STUDY OF POSITRON ANNIHILATION ONE DIMENSION ANGULAR-CORRELATION RADIATION ON POLYCRYSTAL Na^+ CONDUCTOR Na_5Y_(1-x)Cr_xSi_4O_(12)

With positron annihilation radiation one dimension angular-correlation device, it is measured that positron annihilation radiation one dimension angular-correlation curves of polycrystal sodium ion conductor Na5Y1-x CrxSi4O12 (NYCS) system. After electron momentum distribution curves are normalized, linear parameters are calculated. The parameters H, W and S show the change of Na+ ion vacancy concentration in NYCS series samples. The results show that parameters H, W and S of one dimension angular-correlation curves of those samples vary greatly with Cr2O3 contents. With Cr2O3 content increasing, H and S parameters increase, but W decreases, and reaches extremes at x=0.05; then with Cr2O3 adding continually, parameters H and S decrease gradually, parameter W increases gradually. This shows that, in addtion to Cr2O3, the conductivity has close relation with the concentration of Na+ ion vacancy.

A NOTE ON THE ASYMPTOTICS OF THE POLYMER MEASURES IN ONE DIMENSION

Given g∈(0,∞), we prove thatfor some constant C∈(0,∞), where (g, T) is the polymer measure defined on C_0([0, T]→R^1), and {W(t)}t∈[0,T] is the corresponding coordinate process.

Flexible One-Dimensional Nanostructures:A Review

This review discusses the recent reports on one-dimensional(1D) nanostructures with unusual flexibility.We discuss the importance that flexibility could have in future applications of nanowires and other nanostructures,and detail the two main approaches that have been followed to this day to synthesize highly flexible 1D nanostructures.One approach is based on making crystals in which one or two dimensions of the structure are comparable in size with the unit cell.Such thinness has been shown to provide unusual flexibility.The other approach conjoins hard nanostructures with flexible joints.

A brief review on one-dimensional topological insulators and superconductors

Recently one-dimensional topological phases are gaining increasing attentions. Like two- and three-dimensional ones, Onedimensional systems are important in a complete understanding of the topological properties. One-dimensional topological phases have been realized using current experimental setups. Specially the signatures of Majorana fermions have been observed in onedimensional topological superconductors engineered with Rashiba nanowires. From the many studies, the paper reviews typical theoretical models of one-dimensional topological insulators and superconductors. For one-dimensional topological insulators, we introduce the Su-Schrieffer-Heeger, superlattices and Creutz models, while for topological superconductors the Kitaev model and Rashiba nanowire are introduced. These models not only provide an overview of one-dimensional topological phases, but also are the starting points for further studies.

The Meaning of an Infinitely Great Velocity

An instantaneous velocity where a moment of the clock only corresponds to an arbitrary distance or position in space cannot be implied in Axiom 1, but it indicates that there is only one dimensional existence, space or time, where a certain moment only corresponds to itself specifically, not to any other time or any given length of space. Further, a definition of velocity that consists of two dimensions representing the relationship between space and time is not valid and there is only one-dimensional space or time that is independent of each other in Axiom 1. As a result, the principle of relativity and the principle of the constant velocity of light are replaced by the principle of an inertial system and the principle of universal invariant velocity in Axiom 1. Unlike two dimensions whose magnitude is determined by the ratio, the magnitude of a single dimension is determined by the unit values of one dimension, which indicates that an infinitely great velocity is meaningless. Further, if the two inertial systems are infinite versus finite in Axiom 3, then this extension of the infinitely great velocity can be defined as inextensible.

Pointwise decaying rate of large perturbation around viscous shock for scalar viscous conservation law

In this paper, we consider the large perturbation around the viscous shock of the scalar conservation law with viscosity in one dimension case. We divide the time region into t ≤T0 and t 〉 To for a fixed constant To when applying energy method. Since To is fixed, the case t ≤ To is easy to deal with and when t 〉 To, from the decaying property of the solution, there is a priori estimate for the solution. Thus we can succeed to control the nonlinear term and get the pointwise estimate for the perturbation by the weighted energy method.

1D Ceria Nanomaterials:Versatile Synthesis and Bio-application

Ceria has emerged as a fascinating and lucrative material in bio-application,for instance,disease treatment,bioimaging and drug delivery due to its abilities of transforming oxidation states between Ce4+and Ce3+and scavenging free radicals,which can produce biological effect,such as being potentially antioxidant towards reactive oxygen species.Recently,many studies about one dimension（ID） CeO2nanomaterials have received much attention because of the unique properties of their length and aspect ratio.We highlight here current research activities focused on the bio-application of 1D ceria nanomaterials.The synthesis methods of 1D cerium oxide nanomaterials were introduced.Several synthesis routes,including template,hydrothermal,sonochemical and other methods,were then discussed with examples developed by recent research.The differences among these methods were also analyzed.This review provides a comprehensive introduction to the synthesis of 1D ceria,its potential applications in biological fields and perspectives on this exciting realm.