关于一类常微分方程亚纯解的存在性

本文运用Ｎｅｖａｎｌｉｎｎａ值分布理论，解决了具一项控制系数Ｐｎ或Ｐｏ的微分方程亚纯解的存在性与可能的个数问题．同时举例说明所给结果是精确的．本文完善了Ｇ．Ｇｕｎｄｅｒｓｅｎ和Ｉ．Ｌａｉｎｅ等人的工作．     

一类非线性Chandrasekhar H-方程的正解

本文通过研究一类非线性算子方程解的存在性，建立了一类出现在辐传理论与气体动力学中的非线性ＣｈａｎｄｒａｓｅｋｈａｒＨ－方程正解或负解的存在性定理．本文的几个定理包含或改进了ＲｉｃｈａｒｄＷ．Ｌｅｇｇｅｔｔ和Ｃ．Ａ．Ｓｔｕａｒｔ等人的一些已知结果．     

SPH方法中的Riemann解与人工粘性

本文描述了光滑粒子动力学方法的人工粘性和Riemann解方法,分析了Godunov方法与传统人工粘性方法的耗散项．给定一种人工粘性,总可以找到一种相应的Riemann解法器,使得它们的耗散项在形式上几乎相同．本文利用各种近似Riemann解构造了相应的新的人工粘性．这些新的粘性,无需人工调节粘性系数．本文完成了多个数值试验,比较了使用传统人工粘性方法与Riemann解方法的不同．采用新的人工粘性,辅助热通量粘性,可以获得令人满意的计算结果．     

三维与二维晶体生长控制方程的精确解

本文通过将未知函数展开成复数形式的Fourier级数,求出了一类二阶偏微分方程的三角级数形式的解析解,并严格证明了其收敛性．三维稳态与二维稳态和二维非稳态晶体生长控制方程都是这类二阶偏微分方程特例．利用这一特点,本文求出了三维稳态与二维稳态和二维非稳态晶体生长控制方程的解析解．理论结果有助于揭示稳态晶体生长的本质特性．本文还给出了三维非稳态晶体生长控制方程的解析解．     

一类非线性方程的定性分析

本文研究非线性微分方程当ｑ＝２时，文［１］进行了研究．本文对一般的系统（Ｅ）αｑ进行了定性研究．     

用L~2能量法研究粘性守恒律解的渐近性态(英文)

本文讨论单个粘性守恒律方程与具有粘性的ｐ方程组的Ｃａｕｃｈｙ问题．根据初始资料的不同情形,其相应的Ｒｉｅｍａｎｎ问题以疏散波,激波或它们的迭加为弱解．本文的目的是指出Ｃａｕｃｈｙ问题的解将分别趋于疏散波,激波或它们的迭加．本文基本方法是能量积分法．文中综述了现有的成果,也提出了一些未解决的问题．     

一个模糊评估模型及其应用(英文)

本文在文［１］，文［２］的基础上，提出了一个适用于质量评估的有序二元对比模糊评估模型．它比现有的方法更切合实际．同时本文论述了在具体操作中所应注意的问题．     

关于矩阵特征值问题向后误差分析的注记

本文研究实矩阵关于复近似特征对的范数型向后误差．在复扰动情形,这个问题已被Higham 等学者解决．本文研究实扰动情形．结果表明,通常情况下,两种情形差别不大,但在某些情形,二者可以相差很大．作为推广,我们还讨论了矩阵多项式的相应问题．文中的一个结果部分地解决了D．J．Higham和N．J．Higham 1999年提出的一个待解决的问题．     

Pachpatte几个非线性二元积分不等式的推广

本文建立了几个ｎ元非线性积分不等式解的估计．在ｎ＝２的特殊情况改进并推广了 Ｐａｃｈｐａｔｔｅ Ｂ． Ｇ．［５,９,１０］的五个定理．举例说明了结果的应用．     

近程空中目标航路研究

本文在等加速俯冲飞行假定下．分析了近程空中目标航路的特点，并据此提出了目标航路模型．经过投影变换，把目标航路模型转化为二次函数．从而使目标航路的滤波及预报问题得到简化．采用进推最小二乘(RLS)原理．给出了目标航路的在线滤波器及预报器．最后．对本文方法进行了仿真．并对仿真结果进行了分析．     

有保护区的海洋渔业资源离散动力学模型分析

假设海洋渔业资源分属于保护区和非保护区两个区域,本文建立一个渔业资源储量-捕捞力度模型,用聚合方法得到一个简化的离散动力系统,从而分析正不动点的存在性、稳定性以及关于保护区面积比例的局部分叉,运用中心流形定理分析平衡点的局部稳定性,并用数值模拟验证不动点的局部分叉.最后,用全局分析方法分析保护区面积比例变化对可行吸引域的结构和大小的影响,从而揭示保护区对渔业资源可持续利用的影响.     

Optimum control laws in a non-autonomous dynamic model of a gas field

A model of gas field development described as a nonlinear optimum control problem with an infinite planning horizon is considered. The Pontryagin maximum principle is used to solve it. The theorem on sufficient optimumity conditions in terms of constructions of the Pontryagin maximum principles is used to substantiate the optimumity of the extremal solution. A procedure for constructing the optimum solution by dynamic programming is described and is of some methodological interest. The obtained optimum solution is used to construct the Bellman function. Reference is made to a work containing an economic interpretation of the problem.     

