关于一类二次哈密尔顿系统在二次扰动下的极限环个数问题

本文研究了一类具有两个鞍点和一个中心的通用二次哈密尔顿向量场在二次扰动下的三参数开折，证明极限环的最小上界为２。     

A model study for the steady state error of numerical approximations of inviscid flow equations on Cartesian grid

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. In this paper we consider the influence of the refined interfaces on the steady state errors for second‐order three‐point difference approximations of flow equations. Since the various characteristic components of the Euler equations should behave similarly on such grids with regard to refinement‐induced errors, it is sufficient enough to conduct the analysis on a scalar model problem. The error we consider is a global error, different to local truncation error, and reflects the interaction between multiple interfaces. The steady state error will be compared to the errors on smooth refinement grids and on uniform grids. The conclusion seems to support the numerical findings of Yamaleev and Carpenter (J. Comput. Phys. 2002; 181: 280–316) that refinement does not necessarily reduce the numerical error. Copyright © 2005 John Wiley & Sons, Ltd.     

Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.     

复注及多孔注浆理论研究

针对柱面注浆方式，研究了有关渗透注浆的单孔复注及不同方式布孔时多孔注浆的相互影响等问题，推导出一些有价值的岩体注浆理论公式，可用于指导现场注浆工程的设计与施工．     

Polyelectrolyte complexes. VI. Polycation structure,polyanion molar mass,and polyion concentration effects on complex nanoparticles based on poly(sodium 2‐acrylamido‐2‐methylpropanesulfonate)

The formation and characterization of some interpolyelectrolyte complex (IPEC) nanoparticles based on poly(sodium 2‐acrylamido‐2‐methylpropanesulfonate) (NaPAMPS), as a function of the polycation structure, polyanion molar mass, and polyion concentration, were followed in this work. Poly(diallyldimethylammonium chloride) and two polycations (PCs) containing (N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride) units in the backbone (PCA₅ and PCA₅D₁) were used as starting polyions. The complex stoichiometry, (n^?/n⁺)_iso, was pointed out by optical density at 500 nm (OD₅₀₀), polyelectrolyte titration, and dynamic light scattering. IPEC nanoparticle sizes were influenced by the polycation structure and polyanion molar mass only before the complex stoichiometry, which was higher for the more hydrophilic polycations (PCA₅ and PCA₅D₁) and for a higher NaPAMPS molar mass, and were almost independent of these factors after that, at a flow rate of the added polyion of about 0.28 mL × (mL PC)^?1 × h^?1. The IPEC nanoparticle sizes remained almost constant for more than 2 weeks, both before and after the complex stoichiometry, at low concentrations of polyions. NIPECs as stable colloidal dispersions with positive charges in excess were prepared at a ratio between charges (n^?/n⁺) of 0.7, and their storage colloidal stability, as a function of the polycation structure and polyion concentration (from 0.8 to ca. 7.8 mmol/L), was demonstrated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2495–2505, 2004     

Optical Diffractive Memories: Angular Selectivity and Diffraction Efficiency in Dichromated Gelatin

Two thousand images of resolution 512×512 pixels as a regular matrix pattern of 10×10 elements are stored, where each element is angularly multiplexed 20 times in a 25 μm thickness of dichromated gelatin emulsion without cross-talk effect. The surface area of the matrix is 1 cm². We show good concordance of the angular selectivity between the experimental result and theory. The diffraction efficiency of each 20 multiplexed images is measured and has nearly the same value. Examples of reconstructed images for multiple applications are given, for example, storage of 160,000 images on a 3′1/2 floppy disc format, which is about 100 min of black and white film. Application can be made to automobile cartography and storage of X-ray images as well as weather forecast images. Colored diffractive images are also possible and are illustrated.     

Measurement of storage time, estimation of ion number and study of absorption line profile in a Paul trap

Europium (Eu⁺) ions were confined in a Paul trap and detected by non-destructive method. Storage time of Eu⁺ ions achieved in vacuum was improved by orders of magnitude employing buffer gas cooling. The experimentally detected signal was fitted to the ion response signal and the total number of ions trapped was estimated. It is found that the peak signal amplitude as well as the product of FWHM and the peak signal amplitude is proportional to the total number of trapped ions. The trapped ion secular frequency was swept at different rates and its effect on the absorption line profile was studied both experimentally and theoretically.     

On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

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.