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A (2n)×(2n) complex matrix A in C^(2n×2n) is said to be Hamiltonian if J_nA=(J_nA)^(H), (1) where J_n in R^(2n×2n) is the matrix of the form J_n=[0 I_n; I_n 0], (2) I_n is ...

Since each triplet of Yff circles are congruent and pass through a single point, they obey Johnson's theorem. As a result, in each case, there is a fourth circle congruent to ...

In 1979, Conway and Norton discovered an unexpected intimate connection between the monster group M and the j-function. The Fourier expansion of j(tau) is given by (1) (OEIS ...

The Pippenger product is an unexpected Wallis-like formula for e given by e/2=(2/1)^(1/2)(2/34/3)^(1/4)(4/56/56/78/7)^(1/8)... (1) (OEIS A084148 and A084149; Pippenger 1980). ...

A random permutation is a permutation containing a fixed number n of a random selection from a given set of elements. There are two main algorithms for constructing random ...

Half a circle. The area of a semicircle of radius r is given by A = int_0^rint_(-sqrt(r^2-x^2))^(sqrt(r^2-x^2))dxdy (1) = 2int_0^rsqrt(r^2-x^2)dx (2) = 1/2pir^2. (3) The ...

A mathematical object defined for a set and a binary operator in which the multiplication operation is associative. No other restrictions are placed on a semigroup; thus a ...

A square-free graph is a graph containing no graph cycles of length four. A simple graph is square-free iff c_4=1/8[Tr(A^4)-2m-2sum_(i!=j)a_(ij)^((2))]=0, where A is the ...

For a bivariate normal distribution, the distribution of correlation coefficients is given by P(r) = (1) = (2) = (3) where rho is the population correlation coefficient, ...

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...