On the image of the Burau representation of the IA-automorphism group of a free group

In this paper we study the graded quotients of the lower central series of the image of the IA-automorphism group of a free group by the Burau representation. In particular, we determine their structures for degrees 1 and 2.     

Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.     

Lower bounds on the cardinality of the maximum matchings of planar graphs

Lower bounds on the cardinality of the maximum matchings of planar graphs, with a constraint on the minimum degree, are established in terms of a linear polynomial of the number of vertices. The bounds depend upon the minimum degree and the connectivity of graphs. Some examples are given which show that all the lower bounds are best possible in the sense that neither the coefficients nor the constant terms can be improved.     

Conformity and precision of CO2 densimetry in CO2 inclusions: microthermometry versus Raman microspectroscopic densimetry

To assess the ability of densimetry for CO₂ fluid in CO₂ inclusions, we compare two methods, microthermometry and Raman microspectroscopic densimetry for CO₂. The comparative experiment was performed for nine CO₂ inclusions in three mantle xenoliths. The results are as follows: (1) microthermometry precisely determines CO₂ density with the range of 0.65 to 1.18 g/cm³ compared with Raman microspectroscopic densimetry; (2) CO₂ density obtained by Raman microspectroscopic densimetry is fairly consistent with that by microthermometry; (3) it is hard to determine CO₂ density in CO₂ inclusion with diameter of less than around 3 µm using microthermometry; and (4) microthermometry can be applied only to the CO₂ inclusion whose CO₂ density ranges from around 0.65 to 1.18 g/cm³, whereas the Raman microspectroscopic densimetry is applicable to CO₂ density ranging from 0.1 to 1.24 g/cm³. The above features carry the potential for estimation of depth origin of mantle‐derived rocks. The depth where the rocks were trapped by host magma can be estimated using both geothermometric data and CO₂ fluid density in CO₂ inclusions in the rocks. Typical precisions of density of CO₂ in CO₂ inclusions obtained by the Raman microspectroscopic densimetry (~0.01 g/cm³) and by the microthermometry (< 0.001 g/cm³) correspond to uncertainties in the depth origin of 2.4 km and < 1.7 km, respectively, at 1000 ± 50 °C. In case of the mantle under 750–1250 °C and 1 GPa, the CO₂ fluid has a density ranging from 1.06 g/cm³ to 1.21 g/cm³, which are well measured by the Raman microspectroscopic densimetry. Combination of both densimetries for CO₂ in mantle minerals elucidates the deep structure of the Earth. Copyright © 2012 John Wiley & Sons, Ltd.     

单晶生长炉全局热分析(3)-自由界面形状的影响

本文在平坦自由表面非定常三维全局热分析模型的基础上,考虑自由表面形状的弯曲性,通过大量数值模拟,研究了弯曲自由表面对熔液流动、炉内全局温度场分布等的影响.研究表明:弯曲自由表面更易引起熔液流动振荡,且降低晶体生长界面反转的临界Re数,使结果更接近实际,从而使单晶生长全局热分析模型比前文更完善.     

Endoscopic Observation of Tissue by Narrowband Illumination

We propose a new illumination method for a medical endoscope: narrow band imaging (NBI), in which the spectral bandwidth of the filtered light is narrowed. To confirm how the spectral specifications of the filtered light influence a reproduced image, an experiment was conducted observing the endoscopic images of the back mucosa of a human tongue. In addition, the effect of NBI on endoscopic images was investigated through preliminary clinical tests in colonoscopy and upper gastrointestinal endoscopy. It has been shown that NBI can enhance the capillary pattern and the crypt pattern on the mucosa. These patterns are useful features for diagnosing an early cancer.