Many problems in kinematic synthesis of mechanisms and robots lead naturally to systems of bilinear equations in design parameters. Such systems are typically solved using well-known methods for solutions of systems of polynomial equations, e.g., Dialytic Elimination, Grobner bases, and Polynomial Continuation. This paper presents a new nullspace analysis method for solving a system of bilinear...

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/ ), where > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We use this result to resolve several open ...

We consider a random polynomial system with m equations and m real unknowns. Assume all equations have the same degree d and the law on the coefficients satisfies the Kostlan-Shub-Smale hypotheses. It is known that E(N) = d where N denotes the number of roots of the system. Under the condition that d does not grow very fast, we prove that lim supm→+∞ V ar( N dm/2 ) ≤ 1. Moreover, if d ≥ 3 then ...

The primitive equations (PEs) of the atmosphere and the oceans without viscosity are considered. These equations are not well-posed for any set of local boundary conditions. In space dimension 2.5 a set of nonlocal boundary conditions has been proposed in [4]. The present article is aimed at testing the validity of these boundary conditions with physically relevant data. The issues tested are t...

By a deficient polynomial system of n polynomial equations in n unknowns we mean a system that has fewer solutions than that predicted by the total degree, or the Bézout number, of the system. If the system is mhomogeneous, the Bézout number can be considerably reduced. In this paper, we introduce a homotopy for numerically determining all isolated solutions of deficient m-homogeneous systems. ...

A general formula is given for the conditional mean in terms of higher order statistics. Using this formula, a general scheme for nonlinear system identi cation is introduced including a broad range of nonlinearities which depends on the probability density function of the input. As a special case of that general scheme, the polynomial system identi cation problem is treated. It is shown that o...

In this article the instability of single phase flow in a circular pipe from laminar to turbulence regime has been investigated. To this end, after finding boundary conditions and equation related to instability of flow in cylindrical coordination system, which is called eigenvalue Orr Sommerfeld equation, the solution method for these equation has been investigated. In this article Chebyshev p...

Given a polynomial ideal and a term order, there is a unique reduced Grr obner basis and, for each polynomial, a unique normal form, namely the smallest (w.r.t. the term order) polynomial in the same coset. We consider the problem of nding this normal form for any given polynomial, without prior computation of the Grr obner basis. This is done by transforming a representation of the normal form...

One of the key questions in contemporary applied cryptography is whether there exist an efficient algorithm for solving the discrete logarithm problem in elliptic curves. The primary approach for this problem is to try to solve a certain system of polynomial equations [44]. Current attempts try to solve them directly with existing software tools which does not work well due to their very loosel...