Volume 102, Issue 1
April 1992, pages 1-81
pp 1- April 1992
pp 1-12 April 1992
For suitable functionsH = H(T) the maximum of¦(ζ(σ + it))z¦ taken overT≤t≤T + H is studied. For fixed σ(1/2≤σ≤l) and fixed complex constantsz “expected lower bounds” for the maximum are established.
pp 13-22 April 1992
We extend the notion of a parabolic vector bundle on a smooth curve to define generalized parabolic sheaves (GPS) on any integral projective curve X. We construct the moduli spacesM(X) of GPS of certain type onX. IfX is obtained by blowing up finitely many nodes inY then we show that there is a surjective birational morphism from M(X) to M (Y). In particular, we get partial desingularisations of the moduli of torsion-free sheaves on a nodal curveY.
pp 23-27 April 1992
In this paper we study the non-existence of nodal solutions for critical Sobolev exponent problem-div(|∇u|m−2∇u)=|u|p-1u+|u|q-1u inB(R)u = 0 on ∂B(R) whereB(R) is a ball of radiusR in ℝn.
pp 29-47 April 1992
In this paper we consider scalar convex conservation laws in one space variable in a stripD =(x, t): 0 ≤x ≤1,t > 0 and obtain an explicit formula for the solution of the mixed initial boundary value problem, the boundary data being prescribed in the sense of Bardos-Leroux and Nedelec. We also get an explicit formula for the solution of weighted Burgers equation in a strip.
pp 49-51 April 1992
A simpler example of regular space that is not completely regular is attempted.
pp 53-58 April 1992
In this paper two theorems on ¦ N,pn;δ¦k summability factors, which generalize the results of Bor  on ¦ N,pn¦k summability factors, have been proved.
pp 59-71 April 1992
In this paper we study maximal monotone differential inclusions with memory. First we establish two existence theorems; one involving convex-valued orientor fields and the other nonconvex valued ones. Then we examine the dependence of the solution set on the data that determine it. Finally we prove a relaxation theorem.
pp 73-81 April 1992
Gronwall’s inequality has many extensions and analogues among them the discrete one. In this paper we present theorems which look like Gronwall’s lemma in the classical propositional calculus.