New Acceleration of Nearly Optimal Univariate Polynomial Root-findERS

Univariate polynomial root-finding has been studied for four millennia and is still the subject of intensive research. Hundreds of efficient algorithms for this task have been proposed. Two of them are nearly optimal. The first one, proposed in 1995, relies on recursive factorization of a polynomial, is quite involved, and has never been implemented. The second one, proposed in 2016, relies on subdivision iterations, was implemented in 2018, and promises to be practically competitive, although user's current choice for univariate polynomial root-finding is the package MPSolve, proposed in 2000, revised in 2014, and based on Ehrlich's functional iterations. By proposing and incorporating some novel techniques we significantly accelerate both subdivision and Ehrlich's iterations. Moreover our acceleration of the known subdivision root-finders is dramatic in the case of sparse input polynomials. Our techniques can be of some independent interest for the design and analysis of polynomial root-finders.Comment: 89 pages, 5 figures, 2 table

Color television system for a manned space base Progress report

Color television system for manned space statio

Model validation of spatiotemporal systems using correlation function tests

Model validation is an important and essential final step in system identification. Although model validation for nonlinear temporal systems has been extensively studied, model validation for spatiotemporal systems is still an open question. In this paper, correlation based methods, which have been successfully applied in nonlinear temporal systems are extended and enhanced to validate models of spatiotemporal systems. Examples are included to demonstrate the application of the tests

The development of a three-dimensional partially elliptic flow computer program for combustor research

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted

Tuning electronic structure of graphene via tailoring structure: theoretical study

Electronic structures of graphene sheet with different defective patterns are investigated, based on the first principles calculations. We find that defective patterns can tune the electronic structures of the graphene significantly. Triangle patterns give rise to strongly localized states near the Fermi level, and hexagonal patterns open up band gaps in the systems. In addition, rectangular patterns, which feature networks of graphene nanoribbons with either zigzag or armchair edges, exhibit semiconducting behaviors, where the band gap has an evident dependence on the width of the nanoribbons. For the networks of the graphene nanoribbons, some special channels for electronic transport are predicted.Comment: 5 figures, 6 page