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A coordinate system (mu,nu,psi) given by the coordinate transformation x = (mucospsi)/(mu^2+nu^2) (1) y = (musinpsi)/(mu^2+nu^2) (2) z = nu/(mu^2+nu^2) (3) and defined for ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

Doob (1996) defines a stochastic process as a family of random variables {x(t,-),t in J} from some probability space (S,S,P) into a state space (S^',S^'). Here, J is the ...

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

In Minkowski space, a twistor may be defined as a pair consisting of a spinor field and a complex conjugate spinor field satisfying the twistor equation.

The nth coefficient in the power series of a univalent function should be no greater than n. In other words, if f(z)=a_0+a_1z+a_2z^2+...+a_nz^n+... is a conformal mapping of ...

A hyperbolic knot is a knot that has a complement that can be given a metric of constant curvature -1. All hyperbolic knots are prime knots (Hoste et al. 1998). A prime knot ...

The coordinates representing any point of an n-dimensional affine space A by an n-tuple of real numbers, thus establishing a one-to-one correspondence between A and R^n. If V ...

A special nonsingular map from one manifold to another such that at every point in the domain of the map, the derivative is an injective linear transformation. This is ...

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...