极小子群的中心化子与群的p-可解性

得到G为p-可解的一些充分条件.设p是一个固定的奇素因子,如果对G的每个p阶子群X,或X(?)G,或|G:C_G(X)|为素数的方幂.则G是p-可解.从而推广了李世荣的一个定理.     

有限群的弱m-正规子群

定义了有限群G的弱m-正规子群,并在此定义下,赋予有限群的子群的诸多性质,得出(1)若G的Sylow-子群在G中弱m-正规,且至少有一个Sylow-子群在G的极大子群M中正规,则M为可解群.(2)若有限群G的Sylow-子群都是弱m-正规的,且在G的极大子群M中没有正规的Sylow-子群,则M是非可解的.(3)设有限群G的Sylow-子群都是弱m-正规的,G的极大子群M可解的充分必要条件是至少有一个Sylow-子群在M中正规.(4)若G的Sylow-子群都在G中弱m-正规,且至少有一个Sylow-子群在G的极大子群M中正规,M至少有3个不同的素因子,则G可解.(5)设M为G的任一极大子群,且M为可解群.若M的每个Sylow-子群非循环且它们的极大子群都在G中弱m-正规,则G可解.     

完全多部图的拉普拉斯特征多项式

研究拉普拉斯整图的存在性问题.用A(G)表示有n个顶点的简单图G的邻接矩阵,D(G)表示图G的顶点度对角矩阵.图G的拉普拉斯矩阵为L(G)=D(G)-A(G).通过研究完全多部图Kp1,p2,…,pr的拉普拉斯特征多项式,得到了所有的完全多部图Kp1,p2.…pr都是拉普拉斯整图.     

有限群p-可解的几个充分条件

子群的中心化子对群的结构有很强的控制作用.对有限群G的极小子群的中心化子赋予较弱的条件,得到G的p-可解的充分条件.在一定程度推广了李世荣的结果.     

一类拟正则半群的性质和特征

定义了一类拟正则半群,即拟右半群.利用拟正则半群和左中心幂等元的性质,证明了S为拟右半群时,(1)S为拟完全正则半群;(2)RegS为完全正则半群;(3)R*为S上的最小半格同余;(4)RegS上的每个R-类Tα为右群;(5)TαGα×Eα,其中Gα为群,Eα为右零半群.在此基础上得到了3个等价命题:若S为具有左中心幂等元半群,则(1)S为拟右半群;(2)S为拟完全正则的,RegS为S的理想;(3)S为右群强半格的诣零理想扩张.     

双孢蘑菇SCAR标记的建立及在菌株群鉴定中的应用

根据15条具有菌株群特异性的SRAP、ISSR、RAPD扩增产物DNA条带测序结果,设计64对SCAR引物,其中6对引物能成功扩增出目的条带,即有6条特异片段(A、C、E、G、H、J)被成功转化为SCAR标记.通过这6个SCAR标记的不同组合,将40个双孢蘑菇菌株分为9个类群和6个类群,与基于SRAP、ISSR、RAPD资料的聚类分析结果的组间距离值取13和16时的分类结果完全吻合.对A片段的SCAR-PCR检测结果是:可从40个双孢蘑菇菌株中鉴别出双孢蘑菇333号菌株(编号01).     

两类半群的整体决定性

证明两类半群G0和G’都是整体决定的．设G是群,P是G的单位元．记GO—GU{0}为由G添加一个零元0所得的半群,即G0是0一群．记G’=GU（1）为由G另外添加了一个幺元1所得的半群,注意1≠e,且1是半群G’的幺元．设Go为由所有G0所构成的半群类和G1为由所有G’所构成的半群类．     

偶数顶点不含四圈图的无符号拉普拉斯谱半径

G是一个简单图,矩阵Q（G）=D（G）＋A（G）记为图G的无符号拉普拉斯谱半径,其中D（G）和A（G）分别为对角元素为图G顶点度的对角阵和图G的邻接矩阵．本文证明了图G是偶数顶点不含四圈的图,G。是G中有最大无符号拉普拉斯谱半径的图,p＆G。的无符号拉普拉斯谱半径,则p3-p2,z-1）p＋1-或＋d∑（d。＋以）反≤0,对于u∈V（G。）．     

关于有限群极大子群的CI-截和Deskins完备的一个注记

设G是有限群，M是G的极大子群．令K／N是G的一个主因子，K≤M而N（2=M，称MnN／K为M的一个CI-截，M的所有CI-截都同构．M在G中的一个完备是G的一个子群C，如果C（z=M，而C的每个G不变真子群都在M中．应用这些概念，本文得到了有关有限群可解性的新结论．     

一类椭圆变分不等式双侧障碍问题解的正则性

设 G是 n维欧几里得空间 En中的有界区域 ,令　 K ={u,u - u0 ∈ W1 ,p(G) ,φ1 (x)≥ u(x)≥φ2 (x) ,x∈ G}其中 u0 对任意的 x∈ G满足φ1 (x)≥ u0 (x)≥φ2 (x)。采用与以往不同的方法 ,研究了椭圆变分不等式　∫G{ (v - u) .A(x,u, u) (v - u) B(x,u, u) }dx≥ 0 , v∈ K在 A,B满足较为广泛的结构条件下 ,得到了其双侧障碍问题解的正则性 ,并推广、改进了 Mu J和 Zimer的主要结果 .     

