关于指数率Logistic方程在无限柱体内的波前解的存在性

与一维空间中研究连接两个常数的波前解的存在性不同的是,本文建立了在多维无限长的柱体内连接两个曲面的单调行波解的存在性.相应的模型是一种具有指数率的Logistic方程.所用的方法是一种改进了的单调性方法.本文的研究结果对自然界中波的实际传播行为给出了有益的启示.     

Tail Bounds for the Supremums of Empirical Processes over Unbounded Classes of Functions

So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetrization idea and a new method of truncating the original probability space; the exponential bounds of the tail probabilities for the supremum of the empirical process over an unbounded class of functions are obtained. The exponential bounds can be used to establish laws of the logarithm for the empirical processes over unbounded classes of functions.     

Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings

In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767-773] in condition αn∈(0,1], and also strong and weak convergence theorem of a finite family of strictly pseudocontractive mappings of Browder-Petryshyn type is obtained. The results presented extend and improve the corresponding results of M.O. Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73-81].     

Higher-order spectral analysis and weak asymptotic stability of convex processes

This paper deals with the asymptotic stability analysis of a discrete dynamical inclusion whose right-hand side is a convex process. We provide necessary and sufficient conditions for weak asymptotic stability, and obtain sharp estimates for the asymptotic null-controllability set. These estimates involve not only standard, but also higher-order spectral information on the convex process and its adjoint.     

Near-Field and Polarized Evanescent Field Excited Fluorescence of Self-Organized Particle Arrays of Organic Dye

A wetting/dewetting process was utilized to prepare self-organized organic dye particles of micrometer and submicrometer size. Near-field scanning optical microscopy successfully identified near-field excited near-field fluorescence from single particles. The majority of the small particles with diameters around 2 mm or less, however, did not show fluorescence under near-field observation. In contrast, far-field fluorescence, when excited by a polarized evanescent field, was observed, with the intensity depending on the excitation polarization, indicating that molecules' transition moment within dye particles was oriented parallel to the substrate surface. Single particle fluorescence spectrum consistently showed an identical sharp peak with a large redshift, indicating that the particles were composed of identical dye aggregates similar to J-aggregates. These observations suggest that the near-field at the probe tip was polarized parallel to the probe axis. Another observation, that molecules were oriented in a similar direction among adjacent particles, suggests that the dewetting process contributed to the alignment of the molecular direction among adjacent particles, which further proves that the present specimen was formed by a self-organizing mechanism.     

Size exclusion chromatography with dual-beam refractive index gradient detection of polystyrene samples

Non-aqueous size exclusion chromatography (SEC) of polystyrenes (as model analytes) is examined using the microscale molar mass sensor (μ-MMS) for detection. The μ-MMS is combined with SEC to demonstrate this simultaneously universal and molar mass selective detection method for polymer characterization. The μ-MMS is based on measuring the refractive index gradient (RIG) at two positions (upstream and downstream) within a T-shaped microfluidic channel. The RIG is produced from a sample stream (eluting analytes in the mobile phase) merging with a mobile phase stream (mobile phase only). The magnitude of the RIG is measured as a probe beam deflection angle and is related to analyte diffusion coefficient, the time allowed for analyte diffusion from the sample stream toward the mobile phase stream, and the bulk phase analyte refractive index difference relative to the mobile phase. Thus, two deflection angles are measured simultaneously, the upstream angle and the downstream angle. An angle ratio is calculated by dividing the downstream angle by the upstream angle. The μ-MMS was found to extend the useful molar mass calibration range of the SEC system (nominally limited by the total exclusion and total permeation regions from ∼100,000 g/mol to ∼800 g/mol), to a range of 3,114,000-162 g/mol. The injected concentration LOD (based on 3 s statistics) was 2 ppm for the upstream detection position. The point-by-point time-dependent ratio, termed a ‘ratiogram’, is demonstrated for resolved and overlapped peaks. Within detector band broadening produces some anomalies in the ratiogram shapes, but with highly overlapped distributions of peaks this problem is diminished. Ratiogram plots are converted to molar mass as a function of time, demonstrating the utility of SEC/μ-MMS to examine a complex polymer mixture.     

Investigation of Scale Exponents of Complete and Incomplete Aggregation-Annihilation Processes

The complete and incomplete aggregation-annihilation processes are investigated with the method of generating function, and the scale exponents are obtained exactly. We find that the scale exponents of incomplete aggregation-annihilation process are different from the previous exponents obtained by different methods. The time dependence of the total number of clusters and the total mass of clusters are analytically obtained.