参数化设计中确定参数有效范围的吴特征列方法

参数化CAD设计中,需要对给定的草图进行修改进而得到满足设计者需求的模型.然而,在修改参数值时,常常由于给定的参数值不合理,而导致无法重新生成几何图形.利用吴特征列方法从代数可解的角度给出了一个在参数化设计中确定参数的有效范围的算法.实例的分析计算,证明算法是可行的.     

星形箭图偏周期预投射代数的Hilbert级数

设△是一个有限无圈的箭图.引入了由Δ所决定的偏周期预投射代数,它是一个定义在周期为p的稳定平移箭图Z△/(τ~p)上的代数,记为Π_(Q(Δ,p),J).当周期p=1时,偏周期预投射代数就是偏预投射代数.我们推广了Eting和Eu的方法并得到无圈的星形箭图△所决定的偏周期预投射代数Π_((Q(Δ,p)),J)的Hilbert级数的计算公式.     

M/M/1/m系统算子的本征值特性(m=4,5)

研究了m=4,5时,M/M/1/m算子本征值特性:二者相应本征值的代数重均为1;二者相应的系统算子的非零本征值相互交替;后者的最大非零本征值逐渐靠近0点;另外给出了m=4,5时,相应的p_0(t)图像.     

On F-almost split sequences

Let A be an Artinian algebra and F an additive subbifunctor of Ext,（-, -） having enough projectives and injectives. We prove that the dualizing subvarieties of mod A closed under F-extensions have F-almost split sequences. Let T be an F-cotilting module in mod A and S a cotilting module over F = End（T）. Then Horn（-, T） induces a duality between F-almost split sequences in ⊥FT and almost sl31it sequences in ⊥S, where addrS = Hom∧（f（F）, T）. Let A be an F-Gorenstein algebra, T a strong F-cotilting module and 0→A→B→C→0 and F-almost split sequence in ⊥FT.If the injective dimension of S as a Г-module is equal to d, then C≌（ΩCM^-dΩ^dDTrA^＊）^＊,where（-）^＊=Hom（g,T）.In addition, if the F-injective dimension of A is equal to d, then A≌ΩMF^-dDΩFop^-d TrC≌ΩCMF^-d ≌F^d DTrC.     

Fock空间上的对偶Toeplitz代数

通过符号映射研究Fock空间之正交补空间上对偶Toeplitz代数的结构,得到了Fock空间上对偶Toeplitz代数的一个短正合序列.并研究了对偶Toeplitz算子谱的性质.     

Automorphism group and representation of a twisted multi-loop algebra

Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie algebra. Recently we have studied the universal central extension, derivations and its vertex operator representations. In the present paper we study the automorphism group and bosonic representations ofL（t1, t2, 1）.     

Realizing enveloping algebras via varieties of modules

By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra L（A） generated by indecomposable constructible sets in the varieties of modules for any finite- dimensional C-algebra A. We obtain a geometric realization of the universal enveloping algebra R（A） of L（A）, this generalizes the main result of Riedtmann. We also obtain Green＇s formula in a geometric form for any finite-dimensional C-algebra A and use it to give the comultiplication formula in R（A）.     

ACCURATE ATTENUATION CORRECTION FOR ALGEBRAIC RECONSTRUCTION TECHNIQUE IN SPECT

We present a new iterative reconstruction algorithm to improve the algebraic reconstruction technique （ART） for the Single-Photon Emission Computed Tomography. Our method is a generalization of the Kaczmarz iterative algorithm for solving linear systems of equations and introduces exact and implicit attenuation correction derived from the attenuated Radon transform operator at each step of the algorithm. The performances of the presented algorithm have been tested upon various numerical experiments in presence of both strongly non-uniform attenuation and incomplete measurements data. We also tested the ability of our algorithm to handle moderate noisy data. Simulation studies demonstrate that the proposed method has a significant improvement in the quality of reconstructed images over ART. Moreover, convergence speed was improved and stability was established, facing noisy data, once we incorporate filtration procedure in our algorithm.     

巧用向量解解析几何问题

平面向量融数形于一体,具有代数、几何的双重身份,既是中学数学知识的一个交汇点,又是联系多种知识的媒介．巧用平面向量,能妙解许多看似与平面向量无关的解析几何问题,下面举例说明．     

n-李代数的结构

主要研究特征为2的代数闭域上(n+1)维n-李代数的结构,给出了(n+1)维n-李代数的分类,描述了其可解性与幂零性,刻画了(n+1)维n-李代数的导子代数与内导子代数的结构.