具有热储备的并行可修系统稳态解的最优控制

研究了具有热储备的并行可修复系统中,其稳定解的最优控制问题,并给出了其最优解的存在唯一性.     

On a stochastic wave equation with unilateral boundary conditions

We prove the existence and uniqueness of solutions to the initial boundary value problem for a one-dimensional wave equation with unilateral boundary conditions and random noise. We also establish the existence of an invariant measure.

     

Application of Homotopy Perturbation Method and Variational Iteration Method to Nonlinear Oscillator Differential Equations

In this paper, homotopy perturbation method (HPM) and variational iteration method (VIM) are applied to solve nonlinear oscillator differential equations. Illustrative examples reveal that these methods are very effective and convenient for solving nonlinear differential equations. Moreover, the methods do not require linearization or small perturbation. Comparisons are also made between the exact solutions and the results of the homotopy perturbation method and variational iteration method in order to prove the precision of the results obtained from both methods mentioned.     

向量优化问题有效解的稳定性

运用标量化的方法,通过锥正定真有效解的上半连续性讨论了无限维赋范空间中锥有效解的部分上半连续性,证明了锥有效解的通有稳定性.在此基础上,进一步证明,在Baire纲的意义下,绝大多数的向量优化问题至少存在一个锥正定真有效解是本质的有效解,换句话说,绝大多数的向量优化问题锥有效解是几乎下半连续的.     

一类具偏差变元的二阶微分方程周期解

By using the theory of coincidence degree,we study a kind of periodic solutions to second order differential equation with a deviating argument such as x"(t) f(x'(t)) h(x(t))x'(t) g(x(t-τ(t)))=p(t),some sufficient conditions on the existence of periodic solutions are obtained.     

积因子求权重层次分析法在城市排序中的应用

克服传统层次分析法确定因素权重主观性太强的不足,结合积因子方法给出了积因子赋值求权重层次分析法,并利用该方法对黑龙江省各城市按可持续发展指标进行排序,得到符合实际的结果.     

广义变系数Kdv方程的对称及其群不变解

利用经典李对称的方法对广义变系数Kdv方程进行研究,利用这种方法得到了该方程的一个新的精确解,这种方法的基本思路是通过对称约化将原来较难求解的偏微分方程转化为较易求解的常微分方程进行求解.实例证明这种方法具有一般性,适合于求一大类变系数的非线性演化方程.     

Nonstandard perturbation approximation and travelling wave solutions of nonlinear reaction diffusion equations

This paper deals with the construction of a nonstandard numerical method to compute the travelling wave solutions of nonlinear reaction diffusion equations at high wave speeds. Related general properties are studied using the perturbation approximation. At high wave speed the perturbation parameter approaches to zero and the problem exhibits a multiscale character. That is, there are thin layers where the solution varies rapidly, while away from these layers the solution behaves regularly and varies slowly. Most of the conventional methods fail to capture this layer behavior. Thus, the quest for some new numerical techniques that may handle the travelling wave solutions at high wave speeds earns relevance. In this paper, one such parameter robust nonstandard numerical scheme is constructed, in the sense that its numerical solution converges in the maximum norm to the exact solution uniformly well for all finite wave speeds. To overcome the difficulty due to the nonlinearity, the problem is linearized using the quasilinearization process followed by nonstandard finite difference discretization. An extensive amount of analysis is carried out which uses a suitable decomposition of the error into smooth and singular component and a comparison principle combined with appropriate barrier functions. The error estimates are obtained, which ensures uniform convergence of the method. A set of numerical experiment is carried out in support of the predicted theory that validates computationally the theoretical results. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

The locally conservative Galerkin (LCG) method for solving the incompressible Navier–Stokes equations

In this paper, the locally conservative Galerkin (LCG) method (Numer. Heat Transfer B Fundam. 2004; 46 :357–370; Int. J. Numer. Methods Eng. 2007) has been extended to solve the incompressible Navier–Stokes equations. A new correction term is also incorporated to make the formulation to give identical results to that of the continuous Galerkin (CG) method. In addition to ensuring element‐by‐element conservation, the method also allows solution of the governing equations over individual elements, independent of the neighbouring elements. This is achieved within the CG framework by breaking the domain into elemental sub‐domains. Although this allows discontinuous trial function field, we have carried out the formulation using the continuous trial function space as the basis. Thus, the changes in the existing CFD codes are kept to a minimum. The edge fluxes, establishing the continuity between neighbouring elements, are calculated via a post‐processing step during the time‐stepping operation. Therefore, the employed formulation needs to be carried out using either a time‐stepping or an equivalent iterative scheme that allows post‐processing of fluxes. The time‐stepping algorithm employed in this paper is based on the characteristic‐based split (CBS) scheme. Both steady‐ and unsteady‐state examples presented show that the element‐by‐element formulation employed is accurate and robust. Copyright © 2007 John Wiley & Sons, Ltd.     

Euler's Problem Revisited: 222 Years Later

This paper furnishes several closed-form solutions for the buckling eigenvalue problem of the columns with variable flexural rigidity along the axis. The column is either under uniformly distributed axial load or under concentrated compressive load. Sommario. Questo lavoro fornisce diverse soluzioni in forma chiusa per il problema agli autovalori dell'instabilità di colonne con rigidezza flessionale variabile lungo l'asse. La colonna è soggetta ad un carico assiale unifor-memente distribuito oppure ad una forza di compressione concentrata.