Until now, several methods have been developed to compute the domains of attraction for stationary points of polynomial non-linear systems. For the case of non-polynomial systems, though, this question is still open. In this paper a new method, based on Lyapunov’s stability theory and the theorem of Ehlich and Zeller, is presented for the computation of domains of attraction of non-polynomial s...

The generalized Liénard polynomial differential systems are the of form x′ = y, y′ − f(x)y g(x), where f and g polynomials. We characterize all having an invariant algebraic curve. show that first four higher coefficients in variable defining curve, determine completely system. This fact does not hold for arbitrary systems. Primary 34A05. Secondary 34C05, 37C10.

We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the so-called decision maker’s approach in which both criteria are combined into a single (usually non-linear) objective function. Previous work by Papadimitriou and Yannakakis showed how to efficiently approximate the Pareto curv...

We derive a new explicit formula in terms of sums over graphs for the $n$-point correlation functions general formal weighted double Hurwitz numbers coming from Kadomtsev-Petviashvili tau hypergeometric type (also known as Orlov-Scherbin partition functions). Notably, we use change variables suggested by associated spectral curve, and our turns out to be polynomial expression certain small set ...

It is shown that a simple closed curve in $${\mathbb {C}}^n$$ uniform limit of rectifiable curves each which has nontrivial polynomial hull itself hull. In case the rectifiable, to be hulls. also every , $$n\ge 2$$ can approximated total variation norm by polynomially convex, coincides with original except on an arbitrarily small segment. As corollary, it arc contained curve.

let $g$ be a simple graph of order $n$‎. ‎we consider the‎ ‎independence polynomial and the domination polynomial of a graph‎ ‎$g$‎. ‎the value of a graph polynomial at a specific point can give‎ ‎sometimes a very surprising information about the structure of the‎ ‎graph‎. ‎in this paper we investigate independence and domination‎ ‎polynomial at $-1$ and $1$‎.

Cryo-electron microscopy (Cryo-EM) is a powerful technique to produce 3-dimensional density maps for large molecular complexes. Although many atomic structures have been solved from cryo-EM density maps, it is challenging to derive atomic structures when the resolution of density maps is not sufficiently high. Geometrical shape representation of secondary structural components in a medium-resol...

An algebraic curve is defined as the zero set of a multivariate polynomial. We consider the problem of fitting an algebraic curve to a set of vectors given an additional set of vectors labelled as interior or exterior to the curve. The problem of fitting a linear curve in this way is shown to lend itself to a support vector representation, allowing non-linear curves and high dimensional surface...

In this paper a class of quartic trigonometric Bézier curve, called QT Bézier curve, with two shape parameters is presented. These curves not only inherit most properties of the usual quartic Bézier curves in the polynomial space, but also enjoy some other advantageous properties for shape modelling. The shape of the curve can be adjusted by altering the values of shape parameters while the con...

If K is a hyperbolic knot in the oriented S3, an algebraic component of its character variety containing the holonomy of the complete hyperbolic structure of finite volume of S3 \ K is an algebraic curve (excellent component K). The traces of the peripheral elements of K define polynomial functions in K. These functions are related in pairs by canonical polynomials. These peripheral polynomials...