Elegant Inceben Gaussian beams in a quadratic-index medium

Elegant Ince—Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince—Gaussian beams and they display better symmetry between the Ince-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince—Gaussian beams are discussed.     

Geometry of Cubic and Quartic Hypersurfaces over Finite Fields

Let YPⁿ be a cubic hypersurface defined over GF(q). Here, we study the Finite Field Nullstellensatz of order [q/3] for the set Y(q) of its GF(q)-points, the existence of linear subspaces of PG(n,q) contained in Y(q) and the possibility to join any two points of Y(q) by the union of two lines of PG(n,q) entirely contained in Y(q). We also study the existence of linear subspaces defined over GF(q) for the intersection of Y with s quadrics and for quartic hypersurfaces.     

(APD)-property of -algebras by extensions of -algebras with (APD)

A unital -algebra is said to have the (APD)-property if every nonzero element in has the approximate polar decomposition. Let be a closed ideal of . Suppose that and have (APD). In this paper, we give a necessary and sufficient condition that makes have (APD). Furthermore, we show that if and or is a simple purely infinite -algebra, then has (APD).

     

Extraction of bulk wave characteristics from a pulsed ultrasonic polar scan

The pulsed ultrasonic polar scan (P-UPS) technique provides a map with characteristic contours reflecting the critical bulk wave angles, which directly relate to the in-plane elastic properties of the insonified material spot. Besides these contours, additional information is captured in a P-UPS experiment which has particular importance for the inspection of anisotropic materials. By extensive post-processing on a single P-UPS experiment, we successfully extracted the local directional (i) critical bulk wave angles, (ii) phase velocity profiles, (iii) slowness curves, (iv) walk-off angles and (v) energy velocity profiles, for the three different polarization states of bulk waves. The procedure is demonstrated and discussed for an isotropic aluminum sample as well as an autoclave manufactured orthotropic _[0]8${\left[0\right]}_8$ carbon/epoxy laminate. In addition, a numerical and experimental investigation of the role of the immersion liquid as a lens for the P-UPS result is performed. This lensing effect permits to zoom in/out on the P-UPS fingerprint, hence broadening the class of materials which can be inspected by the P-UPS technique.     

Well-Posedness of A Compressible Gas-Liquid Model for Deepwater Oil Well Operations

The main purpose of this paper is two-fold: (i) to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71 (2011), pp. 2014–2047]; (ii) to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58 (2004), pp. 719–731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.     

平行映射下保测地线的曲面

利用古典微分几何方法,讨论了在平行映射下测地线不变的曲面若干局部性质;研究了该类曲面的测地坐标系,并最终得出满足该条件的曲面只有三类.     

A spherical higher-order finite-difference time-domain algorithm with perfectly matched layer

A higher-order finite-difference time-domain（HO-FDTD） in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain（FDTD） and the multiresolution time-domain（MRTD） schemes with respect to memory requirements and CPU time. Moreover, the Berenger＇s perfectly matched layer（PML） is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML.     

Iron‐mediated AGET ATRP of methyl methacrylate in the presence of polar solvents as ligands

The polar solvents, N‐methylpyrrolidone (NMP), N,N‐dimethylformamide (DMF), and acetonitrile (CH₃CN) were used as ligands for iron(III)‐mediated activators generated by electron transfer atom transfer radical polymerizations (AGET ATRPs) of methyl methacrylate (MMA) with various initiators and reducing agents. Polymerizations were conducted with a molar ratio of [MMA]₀/[initiator]₀/[FeBr₃]₀/[reducing agent]₀ = 100:1:1:0.5 and a volume ratio of MMA/solvent = 2:1 at 60 °C to investigate the effects of initiator, solvent and reducing agent, and most of the systems showed the typical features of “living”/controlled radical polymerization. In order to get a deeper understanding of the mechanism, the amount of the reducing agent was changed to study the polymerization behavior. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1020–1027