在可交换四元数空间中的双曲方程的特征边值问题

讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.     

代数体函数的定理

本文定义并研究了代数体函数的加法．结合杨乐的方法,将仪洪勋联系重值的亚纯函数唯一性定理推广到多值的代数体函数．     

Euler characteristic and related measures for random geometric sets

By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.     

Near field imaging in microwave regime using double layer split-ring resonator based metamaterial

A planar metamaterial structure consisting of two layers of split-ring resonator (SRR) arrays is demonstrated to form the image of a point source with subwavelength resolution. The source frequency is swept through the resonance gap of the metamaterial layers and the lateral field intensity distribution is recorded on the transmission side of the metamaterial. When the source is tuned to the resonance frequency of SRRs, the metamaterial acts as a high permeability medium and a distinct image with subwavelength resolution in the lateral direction is obtained. Increasing the distance between the individual SRR layers reduces the interlayer coupling, and the intensity and spatial resolution of the image decrease rapidly.     

Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

确定线性偏微分方程组可积系统的对合特征集方法

基于Ritt-Wu特征集方法和Riquier-Janet理论,给出一种将线性微分方程组化成简单标准形式的有效算法．该算法通过消去冗余和添加可积条件获得线性微分方程组的完全可积系统(有形式幂级数解)或不相容判定．该算法不仅适用于常系数的线性偏微分方程组,而且对于变系数(以函数为系数)仍然有效．作者还给出了完全可积系统判定定理及其严格证明．     

Novel radical‐responsive MRI contrast agent based on paramagnetic liposomes

A novel, radical responsive MRI contrast agent based on a gadolinium chelate conjugated to a liposome through a disulfide linker was synthesized, with the aim of pursuing the in vivo mapping of radicals. The liposome was prepared by incorporating a thiol‐activated phospholipid, which was subsequently reacted with a gadolinium chelate containing a free thiol group. The long reorientational motion of the supramolecular adduct endows the paramagnetic agent with a relaxivity significantly higher than that of the free complex. The disulfide bond represents a radical‐sensitive moiety and a large decrease in contrast efficacy (T₁ relaxivity) is shown upon its cleavage. A preliminary assessment of the system was made by means of in vitro gamma‐irradiation and thiol–disulfide bond exchange with dithiothreitol. Both methods showed a clear dose‐dependent decrease in T₁‐relaxivity. Copyright © 2003 John Wiley & Sons, Ltd.     

Mathematical topographical correction of XPS images using multivariate statistical methods

For rough heterogeneous samples, the contrast observed in XPS images may result from both changes in elemental or chemical composition and sample topography. Background image acquisition and subtraction are frequently utilized to minimize topographical effects so that images represent concentration variations in the sample. This procedure may significantly increase the data acquisition time. Multivariate statistical methods can assist in resolving topographical and chemical information from multispectral XPS images. Principal component analysis (PCA) is one method for identification of the highest correlation/variation between the images. Topography, which is common to all of the images, will be resolved in the first most significant component. The score of this component contains spatial information about the topography of the surface, whereas the loading is a quantitative representation of the topography contribution to each elemental/chemical image. The simple‐to‐use self‐modelling mixture analysis (Simplisma) method is a pure variable method that searches for the source of most differences in the data and therefore has the potential to distinguish between chemical and topographical phases in images. The mathematical background correction scheme is developed and validated by comparing results to the experimental background correction for samples with differing degrees of topography. Copyright © 2004 John Wiley & Sons, Ltd.     

Surface profile measurement of low-frequency vibrating objects using temporal analysis of fringe pattern

A simple and accurate algorithm (phase scanning method) is proposed for 3D surface contouring and dynamic response determination of a vibrating object. A sinusoidal fringe pattern is projected onto a low-frequency vibrating object by a programmable liquid crystal display projector. The fringe patterns are captured by a high-speed CCD camera with a telecentric gauging lens. Phase values are evaluated point by point using phase scanning method. From the phase values of each point on the object, the contour of the specimen at different instants of vibration can be retrieved. In this paper, a small vibrating coin is used to demonstrate the validity of the method and the experimental results are compared with test results on a stationary coin using four-step phase shifting and fast Fourier transform methods. The technique is especially useful in applications where the vibrating object has a complicated shape.     

斐索型光学合成孔径系统近轴成像条件研究

从几何光学理论出发，详细推导了斐索型光学合成孔径成像系统的近轴非相干成像条件，即子望远系统的角放大率等于系统的线性缩放因子。对于焦平面上的像点而言，合成孔径成像系统可等效为一个带有特殊形状孔径光阑的望远系统，这要求该孔径光栏的开口形状和位置分布与合成孔径成像系统各子系统孔径大小和位置分布相一致。我们由此得到了斐索型合成孔径成像系统的主要约束条件。