Littlewood-Paley g_λ*-函数在弱Hardy空间中的有界性

在弱核条件下证明了Littlewood-Paley g_λ*-函数为(H~1,∞,L~1,∞)型的有界算子,其中H~1,∞和L~1,∞分别为弱H~1空间和弱L~1空间.     

ON THE INITIAL-BOUNDARY VALUE PROBLEM FOR THE SYSTEM OF MULTI-DIMENSIONAL GENERSALIZED BBM EQUATIONS AND KdV EQUATIONS

The Benjamin-Bona-Mahony (BBM) equationu_1+UU_x-u_(xxt)=0and the Korteweg-de Vries (KdV) equationu_1+uu_z+u_(xxx)=0have both been proposed as models for long waves in nonlinear dispersive systems and the Cauchy's problemwas studied for the above equations.1 We consider the periodic boundary value problem for the system of n-dimensional generalized BBMequationswhere be a n-dimensional cube with21 in each direction,and _0(x) is a n-dimensional periodic functional     

完全阿基米德半群上关系H~*(英文)

给出了完全阿基米德半群上关系H~*是同余的若干等价条件.     

Yetter-Drinfeld拟余模范畴上的Hopf拟余模

设H是■上的有限维Hopf余拟群,则它的线性对偶空间H~*是■上的一个Hopf拟群。进一步地,H~*有一个■上的右H-Hopf拟余模结构。     

H~∞最优混合灵敏度问题

本文给出了一种H~∞最优混合灵敏度问题的解,其方法是将混合灵敏度H~∞最优问题转化成已熟悉的“A course in H~∞ control theory”的结果.     

H—Galois代数同构类和Harrison上同调群

<正> 若K是一个具有单位元的可换环,K—双代数(H,μ,η,△,ε)具有对极正[1]时称为Hopf代数[2],△:H→H(?)H表示上乘法或者对角映射,ε:H→K表示上单位或者扩张映射。本文自始至终假定H是一个秩为2的自由—K模。在H中存在一个元素x,使得ε(x)=0,它是kerε的生成元,并且1,x是H的一个基。H~*是k—模H的对偶,Φ是H~*的元素,使得Φ(1)=0,Φ(x)=1,ε和中构成H~*关于K的一个基,对偶于H的基1,x。H~*也是K上的一个Hopf代数,ε是H~*的单位元。在K中存在元素p、q,使得x~2=qx,△x=1(?)x+x(?)1+px(?)x,pq+2=0。     

A Coquasi—Hopf Algebra H^＊ ◇φH

A Coquasi-Hopf Algebra H~* ◇_ΦH&&&&     

扭曲冲积的同调维数

当H是半单的Hopf代数及其对偶H~*是幺模的Hopf代数时,通过构造可分扩张A~*H/A,利用比较法得到了扭曲冲积A~*H的整体维数、弱维数和有限维数小于或等于子代数A的整体维数、弱维数和有限维数.所得结果与著名的有限维数猜想有一定的联系.     

Asymmetry for Convex Body of Revolution

In this paper, we study the Minkowski measure of asymmetry for n-dimensional convex bodies of revolution( n ≥3). We show that among all n-dimensional convex bodies of revolution, the bodies which generated by isosceles triangles are the most asymmetric ones. Also, we study the asymmetry for n-dimensional constant width bodies of revolution.     

具不变向量场的齐次黎曼空間

(四) 空間类型的决定我們回到(二)中所描述的齐次黎曼实間的决定,恢复(一)、(二)中所用的記号,在沒有誤会的情形下,我們也沿用一些(三)中所用的記号,由于情况的复杂,我們分兩节来处理这个問題,在本节中我們討論作用于平面E_(n-q)上的群H的可换旋轉群H~*只含恒等变換的情形及H~*为單参数的情形。     

弱Hopf代数上的β-特征代数

考虑了弱Hopf代数上的β-特征代数.当H是有限维弱Hopf代数时,给出了g∈C_β(H) (C_β(H)是H~* 的β-特征)的一个充要条件,并研究了弱Hopf代数上的β-广义特征代数.     

