THE GENERAL SCHEME FOR HIGHER－ORDER DECOMPOSITIONS OF ZERO－CURVATURE EQUATIONS ASSOCIATED WITH■（2）

ＴＨＥＧＥＮＥＲＡＬＳＣＨＥＭＥＦＯＲＨＩＧＨＥＲ－ＯＲＤＥＲＤＥＣＯＭＰＯＳＩＴＩＯＮＳＯＦＺＥＲＯ－ＣＵＲＶＡＴＵＲＥＥＱＵＡＴＩＯＮＳＡＳＳＯＣＩＡＴＥＤＷＩＴＨ■（２）￥ＺＥＮＧＹＵＮＢＯ（曾云波）（ＤｅｐｏｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａ...     

GLOBAL ATTRACTIVITY OF LINEAR NON－AUTONOMOUS NEUTRAL DIFFERENTIAL－DIFFERENCE EQUATIONS

ＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＯＦＬＩＮＥＡＲＮＯＮ－ＡＵＴＯＮＯＭＯＵＳＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬ－ＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＳＨＥＸＵＥＺＨＯＮＧ（何学中）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｎｉｎｇｘｉ...     

FOURIER－CHEBYSHEV SPECTRAL METHOD FOR SOLVING THREE－DIMENSIONAL VORTICITY EQUATION

ＦＯＵＲＩＥＲ－ＣＨＥＢＹＳＨＥＶＳＰＥＣＴＲＡＬＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＶＯＲＴＩＣＩＴＹＥＱＵＡＴＩＯＮＧＵＯＢＥＮＹＵ（郭本瑜）；ＬＩＪＩＡＮ（李健）；ＭＡＨＥＰＩＮＧ（马和平）（Ｄｅｐａｒｔｍｅｎｔｏ...     

A NOTE ON REGULARITY AND EXISTENCE OF SOLUTIONS FOR A CLASS OF NON－UNIFORMLY DEGENERATE ELLIPTIC EQUATIONS

ＡＮＯＴＥＯＮＲＥＧＵＬＡＲＩＴＹＡＮＤＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮ－ＵＮＩＦＯＲＭＬＹＤＥＧＥＮＥＲＡＴＥＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＬＩＪＵＮＪＩＥ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＺｈｅｊｉａｎｇＵｎｉ...     

SOLVXBILITY OF FORWARD－BACKWARD SDES AND THE NODAL SET OF HAMILTON－JACOBI－BELLMAN EQUATIONS

ＳＯＬＶＸＢＩＬＩＴＹＯＦＦＯＲＷＡＲＤ－ＢＡＣＫＷＡＲＤＳＤＥＳＡＮＤＴＨＥＮＯＤＡＬＳＥＴＯＦＨＡＭＩＬＴＯＮ－ＪＡＣＯＢＩ－ＢＥＬＬＭＡＮＥＱＵＡＴＩＯＮＳ￥ＭＡＪＩＮ；ＹＯＮＧＪＩＯＮＧＭＩＮＡｂｓｔｒａｃｔ：Ｔｈｅｓｏｌｖａｂｉｌｉｔｙｏｆ...     

THE ERRORS ESTIMATION OF THE CHEBYSHEV SPECTRAL－DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORTICITY EQUATION

ＴＨＥ　ＥＲＲＯＲＳ　ＥＳＴＩＭＡＴＩＯＮ　ＯＦ　ＴＨＥ　ＣＨＥＢＹＳＨＥＶ　ＳＰＥＣＴＲＡＬ－ＤＩＦＦＥＲＥＮＣＥ　ＭＥＴＨＯＤ　ＦＯＲ　ＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬ　ＶＯＲＴＩＣＩＴＹ　ＥＱＵＡＴＩＯＮＴＨＥＥＲＲＯＲＳＥＳＴＩＭＡＴＩＯＮＯＦ...     

ON THE DIFFERENTIABILITY OF THE PARITY PROGRESSIVE POPULATION SEMIGROUP

ＯＮＴＨＥＤＩＦＦＥＲＥＮＴＩＡＢＩＬＩＴＹＯＦＴＨＥＰＡＲＩＴＹＰＲＯＧＲＥＳＳＩＶＥＰＯＰＵＬＡＴＩＯＮＳＥＭＩＧＲＯＵＰ￥ＳＨＩＤＥＭＩＮＧＡＮＤＹＡＮＧＬＵＳＨＡＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅ...     

UNIFORM STABILITY AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS

ＵＮＩＦＯＲＭＳＴＡＢＩＬＩＴＹＡＮＤＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＳＯＬＵＴＩＯＮＳＯＦ２－ＤＩＭＥＮＳＩＯＮＡＬＭＡＧＮＥＴＯＨＹＤＲＯＤＹＮＡＭＩＣＳＥＱＵＡＴＩＯＮＳＺＨＡＮＧＬＩＮＧＨＡＩＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

GLOBAL STRUCTURE OF THE ORBITS OF A KIND OF N－DIMENSIONAL COMPETITIVE SYSTEMS

ＧＬＯＢＡＬＳＴＲＵＣＴＵＲＥＯＦＴＨＥＯＲＢＩＴＳＯＦＡＫＩＮＤＯＦＮ－ＤＩＭＥＮＳＩＯＮＡＬＣＯＭＰＥＴＩＴＩＶＥＳＹＳＴＥＭＳ￥ＣｈｅｎｇＣｈｕｎ－ｃｈｏｒ，Ｌｉｔｗｉｎ（郑振初）（ＨｏｎｇＫｏｎｇＩｎｓｔｉｔｕｔｅｏｆＥｄｕｃａｔｉｏｎ，香港...     

