推广的Boussinesq方程和KdV方程——Painlevé性质,Bcklund变换和Lax对

本文从Kadomtsev-Petviashvili方程的对称性约化出发,得到了具有任意函数作为变系数的推广的Boussinesq方程和推广的KdV方程.利用Weiss和Kruskal等建立的奇性分析方法,我们证明了这两个方程可积的充分条件:Painlevé性质。得到了这两个方程的Bcklund变换和奇性流形方程(推广的Schwartz-Boussinesq方程和Schwartz-KdV方程)。并由此将这两个方程线性化,即给出这两个方程的Lax对并包含有明显的与时间无关的任意谱参数。     

不可压流体的边界层问题

研究三维有界区域在边界上有流动的不可压流体的边界层问题,导出了Navier-Stokes方程区域内部的近似方程(Euler方程和线性化的Euler方程)和边界附近近似的方程(零阶边界层方程与一阶边界层方程),证明了这种近似的合理性.     

Navier-Stokes方程与Euler方程的稳定性比较

比较了Navier-Stokes 方程和Euler方程的稳定性;并以它们的典型初值问题为例,分析了Navier-Stokes方程和Euler方程稳定性不同的原因．     

几种广义非线性发展方程的新解

本文研究了构造了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解的问题.利用三种辅助方程及其新解,获得了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解.这些解由双曲余割函数、双曲正切函数、双曲正割函数、双曲余切函数和余割函数组成.     

应用(1/G)-展开法求解五阶KdV方程

本篇论文首次提出(1/G) -展开法,用于求解非线性演化方程的行波解.将该法应用于五阶KdV方程的求解,当参数满足一定条件时,该方程可化为Sawada-Kotera (SK)方程、Caudrey-Dodd-Gibbon(CDG)方程、Kaup-Kupershmidt (KK)方程、Lax方程和Ito方程.其解可被表示为...     

非线性波方程新的显式精确解

利用Darboux和一个可化为标准Bernoulli方程的4阶常微分方程,统一地处理了三个著名方程KdV方程,Kadomtsev-Petviashvili(KP)方程和Hirota-Satsuma(HS)方程的求解问题.给出了这些方程一批新的具有更为丰富形式的精确解,其中包括孤波解和行波解.     

有界区域上的粘性分离法

用分步法求解Navier-Stokes方程的初边值问题。在每一个时间区间内,将原方程分解为没有扩散项的Euler方程和没有对流项的扩散方程,证明了近似解的收敛性。与通常的方法不同的是,我们用一个非齐次扩散方程代替了齐次扩散方程。本文是一系列文章的第一篇,讨论线性化的方程。     

脉冲强迫非线性时滞微分方程的渐近性

本文研究一类脉冲强迫非线性时滞微分方程的渐近性,所得结果不仅适用于线性方程和非线性方程,强迫方程和非强迫方程,脉冲方程和非脉冲方程,而且改进了最近文献［８］的主要结果．     

利用Riccati方程求解Burgers方程

应用李群理论中的伸缩变换群,把非线性二阶偏微分方程-Burgers方程转化为非线性非齐次一阶常微分方程-Riccati方程,将Riccati方程转化为Bernoulli方程和齐次线性二阶常微分方程,从而找到了Riccati方程的许多解,最后进一步求出了Burgers方程许多新的解析解.     

一类非线性发展方程的显式精确解

提出了寻求非线性发展方程行波解新的辅助方程法,作为实例通过选取变系数Bernoulli方程作为辅助常微分方程,并借助于计算机系统Mathematica和齐次平衡原则,求解了一类非线性发展方程,得到了该方程的新的显式精确解.所用方法可应用到其它类似方程的求解.     

