二阶中立型微分方程的区间振动准则

利用平均函数技巧 ,对二阶中立型微分方程 [a(t) (x(t) p(t)x(t-τ) )′]′ q(t)f[x(t) ,x(t-σ) ]g[x′(t) ]=0建立了一些区间振动准则 ,这些振动准则不同于已知依赖于整个区间 [t0 ,∞ )的性质的结果 ,而是仅依赖于 [t0 ,∞ )上的子区间列的性质     

具有阻尼项的二阶非线性微分方程的区间振动准则

本文研究一类具有阻尼项的二阶非线性微分方程,利用平均函数和一个广义Riccati变换,得到了该方程的新的区间振动准则,这些准则不同于已知的依赖于整个区间[t0,∞)的性质的结果,而是仅依赖于区间[t0,∞)的子区间列的性质．所得结果推广和改进了Kong的振动准则．特别,还给出了几个例子以说明本文所得结果的优越性．     

二阶半线性常微分方程的区间振动准则

通过利用平均函数及 Ｈａｒｄｙ ，Ｌｉｔｔｌｅｗｏｏｄ和 Ｐｏｌｙａ不等式，对二阶半线性微分方程建立了一些新的区间振动准则，这些准则不同于已知的依赖于整个区间[ｔ０，∞）的性质的结果，而是仅依赖于区间[ｔ０，∞）的子区间列的性质．所得结果推广和改进了 Ｋａｍｅｎｅｖ，Ｋｏｎｇ，Ｌｉ和 Ｙｅｈ及 Ｐｈｉｌｏｓ的振动准则，同时也可应用于以前所不能处理的某些情形，如特别，还给出了几个例子以说明本文所得结果优越性．     

二阶中立型Emden-Fowler方程的区间振动准则

利用Riccati变换及积分平均技巧,建立了一类具有多个时滞的中立型Emden-Fowler方程的区间振动准则,这些准则不同于已知的依赖于整个[t_0,∞)性质的结果,而是仅依赖于[t_0,∞)的子区间列的性质,结果推广并改进了一些已有的结果.     

二阶矩阵微分系统振动的区间准则

本文研究了二阶矩阵微分系统的振动性：（Ｐ（ｔ）Ｙ＇）＇＋Ｑ（ｔ）Ｙ＝ ０,ｔ∈［ｔ０,∞）,其中Ｐ,Ｑ,Ｙ是ｎ×ｎ实矩阵函数,Ｐ（ｔ）,Ｑ（ｔ）是对称的且Ｐ（ｔ）正定．所得的准则仅依赖于系统在［ｔ０,∞）的一个子区间序列的信息而有别于已知的大多数结论,我们的结果更精确,并能应用于判别如极端情形．     

线性矩阵Hamilton系统振动性的区间判据

采用两种不同的方法,得到了线性矩阵Hamilton系统的振动性判据.这些振动性判据仅依赖于系数矩阵在[to,∞)的某些子区间上的性质,从而改进并推广了许多已知的Kamenev型振动准则.     

具有正负系数的中立型方程的振动性

讨论中立型方程d/dt[x(t)-R(t)x(t-r)] P(t)x(t-t)-Q(t)x(t-δ）=0,（*）其中P,Q,R∈C[（to,∞）,R∧ ）,r,τ,δ∈（0,∞）,τ≥δ,在允许R（t） ∫∧tt=τ δQ（u）du-1变号的情况下得到（*）的所有解振动的判据。     

高阶中立型非线性时滞微分方程振动及非振动性

考虑中立型微分方程其中n≥1为奇数,P∈C（[to,∞）,R）,τ＞0,σi≥0,fi∈C（[to,∞）×R,R）,i＝1,2,……,m本文在允许P（t）－1振动的情况下获得了此方程所有解振动及存在正解的充分条件作为应用,证明了方程所有解振动（ηπ＜β）或存在最终正解（ηπ＞β,其中C＞0,β＞0.     

