Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex Euclidean space

We treat m-dimensional real submanifolds M of complex space forms ̿M when the maximal holomorphic tangent subspace is (m−1)-dimensional. On these manifolds there exists an almost contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX,Y)−h(X,FY) = g(FX,Y)η, η∊ T⊥(M), on the structure F and on the second fundamental form h of these submanifolds. Especially when the ambient space ̿M is a complex Euclidean space, we obtain a complete classification of submanifolds M which satisfy these conditions.Mathematics Subject Classifications (2000): 53C15, 53C40, 53B20.     

Weak logarithmic Sobolev inequalities and entropic convergence

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner inequalities, etc.). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincaré inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.      

Some Oscillatory Singular Integrals on Herz-type Spaces (Ⅱ)

In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the Lebesgue spaceL1(Rn).     

三维Minkowski空间中的曲面及其可积性

利用可积系统的思想,借助三维Minkowski空间L3的矩阵模型,研究了L3中具有调和逆平均曲率的类空曲面和洛伦兹调和逆平均曲率类时曲面的可积性及其形变.     

N = 4 Supersymmetric (Dyonic) Hypermultiplets in String Theory

In four-dimensional N = 4 supersymmetric gauge theory, we obtain an exact metric on the moduli space of quantum vacua and analyze the spectra of BPS states in weak as well as in strong coupling regions. Identifying the hypermultiplet of the dyonic state as a string stretched between D₃-brane probe and a 7-brane, we demonstrate that the two hypermultiplets, which become massless at two singularities in supersymmetric theory, correspond to open strings beginning on the D₃-brane and ending on the respective 7-brane.     

A Sufficient Condition for Interolation by Functions in A~P(φ) (1

肖杰  赵大蕻 《数学季刊》1992,(4)

小间隙高放大多丝室及其放电机制

对以强猝灭气体工作的小间隙多丝室及其放电机制进行了研究,实验表明,因为工作在饱和模式区,这种室同时具有很高的气体放大和相当快的时间特性.文中探讨了放电机制,雪崩中空间电荷效应以及电离光子的产生和作用是重要的因素,而其中后一因素又受到强猝灭气体的抑制.     

绝对连续测度的Loeb代数

It is proved that if μ and v be finite measures on a measurable space (X,S) and v is absolutely continuous with respect to v, then it is holds that L(^*S,^*v) C L(^*S,^*v), while L(^*S,^*v) and L(^*S,^*v) are the Loeb algebras with respect to measure spaces (X,S,μ) and(X,S,μ).     

Fixed Point Theorems on Product Topological Spaces and Applications

A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.     

加权Bergman空间上小Hankel算子的Schatten类

讨论了 C\+n 中有界对称域的加权Bergman空间上符号属于 L\+2\-a(Ω, dV\-λ) 的小Hankel算子, 利用符号 Φ 的某种积分变换,给出了小Hankel算子 h\-Φ 属于Schatten理想 S\-p 的特征.