On cyclic biquadratic fields related to a problem of Hasse

In this note we shall prove that there exist infinitely many cyclic biquadratic fieldsK whose integral bases are neither {1, , ², } nor {1, , , ³) for any numbers , inK. Next, we shall construct infinitely many cyclic biquadratic fieldsK which have the index 1, but still have not the integral basis {1, , ², ³) for every inK. Finally we shall give a class of biquadratic fields for a problem of Hasse concerning an integral basis.     

Tables of octic fields with a quartic subfield

We describe the computation of extended tables of degree 8 fields with a quartic subfield, using class field theory. In particular we find the minimum discriminants for all signatures and for all the possible Galois groups. We also discuss some phenomena and statistics discovered while making the tables, such as the occurrence of 11 non-isomorphic number fields having the same discriminant, or several pairs of non-isomorphic number fields having the same Dedekind zeta function.

     

On some Hasse Principles over formally real fields

Mathematische Zeitschrift -     

On a combinatorial problem related to permanents

Some numerical results will be presented concerning the largest and smallest values of square permanents containing the integers 1, 2, 3, ...,n ² n=1(1)8.Dedicated to Peter Naur on the occasion of his 60th birthday     

On a certain problem of integral geometry

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 53, pp. 95–99, 1990.     

On a problem related to the Vandermonde determinant

This short note describes new properties of the elementary symmetric polynomials, and reveals that the properties give an answer to the conjecture raised by El-Mikkawy in [M.E.A. El-Mikkawy, On a connection between the Pascal, Vandermonde and Stirling matrices—II, Appl. Math. Comput. 146 (2003) 759-769].     

On a certain approach to the problem orientation of electronic computers

Journal of Mathematical Sciences -     

On a certain nonlocal problem for a hyperbolic equation

The author proves the existence and uniqueness of a generalized solution of a nonlocal problem with an integral condition for a hyperbolic equation with n spatial variables. This work is a continuation of the studies started in [3–5], where the solvability problem of nonlocal problems with an integral condition was studied for hyperbolic equations on the plane. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.     

On certain co-H spaces related to Moore spaces

We show that certain co- spaces, constructed by Anick and Gray, carry a homotopy co-associative and co-commutative co- structure.

     

On certain integral inequalities related to Opial's inequality

The aim of the present paper is to establish some new integral inequalities involving three functions and their derivatives which in the special cases yield the well known Opial inequality and some of its generalizations.