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The first Debye function is defined by D_n^((1))(x) = int_0^x(t^ndt)/(e^t-1) (1) = x^n[1/n-x/(2(n+1))+sum_(k=1)^(infty)(B_(2k)x^(2k))/((2k+n)(2k!))], (2) for |x|<2pi, n>=1, ...

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

Informally, an L^2-function is a function f:X->R that is square integrable, i.e., |f|^2=int_X|f|^2dmu with respect to the measure mu, exists (and is finite), in which case ...

For a given signal, the power spectrum gives a plot of the portion of a signal's power (energy per unit time) falling within given frequency bins. The most common way of ...

Let a discrete distribution have probability function p_k, and let a second discrete distribution have probability function q_k. Then the relative entropy of p with respect ...

An equilibrium minimal surface for a crystal or drop which has the least anisotropic surface free energy for a given volume. It is the anisotropic analog of a sphere. In the ...

The van der Pol equation is an ordinary differential equation that can be derived from the Rayleigh differential equation by differentiating and setting y=y^'. It is an ...

p^~=|phi_i(x)><phi_i(t)| (1) p^~sum_(j)c_j|phi_j(t)>=c_i|phi_i(x)> (2) sum_(i)|phi_i(x)><phi_i(x)|=1. (3)

Let G be a subgroup of the modular group Gamma. Then an open subset R_G of the upper half-plane H is called a fundamental region of G if 1. No two distinct points of R_G are ...