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).     

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.     

Control of self‐organized low‐dimensional morphology in poly(styrene‐b‐4vinylpyridine)/polystyrene blend thin films

The surface morphologies of poly(styrene‐b‐4vinylpyridine) (PS‐b‐P4VP) diblock copolymer and homopolystyrene (hPS) binary blend thin films were investigated by atomic force microscopy as a function of total volume fraction of PS (?_PS) in the mixture. It was found that when hPS was added into symmetric PS‐b‐P4VP diblock copolymers, the surface morphology of this diblock copolymer was changed to a certain degree. With ?_PS increasing at first, hPS was solubilized into the corresponding domains of block copolymer and formed cylinders. Moreover, the more solubilized the hPS, the more cylinders exist. However, when the limit was reached, excessive hPS tended to separate from the domains independently instead of solubilizing into the corresponding domains any longer, that is, a macrophase separation occurred. A model describing transitions of these morphologies with an increase in ?_PS is proposed. The effect of composition on the phase morphology of blend films when graphite is used as a substrate is also investigated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3496–3504, 2004     

A Quantum Chemical Study on Recognition of Nitro-phenols by Calix[n]arenes

A PM3 calculation in vacuum of the inclusion complexation ofo-, m-, p-nitro-phenol with calix[n]arenes is performedsuccessfully. The pathways for inclusion process are describedand the most probable structures of the 1:1 complex are soughtthrough a potential energy scan. The energy differences betweenthe inclusion complexes and the hosts, by calculation, show thatthe most stable complexation is calix[4]-p-nitro phenol andcalix[6]-m-nitro phenol.     

One-pot Synthesis of 2, 5-Disubstituted Oxazoles Using Poly[styrene（iodosodiacetate）]

2,5-Disubstituted oxazoles were prepared conveniently by treatment of aromatic α-methyl ketones and nitriles with poly[styrene(iodosodiacetate)] in one-pot process.     

A jet appearing when a black hole event horizon touches the rindler horizon

The Hawking effect of a nonuniformly rectilinearly accelerating Kinnersley black hole is studied. Its horizons are rotationally symmetric. Its Hawking temperature depends not only on the time, but also on the polar angle. When a Kinnersley black hole touches its Rindler horizon, the Hawking temperature at the contact point is reduced to zero. But at the opposite pole of the black hole, the Hawking temperature increases rapidly. A jet appears as a tail of the accelerating black hole.     

KDP晶体三倍频实验和分析

报道了ＫＤＰ晶体中的三倍频产生的实验研究，计算了比较了直接三倍频过程和级联过程对ＫＤＰ晶体三阶有效非线性系数的贡献，并探讨了ＫＤＰ作为非线性晶体材料三阶非线性系数测量基准的可行性。