Field theoretical approach to gravitational waves

The aim of these notes is to give an accessible and self‐contained introduction to the theory of gravitational waves as the theory of a relativistic symmetric tensor field in a Minkowski background spacetime. This is the approach of a particle physicist: the graviton is identified with a particular irreducible representation of the Poincaré group, corresponding to vanishing mass and spin two. It is shown how to construct an action functional giving the linear dynamics of gravitons, and how General Relativity can be obtained from it. The Hamiltonian formulation of the linear theory is examined in detail. We study the emission of gravitational waves and apply the results to the simplest case of a binary Newtonian system.     

基础化学双语教学新模式的调查分析

针对目前我国大学基础化学双语教学中存在的师资、学生和教材等方面的问题,结合我校学生专业基础知识和外语水平等特点,提出了“专业基础扎实统一,外教拓展重点提高”的普通化学原理双语课程教学新模式。对我校近年来基础化学课程双语教学情况进行问卷调查研究,分析在双语教学过程中存在的一些问题,并提出切实可行的建议,不断思考、总结并探讨适合基础专业课程双语教学的合理定位与授课方法。     

经典质点动力学方程的形式探讨

根据因果一致原理,重新构建了质点动力学的形式体系,由此得到了新的质点动力学方程.为了从更基本层次理解和导出这一方程,采纳的一个自然简单的假定是承认一个绝对空间背景的存在.实际上,由于时空的绝对背景必然和时空的相对标度相区分,一个绝对背景的存在既可以在最大程度上和狭义相对论的逻辑基础相容,又最精简地保留了基于直观经验的直觉性认识.除此之外,绝对背景也可以看作为是牛顿绝对时空观的潜在组成部分.在新质点动力学方程的应用过程中,不再需要以惯性系为适用前提,也无需人为地手放进虚拟的惯性力.从而实现了质点动力学方程在任何（相对背景）无自转的实际参考系中保持形式不变.而惯性力的本质就是参考物体所受到的真实力.分析表明,新的质点动力学方程能够自然地和作为牛顿第二定律实证基础的经验规律相契合,但是在形式上,质点动力学方程从伽利略相对性推广到了一个更切合实际的适度广义的相对性原理.     

Astrophysical Dynamics and Cosmology

First, the essence of a physical theory for a multilevel system is through coupling different physical laws in different levels by a symmetry-breaking principle, rather than through a unification using larger symmetry. In astrophysical dynamics, the symmetry-breaking mechanism and the coupling are achieved by prescribing the coordinate system so that the laws of fluid dynamics and heat conductivity are coupled with gravitational field equations. Another important ingredient in modeling fluid motion in astrophysics is to use the momentum density field to replace the velocity field as the state function of cosmic objects. Second, by applying the new symmetry-breaking mechanism and the new coupled astrophysical dynamics model, we rigorously prove a basic theorem on black holes: Assume the validity of the Einstein theory of general relativity, then black holes are closed, innate and incompressible. Third, we prove a theorem on structure of universes. Assume the Einstein theory of general relativity, and the principle of cosmological principle that the universe is homogeneous and isotropic. Then we show that 1) all universes are bounded, are not originated from a Big-Bang, and are static; and 2) The topological structure of our Universe can only be the 3D sphere. Also, thanks to the basic properties of black holes, we show that our results on our Universe resolve such fundamental problems as dark matter and dark energy, redshifts and CMB. Fourth, we discovered that both supernovae explosion and AGN jets, as well as many astronomical phenomena, are due to combined relativistic, magnetic and thermal effects. The radial temperature gradient causes vertical Bénard convection cells, and the relativistic viscous force (via electromagnetic, the weak and the strong interactions) gives rise to an huge explosive radial force near the Schwarzschild radius, leading e.g. to supernovae explosion and AGN jets.     

Global results for an HIV/AIDS model with multiple susceptible classes and nonlinear incidence

In this paper, an HIV/AIDS epidemic model is proposed in which there are two susceptible classes. Two types of general nonlinear incidence functions are employed to depict the scenarios of infection among cautious and incautious individuals. Qualitative analyses are performed, in terms of the basic reproduction number $\R_0$, to gain the global dynamics of the model: the disease-free equilibrium is of global asymptotic stability when $\R_0\leq 1$; a unique endemic equilibrium exists and globally asymptotically stable $\R_0> 1$. The introduction of cautious susceptible and the resulting multiple transmission functions has positive effect on HIV/AIDS prevalence. Numerical simulations are carried out to illustrate and extend the obtained analytical results.     

Identification of source term for the Rayleigh‐Stokes problem with Gaussian random noise

In this paper, we study an inverse source problem for the Rayleigh‐Stokes problem for a generalized second‐grade fluid with a fractional derivative model. The problem is severely ill‐posed in the sense of Hadamard. To regularize the unstable solution, we apply a general filter method for constructing regularized solution, and the convergence rate of this method also has been investigated.     

Nonlinear semigroup approach to transport equations with delayed neutrons

This paper deal with a nonlinear transport equation with delayed neutron and general boundary conditions. We establish, via the nonlinear semigroups approach, the existence and uniqueness of the mild solution, weak solution, strong solution and local solution on L~p-spaces(1 ≤ p +∞). Local and non local evolution problems are discussed.     

General linear-fractional branching processes with discrete time

We study a linear-fractional Bienaymé–Galton–Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads to the linear-fractional distribution formula for an arbitrary observation time, which allows us to establish transparent limit theorems for the subcritical, critical and supercritical cases. Our results extend recent findings for the linear-fractional branching processes with countably many types.     

Degree Sequences Beyond Power Laws in Complex Networks

Many complex networks possess vertex-degree distributions in a power-law form of $ck^{-\gamma}$, where $k$ is the degree variable and $c$ and $\gamma$ are constants. To better understand the mechanism of power-law formation in real-world networks, it is effective to analyze their degree variable sequences. We had shown before that, for a scale-free network of size $N$ ,if its vertex-degree sequence is $k_11$ , then the length $l$ of the vertex-degree sequence is of order $logN$ . In the present paper, we further study complex networks with more general distributions and prove that the same conclusion holds even for non-network type of complex systems. In addition, we support the conclusion by verifying many real-world network and system examples. We finally discuss some potential applications of the new finding in various fields of science, technology and society.     

开展普通物理双语教学的经验、体会和教训

介绍了近几年来在开展普通物理双语教学过程中取得的一些经验、体会和教训．我们教学的基本方针是一切为了学生的进步,调动学生的积极性,与国际接轨,为将来学生能更好地学习、交流和开展科学研究做好准备．在教学中,我们使用了国外原版教材,并用英语授课,采取灵活的教学方式．尽管我们在逐渐加强英语教学的力度,但在目前,我们的英语教学仍是中文教学的辅助部分．