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A curve alpha on a regular surface M is a principal curve iff the velocity alpha^' always points in a principal direction, i.e., S(alpha^')=kappa_ialpha^', where S is the ...

The index I associated to a symmetric, non-degenerate, and bilinear g over a finite-dimensional vector space V is a nonnegative integer defined by I=max_(W in S)(dimW) where ...

The derivative (deltaL)/(deltaq)=(partialL)/(partialq)-d/(dt)((partialL)/(partialq^.)) appearing in the Euler-Lagrange differential equation.

The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a ...

The probability that a random integer between 1 and x will have its greatest prime factor <=x^alpha approaches a limiting value F(alpha) as x->infty, where F(alpha)=1 for ...

The radius of a polygon's incircle or of a polyhedron's insphere, denoted r or sometimes rho (Johnson 1929). A polygon possessing an incircle is same to be inscriptable or ...

A method for numerical solution of a second-order ordinary differential equation y^('')=f(x,y) first expounded by Gauss. It proceeds by introducing a function delta^(-2)f ...

The solutions to the Riemann P-differential equation are known as the Riemann P-series, or sometimes the Riemann P-function, given by u(z)=P{a b c; alpha beta gamma; alpha^' ...

A cusp catastrophe is a catastrophe which can occur for two control factors and one behavior axis. The cusp catastrophe is the universal unfolding of the singularity f(x)=x^4 ...

The equations defined by q^. = (partialH)/(partialp) (1) p^. = -(partialH)/(partialq), (2) where p^.=dp/dt and q^.=dq/dt is fluxion notation and H is the so-called ...