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Bin Han 《Advances in Computational Mathematics》2006,24(1-4):375-403
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
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Cory J. Hill Baohua Yang Rui Q. Yang 《Physica E: Low-dimensional Systems and Nanostructures》2004,20(3-4):486
Mid-IR type-II interband cascade lasers were demonstrated in pulsed mode at temperatures up to 325 K and in continuous mode up to 200 K. At 80 K, the threshold current density was 8.9 A/cm2 and a continuous wave output power of 140 mW/facet was obtained. 相似文献
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Kerr介质中级联三能级原子与压缩相干态相互作用的光子统计演化 总被引:6,自引:0,他引:6
本文研究了存在Kerr介质的高Q腔中压缩相干态与级联三能级原子相互作用的光子统计演化规律,讨论了光场参数、Kerr介质及相干振幅对平均光子数的影响. 相似文献
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George R. Newkome Gregory R. Baker James K. Young James G. Traynham 《Journal of polymer science. Part A, Polymer chemistry》1993,31(3):641-651
Cascade (dendritic) polymers are discrete, highly branched, monodisperse polymers that possess branching patterns described by a mathematical progression. A systematic nomenclature that accurately represents these molecules is described. © 1993 John Wiley & Sons, Inc. 相似文献
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Tandem cascade reactions of allylazides and olefinic dipolarophiles to give cis‐fused 2,3,7‐triazabicyclo [3.3.0]octenes ( 5, 6 or 7 ) are reported. Therein, an intermolecular dipolar cycloaddition of azide and alkene gave a triazoline which was followed by isomerization of the triazoline to a diazoester ( 4 ) and then an intramolecular dipolar cycloaddition from the diazo functional group and the double bond in 4 to give 5 . Compound 5 may further more undergo a Michael addition to give 7‐substituted‐ 2,3,7‐ triazabicyclo [3.3.0]oct‐2‐ene ( 6 ) or a tautomerization to give 2,3,7‐triazabicyclo[3.3.0]oct‐3‐ene ( 7 ). The reaction may be manipulated to stop at a particular stage by adopting a suit able solvent or an appropriate temperature. 相似文献
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Following a freeze-thaw cycle, and the treatment of Rhodopseudomonas sphaeroides withthe nonionic detergent Lubrol PX, the permeabilized cell suspensions can be assayed directlyboth for the intracellular levels of glutamine synthetase and the state of adenylylation(i.e. the average number n of adenylylated subunits/dodecameric molecules). It seems that all components of the bicycle system are retained if cells grown with lowconcentrations of a?monia as the sole nitrogen source are used. The value of n was depend-ent upon the concentration of substrates (ATP, Pi) and allosteric effectors (ATP, gluta-mine and α-ketoglutarate) of adenylyltransferase. The value of n affected by UTP, thespecific substrate of the uridylyltransferase shows first the evidence that the bicycle cascadecontrol system studied in Escherichia coli may exist in this phototrophic bacterium. 相似文献