• Volume 110, Issue 1

February 2000,   pages  1-120

• Intermediate Jacobians and Hodge Structures of Moduli Spaces

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

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

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 :

• obtain a simple model form for a representative from each equivalence class in 𝐵(2, 𝑛),
• obtain necessary conditions for two such model connections' in 𝐵(2, 𝑛) to be themselves equivalent,
• show that 𝐵(2, 𝑛) contains a (3𝑛 - 6)-parameter family of pairwise inequivalent connections, and
• 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

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

In this paper a necessary and sufficient condition has been obtained for $\sum_{a_n\epsilon_n}$ to be summable $|\overline{N}, q|$ whenever $\sum_{a_n}$ is bounded (𝑁, 𝑝, 𝑞).

• Construction of Wachspress Type' Rational Basis Functions over Rectangles

In the present paper, we have constructed rational basis functions of 𝐶0 class over rectangular elements with wider choice 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

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

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 the classical decay laws for weak spherical and cylindrical shocks.

• Slow Rotation of a Sphere with Source at its Centre in a Viscous Fluid

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 component 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.

• # Proceedings – Mathematical Sciences

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