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Algebraic Sum

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Brigitte Hiller – One of the best experts on this subject based on the ideXlab platform.

  • collective modes and current Algebraic Sum rules in nuclear medium
    arXiv: Nuclear Theory, 1998
    Co-Authors: Wojciech Broniowski, Brigitte Hiller
    Abstract:

    In-medium Sum rules following from the chiral charge algebra of QCD are reviewed, and new Sum rules are derived. The new Sum rules relate the I^G(J^{PC})=1^-(0^{++}) excitations (quantum numbers of a_0(980)) to the scalar and isovector densities, and are nontrivial for the isospin-asymmetric medium. We present an extensive illustration of the Sum rules with help of quark matter in the Nambu-Jona–Lasinio model. Collective excitations different from the usual meson branches (spin-isospin sound modes) are shown to contribute significantly to the Sum rules and to play a crucial role in the limit of vanishing current quark masses.

  • Collective modes and current-Algebraic Sum rules in nuclear medium
    Nuclear Physics A, 1998
    Co-Authors: Wojciech Broniowski, Brigitte Hiller
    Abstract:

    Abstract In-medium Sum rules following from the chiral charge algebra of QCD are reviewed, and new Sum rules are derived. The new Sum rules relate the I g (J pc ) = 1 − (0 ++ ) excitations (quantum numbers of a 0 (980)) to the scalar and isovector densities, and are non-trivial for the isospin-asymmetric medium. We present an extensive illustration of the Sum rules with the help of quark matter in the Nambu-Jona-Lasinio model. Collective excitations different from the usual meson branches (spin-isospin sound modes) are shown to contribute significantly to the Sum rules and to play a crucial role in the limit of vanishing current quark masses.

Toka Diagana – One of the best experts on this subject based on the ideXlab platform.

Wojciech Broniowski – One of the best experts on this subject based on the ideXlab platform.

  • collective modes and current Algebraic Sum rules in nuclear medium
    arXiv: Nuclear Theory, 1998
    Co-Authors: Wojciech Broniowski, Brigitte Hiller
    Abstract:

    In-medium Sum rules following from the chiral charge algebra of QCD are reviewed, and new Sum rules are derived. The new Sum rules relate the I^G(J^{PC})=1^-(0^{++}) excitations (quantum numbers of a_0(980)) to the scalar and isovector densities, and are nontrivial for the isospin-asymmetric medium. We present an extensive illustration of the Sum rules with help of quark matter in the Nambu-Jona–Lasinio model. Collective excitations different from the usual meson branches (spin-isospin sound modes) are shown to contribute significantly to the Sum rules and to play a crucial role in the limit of vanishing current quark masses.

  • Collective modes and current-Algebraic Sum rules in nuclear medium
    Nuclear Physics A, 1998
    Co-Authors: Wojciech Broniowski, Brigitte Hiller
    Abstract:

    Abstract In-medium Sum rules following from the chiral charge algebra of QCD are reviewed, and new Sum rules are derived. The new Sum rules relate the I g (J pc ) = 1 − (0 ++ ) excitations (quantum numbers of a 0 (980)) to the scalar and isovector densities, and are non-trivial for the isospin-asymmetric medium. We present an extensive illustration of the Sum rules with the help of quark matter in the Nambu-Jona-Lasinio model. Collective excitations different from the usual meson branches (spin-isospin sound modes) are shown to contribute significantly to the Sum rules and to play a crucial role in the limit of vanishing current quark masses.

Tomasz Weiss – One of the best experts on this subject based on the ideXlab platform.

  • On the Ramseyan properties of some special subsets of {$2\sp ømega$} and their Algebraic Sums
    Journal of Symbolic Logic, 2002
    Co-Authors: Andrzej Nowik, Tomasz Weiss
    Abstract:

    We prove the following theorems: 1. If X ⊆ 2 ω is a γ -set and Y ⊆2 ω is a strongly meager set, then X + Y is Ramsey null. 2. If X ⊆2 ω is a γ -set and Y belongs to the class of sets, then the Algebraic Sum X + Y is an set as well. 3. Under CH there exists a set X ∈ MGR * which is not Ramsey null.

  • the Algebraic Sum of a set of strong measure zero and a perfectly meager set revisited
    East-West Journal of Mathematics, 2000
    Co-Authors: Andrzej Nowik, Tomasz Weiss
    Abstract:

    We present simple proofs of the following theorems: It is consistent with ZFC that there are a strongly measure zero set X, and a set Y \in \bar{AFC} such that X+Y contains a perfect set. It is consistent with ZFC that there are a setXof universal measure zero, and a strongly meager setY such that X+Y contains a perfect set.

  • The Algebraic Sum of sets of real numbers with strong measure zero sets
    Journal of Symbolic Logic, 1998
    Co-Authors: Andrzej Nowik, Marion Scheepers, Tomasz Weiss
    Abstract:

    We prove the following theorems:(1) If X has strong measure zero and if Y has strong first category, then their Algebraic Sum has property S0.(2) If X has Hurewicz’s covering property, then it has strong measure zero if, and only if, its Algebraic Sum with any first category set is a first category set.(3) If X has strong measure zero and Hurewicz’s covering property then its Algebraic Sum with any set in is a set in . ( is included in the class of sets always of first category, and includes the class of strong first category sets.)These results extend: Fremlin and Miller’s theorem that strong measure zero sets having Hurewicz’s property have Rothberger’s property, Galvin and Miller’s theorem that the Algebraic Sum of a set with the γ-property and of a first category set is a first category set, and Bartoszyfnski and Judah’s characterization of -sets. They also characterize the property (*) introduced by Gerlits and Nagy in terms of older concepts.

Ke-qiu Chen – One of the best experts on this subject based on the ideXlab platform.