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1.
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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Sameerah Jamal 《Journal of Differential Equations》2019,266(7):4018-4026
A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions. 相似文献
4.
Alessandro Morando Paola Trebeschi Tao Wang 《Journal of Differential Equations》2019,266(9):5397-5430
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme. 相似文献
5.
Metabolic profiles of dioscin in rats revealed by ultra‐performance liquid chromatography quadrupole time‐of‐flight mass spectrometry 下载免费PDF全文
He Zhu Jin‐Di Xu Qian Mao Hong Shen Ming Kong Jian‐Ping Chen Song‐Lin Li 《Biomedical chromatography : BMC》2015,29(9):1415-1421
Dioscin (DIS), one of the most abundant bioactive steroidal saponins in Dioscorea sp., is used as a complementary medicine to treat coronary disease and angina pectoris in China. Although the pharmacological activities and pharmacokinetics of DIS have been well demonstrated, information regarding the final metabolic fates is very limited. This study investigated the in vivo metabolic profiles of DIS after oral administration by ultra‐performance liquid chromatography quadrupole time‐of‐flight mass spectrometry method. The structures of the metabolites were identified and tentatively characterized by means of comparing the molecular mass, retention time and fragmentation pattern of the analytes with those of the parent compound. A total of eight metabolites, including seven phase I and one phase II metabolites, were detected and tentatively identified for the first time. Oxidation, deglycosylation and glucuronidation were found to be the major metabolic processes of the compound in rats. In addition, a possible metabolic pathway on the biotransformation of DIS in vivo was proposed. This study provides valuable and new information on the metabolism of DIS, which will be helpful for further understanding its mechanism of action. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
6.
Studies on metabolism of total glucosides of paeony from Paeoniae Radix Alba in rats by UPLC‐Q‐TOF‐MS/MS 下载免费PDF全文
Wenli Cao Xinguo Wang Haojie Li Xuliang Shi Wencheng Fan Shaohua Zhao Minyan Liu Liying Niu 《Biomedical chromatography : BMC》2015,29(11):1769-1779
Total glucosides of paeony are the active constituents of Paeoniae Radix Alba. In this study, a novel strategy was proposed to find more metabolites and the differences between paeoniflorin, albiflorin and total glucosides of paeony (TGP). This strategy was characterized as follows: firstly, the animals were divided into three groups (paeoniflorin, albiflorin and TGP) to identify the source of TGP metabolites from paeoniflorin or albiflorin; secondly, a generic information‐dependent acquisition scan for the low‐level metabolites was triggered by the multiple mass defect filter and dynamic background subtraction; thirdly, the metabolites were identified with a combination of data‐processing methods including mass defect filtering, neutral loss filtering and product ion filtering; finally, a comparative study was used in the metabolism of paeoniflorin, albiflorin and TGP. Based on the strategy, 18 metabolites of TGP, 10 metabolites of paeoniflorin and 13 metabolites of albiflorin were identified respectively. The results indicated that the hydrolysis, conjugation reaction and oxidization were the major metabolic pathways, and the metabolic sites were the glycosidic linkage, the ester bond and the benzene ring. This study is first to explore the metabolism of TGP, and these findings enhance our understanding of the metabolism and the interactions of paeoniflrin and albiflorin in TGP. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
7.
Michel Hébert 《Archive for Mathematical Logic》1991,31(2):133-143
Summary We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories are nonuniform. 相似文献
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几率量子隐形传态的离子阱方案 总被引:2,自引:0,他引:2
本文提出了一个在分别囚禁于不同离子阱中的两个离子间实现几率量子隐形传态的简单方案,Alice对离子1和离子2的内态进行联合测量并通过经典通道告诉Bob测量结果,Bob利用一束经典驻波场激光与离子3相互作用并控制相互作用的时间就能够在离子3上最佳几率地重现离子1的初始内态. 相似文献
10.
Using Brown's construction (J. Algebra 15 (1970) 103) of an exact 6-term sequence for a fibration of groupoids we show how an exact 9-term sequence can be associated to a fibration of bigroupoids. Applications to topology and algebra are given. 相似文献