here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

We propose the representability hierarchy of algebraic functions over C, which relates classic questions like the unsolvability of the quintic by radicals to unresolved questions like Hilbert’s 13th problem in its original algebraic form. We construct the theory of algebraic functions via both superpositions and algebraic geometry and then justify the known positions of the universal algebraic ...

1 Algebraic sets, affine varieties, and the Zariski topology 4 1.1 Algebraic sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Hilbert basis theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Zariski topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Proof that affine algebraic sets form closed sets on a t...

This paper extends the modified affine arithmetic in matrix form method for bivariate polynomial evaluation and algebraic curve plotting in 2D to modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting in 3D. Experimental comparison shows that modified affine arithmetic in tensor form is not only more accurate but also much faster than affin...

The ability of a multibody dynamic model to accurately predict the response of a physical system relies heavily on the use of appropriate system parameters in the mathematical model. Thus, the identification of unknown system parameters (or parameters that are known only approximately) is of fundamental importance. If experimental measurements are available for a mechanical system, the paramete...

Traditional methods for algebraic manipulation of polynomials in Bernstein form try to obtain an explicit formula for each coefficient of the result of a given procedure, such us multiplication, arbitrarily high degree elevation, composition, or differentiation of rational functions. Whereas this strategy often furnishes involved expressions, these operations become trivial in terms of convolut...

The turbulent mass ux, or equivalently the uctuating Favre velocity mean, appears in the rst and second moment equations of compressible k " and Reynolds stress closures. Mathematically it is the di erence between the unweighted and density-weighted averages of the velocity eld and is therefore a measure of the e ects of compressibility through variations in density. It appears to be fundamenta...

We propose an algorithm for interactive ray-casting of algebraic surfaces of high degree. A key point of our approach is a polynomial form adapted to the view frustum. This so called frustum form yields simple expressions for the Bernstein form of the ray equations, which can be computed efficiently using matrix products and pre-computed quantities. Numerical root-finding is performed using B-s...

This paper describes how a commonly used canonical form for linear differential-algebraic equations can be computed using numerical software from the linear algebra package LAPACK. This makes it possible to automate for example observer construction and parameter estimation in linear models generated by a modeling language like Modelica.

The quantum damped harmonic oscillator is described by the master equation with usual Lindblad form. The equation has been solved completely by us in arXiv : 0710.2724 [quant-ph]. To construct the general solution a few facts of representation theory based on the Lie algebra su(1, 1) were used. In this paper we treat a general model described by a master equation with generalized Lindblad form....