报酬函数及转移速率族均非一致有界的连续时间折扣马氏决策规划

本文首次在报酬函数及转移速率族均非一致有界的条件下，对可数状态空间，可地动集的连续时间折扣马氏决策规划进行研究，文中引入一类新的无界报酬函数，在一类新的马氏策略中，讨论了最优策略的存在性及春结构，除证明了在有界报酬和一致有界转移速率族下成立的主要结果外，本文还得到一些重要结论。     

JOINT MODEL AND CRITERION OPTIMAL EXPERIMENT DESIGN

In this paper,a new optimal design criterion--joint model and criterion optimal de-sign criterioon is put forward. The design that is subject to this criterion satisfies many kinds of lin-ear optimal criterion and D-optimal criterion on several experiment models at the same time. Theequivalent condition of this optimal design is given. Its iterative algorithm and the algorithm cover-genee are stated.     

Constrained Markov decision processes with total cost criteria: Occupation measures and primal LP

This paper is the third in a series on constrained Markov decision processes (CMDPs) with a countable state space and unbounded cost. In the previous papers we studied the expected average and the discounted cost. We analyze in this paper the total cost criterion. We study the properties of the set of occupation measures achieved by different classes of policies; we then focus on stationary policies and on mixed deterministic policies and present conditions under which optimal policies exist within these classes. We conclude by introducing an equivalent infinite Linear Program.     

Nonstationary denumerable state Markov decision processes – with average variance criterion

In this paper, we consider the nonstationary Markov decision processes (MDP, for short) with average variance criterion on a countable state space, finite action spaces and bounded one-step rewards. From the optimality equations which are provided in this paper, we translate the average variance criterion into a new average expected cost criterion. Then we prove that there exists a Markov policy, which is optimal in an original average expected reward criterion, that minimizies the average variance in the class of optimal policies for the original average expected reward criterion.     

Recent results on conditions for the existence of average optimal stationary policies

This paper concerns countable state space Markov decision processes endowed with a (long-run expected)average reward criterion. For these models we summarize and, in some cases,extend some recent results on sufficient conditions to establish the existence of optimal stationary policies. The topics considered are the following: (i) the new assumptions introduced by Sennott in [20–23], (ii)necessary and sufficient conditions for the existence of a bounded solution to the optimality equation, and (iii) equivalence of average optimality criteria. Some problems are posed.This research was partially supported by the Third World Academy of Sciences (TWAS) under Grant No. TWAS RG MP 898-152.     

Continuous time Markovian decision processes average return criterion

Continuous time Markovian decision models with countable state space are investigated. The existence of an optimal stationary policy is established for the expected average return criterion function. It is shown that the expected average return can be expressed as an expected discounted return of a related Markovian decision process. A policy iteration method is given which converges to an optimal deterministic policy, the policy so obtained is shown optimal over all Markov policies.     

Uncertain agency models with multi-dimensional incomplete information based on confidence level

This paper discusses a principal–agent problem with multi-dimensional incomplete information between a principal and an agent. Firstly, how to describe the incomplete information in such agency problem is a challenging issue. This paper characterizes the incomplete information by uncertain variable, because it has been an appropriate tool to depict subjective assessment and model human uncertainty. Secondly, the relevant literature often used expected-utility-maximization to measure the two participators’ goals. However, Ellsberg paradox indicates that expected utility criterion is not always appropriate to be regarded as decision rule. For this reason, this paper presents another decision rule based on confidence level. Instead of expected-utility-maximization, the principal’s aim is to maximize his potential income under the acceptable confidence level, and the agent’s aim depends on whether he has private information about his efforts. According to the agent’s different decision rules, three classes of uncertain agency (UA) models and their respective optimal contracts are presented. Finally, a portfolio selection problem is studied to demonstrate the modeling idea and the viability of the proposed UA models.     

允许投资组合条件下概率准则

概率准则具有一定的现实意义，其投资决策是以期望贴现资产为导向的．本文讨论了完备标准动态金融市场中在允许投资组合条件下的概率准则问题，得到了准则函数，贴现资产过程以及最优允许投资组合过程的解析表达式．期望贴现资产越大，准则函数越小。     

Split-plot designs with general minimum lower-order confounding

Split-plot designs have been widely used in industrial experiments.Up to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) criterion.Recently,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et al.proposed a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) theory.It is proved that,the GMC criterion selects optimal designs ...     

