GLOBAL CLASSICAL SOLUTIONS WITH SMALL INITIAL TOTAL VARIATION FOR QUASILINEAR HYPERBOLIC SYSTEMS

By means of the continuous Glimm functional,a proof is given on the global existence ofclassical solutions to Cauchy problem for general first order quasilinear hyperbolic systems withsmall initial total rariation.     

单调性条件在Fourier级数收敛性中的最终推广:历史、发展、应用和猜想

为了对Fourier级数进行近似计算和有效应用,必须研究其收敛性,这个课题有长久的历史,形成了数学分析中吸引包括许多著名数学家在内的学者研究的一条热烈但困难的主流.其中,在三角级数(Fourier级数)一致收敛性和平均收敛性问题中人们一直关心Fourier系数的单调递减条件最终的推广.这个开始于英国Chaundy-Jollife(1916年)和Young(1913年)的工作最近出现了突破性的进展,产生了许多完善的结果.本文将对这方面的历史、发展给出综述,并重点介绍最近的应用成果,并对以后的工作给出研究思路和线索.     

低压闪蒸液滴形态和温度变化的研究

将液滴在常压下突然置于低压环境中,液滴由最初的平衡状态变成过热状态,发生闪蒸.本文实验研究了低压闪蒸液滴内部形态和温度的变化,系统描述了液滴闪蒸过程中的各种形态变化,总结了稳态闪蒸和稳态结冰过程中环境压力和初始温度对温度变化的影响.实验结果表明液滴闪蒸分六种形态.稳态闪蒸中环境压力越低,液滴的最终温度也越低;液滴的初始温度越高,降到最低温度的时间越长.稳态结冰过程中,液滴初始温度增加,液滴结冰温度和结冰回升最高温度也随之增加;液滴的结冰温度和回升最高温度随环境压力的增高而减小.     

交替三线性分解算法结合高效液相色谱法同时测定水杨酸与龙胆酸

利用交替三线性分解算法(ATLD)与高效液相色谱法相结合,在色谱保留时间为0.662 8~0.949 5min(间隔1/150 min)、紫外吸收波长为268~332 nm(间隔2 nm)且在未知干扰物2,3-二羟基苯甲酸存在下,同时测定了水溶液中光谱及色谱严重重叠的水杨酸(SA)和龙胆酸(GA)的含量,回收率分别为(102.2±6.7)%,(102.1±4.1)%,分辨结果与实际结果一致。研究结果表明:该方法定量快速准确、实验操作步骤简单,说明ATLD算法收敛快速稳定,对复杂体系中组分数估计不敏感,能有效解决色谱中的二阶校正问题。     

A statistical dynamics approach to the study of human health data: Resolving population scale diurnal variation in laboratory data

Statistical physics and information theory is applied to the clinical chemistry measurements present in a patient database containing 2.5 million patients' data over a 20-year period. Despite the seemingly naive approach of aggregating all patients over all times (with respect to particular clinical chemistry measurements), both a diurnal signal in the decay of the time-delayed mutual information and the presence of two sub-populations with differing health are detected. This provides a proof in principle that the highly fragmented data in electronic health records has potential for being useful in defining disease and human phenotypes.     

Full fitting analysis of the relative intermediate form factor measured by neutron spin echo

This paper describes the dynamics of a water-in-oil microemulsion from the dilute to the dense droplet region. Using the relative intermediate form factor method for neutron spin echo data analyses [M. Nagao, H. Seto, Phys. Rev. E 78 (2008) 011507], the shape and structure fluctuations of a droplet microemulsion are successfully decoupled. In the previous paper, we used the first cumulant analysis of the shape fluctuation model, while the full fitting form of the same model is applied in this paper. The final results of the fittings using the first cumulant approximation and the full form of the model are almost identical, and therefore, the validity of the method is strengthened. The estimated bending modulus of the surfactant membrane, κ, is basically the same, within the experimental errors, in the previous and present results. The κ is not affected much by an increase of the droplet concentration. A clear dynamic slowing down of the water droplets is highlighted at the length scale corresponding to the inter-droplet distance from the structure fluctuation analysis.     

Effects of composition grading at heterointefaces and layer thickness variations on Bragg mirror quality

GaAs/AlAs Bragg mirrors on GaAs with varied number of layer pairs were grown, by molecular beam epitaxy (MBE), to be applied for semiconductor saturable absorber mirrors (SESAMs) and intensity modulators. Due to the random variation of the growth rate, substrate surface roughness, and interdiffusion at the interfaces, precise control of the growth conditions of deposited layers poses a serious problem. Usually, thickness variations and composition grading at the heterointefaces result in variations of the mirror reflectivity. In this paper, the high resolution X-ray diffraction (HRXRD), optical reflectance, Rutherford backscattering/channelling (RBS), supported by numerical evaluation methods were employed to determine both the exact thickness of each layer and the composition grading at the interface between succeeding layers of GaAs/AlAs-based mirrors. To reduce ambiguity and to speed up the analysis, the rocking curves and RBS spectra were simulated concurrently, using results of one simulation to verify the others. This process was carried out until the best fit between experimental and calculated curves was achieved. The complementary use of both methods results in improved sensitivity and makes the whole process of evaluation of the thickness variation of each layer and the size of the composition grading at the interfaces less time consuming.     

Propagation of light in(2+1)-dimensional nonlinear optical media with spatially inhomogeneous nonlinearities

The(2 1)-dimensional nonlinear Schr(o)dinger(NLS)equation with spatially inhomogeneous nonlinearities is investigated,which describes propagation of light in(2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities.New types of optical modes and nonlinear effects in optical media are presented numerically.The results reveal that the regular split of beam can be obtained in (2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities,by adjusting the guiding parameter.Furthermore,the stability of beam regular split is discussed numerically,and the results reveal that the beam regular split is stable to the finite initial perturbations.