Çakmak, Ali; Karacan, Murat Kemal; Kiziltug, Sezai; Yoon, Dae Won

Çakmak, Ali; Karacan, Murat Kemal; Kiziltug, Sezai; Yoon, Dae Won

In this paper, we classify translation surfaces in the three dimensional Galilean space G3 satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the second fundamental form of the surface. We also give explicit forms of these surfaces.

Yağmur, Nihat

In this work we present some geometric properties (like star-likeness and convexity of order α and also close-to-convexity of order (1 + α) /2) for normalized of Lommel functions of the first kind. In order to prove our main results, we use the technique of differential subordinations and some inequalities. Furthermore, we present some applications of convexity involving Lommel functions associated with the Hardy space of analytic functions, i.e., we obtain conditions for the function hμ, ν(z) to belong to the Hardy space Hp.

Koşan, Muhammet Tamer; Özdin, Tufan

A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let τ = (Tτ, Fτ) be a hereditary torsion theory such that Tτ = Mod-R. Then every τ-torsionfree R-module satisfies (P) if and only if S =R/τ(R) is a division ring. (2) Let K be a hereditary pre-torsion class of modules. Then every module in K satisfies (P) if and only if either K = {0} or S = R/ SocK(R) is a division ring, where SocK(R) = ∩{I ≤ RR: R/I ∈ K}.