This paper uses the notion of Galois-connection to examine the relation between valuation-spaces and logics. Every valuation-space gives rise to a logic, and every logic gives rise to a valuation space, where the resulting pair of functions form a Galois-connection, and the composite functions are closureoperators. A valuation-space (resp., logic) is said to be complete precisely if it is Galoi...

A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector...

Using Penrose's binor calculus for SU (2) (SL(2; C)) tensor expressions, a graphical method for the connection representation of Euclidean Quantum Gravity (real connection) is constructed. It is explicitly shown that: (i) the recently proposed scalar product in the loop-representation coincide with the Ashtekar-Lewandowski cylindrical measure in the space of connections; (ii) it is possible to ...

An all{to{all broadcast algorithm that exploits concurrent communication on all channels of the Connection Machine system CM{200 binary cube network is described. Issues in integrating a physical all{to{all broadcast between processing nodes into a language environment using a global address space is dicussed. Timings for the physical broadcast between nodes, and the virtual broadcast are given...

We develop a new model of a spinning particle in Brans-Dicke space-time using a metric-compatible connection with torsion. The particle's spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an autoparallel of the metric-compatible connection) when neglecting spin-curvature coupling.

We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss-Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove that the eigenvalues of the Gauss-Manin connection are integral linear combinations of the weights which define the local system.

We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a nonresonant complex rank one local system. Aomoto and Kita determined this GaussManin connection for arrangements in general position. We use their results and an algorithm constructed in this paper to determine this Gauss-Manin connection for all arrangements.

We develop a new model of a spinning particle in Brans-Dicke space-time using a metric-compatible connection with torsion. The particle's spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an autoparallel of the metric-compatible connection) when neglecting spin-curvature coupling.

In this paper we propose a new geometric interpretation for General Relativity (GR). It has always been presumed that the gravitational field is described in GR by a Levi-Civita connection. We suggest that this may not necessarily be the case. We show that in the presence of an arbitrary affine connection, the gravitational field is described as nonmetricity of the affine connection. An affine ...

In this paper, we have studied warped products and multiply warped product on quasi-Einstein manifold with semi-symmetric nonmetric connection. Then we have applied our results to generalized Robertson-Walker space times with a semi-symmetric non-metric connection.