My agents love to conform: Norms and emotion in the micro-macro link

This contribution investigates the function of emotion in relation to norms, both in natural and artificial societies. We illustrate that unintentional behavior can be normative and socially functional at the same time, thereby highlighting the role of emotion. Conceiving of norms as mental objects we then examine the role of emotion in maintaining and enforcing such propositional attitudes. The findings are subsequently related to social structural dynamics and questions concerning micro-macro linkage, in natural societies as well as in artificial systems. Finally, we outline the possibilities of an application to the socionic multi-agent architecture SONAR. Christian von Scheve graduated in Sociology with minors in Psychology, Economics, and Political Science at the University of Hamburg, where he also worked as a research assistant at the Institute of Sociology. Currently, he is a 3rd year PhD student at the University of Hamburg. He was a Fellow of the Research Group “Emotions as Bio-Cultural Processes” at the Center for Interdisciplinary Research (ZiF) at Bielefeld University. In his doctoral thesis he develops an interdisciplinary approach to emotion and social structural dynamics, integrating emotion theories from the neurosciences, psychology, and the social sciences. He has published on the role of emotion in large-scale social systems, human-computer interaction, and multi-agent systems. He is co-editor of a forthcoming volume on emotion regulation. Daniel Moldt received his BSc in Computer Science/Software Engineering from the University of Birmingham (England) in 1984, graduated in Informatics at the University of Hamburg, with a minor in Economics in 1990. He received his PhD in Informatics from the University of Hamburg in 1996, where he has been a researcher and lecturer at the Department of Informatics since 1990. Daniel Moldt is also the head of the Laboratory for Agent-Oriented Systems (LAOS) of the theoretical foundations group at the Department of Informatics. His research interests focus on theoretical foundations, software engineering and distributed systems with an emphasis on agent technology, Petri nets, specification languages, intra- and inter-organizational application development, Socionics and emotion in informatics. Julia Fix is currently a PhD student at the Theoretical Foundations of Computer Science Group, Department for Informatics at the University of Hamburg. She studied Informatics and Psychology at the University of Hamburg, with an emphasis on theoretical foundations of multi-agent systems and wrote her diploma theses about emotional agent systems. Her current research interests focus on conceptual challenges and theoretical foundations of modelling emotions in multi-agent systems, emotion-based norm enforcement and maintenance, and Socionics. A further research focus are Petri nets, in particular the use of Petri-net modelling formalisms for representing different aspects of emotion in agent systems. Rolf von Lüde is a professor of Sociology at the University of Hamburg with a focus in teaching and research in Sociology of Organizations, Work and Industry since 1996. He graduated in Economics, Sociology, and Psychology, and received his doctorate in Economics and the venia legendi in Sociology from the University of Dortmund. His current research focuses on labor conditions, the organization of production, social change and the educational system, the organizational structures of university, Socionics as a new approach to distributed artificial intelligence in cooperation with computer scientists, new public management, and emotions and social structures. Rolf von Lüde is currently Head of Department of Social Sciences and Vice Dean of the School of Business, Economics and Social Sciences, University of Hamburg.     

Modeling and simulation of severe slugging in air-water systems including inertial effects

A mathematical model and numerical simulations corresponding to severe slugging in air-water pipeline-riser systems are presented. The mathematical model considers continuity equations for liquid and gas phases, with a simplified momentum equation for the mixture. A drift-flux model, evaluated for the local conditions in the riser, is used as a closure law. In many models appearing in the literature, propagation of pressure waves is neglected both in the pipeline and in the riser. Besides, variations of void fraction in the stratified flow in the pipeline are also neglected and the void fraction obtained from the stationary state is used in the simulations. This paper shows an improvement in a model previously published by the author, including inertial effects. In the riser, inertial terms are taken into account by using the rigid water-hammer approximation. In the pipeline, the local acceleration of the water and gas phases are included in the momentum equations for stratified flow, allowing to calculate the instantaneous values of pressure drop and void fraction. The developed model predicts the location of the liquid accumulation front in the pipeline and the liquid level in the riser, so it is possible to determine which type of severe slugging occurs in the system. A comparison is made with experimental results published in literature including a choke valve and gas injection at the bottom of the riser, showing very good results for slugging cycle and stability maps. Simulations were also made assessing the effect of different strategies to mitigate severe slugging, such as choking, gas injection and increase in separation pressure, showing correct trends.     

Orlicz型序列空间的暴露性

对赋Luxember范数或Orlicz范数的Orlicz型序列空间,诸如古典的、广义的及参数式的,本文总结、补充、比较列出了暴露点及暴露性的充分必要刻画,并对以往结果中的错误进行了修正,从而在序列空间方面系统地完成了有关暴露性的刻画。     

Financial Risk Modelling and Econometric Inference

In finance, the explicit modelling of uncertainty takes on a particularly important role. The values of financial derivatives increase in the return volatility of the underlying security. This notion requires a concept of volatility and hence uncertainty. In addition, the choice between modelling in discrete and continuous time is not arbitrary, since it corresponds to a distinction between incomplete and complete markets, respectively, and this distinction matters for asset pricing, financial risk modelling, and inference. Risk and volatility are closely connected, and implied volatility, volatility forecasting, volatility in term structure models, stochastic volatility, and portfolio analysis are considered and related to a more general interplay between cross-sectional and dynamic aspects in finance. Stocks, bonds, and options are considered and placed in the context of efficiency and separation in inference.     

PANEL DISCUSSIONS

Representations of mathematical concepts play an important role in understanding: both in helping learners understand the to-be-learned material and in facilitating teachers’ understanding of pedagogical processes which, in turn, are involved in developing learners’ understanding. In this paper, we report on work with a cohort of pre-service primary teachers, with the aim of developing their understanding of mathematics, their confidence in their subject knowledge and their confidence in teaching mathematics. This was attempted through the introduction and use of a ‘representational approach’ to the teaching of the mathematical concepts required of teachers training to teach in primary schools in the UK. We present the results of attitude measures and a follow-up qualitative questionnaire in identifying whether and how the use of this representational approach supported pre-service teachers’ understanding and their confidence in teaching mathematics. The results suggest that the representational approach used had a positively significant impact on the attitudes towards studying and teaching mathematics.     

