可解内生生育率的C-K模型

Abstract. In this paper,a C-K model with solvable endogenous fertility under the strongly addi-tive utility function is presented. The discrimination conditions of the existence of the nonzerosteady states are given. Under a kind of utility function and production function,we prove thatthese conditions are satisfied and the economy at least has an optimal growth path. The position-al relationship of the multiple steady states on the plane is discussed when multiple steady statesand multiple growth paths exist. By numerical analysis ,the fertility decreses with the per capitacapital and per capita consumption increasing and increases with the per capita capital and percapita consumption decreasing on the economic growth path are obtained.     

EXISTENCE AND REGULARITY OF SOLUTIONS TO MODEL FOR LIQUID MIXTURE OF ^3HE-^4HE

Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper.First,it is proved that this system possesses a unique global weak solution in H 1(,C × R) by using Galerkin method.Secondly,by using an iteration procedure,regularity estimates for the linear semigroups,it is proved that the model for liquid mixture of 3He-4He has a unique solution in Hk(,C × R) for all k ≥ 1.     

OPTIMAL IMPULSIVE CONTROL IN COMPETITIVE SYSTEM

In this paper,the impulsive exploitation of two species periodic competitive system is considered.First,we show that this type of system with impulsive har- vesting has a unique positive periodic solution,which is globally asymptotically stable.Further,by choosing the maximum total revenues as the management objective,we investigate the optimal harvesting policies for periodic competi- tive system with impulsive harvesting.Finally,we obtain the optimal time to harvest and optimal population level.     

UTILITY TRAP THEOREM FOR SUBJECTIVE DECISION

In this paper, We give a mathematical model for decision With multiple goals at hierarchy process. We study problems arising from the non-program decision. Decision theory is concerned with selecting an alternative among a set of of alternatives, A choice of a optimal action is determined by choosing the action having the highest expected utility. The expected utility of each action is determined by the utility of event with its probability of occurence.     

动态投入产出系统的稳定性分析

The dynamic input-output model is well known in economic theory and practice. In this paper, the asymptotic stability and balanced growth solutions of the dynamic input-output system are considered. Under some natural assumptions which do not require the technical coefficient matrix to be indecomposable,it has been proved that the dynamic input-output system is not asymptotically stable and the closed dynamic input-output model has a balanced growth solution.     

Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm

In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.     

A SOLVABLE ONE-DIMENSIONAL ALLOCATION DECISION MODEL OF RENEWABLE RESOURCES

In the paper, the determinate atlecation decision model and the probabilistic allocation decision model of a kind of renewable resource are separatly studied by means of dynamic programming, and the optimal allocation policy is given under some special conditions.     

Optimal models with maximizing probability of first achieving target value in the preceding stages

Decision makers often face the need of performance guarantee with some sufficiently high probability. Such problems can be modelled using a discrete time Markov decision process (MDP) with a probability criterion for the first achieving target value. The objective is to find a policy that maximizes the probability of the total discounted reward exceeding a target value in the preceding stages. We show that our formulation cannot be described by former models with standard criteria. We provide the properties of the objective functions, optimal value functions and optimal policies. An algorithm for computing the optimal policies for the finite horizon case is given. In this stochastic stopping model, we prove that there exists an optimal deterministic and stationary policy and the optimality equation has a unique solution. Using perturbation analysis, we approximate general models and prove the existence of e-optimal policy for finite state space. We give an example for the reliability of the satellite sy     

FORMATION OF NECROTIC CORES IN THE GROWTH OF TUMORS： ANALYTIC RESULTS

In this article, the author studies the mechanism of formation of necrotic cores in the growth of tumors by using rigorous analysis of a mathematical model. The model modifies a corresponding tumor growth model proposed by Byrne and Chaplain in 1996, in the case where no inhibitors exist. The modification is made such that both necrotic tumors and nonnecrotic tumors can be considered in a joint way. It is proved that if the nutrient supply is below a threshold value, then there is not dormant tumor, and all evolutionary tumors will finally vanish. If instead the nutrient supply is above this threshold value then there is a unique dormant tumor which can either be necrotic or nonnecrotic, depending on the level of the nutrient supply and the level of dead-cell dissolution rate, and all evolutionary tumors will converge to this dormant tumor. It is also proved that, in the second case, if the dormant tumor is necrotic then an evolutionary tumor will form a necrotic core at a finite time, and if the dormant tumor is nonnecrotic then an evolutionary tumor will also be nonnecrotic from a finite time.     

OPTIMAL CONTROL PROBLEM FOR A PERIODIC PREDATOR-PREY MODEL WITH AGE-DEPENDENCE

In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur's theorem and optimality condition is derived by means of normal cone.     

具有内生人口规模的城市经济增长模型

本文研究了城市经济增长与人口规模的相互关系.通过引入含消费与舒适度的双变量效用函数,提出了城市居民效用最大化问题.利用动态优化与动力系统,得出描述模型的二维动力系统,具有唯一双曲型平衡点和优化问题存在唯一最优增长路径.因而,对城市经济增长存在最优的人口规模.     

