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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 ...

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

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

The function lambda(n)=(-1)^(Omega(n)), (1) where Omega(n) is the number of not necessarily distinct prime factors of n, with Omega(1)=0. The values of lambda(n) for n=1, 2, ...

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is ...

A problem is assigned to the NP (nondeterministic polynomial time) class if it is solvable in polynomial time by a nondeterministic Turing machine. A P-problem (whose ...

The question of whether a solution to a given problem exists. The existence problem can be solved in the affirmative without actually finding a solution to the original ...

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means ...

A problem is assigned to the P (polynomial time) class if there exists at least one algorithm to solve that problem, such that the number of steps of the algorithm is bounded ...

A problem in the theory of algebraic invariants that was solved by Hilbert using an existence proof.