A uniqueness theorem for a free boundary problem

In this paper, we prove a uniqueness theorem for a free boundary problem which is given in the form of a variational inequality. This free boundary problem arises as the limit of an equation that serves as a basic model in population biology. Apart from the interest in the problem itself, the techniques used in this paper, which are based on the regularity theory of variational inequalities and of harmonic functions, are of independent interest, and may have other applications.

     

Beam Combination using Stimulated Brillouin Scattering for the Ultimate High Power-Energy Laser System Operating at High Repetition Rate over 10 Hz for Laser Fusion Driver

After the laser was invented in 1960, a phase conjugation mirror has been respected to be the most fantastic one for the laser resonator composition because it can compensate any distortions of the laser beams occurred by the many inhomogenuities of the laser media and optical components. Among the many phase conjugation configurations, the stimulated Brillouin scattering phase conjugation mirror is the most simple one and many researchers have tried to utilize it to develop high power/energy laser systems. For realizing a high energy/power laser system the thermal problem is the most difficult to solve, and some researchers suggested a beam combination technique to reduce the thermal load of the big laser media to many small sized ones. To accomplish the beam combination using stimulated Brillouin scattering phase conjugation mirrors (SBS-PCMs), it is necessary to lock/control the phases of the SBS-PCMs. And some researchers have developed several ways for it, but they can lock the phases of a limited number of beams overlapped at the foci less than 5, or lock the phases by back-seeding technique but it loses the phase conjugation characteristics. For realization of the laser fusion driver, it is necessary to combine more than 10 or 100 beams. And the authors have developed recently a new phase controlling/locking technique which is isolated and independent totally from other beams and it can be applied to an unlimited number of beams in principle.     

Synthesis of TiO2–SiO2/polymer core–shell microspheres with a microphase‐inversion method

A novel microphase‐inversion method was proposed for the preparation of TiO₂–SiO₂/poly(methyl methacrylate) core–shell nanocomposite particles. The inorganic–polymer nanocomposites were first synthesized via a free‐radical copolymerization in a tetrahydrofuran solution, and the poor solvent was added slowly to induce the microphase separation of the nanocomposite and result in the formation of nanoparticles. The average particle sizes of the microspheres ranged from 70 to 1000 nm, depending on the reaction conditions. Transmission electron microscopy and scanning electron microscopy indicated a core–shell morphology for the obtained microspheres. Thermogravimetric analysis and X‐ray photoelectron spectroscopy measurements confirmed that the surface of the nanocomposite microspheres was polymer‐rich, and this was consistent with the core–shell morphology. The influence of the synthetic conditions, such as the inorganic composition and the content of the crosslinking monomer, on the particle properties was studied in detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3911–3920, 2006     

A highly sensitive and rapid assay for protein determination in human urine and penicillin using a Rayleigh light-scattering technique with benzeneazo-8-acetylamino-1-naphthol-3,6-disulfonic acid sodium salt.

A simple and sensitive method was conducted for the determination of trace amounts of proteins with benzeneazo-8-acetylamino-1-naphthol-3,6-disulfonic acid sodium salt (azophloxine, AP) using a Rayleigh light-scattering (RLS) technique. At pH 2.60 and in the presence of an emulsifier OP microemulsion, the RLS of AP can be greatly enhanced by proteins, owing to the interaction between AP and protein. The enhanced intensity is proportional to the concentration of proteins. Four proteins, including bovine serum albumin (BSA), human serum albumin (HSA), lysozyme (Lys) and gamma globulin (gamma-G) have been tested. For example, the linear range of BSA was 0 - 0.06 microg mL(-1) with detection limits of 2.38 ng mL(-1). The method was applied to the analysis of protein in human urine and penicillin samples with satisfactory results. The relative standard deviation was in all instances less than 4.0%, and the recovery was in the range of 97.5 - 104%.     

纤维素基磁性聚偕胺肟树脂吸附锂

研究了氯化锂浓度、树脂含量和溶液的ＰＨ对碱式纤维素基磁性聚偕胺肟树脂吸附Ｌｉ＾＋离子能力的影响。在适当条件下，每个偕胺肟基可吸附两个Ｌｉ＾＋离子。     

LB膜中螺吡喃材料的光学性质研究

利用ＬＢ技术制备螺吡喃有序分子膜，研究了气液界面上螺吡喃材料在不同成份和不同ｐＨ值亚相时的成膜行为，着重研究了螺吡喃在ＬＢ膜这个特殊介质环境中不同于溶液的光致变色机理和光学性质     

The measurements of correlation times of molecules adsorbed on silica gel,alumina and charcoal using NOESY and MAS NMR

The correlation times (τ_c) and cross relaxation rates of toluene, dimethylformamide, tetrahydrofuran, water-acetone and water-dioxane adsorbed on silica gel, alumina and charcoal were obtained by measurements of the integrated intensities of cross and diagonal peaks in their NOESY spectra. The (τ_c) of the above mentioned systems is in the range of 10^?6?10^?9 s, much longer than that in the liquid (10^?12?10^?14 s). It was found that intramolecular rotation of toluene adsorbed on charcoal is slower than that on SiO₂, Al₂O₃ and the inversion of α and β protons in tetrahydrofuran is very fast (τ_c = 1.76×10^?9 s). The cross relaxation plays an important role in the relaxation of molecules adsorbed on solid surfaces with low electron densities.     

Notes on polynomial levelability

We consider the polynomial levelability with respect to approximation algorithms (PLAA). A setA isPLAA if given any approximation algorithm forA and a polynomialp, there are another approximation algorithm forA and a polynomialq such that for infinitely many inputsx, acceptsx but has running time greater thanp(|x|) and acceptsx within timeq(|x|). In this paper, an algorithm is called an approximation algorithm forA if the symmetric differenceA L() is sparse, whereL() is the set of strings recognized by. We prove that all naturalNP-complete sets arePLAA unlessP=NP and allEXP-complete sets arePLAA.This work was supported in part by the NSF under Grant DCR 83-12472 and was done while the author studied at the Department of Mathematics, University of California at Santa Barbara. The work was also supported by Chinese National Science Foundation