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171.
172.
The problem of detecting the homoclinic orbits of an initially straight buckled beam is addressed. Two families of boundary conditions are identified and investigated in detail. For the first family, the homoclinic orbits belong to a planar invariant manifold, and are easily computed in closed form. For the second family, the manifold is no longer planar, and is detected via the non-linear normal modes technique by obtaining approximate expressions which are sufficient to highlight the effects of the non-flatness. A hierarchy of reduced order, single degree of freedom, models is determined. These are obtained by taking into account increasing degrees of non-linearity in the potential energy, which allow for a more and more refined computation of the homoclinic solution. The various models are compared with each other and discussed in detail, and the non-planarity of the manifold is illustrated through examples. 相似文献
173.
174.
175.
Gongyun Zhao 《Mathematical Programming》1995,68(1-3):49-71
In this paper we study higher-order interior point algorithms, especially power-series algorithms, for solving linear programming problems. Since higher-order differentials are not parameter-invariant, it is important to choose a suitable parameter for a power-series algorithm. We propose a parameter transformation to obtain a good choice of parameter, called ak-parameter, for general truncated powerseries approximations. We give a method to find ak-parameter. This method is applied to two powerseries interior point algorithms, which are built on a primal—dual algorithm and a dual algorithm, respectively. Computational results indicate that these higher-order power-series algorithms accelerate convergence compared to first-order algorithms by reducing the number of iterations. Also they demonstrate the efficiency of thek-parameter transformation to amend an unsuitable parameter in power-series algorithms.Work supported in part by the DFG Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung. 相似文献
176.
George A. Anastassiou Sorin G. Gal 《Journal of Computational Analysis and Applications》1999,1(1):3-23
In recent articles the first author and H. Gonska [e.g., see G. Anastassiou, C. Cottin, and H. Gonska, Global smoothness of approximating functions, Analysis, 11, 43–57 (1991); G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)] studied global smoothness preservation by some univariate and multivariate linear operators over compact domains and
n
, n 1. In particular, they studied a very general positive linear integral type operator [e.g., see G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)] over
n
that was introduced through a convolution-like integration of another general positive linear operator with a scaling-type function. In this article the authors, among others, extend and generalize [G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)]. Also certain new similar but more general integral operators are introduced and studied. These operators arise in a natural way, and for all these sufficient conditions are given for shift invariance, preservation of higher-order global smoothness and sharpness of the related inequalities, convergence to the unit using the first modulus of continuity, shape preservation, and preservation of continuous probabilistic distribution functions. Several examples of very general specialized operators, old and new, are given that satisfy all the above properties. 相似文献
177.
In this paper, we investigate a Langevin model subjected to stochastic intensity noise (SIN), which incorporates temporal fluctuations in noise-intensity. We derive a higher-order Fokker-Planck equation (HFPE) of the system, taking into account the effect of SIN by the adiabatic elimination technique. Stationary distributions of the HFPE are calculated by using the perturbation expansion. We investigate the effect of SIN in three cases: (a) parabolic and quartic bistable potentials with additive noise, (b) a quartic potential with multiplicative noise, and (c) a stochastic gene expression model. We find that the existence of noise-intensity fluctuations induces an intriguing phenomenon of a bimodal-to-trimodal transition in probability distributions. These results are validated with Monte Carlo simulations. 相似文献
178.
This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial data and periodic boundary condition.Motivated by the works of Thomann and Tzvetkov(Nonlinearity,23(2010),2771–2791),Tzvetkov(Probab.Theory Relat.Fields,146(2010),4679–4714),Burq,Thomann and Tzvetkov(Ann.Fac.Sci.Toulouse Math.,27(2018),527–597),the authors first construct the Borel measure of Gibbs type in the Sobolev spaces with lower regularity,and then establish the existence of global solution to the equation with the helps of Prokhorov compactness theorem,Skorokhod convergence theorem and Gibbs measure. 相似文献
179.
The Darboux transformation of a 3 × 3 spectral problem which is associated with the higherorder nonlinear SchrSdinger equation is given. Some solutions of the higher-order nonlinear Schroedinger equation are provided by taking different “seeds“. 相似文献
180.