Pointwise Pseudo-Orbit Tracing Property and Its Application

In this paper, the pointwise pseudo-orbit tracing property is defined on a compact metric space, and it is a generalization of pseudo-orbit tracing property. As applications, we prove the following results: (i) If / has pointwise pseudo-orbit tracing property, for any k ∈ Z+, and fk is chain transitive, then for any k ∈ Z+, fk has open set transitive ; (ii) If f has pointwise pseudo-orbit tracing property, and for any n ∈ Z+,fn is chain transitive, then f has sensitive dependence on initial conditions; (iii) If f is open set mixing and has pointwise pseudo-orbit tracing property, then f has property P; (iv) Let f : (X, d) →(X, d) be a homeomophism, then f is pointwise pseudo-orbit tracing property if and only if the shift map σf is pointwise pseudo-orbit tracing property.

Topological Stability and Pseudo-orbit Tracing Property for Homeomorphisms on Uniform Spaces

In this paper,we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces.We introduce the concept of topological stability for homeomorphisms on compact uniform spaces and prove that if a homeomorphism on a compact uniform space is expansive and has pseudo-orbit tracing property,then it is topologically stable.Moreover,we discuss the topological stability for homeomorphisms on uniform spaces from the view of localization.We introduce definitions of topologically stable point and shadowable point for homeomorphisms on uniform spaces and show that every shadowable point of an expansive homeomorphism on a compact uniform space is topologically stable.

Pointwise Pseudo-Orbit Tracing Property and Chaos

In this article, we discuss the relationship between pointwise pseudo-orbit tracing property and chaotic properties such as topological mixing. When f has pointwise pseudo-orbit tracing property, we give some equal conditions of uniform positive entropy and completely positive entropy.

Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2) flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2) flows.

Effect of Trace Sc and Zr on the Mechanical Properties and Microstructure of A1 Alloy 2618

An experimental 2618(Al-Cu-Mg-Fe-Ni) alloy added with trace Sc and Zr was prepared by ingot metallurgy (IM) method. The aging behavior of the alloy was studied by Vickers hardness measurement at 200℃ and 300℃. and the tensile properties of alloy specimens were measured at 20℃, 200℃, 250℃ and 300℃. The microstructure was observed by using optical microscope, SEM and TEM. It was found that the addition of Sc and Zr to 2618 alloy resulted in a primary Al_3(Sc,Zr) phase which could refine the grain because it acts as nuclei of heterogeneous crystallization in the melt during solidification. The secondary Al_3(Sc,Zr) particles were full coherent with matrix and had obvious precipitation hardening effect. They also made the S' phase precipitate more homogeneous. So the strength of alloy increases at both ambient and elevated temperatures without a decrease of ductility. The ductile fracture of alloy occurs by microvoid nucleation, growth and coalescence, so the microvoid coalescence is the dominant fracture mechanism.

THE APOTP AND NON-WANDERING HOMEOMORPHISM

We introduce the concept of asymptotic pseudo orbit tracing property (APOTP) and obtain a new condition by the APOTP for which a homeomor-phism is a non-wandering homeomorphism.

Hylocomium splendens (Hedw.) B.S.G.and Pleurozium schreberi (Brid.) Mitt.as trace element bioindicators:Statistical comparison of bioaccumulative properties

The principal objective of this study was to compare bioaccumulative properties of two terrestrial moss species Hylocomium splendens and Pleurozium schreberi from the Kielce area （south-central Poland）, using various statistical techniques. Forty-six moss samples from 23 sampling sites located within the city limits were analyzed for 33 trace elements. The results indicated that 17 elements （Ba, Ce, Co, Cu, Eu, Fe, Gd, Hg, La, Mo, Nd, Ni, Pb, Pr, Sm, V, Y） dominated in H. splendens, whereas only three elements （Mn, Sr, Zn） occurred in excessive amounts in P. schreberi. No differences in the distribution pattern of Dy, Er, Ho, Sn, Tb, Th and Yb were observed. The element concentration ratio （PI/Hy） varied from 0.50 to 1.19. For 14 elements （Ce, Co, Cu, Fe, Gd, Hg, La, Mo, Nd, Ni, Pb, Sm, Th, V）, PI/Hy 〈 1; for 4 elements （Cd, Mn, Sr, Zn）, PI/Hy 〉 1; for 7 elements （Ba, Dy, Er, Eu, Pr, Y, Yb）, PI/Hy = equalled 1. Czekanowski＇s method showed similarities in rare earth element concentrations for both moss species. The cluster analysis exhibited three significant clusters at D link /D max × 100 〈 50 for both moss species. Strong positive Spearman correlations between both moss species were recorded for the following pairs：Ba-Ba, Co-Co, Er-Er, Eu-Eu, Gd Gd, Mn-Mn, Ni-Ni, Pb-Pb, Pr-Pr, Sm-Sm, Th-Th, Y-Y, and Yb-Yb. Nonparametric tests （Sign test, Wilcoxon tests） showed statistically significant differences only for Cd, Ce, Co, Cu, Hg, Mo, Ni, Pb and Sr. The scanning electron microscope study of H. splendens and P. schreberi revealed a different morphology of these species with no injuries.