最优预测与因果关系检验

本文从信息论角度出发 ,给出了一个新的准则 ,并且证明在正态假设条件下 ,此时的最优预测与最小二乘意义下的最优预测相同 .最后 ,将此准则应用到因果关系的检验     

Borel状态空间非平稳MDP的平均方差准则

本文考虑具有 Ｂｏｒｅｌ状态空间和行动空间非平稳 ＭＤＰ的平均方差准则．首先,在遍历条件下,利用最优方程,证明了关于平均期望目标最优马氏策略的存在性．然后,通过构造新的模型,利用马氏过程的理论,进一步证明了在关于平均期望目标是最优的一类马氏策略中,存在一个马氏策略使得平均方差达到最小．作为本文的特例还得到了 Ｄｙｎｋｉｎ Ｅ． Ｂ．和 Ｙｕｓｈｋｅｖｉｃｈ Ａ． Ａ．及 Ｋｕｒａｎｏ Ｍ．等中的主要结果．     

Homogeneous and strictly homogeneous criteria for partial structures

The Galois closure on the set of relations invariant to all finite partial automorphisms (automorphisms) of a countable partial structure is established via quantifier-free infinite predicate languages (infinite languages with finite string of quantifiers respectively). Based on it the homogeneous and strictly homogeneous criteria for a countable partial structure as well as an ultrahomogeneous criterion for a countable relational structure are found. Next it is shown that infinite languages with a finite string of quantifiers cannot determine the corresponding Galois closure for relations invariant to all automorphisms of an uncountable partial structure.     

Continuous time Markov decision programming with average reward criterion and unbounded reward rate

This paper deals with the continuous time Markov decision programming (briefly CTMDP) with unbounded reward rate. The economic criterion is the long-run average reward. To the models with countable state space and compact metric action sets, we present a set of sufficient conditions to ensure the existence of the stationary optimal policies.This paper was prepared with the support of the National Youth Science Foundation.     

平面应力状态断裂强度的椭圆准则分析

简要分析了近年来提出的一个断裂准则——椭圆准则的基本特征,导出了它在主应力坐标系下的基本方程.根据所导出的基本方程,获得了平面应力条件下椭圆准则理论断裂强度曲线的完整描述关系,并分析讨论了破坏发生的方位及断裂形式与材料本征力学性质参数之间的联系.与既有理论结果及实验现象的对比解释了椭圆准则在材料相关参数确定方面的局限性.当应力状态相关材料特征参数在拉伸区和压缩区均作为常数时,获得了铸铁和混凝土平面应力状态下的断裂强度曲线.与相关实验数据的对比表明,它们在拉伸区能较好地吻合,但压缩区的差异十分显著,进一步证实了材料特征参数随应力状态变化规律对椭圆准则发展的必要性.     

Hurwicz model of uncertain optimal control with jump

How to choose the optimization criterion of the objective function is an important issue for uncertain optimal control. The Hurwicz criterion is a flexible optimization criterion attempting to find the intermediate area between the extremes posed by the optimistic and pessimistic criteria. Based on uncertainty theory, in this paper, we establish a new uncertain optimal control model with jump by making use of Hurwicz criterion to optimize an uncertain objective function. By applying Bellman's principle of optimality, the principle of optimality for the proposed model is presented and then the equation of optimality is derived. Finally, an example is given to show the the effectiveness of the results obtained.     

回归系数的广义岭型主相关估计及其优良性

In this paper, we propose a new biased estimator of the regression parameters, the generalized ridge and principal correlation estimator. We present its some properties and prove that it is superior to LSE （least squares estimator）, principal correlation estimator, ridge and principal correlation estimator under MSE （mean squares error） and PMC （Pitman closeness） criterion, respectively.     

Mixed eigenvalues of discrete p-Laplacian

This paper deals with the principal eigenvalue of discrete p-Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequalities. The main goal is the quantitative estimates of the eigenvalue. The paper begins with the case having reflecting boundary at origin and absorbing boundary at infinity. Several variational formulas are presented in different formulation： the difference form, the single summation form, and the double summation form. As their applications, some explicit lower and upper estimates, a criterion for positivity （which was known years ago）, as well as an approximating procedure for the eigenvalue are obtained. Similarly, the dual case having absorbing boundary at origin and reflecting boundary at presented at the end of Section 2 to infinity is also studied. Two examples are illustrate the value of the investigation.     

Recurrence set-relations in stochastic multiobjective dynamic decision processes

Finite horizon stochastic dynamic decision processes with R^p valued additive returns are considered. The optimization criterion is a partial-order preference relation induced from a convex cone in R^p . The state space is a countable set, and the action space is a compact metric spaces. The optimal value function, which is of a set-valued mapping, is defined. Under certain assumptions on the continuity of the reward vector and the transition probability, a system of a recurrence set-relations concerning the optimal value functions is given.