LIMIT SETS OF A CLASS OF FOUR-DIMENSIONAL COMPETITIVE SYSTEMS

ＬＩＭＩＴＳＥＴＳＯＦＡＣＬＡＳＳＯＦＦＯＵＲ－ＤＩＭＥＮＳＩＯＮＡＬＣＯＭＰＥＴＩＴＩＶＥＳＹＳＴＥＭＳＲｕａｎＪｉａｎｃｈｅｎｇ（阮建成）（ＪｉｎａｎＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ａ．Ｊ．Ｓｃｈｗａｒｔｚ［９］ｓｔｕｄｉｅｄＣ２ｄｙｎａ...     

HORSESHOE EFFECT AND TOPOLOGICAL ENTROPYOFONE－DIMENSIONALMAPS

ＨＯＲＳＥＳＨＯＥＥＦＦＥＣＴＡＮＤＴＯＰＯＬＯＧＩＣＡＬＥＮＴＲＯＰＹＯＦＯＮＥ－ＤＩＭＥＮＳＩＯＮＡＬＭＡＰＳ＊ＸＩＬＩＦＥＮＧＡｂｓｔｒａｃｔ．Ｉｎｔｈｉｓｐａｐｅｒ，ｆｏｒａｎｙｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎｆ：［０，１］→［０，１］，...     

关于不同分布两两NQD列的Jamison型加权乘积和的强稳定性

本文讨论了不同分布两两ＮＱＤ列的Ｊａｍｉｓｏｎ型加权乘积和的强稳定性及乘积和的Ｍａｒｃｉｎｋｉｅｗｉｃｚ型强大数律,推广并改进了Ｅｔｅｍａｄｉ［１］关于不同分布两两独立列部分和的工作及Ｍａｔｕｌａ［２］,王岳宝等［３］关于同分布两两ＮＱＤ列部分和的工作．     

Stability of Periodic Solutions of Ordinary Differential Equations in Banach Spaces

§１．ＤｅｆｉｎｉｔｉｏｎｓａｎｄＮｏｔａｔｉｏｎｓＬｅｔＥｂｅａｒｅａｌＢａｎａｃｈｓｐａｃｅ,ａｎｄｌｅｔｘ,ｙ∈Ｅ．Ｔｈｅｄｉｒｅｃｔｉｏｎａｌｄｅｒｉｖａｔｉｖｅ［ｘ,ｙ］－ｏｆｘａｎｄｙｉｓｄｅｆｉｎｅｄｂｙ（ｆｏｒｍｏｒｅｄｅｔａｉｌｓｓ...     

EMBEDDING FLOWS AND SMOOTH CONJUGACY

ＥＭＢＥＤＤＩＮＧＦＬＯＷＳＡＮＤＳＭＯＯＴＨＣＯＮＪＵＧＡＣＹＺＨＡＮＧＭＥＩＲＯＮＧＬＩＷＥＩＧＵＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＭａｒｃｈ２３，１９９４．ＲｅｖｉｓｅｄＮｏｖｅｍｂｅｒ１，１９９５．ＤｅｐａｒｔｍｅｎｔｏｆＡｐ...     

Riccati微分方程的可积条件

Ｉｎ１９９８,ＺｈａｏＬｉｎｌｏｎｇ［１］ｏｂｔａｉｎｅｄｔｈｅｉｎｔｅｇｒａｂｌｅｃｏｎｄｉｔｉｏｎ：Ｒ＝１αγＰｅ２∫（Ｑ－βＤ）ｄｘ　　　（α,β,γｉｓｃｏｎｓｔ）．（１）ＦｏｒＲｉｃｃａｔｉｅｑｕａｔｉｏｎ：ｙ′＝ｐ（ｘ）ｙ２＋Ｑ（ｘ）ｙ＋Ｒ（ｘ）　　（ＰＲ≠０）．（２）　　Ｈｅｒｅｔｈｅｎｅｗｉｎｔｅｇｒａｂｌｅｃｏｎｄｉｔｉｏｎｓｉｓｇｉｖｅｎ：Ｌ［ｙ０］＝１αγＰｅ２∫（Ｑ＋２ｙ０ｐ－βＤ）ｄｘ．（３）Ｌ［ＡＢ＋ｙ０］＝１αγ（ＡＢ）２Ｌ［ｙ０］ｅ２∫（２ＢＡＬ［ｙ０］＋Ｑ＋２ｙ…     

