Recollement of Triangulated Categories

代数表示论是近三十多年来代数学的一个新的重要分支.目前,代数表示论发展的特点之一就是与代数几何的交叉和渗透.其中,沟通代数表示论和代数几何的桥梁是三角范畴(导出范畴)的理论体系.在这一理论体系中,Beilinson,Bernstain和Deligne在上个世纪八十年代初提出的三角范畴的recollement和t-结构起着关键性的作用.本学位论文围绕recollement与t-结构展开研究.全文共分成四章.在第一章,我们对与论文有关的研究背景起源及发展动态作简要介绍,并阐述本文的主要工作与已有成果的关系.在第二章,我们考虑在已知三个三角范畴和四个正合函子的情况下,构造新的recollement....The theory of representations of algebras is one of the mostimportant branches of algebra during the last thirty years.Recently, one of the developement characters of the theory ofrepresentations of algebras is the intersection and penetration withthe algebraic geometry. And, the bridge establishing the relationbetween the theory of representations of algebras and the algebraicgeometry is the the...学位：理学硕士院系专业：数学科学学院数学与应用数学系_基础数学学号：20042300

三角范畴的有界t2结构与遗传Abel 范畴

研究三角范畴有界t2结构的心. 证明了对于给定的三角范畴D 的有界t2结构( D≤0 , D≥0 ) ,如果对于D 中任意的一个不可分解对象X ,满足X ∈D≤0 ,或者X ∈D≥1 ,则此t2结构的心是遗传的. 进一步地,得到了由遗传Abel 范畴A 的可裂挠对( T , F) 导出的Db ( A) 上有界t2结构的心也是遗传的Abel 范畴.国家自然科学基金(10671161

Comparison of gene frequencies of 15 STR loci between patients with primary gastric adencarcinomas and the unrelated locals from Xiamen

目的比较15个短串联重复序列(STR)基因座基因频率在原发性胃腺癌患者和厦门地区正常人群中的分布,推测与胃腺癌相关的基因。方法123份血样采自本地区无癌家族史的健康人群,39份血样采自本地区胃腺癌患者。用聚合酶链反应(PCR)复合扩增结合四色荧光检测方法对血样DNA进行基因型分析,调查本地区健康人群和胃腺癌患者人群的基因频率分布,并根据两者的该15个基因座等位基因频率分布的差异性,推测易感连锁和抗性连锁的等位基因。结果厦门地区胃腺癌患者的TH01、vWA和FAG基因座的等位基因的分布与该地区健康人群比较差异有统计学意义(P<0·01)。在个别等位基因比较中,胃腺癌人群TH01-7的基因频率为0·0385,健康人群TH01-7的基因频率为0·2642,两者差异有统计学意义(P<0·01),相对危险度(RR)=0·1115;胃腺癌人群vWA-15基因频率0·0513,健康人群vWA-15的基因频率0·2927,两者差异有统计学意义(P<0·01),RR=0·1307;胃腺癌人群FAG-18的基因频率为0·1026,健康人群FAG-18的基因频率为0·0163,两者差异有统计学意义(P<0·01),RR=6·8998。结论TH01-7与胃腺癌相关联,其附近可能存在胃腺癌抗性基因;vWA-15附近有可能存在与胃腺癌相关的抗性基因;FAG-18与胃腺癌相关联,其附近可能存在胃腺癌易感基因。Objective To compare the gene frequencies of 15 STR loci between patients with primary gastric adencarcinomas and the unrelated locals from Xiamen in order to search for the genes correlated to the gastric adencarcinomas.Methods The control group consisted of 123 unrelated locals and the testing group was composed of 39 gastric adencarcinomas suffers. All genotypes of the sample DNA were analyzed by gene scan technology and multiplex PCR method with 4-colored fluorescence-labeled primers. All the polymorphic alleles of these 15 STR loci in unrelated healthy locals and patients with primary gastric adencarcinomas had been investigated. The sensitive or resistant genetic factors were inferred according to the statistical difference with distribution of allele frequencies.Results It showed that there were statistic differences (P<0.01)between controls and testing groups in allele frequencies of the three loci: TH01, vWA and FAG. The further exploration of the separated locus revealed that the gene frequency of TH01-7 in the gastric adencarcinomas suffers was 0.0385,but 0.2642 in the control group[P<0.01 and relative risk(RR)=0.1115];the gene frequency of vWA-15 in the gastric adencarcinomas suffers was 0.0513,but 0.2927 in the control group(P<0.01 and RR=0.1307);the gene frequency of FAG-18 in the gastric adencarcinomas suffers was 0.1026,but 0.0163 in the control group(P<0.01 and RR= 6.8998). Conclusions It is very possible that TH01 alleles may be associated with gastric adencarcinomas and it is possible that there is a resistant gene to gastric adencarcinomas near the region of TH01-7 locus; there is a resistant gene of gastric adencarcinomas near the region of vWA-15 locus; FAG alleles may be associated with gastric adencarcinomas and perhaps there is a sensitive gene of gastric adencarcinomas near FAG-18 locus

