Symplecton for U_h(sl(2)) and representations of SL_h(2)

Polynomials of boson creation and annihilation operators which form irreducible tensor operators for Jordanian quantum algebra U_h(sl(2)), called h-symplecton, are introduced and their properties are investigated. It is shown that many properties of symplecton for Lie algebra sl(2) are extended to h-symplecton. The h-symplecton is also a basis of irreducible representation of SL_h(2) dual to U_h(sl(2)). As an application of the procedure used to construct h-symplecton, we construct the representation bases of SL_h(2) on the quantum h-plane.Comment: 20 pages, LaTeX2e, no figures, to be published in J.Math.Phy

Strong magnetic field enhancement of spin triplet pairing arising from coexisting 2kF2k_F spin and 2kF2k_F charge fluctuations

We study the effect of the magnetic field (Zeeman splitting) on the triplet pairing. We show generally that the enhancement of spin triplet pairing mediated by coexisting $2k_F$ spin and $2k_F$ charge fluctuations can be much larger than in the case of triplet pairing mediated by ferromagnetic spin fluctuations. We propose that this may be related to the recent experiment for (TMTSF)$_2$ClO$_4$, in which a possibility of singlet to triplet pairing transition has been suggested.Comment: 5 page

International Financial Regulatory Standards and Human Rights: Connecting the Dots

This paper’s hypothesis is that the international standard setting bodies (SSBs) could improve the quality of their international standards by incorporating a human rights analysis. It focuses on five SSBs and seven of their international standards and its findings include the following: First, the standards all implicate the right of non-discrimination, and the rights to information, privacy and an effective remedy. Second, they each raises economic, social and cultural rights issues, including the obligation to allocate ‘maximum available resources’ to the progressive realization of economic, social and cultural rights; the human rights responsibilities of private actors exercising delegated regulatory authority, and the need for financial decision-makers to account for all the impacts and risks of their decisions and actions. Third, the SSBs’ failure to utilize such international standards as the UNGPs, the PRI, and the Equator Principles means that they have not comprehensively addressed the risk factors facing the financial sector. Fourth, the benefits that the SSBs gain from utilizing a human rights analysis outweigh their costs. Fifth, there are manageable risks to human rights if the financial sector adopts a human rights approach

Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]

Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be expressed in terms of the $Q$-Hahn polynomials. We next investigate representations of the quantum supergroup OSp_q(1/2) which are not well-defined in the classical limit. Employing the universal T-matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in all cases. Using the Clebsch-Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even dimensional representations of the quantum supergroup OSp_q(1/2).Comment: 16 pages, no figure

A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we proposed a lattice dynamic treatment for the total potential energy for single-walled carbon nanotubes (SWCNT's) which is, apart from a parameter for the non-linear effects, extracted from the vibrational energy of the planar graphene sheet. Based upon the proposal, we investigated systematically the relaxed lattice configuration for narrow SWCNT's, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties respected to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. Particularly, we verified that the relaxation effect brings the bond length longer and the frequencies of various optical vibrational modes softer; Our calculation provides the evidence that the Young's modulus of armchair tube exceeds that of the planar graphene sheet, and the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of the graphite; The calculated radial breathing modes for the ultra narrow tubes with diameter range between 0.2 - 0.5 nm coincide the experimental results and the existing {\it ab initio} calculations with satisfaction; For narrow tubes of diameter 2 nm, the calculated frequencies of optical modes in tubule tangential plane as well as those of radial breathing modes are also in good agreement with the experimental measurement. In addition, our calculation shows that various physical quantities of relaxed SWCNT's can actually be expanded in terms of the chiral angle defined for the correspondent ideal SWCNT's.Comment: 9 pages, 7 figure

Quantization of Lie-Poisson structures by peripheric chains

The quantization properties of composite peripheric twists are studied. Peripheric chains of extended twists are constructed for U(sl(N)) in order to obtain composite twists with sufficiently large carrier subalgebras. It is proved that the peripheric chains can be enlarged with additional Reshetikhin and Jordanian factors. This provides the possibility to construct new solutions to Drinfeld equations and, thus, to quantize new sets of Lie-Poisson structures. When the Jordanian additional factors are used the carrier algebras of the enlarged peripheric chains are transformed into algebras of motion of the form G_{JB}^{P}={G}_{H}\vdash {G}_{P}. The factor algebra G_{H} is a direct sum of Borel and contracted Borel subalgebras of lower dimensions. The corresponding omega--form is a coboundary. The enlarged peripheric chains F_{JB}^{P} represent the twists that contain operators external with respect to the Lie-Poisson structure. The properties of new twists are illustrated by quantizing r-matrices for the algebras U(sl(3)), U(sl(4)) and U(sl(7)).Comment: 24 pages, LaTe

Effect of heuristics on serendipity in path-based storytelling with linked data

Path-based storytelling with Linked Data on the Web provides users the ability to discover concepts in an entertaining and educational way. Given a query context, many state-of-the-art pathfinding approaches aim at telling a story that coincides with the user's expectations by investigating paths over Linked Data on the Web. By taking into account serendipity in storytelling, we aim at improving and tailoring existing approaches towards better fitting user expectations so that users are able to discover interesting knowledge without feeling unsure or even lost in the story facts. To this end, we propose to optimize the link estimation between - and the selection of facts in a story by increasing the consistency and relevancy of links between facts through additional domain delineation and refinement steps. In order to address multiple aspects of serendipity, we propose and investigate combinations of weights and heuristics in paths forming the essential building blocks for each story. Our experimental findings with stories based on DBpedia indicate the improvements when applying the optimized algorithm

Laughlin states on the Poincare half-plane and its quantum group symmetry

We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.Comment: 9 pages,Late

Electron-phonon effects and transport in carbon nanotubes

We calculate the electron-phonon scattering and binding in semiconducting carbon nanotubes, within a tight binding model. The mobility is derived using a multi-band Boltzmann treatment. At high fields, the dominant scattering is inter-band scattering by LO phonons corresponding to the corners K of the graphene Brillouin zone. The drift velocity saturates at approximately half the graphene Fermi velocity. The calculated mobility as a function of temperature, electric field, and nanotube chirality are well reproduced by a simple interpolation formula. Polaronic binding give a band-gap renormalization of ~70 meV, an order of magnitude larger than expected. Coherence lengths can be quite long but are strongly energy dependent.Comment: 5 pages and 4 figure

Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.Comment: 10 pages, 4 figure