Analysis for some properties of discrete time Markov decision processes

This paper investigates properties of the optimality equation and optimal policies in discrete time Markov decision processes with expected discounted total rewards under weak conditions that the model is well defined and the optimality equation is true. The optimal value function is characterized as a solution of the optimality equation and the structure of optimal policies is also given.     

Orientation and conformation of two [6]carbohelicenes in stretched polystyrene and a thermoresponsive polyaspartate

Two functionalized [6]carbohelicenes, one of which was also available in its two enantiomeric pure forms, were oriented in stretched polystyrene in CDCl₃, and in a recently introduced chiral thermoresponsive lyotropic polyaspartate (poly(benzyl)_0.5(phenethyl)_0.5-L-aspartate) in C₂D₂Cl₄. From the resulting ¹H,¹³C residual dipolar couplings, the helical pitch of a methylated [6]carbohelicene was determined and found to be in agreement with theoretical predictions and existing crystal structures (d(C2,C2′) ≈ 4.3 Å). For a second [6]carbohelicene with para-methoxyphenyl substituents, a clear conformational preference of the substituents was observed. The orientational properties of the two helicene enantiomers in the chiral polyaspartate are very similar, but both drastically change around 306 K. We suggest this behavior is due to an unusual phase transition in the liquid crystal.     

Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.     

Joint L1/Lp-regularized minimization in video recovery of remote sensing based on compressed sensing

L₁ regularization and L_p regularization are proposed for processing recovered images based on compressed sensing (CS). L₁ regularization can be solved as a convex optimization problem but is less sparse than L_p (0 < p < 1). L_p regularization is sparser than L₁ regularization but is more difficult to solve. This paper proposes joint L₁/L_p (0 < p < 1) regularization, which combines L_p regularization and L₁ regularization. This joint regularization is applied to recover video of remote sensing based on CS. Joint regularization is sparser than L₁ regularization but is as easy to solve as L₁ regularization. A linearized Bregman reweighted iteration algorithm is proposed to solve the joint L₁/L_p regularization problem. The performance and capabilities of the linearized Bregman algorithm and linearized Bregman reweighted algorithm for solving the joint L₁/L_p regularization model are analyzed and compared through numerical simulations.     

A computational method for geometric optimization of enhanced heat transfer devices based upon entropy generation minimization

A computational fluid dynamics‐based optimization methodology is developed, appropriate for the geometric optimization of enhanced heat transfer devices based upon the principle of entropy generation minimization, in which the objective function is evaluated from a flow field obtained by computational simulation. A quasi‐Newton optimization procedure is employed, with computation of the objective function gradients based upon a finite difference approach. The optimization procedure is developed to be general with regard to the choice of objective function, the details of the problem under consideration, and the computational methodology employed in solving the fluid flow and heat transfer problems. A novel implementation of a Taylor series‐based procedure for the fast solution of nearby problems is presented, which is found to greatly benefit the efficiency of the present methodology. Finally, a numerical experiment is presented, illustrating the use of the present method in the geometric optimization of a practical enhanced heat transfer device on the basis of the criterion of entropy generation minimization. The optimization of the fin spacing of a simple plate fin heat sink is considered, and a comparison of the computational results with results obtained by analytical optimization based upon empirical friction factor and Nusselt number correlations is given. Copyright © 2012 John Wiley & Sons, Ltd.     

The first principles investigation of ferrite magnetic response with mismatch stress

The quasi-ferrite model is proposed and an appropriate PBE exchange functional with the spin density functional theory(SDFT) is selected for the calculation of the relation between magnetic moment and residual stress in ferrite using a quantum mechanics code. The relationship between ferrite magnetism and the carbon content is determined,and then a ferrite interstitial solid solution(ISS) model in a low carbon concentration state is replaced with an α- Fe model in the case of majority magnetic calculation. The band structure of the loaded-Fe is compared with that of the unloaded α-Fe. The comparison shows that the energy of Fe atomic 3d orbital changes a little,while the energy of electron orbital of iron core below 3d almost keeps unchanged. The relationship between the magnetic moment and the stress appears intermittent due to the Bragg total reflection. The change in the magnetic moment due to lattice mismatch is much larger than that caused by mechanical loading.     

处理噪声问题的泰勒展开交替最小化算法

为了处理图像、计算机视觉和生物信息等领域中广泛存在的稀疏大噪声和高斯噪声问题,提出了一种利用交替方向最小化思想求解主成分追求松弛模型的泰勒展开交替最小化算法(TEAM).采用推广泰勒展开和收缩算子等技术推导出低秩矩阵和稀疏大噪声矩阵的迭代方向矩阵,加入连续技术提高算法的收敛速率,设计出TEAM算法的求解步骤.实验中,将TEAM算法与该领域的顶级算法作分析对比.结果表明,TEAM算法时间优势明显,误差优势略好.     

New simple exact penalty function for constrained minimization

By adding one variable to the equality-or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.     

Some properties and applications of cumulative Kullback–Leibler information

The cumulative Kullback–Leibler information has been proposed recently as a suitable extension of Kullback–Leibler information to the cumulative distribution function. In this paper, we obtain various results on such a measure, with reference to its relation with other information measures and notions of reliability theory. We also provide some lower and upper bounds. A dynamic version of the cumulative Kullback–Leibler information is then proposed for past lifetimes. Furthermore, we investigate its monotonicity property, which is related to some new concepts of relative aging. Moreover, we propose an application to the failure of nanocomponents. Finally, in order to provide an application in image analysis, we introduce the empirical cumulative Kullback–Leibler information and prove an asymptotic result. Copyright © 2015 John Wiley & Sons, Ltd.