Structures and magnetic properties of Fe and Ni monoatomic chains encapsulated by an Au nanotube

Structures and magnetic properties of transition metal （TM） Fe or Ni monoatomic chains （MACs） encapsulated by a Au （5, 5） nanotube （Fe@Au and Ni@Au） are investigated using the density functional theory （DFT）. The calculated results show that both Fe@Au and Ni@Au prefer to adopt ferromagnetic （FM） orders as ground states. In particular, the Fe@Au keeps the magnetic properties of free-standing Fe MAC, indicating that this system may be viewed as a new candidate in electromagnetic devices.

The Asymptotic Average Shadowing Property and Its Applications

Let (X, d) be a bounded metric space and f : X → X be a uniformly continuous surjection. For a given dynamical system (X, f) which may not be compact, we investigate the relation between the asymptotic average shadowing property(AASP), transitivity and mixing. If f has the AASP, then the following statements hold: (1) f n is chain transitive for every positive integer n; (2) If X is compact and f is an expansive homeomorphism, then f is topologically weakly mixing; (3) If f is equicontinuous, then f is topologically weakly mixing; (4) If X is compact and f is equicontinuous, then f ×f is a minimal homeomorphism. We also show that the one-sided shift map has the AASP and the identity map 1 X does not have the AASP. Furthermore, as its applications, some examples are given.

Contraction Integrated Semigroups and Their Applicationto Continuous-time Markov Chains

We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.

A Markov chain model of mixing kinetics for ternary mixture of dissimilar particulate solids

This paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov chain model is proposed to describe the process. At each time step, the exchange of particulate solids between the cells of the chain is divided into two virtual stages. The first is pure stochastic mixing accompanied by downward segregation. Upon the completion of this stage, some of the cells appear to be overfilled with the mixture, while others appear to have a void space. The second stage is related to upward segregation. Components from the overfilled cells fill the upper cells （those with the void space） according to the proposed algorithm. The degree of non-homogeneity in the mixture （the standard deviation） is calculated at each time step, which allows the mixing kinetics to be described. The optimum mixing time is found to provide the maximum homogeneity in the ternary mixture. However, this “common” time differs from the optimum mixing times for individual components. The model is verified using a lab-scale vibration vessel, and a reasonable correlation between the calculated and experimental data is obtained

Liquid crystal character controlled by complementary discotic molecules mixtures： Columnar stacking type and mesophase temperature range

In this work, the mesophase properties were tuned via mixing two discotic molecules with structural complementarity. Compared with the liquid crystalline hexakis（n-hexyloxy）triphenylene（H6TP）materials（columnar hexagonal phase from 53 ℃ to 91 ℃）, mesophase types as well as phase transition temperatures varied with the introduction of crystalline hexaazatriphenylene derivative（PBH）molecules. The introduction of less than 33% amount of PBH disrupted the columnar hexagonal phase formed by H6 TP remarkably, followed by the decreased clearing temperatures of liquid crystals. As the PBH amount was further increased, the destroyed columnar hexagonal phase was turned into the columnar rectangular phase, in which H6 TP and PBH molecules together formed the columnar mesophase. The formation of new mesophase contributed to the enlarged mesophase temperature（from44 ℃ to 144 ℃）. We speculated that the alkyl chains interaction induced by the PBH component competed with the strong p–p stacking between H6 TP molecules, thus altering the liquid crystalline properties including mesophase types and phase transition temperatures.

On the hyperbolicity of flows

Let X be a C1 vector field on a compact boundaryless Riemannian manifold M（dim M≥2）,and A a compact invariant set of X.Suppose that A has a hyperbolic splitting,i.e.,T∧M = Es Eu with Es uniformly contracting and Eu uniformly expanding.We prove that if,in addition,A is chain transitive,then the hyperbolic splitting is continuous,i.e.,A is a hyperbolic set.In general,when A is not necessarily chain transitive,the chain recurrent part is a hyperbolic set.Furthermore,we show that if the whole manifold M admits a hyperbolic splitting,then X has no singularity,and the flow is Anosov.