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991.
M. L. Puterman 《Journal of Optimization Theory and Applications》1977,22(1):103-116
In this paper, we consider the problem of optimally controlling a diffusion process on a closed bounded region ofR
n with reflection at the boundary. Employing methods similar to Fleming (Ref. 1), we present a constructive proof that there exists an optimal Markov control that is measurable or lower semicontinuous. We prove further that the expected cost function corresponding to the optimal control is the unique solution of the quasilinear parabolic differential equation of dynamic programming with Neumann boundary conditions and that there exists a diffusion process (in the sense of Stroock and Varadhan) corresponding to the optimal control.This work was partially supported by the National Science Foundation, Grant No. GK-18339, by the Office of Naval Research, Grant No. NR-042-264, and by the National Research Council of Canada, Grant No. A3609.The author would like to thank S. R. Pliska, J. Pisa, and N. Trudinger for helpful suggestions. He is especially grateful to Professor A. F. Veinott, Jr., for help and advice in the preparation of the doctoral dissertation, on which part of this paper is based. Finally, he wishes to thank one of the referees for the careful reading and constructive comments on an earlier version of this paper. 相似文献
992.
993.
It is known that the classical capillary pressure-saturation relationship may be deficient under non-equilibrium conditions when large saturation changes may occur. An extended relationship has been proposed in the literature which correlates the rate of change of saturation to the difference between the phase pressures and the equilibrium capillary pressure. This linear relationship contains a damping coefficient, \tau, that may be a function of saturation. The extended relationship is examined at the macro-scale through simulations using the two-phase simulator MUFTE-UG. In these simulations, it is assumed that the traditional equilibrium relationship between the water saturation and the difference in fluid pressures holds locally. Steady-state and dynamic numerical experiments are performed where a non-wetting phase displaces a wetting phase in homogeneous and heterogeneous domains with varying boundary conditions, domain size, and soil parameters. From these simulations the damping coefficient can be identified as a (non-linear) function of the water saturation. It is shown that the value of increases with an increased domain size and/or with decreased intrinsic permeability. Also, the value of for a domain with a spatially correlated random distribution of intrinsic permeability is compared to a homogeneous domain with equivalent permeability; they are shown to be almost equal. 相似文献
994.
995.
B. Blackadar recently proved that any full corner in a unital C*-algebra has K-theoretic stable rank greater than or equal to the stable rank of . (Here is a projection in , and fullness means that .) This result is extended to arbitrary (unital) rings in the present paper: If is a full idempotent in , then . The proofs rely partly on algebraic analogs of Blackadar's methods and partly on a new technique for reducing problems of higher stable rank to a concept of stable rank one for skew (rectangular) corners . The main result yields estimates relating stable ranks of Morita equivalent rings. In particular, if where is a finitely generated projective generator, and can be generated by elements, then .
996.
M. Barraa 《Proceedings of the American Mathematical Society》2005,133(6):1723-1726
Let and denote two -tuples of operators with and Let denote the elementary operators defined on the Hilbert-Schmidt class by We show that
Here is the essential numerical range, is the joint numerical range and is the joint essential numerical range.
Here is the essential numerical range, is the joint numerical range and is the joint essential numerical range.
997.
This study investigates how to dynamically allocate resources with a given budget for advertising through Web portals using keyword-activated banner ads on the Internet. Identifying the factors that affect the potential number of banner ad clickthroughs in each portal, we show that the process of budget allocation between the two types of portals (generic vs specialized) that leads to the largest banner clicksthrough in the long run is an optimal control problem. Using techniques of dynamic programming, we find analytical solutions for the optimal budgeting decisions. Our analysis shows that an advertisers optimal portal budgeting depends nonlinearly on the number of visitors who type the same trigger keyword and the average clicksthrough rates, as well as on the advertiser and ad effectiveness. Further, we find that the maximal number of banner clickthroughs from both portals, at time t, depends on the remaining budget until the end of the planning period. The analytical results have useful managerial insight. One of the interesting features of our solution shows that, while a large visitor base may favor the generic portal, other parameters may affect it unfavorably: e.g., lower clickthrough rates of keyword banners from a more heterogeneous audience. Using a specificaction that is consistent with empirical observations, we show that, in the long run, an advertiser must always spend more ad money at the specialized portal. 相似文献
998.
O.?E.?Barndorff-NielsenEmail author N.?N.?Leonenko 《Methodology and Computing in Applied Probability》2005,7(3):335-352
Stationary processes with prescribed one-dimensional marginal laws and long-range dependence are constructed. The asymptotic
properties of the spectral densities are studied. The possibility of Mittag-Leffler decay in the autocorrelation function
of superpositions of Ornstein-Uhlenbeck type processes is proved.
AMS 2000 Subject Classification Primary 60E07, 60G10, 60G18
Secondary 62M10, 62P05
Supported by the Danish National Research Foundation and EPSRC grant RCMT091.
Partially supported by the ARC grants DP 0345577, DP0559807 and EPSRC grant RCMT091. 相似文献
999.
Metastability in the Ising model is studied in two ways. In a dynamical Monte Carlo model, metastable magnetization and lifetime are measured for various magnetic fields and low temperatures. Following up a proposed relation between analytic continuation of transfer matrix eigenvalues and metastability, transfer matrix eigenvalues are studied. We examine the extent to which these approaches agree. The Monte Carlo data also provide quantitative support for the critical droplet model for decay. 相似文献
1000.
李继猛 《浙江大学学报(理学版)》1959,46(3):309-314
研究了时标上的一类具有阻尼项的二阶广义Emden-Fowler型泛函动态方程的振荡性,利用时标上的微积分理论和广义的Riccati变换及不等式技巧,建立了该方程振荡的若干判别准则, 推广且改进了一些已有的结果,并用具体实例来说明本文的主要结论。 相似文献