Given a finite state space E, we build a universal dilation for all possible discrete time Markov chains on E, homogeneous or not: we introduce a second system (an “environment”) and a deterministic invertible time-homogeneous global evolution of the system E with this environment such that any Markov evolution of E can be realized by a proper choice of the initial (random) state of the environ...

The aim of belief merging is to merge conflicting information while preserving as much of it as possible. Most proposals in the literature work with knowledge bases expressed in propositional logic. We propose a new framework for merging knowledge bases expressed in (subsets of) first-order logic. Dilation operators (a concept originally introduced by Bloch and Lang) are employed and developed,...

PURPOSE To evaluate the intra- and interobserver reproducibility of peripapillary retinal nerve fiber layer (RNFL) thickness measurements before and after pupil dilation using spectral-domain optical coherence tomography (SD-OCT). METHODS In this observational case series, 44 eyes of 44 healthy subjects were scanned by two trained operators on the same day, using Cirrus SD-OCT (Carl Zeiss Med...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

Considerable interest exists in understanding the framework of weighted inequalities for differential operators and the Fourier transform, and the application of quantitative information drawn from these inequalities to varied problems in analysis and mathematical physics, including nonlinear partial differential equations, spectral theory, fluid mechanics, stability of matter, stellar dynamics...

We review current research in the field of categorical quantum mechanics. We place the category of relations within the same categorical framework and point out the similarities with the category of Hilbert spaces. Subsequently, we provide a categorical model for investigating the spectral theorem (as provided in [22]), within the context of an internally diagonalisable element and apply these ...

In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which based on the method of Pavlov and define its characteristic function. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of...