Computable Carathéodory Theory

The conformal Riemann mapping of the unit disk onto a simply-connected domain W is a central object of study in classical Complex Analysis. The first complete proof of the Riemann Mapping Theorem given by P. Koebe in 1912 is constructive, and theoretical aspects of computing the Riemann map have been extensively studied since. Carathéodory Theory describes the boundary extension of the Riemann map. In this paper we develop its constructive version with explicit complexity bounds.     

Cremona transformations and diffeomorphisms of surfaces

We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational, then Aut(X), the group of algebraic automorphisms, is dense in Diff(X), the group of self-diffeomorphisms of X.     

On upper bounds on stable commutator lengths in mapping class groups

We give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating curve on an oriented closed surface of genus 2 are not equal to each other.     

Using X-PEEM to study biomaterials: Protein and peptide adsorption to a polystyrene–poly(methyl methacrylate)-b-polyacrylic acid blend

Recent synchrotron-based soft X-ray photoemission electron microscopy (X-PEEM) studies of protein and peptide interaction with phase segregated and patterned polymer surfaces in the context of optimization of candidate biomaterials are reviewed and a study of a new system is reported. X-PEEM and atomic force microscopy (AFM) were used to investigate the morphology of a phase-segregated thin film of a polystyrene/poly(methyl methacrylate)-b-polyacrylic acid (PS/PMMA-PAA) blend, and its interactions with negatively charged human serum albumin (HSA) and positively charged SUB-6 (a cationic antimicrobial peptide, RWWKIWVIRWWR-NH₂) at several pHs. At neutral pH, where the polymer surface is partially negatively charged, HSA and SUB-6 peptide showed contrasting adsorption behavior which is interpreted in terms of differences in their electrostatic interactions with the polymer surface.     

A new spectral calibration method for Fourier domain optical coherence tomography

Spectral calibration is important for a Fourier domain optical coherence tomography (FD-OCT) system. A new spectral calibration method for FD-OCT is presented. Through the iterated mapping of spectral interferograms detected by an optical spectrum analyzer and the CCD grating spectrometer, multiple groups of calibration coefficients are obtained. By comparing the effects of these coefficients on improving the amplitude of the axial point spread function (PSF), optimum coefficients are obtained. In this method, no additional calibration laser source is needed, reducing the complexity of the system. The cross-sectional images of a glass plate in milk are acquired, and the experimental results indicate that the axial resolution and signal-to-noise ratio (SNR) are effectively improved with the proposed spectral calibration method.     

线性同余人字映射组合产生均匀随机数

研究了线性同余法与人字映射组合随机数发生器 :xn=Axn-1(mod M) ,wn=2 xn,　 xn≤ 0 .5 M,wn=2 (M-xn) +1 ,　 xn>0 .5 M,yn=wn/ M.该组合发生器比相应的线性同余法在空间结构上有明显改善 ,并通过统计检验     

Micro-Raman mapping on an anatase TiO2 single crystal with a large percentage of reactive (0 0 1) facets

After it has been successfully synthesized in 2008, so far, no Raman investigations on the micro-sized anatase TiO₂ single crystal which has a large percentage of the reactive (0 0 1) facets have been conducted to the best of our knowledge. In the present work, this unique anatase TiO₂ single crystal was investigated by noninvasive and nondestructive Raman mapping technique. Raman images of both non-polarized and polarized measurements showed that the Raman features of the crystal varied with measurement position. The differences among the Raman spectra measured on different crystal facets were believed to result from the orientations and the symmetry rules. Whereas the differences among those measured at different points of the same crystal facet under the same measurement condition were supposed to indicate the defects of the crystal structure, such as oxygen vacancies, local lattice disorder etc. Furthermore, the appearance of the two second order Raman peaks of 803 and 918 cm⁻¹ as well as the blue-shift of 395 cm⁻¹ peak implies the anharmonicity of the crystal structure, which is also probably caused by the crystal defects. Our results provide useful information about the structure of this unique anatase TiO₂ material, and could be complementary to those that acquired by other characterization techniques.     

Laser-induced breakdown spectroscopy applications in the steel industry: Rapid analysis of segregation and decarburization

Rapid chemical analysis is increasingly a prerequisite in the steel making industry, either to check that a steel product complies with customers' specifications, or to investigate the presence of defects that may lead to mechanical property failure of the product. Methods conventionally used for assessment, such as the monitoring of decarburization and segregation, performed by chemical etching of a polished surface followed by optical observation, tend to be relatively fast, simple and applicable to large sample areas; however, the information obtained is limited to the spatial extent of the defect. Other techniques, such as electron probe microscopy and scanning electron microscopy — energy dispersive X-ray, can be used for providing detailed chemical composition at the micro-scale, for a better understanding of the mechanisms involved; however, their use is limited to analyzing comparatively very small sample areas (typically a few mm²).     

模糊保并、保交映射的隶属函数

模糊关系与算子合成构成了模糊映射，即将模糊集映射为模糊集。本文证明了模糊保并、保交映射的隶属函数可以表示为模糊关系与算子的合成。     

模糊映射的完全广义混合型强变分包含

研究一类新的关于模糊映射的完全广义混合型强变分包含问题，给出解的逼近算法，证明这类问题解的一个存在定理和序列收敛定理。