The structure of invertible substitutions on a three-letter alphabet

We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a finite set of invertible substitutions such that any invertible substitution can be written as I_wσ₁σ₂σ_k, where I_w is the inner automorphism associated with w, and for 1jk. As a consequence, M is the matrix of an invertible substitution if and only if it is a finite product of non-negative elementary matrices.     

On invertible substitutions with two fixed points

Let ? be a primitive substitution on a two-letter alphabet {a,b} having two fixed points ξ_a and ξ_b. We show that the substitution ? is invertible if and only if one has ξ_a=abξ and ξ_b=baξ. To cite this article: Z.-X. Wen et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 727–731.     

CdSe/ZnS-labeled carboxymethyl chitosan as a bioprobe for live cell imaging

A simple and convenient method for the construction of CdSe/ZnS-labeled polysaccharides as bioprobes were developed, which are highly biocompatible and photostable, and have been proven to be suitable for live cell imaging.     

On the leading term and the degree of the polynomial trace mapping associated with a substitution

Using the trace mapping and the reduced trace mapping associated with a substitution, one obtaines the spectral properties of one-dimensional Schrödinger operators of the formH=–+V onl ², where is the discrete Laplacian andV is a diagonal operator with elements derived from a substitution rule. In particular, the reduced trace mapping is closely related to the leading term of the original trace mapping. In this paper, the explicit expression of the leading term is given and its properties are discussed.     

Study on interaction between drug and membrane by using liposome coated zirconia-magnesia chromatography

The interactions between drug molecules and membrane were studied using the new chromatography stationary phase of liposome coated zirconia–magnesia. log K_s(ZrO₂–MgO) on this new chromatography for some drugs, compared with that on liposome coated silica chromatography and other reported data, fair correlations were observed between them when excluding effect of special adsorption. log K_s(ZrO₂–MgO) values for barbitalum, diazepam, benzene, benzocaine and toluene correlated well with corresponding values on liposome coated silica chromatography (R = 0.99778, P < 0.001; R = 0.98229, P < 0.003; R = 0.9985, P < 0.0001; R = 0.99925, P < 0.0001, pH value of mobile phase at pH 7.4, 7.0, 6.4 and 5.4, respectively). They also correlated well with the literature data on immobilized artificial membrane chromatography (R = 0.99999, P < 0.004 at pH 7.4) and liposome chromatography (R = 0.99994, P < 0.008) for procaine, lidocaine and bupivacaine. Liposome coated zirconia–magnesia chromatography can thus be used for studying drug–membrane interaction and prediction of drug absorption as another liposome chromatography method.     

High-performance liquid chromatography of some basic drugs on a n-octadecylphosphonic acid modified magnesia-zirconia stationary phase

The high-performance liquid chromatographic behavior of some basic drugs was studied on a n-octadecylphosphonic acid modified magnesia-zirconia (C18PZM) stationary phase. The effect of mobile phase variables such as methanol content, ionic strength, and pH on their chromatographic behavior was investigated. The retention mechanism of basic drugs on the stationary phase was elucidated. The results indicate that both hydrophobic and cation-exchange interactions contribute to solute retention under most chromatographic conditions. The inherent Br?nsted-acid sites and also the adsorbed Lewis base anionic buffer constituents on accessible ZM surface Lewis acid sites play a role in the retention of ionized solutes by cation-exchange interaction. However, especially at high mobile phase pH, the retention of basic drugs depends mainly on hydrophobic interactions between solutes and support. Separations of the basic drugs on the C18PZM phase by a predominantly reversed-phase retention mode were very promising. The mixed-mode retention feature on this phase, as a result of the adsorbed Lewis base anionic buffer constituents acting as sites for cation-exchange, could also be very useful, e.g. for enhancing the chromatographic selectivity of such analytes. The C18PZM seems to be an excellent alternative to silica-based reversed-phase stationary phase for the separation of strongly basic solutes.     

