Volume 111, Issue 2
May 2001, pages 139-247
pp 139-149 May 2001
We propound a descent principle by which previously constructed equations over GF(qn)(X) may be deformed to have incarnations over GF(q)(X) without changing their Galois groups. Currently this is achieved by starting with a vectorial (= additive)q-polynomial ofq-degreem with Galois group GL(m, q) and then, under suitable conditions, enlarging its Galois group to GL(m, qn) by forming its generalized iterate relative to an auxiliary irreducible polynomial of degreen. Elsewhere this was proved under certain conditions by using the classification of finite simple groups, and under some other conditions by using Kantor’s classification of linear groups containing a Singer cycle. Now under different conditions we prove it by using Cameron-Kantor’s classification of two-transitive linear groups.
pp 151-161 May 2001
In this paper we do phrase the obstruction for realization of a generalized group character, and then we give a classification of Clifford systems in terms of suitable low-dimensional cohomology groups.
pp 163-172 May 2001
LetX be an integral projective curve andL ∃ Pica(X),M ∃ Picb (X) with h1(X, L)= h1(X, M) = 0 andL, M general. Here we study the rank of the multiplication map μL,M:H0(X,L)⊗H0(X,M)→H0(X,L⊗M). We also study the same problem whenL andM are rank 1 torsion free sheaves onX. Most of our results are forX with only nodes as singularities.
pp 173-178 May 2001
We give some conditions under which the periods of a self map of an algebraic variety are bounded.
pp 179-201 May 2001
In this paper we consider some Anderson type models, with free parts having long range tails and with the random perturbations decaying at different rates in different directions and prove that there is a.c. spectrum in the model which is pure. In addition, we show that there is pure point spectrum outside some interval. Our models include potentials decaying in all directions in which case absence of singular continuous spectrum is also shown.
pp 203-219 May 2001
In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with miltipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.
pp 221-227 May 2001
In this paper, we give a simple alternative proof of a Tauberian theorem of Hardy and Littlewood (Theorem E stated below, ).
pp 229-239 May 2001
We give a necessary and sufficient condition for proximinality of a closed subspace of finite codimension in c0-direct sum of Banach spaces.
pp 241-247 May 2001
The purpose of this paper is to prove a common fixed point theorem, from the class of compatible continuous maps to a larger class of maps having weakly compatible maps without appeal to continuity, which generalizes the results of Jungck , Fisher , Kang and Kim , Jachymski , and Rhoades .