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21.
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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Interactions of Pt‐ttpy with G‐Quadruplexes Originating from Promoter Region of the c‐myc Gene Deciphered by NMR and Gel Electrophoresis Analysis 下载免费PDF全文
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Experimental and Theoretical Studies on the Rearrangement of 2‐Oxoazepane α,α‐Amino Acids into 2′‐Oxopiperidine β2,3,3‐Amino Acids: An Example of Intramolecular Catalysis 下载免费PDF全文
Dr. Diego Núñez‐Villanueva Dr. M. Ángeles Bonache Laura Lozano Dr. Lourdes Infantes Prof. José Elguero Prof. Ibon Alkorta Prof. M. Teresa García‐López Dr. Rosario González‐Muñiz Dr. Mercedes Martín‐Martínez 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(6):2489-2500
Enantiopure β‐amino acids represent interesting scaffolds for peptidomimetics, foldamers and bioactive compounds. However, the synthesis of highly substituted analogues is still a major challenge. Herein, we describe the spontaneous rearrangement of 4‐carboxy‐2‐oxoazepane α,α‐amino acids to lead to 2′‐oxopiperidine‐containing β2,3,3‐amino acids, upon basic or acid hydrolysis of the 2‐oxoazepane α,α‐amino acid ester. Under acidic conditions, a totally stereoselective synthetic route has been developed. The reordering process involved the spontaneous breakdown of an amide bond, which typically requires strong conditions, and the formation of a new bond leading to the six‐membered heterocycle. A quantum mechanical study was carried out to obtain insight into the remarkable ease of this rearrangement, which occurs at room temperature, either in solution or upon storage of the 4‐carboxylic acid substituted 2‐oxoazepane derivatives. This theoretical study suggests that the rearrangement process occurs through a concerted mechanism, in which the energy of the transition states can be lowered by the participation of a catalytic water molecule. Interestingly, it also suggested a role for the carboxylic acid at position 4 of the 2‐oxoazepane ring, which facilitates this rearrangement, participating directly in the intramolecular catalysis. 相似文献
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Caesium carbonate supported on hydroxyapatite‐encapsulated Ni0.5Zn0.5Fe2O4 nanocrystallites as a novel magnetically basic catalyst for the one‐pot synthesis of pyrazolo[1,2‐b]phthalazine‐5,10‐diones 下载免费PDF全文
Behrooz Maleki Samaneh Barat Nam Chalaki Samaneh Sedigh Ashrafi Esmail Rezaee Seresht Farid Moeinpour Amir Khojastehnezhad Reza Tayebee 《应用有机金属化学》2015,29(5):290-295
A novel nanomagnetic basic catalyst of caesium carbonate supported on hydroxyapatite‐coated Ni0.5Zn0.5Fe2O4 magnetic nanoparticles (Ni0.5Zn0.5Fe2O4@HAP‐Cs2CO3) was prepared. This new catalyst was fully characterized using Fourier transform infrared spectroscopy, transmission and scanning electron microscopy, X‐ray diffraction and vibrating sample magnetometry techniques, and then the catalytic activity of this catalyst was investigated in the synthesis of 1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione derivatives. Also, Ni0.5Zn0.5Fe2O4@HAP‐Cs2CO3 could be reused at least five times without significant loss of activity and could be recovered easily by applying an external magnet. Thus, the developed nanomagnetic catalyst is potentially useful for the green and economic production of organic compounds. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Functional Binding Surface of a β‐Hairpin VEGF Receptor Targeting Peptide Determined by NMR Spectroscopy in Living Cells 下载免费PDF全文
Dr. Donatella Diana Anna Russomanno Dr. Lucia De Rosa Dr. Rossella Di Stasi Dr. Domenica Capasso Dr. Sonia Di Gaetano Dr. Alessandra Romanelli Dr. Luigi Russo Dr. Luca D. D'Andrea Prof. Roberto Fattorusso 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(1):91-95
In this study, the functional interaction of HPLW peptide with VEGFR2 (Vascular Endothelial Growth Factor Receptor 2) was determined by using fast 15N‐edited NMR spectroscopic experiments. To this aim, 15N uniformly labelled HPLW has been added to Porcine Aortic Endothelial Cells. The acquisition of isotope‐edited NMR spectroscopic experiments, including 15N relaxation measurements, allowed a precise characterization of the in‐cell HPLW epitope recognized by VEGFR2. 相似文献
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Given an ‐vertex pseudorandom graph and an ‐vertex graph with maximum degree at most two, we wish to find a copy of in , that is, an embedding so that for all . Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in . Here, we provide a deterministic polynomial time algorithm that finds a given in any suitably pseudorandom graph . The pseudorandom graphs we consider are ‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, . A ‐bijumbled graph is characterised through the discrepancy property: for any two sets of vertices and . Our condition on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications. 相似文献