Spacetime tangent bundle with torsion

It is demonstrated explicitly that the bundle connection of the Finslerspacetime tangent bundle can be made compatible with Cartan's theory of Finsler space by the inclusion of bundle torsion, and without the restriction that the gauge curvature field be vanishing. A component of the contorsion is made to cancel the contribution of the gauge curvature field to the relevant component of the bundle connection. Also, it is shown that the bundle manifold remains almost complex, and that the almost complex structure can be made to have a vanishing covariant derivative if additional conditions on the torsion are satisfied. However, the Finsler-spacetime tangent bundle remains complex only if the gauge curvature field vanishes.     

Solution to torsion relations in finsler-spacetime tangent bundle

In the Finsler-spacetime tangent bundle, a simple solution is determined to the torsion relations that were obtained previously to maintain (1) compatibility with Cartan's theory of Finsler space, (2) the almost complex structure, and (3) the vanishing of the covariant derivative of the almost complex structure.     

Lifting geometric objects to a cotangent bundle, and the geometry of the cotangent bundle of a tangent bundle

We show that the cotangent bundle T^*T of the tangent bundle of any differentiable manifold carries an integrable almost tangent structure which is generated by a natural lifting procedure from the canonical almost tangent structure (vertical endomorphism) of T . Using this almost tangent structure we show that T^*T is diffeomorphic to a tangent bundle, namely TT^* . This provides a new and geometrically instructive proof of a result of Tulczyjew, which has applications in Lagrangian and Hamiltonian dynamics and in field theory The requisite general definitions and results concerning liftings of geometric objects from a manifold to its cotangent bundle are given. As an application, we shed new light on the meaning of so-called adjoint symmetries of second-order differential equations.     

Collapsing of connected sums and the eigenvalues of the Laplacian

We study the behavior of the eigenvalues of the Laplacian acting on functions when one side of a connected sum of two closed Riemannian manifolds collapses to a point. We prove that the eigenvalues converge to those of the limit space, by using the method of Anné and Colbois. From this, we obtain a gluing theorem for the eigenvalues.     

Comments on the unification of electromagnetism and gravitation through “Generalized Einstein manifolds”

Akbar-Zadeh [J. Geom. Phys. 17 (1995) 342] has recently proposed a new geometric formulation of Einstein-Maxwell system with source in terms of what are called “Generalized Einstein manifolds”. We show that, contrary to the claim, Maxwell equations have not been derived in this formulation, and that the assumed equations can be identified only as source-free Maxwell equations in the proposed geometric setup. A genuine derivation of source-free Maxwell equations is presented within the same framework. We draw a conclusion that the proposed unification scheme can pertain only to source-free situations.     

Critical remarks on Finsler modifications of gravity and cosmology by Zhe Chang and Xin Li

I do not agree with the authors of papers arXiv:0806.2184 and arXiv:0901.1023v1 (published in [Zhe Chang, Xin Li, Phys. Lett. B 668 (2008) 453] and [Zhe Chang, Xin Li, Phys. Lett. B 676 (2009) 173], respectively). They consider that “In Finsler manifold, there exists a unique linear connection – the Chern connection … It is torsion freeness and metric compatibility …”. There are well-known results (for example, presented in monographs by H. Rund and R. Miron and M. Anastasiei) that in Finsler geometry there exist an infinite number of linear connections defined by the same metric structure and that the Chern and Berwald connections are not metric compatible. For instance, the Chern's one (being with zero torsion and “weak” compatibility on the base manifold of tangent bundle) is not generally compatible with the metric structure on total space. This results in a number of additional difficulties and sophistication in definition of Finsler spinors and Dirac operators and in additional problems with further generalizations for quantum gravity and noncommutative/string/brane/gauge theories. I conclude that standard physics theories can be generalized naturally by gravitational and matter field equations for the Cartan and/or any other Finsler metric compatible connections. This allows us to construct more realistic models of Finsler spacetimes, anisotropic field interactions and cosmology.     

An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting parallel one-form

An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold of positive scalar curvature admitting a parallel one-form is found. The possible universal covering spaces of the manifolds on which the smalles possible eigenvalue is attained are also listed. Moreover, a complete classification of the compact odd-dimensional manifolds whose universal covering space is Sⁿ⁻¹ × is given in the limiting case. All such manifolds are diffeomorphic but not necessarily isometric to Sⁿ⁻¹ × S¹.     

