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《Indagationes Mathematicae》2021,32(1):55-85
We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows. 相似文献
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A finite support product of clones of Jensen's minimal singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals. 相似文献
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Liang Zhao 《Journal of Differential Equations》2019,266(9):5615-5624
In this paper, let be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation where are real constants. 相似文献
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Pu Duan Bo Zhi Luke Coburn Christy L. Haynes Klaus Schmidt-Rohr 《Magnetic resonance in chemistry : MRC》2020,58(11):1130-1138
The composition of fluorescent polymer nanoparticles, commonly referred to as carbon dots, synthesized by microwave-assisted reaction of citric acid and ethylenediamine was investigated by 13C, 13C{1H}, 1H─13C, 13C{14N}, and 15N solid-state nuclear magnetic resonance (NMR) experiments. 13C NMR with spectral editing provided no evidence for significant condensed aromatic or diamondoid carbon phases. 15N NMR showed that the nanoparticle matrix has been polymerized by amide and some imide formation. Five small, resolved 13C NMR peaks, including an unusual ═CH signal at 84 ppm (1H chemical shift of 5.8 ppm) and ═CN2 at 155 ppm, and two distinctive 15N NMR resonances near 80 and 160 ppm proved the presence of 5-oxo-1,2,3,5-tetrahydroimidazo[1,2-a]pyridine-7-carboxylic acid (IPCA) or its derivatives. This molecular fluorophore with conjugated double bonds, formed by a double cyclization reaction of citric acid and ethylenediamine as first shown by Y. Song, B. Yang, and coworkers in 2015, accounts for the fluorescence of the carbon dots. Cross-peaks in a 1H─13C HETCOR spectrum with brief 1H spin diffusion proved that IPCA is finely dispersed in the polyamide matrix. From quantitative 13C and 15N NMR spectra, a high concentration (18 ± 2 wt%) of IPCA in the carbon dots was determined. A pronounced gradient in 13C chemical-shift perturbations and peak widths, with the broadest lines near the COO group of IPCA, indicated at least partial transformation of the carboxylic acid of IPCA by amide or ester formation. 相似文献
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In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation with the critical situation that on g and p, where , is periodic and is bounded. 相似文献
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Algebra matrix and similarity classification of operators 总被引:1,自引:0,他引:1
ZHANG Zilong & LI Yucheng Department of Mathematics Hebei Normal University Shijiazhuang China 《中国科学A辑(英文版)》2006,49(3):398-409
In this paper, by the Gelfand representation theory and the Silov idempotents theorem, we first obtain a central decomposition theorem related to a unital semi-simple n-homogeneous Banach algebra, and then give a similarity classification of two strongly irreducible Cowen-Douglas operators using this theorem. 相似文献