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941.
942.
A finite difference approximation to a
hierarchical size-structured model with nonlinear growth,
mortality and reproduction rates is developed.
Existence-uniqueness of the weak solution to the model is
established and convergence of the finite-difference approximation
is proved. Simulations indicate that the monotonicity assumption on the
growth rate is crucial for the global existence of weak solutions.
Numerical results testing the efficiency of this
method in approximating the long-time behavior of the model are
presented. 相似文献
943.
Zhen-hua Guo 《应用数学学报(英文版)》2005,21(4):637-654
In this paper, we study the large time asymptotic behavior of solutions to both the Cauchy problem and the exterior problem of the Stokes approximation equations of two dimensional compressible flows. 相似文献
944.
Walter J. Gutjahr 《Methodology and Computing in Applied Probability》2006,8(1):105-133
An analytical framework for investigating the finite-time dynamics of ant colony optimization (ACO) under a fitness-proportional
pheromone update rule on arbitrary construction graphs is developed. A limit theorem on the approximation of the stochastic
ACO process by a deterministic process is demonstrated, and a system of ordinary differential equations governing the process
dynamics is identified. As an example for the application of the presented theory, the behavior of ACO on three different
construction graphs for subset selection problems is analyzed and compared for some basic test functions. The theory enables
first rough theoretical predictions of the convergence speed of ACO.
AMS 2000 Subject classification 68W20, 68W40 相似文献
945.
本文引进了一类重要的多元和型积分算子,它们具有保线性,讨论了它们的逼近性质。利用插补空间方法,建立了多元和型积分算子逼近的正定理和逆定理,给出了其逼近度与函数光滑性间的关系。 相似文献
946.
根据原子分子反应静力学和群论,确定TiH2,TiD2和TjT2的基电子状态为^3A2.应用基函数6-311G^**和密度泛函理论B3P86方法,全电子计算了氢同位素分子及其钛化物的能量E、定容热容Cv和熵S应用电子振动近似理论,即用单个分子TiH2,TiD2和TjT2中的电子和振动能量和熵近似代表他们处于固态时的能量和熵,计算所得到的金属钛的氢化热力学函数△Hc^0,△S^0,△G^0以及平衡压力与温度的关系,与文献符合很好,这表明电子振动近似理论的可应用性,选用金属钛作为中子靶是很正确的。 相似文献
947.
Let be a one-parameter family of positive integral operators on a locally compact space . For a possibly non-uniform partition of define a finite measure on the path space by using a) for the transition between any two consecutive partition times of distance and b) a suitable continuous interpolation scheme (e.g. Brownian bridges or geodesics). If necessary normalize the result
to get a probability measure. We prove a version of Chernoff's theorem of semigroup theory and tightness results which yield
convergence in law of such measures as the partition gets finer. In particular let be a closed smooth submanifold of a manifold . We prove convergence of Brownian motion on , conditioned to visit at all partition times, to a process on whose law has a density with respect to Brownian motion on which contains scalar, mean and sectional curvatures terms. Various approximation schemes for Brownian motion on are also given.
相似文献
948.
H.O. Di Rocco D.I. Iriarte J.A. Pomarico H.F. Ranea Sandoval R. Macdonald 《Journal of Quantitative Spectroscopy & Radiative Transfer》2007,105(1):68-83
In this work we present a method for determining the optical parameters of turbid media, namely its absorption coefficient (μa) and its reduced scattering coefficient . It is based on the measurement of CW transmittance profiles and analysis of the experimental data by a theoretical model based on the diffusion approximation (DA) of the radiative transfer equation (RTE). The method developed has been investigated with solid polymer probes but it could be applied for liquid materials as well. Experimental results are presented and compared to those of other authors together with a discussion about the accuracy of measurements. In addition, measurements using integrating spheres as well as Monte Carlo simulations are also presented to validate these results. 相似文献
949.
In two-phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and, to simplify the analysis, Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. © 2022 Wiley Periodicals, Inc. 相似文献
950.
This research study deals with the numerical solutions of linear and nonlinear time-fractional subdiffusion equations of distributed order. The main aim of our approach is based on the hybrid of block-pulse functions and shifted Legendre polynomials. We produce a novel and exact operational vector for the fractional Riemann–Liouville integral and use it via the Gauss–Legendre quadrature formula and collocation method. Consequently, we reduce the proposed equations to systems of equations. The convergence and error bounds for the new method are investigated. Six problems are tested to confirm the accuracy of the proposed approach. Comparisons between the obtained numerical results and other existing methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method. 相似文献