ON THE CONCAVE φ-INEQUALITIES FOR NONNEGATIVE SUBMARTINGALES

Let φ1, φ2 be nonnegative nondecreasing functions, and φl be concave. The authors prove the equivalence of the following two conditions:(i) Eφ1 (Mf) ≤ cEφ2(Zo+A∞) for every nonnegative submartingale f = (fn)n≥0 with it's Doob's Decomposition: f = Z + A, where Z is a martingale in L1 and A is a nonnegative incrasing and predictable process.(ii) There exists positive constants c, to such that ft∞φ1(s)/s2 ds ≤ c φ2(t)/t, t ＞ to.When φ1 = φ2 the condition (ii) above is equivalent to the classical condition -Pφ＜1. As a consequence, for a concave function φ, -Pφ＜ 1 if and only if Eφ1 (Mf) ≤ cEφ2 (Z0 + A∞)for every nonnegative submartingale f.     

SOME NEW RESULTS ON MARTINGALE INEQUALITIES AND GEOMETRY IN BANACH SPACES

Here we shall state some new results in Banach-space-valued martingale theory and the geometry of Banach spaces which have been obtained since 1986. The topics covered include investigations on nine parts: (1) A basic theorem, (2) Good λ-inequalities, (3) Φ-inequalities, (4) Local convergence, (5) BMO and bounded-     

Hydrothermal Synthesis and Structure of a Mixed-valence Polyoxotungstate Decorated by Copper(I) Coordination Group, [Cu(en)_2H_2O]_2[{Cu(en)_2}HPW_(12)O_(40)]·2H_2O

1 INTRODUCTION Polyoxometalates (POMs) are early transition metal oxygen clusters and have aroused much inte- rest because of their discrete structures of definite sizes, shapes[1] and potential applications in cata- lysis, medicine, materials science, g…     

小指标B值鞅空间与原子分解

建立了一系列Banach空间值鞅的原子分解定理,并讨论了若干小指标鞅空间之间的相互嵌入关系,结果与Banach空间的凸性和光滑性有密切联系.     

WEIGHTED INEQUALITIES FOR THE GEOMETRIC MAXIMAL OPERATOR ON MARTINGALE SPACES

In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M0^＊, then they give sufficient conditions under which the equality M0=MM0^＊ holds, and characterize the equivalent relations between the weak or strong type weighted inequality and the property of W∞-weight or W∞^＊-weight for the geometrical maximal operator in the case of two-weight condition. What should be mentioned is that the new operator-the geometrical minimal operator is equal to the limitation of the minimal operator sequence, and the results for the minimal operator proved in [12] makes the proof elegant and evident.     

梯形直觉模糊数集成算子及在决策中的应用研究

在直觉模糊集理论基础上,用梯形模糊数表示直觉模糊数的隶属度和非隶属度,进而提出了梯形直觉模糊数;然后定义了梯形直觉模糊数的运算法则,给出了相应的证明,并基于这些法则,给出了梯形直觉模糊加权算数平均算子(TIFWAA)、梯形直觉模糊数的加权二次平均算子(TIFWQA)、梯形直觉模糊数的有序加权二次平均算子(TIFOWQA)、梯形直觉模糊数的混合加权二次平均算子(TIFHQA)并研究了这些算子的性质;建立了不确定语言变量与梯形直觉模糊数的转化关系,并证明了转化的合理性;定义了梯形直觉模糊数的得分函数和精确函数,给出了梯形直觉模糊数大小比较方法;最后提供了一种基于梯形直觉模糊信息的决策方法,并通过实例结果证明了该方法的有效性。     

THE MINIMAL OPERATOR AND WEIGHTED INEQUALITIES FOR MARTINGALES

In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities hold.     

ATOMIC DECOMPOSITION FOR B-VALUED R.V. SEQUENCE SPACES

In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.     

Bergman空间上的复合算子的范数

本文研究了Bergman空间上的复合算子的范数与再生核的关系,证明了紧复合算子C的范数‖C‖=sup{‖C*kw‖:w∈D}的充要条件是(0)=0或是仿射映射,即(z)=sz+t,s,t是满足|s|+|t|<1的常数,其中kw为Bergman空间的规范再生核, C*是C的共轭算子.