Growth Theorem and the Radius of Starlikeness of Close-to-Spirallike Functions

AMS Subj. Classification: 30C4

Koebe domain of starlike functions of complex order with Montel normalization

Let S*(1-b), (b 0 complex) denote the class of functions f(z) = z + a2z2 + ... analytic in D = {z : |z| < 1} which satisfies for z = eiθ D, f(z) / z 0 in D, and Re[1 + 1/b(z f\u27(z) / f(z) - 1)] > 0. The aim of this paper is to give the Koebe domain of the above mentioned class

Koebe domain of starlike functions of complex order with Montel normalization

Let S*(1-b), (b 0 complex) denote the class of functions f(z) = z + a2z2 + ... analytic in D = {z : |z| < 1} which satisfies for z = eiθ D, f(z) / z 0 in D, and Re[1 + 1/b(z f\u27(z) / f(z) - 1)] > 0. The aim of this paper is to give the Koebe domain of the above mentioned class

Order quantity and pricing decisions in linear cost inventory systems

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent Univ., 1992.Thesis (Ph.D.) -- -Bilkent University, 1992.Includes bibliographical references leaves 83-84.The primary concern of this study is to reveal the fundamental characteristics of the linear cost inventory model where price is a decision variable in addition to procurement quantity. In this context, the optimal solution must not only strike a balance between leftovers and shortages, but also simultaneously search for the best pricing alternative within the low price high demand and high price low demand tradeoff. To some extent, this problem has been studied in the literature. However, it seems that, there is a need to improve the model in order to understand the decision process better. To this end, optimal decisions must be characterised under a more general problem setting than it has been assumed in the existing models. In this study, we employ such a general model. The overall decision problem can be formulated under a dynamic programming structure. It follows that, the single period model is the basis of this periodic decision model. For this reason, we concentrate first on this problem. Having characterised the optimal solution to this basic model we extend the decision model to account for the multi-period setting. It is established with the results of this study that the decision problem in question is understood better. It is found that the characteristics of the optimal decision under the proposed model can be substantially different from the properties of the optimal solution of the corresponding classical model where there is no pricing decision. The primary reason for this is the fact that when there is a shortage in any period, the price that is set in this period could affect the future revenue which must be accounted in the overall decision problem. That is in a general model, price is an information which has an economic value that is transferred from one period to another just like transfering inventories or backlogs to future periods.Polatoglu, Lutfi HakanPh.D

Essential-oil composition of Isatis floribunda Boiss. ex Bornm. aerial parts from Turkey

There is just one article in the literature in regard to the essential-oil composition of Isatis floribunda Boiss. ex Bornm. (Brassicaceae). Previously, a flower and root extract of I. floribunda was reported to be rich in phenolic compounds, especially chlorogenic acid, p-coumaric acid and quercetin [1]. The current study aims to provide information about the essential-oil composition of aerial parts of I. floribunda. Isatis floribunda was collected from Ankara-Beypazarı. The essential oil was obtained by hydrodistillation of the air-dried aerial parts using a Clevenger apparatus for 3 h. The essential-oil yield was 0.03 mL per 100 g of plant material. The essential oil was trapped in n-hexane (1 mL) dried over anhydrous Na2SO4 and analyzed directly by GC-MS without further dilution. The essential oil was analyzed with an Agilent 5977 MSD GC-MS system operating in EI mode; injector and MS transfer line temperatures were set at 250 °C. Splitless injection was used in the analysis. Innowax FSC column (60 m x 0.25 mm, 0.25 µm film thickness) and helium as the carrier gas (1 mL/min) were used in GC-MS analyses. The oven temperature program was: 60 °C for 10 min and then raised to 220 °C at a rate of 4 °C/min, afterwards the temperature was kept constant at 220 °C for 10 min and then raised to 240 °C at a rate of 1 °C/min. Mass spectra were recorded at 70 eV with the mass range m/z 35-425. Relative amounts of the separated compounds were calculated from the integration of the peaks in MS chromatograms. Identification of essential-oil components was carried out by comparison of their retention indices (RI), relative to a series of n-alkanes (C5 to C30), with the literature values, as well as by mass spectral comparison. The aerial parts essential oil of I. floribunda yielded an essential oil that is rich in n-alkanes and saturated fatty acids. The major components of the essential oil were dodecanoic acid (28.6%), nonacosane (11.0%), hexadecanoic acid (10.0%), tetradecanoic acid (8.4%), methyl octadecanoate (4.8%), decanoic acid (4.6%), and hexahydrofarnesyl acetone (3.5%). We believe our study will stimulate further research on the chemistry of this species