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The complexity of a process or algorithm is a measure of how difficult it is to perform. The study of the complexity of algorithms is known as complexity theory. In general, ...

A Julia set J consisting of a set of isolated points which is formed by taking a point outside an underlying set M (e.g., the Mandelbrot set). If the point is outside but ...

A linear functional defined on a subspace of a vector space V and which is dominated by a sublinear function defined on V has a linear extension which is also dominated by ...

The bifurcation of a fixed point to a limit cycle (Tabor 1989).

An invariant set S subset R^n is said to be a C^r (r>=1) invariant manifold if S has the structure of a C^r differentiable manifold (Wiggins 1990, p. 14). When stable and ...

A method which can be used to solve the initial value problem for certain classes of nonlinear partial differential equations. The method reduces the initial value problem to ...

The so-called generalized Kadomtsev-Petviashvili-Burgers equation is the partial differential equation ...

An algorithm in control theory introduced by Kalman (1960) and refined by Kalman and Bucy (1961). It is an algorithm which makes optimal use of imprecise data on a linear (or ...

A pair of linear operators L and A associated with a given partial differential equation which can be used to solve the equation. However, it turns out to be very difficult ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...