Classical and Nonclassical Dynamic Problems of Sandwich Shells with a Transversely Soft Core

Based on the hypothesis of similarity of transverse displacements in thin-walled sandwich shells with a transversely soft core under dynamic and static loads, refined geometrically nonlinear dynamic equations of motion are constructed in the case of large variations in the parameters of the stress-strain state (SSS) in the tangential directions. For shells structurally symmetric across the thickness and loaded with initial static loads, linearized dynamic equations are derived, which, upon introducing the synphasic and antiphasic functions of displacements and forces, can be used to describe the synphasic and antiphasic buckling forms in the transverse and tangential directions. For nonshallow cylindrical and shallow spherical shells, the nonclassical problems on all possible vibration forms realized at zero indices of variability of the SSS parameters in the tangential directions are formulated and solved. For shallow shells of symmetric structure, the resolving equations are obtained by introducing, instead of tangential displacements and transverse tangential stresses in the core, the corresponding potential and vortex functions.     

商科型高校理工类研究生创新能力的培养

目前,研究生教育处于我国高等教育的最高层次,肩负着为国家发展培养高技术专业型人才的重要任务.尤其是在各国竞争愈发激烈的今天,理工类研究生更是在未来国家现代化建设、科技创新中发挥着重要作用.但是,由于近几年研究生招生规模的逐渐扩大,研究生的培养模式、培养质量等方面出现了许多亟待解决的问题.从商科型高校理工类研究生的培养现状出发,通过运用文献法和归纳法,本文对当前研究生培养过程中存在的问题进行分析,并针对学生创新能力的培养,从学校、导师和学生自身三方面给出了相应的解决措施,着重强调了数学建模在理工类研究生创新能力培养过程中所发挥的重要作用.最后,以湖南工商大学近几年在理工类研究生创新能力培养实践中所采取的主要举措以及取得的成效来进一步论证本文所提出措施的有效性.     

黑龙江漠河地区冰雪情自动监测系统的设计与应用

基于空气、冰、雪与水物理特性的差异,设计了适应高寒地区内陆河道冰雪情定点自动检测的传感器和数据采集系统设备.该系统被安装在黑龙江省漠河县北极村水位站黑龙江河道断面,进行了3个半月的冰雪情定点连续监测,获取了系统的黑龙江河道内部冰水情以与积雪深度现场数据.采集数据完整地反映了黑龙江河道冬季冰层和雪层生消变化过程,为分析高寒地区冬季冰雪情变化规律以及春季凌汛预警提供了科学的预测数据,并探索出了一种适合野外恶劣环境下工程应用的冰雪情检测方法和系统设备.     

Modelling the steady-state effluent characteristics of the TNCU process under different return mixed liquid

The Activated Sludge Model No. 2d (ASM2d) was employed and modified to predict the effluent qualities of the modified enhanced biological phosphate removal (EBPR) system – TNCU. The TNCU process was composed of anaerobic/anoxic/oxide (A2O) process and rotating biological contactors (RBC) in each reactor. There were three modifications for the model in this study: (1) the biosorption effect of the soluble COD, (2) the ammonification of the organic nitrogen in influent wastewater, and (3) the growth of the heterotrophic organisms in the anaerobic tank. The influent wastewater qualities were fixed, the ratios of return sludge and SRT were 0.5 and 11 days, and the model plant was operated at three different mixed liquid recycling ratios (MLRR, 0.5, 1.25, 2). When a steady state was reached, the comparisons between the measured values and the model predicted values in each test were made. It shows a good consistency between them. According to the consistent results, the biosorption effect of the soluble COD and the ammonification of the organic nitrogen in influent wastewater were the important effects in activated sludge system. Additionally, the heterotrophic organisms might grow in the anaerobic tank. The heterotrophic organisms, phosphorus accumulating organisms and autotrophic organisms would decrease in the anaerobic tanks because the lysis reactions were the major reactions in the anaerobic tanks. They would increase in the aerobic tanks. Furthermore, it was indirectly proved that the denitrifying PAOs existed in the EBPR system.     

非参数秩检验在宿舍因素对学风影响中的应用

学风建设是大学教育教学管理中的重要环节,对学生的学习成绩、顺利毕业和就业等都有至关重要的影响。宿舍是学生学习和生活的重要场所,本文应用非参数统计秩检验和中位数检验研究了宿舍对学生学业成绩的影响,得到目前大学宿舍因素对学生学业成绩的影响高度显著,进而建议高等学校应加强学生宿舍管理,把宿舍作为学风建设的重要环节。