Scalar Curvature Rigidity for Asymptotically Locally Hyperbolic Manifolds

Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac operator defined with respect to the Killing connection. The existence of asymptotic Killing spinors is related to the spin structure on the end. The expression for the mass is calculated and proven to vanish for conformally compact Einstein manifolds with conformal boundary a spherical space form, giving rigidity. In the four dimensional case, the signature of the manifold is related to the spin structure on the end and explicit formulas for the relevant invariants are given.     

Commuting Operators and Separation of Variables for Laplacians of Projectively Equivalent Metrics

Let two Riemannian metrics g and g on one manifold M ⁿ have the same geodesics (considered as unparameterized curves). Then we can construct invariantly n commuting differential operators of second order. The Laplacian _g of the metric g is one of these operators. For any x M ⁿ , consider the linear transformation G of T _x M ⁿ given by the tensor g ^Ig_j . If all eigenvalues of G are different at one point of the manifold then they are different at almost every point; the operators are linearly independent and their symbols are functionally independent. If all eigenvalues of G are different at each point of a closed manifold then it can be covered by the n-torus and we can globally separate the variables in the equation _g f = f on this torus.     

Projectively Equivariant Quantization Map

Let M be a manifold endowed with a symmetric affine connection . The aim of this Letter is to describe a quantization map between the space of second-order polynomials on the cotangent bundle T* M and the space of second-order linear differential operators, both viewed as modules over the group of diffeomorphisms and the Lie algebra of vector fields on M. This map is an isomorphism, for almost all values of certain constants, and it depends only on the projective class of the affine connection .     

Classical integrability of strings in γ-deformed backgrounds

This paper considers classical strings propagating in γ-deformed AdS3 γ S^3 backgrounds generated by certain shift T-dualities accompanied （TsT） transformations on S^3 and AdS3, respectively. It finds that the U（1） currents of strings with the twisted boundary conditions are equal to those in γ-deformed backgrounds generated by TsT transformations on both S3 and ADS3. Applying the TsT transformations, it derives the local Lax connections and the monodromy matrices in γ-deformed backgrounds with the spectral parameter which ensure the classical integrability of the string theories.     

一种基于同步传输机制的混合保护方式研究

随着同步数字体系（SDH）多业务平台的日趋发展，传统的SDH保护方式已无法满足现在的需要。提出了一种混合保护方式，在同一个环内实现子网连接保护和两纤双向复用段保护，可实现对高阶和低阶业务的同时兼顾，解决SDH多业务平台的保护问题。该方法在实践中取得了良好的效果。     

科学级CCD并联过采样低噪声模拟信号通道

根据CCD相机模拟通道噪音的非相关性，提出通过并联多个相同的模拟通道来降低模拟通道噪音的方法，并对此进行实验研究。通过实验测定实验装置中噪音的分布情况,得出并联双通道和并联三通道时噪音的改善因子为1.354和1.65，符合理论值。实验还显示，改善因子随模拟通道中可编程增益放大器增益的增加而减小，并对此现象进行分析。通过对改善因子与理论值的偏差进行分析，指出电源噪音、较高的转换速度及温升是造成偏差的主要原因。     

Harmonic Maps into the Moduli Spaces of Flat Connections

It is proved in this paper that, under reasonable assumptions, for each given harmonic map into the moduli spaces of flat connections, there exists one corresponding smooth family of Yang–Mills solutions approaching to the given harmonic map as the parameter tends to zero.     

大学无机化学与高中化学知识衔接——以原子结构与元素周期表为例

原子结构理论是高中化学和大学无机化学的重要组成部分和学习难点,教学过程中如何较好地衔接高中阶段知识与大学无机化学课程尤为重要。本文以原子结构和元素周期表知识点为例,以2019版高中人教版教材和北师大版的无机化学教材内容讨论高中化学知识与大学化学知识的衔接问题,依据作者的教学实践提出若干建议,为大学无机化学原子结构与元素周期表知识点的教学提供参考,同时帮助大一学生顺利完成知识的衔接过渡和培养学生独立思考、自主学习的能力。     

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.     

Z_2拓扑不变量与拓扑绝缘体

文章回顾了几种Z2拓扑数的计算方法,并详细介绍了一种用非阿贝尔贝里联络表示绝缘体Z2不变量的计算方法.这种方法可以确定出一般能带绝缘体的拓扑性质,而不需要限定波函数的规范.利用这种新方法,文章作者计算了二维石墨烯(graphene)系统的Z2拓扑数,得到了和以前研究相一致的结论.