多复变解析Toeplitz算子的换位

本文证明了如果φ是C~n中的单位球B_n上非常值的有界解析函数,在单位球面S_n上连续,φ是S_n上的有界解析函数,T_(φ*)和T_φ交换,则φ是B_n上某个解析函数的边界值.另外还讨论了两个Toeplitz算子的换位.     

二阶非线性微分方程边值问题的同伦分析解

研究了结合变量替换应用同伦分析方法,去求解二阶非线性微分方程的两点边值问题,并得到了逼近解析解的函数级数形式.给出了应用同伦分析方法求解二阶非线性问题的三个实例,显示了同伦分析方法可以比较有效地求解非线性问题.     

一类复代数微分方程解的解析式

利用亚纯函数的Nevanlinna值分布理论和微分代数知识,研究了一类高阶代数微分方程解的解析式问题,该类高阶微分方程解的解析式被得到.     

非线性规划的不使用导数的解析方法—统一探讨

本文从统一的角度给出了解约束优化问题的修正的解析方法,即用梯度的近似值代替梯度的解析方法,并在较弱的条件下证明了其全局收敛性。本文结果扩大了解析方法的应用范围,为优化算法的实现提供了理论依据.     

解析Morrey域的若干刻画

研究了导数的对数属于解析Morrey空间的单叶函数,并建立了解析Morrey域的若干新刻画.     

应用虚拟功的互等定理求解均载悬臂厚矩形板的弯曲

悬臂矩形板的弯曲问题一直是平板经典理论中的著名难题,利用中厚板虚拟功的互等定理,借助付宝连提出的角点静力边界条件,得到了均布载荷作用下悬臂厚矩形板弯曲的封闭解析解,并采用现代数值方法和计算软件对所得解析解进行了数值计算.结果表明功的互等法是求解中厚板弯曲问题的一个简明有效的方法.     

上半空间中修改的Poisson积分和Green位势的例外集

本文刻画了修改的Poisson积分和的Green位势在上半空间中的例外集.所得结论推广了关于解析函数、调和函数和超调和函数增长性质的已有结果.     

非线性阻尼力引起破裂路径的分岔

将Rayleigh波的线性阻尼机理拓展到非线性.对选定的模型寻求解析解.这些解析解描绘出破裂路径的不寻常分岔,还与反孤立子和孤立子的交点有关.     

环形蓄热片相变材料固化时热传导问题的Green函数瞬时解

当环形蓄热片为相变材料所固化时,应用Green函数法分析其瞬时的温度分布.在一个柱形壳体中存储该相变材料(PCM),蓄热片上固体相变材料的厚度随时间而变化,并由Megerlin法求得.找到模型用Bessel方程构成的分析解,讨论了3种不同类型的边界条件,给出了解析解和数值解的比较.结果表明,所有情况下得到的蓄热片温度分布精度是令人满意的.     

一类Dirichlet边值逆问题

给出解析函数的一类Dirichlet边值逆问题的数学提法.依据解析函数Dirichlet边值问题和广义Dirichlet边值问题的理论,讨论了此边值逆问题的可解性.利用解析函数Dirichlet边值问题的Schwarz公式,给出了该边值逆问题的可解条件和解的表示式.     

Analytical and experimental evaluation of stresses in elastic annuli subjected to three-point loading on the outer surface

An analytical solution based on the implementation of the Fourier series is presented for the full-field analysis of stresses in an annular plate subjected to external force loadings uniformly distributed over three small segments of the outer periphery when two of those segments are symmetrical about the diameter passing through the center of the third segment. This problem refers to an annular plate which rests upon two equidistant platens when compressed by a vertical locally-distributed force. The obtained theoretical results are compared with a series of photoelastic experiments for different distances between the loaded segments of the rim.  The feasibility of the mathematical model for the mixed-type boundary conditions is analyzed by comparison of the experimental results, the theoretical analysis, and FEM numerical simulation.     

大气运动基本方程组的解析解

在已知大气运动基本方程于光滑函数类中具有最好的稳定性前提下,讨论了它的局部解的解空间构造．根据它的解空间构造,分析了这个方程具有代表性和应用性的第三初值问题,在解析函数类中给出了适定的第三初值问题的解析解的计算方法以及具体的关系表达式,在局部解意义下完整的解决了这一点初值问题的解析解所涉及的理论与计算问题．指出其它类型定解问题都可以仿照文中的计算方法和步骤,求出所需要的稳定的解析解．     

Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux

In this paper, a powerful analytical method, called homotopy analysis method (HAM) is used to obtain the analytical solution for a nonlinear ordinary deferential equation that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. Nonlinear ODE which is obtained by similarity solution has been solved through homotopy analysis method (HAM). The main objective is to propose alternative methods of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The obtained analytical solution in comparison with the numerical ones represents a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region.     

