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An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...

A filtration of ideals of a commutative unit ring R is a sequence of ideals ... subset= I_2 subset= I_1 subset= I_0=R, such that I_iI_j subset= I_(i+j) for all indices i,j. ...

A closed curve associated with a knot which is displaced along the normal by a small amount. For a knot K parameterized as x^mu(s) for 0<=s<=L along the length of the knot by ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

For a unit speed curve on a surface, the length of the surface-tangential component of acceleration is the geodesic curvature kappa_g. Curves with kappa_g=0 are called ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

Let X be a continuum (i.e., a compact connected metric space). Then X is hereditarily unicoherent provided that every subcontinuum of X is unicoherent. Any hereditarily ...

The mean triangle area of a triangle picked inside a regular hexagon with unit area is A^_=289/3888 (Woolhouse 1867, Pfiefer 1989). This is a special case of a general ...

A k×m×n hexagonal grid graph is a graph of adjoined hexagons consisting of k hexagons along the horizontal triangular axis, m along the northeast axis, and n along the ...