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The function [x] which gives the smallest integer >=x, shown as the thick curve in the above plot. Schroeder (1991) calls the ceiling function symbols the "gallows" because ...

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

Clebsch-Gordan coefficients are mathematical symbol used to integrate products of three spherical harmonics. Clebsch-Gordan coefficients commonly arise in applications ...

The conjugate transpose of an m×n matrix A is the n×m matrix defined by A^(H)=A^_^(T), (1) where A^(T) denotes the transpose of the matrix A and A^_ denotes the conjugate ...

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, ...

For vectors u=(u_x,u_y,u_z) and v=(v_x,v_y,v_z) in R^3, the cross product in is defined by uxv = x^^(u_yv_z-u_zv_y)-y^^(u_xv_z-u_zv_x)+z^^(u_xv_y-u_yv_x) (1) = ...

The Dehn invariant is a constant defined using the angles and edge lengths of a three-dimensional polyhedron. It is significant because it remains constant under polyhedron ...

The Dirichlet eta function is the function eta(s) defined by eta(s) = sum_(k=1)^(infty)((-1)^(k-1))/(k^s) (1) = (1-2^(1-s))zeta(s), (2) where zeta(s) is the Riemann zeta ...

The most general forced form of the Duffing equation is x^..+deltax^.+(betax^3+/-omega_0^2x)=gammacos(omegat+phi). (1) Depending on the parameters chosen, the equation can ...

The Egyptian Mathematical Leather Roll (EMLR), dates to the Middle Kingdom, and was purchased in Egypt in 1858 by Henry Rhind, near the time when the Rhind papyrus was ...