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The number of alternating permutations for n elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on n elements for which the ...

A partial order defined by (i-1, i), (i+1, i) for odd i.

A robust nonparametric test which is an alternative to the paired t-test. This test makes the basic assumption that there is information only in the signs of the differences ...

int_a^b(del f)·ds=f(b)-f(a), where del is the gradient, and the integral is a line integral. It is this relationship which makes the definition of a scalar potential function ...

The mathematical study of a nonlinear equation f(phi)=y, where f maps from a Hilbert space X to a Hilbert space Y and y in Y which abstracts the construction of optical ...

The following three pieces of information completely determine the homeomorphic type of a surface (Massey 1996): 1. Orientability, 2. Number of boundary components, 3. Euler ...

On the class of topological spaces, a homeomorphism class is an equivalence class under the relation of being homeomorphic. For example, the open interval (-pi/2,pi/2) and ...

An extension ring R subset= S such that every element of S is integral over R.

The throwing and catching of multiple objects such that at least one is always in the air. Some aspects of juggling turn out to be quite mathematical. The best examples are ...

D_(KY)=j+(sigma_1+...+sigma_j)/(|sigma_(j+1)|), (1) where sigma_1<=sigma_n are Lyapunov characteristic exponents and j is the largest integer for which ...