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1.
The problem is considered of finding the mechanical impedances of reinforcing ribs of various shapes. The rib is modeled by a narrow plate. The thickness of the rib (the thickness of the plate from which the rib is made) is thus considered small as compared with the height of the rib (the width of the plate). The height of the rib h is assumed small as compared with the lengths of waves propagating in the material of the plate. One of the edges of the rib is assumed to be free of stresses. The matrix giving the relation between the stresses and the velocities of displacements on the second (loaded) edge is called the impedance matrix. An algorithm is proposed for computing the coefficients of the expansion of the impedance matrix in a Taylor series in powers of h. The method is illustrated by the computation of the mechanical impedances of rectilinear and annular reinforcing ribs.  相似文献   

2.
Summary From measurements of two transfer impedances the resistivity of arbitrarily shaped discs may be determined for simply connected, but not for multiply connected regions. As an example of a doubly connected region the transfer impedance of a circular ring is computed. All doubly connected regions may be mapped conformally onto a circular ring.  相似文献   

3.
Electromagnetic scattering by a smooth convex impedance cone   总被引:1,自引:0,他引:1  
The problem of the diffraction of an electromagnetic planewave by a convex cone of arbitrary smooth cross-section withimpedance (Leontovich) boundary conditions is studied. The vectorproblem is reduced to that for the Debye potentials. By meansof Kontorovich–Lebedev integrals, two spectral functionsare introduced and the corresponding boundary value problemis formulated. The spectral functions for the potentials arefound to satisfy the Helmholtz equations on the unit sphereand to be coupled through non-traditional boundary conditionsof the impedance type with shifts on the spectral variable.The use of the Green theorem permits us to establish an integralformulation of the boundary value problem for the spectral functions.The formal asymptotic solution of the problem is then givenfor the case of a narrow cone. For this, two different methodsare given: a method of perturbation applied to the spectralintegral equations and an adaptation of the method of matchingthe asymptotic series in spectral domain. Both methods leadto the same closed-form result for the leading term of the scatteringdiagram asymptotics.  相似文献   

4.
An asymptotic theory is presented for the analysis of surfacewave propagation at high frequencies. The theory is developedfor scalar surface waves satisfying an impedance boundary conditionon a surface, which may be curved and, whose impedance may bevariable. A surface eikonal equation is derived for the phaseof the surface wave field, and it is shown that the wave fieldpropagates over the surface along the surface rays, which arethe characteristics of the surface eikonal equation. The wavefield in space is found by solving certain eikonal and transportequations with the aid of complex rays. The theory is then appliedto several examples: axial waves on a circular cylinder, sphericallysymmetric waves on a sphere, waves on a circular cone with avariable impedance, and waves on the plane boundary of an inhomogeneousmedium. In each case it is found that the asymptotic expansionof the exact solution agrees with the asymptotic solution.  相似文献   

5.
具有扩散影响的Hopfield型神经网络的全局渐近稳定性   总被引:1,自引:0,他引:1  
对具有扩散影响的Hopfield型神经网络平衡点的存在唯一性和全局渐近稳定性进行了研究.在激活函数单调非减、可微且关联矩阵和Liapunov对角稳定矩阵有关时,利用拓扑度理论得到了系统平衡点存在的充分条件.通过构造适当的平均Liapunov函数,分析了系统平衡点的全局渐近稳定性.所得结论表明系统的平衡点(如果存在)是全局渐近稳定的而且也蕴含着系统的平衡点的唯一性.  相似文献   

6.
The electromagnetic scattering of the surface wave by a rectangular impedance cylinder located on an infinite reactive plane is considered for the case that the impedances of the horizontal and vertical sides of the cylinder can have different values. Firstly, the diffraction problem is reduced into a modified Wiener–Hopf equation of the third kind and then solved approximately. The solution contains branch‐cut integrals and two infinite sets of constants satisfying two infinite systems of linear algebraic equations. The approximate analytical or numerical evaluations of corresponding integrals and numerical solution of the linear algebraic equation systems are obtained for various values of parameters such as the surface reactance of the plane, the vertical and horizontal wall impedances, the width and the height of the cylinder. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

7.
We obtain asymptotic formulas for all the moments of certain arithmetic functions with linear recurrence sequences. We also apply our results to obtain asymptotic formulas for some mean values related to average orders of elements in finite fields.  相似文献   

8.
Robust discrimination under a hierarchy on the scatter matrices   总被引:1,自引:0,他引:1  
Under normality, Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] investigated the asymptotic properties of the quadratic discrimination procedure under hierarchical models for the scatter matrices, that is: (i) arbitrary scatter matrices, (ii) common principal components, (iii) proportional scatter matrices and (iv) identical matrices. In this paper, we study the properties of robust quadratic discrimination rules based on robust estimates of the involved parameters. Our analysis is based on the partial influence functions of the functionals related to these parameters and allows to derive the asymptotic variances of the estimated coefficients under models (i)-(iv). From them, we conclude that the asymptotic variances verify the same order relations as those obtained by Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] for the classical estimators. We also perform a Monte Carlo study for different sample sizes and different hierarchies which shows the advantage of using robust procedures over classical ones, when anomalous data are present. It also confirms that better rates of misclassification can be achieved if a more parsimonious model among all the correct ones is used instead of the standard quadratic discrimination.  相似文献   

9.
讨论了二元函数中值定理中间值的渐近性质,给出了一个相关反问题的解.  相似文献   

10.
主要讨论非线性时变系统的一致渐近稳定性,给出Aeyels-Peuteman类型的Matrosov定理定理.与一般的关于一致渐近稳定性的Matrosov定理不同,对Lyapunov函数的要求是不必可微的,并且Lyapunov函数的导数不必严格小于等于零.  相似文献   

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