Since recognizable tree languages are closed under the rational operations, every regular tree expression denotes a recognizable tree language. We provide an alternative proof to this fact that results in smaller tree automata. To this aim, we transfer Antimirov’s partial derivatives from regular word expressions to regular tree expressions. For an analysis of the size of the resulting automato...

A regular surface is a closed genus g surface defined as the tubular neighbourhood of the edge graph of a regular map. A regular map is a family of disc type polygons glued together to form a 2-manifold which is flag transitive. The visualization of this highly symmetric surface is an intriguing and challenging problem. Unlike regular maps, regular surfaces can always be visualized as 3D embedd...

in recent years, many changes have been observed in buying culture of customers and developing chain stores in iran. moreover, need to be more competition in business environments made necessary the stablishment of chain stores, the creation of competitive advantage and long relations to the costumers. regular marketing is a response to stores requirement when establishing such a win-win long r...

In this paper, we mainly study various notions of regularity for a finite collection {C1, · · · , Cm} of closed convex subsets of a Banach space X and their relations with other fundamental concepts. We show that a proper lower semicontinuous function f on X has a Lipschitz error bound (resp., Υ-error bound) if and only if the pair {epi(f), X×{0}} of sets in the product space X × R is linearly ...

Under the assumption that δ is a Woodin cardinal and GCH holds, I show that if F is any class function from the regular cardinals to the cardinals such that (1) κ < cf(F (κ)), (2) κ < λ implies F (κ) ≤ F (λ), and (3) δ is closed under F , then there is a cofinality-preserving forcing extension in which 2 = F (γ) for each regular cardinal γ < δ, and in which δ remains Woodin. Unlike the analogou...