JAEM 2018, Vol 8, No 1a

New characterizations of spacelike curves on timelike surfaces through the link of specific frames

Mon, 01 Jan 2018 00:00:00 GMT

New characterizations of spacelike curves on timelike surfaces through the link of specific frames Ünlütürk, Yasin; Yılmaz, Süha In this work, considering a regular spacelike curve on a smooth timelike surface in Minkowski 3-space, we investigate relations between the mentioned curve’s Darboux and Bishop frames on the timelike surface. Next we obtain Darboux vector of the regular spacelike curve in terms of Bishop apparatus. Thereafter, translating the Darboux vector to the center of the unit sphere, we determine aforementioned spacelike curve. Moreover, we investigate this spherical image’s Frenet-Serret and Bishop apparatus and illustrate our results with two examples.

On the moments for ergodic distribution of an inventory model of type (s; S) with regularly varying demands having infinite variance

Mon, 01 Jan 2018 00:00:00 GMT

On the moments for ergodic distribution of an inventory model of type (s; S) with regularly varying demands having infinite variance Bektaş Kamışlık, Aslı; Kesemen, Tülay; Khaniyev, Tahir In this study a stochastic process X(t) which represents a semi Markovian inventory model of type (s,S) has been considered in the presence of regularly varying tailed demand quantities. The main purpose of the current study is to investigate the asymptotic behavior of the moments of ergodic distribution of the process X(t) when the demands have any arbitrary distribution function from the regularly varying subclass of heavy tailed distributions with infinite variance. In order to obtain renewal function generated by the regularly varying random variables, we used a special asymptotic expansion provided by Geluk [14]. As a first step we investigate the current problem with the whole class of regularly varying distributions with tail parameter 1 < ? < 2 rather than a single distribution. We obtained a general formula for the asymptotic expressions of n th order moments (n = 1, 2, 3, . . .) of ergodic distribution of the process X(t). Subsequently we consider this system with Pareto distributed demand random variables and apply obtained results in this special case.

Generalized Hankel determinant for a general subclass of univalent functions

Mon, 01 Jan 2018 00:00:00 GMT

Generalized Hankel determinant for a general subclass of univalent functions Yalçın, Sibel; Altınkaya, Şahsene; Owa, Shigeyoshi Making use of the generalized Hankel determinant, in this work, we consider a general subclass of univalent functions. Moreover, upper bounds are obtained for |a3 ? µa2 2|, where µ ? R.

Maximal graphs of the first reverse Zagreb beta index

Mon, 01 Jan 2018 00:00:00 GMT

Maximal graphs of the first reverse Zagreb beta index Ediz, Süleyman The reverse vertex degree of a vertex v of a simple connected graph G defined as; cv = ? ? dv + 1 where ? denotes the largest of all degrees of vertices of G and dv denotes the number of edges incident to v. The first reverse Zagreb beta index of a simple connected graph G defined as; CM?1 (G) = P uv?E(G)(cu + cv). In this paper we characterized maximal graphs with respect to the first reverse Zagreb beta index.