不同模量横力弯曲梁的解析解

选择处于平面复杂应力状态下横力弯曲梁,对结构进行了中性层的判定,推导出中性轴、正应力、剪应力、位移的计算公式,得到如下结论:对于复杂应力状态下的不同模量弹性弯曲梁,其中性轴位置与剪应力无关,因此用正应力作为判据而得到解析解,改进了以往用主应力判定中性点的多次循环的计算方法．把解析解的结果与经典力学同模量理论,以及有限元数值解进行了比较,结果表明:解析解很好地考虑了拉压不同模量的效应．还提出了对不同模量结构的计算修正以及对结构优化的思想．     

Analytical solutions of a class of optimum orbit modifications

This paper presents the complete analytical solution of several fundamental problems in orbital correction. The initial orbit is represented by a given point in the phase space, while the final orbit is constrained to stay in a given curve which can be bounded, unbounded, or composed of a finite number of segments of different curves. The inclusion of atmospheric maneuver as part of the optimum process is discussed; its analytical treatment can be carried out by modifying the final state to include the set of orbits having their perigee at the boundary of the atmosphere.The selection of the apogee and perigee distances as state variables gives a symmetric form to the problem and results in a linear differential equation of the first order for the ratio of the adjoint variables. The introduction of a curve of comparison, called the separatrix, facilitates the discussion of the existence of a corner on an optimal trajectory.This work was supported by NASA Contract No. NASr 54(06).     

不同模量弯压柱的解析解

依据不同模量弹性理论用流动坐标系及分段积分法导出复合荷载作用下弯压柱的解析解,建立了中性轴、应力、应变、位移的计算公式,并编制相应的有限元程序进行计算,与解析解进行误差对比．最后对不同模量计算结果与经典力学同模量计算结果进行分析对比,得出两种理论计算结果的差异,并提出对该类结构计算的合理建议．     

Boundary element solution of the two-dimensional groundwater flow equation with stochastic free surface boundary condition

An innovative approach to the approximate solution of stochastic partial differential equations in groundwater flow is presented. The method uses a formulation of the Ito's lemma in Hilbert spaces to derive partial differential equations satisfying the moments of the solution process. Since the moments equations are deterministic, they could be solved by any analytical or numerical method existing in the literature. This permits the analysis and solution of stochastic partial differential equations occurring in two-dimensional or three-dimensional domains of any geometrical shape. The method is tested for the first time in the present paper through a practical application in a sandy phreatic aquifer at the Chalk River Nuclear Laboratories, Ontario, Canada. The equation solved is the two-dimensional LaPlace equation with a dynamic, randomly perturbed, free surface boundary condition. The moments equations are derived and solved by using the boundary integral equation method. A comparison is made with a previous analytical solution obtained by applying the randomly forced one-dimensional Boussinesq equation, and some observations on modeling procedures are given.     

饱和土体自重固结问题的相似解

采用了比以往更为普遍的土体物理力学性质假设,利用Hopf-Cole变换方法求得了厚层土体在自重应力作用下的非线性固结问题的完整解析解答．通过试验数据,将该解答与传统的大应变线性固结理论解答和基于实验数据的有限元数值解答相比较,结果表明,该解答能够更好地描述土体的实际固结过程,而由线性化固结理论所得的解答对固结过程中的沉降量和固结度的估计偏小．     

The method of differential quadrature for transient nonlinear diffusion

Numerical solutions to transient nonlinear diffusion problems are obtained by the method of differential quadrature. The accuracy of the solutions is inferred by comparison with the analytical solution for the linear case. The particular problems associated with general boundary conditions are handled by the use of integral methods. Examples from heat diffusion include composite media and radiation-enhanced conduction.     

The comparison of two reliable methods for accurate solution of time‐fractional Kaup–Kupershmidt equation arising in capillary gravity waves

In this paper, we compared two different methods, one numerical technique, viz Legendre multiwavelet method, and the other analytical technique, viz optimal homotopy asymptotic method (OHAM), for solving fractional‐order Kaup–Kupershmidt (KK) equation. Two‐dimensional Legendre multiwavelet expansion together with operational matrices of fractional integration and derivative of wavelet functions is used to compute the numerical solution of nonlinear time‐fractional KK equation. The approximate solutions of time fractional Kaup–Kupershmidt equation thus obtained by Legendre multiwavelet method are compared with the exact solutions as well as with OHAM. The present numerical scheme is quite simple, effective, and expedient for obtaining numerical solution of fractional KK equation in comparison to analytical approach of OHAM. Copyright © 2016 John Wiley & Sons, Ltd.