On generalized Lax equation of the Lax triple of KP Hierarchy

In terms of the operator Nambu 3-bracket and the Lax pair (L, B_n) of the KP hierarchy, we propose the generalized Lax equation with respect to the Lax triple (L, B_n, B_m). The intriguing results are that we derive the KP equation and another integrable equation in the KP hierarchy from the generalized Lax equation with the different Lax triples (L, B_n, B_m). Furthermore we derive some no integrable evolution equations and present their single soliton solutions.     

共面不对称条件下低能电子碰撞电离Ar(3p)的三重微分截面

采用修正的扭曲波玻恩近似方法, 在共面不对称几何条件下, 计算了能量为70.8 eV电子与Ar(3p)碰撞电离的(e, 2e)三重微分截面, 并与最新实验数据进行了比较. 结果表明电子交换效应和后碰撞相互作用在低能电子碰撞的(e, 2e)过程中起着重要作用. 关键词： (e,2e)三重微分截面 扭曲波玻恩近似 后碰撞相互作用 电子交换效应     

空间用GaInP/GaAs/In0.3Ga0.7 As(1 eV)倒装三结太阳电池研制

采用阶变缓冲层技术 (step-graded) 外延生长了具有更优带隙组合的倒装GaInP/GaAs/In_0.3Ga_0.7As(1.0 eV) 三结太阳电池材料, TEM和HRXRD测试表明晶格失配度为2%的In_0.3Ga_0.7As 底电池具有较低的穿透位错密度和较高的晶体质量, 达到太阳电池的制备要求. 通过键合、剥离等工艺制备了太阳电池芯片. 面积为 10.922 cm² 的太阳电池芯片在空间光谱条件下转换效率达到32.64% (AM0, 25 ℃), 比传统晶格匹配的 GaInP/GaAs/Ge(0.67 eV) 三结太阳电池的转换效率提高3个百分点. 关键词： 太阳电池 三结 倒装结构     

Dielectric assembly of a collagen-model polypeptide in a triple helix

In expectation of the formation of a thermally stable, dielectric supramolecular assembly of a polypeptide with an amino acid sequence similar to that of type-2 collagen, a sequential polypeptide consisting of the repetition of the Pro-Pro-Gly tripeptide was synthesized by solid-phase synthesis. Column chromatography of an ethanol solution of (Pro-Pro-Gly)₁₀ NH₂ showed the presence of a double helix or triple helix of the polypeptide. The pattern of a circular dichroism (CD) spectrum of an ethanol solution of (Pro-Pro-Gly)₁₀ NH₂ was very similar to that of an aqueous solution of (Pro-Pro-Gly)₁₀ OH, strongly suggesting the presence of a triple helix of the polypeptide in ethanol. An oriented monolayer assembly of (Pro-Pro-Gly)₁₀ NH₂ was formed on a thin gold film. The distribution of surface unevenness and the surface potential were investigated with Kelvin force microscopy. The rising spots carried an electric potential from room temperature to 150 °C. The correspondence showed the usefulness of the oriented monolayer of the sequential polypeptide materials for thermally stable, dielectric nanodevices. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3632–3639, 2003     

Subgroups of Free Groups: a Contribution to the Hanna Neumann Conjecture

We prove that the strengthened Hanna Neumann conjecture, on the rank of the inter-section of finitely generated subgroups of a free group, holds for a large class of groups characterized by geometric properties. One particular case of our result implies that the conjecture holds for all positively finitely generated subgroups of the free group F(A) (over the basis A), that is, for subgroups which admit a finite set of generators taken in the free monoid over A.     

Plutonium Predominance-Region Diagram

The oxidation number and the pH are used to construct a predominance-region diagram for soluble plutonium. Features of the diagram can be verified by means of rearrangement equations for plutonium.     

Coexistence of Differently Capped Trigonal Prismatic C2@Ag7 Cages in a Triple Salt of Silver(I) Acetylide

The new silver(I) triple salt 2Ag₂C₂·AgF·9AgNO₃·H₂O was prepared by dissolving Ag₂C₂ in an aqueous solution of AgNO₃ and AgBF₄. Its crystal structure contains two kinds of monocapped trigonal prismatic C₂@Ag₇ cages, with the capping atom occurring on one triangular face or one rectangular face.     

Type II non-commutative geometry. I. Dixmier trace in von Neumann algebras

We define the notion of Connes-von Neumann spectral triple and consider the associated index problem. We compute the analytic Chern-Connes character of such a generalized spectral triple and prove the corresponding local formula for its Hochschild class. This formula involves the Dixmier trace for II_∞ von Neumann algebras. In the case of foliations, we identify this Dixmier trace with the corresponding measured Wodzicki residue.     

New Modular Relations for the Göllnitz-Gordon Functions

We attempt to obtain new modular relations for the Göllnitz-Gordon functions by techniques which have been used by L. J. Rogers, G. N. Watson, and D. Bressoud to prove some of Ramanujan's 40 identities. Also, we give new proofs for some modular relations for the Göllnitz-Gordon functions which have been previously established by using results from L. Rogers and D. Bressoud. Finally, we give applications of those new modular relations to the theory of partitions.     

The Local Index Formula for SU q (2)

We discuss the local index formula of Connes–Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula. (Received: January 2005)