Table of contents

In this paper local measures are associated to Dirichlet series of certain cusp forms on over a -field. In certain cases the measures are proved to be bounded. This guarantees the existence of -adic Mellin transform. Bibliograhy: 4 titles.

Passage from the category of modules to the derived category gives insight into some classical results of homological dimension theory, and also yields a proof of the nondegeneracy of the Yoneda multiplication , where the argument is a noetherian module (or a finite complex with noetherian homology) and is a regular local ring. Bibliography: 9 titles.

This paper consists of two sections. In § 1 maximal, almost maximal, and complete valuation rings are characterized in terms of the decomposability of torsion-free modules of rank 2. In § 2 an attempt is made to describe the maximal -orders in the matrix ring , where is a valuation ring of height 1 in the field . Also, § 2 contains a generalization to a matrix algebra over a field of the well-known fact that a maximal subring of a field is either a field or a valuation ring of

height 1.

Bibliography: 9 titles.

Let be an alphabet and let be an -code, i.e. a set consisting of words in the alphabet ; let denote the length of a word . Suppose that , that is the alphabet of the message language, and , , , is an alphabetic encoding,

characterizes the smallest number of comparisons which are needed to solve the problem of being one-to-one for the -code in the worst case when the size of the input information (the unit of measurement is a comparison of letters from ). It is proved that . We show that a nonhomogeneous equation in words in three unknowns has at most one nontrivial solution, up to isomorphism. Bibliography: 10 titles.

In this paper bounded and almost periodic (in the sense of Bohr and in the sense of Stepanov) solutions of evolutionary variational inequalities with monotone operators are investigated. Natural existence and uniqueness theorems are obtained for such solutions. The regularity with respect to time of bounded solutions is also studied in the appropriate spaces. Bibliography: 19 titles.

In this article the author proves that for any holomorphic mapping the set

of hyperplanes deficient in the Valiron sense forms a polar set. This gives a positive answer to a question posed by Griffiths and King. Bibliography: 16 titles.

This paper constructs an example of a weight function on the interval such that , , whereas the corresponding sequence of orthonormal polynomials is unbounded at . Bibliography: 6 titles.

Suppose denotes a -subgroup of order of a group which is different from its normalizer in . A criterion for the simplicity of a group is obtained which includes the theorems of Feit and Ito on Zassenhaus groups of even degree and which is used to prove the following Theorem. If and the order of the centralizer of each nonidentity element of in is odd, then . It is proved that if has a complement in and if does not divide , then has a nilpotent invariant complement in , and if is complemented by a Frobenius subgroup in the simple group , then , . Related to the results of Brauer, Leonard, and Sibley on finite linear groups is the following Theorem.If the degree of each irreducible constituent of some faithful complex character of is less than , then either or , . Other results connected with the above theorems are also obtained. Bibliography: 24 titles.