Necessary conditions for optimal control problems with bounded state by a penalty method

Necessary conditions are derived for a general relaxed control problem with unilateral state constraint. The results are also valid for ordinary controls that are solutions of the relaxed problem.A penalty is imposed to change the constrained problem into a sequence of unconstrained problems. The assumptions are on the data of the problem and do not requirea priori verification of hypotheses involving the optimal solution.     

Convergence of a strong variational algorithm for relaxed controls involving a class of hyperbolic systems

In this paper, we consider a class of optimal control problems involving linear hyperbolic partial differential equations with Darboux boundary conditions. A strong variational algorithm has been obtained for solving this class of optimal control problems in a previous paper by the third and the first authors. It was also shown that anyL accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that the control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problems.This work was partially supported by the Australian Research Grant Committee, and was done during the period when Z. S. Wu and K. G. Choo were Honorary Visiting Fellows in the School of Mathematics at the University of New South Wales, Australia.     

A system of general nonlinear variational inclusions in Banach spaces

A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces.     

等几何修正准凸无网格法

采用等几何B样条基函数的多项式再生条件对无网格形函数的多项式再生条件进行了修正,使得无网格形函数的负值部分明显减少,在域内趋于非负函数,即等几何修正准凸无网格形函数。该准凸无网格形函数仍然具有与传统再生核无网格形函数相似的构造形式,数值实现比较便捷,同时该准凸无网格形函数的多项式再生条件具有准确的修正系数,无需引入额外的人工节点松弛参数。更重要的是,等几何修正准凸无网格形函数可在确保形函数高阶光滑的前提下减小相对支持域,提高计算效率。最后,基于等几何修正准凸无网格形函数对杆梁和膜板结构进行了伽辽金无网格振动分析。结果表明,与标准再生核无网格法相比,等几何修正准凸无网格法具有更优的计算精度。     

求解广义混合隐拟平衡问题的预测修正算法

引入和研究了一类新的具有四元函数的广义混合隐拟平衡问题．这类平衡问题包含了很多已知的广义平衡问题和广义混合隐拟变分不等式问题作为很特殊的情形．利用辅助原理技巧建议和分析了求解广义混合隐拟平衡问题的预测修正迭代算法．所建议算法的收敛性仅需要映象的连续性和部分松弛强单调性．     

线性方程组的异步松弛迭代法*

本文考虑解线性方程组经典迭代法的异步形式,对系数矩阵为H矩阵,给出了异步迭代过程收敛性的充分条件,这不仅降低了文献[3]对系数矩阵的要求,而且收敛区域比文献[3]的大.     

Optimal Control Problems of Phase Relaxation Models

This work is concerned with optimal control problems with convex cost criterion governed by the relaxed Stefan problem with or without memory. The existence of an optimal control is proved and necessary conditions for a given function to be an optimal control are found. Moreover, an asymptotic analysis is performed as the time relaxation parameter tends to zero.     

DNA tertiary structure and changes in DNA supercoiling upon interaction with ethidium bromide and gyrase monitored by UV resonance Raman spectroscopy

The tertiary structure of DNA is important for many of its biological functions. In this work supercoiled and relaxed forms of purified plasmid DNA pBR322 in dilute aqueous solutions are investigated by means of UVRR spectroscopy to assess changes in B‐DNA conformation. Spectral variation in the CO and exocyclic NH₂ vibration above 1600 cm⁻¹ indicate changes in hydrogen bonding. A minor shift of the CN stretching mode of adenosine and guanosine at 1487 cm⁻¹ supports these findings. Changes in ribose conformation are visible in the spectral region 1320–1360 cm⁻¹ by vibrational coupling of the ribose pucker to the vibrations of the purine and pyrimidine bases. The intercalating phenanthridinium drug ethidium bromide is known to reduce the negative supercoiling of DNA. This change in DNA topology is reflected in variations of the UVRR marker bands of DNA identified above. Principal component analysis helped to extract the features of interest from the complex spectra of the intercalation complex. Within the bacterial cells the change in DNA topology is achieved by the action of topoisomerases. In this work, the DNA‐binding subunit GyrA of the enzyme gyrase was extracted from E. coli and applied to relaxed and supercoiled pBR322. The observed changes in the vibrational signature of the relaxed DNA in the presence of GyrA indicate a change of topology towards the supercoiled form. With already supercoiled DNA no further change in DNA topology is observed. Copyright © 2007 John Wiley & Sons, Ltd.     

Constituent analysis of stress memory in semicrystalline polyurethane

Similar to shape memory, the stress in a stimulus responsive polymer can also be programmed, stored, and retrieved reversibly upon an external stimulus, and known as stress memory. Herein, the stress analysis in a semicrystalline polyurethane is investigated to unveil the total stress–strain components of the memory polymer. The evolution of stress under different temperature and strain levels is determined experimentally. A constitutive model based on phase transition was further used to predict and characterize the individual stress components during the thermomechanical process. In contrast to earlier models, a new approach of using relaxed modulus (RM) has been proposed to predict the stress components in tensile programming condition. The predicted results are having significant agreement with the experimental data. The quantitative stress analysis can help in engineering the products more precisely, where the controllable stimulus responsive stress is needed in multidisciplinary arenas such as pressure garments, massage devices, and artificial muscles etc. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 941–947