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Let alpha(z),gamma(z):(a,b)->R^3 be curves such that |gamma|=1 and alpha·gamma=0, and suppose that alpha and gamma have holomorphic extensions alpha,gamma:(a,b)×(c,d)->C^3 ...

For every p, the kernel of partial_p:C_p->C_(p-1) is called the group of cycles, Z_p={c in C_p:partial(c)=0}. (1) The letter Z is short for the German word for cycle, ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

Let the absolute frequencies of occurrence of an event in a number of class intervals be denoted f_1, f_2, .... The cumulative frequency corresponding to the upper boundary ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...

The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore ...

A holyhedron is polyhedron whose faces and holes are all finite-sided polygons and that contains at least one hole whose boundary shares no point with a face boundary. D. ...

A fractal curve, also called the C-curve (Gosper 1972). The base curve and motif are illustrated below. Duvall and Keesling (1999) proved that the Hausdorff dimension of the ...

The problem of finding the strategy to guarantee reaching the boundary of a given region ("forest") in the shortest distance (i.e., a strategy having the best worst-case ...

Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U such that |f(z_0)|>=|f(z)| for all z in U, then f is constant. The ...