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Murata's constant is defined as C_(Murata) = product_(p)[1+1/((p-1)^2)] (1) = 2.82641999... (2) (OEIS A065485), where the product is over the primes p. It can also be written ...

Knuth (2008, p. 44) terms the 24-vertex graph based on the notes of the musical scale illustrated above the "musical graph." This graph can be seen to be the 24-vertex case ...

Consider a reference triangle DeltaABC with circumcenter O and orthocenter H, and let DeltaA^*B^*C^* be its reflection triangle. Then Musselman's theorem states that the ...

Given an original knot K, the knots produced by mutations together with K itself are called mutant knots. Mutant knots are often difficult to distinguish. For instance, ...

Consider a knot as being formed from two tangles. The following three operations are called mutations. 1. Cut the knot open along four points on each of the four strings ...

Let Omega be a space with measure mu>=0, and let Phi(P,Q) be a real function on the product space Omega×Omega. When (mu,nu) = intintPhi(P,Q)dmu(Q)dnu(P) (1) = ...

The mutual information between two discrete random variables X and Y is defined to be I(X;Y)=sum_(x in X)sum_(y in Y)P(x,y)log_2((P(x,y))/(P(x)P(y))) (1) bits. Additional ...

n events are said to be mutually exclusive if the occurrence of any one of them precludes any of the others. Therefore, for events X_1, ..., X_n, the conditional probability ...

Let M be a sigma-algebra M, and let lambda_1 and lambda_2 be measures on M. If there exists a pair of disjoint sets A and B such that lambda_1 is concentrated on A and ...

A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...