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The Remez algorithm (Remez 1934), also called the Remez exchange algorithm, is an application of the Chebyshev alternation theorem that constructs the polynomial of best ...

The q-analog of the Pochhammer symbol defined by (a;q)_k={product_(j=0)^(k-1)(1-aq^j) if k>0; 1 if k=0; product_(j=1)^(|k|)(1-aq^(-j))^(-1) if k<0; ...

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

"Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. ...

For any system that seeks to minimize a function, only seven different local forms of catastrophe "typically" occur for four or fewer variables: 1. Fold catastrophe, 2. Cusp ...

The absolute value of a real number x is denoted |x| and defined as the "unsigned" portion of x, |x| = xsgn(x) (1) = {-x for x<=0; x for x>=0, (2) where sgn(x) is the sign ...

The dumbbell curve is the sextic curve a^4y^2=x^4(a^2-x^2). (1) It has area A=1/4pia^2 (2) and approximate arc length s approx 5.541a. (3) For the parametrization x = at (4) ...

A catastrophe which can occur for three control factors and two behavior axes. The elliptical umbilic is catastrophe of codimension 3 that has the equation ...

A catastrophe which can occur for one control factor and one behavior axis. It is the universal unfolding of the singularity f(x)=x^3 and has the equation F(x,u)=x^3+ux.

A catastrophe which can occur for three control factors and two behavior axes. The hyperbolic umbilic is the universal unfolding of the function germ f(x,y)=x^3+y^3. The ...