具连续变量的中立型差分方程的振动性

本文研究如下具有连续变量的中立型差分方程△（y（t）-p（t）y（t-τ）） q（t）y（t-σ0=0,t≥to(*)其中q(t）∈C[to,∞）,R∧ ）,τ,σ是非负实数的解的振动性,获得了方程（*）的每个解都振动的若干充分条件,改进了文献中的结果。     

非线性中立型时滞方程解的全局渐近稳定性和振动性

本文研究非线性中立型时滞微分方程N( t) =N( t) [a( t) -b( t) N ( t-τ) -c( t) N( t-σ) -d( t) N ( t) ],t≥ t0 ,( E)其中τ,σ∈ [0 ,∞ ) ,a( t) ,b( t) ,d( t)∈ C1( [t0 ,∞ ) ,R+) ,c( t)∈ C( [t0 ,∞ ) ,k) ,得到方程 ( E)的正解关于正常数平衡点全局渐近稳定和振动的充分条件 .本文所用方法与其他文献不同 ,所得结果发展了一些文献的结果 ,其中定理 ( 2 .3)回答了由 Y.Kuang and A.Feldstein所提出的一个公开问题 .     

房地产业对中国经济真的那么重要吗？

为恰当评估房地产业对中国经济的重要性,通过编制2002、2007和2012年中国社会核算矩阵,进行乘数分解和结构化路径分析的结果表明:房地产业对行业总产出、劳动力和资本报酬、居民和企业收入的拉动作用极低。房地产业主要对金融业、租赁和商务服务业、建筑业以及金属冶炼与压延加工业四个行业的产出影响比较显著,对前三个行业主要是直接的一步式影响,与房地产业紧密相关的产业链条并不长。房地产业对要素报酬和机构收入的拉动总效应极小,且主要是开环效应,与此同时,房地产业主要通过自身和金融业影响要素报酬进而影响机构收入,特别是对资本报酬和企业收入的影响简单、直接,高度依赖这两条基础路径。土地出让金和房地产有关税收已成为地方政府的主要收入来源。房地产开发和运营商、金融机构和地方政府已成为房地产业发展过程中最主要的利益相关方。     

Topological transformation groups of manifolds over non-Archimedean fields,their representations,and quasi-invariant measures,II

Diffeomorphism groups and loop groups of manifolds on Banach spaces over non-Archimedean fields are defined. Moreover, for these groups, finite-and infinite-dimensional manifolds over the corresponding fields are considered. The group structure, the differential-geometric structure, and also the topological structure of diffeomorphism groups and loops groups are studied. We prove that these groups do not locally satisfy the Campbell-Hausdorff formula. The principal distinctions in the structure for the Archimedean and classical cases are found. The quasi-invariant measures on these groups with respect to dense subgroups are constructed. Stochastic processes on topological transformation groups of manifolds and, in particular, on diffeomorphism groups and on loop groups and also the corresponding transition probabilities are constructed. Regular, strongly continuous, unitary representations of dense subgroups of topological transformation groups of manifolds, in particular, those of diffeomorphism group and loop groups associated with quasi-invariant measures on groups and also on the corresponding configurational spaces are constructed. The conditions imposed on the measure and groups under which these unitary representations are irreducible are found. The induced representations of topological groups are studied by using quasi-invariant measures on topological groups. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 18, Functional Analysis, 2006.     

