On the Summability of Formal Solutions of Linear Partial Differential Equations

We investigate the existence and the Borel summability of formal power series in one variable with holomorphic coefficients, solutions of linear partial differential equations which are not of Kowalewski type in the complex domain. Sufficient conditions are given in terms of the shape of the partial differential equations and initial conditions. Existence and asymptotic behavior of local sectorial holomorphic solutions of these linear partial differential equations are obtained as a by-product. 2000 Mathematics Subject Classification. 35C10, 35C20. This research was partially supported by a Marie Curie Fellowship of the European Community programme “Improving Human Research Potential” under contract number HPMF-CT-2002-01818.     

Formal Fundamental Solutions of Irregular Singular Differential Equations Depending Upon Parameters

Given a system of linear differential equations with a pole, say at z = 0, it is well known that the system has a formal fundamental solution which is the product of a formal power series in a root of z, a matrix power of z, and the exponential of a polynomial in a root of z ^–1. Suppose that the system depends analytically upon several parameters in a neighborhood of some point in the parameter space. Then the question arises whether there exists an analytic formal fundamental solution, i.e., a formal fundamental solution whose coefficients are analytic in the parameters in a possible smaller neighborhood of the given point. In 1985, Babbitt and Varadarajan treated this problem together with that of the deformation of nilpotent matrices over rings. They assume that the exponential parts of the formal fundamental solutions are well behaved in some precise sense. In the present paper I will provide constructive proofs of their theorems on formal fundamental solutions and in this way also improve them slightly. Furthermore I will give a condition for well behaved exponential parts – and hence for the existence of an analytic formal fundamental solution – which can be expressed solely in terms of the given equation.     

On the Summability of Formal Solutions of Nonlinear Partial Differential Equations with Shrinkings

We investigate the existence and Borel summability of formal power series in one variable with holomorphic coefficients, solutions of nonlinear partial differential equations with shrinkings having non-Kowalewski type in the complex domain. Sufficient conditions are given in terms of the shape of the functional partial differential equations and initial conditions. The existence and asymptotic behavior of local sectorial holomorphic solutions of these nonlinear functional partial differential equations are obtained as a by-product. We apply the results to the study of asymptotic the behavior of solutions of some advanced-argument partial differential equations in a neighborhood of infinity.      

On Analytic Continuation of Solutions of Linear Partial Differential Equations

We study analytic continuation properties of solutions of linear partial differential equations of Cauchy–Kowalewski type, with respect to one complex variable in sectors of infinite radius. Growth estimates are also investigated. 2000 Mathematics Subject Classification. 35C10, 35C20.     

Algorithms for Formal Reduction of Vector Field Singularities

We present several algorithms transforming a Pfaffian form of the following type:

On the Controllability Problem Arising in Financial Mathematics

This paper deals with the approximate controllability problem for a parabolic equation defined for . It is possible to find a sequence of initial conditions with given compact support such that traces at of corresponding solutions converge to the trace of a given solution. We obtain estimates of the rate of this convergence. These estimates are constructed in terms of eigenvalues of certain compact operator.     

On Properties of Solutions to Nonlinear Parabolic Equations of the Second Order

A quasilinear elliptic problem is considered for which conditions for existence and nonexistence of positive solutions are discussed.     

On the Representations of Solutions of the Theory of Thermoelasticity with Microtemperatures

In the present paper the linear theory of thermoelasticity with microtemperatures is considered. First, the representation of Galerkin type solution of equations of motion is obtained. Then, the representation theorem of Galerkin type of the system of equations of steady oscillations (vibrations) is presented. Finally, the general solution of the system of homogeneous equations of steady oscillations in terms of nine metaharmonic functions is established.     

Thermal Buckling Analysis of a Mindlin Rectangular FGM Microplate Based on the Strain Gradient Theory

This article is aimed at developing a nonclassical Mindlin rectangular functionally graded material (FGM) microplate based on the strain gradient theory (SGT) to study the thermal buckling behavior of microplates with different boundary conditions. This theory comprises material length scale parameters to interpret size effects. The developed model encompasses classical and modified couple stress Mindlin microplate models, if all the material length scale parameters or two of them are taken to be zero, respectively. The Mindlin rectangular FGM microplate is considered to be made of a mixture of metal and ceramic of which the volume fraction is described through a power low function. According to Hamilton's principle and the generalized differential quadrature (GDQ) method, the stability equations and associated boundary conditions are obtained and discretized, respectively. Current formulations provide a possibility to have all types of boundary conditions which herein, FGM microplates with three commonly used boundary conditions are considered. Three different types of thermal loads including uniform, linear and nonlinear temperature rises along the thickness of FGM microplates are considered. The dimensionless critical buckling temperature difference (DCBTD) predicted by SGT is compared with that of modified couple stress theory (CST) and classical theory (CT) which it is found that CST and CT underestimate the DCBTD. Also, effects of the boundary conditions, length scale parameter and material gradient index of FGM microplates on the DCBTD are judiciously investigated.     

