关于群的方次数的若干结果

群的方次数是群论中的一个基本概念,它反映了群的元素阶的性质特征.通过对群的方次数的初步探讨,得到结论:若群G的元素阶均有限,且sup|a|a∈G=sup|a|a∈G(G),则群G的方次数expG=sue|a|a∈C(G).并进一步用方次数刻划了群的结构.     

循环群与不可交换群的阶初探

初学群论往往需要通过许多具体例子来理解群的概念.周知,在群的定义中,并不要求运算是交换的,即不要求ab=ba普遍成立.如果在群G中ab=ba普遍成立,那么G称为交换群或阿贝耳(Abel)群.有限群G所含元素的个数称群G的阶,记为|G|.本文探讨循环群的阶及不可交换群,最低阶数为6的具体例子.     

约化群对约化型齐性空间的真作用

研究了约化群对约化型齐性空间G/H作用的真不连续性,通过实例G=SL(n,R),H=SL(m,R),L=SL(2,R)验证了L对齐性空间G/H作用是真不连续的.     

最高阶元素个数对有限群结构的影响

我们讨论了群的最高阶元素个数为4p2的有限群G,得到：设M（G）I=4p2,n=2p或者n=2P2,其中p是素数,则G是可解群．     

拓扑指数mG与卤化物的晶格能和标准生成焓的关系

在Randic分子价连接性拓扑指数的基础上,将Randic的δi修改为原子结构特征参数δi'(δi'=Zi2×(Xpi)0.5/ni其中Zi,Xpi,ni分别为原子i的氧化数,Pauling电负性和所处的周期数),构建了无机分子的连接性指数mG(mG=∑(δi'×δj'×δk'×…)0.5),其具有优异的结构选择性,用其0,1阶指数0G、1G及(0G)2与碱金属卤化物的晶格能、过渡元素卤化物的标准生成焓相关联,拟合得到两个回归方程(U=403.86+899.5081G,△fHm⊙=33.571+139.644(0G)2-400.7351G),相关系数分别为0.9954、0.9680,预测取得了较好的结果.     

｜M（G）｜=8p，n=2p的有限群

本文讨论了最高阶元素个数为｜M（G）｜=8p,最高阶为k的循环子群个数n=2p的有限群G,得到了结论：设G是最高阶元素个数为8p,且n=2p的有限群,其中p素数,则G是可解群,除非G≌A5。     

P_n×P_m图的邻点可区别全染色和邻点强可区别全染色

对Pn×Pm图的邻点可区别全染色和邻点强可区别全染色问题进行了探讨,给出了染色数公式Xat(Pn×Pm)={4 n=m=2 5 n=2 m≥3,ast(pn×pm)=6 n≥3 n≥3{5 n=m=25 n=2 m≥3 6 n≥3 m≥3     

有限群的s-正规子群与可解性

群G的一个子群H称为在G中s-正规，如果存在G的一个次正规子群尼使得G=HK且H∩K≤HSG，其中SG=〈Hi／Hi在G中次正规且Hi包含于H〉．利用子群的s-正规性对有限群结构的影响，给出了有限群可解的若干充分条件．     

共轭置换子群对有限群可解性的影响

群G的子群H称为G的共轭置换子群,若H^gH=HH^g,对任意g∈G都成立.利用共轭置换子群的定义和性质给出了有限群成为可解群的几个充分条件.     

关于交换群的充分条件

利用指数及群同态的性质给出交换群的几个充分条件。证明了若G的指数为n ,则G为交换群当且仅当n=2；若ψ（x)=x^n为群G上单同态映射，则当n=3,2,-1时或φ（x)=x^n-1，是G上单射或满映射时G为交换群。     

四阶非线性方程两点边值问题

本文应用复合度的方法在f(x,y,z,u)无界的条件下证明了一般的四阶方程y=f(x,y,y′,y″) (*)在边界条件y(0)=A_1,y(1)=A_2,y″(0)=B_1,y″=B(_2或y(0))=A_1,y(1)=A_2,y″(0)=B_1,y(1)=B_2下解的存在性。     

一类变系数线性系统的稳定性

<正> 变系数动力系统运动稳定性是现代化生产中急待解决的一个课题,我国有不少学者正从事于这一课题的研究〔1—4〕,美国Lefschetz动力研究中心仍然把变系数线性系统的运动稳定性作为重要的研究项目之一。文〔3〕利用分解理论研究了缓变系统与子系统呈对称型的大系统的稳定性。本文放宽了对子系统为对称及缓变的要求,沿用分解理论研究了一类仿拟反对称系统平凡解的稳定性。     

