ZIF-8/改性聚丙烯腈电纺纳米纤维的制备及其高效去除水中孔雀石绿

通过原位生长方法，将最常见的金属有机骨架（MOFs）——沸石咪唑酯骨架材料（ZIF‐8）固定到羧甲基化聚丙烯腈静电纺丝纳米纤维（PAN‐COOH NFs）表面，得到ZIF‐8/PAN‐COOH NFs。通过扫描电子显微镜（SEM）、能量色散光谱（EDS）、X射线粉末衍射（XRD）和傅里叶变换红外光谱（FTIR）对合成的ZIF‐8/PAN‐COOH NFs形貌和结构进行表征，并深入研究ZIF‐8/PAN‐COOHNFs从废水中去除孔雀石绿（MG）的性能。研究发现： ZIF‐8/PAN‐COOH NFs对MG的吸附符合拟二级动力学方程，吸附过程可采用Langmuir等温线模型拟合，其对MG的最大吸附容量可达3 604 mg·g^-1。此外，ZIF‐8/PAN‐COOH NFs在染料吸附实验中表现出良好的分离功能和重复利用性。     

The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers

In this paper, we give a systematical study of the local structures and fractal indices of the limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers. For a given Pisot number in the interval (1,2), we construct a finite family of non-negative matrices (maybe non-square), such that the corresponding fractal indices can be re-expressed as some limits in terms of products of these non-negative matrices. We are especially interested in the case that the associated Pisot number is a simple Pisot number, i.e., the unique positive root of the polynomial x^k-x^k-1-…-x-1 (k=2,3,…). In this case, the corresponding products of matrices can be decomposed into the products of scalars, based on which the precise formulas of fractal indices, as well as the multifractal formalism, are obtained.     

涂层界面结合强度检测研究（I）：涂层结合界面应力的理论分析

利用激光划痕测试法和弯曲应力理论，建立了涂层结合界面应力的理论模型，推导出结合界面剪应力、正应力和剥离应力分布公式，分析了结合界面应力产生的机理．理论分析结果表明，界面正应力主要集中在界面中心区域内，而在界面边缘附近，正应力迅速下降，在界面边缘处其值降为0；剪应力和剥离应力主要集中在界面边缘区域内，在远离界面边缘区域，剪应力和剥离应力则迅速下降；涂层中正应力和涂层厚度、基体厚度以及杨氏模量无关，界面间剪应力以及剥离应力随涂层厚度增加而增加，并且由涂层与基体厚度以及杨氏模量所共同决定．     

Axisymmetry Breaking to Travelling Waves in the Cylinder with Partially Heated Sidewall

The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A = 2 and Prandtl number Pτ=0.021. The flow develops from the steady toroidal pattern beyond the first instability threshold, breaks the axisymmetric state at a Rayleigh number near 2000, and transits to standing or travelling azimuthal waves. A new result is observed that a slightly unstable flow pattern of standing waves exists and will transit to stable travelling waves after a long time evolution. The onset of oscillations is associated with a supercritical Hopf bifurcation in a system with O（2） symmetry.     

《超声提取及其应用》简介

功率超声在工业、农业、军事、医疗、环保、美容等各方面的应用日益广泛，相关著作也多有出版；然而，作为功率超声的一个新的应用领域利用超声波的能量，加速或加强从植物、动物、矿物等物质中提取特定成分过程的超声提取技术，国内尚无专著问世。     

When is the union of two unit intervals a self-similar set satisfying the open set condition?

Let U _λ be the union of two unit intervals with gap λ. We show that U _λ is a self-similar set satisfying the open set condition if and only if U _λ can tile an interval by finitely many of its affine copies (admitting different dilations). Furthermore, each such λ can be characterized as the spectrum of an irreducible double word which represents a tiling pattern. Some further considerations of the set of all such λ’s, as well as the corresponding tiling patterns, are given. The first author was partially supported by the RGC grant and the direct grant in CUHK, Fok Ying Tong Education Foundation and NSFC (10571100). The second author was partially supported by NSFC (70371074) and NFSC (10571104).