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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 ...

Operations research is a vast branch of mathematics which encompasses many diverse areas of minimization and optimization. Thousands of books have been written worldwide on ...

Wavelets are a class of a functions used to localize a given function in both space and scaling. A family of wavelets can be constructed from a function psi(x), sometimes ...

Given a pick-7 lottery with 23 numbers that pays a prize to anyone matching at least 4 of the 7 numbers, there is a set of 253 tickets that guarantees a win. This set ...

An idealized coin consists of a circular disk of zero thickness which, when thrown in the air and allowed to fall, will rest with either side face up ("heads" H or "tails" T) ...

Roman numerals are a system of numerical notations used by the Romans. They are an additive (and subtractive) system in which letters are used to denote certain "base" ...

A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...

Probability and Statistics

An Abelian category is a category for which the constructions and techniques of homological algebra are available. The basic examples of such categories are the category of ...

The dihedral group D_3 is a particular instance of one of the two distinct abstract groups of group order 6. Unlike the cyclic group C_6 (which is Abelian), D_3 is ...