The Kloosterman problem for binary Hermitian lattices

A Hermitian lattice over an imaginary quadratic field $\mathbb {Q}(\sqrt{-m})$ is called almost universal if it represents all but finitely many positive integers. We investigate almost universal binary Hermitian lattices and provide a Bochnak-Oh type criterion on almost universality. In particular, all almost universal $p$ -anisotropic binary Hermitian lattices are universal, and we give the complete list of all such Hermitian lattices.     

Leader‐following consensus problem of heterogeneous multi‐agent systems with nonlinear dynamics using fuzzy disturbance observer

This article considers the leader‐following consensus problem of heterogeneous multi‐agent systems. The proposed multi‐agent system is consisted of heterogeneous agents where each agents have their own nonlinear dynamic behavior. To overcome difficulty from heterogeneous nonlinear intrinsic dynamics of agents, a fuzzy disturbance observer is adopted. In addition, based on the Lyapunov stability theory, an adaptive control method is used to compensate the observation error caused by the difference between the unknown factor and estimated values. Two numerical examples are given to illustrate the effectiveness of the proposed method. © 2013 Wiley Periodicals, Inc. Complexity 19: 20–31, 2014     

LENTICULAR NONCOMMUTATIVE TORI

All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than     

A study on structural formation and optical property of wide band-gap Be0.2Zn0.8O layers grown by RF magnetron co-sputtering system

Wide band-gap BeZnO layers were grown on Al₂O₃ (0 0 0 1) substrate using radio-frequency magnetron co-sputtering. The rate of Be_xZn_1−xO crystallized as a hexagonal structure was x=0.2. From the X-ray photoelectron spectroscopy measurement, the O–Zn bonds relating the crystal structure and the Be–O bonds related to the deviation of the stoichiometry in the BeZnO layer were caught at 530.4 and 531.7 eV in the O 1s spectrum, respectively. Thus, the observance on the Be 1s peak of 113.2 eV associated with the bonding Be–O indicates that the sputtered Be atoms are substituted for the host-lattice site in ZnO. This Be–O bonding shows a relatively low intense and broadening spectrum caused by large fluctuation of Be content in the BeZnO layer. From the photoluminescence and transmittance measurement, the free exciton and the neutral donor-bound exciton (D⁰, X) emissions were observed at 3.7692 and 3.7313 eV, respectively, and an average transmittance rate over 95% was achieved in a wide ultraviolet (UV)–visible region. Also, the binding energy for the (D⁰, X) emission was extracted to be 37.9 meV. Through the wide band-gap material BeZnO, we may open some possibilities for fabricating a ZnO-based UV light-emitting diode to be utilized as a barrier layer comprised of the ZnO/BeZnO quantum well structure and/or an UV light emitting material itself.     

Generalized matching theorems for closed coverings of convex sets

In this paper we use fixed point and coincidence theorems due to Park [8] to give matching theorems concerning closed coverings of nonempty convex sets in a real topological vector space. Our new results extend previously given ones due to Ky Fan [2], [3], Shih [10], Shih and Tan [11], and Park [7].     

A note on envelopes of homotopies

In this article, we deal with the notion of the envelopes of homotopies which is the generalized version of functional envelopes in discrete dynamical systems. We prove the stability for envelopes of homotopies in complete normed algebra and we get the stabilities of the derivation and the extended derivation for the notion in the spaces.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.