Banach空间上凸集的凸性

以Banach空间的一般凸集为研究对象,将Banach空间的凸性研究推广到了内部非空的凸集上．打破了从单位球出发研究Banach空间几何的具有局限性的研究方法,给出了严格凸集的若干特征刻画及性质,并得到了严格凸集和光滑集之间的对偶定理．     

拟多项式的迭代

讨论了更广泛的拟多项式映射,研究了拟多项式的迭代,证明了关于逃逸集,充满 Julia集和Julia集的几个定理.推广了多项式动力系统的相关结果.     

集值拟鞅和集值一致渐近鞅

本文讨论了集值拟鞅和集值一致渐近鞅,证明了集值拟鞅与集值一致渐近鞅的选样定理,对于集值一致渐近鞅得到了一些收敛性结果,并由此刻化了空间的 Radon-Nikodym性质.     

一种新的集合序列收敛性

本我们引进了无穷维Ｂａｎａｃｈ空间中的一种新的集合序列收敛性概念,讨论了它与其它收敛性概念的关系。另外,我们还研究了集合序列根限的Ｍｉｎｋｏｗｓｋｉ和。     

E-凸Fuzzy集和E-反凸Fuzzy集

研究了广义凸Fuzzy集和广义反凸Fuzzy集以及它们的性质。通过将凸Fuzzy集和E-凸集相结合,提出了一种新的广义凸Fuzzy集———E-凸Fuzzy集,使得凸Fuzzy集成为它的特例,并对E-凸Fuzzy集的性质进行了初步研究。然后,类似地,通过将反凸Fuzzy集和E-凸集相结合,提出了一种新的广义反凸Fuzzy集———E-反凸Fuzzy集,使得反凸Fuzzy集成为它的特例,并对E-反凸Fuzzy集的性质进行了初步研究。     

关于集值Pramart的某些结果

本文引进了Boohner可积函数空间L~1[Ω;X]中子集的可分解包的概念,给出了集值随机变量族本性上确界的定义及基本性质。以此为基础,研究了集值Pramart的性质;用类似于实值Snell包的方法给出了集值superpramart的上鞅逼近,证明了集值superpramart在Kuratowski-Mosco意义下的收敛定理。     

扩张不变集相对非自治扰动的稳定性

本文研究了自映射的扩张不变集在Ｃ￣０非自治扰动和Ｃ￣１非自治扰动下的稳定性质。     

具有变时滞Hopfield型神经网络的正不变集与吸引集

研究了具有变时滞Hopfield型神经网络的正不变集与吸引集，获得了正不变集与吸引集存在性的充分判据。     

集合上的递归函数

本文在Ｊｅｎｓｅｎ和Ｋａｒｐ工作的基础上引进了集合上的递归函数的概念．研究了递归集函数的初步性质，讨论了递归集函数与Ｊｅｎｓｅｎ和Ｋａｒｐ定义的原始递归集函数及递归数论函数之间的关系，并给出了ＺＦＣ的可定义集模型上递归集函数的范式定理．     

导集运算及其条件的独立性

对点集拓扑学中由导集运算决定拓扑的方法进行了讨论,给出了导集运算的定义,导集运算决定拓扑定理,并讨论了导集运算中条件的相互独立性.进一步完善了点集拓扑学中有关导集概念的内容.     

角蛋白16和17在部分表皮肿瘤中的表达和意义

目的 研究角蛋白16 和17（K16、K17）在部分表皮肿瘤中的表达和意义。方法 采用免疫组化法检测K16、K17在正常皮肤、脂溢性角化病、日光性角化病、皮角、基底细胞癌、鳞状细胞癌中的表达。结果 K16、K17 在正常皮肤表皮各层呈阴性表达;在脂溢性角化病表皮各层中除了角质层外大多呈阳性表达;在日光性角化病表皮K16 均不表达,K17 除了角质层外在其他各层也不表达;K16 在皮角表皮棘层呈强阳性表达,但在其他各层均呈阴性表达,K17 在皮角表皮各层基本呈阳性或强阳性表达;在基底细胞癌中,K16、K17除了在棘层呈弱阳性表达外,在其他各层均呈阴性表达;在鳞状细胞癌中,K16 在基底层呈阴性表达,但在其他各层及K17 在表皮全层均呈阳性或强阳性表达。K16 除基底层外在肿瘤表皮其他各层表达比较差异均有统计学意义（均P＜0.05）;K17 在表皮各层表达差异均有统计学意义（均P＜0.05）。结论 K16、K17的表达状况可为表皮肿瘤的鉴别诊断提供病理学方面的依据。     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

政府花费改变对经济影响的理论分析

本文采用无限期内生时间偏好率模型,研究了政府花费对经济的影响.指出长期的政府花费增加可以使资本存量水平上升,消费水平下降和债券持有量上升;同时,短期分析表明政府花费增加可以减少初始投资率,增加政府债务率水平;但短期的政府花费增加同样导致资本存量水平上升,消费水平下降和债务水平的增加.     

