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A multistable polyhedron is a polyhedron that can change form from one stable configuration to another with only a slight transient nondestructive elastic stretch (Goldberg ...

Let f:R×R->R be a one-parameter family of C^3 maps satisfying f(-x,mu)=-f(x,mu) (1) (partialf)/(partialx)|_(mu=0, x=0)=0 (2) (partial^2f)/(partialxpartialmu)|_(mu=0, x=0)>0 ...

For the rational curve of an unperturbed system with rotation number r/s under a map T (for which every point is a fixed point of T^s), only an even number of fixed points ...

If the faces of a convex polyhedron were made of metal plates and the polyhedron edges were replaced by hinges, the polyhedron would be rigid. The theorem was stated by ...

A shaky polyhedron is a non-rigid concave polyhedron which is only infinitesimally movable. Jessen's orthogonal icosahedron is a shaky polyhedron (Wells 1991).

Let f:R×R->R be a one-parameter family of C^2 maps satisfying f(0,mu)=0 (1) [(partialf)/(partialx)]_(mu=0,x=0)=0 (2) [(partial^2f)/(partialxpartialmu)]_(0,0)>0 (3) ...

To predict the result of a measurement requires (1) a model of the system under investigation, and (2) a physical theory linking the parameters of the model to the parameters ...

Differential Geometry

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...