules. Finally, we consider almost excellent extensions of rings. These extend the corresponding results in [10] as well.

17 ref

014425   Wei C (School of Mathematical Sciences, Ocean China Univ, Qingdao 266 071, People's Republic of China, Email: weicgqd@yahoo.com.cn) : Equivalence relations of AF -algebra extensions. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 209-15.

In this paper, authour consider equivalence relations of C*-algebra extensions and describe the relationship between the isomorphism equivalence and the unitary equivalence. Authour also show that a certain group homomorphism is the obstruction for these equivalence relations to be the same.

15 ref

014424   Wei C (School of mathematical Sciences, Ocean China Univ, Qingdao 266071, People's republic of China) : Homomorphisms between C*-algebra extensions. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 97-104.

In this paper author considered the question when a homomorphism between two extension algebras preserves the essential ideal in the corresponding extension. Some conditions of two essential extensions being isomorphic are given. We also describe the relationship between the induced extensions and the Kasparov products and give the completely positive liftings of the induced extensions.

15 ref

014423   Wang H;Jiang Y (Applied Mathematics Dep, Hunan Univ, Changsha 410082, People's Republic of China, Email: hncswhua@163.com) : Discreteness criteria in PU (1, n; C). Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 243-8.

Discreteness for non-elementary subgroups in PU (1, n; C), and several discreteness criteria are obtained.

13 ref

014422   Veera Krishna M;Suneetha S V;Malashetty S G (Mathematics Dep, Rayalaseema Univ, Kurnool-518 002) : Hydro magnetic flow of a couple stress fluid through a porous medium in a rotating parallel plate channel. Ultra Scient phys Sci 2010, 22(2), 369-76.

Discusse the steady hydro magnetic flow of a couple stress fluid in a rotating parallel plate channel in a porous medium under the influence of a uniform transverse magnetic field. The perturbations are created by a constant pressure gradient along the plates. The equations for the couple stress fluid flow in the porous medium are based on Brinkman's model. The exact solution of the velocity in the porous medium is analytically derived, its behaviour computationally discussed with reference to the various governing parameters. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed.

8 illus, 2 tables, 11 ref

014421   Vasanthi B;Sattanathan R (NO, Vinayaka Missions Univ, Salem, Tamil Nadu, Email: valliaya@yahoo.co.in) : Graceful labelling of graphs obtained from non-graceful books with square pages. Ultra Scient phys Sci 2010, 22(2), 347-50.

Graceful labelling is one of the best known labelling methods of graphs. Despite the large number of papers published on the subject of graceful labelling, there are still more number of open problems existing to explore its gracefulness. In this paper, we present the graceful labelling of new graphs obtained from non-graceful book graphs with square pages.

5 illus, 8 ref

014420   Szal B (Faculty of Mathematics, Computer Science and Econometrics, Zielona Gora Univ, 65-516 Zielona Gora, ul. Szafrana 4a, Poland, Email: b.szal@wmie.uz.zgora.pl) : Embedding relations connected with strong approximation of Fourier series. Proc Indian Acad Sci-Mathl Sci 2010, 120(5), 563-82.

Considers the embedding relation between the class W^qH^ωβ, including only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions. Establishes an improvement of a recent theorem of Le and Zhou which is a generalization of Tikhonov's results. Also extend the Leindler theorem concerning sequences of Fourier coefficients.

17 ref

014419   Subbiah M;Ganesh V (Mathematics Dep, Pondicherry Univ, Pondicherry Univ, Kalapet, Pondicherry-605 014) : On short wave stability and sufficient conditions for stability in the extended rayleigh problem of hydrodynamic stability. Proc Indian Acad Sci-Mathl Sci 2010, 120(3), 387-94.

