环F3+vF3上的循环码与常循环码

本文研究了环F₃+vF₃上的循环码与常循环码.通过环F₃+vF₃与域F₃上的循环码之间关系,证明了环F₃+vF₃上循环码是由一个多项式生成的.最后,用类似的方法,得到了环F₃+vF₃上v-常循环码也是由一个多项式生成的.     

三维稳态磁流体动力学方程的Liouville定理

研究了三维稳态磁流体动力学方程的Liouville定理.首先由能量估计建立了一个Caccioppoli型不等式，再结合Sobolev嵌入得到了Liouville定理成立的3个充分条件，其中一个充分条件表明：若三维稳态磁流体动力学方程的光滑解(u,b)∈L^p,3/2相似文献   

3维Lorentz空间中的类时Willmore曲面

设R³₁ 为3维Lorentz空间，装备有Lorentz内积Q³是R³₁的共形紧致化, 由R³₁加上一个无穷远光锥C_∞构成. Q³拥有一个标准的Lorentz共形度量，并且它的共形变换群同构于Lorentz群O(3,2)/{±1}. 研究Q³中类时曲面的共形不变量和Willmore曲面的对偶定理.设M (?) R³₁是一个类时曲面,n是它的单位 法向量．对任意p ∈ M,定义S1 2(p)={X∈R³₁｜(X-c(p),X-c(p))=H(p)-2}, 其中c(p)=P+H(p)-1n(p)∈ R³₁,H(p)为曲面在p点的中曲率,则S1 2(p)是 R³₁中的一个单叶双曲面,它与曲面M在p点相切,并有相同的中曲率．曲面族 {S1 2(p),p∈M}有两个不同的包络面,一个是曲面M本身,另一个记为(M)(称 为曲面M的导出曲面)．设M是一个Willmore曲面,证明了如果M的导出曲面 (M)是一个点,则M一定共形等价于R³₁中的一个极小曲面;如果M的导出曲面 (M)非退化,则(M)也是一个Willmore曲面,并且(M)=M．     

BaTiO3 /SrTiO3超晶格的激光分子束外延生长与二阶光学非线性研究

使用激光分子束外延 ,在SrTiO₃ ( 1 0 0 )单晶衬底上成功生长了一系列c轴取向的 ,具有原子量级控制精度的BaTiO₃/SrTiO₃超晶格 .利用晶格失配导致的薄膜表面台阶密度的周期性变化 ,讨论了反射式高能电子衍射 (RHEED)强度在BaTiO₃ 层和SrTiO₃ 层中的周期性调制 .系统研究了二阶非线性光学极化率同超晶格结构的关系 .实验测量和理论拟合结果表明 ,BaTiO₃ /SrTiO₃ 超晶格的二阶非线性光学极化率显著增强 ,其最大值比BaTi₃体单晶提高一个数量级以上 .从应力导致的晶格畸变和极化增强出发 ,讨论了二阶光学非线性增强的物理机制     

正整数的一类三分拆的应用

利用正整数n的一类特殊的3分拆n=n1+n2+n3,n1>n2>n3≥1,且n2+n3>n1的Ferrers图将不定方程4x1+3x2+2x3=n(n≥9)的正整数解与这种分拆联系起来,从而得到了该不定方程的正整数解数公式;同时也给出了正整数n的一类4分拆的计数公式.此外,还给出了周长为n的整边三角形的计数公式的一个简单证明.     

