差商算子的多尺度分解与B样条级数的非均匀细分算法

This paper presents a decomposition scheme of the m-th order divided difference operator on non-uniform knots. Through it we introduce a subdivision algorithm of arbitrary B-spline series. Two numerical experiments on function approximation and curve fitting are given to show the efficiency of our algorithm.     

Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

This paper studies a low order mixed finite element method (FEM) for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q ₁ ^rot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H ¹-norm and the pressure in the L ²-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.     

Singular Hartree equation in fractional perturbed Sobolev spaces

We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.     

非平稳市场中适应性在线投资组合策略设计与分析

考虑到股票市场的表现往往是非平稳的, 过去较长时间的股票价格对当前的投资决策影响较小, 因此基于近期股票价格数据设计在线投资组合策略. 首先, 将上一期的策略与固定长度的股票价格近期数据对应的最优定常再调整策略加权平均, 设计了一个在线投资组合策略. 其次, 进一步采用在线学习的方法选择加权平均的权重, 设计了一个适应性的在线投资组合策略. 利用实际股票价格数据对构造的策略进行数值分析, 结果表明与基准策略和已有的在线投资组合策略相比, 设计的策略具有较好的性能.     

Collision-induced rovibrational energy transfer in small polyatomic molecules: the role of intramolecular perturbations

ABSTRACT

Various forms of time-resolved optical double-resonance spectroscopy facilitate rotationally resolved measurements of collision-induced intramolecular vibration-to-vibration (V–V) energy-transfer processes, which take a gas-phase polyatomic molecule from one distinct rovibrational energy level to another. Of longstanding mechanistic interest are questions concerning the extent to which such V–V energy transfer (ET) may be influenced by intramolecular perturbations – notably Fermi resonance (and other anharmonic mixing effects) and Coriolis coupling – within polyatomic molecular rovibrational manifolds of interest. It is evident that quantum-mechanical interference effects can arise, either inhibiting or enhancing the probability of collision-induced ET in perturbed rovibrational manifolds of certain small gas-phase polyatomic molecules, notably CO₂, D₂CO and C₂H₂. This article focuses on a blend of high-resolution rovibrational spectroscopy (characterising initial and final molecular levels and their intramolecular perturbations) and collision dynamics (with colliding molecules defined in terms of isolated-molecule spectroscopic basis states). It aims to offer fresh insights and to consider some apparent mechanistic anomalies (e.g. collision-induced quasi-continuous background effects in the 4ν_CH rovibrational manifold of C₂H₂). Various reported experiments and related theoretical treatments are critically re-examined, in order to pose and address mechanistic questions some of which still challenge detailed understanding.     

Effect of resonant magnetic perturbations on edge plasma parameters in the STOR-M tokamak

Edge plasma properties have been modified in the Saskatchewan Torus-Modified tokamak by means of resonant magnetic perturbations (RMP). It has been found that the radial profiles of ion saturation current and floating potential in the edge region can be modified by an externally applied static (m?=?2, n?=?1) RMP field. An increase in the pedestal plasma density (n) and more negative electric field (E_r) have been observed in the plasma edge region. It is believed that the RMP field altered the plasma transport in the edge and scrape-off layer regions, leading to a higher density pedestal and a potential drop in some cases. During the enhanced confinement phase, it is possible to identify a region where intermittent transport events, the so-called blobs, are created and the holes of lower density left behind.     

Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations

A convenient and universal residue calculus method is proposed to study the stochastic response behaviors of an axially moving viscoelastic beam with random noise excitations and fractional order constitutive relationship, where the random excitation can be decomposed as a nonstationary stochastic process, Mittag-Leffler internal noise, and external stationary noise excitation. Then, based on the Laplace transform approach, we derived the mean value function, variance function and covariance function through the Green's function technique and the residue calculus method, and obtained theoretical results. In some special case of fractional order derivative α , the Monte Carlo approach and error function results were applied to check the effectiveness of the analytical results, and good agreement was found. Finally in a general-purpose case, we also confirmed the analytical conclusion via the direct Monte Carlo simulation.     

Breather Dynamics of the Sine-Gordon Equation

This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity. The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.     

Perturbations of Multipliers of Systems of Periodic Ordinary Differential Equations

The paper deals with periodic systems of ordinary differential equations (ODEs). A new approach to the investigation of variations of multipliers under perturbations is suggested. It enables us to establish explicit conditions for the stability and instability of perturbed systems.     

Existence of traveling wave solutions for a nonlinear dissipative-dispersive equation

In this paper, we consider a dissipative-dispersive nonlinear equation appliable to many physical phenomena. Using the geometric singular perturbation method based on the theory of dynamical systems, we investigate the existence of its traveling wave solutions with the dissipative terms having sufficiently small coefficients. The results show that the traveling waves exist on a two-dimensional slow manifold in a three-dimensional system of ordinary differential equations （ODEs）. Then, we use the Melnikov method to establish the existence of a homoclinic orbit in this manifold corresponding to a solitary wave solution of the equation. Furthermore, we present some numerical computations to show the approximations of such wave orbits.