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1.
实值二维信号可以用四元数来表示,因此,四元数的尺度函数和小波的构造就成为分析二维信号的关键.引入了四元数小波包的概念,并且借助于四元数多分辨分析和四元数尺度函数和四元数小波函数的概念和若干公式,给出并构造了一类四元数正交小波包的构造方法,得到了四元数正交小波包的3个正交性公式,最后,利用四元数正交小波包给出了L^2(R...  相似文献   

2.
依据分裂四元数的概念,首先,给出了分裂四元数的实表示矩阵形式,将对分裂四元数的研究转化为实数域上四阶矩阵的研究;其次,根据分裂四元数不同的极表示形式,得到了分裂四元数实表示矩阵相应的棣莫弗定理,推广了欧拉公式,并给出了单位分裂四元数的实表示矩阵方程的求根公式.最后,通过算例验证了结论的正确性.  相似文献   

3.
胡贵军 《数学大王》2007,(15):10-13
第三回唐四藏略施小计 不孝子痛改前非 上回说到四狮兄弟因为分割领地不公而差点兄弟反目.幸亏小圣及时出面相助,才得以平息."功夫不负有心人",四藏经过一夜的苦思冥想之后,终于找出了解决办法.四狮兄弟真是感激不尽,告别了四狮兄弟后,四人继续西行.正好和贝卡他们相遇了.  相似文献   

4.
研究了包含η-厄尔米特矩阵的四元数矩阵方程组.用四元数矩阵的秩和广义逆给出了一个包含η-厄尔米特矩阵的四元数矩阵方程组相容的充分必要条件.进一步地,用四元数矩阵的广义逆给出了这个四元数矩阵方程组的通解表达式.  相似文献   

5.
四元数矩阵的实表示与四元数矩阵方程   总被引:7,自引:0,他引:7  
四元数矩阵与四元数矩阵方程在力学和工程问题的理论研究和实际数值计算中都起到重要的作用.该文借助四元数矩阵的实表示方法,研究了一般四元数矩阵方程AXB-CYD=E的解的问题,给出了一种求解四元数矩阵方程的算法技巧.该文还得到了四元数矩阵的Roth's定理.  相似文献   

6.
通过分析四站保障的影响因素,提出军用机场四站保障指标体系构建方法,运用系统分析法和Delphi法建立了四站保障指标体系,并形成军用机场四站保障效能评估方法,运用可能一满意度及层次分析等方法建立了军用机场四站保障效能评估模型.  相似文献   

7.
把友向量的概念推广到分裂四元数环上,借助分裂四元数的复表示研究了分裂四元数的一系列代数性质,并给出了相应问题的论证方法,从而建立了一套分裂四元数力学的简单数学方法.  相似文献   

8.
本文给出了四元数矩阵惯性的定义,讨论了四元数体上Lyapunov矩阵方程的唯一解,推广了一般惯性定理、Lyapunov稳定性定理、Carlson-Schneider定理、Stein稳定性定理等一些重要的结果到四元数矩阵,同时得出了四元数体上稳定矩阵的一些判别条件.  相似文献   

9.
利用i-共轭重新定义了分裂四元数矩阵的共轭转置,在此基础上借助复表示和友向量研究了分裂四元数矩阵的奇异值分解,并利用所得结果解决了分裂四元数矩阵的极分解和分裂四元数矩阵方程AXB-CYD=E.  相似文献   

10.
利用最大平面图着色的"简化降阶法",对一定拓扑结构的"另一个25阶最大平面图"G′_(M25)进行了着色运作.先逐点"降阶",再逐点"着色、升阶、着色",直至获得G′_(M25)的四色着色方案.由于着色过程中,有些点的着色是可以选择的,在这些点作任意选色后,只是找出其中的二个G′_(M25)的四色着色方案,即"四色着色方案壹"和"四色着色方案贰"(其他的四色着色方案未作求解).然后,在"四色着色方案壹"和"四色着色方案贰"的基础上,利用多层次的"二色交换法",相应地分别求出了G′_(M25)的二个相近四色着色方案集,即"相近四色着色方案集壹"和"相近四色着色方案集贰".在"相近四色着色方案集壹"中,含有72个不同的四色着色方案;在"相近四色着色方案集贰"中,含有156个不同的四色着色方案.文中对这二个相近四色着色方案集进行了分析,得到了有意义的结果.  相似文献   

