一类夹心变换半群的正则元

设T_X是非空集合X上全变换半群,E是X上等价关系,则T_?(X)={f∈T_X:?_x,y∈X,(f(x),f(y))∈E?(x,y)∈E}是T_X的反射等价关系的子半群.取定θ∈T_?(X),在T_?(X)上定义新的运算°为f°g=fθg,其中fθg表示一般意义上映射f、θ、g的复合.关于这个运算°,T_?(X)成为夹心变换半群T_?(X;θ).本文刻画了它的正则元,给出了T_?(X;θ)是正则半群的充要条件.     

保序自映射半群的同余

设X为偏序集(T_0A-空间),S(X)表示X上保序(连续)自映射作成的半群.本文通过讨论T_0A-空间上的S-关系来研究半群S(X)上的同余格,得到一些有趣的结果.     

TE(X)的由幂等元生成的子半群

设X为有限集合,()X为X上的全变换半群,设E为X上任一非平凡等价关系,变换半群TE(X)定义为TE(X)={f∈()X:()(a,b)∈E,(f(a),f(b))∈E}.讨论了半群TE(X)的由幂等元生成的子半群T2,以及由亏值为1的幂等元作为生成元时,T2的极小生成元集,并且求出了这个极小生成集的元素个数.     

富足变换半群

讨论了集X上变换之间的L*关系.证明了X上变换半群S是abundant(富足)半群,任一个半群均可以嵌入一abundant半群中.同时也讨论了几种特殊的abundant子半群等.     

集合I到集合Λ上的二元关系半群ρθ(I×Λ)的生成集和Green-关系

设集合I,Λ是任意的非空集合. 当θ=×'×I(∪)Λ×I时, 本文获得了半群ρθ(I×Λ)的非可解元和不可约生成集, 并且给出了半群ρθ(I×Λ)的Green-关系, 最后讨论了半群ρθ(I×Λ)的一些特殊计数.     

OT(X,Y;θ)的一类特殊子半群Me及其极大（小）元

由于保序夹心半群OT(X,Y;θ)的幂等元集E(OT(X,Y;θ))不构成子半群，对E(OT(X,Y;θ))加某些限制条件后，得到幂等元集E(OT(X,Y;θ))的真子集Me，证明了Me是半群OT(X,Y;θ)的子半群，讨论了Me在自然偏序下的一些结论，此外，还描述了子半群Me的极大(极小)元与覆盖元。
     

半群PO(X,Y,θ)的格林关系及正则元

设X和Y是有限非空集合,PO(X,Y)表示从X到Y的所有部分保序映射构成的集合.取定θ∈PO(Y,X),在PO(X,Y)上定义运算,如:αβ=αθβ,则(PO(X,Y),)是一个半群,称为有限部分保序夹心半群,记为PO(X,Y,θ).半群PO(X,Y,θ)的格林关系及其正则元被刻划了.     

O(X)的幂等元中心化子的格林关系

设ρ是有限非空集X上的一个凸等价关系,R是商集X/ρ的一个横截集.对X上的保序全变换半群O(X)的子半群O(X,ρ,R)={α∈O(X)|RαR且(x,y)∈ρ(xα,yα)∈ρ},在此证明了O(X,ρ,R)是O(X)的以幂等元为中心的子半群,并且刻划出它的格林关系.     

半群S(X.θ)中的正则元(Ⅰ)

半群S中的元素a是正则元，如果存在b∈S，使aba=a．正则元是半群中重要且特殊的元素，对确定半群的结构起着关键作用．对于任意的非空集合X，策划了半群T(X．θ)上的正则元，明确了正则元本质．其结论为刻划半群S(X．θ)的正则元提供了理论基础．     

一类有限变换半群的Green关系

在[5]中作者考察过一类变换半群，即TE（X）{f∈Fx,任意（a,b)∈E，（f(a),f(b))∈E}，这里E是集合X上任一等价关系，当X带上以所有E类为基的拓扑时，TE(X)恰是拓扑空间X上的连续自映半群。本文讨论了半群TE（X）上的Green关系，并且当X为有限集，E是单等价关系时，给出了全部Green关系的刻划。     

直径图为11圈的7距离集研究

如果平面点集X中的任意两点确定的互异距离数为k,则称X为k距离集。用d(x,y)表示平面上互异两点x,y之间的距离,记X中的最大距离为直径D=D(X)。直径图DG(XD)是由X中所有直径构成的图,XD表示其顶点集。讨论了当X是一个7距离集时,直径图DG(XD)的构型。利用DG(XD)中最多包含一个圈,且只能为奇圈的特性,以及直径所具有的特殊性,证得当直径图为11圈时,其顶点集XD恰好为某正十一边形的顶点集。     

An adherence semigroup

By a dynamical system we mean a pair of (X,T), whereX is compact Hausdorff space. In this paper we define an adherence semigroupA(X,T--X ^x, which is the set of all pointwise limit of subnets of(T ⁿ)n∈N. We will prove some commonness between adherence semigroup and Ellis semigroup. Foundation item: Supported by the Special Funds for Major State Basic Research Projects Biography: Niu Min(1979-), female, Ph. D candidate, research interest: fractal geometry.     

A local asymptotic behavior for ruin probability in the renewal risk model

Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.     

