This paper is a continuation of [1] where the classical model was analyzed. Discussed are some quantization problems of two-dimensional affinely rigid body with the double dynamical isotropy. Considered are highly symmetric models for which the variables can be separated. Some explicit solutions are found using the Sommerfeld polynomial method.

The direct geometrico-static problem of cable-driven parallel robots with 5 cables is presented. The study provides procedures for the identification of all equilibrium poses of the end-effector when cable lengths are assigned. A leastdegree univariate polynomial in the ideal governing the problem is obtained, thus showing that the latter has 140 solutions in the complex field. By a continuatio...

Let a = (an)n≥1 be a periodic sequence, Fa(s) the meromorphic continuation of P n≥1 an/n , and Na(σ1, σ2, T ) the number of zeros of Fa(s), counted with their multiplicities, in the rectangle σ1 < Re s < σ2, | Im s| ≤ T . We extend previous results of Laurinčikas, Kaczorowski, Kulas, and Steuding, by showing that if Fa(s) is not of the form P (s)Lχ(s), where P (s) is a Dirichlet polynomial and ...

This paper presents a branch & cut algorithm to nd all isolated solutions of a system of polynomial constraints. Our ndings show that fairly straightforward reenements of interval methods inspired by AI constraint propagation techniques result in a multivariate root nding algorithm that is competitive with continuation methods on most benchmarks and which can solve a variety of systems that are...

Homotopy continuation is an efficient tool for solving polynomial systems. Its efficiency relies on utilizing adaptive stepsize and adaptive precision path tracking, and endgames. In this article, we apply homotopy continuation to solve steady state problems of hyperbolic conservation laws. A third-order accurate finite difference weighted essentially non-oscillatory (WENO) scheme with Lax-Frie...

Constructions of wavelets and prewavelets over triangulations with an emphasis of the continuous piecewise polynomial setting are discussed. Some recent results on piecewise linear prewavelets and orthogonal wavelets are presented. c © 2003 Elsevier Science B.V. All rights reserved.

Introduction. The purpose of this paper is to find explicit formulas for those terms in the trace formula which arise from Eisenstein series. The paper is a continuation of [l(g)]. (We refer the reader to the introduction of [l(g)] for a general discussion as well as a description of the notation we will use below.) We have already solved the most troublesome analytic problem. The difficulties ...

by Daniel James Bates Homotopy continuation techniques may be used to approximate all isolated solutions of a polynomial system. More recent methods which form the crux of the young field known as numerical algebraic geometry may be used to produce a description of the complete solution set of a polynomial system, including the positive-dimensional solution components. There are four main topic...

We critique a Padé analytic continuation method whereby a rational polynomial function is fit to a set of input points by means of a single matrix inversion. This procedure is accomplished to an extremely high accuracy using a novel symbolic computation algorithm. As an example of this method in action, it is applied to the problem of determining the spectral function of a single-particle therm...