A note on strongly π-regular rings

Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that x ⁿ=x ^{n +1} y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and x ^m=x ⁿ. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

On α-I-continuous and α-I-open functions

Montgomery and Vaughan improved a theorem of Erd?s and Fuchs for an arbitrary sequence. Sárközy extended this theorem of Erd?s and Fuchs for two arbitrary sequences which are "near" in a certain sense. Using the idea of Jurkat (differentiation of the generating function), we will extend similarly the result of Montgomery and Vaughan for "sufficiently near" sequences.     

An exponentially fitted special second-order finite difference method for solving singular perturbation problems

An exponentially fitted special second-order finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. A fitting factor is introduced in a tri-diagonal finite difference scheme and is obtained from the theory of singular perturbations. Thomas Algorithm is used to solve the system and its stability is investigated. To demonstrate the applicability of the method, we have solved several linear and non-linear problems. From the results, it is observed that the present method approximates the exact solution very well.     

Controllability of Functional Integro-Differential Inclusions with an Unbounded Delay

In this paper, a sufficient condition is established for the controllability of neutral functional integro-differential inclusions with an unbounded delay in Banach spaces. The approach used is a fixed-point theorem for condensing maps due to Martelli and the theory of analytic semigroup of linear operators. Communicated by F. Zirilli Research supported by NNSF of China, by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China, and by the Qing Lan Talent Engineering Fund QL-05-164 of Lanzhou Jiaotong University. The authors are grateful to Professor F. Zirilli and two anonymous referees for valuable suggestions improving this paper.     

On the validity of the amphoteric-defect model in gallium arsenide and a criterion for Fermi-level pinning by defects

Using the theoretically calculated point-defect total-energy values of Baraff and Schlüter in GaAs, anamphoteric-defect model has been proposed by Walukiewicz to explain a large number of experimental results. The suggested amphoteric-defect system consists of two point-defect species capable of transforming into each other: the doubly negatively charged Ga vacancyV _Ga ^2– and the triply positively charged defect complex (AS_Ga+V _As)³⁺, with As_Ga being the antisite defect of an As atom occupying a Ga site andV _As being an As vacancy. When present in sufficiently high concentrations, the amphoteric defect systemV _Ga ^2– /(As_Ga+V _As)³⁺ is supposed to be able to pin the GaAs Fermi level at approximately theE _v +0.6 eV level position, which requires that the net free energy of theV _Ga/(As_Ga+V _As) defect system to be minimum at the same Fermi-level position. We have carried out a quantitative study of the net energy of this defect system in accordance with the individual point-defect total-energy results of Baraff and Schlüter, and found that the minimum net defect-system-energy position is located at about theE _v +1.2 eV level position instead of the neededE _v +0.6 eV position. Therefore, the validity of the amphoteric-defect model is in doubt. We have proposed a simple criterion for determining the Fermi-level pinning position in the deeper part of the GaAs band gap due to two oppositely charged point-defect species, which should be useful in the future.     

Linear optical switching in a FLC/waveguide composite device

A fast electrooptic modulation in a polymer waveguide using a ferroelectric liquid crystal has been proposed. In this device, the surface stabilized ferroelectric liquid crystal and the soft mode ferroelectric liquid crystal are used as an active material on the passive polymer waveguide, and electrooptic switching is realized by controlling the total reflection at the polymer waveguide-liquid crystal interface. The response time is of the order of several microseconds. The analogue electrooptic modulation in the waveguide is realized using the field induced linear molecular tilt of the electroclinic effect in the soft mode ferroelectric liquid crystal.     

Measurement of intense microwave field patterns using a neon glow indicator lamp

A novel method using small neon glow lamps with electrodes is developed for measuring intense microwave field patterns. When the lamp axis coincide with the electric field direction, the lamp discharge starts at the feeblest microwave electric field strength. Therefore, the lamp axis shows the field direction and the discharge starting indicates the field strength. The field strength for starting the microwave discharge is less than the strength for AC discharge, because of its low loss discharge mechanism. In the experiments using a microwave oven, it has been demonstrated again comparing with the simulated results that the method is able to use for measuring the intense electric field strength and direction.     

A precision measurement of the hyperfine structure of87Sr+

The ground state hyperfine splitting of⁸⁷Sr⁺ was measured with a precision of 1×10^–8. The experiments were performed with an RF ion trap connected to an ISOL (isotope separator on-line), where all the possible transitions between Zeeman sublevels were observed by a laser-microwave double resonance method. The magnetic dipole hyperfine constant was determined to beA=–1 000 473.673 (11) kHz.