Chaotic electronic scattering with He(+)

We investigate classical electronic collisions with a He(+) ion. Scattering functions, such as the scattering angle, collisional time, or energy of the outgoing electron, all exhibit an interesting hierarchial self-similar structure, which can be interpreted in terms of the indefinite number of electronic returns to the vicinity of the nucleus, encounters between electrons, and Keplerian excursions of electrons during the collisional processes. Based on this mechanism a binary coding is introduced to organize the dynamics of this three-body system and to provide an understanding of the self-similarity among generations of scale magnification, which yields escape rates that vary with the sectional cut into the parameter space. The self-similarity displayed within a single generation, on the other hand, can be simply tied to the periods of the two independent electronic excursions. The physical interpretation and the symbolic dynamics introduced here are generally useful for three-body collisional systems, including atomic, molecular, or stellar collisions.     

Constructive methods of approximation by ridge functions and radial functions

Let be a univariant function, and letg(x) be the average of (x,u) asu runs over the unit sphere in ⁿ . We give a necessary and sufficient condition forg to be a kernel function, i.e., thatg be inL ¹ ( ⁿ ) and have integral 1. The result is used to give a constructive proof of the density of the ridge functions based upon the function .     

On small zeros of quadratic forms over finite fields (II)

Let be a quadratic form with integer coefficients and letp denote a prime. Cochrane^[1] proved that ifn≥4 then has a solution satisfying , where . The aim of the present paper is to generalize the above result to finite fields.     

用超临界气体抽提方法研究抚顺烟煤的组成和结构——Ⅰ.抽出物的分离及GC、GC/MS分析

将抚顺烟煤用甲苯作溶剂,在半连续抽提装置上,于350℃、20MPa条件下,进行超临界气体抽提。抽出物先分离成油、沥青烯及前沥青烯三个族组份,再用离子交换树脂、硅胶柱色谱作进一步分离。GC和GC/MS的分析结果表明,油段分中存在正构烷烃(C_(13)—C_(31))、类异戊二烯化合物及长链烷基苯系列,这些化合物可提供抚顺烟煤的地球化学信息。     

Spectroscopic studies on 2,3,4,5-tetraphenylpyrylium salts with and without silver (I)-bridged structures

Two novel phenylated pyrylium compounds, silver (I)-bridged 2,3,4,5-tetraphenylpyrylium perchlorate (P1) and its silver (I)-free pyrylium ligand (P2) were prepared from 1,2,3,4-tetraphenylcyclopentadiene to examine their spectroscopic behaviors. The UV/vis absorption and fluorescent emission spectra of P1 and P2, measured in three solvents (acetonitrile, dichloromethane and toluene), reveal that the photophysical behaviors are closely related to silver (I) fragment, and strongly dependent on solvent polarity. In polar acetonitrile, P1 displays longer absorption wavelength and much lower fluorescent emission intensity than P2, although they exhibit much similarity in shape. In contrast, in nonpolar toluene, while P2 shows an apparent absorption band at 338 nm, P1 displays a tail-like line without absorption band observed. All the spectra obtained indicate a better coplanarity and a stronger intra-molecular charge transfer in P1 due to the effect of silver (I) fragment. Additionally, the 1H NMR spectra of P1 and P2, which were recorded under the same conditions, indicate that the silver (I) fragment reinforces pyrylium ring's capacity to localize the formal positive charge within the heterocyclic ring.     

Efficient degradation of organic pollutants mediated by immobilized iron tetrasulfophthalocyanine under visible light irradiation

Supported iron tetrasulfophthalocyanine can efficiently catalyze the degradation of organic pollutants by H2O2 under visible light irradiation in an aqueous solution, and the catalyst can be easily recycled without apparent loss of activity.