A note on the existence of multiple solutions for a class of systems of second order ODEs

We prove the existence of multiple solutions for some systems of second order ODEs with Dirichlet boundary conditions. Such systems are obtained by coupling scalar ODEs with different growth conditions. The proof relies on a global continuation technique.     

Persistent spectral hole-burning in a -doped aluminosilicate glass from 8 to 295 K: Study of the burning and refilling kinetics, and of optical dephasing

High-temperature persistent spectral hole-burning (PSHB), up to room temperature, has been observed in a Eu ³⁺ -doped aluminosilicate glass using a high peak-power nanosecond dye laser. Spontaneous refilling as well as thermal cycling measurements show that at least two mechanisms, a fast and a slow one, are involved in our sample. We suggest that the fast or “easy” component may correspond to a non-photochemical local rearrangement of the host or to photoreduction of the Eu ³⁺ ions and that the second one leading to very stable photoproducts may correspond to transfer of an electron over a sizable distance through a several-step process. The mechanisms we suggest agree with light-induced hole refilling measurements. Line broadening mechanisms are discussed and the temperature-dependent part of the homogeneous width and of the spectral shift is interpreted in terms of a two-phonon (Raman) process involving pseudo-local phonons. Received 28 July 1999     

Experiments on 40 Gb/s Transmission with Wavelength Conversion: Results from the IST ATLAS Project

In this article we report the main experimental results obtained in the framework of the IST ATLAS project regarding the transmission at 40 Gb/s over long terrestrial links, including the frequency conversion of a signal. We report the single-channel 40 Gb/s transmission over a link 500 km long with an amplifier spacing of 100 km, both with G.652 fibers and G.653 fibers by periodically compensating the chromatic dispersion with dispersion-compensating fibers. We report the single-channel transmission at 40 Gb/s, also, after the wavelength conversion of a channel with both PPLN and semiconductor optical amplifier devices. In particular, 500 km distances are obtained with PPLN wavelength conversion and 300 km distances with semiconductor optical amplifiers. Some results have been reported for electronic devices operating at 40 Gb/s.     

Affect control theory: An assessment*

This paper reviews affect control theory's major strengths, the contributions of recent work to its growth, and the most promising avenues for future work. Affect control theory's strengths include (1) the precision of its mathematical statement and empirical base (especially when compared with earlier interpretive sociologies), (2) its ability to link the internal processing that generates social action to the socio‐cultural system upon which that action is based, and (3) the generality that allows a parsimonious explanation of a wide range of processes and previous research findings. Recent advances provide (1) new, more accurate impression‐change formulas, (2) the expansion of the theory to encompass settings, emotions, and traits, (3) new dictionaries of evaluation, potency and acitivity meanings and (4) tests of the theory using likelihood judgments, verbal scenarios and actual behavior of naive experimental subjects. Further work must include links to cognitive structures that will further delineate definition of situation and behavior selection processes. In addition, integration of affect control theory with new sociological work on the development of shared social knowledge and on institutionalized production systems expand the theory in useful ways. Finally, new work must find innovative and convincing ways to test simulation outcomes using both verbal accounts and behavior.     

线性离散事件动态系统的可达性

可达性是动态系统的重要性质之一。本文讨论离散事件动态系统的可达性,给出了系统完全可达的充要条件,得到了利用系统的特征矩阵判断系统可达性的判据,证明了系统可按可达性进行分解、状态反馈不影响系统可达性等结论,还进一步讨论了一类流水线生产加工系统的可达性,本文的结果对于这类系统的分析和控制是有意义的。     

Polymer adsorption on heterogeneous surfaces

The adsorption of a single ideal polymer chain on energetically heterogeneous and rough surfaces is investigated using a variational procedure introduced by Garel and Orland (Phys. Rev. B 55, 226 (1997)). The mean polymer size is calculated perpendicular and parallel to the surface and is compared to the Gaussian conformation and to the results for polymers at flat and energetically homogeneous surfaces. The disorder-induced enhancement of adsorption is confirmed and is shown to be much more significant for a heterogeneous interaction strength than for spatial roughness. This difference also applies to the localization transition, where the polymer size becomes independent of the chain length. The localization criterion can be quantified, depending on an effective interaction strength and the length of the polymer chain. Received: 29 October 1997 / Revised: 19 December 1997 / Accepted: 6 March 1998     

Some computational methods for systems of nonlinear equations and systems of polynomial equations

This paper gives a brief survey and assessment of computational methods for finding solutions to systems of nonlinear equations and systems of polynomial equations. Starting from methods which converge locally and which find one solution, we progress to methods which are globally convergent and find an a priori determinable number of solutions. We will concentrate on simplicial algorithms and homotopy methods. Enhancements of published methods are included and further developments are discussed.     

一类抽象算子方程组的迭代解及其应用

在Banach空间中, 利用半序方法讨论了一类抽象算子方程组解的存在唯一性, 推广和统一了以前的一些结果. 然后应用到 Banach 空间非线性积分方程组, 得到了方程组的唯一解, 构造了收敛于方程组唯一解的迭代序列并给出了相应的误差估计.     

Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems

In this paper, a gap function for a system of vector equilibrium problems is introduced and studied. Some necessary and sufficient conditions for the system of vector equilibrium problems are established. Characterizations of the solutions set for the system of vector equilibrium problems are also derived. Furthermore, some existence results of solutions for the system of vector equilibrium problems are proved. This work was supported by the National Natural Science Foundation of China, the Youth Foundation, Sichuan Education Department of China, the National Natural Science Foundation, Sichuan Education Department of China (2004C018), and a grant from the National Science Council of ROC.