Homotopy of Non-Modular Partitions and the Whitehouse Module

We present a class of subposets of the partition lattice _n with the following property: The order complex is homotopy equivalent to the order complex of _n – 1, and the S _n -module structure of the homology coincides with a recently discovered lifting of the S _n – 1-action on the homology of _n – 1. This is the Whitehouse representation on Robinson's space of fully-grown trees, and has also appeared in work of Getzler and Kapranov, Mathieu, Hanlon and Stanley, and Babson et al.One example is the subposet P _n ⁿ – 1 of the lattice of set partitions _n , obtained by removing all elements with a unique nontrivial block. More generally, for 2 k n – 1, let Q _n ^k denote the subposet of the partition lattice _n obtained by removing all elements with a unique nontrivial block of size equal to k, and let P _n ^k = _{i = 2} ^k Q _n ⁱ . We show that P _n ^k is Cohen-Macaulay, and that P _n ^k and Q _n ^k are both homotopy equivalent to a wedge of spheres of dimension (n – 4), with Betti number . The posets Q _n ^k are neither shellable nor Cohen-Macaulay. We show that the S _n -module structure of the homology generalises the Whitehouse module in a simple way.We also present a short proof of the well-known result that rank-selection in a poset preserves the Cohen-Macaulay property.     

Construction of Certain Cyclic Distance-Preserving Codes Having Linear-Algebraic Characteristics

An ordered list of binary words of length n is called a distance-preserving m, n-code, if the list distance between two words is equal to their Hamming distance, for distances up to m. A technique for constructing cyclic m, n-codes is presented, based on the standard Gray code and on some simple tools from linear algebra.     

On the Approximation of Functions on Locally Compact Abelian Groups

Questions of approximative nature are considered for a space of functions L ^p(G, ), 1 p , defined on a locally compact abelian Hausdorff group G with Haar measure . The approximating subspaces which are analogs of the space of exponential type entire functions are introduced.     

乳化液喷雾与微爆现象的激光全息实验研究

本文采用离轴高速多脉冲红宝石激光全息摄影仪研究高温高压环境中乳化液喷雾的雾化和蒸发过程,记录方式为象面全息方式,再现时分别采用激光和白光光源。实验发现:在适当的温度压力条件下,乳化液喷雾可以发生微爆现象,微爆呈团状,又称“团状微爆”,也称为“二次雾化”,微爆能量可以将众多的小液滴及液滴碎片抛出液束区,有效地改善液体与环境气体的混合过程,具有重要的理论意义和实用价值。     

Uniform Growth of Polycyclic Groups

We prove that polycyclic groups have uniform exponential or polynomial growth.     

Backscattering wave mode analysis of an elastic tube and parameter reconstruction

I.IntroductionInthestudyofundcrwatcrtargctidcntification,moreandmoreattentionhasbcenpaidtotheinversescatteringprob1cm.Alargekindofobjcctscanbesimplificdintocylinders,spheresore11ipsoidswhilcstudyingtheirscattcringficIds.Thedirectprob1cmhasbeendeve1opedwel1andpcop1caredevotingtothcstudyofthcinvcrscprob1emfortargctidentification.Thedirectprob1emofthescatteringfrome1asticcylindcrsortubcsandtheinverseproblcmofthescat-teringfromsofttubcshavebccninvcstigatcd.['-']Inthispapcr,thedircctandinvcrsepro…     

多光谱全色分色棱镜的胶合

论述了多光谱全色分色棱镜组的胶合工艺。该棱镜组是由６块非标准角棱镜、１块底板和４块滤色镜共１１个零件所组成。该棱镜组各出射面与入射面之间的角度允差要求≤１０″，各通光面与底板底面之间的垂直度要求⊥≤１０″，棱镜中间还有两处空气隙，空气隙的宽度要求为Ｌ＝０．０５ｍｍ。另外，各棱镜在主光路方向上还有距离（光程）要求，因此该棱镜组的胶合工作成了该项任务加工中一个比较关键的技术。     

Null-quadrics of codimension 4 in ℂ7

In this paper we study the automorphisms of nondegenerate quadrics of type (4, 3). In particular, we classify the so-called null-quadrics (we prove that there are exactly two null-quadrics up to equivalence), and find their automorphism groups. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 657–665, November, 1997. Translated by S. S. Anisov     

THE COMPLETE LANGLANDS PARAMETERS CORRESPONDING TO THE REPRESENTATIONS OF THE CLASSICAL GROUPS WITH INTEGRAL REGULAR INFINITESIMAL CHARACTERS

1.CompleteLanglandsParametersandL-PacketsInthissectionwereviewsomebasicfactsfrom[1].Wedenotethesetsofrealnumbers,complexnumbersandintegersbyR,CandZ,respectively.SupposethatGisaconnectedcomplexreductivealgebraicgroup.WehaveanextendedgrouPGrforG,andvGrisanE-groupforGr.WedenotethesetofLanglandsparametersandthesetofgeometricparametersforvGrbYp(vG')andX(VG'),respectively.ThereisanaturalmapfromP(VG')toX(vG').ItinducesabijectionfromequivalenceclassesofLanglandsparameterstogeometricparamet…     

格序群的扭自由根式格

证明了发下结果；格序群的扭自由根式全体构成一个完备格县这个格满足并无限分配律，所有主扭自由根式构成这个格的一个理想。