The method of the canonical connection introduced by Maier and Ullman provides an optimal procedure for query processing in universal-relation databases. We present an algorithm for computing canonical connections in a database scheme which is more efficient than the classical algorithm based on tableau reduction. Moreover, with a slight modification of the algorithm we obtain a join plan which...

A new finite atlas of overlapping balanced canonical forms for multivariate discrete-time loss-less systems is presented. The canonical forms have the property that the controllability matrix ispositive upper triangular up to a suitable permutation of its columns. This is a generalization of asimilar balanced canonical form for continuous-time lossless systems. It is shown that this...

We discuss the notion of uniform canonical bases, both in an abstract manner and specifically for the theory of atomless Lp lattices. We also discuss the connection between the de nability of the set of uniform canonical bases and the existence of the theory of beautiful pairs (i.e., with the nite cover property), and prove in particular that the set of uniform canonical bases is de nable in al...

We investigate the connection between propositional proof systems and their canonical pairs. It is known that simulations between proof systems translate to reductions between their canonical pairs. We focus on the opposite direction and study the following questions. Q1: Where does the implication [can(f) ≤ m can(g) ⇒ f ≤s g] hold, and where does it fail? Q2: Where can we find proof systems of...

In a recent paper, a new 3-parameter class of Abel type equations, so-called AIR, all of whose members can be mapped into Riccati equations, is shown. Most of the Abel equations with solution presented in the literature belong to the AIR class. Three canonical forms were shown to generate this class, according to the roots of a cubic. In this paper, a connection between those canonical forms an...

Several new insights into the canonical quantization of general relativity have been acquired using Ashtekar-like variables [1]. Originally, this consisted in basing the theory on a canonical pair formed by a set of (densitized) triads Ẽ i , and a (complex) SU(2) connection A i a ≡ Γ i a + iK i a, where Γ i a is the spin connection compatible with the triads and K a = KabE bi where Kab is the e...

We study the quaternion CR-submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR-submanifold. 2000 Mathematics Subject Classification. 53C20, 53C21, 53C25.

In this paper we explore the connection between semi-classical and quantum Birkhoff canonical forms (BCF) for Schrödinger operators. In particular we give a ”non-symbolic” operator theoretic derivation of the quantum Birkhoff canonical form and provide an explicit recipe for expressing the quantum BCF in terms of the semi-classical BCF.

Canonical transformations are studied in the bosonic Fock space using coherent and ultracoherent vectors. The connection between the Weyl operator and the homogeneous canonical transformations (Bogoliubov transformations) is presented. The unitary ray representation of the symplectic group is defined in the bosonic Fock space by the action of the group on the ultracoherent vectors.