CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).     

SOME TOPICS ON WAVELET ANALYSIS

A review of the advance in the theory of wavelet analysis in recent years is given.     

多个尺度函数产生的多分辨率分析

本文考虑一般细分方程ψｉ（ｘ）＝Σ１≤ｊ≤ＮΣｋ∈Ｚｃｉｊ（ｋ）ψｊ（２ｘ－ｋ），解的存在性，正则性和稳定性，及｛ψｉ｝１≤ｉ≤Ｎ产生Ｌ＾ｐ多分辨率分析的条件。     

Anion-Exchange-Driven Disassembly of a SiO(2)/CTAB Composite Mesophase: the Formation of Hollow Mesoporous Silica Spheres

Silica-based surfactant/inorganic composite mesophases have been extremely studied. In this work, we developed a mild method to realize the room-temperature disassembly of a SiO(2)/cetyltrimethylammonium bromide (CTAB) mesophase in a neutral medium. Using KMnO(4) as a typical etching agent, SiO(2)/CTAB mesophase spheres were partially disassembled into normal or rattle-type hollow structures. The disassembly of the SiO(2)/CTAB spheres was supposed to be driven by anion exchange between permanganate and silicate ions. This unique method makes possible the selective etching of a SiO(2)/CTAB mesophase over a SiO(2) phase.     

Compactly Supported Tight Affine Frames with Integer Dilations and Maximum Vanishing Moments

When a cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L ²=L ²(R) with dilation integer factor M2, the standard matrix extension approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The notion of vanishing moment recovery (VMR) was introduced in our earlier work (and independently by Daubechies et al.) for dilation M=2 to increase the order of vanishing moments. This present paper extends the tight frame results in the above mentioned papers from dilation M=2 to arbitrary integer M2 for any compactly supported M-dilation scaling functions. It is shown, in particular, that M compactly supported tight frame generators suffice, but not M–1 in general. A complete characterization of the M-dilation polynomial symbol is derived for the existence of M–1 such frame generators. Linear spline examples are given for M=3,4 to demonstrate our constructive approach.     

Limit cycle for cubic system of Kolmogorov type with a conic algebraic trajectory

In this paper we study the existence of limit cycle for cubic system ()₃, of Kolmogorov type with a conic algebraic trajectory

铅影响儿童健康

对１９９３年６月至１９９６年６月因体弱多病，生长发育矮小等来诊的３５１例儿童作了血铅测查和临床全征分析，以期引起儿科临床医师重视。