用于激光推进的高功率激光器的选择

 从激光推进的要求出发，阐述了用于激光推进的高功率激光器的选择原则，即激光器必须满足：（1）高的平均功率和峰值功率；（2）高的单脉冲能量；（3）高的重复频率；（4）优良的大气传输特性。主要分析了目前YAG固体激光器、自由电子激光器和TEA脉冲CO₂激光器的特点，通过上述4个方面性能的比较，认为在目前水平下，TEA脉冲CO₂激光器是进行激光推进的首选强激光源，其优点表现在：功率可达10kW量级，单脉冲能量可达0.5~1kJ，重复频率为20~40Hz；激光波长处于大气传输窗口，对大气变化不敏感；工作物质快速流动，不存在热透镜效应和破坏阈值；相关光学元件易于制造；光束质量较好；运行成本低。     

Crystal Structures of Two Potential Tumor Imaging Agents and Therapeutic Agents Copper（Ⅱ） Ternary Complexes with Salicylidene-tyrosinato Schiff Base and Nitrogen-donor Chelating Lewis Base

The crystal structures of two potential tumor imaging agents and therapeutic agents -copper(Ⅱ) complexes with salicylidene-tyrosinato Schiff base and nitrogen-donor chelating Lewis base, [Cu(sal-tyr)(bipy)] 1 and [Cu(sal-tyr)(phen)]2CH3OH 2 are presented. Our work is helpful to get deep understanding of novel 64Cu tumor imaging agents and therapeutic agents.     

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].     

Pseudorandom properties of prime factors

In this paper we study some pseudo-random properties related to the prime factors of integers. We prove some results concerning the well distribution of the greatest prime factor modulo 4, and give some computational insight on the correlations, which seem to be beyond reach of proof.