Interior Operators and Topological Connectedness

Abstract

A categorical notion of interior operator is used in topology to define connectedness and disconnectedness with respect to an interior operator. A commutative diagram of Galois connections is used to show a relationship between these notions and Arhangelskii and Wiegandt's notions of connectedness and disconnectedness with respect to a subclass of topological spaces. Examples are included.     

LEFT-INVARIANT PSEUDO-EINSTEIN METRICS ON LIE GROUPS

In this article, we focus on left-invariant pseudo-Einstein metrics on Lie groups. To begin with, we give some examples of pseudo-Einstein metrics on Lie groups. Also we calculate the Levi-civita connection, and then Ricci tensor associated with left-invariant pseudo-Riemannian metrics on the unimodular Lie groups of dimension three. Furthermore, we show that the left-invariant pseudo-Einstein metric on SL(2) is unique up to a constant. At last, we study the left-invariant pseudo-Riemannian metrics on compact Lie groups and classify the pseudo-Einstein metrics on the low-dimensional compact Lie groups.     

A U（4） QCD Model Using Generalized Yang-Mills Theory

Generalized Yang-Mills theory has a covariant derivative which contains both vector and pseudoscalar gauge bosons. Based on this theory, we construct a U（4） strong interaction model. By using this U（4） generalized Yang-Mills model, we obtain that mesons can be realized as the colorless pseudoscalar gauge bosons. We also obtain a gauge potential solution which can be used to explain the asymptotic behavior and color confinement.     

Dynamical Symmetry Breaking of Maximally Generalized Yang-Mills Model and Its Restoration at Finite Temperatures

In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.     

化学专业学术型硕士研究生培养与本科科研训练有效衔接的探究

阐述了高水平学术型硕士研究生培养与本科科研体验衔接的基本情况,以化学专业为例,就学术型硕士培养与本科创新性科研实践的衔接模式进行了详细的剖析,指出2者的衔接有助于高层次、高科研水平与高创新能力的硕士研究生培养。     

大学化学与高中化学的衔接教学——以原子结构知识为例

高中的和大学的学习方法差异巨大,使学生难以快速适应大学无机化学的教学。以原子结构知识的学习为例,展开高中化学与大学化学的衔接教学研究,通过找准切入点、提出问题、初识基本知识、原理详解、实例练习等环节,可以顺利完成知识的衔接过渡,同时培养学生独立思考和自主学习的能力。     

Tensor Fields of Type (0, 2) on the Tangent Bundle of a Riemannian Manifold

To any (0, 2)-tensor field on the tangent bundle of a Riemannian manifold, we associate a global matrix function. Based on this fact, natural tensor fields are defined and characterized, essentially by means of well-known algebraic results. In the symmetric case, this classification coincides with the one given by Kowalski–Sekizawa; in the skew-symmetric one, it does with that obtained by Janyka.     

The unitary connections on the complex Grassmann manifold

In the complex Grassmann manifold ℱ(m,n), the space of complexn-planes passes through the origin of C^m+n; the local coordinate of the space can be arranged into anm ×n matrixZ. It is proved that