• 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 FoxH-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

LetR be a commutative noetherian ring and ƒ1, …, ƒr ∃ R. In this article we give (cf. the Theorem in §2) a criterion for ƒ1, …, ƒr to be regular sequence for a finitely generated module overR which strengthens and generalises a result in [2]. As an immediate consequence we deduce that if V(g1, …,gr) ⊆ V(ƒ1, …, ƒr) in SpecR and if ƒ1, …, ƒr is a regular sequence inR, theng1, …,gr is also a regular sequence inR.

• Picard groups of the moduli spaces of semistable sheaves I

We compute the Picard group of the moduli spaceU′ of semistable vector bundles of rankn and degreed on an irreducible nodal curveY and show thatU′ is locally factorial. We determine the canonical line bundles ofU′ andUL, the subvariety consisting of vector bundles with a fixed determinant. For rank 2, we compute the Picard group of other strata in the compactification ofU′.

• 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

Leth be a complete metric of Gaussian curvature K0 on a punctured Riemann surface of genusg ≥ 1 (or the sphere with at least three punctures). Given a smooth negative functionK withK =K0 in neighbourhoods of the punctures we prove that there exists a metric conformal toh 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 subspaceS 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 thatS is closed inL2 (M) and that if a sequence of functions fn in ƒn converges inL2(M), then so do the partial derivatives of the functions ƒn.

• Cowling-price theorem and characterization of heat kernel on symmetric spaces

We extend the uncertainty principle, the Cowling-Price theorem, on noncompact Riemannian symmetric spacesX. We establish a characterization of the heat kernel of the Laplace-Beltrami operator onX from integral estimates of the Cowling-Price type.

• Geometry of good sets inn-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 spacesE andF. We show that ifF has a copy of c0, then π1 (E, F) will have a copy of c0, and under some conditions ifE 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.

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