线性方程组几种解结构

本文对线性方程组的一般解,最小二乘解、极小范数解和极小范数最小二乘解分别进行了讨论,并得出它们的表出形式。     

关于丢番图方程x2±xy+y2=p

设p是形如6k+1的正素数,运用数论方法及计算机程序,获得了丢番图方程x2-xy+y2=p在p<100000时的满足x相似文献   

边界单元法三维应力分析计算程序

以三维弹性力学问题的基本解 (Kelvin解 )为基础开发了边界单元法三维弹性应力分析计算程序 ,并对其进行了验证。结果表明 ,该程序可用来求解三维弹性应力问题 ,尤其适用于三维应力集中问题。程序中采用动态分配内存 ,自动选点积分 ,并利用分块解法求解方程组 ,有效地节省了计算机资源 ,扩大了求解问题的规模。     

叠加势V(r)=A_1r~6+A_2r~2+B_2r~(-4)+B_1r(-6)径向Schrdinger方程的解析解

采用连分法得到了幂函数与逆幂函数V(r)=A1r6+A2r2+B2r-4+B1r-6的叠加势径向Schrodinger方程的 解析解.     

An Investigation of Stimulating the Autoclave Curing Process of Resin Matrix／Fiber Reinforced Composite Material, Ⅰ ： Process model

A mathematical model is made which describes the curing process of composites constructed from continuous fiber-reinforced, thermosetting resin matrix prepreg materials, and the consoli-dation of the composite is developed. The model provides the variation of temperature distribu-tion, the entre reaction process in the resin, the resin flow and fibers stress inside the composite,and the void variation and the residual stress distribution. It can be used to illustrate the mecha-nism of curing process and optimize the cure cycle of composite material in order to ensure the quality of a product.     

C_0-半群的脉冲扰动与一类半线性脉冲发展方程(英文)

研究无限维Banach空间中一半群的脉冲扰动及一类非线性脉冲系统的温和解的存在性、唯一性、正则性和连续依赖性,最后给出例子加以说明。     

Dynamical framework with blocking topography coordinates for atmospheric GCM and its validation

The dynamical framework with Blocking Topography Coordinates (hereafter, BTC), which is suited to handle the steep topography for the atmospheric general circulation models, is presented in this paper, together with its validation results. The integral properties of both the differential and finite-difference equations for the BTC dynamical core are: gross mass conservation, quadratic conservation for advection terms, Coriolis force does not change the kinetic energy, conservation of total available energy. The improved nonlinear iteration scheme is utilized for the time-integration. The energy conservation for BTC dynamical core is validated by using the integration results from 9-layer and 21-layer version respectively. Comparison results show that, the changes of the kinetic energy and total available potential energy during the integration are quite close for both the BTC dynamical framework and the dynamical framework of IAP 9-level and IAP 21-level AGCM, and this may suggest that the BTC dynamical core can be used for long-term integration with good computational stability. Furthermore, the BTC dynamical core has the advantage over the terrain following (sigma) coordinates in its better representation of the influence of the large-scale topography on the atmospheric general circulation. Finally, the correctness and reasonableness of the BTC dynamical core has been further proved by the numerical simulation of the topography influence on the quasi-stationary planetary wave with 21-layer version of BTC dynamical framework.     

An iterative algorithm in potential-field inversion

1　Principle and MethodAll the problems of potential- field inversioncan be concluded that of solving nonlinear functionas follows:b =f( x) ( 1 )where x =( x1,x2 ,… .xn) T,xj( j =1 ,2 ,… ,n)indicate geometricparameters and physical parame-ters of the object;b=( b1,b2 ,… ,bm) T,bi( i=1 ,2 ,… ,m) indicate potential- field measurements.Main algorithms for expression( 1 ) are leastsquare method ( include damping least squaremethod ) ,gradient method ( conjugate gradientmethod and variable met…     

关于常微分方程初值问题数值解误差的探讨

引用B样条插值函数讨论了一阶常微分方程初值问题的数值解 ,给出一个隐式近似求解公式 ,并得到此公式的局部截断误差为O(h5) ,整体截断误差为O(h4 ) .在此基础上又给出了一个校正显式求解公式 ,其局部截断误差为O(h4 ) .     

(3+1)维NNV方程的精确解

引入一个简单的变换，把(3 1)维Nizhnik-Novikov-Vesdov(NNV)方程化为一维KdV方程，从而通过已知KdV方程的解得到(3 1)维NNV方程的若干精确解。这种方法可以推广开来，方便地建立起某一高维方程和其它低维非线性方程的联系，然后通过求解低维的非线性方程找到高维非线性方程的精确解。