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131.
M Riedel 《Journal of multivariate analysis》1985,16(2):241-252
Let X1, X2,…, be independent, identically distributed random variables. Suppose that the linear forms L1 = Σj=1∞ajXj and L2 = Σj=1∞bjXj exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X1 is normally distributed are presented. The result is an extension of a theorem of Linnik (Ukrainian Math. J.5 (1953), 207–243, 247–290) concerning the case that the linear forms L1 and L2 have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions. 相似文献
132.
A decision scheme for the interpretation of spectra from wavelength dispersive X-ray fluorescence spectrometry is described that encompasses elements from three areas of artificial intelligence: fuzzy logic, rule based expert systems and neural net technology.After transforming the recorded spectra to line spectra by appropriate background correction a reasoning scheme is applied that takes into account not only the observed spectra, but also the recording conditions and prior spectroscopic information regarding the relative emission probabilities and the usefulness of the different lines for the purpose of element identification. The latter is done on the basis of a previously described scheme to compute conditional a posteriori Bayes probabilities for a mean matrix. These different pieces of information are then assembled into a battery of fuzzy rules. The importance of the rules as well as the importance of the X-ray lines is determined in a training process, similar to the one in a feedforward back-propagation network.To further stabilize the results this network is pruned in a second training cycle. This, however, had little effect on the quality of interpretation.The advantages of this approach to the interpretation of X-ray spectra over older ones are numerous: the system adapts itself to better interpret spectra that are of greater importance to a laboratory as these are better represented in the training set; the fuzzy logic is capable of working with incomplete and uncertain knowledge, and the neural network results based on these fuzzy rules is readily interpretable by the X-ray spectroscopist as every rule can be expressed also in natural language as in any classical rule based system.On leave from Silesian University, Katowice, Poland 相似文献
133.
The Fourier transform far infrared spectra of oxalate hydrates of whole rare-earth series except Pm and Sc are investigated in the range of 100-400 cm~(-1). The assignment of vibrational frequencies is made on the basis of normal coordinate analysis using our NORVIB program. The model used for the hghter elements of the lanthanide series (La to Eu) is based on the crystal structure of Nd_2(C_2O_4)_3. 10H_2O, in which each lanthanide ion is surrounded by nine O atoms, six from three oxalate ions and three from Water molecules.The model adopted for the heavier elements of the lanthanide series (Gd to Lu) and Ytterbium is based on the crystal structure of Yb_2(C_2O_4)_3· 6H_2O, in which each ion is surrounded by eight atoms, six from three oxalate ions and two from water molecules. The variation of the metal-ligand frequencies and force constants with the atomic numbers of lanthanides is plotted and discussed. 相似文献
134.
二组分混合物的最小流化特性 Ⅰ.混合/分离状态与最小流化空隙率 总被引:1,自引:0,他引:1
分析了二组分混合物的3种混合/分离状态及在完全混合时发生连续相转变的极限组成。提出一个判别非等密度体系混合/分离状态的法则与确定混合物空隙率简易可行的随意松散堆积方法。 相似文献
135.
We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them. 相似文献
136.
Yuan-zeXu Yi-binXu 《高分子科学》2005,(2):147-153
The evolution and the origin of “solid-like state” in molten polymer/clay nanocomposites are studied. Using polypropylene/clay hybrid (PPCH) with sufficient maleic anhydride modified PP (PP-MA) as compatibilizer, well exfoliation yet solid-like state was achieved after annealing in molten state. Comprehensive linear viscoelasticity and non-linear rheological behaviors together with WAXD and TEM are studied on PPCH at various dispersion stages focusing on time,temperature and deformation dependencies of the “solid-like” state in molten nanocomposites. Based on these, it is revealed that the solid-structure is developed gradually along with annealing through the stages of inter-layer expansion by PP-MA,the diffusion and association of exfoliated silicate platelets, the formation of band/chain structure and, finally, a percolated clay associated network, which is responsible for the melt rigidity or solid-like state. The network will be broken down by melt frozen/crystallization and weakened at large shear or strong flow and, even more surprisingly, may be disrupted by using trace amount of silane coupling agent which may block the edge interaction of platelets. The solid-like structure causes characteristic non-linear rheological behaviors, e.g. residual stress after step shear, abnormal huge stress overshoots in step flows and, most remarkably, the negative first normal stress functions in steady shear or step flows. The rheological and structural arguments challenge the existing models of strengthened entangled polymer network by tethered polymer chains connecting clay particles or by chains in confined melts or frictional interaction among tactoids. A scheme of percolated networking of associated clay platelets, which may in band form of edge connecting exfoliated platelets, is suggested to explain previous experimental results. 相似文献
137.
In this study, local least squares (LLS) and principal component analysis (PCA) were applied to deal with the disturbances in a data set of chromatographic fingerprints after necessary data transformations. It has been demonstrated that PCA with standard normal variate (SNV) transformation of data led to meaningful classification of 33 different Erigeron breviscapus herbal samples. The result was also corroborated by variance squares discriminant method. The quality of herbal objects was further evaluated, and the causes of this fact have been explained from a chemical point of view. At the same time, it implied an idea for qualitative evaluation of the herbal objects with a common class pattern of chromatographic fingerprints. 相似文献
138.
Xiufang Xu Guichang Wang Xuezhuang Zhao Yinming Pan Yunxiao Liang Zhenfeng Shang 《Journal of mathematical chemistry》2007,41(2):143-160
In this paper, the fuzzy symmetry of some prototypical linear molecules has been analyzed. The results show that some molecular
orbitals (MOs) are less symmetrical but some others are more symmetrical than the molecular skeleton, which the MOs correspond
to. The membership functions of space inversion for MOs are closely related to the chemical characteristics of the MOs. Sometimes,
although the symmetry of a molecular skeleton is not obvious, however that of some MO is quite obvious. The membership functions
of the fuzzy inversion symmetry depend on the choice of the position of the center of inversion. As compared to those of diatomic
molecules and linear tri-atomic molecules, the linear polyatomic molecules in which a distinctive fuzzy symmetry of space
translation may exist, and thus a significant effect on their properties can be expected. 相似文献
139.
140.
K. Osaki T. Inoue T. Uematsu Y. Yamashita 《Journal of Polymer Science.Polymer Physics》2002,40(10):1038-1045
Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τRZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τL > τRZ) and a high‐frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ1) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K‐BKZ) equation with the damping function h(γ) = (1 + 0.2γ2)?1/2, where γ is the magnitude of shear. Contributions to η and Ψ1 from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τst = τ + (τRZ ? τ)/(1 + 0.35τRZ γ˙) instead of τRZ. Here, γ˙ is the rate of shear, and τ is the τRZ value at the infinite dilution limit. η and Ψ1 at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol?1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002 相似文献