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.

An Ultra-fast DOA Estimator with Circular Array Interferometer Using Lookup Table Method

The time-consuming phase ambiguity resolution makes the uniform circular array (UCA) interferometer not suitable for real-time direction-of-arrival (DOA) estimation. This paper introduces the lookup table (LUT) method to solve this problem. The key of the method is that we look up the ambiguity numbers instead of the eventual DOA from the table, and then the DOA is obtained by relatively small amount of calculation. This makes it possible that we are able to shrink the table size while maintain the DOA estimation accuracy. The table addresses cover all possible measured phase differences (PDs), which enables the method to be free of spatial scanning. Moreover, without adding frequency index to the lookup table, the estimator can realize wideband application. As an example, a field-programmable gate array (FPGA) based DOA estimator with the estimation time of 180 ns is presented, accompanied by the measured results. This method possesses the advantages of ultra-high speed, high accuracy and low memory usage

A study of XML in the library science curriculum in Taiwan and South East Asia

This paper aims to investigate the current XML-related courses available in 96 LIS schools in South East Asia and Taiwan’s 9 LIS schools. Also, this study investigates the linkage of library school graduates in Taiwan who took different levels of XML-related education (that is XML arranged as an individual course or XML arranged as a section unit in courses) and their professional qualification. Research questions include what is the availability of XML-related courses in countries in Taiwan and South East Asia? What are Taiwan LIS graduates’ views on degree of XML-related courses satisfaction, cognition of learning XML technology, and views of XML-related courses? What is the linkage of Taiwan LIS graduates who studied different levels of XML-related education and their professional qualifications? This study applies 3 research methodologies: information gathering from the internet; questionnaire surveys; in-depth interviews. Results of the analysis show that LIS schools should provide optional XML-related courses with practical sessions, and library associations should provide regular XML-related continuing education to enhance LIS students’ professional qualifications