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product_(i)dp_idq_i, where p_i and q_i are momenta and positions of particles.

This is proven in Rademacher and Toeplitz (1957).

A Liouville Space, also known as line space or "extended" Hilbert space, it is the Cartesian product of two Hilbert spaces.

The lengths of the tangents from a point P to a conic C are proportional to the cube roots of the radii of curvature of C at the corresponding points of contact.

An elliptic function with no poles in a fundamental cell is a constant.

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

A function f(x) satisfies the Lipschitz condition of order beta at x=0 if |f(h)-f(0)|<=B|h|^beta for all |h|<epsilon, where B and beta are independent of h, beta>0, and alpha ...

A function f such that |f(x)-f(y)|<=C|x-y| for all x and y, where C is a constant independent of x and y, is called a Lipschitz function. For example, any function with a ...

int_0^inftye^(-ax)J_0(bx)dx=1/(sqrt(a^2+b^2)), where J_0(z) is the zeroth order Bessel function of the first kind.

A statement letter or a negation of a statement letter (Mendelson 1997, p. 30).