11.
Under suitable regularity conditions, it is shown that a third order asymptotically efficient estimator is fourth order asymptotically efficient in some class of estimators in the sense that the estimator has the most concentration probability in any symmetric interval around the true parameter up to the fourth order in the class. This is a resolution of the conjecture by Ghosh (1994, Higher Order Asymptotics, Institute of Mathematical Statistics, Hayward, California). It is also shown that the bias-adjusted maximum likelihood estimator is fourth order asymptotically efficient in the class.  相似文献   

12.
In this article, we extend the fourth‐order compact boundary scheme in Liao et al. (Numer Methods Partial Differential Equations 18 (2002), 340–354) to a 3D problem and then combine it with the fourth‐order compact alternating direction implicit (ADI) method in Gu et al. (J Comput Appl Math 155 (2003), 1–17) to solve the 3D reaction‐diffusion equation with Neumann boundary condition. First, the reaction‐diffusion equation is solved with a compact fourth‐order finite difference method based on the Padé approximation, which is then combined with the ADI method and a fourth‐order compact scheme to approximate the Neumann boundary condition, to obtain fourth order accuracy in space. The accuracy in the temporal dimension is improved to fourth order by applying the Richardson extrapolation technique, although the unconditional stability of the numerical method is proved, and several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed new algorithm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013  相似文献   

13.
A fourth order differential operator with summable coefficients and some boundary conditions is considered. Asymptotics of solutions to a fourth order differential equation is studied. The equation for eigenvalues is also studied and an asymptotics of the eigenvalues of the considered boundary value problem is obtained.  相似文献   

14.
A cubic spline method is described for the numerical solution of a two-point boundary value problem, involving a fourth order linear differential equation. This spline method is shown to be closely related to a known fourth order finite difference scheme.  相似文献   

15.
By using a special interpolation operator developed by Girault and Raviart (finite element methods for Navier‐Stokes Equations, Springer‐Verlag, Berlin, 1986), we prove that optimal error bounds can be obtained for a fourth‐order elliptic problem and a fourth‐order parabolic problem solved by mixed finite element methods on quasi‐uniform rectangular meshes. Optimal convergence is proved for all continuous tensor product elements of order k ≥ 1. A numerical example is provided for solving the fourth‐order elliptic problem using the bilinear element. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006  相似文献   

16.
Lie’s invariant criteria for determining whether a second order scalar equation is linearizable by point transformation have been extended to third and fourth order scalar ordinary differential equations (ODEs). By differentiating the linearizable by point transformation scalar second order ODE (respectively third order ODE) and then requiring that the original equation holds, what is called conditional linearizability by point transformation of third and fourth order scalar ODEs, is discussed. The result is that the new higher order nonlinear ODE has only two arbitrary constants available in its solution. One can use the same procedure for the third and fourth order extensions mentioned above to get conditional linearizability by point or other types of transformation of higher order scalar equations. Again, the number of arbitrary constants available will be the order of the original ODE. A classification of ODEs according to conditional linearizability by transformation and classifiability by symmetry are proposed in this paper.  相似文献   

17.
The Paneitz operator is a fourth order differential operator which arises in conformal geometry and satisfies a certain covariance property. Associated to it is a fourth order curvature – the Q-curvature.  相似文献   

18.
A fourth order fourstep ADI method is described for solving the systems of ordinary differential equations which are obtained when a (nonlinear) parabolic initial-boundary value problem in two dimensions is semi-discretized. The local time-discretization error and the stability conditions are derived. By numerical experiments it is demonstrated that the (asymptotic) fourth order behaviour does not degenerate if the time step increases to relatively large values. Also a comparison is made with the classical ADI method of Peaceman and Rachford showing the superiority of the fourth order method in the higher accuracy region, particularly in nonlinear problems.  相似文献   

19.
We consider a system of M(≥2) singularly perturbed equations of reaction-diffusion type coupled through the reaction term. A high order Schwarz domain decomposition method is developed to solve the system numerically. The method splits the original domain into three overlapping subdomains. On two boundary layer subdomains we use a compact fourth order difference scheme on a uniform mesh while on the interior subdomain we use a hybrid scheme on a uniform mesh. We prove that the method is almost fourth order ε-uniformly convergent. Furthermore, we prove that when ε is small, one iteration is sufficient to get almost fourth order ε-uniform convergence. Numerical experiments are performed to support the theoretical results.  相似文献   

20.
We show that a class of regular self-adjoint fourth order boundary value problems (BVPs) is equivalent to a certain class of matrix problems. Conversely, for any given matrix problem in this class, there exist fourth order self-adjoint BVPs which are equivalent to the given matrix problem. Equivalent here means that they have exactly the same spectrum.  相似文献   

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