乘积空间上的分数次积分算子

本文把乘积空间上的分数次积分算子的核推广为非乘积型的核,考虑卷积算子的到有界性,同时考虑了T的到的有界性。     

Group outcome: The relationship between group learning outcome,attributional style,academic achievement,and self-concept

Six classes of grade seven students (N = 181) participated in field research which explored the consequences of group outcome (successful, unsuccessful) for individuals learning mathematics cooperatively using Student Teams-Achievement Divisions. In addition, we explored the effects of within-class prior mathematics achievement (low, low-medium, high-medium, high) as well as attributional style (learned-helpless, mastery-oriented). The dependent variables were mathematics achievement, causal attributions, and self-concept. There were two interactions: Group Outcome × Attributional Style on achievement, and Within-Class Prior Mathematics Achievement × Group Outcome on achievement and self-concept. Learned-helpless students from unsuccessful groups learned significantly less than learned-helpless students from successful groups. Low prior achievement students from unsuccessful groups learned significantly less than low prior achievers from successful groups. In contrast, there was no significant relationship between group outcome and individual post-test achievement for mastery-oriented students or for students high in prior within-class achievement.     

Integrating mindfulness and connection practices into preservice teacher education improves classroom practices

Teachers vary in their ability to enact effective teaching practices. We randomly assigned 88 early education preservice teachers to standard teacher education or teacher education plus a 9-week mindfulness-based intervention. Using the Classroom Assessment Scoring System (CLASS) as our primary outcome, we assessed effective teaching practices at baseline and at a 6-month follow-up that occurred during full-time student teaching. Mindfulness, negative affect, and well-being were assessed at baseline, post-test, and follow-up. At follow-up, we observed significant GROUP × time interactions on all major CLASS domains: Instructional supports, Emotional supports, and Classroom organization favoring the intervention group (Cohen's d's 0.53–0.65). Daily mindfulness practice was significantly associated with intervention group improvements on Instructional supports (r = .39) and Classroom organization (r = .38). No group differences were observed on negative affect or well-being. Implications for teacher education are discussed.     

一类非退化广义Q—全纯矩阵值函数

本文研究一类非退化m×m阶复值函数矩阵W(Z),它满足矩阵形式的平面一阶偏微分方程组这里A.B.Q都是m×m阶复值函数矩阵,W(z)是未知的,在Q(z)可自交换、Holder连续且特征值的模不等于1的条件下,W(z)称为广义Q-全纯矩阵值函数。本文建立了非退化广义Q-纯矩阵值函数的若干基本定理。     

Short-term memory for order but not for item information is impaired in developmental dyslexia

Recent findings suggest that people with dyslexia experience difficulties with the learning of serial order information during the transition from short- to long-term memory (Szmalec et al. Journal of Experimental Psychology: Learning, Memory, & Cognition 37(5): 1270-1279, 2011). At the same time, models of short-term memory increasingly incorporate a distinction of order and item processing (Majerus et al. Cognition 107: 395-419, 2008). The current study is aimed to investigate whether serial order processing deficiencies in dyslexia can be traced back to a selective impairment of short-term memory for serial order and whether this impairment also affects processing beyond the verbal domain. A sample of 26 adults with dyslexia and a group of age and IQ-matched controls participated in a 2?×?2?×?2 experiment in which we assessed short-term recognition performance for order and item information, using both verbal and nonverbal material. Our findings indicate that, irrespective of the type of material, participants with dyslexia recalled the individual items with the same accuracy as the matched control group, whereas the ability to recognize the serial order in which those items were presented appeared to be affected in the dyslexia group. We conclude that dyslexia is characterized by a selective impairment of short-term memory for serial order, but not for item information, and discuss the integration of these findings into current theoretical views on dyslexia and its associated dysfunctions.     

分次zip环与SPlit-null扩张(英文)

本文定义并讨论了分次zip环,讨论了交换环的Split—null扩张的zip性,推广了C.Faith的部分结果。     

一类半正定阵的反问题

本文给出了矩阵方程AX=B的反问题在半正定矩阵(未必对称)类中有解的充要条件,并在有解时给出其解的表达式。     

Determination of Trace Molybdenum（VI） by Oscillographic Potentiometric Catalyzing Kinetic Method of Simplex Optimization

1　Introduction　Ahugeamountofliteratureexistsonthestudyofi dentifyingtracemetalionsbymeansofspectropho tometry[1 3] ,fluorimetry[4 6 ] aswellas polarogra phy[7 9] ,whichhaveactiononlocatingtheendpointoftheindicatingreaction .Howeverbothspectropho tometryandfluorimetryareeasytobeinterferedbycolororprecipitation ,whilepolarographyhasanissueofmercurypollution .Thecatalyzingkineticanalysishasthecharacteristicsofhighsensitivityandspeedi ness.Oscillographicpotentiometryisasimpleintu itionisticanal…