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.     

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.     

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

ＩｎｔｒｏｄｕｃｔｉｏｎＡｓａｍａｔｅｒｉａｌｕｎｄｅｒｇｏｅｓｉｒｒｅｖｅｒｓｉｂｌｅｂｅｈａｖｉｏｒ,ｉｔｓｍｉｃｒｏｓｔｒｕｃｔｕｒｅｗｉｌｌｃｈａｎｇｅ .Ｐａｒｔｉｃｕｌａｒｌｙ ,ｔｈｅｓｉｎｇｌｅｃｒｙｓｔａｌｖｏｌｕｍｅｆｒａｃｔｉｏｎｏｆａｐｏｌｙｃｒｙｓｔａｌ,ｗｈｉｃｈｉｓｍａｔｈｅｍａｔｉｃａｌｌｙａｓｃａｌａｒｆｕｎｃｔｉｏｎｏｎｔｈｅｒｏｔａｔｉｏｎｇｒｏｕｐａｎｄｉｓｃａｌｌｅｄａＣＯＤＦ (ｃｒｙｓｔａｌｏｒｉｅｎｔａｔｉｏｎｄｉｓｔｒｉｂｕｔｉｏｎｆｕｎｃｔｉｏｎ) ,ｃ…     

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.     

Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor

Third order three-dimensional symmetric and traceless tensors play an important role in physics and tensor representation theory. A minimal integrity basis of a third order three-dimensional symmetric and traceless tensor has four invariants with degrees two, four, six, and ten, respectively. In this paper, we show that any minimal integrity basis of a third order three-dimensional symmetric and traceless tensor is also an irreducible function basis of that tensor, and there is no syzygy relation among the four invariants of that basis, i.e., these four invariants are algebraically independent.     

Aharonov—Anandan phase gate in sub Hilbert space of a coupling flux qubits system

We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimension Hilbert space of a coupling flux qubits system to a 2-dimension subspace spanned by two dressed states |01> and |10>. In this subspace, we illustrate how to generate an Aharnov--Anandan phase, based on which, we can construct a NOT gate (as effective as a C-NOT gate) in this coupling flux qubits system. Finally, the fidelity of the NOT gate is also calculated in the presence of the simulated classical noise.     

集值下鞅的Doob分解的注记

基于(X,‖.‖)为可分的Banach空间,X*为其对偶空间,X*可分,讨论集值增过程与实值增过程之间的关系,研究超空间上代数运算的若干性质,利用支撑函数,得出集值下鞅可Doob分解的二个充要条件,改进和推广了已往的结果。     

Preparation of Size Controllable Polypyrrole Sub‐Microcapsules Using SEBS Copolymer as the Building Block

Summary: SEBS is used as building blocks to fabricate size controllable polypyrrole (PPy) capsules. Polypyrrole shells grow on the surfaces of the size controllable oxidant sub‐microparticles dispersed in the solution cast film of a SEBS copolymer by vapor phase polymerization. After washing in ethanol, PPy sub‐microcapsules dispersed in a SEBS matrix are obtained. This technique shows advantages of lower cost and less pollution, as compared with the gold‐template method reported in the literature.

A TEM image of polypyrrole sub‐microcapsules dispersed in a SEBS matrix.     

Quantum State Transfer in Engineered Spin Chain under Influence of Spatially Distributed Environment

It has been shown that a quantum state could be perfectly transferred via a spin chain with engineered ``always-on interaction". In this paper, we study a more realistic problem for such a quantum state transfer (QST) protocol, how the efficacy of QST is reduced by the quantum decoherence induced by a spatially distributed environment. Here, the environment is universally modeled as a bath of fermions located in different positions. By making use of the irreducible tensor method in angular momentum theory, we investigate the effect of environment on the efficiency of QST for both cases at zero and finite temperatures. We not onlyshow the generic exponential decay of QST efficiency as the number of sites increase, but also find some counterintuitive effect, the QST can be enhanced as temperature increases in some cases.     

唯一分解整环R上不可约多项式的一个判别准则

本获得了一个判别唯一分解整环R及其商域Q上的n次（n＞2)多项式不可约的充分条件。