Convex duality for finite-fuel problems in singular stochastic control

Upon introducing a finite-fuel constraint in a stochastic control system, the convex duality formulation can be set up to represent the original singular control problem as a minimization problem over the space of vector measures at each level of available fuel. This minimization problem is imbedded tightly into a related weak problem, which is actually a mathematical programming problem over a convex,w*-compact space of vector-valued Radon measures. Then, through the Fenchel duality principle, the dual for the finite-fuel control problems is to seek the maximum of smooth subsolutions to a dynamic programming variational inequality. The approach is basically in the spirit of Fleming and Vermes, and the results of this paper extend those of Vinter and Lewis in deterministic control problems to the finite-fuel problems in singular stochastic control. Meanwhile, we also obtain the characterization of the value function as a solution to the dynamic programming variational inequality in the sense of the Schwartz distribution.The author is much indebted to Professor Wendell H. Fleming for his constant support and many helpful discussions during the preparation of this paper.     

Cellulose-poly(vinyl pyrrolidone) blends studied by scanning electron microscopy and dynamic mechanical measurements

New polymer blends based on cellulose and poly(vinyl pyrrolidone) (PVP) were obtained using a mixture of N=methyl morpholine N-oxide (NMMO) and dimethylsulfoxide (DMSO) as a common solvent system. Materials are obtained after the removing of NMMO-DMSO in three of their different solvents, namely i) H₂O, ii) a mixture 95/5 vol/vol hexamethyl phosphororri amide (HMPA) DMSO and iii) a mixture of 95/5 vol/vol dioxan/water.Scanning electron microscopy techniques were extensively used and lead to the conclusion that all these blends in the composition range 25/75 w/w to 75/25 w/w cellulose/PVP are two-phase systems in which cellulose forms a continuous phase. Preliminary results from calorimetric and dynamic mechanical measurements confirm these observations. Furrthermore, it is shown that using dioxanwater preserves the initial cellulose PVP composition, allowing to get blends with the desired PVP fraction. Although it is not the case with HMPA/DMSO which dissolves a part of PVP, its use leads to assymmetric, porous structures.     

Effect of AlN content on the performance of brominated epoxy resin for printed circuit board substrate

Polymer matrix composites, based on brominated epoxy, a type of material widely used in printed circuit boards (PCBs), as matrix and AlN particle as filler were prepared. The influences of AlN content on the mechanical, thermal, and electrical properties of the composites were investigated by uniaxial tensile test, TMA, thermal conductivity measurement, DMA, and dielectric properties measurement. It was found that the properties of composites monotonically varied with AlN content except that maximum tensile strength and strain of composites corresponded to a filler content of 10 wt %. The results of DMA also showed the AlN reinforcement was more pronounced above T_g, and the peak area of tan δ versus T curves decreased with AlN content, which implied the damping capacity of the composite gradually decreased. The increase in T_g and decrease in damping were probably due to strong interaction between the AlN and epoxy matrix inhibiting the mobility of the epoxy chain. In addition, different theoretical models reported in the literature were used to predict the E, CTE, k, and D_k, and compared with the experimental data. Finally, suitable models were recommended in the present materials system. For the significant improvement of performance of epoxy, we can conclude that these composite materials may be promising for PCB substrate. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1662–1674, 2007     

双模SU（1,1）相干态场与级联三能级原子相互作用的动力学

讨论了关联双模ＳＵ（１，１）相干态场与级联三能级原子的相互作用对原子动力学行为的影响，也研究了双模场的量广场的量子统计性质随时间的演化。通过数值计算，发现了一些新的演化规律。     

求解交变载荷下异形板动力响应的Gurtin半解析法

该方法以Ｇｕｒｔｉｎ变分原理为基础，在空间域作有限元离散，时间域取级数。本文研究了在交变载荷ｑ（ｘ，ｙ，ｔ）＝Ｐ（ｘ，ｙ）ｓｉｎωｔ作用下任意形状板时域级数的取法，使得各种支承条件的动力响应问题均可由本计算模式得到具有相当精度和效率的解。     

Two-phase optimization of coal strategies at a power station

Development of optimal coal mining and stockpiling strategies for a new 960 MW thermal power station depends strongly on the operation of New Zealand's mixed hydro/thermal power system. To overcome the large dimensionality of the problem the optimization proceeds in two phases for each future scenario studied. Phase 1 finds optimal hydro operating strategies with thermal generation in merit order of marginal fuel costs. It uses stochastic dynamic programming. The hydro generating strategies are used as input to the phase 2 stochastic simulation of the coal mining and stockpiling operation at the new thermal station. Finally, a strategy is identified which is a priori best over all future scenarios of industrial development and oil prices studied.     

OPTIMAL RECOVERY OF A SHARED RESOURCE STOCK: A DIFFERENTIAL GAME MODEL WITH EFFICIENT MEMORY EQUILIBRIA

We consider an optimal two-country management of depleted transboundary renewable resources. The management problem is modelled as a differential game, in which memory strategies are used. The countries negotiate an agreement among Pareto efficient harvesting programs. They monitor the evolution of the agreement, and they memorize deviations from the agreement in the past. If the agreement is observed by the countries, they continue cooperation. If one of the countries breaches the contract, then both countries continue in a noncooperative management mode for the rest of the game. This noncooperative option is called a threat policy. The credibility of the threats is guaranteed by their equilibrium property. Transfer or side payments are studied as a particular cooperative management program. Transfer payments allow one country to buy out the other from the fishery for the purpose of eliminating the inefficiency caused by the joint access to the resources. It is shown that efficient equilibria can be reached in a class of resource management games, which allow the use of memory strategies. In particular, continuous time transfer payments (e.g., a share of the harvest) should be used instead of a once-and-for-all transfer payment.     

Hybrid algorithm for sequencing with bicriteria

This paper presents a solution algorithm for a single machine scheduling problem with two criteria: total tardiness and total flow time. Theoretical results of precedence properties which are respected by all nondominated schedules are first derived. These precedence properties are then incorporated into a multiple-criteria dynamic programming framework to improve the computational efficiency. Results of the computational experiment and the average behavior (computation time and efficiency) of the algorithm are reported.This investigation was supported in part by University of Kansas General Research Allocation No. 3470-20-0038 and the University of Kansas School of Business Research Fund provided by the Fourth National Bank and Trust Company, Wichita. The ideas and opinions expressed herein are solely those of the author. The author especially wants to thank Professor P. L. Yu for valuable comments on an earlier draft of this paper.     

Optimal control of diffusion processes with reflection

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.     

Macro-Scale Dynamic Effects in Homogeneous and Heterogeneous Porous Media

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.