关于具有常平均曲率和数量曲率超曲面的Mbius几何的一个注记

设x:M→Sn 1(n≥3)是n 1-维单位球中的无脐点超曲面, Mobius不变量G,Φ,A和B分别表示x的Mobius度量, Mobius形式, Blaschke形式和Mobius第二基本形式．本文证明了如果x的Mobius形式Φ平行,并且A λG μB=0,其中λ,μ分别是定义在M上的光滑函数,那么Φ=0,由此及李海中、王长平(2003年)文献中的分类定理给出了Sn 1中具有平行的Mobius形式及满足A λG μB=0的超曲面的分类．此结果推广了他们及张廷枋(2003年)文献中的结果．     

Local and global solutions of the Chern-Simons-Higgs system

We study low regularity solutions of the Chern-Simons-Higgs equations. The Lorentz gauge condition makes them hyperbolic equations with the null form. Under the Coulomb gauge condition they are formulated in the hyperbolic equation coupled with elliptic equation. The div-curl decomposition is used in the temporal gauge.     

充分发挥计算机辅助教学作用

本文就计算机在物理实验方面的辅助教学进行了较为深刻的研究和探索，并提出可行性的方案。     

三硼酸锂晶体的生长形态

用自由生长系统研究了三硼酸锂ＬｉＢ_３Ｏ_５（ＬＢＯ）晶体的实际生长形态。实验表明，它的各晶面簇的重要性的顺序为：｛１１０｝＞｛０１１｝＞｛２０１｝＞｛１１１｝。讨论了ＬＢＯ晶体的生长习性与内部结构之间的关系并应用负离子配位多面体理论模型解释了ＬＢＯ晶体的生长形态。     

Quantum chemistry investigation on the active site of Mn-SOD

In this paper, we carried out a theoretical study on the active site structures of the Mn-SOD with ab initio Hartree–Fock SCF method, and analyzed the molecular orbital energies, charges and atomic orbital contribution to the frontier molecular orbital.     

Rheological properties of multisticker associative polyelectrolytes in semidilute aqueous solutions

Multisticker associative polyelectrolytes of acrylamide (≈86 mol %) and sodium 2‐acrylamido‐2‐methylpropanesulfonate (≈12 mol %), hydrophobically modified with N,N‐dihexylacrylamide groups (≈2 mol %), were prepared with a micellar radical polymerization technique. This process led to multiblock polymers in which the length of the hydrophobic blocks could be controlled through variations in the surfactant‐to‐hydrophobe molar ratio, that is, the number of hydrophobes per micelle (N_H). The rheological behavior of aqueous solutions of polymers with the same molecular weight and the same composition but with two different hydrophobic block lengths (N_H = 7 or 3 monomer units per block) was investigated as a function of the polymer concentration with steady‐flow, creep, and oscillatory experiments. The critical concentration at the onset of the viscosity enhancement decreased as the length of the hydrophobic segments in the polymers increased. Also, an increase in the N_H value significantly enhanced the thickening ability of the polymers and affected the structure of the transient network. In the semidilute unentangled regime, the behavior of the polymer with long hydrophobic segments (N_H = 7) was studied in detail. The results were well explained by the sticky Rouse theory of associative polymer dynamics. Finally, the viscosity decreased with an increase in the temperature, mainly because of a lowering of the sample relaxation time. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1640–1655, 2004     

THERMODYNAMIC STUDY OF ADSORPTION OF PHENOLIC COMPOUNDS FROM AQUEOUS SOLUTION BY A WATER-COMPATIBLE HYPERCROSSLINKED POLYMERIC ADSORBENT

Equilibrium data for the adsorption of phenolic compounds, i.e., phenol, p-cresol, p-chlorophenol and p-nitrophenol from aqueous solutions by a water-compatible hypercrosslinked polymeric adsorbent (NJ-8) within temperature range of 283-323 K were obtained and correlated with a Freundlich-type of isotherm equation, so that equilibrium constants KF and n were obtained. The capacities of equilibrium adsorption for all the four phenolic compounds on the NJ-8 from aqueous solutions are around 2 times as high as those of Amberlite XAD-4, which may be attributed to the unusual micropore structure and the partial polarity on the network. The values of the enthalpy (always negative) are indicative of an exothermic process, which manifests the adsorption of all the four phenolic compounds on the two polymeric adsorbents to be a process of physical adsorption. The negative values of free energy change show that the solute is more concentrated on the adsorbent than in the bulk solution. The absolute free energy values of adsorption for NJ-8 are always higher than those for Amberlite XAD-4, which indicates that phenolic compounds are preferentially adsorbed on NJ-8. The negative values of the adsorption entropy are consistent with the restricted mobilities of adsorbed molecules of phenolic compounds as compared with the molecules in solution. The adsorption entropy values of phenolic compounds for NJ-8 are lower than those for Amberlite XAD-4, which means the micropores of NJ-8 require more orderly arranged adsorbate.     

Contravariant forms and extremal projectors

Tensor product of irreducible modules of highest weight over a semi-simple quantum group is completely reducible if and only if a natural contravariant form is non-degenerate when restricted to the span of singular vectors. We express this restriction through the extremal projector of the quantum group providing a computationally feasible criterion for complete reducibility of tensor products.