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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
2.
3.
We prove that to most of the known hypercyclic operators A on separable Banach spaces there exist compact (compact convex, compact connected) subsets K of E such that each compact (compact convex, compact connected) subset of E can be approximated with respect to Hausdorff's distance by for suitable .
Received July 8, 1997, in final form October 17, 1997 相似文献
4.
M. Brokate D. Rachinskii 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(4):385-411
The paper is concerned with the study of plasticity models described by differential equations with stop and play operators.
We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the
vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another
class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions.
The paper was written during the research stay of D. Rachinskii at the Technical University Munich supported by the research
fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grant No. 01-01-00146, 03-01-00258), and the Grants of the President of Russia (Grant No. MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged. 相似文献
5.
Saida Sultanic 《Integral Equations and Operator Theory》2006,55(4):573-595
The central question of this paper is the one of finding the right analogue of the Commutant Lifting Theorem for the Bergman
space La2. We also analyze the analogous problem for weighted Bergman spaces La,α2, − 1 < α < ∞. 相似文献
6.
Kunyu Guo 《Journal of Functional Analysis》2004,213(2):380-411
This paper mainly concerns defect operators and defect functions of Hardy submodules, Bergman submodules over the unit ball, and Hardy submodules over the polydisk. The defect operator (function) carries key information about operator theory (function theory) and structure of analytic submodules. The problem when a submodule has finite defect is attacked for both Hardy submodules and Bergman submodules. Our interest will be in submodules generated by polynomials. The reason for choosing such submodules is to understand the interaction of operator theory, function theory and algebraic geometry. 相似文献
7.
In this paper we relate the operators in the operator representations of a generalized Nevanlinna function N(z) and of the function −N(z)−1 under the assumption that z=∞ is the only (generalized) pole of nonpositive type. The results are applied to the Q-function for S and H and the Q-function for S and H∞, where H is a self-adjoint operator in a Pontryagin space with a cyclic element w, H∞ is the self-adjoint relation obtained from H and w via a rank one perturbation at infinite coupling, and S is the symmetric operator given by S=H∩H∞. 相似文献
8.
The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays, etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation. 相似文献
9.
温度对PSⅡCP4 7/D1/D2/Cytb559复合物荧光光谱特性的影响 总被引:3,自引:3,他引:0
采用激励光源为514.5 nm的分幅扫描单光子计数荧光光谱装置对经20℃、42℃和48℃不同温度处理后的反应中心复合物CP47/D1/D2/Cyt b559的荧光光谱特性进行了研究.经解析,获得不同温度处理后,CP47/D1/D2/Cyt b559复合物最大峰值未发生变化,均在682 nm,说明Chla670的能量都由Chla682接收,但损耗愈来愈小,在48℃时,损耗程度最小,而其荧光百分比未发生多大变化.振动副带~700 nm和~740 nm的中心波长都发生蓝移,在不同温度下分别为:20℃ 703 nm,749 nm;42℃ 697 nm,744 nm;48℃ 694 nm,740 nm.因此可以推测温度的升高,影响了CP47/D1/D2/Cyt b559色素蛋白的二级结构以及色素分子的空间位置,使最大峰值处的荧光强度逐渐降低,振动副带逐渐蓝移.42℃的温度已造成影响,48℃影响较大. 相似文献
10.
On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form
We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12]. 相似文献