Regularity of multiwavelets

The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L _p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.     

Numerical algorithms for uniform Airy-type asymptotic expansions

Airy-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing the asymptotic series. One method is based on expanding the coefficients of the asymptotic series in Maclaurin series. In the second method we consider auxiliary functions that can be computed more efficiently than the coefficients in the first method, and we do not need the tabulation of many coefficients. The methods are quite general, but the paper concentrates on Bessel functions, in particular on the differential equation of the Bessel functions, which has a turning point character when order and argument of the Bessel functions are equal.     

Explicit generalized zolotarev polynomials with complex coefficients

We give explicitly a class of polynomials with complex coefficients of degreen which deviate least from zero on [−1, 1] with respect to the max-norm among all polynomials which have the same,m + 1, 2m ≤n, first leading coefficients. Form=1, we obtain the polynomials discovered by Freund and Ruschewyh. Furthermore, corresponding results are obtained with respect to weight functions of the type 1/√ρl, whereρl is a polynomial positive on [−1, 1].     

分子筛组装单质半导体碲的拉曼光谱

无机介孔材料MCM41是高有序,直孔道介孔分子筛,具有孔径约4nm的一维均匀孔道,孔壁厚约1nm,介孔体积可达40%,是一种很理想的组装材料主体。半导体碲位于第Ⅵ族,其六方相的晶格排列呈螺旋链状结构。本文采用固相合成反应方法,将单质半导体碲成功地组装在MCM41介孔分子筛中。在组装体中,单质半导体碲保持着六方相的晶体结构,其拉曼晶体振动表现出纳米晶体的结构特征。真空热处理实验表明,组装体具有良好的热稳定性。Te的六方相和所具有的独特的螺旋链状结构使Te分子很容易进入MCM41的直孔道内,同时MCM41均匀而规则的直孔道限制了Te螺旋链的随机排列,因而被组装在直孔道内的Te能螺旋链式生长,形成一维半导体纳米晶体,排列均匀,尺寸单一,具有稳定的空间构型     

On the Shintani zeta function for the space of binary quadratic forms

Partially supported by NSF Grant DMS-8803085, DMS-8610730     

Ce-MCM-48立方介孔分子筛结构的光谱表征

在碱性条件下,以混合模板剂pH调节水热合成了掺入铈的介孔分子筛Ce-MCM-48,并采用XRD,DRUV-Vis(紫外-可见漫反射),FTIR,XRF结合BET等测试手段对样品进行表征。实验结果表明,采用本方法所合成的掺铈介孔材料仍保持立方介孔的有序结构,同时适量的铈的掺入和pH调节使分子筛的有序性及吸附性能得到改善,晶胞参数增大,孔径更均一,孔壁增厚。从而可推出Ce-MCM-48的热稳定性、水热稳定性、催化活性及择形选择性可得到提高。掺入的铈以四配位状态高度分散在介孔的有序结构当中。红外光谱表明不同量的铈的掺入对骨架硅的各种振动扰动程度不同。     

超声波对合成介孔材料Al-MCM-41的有序度的影响

在超声频率为20 kHz,电功率为500 W的超声波作用下,分别以Al（NO₃）₃和Al₂ （SO₄）₃做铝源合成了具有不同Si/Al比的Al-MCM-41。XRD结果显示,尽管超声波作用下,掺杂杂原子Al也要降低介孔材料的有序度,但其有序度降低的程度比普通水热法要小,超声波的辅助可以在同样反应时间内得到比普通水热法具有更高有序度的Al-MCM-41,即在掺杂过程中,超声波要比普通搅拌有利于介孔材料保持其骨架稳定性。此外考察了超声波作用时间对产品有序度和粒度的影响。     

载体MCM-41对Tb(aspirin)3phen发光性能的影响

在室温下,乙二胺环境中合成了高度有序的介孔材料MCM-41,并将经热处理的发光客体Tb(aspi-rin)3phen组装进其孔道,通过激发发射光谱对其光致发光性能进行了研究。结果表明,Tb(aspirin)3phen240～375 nm区间的宽激发峰归属于配体aspirin羰基n→π*跃迁、苯环π→π*跃迁,和phen的杂菲基团吸收,Tb3 的特征发射是由于Antenna效应引起的。相对于纯Tb(aspirin)3phen,Tb(aspirin)3phen-MCM-41B和Tb(aspirin)3phen/MCM-41A的激发谱带出现了明显的分裂,而Tb(aspirin)3phen-MCM-41A只在353nm处剩下了相对较窄的单峰。Tb(aspirin)3phen-MCM-41B,Tb(aspirin)3phen/MCM-41A和Tb(aspirin)3phen-MCM-41A的短波段激发峰依次减弱消失,长波段激发峰逐渐增强,而405 nm发射峰强度IL和544 nm发射峰强度ILn的比值I(I=IL/ILn)依次减小。MCM-41骨架与Tb(aspirin)3phen成键后,不同程度降低了配体aspirin和phen单重态S1和三重态T1能级,且对phen的影响大于aspirin。不同的MCM-41表面晶格场对配体能级的影响顺序为:MCM-41B外表面>MCM-41A外表面>MCM-41A内表面。I值可定性表示MCM-41表面晶格场对配体能级影响程度和MCM-41表面Tb(aspirin)3phen的含量。     

Nuclear Spin–Lattice Relaxation of Single Crystal Sr14Cu24O41

Nuclear spin–lattice relaxation rate T ₁ ⁻¹ has been measured for the ladder sites of two single crystals Sr₁₄Cu₂₄O₄₁ (Sr14-A,B) by ⁶³Cu NMR/NQR. The hole localization around 100 K appears as a peak in the T variation of T ₁ ⁻¹(NQR). On the other hand, it is suppressed in the T ₁ ⁻¹ (NMR) data under the magnetic field H ∼ 11 T, and a new peak appears around 20 K. T ₁ ⁻¹(NMR) around the peak is more enlarged for Sr14-B than for Sr14-A. Hence, holes on the ladders of Sr14-B tend to be more localized. This is considered to be an origin for the occurrence of the magnetic order in Sr14-B under H ∼ 11 T.     

Optimization of profenofos organophosphorus pesticide degradation by zero-valent bimetallic nanoparticles using response surface methodology

This study synthesized bimetallic Fe/Ni nanoparticles and used them for catalytic degradation of profenofos, an organophosphorus pesticide. This novel bimetallic catalyst (Fe/Ni) was characterized by scanning electron microscopy (SEM), energy-dispersive X-ray analysis spectroscopy (EDAX) and X-ray diffraction (XRD). The bimetallic nano-catalyst was prepared at diameters of 20–50 nm and was shown to effectively degrade profenofos. A three-factor central composite design combined with response surface methodology was used to maximize profenofos removal using the bimetallic system. A quadratic model was built to predict degradation efficiency. ANOVA was used to determine the significance of the variables and interactions between them. Good correlation between the experimental and predicted values was confirmed by the high F-value (16.38), very low P-value (<0.0001), non-significant lack of fit, an appropriate coefficient of determination (R² = 0.936) and adequate precision (14.75). The highest removal rate attained was 94.51%.