五边方程的集合理论解(英文)

本文给出五边方程的集合理论解.假设V作用在有限群的张量积G(?)G上,满足五边方程V12V13V23=V23V12,则在给定条件下,V由三元组(a,d,p)惟一确定,其中a,d,p是G到自身的群同态。由此给出了V的分类.

帆边方程的拟合与风压中心的计算

根据帆船运动系统中船帆的客观现状，本文提出了一个帆边方程的分段带约束拟合方法，进而对Ｌａｓｅｒ型船帆的风压中心进行数值计算。

Oscillation of Systems of Parabolic Differential Equations with Deviating Arguments

To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.

A Class of the Singularly Perturbed Boundary Value Problems for Elliptic Equation with a Super Surface of Turning Point in n-dimensional Space

In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.

COMPACT FOUR-COMPONENT 2-D FDFD METHOD WITH EQUIVALENT SURFACE IMPEDANCE BOUNDARY CONDITION FOR MULTILAYER METAL-COATED WAVEGUIDE

A compact four-component two-dimensional （2-D） finite-difference frequency domain （FDFD） method with the equivalent surface impedance boundary condition is used to analyze the dispersion characteristics of multilayer metal-coated waveguides. According to the equivalent surface impedance boundary condition,the relationship between transverse field components on the boundary can be easily depicted. Once the eigen equation is solved,the propagation constant can be obtained as the eigen value for a given frequency. Results of the proposed method agaree well with those of high frequency structure simulator（HFSS）.

Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations

The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.

Analysis of complicated structure seismic wave fields

In western China seismic wave fields are very complicated and have low signal to noise ratio.In this paper,we focus on complex wave field research by forward modeling and indicate that density should not be ignored in wave field simulation if the subsurface physical properties are quite different.We use the acoustic wave equation with density in the staggered finite-difference method to simulate the wave fields.For this purpose a complicated geologic structural model with rugged surfaces,near-surface low-velocity layers,and high-velocity outcropping layers was designed.Based on the instantaneous wave field distribution,we analyzed the mechanism forming complex wave fields.The influence of low velocity layers on the wave field is very strong.A strong waveguide occurs between the top and base of a low velocity layer,producing multiples which penetrate into the earth and form strong complex wave fields in addition to reflections from subsurface interfaces.For verifying the correctness of the simulated wave fields,prestack depth migration was performed using different algorithms from the forward modeling.The structure revealed by the stacked migration profile is same as the known structure.

The Singularly Perturbed Boundary Value Problems for Elliptic Equation with Turning Point

The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.

Oscillatory Criteria for a Class of Boundary Value Problem of Nonlinear Hyperbolic Equations *L

Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.

求超静定结构位移的捷径

用莫尔积分求超静定结构的位移,对初学者来说往往采取解两个超静定问题的方法.实际上这是不必要的.下面我们举例说明之.

A study of perfectly matched layers for joint multicomponent reverse-time migration

Reverse-time migration in finite space requires effective boundary processing technology to eliminate the artificial truncation boundary effect in the migration result.On the basis of the elastic velocity-stress equations in vertical transversely isotropic media and the idea of the conventional split perfectly matched layer（PML）,the PML wave equations in reverse-time migration are derived in this paper and then the high order staggered grid discrete schemes are subsequently given.Aiming at the＂reflections＂from the boundary to the computational domain,as well as the effect of seismic event＇s abrupt changes at the two ends of the seismic array,the PML arrangement in reverse-time migration is given.The synthetic and real elastic,prestack,multi-component,reverse-time depth migration results demonstrate that this method has much better absorbing effects than other methods and the joint migration produces good imaging results.

Blow-up of Solution for a Nonlinear Hyperbolic Equation

In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.

擂题(9)、(8)的有关问题通告

一、关于擂题(9)看过擂题(9)的评注,特别是知道供题人对擂题(9)未有纯几何直接证法而“深感遗憾之惑”(胡安礼)后,又有不少读者来信、来稿,要攻下纯几何直接证明这个堡垒.在这批来稿中,除徐长海先生、万喜人先生的两个证明外,其它的来槁仍不理想.

关于几个几何定值问题

引理1 设两已知点p1（x1,y1）、p2（x2,y2）的连线交直线Ax+By+c=0于点P（P2不在此直线上）.

Singular Perturbation of Two Points Boundary Value Problems for a Class of Third Order Quasilinear Differential Equations

In this paper, the fixed-point Theorem i s used to estimate an asymptotic solution of boundary value problems for a class o f third order quasilinear differential equation and the uniformly valid asymptot ic expansion of solution of any orders including boundary layer is obtained.

Optimal Boundary Control Method for Domain Decomposition Algorithm

To study the domain decomposition algorithms for the equations of elliptic type, the method of optimal boundary control was used to advance a new procedure for domain decomposition algorithms and regularization method to deal with the ill posedness of the control problem. The determination of the value of the solution of the partial differential equation on the interface——the key of the domain decomposition algorithms——was transformed into a boundary control problem and the ill posedness of the control problem was overcome by regularization. The convergence of the regularizing control solution was proven and the equations which characterize the optimal control were given therefore the value of the unknown solution on the interface of the domain would be obtained by solving a series of coupling equations. Using the boundary control method the domain decomposion algorithm can be carried out.

On the Blowing-up Behaviours for Nonlirear Wave Equations

This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite time to the mixed problems with respect to Neumann boundary and Dirichlet boundary for various nonlinear conditions and initial value conditions which usually meet.

A Boundary Integral Equation Approach for Boundary Problem of Laplace Equation

Using the second Green formula, the boundary problem of Laplace equation satisfied by potential function of static electric field is transformed to the problem of the boundary integral equation, and then a boundary integral equation approach is established by partitioning boundary using linear boundary element.

MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects

Combined effects of Soret(thermal-diffusion) and Dufour(diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained.Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.

A Boundary Value Problem for Second Order Functional Differential Equations with Impulses

Aim To investigate the boundary value problem for second order functional differentiai equations with impulses. Methods The fixed point principle was used to establish our results. Results and Conclusion The results of the esistence, the uniqueness and the continuous dependence on aprameter of soiutions of the boundary value problems for second order functional differential equations with impulses are obtained.