伸缩因子为s的尺度函数傅里叶变换的支集

主要构造出了一类sd-集但非Wsd-集．同时,我们使用一种新方法,推广了一些已知的结果．基于这些结果,系统地揭示了sd-尺度函数的傅里叶变换的支集与闭球的关系．     

Directional Haar wavelet frames on triangles

Traditional wavelets are not very effective in dealing with images that contain orientated discontinuities (edges). To achieve a more efficient representation one has to use basis elements with much higher directional sensitivity. In recent years several approaches like curvelets and shearlets have been studied providing essentially optimal approximation properties for images that are piecewise smooth and have discontinuities along C²-curves. While curvelets and shearlets have compact support in frequency domain, we construct directional wavelet frames generated by functions with compact support in time domain. Our Haar wavelet constructions can be seen as special composite dilation wavelets, being based on a generalized multiresolution analysis (MRA) associated with a dilation matrix and a finite collection of ‘shear’ matrices. The complete system of constructed wavelet functions forms a Parseval frame. Based on this MRA structure we provide an efficient filter bank algorithm. The freedom obtained by the redundancy of the applied Haar functions will be used for an efficient sparse representation of piecewise constant images as well as for image denoising.     

激光辐照不规则空间碎片冲量矢量计算

研究了不规则空间碎片受激光辐照后的冲量变化。利用不论激光入射方向如何,烧蚀反喷方向始终沿着烧蚀平面法向方向这个实验现象,同时,根据NASA对于空间碎片形状的基本划分,分别计算了球体、柱形体和立方体受激光辐照后的冲量变化情况。计算结果表明:对于球体和立方体,无论激光辐照方向如何变化,冲量方向总是和辐照方向相同,冲量大小和垂直辐照相同材料的平板分别成固定比例关系;而对于柱形体,冲量大小和方向随着激光辐照方向变化而变化。     

Stability of wavelet frames with matrix dilations

Under certain assumptions we show that a wavelet frame

in remains a frame when the dilation matrices and the translation parameters are perturbed. As a special case of our result, we obtain that if is a frame for an expansive matrix and an invertible matrix , then is a frame if and for sufficiently small 0$">.

     

Dixmier traces of operators on Banach and Hilbert spaces

We present a simple approach to the theory of traces on the Marcinkiewicz operator ideal Particular attention is paid to the Dixmier traces, which may be obtained from both dilation‐invariant functionals and shift‐invariant functionals on $\mathfrak l_\infty$. Since the concept of positivity does not make sense for traces defined on operator ideals over Banach spaces, traces are not assumed to be positive in the Hilbert space setting, as well. This standpoint raises some new problems. The present studies will be continued in 35 , 36 .     

复杂背景下运动目标的光学相关识别

在应用光电混合联合变换相关器实现运动目标相关识别的过程中,针对目标与模板由于运动所产生的差异和复杂背景影响相关器识别率的问题,采用了一种以高斯函数的一阶导数做小波多尺度边缘提取和形态学膨胀进行边缘加粗处理相结合的方法。这种方法可充分利用小波多尺度的特点,使得提取后的边缘在抑制噪声的同时,能保留更多的细节信息,明显改善复杂背景下运动目标的相关识别问题。对以低对比度和小目标为特点的动态序列进行光学相关实验,结果表明,这种方法能有效增强探测目标的相关峰亮度,验证了算法对复杂背景下运动目标识别的可行性。     

Sorption and partial molar volumes of gases in poly(ethylene-co-vinyl acetate)

Sorption and dilation properties of polymer-gas systems involving poly(ethylene-co-vinyl acetate) and N₂, CH₄, or CO₂, have been investigated at pressures up to 50 atm at temperatures of 10–40°C. Sorption isotherms for low-solubility gases (i.e., CH₄ and N₂) can be described by Henry's law, and those for high-solubility gas (i.e., CO₂) by Flory-Huggins dissolution equation. Dilation isotherms are similar in contour to the corresponding sorption isotherms. From the obtained sorption and dilation data, partial molar volumes of the gases in the polymer were determined as a function of temperature. Thermal expansivity of dissolved CO₂ molecules was estimated at ca. 2.4 × 10^?3°C^?1 from the temperature dependence of partial molar volume. The expansivity is smaller than that of liquid CO₂ and larger than those of the polymer and organic liquids. © 1994 John Wiley & Sons, Inc.     

Dilation of poly[1-(trimethylsilyl)-1-propyne] during sorption of n-nonane

The linear expansion and contraction in the principal planar directions of poly[1-(trimethylsilyl)-1-propyne] film were measured concurrently with the sorption of n-nonane at 35°C. After the first sorption cycle, in which the polymer exhibited markedly nonisotropic volumetric dilation, the polymer expanded and contracted reproducibly during subsequent multiple sorption and desorption cycles. These reversible dilation isotherms were reproducible from sample to sample. The fractional change in length was identical in arbitrarily selected, orthogonal directions in the plane of the film, suggesting that the expansion and dilation of the sample are isotropic. When plotted versus the activity of n-nonane, the linear expansions in the plane of the film are slightly concave to the activity axis, reaching levels over 10% at the highest activities. The experimental partial specific volume of the polymer is near its pure component value but that of the penetrant is much less than its pure component value. Moreover, the magnitude of dilation observed is described rather closely by the dilation which would result solely from the Henry's law portion of sorption, assuming zero volume-change of mixing. These results are consistent with the explicit notions of “hole-filling” associated with the Langmuir mode in the dual-mode model. © 1993 John Wiley & Sons, Inc.     

Nonlinear optimization simplified by hypersurface deformation

A general strategy is advanced for simplifying nonlinear optimization problems, the ant-lion method. This approach exploits shape modifications of the cost-function hypersurface which distend basins surrounding low-lying minima (including global minima). By intertwining hypersurface deformations with steepest-descent displacements, the search is concentrated on a small relevant subset of all minima. Specific calculations demonstrating the value of this method are reported for the partitioning of two classes of irregular but nonrandom graphs, the prime-factor graphs and the pi graphs. We also indicate how this approach can be applied to the traveling salesman problem and to design layout optimization, and that it may be useful in combination with simulated annealing strategies.     

Overlap Integrals Between Irregular Solid Harmonics and STOs Via the Fourier Transform Methods

In this paper, a unified analytical and numerical treatment of overlap integrals between Slater type orbitals (STOs) and irregular Solid Harmonics (ISH) with different screening parameters is presented via the Fourier transform method. Fourier transform of STOs is probably the simplest to express of overlap integrals. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals as finite sums and infinite series of STOs, ISHs, Gegenbauer, and Gaunt coefficients. The another mathematical tools except for Fourier transform have used partial-fraction decomposition and Taylor expansions of rational functions. Our approach leads to considerable simplification of the derivation of the previously known analytical representations for the overlap integrals between STOs and ISHs with different screening parameters. These overlap integrals have also been calculated for extremely large quantum numbers using Gegenbauer, Clebsch-Gordan and Binomial coefficients. The accuracy of the numerical results is quite high for the quantum numbers of Slater functions, irregular solid harmonic functions and for arbitrary values of internuclear distances and screening parameters of atomic orbitals.