9,470 research outputs found
The Budget-Constrained Functional Dependency
Armstrong's axioms of functional dependency form a well-known logical system
that captures properties of functional dependencies between sets of database
attributes. This article assumes that there are costs associated with
attributes and proposes an extension of Armstrong's system for reasoning about
budget-constrained functional dependencies in such a setting.
The main technical result of this article is the completeness theorem for the
proposed logical system. Although the proposed axioms are obtained by just
adding cost subscript to the original Armstrong's axioms, the proof of the
completeness for the proposed system is significantly more complicated than
that for the Armstrong's system
Quantum integrable systems and representations of Lie algebras
In this paper the quantum integrals of the Hamiltonian of the quantum
many-body problem with the interaction potential K/sinh^2(x) (Sutherland
operator) are constructed as images of higher Casimirs of the Lie algebra gl(N)
under a certain homomorphism from the center of U(gl(N)) to the algebra of
differential operators in N variables. A similar construction applied to the
affine gl(N) at the critical level k=-N defines a correspondence between higher
Sugawara operators and quantum integrals of the Hamiltonian of the quantum
many-body problem with the potential equal to constant times the Weierstrass
function. This allows one to give a new proof of the Olshanetsky-Perelomov
theorem stating that this Hamiltonian defines a completely integrable quantum
system. We also give a new expression for eigenfunctions of the quantum
integrals of the Sutherland operator as traces of intertwining operators
between certain representations of gl(N).Comment: 17 pages, no figure
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