稀土粉末Eu∶Y_2O_3的自由感应衰减量子拍

稀土固体是重要的激光和光电子材料。目前 ,由于以宽带信号和太赫兹比特数据传输率为特征的信息技术的发展 ,稀土固体材料的相干瞬态动力学过程成为宽带与高速信息光子学的基本物理问题之一。研究了室温下稀土粉末样品Eu3+ ∶Y2 O3自由感应衰减的相干瞬态光谱 ,这有助于理解有效的光吸收动力学、激发态弛豫、相干能量传递和超短光脉冲在稀土固体中的传播。用一对紫外飞秒相干光脉冲作用于稀土粉末样品Eu3+ ∶Y2 O3,然后监测物质激发态的布居数随两个激发脉冲之间的延时的变化 ,测量到其自由感应衰减量子拍 (FID) ,从拍频周期分析确定了其能级精细结构 ,能级的退相时间长达皮秒量级。理论分析和实验结果符合得很好。对稀土离子的量子干涉的研究 ,表明其在受激受控光放大方面具有潜在的应用前景     

Yb~(3+)∶Pr~(3+)∶ZBLAN光纤中4f5d上转换激发的理论研究

利用粒子数速率方程和相关的辐射跃迁理论,计算了Yb3+∶Pr3+∶ZBLAN光纤中Pr3+离子4f5d能级两步上转换激发的动力学过程。得到不同Pr3+掺杂浓度下,激发光的光谱强度和粒子数密度的纵向分布和有效光纤长度随激发光的光谱强度的变化关系。另外,还得到了4f5d荧光强度与入射光强、光纤长度和Pr3+掺杂浓度的关系,给出了激发效率与激发光的光谱强度和Pr3+掺杂浓度的关系。     

利用爆磁压缩发生器产生高功率脉冲高电压

 爆磁压缩发生器产生脉冲高电压技术可以用于产生高功率微波及强电磁脉冲的实验研究。给出了利用螺旋型爆磁压缩发生器（HEMG）驱动电爆炸丝功率调节系统产生高功率脉冲高电压的实验方法和主要的结果。在利用HEMG驱动电爆炸丝断路开关（EEOS）产生脉冲高电压实验中，获得了最高电压700~800kV,功率大于20GW的脉冲输出。     

On division rings with algebraic commutators of bounded degree

We shall answer several questions concerning additive or multiplicative commutators in a division ring which are algebraic of bounded degree over its center.     

Seizure warning algorithm based on optimization and nonlinear dynamics

There is growing evidence that temporal lobe seizures are preceded by a preictal transition, characterized by a gradual dynamical change from asymptomatic interictal state to seizure. We herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing EEG signals. Such, the algorithm constitutes a seizure warning system. The algorithm estimates STL_max, a measure of the order or disorder of the signal, of EEG signals recorded from individual electrode sites. The optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures. Specifically, a quadratically constrained quadratic 0-1 programming problem is formulated to identify critical electrode sites. The automated seizure warning algorithm was tested in continuous, long-term EEG recordings obtained from 5 patients with temporal lobe epilepsy. For individual patient, we use the first half of seizures to train the parameter settings, which is evaluated by ROC (Receiver Operating Characteristic) curve analysis. With the best parameter setting, the algorithm applied to all cases predicted an average of 91.7% of seizures with an average false prediction rate of 0.196 per hour. These results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes.Mathematics Subject Classification (1991):20E28, 20G40, 20C20     

On Einstein four-manifolds with <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-actions

We study closed Einstein 4-manifolds which admit S¹ actions of a certain type, i.e., warped products. In particular, we classify them up to isometry when the fixed point of the S¹ action satisfies certain natural geometric conditions. The proof uses the Bochner-Weitzenböck formula for 1-forms and the theory of minimal surfaces in 3-manifolds.in final form: 22 January 2003     

Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal     

Bounded Positive Solutions of Schrödinger Equations in Two-Dimensional Exterior Domains

We prove under quite general assumptions the existence of a bounded positive solution to the semilinear Schrödinger equation in a two-dimensional exterior domain.     

On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].