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A two-dimensional map also called the Taylor-Greene-Chirikov map in some of the older literature and defined by I_(n+1) = I_n+Ksintheta_n (1) theta_(n+1) = theta_n+I_(n+1) ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

The angle of attack alpha of a surface is measured as the angle between the direction of fluid flow relative to the surface, and the line in the direction of normal fluid ...

A Bloch vector is a unit vector (cosphisintheta, sinphisintheta, costheta) used to represent points on a Bloch sphere.

For a curve with first fundamental form ds^2=Edu^2+2Fdudv+Gdv^2, (1) the Gaussian curvature is K=(M_1-M_2)/((EG-F^2)^2), (2) where M_1 = |-1/2E_(vv)+F_(uv)-1/2G_(uu) 1/2E_u ...

A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...

A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.

Let r be the correlation coefficient. Then defining z^'=tanh^(-1)r (1) zeta=tanh^(-1)rho, (2) gives sigma_(z^') = (N-3)^(-1/2) (3) var(z^') = 1/n+(4-rho^2)/(2n^2)+... (4) ...