Hereditary optimal control problems: Numerical method based upon a padé approximation

In this paper, we consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argumentx(t – ). In our approximation scheme, we first replace the variable with an augmented statey(t) x(t - ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four problems are solved to illustrate the validity and usefulness of this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant NCC-2-106.     

Tactical problems involving uncertain actions

The purpose of this paper is to solve anm-silent versusn-silent duel with arbitrary accuracy functionsP andQ which are continuously differentiable in [0, 1] with positive derivatives in (0, 1) and such thatP(0)=Q(0)=0,P(1)(0, 1),Q(1)(0, 1). The game can be interpreted as a game in which the players know only that the numbers of their actions have binomial distribution.Part of this paper was written during the author's stay at the Institute of Statistics and Mathematical Economics, University of Karlsruhe, FRG. The author wishes to thank Prof. S. Trybua, Technical University of Wrocaw, Poland, for helpful discussion in preparing the paper and Prof. D. Pallaschke, University of Karlsruhe, FRG, for help in preparing the numerical example.     

Optimal virtual orbitals to relax wave functions built up with transferred extremely localized molecular orbitals

Extremely localized molecular orbitals (ELMOs), namely orbitals strictly localized on molecular fragments, are easily transferable from one molecule to another one. Hence, they provide a natural way to set up the electronic structure of large molecules using a data base of orbitals obtained from model molecules. However, this procedure obviously increases the energy with respect to a traditional MO calculation. To gain accuracy, it is important to introduce a partial electron delocalization. This can be carried out by defining proper optimal virtual orbitals that supply an efficient set for nonorthogonal configurations to be employed in VB-like expansions.     

Drug metabolite cluster centers-based strategy for comprehensive profiling of Neomangiferin metabolites in vivo and in vitro and network pharmacology study on anti-inflammatory mechanism

Neomangiferin (NMF) is an extremely special xanthone that could be simultaneously attributed to C-glycoside and O-glycoside with a variety of biological activities, such as anti-inflammatory, antitumor, antipyretic, and so on. So far as we know, the metabolism profiling has been insufficient until now. Herein, Drug Metabolite Cluster Centers (DMCCs)-based Strategy has been developed to profile the NMF metabolites in vivo and in vitro. Firstly, the DMCCs was proposed depending on literature-related and preliminary analysis results. Secondly, the specific metabolic rule was implemented to screen the metabolites of candidate DMCCs from the acquired Ultra High Performance Liquid Chromatography Quadrupole Exactive Orbitrap Mass Spectrometry (UHPLC-Q-Exactive Orbitrap MS) data by extracted ion chromatography (EIC) method. Thirdly, candidate metabolites were accurately and tentatively identified according to the pyrolysis law of mass spectrometry, literature reports, comparison of reference substances, and especially the diagnostic product ions (DPIs) deduced preliminarily. Finally, network pharmacology was adopted to elucidate the anti-inflammatory action mechanism of NMF on the basis of DMCCs. As a result, 3 critical metabolites including NMF, Mangiferin (MF) and Norathyriol (NA) were proposed as DMCCs, and a total of 61 NMF metabolites (NMF included) were finally screened and characterized coupled with 3 different biological sample preparation methods including solid phase extraction (SPE), acetonitrile precipitation and methanol precipitation. Among them, 32 metabolites were discovered in rat urine, 30 in rat plasma, 12 in rat liver, 9 metabolites in liver microsomes and 8 in rat faeces, respectively. Our results also illustrated that NMF primarily underwent deglucosylation, glucuronidation, methylation, sulfation, dihydroxylation and their composite reactions in vivo and in vitro. Additionally, network pharmacology analysis based on DMCCs revealed 85 common targets of disease-metabolites, and the key targets were TNF, EGFR, ESR1, PTGS2, HIF1A, IL-2, PRKCA and PRKCB. They exerted anti-inflammatory effects mainly through the pathways of inflammatory response, calcium-dependent protein kinase C activity, nitrogen metabolism, pathways in cancer and so on. In general, our study constructed a novel strategy to comprehensive elucidate the biotransformation pathways of NMF in vivo and in vitro, and provided vital reference for further understanding its anti-inflammatory action mechanism. Moreover, the established strategy could be generalized to the metabolism and action mechanism study of other natural products.     