A Note on a Nonlinear Model of a Piezoelectric Rod

If piezoceramics are excited by weak electric fields a nonlinear behavior can be observed, if the excitation frequency is close to a resonance frequency of the system. To derive a theoretical model nonlinear constitutive equations are used, to describe the longitudinal oscillations of a slender piezoceramic rod near the first resonance frequency. Hamilton's principle is used to receive a variational principle for the piezoelectric rod. Introducing a Rayleigh Ritz ansatz with the eigenfunctions of the linearized system to approximate the exact solution leads to nonlinear ordinary differential equations. These equations are approximated with the method of harmonic balance. Finally it is possible to calculate the amplitudes of the displacements numerically. As a result it is shown, that the Duffing type nonlinearities found in measurements can be described with this model.     

Constructing a monotonic quadratic objective function in n variables from a few two-dimensional indifferences

We develop a model for constructing quadratic objective functions in n target variables. At the input, a decision maker is asked a few simple questions about his ordinal preferences (comparing two-dimensional alternatives in terms `better', `worse', `indifferent'). At the output, the model mathematically derives a quadratic objective function used to evaluate n-dimensional alternatives.Thus the model deals with some imaginary decisions (criteria aggregates) at the input, and disaggregates the decision maker's preference into partial criteria and their cross-correlations (=a quadratic objective function). Therefore, the model provides an approximation step which is next to the disaggregation of a preference into additively separable linear criteria with weight coefficients.The model is based on least squares fitting a quadratic indifference hypersurface (if n=2, indifference curve) to several alternatives which are supposed to be equivalent in preference. The resulting ordinal preference is independent of the cardinal utility scale used in intermediate computations which implies that the model is ordinal. The monotonicity of the quadratic objective function is implemented by means of a finite number of linear constraints, so that the computational model is reduced to restricted least squares.In illustration, we construct a quadratic objective function of German economic policy in four target variables: inflation, unemployment, GNP growth, and increase in public debt. This objective function is used to evaluate the German economic development in 1980–1994.In another application, we construct a quadratic objective function of ski station customers. Then it is used to adjust prices of 10 ski stations to the South of Stuttgart.In Appendix A we provide an original fast algorithm for restricted least squares and quadratic programming used in the main model.     

Managerial Judgement in a Competitive Bidding Model

The basic Friedman model is extended to allow for bias in cost estimates and the use of management judgement on market trends. The estimated mean bid is used as a parameter. Simulation, using data from four construction companies, is used to evaluate the performance of the resulting model. A sensitivity analysis is used to determine the required accuracy for the management estimate. A brief account is given of the introduction of the model as a practical tool of top management in a major construction firm.     

Modelling and resonance of a flexible rod using a floating reference frame

A direct variational approach with a floating frame is presented to derive the ordinary differential equations of motion of a flexible rod, constant crank speed slider-crank mechanism. Potential energy terms contained in the derivation include beam-bending energy and energy in foreshortening of the rod tip (which were selected because of the importance of these terms in a pinned-pinned rod parametric resonance). A symbolic manipulator code is used to reduce the constrained equations of motion to unconstrained nonlinear equations. A linearized version of these equations is used to explore parametric resonance stability-instability zones by a monodromy matrix technique.     

Discretization of a convection-diffusion equation

The unsteady convection-diffusion equation with constant coefficientsadmits an exact solution in the form of a convolution integral,which provides an explicit representation of the evolution operatorthrough one time step. This is used to unify many numericalschemes for the equation, showing interrelationships betweenfinite difference and finite element schemes and presentinga general framework for detailed error analysis. In particular,the upwind scheme, Lax Wendroff, QUICKEST, the ECG schemes andCrank Nicolson are all members of a family that includes powerfulnew schemes. Fourier analysis is used to obtain practical stabilityregions and some insights into accuracy; and the Peano kerneltheorem is also used to derive rigorous error bounds that canbe generalized to irregular meshes.     

Irradiation of a cone by a magnetic dipole

Th electromagnetic field produced by a magnetic dipole in thepresence of a perfectly conducting cone of arbitrary cross-sectionis determined. The solution is used to find out how a currenton the cone travelling towards the apex is reflected. Some valuesof the reflection coefficient are calculated. In particular,it is shown that there is a sort of resonance with the reflectionincreasing significantly as the cone approaches a plane.     

The approximate solution of a class of Fredholm integral equations with a weakly singular kernel

A method for finding the numerical solution of a weakly singular Fredholm integral equation of the second kind is presented. The Taylor series is used to remove singularity and Legendre polynomials are used as a basis. Furthermore, the Legendre function of the second kind is used to remove singularity in the Cauchy type integral equation. The integrals that appear in this method are computed in terms of gamma and beta functions and some of these integrals are computed in the Cauchy principal value sense without using numerical quadratures. Four examples are given to show the accuracy of the method.     

Simulating of a pressing process of a viscoelastic polymer melt

A well known and often used method to obtain anisotropic polymer films is the so-called pressing process. Here, films are squeezed under high temperatures, pressure and deformation rates. To simulate such a process, the polymeric matrix is treated as a non-Newtonian, viscoelastic melt. The modeling of such melts is done with the anisotropic molecule movement tensor generalization of the Maxwell Model for high deformation rates. The viscoelastic flow simulations are done with DEVSS stabilization techniques and an ALE based dynamic mesh Method. In this work we present simulations in order to show the difference between classical approaches using a generalized Newtonian viscosity to model the melt and the used viscoelastic models. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)