Vol. 8 No. 2 (2016)

Published: 2016-12-22

Articles

  • Articles

    Characterizing trees in property-oriented concept lattices

    Hua Mao
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    Abstract

    Property-oriented concept lattices are systems of conceptual clusters called property-oriented concepts, which are partially ordered by the subconcept/superconcept relationships. Property-oriented concept lattices are basic structures used in formal concept analysis. In general, a property-oriented concept lattice may contain overlapping clusters and is not to be a tree construction. Additionally, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output property-oriented concept lattice to form a tree after one removes its greatest element. After applying to input data for which the associated property-oriented concept lattice is a tree, we present an algorithm for computing property-oriented concept lattices.

     

    References
  • Articles

    Principal filters of some ordered $\Gamma$-semigroups

    Niovi Kehayopulu, Michael Tsingelis
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    Abstract

    For an intra-regular or a left regular and left duo ordered $\Gamma$-semigroup $M$, we describe the principal filter of $M$ which plays an essential role in the structure of this type of $po$-$\Gamma$-semigroups. We also prove that an ordered $\Gamma$-semigroup $M$ is intra-regular if and only if the ideals of $M$ are semiprime and it is left (right) regular and left (right) duo if and only if the left (right) ideals of $M$ are semiprime.

     

    References
  • Articles

    Perturbations of Operator Banach frames in Banach spaces

    Chander Shekhar, Shiv Kumar Kaushik
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    Abstract

    Casazza and Christensen \cite{BB} studied perturbation of operators in the context of frames. Also, Chistensen and Heil \cite{DD} studied perturbation of frames and atomic decompositions. In the present paper, we study perturbation of operator Banach frames (OBFs) for Banach spaces and obtained perturbation results for operator Banach frames and operator Bessel sequences. Also, we give a condition under which the sum of finite number of sequences of operators is an OBF by comparing each of the sequences with another system of OBFs. Finally, we define similar OBFs and prove that if a sequence of operators is similar to an OBF, then it has to be an OBF.

     

    References
  • Articles

    On a Convergence of Modified Fourier-Pade Approximations

    Tigran Bakaryan
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    Abstract

    We consider convergence acceleration of the modified Fourier expansions by trigonometric-rational corrections which lead to modified Fourier-Pade approximations. Exact constants of the asymptotic errors are derived for smooth functions and comparison with the corresponding errors of the modified Fourier expansions is performed.

    References