Considers the extended Rayleigh problem of hydrodynamic stability dealing with the stability of inviscid homogeneous shear flows in sea straits of arbitrary cross section. Proved a short wave stability result, namely, if k <62> 0 is the wave number of a normal mode then k <62> k_c (for some critical wave number k_c) implies the stability of the mode for a class of basic flows. Furthermore, if K (z) = [-(U"₀-T₀U'₀)]/[U₀-U_0s], where U₀ is the basic velocity, T₀ (a constant) the topography and prime denotes differentiation with respect to vertical coordinate z then Proved that a sufficient condition for the stability of basic flow is 0 <60> K(z) ≤ (π²/D² + T²₀/4), where the flow is 0 <60> K (z) ≤ (π²/D² + T²₀/4), where the flow domain is 0 ≤ z ≤ D.

9 ref

014418   Stefanovic N;Milosevic M (Group for Intelligent Systems, Faculty of Mathematics, Belgrade Univ, Studentski Trg 16, 11000 Beograd, Serbia, Email: stenedjo@gmail.com) : Very simple proof of Pascal's hexagon theorem and some applications. Proc Indian Acad Sci-Mathl Sci 2010, 120(5), 619-29.

In this article authors present a simple and elegant algebraic proof of Pascal's hexagon theorem which requires only knowledge of basics on conic sections without theory of projective transformations. Also, we provide an efficient algorithm for finding an equation of the conic containing five given points and a criterion for verification whether a set of points is a subset of the conic.

4 ref

014417   Sreekumar R (Mathematics Dep, S.D. College, Alleppey(Dist)-688 003, Email: dr.sreekumar@gmail.com) : Some generalized metric spaces. Sci Soc 2010, 8(1), 31-8.

The theory of 'Generalized Metric Spaces' is closely related to 'metrization theory'. These classes often appear in theorems, which characterize metrizability in terms weaker topological properties. Any class of spaces defined by a property possessed by all metric spaces could technically be called as a class of 'generalized metric spaces'. But the term is meant for classes, which are 'close' to metrizable spaces in some sense. They can be used to characterize the images or pre images of metric spaces under certain kinds of mappings. The class of spaces like Borges's wl-spaces, Arhangelskii's p-spaces, Okuyama's σ -spaces have major roles in the theory of generalized metric spaces. They have appeared as a 'factor' in many metrization theorems. In this paper we introduce the fuzzy analogue of the above spaces and study their relationships.

8 ref

014416   Soykan Y (Mathematics Dep, Art and Science Faculty, Zonguldak Karaelmas Univ, 67100, Zonguldak, Turkey, Email: yuksel_soykan@hotmail.com) : Eigenvalue estimates of positive integral operators with analytic kernels. Proc Indian Acad Sci-Mathl Sci 2010, 120(3), 333-50.

In this paper, we exhibit canonical positive definite integral kernels associated with simply connected domains. We give lower bounds for the eigenvalues of the sums of such kernels.

13 ref

014415   Soner N D;Chaluvaraju B;Srivastava J P (Mathematics Dep, Mysore Univ, Manasagangotri, Mysore-570 006) : Roman edge domination in graph. Proc Natn Acad Sci India-Sect A 2009, 79(Pt1), 45-50.

In this paper, we initiate a study on roman edge dominating function and roman edge domination number and its exact values for some standard graphs have been established. Also its relationship with other parameters is investigated.

1 illus, 10 ref

014414   Singh T;Chaubey R (Applied Mathematics Dep, Institute of Technology, Banaras Hindu Univ, Varanasi, Email: drtrilokisingh@yahoo.co.in) : Bianchi type-I, III, V, VIo and Kantowski-sachs universes in self-condition cosmology. Proc Natn Acad Sci India-Sect A 2009, 79(Pt1), 71-89.

The solution of Einstein's equation in presence of a self-creation cosmology in Brans-Dicke theory have been obtained for Bianchi type-I, III, V, VIo and Kantowski-Sachs (KS) universes in the quadrature form. Some physically interesting cases have been studied in detail.

