• Volume 114, Issue 2

May 2004,   pages  99-215

• On a New Unified Integral

In the present paper we derive a unified new integral whose integrand contains products of Fox 𝐻-function and a general class of polynomials having general arguments. A large number of integrals involving various simpler functions follow as special cases of this integral.

• A Criterion for Regular Sequences

Let 𝑅 be a commutative noetherian ring and $f_1,\ldots,f_r \in R$. In this article we give (cf. the Theorem in $\mathcal{x}$2) a criterion for $f_1,\ldots,f_r$ to be regular sequence for a finitely generated module over 𝑅 which strengthens and generalises a result in [2]. As an immediate consequence we deduce that if $V(g_1,\ldots,g_r) \subseteq V(f_1,\ldots,f_r)$ in Spec 𝑅 and if $f_1,\ldots,f_r$ is a regular sequence in 𝑅, then $g_1,\ldots,g_r$ is also a regular sequence in 𝑅.

• Picard Groups of the Moduli Spaces of Semistable Sheaves I

We compute the Picard group of the moduli space 𝑈′ of semistable vector bundles of rank 𝑛 and degree 𝑑 on an irreducible nodal curve 𝑌 and show that 𝑈′ is locally factorial. We determine the canonical line bundles of 𝑈′ and 𝑈′L, the subvariety consisting of vector bundles with a fixed determinant. For rank 2, we compute the Picard group of other strata in the compactification of 𝑈′.

• Twisted Holomorphic Forms on Generalized Flag Varieties

In this paper we prove some vanishing theorems for the twisted Dolbeault cohomology of the complete flag varieties associated to a simple, simply connected algebraic group.

• A Complete Conformal Metric of Preassigned Negative Gaussian Curvature for a Punctured Hyperbolic Riemann Surface

Let ℎ be a complete metric of Gaussian curvature 𝐾0 on a punctured Riemann surface of genus 𝑔 ≥ 1 (or the sphere with at least three punctures). Given a smooth negative function 𝐾 with 𝐾=𝐾0 in neighbourhoods of the punctures we prove that there exists a metric conformal to ℎ which attains this function as its Gaussian curvature for the punctured Riemann surface. We do so by minimizing an appropriate functional using elementary analysis.

• Limits of Functions and Elliptic Operators

We show that a subspace 𝑆 of the space of real analytical functions on a manifold that satisfies certain regularity properties is contained in the set of solutions of a linear elliptic differential equation. The regularity properties are that 𝑆 is closed in $L^2(M)$ and that if a sequence of functions $f_n$ in 𝑆 converges in $L^2(M)$, then so do the partial derivatives of the functions $f_n$.

• Cowling–Price Theorem and Characterization of Heat Kernel on Symmetric Spaces

We extend the uncertainty principle, the Cowling–Price theorem, on non-compact Riemannian symmetric spaces 𝑋. We establish a characterization of the heat kernel of the Laplace–Beltrami operator on 𝑋 from integral estimates of the Cowling–Price type.

• Geometry of Good Sets in 𝑛-Fold Cartesian Product

We propose here a multidimensional generalisation of the notion of link introduced in our previous papers and we discuss some consequences for simplicial measures and sums of function algebras.

• Containment of 𝑐0 and 𝑙1 in 𝛱1(𝐸, 𝐹)

Suppose 𝛱1(𝐸, 𝐹) is the space of all absolutely 1-summing operators between two Banach spaces 𝐸 and 𝐹. We show that if 𝐹 has a copy of 𝑐0, then 𝛱1(𝐸, 𝐹) will have a copy of 𝑐0, and under some conditions if 𝐸 has a copy of 𝑙1 then 𝛱1(𝐸, 𝐹) would have a complemented copy of 𝑙1.

• Unsteady Stokes Equations: Some Complete General Solutions

The completeness of solutions of homogeneous as well as non-homogeneous unsteady Stokes equations are examined. A necessary and sufficient condition for a divergence-free vector to represent the velocity field of a possible unsteady Stokes flow in the absence of body forces is derived.

• A Variational Proof for the Existence of a Conformal Metric with Preassigned Negative Gaussian Curvature for Compact Riemann Surfaces of Genus >1

• # Proceedings – Mathematical Sciences

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