非线性椭圆型方程组边值问题的可解性

研究椭圆型方程组Dirichlet边值问题的可解性,利用不动点定理证明了上述问题存在上、下解情形,存在有界非负解,并利用该结论讨论了带参数的椭圆型方程组Dirichlet边值问题通过寻找该问题的上、下解,证明了正参数充分小时,这个问题存在有界正解.这里非线性函数在+∞处可以是超线性的,从而证明了部分椭圆型方程组边值问题中非线性项为超线性时,有界正解的存在性.同时,作为定理的应用,给出了实例.     

具有时滞的非线性微分方程的概周期解的存在性及唯一性

本文研究了一类具有时滞的非线性微分方程的有界解及概周期解的存在性及唯一性问题。利用变量替换和不动点方法及逼近法,我们得到了此类方程有界解和概周期解的存在性及唯一性的一些有趣的新结果。我们的结果大大改进和推广了文［２］的主要结果。     

一般有界区域上次线性椭圆方程改进的正解估计

在一般有界区域上，建立了次线性椭圆方程广义Ｄｉｒｉｃｈｌｅｔ问题改进的正解估计和有界强解的存在性定理．     

泛函微分方程解的指数渐近稳定性与有界性

本文研究了具有有限时滞中立型泛函微分方程解的有界性问题 ,得到了方程解的指数渐近稳定性蕴涵有界解的存在性的新的结果     

局部扰动半平面上的散射问题

该文讨论半平面上有局部扰动情况下的散射问题．通过位势理论,应用边界积分方程的方法研究了该问题解的存在与唯一性．主要方法是运用对称反射,使该无界区域上的散射问题变成一个有界区域上的散射问题,只是这一有界区域的边界不光滑．通过仔细分析相应的边界积分算子,作者得到了其解的存在与唯一性．     

一类具有退化系数鞅问题解的唯一性

该文首先在系数有界的条件下,证明了一类具有退化系数鞅问题解的存在唯一性.然后借助于函数变换,指出系数有界条件可以被弱化.     

泛函微分方程解的指数渐近稳定性与有界性

本研究了具有有限时滞中立型泛函微分方程解的有界性问题，得到了方程解的指数渐近稳定性蕴涵有界解的存在性的新的结果。     

共振情况下m点p-Laplacian算子边值问题解的存在性

本文研究了在共振情况下m点P-Laplacian算子边值问题解的存在性问题.在非线性项f(t,u,v)有界的条件下,根据Mawhin的连续定理和m点P-Laplacian算子的边值问题的上下解理论,得出共振问题解的存在的结论.     

具有温和阻尼的非线性热弹耦合系统的整体吸引子

本文研究有界区域下带有温和阻尼的非线性热弹耦合系统的整体解的适定性和整体吸引子的问题.首先,利用Faedo-Galerkin的方法,证明初边值问题弱解的适定性,其次根据解的适定性构造了动力系统,最后给出系统有界吸收集的存在性和半群的一致紧性,证明了系统整体吸引子的存在性.     

有界域和半无界域上广义Kawahara方程的初边值问题

本文在有界区域和半无界区域上研究广义Kawahara方程的初边值问题,运用能量积分方法、不等式技巧和嵌入定理建立解的先验估计,结合压缩映射原理证明了在有界区域上整体正则解的存在性和唯一性;同时得到当时间趋于无穷时,解的L2范数具有指数衰减性;并且在加强的初边值条件下,借助不等式技巧证得在有界区域上存在与有界域长度无关的整体正则解,以及在半无界域上同样存在唯一的整体正则解.     

On Order Bounded Subsets of Locally Solid Riesz Spaces

In a topological Riesz space there are two types of bounded subsets: order bounded subsets and topologically bounded subsets. It is natural to ask (1) whether an order bounded subset is topologically bounded and (2) whether a topologically bounded subset is order bounded. A classical result gives a partial answer to (1) by saying that an order bounded subset of a locally solid Riesz space is topologically bounded. This paper attempts to further investigate these two questions. In particular, we show that (i) there exists a non-locally solid topological Riesz space in which every order bounded subset is topologically bounded; (ii) if a topological Riesz space is not locally solid, an order bounded subset need not be topologically bounded; (iii) a topologically bounded subset need not be order bounded even in a locally convex-solid Riesz space. Next, we show that (iv) if a locally solid Riesz space has an order bounded topological neighborhood of zero, then every topologically bounded subset is order bounded; (v) however, a locally convex-solid Riesz space may not possess an order bounded topological neighborhood of zero even if every topologically bounded subset is order bounded; (vi) a pseudometrizable locally solid Riesz space need not have an order bounded topological neighborhood of zero. In addition, we give some results about the relationship between order bounded subsets and positive homogeneous operators.     

