一类高阶差分方程系统的稳定性

研究了一类具有初值的高阶差分方程系统平衡点的稳定性问题,得到了平衡点处稳定、局部渐近稳定性、全局渐近稳定性的充分条件,讨论了正平衡点处解的振动性问题.

一类高维指数型差分方程正解的渐近性

研究一类高维指数型差分方程模型x_(n+1)^(i)=a_i+b_ix_(n-1)^(i+1)e^(-x(ni)(i=1,2,…,m)正解的渐近性,其中a_i和b_i是正常数,且初始值x_(-1)^(i)和x_0^(i)是正实数值,x_(n-1)^(m+1)=x_(n-1)^(1)(n=0,1,2,…),获得该方程正平衡点的存在唯一性及正解的有界性、持久性和收敛性的一些充分条件,所得结果推广了已有文献的相关结论.

NWP卡尔曼滤波光伏功率的预测模型

针对超短期光伏功率预测问题,提出一种基于NWP的卡尔曼滤波光伏功率预测模型。将太阳总辐照度视为系统状态变量,光伏发电功率视为系统观测量,利用实测数据拟合确定预测模型的观测方程,引入激励噪声作为控制方程输入量,确定系统差分控制方程,在递推迭代过程中,应用测量功率数据实时修正和限制系统剩余白噪声,实现光伏功率的超短期预测。结果表明,模型的预测误差除个别畸点幅值较大外,其余点误差都在6%以内,天气晴朗时在2%以内,呈现出较好的准确性。

Stochastic Optimal Control of First-Passage Failure for Rectangular Thin Plate Vibration Model under Gaussian White-Noise Excitations

A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito stochastic differential equation for the system is obtained by applying the stochastic averaging method for quasi-nonintegrable Hamiltonian systems. The conditional reliability function and conditional probability density are both gained by solving the backward Kolmogorov equation numerically. Finally, a stochastic optimal control model is proposed and solved. The numerical results show the effectiveness of this method.

Stochastic prediction and control to methane in coalmine

The ventilation system plays an essential role in underground workings, and improvements in dilution effect to stochastic methane build-up at cul-de-sac of a coalmine require the installation of mixed ventilation system. For 4-12-1 I N02.8A centrifugal ventilation fan, the characteristic operating function of its mixed ventilation system is calculated from ventilation quantity and total pressure in the actual working status. At cul-de-sac of the reference coalmine, the evolution of methane concentration is a compound Poisson process and equivalent to a Brownian motion for Gaussian distributed increments. Solution of stochastic differential equation driven by mixed ventilation system, with dilution equation for its closure, provides parameters of mine ventilation system for keeping methane concentration within the permissible limit at cul-de-sac of the reference coalmine. These results intend to shed some light on application of blowing-sucking mixed ventilation systems in underground workings, and establish stochastic trends to consider methane control in coalmines.

Application of Homotopy Analysis Method to Solve Relativistic Toda Lattice System

In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations.

Lie Point Symmetries of Differential-Difference Equations

In this paper, the classical Lie group approach is extended to find some Lie point symmetries of differentialdifference equations. It reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.

New Ansaetze for Obtaining Exact Solutions of Nonlinear Schroedinger-Type Equation

We propose two simple ansaetze that allow us to obtain different analytical solutions for two generalizeal versions of the nonlinear Schrodinger equation, such as the averaged dispersive-managed fiber system equation and the extended nonlinear Schrodinger equation which describe the femtosecond pulse propagation in monomode optical fiber. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media.

Some New Lie Symmetry Groups of Differential-Difference Equations Obtained from a Simple Direct Method

In this paper,based on the symbolic computing system Maple,the direct method for Lie symmetry groupspresented by Sen-Yue Lou [J.Phys.A:Math.Gen.38 (2005) L129] is extended from the continuous differential equationsto the differential-difference equations.With the extended method,we study the well-known differential-difference KPequation,KZ equation and (2+1)-dimensional ANNV system,and both the Lie point symmetry groups and the non-Liesymmetry groups are obtained.

Saint-Venant Fractional Equation and Hydraulic Gradient

The overall objectives to support analytically the mathematical background of hydraulics, linking the Navier-Stokes with hydraulic formulas, which origin is experimental but have wide and varied application. This, leads us study the inverse problem of the coefficients of differential equations, such as equations of the porous medium, Saint-Venant, and Reynolds, and accordingly with the order of derivatives. The research led us to see that the classic version suffers from a parameter that reflects the fractal and non-local character of the viscous interaction. Motivated by the concept of spatial occupancy rate, the authors set forth Navier-Stokes＇s fractional equation and the authors obtain the fractional Saint-Venant. In particular, the hydraulic gradient, or friction, is conceived as a fractional derivative of velocity. The friction factor is described as a linear operator acting on speed, so that the information it contains is transferred to the order of the derivative, so that the same is linearly related to the exponent of the friction factor. It states Darcy＇s non-linear law. The authors take a previous result that describes the nonlinear flow law with a leading term that contains a hyper-geometric function, whose parameters depend on the exponent of the friction factor and the exponent of the hydraulic radius. It searches the various laws of flow according to the best known laws of hydraulic resistance, such as Chezy and Manning.

Simulation of Reciprocating Compressor Start-up and Shut-down under Loaded and Unloaded Conditions

During the start-up and shut-down phase of reciprocating compressors, the loads on all components of driven train system are very high. In this paper a method for calculating the forces on coupling, e-motor, crank shaft as well other components of the system will be described. The modelling of the electrical induction motor, coupling, crank shaft, damper as well as the compressor resistance torque are extremely important in simulating start-up and shut-down of reciprocating compressor. Furthermore the switching torque of the electrical motor and the instantaneous moment of inertia of the reciprocating compressor crank gear are important as well. The transient start-up and shut-down process under loaded and unloaded conditions is described using a non-linear differential equation for driven train system： E-motor--coupling--flywheel--reciprocating compressor--damper. Shaft torsional moments on the drive train and especially on the coupling, whether elastic or stiff, can then only be calculated using numerical simulation. This paper will describe some of the key elements in modelling, simulating and measurements of drive train start-up and shut-down carried out on already operational piston compressor units.

On the solutions and periodic nature of some systems of difference equations

In this paper, we consider the solution of the following rational systems of difference equations：xn＋1=zn-1xn-2/xn-2±yn,yn＋1=xn-1yn-2/yn-2±zn,zn＋1=yn-1zn-2/zn-1±xn,where initial conditions are nonzero real numbers.

Integrable discretization of soliton equations via bilinear method and Backlund transformation

We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method.This approach is mainly based on the compatibility between an integrable system and its B¨acklund transformation.We apply this procedure to several equations,including the extended Korteweg-deVries(Kd V)equation,the extended Kadomtsev-Petviashvili(KP)equation,the extended Boussinesq equation,the extended Sawada-Kotera(SK)equation and the extended Ito equation,and obtain their associated semidiscrete analogues.In the continuum limit,these differential-difference systems converge to their corresponding smooth equations.For these new integrable systems,their B¨acklund transformations and Lax pairs are derived.

Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations

A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectie map and a completely integrable tinite-dimensionai Hamiltonian system.