present study seeks to investigate the existing canonical correlation among the effective factors including x variables that consist of environmental factors, inter-organizational factors and the creation factors of the perceptual value; on the components of competitiveness, as well as y variables consisting of enterprise performance against the market, the customers and the internal performanc...

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SUq(2) . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector...

Canonical quantization of three dimensional gravity in the first order formalism suggests that one should allow singular solutions. This paper addresses the importance of singular solutions in the path integral approach to quantum gravity. Using a simple ansatz for the dreibein and the spin connection in the de-Sitter and the anti-de-Sitter spaces we propose that the sum over the 3D manifolds i...

This is a survey on recent joint work with A.R. Gover on the geometry of non–degenerate CR manifolds of hypersurface type. Specifically we discuss the relation between standard tractors on one side and the canonical Cartan connection, the construction of the Fefferman space and the ambient metric construction on the other side. To put these results into perspective, some parts of the general th...

We associate a canonical unital involutive quantale to a topological groupoid. When the groupoid is also étale, this association is compatible with but independent from the theory of localic étale groupoids and their quantales [19] of P. Resende. As a motivating example, we describe the connection between the quantale and the C∗-algebra that both classify Penrose tilings, which was left as an o...

We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H [ 2 . For the case H> 2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the...

An anomaly-free operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is entirely free of factor ordering singularities and can be defined in symmetric and non-symmetric form. We work in the real connection representation and obtain a well-defined quantum theory. We compu...

Various frameworks that generalise the notion of contextuality in theories of physics have been proposed; one is the sheaf-theoretic approach by Abramsky and Brandenburger; an other is the equivalence-based approach by Spekkens. We show that these frameworks are equivalent for scenarios with preparations and measurements, whenever factorizability is justified. This connection gives rise to a ca...

We provide a direct computation of the $F$-pure threshold degree four homogeneous polynomial in two variables and, more generally, certain polynomials with distinct roots. The depends on whether cross ratio roots satisfies specific M\"{o}bius transformation Legendre polynomial. then make connection between long lasting open question, involving relationship and log canonical threshold, over $\ma...

We discuss the application of an assumptionbased truth maintenance system to the construction of a circumscriptive theorem prover, showing that the connection discovered by Reiter and de Kleer between assumption-based truth maintenance and prime implicants relates to the notions of minimality appearing in nonmonotonic reasoning. The ideas we present have been implemented, and the resulting syst...