多元函数空间的对称分解

引进一种多元函数空间的对称分解方法,并讨论了由对称算符组成的正交幂等系统的简单构造.     

有关E'-矩阵的若干注记

The class of E'-matrices introduced in [4] is a subclass of Q0-matrices whose proper principal submatrices are Q-matrices. In this paper, we investigate the relation of the class E' to other known matrix classes and obtain a series of necessary and sufficient conditions for E'-matrices.     

锥中上调和函数的Riesz 分解定理及其应用

本文给出了锥中上调和函数的Riesz 分解定理. 同时, 得到了它在锥中无穷远点处的增长性质, 并且刻画了其例外集的几何性质. 作为应用, 我们证明了锥内次调和函数的Phragmén-Lindelöf 型定理.     

On representations of real Jacobi groups

We consider a category of continuous Hilbert space representations and a category of smooth Fr’echet representations,of a real Jacobi group G.By Mackey’s theory,they are respectively equivalent to certain categories of representations of a real reductive group L.Within these categories,we show that the two functors that take smooth vectors for G and for L are consistent with each other.By using Casselman-Wallach’s theory of smooth representations of real reductive groups,we define matrix coefficients for distributional vectors of certain representations of G.We also formulate Gelfand-Kazhdan criteria for real Jacobi groups which could be used to prove multiplicity one theorems for Fourier-Jacobi models.     

有限域上一类三项式的研究

利用有限域理论,按照扩张次数k的奇偶性,研究了p~k元域上一类三项式的可约性判定问题,并在一定的条件下给出了该类三项式的一个分解式,最后给出了两种利用此类三项式构造新的不可约多项式的方法.     

Fe3O4/β-CD的高压电学性质研究

 高压下的电学性质测量是获得材料物理性质的有效手段。利用集成在金刚石对顶砧上的薄膜微电路,测量了高压下Fe₃O₄/β-CD（β-糊精）的电导率,并分析了电导率随压力的变化关系。在0～39.9 GPa范围内,Fe₃O₄/β-CD的电导率随压力的增加而逐渐增大,并呈半导体的特征;而在17.0 GPa处其电导率发生突变,表明样品发生了高压相变。在卸压过程中,电导率随压力的变化呈线性关系,并且卸压后样品的电导率不能回到最初的状态,推测这是一个不可逆的高压结构相变。     

ORIENTATION DISTRIBUTION FUNCTIONS FOR MICROSTRUCTURES OF HETEROGENEOUS MATERIALS (Ⅱ)──CRYSTAL DISTRIBUTION FUNCTIONS AND IRREDUCIBLE TENSORS RESTRICTED BY VARIOUS MATERIAL SYMMETRIES

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算子的酉等价与换位代数的K0-群

We show that two irreducible operators on Н are unitarily equivalent if and only if W^*（AФB)‘≌M2(C), and give an answer to the open question posed by J. B. Conway (Subnormal Operators, 7r Pitman, Advanced Publishing Program,Boston, London, Melbourne, 1981) for irreducible operator. We also show that if T, T1 and T2 are irreducible operators with TФT1≌TФT2, then T1≌T2. Finally, we show that K0(A(D))≌Z, giving a new result on the Ko-group of Banach algebras.     

ORIENTATION DISTRIBUTION FUNCTIONS FOR MICROSTRUCTURES OF HETEROGENEOUS MATERIALS (Ⅱ)──CRYSTAL DISTRIBUTION FUNCTIONS AND IRREDUCIBLE TENSORS RESTRICTED BY VARIOUS MATERIAL SYMMETRIES

The explicit representations for tensorial Fourier expansion of 3-D crystal orientation distribution functions (CODFs) are established. In comparison with that the coefficients in the mth term of the Fourier expansion of a 3-D ODF make up just a single irreducible mth-order tensor, the coefficients in the mth term of the Fourier expansion of a 3-D CODF constitute generally so many as 2m + 1 irreducible mth-order tensors. Therefore, the restricted forms of tensorial Fourier expansions of 3-D CODFs imposed by various micro- and macro-scopic symmetries are further established, and it is shown that in most cases of symmetry the restricted forms of tensorial Fourier expansions of 3-D CODFs contain remarkably reduced numbers of mth-order irreducible tensors than the number 2m + 1. These results are based on the restricted forms of irreducible tensors imposed by various point-group symmetries, which are also thoroughly investigated in the present part in both 2- and 3-D spaces.     

Growth Diversity in One Dimensional Fluctuating Interfaces

A set of one dimensional interfaces involving attachment and detachment of k-particle neighbors is studied numerically using both large scale simulations and finite size scaling analysis. A labeling algorithm introduced by Barma and Dhar in related spin Hamiltonians enables to characterize the asymptotic behavior of the interface width according to the initial state of the substrate. For equal deposition-evaporation probability rates it is found that in most cases the initial conditions induce regimes of saturated width. In turn, scaling exponents obtained for initially flat interfaces indicate power law growths which depend on k. In contrast, for unequal probability rates the interface width exhibits a logarithmic growth for all k>1 regardless of the initial state of the substrate.