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The fundamental group of an arcwise-connected set X is the group formed by the sets of equivalence classes of the set of all loops, i.e., paths with initial and final points ...

Two geometric figures are said to be concentric if their centers coincide. The region between two concentric circles is called an annulus. The following table summarizes some ...

Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the triangle are known as Malfatti circles. The Malfatti configuration ...

Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

An exponential sum of the form sum_(n=1)^Ne^(2piiP(n)), (1) where P(n) is a real polynomial (Weyl 1914, 1916; Montgomery 2001). Writing e(theta)=e^(2piitheta), (2) a notation ...

A diafix of a string T=s_1s_2...s_N is a substring s_(i+1)...s_(N-i) (0<=i<N/2). It is therefore not a first (prefix) or last (suffix) part of a string, but rather is a ...

A hyperstring is a simple semi-Hamiltonian acyclic digraph (V,E) with a labeling of the edges in E such that, for all vertices i,j,p,q in V, either pi(i,j)=pi(p,q) or pi(i,j) ...

Transparallel processing refers to this search for regularities in O(2^N) strings as if only one string of length N were concerned (as is possible if the strings form a ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

Data resulting from the observation of a population on a number of variables over time. Whenever observations are made more than once, the data is considered to be ...