Semicrossed products generated by two commuting automorphisms

We study the semicrossed product of a finite dimensional C^*-algebra by two types of commuting automorphisms, and identify them with matrix algebras of analytic functions in two variables. We look at the connections with semicrossed products by Z_+ actions.Comment: 15 page

Tapping Into Creativity: A/R/Tography as a Research Methodology Underpinning Teacher Education

Educational research within teacher education has become a must, where there is emphasis on ‘teacher as researcher’, with action research as their methodology. Yet, many teachers may not have embarked on any form of research prior to educational programmes designed to enhance their pedagogy and impact their practice. There is also a question around the methodologies they are introduced to, which at times fail to hone in on the very characteristic and golden thread of their profession: creativity. This article reintroduces the concept of a/r/tography, not only as a methodology from art-based education in its own right, but also as one that can be used as a hybridised practice-oriented and action research-based methodology within teacher education. Not just for dissertation or research purposes, but as something that should underpin all programme curriculum and pedagogy designed for the education of teachers

The Stable Manifold Theorem for Stochastic Differential Equations

We formulate and prove a {\it Local Stable Manifold Theorem\/} for stochastic differential equations (sde's) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and It\^o-type equations are treated. Starting with the existence of a stochastic flow for a sde, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution. For Stratonovich sde's, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating sde. The proof of the stable manifold theorem is based on Ruelle-Oseledec multiplicative ergodic theory

Quantum Hall Droplets on Disc and Effective Wess-Zumino-Witten Action for Edge States

We algebraically analysis the quantum Hall effect of a system of particles living on the disc ${\bf B}^1$ in the presence of an uniform magnetic field $B$. For this, we identify the non-compact disc with the coset space $SU(1,1)/U(1)$. This allows us to use the geometric quantization in order to get the wavefunctions as the Wigner ${\cal D}$-functions satisfying a suitable constraint. We show that the corresponding Hamiltonian coincides with the Maass Laplacian. Restricting to the lowest Landau level, we introduce the noncommutative geometry through the star product. Also we discuss the state density behavior as well as the excitation potential of the quantum Hall droplet. We show that the edge excitations are described by an effective Wess-Zumino-Witten action for a strong magnetic field and discuss their nature. We finally show that LLL wavefunctions are intelligent states.Comment: 18 pages, clarifications and misprints corrected, version published in IJGMM

Simulation of brittle damage for fracture process of endodontically treated tooth

The mechanics of brittle damage in porcelain of an endodontically treated maxilla incisor tooth was simulated using finite element method (FEM). For this purpose a very complex composite structure of endodontically treated tooth is simulated under transverse loading. Three dimensional (3D) model of human maxilla incisor tooth root was developed based on Computed Tomography (CT) scan images. Crown, core cement, resin core, dental post, post cement and dentin were created using SolidWorks software, and then the model was imported into ABAQUS-6.9EF software for nonlinear behavior analysis. This study utilizes finite element method to simulate onset and propagation of crack in ceramic layer (porcelain) by the cause of both tension and compression loading related to complexity of the geometry of tooth implant. The simulation has been done using brittle damaged model available in ABAQUS/Explicit in quasi-static load condition. The load-displacement response of whole structure is measured from the top of porcelain by controlling displacement on a rigid rod. Crack initiated at the top of porcelain bellow the location of the rod caused by tension damage at equivalent load of 590 N. Damage in porcelain accounts for up to 63% reduction of whole structure stiffness from the undamaged state. The failure process in porcelain layer can be described by an exponential rate of fracture energy dissipation. This study demonstrated that the proposed finite element model and analysis procedure can be use to predict the nonlinear behavior of tooth implant

Mass-Galaxy offsets in Abell 3827, 2218 and 1689: intrinsic properties or line-of-sight substructures?

We have made mass maps of three strong-lensing clusters, Abell 3827, Abell 2218 and Abell 1689, in order to test for mass-light offsets. The technique used is GRALE, which enables lens reconstruction with minimal assumptions, and specifically with no information about the cluster light being given. In the first two of these clusters, we find local mass peaks in the central regions that are displaced from the nearby galaxies by a few to several kpc. These offsets {\em could\/} be due to line of sight structure unrelated to the clusters, but that is very unlikely, given the typical levels of chance line-of-sight coincidences in $\Lambda CDM$ simulations --- for Abell 3827 and Abell 2218 the offsets appear to be intrinsic. In the case of Abell 1689, we see no significant offsets in the central region, but we do detect a possible line of sight structure: it appears only when sources at z\ga 3 are used for reconstructing the mass. We discuss possible origins of the mass-galaxy offsets in Abell 3827 and Abell 2218: these include pure gravitational effects like dynamical friction, but also non-standard mechanisms like self-interacting dark-matter.Comment: 14 pages, 9 figures; Accepted for publication in MNRA

Highly efficient spin-orbit torque and switching of layered ferromagnet Fe3GeTe2

Among van der Waals (vdW) layered ferromagnets, Fe3GeTe2 (FGT) is an excellent candidate material to form FGT/heavy metal heterostructures for studying the effect of spin-orbit torques (SOT). Its metallicity, strong perpendicular magnetic anisotropy built in the single atomic layers, relatively high Curie temperature (Tc about 225 K) and electrostatic gate tunability offer a tantalizing possibility of achieving the ultimate high SOT limit in monolayer all-vdW nanodevices. The spin current generated in Pt exerts a damping-like SOT on FGT magnetization. At about 2.5x1011 A/m2 current density,SOT causes the FGT magnetization to switch, which is detected by the anomalous Hall effect of FGT. To quantify the SOT effect, we measure the second harmonic Hall responses as the applied magnetic field rotates the FGT magnetization in the plane. Our analysis shows that the SOT efficiency is comparable with that of the best heterostructures containing three-dimensional (3D) ferromagnetic metals and much larger than that of heterostructures containing 3D ferrimagnetic insulators. Such large efficiency is attributed to the atomically flat FGT/Pt interface, which demonstrates the great potential of exploiting vdW heterostructures for highly efficient spintronic nanodevices