Conservation Laws of K(m, n) and mK(m, n) Equations

Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2, n) equations and mnK(m, n) equations are found by using of this approach and some new results have been obtained.     

Molecular scale structure formation by folding

A conception of a structure formation suitable for nano-technology is proposed, which is programmable and suitable for mass production-like lithography. This conception utilizes the controlled folding of chains like the scan-lines of television. Its possibility and property were studied theoretically using the modeled chains consist of beads. By adopting the interaction among the beads which can distinguish the kind of the partner by its polarity and is chiral to break the chiral symmetry of the folded state, the special chains which have the unique ground states could be designed. In these ground states, the chains are folded like the scan-lines of television. The thermodynamic properties of the suggested chains were studied by the Monte Carlo simulations and the suggested chains showed the phase-transition-like behavior which is distinct compared to both the random chains and the chain that has only the non-specific attraction. The size dependence and the effects of adding the non-specific attraction and modifying the border of the folded conformation were also studied.     

BNCT蒙特卡洛剂量计算的混合网格算法研究

在硼中子俘获治疗(BNCT)的蒙特卡洛(MC)剂量计算中,通常使用单一的网格模式,如16mm,8mm,4mm.使用细网格计算资源太大,使用粗网格,计算精度不够,为此,根据粒子穿透深度和计数量的变化梯度,采用混合网格模拟计算,达到了细网格的精度,时间仅为细网格的37%.     

Synthese und Struktur von γ-Halogenpropyl-octa(silasesquioxanen)

Synthesis and Structures of γ-Halopropyl-octa(silasesquioxanes) As a more rapid and versatile synthetic approach, we have studied the FeCl₃-catalyzed hydrolytic polycondensation of suited trichlorosilanes in a biphasic system which yields e.g. the new octa(silasesquioxane) (BrCH₂CH₂CH₂)₈Si₈O₁₂.     

The Classification of Exponential Paths in Sp(2)

众所周知，四阶以上辛群中指数型道路的Ｍａｓｌｏｖ指标可以取任意整数．本文给出了二阶辛群中指数型道路的分类及其Ｍａｓｌｏｖ指标的取值范围，指出了与高阶情形的不同之处．     

Scale functions on $p$-adic Lie groups

Let G be a p-adic Lie group. Then G is a locally compact, totally disconnected group, to which Willis [14] associates its scale function G : G→ℕ. We show that s can be computed on the Lie algebra level. The image of s consists of powers of p. If G is a linear algebraic group over ℚ _p , s(x)=s(h) is determined by the semisimple part h of x∈G. For every finite extension K of ℚ _p , the scale functions of G and H:=G(K) are related by s _H ∣ _G =s _G ^{[ K :ℚ} _p ^]. More generally, we clarify the relations between the scale function of a p-adic Lie group and the scale functions of its closed subgroups and Hausdorff quotients. Received: 20 February 1997; Revised version: 18 May 1998     

LIPSCHITZ STABILITY OF GENERAL CONTROL SYSTEMS Ⅱ.IN TERMS OF TWO MEASURES

1IntroductionStabilityintermsoftwomeasures,thisconceptenableustounifyava-rietyofstabilityconceptsandtoofferageneralandunifiedframeworkforinvestigationofstabilitytheory.AndtheoriginalLiapunovtheoremshavebeenextended,generalizedandweakenedinvariousaspects[3…     

Gaudin Model,KZ Equation and an Isomonodromic Problem on the Tours

This Letter presents a construction of isospectral problems on the torus. The construction starts from an SU(n) version of the XYZ Gaudin model recently studied by Kuroki and Takebe within the context of a twisted WZW model. In the classical limit, the quantum Hamiltonians of the generalized Gaudin model turn into classical Hamiltonians with a natural r-matrix structure. These Hamiltonians are used to build a nonautonomous multi-time Hamiltonian system, which is eventually shown to be an isomonodromic problem on the torus. This isomonodromic problem can also be reproduced from an elliptic analogue of the KZ equation for the twisted WZW model. Finally, a geometric interpretation of this isomonodromic problem is discussed in the language of a moduli space of meromorphic connections.     

关于多目标数学规划的最优性条件

本文讨论定义于Ｂａｎａｃｈ空间的多目标数学规划，得到一些ε－最优解和（弱）有效解的必要条件，充分条件和必要充分条件。