Development and prevalidation of a method for phenol determination by solid-phase spectrophotometry

A simple, sensitive and rapid solid-phase spectrophotometric procedure was developed for the determination of traces of phenol with 4-aminoantipyrine as a reagent (AAP-SPS), and the optimal experimental conditions were established. This method was performed by sorption and direct absorbance measurements of the product phenol-AAP sorbed on the anion-exchanger Dowex 1-X4 (0.2 g) at 495 nm (absorption maximum) and 700 nm (non-absorption wavelength). The sensitivity offered by the AAP-SPS procedure was higher by a factor of 40 compared with the respective conventional spectrophotometric method. Metrological characteristics were established using a prevalidation strategy. The AAP-SPS procedure is characterized by a linear calibration function in the working range of 0.05–0.50 μmol, low standard deviation of procedure (±0.012), low limit of determination (0.021 μmol), and favorable random (±0.85 to ±11.27%) and systematic deviations (−4.55 to +11.50%). Moreover, the accuracy of the system investigated by the recovery test is acceptable (99–102%). Favorable working and performance characteristics make the new SPS method ideal for phenol monitoring in pharmaceutical preparations as well as other matrices.     

Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems

This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.     

Construction of Spatiotemporal-Coupling Optimal Low-Dimensional Dynamical Systems for Compressible Navier-Stokes Equations; [可压缩 Navier-Stokes 方程的时空耦合优化低维动力系统建模方法]北大核心CSCD

For the low-dimensional dynamical system model to study dynamics properties of Navier-Stokes equations, it is very important that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. However, to date, there is no universal approach to ensure this purpose for general problems. Herein, it is found that any low-dimensional model based on spatial bases, such as proper orthogonal decomposition bases, optimal spatial bases, and other classical spatial bases, is not predictable, i.e., the error increases with the time evolution of the flow field. With the theoretical framework for building optimal dynamical systems and the new concept of spatiotemporal-coupling spectrum expansion, the low-dimensional model for compressible Navier-Stokes equations was constructed to approximate the numerical solution to large-eddy simulation equations, and the numerical results and novel time evolution of spatiotemporal-coupling bases were given. The entire field error is typically below 10−2%, and the average error at each grid point is below 10−8%. The spatiotemporal-coupling optimal low-dimensional dynamical systems can ensure that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. Therefore, characteristic dynamics properties of spatiotemporal-coupling optimal low-dimensional dynamical systems are the same as those of real flow. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Lamination Design Optimization for Continuous Fiber Reinforced Composites of Variable Thicknesses北大核心CSCD

由于具备高的比强度、比刚度,利用连续纤维增强复合材料代替传统金属材料以实现结构轻量化正受到设计者们的广泛关注。然而,结构的复杂性给复合材料的铺层设计与优化带来了很大的挑战。针对航空用复合材料铺层设计约束多的问题,通过逐步构建设计变量准确表达结构的铺层信息。基于经典遗传算法框架,结合各设计变量特点,定义了铺层优化算法中的遗传算子,通过引入“修复”策略保证了每一代解都能满足设计约束,分布在可行域区间内。最后利用精英保留策略提高了算法的局部寻优能力,可以降低复杂复合材料结构铺层设计的计算成本。通过解决经典benchmark问题并与已有优化结果的比较,验证了前述铺层优化算法的全局、局部寻优能力,为工程实际中的复合材料铺层设计优化提供了理论支撑。     

化学教学内容情感性艺术处理的策略

化学教学内容是教学系统的基本要素之一。对教学内容作情感性艺术处理,显示了教师高超的化学教学艺术。其艺术策略分为:一是巧妙组织教学内容来调节学生的学习心向,包括心理匹配策略、超出预期策略;二是有效地利用教学内容中的情感资源来陶冶学生的情操,包括展示情感策略、发掘情感策略、诱发情感策略、赋予情感策略。     

绿色产品零售企业与市场消费者策略选择演化分析

线上线下结合营销模式有效缓解了流通渠道不畅和营销方式单一的问题,进而促进绿色产品消费。在相关假设的基础上,通过构建绿色产品零售企业和市场消费者的演化博弈模型,重现博弈主体的动态演进过程。研究结果表明,在线上线下结合营销模式中,绿色产品零售企业与消费者演化博弈系统存在两个可能的均衡状态,分别是O{维持传统营销策略,使用传统渠道购买产品}、C{建立线上营销策略,使用线上渠道购买产品}。演化博弈系统的演进受到9个相关因素的干扰,这些因素通过影响博弈主体的收益、成本及潜在的风险损失等发生作用。在理论推导的基础上,以被调研的A绿色产品零售企业为样本进行数值模拟,验证理论推导的正确性,给出上述影响因素的作用强度。