Intermediate Jacobians and Hodge structures of moduli spaces

DONU ARAPURA and PRAMATHANATH SASTRY*
Department of Mathematics, Purdue University, West Lafayette, In 47907-1395, USA
*The Mehta Research Institute, Chhatnag, Jhusi, Allahabad 221 506, India
Email: dvb@math.purdue.edu; pramath@mri.ernet.in

The mixed Hodge structure on the low degree cohomology of the moduli space of vector bundles on a curve is studied. Analysis of the third cohomology yields a new proof of a Torelli theorem.

An intrinsic approach to Lichnerowicz conjecture

AKHIL RANJAN
Department of Mathematics, Indian Institute of Technology, Mumbai 400076, India
Email: aranjan@math.iitb.ernet.in

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids the nice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.

Connections for small vertex models

R SRINIVASAN
Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad 211 019, India

This paper is a first attempt at calssifying connections on small vertex models i.e., commuting squares of the form displayed in (1.2) below. More precisely if we let B(k, n) denote the collection of matrices W for which (1.2) is a commuting square then, we : (i) obtain a simple model form for a representative from each equivalence class in B(2, n), (ii) obtain necessary conditions for two such 'model connections' in B(2, n) to be themselves equivalent, (iii) show that B(2, n) contains a (3n – 6)-parameter family of pairwise inequivalent connections, and (iv) show that the number (3n – 6) is sharp. Finally, we deduce that every graph that can arise as the principal graph of a finite depth subfactor of index 4 actually arises for one arising from a vertex model corresponding to B(2, n) for some n.

Transformation semigroup compactifications and norm continuity of weakly almost periodic functions

A JALILIAN and M A POURABDOLLAH
Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran

We prove if there exists a separately continuous action of a topologically right simple semitopological semigroup S on a topologoical space X and if S acts topologically surjective on X then each weakly almost periodic function on X, with respect to S, is left norm continuous.

On (N, p, q) summability factors of infinite series

NIRANJAN SINGH and NEETA SHARMA
Department of Mathematics, Kurukshetra University, Kurukshetra 136 119, India

In this paper a necessary and sufficient condition has been obtained for Sa_ne_n to be summable |N, q| whenever Sa_n is bounded (N, p, q).

Construction of 'Wachspress type' rational basis functions over rectangles

P L POWAR and S S RANA
Department of Mathematics and Computer Science, R.D. University, Jabalpur 482 001, India

 In the present paper, we have constructed rational basis functions of C⁰ class over rectangular elements with widerchoice of denominator function. This construction yields additional number of interior nodes. Hence, extra nodal points and the flexibility of denominator function suggest better approximation.

A direct heuristic algorithm for linear programming

S K SEN and A RAMFUL*
Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore 560 012, India
*Department of Mathematics, University of Mauritius, Reduit, Mauritius

An O(n³) mathematically non-iterative heuristic procedure that needs no artificial variable is presented for solving linear programming problems. An optimality test is included. Numerical experiments depict the utility/scope of such a procedure.

An approximate solution for spherical and cylindrical piston problem

S K SINGH and V P SINGH
Centre for Aeronautical System Studies and Analyses, New Thippasandra P.O., Bangalore 560 075, India
Email: drvpsingh@hotmail.com

A new theory of shock dynamics (NTSD) has been derived in the form of a finite number of compatibility conditions along shock rays. It has been used to study the growth and decay of shock strengths for spherical and cylindrical pistons starting from a non-zero velocity. Further a weak shock theory has been derived using a simple perturbation method which admits an exact solution and also agrees with theclassical decay laws for weak spherical and cylindrical shocks.

Slow rotation of a sphere with source at its centre in a viscous fluid

SUNIL DATTA and DEEPAK KUMAR SRIVASTAVA
Department of Mathematics and Astronomy, Lucknow University, Lucknow 226 007, India

In this note, the problem of a sphere carrying a fluid source at its centre and rotating with slow uniform angular velocity about a diameter is studied. The analysis reveals that only the azimuthal componennt of velocity exists and is seen that the effect of the source is to decrease it. Also, the couple on the sphere is found to decrease on account of the source.