凸显“本质联系证据推理”的离子键与共价键教学

针对离子键与共价键在教学中存在本质分离、联系割裂和忽视“证据推理”素养发展目标的问题,依据元素周期律中金属性和非金属性的递变规律进行推理,并寻找证据进行证实或证伪,以认清离子键与共价键的静电作用的成键本质和辩证统一的关系,发展学生证据推理的核心素养,提高学生的逻辑思维能力。     

Kaehler流形上的Hamilton力学

利用力学原理、现在微分几何理论和高等微积分把Hamihon力学推广至Kaehler流形上，建立Kaehler流形上Hamihon力学，并得到Hamilton向量场、Hamihon方程等复的数学形式．     

Upper bound involving parameter σ 2 for the rainbow connection number

Let G be a connected graph of order n. The rainbow connection number rc（G） of G was introduced by Chartrand et al. Chandran et al. used the minimum degree of G and obtained an upper bound that rc（G） 〈_ 3n/（ δ＋ 1） - 3, which is tight up to additive factors. In this paper, we use the minimum degree-sum a2 6n of G to obtain a better bound rc（G） _〈 - 8, especially when is small （constant） but a2 is large （linear in n）.     

Stress-energy connection and cosmological constant problem

We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate modification of the spacetime connection, we obtain varied geometrodynamical equations which properly comprise the usual gravitational field equations with, however, Planck-suppressed, non-local, higher-dimensional additional terms. The prime novelty brought about by the formalism is that, the vacuum energy does act not as the cosmological constant but as the source of the gravitational constant. The formalism thus deafens the cosmological constant problem by channeling vacuum energy to gravitational constant. Nevertheless, quantum gravitational effects, if any, restore the problem via the graviton and graviton-matter loops, and the mechanism proposed here falls short of taming such contributions to cosmological constant.     

A model of unified quantum chromodynamics and Yang-Mills gravity

Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging T (4) × [SU (3)] color in flat space-time, we have a unified model of chromo-gravity with a new tensor gauge field, which couples universally to all gluons, quarks and anti-quarks. The space-time translational gauge symmetry assures that all wave equations of quarks and gluons reduce to a Hamilton-Jacobi equation with the same ’effective Riemann metric tensors’ in the geometric-optics (or classical) limit. The emergence of ef f ective metric tensors in the classical limit is essential for the unified model to agree with experiments. The unified model suggests that all gravitational, strong and electroweak interactions appear to be dictated by gauge symmetries in the generalized Yang-Mills framework.     

Characterization of Levi-Civita and Newton–Cartan connections in dimension 2

In dimension 2, we give a local characterization of Levi-Civita connections, improving a result by G. Thompson (1991), and of Newton–Cartan connections (connections which are limit of Levi-Civita connections).     

超对称自对偶杨─Mills模型

本文构造并研究了一个新的４维Ｎ＝１超对称模型──超对称自对偶杨－Ｍｉｌｌｓ模型．该模型的运动方程相当于４维起空间中相应于ＣＰ３，４中一点的超平面上曲率为零的条件．根据这一几何解释，我们构造了模型的线性系统．另外，为说明其动力学内涵，还给出了相应的作用量     

伏安法测量电阻的误差分析

本文给出伏安法测量电阻时，安培计内、外接法的定量选择公式，定量地描绘了使测量误差在允许范围所需要采取的具体措施。     

A singularity removal theorem for Yang-Mills fields in higher dimensions

In four and higher dimensions, we show that any stationary admissible Yang-Mills field can be gauge transformed to a smooth field if the norm of the curvature is sufficiently small. There are three main ingredients. The first is Price's monotonicity formula, which allows us to assert that the curvature is small not only in the norm, but also in the Morrey norm . The second ingredient is a new inductive (averaged radial) gauge construction and truncation argument which allows us to approximate a singular gauge as a weak limit of smooth gauges with curvature small in the Morrey norm. The second ingredient is a variant of Uhlenbeck's lemma, allowing one to place a smooth connection into the Coulomb gauge whenever the Morrey norm of the curvature is small; This variant was also proved independently by Meyer and Rivière. It follows easily from this variant that a -connection can be placed in the Coulomb gauge if it can be approximated by smooth connections whose curvatures have small Morrey norm.