Dynamic investment strategies with demand-side and cost-side risks

Investments in cost reductions are critical for the long run success of companies that operate in dynamic and stochastic market environments. This paper studies optimal investment in cost reductions as a real option under the assumption that a single firm faces two different sources of risk, stochastic demand and input prices. We derive optimal investment strategies for a monopoly as well as a firm in a perfectly competitive market and show that in case of high marginal costs, cost reductions take place earlier in competitive than in monopoly markets. While the existence of an option to invest in cost reductions increases firm value it also increases a firm’s systematic risk. Risk can be smaller in a monopolistic than in a competitive industry.     

Steenrod squares in Cotor

It is first shown that the comparison theorem in relative homological algebra is the only tool to be used for introducing Steenrod operations in Cotor as well as in Ext. Then, the interaction of the operations in both functors is discussed in full detail. Some basic properties of the operations are given in the last section of the paper.The authors would like to thank a referee for his suggestion to reorganize their paper in the present form.This work is supported in part by NSF research grant GP-9585.     

Matrices that commute with their derivative. On a letter from Schur to Wielandt

We examine when a matrix whose elements are differentiable functions in one variable commutes with its derivative. This problem was discussed in a letter from Schur to Wielandt written in 1934, which we found in Wielandt’s Nachlass. We present this letter and its translation into English. The topic was rediscovered later and partial results were proved. However, there are many subtle observations in Schur’s letter which were not obtained in later years. Using an algebraic setting, we put these into perspective and extend them in several directions. We present in detail the relationship between several conditions mentioned in Schur’s letter and we focus in particular on the characterization of matrices called Type 1 by Schur. We also present several examples that demonstrate Schur’s observations.     

Rawlsian altruism with perfect discrimination leads to social efficiency

Recent studies draw attention on the highly specialized capacity of human beings in recognizing altruists versus cheaters in social interactions. These results hint at the existence of specialized abilities that support discriminating behavior in strategic interactions. In this paper, we explore the implications of discriminating behavior in the study of the indirect evolutionary selection of selfish versus altruistic motivations in the context of generic 2×2 base games, and in particular for coordination and cooperation scenarios. We find that inequality averse (Rawlsian) altruism can enforce under rather general conditions socially optimal outcomes, including cases where selfishness cannot, such as in prisoner’s dilemmas. Inequality seeking (Nietzschian) altruism in no case improves upon Rawlsian altruism in terms of social optimality of outcomes, and often does worse. In the cooperation scenario in particular, Nietzschean altruism never manages to implement the cooperative outcome. Under perfect discrimination, moreover, inequality averse (Rawlsian) altruism often evolves at the expense of selfishness. These results suggest that the development of sophisticated discrimination abilities may be strongly adaptive in supporting fairness-oriented forms of pro-sociality in humans in the context of social dilemmas and coordination problems.     

中国股票市场横截面收益率的可预测性研究——兼与美国对比

本文旨在检验中国股票市场横截面收益的可预测性。我们选取了15个公司层面的特征指标作为变量,现有文献已经发现这些指标在美国股票市场上具有预测横截面股票收益的能力。我们检验这些变量在中国股票市场是否可以用来预测股票收益,样本的时间区间为1996~2015年。我们发现这些变量在中国股票市场对股票横截面收益的预测能力是相对较弱的。我们对中国股票市场的弱可预测性提出了两种可能的解释:其一,可能是收益预测因子在中国股票市场中的同质性比在美国股票市场中更强;其二,在中国股票市场中股票价格的无效率程度比较高。两种解释我们都找到了实证依据来支撑。     

Entanglement,fidelity and quantum chaos in cavity QED

Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality microcavity is studied. We consider the strongly coupled atom–field system as a quantum–classical hybrid with dynamically coupled quantum and classical degrees of freedom. We show that, even in the absence of any other interaction with environment, the coupling of quantum and classical degrees of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. Chaos manifests itself in the atomic external degree of freedom as a random walking of an atom inside a cavity with prominent fractal-like behavior and in the quantum atom–field degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependences of variance of quantum entanglement and of the maximum Lyapunov exponent on the detuning of the atom–field resonance correlate strongly. It is shown that the Jaynes–Cummings dynamics can be unstable in the regime of chaotic walking of an atom in the quantized field of a standing wave in the absence of any other interaction with environment. Quantum instability manifests itself in strong variations of quantum purity and entropy and in exponential sensitivity of fidelity of quantum states to small variations in the atom–field detuning. It is quantified in terms of the respective classical maximal Lyapunov exponent that can be estimated in appropriate in–out experiments. This result provides a quantum–classical correspondence in a closed physical system.