Fourier analysis of the approximation power of principal shift-invariant spaces

The approximation order provided by a directed set {S _h } _h>0 of spaces, each spanned by thehZ ^d -translates of one function, is analyzed. The nearoptimal approximants of [R2] from eachs _h to the exponential functions are used to establish upper bounds on the approximation order. These approximants are also used on the Fourier transform domain to yield approximations for other smooth functions, and thereby provide lower bounds on the approximation order. As a special case, the classical Strang-Fix conditions are extended to bounded summable generating functions.The second part of the paper consists of a detailed account of various applications of these general results to spline and radial function theory. Emphasis is given to the case when the scale {s _h } is obtained froms ₁ by means other than dilation. This includes the derivation of spectral approximation orders associated with smooth positive definite generating functions.     

Remez-, Nikolskii-, and Markov-type inequalities for generalized nonnegative polynomials with restricted zeros

Sharp Remez-, Nikolskii-, and Markov-type inequalities are proved for functions of the form

A family of Hermite interpolants by bisection algorithms

A two point subdivision scheme with two parameters is proposed to draw curves corresponding to functions that satisfy Hermite conditions on [a, b]. We build two functionsf andf ¹ on dyadic numbers and for some values of the parameters,f is in ¹ withf ¹=f. Examples are provided which show how different the curves can be.     

A note on debye potentials for spherically gyrotropic media

The Debye potentials are generalized to the case of electromagnetic fields in spherically gyrotropic media. A medium is called spherically gyrotropic if it is locally gyrotropic with the distinguished axis having a radial direction determined by a central point. Expressions for electromagnetic fields in terms of the generalized potentials are presented and the system of differential equations for the potentials is derived. The results are summarized in the form of a theorem. Basic facts about the Debye potentials in isotropic media are recalled.     

Fabrication of MCM-41 mesoporous silica through the self-assembly supermolecule of β-CD and CTAB

Using the self-assembly β-cyclodextrin (β-CD) and cetyltrimethylammonium bromide (CTAB) as structure-directing agents, high-quality ordered MCM-41 silicas have been prepared. Small-angle X-ray diffraction (SXRD), N₂ adsorption-desorption and scanning electron microscope (SEM) techniques were used to characterize the calcined samples. Results showed that the pore structure of the resulting mesoporous silica belonged to the two-dimensional hexagonal structure (space group p6mm). The high-quality hexagonal structure was formed as n?1 (n denotes molar ratio of β-CD to CTAB). N₂ adsorption-desorption curves revealed type IV isotherms, H4 hysteresis loops, for all samples, and H1 hysteresis loops for samples at n=0, 0.1, 1 and 2, respectively. The pore size and the pore wall thickness of the samples increased with the increase in n values, respectively.     

疏水改性MCM-41对甲草胺缓释性能的影响

采用浸渍法将甲草胺吸附到纯硅MCM-41(M41)介孔材料中, 以六甲基二硅氮烷(HMDS)为表面改性剂, 通过气-固反应对吸附了甲草胺的M41材料(Ach/M41)进行疏水改性, 得到了既具有高载药性又能有效延缓甲草胺释放的缓释体系Ach/TMS-M41. XRD、低温N₂吸附/脱附、FT-IR和TG等分析结果表明, 甲草胺在M41中的吸附量高达0.381 g·g^-1(质量分数为27.6%), 此时M41仍保持原有的孔道结构, 且甲草胺能完全分散于M41孔道中. 分别对Ach/M41和Ach/TMS-M41在水中的缓释性能进行了测试, 甲草胺释放率分别为62%和38.1%, 表明疏水改性对延缓甲草胺释放有较好的效果. 而且, 介孔材料孔壁对甲草胺具有明显的紫外屏蔽保护作用.     

介孔分子筛V-MCM-41的水热法制备与合成机理

 以十六烷基三甲基溴化铵为模板剂,廉价的工业级高模数比(3.3)的硅酸钠为硅源,通过水热法合成了V-MCM-41介孔分子筛. 考察了合成条件对产物织构的影响,并采用低温氮吸附法分析探讨了介孔分子筛V-MCM-41的合成机理. 结果表明,模板剂用量、 pH值、加料方式、晶化温度、晶化时间、陈化时间和焙烧气氛等合成条件对介孔分子筛的制备均有影响,其中晶化温度、 pH值和模板剂用量的影响最为明显. X射线衍射谱表明合成的介孔分子筛具有六方晶体结构. 红外光谱和紫外可见光谱表明V进入了介孔分子筛的骨架结构.     

A novel heterogeneous nanocatalyst: 2‐Methoxy‐1‐phenylethanone functionalized MCM‐41 supported Cu(II) complex for C‐S coupling of aryl halides with thiourea

An environmentally friendly copper‐based catalyst supported on 2‐Methoxy‐1‐phenylethanone functionalized MCM‐41 was prepared and characterized by FT‐IR, FE‐SEM, TEM, XRD, EDX, BET and ICP techniques. The catalyst was applied for the C?S cross‐coupling reaction of aryl halides with thiourea. Corresponding products were produced in good yields in aerobic conditions. The catalyst could be recovered and recycled for several times.     

Pd(0)-guanidine@MCM-41: a very effective catalyst for rapid production of bis (pyrazolyl)methanes

In this research, a rapid, green and efficient protocol for synthesis of bis (pyrazolyl)methane derivatives in the presence of Pd(0)-guanidine@MCM-41 catalysts under solvent-free conditions by the following two methods has been reported: (i) via the one-pot pseudo five-component reaction among phenylhydrazine (2 equivalents), ethyl acetoacetate (2 equivalents) and aromatic aldehydes (1 equivalent); and (ii) the one-pot pseudo three-component reaction between 3-methyl-1-phenyl-1H-pyrazol-5(4H)-one (2 equivalents) and aromatic aldehydes (1 equivalent). Some advantages of this protocol include: green conditions, extremely short times, high efficiency, proper one-pot operation, generality of method, easy work-up and recyclability, and reusability of the catalyst up to five times without significant loss in catalytic activity.