We study fusion rings for degenerate minimal models (p = q) for N = 0, N = 1 and N = 2 (super)conformal algebras. In the first part we consider a family of modules for the Virasoro vertex operator algebra L(1, 0), and show that a fusion ring of the family is isomorphic to a Grothendieck ring Rep(sl(2,C)). In the second part, we used similar methods for the family of modules for N = 1 Neveu Schw...

We construct a structure-preserving signature scheme that is selectively randomizable and works in all types of bilinear groups. We give matching lower bounds showing that our structure-preserving signature scheme is optimal with respect to both signature size and public verification key size. State of the art structure-preserving signatures in the asymmetric setting consist of 3 group elements...

Today, data outsourcing to the clouds is a popular computing paradigm, and enabling efficient and trustworthy outsourcing becomes critically important as many emerging cloud applications are increasingly security-sensitive, such as healthcare, finance, etc. One of the promising techniques is authentication data structure (ADS). Most existing ADSs are not log-structured, yet cloud storage system...

In this study the structure for O-minimal expansions of groups is considered Let be an o-minimal expansion of an ordered group (R,0,1,+,<) with distinguished positive element 1. We first prove that the following are equivalent: (1) is semibounded, (2) has no poles, (3) cannot define a real closed field with domain R and order <, (4) is eventually linear and (5) every –definable set is a finit u...

The aim of this article is to study the concept of unique solvability of max-min fuzzy neutrosophic soft matrix equation and strong regularity of fuzzy neutrosophic soft matrices over Fuzzy Neutrosophic Soft Algebra (FNSA). A Fuzzy Neutrosophic Soft Matrix (FNSM) is said to have Strong, Linear Independent (SLI) column (or, in the case of fuzzy neutrosophic soft square matrices, to be strongly r...

Pathways are a universal paradigm for functionally describing cellular processes. Even though advances in high-throughput data generation have transformed biology, the core of our biological understanding, and hence data interpretation, is still predicated on human-defined pathways. Here, we introduce an unbiased, pathway structure for genome-scale metabolic networks defined based on principles...

We consider A-series modular invariant Virasoro minimal models on the upper half plane. From Lewellen's sewing constraints a necessary form of the bulk and boundary structure constants is derived. Necessary means that any solution can be brought to the given form by rescaling of the fields. All constants are expressed essentially in terms of fusing (F-) matrix elements and the normalisations ar...

The chiral vertex operators for the minimal models are constructed and used to define a fusion product of representations. The existence of com-mutativity and associativity operations is proved. The matrix elements of the associativity operations are shown to be given in terms of the 6-j symbols of the weak quasitriangular quasi-Hopf algebra obtained by truncating U q (sl(2)) at roots of unity.