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.     

改性壳聚精膜用于醇水混合液分离的研究──Ⅲ．超细粉末填充壳聚精膜

首次制备了用Ｓｉ３Ｎ４，ＳｉＯ２，ＴｉＨ４超细粉末填充的改性壳聚精膜，并将其用于乙醇／水混合液的分离中。实验表明壳聚糖膜经超细粉末填充后强度增大，溶胀度减小。用于乙醇／水混合液渗透蒸发分离时，分离因子和渗透通量都有提高，并在填充量为１６．７％附近出现极大值。随着料液中乙醇含量的增大，渗透通量减小，分离因子增大；随着料液温度的升高渗透通量显著增大，分离因子则稍有下降。并简单讨论了超细粉末在乙醇／水混合液分离中的作用。     

矿渣粉加固粉土的理论分析及路用性能研究

提出了矿渣粉加固粉土的相关理论。将矿渣粉在加固土中的作用归结为火山灰胶凝效应和微集料填充效应,而火山灰胶凝效应又可进一步归结为水化作用、激发作用和离子交换作用;认为微集料填充效应与矿渣粉细度极为相关;用框图归纳了矿渣粉加固土的两种作用效应。进行了矿渣粉、石灰粉加固土无侧限饱水抗压强度、水稳定性、冻稳定性、温度收缩和干燥收缩等路用性能试验,并进行比较。结果表明,矿渣粉加固土所测路用性能指标优于石灰粉加固土。为工程应用提供了试验依据。     

用于同步辐射光源的成像板粉末衍射系统

报道了我们研制的一套成像板粉末衍射装置,对其误差来源进行了详细的分析讨论,并与衍射仪进行了比较.该装置的半径为143.3mm,最大测量角度范围不160°，最大角度(2q )偏差小于0.03°,这些性能指标已被实验所证实,完全可应用于粉末衍射全谱的测量.     

Structures and syntheses of layered and framework amine-bearing uranyl phosphate and uranyl arsenates

Two hydrated uranyl arsenates and a uranyl phosphate were synthesized by hydrothermal methods in the presence of amine structure-directing agents and their structures determined: (N₂C₆H₁₄)[(UO₂)(AsO₄)]₂(H₂O)₃, DabcoUAs, {NH(C₂H₅)₃}[(UO₂)₂(AsO₄)(AsO₃OH)], TriethUAs, and (N₂C₄H₁₂)(UO₂)[(UO₂)(PO₄)]₄(H₂O)₂, PiperUP. Intensity data were collected at room temperature using MoKα X-radiation and a CCD-based area detector. The crystal structures were refined by full-matrix least-squares techniques on the basis of F² to agreement indices (DabcoUAs, TriethUAs, PiperUP) wR₂=5.6%, 8.3%, 7.2% for all data, and R₁=2.9%, 3.3%, 4.0%, calculated for 1777, 5822, 9119 unique observed reflections (|F_o|?4σ_F), respectively. DabcoUAs is monoclinic, space group C2/m, Z=2, a=18.581(1), b=7.1897(4), c=7.1909(4) Å, β=102.886(1)°, V=936.43(9) Å³, D_calc=3.50 g/cm³. TriethUAs is monoclinic, space group P2₁/n, Z=4, a=9.6359(4), b=18.4678(7), c=10.0708(4) Å, β=92.282(1)°, V=1790.7(1) Å³, D_calc=3.41 g/cm³. PiperUP is monoclinic, space group Pn, Z=2, a=9.3278(4), b=15.5529(7), c=9.6474(5) Å, β=93.266(1)°, V=1397.3(1) Å³, D_calc=4.41 g/cm³. The structure of DabcoUAs contains the autunite-type sheet formed by the sharing of vertices between uranyl square bipyramids and arsenate tetrahedra. The triethylenediammonium cations are located in the interlayer along with two H₂O groups and are disordered. Both TriethUAs and PiperUP contain sheets formed of uranyl pentagonal bipyramids and tetrahedra (arsenate and phosphate, respectively) with the uranophane sheet-anion topology. In TriethUAs, triethlyammonium cations are located in the interlayer. In PiperUP, the sheets are connected by a uranyl pentagonal bipyramid that shares corners with phosphate tetrahedra of adjacent sheets, resulting in a framework with piperazinium cations and H₂O groups in the cavities of the structure.     

多重向量值正交小波包

本文引入多重向量值小波包的概念,提供一类多重向量值正交小波包的构造方法,并运用积分变换和算子理论,讨论了多重向量值正交小波包的性质．利用多重向量值正交小波包,构造了空间L2(R,Cs×s)的新的正交基．     

TiO2 粉末催化剂光催化降解室内 空气中有机污染物

本文制备了一系列 TiO2粉末催化剂, 用光催化法降解室内空气中各种微量有机污染物,最终降解率 接近 100%. 考察了晶型对光催化剂性能的影响, 结果表明,锐钛矿型 TiO2 的催化性能最好. 最后,分析了 TiO2 光催化反应机理.     

Rebuilding of metal components with laser cladding forming

Laser cladding forming (LCF) is a novel powerful tool for the repairing of metal components. Rebuilding of V-grooves on medium carbon steel substrates has been carried out with laser cladding forming technique using stainless steel powder as the cladding material. Microstructure of the deposited layers has been characterized using optical microscopy (OM), scanning electron microscopy (SEM), energy dispersive X-ray microanalysis (EDAX), electron probe microanalysis (EPMA) and X-ray diffraction (XRD). Mechanical properties of the rebuilt V-groove samples have been evaluated by tensile and impacting tests and microhardness measurement. Experimental results show that good fusion bonding between the rebuilt layers and the substrate has been formed, and the microstructure of the cladding layers is mainly composed of fine, dense and defect-free epitaxial columnar dendrites. Due to the effect of grain size refinement, the tensile strength, impacting toughness, elongation and microhardness of the rebuilt samples have been greatly enhanced compared to those of the substrate. Microhardness is also very uniform throughout the rebuilt regions. With the growth of the deposited layers, the microhardness increases gradually. The good ductility of the deposited regions is verified by the SEM fracture analysis.