Let g be a reductive Lie algebra over C. We say that a g-module M is a generalized Harish-Chandra module if, for some subalgebra k ⊂ g, M is locally k-finite and has finite k-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when k is a Cartan subalgebra. We ...

We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the subalgebra. Moreover, the rationality and the C2-cofiniteness of the subalgebra are established. Our result contains the case of the vertex operator algebra ...

This paper proposes a novel adaptive control law for nonlinear systems using Takagi-Sugeno fuzzy system. Takagi-Sugeno fuzzy system is used to identify nonlinear system components theta alpha and theta beta. Stable Indirect Adaptive control law is such that it has two control components one is certainty equivalence control and other is sliding mode control. Sliding mode controller is used to en...

A statistical analysis of Type-1 and Interval Type-2 Fuzzy Logic in dynamic parameter adaptation in the Bee Colony Optimization algorithm (BCO) is presented in this paper. The Bee Colony Optimization meta-heuristic belongs to the class of Nature-Inspired Algorithms. The objective of the work is based on the main reasons for the analysis of the approach with Interval Type-2 Fuzzy Logic to find t...