We introduce the notions of Jacobson radical of a Γ−semiring and semisimple Γ−semiring and characterize them via operator semirings. AMS Mathematics Subject Classification (2000): 16Y60, 16Y99, 20N10

We prove that a space with a σ-weakly hereditarily closurepreserving sn-network is sn-first countable. As an application of this result, we prove that a Lindelöf space with a σ-weakly hereditarily closurepreserving sn-network is sn-second countable. The above results answer some questions posed by L. Yan. AMS Mathematics Subject Classification (2000): 54D20, 54D65, 54E20, 54E99

In this paper we introduce the concept of fuzzy generalized bi-ideal of a Γsemigroup, which is an extension of the concept of a fuzzy bi-ideal of a Γsemigroup and characterize regular Γ-semigroups in terms of fuzzy generalized bi-ideals. AMS Mathematics Subject Classification(2000): 08A72, 20M12, 3F55

We obtain the further characterizations and properties of weakly open functions in bitopological spaces due to Jelić [5]. AMS Mathematics Subject Classification (2000): 54C10, 54E55

In this paper, we first show that for any fixed D(−1)-triple {1, b, c} with b < c, there exist at most two d’s such that {1, b, c, d} is a D(−1)-quadruple with c < d. Using this result, we further show that there exist at most 10 D(−1)-quadruples. AMS subject classifications: 11D09, 11D45

defined in [13]. We give the generating functions, some representation and the congruences of the function Ki(z). Also, we present some inequalities for the function Ki(x) for positive values of x. AMS Mathematics Subject Classification (2000): 11B34, 11B50, 11B37.

If T and S are quasisimilar bounded operators on Banach spaces, we prove that each closed-and-open subset of the lower semiBrowder essential spectrum of T intersects one special part of the upper semi-Browder essential spectra of T and S. AMS Mathematics Subject Classification (1991): 47A53, 47A10

Two classes of linear involutory semigroups We construct two classes of involutory semigroups, which together with two already known generating rules yield n linear involutory semigroups of order n, where 2n = 2 n+2 ? 1 2 (n + 1)(n + 6) ; 2n+1 = 3 2 n+1 ? 1 2 (n 2 + 9n + 10) (1) for n 1. By the way, we extend the rule for the construction of linear archimedian involutory semigroups in L. Berg a...

AMS Subject Classification 58F15

We study steady states of Stefan-type problems in the plane with the Gibbs-Thomson correction involving general anisotropic energy density function. By a local analysis we prove the global result showing that the solution is the Wulff shape. The key element is a stability result which enables us to approximate singular models by regulars ones. keywords: Stefan-type problems, singular interfacia...