公理化局部有限空间中映射连续性的扩展

用公理化方法研究了局部有限空间中的连续映射及其扩张问题。给出了局部有限空间的公理化定义方法;利用邻近关系研究了局部有限空间中的连续映射、同胚和局部同胚等问题;通过对局部有限空间变形的研究,定义了局部有限空间的一种特殊收缩核,有效地解决了局部有限空间中连续映射的扩张问题。     

Structural and thermodynamic properties of AlB2 compound

We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter (HGH) scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB₂ compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Debye model, obtained successfully are the dependences of the normalized lattice parameters a/a₀ and c/c₀ on pressure P, the normalized primitive cell volume V/V₀ on pressure P, the variation of the thermal expansion α with pressure P and temperature T, as well as the Debye temperature \Theta_D and the heat capacity C_V on pressure P and temperature T.     

Extrusion of pastes with a piston extruder for the determination of the local solid and fluid concentration, the local porosity and saturation and displacement profiles by means of NMR imaging

 Nuclear Magnetic Resonance (NMR) was used to investigate the extrusion behaviour of PTFE pastes in a ram extruder. By means of ¹H-NMR imaging (MRI) it is possible to determine the local proton density and therefore, the local fluid concentration. The ¹⁹F-MRI provides the local solid concentration. Thus the local saturation and the local porosity can be calculated with the information of the local fluid and solid concentration. Furthermore displacement profiles can be derived from NMR images by means of correlation techniques without any preparation or marking of the pastes. Received: 8 May 2000   Accepted: 1 May 2001     

论联省自治的原动力

联省自治的产生是资产阶级联省自治派和地方军阀产生合力的结果。但是，联省自治思潮与运动一开始就将斗争锋芒直指北洋军阀专制主义中央集权和地方军阀的地方割据。资产阶级联省自治派是联省自治思潮的鼓吹者、联省自治团体的组织者、联省自治运动的直接发动者，因而是运动的原动力，地方军阀则是附合者，而且是别有用心的。     

Co-P非晶态合金电子性质和局域结构的理论研究

根据Co P非晶态合金结构的短程有序和结构中可能存在P -P相互作用的实验事实 ,选择了单磷原子簇模型ConP(n =1～ 5 )和双磷原子簇模型ConP2 (n =1～ 4 ) ,用密度泛函理论方法对其进行计算 .结果表明 ,在单磷Co2 P( 2 ) 、Co3 P( 1) 及Co4P( 2 ) 模型体系中 ,Co原子供给P原子电子 ,与电负性规则一致 ,同时Co和P之间具较强化学作用 ,可以形成稳定的原子簇 ;而在双磷和单磷原子簇Co5P( 1) 模型体系中 ,形成的原子簇不稳定 ,采用单磷Co2 P( 2 ) 、Co3 P( 1) 及Co4P( 2 ) 模型能较好地反映Co P非晶态合金的结构特点 .     

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u = uk((e)u)α

This paper undertakes a systematic treatment of the low regularity local wellposedness and ill-posedness theory in Hs andHs for semilinear wave equations with polynomial nonlinearity in u and (e)u. This ill-posed result concerns the focusing type equations with nonlinearity on u and (e)tu.     

Generating Quadratic Pseudo-Anosov Homeomorphisms of Closed Surfaces

In this note, we show that given a closed, orientable genus-g surface S _g , any hyperbolic toral automorphism has a positive power which induces a quadratic, orientable pseudo-Anosov homeomorphism on S _g . To show this, we lift Anosov toral automorphisms through a ramified topological covering and present the lifted homeomorphism via a standard set of Lickorish twists. This construction provides a general method of producing pseudo-Anosov maps of closed surfaces with predetermined orientable foliations and quadratic dilatation. Since these lifted automorphisms have orientable foliations, this construction is a sort of converse to that of Franks and Rykken [Trans. Amer. Math. Soc. 1999], who established that one can associate to a quadratic pseudo-Anosov homeomorphism with oriented unstable foliation a hyperbolic toral automorphism.     

Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

On the influence of the surfactant''s polar group on the local and terminal velocities of bubbles

The local and the terminal velocities, the size and the degree of bubbles’ shape deformations were determined as a function of distance from the position of the bubble formation (capillary orifice) in solutions of n-octyltrimethylammonium bromide, n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside and n-octanoic acid.

These surface-active compounds have different polar groups but an identical hydrocarbon chain (C8) in the molecule. The motion of the bubbles was monitored and recorded using a stroboscopic illumination, a CCD camera, and a JVC professional video. The recorded bubble images were analyzed by the image analysis software. The bubbles accelerated rapidly and their shape was deformed immediately after detachment from the capillary. The extent of the bubbles’ shape deformation (ratio of horizontal and vertical diameters) was 1.5 in distilled water and dropped rapidly down to a level of ca. 1.05–1.03 with increasing surfactant concentration. After the acceleration period the bubbles either attained a constant value of the terminal velocity (distilled water and high concentrations of the solutions), or a maximum in the velocity profiles was observed (low concentrations). The values of the terminal velocity diminished drastically with increasing concentration, from the value of 35 cm/s in water down to about 15 cm/s, while the bubble diameter decreased by ca. 10% only. The surfactant adsorption at the surface of the bubbles was evaluated and the minimum adsorption coverages required to immobilize the bubbles’ surface were determined. It was found that this minimum adsorption coverage was ca. 4% for n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside, n-octanoic acid and 25% for n-octyltrimethylammonium bromide. The difference in the adsorption coverage together with the surfactants’ surface activities indicate that it is mainly the adsorption kinetics of the surfactants that governs the fluidity of interfaces of the rising bubbles.