Frame Wavelets with Compact Supports for L^2（R^n）

The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.     

Synthesis and nuclear magnetic resonance analysis of starch‐g‐poly(1,4‐dioxan‐2‐one) copolymers

A new biodegradable starch graft copolymer, starch‐g‐poly(1,4‐dioxan‐2‐one), was synthesized through the ring‐opening graft polymerization of 1,4‐dioxan‐2‐one onto a starch backbone. The grafting reactions were conducted with various 1,4‐dioxan‐2‐one/starch feed ratios to obtain starch‐g‐poly(1,4‐dioxan‐2‐one) copolymers with various poly(1,4‐dioxan‐2‐one) graft structures. The microstructure of starch‐g‐poly(1,4‐dioxan‐2‐one) was characterized in detail with one‐ and two‐dimensional NMR spectroscopy. The effect of the feed composition on the resulting microstructure of starch‐g‐poly(1,4‐dioxan‐2‐one) was investigated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3417–3422, 2004     

Reply to the comment on: ‘Magnetoresistance in La1−xCaxMnO3(0≤x<0.4)’

The author of the comment objects to the characterization and the interpretation of magnetoresistance (MR) effects observed by us in La_1−xCa_xMnO₃ (0≤x<0.4) samples. In this reply, arguments are used to show that the samples' characterization and explanation of the MR by considering the role of the short-charge ordering (CO) regions and magnetic domains are reasonable and acceptable.     

多元K-拟全纯函数及其正规定则

研究函数族的正规性定则是复变函数论中的一个重要且有意义的工作．引进多元K-拟全纯函数的定义，并给出了多元K-拟全纯函数族的一个正规定则．     

Dimensionally and thermally stable polymer,containing disordered graphitic structure and adamantane

In an attempt to develop a low‐k interlayer dielectric, adamantane‐diphenyldiethynyl moiety containing oligomer is prepared. Oligomerization of 1,3,5,7‐tetrakis[3/4‐ethynylphenyl]adamantane ( 4 ) is accomplished by a Glaser–Hay oxidative coupling with 1,3,5‐triethynylbenzene and phenylacetylene end‐capping agent. The CHCl₃ soluble oligomer is then thermally treated by step‐curing at 200, 300, 380, and 450 °C for 30 min at each temperature under nitrogen flow to render a shiny void‐free black polymer. TGA analysis indicates that the polymer is stable under nitrogen up to 500 °C with a marginal decomposition up to 800 °C. Solid‐state ¹³C NMR, Raman scattering, and FTIR are used to characterize the structure of the polymer. The polymer consists of amorphous carbon networks with the adamantane moieties and nanosized graphitic regions (clusters), which are generated from the thermal crosslinking of the diphenyldiethynyl units. It shows a remarkably low linear coefficient of thermal expansion (～25 ppm/°C), presumably due to the presence of the disordered graphitic structure. Its high density (～1.21 g/cm³), refractive index (～1.80 at 632 nm), and Young's modulus (～17.0 GPa) are also consistent with the interpretation. This study reveals important details about the effect of microscopic structure on the macroscopic properties of the highly crosslinked polymer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6909–6925, 2006     

A study of electrostatic spring softening for dual-axis micromirror

Electrostatic spring softening is an important characteristic of electrostatically actuated dual-axis micromirror, since it lowers the resonant frequencies. This paper presents an approach based on approximating the electrostatic forces by the first-order Taylor's series expansion to investigate this characteristic. The dual-axis micromirror studied in this paper has three motion modes, two torsional (about x- and y-axis, respectively) and one translational (about z-axis). The stiffnesses of all these modes are softened by a DC bias voltage applied to the mirror plate. The resonant frequencies are lowered with the increment of the bias voltage. The relationship of the bias voltage and the resonant frequencies of all the motion modes is derived. The analytical results show that the resonant frequency curves are affected by the capacitor geometries, i.e. the gap between the mirror plate and the electrodes and the electrodes size. The lowering curves drop slowly when the bias voltage is small. While for large bias voltage, the lowering curves drop rapidly. The experiment results are consistent with those obtained by the analytical approach.     

Two-Scale Homogeneous Functions in Wavelet Analysis

Two-scale homogeneous functions are functions hh satisfying h(x) = \gl h(2 x)h(x) = \gl h(2 x) for some constant \gl\gl. They form a class of special functions and include homogeneous polynomials. In this article we investigate two-scale homogeneous functions that are contained in a shift-invariant space S(f)S(\phi) where f\phi is an rr-vector of functions and satisfies a vector refinement equation. The structure of these functions is analyzed. In particular, we establish a one-to-one correspondence between these two-scale homogeneous functions with order \gl\gl and the left eigenvectors of a finite matrix (derived from the mask for f\phi) associated with eigenvalue \gl\gl.     

一种非刚性医学图像点匹配方法

提出了一种非刚性点匹配的算法并把其运用于医学图像配准．该算法采用信号滤波的方法来获得点集间的匹配信息，并运用松弛标记法将各点邻域关系对模糊的匹配信息进行迭代获得明确的匹配关系．在此基础上，利用高斯径向基函数来描述点模式间的弹性形变，在基本的迭代框架下实现问题的求解．实验结果显示在形变程度为5％、出格点比率50％和噪声标准差为5％的情况下该算法的匹配误差能控制在0．13以下，表明了该算法的鲁棒性和有效性，较好地解决了医学非刚性形变的点匹配问题．     

An Improved Extra-Gradient Method for Minimizing a Sum of p-norms—A Variational Inequality Approach

This paper presents a variational inequality (VI) approach to the problem of minimizing a sum of p-norms. First the original problem is reformulated as an equivalent linear VI. Then an improved extra-gradient method is presented to solve the linear VI. Applications to the problem of p-norm Steiner Minimum Trees (SMT) shows that the proposed method is effective. Comparison with the general extra-gradient method is also provided to show the improvements of the new method.     

Phenylene vinylene‐based electroluminescent polymers with electron transport block in the main chain

We report a new route for the design of soluble phenylene vinylene (PV) based electroluminescent polymers bearing electron‐deficient oxadizole (OXD) and triazole (TZ) moieties in the main chains with the aryloxy linkage. Both series of the PV‐based polymers were prepared by Wittig reaction. By properly adjusting the OXD and/or TZ content through copolymerization, we can achieve an enhanced balance of hole‐ and electron injections, such that the device efficiency is significantly improved. Light‐emitting diodes fabricated from P1, P2, P3, P4, P5, P6, and P7 with the configuration of Indium–Tin Oxide (ITO)/Poly (styrene sulfonic acid) doped poly (ethylenedioxythiophene) (PEDOT)/polymer/Ca/Al, emit bright green light with the maximum peak around 500 nm. For the device using the optimal polymer (P4) as emitting layer, a maximum brightness of 1300 cd/m² at 20 V and a maximum luminance efficiency of 0.325 cd/A can be obtained. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3469–3478, 2006