Addendum to “Drinfeld Realization of Twisted Quantum Affine Algebras”

We provide necessary details to several arguments that appeared in our previous paper “Drinfeld Realization of Twisted Quantum Affine Algebras,” Commun. Algebra 35 (2007) 3683–3698.     

On Affine Normal Forms and a Classification of Homogeneous Surfaces in Affine Three-Space

We classify homogeneous surfaces in real and complex affine three-space. This is achieved by choosing affine coordinates so that the surface is defined by a function whose Taylor series is in a preferred normal form.     

激光半主动导引头光学系统分析

对陀螺-光学耦合式导引头中两种结构的光学系统进行分析,得出它们有不同的反射镜摆动角与跟踪场比,导出目标偏离视线的计算公式,并进行计算分析,最后讨论离焦探测器浸没问题。     

The validity of high-pass angular spectrum filter in solid immersion lens system

应用矢量方法计算了具有高通角谱滤波器的固体浸没透镜（SIL）系统的焦场分布。数值结果显示，对于径向（角向）偏振输入光，高通角谱滤波器可以减小SIL系统的光斑（暗斑）大小。然而，对于线性偏振输入光，简单的高通角谱滤波器不能够优化SIL系统的光场分布，也不能够改进系统的光存储密度。     

Functional equations for transfer-matrix operators in open Hecke chain models

We consider integrable open chain models formulated in terms of the generators of affine Hecke algebras. We use the fusion procedure to construct the hierarchy of commutative elements, which are analogues of the commutative transfer matrices. These elements satisfy a set of functional relations generalizing functional relations for a family of transfer matrices in solvable spin chain models of the U_q(gl(n|m)) type. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 219–236, February, 2007.     

Crystallized structure for level 0 part of modified quantum affine algebra Uq (sl2)

Crystal base of the level 0 part of the modified quantum affine algebra Uq(sl2)_0 is given by path. Weyl group actions, extremal vectors and crystal structure of all irreducible components are described explicitly.     

Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems

This paper provides an analysis of the polynomiality of primal-dual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu’s scaled Lipschitz condition, but is also applicable to mappings that are not monotone. We show that a family of primal-dual affine scaling algorithms generates an approximate solution (given a precision ε) of the nonlinear complementarity problem in a finite number of iterations whose order is a polynomial ofn, ln(1/ε) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in Jansen et al., SIAM Journal on Optimization 7 (1997) 126–140. Research supported in part by Grant-in-Aids for Encouragement of Young Scientists (06750066) from the Ministry of Education, Science and Culture, Japan. Research supported by Dutch Organization for Scientific Research (NWO), grant 611-304-028     

微分流形上的变换群

本文主要讨论如何把仿射Ｋｉｌｌｉｎｇ向量场、共形Ｋｉｌｌｉｎｇ向量场和射影Ｋｉｌｌｉｎｇ向量场推广成为四种张量场．我们得到了仿射Ｋｉｌｌｉｎｇｐ（≥１）形式和射影Ｋｉｌｌｉｎｇｐ（≥１）形式的多种定义，文献［１］中的定义仅是其中之一．     

Affine surfaces in R 4 with planar geodesics with respect to the affine metric

It is proved that non-degenerate surfaces in R ⁴ with planar geodesics are only the complex paraboloid and the product of two parabolas. An erratum to this article is available at .     

Torsion in Boundary Coinvariants and K -Theory for Affine Buildings

Let (G, I, N, S) be an affine topological Tits system, and let Γ be a torsion-free cocompact lattice in G. This article studies the coinvariants H ₀(Γ; C(Ω,Z)), where Ω is the Furstenberg boundary of G. It is shown that the class [1] of the identity function in H ₀(Γ; C(Ω, Z)) has finite order, with explicit bounds for the order. A similar statement applies to the K ₀ group of the boundary crossed product C ^*-algebra C(Ω)Γ. If the Tits system has type ? ₂, exact computations are given, both for the crossed product algebra and for the reduced group C ^*-algebra.