An (m+1)-step iterative method of convergence order (m+2) for linear complementarity problems

In this paper, we present an (m+1)-step iterative method of convergence order (m+2) for solving linear complementarity problems. The proposed iterative method is simple and easy to construct, and requiring only third Fréchet differentiation. Computational efficiency in its general form is discussed and a comparison between the efficiency of the proposed method and existing ones is made. The performance is tested through numerical experiments on some test problems.     

Das Atomgewicht des Neodyms

Ohne Zusammenfassung     

New diffusion-edited NMR experiments to expedite the dereplication of known compounds from natural product mixtures

[reaction: see text] We present two new diffusion-edited NMR experiments, improved DECODES and HETDECODES, that sort the constituents in a mixture by their individual diffusion coefficients. These experiments should allow the partial NMR spectral assignment and cursory structure elucidation of compounds in a complex mixture as an aid in the dereplication of known or nuisance compounds.     

IMPROVEMENT OF THE SEMI-ANALYTICAL METHOD, FOR DETERMINING THE GEOMETRICALLY NON-LINEAR RESPONSE OF THIN STRAIGHT STRUCTURES. PART I: APPLICATION TO CLAMPED-CLAMPED AND SIMPLY SUPPORTED-CLAMPED BEAMS

In a previous series of papers (Benamar 1990 Ph.D. Thesis, University of Southampton; Benamaret al. 1991 Journal of Sound and Vibration149, 179-195;164, 399-424 [1-3]) a general model based on Hamilton's principle and spectral analysis has been developed for non-linear free vibrations occurring at large displacement amplitudes of fully clamped beams and rectangular homogeneous and composite plates. The results obtained with this model corresponding to the first non-linear mode shape of a clamped-clamped (CC) beam and to the first non-linear mode shape of a CC plate are in good agreement with those obtained in previous experimental studies (Benamaret al. 1991 Journal of Sound and Vibration 149, 179-195;164, 399-424 [2, 3]). More recently, this model has been re-derived (Azar et al. 1999 Journal of Sound and Vibration224, 377-395; submitted [4, 5]) using spectral analysis, Lagrange's equations and the harmonic balance method, and applied to obtain the non-linear steady state forced periodic response of simply supported (SS), CC, and simply supported-clamped (SSC) beams. The practical application of this approach to engineering problems necessitates the use of appropriate software in each case or use of published tables of data, obtained from numerical solution of the non-linear algebraic system, corresponding to each problem. The present work was an attempt to develop a more practical simple “multi-mode theory” based on the linearization of the non-linear algebraic equations, written on the modal basis, in the neighbourhood of each resonance. The purpose was to derive simple formulae, which are easy to use, for engineering purposes. In this paper, two models are proposed. The first is concerned with displacement amplitudes of vibrationW_max /H, obtained at the beam centre, up to about 0·7 times the beam thickness and the second may be used for higher amplitudes W_max/H up to about 1·5 times the beam thickness. This new approach has been successfully used in the free vibration case to the first, second and third non-linear modes shapes of CC beams and to the first non-linear mode shape of a CSS beam. It has also been applied to obtain the non-linear steady state periodic forced response of CC and CSS beams, excited harmonically with concentrated and distributed forces.     

Embedding Uq(sl(2)) and Sine Algebras in Generalized Clifford Algebras

We establish the connection between certain quantum algebras and generalizedClifford algebras (GCA). To be precise, we embed the quantum tori Lie algebraand U _q (sl(2)) in GCA.     

Synthesis,characterization, and photovoltaic properties of dithienylbenzobisazole‐dithienylsilole copolymers

Three conjugated polymers comprised of dioctyl‐dithieno‐[2,3‐b:2',3'‐d]silole and a donor‐acceptor‐donor triad of either cis‐benzbisoxazole, trans‐benzobisoxazole or trans‐benzobisthiazole were synthesized via the Stille cross‐coupling reaction. The impact of varying the heteroatoms and/or the location within the benzobisazole moiety on the optical and electronic properties of the resulting polymers was evaluated via cyclic voltammetry and UV‐Visible spectroscopy. All of the polymers have similar optical band‐gaps of ～1.9 eV and highest occupied molecular orbital levels of ? 5.2 eV. However, the lowest unoccupied molecular orbitals (LUMO) ranged from ? 3.0 to ? 3.2 eV. Interestingly, when the polymers were used as donor materials in bulk‐heterojunction photovoltaic cells with PC₇₁BM as the electron‐acceptor, the benzobisoxazole‐based polymers gave slightly better results than the benzobisthiazole‐containing polymers with power conversion efficiencies up to 3.5%. These results indicate that benzobisoxazoles are promising materials for use in OPVs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1533–1540     

COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL

Let m be a positive integer and B be the unit ball of Rn(n ≥ 2). We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem(-△)mu = a1(x)uα1+ a2(x)uα2, lim|x|→1u(x)(1- |x|)m-1= 0,where α1, α2 ∈(-1, 1) and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.