The conceptual and formal structure of quantum mechanics is analysed from the point of view of the dynamics of distinctions, occcuring during the observation process. The Hilbert space formalism is simplified with the help of the concept of closure: closure of an eigenstate under an operator is generalized to the linear closure of a subset of states, and this is further simplified to orthogonal...

The closure ordinal of a formula of modal μ-calculus μXφ is the least ordinal κ, if it exists, such that the denotation of the formula and the κ-th iteration of the monotone operator induced by φ coincide across all transition systems (finite and infinite). It is known that for every α < ω there is a formula φ of modal logic such that μXφ has closure ordinal α [3]. We prove that the closure ord...

Often the structure of discrete sets can be described in terms of a closure operator. When each closed set has a unique minimal generating set (as in convex geometries in which the extreme points of a convex set generate the closed set), we have an antimatroid closure space. In this paper, we show there exist antimatroid closure spaces of any size, of which convex geometries are only a sub-fami...

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This paper presents characterizations of M-fuzzifying matroids bymeans of two kinds of fuzzy operators, called M-fuzzifying derived operatorsand M-fuzzifying difference derived operators.

We introduce and investigate the orbit-closed $C$-numerical range, a natural modification of range an operator introduced for $C$ trace-class by Dirr vom Ende. Our is conservative theirs because these two sets have same closure even coincide when finite rank. Since Ende's results concerning depend only on its closure, our inherits properties, but we also establish more. For selfadjoint, Ende we...

There has been renewed interest in recent years in McKinsey and Tarski’s interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the modal mu-calculus and to a logic of tangled closure operators that was developed by Fernández-Duque after these two languages had been shown by Dawar and Ot...

There has been renewed interest in recent years in McKinsey and Tarski’s interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the modal mu-calculus and to a logic of tangled closure operators that was developed by Fernández-Duque after these two languages had been shown by Dawar and Ot...

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means a q-difference operator. Some properties the in this subclass, such as sufficient and necessary conditions, coefficient estimates, growth distortion theorems, radius starlikeness convexity, partial sums closure are investigated.

Introduction: The most common type of velopharyngeal valve (VPV) closure is a matter of controversy.The aim of this study was to estimate the most common type of VPV closure, including identification of the type and grade of VPV closure among Egyptian children.  Materials and Methods: This study included patients who were candidates for adenotonsillectomy. In these cases, video-nasoendoscopy an...