极限环的表达式和计算

本文提出一种解析法和数值法相结合的方法，用来计算多项式微分系统的极限环，极限环表示为x=∑k≥0(ak cos kφ bk sin kφ),y=∑k≥0(ck cos kφ dk sin kφ)，先用解析法求出小参数时极限环的初始表达式，然后用增量法和迭代法求出任意参数时极限环满足给定精度的表达式，半稳定极限环和分叉值也可以计算。     

可靠度的M-Bayes可信限及其性质

以前作者提出了一种新的参数估计方法-M-Bayes可信限法,并且给出了可靠度的M-Bayes可信下限的估计.给出了另一个可靠度的M-Bayes可信下限的估计,并给出了M-Bayes可信下限的性质一可靠度的两个M-Bayes可信下限与经典置信下限的关系.最后,给出一个例子,从这个例子可以看出本文提出的方法可行且便于应用.     

M-BAYESIAN CREDIBLE LIMIT METHOD OF PARAMETER AND ITS APPLICATION

This article develops a new method, named M-Bayesian credible limit method, to estimate reliability parameter. In the article, the M-Bayesian credible limit method of failure rate is derived for zero-failure data from products with exponential distribution. Relations between M-Bayesian credible limit and other classical confidence limits are discussed. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.     

M-BAYESIAN CREDIBLE LIMIT METHOD OF PARAMETER AND ITS APPLICATION

This article develops a new method, named M-Bayesian credible limit method, to estimate reliability parameter. In the article, the M-Bayesian credible limit method of failure rate is derived for zero-failure data from products with exponential distribution. Relations between M-Bayesian credible limit and other classical confidence limits are discussed. Finally, the new method isapplied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.     

Investment timing and optimal capacity choice for small hydropower projects

This paper presents a method for assessing small hydropower projects that are subject to uncertain electricity prices. We present a real options-based method with continuous scaling, and we find that there is a unique price limit for initiating the project. If the current electricity price is below this limit it is never optimal to invest, but above this limit investment is made according to the function for optimal size. The connection between the real option and the physical properties of a small hydropower plant is dealt with using a spreadsheet model that performs a technical simulation of the production in a plant, based on all the important choices for such a plant. The main results of the spreadsheet are simulated production size and the investment costs, which are in turn used for finding the value of the real option and the price limit. The method is illustrated on three different Norwegian small hydropower projects.     

Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis

In this paper, we present a method of higher-order analysis on bifurcation of small limit cycles around an elementary center of integrable systems under perturbations. This method is equivalent to higher-order Melinikov function approach used for studying bifurcation of limit cycles around a center but simpler. Attention is focused on planar cubic polynomial systems and particularly it is shown that the system studied by ?o?a?dek (1995) [24] can indeed have eleven limit cycles under perturbations at least up to 7th order. Moreover, the pattern of numbers of limit cycles produced near the center is discussed up to 39th-order perturbations, and no more than eleven limit cycles are found.     

电机工程中一类非线性振动方程的渐近分析

本文采用文［１］中提出的修正的方法，研究电机工程中一类非线性振动方程，定量地给出了存在极限环的参数范围以及极限环的振幅，并判定该极限环是不稳定的，这些结果与已知的定性分析结果完全一致，从而进一步证实了上述渐近方法的有效性。     

A new method for parameter sensitivity estimation in structural reliability analysis

For the parameter sensitivity estimation with implicit limit state functions in the time-invariant reliability analysis, the common Monte Carlo simulation based approach involves multiple trials for each parameter being varied, which will increase associated computational cost and the cost may become inevitably high especially when many random variables are involved. Another effective approach for this problem is featured as constructing the equivalent limit state function (usually called response surface) and performing the estimation in FORM/SORM. However, as the equivalent limit state function is polynomial in the traditional response surface method, it is not a good approximation especially for some highly non-linear limit state functions. To solve the above two problems, a new method, support vector regression based response surface method, is therefore presented in this paper. The support vector regression algorithm is employed to construct the equivalent limit state function and FORM/SORM is used in the parameter sensitivity estimation, and then two illustrative examples are given. It is shown that the computational cost of the sensitivity estimation can be greatly reduced and the accuracy can be retained, and results of the sensitivity estimation obtained by the proposed method are in satisfactory agreement with those computed by the conventional Monte Carlo methods.     

Analysis of Hermite subdivision using piecewise polynomials

In this paper we begin to explore a new method of analyzing the regularity of Hermite subdivision schemes that are defined from local polynomial interpolants. The idea of the method is to view the limit of the scheme as the limit of splines formed by these local interpolants rather than as the limit of polygons. We demonstrate the success of the method by obtaining the precise Hölder regularity of the simple, but non-trivial scheme in which the data are uniformly spaced and the refinement rule is defined by quintic interpolation of four values and two derivatives.     

多自由度非线性振动系统的内共振

本文研究多自由度非线性自治系统的周期解问题,我们推广了KBM[1]法,本方法可以求得极限环的相图,振幅,周期及其稳定性.     

An extended sequential limit analysis based on moving coordinates for pressurized spherical cap membranes with large shape change

Sequential limit analysis (SLA) is an effective and normally used method to calculate the plastic limit load of structures with large deformation. However, attribute to the assumption of neglecting the changing behavior of shape and plane stress direction, the conventional SLA method would be inaccurate in the plastic response prediction for the large-shape-change structures, especially for the pressurized spherical cap. This research develops a novel analytical model for the pressurized spherical cap based on the advanced SLA method, which features introducing the moving coordinate system and considering of the changing behavior of shape and plane stress direction into the conventional method. With the proposed method, the effects of geometry and material parameters on the plastic limit load are analyzed. Compared with the validating FE simulation results of ABAQUS software, the newly extended SLA method performances a more precise prediction of the load deflection response and plastic limit load than the normal one. Due to the limit yield degree and bending moment, the accuracy of the new model will increase with the increase of yield strength and radius. The larger the initial deflection of the pressurized spherical cap is, the smaller the relative error between the analysis results of advanced SLA and FE method is. Moreover, this newly proposed SLA remains effective and accurate within a wide range of the initial thickness-curvature radius ratio, especially for low elasticity modulus materials.     

