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2.
《Indagationes Mathematicae》2021,32(6):1229-1239
3.
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
4.
An M/G/1 retrial queueing system with additional phase of service and possible preemptive resume service discipline is considered. For an arbitrarily distributed retrial time distribution, the necessary and sufficient condition for the system stability is obtained, assuming that only the customer at the head of the orbit has priority access to the server. The steady-state distributions of the server state and the number of customers in the orbit are obtained along with other performance measures. The effects of various parameters on the system performance are analysed numerically. A general decomposition law for this retrial queueing system is established. 相似文献
5.
J.V.P. de OliveiraA.V. Cardona M.T. VilhenaR.C. Barros 《Journal of Quantitative Spectroscopy & Radiative Transfer》2002,73(1):55-62
We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTSN) methods applied to the radiative transfer equation in the discrete ordinates (SN) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” SN problems by using the LTSN method. We show some numerical experiments for a typical model problem. 相似文献
6.
Zhong-Qing Wang 《Journal of Mathematical Analysis and Applications》2002,274(1):374-403
An orthogonal system of rational functions is discussed. Some inverse inequalities, imbedding inequalities and approximation results are obtained. Two model problems are considered. The stabilities and convergences of proposed rational spectral schemes and rational pseudospectral schemes are proved. The techniques used in this paper are also applicable to other problems on the whole line. Numerical results show the efficiency of this approach. 相似文献
7.
Mariano J. Valderrama 《商业与工业应用随机模型》1991,7(1):93-106
Alternative procedures for representing a stochastic signal as a denumerable series with uncorrelated terms are developed. The study includes considerations about parametric rescaling and its repercussions on the orthogonal expansion, as well as numerical techniques for approaching such an expansion. In addition, applications to the Gaussian characterization of stochastic signals, filtering and stochastic modelling are treated. 相似文献
8.
T-型树谱唯一性的一个简单刻画 总被引:1,自引:0,他引:1
图G称为谱唯一的,如果任何与G谱相同的图一定与G同构.一棵树称为T-型树如果其仅有一个最大度为3的顶点.本文给出了T-型树谱唯一性的一个简单刻画,从而完全解决了T-型树的谱唯一性问题. 相似文献
9.
《组合设计杂志》2002,10(5):283-293
An Orthogonal Double Cover (ODC) of the complete graph Kn by an almost‐hamiltonian cycle is a decomposition of 2Kn into cycles of length n?1 such that the intersection of any two of them is exactly one edge. We introduce a new class of such decompositions. If n is a prime, the special structure of such a decomposition allows to expand it to an ODC of Kn+1 by an almost‐hamiltonian cycle. This yields the existence of an ODC of Kp+1 by an almost‐hamiltonian cycle for primes p of order 3 mod 4 and its eventual existence for arbitrary primes p. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 283–293, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10011 相似文献
10.
This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.