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41.
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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Chemical versus Electrochemical Synthesis of Carbon Nano‐onion/Polypyrrole Composites for Supercapacitor Electrodes
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Olena Mykhailiv Monika Imierska Martyna Petelczyc Prof. Dr. Luis Echegoyen Dr. Marta E. Plonska‐Brzezinska 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(15):5783-5793
The development of high‐surface‐area carbon electrodes with a defined pore size distribution and the incorporation of pseudo‐active materials to optimize the overall capacitance and conductivity without destroying the stability are at present important research areas. Composite electrodes of carbon nano‐onions (CNOs) and polypyrrole (Ppy) were fabricated to improve the specific capacitance of a supercapacitor. The carbon nanostructures were uniformly coated with Ppy by chemical polymerization or by electrochemical potentiostatic deposition to form homogenous composites or bilayers. The materials were characterized by transmission‐ and scanning electron microscopy, differential thermogravimetric analyses, FTIR spectroscopy, piezoelectric microgravimetry, and cyclic voltammetry. The composites show higher mechanical and electrochemical stabilities, with high specific capacitances of up to about 800 F g?1 for the CNOs/SDS/Ppy composites (chemical synthesis) and about 1300 F g?1 for the CNOs/Ppy bilayer (electrochemical deposition). 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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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
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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