We investigate the notion of dilation of a propositional theory based on neighbourhoods in a generalized approximation space. We take both a semantic and a syntactic approach in order to define a suitable notion of theory dilation in the context of approximate reasoning on the one hand, and a generalized notion of forgetting in propositional logic on the other hand. We place our work in the con...

For many Markov semigroups dilations in the sense of Hudson and Parthasarathy, that is a dilation which is a cocycle perturbation of a noise, have been constructed with the help of quantum stochastic calculi. In these notes we show that every Markov semigroup on the algebra of all bounded operators on a separable Hilbert space that is spatial in the sense of Arveson, admits a Hudson-Parthasarat...

A well-known clustering algorithm is K-means. This algorithm, besides advantages such as high speed and ease of employment, suffers from the problem of local optima. In order to overcome this problem, a lot of studies have been done in clustering. This paper presents a hybrid Extended Cuckoo Optimization Algorithm (ECOA) and K-means (K), which is called ECOA-K. The COA algorithm has advantages ...

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}...

We discuss the fundamentals of classical particle scattering of a two body system in forces which are 0 (r~~) at infinity along with their Lipshitz constants. We prove asymptotic completeness for this two-body case. Of particular interest is the fact that in the absence of control on Lipshitz constants at oo, two solutions of the interacting equation may be asymptotic to the same free solution ...

Morphological image processing is well known as an efficient methodology for image processing and computer vision. With the wide use of color in many areas, the interest on the color perception and processing has been growing rapidly. Many models have been proposed to extend morphological operators to the field of color images, dealing with some new problems not present previously in the binary...