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81.
本文提出了一种用于光弹性复合材料的简化应变——光学定律。按照这一简化定律。模型材料的主应变差和主应变方向只要利用光弹性实验测出的等差线与等倾线即可求得。些是一种正交异性光弹性分析的近似方法,这一方法所得结果与实验数据比较,最大误差在10%左右。由于采用简化应变——光学定律使得正交异性光弹性分析工作大为简便,因此它是一种适合于工程应用的近似方法。 相似文献
82.
基于抽取和连续投影算法的可见近红外光谱变量筛选 总被引:1,自引:0,他引:1
大多数短波CCD硅检测器为2 048或3 648像元,相邻波长间隔小,预处理算法对其适用性差.本文在600.09~980.47 nm光谱范围内,采用等间隔抽取方法重构光谱矩阵.经不同光谱预处理后,分别采用遗传算法(GA)和连续投影算法(SPA),筛选偏最小二乘法(PLS)建模变量.采用留一法交叉验证评价模型的预测能力,... 相似文献
83.
以同伦近似对称法为理论依据研究了远场模型方程, 通过归纳各阶相似约化解和各阶相似约化方程的通式构造相应的同伦级数解. 各阶相似约化方程均为线性变系数常微分方程, 并且可以从零阶开始依次求解. 同伦模型中的辅助参数影响同伦级数解的收敛性.
关键词:
同伦近似对称法
远场模型方程
同伦级数解 相似文献
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86.
Mathew Baxter Robert A. Van Gorder 《Mathematical Methods in the Applied Sciences》2014,37(11):1642-1651
We consider wave solutions to nonlinear sigma models in n dimensions. First, we reduce the system of governing PDEs into a system of ODEs through a traveling wave assumption. Under a new transform, we then reduce this system into a single nonlinear ODE. Making use of the method of homotopy analysis, we are able to construct approximate analytical solutions to this nonlinear ODE. We apply two distinct auxiliary linear operators and show that one of these permits solutions with lower residual error than the other. This demonstrates the effectiveness of properly selecting the auxiliary linear operator when performing homotopy analysis of a nonlinear problem. From here, we then obtain residual error‐minimizing values of the convergence control parameter. We find that properly selecting the convergence control parameter makes a drastic difference in the magnitude of the residual error. Together, appropriate selection of the auxiliary linear operator and of the convergence control parameter is shown to allow approximate solutions that quickly converge to the true solution, which means that few terms are needed in the construction of such solution. This, in turn, greatly improves computational efficiency. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
87.
Zhenbin Fan 《Optimization》2014,63(8):1205-1217
In this paper, we study the approximate controllability of a linear fractional differential equation by using the method of regularization of Tikhonov. New concepts and results about controllability are established. Then, under the condition of the positivity of the controllability operator, we obtain that the linear system can be steered to an arbitrary small neighbourhood of the fractional integral of the state at final time. 相似文献
88.
本文研究了矩阵方程AX = B 的Hermitian R-对称最大秩和最小秩解问题. 利用矩阵秩的方法, 获得了矩阵方程AX = B有最大秩和最小秩解的充分必要条件以及解的表达式, 同时对于最小秩解的解集合, 得到了最佳逼近解. 相似文献
89.
Panayot S. Vassilevski Ludmil T. Zikatanov 《Numerical Linear Algebra with Applications》2014,21(3):297-315
Motivated by the increasing importance of large‐scale networks typically modeled by graphs, this paper is concerned with the development of mathematical tools for solving problems associated with the popular graph Laplacian. We exploit its mixed formulation based on its natural factorization as product of two operators. The goal is to construct a coarse version of the mixed graph Laplacian operator with the purpose to construct two‐level, and by recursion, a multilevel hierarchy of graphs and associated operators. In many situations in practice, having a coarse (i.e., reduced dimension) model that maintains some inherent features of the original large‐scale graph and respective graph Laplacian offers potential to develop efficient algorithms to analyze the underlined network modeled by this large‐scale graph. One possible application of such a hierarchy is to develop multilevel methods that have the potential to be of optimal complexity. In this paper, we consider general (connected) graphs and function spaces defined on its edges and its vertices. These two spaces are related by a discrete gradient operator, ‘Grad’ and its adjoint, ‘ ? Div’, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then, a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ?2‐projection QH onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection πH from the original edge‐space onto a properly constructed coarse edge‐space associated with the edges of the coarse graph. The projections πH and QH commute with the discrete divergence operator, that is, we have Div πH = QH div. The respective pair of coarse edge‐space and coarse vertex‐space offer the potential to construct two‐level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian, which utilizes the discrete divergence operator. The performance of one two‐level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
90.
引入了拟绝对-*-k-仿正规算子,获得了拟绝对-*-k-仿正规算子的一个充要条件.并证明了拟绝对-*-k-仿正规算子在0≤k≤1上是有限上升的,作为此性质的应用,证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则Weyl谱和本质近似点谱的谱映射定理成立.最后证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则σ_(ja)(T)\{0}=σ_a(T)\{0}. 相似文献