Solutions in Sobolev spaces of vector refinement equations with a general dilation matrix

In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space W_p^k(ℝ^s) (1≤p≤∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented. Rate of convergence of vector cascade algorithms in a Sobolev space W_p^k(ℝ^s) will be investigated. When the dilation matrix is isotropic, a characterization will be given for the L_p (1≤p≤∞) critical smoothness exponent of a refinable function vector without the assumption of stability on the refinable function vector. As a consequence, we show that if a compactly supported function vector φ∈L_p(ℝ^s) (φ∈C(ℝ^s) when p=∞) satisfies a refinement equation with a finitely supported matrix mask, then all the components of φ must belong to a Lipschitz space Lip(ν,L_p(ℝ^s)) for some ν>0. This paper generalizes the results in R.Q. Jia, K.S. Lau and D.X. Zhou (J. Fourier Anal. Appl. 7 (2001) 143–167) in the univariate setting to the multivariate setting. Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 42C20, 41A25, 39B12. Research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) under Grant G121210654.     

用13CNMR研究聚甲基丙烯酸锡酯的立构序列分布

本文测定了自由基型溶液聚合的聚甲基丙烯酸三甲基锡酯(PTMTM),聚甲基丙烯酸三乙基锡酯(PTETM)和聚甲基丙烯酸三丁基锡酯(PTBTM)的¹³C-NMR谱,对其C-2谱扩展分峰,计算立构序列,从定量数据表明,聚合物样品的空间立构富于或稍富于间规立构,随取代基的体积增大而趋于无规分布,作者认为受空间位阻效应和分子内或分子间形成配位键的影响。     

薄相屏闪烁的数值分析

本文在弱闪烁条件下，利用广泛适用于星际闪烁、行星际闪烁和电离层闪烁的薄相屏理论，以行星际闪烁为算例，对薄相屏闪烁进行了数值分析。结果表明：垂直于介质运动方向上的不规则结构的大小对闪烁有着重要的影响，直接表现在频谱的变化趋势和振荡幅度的不同。尤其是当小于Ｆｒｅｓｎｅｌ尺度时，数值计算表明此时没有闪烁发生。     

RS码频域编译码的计算机模拟

频域编译码是近年来由Ｂｌａｈｕｔ等人提出来的纠错码编译方法。本文介绍了在时域和频域编译ＲＳ码的基本方法，并给出了在移动信息道的简单分群Ｍａｒｋｏｖ模型下频域编译码的计算机模拟方法和结果。     

Application of asymptotic waveform evaluation to eigenmode expansion method for analysis of simultaneous switching noise in printed circuit boards (PCBs)

In this paper, the asymptotic waveform evaluation (AWE) technique is first applied to the conventional eigenmode expansion method for characterizing a power/ground (P/G) plane pair and analyzing the simultaneous switching noise on such plane pairs for printed circuit boards or multichip modules. The application of AWE avoids a large number of iterations in computing the impedance frequency response of a P/G plane pair structure and greatly reduces the computation time. Meanwhile, to obtain an accurate solution in an entire frequency range, we employ the complex frequency hopping technique which can help select multiple expansion points. In addition, the proposed approach can also be used to characterize the P/G plane pair structures with irregular shapes. Three examples demonstrate its high efficiency and good accuracy.     

北京自由电子激光最近进展──实现饱和振荡

北京自由电子激光(BFEL)装置于1993年底在10.68μm处实现了饱和振荡.输出激光能量为3mJ,饱和平顶宽度2μs.对应饱和振荡平均功率为210kW(宏脉冲),峰值功率约为20MW,比自发辐射高8个量级,单程小讯号净增益为24%,转换效率为0.45%,与理论预期结果相符.光束质量接近衍射极限.目前装置可工作于9-11μm.     

Efficiency improvement of near-ultraviolet InGaN LEDs using patterned sapphire substrates

The use of conventional and patterned sapphire substrates (PSSs) to fabricate InGaN-based near-ultraviolet (410 nm) light-emitting diodes (LEDs) was demonstrated. The PSS was prepared using a periodic hole pattern (diameter: 3 /spl mu/m; spacing: 3 /spl mu/m) on the (0001) sapphire with different etching depths. From transmission-electron-microscopy and etch-pit-density studies, the PSS with an optimum pattern depth (D/sub h/=1.5 /spl mu/m) was confirmed to be an efficient way to reduce the thread dislocations in the GaN microstructure. It was found that the output power increased from 8.6 to 10.4 mW, corresponding to about 29% increases in the external quantum efficiency. However, the internal quantum efficiency (@ 20 mA) was about 36% and 38% for the conventional and PSS LEDs, respectively. The achieved improvement of the output power is not only due to the improvement of the internal quantum efficiency upon decreasing the dislocation density, but also due to the enhancement of the extraction efficiency using the PSS. Finally, better long-time reliability of the PSS LED performance was observed.     

Super-Wavelets and Decomposable Wavelet Frames

A wavelet frame is called decomposable whenever it is equivalent to a superwavelet frame of length greater than one. Decomposable wavelet frames are closely related to some problems on super-wavelets. In this article we first obtain some necessary or sufficient conditions for decomposable Parseval wavelet frames. As an application of these conditions, we prove that for each n > 1 there exists a Parseval wavelet frame which is m-decomposable for any 1 < m ≤ n, but not k-decomposable for any k > n. Moreover, there exists a super-wavelet whose components are non-decomposable. Similarly we also prove that for each n > 1, there exists a Parseval wavelet frame that can be extended to a super-wavelet of length m for any 1 < m ≤ n, but can not be extended to any super-wavelet of length k with k > n. The connection between decomposable Parseval wavelet frames and super-wavelets is investigated, and some necessary or sufficient conditions for extendable Parseval wavelet frames are given.     

Time resolved spectroscopic NMR imaging using hyperpolarized Xe

We have visualized the melting and dissolution processes of xenon (Xe) ice into different solvents using the methods of nuclear magnetic resonance (NMR) spectroscopy, imaging, and time resolved spectroscopic imaging by means of hyperpolarized ¹²⁹Xe. Starting from the initial condition of a hyperpolarized solid Xe layer frozen on top of an ethanol (ethanol/water) ice block we measured the Xe phase transitions as a function of time and temperature. In the pure ethanol sample, pieces of Xe ice first fall through the viscous ethanol to the bottom of the sample tube and then form a thin layer of liquid Xe/ethanol. The xenon atoms are trapped in this liquid layer up to room temperature and keep their magnetization over a time period of 11 min. In the ethanol/water mixture (80 vol%/20%), most of the polarized Xe liquid first stays on top of the ethanol/water ice block and then starts to penetrate into the pores and cracks of the ethanol/water ice block. In the final stage, nearly all the Xe polarization is in the gas phase above the liquid and trapped inside the pores. NMR spectra of homogeneous samples of pure ethanol containing thermally polarized Xe and the spectroscopic images of the melting process show that very high concentrations of hyperpolarized Xe (about half of the density of liquid Xe) can be stored or delivered in pure ethanol.