Homogenisation and spectral convergence of a periodic elastic composite with weakly compressible inclusions

A two-phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the two-scale limit is found to solve a Stokes type problem and shown to have no microscopic oscillations when the composite is subjected to body forces that are microscopically irrotational. The composites spectrum is analysed and shown to converge, in an appropriate sense, to the spectrum of the two-scale limit problem. A characterisation of the two-scale limit spectrum is given in terms of the limit macroscopic and microscopic behaviours.     

最短时限最少耗费的缺省指派问题及决策求解

文章指出了存在于军事决策与管理科学中最短时限最少耗费的缺省指派问题，并对其进行了深入的理论研究。论证了逼近最短时限的一个重要的定理及联系最短时限、最少耗费缺省指派最优解与经典指派问题最优解之间的相关性定理。据此首次建立了求解最短时限、最少耗费缺省指派的决策方法。这一方法可被广泛地应用于军事决策中进攻目标最优缺省选择与经济建设中工程最优缺省立项尽快见效等方面的一类新的科学决策。     

Global stability and oscillations of dynamical systems describing synchronous electrical machines

A new mathematical model for a synchronous machine with strong excitation control is proposed. The limit load problem for synchronous machines is considered. The limit admissible load is estimated by the nonlocal reduction method. Criteria for the existence of circular solutions and limit cycles of the second kind for the model of a synchronous machine are obtained.     

万因斯坦-钱伟长法的应用——简支与固支混合边界矩形板基频上下限

本文将边界条件放松法[1][2]应用于简支与固支混合边界矩形板,求得此类板的基频下限值.文中还设计了一种能满足位移边界条件的多项式作为振型试函数,从而用里兹法得到相应的上限值.具体算例得到了满意的结果.最后本文指出,通常用力法迭加法得到的此类板的所谓精确解,若考虑实际计算的级数截断误差,本质上是一种下限解.     

Bifurcations of limit cycles in a Z 4-equivariant quintic planar vector field

In this paper, a Z4-equivariant quintic planar vector field is studied. The Hopf bifurcation method and polycycle bifurcation method are combined to study the limit cycles bifurcated from the compounded cycle with 4 hyperbolic saddle points. It is found that this special quintic planar polynomial system has at least four large limit cycles which surround all singular points. By applying the double homoclinic loops bifurcation method and Hopf bifurcation method, we conclude that 28 limit cycles with two different configurations exist in this special planar polynomial system. The results acquired in this paper are useful for studying the weakened 16th Hilbert＇s Problem.     

The limit cycles of a second-order system of differential equations: The method of small forms

In this paper we investigate the existence of limit cycles of a system of the second-order differential equations with a vector parameter.We propose a method for representing a solution as a sum of forms with respect to the initial value and the parameter; we call this technique the method of small forms. We establish the conditions under which a sufficiently small neighborhood of the equilibrium point contains no limit cycles. We construct a polynomial, whose positive roots of odd multiplicity define the lower bound for the number of cycles, and simple positive roots (other positive roots do not exist) define the number of limit cycles in a sufficiently small neighborhood of the equilibrium point.We prove theorems, whose conditions guarantee that a positive root of odd multiplicity defines a unique limit cycle, but a positive root of even multiplicity defines exactly two limit cycles.We propose a method for defining the type of the stability of limit cycles.     

Limit cycles for a perturbation of a quadratic center with symmetry

To estimate the number of limit cycles appearing under a perturbation of a quadratic system that has a center with symmetry, we use the method of generalized Dulac functions. To this end, we reduce the perturbed system to a Liénard system with a small parameter, for which we construct a Dulac function depending on the parameter. This permits one to estimate the number of limit cycles in the perturbed system for all sufficiently small parameter values. We find the Dulac function by solving a linear programming problem. The suggested method is used to analyze four specific perturbed systems that globally have exactly three limit cycles [i.e., the limit cycle distribution 3 or (3, 0)] and two systems that have the limit cycle distribution (3, 1) (i.e., one nest around each of the two foci).     

Computing the weak limit of KdV

The solution of the KdV equation with single-minimum initial data has a zero-dispersion limit characterized by Lax and Levermore as the solution of an infinite-dimensional constrained quadratic minimization problem. An adaptive numerical method for computing the weak limit from this characterization is constructed and validated. The method is then used to study the weak limit. Initial simple experiments confirm theoretical predictions, while experiments with more complicated data display multiphase behavior considerably beyond the scope of current theoretical analyses. The method computes accurate weak limits with multiphase structures sufficiently complex to provide useful test cases for the calibration of numerical averaging algorithms. © 1994 John Wiley & Sons, Inc.     

关于求解极限的若干思考

无穷小等价替换是计算极限一种常用且好用的方法,但要求替换项在极限点的某个邻域内没有零点,文章证明了函数在极限点的任意邻域都出现零点时,满足一定条件,等价替换仍可实施.另外利用极坐标计算二元函数极限时有诸多的限制,文章针对一类特殊函数给出了应用极坐标便于计算应用的若干结论.