We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

The Multiplier Hopf Group Coalgebra was introduced by Hegazi in 2002 [] as a generalization of Hope group caolgebra, introduced by Turaev in 2000 [], in the non-unital case. We prove that the concepts introduced by A.Van Daele in constructing multiplier Hopf algebra [3] can be adapted to serve again in our construction. A multiplier Hopf group coalgebra is a family of algebras A = {A α } α∈π , ...

TSVETKOV, Ts., Ts. TAKEVA and A. SOLAK, 2006. To the problem of experimental hibernation I. About the role of endogenous hibernation trigger. Bulg. J. Agric. Sci., 1-5 Experimented 24 white mice (Mus Musculus), divided into 2 groups of twelve. The fist 12 animals have been injected intraperitoneal (i.p.) with blood plasma (in different doses) from ground squirrels by the time of deep hibernatio...

We introduce and study the concept of a bornological quantum group. This generalizes the theory of algebraic quantum groups in the sense of van Daele from the algebraic setting to the framework of bornological vector spaces. Working with bornological vector spaces, the scope of the latter theory can be extended considerably. In particular, the bornological theory covers smooth convolution algeb...

Algebraic quantum groupoids have been developed by two of the authors this note (AVD and SHW) in a series papers [A. Van Daele S. Wang, Weak multiplier Hopf algebras. Preliminaries, motivation basic examples, Banach Center Publ. 98 (2012) 367–415; A. algebras I. The main theory, J. Reine Angew. Math. 705 (2015) 155–209; II. source target algebras, preprint (2014), arXiv: 1403.7906v2 [math.RA]; ...