Dispersion characteristics of transverse surface waves in piezoelectric coupled solid media with hard metal interlayer

The propagation of transverse surface waves in a piezoelectric layer/metal substrate system with one or multiple hard metal interlayer(s) is investigated analytically. The general dispersion equations for the existence of the waves are obtained in a simple mathematic form for class 6 mm piezoelectric materials. The presence of a hard metal interlayer can not only get rid of the undesired mode appearing in the case without an interlayer but shorten the existence range of the phase velocity within which a nonleaky but dispersive mode exists. The effects of the hard interlayer on the phase velocity can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.     

Numerical simulation of nonlinear magnetic-mechanical-electric coupling effect in laminated magnetoelectric composites

Considering the significant nonlinear magnetoelectric (ME) characteristics in laminated ME composites, we build a numerical model of magnetic-mechanical-electric coupling effect based on the nonlinear magnetostrictive constitutive relation. The change of the ME field coefficients with bias magnetic field predicted by this model shows good agreement with the experimental result, both qualitatively and quantitatively. Furthermore, this paper considers and predicts the magnetoelectric conversion charateristics of laminated ME composites, calculates and analyzes the influence of the thickness ratio of magnetostrictive layer, the geometrical size of laminated composites, the saturation magnetization, and the types of piezoelectric materials on the ME conversion coefficient of ME laminated composites. We believe that this research provides a theoretical basis for the production of magnetoelectric devices with good magnetoelectric conversion characteristics.     

F-theory grand unification at the colliders

We predict the exact gaugino mass relation near the electroweak scale at one loop for gravity mediated supersymmetry breaking in F-theory SU(5) and SO(10) models with UY(1) and U(1)_B−L fluxes, respectively. The gaugino mass relation introduced here differs from the typical gaugino mass relations studied thus far, and in general, should be preserved quite well at low energy. Therefore, these F-theory models can be tested at the Large Hadron Collider and future International Linear Collider. We present two typical scenarios that satisfy all the latest experimental constraints and are consistent with the CDMS II experiment. In particular, the gaugino mass relation is indeed satisfied at two-loop level with only a very small deviation around the electroweak scale.     

On the regularity of orientable matroids

We present two characterizations of regular matroids among orientable matroids and use them to give a measure of “how far” an orientable matroid is from being regular.     

Multi-graded nilpotent tuples

We discuss multi-graded nilpotent tuples of multi-graded vector spaces which are a generalization of graded nilpotent pairs. The multi-grading yields a natural notion of a shape of such tuple and our main interest is to answer the question “Is the number of multi-graded nilpotent tuples of a fixed shape, up to base change in the homogeneous components, finite?” Our methods make use of a translation to the class of so-called “Multi-staircase algebras” and we classify their representation types.     

Fixed-Point Theorems for Generalized Nonexpansive Mappings

Using the concept of asymptotic center we obtain the existence of fixed points having preassigned location for a wider class of asymptotic nonexpansive mappings in a uniformly convex Banach space. This generalization leads us to get a recent result of Alfuraidan and Khamsi for continuous monotone asymptotic nonexpansive mappings as well as the classical fixed-point result of Geobel and Kirk for asymptotic nonexpansive mappings in a uniformly convex Banach space. Also we prove a fixed-point theorem for order preserving continuous maps on a quasiordered closed convex subset of a uniformly convex Banach sapce having monotone norm.     

Center for Elliptic Quantum Group Eτ,η(sln)

We give the center of the elliptic quantum group in general cases. Based on the dynamical Yang-Baxter relation and the fusion method, we prove that the center commutes with all generators of the elliptic quantum group. Then for a kind of assumed form of these generators, we find that the coefficients of these generators form a new type of closed algebra. We also give the center for the algebra.     

Banaschewski’s theorem for generalized <Emphasis Type="Italic">MV</Emphasis>-algebras

A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element. This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002. The work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information (grant I/2/2005).     

Weakly Implicative (Fuzzy) Logics I: Basic Properties

This paper presents two classes of propositional logics (understood as a consequence relation). First we generalize the well-known class of implicative logics of Rasiowa and introduce the class of weakly implicative logics. This class is broad enough to contain many “usual” logics, yet easily manageable with nice logical properties. Then we introduce its subclass–the class of weakly implicative fuzzy logics. It contains the majority of logics studied in the literature under the name fuzzy logic. We present many general theorems for both classes, demonstrating their usefulness and importance.The work was supported by grant A100300503 of the Grant Agency of the Academy of Sciences of the Czech Republic and by Institutional Research Plan AVOZ10300504.