We study Fréchet differentiable stable operators in real Banach spaces. We present the theory of linear and nonlinear stable operators in a systematic way and prove solvability theorems for operator equations with differentiable expanding operators. In addition, some relations to the theory of monotone operators in Hilbert spaces are discussed. Using the obtained solvability results, we formula...

The purpose of this paper is using Korpelevich’s extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approxima...

Let P be a Poisson algebra with Lie bracket {,} over field F of characteristic p≥0. In this paper, the structure is investigated. particular, if solvable respect to its bracket, then we prove that ideal J generated by all elements {{{x1,x2},{x3,x4}},x5} x1,…,x5∈P associative nilpotent index bounded function derived length P. We use result further and p≠2, {P,P}P nil.

The notion of solvability in the call-by-value-calculus is deened and completely characterized, both from an operational and a logical point of view. The operational characterization is given through a reduction machine, performing the classical-reduction, according to an innermost strategy. In fact, it turns out that the call-by-value reduction rule is too weak for capturing the solvability pr...

Attila Bérczes (University of Debrecen): On arithmetic properties of solutions of norm form equations. Abstract. Let α be an algebraic number of degree n and K := Q(α). Consider the norm form equation NK/Q(x0 + x1α+ x2α + . . .+ xn−1α) = b in x0, . . . , xn−1 ∈ Z. (1) Let H denote the solution set of (1). Arranging the elements of H in an |H| × n array H, one may ask at least two natural questi...

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...

The known facts about solvability of equations over groups are considered from a more general point of view. A generalized version of the theorem about solvability of unimodular equations over torsion-free groups is proved. In a special case, this generalized version become a multivariable variant of this theorem. For unimodular equations over torsion free groups, we prove an analogue of Magnus...

This paper contains two results on the Lp regularity problem on Lipschitz domains. For second order elliptic systems and 1 < p < ∞, we prove that the solvability of the Lp regularity problem is equivalent to that of the Lp ′ Dirichlet problem. For higher order elliptic equations and systems, we show that if p > 2, the solvability of the Lp regularity problem is equivalent to a weak reverse Höld...

Let ` ) → k. It has long been known that −1 ∼= ∫ W J̃ ( e, . . . , 1 ‖Θ‖ ) dl

We investigate a new type of graph inequality (in the tradition of Cvetković, Simić, and Capobianco) which is based on the subgraph relation and which allows as terms fixed graphs, graph variables with specified vertices, and the operation of identifying vertices. We present a simple graph inequality which does not have a solution, and show that the solvability of inequalities with only one gra...