On linearly Lindelöf and strongly discretely Lindelöf spaces

We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed , and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.

     

Some rapidly converging series for

For a natural number , the author derives several families of series representations for the Riemann Zeta function . Each of these series representing converges remarkably rapidly with its general term having the order estimate:

Relevant connections of the results presented here with many other known series representations for are also pointed out.

     

Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps

Let be a nonempty closed convex subset of a real Banach space and be a Lipschitz pseudocontractive self-map of with . An iterative sequence is constructed for which as . If, in addition, is assumed to be bounded, this conclusion still holds without the requirement that Moreover, if, in addition, has a uniformly Gâteaux differentiable norm and is such that every closed bounded convex subset of has the fixed point property for nonexpansive self-mappings, then the sequence converges strongly to a fixed point of . Our iteration method is of independent interest.

     

Lasing action in air induced by ultra-fast laser filamentation

The backscattered fluorescence of nitrogen from filaments generated by intense ultra-fast Ti:sapphire laser pulses propagating in air is studied. The backscattered fluorescence from N₂ molecules and ions show an exponential increase with increasing filament length, indicating amplified spontaneous emission. Received: 11 October 2002 / Revised version: 3 December 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +1-418/6562-623, E-mail: qluo@phy.ulaval.ca     

Femtosecond pump-probe experiments on non-stoichiometric sodium-fluoride clusters

In this paper we present two-color pump and probe spectroscopy on Na₂F, the smallest of the non-stoichiometric sodium-fluoride clusters (Na_nF_n-1), in molecular beams by employing femtosecond laser pulses. The molecules were pumped into the first excited state by one photonic transition and consecutively ionized from there by the second photon. We resolved the wavepacket oscillatory motion involving periodical structural rearrangements in the first excited state of Na₂F with a period of 185 fs. The time-resolved experiments show that sodium fluoride clusters provide interesting features which can be manipulated in optimal control experiments.     

-actions whose fixed data has a section

Given a collection of real vector bundles over a closed manifold , suppose that, for some is of the form , where is the trivial one-dimensional bundle. In this paper we prove that if is the fixed data of a -action, then the same is true for the Whitney sum obtained from by replacing by . This stability property is well-known for involutions. Together with techniques previously developed, this result is used to describe, up to bordism, all possible -actions fixing the disjoint union of an even projective space and a point.     

色散耦合道光学模型对28Si的核子散射数据分析

在光学势中引入色散关系, 相比于通常的耦合道光学模型, 极大地减少了光学势 参数的个数. 采用基于软旋转子模型的耦合道方法对较轻形变核²⁸Si核的中子和质子散射实验数据进行了计算分析, 拟合得到一组色散光学势参数. 计算的中子总截面、以及中子、质子的弹性与非弹性散射微分截面与实验数据有较好的符合.     

19F-NMR进展

19F-NMR技术由于其化学位移范围大、不易出现峰重叠及灵敏度高等优点,自上个世纪50年代出现以来,在分析光学异构体,生命科学等研究中有其特殊意义.在体内核磁共振技术中,19F-NMR与其他方法相比,在不损伤样品的条件下,就可进行实时定量监测.近30年,引人氟代指示剂进行体内19F-NMR的研究,含氟生物活性物质以及含氟材料的研究受到很大的重视,19F-NMR技术及其应用发展起来.从近10年的情况来看,含氟生物活性物质的研究以及在医药、农药和具有优异性能的含氟材料的研究应用受到很大的重视,这是近期19F-NMR研究发展的一个主要特点.     

Adsorption and manipulation of carbon onions on highly oriented pyrolytic graphite studied with atomic force microscopy

Carbon onions produced by DC arc discharge method were deposited on highly oriented pyrolytic graphite (HOPG) surface and their adsorption and manipulation was studied using an atomic force microscopy (AFM). Well-dispersed adsorption of carbon onions on HOPG surface was obtained and aggregations of onions were not observed. The van der Waals interaction between the onion and HOPG surface and that between two onions, were calculated and discussed using Hamaker's theory. The manipulation of adsorbed onions on HOPG surface was realized using the AFM in both the raster mode and the vector mode. The controllability and precision of two manipulation modes were compared and the vector mode manipulation was found superior, and is a useful technique for the construction of nano-scale devices based on carbon onions.     

Dynamic single-mode and modulation characteristics analyses for λ/4 phase-shifted distributed feedback lasers with chirped grating

The dynamic single-mode and modulation performance of λ/4 phase-shifted distributed feedback laser diode with chirped grating (QWS-CG-DFB) are analyzed theoretically. The numerical simulation shows that, in contrast to purely QWS-DFB laser, the enhanced dynamic single-mode suppression ratio (SMSR) can be reached by QWS-CG-DFB laser. Under the smaller biasing current, the modulation band-width in presence of chirped grating is narrower, this difference shrinks for larger biasing current. For large signal modulation, the chirped grating is helpful to increase the output extinction ratio, but worsens the frequency chirping. The good dynamic characteristic can be obtained by selecting system parameters reasonably.