In this paper, a topological space based on LI-ideals of a lattice implication algebra is constructed, and its topological properties, such as separability, compactness and connectedness are discussed.
In this paper, the authors introduce and study the concept of （1, 2）^＊-generalized closed sets with respect to an ideal in a bitopological space. Also, some characterizations and applications of（1, 2）^＊-generali...In this paper, the authors introduce and study the concept of （1, 2）^＊-generalized closed sets with respect to an ideal in a bitopological space. Also, some characterizations and applications of（1, 2）^＊-generalized closed sets are given.展开更多
For a continuous domain D, some characterization that the convex powerdomain CD is adomain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it isproved that the set of the maximal points Ma...For a continuous domain D, some characterization that the convex powerdomain CD is adomain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it isproved that the set of the maximal points Max(CD) of CD with the relative Scott topology ishomeomorphic to the set of all Scott compact subsets of Max(D) with the topology induced bythe Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.展开更多
Magnetic field topology frozen in ideal magnetohydrodynamics （MHD） and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete de...Magnetic field topology frozen in ideal magnetohydrodynamics （MHD） and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics： Eulerian and La- grangian descriptions of three dimensional （3D） MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clar- ifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global con- straint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low-fl limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results field notwithstanding the small resistivity. Strong Faraday in sheet dissipation, resistive heating and topological changes in the induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun＇s corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit. A cylindrical initial-boundary value problem provides specificity in the general MHD ideas presented.展开更多
基金Supported by the National Natural Science Foundation of China(60474022)Supported by the Henan Innovation Project For University Prominent Research Talents(2007KYCX018)
文摘In this paper, a topological space based on LI-ideals of a lattice implication algebra is constructed, and its topological properties, such as separability, compactness and connectedness are discussed.
文摘In this paper, the authors introduce and study the concept of （1, 2）^＊-generalized closed sets with respect to an ideal in a bitopological space. Also, some characterizations and applications of（1, 2）^＊-generalized closed sets are given.
基金Project supported by the National Natural Science Foundation of Chian(No.19831040),the Doctoral Programme Foundation of the Ministry of Education of China(No.2000061019)and the 973 Project by the Science Commission of China.
文摘For a continuous domain D, some characterization that the convex powerdomain CD is adomain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it isproved that the set of the maximal points Max(CD) of CD with the relative Scott topology ishomeomorphic to the set of all Scott compact subsets of Max(D) with the topology induced bythe Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.
基金The National Center for Atmospheric Researchis sponsored by the US National Science Foundation
文摘Magnetic field topology frozen in ideal magnetohydrodynamics （MHD） and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics： Eulerian and La- grangian descriptions of three dimensional （3D） MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clar- ifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global con- straint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low-fl limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results field notwithstanding the small resistivity. Strong Faraday in sheet dissipation, resistive heating and topological changes in the induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun＇s corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit. A cylindrical initial-boundary value problem provides specificity in the general MHD ideas presented.
