Given a homotopy connecting two polynomial systems we provide a rigorous algorithm for tracking a regular homotopy path connecting an approximate zero of the start system to an approximate zero of the target system. Our method uses recent results on the complexity of homotopy continuation rooted in the alpha theory of Smale. Experimental results obtained with the implementation in the numerical...

The interval Newton's method in conjunction with generalized bisection, as implemented in the public domain mftware program INTBIS by Kearfott and Novoa, is a method of miring single and simultaneous nonlinear equatiom. In this paper, this method is used m solve 15 test problems from different chemical engineering application areas, and an ill-scaled tramcendentai equation. The interval method ...

Combinig the harmonic balance method (HBM) and a continuation method is a well-known technique to follow the periodic solutions of dynamical systems when a control parameter is varied. However, since deriving the algebraic system containing the Fourier coefficients can be a highly cumbersome procedure, the classical HBM is often limited to polynomial (quadratic and cubic) nonlinearities and/or ...

searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Hi...

the topological index of a graph g is a numeric quantity related to g which is invariant underautomorphisms of g. the vertex pi polynomial is defined as piv (g)  euv nu (e)  nv (e).then omega polynomial (g,x) for counting qoc strips in g is defined as (g,x) =cm(g,c)xc with m(g,c) being the number of strips of length c. in this paper, a new infiniteclass of fullerenes is constructed. the ...

searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Hi...

searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Hi...

searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Hi...

Array-based Discovery of Aptamer Pairs Report Title Affinity reagent pairs that recognize distinct epitopes on a target protein can greatly improve the sensitivity and specificity of molecular detection. Importantly, such pairs can be conjugated to generate reagents that achieve twosite “bidentate” target recognition, with affinities greatly exceeding either monovalent component. DNA aptamers a...

Homotopies for polynomial systems provide computational evidence for a challenging instance of a conjecture about whether all solutions are real. The implementation of SAGBI homotopies involves polyhedral continuation, at deformation and cheater's ho-motopy. The numerical diiculties are overcome if we work in the true synthetic spirit of the Schubert calculus by selecting the numerically most f...