This article presents several numerical algorithms for computations in sheaf cohomology. Let X be an algebraic set defined by a system of homogeneous multivariate polynomials with coefficients in C. Let C be a union of reduced, irreducible pure-dimensional curve components of X. The first algorithm computes the dimension of the first cohomology of any twist of the ideal sheaf of C. Let D be a r...

The optimal attitude estimate is often defined as the solution to a minimization problem. When the objective function of the minimization problem is quadratic in the attitude matrix or equivalently quartic in the attitude quaternion, for example, in GPS attitude determination, gradient-based iterative algorithms are usually used, which can only find the local minimizer. A novel numerical method...

An algorithm is given to compute the real points of the irreducible one-dimensional complex components of the solution sets of systems of polynomials with real coefficients. The algorithm is based on homotopy continuation and the numerical irreducible decomposition. An extended application is made to Griffis-Duffy platforms, a class of Stewart-Gough platform robots. 2000 Mathematics Subject Cla...

Quasipolynomials arise in a number of applications, and in particular as the characteristic equation associated with systems of delay differential equations. Quasipolynomial equations are generally difficult to solve, and most often must be solved numerically. In the non-trivial case, quasipolynomials have an infinite number of roots in the complex plane. We present a new numerical method for f...

This paper describes a new implementation of an algorithm to find all isolated Nash equilibria in a finite strategic game. The implementation uses the game theory software package Gambit to generate systems of polynomial equations which are necessary conditions for a Nash equilibrium, and polyhedral homotopy continuation via the package PHCpack to compute solutions to the systems. Numerical exp...

In this paper we study that the q-Euler numbers and polynomials are analytically continued to Eq(s). A new formula for the Euler’s q-Zeta function ζE,q(s) in terms of nested series of ζE,q(n) is derived. Finally we introduce the new concept of the dynamics of analytically continued q-Euler numbers and polynomials. 2000 Mathematics Subject Classification 11B68, 11S40 Key wordsq-Bernoulli polynom...

We analyze an immersed interface finite element method based on linear polynomials on noninterface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken H1-norm and L2-norm.

This is the continuation of the paper [4]. We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-p...

We present an explicit product formula for the spherical functions of the compact Gelfand pairs (G,K1) = (SU(p+ q), SU(p)× SU(q)) with p ≥ 2q, which can be considered as the elementary spherical functions of one-dimensional K-type for the Hermitian symmetric spaces G/K with K = S(U(p)× U(q)). Due to results of Heckman, they can be expressed in terms of Heckman-Opdam Jacobi polynomials of type B...

This is the continuation of Montes’ paper ‘‘On the canonical discussion of polynomial systems with parameters’’. In this paper, we define the Minimal Canonical Comprehensive Gröbner System of a parametric ideal and fix under which hypothesis it exists and is computable. An algorithm to obtain a canonical description of the segments of the Minimal Canonical CGS is given, thus completing the whol...