6 ref

014413   Singh R N;Pandey K P;Pandey M K (Mathematical Sciences Dep, A.P.S. Univ, Rewa-486 003, Email: rnsinghmp@rediffmail.com) : On a type of quarter-symmetric non-metric connection in an sp-Sasakian manifold. Proc Natn Acad Sci India-Sect A 2009, 79(Pt1), 109-15.

Studied a type of quarter-symmetric non-metric connection in an sp-Sasakian manifold. It is shown that projective curvature tensor is invariant with respect to the transformation considered.

7 ref

014412   Shrivastava S (Mathematics Dep, Government Model Science College, Rewa-486 001) : Certain integrals and expansion formulae involving Horn function of two variables and Fox's H-function. Proc Natn Acad Sci India-Sect A 2009, 79(Pt1), 117-23.

Some finite integrals involving Horn's function and Fox's H-function of two variables have been evaluated. Three integrals have been utilized to establish the expansion formulae for Fox's H-function in series involving Jacobi-polynomials. A few particular cases of interest have also been discussed.

12 ref

014411   Shirali S A (NO, Rishi Valley School, Rishi Valley-517 352, Email: shailesh.shirali@gmail.com) : Madhava, gregory, Leibnitz, and sums of two squares. Resonance 2010, 15(2), 116-23.

Describes a connection between the Gregory-Leibnitz series for pi and the representations of positive integers as sums of two squares. It emerges from a study of the geometry of lattice points in the plane.

1 illus, 6 ref

014410   Rosebrock S (NO, Education Univ, Postfach 11 10 62, 760 60, Email: rosebrock@ph-karlsruhe.de) : On the complexity of labeled oriented trees. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 11-8.

Defined a notion of complexity for labeled oriented trees (LOTs) related to the bridge number in knot theory and prove that LOTs of complexity 2 are aspherical. Also present a class of LOTs of higher complexity which is aspherical, give an upper bound for the complexity of labeled oriented intervals and study the complexity of torus knots.

4 illus, 9 ref

014409   Ren D;Lu Y (Mathematics and Statistics School, Southwest Univ, Chongqing 400715, People's Republic of China, Email: dongmei.ren@gmail.com) : Mean value estimates of the error terms of lehmer problem. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 507-13.

Let p be an odd prime and a be an integer coprime with p. Denote by N (a, p) the number of pairs of integers b, c with be = a(mod p), 1 ≤ b, c <60> p and with b, c having different parity. The main purpose of this paper is to study the mean square value problem of (N (a, p) - 1/2(p - 1)) over interval (N, N + M] with M, N positive integers by using the analytic methods, and finally by obtaining a sharp asymptotic formula.

7 ref

014408   Ravindra Kumar;Singh K K;Sharma A K (NO, , 616, Pal Colony, Near Shesh Cold Store, Ashok Nagar, Etawah-206 001, Email: rkpl.maths@gmail.com) : Magneto-hydrodynamic unsteady laminar flow of higher order visco-elastic fluid through porous medium in a right circular cylinder. Ultra Scient phys Sci 2010, 22(1), 169-78.

The aim of the present paper is to investigate the unsteady laminar flow of a conducting higher order visco-elastic [Oldroyd (1958) model] fluid through porous medium in a right circular cylinder under the influence of an uniform magnetic field applied perpendicular to flow of fluid i.e. in the azimuthal direction. The problem has been solved in the generalised visco-elastic model and the velocity field has been derived analytically in the closed form. The particular cases corresponding to first order visco-elastic Oldroyd, Maxwell, Rivlin-Ericksen models and ordinary viscous fluids have been derived for velocity field. Numerical work has been done and tables are given for particular case I Oldroyd visco-elastic liquid of first order. Graphs have also been plotted for the same, to visualise the physical situation of the flow of liquid.