A criterion based on computational singular perturbation for the identification of quasi steady state species: A reduced mechanism for methane oxidation with NO chemistry

A criterion based on computational singular perturbation (CSP) is proposed to effectively distinguish the quasi steady state (QSS) species from the fast species induced by reactions in partial equilibrium. Together with the method of directed relation graph (DRG), it was applied to the reduction of GRI-Mech 3.0 for methane oxidation, leading to the development of a 19-species reduced mechanism with 15 lumped steps, with the concentrations of the QSS species solved analytically for maximum computational efficiency. Compared to the 12-step and 16-species augmented reduced mechanism (ARM) previously developed by Sung, Law & Chen, three species, namely O, CH₃OH, and CH₂CO, are now excluded from the QSS species list. The reduced mechanism was validated with a variety of phenomena including perfectly stirred reactors, auto-ignition, and premixed and non-premixed flames, with the worst-case error being less than 10% over a wide range of parameters. This mechanism was then supplemented with the reactions involving NO formation, followed by validations in both homogeneous and diffusive systems.     

基于博弈论的煤矿安全管理问题

借助博弈论这个媒介,为中国政府与煤矿企业之间建立了一个博弈模型,以改进、完善煤矿生产安全管理制度,并提出一系列有效管理措施及方法,帮助加强对煤矿生产的管理水平,促进煤矿事业蓬勃发展。     

汽轮发电机组动静碰摩的奇异谱理论与小波分析诊断方法研究

作者利用奇异谱对汽轮发电机组转子动碰摩的振动信号进行了分析,剔除信号中因不平衡等邦联所产生的平滑部分、抑制噪声;并运用连续小波变换对信号进行分析。通过多尺度分析形成等高线图,使碰摩故障特征在相应的等高图上得以体现出来。作者还比较了相似频谱特征的两类故障信号的小波变换等高线特征,总结了碰摩故障小波变换等高线分析特征,得到了理想的分析结果,为汽轮发电机组碰摩故障识别提供了新的思路;同时讨论了运用小波变     

On the Stokes Phenomenon for Holomorphic Solutions of Integro-Differential Equations with Irregular Singularity

We study the Stokes phenomenon for sectorial holomorphic solutions of linear integro-differential equations in two variables t, z with irregular singularity at t = 0. More precisely, we give sufficient conditions on the coefficients of the equations and initial conditions under which the Stokes transition functions can be expressed as the generalized Laplace transform of a convergent series of hyperfunctions defined on half-lines in .      

气固两相流中颗粒轨道运动方程的一组分析解

在气固两相流场的单元体内建立了描述颗粒沿轨道运动的控制方程,针对不同Ｒｅｙｎｏｌｄｓ数范围内的气体－颗粒阻力系数表达式,导出了颗粒运动方程的一组分析解,在采用颗粒轨道或随机轨道模型时,它们可用于计算流场网格单元控制体或湍流随机涡团内颗粒运动的速度和轨迹。     

The application of the homotopy perturbation method to one-phase inverse Stefan problem

In this paper, the application of the homotopy perturbation method for solving the inverse Stefan problem is presented. This problem consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of the functions describing temperature and heat flux on the boundary, when the position of the moving interface is known.     

Fundamental Solutions in the Theory of Thermoelasticity for Solids with Double Porosity

In this article, the linear theory of thermoelasticity for solids with double porosity is considered. The fundamental solutions for the systems of steady vibrations (including quasi-static case) and equilibrium equations are constructed by means of elementary functions; the basic properties of such solutions are also established.     

Bounds for the Vanishing Order for Solutions of a Linear Differential System

We provide upper bounds for the order of vanishing of a polynomial restricted to a solution of a linear differential system through a nonsingular point. We deduce an estimate on the maximum order of inflection of the trajectories of a linear nonautonomous vector field.     

Forecasting of peak electricity demand in Mauritius using the non-homogeneous Gompertz diffusion process

In this study, the non-homogeneous Gompertz diffusion process (NHGDP) is used to model the monthly peak electricity demand in Mauritius in order to predict the future values on the basis of a Genetic Algorithm (GA) approach. Our model is developed based a key economic indicator which is the gross domestic product (GDP) and the weather factors such as temperature, hours of sunshine and humidity. Genetic Algorithm then searches for the best coefficients by minimizing the root mean square error. Monthly data from January 2005 to December 2008 are considered to test the model. Finally, the Artificial Neural Network (ANN) is used to forecast each independent variable for the year 2009 and the NHGDP model is validated for that year. Our results show that the model provides an accurate and reliable prediction for the monthly peak electricity demand in Mauritius.     

灰色自记忆模型在年径流预测中的应用

为探索提高年径流预测精度的简单有效途径,以GM(1,1)微分方程为动力核建立了灰色自记忆模型,并应用于寸滩站年径流的拟合和预测中,取得了良好的效果。与组合模型相比,该模型结构简单并具有较高的拟合和预测精度,可应用于年径流序列的预测之中。