Feedback minimization of first-passage failure of quasi non-integrable Hamiltonian systems

The non-linear stochastic optimal control of quasi non-integrable Hamiltonian systems for minimizing their first-passage failure is investigated. A controlled quasi non-integrable Hamiltonian system is reduced to an one-dimensional controlled diffusion process of averaged Hamiltonian by using the stochastic averaging method for quasi non-integrable Hamiltonian systems. The dynamical programming equations and their associated boundary and final time conditions for the problems of maximization of reliability and of maximization of mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The dynamical programming equations for maximum reliability problem and for maximum mean first-passage time problem are finalized and their relationships to the backward Kolmogorov equation for the reliability function and the Pontryagin equation for mean first-passage time, respectively, are pointed out. The boundary condition at zero Hamiltonian is discussed. Two examples are worked out to illustrate the application and effectiveness of the proposed procedure.     

针对限制幅值磁共振脉冲的优化设计

在磁共振脉冲优化领域,优化脉冲普遍存在幅值过大的问题,这极大地限制了优化脉冲的使用范围。为了限制优化脉冲的幅值,扩大其应用范围,提出了一种基于L-BFGS-B数值算法的脉冲优化设计方法。首先基于Liouville-von Neuman方程,使用最优控制思想构建优化模型;然后使用L-BFGS-B算法,在限制幅值的条件下对优化模型进行数值迭代求解;最后以脉冲的激发效率以及激发轮廓的均匀性作为衡量优化脉冲优劣的标准对该方法进行仿真和实验验证。结果表明,采用该方法获得的优化脉冲在幅值被限制的前提下,仍能获得较传统磁共振脉冲更好的共振激发效果,进而增强信号的灵敏度,提高图像的质量。     

基于背景最佳滤波尺度的红外图像复杂度评价准则

提出一种基于背景最佳滤波尺度的红外图像复杂度评价准则来解决传统方法评价背景效果较差的问题. 同时, 这种方法还可以为红外图像滤波提供最佳高通滤波尺度信息, 从而对红外图像进行性能最佳滤波. 首先, 生成高斯仿真目标并与红外图像进行融合, 获得包含仿真目标及真实红外背景的图像. 然后, 在不同高斯滤波尺度下对图像滤波, 并计算滤波后仿真目标的信噪比. 最后, 取滤波后目标信噪比最大时的滤波尺度作为背景最佳滤波尺度, 使用该尺度可评价红外图像的复杂度. 另外, 本文还使用数学模型推导了红外图像最佳滤波尺度, 得出最佳滤波尺度的数学表达式. 大量实验表明: 1) 本文推导的最佳滤波尺度数学表达式与实验曲线吻合. 2) 这种方法在评价红外图像复杂度方面比传统的基于信息熵的方法效果要好很多. 并且这种方法获取的红外背景复杂度为滤波最佳尺度, 可以直接利用这项指标对图像进行最佳滤波从而更好地检测弱小目标. 3) 仿真目标尺度越大, 最佳滤波尺度也会相应增大. 因此, 在评价图像复杂度时, 应使用相同尺度的仿真目标, 不同图像之间才具备可比性. 同时, 最佳滤波尺度与仿真目标的强度无关. 4) 本文算法使用的滤波器宜用高斯及Butterworth高通滤波器实现. 5) 本文提出的方法不仅可以有效分析红外视频的复杂度, 并且可以通过复杂度的变化分析图像内容的突变.     

Iterative approximation of fixed points of Prešić operators on partial metric spaces

We study the convergence of the Pre?i? type k‐step iterative method for a class of operators satisfying Pre?i? type contractive conditions on the setting of partial metric spaces. Some examples are presented to illustrate our obtained results. As applications of the presented convergence theorems, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.     

