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

The ordinary differential equation y^('')-(a+bk^2sn^2x+qk^4sn^4x)y=0, where snx=sn(x,k) is a Jacobi elliptic function (Arscott 1981).

The Enneper surfaces are a three-parameter family of surfaces with constant negative curvature (and nonconstant mean curvature). In general, they are described by elliptic ...

Two metrics g_1 and g_2 defined on a space X are called equivalent if they induce the same metric topology on X. This is the case iff, for every point x_0 of X, every ball ...

An integer d is a fundamental discriminant if it is not equal to 1, not divisible by any square of any odd prime, and satisfies d=1 (mod 4) or d=8,12 (mod 16). The function ...

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 ...

The modular group Gamma is the set of all transformations w of the form w(t)=(at+b)/(ct+d), where a, b, c, and d are integers and ad-bc=1. A Gamma-modular function is then ...

A hyperbolic fixed point of a differential equation is a fixed point for which the stability matrix has eigenvalues lambda_1<0<lambda_2, also called a saddle point. A ...

The hyperbolic polar sine is a function of an n-dimensional simplex in hyperbolic space. It is analogous to the polar sine of an n-dimensional simplex in elliptic or ...

A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...