BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and general shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r*which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if |r| ≥ r*; while they appear as damped oscillatory waves if |r| r*. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory solutions according to the orbits evolution relation corresponding to the component u(ξ) in the global phase portraits, and then obtain the approximate solutions(u(ξ), H(ξ)). Furthermore,by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions.     

Impact analysis of maritime cabotage legislations on liner hub-and-spoke shipping network design

Maritime cabotage is a legislation published by a particular coastal country, which is used to conduct the cargo transportation between its two domestic ports. This paper proposes a two-phase mathematical programming model to formulate the liner hub-and-spoke shipping network design problem subject to the maritime cabotage legislations, i.e., the hub location and feeder allocation problem for phase I and the ship route design with ship fleet deployment problem for phase II. The problem in phase I is formulated as a mixed-integer linear programming model. By developing a hub port expanding technique, the problem in phase II is formulated as a vehicle routing problem with pickup and delivery. A Lagrangian relaxation based solution method is proposed to solve it. Numerical implementations based on the Asia–Europe–Oceania shipping services are carried out to account for the impact analysis of the maritime cabotage legislations on liner hub-and-spoke shipping network design problem.     

Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data

In this paper we present an error estimate for the explicit Runge-Kutta discontinuous Galerkin method to solve a linear hyperbolic equation in one dimension with discontinuous but piecewise smooth initial data. The discontinuous finite element space is made up of piecewise polynomials of arbitrary degree $k\ge 1$ , and time is advanced by the third order explicit total variation diminishing Runge-Kutta method under the standard CFL temporal-spatial condition. The $L^2(\mathbb R \backslash \mathcal R _T)$ -norm error at the final time $T$ is optimal in both space and time, where $\mathcal R _T$ is the pollution region due to the initial discontinuity with the width $\mathcal O (\sqrt{T\beta }h^{1/2}\log (1/h))$ . Here $h$ is the maximum cell length and $\beta $ is the flowing speed. These results are independent of the time step and hold also for the semi-discrete discontinuous Galerkin method.     

平衡指数损失函数下的信度保费

在经典的信度保费模型中,得到的信度保费估计均是考虑的是纯保费,然而在保险实务中,保险公司收取的保费不可能是纯保费,必须具有正的安全负荷.在平衡指数损失函数下,研究了多合同的信度保费模型.利用正交投影方法,得到了未来保费的信度估计.最后对估计进行了数值模拟.     

The defocusing energy-supercritical Hartree equation

In this paper,we study the global well-posedness and scattering problem for the energysupercritical Hartree equation iut+Δu.(|x|.γ.|u|2)u=0 with γ4 in dimension d γ.We prove that if the solution u is apriorily bounded in the critical Sobolev space,that is,u ∈Lt∞(I;Hxsc(Rd)) with sc:= γ/2.11,then u is global and scatters.The impetus to consider this problem stems from a series of recent works for the energy-supercritical nonlinear wave equation(NLW) and nonlinear Schrdinger equation(NLS).We utilize the strategy derived from concentration compactness ideas to show that the proof of the global well-posedness and scattering is reduced to disprove the existence of three scenarios:finite time blowup;soliton-like solution and low to high frequency cascade.Making use of the No-waste Duhamel formula,we deduce that the energy of the finite time blow-up solution is zero and so get a contradiction.Finally,we adopt the double Duhamel trick,the interaction Morawetz estimate and interpolation to kill the last two scenarios.     

Explicit Stationary Distribution of the （L, 1）-reflecting Random Walk on the Half Line

In this paper,we consider the（L,1） state-dependent reflecting random walk（RW） on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for（positive） recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the（L,1）-random walk.     

Subalgebras of FA-presentable algebras

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FA-presentable algebra with a single unary operation is itself FA-presentable. Furthermore, it is proven that the class of unary FA-presentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable.     

The representation of fractional powers of coercive differential operators

In this paper, under the definition of fractional powers by Straub, we will give the representation of fractional powers of coercive differential operators by using pseudo differential operators.     

基于保守决策偏好的犹豫模糊余弦优化投影决策方法

针对犹豫模糊信息下的多属性决策问题,提出了余弦优化投影方法,将投影夹角定义为决策者的风险偏好,并设置了态度参数用于调节决策者的心理变化,通过灵活描述决策者的保守心理,改进了投影法仅考虑投影长度的不足,使决策者可通过投影长度和投影夹角对备选方案进行综合判断。算例验证了方法的合理性和可行性。     

Inexact inverse subspace iteration for generalized eigenvalue problems

n this paper, we present an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax=λBx. We first formulate a version of inexact inverse subspace iteration in which the approximation from one step is used as an initial approximation for the next step. We then analyze the convergence property, which relates the accuracy in the inner iteration to the convergence rate of the outer iteration. In particular, the linear convergence property of the inverse subspace iteration is preserved. Numerical examples are given to demonstrate the theoretical results.