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Let ad=bc, then Hirschhorn's 3-7-5 identity, inspired by the Ramanujan 6-10-8 identity, is given by (1) Another version of this identity can be given using linear forms. Let ...

Suppose that A is a Banach algebra and X is a Banach A-bimodule. For n=0, 1, 2, ..., let C^n(A,X) be the Banach space of all bounded n-linear mappings from A×...×A into X ...

The Hodge conjecture asserts that, for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually rational linear ...

A geometric theorem related to the pentagram and also called the Pratt-kasapi theorem. It states ...

A function phi(t) satisfies the Hölder condition on two points t_1 and t_2 on an arc L when |phi(t_2)-phi(t_1)|<=A|t_2-t_1|^mu, with A and mu positive real constants. In some ...

Let 1/p+1/q=1 (1) with p, q>1. Then Hölder's inequality for integrals states that int_a^b|f(x)g(x)|dx<=[int_a^b|f(x)|^pdx]^(1/p)[int_a^b|g(x)|^qdx]^(1/q), (2) with equality ...

Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

A minimal embedded surface discovered in 1992 consisting of a helicoid with a hole and handle (Science News 1992). It has the same topology as a punctured sphere with a ...

The Hofstadter ellipses are a family of triangle ellipses introduced by P. Moses in February 2005. The Hofstadter ellipse E(r) for parameter 0<r<1 is defined by the trilinear ...

The r-Hofstadter triangle of a given triangle DeltaABC is perspective to DeltaABC, and the perspector is called the Hofstadter point. The triangle center function is ...