A solution of the global controllability problem for a class of nonlinear control systems of the Volterra integro-differential equations is presented. It is proven that there exists a family of continuous controls that solve the global controllability problem for the considered class and...

In a series of papers, an approach to field theory is developed in which matter appears by interpreting source-free (homogeneous) fields over a 6-dimensional space of signature (3,3), as interacting (inhomogeneous) fields in spacetime. The extra dimensions are given a physical meaning as...

In [3, Theorem 3] it is proved that for a ring homomorphism : → such that () = for all ideals of , given any chain of prime ideals ℘ ⊆ ℘ ⊆ … ℘ in there exists a chain of prime ideals ⊆ ⊆ … in such that () = ℘. Here, under the weaker assumption (℘) = ℘ for all prime...

The main aim of this monograph is to survey some recent results obtained by the author related to reverses of the Schwarz, triangle and Bessel inequalities. Some Grüss' type inequalities for orthonormal families of vectors in real or complex inner product spaces are presented as well....

The twin prime conjecture is a historically unsolved problem. Different from many previous approaches, this paper uses a 2-D mapping of odd numbers and subsequently transforms the 2-D mapping to reveal some base pattern regularity. Based on the repetitive base pattern analysis, a ratio, twin...

This paper is really an attempt to solve the age-old problem of the Goldbach Conjecture, by first restating it in terms of primes of the form 2x-q (where q is a prime less than or equal to x) and then proving the restated theorem. Restating the problem merely requires us to ask the question:...

In this paper a theorem concerning the general matrix triplet (, , ) where and are matrices over an arbitrary division ring with compatible dimensions × , × , × , respectively, is given. The equivalence near-canonical form of the matrix triplet () mentioned above is proposed and a practical...

We present a result on summability of power series in one variable, whose coefficients are holomorphic functions of several other complex variables. This result then is applied to the Cauchy problem for the heat equation in several spatial variables

Necessary and sufficient conditions are obtained for bilateral weighted shifts to be near subnormal . As an application of the main results, many new answers to the Hilbert space problem 160 are presented at the end of the paper