Transit passenger origin-destination estimation in congested transit networks with elastic line frequencies

This paper deals with the transit passenger origin-destination (O-D) estimation problem by using updated passenger counts in congested transit networks and outdated prior O-D matrix. A bilevel programming approach is extended for the transit passenger O-D updating problem where the upper-level problem seeks to minimize the sum of error measurements in passenger counts and O-D matrices, while the lower level is the stochastic user equilibrium assignment problem for congested transit networks. The transit assignment framework is based on a frequency-adaptive transit network model in this paper, which can help determine transit line frequencies and the network flow pattern simultaneously in congested transit networks. A heuristic solution algorithm is adapted for solving the transit passenger O-D estimation problem. Finally, a numerical example is used to illustrate the applications of the proposed model and solution algorithm. The work described in this paper was mainly supported by two research grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project No. PolyU 5143/03E and PolyU 5040/02E).     

Resonant frequencies for a narrow strip grating

This paper deals with the existence and the distribution of the resonances associated with the Maxwell system in a periodic infinite structure, obtained by loading a substrate with a periodic perturbation. We give an integral formulation of the homogeneous diffraction problem. By boundary integral operators method, the existence and distribution of resonances is reduced to the determination of the characteristic values of two meromorphic operator valued functions. We give existence results on complex resonances close to the resonances of the substrate and also on real resonances. Copyright © 1999 John Wiley & Sons, Ltd.     

Resonant response of a strong electromagnetic wave beam to a gravitational wave in a static magnetic field

Concrete forms of resonant response (ER) for a strong electromagnetic (EM) wave beam (photon flux) propagating in a static magnetic field to a standing gravitational wave (gravitons) are given, and the corresponding perturbation solutions and resonant conditions are obtained. It is found that perturbed EM fields (PEMFs) contain three new components with frequencies Io,* w,l and ωP_g respectively. In the case of ω_e⋙ω_g, the PEMFs are manifested as the EM wave beams with frequency ω_e and a standing EM wave with ω_g. The former and the background EM wave beam (BE-MWB) have the same propagating direction, while in the case of ω_g⋙ω_e, all PEMFs are expressed as the standing EM waves with frequency ω_g. The resonant response occurs in two cases of ω_e = 1/2 ω_g andω_e, = ω_g only. Then not only the first order perturbed energy fluxes (PEFs) propagating in the same and opposite directions of the BEMWB can be generated, but also radial and tangential PEFs which are perpendicular to the above directions can be produced. This effect might provide a new way for the EM detection of the gravitational waves (GWs). Moreover, the possible schemes of displaying perturbed effects induced by the standing GW withh = 10^-33 - 10^-35 and λ_g = 0.1 m at the level of the single photon avalanche and in a typicla laboratory dimension are reviewed.     

一个曲面波方程的精确解

Abstract. Some exact travelling wave solutions and rational travelling wave solutions of a sur-face wave equation in a convecting fluid are given in this paper.     

Resonant wave motion in a non-homogeneous system

A nonlinear theory of resonant wave motion in an inhomogeneous system (arising from different mechanical applications) is considered. Depending on the magnitude of the influence of inhomogeneity two different situations are encountered. The system may behave either as a nonlinear one-degree-of-freedom oscillator exhibiting a response curve with either soft or hard spring behaviour or for a sufficiently small influence of inhomogeneity, there are periodic shock waves in a certain frequency band about the linear resonance frequency, a phenomenon that is familiar from homogeneous systems like a gas filled tube being excited close to resonance.     

Exterior dirichlet problem for the reduced wave equation: asymptotic analysis of low frequencies

The order of convergence for the low frequency asymptotics of the exterior Dirichlet problem for the Helmholtz equation with variable, possibly non-smooth coefficients is shown to be Ω², the square of the frequency, except of some singular cases. In these cases the asymptotics are characterized completely by some lower order terms in the spherical harmonics expansion of the solution to the static problem.     

Global solutions for a nonlinear wave equation

In this work the existence of a global solution for the mixed problem associated to the nonlinear equation

is proved in a Hilbert space framework by using Galerkin method.     

Solitary wave solutions and kink wave solutions for a generalized KDV-mKDV equation

Bifurcation method of dynamical systems is employed to investigate solitary wave solutions and kink wave solutions of the generalized KDV-mKDV equation. Under some parameter conditions, their explicit expressions are obtained.     

New travelling wave solutions for a nonlinearly dispersive wave equation of Camassa-Holm equation type

In this paper, the integral bifurcation method is used to study a nonlinearly dispersive wave equation of Camassa-Holm equation type. Loop soliton solution and periodic loop soliton solution, solitary wave solution and solitary cusp wave solution, smooth periodic wave solution and non-smooth periodic wave solution of this equation are obtained, their dynamic characters are discussed. Some solutions have an interesting phenomenon that one solution admits multi-waves when parameters vary.     

Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping

The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with strong damping is considered. We prove that, under suitable assumptions on relaxation functions and certain initial data, the decay rate of the solutions energy is exponential.     

Exact traveling wave solutions for a modified Camassa-Holm equation

In this paper, the bifurcation method of planar dynamical systems is utilized to investigate a modified Camassa-Holm equation. After dividing the parametric space, some explicit parametric conditions are derived for the existence of traveling wave solutions. Several exact traveling solutions are also obtained.     

一类强阻尼波方程解的存在性和爆破性

讨论一类强阻尼波方程解的局部存在性,并利用势井理论研究解的整体存在性和爆破性.     

Estimates for wave and Klein-Gordon equations on modulation spaces

We prove that the fundamental semi-group eit(m 2I+|Δ|)1/2(m = 0) of the Klein-Gordon equation is bounded on the modulation space M ps,q(Rn) for all 0 < p,q ∞ and s ∈ R.Similarly,we prove that the wave semi-group eit|Δ|1/2 is bounded on the Hardy type modulation spaces μsp,q(Rn) for all 0 < p,q ∞,and s ∈ R.All the bounds have an asymptotic factor tn|1/p 1/2| as t goes to the infinity.These results extend some known results for the case of p 1.Also,some applications for the Cauchy problems related to the semi-group eit(m2I+|Δ|)1/2 are obtained.Finally we discuss the optimum of the factor tn|1/p 1/2| and raise some unsolved problems.     

二维空间上一类半线性波动方程的爆破问题

本文用类似于[1]中解决爆破问题的方法，对二维空间上一类半线性波动方程的初值问题证得了：当非线性项F（u）∈C2（R）和初值g（x）∈CO（R2）且满足一定条件时，初值问题不存在全局C2-解．     

Kinks and travelling wave solutions for Burgers-like equations

In this work we develop a variety of Burgers-like equations. We show that these derived equations share some of the travelling wave solutions of the Burgers equation, and differ in some other solutions.     

Solitary wave and chaotic behavior of traveling wave solutions for the coupled KdV equations

Using the method of dynamical systems to study the coupled KdV system, some exact explicit parametric representations of the solitary wave and periodic wave solutions are obtained in the given parameter regions. Chaotic behavior of traveling wave solutions is determined.     

Strong solutions to stochastic wave equations with values in Riemannian manifolds

Let M be a d-dimensional compact Riemannian manifold. We prove existence of a unique global strong solution of the stochastic wave equation , where Y is a C¹-smooth transformation and W is a spatially homogeneous Wiener process on whose spectral measure has finite moments up to order 2.     

Strichartz estimates for the Dunkl wave equation and application

In this paper, we prove dispersive and Strichartz estimates associated for the Dunkl wave equation.