Abstract This research is primarily concerned having the synchronization issue of time-varying delay recurrent neural networks (RNNs) with event-triggered regulation (ETR). ETR may legitimately reduce number control activities performed and amount energy expended. Via L-K functional, Schur complement lemma, linear matrix inequalities (LMIs), other analytic techniques, a sufficient condition for...

The output feedback H∞ control is addressed for a class of continuous-time Markov jump linear systems with the Markov process taking values in an infinite countable set S. We consider that only an output and the jump parameters are available to the controller. Via a certain bounded real lemma, together with some extensions of Schur complements and of the projection lemma, a theorem which charac...

We announce a higher-dimensional generalization of the Bailey Transform, Bailey Lemma, and iterative "Bailey chain" concept in the setting of basic hypergeometric series very well-poised on unitary Ae or symplectic Q groups. The classical case, corresponding to A¡ or equivalently U(2), contains an immense amount of the theory and application of one-variable basic hypergeometric series, includin...

We prove Wigner-Eckart theorem for the irreducible tensor operators for arbitrary Hopf algebras, provided that tensor product of their irreducible representation is completely reducible. The proof is based on the properties of the irreducible representations of Hopf algebras, in particular on Schur lemma. Two classes of tensor operators for the Hopf algebra Ut(su(2)) are considered. The reduced...

Some Schur, Vitali-Hahn-Saks and Nikodým convergence theorems for (l)-group-valued measures are given in the context of (D)-convergence. We consider both the σ-additive and the finitely additive case. Here the notions of strong boundedness, countable additivity and absolute continuity are formulated not necessarily with respect to a same regulator, while the pointwise convergence of the measure...

The aim of this lecture is to recall some standard basic things about the representation theory of finite dimensional algebras and finite groups. First, we recall restriction, induction and coinduction functors. Then we recall the Schur lemma and deduce consequences about the action of the center and the structure of completely reducible representations. Then we explain the structure and repres...

The ring of symmetric functions Λ, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the symmetric group. One may define a coproduct on Λ by the plethystic addition on alphabets. In this way the ring of symmetric functions becomes a Hopf algebra. The Littlewood–...

Abstract. We announce a higher-dimensional generalization of the Bailey Transform, Bailey Lemma, and iterative “Bailey chain” concept in the setting of basic hypergeometric series very well-poised on unitary Al or symplectic Cl groups. The classical case, corresponding to A1 or equivalently U(2), contains an immense amount of the theory and application of one-variable basic hypergeometric serie...

ON THE DIAGONALS OF PROJECTIONS IN MATRIX ALGEBRAS OVER VON NEUMANN ALGEBRAS Soumyashant Nayak Richard V. Kadison The main focus of this dissertation is on exploring methods to characterize the diagonals of projections in matrix algebras over von Neumann algebras. This may be viewed as a non-commutative version of the generalized Pythagorean theorem and its converse (Carpenter’s Theorem) studie...