The fixed point property for multivalued nonexpansive mappings

We show some properties concerning geometrical constants of Banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties.     

Examples of non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property

In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces.     

BOUNDEDNESS OF FRACTIONAL INTEGRALS IN HARDY SPACES WITH NON-DOUBLING MEASURE - In Memory of Professor Sun Yongsheng

Let μ be a Borel measure on Rd which may be non doubling. The only condition that μ must satisfy is μ(Q) ≤ col(Q)n for any cube Q () Rd with sides parallel to the coordinate axes and for some fixed n with 0 ＜ n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H1 (μ).     

Characterization and recognition of generalized clique-Helly graphs

Let p?1 and q?0 be integers. A family of sets F is (p,q)-intersecting when every subfamily F^′⊆F formed by p or less members has total intersection of cardinality at least q. A family of sets F is (p,q)-Helly when every (p,q)-intersecting subfamily F^′⊆F has total intersection of cardinality at least q. A graph G is a (p,q)-clique-Helly graph when its family of (maximal) cliques is (p,q)-Helly. According to this terminology, the usual Helly property and the clique-Helly graphs correspond to the case p=2,q=1. In this work we present a characterization for (p,q)-clique-Helly graphs. For fixed p,q, this characterization leads to a polynomial-time recognition algorithm. When p or q is not fixed, it is shown that the recognition of (p,q)-clique-Helly graphs is NP-hard.     

随机环境中分枝过程的等价定理

给定了随机环境中分枝过程(BPRE)的精确定义,讨论了有关的可测性问题和BPRE的基本性质．在此基础上,证明了BPRE的一个等价定理．     

周期性分层介质高反射区范围的分析与估计

对于具有周期单元的分层介质材料高反射区的波长范围，提供一种简明的估计分析方法.基于Floquet定理，分析了有限周期单元分层介质的光子带隙特性，给出分层介质的高反射区波长范围.讨论了分层介质高反射区和周期单元禁带之间的关系.计算表明，高反射区和周期单元禁带的中心波长彼此一致.并且，随着分层介质周期单元数的增多，高反射区的深度和带宽就越接近于周期单元禁带的深度和宽度.最后，讨论周期分层介质的光子带隙特性与入射角及其与极化的变化关系. 关键词： 分层介质 带隙特性 周期单元 高反射区     

Generalized Physical and SRB Measures for Hyperbolic Diffeomorphisms

In this paper we introduce the notion of generalized physical and SRB measures. These measures naturally generalize classical physical and SRB measures to measures which are supported on invariant sets that are not necessarily attractors. We then perform a detailed case study of these measures for hyperbolic Hènon maps. For this class of systems we are able to develop a complete theory about the existence, uniqueness, finiteness, and properties of these natural measures. Moreover, we derive a classification for the existence of a measure of full dimension. We also consider general hyperbolic surface diffeomorphisms and discuss possible extensions of, as well as the differences to, the results for Hènon maps. Finally, we study the regular dependence of the dimension of the generalized physical/SRB measure on the diffeomorphism. For the proofs we apply various techniques from smooth ergodic theory including the thermodynamic formalism. 2000 Mathematics Subject Classification. Primary: 37C45, 37D20, 37D35, Secondary: 37A35, 37E30     

On then-cutset property

For a partially ordered setP and an elementx ofP, a subsetS ofP is called a cutset forx inP if every element ofS is noncomparable tox and every maximal chain ofP meets {x}∪S. We letc(P) denote the smallest integerk such that every elementx ofP has a cutsetS with ‖S‖?k: Ifc(P)?n we say thatP has then-cutset property. Our results bear on the following question: givenP, what is the smallestn such thatP can be embedded in a partially ordered set having then-cutset property? As usual, 2 ⁿ denotes the Boolean lattice of all subsets of ann-element set, andB _n denotes the set of atoms and co-atoms of 2 ⁿ . We establish the following results: (i) a characterization, by means of forbidden configurations, of whichP can be embedded in a partially ordered set having the 1-cutset property; (ii) ifP contains a copy of 2 ⁿ , thenc(P)?2^[n/2]?1; (iii) for everyn>3 there is a partially ordered setP containing 2 ⁿ such thatc(P)<c(2 ⁿ ); (iv) for every positive integern there is a positive integerN such that, ifB _m is contained in a partially ordered set having then-cutset property, thenm?N.     

p型未掺杂富锌ZnO薄膜的形成和性能研究

以高纯ZnO为靶材,氩气为溅射气体,利用射频磁控溅射技术在石英衬底上生长出纤锌矿结构的富锌ZnO薄膜.薄膜沿(002)择优取向生长,厚约为1.2μm,呈现电绝缘特性.将溅射的ZnO薄膜在10-3Pa,510~1 000 K的温度范围等温退火1 h,室温Hall测量结果表明ZnO薄膜的导电性能经历了由绝缘—n型—p型—n型半导体的变化.XPS测试表明ZnO薄膜的Zn/O离子比随退火温度的升高而降低,但一直是富锌ZnO,说明未掺杂的富锌ZnO也可以形成p型导电.p型未掺杂富锌ZnO薄膜的形成可归因于VZn受主浓度可以克服VO和Zni本征施主的补偿效应.     

Viscometric properties of dilute polystyrene/dioctyl phthalate solutions

We report viscometric data collected in a Couette rheometry on dilute, single‐solvent polystyrene (PS)/dioctyl phthalate (DOP) solutions over a variety of polymer molecular weights (5.5 × 10⁵ ≤ M_w ≤ 3.0 × 10⁶ Da) and system temperatures (288 K ≤ T ≤ 318 K). In view of the essential viscometric features, the current data may be classified into three categories: The first concerns all the investigated solutions at low shear rates, where the solution properties are found to agree excellently with the Zimm model predictions. The second includes all sample solutions, except for high‐molecular‐weight PS samples (M_w ≥ 2.0 × 10⁶ Da), where excellent time–temperature superposition is observed for the steady‐state polymer viscosity at constant polymer molecular weights. No similar superposition applies at a constant temperature but varied polymer molecular weights, however. The third appears to be characteristic of dilute high‐molecular‐weight polymer solutions, for which the effects of temperature on the viscosity curve are further complicated at high shear rates. The implications concerning the relative importance of hydrodynamic interactions, segmental interactions, and chain extensibility with increasing polymer molecular weight, system temperature, and shear rate are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 787–794, 2006