激光照射下铝靶表面汽化压力的测量

 本文分析了会聚自由振荡钕玻璃脉冲激光束辐照平面铝靶的汽化特性。在激光功率密度约10 MW/cm²下，由拍摄激光与靶相互作用产生射流发光的时间积分照片测得靶面的汽化压力约3.6 GPa。把时间积分照片与高速分幅照片比较，证明在激光与靶相互作用一段时间后确实存在着马赫盘。     

不动点集为F=U_(i=1)~mRP_i(1)×HP_i(n)的对合

(M,T)是一个在r维光滑闭流形M上的不平凡光滑对合,它的不动点集为F．本文给出了F=U(i=1)~m RPi(1)×HPi(n)时对合的协边类,其中HP(n)表示n维四元数射影空间．     

S-内射模及S-内射包络

设R是环.设S是一个左R-模簇,E是左R-模.若对任何N∈S,有Ext_R~1(N,E)=0,则E称为S-内射模.本文证明了若S是Baer模簇,则关于S-内射模的Baer准则成立;若S是完备模簇,则每个模有S-内射包络;若对任何单模N,Ext_R~1(N,E)=0,则E称为极大性内射模;若R是交换环,且对任何挠模N,Ext_R~1(N,E)=0,则E称为正则性内射模.作为应用,证明了每个模有极大性内射包络.也证明了交换环R是SM环当且仅当T/R的正则性内射包e(T/R)是∑-正则性内射模,其中T=T(R)表示R的完全分式环,当且仅当每一GV-无挠的正则性内射模是∑-正则性内射模.     

High-resolution electron microscopy observations of continuous precipitates with Pitsch-Schrader orientation relationship in an Mg–Al based alloy and interpretation with the O-lattice theory

High-resolution electron microscopy was applied to analyze the continuous precipitated particles of the γ-Mg₁₇Al₁₂ phase with Pitsch-Schrader OR in the heat-treated AZ91 alloy at 473 K for 8 h. The existence of a continuous precipitated particle with the Pitsch-Schrader OR including the selection of the habit plane and the growth direction in Mg–Al system is rationalized by the constrained coincidence site lattice/constrained complete pattern shift lattice (CCSL/CDSCL) model and the O-lattice theory.     

Qubit Approach to the Topological Degeneracy of 4 and 6-Quasihole Pfaffian Paired Hall State

By virtue of the two-layer picture of Pfaffian pair Hall state, a qubit representation of topological degeneracy for quasiholes excitation is displayed. The non-Abelian feature of states can be manifested readily by the new wave functions. The virtue of this approach is that one does not need to find the equalities of Pfaffians, which is a so tedious task as exemplified for the case of six quasiholes. Then the braiding matrices are also constructed readily by just permutating single-qubit states, which are unitary and hermite.     

The L* Partial Order on the Set of Group Matrices

In this paper,we use the L(o)wner partial order and the star partial order to introduce a new partial order (denoted by "L*") on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L* partial order is a special kind of the core par-tial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.     

Synthesis, Characterization, Optical Properties and Theoretical Studies of Novel Substituted Imidazo[1,5-a]pyridinyl 1,3,4-Oxadiazole Derivatives

Novel imidazo[1,5-a]pyridinyl 1,3,4-Oxadiazole derivatives were synthesized and characterised by IR, ¹H NMR and HRMS.UV-vis absorption and fluorescence properties of these compounds in different solutions showed that the maximal emission wavelength was not significantly changed in different solvents; however, maximum absorption wavelength was blue-shifted with the increase of solvent polarity. Absorption λ_max and emission λ_max was less correlated with substituent groups on benzene rings. The calculated molecular orbital correlates well with their absorption.     

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.     

Model Equations and Traveling Wave Solutions for Shallow-Water Waves with the Coriolis Effect

In the present study, we start by formally deriving the simplified phenomenological models of long-crested shallow-water waves propagating in the equatorial ocean regions with the Coriolis effect due to the Earth’s rotation. These new model equations are analogous to the Green–Naghdi equations, the first-order approximations of the KdV-, or BBM type, respectively. We then justify rigorously that in the long-wave limit, unidirectional solutions of a class of KdV- or BBM type are well approximated by the solutions of the Camassa–Holm equation in a rotating setting. The modeling and analysis of those mathematical models then illustrate that the Coriolis forcing in the propagation of shallow-water waves can not be neglected. Indeed, the CH-approximation with the Coriolis effect captures stronger nonlinear effects than the nonlinear dispersive rotational KdV type. Furthermore, we demonstrate nonexistence of the Camassa–Holm-type peaked solution and classify various localized traveling wave solutions to the Camassa–Holm equation with the Coriolis effect depending on the range of the rotation parameter.