The purpose of this paper is to continue the study initiated in [7] concerning notion pseudo-generalized inverse. In work, we are interested investigating relationship between compactness, finite rank and invertibility for bounded operators. preserving properties products invertible operators also treated related results given. At end paper, discuss some special cases sets n-left inverses a lef...

This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy functions, as simplified forms of the multinomial distribu...

This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy functions, as simplified forms of the multinomial distribu...

The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo simulation techniques for rare-event probability estimation and optimization. In this paper we investigate how these methods can be extended to provide a general non-parametric cross-entropy framework based on φ-divergence distance measures. We show how the χ distance in particular yields a viable alternative to Kull...

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

several characterizations of marshall-olkin generalized distributions, introduced by gui (2013) and by al-saiari et al. (2014) are presented. these characterizations are based on: (i) a simple relationship between two truncated moments ; (ii) the hazard function.

Greatest common divisors and least common multiples of quotients of elements of integral domains have been investigated by Lüneburg and further by Jäger. In this paper we extend these results to invertible fractional ideals. We also lift our earlier study of the greatest common divisor and least common multiple of finitely generated faithful multiplication ideals to finitely generated projectiv...

Many objects in the real world are tubular in shape and this paper is about understanding this object class, which we refer to in the paper as generalized tubes (hereafter GTs). Intuitively, a GT is constructed by sweeping some planar closed curve (the GT cross-section) along a 3D space curve (the GT axis). First, we examine the GT class as a whole and identify two important GT subclasses where...