非线性二阶Neumann边值问题的正解

利用度数理论考察了非线性二阶Neumann边值问题的正解。结论表明这个问题可以具有n个正解,只要非线性项在某些有界集上的高度和增长是适当的,其中n是一个任意的自然数。     

Multiplicity in the partial oxidation of propylene over a copper-molybdena catalyst

Measurement of rates of formation of acrolein and acetaldehyde in the partial oxidation of propylene over a copper molybdate catalyst were made under steady-state and transient modes. These measurements disclosed a rate of product formation multiplicity apparently attributable to the oxidation state of the catalyst and not to surface phenomena usually thought to be the source of hysteresis in catalytic systems.     

OBSERVABLE MULTIPLICITY FEATURES OF INHOMOGENEOUS SOLUTIONS MEASURED BY THE THERMOCHEMIC METHOD: THEORY AND EXPERIMENTS

The thermochemic method, where the catalyst temperature is manipulated by Joule-heating, may falsify the underlying kinetics by inducing inhomogeneous solutions. This work analyzes the multiplicity and stability of these states in a wire with uniform activity with or without gaps in heat conduction. Measurements of integral properties may indicate the existence of inhomogeneities either by the existence of characteristic multiplicity patterns and bifurcation maps or by unique quantitative features

These tests are employed to show that the two intermediate branches, out of four observed in ammonia oxidation, are inhomogeneous solutions induced by lack of communication. The measured bifurcation set, separating the domains of existence of the four states, is mapped in the three dimensional space of reactants concentrations and temperature.     

Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time-scale multiplicity

In this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two-time-scale nonlinear systems. Taking the advantage of the time scale separation, these processes are decomposed into fast subsystem and slow subsystem according to the dynamics. In the proposed method, an approach that combines the approximate solutions obtained from both the fast and slow subsystems to form a composite solution of the original system is proposed. Also, based on the fast and slow subsystems, a distributed state estimation scheme is proposed to handle the implicit time-scale multiplicity. In the proposed design, an extended Kalman filter (EKF) is designed for the fast subsystem and a moving horizon estimator (MHE) is designed for the slow subsystem. In the design, the slow subsystem is only required to send information to the fast subsystem one-directionally. The fast subsystem estimator does not send out any information. The estimators use different sampling times, that is, fast sampling of the fast state variables is considered in the fast EKF and slow sampling of the slow state variables is considered in the slow MHE. Extensive simulations based on a chemical process are performed to illustrate the effectiveness and applicability of the proposed subsystem decomposition and composite estimation architecture.     

SUDDEN DESTABILIZATION OF CONTROLLED CHEMICAL PROCESSES

Input multiplicity occurs when more than one set of inputs can produce the same set of outputs. Input multiple steady states are divided into compatible steady states having process gains of similar sign, and opposed steady stales with process gains of opposite sign. For a system controlled with reset action, only the compatible steady states satisfy the necessary condition for stability. Any disturbance which drives the controlled system from the designed steady state to a less stable or unstable compatible steady state can cause sudden destabilization of the process. Several examples are given of the possible types of behavior resulting from this phenomenon.

Multiple steady states also occur for systems with proportional controllers. For single-input-single-output systems with continuous process characteristics, whether or not reset action is used, two steady states positioned next to each other cannot both be stable under closed-loop control. However, under proportional control, opposed steady states for which 1 + K_cK_p is positive can be stable.     

大学英语写作教学形成性评估中的多元主体研究

将形成性评估引入大学英语写作教学,可以培养学生在写作活动中的自主性与积极性,并更直观地体验自己在写作学习各个方面的进步与提高。英语写作形成性评估体系中的评估主体具有多元化的特征:教师主体设计总体教学目标与评估标准;学生主体在自评与互评环节中承担主要的评估任务;在线评估系统为学生作文的措辞与句式提供建议;档案袋的运用可以对整个评估过程中学生的各项表现进行翔实的记录,为信息反馈提供凭证。各个主体相互独立又彼此关联,共同为学生写作技能的提高提供比较全面与客观的评价与建议,帮助学生在思辨与写作能力方面不断突破与进步。     

HYSTERESIS AND PHASE TRANSITIONS IN A SINGLE PARTIALLY INTERNALLY WETTED CATALYST PELLET: THERMOGRAVIMETRIC STUDIES

The hydrogenation of cyclohexene over palladium supported in a microporous γ-alumina pellet is studied thermogravimetrically with a view to measuring the extent of partial internal wetting associated with the different steady state branches. As many as three steady state branches having significantly different degrees of internal wetting and reaction rates, with transitions between them, are confirmed from observations of catalyst weight change. It is seen that with reduction in catalyst activity the middle branch, obtained by condensation from a vapor filled pellet, is much more prominent without showing an evaporative transition for the range of hydrogen partial pressures used here. The catalyst activity is therefore an important parameter affecting the structure of the steady state branches. Hysteresis effects are found to occur, and the thermogravimetric results also confirm the importance of history in determining the catalyst state. The measured degree of wetting is in accordance with that estimated from a mathematical model incorporating capillary condensation effects in addition to reaction-diffusion phenomena. The same model also satisfactorily interprets the reaction rate variations and transitions seen in the present work.     

非线性三点边值问题对称正解的存在性与多解性

为了研究非线性三点边值问题,利用不动点定理及单调迭代法,探讨了该问题对称正解的存在性与多解性,不仅得到了该边值问题存在2n（n为自然数）个对称正解,而且还给出了逼近于这些解的迭代格式。     

Multiplicity Regions in a Moving‐Bed Reactor: Bifurcation Analysis,Model Extension,and Application for the High‐Temperature Pyrolysis of Methane

This paper reports studies on the bifurcation analysis and the generation of regions of multiplicity in the operation of moving‐bed reactors. The studies were first carried out for a generalized model, which allows the investigation of the effect of various scenarios, such as changes in heat capacity or the number of moles with reaction, as well as the previously unstudied equilibrium and allothermic reactions. The insights gained from this extension were then applied to an actual reaction, namely the high temperature pyrolysis of methane.