一类向后权位移的循环向量

设T是权为{W_n}_0~∞的权位移。通常,T酉等价于由形式幂级数构成的函数空间H~2(β)上的乘子z:f→zf.本文证明,如果T是一个内射单侧权位移,适合r_1(T)=r(T)=1,如果f在单位圆盘的某邻域内解析,则要么f是T~*的循环向量,要么f含于T~*的有限维不变子空间.     

三价镨离子的水解聚合作用的研究

用PH法研究了Pr(No_3)_3在浓度为0.1-0.6M、25℃下的水解平衡,加入NaNo_3调节离子强度为2M。以同配体常数法确定水解平衡时的主要产物及其相应的水解平衡常数,所得结果与用作图外推法的结果极为一致。其水解平衡常数为: Pr~(3+)+H_2o ProH+~(2+)+H~+ lg~*β_(11)=-9.03 2Pr~(3+)+2H_2o Pr_2(oH)_2~(4+)+2H~+ lg~*β_(22)=-15.40     

Numerical analysis on intermittent flow in a longitudinal section of Bingham fluid along a slope

The transition process of intermittent flow in a longitudinal section of Bingham fluid from initial distribution to fully developed state was numerically investigated in this paper. The influences of slope θ. dimensionless runoff Q* and viscosity μ0* on the dimensionless surge speed U* were also presented in a wide range of parameters. By one typical example, the intermittent flow possessed wave characteristics and showed a supercritical flow conformation for a fully developed flow. The distributions of gravity and bed drag along the flow path and the velocity distribution of flow field were also analyzed.     

Propositional Vector Logic System and Its Adequacy Thcorem

With the paradigm of holistic thinking and multiple per-spectives,an overall new understanding of logic is ob-tained for reasoning in collective intelligent systems(CIS).Based on the hypothesis of multiple resolutions ofreasoning in CIS,the logical state of a proposition isgeneralized into an n-dimensional vector whose elementis either 1 or 0.In contrast with classical logic with bina-ry truth-values,a propositional vector logic system isconstructed by introducing new connectives,new axi-oms,and new rules.Adequate sets of connectives areprovided.The soundness theorem and the adequacy the-orem for the vector logic system are shown.     

Characteristic Functions over C*-Probability Spaces

Various properties of the characteristic functions of random variables in a non- commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.     

Matrix transformation of digital image and its periodicity

The periodicity of a general matrix modular transformation is discussed, and a simple proof of a sufficient and necessary condition that a matrix transformation has periodicity is given. Using a block matrix method, the higher dimensional transformation and its inverse are studied, and a simple algorithm for calculating their periods is put forward. The security of n-dimensional Amold transformation and its inverse is also discussed. The results show that the two transformations are applicable in scrambling and recovering images.     

Dirichlet Form of Product of Variational Fractals

completed.□　Lemma2 .2　 Suppose H to be a Hilbert spacewith the inner product ( .,.) H and the relativenorm‖·‖H.If{xn}in H weakly converges tox,then there exists a subsequence {xni}satisfyingthatx - 1k ki=1xni H→ 0 ,　 k→∞ .　The proof can be found in Ref.[9].　 Lemma 2 .3　 Suppose W* to be a symmetricform on D[W],and W* [u]≤ W1[u]for all u∈D[W].If {un}∈D[W]in H converges W1- weak-ly to u,then it converges W* - weakly to u.　The proof can be found in Ref.[8].　 Lemma 2 .4…     

A generalized funk’s section theorem for measures

If L is a star body in R~n whose central(n-i)-slices have the same(n-i)-dimensional measure μ_(n-i)(with appropriate density)as the central(n-i)-slices of an origin-symmetric star body K,then the corresponding n-dimensional measures μ_n of K and L satisfy μ_n(K)≤μ_n(L).This extends a generalized Funk’s section theorem for volumes to that for measures.     

间接调节系统的绝对稳定性

1.引言本文讨论间接调节系统这里我们以大写的拉丁字母A,B,…表示实矩阵,以小写的拉丁字母a,b,…,x,y,…表示列向量,以希腊字母σ,ξ,ψ…表示数量。(x,y)表示向量x和y的内积,以A~*和a~*表示矩阵A和向量a的转置若实对称矩阵H=H~*所对应的二次型(Hx,x)是正定的,我们就记它为H>0;若(Hx,x)≥0对任何向量x成立,就记它为H≥0。以表I示单位矩阵。如果对于任何适合条件