扶手椅型二硫化钼纳米带的电子结构与边缘修饰

采用基于密度泛函理论的第一性原理计算方法, 研究了扶手椅型二硫化钼纳米带的几何构型与电子结构, 发现其稳定性与电子性质敏感地依赖于边缘修饰. 随着边缘修饰的H原子数增加, 纳米带变得更加稳定, 并在间接带隙半导体、半金属和直接带隙半导体之间转变. 纳米带的能带结构和电子态密度显示, 其费米能级附近的能带主要由边缘态贡献. 当二硫化钼纳米带两边用不同数目的H原子修饰时, 纳米带同时具有由这两种修饰引起的边缘态并且两种边缘态的相互影响很小. 研究了三类纳米带带隙与宽度的关系, 对于每个原胞修饰0个或8个H原子的纳米带, 带隙随宽度以3为周期振荡变化; 而对于每个原胞修饰4个H原子的纳米带, 带隙振荡不再具有周期并且振荡幅度变小.     

Z型CdIn2S4/ZnSnO3异质结的构筑及其光催化产氢性能

通过高温煅烧ZnSn(OH)₆前驱体制备了双壳中空立方体结构的ZnSnO₃(ZSO),进而采用水热法将CdIn₂S₄(CIS)纳米晶包裹在ZSO表面,成功制备了CdIn₂S₄/ZnSnO₃(CIS/ZSO)异质催化剂。活性产氢实验结果表明,CIS、ZSO物质的量之比为12%时制备的12% CIS/ZSO具有优异的光催化产氢性能,在3 h内产氢量为1 676.48 μmol·g^-1,分别是ZSO和CIS的12倍和8倍。ZSO光催化析氢反应活性的增强归因于CIS/ZSO异质结构的成功构建,异质界面的形成显著提高了光生电子/空穴对的分离效率,降低了其复合率。通过对电荷转移路径的分析,提出了可能的反应机理。     

Spectrality of infinite convolutions with three-element digit sets

Let \(0< \rho <1\) and let \(\{a_n, b_n\}_{n=1}^\infty \) be a sequence of integers with bounded from upper and lower. Associated with them there exists a unique Borel probability measure \(\mu _{\rho , \{0, a_n, b_n\}}\) generated by the following infinite convolution product

$$\begin{aligned} \mu _{\rho , \{0, a_n, b_n\}}=\delta _{\rho \{0, a_1, b_1\}} *\delta _{\rho ^2 \{0, a_2, b_2\}} *\delta _{\rho ^3 \{0, a_3, b_3\}} *\cdots \end{aligned}$$

in the weak convergence, where \(\delta _E=\frac{1}{\# E}\sum _{e \in E} \delta _e\) and \(\hbox {gcd}(a_n, b_n)=1\) for all \(n \in {{\mathbb {N}}}\). In this paper, we show that \(L^2(\mu _{\rho , \{0, a_n, b_n\}})\) admits an exponential orthonormal basis if and only if \(\rho ^{-1} \in 3{{\mathbb {N}}}\) and  \(\{a_n, b_n\} \equiv \{1, 2\} \ (\mathrm {mod} \ 3)\) for all \(n \in {{\mathbb {N}}}\).

     

水下任意刚性散射体对Bessel波的散射特性分析

本文利用Bessel波的谐波展开式, 采用T矩阵方法的推导思路, 建立了水下任意刚性散射体在Bessel波照射下的声散射场计算公式. 以水下刚性椭球体和两端附连半球的刚性圆柱体为例, 计算了在不同波锥角β 下的反向散射形态函数, 同时, 依据镜反射波和绕行波的干涉物理模型, 给出了预报Bessel波照射下的反向散射形态函数峰峰间隔值的计算模型. 仿真结果表明本文提出的Bessel波照射下反向散射形态函数峰峰间隔值预报方法是准确有效的, 同时也说明, 本文建立的基于T矩阵法计算水下任意刚性散射体在Bessel波束下的声散射场方法是有效的, 这拓展了T矩阵法的应用领域.