Composition operators with linear fractional symbols on vector-valued Bergman spaces

0　IntroductionLetDdenotetheopenunitdiskinthecomplexplaneC , DitsboundaryanddAtheLebesguemeasureonD ,normal izedsothatA(D) =1.ForaBanachspace (X ,‖·‖X) ,wewriteH(D ,X)fortheclassofallX valuedanalyticfunctionsonD .Let1≤ p<∞ ,theX valuedBergmanspaceBp(X)istheclassofallf∈H(D ,X) forwhich‖f‖Bp(X) =∫D‖f(z)‖pXdA(z) 1 /p <∞ (1)IfX =C,thenwewriteBp =Bp(C) fortheclassicalBergmanspaces.Letφ∶D→Dbeananalyticself mapofD .Thenthee quation Cφf=f φdefinesacompositionoperator…     

On the limiting behavior of weighted partial sums for<Emphasis Type="Italic">B</Emphasis> valued martingale difference sequences

Let {X_n, n≥1} be a martingale difference sequence and {a _nk , 1⩽k⩽n,n⩾1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ _k=1 ⁿ a _nk X _k is investigated and some new results are obtained. Foundation item: Supported by the National Natural Sciene Foundation of China (No. 10071058 and No. 10071019) Biography: Gan Shi-xin (1939-), male, Prof lessor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.     

A Large Deviation Principle for the Risk Process with Varying Premium

Let u ∈ R ,for any ω 〉 0, the processes X^ε = {X^ε（t）; 0 ≤ t≤ 1} are governed by the following random evolution equations dX^ε（t）= b（X^ε（t）,v（t））dt-εdSt/ε, where S={St; 0≤t≤1} is a compound Poisson process, the process v={v（t）; 0≤t≤1} is independent of S and takes values in R^m. We derive the large deviation principle for{（X^ε,v（.））; ε〉0} when ε↓0 by approximation method and contraction principle, which will be meaningful for us to find out the path property for the risk process of this type.     

The nonwandering set of some Hénon map

For the Hénon mapT _{a, b}(x, y) = (1 −ax ² +y, bx), Benedicks and Carleson proved that for (a,b) near (2, 0) andb > 0, there exists a setE with positive Lebesgue measure, whose corresponding mapT _{a, b} possesses a strange attractor. Viana conjectured that if (a, b) ∈E, then the nonwandering set of the mapT _a, b Ω(T_{a, b}) = ∧_{a, b},Uq _a, b, where ∧_{a, b}, is the strange attractor, q_a,b is a hyperbolic fixed point in the third quadrant. It is proved that this conjecture holds true for a positive measure set E₁ ⊂E.     

The comparative investigation on redox property and second-order nonlinear response of Keggin-type α-[PM12O39NPh]3− (M = W and Mo) and Mo6NPh

Keggin-type phenylimido-polyoxometalates α-[PM₁₂O₃₉NPh]³⁻ (M = W and Mo) have been systematically investigated on the electronic structures, redox as well as nonlinear optical (NLO) properties by density functional theory (DFT). The strong M≡N bond confirmed by natural bond orbital (NBO) analysis comprises one s bond and two π bonds, the same as Mo≡N in [Mo₆O₁₈NPh]²⁻. Furthermore, phenylimido segment effectively modifies the electronic properties of α-[PM₁₂O₃₉NPh]³⁻. On one hand, when enlarging the inorganic cluster from {Mo₆O₁₈} to {PMo₁₂O₃₉}, the energy gap between HOMO and LUMO in α-[PMo₁₂O₃₉NPh]³⁻ decreased, resulting in enormously anodic shift for the reduction potential, while the excitation energy is less and the total second-order polarizability β ₀ is up to 438-3×10⁻³⁰ esu, which is nearly 10 times larger than that of [Mo₆O₁₈NPh]²⁻. On the other hand, when metal W in α-[PM₁₂O₃₉NPh]³⁻ is substituted by Mo, the interaction between Mo and N is enhanced and the redox ability becomes stronger. The β ₀ value for α-[PMo₁₂O₃₉NPh]³⁻ is more than 5 times higher than that of α-[PW₁₂O₃₉NPh]³⁻. It indicates that changing appropriate metal or enlarging the inorganic cluster will improve the redox properties and second-order nonlinear response. Moreover, the electron transition for three compounds mentioned above occurred mainly from organoimido segment (as the electron donor) to polyanion cluster (as the acceptor). As a result, α-[PMo₁₂O₃₉NPh]³⁻ may be a promising candidate for oxidant and nonlinear optical material. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. Supported by National Natural Science Foundation of China (Grant No. 20573016), Training Fund of NENU’s Scientific Innovation Project (Grant No. NENUSTC07017), Science Foundation for Young Teachers of Northeast Normal University (Grant No. 20070304) and Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT)     

恭城沙田柚果实品质与土壤环境化学的研究

在恭城县城选择三不同情况的沙田柚环境（挂果好，当年产３００多个，挂果一般，当年产５０个，从不挂果，树龄已有８年，结果无望）采样，分析土壤，果实，树枝叶的常量元素和微量元素，结果表明，恭城沙田柚全糖含量平均值达１０％以上，可溶性固形物含量达１７％，柠檬酸０．３１％，糖酸比和固酸比多在３０以上。品质优的沙田柚生长的土壤Ｋ２Ｏ，Ｐ２Ｏ５含量分别为１．８００３％～２．２１２５％和０．１５２４％～０．１８１     

三聚磷酸二氢铝二水物的合成和表征

用磷酸和氢氧化铝为原料制备三聚磷酸二氢铝二水物。用X-衍射、红外光谱、化学分析、DTA-TG结合X-ray分析,证明产品的化学结构式为AlH2P3O10*2H2O。其晶体结构属正交晶系,空间群为PZ1/bZ1/aZ/m,D92h,晶胞参数a=15.919×10-8 cm,b=8.884×10-8cm,c=9.936×10-8 cm,单位晶胞体积V=1 405×10-8 cm3,Z=6。防绣性能测试表明其防锈能力与红丹颜料相当。毒理学试验表明该颜料半致死量LD50=18.0 g/kg(小白鼠),属实际无毒级,符合食品容器及儿童玩具涂装的要求。