Jensen's inequality for g-expectation: part 1

Briand et al. (Electron. Comm. Probab. 5 (2000) 101–117) gave a counterexample and proposition to show that given g,g-expectations usually do not satisfy Jensen's inequality for most of convex functions. This yields a natural question, under which conditions on g, do g-expectations satisfy Jensen's inequality for convex functions? In this paper, we shall deal with this question in the case that g is convex and give a necessary and sufficient condition on g under which Jensen's inequality holds for convex functions. To cite this article: Z. Chen et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Langduin C, a novel dimeric diterpenoid from the roots of Euphorbia fischeriana

Langduin C, a novel dimeric diterpenoid, was isolated from the roots of Euphorbia fischeriana and its structure was established by spectral data and single-crystal X-ray diffraction analysis.     

Analysis on Shack–Hartmann wave-front sensor with Fourier optics

In Shack–Hartmann wavefront sensor (SHWS), the behavior of the irradiance pattern produced by the micro-lens array is important for an accurate centroid estimation. In this paper, the behavior of a micro-lens array in SHWS is analyzed using Fourier optics, and reveals that in addition to the main, expected spots, secondary spots with smaller intensities also appeared as a result of diffraction by the small dimensions of the micro-lens and interference from the different micro-lenses. This result is confirmed by comparing with a irradiance pattern taken from an actual SHWS. The additional error in centroid estimation caused by these secondary spots is discussed and relationship to the parameters of the micro-lens of SHWS is analyzed.     

精选实验素材加强实验教学

多年来人们对实验教学加以重视的同时却陷入了一个误区：只重视做好课堂演示实验和学生分组实验，而忽视了课外小实验的作用．其实，经常性地引导学生自己动手，就地取材，开展课外小实验、小制作，对加强物理实验教学，加深对物理知识的理解，提高学生的分析解决问题的能力，将会起到重要的作用．     

半导体激光器发射光谱实验仪

设计了一种半导体激光器发射光谱实验仪 ,可以用来观测LD发射的荧光光谱、激光光谱 ,以及了解光栅外腔选取单纵模、压窄线宽、波长调谐的机理 .该实验仪结构紧凑 ,物理概念清晰 ,适用于大专院校的光学实验教学     

Buckling of a stiff thin film on a compliant substrate in large deformation

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.     

The effect of micro-morphology of Bi2O3 on catalytic properties of Co/Bi catalyst for wet air oxidation of acetic acid

The novel phase transfer catalysts S-8 [4-(dimethyloctylammonium) propansultan] and DB-X [1,4-bis(triethylmethylammonium)benzene dibromide] were synthesized and employed for high conversion synthesis of dichlorocyclopropane from various olefins.This revised version was published online in December 2005 with corrections to the Cover Date.     

Crystallographic report: Diiodo[tris(2‐pyridyl)amine]mercury(II), [(C5H4N)3N]HgI2

In mononuclear HgI₂[(C₅H₄N)₃N], mercury is tetrahedrally coordinated by two nitrogen atoms of a tris(2‐pyridyl)amine ligand and two iodides. The coordination moieties are connected by weak intermolecular Hg(II)···I interactions to give a one‐dimensional structure. Copyright © 2003 John Wiley & Sons, Ltd.     

A Large Conformational Change of a Bridged b-Cyclodextrin Dimer in Aqueous Solution

As artificial enzymes, the binding constants of cyclodextrins (CDs) and their substrates are expected to be high1. For this purpose, many kinds of bridged cyclodextrin dimers2 whose two cyclodextrins are linked by various spacers have been constructed. It was of interest to make the dimers, whose binding constants would exceed 108dm3/mol3. Up to date, the bridged cyclodextrin dimers have been extensively studied as enzyme models and as molecular receptors4-6. Recently, we synthesized a brid…     

Synthesis of optically active 6-substituted 2-(aminomethyl)chromans

Three novel, optically active, 6-substituted 2-(aminomethyl)chromans were synthesized from readily available chroman 2-carboxylic acid precursors. These chroman-containing primary amines are useful building blocks for the synthesis of chroman-derived pharmaceutical agents.