Practical Criterion for Universal Laws and Practical Methods for Construction of Co-variance Sets

给出相对论力学中普遍定律的实用判别法和协变集的实用构造法,还给出实现非普遍定律的“可导出性”的一种实用方法．

Traces of nonsmooth functions on polyhedral domains

introduced in this paper are the definitions of the traces for a class of nonsmooth functions on polyhedral domains. By analyzing their properties we get the structures of these traces.

FUZZY SOLID SETS FOR MATHEMATICAL MORPHOLOGY AND OPTICAL IMPLEMENTATION

Fuzzy sets in the subject space are transformed to fuzzy solid sets in an increased object space on the basis of the development of the local umbra concept. Further, a counting transform is defined for reconstructing the fuzzy sets from the fuzzy solid sets, and the dilation and erosion operators in mathematical morphology are redefined in the fuzzy solid-set space. The algebraic structures of fuzzy solid sets can lead not only to fuzzy logic but also to arithmetic operations. Thus a fuzzy solid-set image algebra of two image transforms and five set operators is defined that can formulate binary and gray-scale morphological image-processing functions consisting of dilation, erosion, intersection, union, complement, addition, subtraction, and reflection in a unified form. A cellular set-logic array architecture is suggested for executing this image algebra. The optical implementation of the architecture, based on area coding of gray-scale values, is demonstrated. (C) 1995 Optical Society of America

Raman scattering of non-planar graphite: arched edges, polyhedral crystals, whiskers and cones

Planar graphite has been extensively studied by Raman scattering for years. A comparative Raman study of several different and less common non-planar graphitic materials is given here. New kinds of graphite whiskers and tubular graphite cones (synthetic and natural) have been introduced. Raman spectroscopy has been applied to the characterization of natural graphite crystal edge planes, an individual graphite whisker graphite polyhedral crystals and tubular graphite cones. Almost all of the observed Raman modes were assigned according to the selection rules and the double-resonance Raman mechanism. The polarization properties related to the structural features, the line shape of the first-order dispersive mode and its combination modes, the frequency variation of some modes in different carbon materials and other unique Raman spectral features are discussed here in detail.

Large-scale, rapid synthesis and application in surface-enhanced Raman spectroscopy of sub-micrometer polyhedral gold nanocrystals

Macromolecule-protected sub-micrometer polyhedral gold nanocrystals have been facilely prepared by heating an aqueous solution containing poly (N-vinyl-2-pyrrolidone) (PVP) and HAuCl4 without adding other reducing agents. Scanning electron microscopy (SEM), energy-dispersive x-ray spectroscopy (EDX), ultraviolet-visible-near-infrared spectroscopy (UV-vis-NIR), and x-ray diffraction (XRD) were employed to characterize the obtained polyhedral gold nanocrystals. It is found that the 10:1 molar ratio of PVP to gold is a key factor for obtaining quasi-monodisperse polyhedral gold nanocrystals. Furthermore, the application of polyhedral gold nanocrystals in surface-enhanced Raman scattering (SERS) was investigated by using 4-aminothiophenol (4-ATP) as a probe molecule. The results indicated that the sub-micrometer polyhedral gold nanocrystals modified on the ITO substrate exhibited higher SERS activity compared to the traditional gold nanoparticle modified film. The enhancement factor (EF) on polyhedral gold nanocrystals was about six times larger than that obtained on aggregated gold nanoparticles (similar to 25 nm).

Polyhedral oligomeric silsesquioxane nanocomposite thin films via layer-by-layer electrostatic self-assembly

Fabrication of ultrathin polymer composite films with low dielectric constants has been demonstrated. Octa( aminophenyl) silsesquioxane (OAPS) was synthesized and assembled with poly( acrylic acid) (PAA) and poly( styrene sulfonate) (PSS) via a layer-by-layer electrostatic self-assembly technique to yield nanoporous ultrathin films. The OAPS was soluble in water at pH 3 or lower, and suitable pH conditions for the OAPS/PAA and OAPS/PSS assemblies were determined. The multilayer formation process was studied by contact angle analysis, X-ray photoelectron spectroscopy, atomic force microscopy, quartz crystal microgravimetry, UV-vis spectroscopy, and ellipsometry. The multilayer growth was found to be steady and uniform, and the analysis of the film surface revealed a rough topography due to OAPS aggregates. The incorporation of porous OAPS molecules into the thin films significantly lowered their dielectric constants. The OAPS/PAA multilayer thin film thus prepared exhibited a dielectric constant of 2.06 compared to 2.58 for pure PAA film. The OAPS/PAA multilayer film was heated to effect cross-linking between the OAPS and the PAA layers, and the transformation was verified by reflection-absorption Fourier transform infrared spectroscopy.

Polyol-mediated synthesis of polyhedral silver clusters

Besides the spheres, polyhedral silver nanoclusters were prepared by the polyol process with 3-aminopropyl triethoxysilane (APTES). In the process, APTES acts as not only the stabilizer but also the template.