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If 0<=g(x)<=1 and g is nonincreasing on the interval [0, 1], then for all possible values of a and b, int_0^1g(x^(1/(a+b)))dx>=int_0^1g(x^(1/a))dxint_0^1g(x^(1/b))dx.

The series of Sturm functions arising in application of the Sturm theorem.

An algebra S^' which is part of a large algebra S and shares its properties.

A C^infty (infinitely differentiable) manifold is said to be a submanifold of a C^infty manifold M^' if M is a subset of M^' and the identity map of M into M^' is an ...

A p×q submatrix of an m×n matrix (with p<=m, q<=n) is a p×q matrix formed by taking a block of the entries of this size from the original matrix.

A module over a ring that is contained in and has the same addition as another module over the same ring.

The relationship x succeeds (or follows) y is written x≻y. The relation x succeeds or is equal to y is written x>=y.

A real-linear vector space H equipped with a symplectic form s.

A system of equations is any set of simultaneous equations.

A tangent point of two similar curves.