The Bounded t-Structure of Triangulated Categories and Hereditary Abelian Categories

研究三角范畴有界t-结构的心.证明了对于给定的三角范畴D的有界t-结构(D≤0,D≥0),如果对于D中任意的一个不可分解对象X,满足X∈D≤0,或者X∈D≥1,则此t-结构的心是遗传的.进一步地,得到了由遗传Abel范畴A的可裂挠对(T,F)导出的Db(A)上有界t-结构的心也是遗传的Abel范畴.The t-structure of triangulated categories is the promotion of the torsion theory of abelian categories on the triangulated categories,which plays an important role in the study of the algebraic geometry.The heart of the bounded t-structure of triangulated categories is studied in this paper.It is proved that any given bounded t-stucture(D≤0,D≥0) on D satisfies that X∈D≤0,or X∈D≥1,for any indecomposable object X in D.Then the heart of the certain t-structure is hereditary.Moreover,if(T,F) is the splited torsion theory of the hereditary abelian category A,then the heart of the bounded t-structure on the bounded derived category Db(A) deduced by(T,F) is also hereditary abelian category.国家自然科学基金(10671161)资

Synthesis of α-Al_2O_3 Nanopowder

[中文文摘]以AlCl_3·6H_2O为原料,用溶胶—凝胶法制备出Al(OH))3凝胶,反复多次冷冻离心脱水,1180℃煅烧得到纳米级α-Al_2O_3,用x射线粉末衍射(XRD)、透射电镜(TEM)、比表面测定(BET)对产品进行表征,证明产品直径为93nm,并讨论了其原理。[英文文摘]α-Al_2O_3 nanopowder was synthesized by baking the colloid of A1(OH)_3 at 1180℃ after it dehydrated by means of multi-freeze and centrifugal. Using A1_2O_3·6H_2O as raw materials, colloid of Al (OH)_3 was prepared by colloidal chemistry method. The structure and characteristic of the powder were studied by means of XRD, BET and TEM, it was revealed that the average size of α-Al_2O_3 is about 90nm. The formation mechanism of colloid was discussed

Ultra-high energy absorption high-entropy alloy syntactic foam

Metal matrix syntactic foams (MMSFs) are a class of fascinating particulate composites consisting of metal matrix and hollow spheres, which are promising in the light-weight structural and energy absorbing applications. However, the energy absorption capacity of most MMSFs is suffocated inevitably by relatively low strength of traditional metal matrix alloys, such as widely used aluminum and magnesium alloys. Here, we developed a novel MMSF with CoCrFeMnNi high entropy alloy matrix and alumina cenosphere fillers by pressure infiltration, which exhibits an ultra-high energy absorption capacity of 242.8 +/- 20.6 MJ m(-3), among the highest reported values of MMSFs. We show that this exceptional energy absorption capacity stems from excellent combination of high strength of alumina cenospheres and super-large ductility and fracture toughness of CoCrFeMnNi high entropy alloy. These results shed new light into design of advanced light-weight and energy absorbing materials