a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the center of such...

In this paper we present a comparison of the service disciplines in real-time queueing systems (the customers have a deadline before which they should enter the service booth). We state that the more a service discipline gives priority to customers having an early deadline, the least the average stationary lateness is. We show this result by comparing adequate random vectors with the Schur-Conv...

In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, and direct products and also direct limits of groups with topological approach.

Let F be an arbitrary field (of arbitrary characteristic). Let A be a central simple F -algebra endowed with a quadratic pair σ (if charF 6= 2 then σ is simply an orthogonal involution on A). We show that the Witt index of σ over the function field of the Severi-Brauer variety of A is divisible by the Schur index of the algebra A.

The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur function and a single row Schur function in terms of skew Schur functions. Like the classical rule, our rule involves simple additions of boxes to the original skew shape. Our proof is purely combinator...

In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.