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 特征方程
 characteristic equation
 A sufficient and necessary condition for oscillation of difference equation with continuous arguments x(t+τ)-x(t)+∑ from i=1 to m qix(t-σi)=0 where τ,qi,σi ∈(0,∞)(i=1,2,…,m),is established by using the characteristic equation. Furthermore,some explicit conditions for oscillation are obtained. 利用特征方程,得到了关于连续变量差分方程x(t+τ)-x(t)+∑ from i=1 to m qix(t-σi)=0其中τ,qi,σi∈(0,∞)(i=1,2,…,m),所有解振动的充要条件和几个显式的充分条件. 短句来源 The so-called Lucas sequence defined as L_(n+2) = L_(n+1) + L_(n),L_(0) = 2,L1 = 1. It is well known that the Lucas characteristic equation is x2 - x - 1 = 0. In this paper, we study which Lucas numbers can be written as the form of the characteristic equation. Lucas数列L_(n+2)=L_(n+1)+L_n，L_0=2，L_1=1。 它的特征方程是x~2-x-1=0．本文研究了可以表示成特征方程左边的形式的Lucas数。 短句来源 A necessary and sufficient condition for the existence of positive solutions for the linear delay difference equation with variable delaysx_(n+1)-x_n+∑mi=1p_i(n)x_(τ_i(n))=0is established by using generalized characteristic equation,which parallels the theory of delay differential equations. 利用广义特征方程,得出了线性变时滞差分方程xn+1-xn+∑mi=1pi(n)xτi(n)=0正解存在的充分必要条件,这个条件是时滞泛函微分方程相应结论的离散形式. 短句来源 Method for Computing the Characteristic Equation of Rayleigh Surface Wave Dispersion Curve Rayleigh表面波频散曲线的特征方程的计算方法 短句来源 The characteristic equation, for estimation of variance components and the variance—covariance matrix of the estimated compenents are derived for the model of Condition. Adjustment with Constraints (CAC). 本文从附有限制条件的条件平差(the Condition Adjustment with Constraints)的数学模型(简称CAC模型)出发,推导了方差分量估计的特征方程,并给出了方差分量估值的方差—协方差矩阵。 短句来源 更多
 characteristic equations
 The Galerkin Method for the Characteristic Equations of the Singular Integral Equations with Hilbert Kernel 带Hilbert核奇异积分方程特征方程的Galerkin方法 短句来源 There have been Characteristic equations for circular waveguides of the following fundamental forms- CMS-Stratton equation, Brown equation, and BWB-Unger equation. 圆波导的特征方程已有几种基本形式:CMS-Stratton方程、Brown方程、BWB-Unger方程。 短句来源 Modal characteristic equations of mode HE11, TE01, TM01 are analysed with numerical method and their dispersion curves are given. 对HE11、TE01、TM01三个低阶模的特征方程进行了数值计算，给出了它们的色散曲线。 短句来源 This paper gives the characteristic equations of Toeplitz operator on H 2(T 2) . The necessary and sufficient conditions of the operator are discussed. The product of two Toeplitz operators is still a Toeplitz operator. 给出了H2 (T2 )上Toeplitz算子的特征方程 :T zTTz =T ,T wTTw =T ,及两个Toeplitz算子 φ ,ψ∈L∞(T2 ) ,Tφ 和Tψ 的乘积TφTψ 仍为Toeplitz算子的充要条件是 :φ对z、w中零个、一个或两个变量共轭解析 ,ψ对余下变量解析 ,且乘积为Tφψ。 短句来源 we classify 3-rank periodic unit impluse response sequence {gi}0∞ into four categories according to their characteristic equations, and discuss the necessary and sufficient conditions of the existence of 3 dimensional minimal realization respectively. 根据无穷序列{gi}0∞的特征方程将3阶周期序列{gi}0∞分为四类,分别讨论了序列{gi}0∞存在3维最小实现的充要条件。 更多
 secular equation
 The propagation characteristics of magnetostatic forward volume waves (MSFVWs) for a double layered YIG waveguide structure under inclined magnetic field are theoretically studied and the secular equation is obtained. In addition,the dispersion relation and delay characteristics of the coupled mode in two different YIG films are studied by numerical analogue in the range of inclination angle from 5° to 20°. 本文研究了在倾斜静磁场作用下 ,双层YIG薄膜波导结构中静磁体波的传播特性 ,得到了其色散的特征方程 ,计算了磁场倾角从 5°到 2 0°范围内双层波导结构中静磁体波传播的色散关系和延迟特性 . 短句来源 The problem of achieving stable reliability analysis of piezoelectric trusses with random parameters was studied on the basis of the finite element analysis method and stable secular equation. 在有限元分析方法基础上,基于稳定特征方程对随机参数压电桁架结构进行稳定可靠性分析. 短句来源 On the basis of the consideration of the above, the article embarks from the multi-degrees of freedom structure secular equation, in view of the different boundary condition, considered Zhang D Wen method and one general perturbation method two elementary theories methods, and has established the corresponding procedure. 基于以上考虑,本文从多自由度结构特征方程出发,针对不同的边界条件,考虑张德文方法和一种通用矩阵摄动方法两种基本理论方法,并编制了相应的程序。 短句来源 The formulation of Love wave secular equation and displacement distribution in layered soils with sloping layers is developed by using finite element method and analytical method in this paper. 利用有限元法及解析法相结合的方法建立了地基含有倾斜层时Love波弥散特征方程和位移计算公式。 短句来源 The dispersion secular equation of Stoneley waves in two infinite solid media is obtained. The characteristics of Stoneley waves in layered solid media are discussed by using the secular equation. 建立了成层无限固体介质中Stoneley波的特征方程 ,并利用这一特征方程进一步讨论了成层无限固体介质中Stoneley波的特性 . 短句来源 更多