基于Agent仿真的个体有限理性与众包绩效的关系研究

如何筛选有限理性参与者是企业实施众包的关键问题。通过引入个体有限理性,扩展了经典的NK模型,构建了模拟竞赛式众包问题解决过程的多主体仿真模型,研究了个体有限理性水平、个体有限理性系统化程度以及个体有限理性水平标准差对众包绩效的影响。仿真结果显示,个体有限理性水平对提高众包绩效有显著的正向影响,尤其是在任务复杂性较高的情况下;个体有限理性系统化程度和个体有限理性水平标准差对众包绩效也有正向影响,但依赖于个体有限理性水平。当企业有一个复杂性较高的任务时,如果追求所有方案的整体改善,企业需要招募有限理性水平较高的个体,并组成有限理性系统化程度较高且有限理性水平标准差较大的群体;如果追求少数优质方案,企业需要招募有限理性水平较高的个体,并组成有限理性系统化程度较低且有限理性水平标准差较大的群体。     

p-算子空间上的框架逼近和嵌入

介绍了p-算子空间上的p-完全有界框架概念.证明了可分p-算子空间X上存在p-完全有界框架当且仅当X满足p-完全有界逼近性质当且仅当X能够p-完全可补嵌入有p-完全有界基的p-算子空间.对于满足p-完全有界逼近性质的非可分的p-算子空间,还证明了其任意可分子空间均可以p-完全同构嵌入到有p-完全有界框架的p-算子空间.     

Cosine of angle and center of mass of an operator

We consider the notion of real center of mass and total center of mass of a bounded linear operator relative to another bounded linear operator and explore their relation with cosine and total cosine of a bounded linear operator acting on a complex Hilbert space. We give another proof of the Min-max equality and then generalize it using the notion of orthogonality of bounded linear operators. We also illustrate with examples an alternative method of calculating the antieigenvalues and total antieigenvalues for finite dimensional operators.     

超布朗运动与无界区域上一类非线性微分方程

本文得到了超布朗运动的一个极限定理,并用超布朗运动给出了区域D上非线性微分方程的Dirichlet问题与随机Dirichlet问题非负有界解的精确表达式．     

On multiplicities of cocharacters for algebras with superinvolution

In this paper we deal with finitely generated superalgebras with superinvolution, satisfying a non-trivial identity, whose multiplicities of the cocharacters are bounded by a constant. Along the way, we prove that the codimension sequence of such algebras is polynomially bounded if and only if their colength sequence is bounded by a constant.     

On the convergence of a bounded amart and a conjecture of Chatterji

Through the decomposition theorem of Lebesgue and Darst it is possible to define a generalized Radon-Nikodym derivative of a bounded additive set function with respect to a bounded countably additive set function. For a bounded amart the derivatives of the components are shown to converge almost everywhere. This result, together with a characterization of amarts, yields a theorem stated by Chatterji whose proof is incorrect.     

Sublattices of associahedra and permutohedra

Grätzer asked in 1971 for a characterization of sublattices of Tamari lattices. A natural candidate was coined by McKenzie in 1972 with the notion of a bounded homomorphic image of a free lattice—in short, bounded lattice. Urquhart proved in 1978 that every Tamari lattice is bounded (thus so are its sublattices). Geyer conjectured in 1994 that every finite bounded lattice embeds into some Tamari lattice.     

A note on the theorems of paley and stein

We show that, under the conditions of the theorems of Paley and Stein, a system with bounded norms in L∞ can be replaced by a system with bounded norms in the space of functions of bounded mean oscillation.     

Manifolds with Boundary and of Bounded Geometry

For non–compact manifolds with boundary we prove that bounded geometry defined by coordinate–free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas with subordinate partition of unity on manifolds with boundary of bounded geometry and we study the change of geodesic coordinate maps.