Optimal reinsurance under risk and uncertainty

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to the total claims. Thus, if one imposes strictly positive lower bounds for this variable, the reinsurer moral hazard is totally eliminated.Three main contributions seem to be reached. Firstly, necessary and sufficient optimality conditions are given in a very general setting. Secondly, the optimal contract is often a bang–bang solution, i.e., the sensitivity between the retained risk and the total claims saturates the imposed constraints. Thirdly, the optimal reinsurance problem is equivalent to other linear programming problem, despite the fact that risk, uncertainty, and many premium principles are not linear. This may be important because linear problems may be easily solved in practice, since there are very efficient algorithms.     

Nash equilibrium strategies for a defined contribution pension management

This paper studies the time-consistent investment strategy for a defined contribution (DC) pension plan under the mean–variance criterion. Since the time horizon of a pension fund management problem is relatively long, two background risks are taken into account: the inflation risk and the salary risk. Meanwhile, there are a risk-free asset, a stock and an inflation-indexed bond available in the financial market. The extended Hamilton–Jacobi–Bellman (HJB for short) equation of the equilibrium value function and the verification theorem corresponding to our problem are presented. The closed-form time-consistent investment strategy and the equilibrium efficient frontier are obtained by stochastic control technique. The effects of the inflation and stochastic income on the equilibrium strategy and the equilibrium efficient frontier are illustrated by mathematical and numerical analysis. Finally, we compare in detail the time-consistent results in our paper with the pre-commitment one and find the distinct properties of these two results.     

Facile and stereo-controlled synthesis of 2-deoxynojirimycin, Miglustat and Miglitol

A novel and facile synthesis of a series of the biologically significant iminosugar derivatives including 2-deoxynojirimycin, Miglustat and Miglitol is reported. The synthesis features a strategic double inversion mechanism for securing the desired stereochemistry at C5 position of such glucose-type carbohydrate mimetics, representing a practical and remarkable improvement on the previously reported method that suffers from the loss of the stereo-control during the reaction process.     

The effect of boric acid on the vapour liquid equilibrium of aqueous potassium carbonate

Aqueous potassium carbonate has seen renewed interest as a viable solvent for pre and post combustion carbon capture and storage. However, slow reaction kinetics may require the addition of a rate promoter such as boric acid to improve efficiency. The vapour liquid equilibrium of 30 weight percent potassium carbonate with 0, 3 and 5 weight percent boric acid was investigated at 50 and 70 °C using a dynamic inert gas stripping method. By estimating the boric acid reactions an Electrolyte-NRTL model was able to fit this data and literature results very closely.     

Phase equilibrium measurements of structure II clathrate hydrates of hydrogen with various promoters

Phase equilibrium measurements of single and mixed organic clathrate hydrates with hydrogen were determined within a pressure range of 2.0-14.0 MPa. The organic compounds studied were furan, 2,5-dihydrofuran, tetrahydropyran, 1,3-dioxolane and cyclopentane. These organic compounds are known to form structure II clathrate hydrates with water. It was found that the addition of hydrogen to form a mixed clathrate hydrate increases the stability compared to the single organic clathrate hydrates. Moreover, the mixed clathrate hydrate also has a much higher stability compared to a pure hydrogen structure II clathrate hydrate. Therefore, the organic compounds act as promoter materials. The stabilities of the single and mixed organic clathrate hydrates with hydrogen showed the following trend in increasing order: 1,3-dioxolane < 2,5-dihydrofuran < tetrahydropyran < furan < cyclopentane, indicating that both size and geometry of the organic compound determine the stability of the clathrate hydrates.     

单斜BiVO4可见光催化降解甲基橙的形貌效应

以硝酸铋和偏钒酸铵为无机源,NaOH为pH值调节剂,三嵌段共聚物P123为表面活性剂,采用醇-水热法制备了多种形貌的单斜BiVO4.利用X射线衍射、N2吸脱附、扫描电子显微镜、X射线光电子能谱和紫外可见光漫反射等技术表征了其物化性质,并考察了这些BiVO4样品在可见光照射下降解甲基橙的催化活性.结果表明,表面活性剂和溶...