Volume of Hyperbolic 3-Manifolds with Iterated Pseudo-Anosov Amalgamations (Dedicated to Professor Mitsuyoshi Kato on his sixtieth birthday)

Let : be a pseudo-Anosov homeomorphism. We will study an asymptotic behaviour of the volume of closed hyperbolic 3-manifolds N _n obtained from certain 3-manifolds M, M by attaching their boundaries by the n-th iteration ⁿ of .     

荆门热电厂厂区膨胀土等级的可拓评价研究

运用可拓学的基本理论,建立了膨胀土可拓评价模型。以此模型为基础,对荆门热电厂的膨胀土进行了可拓综合评价,并将判别结果与分级膨胀量评价法的判别结果进行了对比,其结果是一致的,说明该方法是可行的。     

基于吸力量测确定膨胀土活动带和裂隙深度

采用M itchell公式和裂隙扩展深度方程两种吸力法确定安康地区膨胀土大气影响深度和裂隙开展深度。其一通过对安康地区两处天然边坡开挖观测井,利用张力计进行不同深度处吸力值的现场量测,根据M itchell提出公式计算大气影响深度;其二根据非饱和土抗拉强度公式,建立膨胀土裂隙扩展深度方程,利用基质吸力量测结果求其理论解。结果表明,安康地区膨胀土吸力变化曲线随深度增加变幅减小,呈“波浪式”推移。M itchell公式确定安康地区膨胀土的大气影响深度为3.35m以内,裂隙深度方程确定裂隙开展深度为3.06³.14m。利用M itchell公式计算大气影响深度与膨胀土断裂理论公式确定的裂隙开展深度结果接近。     

改性膨胀土路堤填筑含水量优化试验研究

在控制含水量的前提下,对分别掺入不同量石灰、不同量水泥改性膨胀土试件进行强度和膨胀量试验,得到不同含 水量及不同石灰(水泥)掺量对改性膨胀土强度和膨胀性的影响,通过对实验所得数据的分析,找出含水量和掺石灰(水泥)剂 量的最佳融合点,并据此对膨胀土路堤填料的改性施工提出了一些有益的建议。     

皖中膨胀土的承载比(CBR)强度特性研究

针对皖中地区高速公路建设中遇到的膨胀土问题,选取合六叶高速公路典型土样开展了系统的承载比（CBR）特性试验研究,并在此基础上探讨了膨胀土作为路基填料的适用性。研究表明:（1）起始含水量对膨胀土CBR值影响显著,CBR最大值对应的含水量高于最佳含水量,且击实功越大,二者差值也越大;（2）CBR膨胀量随起始含水量增大而减小,起始含水量越低,CBR膨胀量就越大,路基的水稳性就越差;（3）当击实功较大时,膨胀土的最佳含水量较小,适合填筑的可变含水量范围较宽,建议现场施工控制采用重型击实标准;（4）在重型击实条件下,将弱膨胀土起始含水量控制在比最优含水量大2%⁴%范围内,能同时满足压实度和CBR值要求以用于填筑下路堤,中膨胀土作为路基填料时必须经过改性处理。研究结果对于在膨胀土地区进行公路建设具有参考意义。     

Random Probability Measures with Given Mean and Variance

This article describes several natural methods of constructing random probability measures with prescribed mean and variance, and focuses mainly on a technique which constructs a sequence of simple (purely discrete, finite number of atoms) distributions with the prescribed mean and with variances which increase to the desired variance. Basic properties of the construction are established, including conditions guaranteeing full support of the generated measures, and conditions guaranteeing that the final measure is discrete. Finally, applications of the construction method to optimization problems such as Plackett's Problem are mentioned, and to experimental determination of average-optimal solutions of certain control problems.     

Quasi-hyperbolic semigroups

We introduce the notion of quasi-hyperbolic operators and C₀-semigroups. Examples include the push-forward operator associated with a quasi-Anosov diffeomorphism or flow. A quasi-hyperbolic operator can be characterised by a simple spectral property or as the restriction of a hyperbolic operator to an invariant subspace. There is a corresponding spectral property for the generator of a C₀-semigroup, and it characterises quasi-hyperbolicity on Hilbert spaces but not on other Banach spaces. We exhibit some weaker properties which are implied by the spectral property.     

Invariant Measures in Free MV-Algebras

MV-algebras can be viewed either as the Lindenbaum algebras of ?ukasiewicz infinite-valued logic, or as unit intervals of lattice-ordered abelian groups in which a strong order unit has been fixed. The free n-generated MV-algebra Free _n is representable as an algebra of continuous piecewise-linear functions with integer coefficients over the unit cube [0, 1] ⁿ . The maximal spectrum of Free _n is canonically homeomorphic to [0, 1] ⁿ , and the automorphisms of the algebra are in 1–1 correspondence with the pwl homeomorphisms with integer coefficients of the unit cube. In this article, we prove that the only probability measure on [0, 1] ⁿ which is null on underdimensioned 0-sets and is invariant under the group of all such homeomorphisms is the Lebesgue measure. From the viewpoint of lattice-ordered abelian groups, this fact means that, in relevant cases, fixing an automorphism-invariant strong unit implies fixing a distinguished probability measure on the maximal spectrum. From the viewpoint of algebraic logic, it means that the only automorphism-invariant truth averaging process that detects pseudotrue propositions is the integral with respect to Lebesgue measure.     

The nonexistence of expansive homeomorphisms of a class of continua which contains all decomposable circle-like continua

A homeomorphism of a compactum with metric is expansive if there is such that if and , then there is an integer such that . It is well-known that -adic solenoids () admit expansive homeomorphisms, each is an indecomposable continuum, and cannot be embedded into the plane. In case of plane continua, the following interesting problem remains open: For each , does there exist a plane continuum so that admits an expansive homeomorphism and separates the plane into components? For the case , the typical plane continua are circle-like continua, and every decomposable circle-like continuum can be embedded into the plane. Naturally, one may ask the following question: Does there exist a decomposable circle-like continuum admitting expansive homeomorphisms? In this paper, we prove that a class of continua, which contains all chainable continua, some continuous curves of pseudo-arcs constructed by W. Lewis and all decomposable circle-like continua, admits no expansive homeomorphisms. In particular, any decomposable circle-like continuum admits no expansive homeomorphism. Also, we show that if is an expansive homeomorphism of a circle-like continuum , then is itself weakly chaotic in the sense of Devaney.