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A twin prime cluster of order n is a collection of 2n consecutive prime numbers such that consecutive pairs form twin primes. Twin prime clusters were discussed by Mudge ...
Let a piecewise smooth function f with only finitely many discontinuities (which are all jumps) be defined on [-pi,pi] with Fourier series a_k = 1/piint_(-pi)^pif(t)cos(kt)dt ...
A Woodall prime is a Woodall number W_n=2^nn-1 that is prime. The first few Woodall primes are 7, 23, 383, 32212254719, 2833419889721787128217599, ... (OEIS A050918), ...
sum_(n=0)^(infty)[(q)_infty-(q)_n] = g(q)+(q)_inftysum_(k=1)^(infty)(q^k)/(1-q^k) (1) = g(q)+(q)_inftyL(q) (2) = g(q)+(q)_infty(psi_q(1)+ln(1-q))/(lnq) (3) = ...
Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p). An s-cluster is an isolated group of s adjacent (i.e., horizontally ...
The projective special unitary group PSU_n(q) is the group obtained from the special unitary group SU_n(q) on factoring by the scalar matrices contained in that group. ...
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Three types of n×n matrices can be obtained by writing Pascal's triangle as a lower triangular matrix and truncating appropriately: a symmetric matrix S_n with (S)_(ij)=(i+j; ...
A d-dimensional discrete percolation model is said to be inhomogeneous if different graph edges (in the case of bond percolation models) or vertices (in the case of site ...
Let K be a number field with r_1 real embeddings and 2r_2 imaginary embeddings and let r=r_1+r_2-1. Then the multiplicative group of units U_K of K has the form ...
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