An elementary approach to optimal discrete-time search strategies

Optimal strategies are known for the finite and infinite horizon discrete-time search with constant unit cost and without recall. These strategies were obtained in the theory of optimal stopping, based on the martingale convergence theorem and other tools from probability theory. We present here an elementary approach to these problems, relying only on routine calculation of expected values. In the finite horizon case, the solution utilizes a simple form of backward induction, in conjunction with a nonlinear dynamical system, to compute the parameters of the optimal strategy. An elementary proof is also given that a simple threshold search is optimal among all strategies with finite expected total cost.     

The optimal control related to Riemannian manifolds and the viscosity solutions to Hamilton–Jacobi–Bellman equations

In this paper we study the optimal stochastic control problem for stochastic differential equations on Riemannian manifolds. The cost functional is specified by controlled backward stochastic differential equations in Euclidean space. Under some suitable assumptions, we conclude that the value function is the unique viscosity solution to the associated Hamilton–Jacobi–Bellman equation which is a fully nonlinear parabolic partial differential equation on Riemannian manifolds.     

On Sequenial Tests of the Bincknial Distribution

In this paper, we consider the detailed characteristics of the standard sequential test of a simple hypothesis versus a single alternative for the case of the binomial distribution. A method is developed which permits evaluation of the associated probabilities of acceptance and/or rejection of the null hypothesis at each stage. From this information, the quantitative features of the test (Operating Characteristic and test termination probability) are completely determined. Curves are presented to facilitate assessment of the sequential procedure in practical cases. A sequential test is compared with a fixed sample size test having approximately the same Operating Characteristic. Wald's approximation for the average sample number is compared with exact values.     

反向映射法在双列圆锥滚子汽车轮毂轴承设计中的应用

通过对比分析国内外双列圆锥滚子汽车轮毂轴承产品系列的结构特征和参考目前国内(单列)圆锥滚子轴承设计方法,分析了反向映射法在双列圆锥滚子汽车轮毂轴承结构设计中的应用。     

Bootstrap prediction intervals in state–space models

Abstract.  Prediction intervals in state–space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, with the true parameters substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty caused by parameter estimation. Second, the Gaussianity of future innovations assumption may be inaccurate. To overcome these drawbacks, Wall and Stoffer [ Journal of Time Series Analysis (2002) Vol. 23, pp. 733–751] propose a bootstrap procedure for evaluating conditional forecast errors that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. In this article, we propose a bootstrap procedure for constructing prediction intervals directly for the observations, which does not need the backward representation of the model. Consequently, its application is much simpler, without losing the good behaviour of bootstrap prediction intervals. We study its finite-sample properties and compare them with those of the standard and the Wall and Stoffer procedures for the local level model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series.     

Cold repeated forming of compact for aluminium foam

A cold repeated forming process of compacts for producing metal foams was developed in order to strongly bond powder particles. In this process, the compact undergoes severe plastic deformation for the strong bonding of particles by repeated backward extrusion and cup compression, and thus the compact largely foams owing to the accumulation of gas released from blowing agents inside the compact during heating. The cold repeated forming process without heating is much simpler than that for the conventional hot extrusion process. The relative density of the foam was decreased by adding silicon powder to the compact, and an aluminium foam having a relative density of 0.27 was obtained using two repeats of backward extrusion and cup compression, 1.5 mass% titanium hydride powder and 4 mass% silicon powder. In addition, a one-piece foam was successively produced from the bonding of two compacts during the foaming in a die. It was found that the cold repeated forming of compacts is effective for the production of metal foams.     

A fast and efficient load flow technique for unbalanced distribution system

This paper presents a fast and efficient load flow technique for unbalanced distribution system. The proposed load flow technique is derived by promulgating the concept of conventional backward forward sweep (BFS) technique of power flow study for distribution system. The proposed technique employs a novel load-impedance matrix (LIM) to calculate the bus voltages in a single step unlike the conventional BFS approach which involves two separate steps (backward sweep and forward sweep) to perform the same and this improvement is claimed as the novelty of this work. This distinctive feature makes the proposed algorithm faster in operation. Nodal voltages, at any iteration, may be calculated, directly, from the values obtained in the previous iteration by utilizing LIM. A simple concept of set theory is adopted here to construct the LIM. Special treatments are also included in this method to analyze weakly meshed systems. The proposed technique is flexible enough to accommodate any sort of changes in the existing network topology through LIM. It is tested on different three-phase balanced and unbalanced radial distribution systems as well as weakly meshed networks for load flow study. A separate case study is also presented to check the validity of the proposed load flow technique for various transformer connections. The obtained results demonstrate the effectiveness of the proposed technique. Furthermore, performance comparison reveals that the proposed algorithm is, computationally, faster and robust than the conventional power flow techniques reported in the recent state-of-the-art literatures.     

Maximum principle for mean-field jump–diffusion stochastic delay differential equations and its application to finance

This paper investigates a stochastic optimal control problem with delay and of mean-field type, where the controlled state process is governed by a mean-field jump–diffusion stochastic delay differential equation. Two sufficient maximum principles and one necessary maximum principle are established for the underlying system. As an application, a bicriteria mean–variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques. Under certain conditions, explicit expressions are provided for the efficient portfolio and the efficient frontier, which are as elegant as those in the classical mean–variance problem without delays.     

一阶谓词逻辑的图形推理法

针对已有一阶谓词逻辑推理方法中存在的推理效率低等问题,研究一种基于谓词/变迁系统的图形推理法。定义了描述谓词间与/或关系的谓词-与/或图,借助谓词-与/或图表示谓词/变迁系统,提出一种实现反向推理的目标制导的图形推理法。该方法推理效率高,较已有的推理方法具有一定的优越性。