3 illus, 3 tables, 17 ref

014407   Rane V V (Mathematics Dep, Institute of Science, 15, Madam Cama Road, Mumabi-400 032, Email: v_v_rane@yahoo.com.in ) : Dirichlet expression for L (1, χ) with general dirichlet character. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 7-9.

In the famous work of Dirichlet on class number formula, L(s, χ) at s = 1 has been expressed as a finite sum, where L(s, χ) is the Dirichlet L-series of a real Dirichlet character. Shows that this expression with obvious modification is valid for the general primitive Dirichlet character χ.

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014406   Rajput U S;Surendra Kumar (Mathematics & Astronomy Dep, Lucknow Univ, Lucknow-226 007, Email: usrajput@sify.com) : MHD flow past an impulsively started infinite vertical porous plate with heat transfer. Ultra Scient phys Sci 2010, 22(1), 85-90.

The aim is to study radiation effects on impulsively started infinite vertical porous plate in the presence of variable temperature. The temperature of plate is made to rise linearly with time. The fluid of our flow model is considered as gray, absorbing-emitting radiation but non- scattering medium.

2 illus, 1 table, 16 ref

014405   Qing T;Wenpeng Z (Mathematics Dep, Northwest Univ, Xi'an, Shaanri, 710 127, Peoples' Republic of China) : Hybird mean value involving Gauss sums and character sums. Indian J pure appl Math 2010, 41(4), 583-94.

Let χ be a Dirichlet character modulo q <62> 2, and L(s, χ) denotes the Dirichlet L-function corresponding to χ. The main purpose of this paper is using the estimate for character sums and the analytic method to study the mean value properties of L/L(1, χ) with the weight of Gauss sums and character sums, and give an interesting mean value formula for it.

9 ref

014404   Panda J P;Mohapatra J K (Mathematics Dep, Institute of Technical Education and Research S 'O' A University, Khandagiri Square, Bhubaneswar-751 030) : Unsteady free convection MHD flow of a second order fluid between two heated plates in a porous medium. Ultra Scient phys Sci 2010, 22(1), 155-62.

The unsteady free convection flow and mass transfer of an electrically conducting second order fluid between two heated vertical plates under the action of transverse magnetic field has been studied. We have considered the flow of an incompressible second order Rivlin Ericksen electrically conducting fluid between two plates. The solution for the fluid velocity, the temperature and the concentration have been obtained analytically. The skin friction and heat flux are also found. The effect of pertinent parameters such as Grashof number, Prandtl number, magnetic parameter, Schmidt number etc. which characterize the flow, heat and mass transfer phenomena have been studied with help of graphs.

3 illus, 8 ref

014403   Panda J P;Dash N;Dash G C (Mathematics Dep, Institute of Technical Education and Research, Siksha 'O' Anusandhan Univ, Khandagiri Square, Bhubneswar-751 030) : Hydromagnetic flow through porous medium of elastico-viscous fluid over a porous plate. Ultra Scient phys Sci 2010, 22(1), 131-6.

In this paper we have considered an electrically conducting fluid exhibiting the character or elastico-viscous over a porous plate. The surrounding medium is packed with a homogenous porous matrix. The analytical expressions for the velocity, temperature are presented. The effects of various physical parameters such as magnetic parameter M, elastic parameter Re, Porosity parameter Kp and rotational parameter E and Rarefaction parameter R are studied with help of graphs.

1 illus, 9 ref

014402   Pal G;Ganguly S (NO, , 5/1, Nandaram Sen, Fisrt Lane, Kolkata-700 005, Email: Ganguly @math.tifr.res.in ) : Integers without large prime factors in short intervals: conditional results. Proc Indian Acad Sci-Mathl Sci 2010, 120(5), 515-24.

18 ref

014401   Pal A (Stat-Math Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata-700 108, Email: abhijit_r@isical.ac.in) : Relatively hyperbolic extensions of groups and cannon-thurston maps. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 57-68.

