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The structure factor S_Gamma of a discrete set Gamma is the Fourier transform of delta-scatterers of equal strengths on all points of Gamma, S_Gamma(k)=intsum_(x in ...

The energy of a graph is defined as the sum of the absolute values of its graph eigenvalues (i.e., the sum of its graph spectrum terms). Other varieties of graph energy are ...

The Delannoy numbers D(a,b) are the number of lattice paths from (0,0) to (b,a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ^, ...

Given a sum and a set of weights, find the weights which were used to generate the sum. The values of the weights are then encrypted in the sum. This system relies on the ...

There exists a positive integer s such that every sufficiently large integer is the sum of at most s primes. It follows that there exists a positive integer s_0>=s such that ...

The improvement of the convergence properties of a series, also called convergence acceleration or accelerated convergence, such that a series reaches its limit to within ...

A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.

5((x^5)_infty^5)/((x)_infty^6)=sum_(m=0)^inftyP(5m+4)x^m, where (x)_infty is a q-Pochhammer symbol and P(n) is the partition function P.

Any linear combination of real spherical harmonics A_lP_l(costheta)+sum_(m=1)^l[A_l^mcos(mphi)+B_l^msin(mphi)]P_l^m(costheta) for l fixed whose sum is not premultiplied by a ...

A self-avoiding polygon containing three corners of its minimal bounding rectangle. The anisotropic area and perimeter generating function G(x,y) and partial generating ...