EXPONENTIAL STABILITY OF LINEAR TIME－VARYING IMPULSIVE DIFFERENTIAL SYSTEMS WITHDELAYS

ＥＸＰＯＮＥＮＴＩＡＬＳＴＡＢＩＬＩＴＹＯＦＬＩＮＥＡＲＴＩＭＥ－ＶＡＲＹＩＮＧＩＭＰＵＬＳＩＶＥＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＷＩＴＨＤＥＬＡＹＳ￥ＧｕａｎＺｈｉｈｏｎｇ（关治洪）；ＬｉｕＹｏｎｇｑｉｎｇ（刘永清）（ＳｏｕｔｈＣｈｉｎａＵｎ...     

Linearized stability analysis of two-dimension Burnett equations

The linearized stability analyses of two-dimension Burnett equations were studied in present paper for the first time. The characteristic stability equation of two-dimension original Burnett equation was first derived and the characteristic curve was achieved. The material derivatives in original Burnett equations are then replaced with the Euler and Navier-Stokes equations. The stabilities of these two alternative Burnett equations are then analyzed. The linearized stability analyses show that the two-dimension original Burnett and Euler-based Burnett equations are not stable while the Navier-Stokes-based Burnett equations are stable. The critical Knudsen number for the original Burnett and Euler-based Burnett equations are 0.074 and 0.353, respectively. These critical Knudsen number are smaller than those of corresponding one-dimension equations. The two-dimension Burnett equations are more unstable than one-dimension equations.     

On the Least Number of Fixed Points of an Equivariant Map

The problem on the least number of fixed points of an equivariant map of a compact polyhedron on which a finite group acts is considered. For such a map, the least number of fixed points and the least number of fixed orbits are estimated in terms of invariants of the type of Nielsen numbers. The estimates obtained are sharp. The results are similar to those of P. Wong, but their assumptions are essentially weaker. Some notations are refined. The proofs are constructive.     

Permutation Tests for Reflected Symmetry

The paper presents a permutation procedure for testing reflected (or diagonal) symmetry of the distribution of a multivariate variable. The test statistics are based in empirical characteristic functions. The resulting permutation tests are strictly distribution free under the null hypothesis that the underlying variables are symmetrically distributed about a center. Furthermore, the permutation tests are strictly valid if the symmetric center is known and are asymptotic valid if the center is an unknown point. The equivalence, in the large sample sense, between the tests and their permutation counterparts are established. The power behavior of the tests and their permutation counterparts under local alternative are investigated. Some simulations with small sample sizes (?20) are conducted to demonstrate how the permutation tests works.     

凹角型区域椭圆边值问题的自然边界归化

In this paper, the natural boundary reduction for some elliptic boundary value problems with concave angle domains and their natural boundary methods are investigated. The natural integral equations and the Poisson integral formulae are given. The finite element methods of the natural integral equations are discussed in details. The convergences of the approximate solutions and their error estimates are obtained. Finally, some numerical examples are presented to show that our methods are effective.     

Stress analysis of orthotropic planes weakened by cracks

The stress fields in an orthotropic infinite plane containing Volterra type climb and glide edge dislocations are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type and are solved for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.     

一类非线性伪抛物型方程的伪谱解法

本文考虑了一类非线性伪抛物型方程的Fourier伪谱方法,建立了该方程的Fourier伪谱方法的半离散格式和全离散格式．并利用Sobolev空间的正交映射理论,给出了这两种格式的误差估计．最后针对全离散格式给出了数值算例,数值结果表明Fourier伪谱格式能正确加解密,且计算误差较小,效率较高,具有较好的稳定性,可用于提高热流密码体制的加解密效率．     

Constitutive Modelling of Resins in the Stiffness Domain

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic.The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.     

与过程相联系的σ-代数流

讨化了σ-代数流的结构,并给出其一般性的结果;归纳出各σ-代数流的相互关系;最后介绍其两个简单应用.     

横观各向同性多孔超弹性矩形板的单向拉伸

利用横观各向同性超弹性材料的广义neo-Hookean应变能函数研究了含有多个微孔的超弹性矩形板在单向拉伸作用下的有限变形和受力分析.给出了含有某种对称性分布的多个微孔的矩形板的变形模式,通过求解该变形模式满足的微分方程,将它用两个参数表示出来.可应用最小势能原理导出变分近似解,从而得到矩形板的变形和应力分布的解析解.分析了板中微孔的增长及微孔边缘应力的分布情况,讨论了板的各向异性程度及微孔的大小和孔间距离的影响,得到了单个、三个及五个微孔板中微孔的增长变形和孔边应力分布的一些基本规律规律,并进行了相互比较.     

A parallel computational scheme with ninth-order multioperator approximations and its application to direct numerical simulation

The properties of ninth-order multioperator compact schemes based on known third-and fifth-order compact approximations are examined. The domains where the multioperators have fixed signs are determined numerically. The numerical results are compared with the exact solution to the Burgers equation. The multioperator schemes are applied to the problem of vortex sheet roll-up.