On the Structure of the B—cocleft Module Coalgebra

§１．　ＴｈｅＥｑｕｉｖａｌｅｎｔＴｈｅｏｒｅｍｏｆｔｈｅＣｒｏｓｓｅｄＣｏｐｒｏｄｕｃｔＬｅｔＣｂｅａｌｅｆｔＨ－ｗｅａｋｌｙｃｏｍｏｄｕｌｅｃｏａｌｇｅｂｒａ［４］ｗｉｔｈｔｈｅｓｔｒｕｃｔｕｒｅρ－Ｃ（ｃ）＝∑ｃ（１）ｃ（２）．ＤｂｅｌｅｆｔＨ－ｍｏｄｕｌｅｃｏａｌｇｅｂｒａ［２］ｗｉｔｈｔｈｅｓｔｒｕｃｔｕｒｅ“”．Ｆｏｒα∈Ｈｏｍκ（Ｃ，ＨＨ）ｄｅｎｏｔｅα（ｃ）＝∑α１（ｃ）α２（ｃ）．Ｄｅｆｉｎｅ△－：ＣＤ→（ＣＤ）（ＣＤ）ａｎｄε－：ＣＤ→κａｓｆｏｌｌｏｗ－ｉ…     

改进HS共轭梯度算法及其全局收敛性

１．引 言 １９５２年 Ｍ．Ｈｅｓｔｅｎｅｓ和Ｅ．Ｓｔｉｅｆｅｌ提出了求解正定线性方程组的共轭梯度法［１］．１９６４年Ｒ．Ｆｌｅｔｃｈｅｒ和Ｃ．Ｒｅｅｖｅｓ将该方法推广到求解下列无约束优化问题： ｍｉｎｆ（ｘ）,ｘ∈Ｒｎ,（１）其中ｆ：Ｒｎ→Ｒ１为连续可微函数,记ｇｋ＝ ｆ（ｘｋ）,ｘｋ∈ Ｒｎ． 若点列｛ｘｋ｝由如下算法产生：其中 βｋ＝［ｇＴｋ（ｇｋ－ｇｋ－１）］／［ｄＴｋ－１（ｇｋ－ｇｋ－１）］．（Ｈｅｓｔｅｎｅｓ－Ｓｔｉｅｆｅｌ）　　（４）则称该算法为 Ｈｅｓｔｅｎｅｓ—Ｓｔｉｅｆｅｌ共轭梯度算…     

The Pell Equations x^2—8y^2=1 and y2—Dz^2=1

ＯｎｔｈｅＰｅｌｌｅｑｕａｔｉｏｎｓｘ２－８ｙ２＝１,　ｙ２－Ｄｚ２＝１（１）ｗｈｅｒｅＤ＞０ｉｓａｓｑｕａｒｅ－ｆｒｅｅｉｎｔｅｇｅｒ．ＣａｏＺｈｅｎｆｕ［１］ｓｈｏｗｅｄｔｈａｔｉｆＤ＝∏ｓｉ＝１Ｐｉ≡１（ｍｏｄ４）ｏｒＤ＝２∏Ｐｉ,１≤ｓ≤４,ｔｈｅｎｔｈｅｅｑｕａｔｉｏｎ（１）ｈａｓｎｏｌｙｐｏｓｉｔｉｖｅｉｎｔｅｇｅｒｓｏｌｕｔｉｏｎｚ＝６（Ｄ＝２·１７）．ＣｈｅｎｇＪｉａｎｈｕａ［２］ｓｈｏｗｅｄｔｈａｔｉｓＤ＝∏ｓｉ＝１Ｐｉ　１≤ｓ≤２,ｔｈｅｎｔｈｅｅｑｕａｔｉｏｎ（１）ｈａｓｏ…     

A CLASS OF FDE WITH DEVIATING ARGUMENT WHICH DEPENDS ON STATE AND RATE OF CHANGE OF THE STATE

ＦｏｒｔｈｅＮｏｎ－Ｒ．Ｎ．Ａ．ＦＤＥ，ｔｈｅｒｅａｒｅｗｉｄｅａｐｐｌｉｃａｔｉｏｎｓ［１］．Ｔｈｅｓｅｅｑｕａｔｉｏｎｓｓｈｏｗａｎｉｍｐａｒｔａｎｔｃｈａｒａｃｔｅｒ，ｗｈｉｃｈｂｏｔｈｐｏｓｉｔｉｖｅａｎｄｎｅｇａｔｉｖｅｄｅｌａｙａｃｔａｓ...     

A Characteristic Mixed Finite Element Two-Grid Method for Compressible Miscible Displacement Problem

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The concentration equation is treated by a mixed finite element method with characteristics (CMFEM) and the pressure equation is treated by a parabolic mixed finite element method (PMFEM). Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations. Moreover, the $L^q$ error estimates are conducted for the pressure, Darcy velocity and concentration variables in the two-grid solutions. Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.     

