On the significance of polarization charge and isomagnetic surface in the interaction between conducting fluid and magnetic field

From the frozen-in field lines concept, a highly conducting fluid can move freely along, but not traverse to, magnetic field lines. We discuss this topic and find that in the study of the frozen-in field lines concept, the effects of inductive and capacitive reactance have been omitted. When admitted, the relationships among the motional electromotive field, the induced electric field, the eddy electric current, and the magnetic field becomes clearer and the frozen-in field line concept can be reconsidered. We emphasize the importance of isomagnetic surfaces and polarization charges, and show analytically that whether a conducting fluid can freely traverse magnetic field lines or not depends solely on the magnetic gradient in the direction of fluid motion. If a fluid does not change its density distribution and shape (can be regarded as a quasi-rigid body), and as long as it is moving along an isomagnetic surface, it can freely traverse magnetic field lines without any magnetic resistance no matter how strong the magnetic field is. When our analysis is applied, the origin of the magnetic field of sunspots can be interpreted easily. In addition, we also present experimental results to support our analysis.Comment: 12 pages, 12 figures, 4 table

Modular invariance for conformal full field algebras

Let V^L and V^R be simple vertex operator algebras satisfying certain natural uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let F be a conformal full field algebra over the tensor product of V^L and V^R. We prove that the q_\tau-\bar{q_\tau}-traces (natural traces involving q_\tau=e^{2\pi i\tau} and \bar{q_\tau}=\bar{e^{2\pi i\tau}}) of geometrically modified genus-zero correlation functions for F are convergent in suitable regions and can be extended to doubly periodic functions with periods 1 and \tau. We obtain necessary and sufficient conditions for these functions to be modular invariant. In the case that V^L=V^R and F is one of those constructed by the authors in \cite{HK}, we prove that all these functions are modular invariant.Comment: 54 page

Full field algebras

We solve the problem of constructing a genus-zero full conformal field theory (a conformal field theory on genus-zero Riemann surfaces containing both chiral and antichiral parts) from representations of a simple vertex operator algebra satisfying certain natural finiteness and reductive conditions. We introduce a notion of full field algebra which is essentially an algebraic formulation of the notion of genus-zero full conformal field theory. For two vertex operator algebras, their tensor product is naturally a full field algebra and we introduce a notion of full field algebra over such a tensor product. We study the structure of full field algebras over such a tensor product using modules and intertwining operators for the two vertex operator algebras. For a simple vertex operator algebra V satisfying certain natural finiteness and reductive conditions needed for the Verlinde conjecture to hold, we construct a bilinear form on the space of intertwining operators for V and prove the nondegeneracy and other basic properties of this form. The proof of the nondegenracy of the bilinear form depends not only on the theory of intertwining operator algebras but also on the modular invariance for intertwining operator algebras through the use of the results obtained in the proof of the Verlinde conjecture by the first author. Using this nondegenerate bilinear form, we construct a full field algebra over the tensor product of two copies of V and an invariant bilinear form on this algebra.Comment: 66 pages. One reference is added, a minor mistake on the invariance under \sigma_{23} of the bilinear form on the space of intertwining operators is corrected and some misprints are fixe

A Discriminatively Learned CNN Embedding for Person Re-identification

We revisit two popular convolutional neural networks (CNN) in person re-identification (re-ID), i.e, verification and classification models. The two models have their respective advantages and limitations due to different loss functions. In this paper, we shed light on how to combine the two models to learn more discriminative pedestrian descriptors. Specifically, we propose a new siamese network that simultaneously computes identification loss and verification loss. Given a pair of training images, the network predicts the identities of the two images and whether they belong to the same identity. Our network learns a discriminative embedding and a similarity measurement at the same time, thus making full usage of the annotations. Albeit simple, the learned embedding improves the state-of-the-art performance on two public person re-ID benchmarks. Further, we show our architecture can also be applied in image retrieval