sl_2(R)上Harish-Chandra模及其应用

将ｓｌ２（Ｒ）上不可约Ｈａｒｉｓｈ－Ｃｈａｎｄｒａ模及ｓｌ２（Ｒ）上不可分解的Ｈａｒｉｓｈ－Ｃｈａｎｄｒａ模进行了完全分类，得到了与ｓｌ２（Ｃ）上模分类的不同形式．作为应用，又构造了实Ｖｉｒａｓｏｒｏ代数的一类新的不可约表示．     

Structure theorem for tournaments omitting N5

A finite tournament T is tight if the class of finite tournaments omitting T is well‐quasi‐ordered. We show here that a certain tournament N₅ on five vertices is tight. This is one of the main steps in an exact classification of the tight tournaments, as explained in [10]; the third and final step is carried out in [11]. The proof involves an encoding of the indecomposable tournaments omitting N₅ by a finite alphabet, followed by an application of Kruskal's Tree Theorem. This problem arises in model theory and in computational complexity in a more general form, which remains open: the problem is to give an effective criterion for a finite set {T₁,…,T_k} of finite tournaments to be tight in the sense that the class of all finite tournaments omitting each of T₁,…,T_k is well‐quasi‐ordered. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 165–192, 2003     

A RELATION BETWEEN THE APPARENT VELOCITY AND THE SPECTRAL POWER OF SUPERLUMINAL RADIO SOURCES

It is proved that the apparent transverse velocities β_(app) and the spectral powers at 10GHz P_(10) of the cores of known superluminal sources are correlated. An interpretation ofthis result within the framework of the relativistic jet model shows that the jet Lorentzfactor γ depends on the intrinsic luminosity of the sources. The probable existence of twosubpopulations of the superluminal sources is shown by a linear regression analysis. "Small"sources f i.e. the sources without extended emission or with a distance from the core tothe outer edge of the lobe<20 kpc, show lower β_(app) than the "large" objects; this can beinterpreted as an orientation effect. Since all BL Lac objects belong to the "small" class,this result sheds new light on such a question as why these sources have lower apparent ve-locities than the "classical" superluminal quasars.     

On the Indecomposable Modules of Uq（sl（2）） Constructed via Ore-extension

Let A be a subalgebra of Uq (sl(2)) generated by K, K-1 and F and Aδ be a subalgebra of Uq (sl(2)) generated by K, K-1 (and also Fd if q is a primitive d-th root of unity with d an odd number). Given an Aδ -module M, a Uq (sl(2))-module AAδ M is constructed via the iterated Ore extension of Uq (sl(2)) in a unified framework for any q. Then all the submodules of AAδ M are determined for a fixed finite-dimensional indecomposable Aδ -module M . It turns out that for some indecomposable Aδ -module M , the Uq (sl(2))-module AAδ M is indecomposable, which is not in the BGG-categories Oq associated with quantum groups in general.     

Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral <Emphasis Type="Italic">su</Emphasis>(2) WZNW Model

A zero modes’ Fock space is constructed for the extended chiral WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping algebra at an even root of unity, and of its infinite dimensional extension by the Lusztig operators We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations of A central result is the characterization of the Grothendieck ring of both and in Theorem 3.1. The properties of the fusion ring in are related to the braiding properties of correlation functions of primary fields of the conformal current algebra model.      

新疆天山北坡典型研究区融雪期地物光谱特征分析

地物的波谱特性乃是整个遥感技术的物理基础,更是遥感技术应用尤其是定量遥感的基石。由于融雪期静态地物与冰-雪-水等动态地物交互存在,地物光谱特征更为复杂。选取了新疆天山北坡乌鲁木齐河流域以及军塘湖流域作为典型研究区,采用美国CID公司生产的CI700便携式野外光谱仪,通过2006年到2009年融雪期大量的野外调查和实地测量,获取了新疆天山北坡典型研究区融雪期典型地物包括各种积雪、冰、水以及土壤的光谱曲线及其变化规律,并对其进行了光谱特征分析。结果表明,融雪期虽然地物类型较为单一,但是因为积雪-冰-水-土壤复杂系统的交互式影响,地物的光谱特性及其变化均较为复杂,给融雪期地表参数的定量遥感研究带来了较大的挑战。对于融雪期复杂地物光谱的系列观测及特征分析无论是对于地物光谱特征基础研究还是定量遥感应用研究均具有重要意义。     

Homotopy Structures for Algebras over a Monad

Let T be a monad over a category A. Then a homotopy structure for A, defined by a cocylinder P : A A, or path-endofunctor, can be lifted to the category A ^T of Eilenberg–Moore algebras over T, provided that P is consistent with T in a natural sense, i.e. equipped with a natural transformation : T P P T satisfying some obvious axioms. In this way, homotopy can be lifted from well-known, basic situations to various categories of algebras for instance, from topological spaces to topological semigroups, or spaces over a fixed space (fibrewise homotopy), or actions of a fixed topological group (equivariant homotopy); from categories to strict monoidal categories; from chain complexes to associative chain algebras. The interest is given by the possibility of lifting the homotopy operations (as faces, degeneracy, connections, reversion, interchange, vertical composition, etc.) and their axioms from A to A ^T , just by verifying the consistency between these operations and : T P P T. When this holds, the structure we obtain on our category of algebras is sufficiently powerful to ensure the main general properties of homotopy.