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A parabolic cyclide formed by inversion of a horn torus when the inversion sphere is tangent to the torus.

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called parabolic if the matrix Z=[A B; B C] (2) ...

A point p on a regular surface M in R^3 is said to be parabolic if the Gaussian curvature K(p)=0 but S(p)!=0 (where S is the shape operator), or equivalently, exactly one of ...

A parabolic cyclide formed by inversion of a ring torus when the inversion sphere is tangent to the torus.

A parabolic cyclide formed by inversion of a spindle torus when the inversion sphere is tangent to the torus.

A point p on a regular surface M in R^3 is said to be planar if the Gaussian curvature K(p)=0 and S(p)=0 (where S is the shape operator), or equivalently, both of the ...

f(z)=k/((cz+d)^r)f((az+b)/(cz+d)) where I[z]>0.

A power series containing fractional exponents (Davenport et al. 1993, p. 91) and logarithms, where the logarithms may be multiply nested, e.g., lnlnx.

The inversion of a ring torus. If the inversion center lies on the torus, then the ring cyclide degenerates to a parabolic ring cyclide.

A function possessing a single period in the complex plane is said to be singly periodic, of often simply periodic. Singly periodic functions include the trigonometric ...