Volume 111, Issue 2
May 2001, pages 139-247
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 of 𝑞-degree 𝑚 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 degree 𝑛. 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.
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.
Let 𝑋 be an integral projective curve and 𝐿 ∈ Pic𝑎(𝑋), 𝑀 ∈ Pic𝑏(𝑋) with ℎ1(𝑋, 𝐿) = ℎ1(𝑋, 𝑀) = 0 and 𝐿, 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 when 𝐿 and 𝑀 are rank 1 torsion free sheaves on 𝑋. Most of our results are for 𝑋 with only nodes as singularities.
We give some conditions under which the periods of a self map of an algebraic variety are bounded.
In this paper we consider some Anderson type models, with free parts having long range tails 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.
In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with multipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.
In this paper, we give a simple alternative proof of a Tauberian theorem of Hardy and Littlewood (Theorem E stated below, ).
We give a necessary and sufficient condition for proximinality of a closed subspace of finite codimension in 𝑐0-direct sum of Banach spaces.
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 generalized the results of Jungck , Fisher , Kang and Kim , Jachymski , and Rhoades .