We continue the recent work of [2] and [25] by showing that whenever the Lévy measure of a spectrally negative Lévy process has a density which is log convex then the solution of the associated actuarial control problem of de Finetti is solved by a barrier strategy. Moreover, the level of the barrier can be identified in terms of the scale function of the underlying Lévy process. Our method app...

Positivity and positive definiteness in algebra of generalized functions are studied. Basic definitions and notions of Colombeau algebra of generalized functions are given and some special classes of positive definite generalized functions on those algebras are introduced. Their relation to distributions is also investigated. AMS Mathematics Subject Classification (2000):

The notion of holomorphic bisectional curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is emloyed to obtain the characterizations of the holomorphic bisectional curvature. For the class of gen...

Let G be a group and τe(G) the set of numbers of elements of G of the same order. In this note it is proved that a group G is isomorphic to PSL2(7) if and only if τe(G) = {1, 21, 56, 42, 48}. AMS Mathematics Subject Classification (2000): 20D60, 20D06

In this paper we introduce the class of R-complex Finsler spaces with (α, β)-metrics and study some important exemples: R-complex Randers spaces, R-complex Kropina spaces. The metric tensor field of a R-complex Finsler space with (α, β)-metric is determined (§2). A special approach is dedicated to the R-complex Randers spaces (§3). AMS Mathematics Subject Classification (2000): 53B40, 53C60

In this paper we study the notion of connectedness in ideal topological spaces. AMS Mathematics Subject Classification (2000): 54A10, 54A05, 54A20

The notion of soft BCI-implicative ideals and BCI-implicative idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft BCI-implicative ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and BCI-implicative idealistic soft BCI-algebras are being related. The intersection, union, “AND” operation and “OR” o...

In this paper, we use the idea of normal family to deal with the uniqueness problems of entire functions that share a rational function with its derivative and get a uniqueness theorem. The conclusions in this paper can be used to improve several known results. Some examples are provided to show that the results presented in this paper are possible. AMS Mathematics Subject Classification (2010)...

The aim of this paper is to relate Thurston’s metric on Teichmüller space to several ideas initiated by T. Sorvali on isomorphisms between Fuchsian groups. In particular, this will give a new formula for Thurston’s asymmetric metric for surfaces with punctures. We also update some results of Sorvali on boundary isomorphisms of Fuchsian groups. AMS Mathematics Subject Classification: 32G15 ; 30F...

We introduce and study the notion of a completely regular ternary semiring. Necessary and sufficient conditions for a ternary semiring to be completely regular are furnished. AMS Mathematics Subject Classification (2010): 16Y30, 16Y99