极小子群的S-正规性对有限群构造的影响

设G为有限群，极小子群在有限群的研究中扮演着一个十分重要的角色．利用极小子群的S-正规性刻划群G的结构，得到一个群p-幂零、幂零的一些充分条件，并推广了一些已知的结果．     

关于Diophantine方程p~(2m)-Dx~2=1

设D是正整数,p是奇素数.运用初等方法讨论了方程p2 m-Dx2=1的正整数解(m,x)的个数,证明了该方程至多有1组正整数解(m,x).     

H型群上的Hardy—Littlewood—Sobolev不等式和Stein-Wiess不等式

研究了H型群上一类带权的HLS不等式,也就是所谓Stein-Wiess不等式,并由此得到了H型群上的HLS不等式．通过建立H型群上一类积-分算子的Lp—p有界性,利用此积分算子与Stein-Wiess不等式的关系,得到所求不等式,从而推广了Heisenberg群上的Stein-Wiess不等式．     

Localization of proteins that are coordinately expressed with Cln2 during the cell cycle

The localization of proteins can give important clues about their function and help sort data from large-scale proteomic screens. Forty-five proteins were tagged with the GFP variant YFP. These proteins were chosen because they are encoded by genes that display strong cell cycle-dependent expression that peaks in G(1). Most of these proteins localize to either the nucleus or to sites of cell growth. We are able to assign new cellular component GO terms to ASF2, TOS4, RTT109, YBR070C, YKR090W, YOL007C, YOL019W and YPR174C. We also have localization data for 21 other proteins. Noteworthy localizations were found for Rfa1p, a member of the DNA replication A complex, and Pri2p and Pol12p, subunits of the alpha-DNA polymerase : primase complex. In addition to its nuclear localization, Rfa1p assembled into cytoplasmic foci adjacent to the nucleus in cells during the G(1)-S phase transition of the cell cycle. Pri2 and Pol12 took on a beaded appearance at the G(1)-S transition and later in the cell cycle were enriched in the nuclear envelope. A new spindle pole body/nuclear envelope component encoded by YPR174 was identified. The cell cycle-dependent abundance of Tos4p mirrored Yox1p and these two proteins were the only proteins that were found exclusively at the G(1)-S phase of the cell cycle. A complete list of localizations, along with images, can be found at our website (http://www.yeastrc.org/cln2/).     

关于数论函数方程σ(x~3)=y~2的一点注记

对于正整数a,设σ(a)是a的所有约数之和.设p是奇素数,r和s是正整数.文中证明了当x=2rps时,若方程σ(x~3)=y~2满足下列条件之一:(ⅰ)2■r,p≡1(mod 6);(ⅱ)2■r,p≡5(mod 6),2|s;(ⅲ)2■rs,p是Fermat数,则σ(x~3)=y~2没有正整数解(x,y).     

Genomic predictions for yield traits in US Holsteins with unknown parent groups

The objective of this study was to assess the reliability and bias of estimated breeding values (EBV) from traditional BLUP with unknown parent groups (UPG), genomic EBV (GEBV) from single-step genomic BLUP (ssGBLUP) with UPG for the pedigree relationship matrix (A) only (SS_UPG), and GEBV from ssGBLUP with UPG for both A and the relationship matrix among genotyped animals (A₂₂; SS_UPG2) using 6 large phenotype-pedigree truncated Holstein data sets. The complete data included 80 million records for milk, fat, and protein yields from 31 million cows recorded since 1980. Phenotype-pedigree truncation scenarios included truncation of phenotypes for cows recorded before 1990 and 2000 combined with truncation of pedigree information after 2 or 3 ancestral generations. A total of 861,525 genotyped bulls with progeny and cows with phenotypic records were used in the analyses. Reliability and bias (inflation/deflation) of GEBV were obtained for 2,710 bulls based on deregressed proofs, and on 381,779 cows born after 2014 based on predictivity (adjusted cow phenotypes). The BLUP reliabilities for young bulls varied from 0.29 to 0.30 across traits and were unaffected by data truncation and number of generations in the pedigree. Reliabilities ranged from 0.54 to 0.69 for SS_UPG and were slightly affected by phenotype-pedigree truncation. Reliabilities ranged from 0.69 to 0.73 for SS_UPG2 and were unaffected by phenotype-pedigree truncation. The regression coefficient of bull deregressed proofs on (G)EBV (i.e., GEBV and EBV) ranged from 0.86 to 0.90 for BLUP, from 0.77 to 0.94 for SS_UPG, and was 1.00 ± 0.03 for SS_UPG2. Cow predictivity ranged from 0.22 to 0.28 for BLUP, 0.48 to 0.51 for SS_UPG, and 0.51 to 0.54 for SS_UPG2. The highest cow predictivities for BLUP were obtained with the most extreme truncation, whereas for SS_UPG2, cow predictivities were also unaffected by phenotype-pedigree truncations. The regression coefficient of cow predictivities on (G)EBV was 1.02 ± 0.02 for SS_UPG2 with the most extreme truncation, which indicated the least biased predictions. Computations with the complete data set took 17 h with BLUP, 58 h with SS_UPG, and 23 h with SS_UPG2. The same computations with the most extreme phenotype-pedigree truncation took 7, 36, and 15 h, respectively. The SS_UPG2 converged in fewer rounds than BLUP, whereas SS_UPG took up to twice as many rounds. Thus, the ssGBLUP with UPG assigned to both A and A₂₂ provided accurate and unbiased evaluations, regardless of phenotype-pedigree truncation scenario. Old phenotypes (before 2000 in this data set) did not affect the reliability of predictions for young selection candidates, especially in SS_UPG2.