Let 1 → (K, K1) → (G,N_G(K₁) → (Q, Q₁) → 1 be a short exact sequence of pairs of finitely generated groups with K a proper non-trivial subgroup of K and K strongly hyperbolic relative to K. Assuming that, for all g ∈ G, there exists k_g ∈ K such that gK₁g^-1 = k_gK₁k^-1_g, we will prove that there exists a quasi-isometric section s: Q → G. Further, we will prove that if G is strongly hyperbolic relative to the normalizer subgroup N_G(K₂) and weakly hyperbolic relative to K[, then there exists a Cannon-Thurston map for the inclusion i: Γ_K → Γ_G.

13 ref

014400   Padmawar V R (Stat-Math. Div, Indian Statistical institute 8th mile, Mysore Road, Bangalore-560 059, Email: vrp@isibang.ac.in) : Is a go-getter better off?. Resonance 2010, 15(1), 32-44.

In this article we first try to answer the question posed in the title in the context of a real life situation. We suggest sequential methods of selecting a member from a given set of individu-J als. We show that these methods indeed assignl 'equal chance' of being selected to all individuals.

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014399   Navin Kumar;Gupta S;Jain T (NO, , D-87, Kundan Kuteer, Kanti-Nagar, Station-Road, Jaipur-302 006, Email: navinkumar.1018@rediffmail.com) : MHD unsteady natural convective walter's memory flow through porous medium with variable suction and heat sink. Ultra Scient phys Sci 2010, 22(1), 191-202.

A Study of unsteady MHD free convective Walter's memory flow of a viscous incompressible fluid through a porous medium past an infinite vertical porous plate in the presence of heat absorbing sink has been made. The porous plate absorbs the fluid with variable velocity. Approximate solutions of governing equations of flow have been derived using successive perturbation technique. The velocity and temperature distributions are derived, discussed and their profiles for various values of physical parameters are shown through graphs. Also, the coefficient of skin-friction and Nusselt number at the vertical porous plate are calculated for various values of physical parameters and presented through table.

10 illus, 1 table, 18 ref

014398   Narayanan K E;Sen S (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: naru@math.iisc.ernet.in) : Segal-Bargmann transform and paley-Wiener theorems on M(2). Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 169-83.

Studies the Segal-Bargmann transform on M(2). The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are investigated. Using a Gutzmer's type formula we characterize the range as a class of functions extending holomorphically to an appropriate domain in the complexification of M(2). We also prove a Paley-Wiener theorem for the inverse Fourier transform.

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014397   Munoz V;Presas F (De Geometria y Topologia Dep, Facultad de Matematicas Complutense de Madrid Univ, 28040, Madrid, Spain, Email: vicente.munoz@mat.ucm.es) : Geometric structures on loop and path spaces. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 417-28.

The loop space associated to a Riemannian manifold admits a quasi-symplectic structure (that is, a closed 2-form which is non-degenerate up to a finite-dimensional kernel). Shows how to construct a compatible almost-complex structure. Finally conditions to have contact structures on loop spaces are studied.

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014396   Moriya B K (Mathematics Dep, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabd-211 019, Email: bhavinomoriya@hir.res.in) : On zero sum subsequences of restricted size. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 395-402.

Let G be a finite abelian group with exp(G) = e. Let s(G) be the minimal integer t with the property that any sequence of t elements in G contains an e-term subsequence with sum zero. Let n, m and r be positive integers and in ≥ 3. Furthermore, γ(C^r_m) = a_r(m - 1) + 1, for some constant a_r depending on r and n is a fixed positive integer such that n ≥ [{m^r(c(r)m - a_r(m - 1) + m - 3) (m - 1) - (m + 1) + (m + l) (a_r + 1)}/{m(m + l)(a_r + 1)}] and s (C^r_n) = (a_r + 1) (n - 1) + 1. In the above lower bound on n, c(r) is the Alon-Dubiner constant. Then s (C^r_nm) = (a_r + l) (nm - 1) + 1.

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