This paper presents a new, compact, canonical representation for arithmetic expressions, called Taylor Expansion Diagram. It can be used to facilitate the verification of RTL specifications and hardware implementations of arithmetic designs, and specifically the equivalence checking of complex algebraic and arithmetic expressions that arise in symbolic verification. This new representation is b...

The sparse matrix/canonical grid (SMCG) Method, which has been shown to be an efficient method for calculating the scattering from one-dimensional and two-dimensional random rough surfaces, is extended to three-dimensional (3-D) dense media scattering. In particular, we study the scattering properties of media containing randomly positioned and oriented dielectric spheroids. Mutual interactions...

We propose techniques for the verification of hybrid systems using template polyhedra, i.e., polyhedra whose inequalities have fixed expressions but with varying constant terms. Given a hybrid system description and a set of template linear expressions as inputs, our technique constructs over-approximations of the reachable states using template polyhedra. Therefore, operations used in symbolic...

For a QCD chiral critical point to exist, the parameter region of small quark masses for which the finite temperature transition is first-order must expand when the chemical potential is turned on. This can be tested by a Taylor expansion of the critical surface (mu,d ,ms)c(μ). We present a new method to perform this Taylor expansion numerically, which we first test on an effective model of QCD...

This paper presents a new, univariate dimension-reduction method for calculating statistical moments of response of mechanical systems subject to uncertainties in loads, material properties, and geometry. The method involves an additive decomposition of a multi-dimensional response function into multiple one-dimensional functions, an approximation of response moments by moments of single random...

In this paper we introduce some new subclasses of the class σ of bi-univalent functions and obtain bounds for the initial coefficients of the Taylor series expansion of functions from the considered classes.

A one-step 4-stage Hermite-Birkhoff-Taylor method of order 12, denoted by HBT(12)4, is constructed for solving nonstiff systems of first-order differential equations of the form y′ = f(x, y), y(x0) = y0. The method uses derivatives y′ to y(9) as in Taylor methods combined with a 4-stage Runge-Kutta method. Forcing an expansion of the numerical solution to agree with a Taylor expansion of the tr...

We prove the Taylor-Kubo formula for a class of isotropic, non-mixing flows with long-range correlation. For the proof, we develop the method of high order correctors expansion.

In this paper , numerical solotion of Abel's integral equationby using the Taylor expanssion of the unknown functionvia collection method based on Sinc is considered...