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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 ...

The specification of a curve, surface, etc., by means of one or more variables which are allowed to take on values in a given specified range.

The only linear associative algebra in which the coordinates are real numbers and products vanish only if one factor is zero are the field of real numbers, the field of ...

An edge of a graph is said to be pendant if one of its vertices is a pendant vertex.

A vertex of a graph is said to be pendant if its neighborhood contains exactly one vertex.

A polycube composed of 5 cubes. There are 29 distinct three-dimensional pentacubes (Bouwkamp 1981). Of these, the 12 planar pentacubes (corresponding to solid pentominoes), ...

The pentagonal cupola is Johnson solid J_5. Its faces consist of 5 equilateral triangles, 5 squares, 1 pentagon, and one decagon. The surface area and volume of the ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

A perfect field is a field F such that every algebraic extension is separable. Any field in field characteristic zero, such as the rationals or the p-adics, or any finite ...