The stable forking conjecture and generic structures

 We prove that for any simple theory which is constructed via Fr?issé-Hrushovski method, if the forking independence is the same as the d-independence then the stable forking property holds. Received: 22 January 2001 / Published online: 19 December 2002 This article is part of the author's D-Phil thesis, written at the University of Oxford and supported by the Ministry of Higher Education of Iran. The author would like to thank the Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran, for its financial support whilst working on this article. Mathematics Subject Classification (2000): 03C45 Key words or phrases: Generic structures – Fr?issé-Hrushovski method – Predimension – Simple theories – Stable theories – Stable forking conjecture     

Highly reflective AlGaAsSb/InP Bragg reflector at 1.55 μm grown by MOVPE

The metalorganic vapor-phase epitaxy growth of a highly reflective 24-pair AlGaAsSb/InP-distributed Bragg reflector (DBR) is reported for the first time. The influence of the growth parameters such as the V/III input ratio, the growth temperature and the pressure, the total H₂ flow, the gas velocity and the switching sequence of the source gases at the interfaces has been deeply investigated and optimized to achieve stable growth conditions. The DBR achieves a reflectivity as high as 99.5% around 1.55 μm, a uniform stable composition, and an excellent crystal quality over the 2 inch wafer, with a surface free of crosshatch and a defect density below 1/cm². For the optical characterizations, measurements of linear and nonlinear reflectivity, transmission, pump-probe and photoluminescence were done. The interfaces and bulk layers of InP/AlGaAsSb/InP heterostructures were analyzed by transmission electron microscopy. High resolution X-ray diffraction measurements were used to determine the composition shift in the growth plane of the DBR. The measurements show the high quality of the growth and demonstrate that thick AlGaAsSb/InP heterostructures can be grown by metalorganic vapor-phase epitaxy (MOVPE), and in particular DBRs above 1.31 μm.     

Nonlinear transient analysis of moderately thick laminated composite sector plates

This study presents a simple formulation for the nonlinear dynamic analysis of shear-deformable laminated sector plates made up of cylindrically orthotropic layers. The non-axisymmetric formulation in cylindrical coordinates is discretized in space domain using two-dimensional Chebyshev polynomials. Houbolt time marching is used for temporal discretization. Quadratic extrapolation is used for linearization along with fixed-point iteration for obtaining the results. Several combinations of simply supported, clamped and free edge conditions are considered. Convergence study has been carried out and the results are compared with the results of square plates. Effects of boundary conditions, moduli ratio, lamination scheme, sector angle and annularity on the transient deflection response are plotted graphically. Transient responses are compared for step, saw-tooth and sinusoidal loadings.     

A note on 4-dimensional locally conformally flat Walker manifolds

A 4-dimensional Walker metric on a semi Riemanian manifold M, for the canonical metric with c = 0, have been investigated by M. Chaichi, E. García—Río and Y. Matsushita. The paper generalizes these notions to the case of constant c ≠ 0. Specially the form of defining functions of this metric in locally conformally flat 4-dimensional Walker manifolds is found.     

Oscillation of solutions of second-order nonlinear differential equations of Euler type

We consider the nonlinear Euler differential equation t²x^″+g(x)=0. Here g(x) satisfies xg(x)>0 for x≠0, but is not assumed to be sublinear or superlinear. We present implicit necessary and sufficient condition for all nontrivial solutions of this system to be oscillatory or nonoscillatory. Also we prove that solutions of this system are all oscillatory or all nonoscillatory and cannot be both. We derive explicit conditions and improve the results presented in the previous literature. We extend our results to the extended equation t²x^″+a(t)g(x)=0.     

Isovector solitons and Maxwell's equations

We present an isovector Lagrangian, which admits stable, nonsingular soliton solutions in three space dimensions. The spherical solution and its total energy are obtained via a variational procedure. An antisymmetric, second-rank tensor is defined in terms of the isovector field and its derivatives. This tensor satisfies Maxwell's equations. The corresponding current is identically conserved and the total charge is topologically quantized.     

The Investigation of Bulk and Surface Polariton Modes in Ga1?xNxAs by Using Infrared Magneto Spectroscopy

We present and discuss infrared magnetoplasma reflectivity and surface polariton modes in Ga_1–xN_xAs. It assumed that the sample is characterized by a magnetoplasma dielectric tensor. Surface polariton dispersion for two component magnetoplasma was calculated from reflectivity spectra data. We detect transverse optic phonon of GaN sublattice in 470 cm^-1. The origin of sharp feature in p-polarization reflectivity about 300 cm^–1 as well as LO phonon frequency of GaAs sublattice is due to Brewster mode. An interesting feature of surface modes in Voigt geometry is nonreciprocalicity, which means that the frequency changes when the direction of propagation is reversed. Also, the infrared magnetoplasma reflectivity of GaNAs should be providing determination of the electrons and heavy holes effective mass and carrier's concentration.     

Special representations of the group SP(4,q) with minimal degrees

Let G be a finite group. Let p(G) denote the minimal degree of a faithful permutation representation ofG and let q(G) and c(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers, respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. The purpose of this paper is to calculate p(G), q(G), c(G) and r(G) for the group SP(4,q). This revised version was published online in June 2006 with corrections to the Cover Date.     

Highly selective PVC-membrane electrodes based on Co(II)-Salen for determination of nitrite ion.

A cobalt(II) derivative was used as a suitable ionophore for the preparation of a polymeric membrane nitrite-selective electrode. The electrode reveals a Nemstian behavior over a very wide NO2- ion concentration range (1.0 x 10(-6)-1.0 x 10(-1) M) and a very low detection limit (5.0 x 10(-7) M). The potentiometric response is independent of the pH of solution in the pH range 4.0-9.5. The electrode shows advantages such as low resistance, fast response and, most importantly, good selectivity relative to a wide variety of inorganic and organic anions. In fact, the selectivity behavior of the proposed NO2- ion-selective electrode shows great improvements compared to the previously reported electrodes for nitrite ion. The proposed electrodes could be used for at least 2 months without any significant changes in potentials. The electrode was successfully applied to the determination of nitrate ion concentrations in sausage and milk samples.