分块矩阵的正定性准则及其应用

本文给出了 3× 3分块矩阵的一个正定性判定准则 ,应用这个准则 ,给出了矩阵方程 (ATXB ,BT×B)=(C ,D)有正定解的充分条件及解的通式     

Navier-Stokes方程初值问题的形式解

给出了R3×R上的Navier_Stokes方程初值问题存在形式解的充要条件 ,同时给出了一个计算实例·     

三次循环域的定义方程及迹型

本文中我们利用迹型作为工具,定出了三次方程x³—ax—b=0定义一个三次循环域的条件。     

几类多圈图的拉普拉斯谱刻画

设图G是一个简单连通图. 如果任何一个与图G同拉普拉斯谱的图都与图G同构,则称图G是由其拉普拉斯谱确定的. 定义了双圈图\theta_{n}(p_1,p_2,\cdots,p_t) 和m 圈图H_n(m\cdot C_3;p_1,p_2,\cdots,p_t). 证明了双圈图\theta_{n}(p)和\theta_{n}(p,q),三圈图H_n(3\cdot C_3;p)和H_n(3\cdot C_3;p,q)分别是由它们的拉普拉斯谱确定的.     

基于Chebyshev多项式零点的Lagrange插值多项式逼近的注记

本文通过一个例子说明了文献[3]中定理6.9的不完善之处,并建立了:若f∈C^r_[-1,1],则     

ContributionsEdge colorings of graphs embeddable in a surface of low genus

In this paper, by using the Discharging Method, we show that any graph with maximum degree Δ 8 that is embeddable in a surface Σ of characteristic χ(Σ) 0 is class one and any graph with maximum degree Δ 9 that is embeddable in a surface Σ of characteristic χ(Σ) = − 1 is class one. For surfaces of characteristic 0 or −1, these results improve earlier results of Mel'nikov.     

On some continuity and differentiability properties of paths of Gaussian processes

The following path properties of real separable Gaussian processes ξ with parameter set an arbitrary interval are established. At every fixed point the paths of ξ are continuous, or differentiable, with probability zero or one. If ξ is measurable, then with probability one its paths have essentially the same points of continuity and differentiability. If ξ is measurable and not mean square continuous or differentiable at every point, then with probability one its paths are almost nowhere continuous or differentiable, respectively. If ξ harmonizable or if it is mean square continuous with stationary increments, then its paths are absolutely continuous with probability one if and only if ξ is mean square differentiable; also mean square differentiability of ξ implies path differentiability with probability one at every fixed point. If ξ is mean square differentiable and stationary, then on every interval with probability one its paths are either differentiable everywhere or nondifferentiable on countable dense subsets. Also a class of harmonizable processes is determined for which of the following are true: (i) with probability one paths are either continuous or unbounded on every interval, and (ii) mean square differentiability implies that with probability one on every interval paths are either differentiable everywhere or nondifferentiable on countable dense subsets.     

A class of infinitely divisible variance functions with an application to the polynomial case

Let be a natural exponential family on ??? with variance function (V, Ω). Here, Ω is the mean domain of and V is its variance expressed in terms of the mean μ ε Ω. In this note we prove the following result. Consider an open interval Ω = (0, b), 0 < b ∞, and a positive real analytic function V on Ω. If V² is absolutely monotone on [0, b) and V has the form μt(μ), where 1 and t is real analytic in a neighborhood of zero, then there exits an infinitely divisible natural exponential family with variance function (V, Ω). We illustrate this result with several examples of general nature.     

肺在酸碱平衡紊乱调节中的数学模型建立

将血浆中[HCO3-]作为自变量、△PaCO2/△[HCO3-]作为因变量,对酸碱平衡紊乱中肺的缓冲作用进行了量化处理并初步建立了数学模型.利用两者间的函数关系,看到:代谢性酸中毒时,随着血浆中[HCO3-]值越来越小,△PaCO2/△[HCO3-]的变化率也越来越小;代谢性碱中毒时,随着血浆中[HCO3-]值越来越大,△PaCO2/△[HCO3-]的变化率越来越小.这一结果完全符合生物学规律.提示这一数学模型对研究酸碱平衡紊乱时,肺代偿调节机制、代偿强度等情况有一定的意义.     

