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A typical vector (i.e., a vector such as the radius vector r) is transformed to its negative under inversion of its coordinate axes. Such "proper" vectors are known as polar ...

Given a module M over a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees module of M with respect to F is ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

A Saunders graphic is a plot of the dth base-b digits of a function f(x,y) as a function of x and y. The plots above show Saunders graphics for the functions ...

Let lambda_1, ..., lambda_n in C be linearly independent over the rationals Q, then Q(lambda_1,...,lambda_n,e^(lambda_1),...,e^(lambda_n)) has transcendence degree at least n ...

The triangle DeltaN_1N_2N_3 formed by joining a set of three Neuberg centers (i.e., centers of the Neuberg circles) obtained from the edges of a given triangle DeltaA_1A_2A_3 ...

An orientable surface with one boundary component such that the boundary component of the surface is a given knot K. In 1934, Seifert proved that such a surface can be ...

A "split" extension G of groups N and F which contains a subgroup F^_ isomorphic to F with G=F^_N^_ and F^_ intersection N^_={e} (Ito 1987, p. 710). Then the semidirect ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_4=f(x_4). Then Simpson's 3/8 rule ...

The square wave, also called a pulse train, or pulse wave, is a periodic waveform consisting of instantaneous transitions between two levels. The square wave is sometimes ...