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A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

A surface parameterized in variables u and v is called smooth if the tangent vectors in the u and v directions satisfy T_uxT_v!=0, where AxB is a cross product.

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

If the difference between the order and the dimension of a series is less than the curve genus, then the series is special.

A three-dimensional knot spun about a plane in four dimensions. Unlike suspended knots, spun knots are smoothly embedded at the poles.

An n×n array is called a square array. Considered as a matrix, a square array is called a square matrix.

A function f(x) is said to be square integrable if int_(-infty)^infty|f(x)|^2dx is finite.

A space which is isomorphic to a Borel subset B of a Polish space equipped with its sigma-algebra of Borel sets.

A point x_0 at which the derivative of a function f(x) vanishes, f^'(x_0)=0. A stationary point may be a minimum, maximum, or inflection point.

If, in a plane or spherical convex polygon ABCDEFG, all of whose sides AB, BC, CD, ..., FG (with the exception of AG) have fixed lengths, one simultaneously increases ...