Solvability of linear equations within weak mixing sets

Solvability of linear equations within the weak mixing sets

We introduce a new class of “random” subsets of natural numbers, WM sets. This class contains normal sets (sets whose characteristic function is a normal binary sequence). We provide necessary and sufficient conditions of solvability of systems of linear equations within every WM subset of N. We also provide a proof of solvability of partition-regular systems (Rado’s systems) within every WM su...

Solvability of Systems of Linear Operator Equations

Let G be a semigroup of commuting linear operators on a linear space S with the group operation of composition. The solvability of the system of equations /,/ = ,■, i = I, ... , r, where /, e G and j e S , was considered by Dahmen and Micchelli in their studies of the dimension of the kernel space of certain linear operators. The compatibility conditions Ijfr = Irfj , i ^ j , are necessar...

Solvability of Systems of Linear Interval Equations

On d-solvability for linear differential equations

The aim of this paper is to investigate the possibility of solving a linear differential equation of degree n by means of differential equations of degree less than or equal to a fixed d, 1 ≤ d < n. This paper recovers and extends work of G. Fano, M. F. Singer and E. Compoint. Representations of algebraic Lie algebras are themain tool. © 2008 Elsevier Ltd. All rights reserved.

Ramsey Properties of Subsets of N Solvability of Linear Diophantine Systems within Wm Sets 16

With my appreciation, I wish to thank my advisor Prof. Hillel Furstenberg for his guidance, support and encouragement during these unforgettable years of learning and research Abstract We associate ergodic properties to some subsets of the natural numbers. For any given family of subsets of the natural numbers one may study the question of occurrence of certain " algebraic patterns " in every s...