Polynomial Solutions to the Diophantine Equation x² + y³ = 6912z²

In this paper, I investigate polynomial solutions to the Diophantine equa­ tion, X² +Y³ = 6912Z², where X = g(x,y), Y = h(x,y) and Z = f(x,y) are polynomials with integer coefficients. The focus is on the greatest common di­ visors for the integer values of these polynomials when the polynomials f (x, y), g(x, y) and h(x, y) are relatively prime in Q[x, y]. However, for a fixed integer pair xo, Yo, the integer values f(x0,y0), g(x0, y0) and h(x0,y0) are not necessarily relatively prime in Z. I investigate the greatest common divisors (GCDs) of these three polynomial values for specific integer pairs x0 and y0· First, I study the cases where y0 = 1 and y0 = 2. For these cases, a complete distri­bution of the GCDs is given. Furthermore, I use the Euclidean Algorithm and Grobner Basis techniques to determine the GCDs for f(x0, y0), g(x0, y0) and h(x0, y0) in Z by obtaining multiples of the GCDs of the polynomials. Then, the results from the cases y0 = 1 and y0 = 2 are generalized to obtain similar properties of the GCDs for all possible integer values of x and y. For the cases where the integer values are not relatively prime, the possible prime divisors of the GCDs and integer bounds for the powers of prime divisors are determined. Finally, polynomial solutions to new Diophantine equations are derived from the original Diophantine equation

Gender discrimination in social studies textbooks

Okul eğitiminin önemli bir aracı olan ders kitaplarının bireylerin birçok toplumsal rollerin yanı sıra cinsiyet rollerini de kazanmalarında etkin rol oynadığı görüşünden yola çıkan bu çalışma, 1928 – 2008 yılları arasında, 6, 7 ve 8. sınıflara yönelik hazırlanan Sosyal Bilgiler ders kitaplarını, toplumsal cinsiyet ayrımcılığı yönünden incelemeyi amaçlamaktadır. Bu ders kitaplarının seçilmesindeki temel neden, Sosyal Bilgiler ders kitaplarının içeriğinin, bireyin toplumsallaşma sürecini ve cinsiyet algısını doğrudan etkileyen konulardan meydana gelmesidir. Kitaptaki tüm metinler taranarak, doküman incelemesi yöntemiyle incelenmiş, sonuçlar niteliksel olarak betimlenmiştir. Based upon the concept that the textbooks, which are crucial materials of the formal education, have an influential role on one's attaining various social role right along with the impact on one's gaining his/her gender role, this work aims to focus on Social Studies textbooks, which were arranged for the 6th, 7th and 8th grade students between 1928-2008, in terms of social gender discrimination. The main reason of the selection of this course book is that the content of Social Studies textbooks cover the process of one's socialization and the topics affecting directly his/her gender perception. Through scanning, all the texts in the book were examined with the method of document review and the results were quantitavely described

A Meta-Analytic Review on Antecedents of Green Product Purchase Intention: An Extended TPB Approach

Owing to the growing attention of consumers towards green-related issues, important number of studies has been devoted to understanding the drivers of green product purchase intention; implying a need to quantitatively synthesize the empirical body of research on the subject. In this sense, extending the theory of planned behavior, the main purpose of this study is to meta-analyze the empirical findings on green product purchase intention and its antecedents. The meta-analytic investigation was performed on 235 effects dependent upon more than 39,000 consumers (N = 39,253). The findings of the meta-analysis reveal that green product purchase intention is most strongly influenced by attitude toward product/brand, followed by brand trust and self-identity, respectively. This research considerably contributes to the pertinent literature by synthesizing and consolidating fragmented empirical evidence on the determinants of green product purchase intention.</p

Time-Dependent Production of Endothelium-Related Biomarkers is Affected Differently in Hemorrhagic and Septic Shocks

Demirel-Yilmaz, Emine/0000-0002-2476-6225; Usanmaz, Suzan E./0000-0002-7096-1347WOS: 000419896200004PubMed: 29019070Shock is associated with inflammation-induced endothelial dysfunction. The aim of this study was to determine time-dependent alteration of blood biomarkers related to endothelial function in hemorrhagic and septic shocks. Hemorrhagic shock was induced by bleeding the animals. A cecal ligation and incision model was used to induce septicemia. Resuscitation was carried out by infusion of lactated Ringer's solution. Resuscitation extended survival time in both shock groups. Blood pressure increased by resuscitation in the hemorrhagic shock but not in the septic shock. While hemorrhage caused a decrease in plasma levels of nitric oxide (NO) and hydrogen sulfide (H2S), asymmetric dimethylarginine (ADMA) and total antioxidant capacity (TAC) levels were increased. Only NO and TAC levels at the late phase were reversed by resuscitation. On the other hand, plasma levels of NO, ADMA, and TAC were increased by septicemia and resuscitation did not alter the septicemia-induced increase. These results indicate that blood biomarkers related to endothelial function were differentially affected by hemorrhage and septicemia. The time scale of biomarker production should be taken into consideration for the diagnostic and therapeutic approaches to these life-threatening diseases.Commission of the Scientific Research Projects of Uludag UniversityUludag University [2008/43]The present study was supported by a grant from The Commission of the Scientific Research Projects of Uludag University (2008/43). We are grateful to Soner Mamuk for the great technical assistance