Related papers: A sufficient condition for existence of iterative …
Some easily verifiable sufficient conditions for the nonexistence of iterative roots for multifunctions on arbitrary nonempty sets are presented. Typically if the graph of the multifunction has a distinguished point with a relatively large…
In this paper we study the existence of continuous solutions and their constructions for a second order iterative functional equation, which involves iterate of the unknown function and a nonlinear term. Imposing Lipschitz conditions to…
The paper is concerned with the completeness problem of root functions of general boundary value problems for first order systems of ordinary differential equations. Namely, we introduce and investigate the class of \emph{weakly regular…
In this paper we investigate iterative roots of strictly monotone upper semi-continuous multifunctions having finitely many jumps. Known results are concerning roots of order 2 for multifunctions of exact one jump. For the general…
Motivated by a question of van der Poorten about the existence of infinite chain of prime numbers (with respect to some base), in this paper we advance the study of sequences of consecutive polynomials whose coefficients are chosen…
Given an order, a commutative ring whose additive group is free of finite rank, a natural computational question is whether a fixed univariate polynomial $f \in \mathbb{Z}[X]$ has a root in this ring. In this paper, we show that the…
We prove that characteristic equations of certain types of delay differential systems, under some mild conditions on their coefficients, can possess infinitely many complex roots.
This paper discusses examples of integral factorial ratios of height 2 or more. It classifies (apart from finitely many examples) such factorial ratios with height 2 and norm at most 1/3, and describes a general result which exhibits more…
We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.
We present a construction of a certain infinite complete partial order (CPO) that differs from the standard construction used in Scott's denotational semantics. In addition, we construct several other infinite CPO's. For some of those, we…
In this paper, we prove that every iterative differential embedding problem over an algebraic function field in positive characteristic with an algebraically closed field of constants has a proper solution.
In this note we consider roots of multivariate polynomials over a finite grid. When given information on the leading monomial with respect to a fixed monomial ordering, the footprint bound [8, 5] provides us with an upper bound on the…
It is desirable that a given continued fraction algorithm is simple in the sense that the possible representations can be characterized in an easy way. In this context the so-called finite range condition plays a prominent role. We show…
In this paper, we classify, up to three possible exceptions, all monic, post-critically finite quadratic polynomials $f(x)\in \mathbb{Z}[x]$ with an iterate reducible module every prime, but all of whose iterates are irreducible over…
The main result of this paper is that the isomorphism for omega-automatic trees of finite height is at least has hard as second-order arithmetic and therefore not analytical. This strengthens a recent result by Hjorth, Khoussainov,…
For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…
We establish a sufficient condition for the ultimate positivity of P-recursive sequences of arbitrary order with a unique dominant root. By additionally verifying finitely many initial terms, the positivity can also be resolved. As an…
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…
The paper studies the question of existence of polynomials with given roots over associative non-commutative rings with identity. It is shown that in the case of an associative division ring for arbitrary n elements of this ring there…
In this article we compare the known dynamical polynomial time algorithm for the game-over attack strategy, to that of the brute force approach; of checking all the ordered rooted subtrees of a given tree that represents a given computer…