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The set of L^p-functions (where p>=1) generalizes L2-space. Instead of square integrable, the measurable function f must be p-integrable for f to be in L^p. On a measure ...

The M'Cay cubic Z(X_3) is a self-isogonal cubic given by the locus of all points whose pedal circle touches the nine-point circle, or equivalently, the locus of all points P ...

Markov's theorem states that equivalent braids expressing the same link are mutually related by successive applications of two types of Markov moves. Markov's theorem is ...

The "mathematical paradigm" is a term that may be applied to the fundamental idea that events in the world can be described by mathematical equations, and that solutions to ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

A nonnegative function g(x,y) describing the "distance" between neighboring points for a given set. A metric satisfies the triangle inequality g(x,y)+g(y,z)>=g(x,z) (1) and ...

Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

A quotient ring (also called a residue-class ring) is a ring that is the quotient of a ring A and one of its ideals a, denoted A/a. For example, when the ring A is Z (the ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...

Given a circular table of diameter 9 feet, which is the minimal number of planks (each 1 foot wide and length greater than 9 feet) needed in order to completely cover the ...