A generalized affine isoperimetric inequality

A purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric inequalities of plane convex geometry: The Blaschke-Santaló inequality and the affine isoperimetric inequality of affine differential geometry.     

Dimension de la mesure d’équilibre d’applications méromorphes

The Journal of Geometric Analysis - Let ? be a dominating meromorphic self-map of a compact Kähler manifold. Assume that the topological degree of ? is larger than the other...     

An upper bound for a Hilbert polynomial on quaternionic Kähler manifolds

In this article we prove an upper bound for a Hilbert polynomial on quaternionic Kähler manifolds of positive scalar curvature. As corollaries we obtain bounds on the quaternionic volume and the degree of the associated twistor space. Moreover, the article contains some details on differential equations of finite type. Part of this article is used in the proof of the main theorem.     

Numerical modeling of a fast-axial-flow CW–CO2 laser

A four-temperature model has been applied on a fast axial flow, longitudinal discharge CO₂ laser. Using Runge–Kutta method, a set of differential equations of the model is numericaly solved. These equations describe the operation of the laser with certain ratio 1:3:6 of the mixture CO₂:N₂: He and average output power of 550 W.The temporal behaviour of the output power and photon density was obtained. The effects of kinetic temperature, coupled mirror reflectivity, gas flow speed, and cavity loss on the output power were studied.Calculated output power was compared with its measured value taken from experiment and a good agreement was observed.     

Numerical simulations of flame propagation and DDT in obstructed channels filled with hydrogen–air mixture

We study flame acceleration and deflagration-to-detonation transition (DDT) in channels with obstacles using 2D and 3D reactive Navier–Stokes numerical simulations. The energy release rate for the stoichiometric H₂–air mixture is modeled by a one-step Arrhenius kinetics. Computations show that at initial stages, the flame and flow acceleration is caused by thermal expansion of hot combustion products. At later stages, shock–flame interactions, Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instabilities, and flame–vortex interactions in obstacle wakes become responsible for the increase of the flame surface area, the energy-release rate, and, eventually, the shock strength. Computations performed for different channel widths d with the distance between obstacles d and the constant blockage ratio 0.5 reproduce the main regimes observed in experiments: choking flames, quasi-detonations, and detonations. For quasi-detonations, both the initial DDT and succeeding detonation reignitions occur when the Mach stem, created by the reflection of the leading shock from the bottom wall, collides with an obstacle. As the size of the system increases, the time to DDT and the distance to DDT increase linearly with d². We also observe an intermediate regime of fast flame propagation in which local detonations periodically appear behind the leading shock, but do not reach it.     

数学建模——培养学生创新能力的重要途径

通过对比传统数学教学方法和数学建模方法,文章指出数学建模既是数学创新教育的需要,也是培养学生创新能力的重要途径,并给出了在数学建模教学过程中培养学生创新思维能力的四种形式.     

基于UML的学生管理系统设计

采用统一建模语言UML,对学生信息管理系统的结构关系建模,阐述了UML在系统 中的可视化建模机制,从不同的层面给出了系统的需求分析及系统设计的整个过程,规范和 扩充了系统的数据,增强了系统交互性．     

基于特征的倍捻锭子有限元建模技术

本文利用基于特征的建模优势对倍捻锭子建立实体有限元模型．完成了锭子从建模到划分网络的前处理工作。     

数学建模思想在教学中的渗透与实践初探

阐述在高等数学课程的教学中渗透数学建模思想的意义,并根据教学实践,介绍了在高等数学教学中渗透数学建模思想的一些实践与认识,提出了在高等数学教学中渗透数学建模思想要注意的几个问题.     

基于信息技术的探索型数学实验教学模式初探

突破传统课堂教学模式，构建以学生自主探究为主线的基于信息技术的探索性数学实验教学模式：“创设情境-数学实验-观察思考-归纳猜想-推理论证-拓展交流”，发展学生的动手操作、自主探究、合作交流和推理能力，提高学生分析问题和解决问题的能力，体现了大力提倡的“自主探究、合作交流、实践创新”学习方式。