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A planar diagram depicting a link (or knot) as a sequence of segments with gaps representing undercrossings and solid lines overcrossings. In such a diagram, only two ...

An algebraic extension K over a field F is a purely inseparable extension if the algebraic number minimal polynomial of any element has only one root, possibly with ...

A flexible polyhedron due to C. Schwabe (with the appearance of having four horns) which flexes from one totally flat configuration to another, passing through intermediate ...

Suppose for every point x in a manifold M, an inner product <·,·>_x is defined on a tangent space T_xM of M at x. Then the collection of all these inner products is called ...

If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...

A self-avoiding walk in which steps may be to the left, right, or straight ahead after a vertical step, but only straight ahead or to the left after a horizontal step. A ...

An extension field of a field F that is not algebraic over F, i.e., an extension field that has at least one element that is transcendental over F. For example, the field of ...

The number of graph edges meeting at a given node in a graph is called the order of that graph vertex.

In the calculus of variations, the condition f_(y^')(x,y,y^'(x_-))=f_(y^')(x,y,y^'(x_+)) must hold at a corner (x,y) of a minimizing arc E_(12).

An automorphism is an isomorphism of a system of objects onto itself. The term derives from the Greek prefix alphaupsilontauomicron (auto) "self" and ...