The entropy theory of symbolic extensions

Fix a topological system (X,T), with its space K(X,T) of T-invariant Borel probabilities. If (Y,S) is a symbolic system (subshift) and :(Y,S)(X,T) is a topological extension (factor map), then the function h_ext on K(X,T) which assigns to each the maximal entropy of a measure on Y mapping to is called the extension entropy function of . The infimum of such functions over all symbolic extensions is called the symbolic extension entropy function and is denoted by h_sex. In this paper we completely characterize these functions in terms of functional analytic properties of an entropy structure on (X,T). The entropy structure is a sequence of entropy functions h_k defined with respect to a refining sequence of partitions of X (or of X×Z, for some auxiliary system (Z,R) with simple dynamics) whose boundaries have measure zero for all the invariant Borel probabilities. We develop the functional analysis and computational techniques to produce many dynamical examples; for instance, we resolve in the negative the question of whether the infimum of the topological entropies of symbolic extensions of (X,T) must always be attained, and we show that the maximum value of h_sex need not be achieved at an ergodic measure. We exhibit several characterizations of the asymptotically h-expansive systems of Misiurewicz, which emerge as a fundamental natural class in the context of the entropy structure. The results of this paper are required for the Downarowicz-Newhouse results [DN] on smooth dynamical systems. Mathematics Subject Classification (2000) Primary: 37B10; Secondary: 37B40, 37C40, 37C45, 37C99, 37D35     

On mappings preserving equilateral triangles

Let E be a Euclidean space, dim E 2. We say that f : E E preserves equilateral triangles if for all triples of points x, y, z E we have We show that if E is a finite-dimensional Euclidean space, dim E 2, f:E E is measurable and preserves equilateral triangles, then it is a similarity transformation (an isometry multiplied by a positive constant). Moreover, in spaces at least three-dimensional we get a similarity transformation without any regularity assumption. Some generalizations as well as some interesting examples are also presented in the paper.     

A Capelli Harish-Chandra homomorphism

For a real reductive dual pair the Capelli identities define a homomorphism from the center of the universal enveloping algebra of the larger group to the center of the universal enveloping algebra of the smaller group. In terms of the Harish-Chandra isomorphism, this map involves a -shift. We view a dual pair as a Lie supergroup and offer a construction of the homomorphism based solely on the Harish-Chandra's radial component maps. Thus we provide a geometric interpretation of the -shift.

     

An Isometric Embedding of Moebius Band with Positive Gaussian Curvature

The main purpose of this paper is to show that there is an isometric embedding from Moebius band to R4 with positive Gaussian curvature.     

On perfectly meager sets in the transitive sense

We prove that assuming one can always find a perfectly meager set, which is not perfectly meager in the transitive sense.

     

Large deviation principle for spatial density of local observables from Gibbs distributions

We establish the large deviation principle characterising, in the thermodynamic limit, the exponential decay rates for the probabilities of macroscopic fluctuations of spatial densities generated by local observables from Gibbs lattice systems with absolutely summable interactions.     

二氧化硫与戊烷的气相光化学反应研究

Baclock等^[1]的研究表明,在SO2与烃的光化学反应体系中,单重态SO2通过系间窜跃转化为三重态SO2参与光化学反应,Penzhorn等^[2,3]的研究表明,在SO2与C4以下气相烃的光化学反应中有多种产物存在,产物的复杂性预示反应为自由基链反应。Smith等^[4]等认为体系中存在烃的逐步氧化,同时证明SO2与烷烃光化学反应中自由基链反应的重要性,文献报道的研究多以凝聚态产物为切入点^[5],为避免器壁对光化学反应的影响,本文以气相物质为研究对象,对挥发性烷烃中结构最简单的戊烷与二氧化硫的光化学反应的气相反应产物,反应机理和影响因素等进行了研究。     

ZnO超微粒子的EPR特性和光催化性能

利用XRD,TEM,XPS和EPR等研究了ZnO超微粒子的EPR特性和光催化性能.前驱物碱式碳酸锌在320,430,550和700℃经热处理制得的ZnO超微粒子粒径分别为13.5,19.3,26.1和38.5nm,属六方晶系纤锌矿结构;室温下ZnO超微粒子表现出稳定的单一谱线的EPR信号,其强度随粒径的增大而减小.而在液氮温度下,ZnO超微粒子的EPR谱具有6条强度不等的超精细谱线,在光催化氧化C₇H₁₆和SO₂过程中,其光催化活性随其EPR信号强度的减小而下降.说明O₂-空位在光催化反应中起重要作用.     

非离子水溶性膦配体的合成及其应用进展

按非离子水溶性膦配体的发展特点,就羟基取代膦配体、天然碳水化合物为母体的膦配体、聚醚基取代的膦配体、具手性中心的膦配体、高分子负载型膦配体、温控相转移膦配体、环糊精改性的膦配体等类型的非离子水溶性膦配体的合成及其在两相催化中的应用作一综述。