Sentence examples for defined by a polynomial from inspiring English sources

Abstract: Algebraic varieties are geometric objects defined by polynomials---you have known many examples since high school, where you learned that a circle can be defined by a polynomial equation such as x^2+y^2=1.

Preliminary results show that at the singularity region, S1, the control-derivative term disappears and the differential equation is degenerated to a center manifold defined by a polynomial (quadratic in general) equation on u.

For a path defined by a polynomial parametric curve r, we show that the (square of the) time optimal feedrate can be determined as a piecewise-rational function of the curve parameter ξ, with break-points corresponding to the roots of certain polynomial equations.

Theorem 4.8 shows that the positivity of the Hankel operator with kernel (1.2) defined by a polynomial P ( x ) is determined by another polynomial Q ( x ) defined by formula (3.4).

Generalizing this problem, one can ask how many lines can be drawn on a quintic Calabi Yau manifold, such as the one illustrated above, which is defined by a polynomial of degree five.

We have designed a new symbolic numeric strategy for computing efficiently and accurately floating point Puiseux series defined by a bivariate polynomial over an algebraic number field.

We address the algebraic problem of analyzing the local topology of each singularity of a plane complex algebraic curve defined by a squarefree polynomial with both exact (i.e. integers or rationals) and inexact data (i.e. numerical values).

When a system is described by higher order differential equations with time as the independent variable, the solution for the homogeneous system is defined by a matrix polynomial eigenproblem.

These functions are defined by a Hermite polynomial modulated with a Gaussian function (1).

These functions are defined by a Hermite polynomial modulated with a Gaussian function as (1).

Note that for the black top roads increase case (plot (a)), the growth is defined by a 2nd order polynomial trend.