 eigenvalue equation
 then use the finite element method to analyse the dielectric loaded resonant cavity ,and get the generalized eigenvalue equation Ax = k02Bx,in matrix B includes the unknownεr′. 然后采用有限元分析的方法来分析介质加载谐振腔,并得到待求广义特征方程Ax = k02Bx,其中B中含有未知数εr′。 短句来源 In this paper, the characteristics of mode fields and optical power coupling among optical fibers of practical 1×3 single-mode optical fiber splitters with a integrative structure of waveguide are derived by using the eigenvalue equation of the symmetric five-layer plannar optical waveguide, and the experimental results are given. 利用五层对称平面介质波导的特征方程，导出了具有波导一体化结构的实际1×3单模光纤分束器的模场特性及其光纤间光耦合特性，并给出了实验结果． 短句来源 In this method. the inverse eigenvalue equation in terms of generalized coordinates is constructed atfirst and then,the unknown local structural parameters are solved by use of optimization methods. 该方法利用复模态综合建立结构在广义坐标下的动力学模型,然后在广义坐标下导出以局部结构参数为未知量的逆特征方程,最后用优化方法求出结构修改参数。 短句来源 Numerical Solution to the Eigenvalue Equation of the Surface Wave on a Lossy Dielectric Plane 有耗介质平面上表面波特征方程的数值解 短句来源 Galerkin method is employed to derive the eigenvalue equation of the shells containing axisymmetrical initial geometrical imperfections. 通过后屈曲分析，应用Galerkin法导出了含有轴对称初始几何缺陷的复合材料圆柱壳的屈曲特征方程。 短句来源 更多

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 characteristic equation
 Examination of the stability of the triangle libration points is reduced to investigation of a characteristic equation of the sixth degree. The problem of the small perturbations of a fiber spun at a given rate onto a bobbin is reduced to a linear integrodifferential equation with retardation whose characteristic equation determines the region of the "draw resonance" instability. The characteristic equation is obtained within linear analysis. Case's method is used to find generalized eigenvectors of the corresponding characteristic equation. The Case approach reduces the equation to a characteristic equation for which generalized eigenvectors and eigenvalues are found. 更多
 characteristic equations
 Some similarity reductions are derived by solving the corresponding characteristic equations. Singular characteristics of standard dynamic blocks, transcendental characteristic equations, and partial spectra of the singular functions were studied. Rozenshtok [4] considers the problem in an adequate statement but, unfortunately, he permitted errors of principle to enter into the writing of the system of characteristic equations; this led to absolutely invalid results. A lax pair for the characteristic equations of averaged many-particle operators The roots of the characteristic equations derived from Rayleigh's equations for surface waves, which were previously interpreted as wave numbers of longitudinal surface waves, do not satisfy the latter equation. 更多
 secular equation
 At the same time, the dispersion relation, which is identical to the secular equation of the Orr-Sommerfeld problem, contains an entire spectrum of solutions not considered in the earlier studies [2-4]. The secular equation with real symmetric positive definite n × n matrix is transformed into a system of n2 quadratic equations for which it is possible to construct a convergent procedure realizing an iterative solution. The secular equation with real symmetric positive definite n × n matrix is transformed into a system of n2 quadratic equations for which it is possible to construct a convergent procedure realizing an iterative solution. For the case of exchange degeneracy in the total spin of the system we give a secular equation that is more compact and convenient for calculations than those obtained earlier. A new equation is presented that expresses first partial derivatives of eigenvalues of the secular equation in terms of first derivatives of coefficients of the secular equation and the eigenvalues themselves. 更多
 eigenvalue equation
 We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schr?dinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space. The eigenvalue equation leads to the differential equation of spheroidal functions. The eigenvalue equation and the frequency characteristic formulas of the input Voltage Stand Wave Ratio (VSWR) are obtained by using the spectral domain method and equivalent circuit method, respectively. The generalized eigenvalue equation governing the hydrodynamic stability of the system was solved using a direct numerical procedure. The eigenvalue equation is formed and the corresponding eigenmodes are presented. 更多
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