The first-order harmonic balance method via first Fourier coefficient is used to construct an approximate frequency-amplitude relation for a Duffing-harmonic oscillator. This relation is in agreement with the result obtained by the Ritz procedure. 相似文献
In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space Wpk(ℝs) (1≤p≤∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented.
Rate of convergence of vector cascade algorithms in a Sobolev space Wpk(ℝs) will be investigated. When the dilation matrix is isotropic, a characterization will be given for the Lp (1≤p≤∞) critical smoothness exponent of a refinable function vector without the assumption of stability on the refinable function
vector. As a consequence, we show that if a compactly supported function vector φ∈Lp(ℝs) (φ∈C(ℝs) when p=∞) satisfies a refinement equation with a finitely supported matrix mask, then all the components of φ must belong to a Lipschitz
space Lip(ν,Lp(ℝs)) for some ν>0. This paper generalizes the results in R.Q. Jia, K.S. Lau and D.X. Zhou (J. Fourier Anal. Appl. 7 (2001) 143–167)
in the univariate setting to the multivariate setting.
Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 42C20, 41A25, 39B12.
Research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) under Grant
G121210654. 相似文献
The photolysis reactions of three compounds commonly used as a sunscreen agents, Parsol 1789 (1-[4-(1,1-dimethylethyl)phenyl]-3-(4-methoxyphenyl)-1,3- propanedione), Oxybenzone ((2-hydroxy-4-methoxyphenyl)phenyl-methanone) and Padimate O (2-ethylhexyl-4-(dimethylamino)benzoate), were investigated to provide a chemical background to aid in the understanding of the photosensitization of the sunscreen agents. Photolysis was carried out in cyclohexane for 70–140 h using a mercury vapor lamp (450W) without excluding oxygen.
Irradation of Parsol 1789 in cyclohexane yielded tert-butylbenzene, p-tert-butylbenzoic acid and p-methoxybenzoic acid; products obtained from the combination of the sunscreen with the solvent included the cyclohexyl esters of p-methoxybenzoic acid, p-tert-butylbenzoic acid and methanoic acid; products obtained from the solvent included cyclohexanol, cyclohexanone and dicyclohexyl ether.
Irradiation of Oxybenzone in the cyclohexane for 100 h produced no detectable products by either gas or liquid chromatographic analysis. Oxybenzone was recovered unchanged and no products were observed from the photoinitiated reaction of oxygen with the solvent.
Irradiation of Padimate O in cyclohexane yielded the ethylhexyl esters of p-aminobenzoic acid, p-monomethylaminobenzoic acid and p-dimethylamino (o/m)-methylbenzoic acid, as well as products from the photoinitiated reaction of oxygen with the solvent. 相似文献
In this paper, a new method of boundary reduction is proposed, which reduces thesteady-state heat transfer equation with radiation. Moreover, a boundary element method is pre-sented for its solution and the error estimates of the numerical approximations are given. 相似文献
Applied Biochemistry and Biotechnology - A novel, anaerobic fermentation process is developed to produce calcium magnesium acetate (CMA) from cheese whey. CMA can be used as a noncorrosive road... 相似文献
Great interests have been accumulated in recent years in the chemistry and biochemistry of nitric oxide (NO) since the remarkable discoveries of its key roles in a wide range of human physiological processes. To elucidate the mechanistic details of NO migration from its donor to its acceptor, it is necessary to determine the Y-NO bind energy that registers the thermodynamic driving force for NO release and capture. In this paper the heterolytic and homolytic N-NO bond dissociation energies [ i. e., △Hhet(N-NO) and △Hhomo(N-NO)] for ten N-nitroso-p-substituted-benzensulfonyl methylamines in acetonitrile are offered, which were obtained from titration calorimetry and thermodynamic cycles, respectively (Scheme 1). 相似文献