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The series z=ln(e^xe^y) (1) for noncommuting variables x and y. The first few terms are z_1 = x+y (2) z_2 = 1/2(xy-yx) (3) z_3 = 1/(12)(x^2y+xy^2-2xyx+y^2x+yx^2-2yxy) (4) z_4 ...

A binary unit of information equal to 8 bits. Unfortunately, the storage of binary numbers in computers is not entirely standardized. Because computers store information in ...

A C-matrix is a symmetric (C^(T)=C) or antisymmetric (C^(T)=-C) C_n (-1,0,1)-matrix with diagonal elements 0 and others +/-1 that satisfies CC^(T)=(n-1)I, (1) where I is the ...

Chebyshev noticed that the remainder upon dividing the primes by 4 gives 3 more often than 1, as plotted above in the left figure. Similarly, dividing the primes by 3 gives 2 ...

A set X whose elements can be numbered through from 1 to n, for some positive integer n. The number n is called the cardinal number of the set, and is often denoted |X| or ...

In the IEEE 754-2008 standard (referred to as IEEE 754 henceforth), a floating-point representation is an unencoded member of a floating-point format which represents either ...

In general, a graph product of two graphs G and H is a new graph whose vertex set is V(G)×V(H) and where, for any two vertices (g,h) and (g^',h^') in the product, the ...

A number n for which the harmonic mean of the divisors of n, i.e., nd(n)/sigma(n), is an integer, where d(n)=sigma_0(n) is the number of positive integer divisors of n and ...

The Krackhardt kite is the simple graph on 10 nodes and 18 edges illustrated above. It arises in social network theory. It is implemented in the Wolfram Language as ...

There are two distinct entities both known as the Lagrange number. The more common one arises in rational approximation theory (Conway and Guy 1996), while the other refers ...