Asymptotic properties of solutions of difference equation of the form ∆xn = anφn(xσ(n)) + bn are studied. Conditions under which every (every bounded) solution of the equation ∆yn = bn is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than m is asymptotically equivalent to some solution...

This paper presents a novel two-frame motion estimation algorithm. The first step is to approximate each neighborhood of both frames by quadratic polynomials, which can be done efficiently using the polynomial expansion transform. From observing how an exact polynomial transforms under translation a method to estimate displacement fields from the polynomial expansion coefficients is derived and...

We prove that if the multipliers of the repelling periodic orbits of a complex polynomial grow at least like n 5+ε , for some ε > 0, then the Julia set of the polynomial is locally connected when it is connected. As a consequence for a polynomial the presence of a Cremer cycle implies the presence of a sequence of repelling periodic orbits with " small " multipliers. Somehow surprisingly the pr...

For any finitely generated torsion-free graded module over a polynomial ring, there exists a homogeneous ideal fitting into an exact sequence similar to a Bourbaki sequence even though its height is not restricted to two.

Let $A$ be an associative algebra over a field of characteristic zero. A central polynomial is the free that takes values $A.$ In this survey, we present some recent results about exponential growth codimension sequence and proper in setting algebras with involution graded by finite group.

In this article, we show that for each property of graphs G in the Polynomial Hierarchy (PH) there is a sequence φ1, φ2, . . . of formulas of the full hybrid logic which are satisfied exactly by the frames in G. Moreover, the size of φn is bounded by a polynomial in n. These results lead to the definition of syntactically defined fragments of hybrid logic whose model checking problem is complet...

A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of r...

Certificates to a linear algebra computation are additional data structures for each output, which can be used by a—possibly randomized— verification algorithm that proves the correctness of each output. Wiedemann’s algorithm projects the Krylov sequence obtained by repeatedly multiplying a vector by a matrix to obtain a linearly recurrent sequence. The minimal polynomial of this sequence divid...

In this paper, we investigate the computational complexity of subgraph reconfiguration problems in directed graphs. More specifically, focus on problem reconfiguring arborescences a digraph, where an arborescence is graph such that its underlying undirected forms tree and all vertices have in-degree at most 1. Given two goal to determine whether there (reconfiguration) sequence between given ea...

A polynomial SDP (semidefinite program) minimizes a polynomial objective function over a feasible region described by a positive semidefinite constraint of a symmetric matrix whose components are multivariate polynomials. Sums of squares relaxations developed for polynomial optimization problems are extended to propose sums of squares relaxations for polynomial SDPs with an additional constrain...