Volume 114, Issue 2
May 2004, pages 99-215
pp 99-101 May 2004
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.
pp 103-106 May 2004
A criterion for regular sequences
LetR be a commutative noetherian ring and ƒ_{1}, …, ƒ_{r} ∃ R. In this article we give (cf. the Theorem in §2) a criterion for ƒ_{1}, …, ƒ_{r} 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(g_{1}, …,g_{r}) ⊆ V(ƒ_{1}, …, ƒ_{r}) in SpecR and if ƒ_{1}, …, ƒ_{r} is a regular sequence inR, theng_{1}, …,g_{r} is also a regular sequence inR.
pp 107-122 May 2004
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′ andU_{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 ofU′.
pp 123-140 May 2004
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.
pp 141-151 May 2004
Leth be a complete metric of Gaussian curvature K_{0} on a punctured Riemann surface of genusg ≥ 1 (or the sphere with at least three punctures). Given a smooth negative functionK withK =K_{0} 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.
pp 153-158 May 2004
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 inL^{2} (M) and that if a sequence of functions fn in ƒ_{n} converges inL^{2}(M), then so do the partial derivatives of the functions ƒ_{n}.
pp 159-180 May 2004
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.
pp 181-197 May 2004
Geometry of good sets inn-fold Cartesian product
A Kłopotowski M G Nadkarni K P S Bhaskara Rao
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.
pp 199-202 May 2004
Containment of c_{0} and ℓ_{1} in π_{1}(E, F)
Suppose π_{1}(E, F) is the space of all absolutely 1-summing operators between two Banach spacesE andF. We show that ifF has a copy of c_{0}, then π_{1} (E, F) will have a copy of c_{0}, and under some conditions ifE has a copy of ℓ_{1} then π_{1} (E, F) would have a complemented copy of ℓ_{1}.
pp 203-213 May 2004
Unsteady stokes equations: Some complete general solutions
A Venkatlaxmi B S Padmavathi T Amaranath
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.
pp 215-215 May 2004 Erratum
Current Issue
Volume 129 | Issue 4
September 2019
© 2017-2019 Indian Academy of Sciences, Bengaluru.