光学非球面二次曲面常数及顶点曲率的研究

受光学非球面制造过程中诸工艺参数的影响,能否保证非球面顶点曲率及二次曲面常数的精度是一个重要问题。基于二次曲面方程,推导出确定光学非球面二次曲面常数k以及顶点曲率半径r的一组算法,并在对一块口径为760mm×200mm标准非球面反射镜的实际测算中进行拟合,经过优化,拟合精度达到Δk=0.015,Δr=0.341mm,从而有效的控制了光学非球面制造过程中的顶点曲率及二次曲面常数的偏差。     

Riemannian curvature on the group of area-preserving diffeomorphisms (motions of fluid) of 2-sphere

Euler's equation for an incompressible fluid filled in a Riemannian manifold D is regarded as a geodesic equation on the group of volume-preserving diffeomorphisms of D provided with a one-sided invariant metric. A negative sectional curvature implies instability of the geodesic with respect to the corresponding flow and perturbation. The exponential growth of the perturbation is estimated from the values of the sectional curvatures.

This paper presents the expression of the components of Riemannian curvature tensor of the group of area-preserving diffeomorphisms of a 2-sphere in explicit formulas through 3 − j coefficients.     

基于梯度与曲率相结合的图像平滑模型的研究

在图像处理过程中, 为了在图像去噪时更好地保留图像边缘细节信息, 首先结合扩散系数和曲率的性质建立了一个曲率平滑模型. 考虑到图像受到噪声污染时曲率会发生显著变化, 将图像的水平集曲率作为一个检测因子代入到上述模型中, 提出了一个梯度与曲率相结合的新模型. 分析与仿真结果表明, 该模型与Perona-Malik模型相比较保留了更多的图像信息, 有效地增强了图像尖锐的边缘, 同时很好地保持了图像的直线和曲线边缘、角点、斜坡和小尺度特征, 是一个理想的模型.     

The quantum harmonic oscillator on the sphere and the hyperbolic plane

A nonlinear model of the quantum harmonic oscillator on two-dimensional space of constant curvature is exactly solved. This model depends on a parameter λ that is related with the curvature of the space. First, the relation with other approaches is discussed and then the classical system is quantized by analyzing the symmetries of the metric (Killing vectors), obtaining a λ-dependent invariant measure dμ_λ and expressing the Hamiltonian as a function of the Noether momenta. In the second part, the quantum superintegrability of the Hamiltonian and the multiple separability of the Schrödinger equation is studied. Two λ-dependent Sturm-Liouville problems, related with two different λ-deformations of the Hermite equation, are obtained. This leads to the study of two λ-dependent families of orthogonal polynomials both related with the Hermite polynomials. Finally the wave functions Ψ_m,n and the energies E_m,n of the bound states are exactly obtained in both the sphere S² and the hyperbolic plane H².     

Solvent and pH Effects on the Sign of the ORD Spectrum of N-Methyl-4-phenyl-7-methoxy-1,2,3,4-tetrahydroisoquinoline in the Visible Spectral Range

It has been described in the literature¹ that the protonation of the nitrogen in 1-benzyl-1,2,3,4-tetraisoquinoline derivatives does not affect the sign of the ORD spectra. We have recently observed² that in the case of several (R) and (S) N-methyl-4-phenyl-1,2,3,4-tetrahydroisoquinol ine derivatives this is true only for the three Cotton effects below 300 nm (the ¹L_b, ¹L_a and ¹B electronic transitions³ of the aromatic moiety), although appreciable variations in intensity and slight shifts in the positions of the extrema were also noticed. On the other hand, the sign of the rotation in the visible spectral range was reversed upon protonation in 0.1N methanolic HCl (or hydrochloride of 1 in methanol).     

