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A topological space X is pathwise-connected iff for every two points x,y in X, there is a continuous function f from [0,1] to X such that f(0)=x and f(1)=y. Roughly speaking, ...

A power series containing fractional exponents (Davenport et al. 1993, p. 91) and logarithms, where the logarithms may be multiply nested, e.g., lnlnx.

A set S with a single point P removed is called a punctured set, written S\{P}.

The study of the implications of chaos for a system in the semiclassical (i.e., between classical and quantum mechanical) regime. In quantum chaos, trajectories do not ...

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

A real matrix is a matrix whose elements consist entirely of real numbers. The set of m×n real matrices is sometimes denoted R^(m×n) (Zwillinger 1995, p. 116).

A vector whose elements are real numbers.

A real vector space is a vector space whose field of scalars is the field of reals. A linear transformation between real vector spaces is given by a matrix with real entries ...

A fraction a/b written in lowest terms, i.e., by dividing numerator and denominator through by their greatest common divisor (a,b). For example, 2/3 is the reduced fraction ...

Let m and m+h be two consecutive critical indices of f and let F be (m+h)-normal. If the polynomials p^~_k^((n)) are defined by p^~_0^((n))(u) = 1 (1) p^~_(k+1)^((n))(u) = ...