The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.

A Model of Low-lying States in Strongly Interacting Electroweak Symmetry-Breaking Sector

It is proposed that, in a strongly-interacting electroweak sector, besides the Goldstone bosons, the coexistence of a scalar state ($H$) and vector resonances such as $A_1$ [$I^G(J^P)=1^-(1^+$)], $V$ [$1^+(1^-)$] and $\omega_H^{}$ [$0^-(1^-)$] is required by the proper Regge behavior of the forward scattering amplitudes. This is a consequence of the following well-motivated assumptions: (a). Adler-Weisberger-type sum rules and the superconvergence relations for scattering amplitudes hold in this strongly interacting sector; (b). the sum rules at $t=0$ are saturated by a minimal set of low-lying states with appropriate quantum numbers. It therefore suggests that a complete description should include all these resonances. These states may lead to distinctive experimental signatures at future colliders.Comment: revised version, to appear in Modern Physics Letters A; file also available via anonymous ftp at ftp://ucdhep.ucdavis.edu/han/sews/lowlying.p

Sampled-data filtering with error covariance assignment

Copyright [2001] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.We consider the sampled-data filtering problem by proposing a new performance criterion in terms of the estimation error covariance. An innovation approach to sampled-data filtering is presented. First, the definition of the estimation covariance e for a sampled-data system is given, then the sampled-data filtering problem is reduced to the Kalman filter design problem for a fictitious discrete-time system, and finally, an effective method is developed to design discrete-time Kalman filters in such a way that the resulting sampled-data estimation covariance achieves a prescribed value. We derive both the existence conditions and the explicit expression of the desired filters and provide an illustrative numerical example to demonstrate the directness and flexibility of the present design metho

Open-closed field algebras

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a \C-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical constructions of open-closed field algebras over V.Comment: 55 pages, largely revised, an old subsection is deleted, a few references are adde

Response-surface-model-based system sizing for nearly/net zero energy buildings under uncertainty

Properly treating uncertainty is critical for robust system sizing of nearly/net zero energy buildings (ZEBs). To treat uncertainty, the conventional method conducts Monte Carlo simulations for thousands of possible design options, which inevitably leads to computation load that is heavy or even impossible to handle. In order to reduce the number of Monte Carlo simulations, this study proposes a response-surface-model-based system sizing method. The response surface models of design criteria (i.e., the annual energy match ratio, self-consumption ratio and initial investment) are established based on Monte Carlo simulations for 29 specific design points which are determined by Box-Behnken design. With the response surface models, the overall performances (i.e., the weighted performance of the design criteria) of all design options (i.e., sizing combinations of photovoltaic, wind turbine and electric storage) are evaluated, and the design option with the maximal overall performance is finally selected. Cases studies with 1331 design options have validated the proposed method for 10,000 randomly produced decision scenarios (i.e., users’ preferences to the design criteria). The results show that the established response surface models reasonably predict the design criteria with errors no greater than 3.5% at a cumulative probability of 95%. The proposed method reduces the number of Monte Carlos simulations by 97.8%, and robustly sorts out top 1.1% design options in expectation. With the largely reduced Monte Carlo simulations and high overall performance of the selected design option, the proposed method provides a practical and efficient means for system sizing of nearly/net ZEBs under uncertainty

Pentaquark Magnetic Moments In Different Models

We calculate the magnetic moments of the pentaquark states from different models and compare our results with predictions of other groups.Comment: 17 pages, no figur

Magnetic Moments of JP=3/2+J^P={3/2}^+ Pentaquarks

If the $J^P$ of $\Theta_5^+$ and $\Xi_5^{--}$ pentaquarks is really found to be ${1\over 2}^+$ by future experiments, they will be accompanied by $J^P={3\over 2}^+$ partners in some models. It is reasonable to expect that these $J^P={3\over 2}^+$ states will also be discovered in the near future with the current intensive experimental and theoretical efforts. We estimate $J^P={3/2}^+$ pentaquark magnetic moments using different models.Comment: 13 page