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A lattice which is built up of layers of n-dimensional lattices in (n+1)-dimensional space. The vectors specifying how layers are stacked are called glue vectors. The order ...

Let a space curve have line elements ds_N, ds_T, and ds_B along the normal, tangent, and binormal vectors respectively, then ds_N^2=ds_T^2+ds_B^2, (1) where ds_N^2 = ...

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

An algorithm for computing the eigenvalues and eigenvectors for large symmetric sparse matrices.

An approximation for the gamma function Gamma(z+1) with R[z]>0 is given by Gamma(z+1)=sqrt(2pi)(z+sigma+1/2)^(z+1/2)e^(-(z+sigma+1/2))sum_(k=0)^inftyg_kH_k(z), (1) where ...

Writing a Fourier series as f(theta)=1/2a_0+sum_(n=1)^(m-1)sinc((npi)/(2m))[a_ncos(ntheta)+b_nsin(ntheta)], where m is the last term, reduces the Gibbs phenomenon. The ...

Let ||f|| be the supremum of |f(x)|, a real-valued function f defined on (0,infty). If f is twice differentiable and both f and f^('') are bounded, Landau (1913) showed that ...

The system of partial differential equations U_t=U·U_(xx)+U·LambdaU.

The Landau-Mignotte bound, also known as the Mignotte bound, is used in univariate polynomial factorization to determine the number of Hensel lifting steps needed. It gives ...

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...