Topological transformation groups of manifolds over non-Archimedean fields,their representations,and quasi-invariant measures. I

Diffeomorphism groups and loop groups of manifolds on Banach spaces over non-Archimedean fields are defined. Moreover, for these groups, finite-and infinite-dimensional manifolds over the corresponding fields are considered. The group structure, the differential-geometric structure, and also the topological structure of diffeomorphism groups and loops groups are studied. We prove that these groups do not locally satisfy the Campbell-Hausdorff formula. The principal distinctions in the structure for the Archimedean and classical cases are found. The quasi-invariant measures on these groups with respect to dense subgroups are constructed. Stochastic processes on topological transformation groups of manifolds and, in particular, on diffeomorphism groups and on loop groups and also the corresponding transition probabilities are constructed. Regular, strongly continuous, unitary representations of dense subgroups of topological transformation groups of manifolds, in particular, those of diffeomorphism groups and loop groups associated with quasi-invariant measures on groups and also on the corresponding configurational spaces are constructed. The conditions imposed on the measure and groups under which these unitary representations are irreducible are found. The induced representations of topological groups are studied by using quasi-invariant measures on topological groups. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 39, Functional Analysis, 2006.     

部分权重信息下对方案有互补偏好的多属性决策法

研究了只有部分权重信息且对方案的偏好信息以模糊互补判断矩阵形式给出的多属性决策问题.首先,基于模糊互补判断矩阵的主观偏好信息,利用转换函数将客观决策信息一致化,建立一个目标规划模型,通过求解该模型得到属性权重,从而利用加性加权法获得各方案的综合属性值,并以此对方案进行排序或择优.提出了一种基于目标规划的多属性决策方法.该方法具有操作简便和易于上机实现的特点.最后,通过实例说明模型及方法的可行性和有效性.     

纯正半群上的强同余及Clifford同余

把Reilly对逆半群的幂等元集合的正规划分的概念推广到纯正半群,用它从另一角度刻画。了纯正半群上强同余的结构.并刻画了具有T关系的两个强同余的联和交的正则核正规系,又讨论了纯正半群上的Clifford同余,给出了最小Clifford同余的刻画.     

Some performance tests of convex hull algorithms

The two-dimensional convex hull algorithms of Graham, Jarvis, Eddy, and Akl and Toussaint are tested on four different planar point distributions. Some modifications are discussed for both the Graham and Jarvis algorithms. Timings taken of FORTRAN implementations indicate that the Eddy and Akl-Toussaint algorithms are superior on uniform distributions of points in the plane. The Graham algorithm outperforms the others on those distributions where most of the points are on or near the boundary of the hull.     

WEIGHTED ESTIMATES FOR MULTIVARIATE HAUSDORFF OPERATORS

In this paper,some weighted estimates for the multivariate Hausdorff operators are obtained.It is proved that the multivariate Hausdorff operators are bounded on L p spaces with power weights,which is based on the boundedness of multivariate Hausdorff operators on Herz spaces,and are bounded on weighted L p spaces with the weights satisfying the homogeneity of degree zero.     

On Induced Mappings

ＯｎＩｎｄｕｃｅｄＭａｐｐｉｎｇｓＣｕｉＨｏｎｇｂｉｎＦａｎＬｅｉＺｈｅｎｇＣｈｏｎｇｙｏｕ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣａｐｉｔａｌＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１０００３７）ＡｂｓｔｒａｃｔＬｅｔＸｂｅ...     

Parallel Newton two‐stage methods based on ILU factorizations for nonlinear systems

Parallel iterative algorithms based on the Newton method and on two of its variants, the Shamanskii method and the Chord method, for solving nonlinear systems are proposed. These algorithms are based on two‐stage multisplitting methods where incomplete LU factorizations are considered as a mean of constructing the inner splittings. Convergence properties of these parallel methods are studied for H‐matrices. Computational results of these methods on two parallel computing systems are discussed. The reported experiments show the effectiveness of these methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Fock-Sobolev空间上有界、紧与S_p-类算子

本文研究Fock-Sobolev空间上稠密定义算子,将这些算子统一表示成积分算子,利用积分算子的方法得到了它们的一个充分条件,并构造反例说此充分条件是非必要的,还得到这些算子为紧算子的两个充分条件.最后构造符号函数在复平面上每一点处本性无界的紧和Sp-类(0p∞)Toeplitz算子.