PbTe(001)表面原子几何结构和电子结构的第一性原理计算

用第一性原理的密度泛函理论计算了PbTe（001）表面的几何结构和电子结构.计算结果表明：PbTe（001）表面不发生重构，但表面几层原子表现出明显的振荡弛豫现象，其中第一、第二层间距减小4.5%，第二、第三层间距增加2.0%，并且表面层原子出现褶皱.表面带隙在X 点，带隙变宽，在基本带隙中不引入新的表面态，而导带底和价带顶附近等多处出现新的表 面共振态；弛豫后费米面处态密度很低，所以表面结构很稳定. 关键词： 密度泛函理论 表面几何结构 表面电子结构 PbTe     

曲率对Rh在锯齿型单壁碳纳米管内外吸附影响的研究

利用密度泛函理论系统的研究了单壁碳纳米管的曲率对Rh原子在锯齿型碳管内外的吸附行为, 发现Rh原子在管外吸附比管内稳定; 随着碳管管径的增加, 曲率减小, 管内外吸附能的差值逐渐减小, 接近Rh原子在石墨烯上的吸附能. 电荷密度分析表明, 由于卷曲效应使碳纳米管管外的电荷密度大于管内, 随着曲率减小, 这种差别逐渐减小. 管内外吸附Rh原子的Bader电荷差值及局域态密度差别亦随着曲率的下降而减小, 这与Rh原子在管内外吸附能的变化规律相一致.     

Effect of low frequency ultrasound on the surface properties of natural aluminosilicates

Structural and surface properties of different natural aluminosilicates (layered, chain and framework structural types) exposed of 20 kHz ultrasound irradiation (0–120 min) in aqueous and 35 wt%. aqueous H₂O₂ dispersions were studied by X-ray diffraction (XRD), dynamic light scattering (DLS), nitrogen adsorption–desorption, thermal analysis, and Fourier transform infrared spectroscopy (FTIR) techniques. It was confirmed that sonication caused slight changes in the structure of investigated minerals whereas their textural properties were significantly affected. The aqueous dispersions of montmorillonite (Mt), clinoptilolite (Zlt), glauconite (Glt) and palygorskite (Pal) were represented by several particles size fractions according to DLS-study. Ultrasound irradiation produced a decrease of the average particle diameter by 4–6 times in water and by 1.3–5 times in H₂O₂ dispersions except for Pal, which underwent strong agglomeration. A significant increase of total pore volume and pore diameter was observed for Glt sonicated in H₂O₂ dispersions whereas for Pal mainly micropore volume sharply increased in both aqueous and H₂O₂ dispersions.     

Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology

We investigate the effect of varying boundary conditions on the renormalization group flow in a recently developed noncommutative geometry model of particle physics and cosmology. We first show that there is a sensitive dependence on the initial conditions at unification, so that, varying a parameter even slightly can be shown to have drastic effects on the running of the model parameters. We compare the running in the case of the default and the maximal mixing conditions at unification. We then exhibit explicitly a particular choice of initial conditions at the unification scale, in the form of modified maximal mixing conditions, which have the property that they satisfy all the geometric constraints imposed by the noncommutative geometry of the model at unification, and at the same time, after running them down to lower energies with the renormalization group flow, they still agree in order of magnitude with the predictions at the electroweak scale.     

The action of the group of bundle-automorphisms on the space of connections and the geometry of gauge theories

Some aspects of the geometry of gauge theories are sketched in this review. We deal essentially with Yang-Mills theory, discussing the structure of the space of gauge orbits and the geometrical interpretation of ghosts and anomalies. Occasionally we deal also with classical gauge theories of gravitation and in particular we study the action of the group of diffeomorphisms on the space of linear connections. Finally we comment on the mathematical interpretation of anomalies in field theories.     

FeS2(100)表面原子几何与电子结构的理论研究

采用密度泛函理论研究了FeS2(100)表面原子几何与电子结构.理论计算结果表明:FeS2(100)表面无弛豫、无重构,是体相原子几何的自然终止.与体相电子结构相比,FeS2(100)表面电子特性明显不同,禁带中央产生新的表面态,且表面态局域性强,主要由Fe原子的3d分波贡献.配位场理论定性分析表明:FeS2(100)完整晶面表面态产生机制是Fe原子的配位数减少、局部对称性下降所致 关键词： 密度泛函理论 表面电子结构 FeS2     

基本物理常数概述及牛顿引力常数的测量

据不完全统计,基本物理常数有160余个之多,覆盖物理学各个领域。自国际科学技术数据委员会(CODATA)1973年首次发表国际推荐值以来,至今已发表了6次推荐值。文章介绍了基本物理常数的分类以及近期发表的基本物理常数领域的主要成就。这些成就及新的突破对物理学和计量学具有重要的意义。牛顿引力常数是测量万有引力的重要常数,具有深远的意义,但其数值极小,因此测量难度很大;二百余年来,科学家精益求精,不断更新方法,以求减小其测量的不确定度。