Lagrangian flows: The dynamics of globally minimizing orbits

The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications.We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma].Reprinted by permission of Addison Wesley Longman Ltd.     

Two Convergence Problems for Monotone Sequences

Eight measures of rate of convergence of monotone sequences of real numbers have been proposed and discussed in a paper by Beyer, Ebanks, and Qualls (Acta Appl. Math. 20 (1990), 267–284). These rates arose in discussions of dynamical systems. In the comparisons of these rates, two problems remained. A complete answer is given to one of the problems and a partial answer is given to the other problem.     

GRIN透镜在细径内窥镜中的应用

介绍在细径内窥镜中ＧＲＩＮ透镜的应用原理及其设计方法。     

Determination of tyrosine traces by adsorption voltammetry of its copper (II) complex

The electrochemical behavior of the copper-tyrosine complex has been studied by linear-sweep adsorption voltammetry. In 0.02 mol/L Na₂HPO₄ buffer solution (pH=9.6), the complex can be adsorped on a hanging mercury drop electrode and reduced at a peak potential of about –0.42 V (vs. SCE). The secondary derivative peak height is linear proportional to the concentration of tyrosine in the range 1.0×10^–7–5.0×10^–5 mol/L. The detection limit is 5×10^–8 mol/L.Project supported by the Provincial Science Foundation of Shandong Province     

Structure and magnetic properties of nanocrystalline ferromagnets (II)

The role of magnetoelastic coupling effects in nanocrystalline ferromagnets is investigated by means of high-field magnetization and Doppler-broadening spectrum measurements. For the nanocrystalline Fe_{73 5}Cu₁Nb₃Si_13.5B₉ alloy, the results show that the pinning effects resulting from the quasidislocation dipole intensely influence the movement of domain wall; by coupling with the magnetostriction the defects-induced stress fields determine the magnetic properties at the early stage of crystallization. In view of the effective anisotropy and magnetoelastic coupling energy the optimal annealing conditions of alloys are discussed.     

The Thresholds of Survival for ann-Dimensional Food Chain Model in a Polluted Environment

The effects of toxicants on the populations for ann-dimensional food chain model in a polluted environment are studied. The thresholds between persistence and extinction of the populations are obtained as functions of model parameters and a time-varying chemical concentration.     

钙钛矿型复合氧化物LaNi_(1-x)Mn_xO_3晶体结构与催化性能的关系

用XRD、IR和TPR等技术研究了钙钛矿型复合氧化物的晶体结构及其反应性能.整个组成范围内,LaNi_(i-x)Mn_xO_3(0.0≤x≤1.0)体系都生成单一钙钛矿相;x=0.0,0.6≤X≤1.0时为菱形晶系,0.2≤x≤0.5为立方晶系.IR和TPR研究表明,晶体结构对B—O键合作用存在较大影响.CO微反考察表明,本体系的催化活性与晶系存在密切关系,晶体对称性越高,反应活性越低.说明钙钛矿型复合氧化物的催化活性与体系活性中心的B—O键合作用能力有关.     

Reflection of Surface Plasmon Polaritons by a Corner Reflector of Negative Index Materials

A novel type of corner reflector for the reflection of surface plasmon polariton (SPP) is proposed. The reflector consists of two layers of compensatory media whose permittivity and permeability take opposite signs to that of the corresponding layer of the SP waveguide. By rigorously solving Maxwell's equations, the reflected SPP is proved to exist. The transverse wave vector of the reflected SPP is always antiparallel to that of the incident SPP and no phase retardation is introduced.     

Effect of borohydride as reducing agent on the structures and electrochemical properties of Pt/C catalyst

In this paper, we found that boron deposited on the surface of support when sodium borohydride used as reducing agent during the preparation of Pt/C catalyst. The deposition of boron markedly reduces particle size of Pt, raises electrochemical active surface (EAS) area of catalyst and electrochemical activity for hydrogen evolution or oxygen reduction reaction (ORR) compared with which prepared using other reducing agents (hydrogen and formaldehyde).     

The optical properties of planar waveguides in LiB3O5 crystals formed by Cu implantation

A planar optical waveguide has been formed in a LiB₃O₅ crystal using 6.0 MeV Cu⁺-ions with a dose of 1 × 10¹⁵ ions/cm² at room temperature. Possible propagating modes were measured at a wavelength of 633 nm using the prism-coupling method. The refractive index profiles of the waveguide were reconstructed by an effective refractive index method and the beam propagation method was used to investigate the properties of the propagation modes in the formed waveguide. The results suggest that the fundamental TE₀ and TM₀ modes may be well-confined and propagate a longer distance inside the waveguide. The implantation process was also simulated using the transport of ions in matter code (TRIM), which indicates that the nuclear energy deposition may be the main factor for the refractive index change.