The paper considers the problem of estimating the unknown input of a nonlinear dynamical system, described by polynomial or rational differential equations, from a finite set of noisy output samples. Without additional information this problem is ill-posed since it is assumed that the unknown function belongs to an infinite-dimensional space. We tackle this difficulty by designing a novel class...

Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for R(si) sufficiently large, which has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. Two constructions of such series are available, one [1...

Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for <(si) sufficiently large, which has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. Two constructions of such series are available, one [1...

Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for R(si) sufficiently large, which has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. Two constructions of such series are available, one [1...

Non Uniform Rational B-splines (NURBs) are proved to be very promising for metamodeling in engineering problems, because they have unique properties such as local modification scheme, strong convex hull property, and infinitely differentiability, etc. Since NURBs are defined by control points, knot vector, and weights associated with control points, the precision of NURBs is influenced by all o...

High resolution space images are becoming more and more important as their resolution and availability improve. Images having a ground pixel size of 0.6 m or 1.0 m are competing with classical aerial photos. The space images cover large areas, reducing the number of control points needed. If rational polynomial coefficients (RPC) are available, the number of control points can be reduced even f...

We prove a special case of a dynamical analogue of the classical Mordell-Lang conjecture. In particular, let φ be a rational function with no superattracting periodic points other than exceptional points. If the coefficients of φ are algebraic, we show that the orbit of a point outside the union of proper preperiodic subvarieties of (P) has only finite intersection with any curve contained in (...