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The nonlinear three-dimensional map X^. = -(Y+Z) (1) Y^. = X+aY (2) Z^. = b+XZ-cZ (3) whose strange attractor is show above for a=0.2, b=0.2, and c=8.0.

|_n]={n for n!=0; 1 for n=0. (1)

If any of the roots of a polynomial are increased, then all of the critical points increase.

The operation of taking an nth root of a number.

The sum of the reciprocals of roots of an equation equals the negative coefficient of the linear term in the Maclaurin series.

There is a one-to-one correspondence between the sets of equivalent correspondences (not of value 0) on an irreducible curve of curve genus p, and the rational collineations ...

The function f(x,y)=(1-x)^2+100(y-x^2)^2 that is often used as a test problem for optimization algorithms (where a variation with 100 replaced by 105 is sometimes used; ...

A generalization of the Runge-Kutta method for solution of ordinary differential equations, also called Kaps-Rentrop methods.

In the illusion illustrated above, when the concentric square borders with rounded edges are rotated slowly, the entire pattern appears to pulsate radially.

The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a ...