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61.
Mathematical Notes - 相似文献
62.
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual. 相似文献
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Knyazev A. A. Karyakin M. E. Krupin A. S. Galyametdinov Yu. G. 《Russian Journal of General Chemistry》2015,85(12):2806-2812
Russian Journal of General Chemistry - Hybrid liquid crystal systems with different ratios of the components have been prepared on the basis of 5,5′-di(heptadecyl)-2,2′-bipyridine... 相似文献
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The European Physical Journal Special Topics - The removal of suspended particles from the interior of a thermocapillary liquid bridge via a finite-particle-size effect restricting the particle... 相似文献
67.
Nano palladium supported on high‐surface‐area metal–organic framework MIL‐101: an efficient catalyst for Sonogashira coupling of aryl and heteroaryl bromides with alkynes 下载免费PDF全文
Manne Annapurna T. Parsharamulu P. Vishnuvardhan Reddy M. Suresh Pravin R. Likhar Mannepalli Lakshmi Kantam 《应用有机金属化学》2015,29(4):234-239
Palladium nanoparticle‐incorporated metal–organic framework MIL‐101 (Pd/MIL‐101) was successfully synthesized and characterized using X‐ray diffraction, nitrogen physisorption, X‐ray photoelectron, UV–visible and infrared spectroscopies, and transmission electron microscopy. The characterization techniques confirmed high porosity and high surface area of MIL‐101 and high stability of nano‐size palladium particles. Pd/MIL‐101 nanocomposite was investigated for the Sonogashira cross‐coupling reaction of aryl and heteroaryl bromides with various alkynes under copper‐free conditions. The reusability of the catalyst was tested for up to four cycles without any significant loss in catalytic activity. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
68.
We study the full counting statistics of transport electrons through a semiconductor two-level quantum dot with Rashba spin–orbit (SO) coupling, which acts as a nonabelian gauge field and thus induces the electron transition between two levels along with the spin flip. By means of the quantum master equation approach, shot noise and skewness are obtained at finite temperature with two-body Coulomb interaction. We particularly demonstrate the crucial effect of SO coupling on the super-Poissonian fluctuation of transport electrons, in terms of which the SO coupling can be probed by the zero-frequency cumulants. While the charge currents are not sensitive to the SO coupling. 相似文献
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We summarize the results of our recent work on Bäcklund transformations (BTs), particularly focusing on the relation between BTs and infinitesimal symmetries. We present a BT for an associated Degasperis–Procesi (aDP) equation and its superposition principle and investigate the solutions generated by applying this BT. Following our general methodology, we use the superposition principle of the BT to generate the infinitesimal symmetries of the aDP equation. 相似文献