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Annals of the Institute of Statistical Mathematics - In this paper, we consider an unbalanced urn model with multiple drawing. At each discrete time step n, we draw m balls at random from an urn...  相似文献   
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We consider sign-changing solutions of the equation \(-\Delta _m u= |u|^{p-1}u\) where \(m\ge 2\) and \(p>1\) in half-space and strips with nonlinear mixed boundary value conditions. We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The main methods used are the integral estimates, the Pohozaev-type identity and the monotonicity formula.  相似文献   
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A high-efficiency microwave irradiation (MW) assisted protocol was proposed to synthesize series SPE-β-CD with specific degree of substitution (DS) in the sodium hydroxide solution. This protocol provided an eco-friendly way to modify the cyclodextrins with bulky sulfopropyl substituent on the purpose of avoiding organic solvents and high quantities of thermal energy. Temperature and energy distribution became more uniform under the new method accordingly. Therefore, not only the reaction time reduced significantly from over 20 h to a few hours, but also the DS increased up according to 1H NMR spectroscopy, MS and elemental analysis results. Most importantly, the effects of reaction parameters on DS were compared both under MW method and conventional heating method, and were sufficiently studied to guarantee the aforementioned results could be better reproduced and DS of products could become more specific through the synthesis process. Products structures were characterized by FT-IR, DSC, and 13C NMR spectroscopy.  相似文献   
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Direct partial oxidation of methane into methanol is a cornerstone of catalysis. The stepped conversion of methane into methanol currently involves activation at high temperature and reaction with methane at decreased temperature, which limits applicability of the technique. The first implementation of copper‐containing zeolites in the production of methanol directly from methane is reported, using molecular oxygen under isothermal conditions at 200 °C. Copper‐exchanged zeolite is activated with oxygen, reacts with methane, and is subsequently extracted with steam in a repeated cyclic process. Methanol yield increases with methane pressure, enabling reactivity with less reactive oxidized copper species. It is possible to produce methanol over catalysts that were inactive in prior state of the art systems. Characterization of the activated catalyst at low temperature revealed that the active sites are small clusters of copper, and not necessarily di‐ or tricopper sites, indicating that catalysts can be designed with greater flexibility than formerly proposed.  相似文献   
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The reaction of hexamethylphosphotriamide or methylphosphonic bis(dimethylamide) compounds with amidines derived from N-Benzimidazoyl imidates 1 leads to (1,2a)benzimidazolo-1,3,5,2-tiazaphosphorine-2-oxides 4 in good yields. If the condensation is realized at room temperature, N-phosphonic amidines 3 can be isolated as intermediates. The isolated compounds 2 , 3 , and 4 are identified by spectroscopic methods: IR, 1 H, 13 C, 31 P, NMR, and M.S.  相似文献   
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Abstract

The hydrolysis kinetics of 14 alkoxy silane coupling agents were carried out in an ethanol:water 80:20 (w/w) solution under acidic conditions and were monitored by 1H, 13C, and 29Si NMR spectroscopy. Acidic conditions were selected in order to enhance the silanol formation and to slow down the self-condensation between the resulting hydrolysed silanol groups. In situ 29Si NMR spectroscopy allowed the determination of the intermediate species as a function of the reaction time. Thus, the following silane coupling agents were studied: 3-methacryloxypropyl trimethoxy silane (MPMS), 3-mercaptopropyl trimethoxy silane (MRPMS), 3-cyanopropyl triethoxy silane (CPES), triethoxy vinyl silane (VES), trimethoxy (2-phenylethyl) silane (PEMS), octyl triethoxy silane (OES), trimethoxy (7-octen-1-yl) silane (OEMS), 3-aminopropyl triethoxy silane (APES), 3-aminopropyl trimethoxy silane (APMS), 3-(2-aminoethylamino)propyl trimethoxy silane, (DAMS), 3-[2-(2-aminoethylamino)-ethylamino]propyl trimethoxy silane (TAMS), 4-amino-3,3-dibutyl trimethoxy silane (ADBMS), trimethoxy [3-(phenylamino)propyl] silane (PAPMS), and triethoxy-3-(2-imidazolin-1-yl) propyl silane (IZPES). A parameter quantifying the grafting potentiality of each silane coupling agent towards OH-rich solid substrates (such as cellulose) was established as a function of the nature of the alkoxy groups (methoxy or ethoxy), as well as that of the fourth substituent (vinyl, aminopropyl, etc.) of the silane studied.

GRAPHICAL ABSTRACT  相似文献   
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In this paper, we introduce and study the Sobolev spaces of exponential type associated with the Weinstein operator, via some elements of harmonic analysis related to this operator. In particular, some properties, including completeness and imbedding theorem, are proved. Finally, using the theory of reproducing kernels, some applications are given for these spaces.  相似文献   
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