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

The Fermion Generations Problem in the Gust in the Free World-Sheet Fermion Formulation

In the framework of the four dimensional heterotic superstring with free fermions we present a revised version of the rank eight Grand Unified String Theories (GUST) which contain the $SU(3)_H$-gauge family symmetry. We also develop some methods for building of corresponding string models. We explicitly construct GUST with gauge symmetry $G = SU(5) \times U(1)\times (SU(3) \times U(1))_H$ and $G = SO(10)\times (SU(3) \times U(1))_H$ or $E(6)\times SU(3)_H$ $\subset E(8)$ and consider the full massless spectrum for our string models. We consider for the observable gauge symmetry the diagonal subgroup $G^{symm}$ of the rank 16 group $G \times G$ $\subset SO(16) \times SO(16)$ or $\subset E(8) \times E(8)$. We discuss the possible fermion matter and Higgs sectors in these theories. We study renormalizable and nonrenormolizable contributions to the superpotential. There has to exist "superweak" light chiral matter ($m_H^f < M_W$) in GUST under consideration. The understanding of quark and lepton mass spectra and family mixing leaves a possibility for the existence of an unusually low mass breaking scale of the $SU(3)_H$ family gauge symmetry (some TeV).Comment: 68 page

The Paths of Unification In The GUST With The G x G Gauge Groups of E(8) x E(8)

In the framework of the four dimensional heterotic superstring with free fermions we discuss the rank eight and/or sixteen Grand Unified String Theories (GUST) which contain the SU(3)_H - gauge family symmetry. We explicitly investigate the paths of the unification in the GUST with gauge symmetry G x G = [SU(5) x U(1) x (SU(3) x U(1))_H]^2. We show that the GUSTs with the G x G gauge group allow to make the scale of unification to be consistent with the string scale M_SU = g_{string} * 5 * 10^17 GeV.Comment: 18 pages, 2 Postscript figures, uses epsf.st

Topological phase in two flavor neutrino oscillations

We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between non-orthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CP conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.Comment: 11 pages, 3 figures, accepted in Phys. Rev.