Θ-type Calderón-Zygmund operators with non-doubling measures

Let µ be a Radon measure on ? ^d which may be non-doubling. The only condition that µ must satisfy is µ(B(x, r)) ≤ Cr ⁿ for all x∈? ^d , r > 0 and for some fixed 0 < n ≤ d. In this paper, under this assumption, we prove that θ-type Calderón-Zygmund operator which is bounded on L ²(µ) is also bounded from L ^∞(µ) into RBMO(µ) and from H _atb ^1,∞ (µ) into L ¹(µ). According to the interpolation theorem introduced by Tolsa, the L ^p (µ)-boundedness (1 < p < ∞) is established for θ-type Calderón-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type Calderón-Zygmund operator with RBMO(µ) function are bounded on L ^p (µ) (1 < p < ∞).     

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.     

具有中间亏指数的线性哈密顿算子的点谱

本文讨论具有任意亏指数d的自伴线性哈密顿算子点谱与对应的线性哈密顿系统的平方可积解之间的关系.若对于某个实开区间中的任意点λ,系统总有d个线性无关解,则它的任何自伴算子的点谱在这个开区间上是不稠密的.     

前向正则模糊神经网络依K-积分模的泛逼近能力

针对前向正则模糊神经网络引进K-拟可加积分和K-积分模概念,应用积分转换定理研究了该网络在K-积分模意义下对模糊值简单函数类的泛逼近能力,进而在有限K-拟可加测度空间上,借助模糊值简单函数为桥梁获得了前向正则模糊神经网络依K-积分模对(u)-可积有界模糊值函数类仍具有泛逼近性.该结果表明前向正则模糊神经网络对连续模糊系统的逼近能力可以推广为对一般可积系统的逼近能力.     

Regular Solution and Lattice Miura Transformation of Bigraded Toda Hierarchy

The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy （BTH）. As a specific example of exponential solutions of the BTH, the authors consider a regular solution for the （1, 2）-BTH with a 3 × 3-sized Lax matrix, and discuss some geometric structures of the solution from which the difference between the （1, 2）- BTH and the original Toda hierarchy is shown. After this, the authors construct another kind of Lax representation of （N, 1）-BTH which does not use the fractional operator of Lax operator. Then the authors introduce the lattice Miura transformation of （N, 1）-BTH which leads to equations depending on one field, and meanwhile some specific examples which contain the Volterra lattice equation （a useful ecological competition model） are given.     

求解二次Lagrangian有限元方程的代数两水平方法

基于矩阵图集的粗化算法,构造一种新的插值算子,提出了瀑布型代数两重网格法;然后结合部分几何信息,提出了求解二次Lagrangian有限元方程的代数两水平方法.数值实验表明该算法稳健性强、计算量更少.     

一些次线性算子在非齐性弱Herz空间中的有界性

本文在具有仅满足增长性条件测度μ的非齐性空间上引入了弱H erz空间,并讨论了某些次线性算子在该空间上的有界性;特别的,我们得到了分数次积分算子的有界性.     

Quantum Hadamard Operators and Their Decomposition Derived by Virtue of IWOP Technique

We introduce the quantum Hadamard operator in continuum state vector space and find that it can be decomposed into a single-mode squeezing operator and a position-momentum mutual transform operator. The two-mode Hadamard operator in bipartite entangled state representation is also introduced, which involves the two-mode squeezing operator and [η〉 ←→｜ξ〉 mutual transformation operator, where [η〉 and ｜ξ〉 are mutual conjugate entangled states. All the discussions are proceeded by virtue of the IWOP technique.     

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco- Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.     

Metric of States

Metric of quantum states plays an important role in quantum information theory. In this letter, we find the deep connection between quantum logic theory and quantum information theory. Using the method of quantum logic, we can get a famous inequality in quantum information theory, and we answer a question raised by S. Gudder.