Finite-Dimensional Representations of the Quantum Superalgebra Uq_{q}[gl(2/2)]: II. Nontypical representations at generic qq

The construction approach proposed in the previous paper Ref. 1 allows us there and in the present paper to construct at generic deformation parameter $q$ all finite--dimensional representations of the quantum Lie superalgebra $U_{q}[gl(2/2)]$. The finite--dimensional $U_{q}[gl(2/2)]$-modules $W^{q}$ constructed in Ref. 1 are either irreducible or indecomposible. If a module $W^{q}$ is indecomposible, i.e. when the condition (4.41) in Ref. 1 does not hold, there exists an invariant maximal submodule of $W^{q}$, to say $I_{k}^{q}$, such that the factor-representation in the factor-module $W^{q}/I_{k}^{q}$ is irreducible and called nontypical. Here, in this paper, indecomposible representations and nontypical finite--dimensional representations of the quantum Lie superalgebra $U_{q}[gl(2/2)]$ are considered and classified as their module structures are analized and the matrix elements of all nontypical representations are written down explicitly.Comment: Latex file, 49 page

A micro-mechanics model for imperfect interface in dielectric materials

The interface between two dielectric bodies is considered imperfect if there are defects (micro-voids and micro-cracks) present on the interface. For such interface, the perfect continuity condition across the interface is no longer valid and its use in analysis becomes questionable. To account for this imperfection, we propose a micro-mechanics model based on the self-consistent scheme, leading to the establishment of a constitutive relationship between the electric displacement and potential discontinuity across the imperfect interface. © 2001 Elsevier Science Ltd.postprin

Irreducible representations of Upq[gl(2/2)]

The two-parametric quantum superalgebra $U_{pq}[gl(2/2)]$ and its representations are considered. All finite-dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and nontypical ones according to a proposition proved in the present paper. This proposition is a nontrivial deformation from the one for the classical superalgebra gl(2/2), unlike the case of one-parametric deformations.Comment: Latex, 8 pages. A reference added in v.

Fractional Chern Insulators from the nth Root of Bandstructure

We provide a parton construction of wavefunctions and effective field theories for fractional Chern insulators. We also analyze a strong coupling expansion in lattice gauge theory that enables us to reliably map the parton gauge theory onto the microsopic Hamiltonian. We show that this strong coupling expansion is useful because of a special hierarchy of energy scales in fractional quantum Hall physics. Our procedure is illustrated using the Hofstadter model and then applied to bosons at 1/2 filling and fermions at 1/3 filling in a checkerboard lattice model recently studied numerically. Because our construction provides a more or less unique mapping from microscopic model to effective parton description, we obtain wavefunctions in the same phase as the observed fractional Chern insulators without tuning any continuous parameters.Comment: 9+3 pages, 6 figures; v2: added refs, amplified discussion of deconfinement, improved discussion of translation invarianc

A finite element approach for computing edge singularities in piezoelectric materials

By using the eigenfunction expansion technique and the weak form of the governing equations for prismatic sectorial domains composed of piezoelectrics and air, an one-dimensional finite element procedure is formulated for computing the eigensolutions of the electromechanical field problem. Generalized displacement and electric potential are taken to be the nodal variables. The resulting global equation is a second order characteristic matrix equation. Validity of the formulation is verified by comparing the computed results with the existing solutions for impermeable cracks and interfacial cracks. Configurations which are of practical interest including conducting cracks, permeable and impermeable notches are studied. © 2001 Elsevier Science Ltd. All rights reserved.postprin

Associations between Moderate-to-Vigorous Physical Activity and Neighbourhood Recreational Facilities: The Features of the Facilities Matter

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Carbonization over PFA-protected dispersed platinum: An effective route to synthesize high performance mesoporous-carbon supported Pt electrocatalysts

An alternative and effective route of synthesizing mesoporous carbon supported Pt nanoparticles is introduced. In reverse order to the conventional synthetic route, carbonization occurs after dispersion of platinum. In this process, H2PtCl6 acts as a Pt source and also serves as a catalyst for the polymerization of furfuryl alcohol (FA). The polymerized FA around the H2PtCl6 nanoparticles functions as a protecting agent and prevents the growth of Pt nanoparticles in the later high temperature carbonization step. The resulting Pt nanoparticles are highly dispersed in the mesoporous carbon structure, CMK3, and give a much higher methanol oxidation current when compared with Pt/CMK3 electrocatalysts prepared via the conventional route. © The Royal Society of Chemistry 2011.postprin

Four- and eight-node hybrid-Trefftz quadrilateral finite element models for helmholtz problem

In this paper, four- and eight-node quadrilateral finite element models which can readily be incorporated into the standard finite element program framework are devised for plane Helmholtz problems. In these models, frame (boundary) and domain approximations are defined. The former is obtained by nodal interpolation and the latter is truncated from Trefftz solution sets. The equality of the two approximations are enforced along the element boundary. Both the Bessel and plane wave solutions are employed to construct the domain approximation. For full rankness, a minimal of four and eight domain modes are required for the four- and eight-node elements, respectively. By using local coordinates and directions, rank sufficient and invariant elements with minimal and close to minimal numbers of domain approximation modes are devised. In most tests, the proposed hybrid-Trefftz elements with the same number of nodes yield close solutions. In absolute majority of the tests, the proposed elements are considerably more accurate than their single-field counterparts. © 2009 Elsevier B.V. All rights reserved.postprin

A semi-analytical finite element method for a class of time-fractional diffusion equations

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