The projection method for computing multidimensional absolutely continuous invariant measures

We present an algorithm for numerically computing an absolutely continuous invariant measure associated with a piecewiseC ² expanding mappingS: on a bounded region R ^N. The method is based on the Galerkin projection principle for solving an operator equation in a Banach space. With the help of the modern notion of functions of bounded variation in multidimension, we prove the convergence of the algorithm.     

A Novel Plasticizer for the Preparation of Thermoplastic Starch

TPS was a biodegradable material based on starch. Starch was an inexpensive and natural renewable polysaccharide, which was widely investigated as the substitute of petroleum-derived plastics. Native starch commonly existed in granule structure with about…     

Synthesis of oligo(p-phenylene vinylene)-porphyrin-oligo(p-phenylene vinylene) triads as antenna molecules for energy transfer

The oligo(p-phenylene vinylene)-porphyrin-oligo(p-phenylene vinylene) (P-OPVn, n=2, 4, where n is the number of phenyl rings) and the complex with Zn²⁺ based on P-OPVn were synthesized for investigating their photophysical properties via UV-vis, voltammetry, steady-state and time-resolved fluorescence spectra. In these molecules two OPV moieties as energy donors were linked to porphyrin center by virtue of Wittig reaction. The detailed studies of photophysical properties indicate that OPV group can act as an antenna unit for effective intramolecular energy transfer.     

Entropy of self-gravitating radiation

We examine the entropy of self-gravitating radiation confined to a spherical box of radiusR in the context of general relativity. We expect that configurations (i.e., initial data) which extremize total entropy will be spherically symmetric, time symmetric distributions of radiation in local thermodynamic equilibrium. Assuming this is the case, we prove that extrema ofS coincide precisely with static equilibrium configurations of the radiation fluid. Furthermore, dynamically stable equilibrium configurations are shown to coincide with local maxima ofS. The equilibrium configurations and their entropies are calculated and their properties are discussed. However, it is shown that entropies higher than these local extrema can be achieved and, indeed, arbitrarily high entropies can be attained by configurations inside of or outside but arbitrarily near their own Schwarzschild radius. However, if we limit consideration to configurations which are outside their own Schwarzschild radius by at least one radiation wavelength, then the entropy is bounded and we find S_max MR, whereM is the total mass. This supports the validity for self-gravitating systems of the Bekenstein upper limit on the entropy to energy ratio of material bodies.     

空间展布体系中由化学反应-扩散-热传导耦合导致的温度场对称破缺

分析了由于化学反应-扩散-热传导耦合而导致的非等温非均匀体系中温度场对称破缺.研究结果表明,在一定的边界条件下,甚至是单组分化学反应-扩散-热传导体系,温度场的这种自组织进程也不可避免.作为温度场结构的一个范例,进一步从解析解及计算机模拟两个方面研究了小展布非等温的Lindeman模型;结果表明,温度场出现时空自组织的阈值不仅与本征参数有关,而且与体系的边界条件及外控约束相关,揭示出了诱发或避免这种温度场时空自组织之途径.     

On strong convergence to 3-D axisymmetric vortex sheets

We consider the 3-D axisymmetric incompressible Euler equations without swirls with vortex-sheets initial data. It is proved that the approximate solutions, generated by smoothing the initial data, converge strongly in provided that they have strong convergence in the region away from the symmetry axis. This implies that if there would appear singularity or energy lost in the process of limit for the approximate solutions, it then must happen in the region away from the symmetry axis. There is no restriction on the signs of initial vorticity here. In order to exclude the possible concentrations on the symmetry axis, we use the special structure of the equations for axisymmetric flows and careful choice of test functions.     

Rectification of excitation with bathochromic shift induced by intense absorption of organic ligands during emission measurement of Eu(III) complex

Bathochromic shift in excitation spectrum was observed during emission measurement of Eu(DBM)(3)Phen containing dilute solution in methyl methacrylate (MMA). Detailed analysis shows that the reason of bathochromic shift is not the formation of molecule aggregation. It is caused by the intense absorption of ligands in the complex. Based on this model, a new method has been established to rectify excitation spectra before emission measurement of systems with different concentration. There exists a critical value of the absorption strength, which is 0.87 from calculation. Higher absorption than this value will cause the bathochromic shift of excitation peak. The wavelength whose absorbance is 0.87 will be the position of the strongest excitation peak. With 200 ppm and 500 ppm Eu(DBM)(3)Phen as the standard sample, relations between relative concentration and wavelength of excitation peak in Eu(DBM)(3)Phen system were deduced and plotted. Theoretical curves are in good agreement with experiment data except extra-dilute concentration, for partial decomplexation of the beta-diketonate and phenanthroline ligands.     

A Phenolic Glucoside from Alangium plantanifolium

Alangium, the sole genus in the family Alangiaceae, has a variety of about 20 species distributed in the tropical and subtropical area of the Eastern Hemisphere, and 13 species are known to occur in the south of China1. A. plantanifolium and A. chinense are used in chinese traditional medicine for the treatment of rheumatalgia, paralysis, cardianeuria, and wound2. Pharmacological studies of the extracts of these two species showed muscular relaxing activity, and anabasine was considered as t…     

微尺度圆管内气体流量的实验测量

以氮气和氦气为工作介质,研究了微尺度(φ=17.6μm,17.9μm)圆管内压力驱动的气体流动,测量了在不同进出口压力下的流量,并与计算值进行了比较.结果表明,即使对于极低Mach数(M=0.003～0.03)流动,其可压缩性仍十分明显,它来源于微尺度效应.在本文的实验参数下,Kundsen数范围为3×10-3～7×10-3,表面滑移不明显,稀薄气体效应可以忽略.     

Synthesis and structural characterization of a novel dimolybdenum(I) compound with mixed‐tribridging ligands: [Bu4N][Mo2(μ‐SPh)2(μ‐Cl(CO6]

A novel mixed‐tribridged dimolybdenum(I) compound [Bn₄N][Mo₂(μ‐SPh)₂(μ‐Cl)(CO)₆] (1) has been synthesized from the reaction of Mo₂(CO)₃(SPh)₂ with BU₄NCl. Compound 1 was characterized by IR, UV‐Vis and ¹H, ¹³C, ⁹⁵Mo NMR spectroscopic analyses. The electrochemical behavior was measured by cyclic voltammetry, indicating a quasi‐reversible two‐electron transfer in one step. The crystal structure determined by X‐ray crystallography shows that 1 contains a [Mo₂(μ‐S)₂(μ‐Cl)]^? core with a planar Mo₂S₂unit and a Cl bridge. The Mo? Mo distance is 0.28709(7) nm, and the Mo‐Cl‐Mo angle is 66.44(4)°. A newface‐sharing bioctahedral structure is discussed.