We study the concept of stabilization with internal loop for infinite-dimensional discrete timevarying systems in the framework of nest algebra. We originally give a parametrization of all stabilizing controllers with internal loop, and it covers the parametrization of canonical or dual canonical controllers with internal loop obtained before. We show that, in practical application, the control...

In the present article, a basis of the coordinate algebra of the multi-parameter quantized matrix is constructed by using an elementary method due to Lusztig. The construction depends heavily on an antiautomorphism, the bar action. The exponential nature of the bar action is derived which provides an inductive way to compute the basis elements. By embedding the basis into the dual basis of Lusz...

2 Using Maple in the study of the canonical formalism of general relativity 17 2. 1 2 CONTENTS Preview This is a review devoted to some results of Algebraic Programming (Computer Algebra-CA) used in treating several problems of general relativity, based mainly on already published articles (see the references). The first chapter presents procedures in REDUCE language using EXCALC package for al...

The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type A. The construction of a basis for the coordinate algebra of the n × n quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a bas...

Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which is obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given. E-mail: [email protected] New E-mail address: [email protected]