5556814
Travelling wave solutions in the generalized Hirota-Satsuma coupled KdV system
By using the bifurcation theory of dynamical systems to the generalized Hirota-Satsuma coupled KdV system, bifurcation parameter sets are shown. Numbers of solitary waves, kink waves and periodic waves are given. Under various parameter conditions, all explicit formulas of solitary wave solutions and kink wave solutions and periodic wave solutions are listed.
29892228
Bifurcations of traveling wave solutions for a class of the generalized Benjamin-Bona-Mahony equation
Abstract By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin–Bona–Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves, finally. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.
11714898
On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation
Abstract This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C 9 1 ⊃ [ C 1 1 + 2 ( C 3 2 ⊃ 2 C 1 2 ) ] . These results in the paper are useful for the study of the weakened Hilbert’s 16th problem.
644571
Parametric inference for progressive Type-I hybrid censored data on a simple step-stress accelerated life test model
This paper considers a simple step-stress accelerated life test model under progressive Type-I hybrid censoring scheme. The progressive Type-I hybrid censoring scheme and statistical method in synthetic accelerated stresses are provided so as to decrease the lifetime and reduce the test cost. An exponentially distributed life of test units and a cumulative exposure model are assumed. The maximum likelihood estimates of the model parameters are obtained using a pivotal quantity. Two useful lemmas and a theorem are given to construct the approximate confidence intervals for the model parameters. Finally, simulation results are provided to assess the method of inference developed in this article. The simulation results show that the method does improve for large sample size.
8986777
Bifurcation method and traveling wave solution to Whitham-Broer-Kaup equation
By using bifurcation method to Whitham-Broer-Kaup shallow water equations, bifurcation parameter sets are shown. Numbers of solitary waves, kink waves and periodic waves are given. Under various parameter conditions, all explicit formulas of solitary wave solutions, kink wave solutions and periodic wave solutions are listed.
7423569
Global Analysis of Stochastic bifurcation in Duffing System
Stochastic bifurcation of a Duffing system subject to a combination of a deterministic harmonic excitation and a white noise excitation is studied in detail by the generalized cell mapping method using digraph. It is found that under certain conditions there exist two stable invariant sets in the phase space, associated with the randomly perturbed steady-state motions, which may be called stochastic attractors. Each attractor owns its attractive basin, and the attractive basins are separated by boundaries. Along with attractors there also exists an unstable invariant set, which might be called a stochastic saddle as well, and stochastic bifurcation always occurs when a stochastic attractor collides with a stochastic saddle. As an alternative definition, stochastic bifurcation may be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value. This definition applies equally well either to randomly perturbed motions, or to p...
20174343
An operator splitting method for variational inequalities with partially unknown mappings
In this paper, we propose a new operator splitting method for solving a class of variational inequality problems in which part of the underlying mappings are unknown. This class of problems arises frequently from engineering, economics and transportation equilibrium problems. At each iteration, by using the information observed from the system, the method solves a system of nonlinear equations, which is well-defined. Under mild assumptions, the global convergence of the method is proved, and its efficiency is demonstrated with numerical examples.
38900432
Fast (Structured) Newton Computations
Many vector-valued functions, representing expensive computations, are also structured computations. In this case the calculation of the Newton step can be greatly accelerated by exploiting this structure. It is often not necessary, nor economic, to form the true Jacobian in the process of computing the Newton step; instead, a more cost-effective auxiliary Jacobian matrix is used. This auxiliary matrix can be sparse even when the true Jacobian matrix is dense; consequently, sparse matrix technology can be used, to great speed advantage, both in forming the auxiliary matrix and in solving the auxiliary linear system.
15359787
Task-Based Dialog Management Using An Agenda
Dialog management addresses two specific problems: (1) providing a coherent overall structure to interaction that extends beyond the single turn, (2) correctly managing mixed-initiative interaction. We propose a dialog management architecture based on the following elements: handlers that manage interaction focussed on tightly coupled sets of information, a product that reflects mutually agreed-upon information and an agenda that orders the topics relevant to task completion.
28282459
The design and characteristics of piezomotors using flexure-hinged displacement amplifiers
Two prototype piezomotors are described in terms of their operational principles, design, construction and some operating characteristics. Both are driven by mechanically amplified piezoelectric stack type actuators. One is a harmonic piezomotor in which the mechanically amplified displacements are used as the wave generator of a harmonic gear drive. The other uses similar mechanical amplifiers to drive a roller clutch motion generator. The requirements for effective mechanical amplifiers are discussed and the performance advantages of piezomotors based on them outlined. It is concluded that such motors can offer useful possibilities for specialist mechatronic applications.
21408324
A Stability Property of T. Chan's Preconditioner
In this short note, we prove that T. Chan's preconditioner proposed in {TChan} [SIAM J. Sci. Statist. Comput., 9 (1988), pp. 766--771] is stable for matrices that are normal and stable.