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The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...

The phrase Tomita-Takesaki theory refers to a specific collection of results proven within the field of functional analysis regarding the theory of modular Hilbert algebras ...

The Wallis formula follows from the infinite product representation of the sine sinx=xproduct_(n=1)^infty(1-(x^2)/(pi^2n^2)). (1) Taking x=pi/2 gives ...

A dozen dozen, also called a gross. 144 is a square number and a sum-product number.

The number 163 is very important in number theory, since d=163 is the largest number such that the imaginary quadratic field Q(sqrt(-d)) has class number h(-d)=1. It also ...

17 is a Fermat prime, which means that the 17-sided regular polygon (the heptadecagon) is constructible using compass and straightedge (as proved by Gauss).

The digits in the number 2187 form the two vampire numbers: 21×87=1827 and 2187=27×81. 2187 is also given by 3^7.

The number 24 is equal to 4! (four factorial). A number puzzle asks to construct 24 in as many ways possible using elementary mathematical operations on three copies of the ...

A generalization of the Lebesgue integral. A measurable function f(x) is called A-integrable over the closed interval [a,b] if m{x:|f(x)|>n}=O(n^(-1)), (1) where m is the ...

The ABC (atom-bond connectivity) energy of a graph is defined as the graph energy of its ABC matrix, i.e., the sum of the absolute values of the eigenvalues of its ABC matrix.