恰有k条非基本边的极小3连通图

设G是简单3连通图．G\e(删除边e)和G/e(收缩边e)都不是简单3连通图,则e称为G的基本边．对于3连通图中的非基本边．Tutte证明了：唯一没有非基本边的简单3连通图是轮．Oxley和Wu确定了至多有3条非基本边的所有极小3连通图以及恰有4条非基本的极小3连通图．Reid与Wu确定了至多有5条非基本边的极小3连通图．在本文中,我们在极小3连通图中定义了三种运算,然后通过轮利用这些运算的逆运算给出恰有k(k■2)条非基本边的极小3连通图的一种构造方法．     

连通的三重Kn-残差图

Erds P,Harary F和Klawe M研究了Kn-残差图,并对连通的m-Kn-残差图提出了一些结论和猜想．利用容斥原理以及集合的运算性质等方法,研究了连通的3-Kn-残差图,得到当顶点最小度为n时,3-Kn-残差图最小阶的计算公式以及相应的唯一极图．当n=2时,得到最小阶为ll以及相应的极图;当n=3时,得到最小阶为20并找到两个不同构的极图,不满足Erdos等提出的结论;当n=4时,得到最小阶为22及相应的极图;当n=8时,可以找到两个不同构的3-Kn-残差图,不满足Erdos等提出的结论;最后证明了当n=9,10时,最小阶分别为48和52以及相应的唯一极图,验证了Erdos等在文献（Residually-complete graphs[J]．Annals of Discrete Mathematics,1980,6：117．123）中提出的结论．     

Edge colorings of graphs embeddable in a surface of low genus

In this paper, by using the Discharging Method, we show that any graph with maximum degree Δ 8 that is embeddable in a surface Σ of characteristic χ(Σ) 0 is class one and any graph with maximum degree Δ 9 that is embeddable in a surface Σ of characteristic χ(Σ) = − 1 is class one. For surfaces of characteristic 0 or −1, these results improve earlier results of Mel'nikov.     

不含三角形的图的λ3-最优性的充分条件

设G=(V,E)是一个连通图,边集S(?)E是一个3-限制性边割,如果G-S是不连通的并且G-S的每个分支至少有三个点.图G的3-限制性边连通度λ_3(G)是G中最小的一个3-限制性边割的基数.图G是λ_3(G)连通的,如果3-限制性边割存在.G是λ_3-最优的,如果λ_3(G)=ξ_3(G),其中ξ_3(G)=min{|[U,(?)]|:U(?)V,|U|=3 and G[U]是连通的).G[U]表示V的子集U的导出子图,(?)=V\U表示U的补.[U,(?)]是一条边的一个端点在U中另一个端点在(?)中的边的集合.本文给出了不含三角形的图是λ_3-最优的一些充分条件.     

3-D network model and its parameter calibration

A material model, whose framework is parallel spring-bundles oriented in 3-D space, is proposed. Based on a discussion of the discrete schemes and optimum discretization of the solid angles, a 3-D network cell consisted of one-dimensional components is developed with its geometrical and physical parameters calibrated. It is proved that the 3-D network model is able to exactly simulate materials with arbitrary Poisson ratio from 0 to 1/2, breaking through the limit that the previous models in the literature are only suitable for materials with Poisson ratio from 0 to 1/3. A simplified model is also proposed to realize high computation accuracy within low computation cost. Examples demonstrate that the 3-D network model has particular superiority in the simulation of short-fiber reinforced composites.     

The 2-(9, 4, 3) and 3-(10, 5, 3) designs

It is shown that there is a unique 2-(9, 4, 3) design with three different extensions to a 3-(10, 5, 3) design. Two of the extensions are isomorphic and have a further extension to the unique 4-(11, 6, 3) design. There is another 2-(9, 4, 3) design with just two extensions to a 3-design. There are 11 2-(9, 4, 3) designs in all, as announced by van Lint, et al. and Stanton et al. There are seven 3-(10, 5, 3) designs of which one is triply transitive, another transitive, and the rest are not transitive but are self-complementary. The transitive 3-designs each have one restriction to a 2-design. Of the non-transitive 3-designs 4 each have two restrictions and the fifth has three.