内生公共支出效用指数的经济优化配置模型

通过将公共投资指数与社会生产总量联系起来,引入含消费与公共支出效用指数的双变量效用函数,提出社会效用最大化问题.求解优化问题得到描述模型的二维动力系统,首先证明了系统存在唯一的均衡点,并利用相图分析了模型存在唯一的最优路径.     

Decentralized Algorithm for Centralized Variational Inequalities in Network Resource Allocation

Decentralized algorithms would be useful for making network resource allocations in large-scale and complex system networks because such networks tend to lack centralized operators and are subject to continuous infrastructure improvements. In this paper, we consider a variational inequality for network resource allocation and devise a decentralized allocation algorithm for it. The proposed algorithm enables each user in the network to decide its own optimal resource allocation in cooperation with other users without using other users’ private information such as their utility functions. Moreover, we present a convergence analysis on the algorithm and apply it to the network resource allocation problem.     

A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin’s irrigation areas, Gansu Province, China. In this study, the irrigation areas’ economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties.     

Arrangement Increasing Resource Allocation

Consider a system composed of several units. The performance of each unit can be affected by providing a portion of a limited amount of costly resources available. An allocation of resources to a unit results in a unit’s response that depends on the level of resources allocated to it and some of its random parameters. In this paper we consider cases where each unit has one or two random parameters. The overall performance of the system is mapped by a function on the vector of responses generated by all the units in the system. Our interest is in identifying the conditions on the response function of the units, the system performance function and the random parameters under which the random system performance as a function of the resource allocation has stochastic arrangement increasing property. This allows one to substantially reduce the number of allocation that needs to be searched to identify an optimal allocation that maximizes the expected utility derived from the system response as a result of the resource allocation.     

Optimization models for assessing the peak capacity utilization of intelligent transportation systems

With limited economic and physical resources, it is not feasible to continually expand transportation infrastructure to adequately support the rapid growth in its usage. This is especially true for traffic coordination systems where the expansion of road infrastructure has not been able to keep pace with the increasing number of vehicles, thereby resulting in congestion and delays. Hence, in addition to striving for the construction of new roads, it is imperative to develop new intelligent transportation management and coordination systems. The effectiveness of a new technique can be evaluated by comparing it with the optimal capacity utilization. If this comparison indicates that substantial improvements are possible, then the cost of developing and deploying an intelligent traffic system can be justified. Moreover, developing an optimization model can also help in capacity planning. For instance, at a given level of demand, if the optimal solution worsens significantly, this implies that no amount of intelligent strategies can handle this demand, and expanding the infrastructure would be the only alternative. In this paper, we demonstrate these concepts through a case study of scheduling vehicles on a grid of intersecting roads. We develop two optimization models namely, the mixed integer programming model and the space-time network flow model, and show that the latter model is substantially more effective. Moreover, we prove that the problem is strongly NP-hard and develop two polynomial-time heuristics. The heuristic solutions are then compared with the optimal capacity utilization obtained using the space-time network model. We also present important managerial implications.     

公债市场波动、消费动态与经济增长——基于递归效用与习惯形成的分析

本文在考虑公债市场波动的经济增长模型中引入递归效用和习惯形成,建立基于递归效用和习惯形成的随机经济增长模型,求得均衡时的最优消费和政府债券需求,讨论递归效用和习惯形成对最优消费和政府债券需求的影响,推导出消费的动态路径和经济增长路径,研究递归效用和习惯形成对消费动态路径和经济增长路径的影响.     

公共资产预算配置的拍卖机制设计

本文探讨在财政部门作为政府出资人的框架下,通过设计一套可行的竞标机制来提高预算项目的配置效率。结合运用机制设计理论和拍卖理论与方法建立竞标机制设计模型,在保证竞标预算单位参与投标和真实显示自己效率的条件下最大化拍卖者——政府出资人的期望效用,并通过求解此模型得到最优的竞标机制。鉴于最优机制在形式上的复杂性,给出了第二高得分拍卖这种最优拍卖方式。最后对公共资产配置预算的规则如何确定才能减少效率损失进行了归纳。     

长江上游集装箱码头泊位——锚地系统配置策略

针对内河集装箱运输增长与内河航道制约所导致的集装箱运输系统运作效率与航运安全问题,讨论长江上游集装箱码头泊位-锚地系统最优配置策略.通过构建码头泊位-锚地系统的船舶候泊排队服务模型,推导出队长水平状态的稳态概率分布,计算出平均等待队长,并建立泊位-锚地系统配置模型,采用数值算例考察相应的最优配置策略和锚泊溢出概率.     

The impact of fat tailed returns on asset allocation

This paper analyzes the asset allocation problem of an investor who can invest in equity and cash when there is time variation in expected returns on the equity. The solution methodology is multistage stochastic asset allocation problem with decision rules. The uncertainty is modeled using economic scenarios with Gaussian and stable Paretian non-Gaussian innovations. The optimal allocations under these alternative hypothesis are compared. Our computational results suggest that asset allocation may be up to 20% different depending on the utility function and the risk aversion level of the investor. Certainty equivalent return can be increased up to .13% and utility can be improved up to .72% by switching to the stable Paretian model.