The method of mixed volume element‐characteristic mixed volume element and its numerical analysis for three‐dimensional slightly compressible two‐phase displacement

Numerical simulation of oil‐water two‐phase displacement is a fundamental problem in energy mathematics. The mathematical model for the compressible case is defined by a nonlinear system of two partial differential equations: (1) a parabolic equation for pressure and (2) a convection‐diffusion equation for saturation. The pressure appears within the saturation equation, and the Darcy velocity controls the saturation. The flow equation is solved by the conservative mixed volume element method. The order of the accuracy is improved by the Darcy velocity. The conservative mixed volume element with characteristics is applied to compute the saturation, that is, the diffusion is discretized by the mixed volume element and convection is computed by the method of characteristics. The method of characteristics has strong computational stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation. Small time truncation error and accuracy are obtained through this method. The mixed volume element simulates diffusion, saturation, and the adjoint vector function simultaneously. By using the theory and technique of a priori estimates of differential equations, convergence of the optimal second order in norm is obtained. Numerical examples are provided to show the effectiveness and viability of this method. This method provides a powerful tool for solving challenging benchmark problems.     

Superconvergence of a combined mixed finite element and discontinuous Galerkin approximation for an incompressible miscible displacement problem

A combined mixed finite element and discontinuous Galerkin approximation for an incompressible miscible displacement problem which includes molecular diffusion and dispersion in porous media is studied. That is to say, the mixed finite element method is applied to the flow equation, and the transport equation is solved by an interior penalty discontinuous Galerkin method. Convolution of the Darcy velocity approximation with the Bramble-Schatz kernel function and averaging are applied in the evaluation of the coefficients in the Galerkin procedure for the concentration. A superconvergence estimate is obtained. Numerical experimental results are presented to verify the theoretical analysis.     

An approximation of incompressible miscible displacement in porous media by mixed finite elements and symmetric finite volume element method of characteristics

A nonlinear system of two coupled partial differential equations models miscible displacement of one incompressible fluid by another in a porous medium. A sequential implicit time‐stepping procedure is defined, in which the pressure and Darcy velocity of the mixture are approximated by a mixed finite element method and the concentration is approximated by a combination of a modified symmetric finite volume element method and the method of characteristics. Optimal order convergence in H¹ and in L² are proved for full discrete schemes. Finally, some numerical experiments are presented. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

A characteristic mixed element method for displacement problems of compressible flow in porous media

A new characteristic mixed element scheme is formulated to solve numerically displacement problems of compressible fluids in porous media. A new mixed finite element method is introduced to solve the pressure equation of parabolic type, in which the mixed element system is symmetric positive definite and the pressure equation is separated from the flux equation. The modified method of characteristics is used to treat convection-dominated diffusion equations of the concentrations. The convergence with optimal accuracy is proved under the general condition. Project supported in part by China State Major Key Project for Basic Researches, Doctoral Station Foundation and TCTPF of China State Education Commission.     

多孔介质可混溶流动问题的混合元与区域分裂特征差分格式

1 引 言 用区域分裂方法求微分方程的数值解,是近年来计算数学领域的—个新方法。这种方法通过分裂区域来减少所处理问题的规模,并实现并行计算,因此,特别适用于大范围的工程技术问题和数学物理问题。本文用这种方法处理平面可混溶不可压缩流动问题其中J=[0.T].u为Darcy速度,p为压力,c为浓度,k为渗透率,μ（c)为流体粘性,c为注入井给定浓度,q为外界源汇项,q~+=max{q,0}.φ为孔隙度。D为扩散矩阵,本文D与u无关。即仅考虑分子扩散,边条件可取为第一或第二类边条件。本文考虑第一类初边值问题     

A splitting positive definite mixed element method for miscible displacement of compressible flow in porous media

A miscible displacement of one compressible fluid by another in a porous medium is governed by a nonlinear parabolic system. A new mixed finite element method, in which the mixed element system is symmetric positive definite and the flux equation is separated from pressure equation, is introduced to solve the pressure equation of parabolic type, and a standard Galerkin method is used to treat the convection‐diffusion equation of concentration of one of the fluids. The convergence of the approximate solution with an optimal accuracy in L²‐norm is proved. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 229–249, 2001     

半导体器件瞬态模拟的对称正定混合元方法

提出具有对称正定特性的混合元格式求解非稳态半导体器件瞬态模拟问题。提出一个最小二乘混合元方法、一个新的具有分裂和对称正定性质的混合元格式和一个解经典混合元方程的对称正定失窃工格式求解电场位势和电场强度方程;提出一个最小二乘混合元格式求解关于电子与空穴浓度的非稳态对流扩散方程,浓度函数和流函数被同时求解;采用标准的有限元方法求解热传导方程。建立了误差分析理论。     

关于求解二相渗流的平面问题的一类新方法

本文提出一类求解二相平面渗流问题的新方法:用有限元法求解关于压力分布的椭圆型方程,然后利用所得的对压力梯度的半解析解,根据已有的饱和度沿流线传播的精确公式求得饱和度场.其主要特点和优点是能克服通常的数值模拟方法所具有的数值弥散,给出准确清晰的水驱油前沿饱和度间断面的位置,并且完全避免了通常必须与压力方程联立求解或交替求解的饱和度方程,从而使计算工作量大大减少.