多重取因子的线性序归结

本文重新定义了有序子句的有序因子,证明了在这种有序因子定义下的提升引理,进而在理论上得到了多重取因子的线性序归结方法的完备性.     

拟线性椭圆型方程Dirichlet问题的无穷多重本征值

本文利用对称形式的山路引理讨论下面的边值问题:和主要研究了λ在零点附近方程解的性态,证明了这时λ为(*)及(**)的无穷多重本征值。本文简报见[9]。     

A constructive proof of a permutation-based generalization of Sperner's lemma

In a recent paper, Gale has given an interesting generalization of the KKM lemma in combinatorial topology. We present a similar generalization of Sperner's well-known lemma and give a constructive proof. The argument uses the familiar idea of following simplicial paths in a triangulation. To demonstrate that the algorithm must work, orientation considerations are necessary. Gale's generalized KKM lemma is derived from the main result. A permutation-based generalization of Brouwer's fixed point theorem is also given.     

On Fractional Brownian Processes

We use Liouville spaces in order to prove the existence of some different fractional -Brownian motion ( 0 < 1 ), or fractional ( , )-Brownian sheets. There are also applications to the Wiener stochastic integral with respect to these -Brownian.     

Solvability results for sublinear functions and operators

In this paper there are stated asymptotic solvability results which yield a Farkas' lemma for sublinear functions and operators. Applications to duality for homogeneous programming and to necessary optimality conditions for nonlinear programming are given. Some closedness conditions used in the paper are also discussed.

---

Zusammenfassung In dieser Arbeit werden asymptotische Lösbarkeitsresultate angegeben, die ein Farkas-Lemma für sublineare Funktionen und Operatoren liefern. Es werden Anwendungen auf die Dualitätstheorie homogener Programme und auf notwendige Optimalitätsbedingungen der nichtlinearen Programmierung angegeben. Einige Abgeschlossenheitsvoraussetzungen, die in der Arbeit benutzt werden, werden diskutiert.

     

上证综合指数混沌模型的动力学特性分析

通过对上海证券综合指数动力学模型的混沌特性进行深入研究,针对模型的混沌特性,应用Schwarz导数对系统的演化过程做了定量描述,利用Sharkovskii定理和符号动力学对模型的相图、分叉图、暗线方程进行了分析,得到了系统的MSS序列,给出该模型不稳定轨道和混沌参数区间的确定方法·为证券市场中的内在规律的研究发展,提供了一个有益的探讨,为非线性混沌动力学理论在经济学的应用做了有益的尝试     

The Morse spectrum of linear flows on vector bundles

For a linear flow on a vector bundle a spectrum can be defined in the following way: For a chain recurrent component on the projective bundle consider the exponential growth rates associated with (finite time) -chains in , and define the Morse spectrum over as the limits of these growth rates as and . The Morse spectrum of is then the union over all components . This spectrum is a synthesis of the topological approach of Selgrade and Salamon/Zehnder with the spectral concepts based on exponential growth rates, such as the Oseledec spectrum or the dichotomy spectrum of Sacker/Sell. It turns out that contains all Lyapunov exponents of for arbitrary initial values, and the are closed intervals, whose boundary points are actually Lyapunov exponents. Using the fact that is cohomologous to a subflow of a smooth linear flow on a trivial bundle, one can prove integral representations of all Morse and all Lyapunov exponents via smooth ergodic theory. A comparison with other spectral concepts shows that, in general, the Morse spectrum is contained in the topological spectrum and the dichotomy spectrum, but the spectral sets agree if the induced flow on the base space is chain recurrent. However, even in this case, the associated subbundle decompositions of may be finer for the Morse spectrum than for the dynamical spectrum. If one can show that the (closure of the) Floquet spectrum (i.e. the Lyapunov spectrum based on periodic trajectories in ) agrees with the Morse spectrum, then one obtains equality for the Floquet, the entire Oseledec, the Lyapunov, and the Morse spectrum. We present an example (flows induced by vector fields with hyperbolic chain recurrent components on the projective bundle) where this fact can be shown using a version of Bowen's Shadowing Lemma.

     

Remarks on the local Hopf's lemma

The paper deals with the problem of extending the recent work of M.S.Baouendi and L.P.Rothschild concerning harmonic functions vanishing to infinite order in the normal direction in balls and half-spaces. Contrary to what one expects, we show that the B.-R. result extends neither to arbitrary domains nor to cases when the normal is replaced by a curve transversal to the boundary. The exact criterion when the result holds in is given.

     

关于单边检验教学中一个问题的讨论

本文对《概率统计》课程中关于单边检验的一个例题所反映的问题进行了讨论,并且建议,统一现行教材中关于单边假设的各种提法。     

A Note on Capacity and Hausdorff Measure in Homogeneous Spaces

ggt We consider analogoues of classical Riesz capacity C and Hausdorff measure H in a homogeneous space (X,d,µ) . We prove that, under mild regularity conditions on (X,d,µ), the usual relations between C and H hold. The key step in the proof is a version of the so called Frostman Lemma in a homogeneous space.