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de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry ...

A symbol used to represent the point and space groups (e.g., 2/m3^_). Some symbols have abbreviated form. The equivalence between Hermann-Mauguin symbols (a.k.a. ...

A bounded operator T:V->W between two Banach spaces satisfies the inequality ||Tv||<=C||v||, (1) where C is a constant independent of the choice of v in V. The inequality is ...

A set S is discrete in a larger topological space X if every point x in S has a neighborhood U such that S intersection U={x}. The points of S are then said to be isolated ...

The hemicube, which might also be called the square hemiprism, is a simple solid that serves as an example of one of the two topological classes of convex hexahedron having 7 ...

A regular skew polyhedron is a polyhedron whose faces and vertex figures are regular skew polygons. There are only three regular skew polyhedra in Euclidean three-space ...

The hat is a caret-shaped symbol commonly placed on top of variables to give them special meaning. The symbol x^^ is voiced "x-hat" (or sometimes as "x-roof") in mathematics, ...

An infinitesimal transformation of a vector r is given by r^'=(I+e)r, (1) where the matrix e is infinitesimal and I is the identity matrix. (Note that the infinitesimal ...

The line integral of a vector field F(x) on a curve sigma is defined by int_(sigma)F·ds=int_a^bF(sigma(t))·sigma^'(t)dt, (1) where a·b denotes a dot product. In Cartesian ...