The complete figure for second order multiple integral problems in the calculus of variations

Notation Throughout this paper Greek indices, , , and Latin indicesi, j, h, k, assume the values 1, ,m, and 1, ,n respectively. The summation convention is operative in respect of both sets of indices.This work was supported by the South African Council for Scientific and Industrial Research.At time of writing Professor Grässer was Visiting Scholar at the University of Arizona, Tucson, Arizona.     

Regularity of weak solutions to rate‐independent systems in one‐dimension

We show that under some appropriate assumptions, every weak solution (e.g. energetic solution) to a given rate‐independent system is of class SBV, or has finite jumps, or is even piecewise C¹. Our assumption is essentially imposed on the energy functional, but not convexity is required.     

Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

Novel and Efficient Oxidation of Benzyl Ethers to Benzaldehydes by DMSO/49% Aq. HBr

Dimethylsulfoxide (DMSO) oxidizes benzyl ethers into corresponding benzaldehydes at 110°C; the reaction is accelerated by 49% aq. HBr. The conditions work well for different aryl‐substituted benzyl ethers. This protocol is inert toward dialkyl ethers.     

A variational approach to second-order approximability of sliding mode control systems

We consider robustness properties of second-order methods for the sliding mode control of nonlinear ordinary differential equations. A new approach is presented based on the theory of well-posed optimization problems. It is shown that the convergence of the real states of the control system to the ideal one is intimately related to Tykhonov well-posedness of suitably defined dynamic optimization problems.     

Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

一维纳米材料Cs0.2WO3和W18O49长度与红外吸收关联性的Mie散射理论推导及实验验证

研究表明二元、三元钨基氧化物的红外吸收性能具有尺寸和形貌依赖性,但还没有普适性的物理学机理及计算方法。本工作基于Mie散射理论,推导了一维材料的长度与光吸收性能之间的关系,通过理论推导计算和实验验证,探究了纳米钨基氧化物的红外吸收性能与颗粒长度的关联性。首先,基于Mie散射理论的推演和计算,揭示了增加纳米Cs_(0.2)WO_3和W_(18)O_(49)材料长度可适度提高其近红外吸收性能的规律。其次,测试了合成的不同长度Cs_(0.2)WO_3纳米棒和W_(18)O_(49)纳米线的红外吸收性能,结果与理论计算及模拟相吻合。其中在2 500～20 000 nm波长范围内Cs_(0.2)WO_3纳米棒和W_(18)O_(49)纳米线随长度的变化趋势不同,Cs_(0.2)WO_3纳米棒的红外吸收性能随长度的增加而增加,而W_(18)O_(49)纳米线的红外吸收性能随长度的增加而减弱。Cs_(0.2)WO_3纳米棒和W_(18)0O_9纳米线的光热效应均随长度的增加而增加,增幅分别达18.5%和12.7%,再次验证了长度效应。     

The turnpike property in finite-dimensional nonlinear optimal control

Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces, the first and the last of which being transient short-time arcs, and the middle piece being a long-time arc staying exponentially close to the optimal steady-state solution of an associated static optimal control problem. We provide in this paper a general version of a turnpike theorem, valuable for nonlinear dynamics without any specific assumption, and for very general terminal conditions. Not only the optimal trajectory is shown to remain exponentially close to a steady-state, but also the corresponding adjoint vector of the Pontryagin maximum principle. The exponential closedness is quantified with the use of appropriate normal forms of Riccati equations. We show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method, or a shooting method. In particular, we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector, not at the initial time, but at the middle of the trajectory.     

混合胺体系中 MCM-49/ZSM-35 复合分子筛的晶化过程

 采用 X 射线衍射、N2 吸附-脱附、扫描电镜和傅里叶变换红外光谱等技术, 研究了 MCM-49/ZSM-35 复合分子筛在 Na2O-SiO2-Al2O3-CHA (环己胺)-HMI (六亚甲基亚胺)-H2O 合成体系中, 先在低温 80 ?C 老化 4 h, 再经 160 ?C 晶化不同时间的演变过程. 结果表明, 在该混合胺体系中, 首先生成 MCM-49 分子筛, 随着晶化时间的延长, 形成 ZSM-35 含量逐渐增加的 MCM-49/ZSM-35 复合分子筛, 最后生成纯 ZSM-35 分子筛; ZSM-35 的生成是以 MCM-49 分子筛的消耗为代价的.     

MCM-49分子筛的合成及其对烷基化反应的催化性能

The MCM 49 zeolite was successfully synthesized using an organic mixture solution (OMS) yielded from hydrogenation of caprolactam as the template instead of the pure hexamethyleneimine (HMI). The OMS contains HMI (76 0%～84 0%), caprolactam (1 0%～10 0%), water, and a few by products. So the synthesis cost of the MCM 49 zeolite decreases obviously. The MCM 49 zeolite synthesized using OMS as the template shows similar crystallinity and purity to that synthesized using pure HMI in conventional process. From the results of NH 3 TPD, N 2 adsorption isotherm, and DTA, it is evident that the MCM 49 zeolite possesses three kinds of acidic centers with different strength, and has a high specific surface area and good thermostability. Furthermore, the MCM 49 zeolite shows good catalytic behavior for the alkylation of benzene with dilute ethylene to ethylbenzene.