Rational Points on Elliptic Curves y^2=x^3+a^3 in f_{p} where p{\equiv}1(mod6) is Prime

In this work, we consider the rational points on elliptic curves over finite fields F_{p}. We give results concerning the number of points on the elliptic curve y^2{\equiv}x^3+a^3(mod p)where p is a prime congruent to 1 modulo 6. Also some results are given on the sum of abscissae of these points. We give the number of solutions to y^2{\equiv}x^3+a^3(modp), also given in ([1], p.174), this time by means of the quadratic residue character, in a different way, by using the cubic residue character. Using the Weil conjecture, one can generalize the results concerning the number of points in F_{p} to F_{p^{r}}.Comment: 9 pages; Keywords: Elliptic curves over finite fields, rational point

THE IMPACT OF FDI, EXPORT, ECONOMIC GROWTH, TOTAL FIXED INVESTMENT ON UNEMPLOYMENT IN TURKEY

The impact of Foreign Direct Investment, export, economic growth and total fixed investment on unemployment in Turkey for the period of 1987-2007 was examined. Johansen cointegration technique was applied to determine long run relationship. The empirical findings suggest that there are two cointegrating vectors during the concerned period of time in Turkey

Inverse problem for Albertson irregularity index

Graph indices have attracted great interest as they give us numerical clues for several properties of molecules. Some indices give valuable information on the molecules under consideration using mathematical calculations only. For these reasons, the calculation and properties of graph indices have been in the center of research. Naturally, the values taken by a graph index is an important problem called the inverse problem. It requires knowledge about the existence of a graph having index equal to a given number. The inverse problem is studied here for Albertson irregularity index as a part of investigation on irregularity indices. A class of graphs is constructed to Show that the Albertson index takes all positive even integers. It has been proven that there exists at least one tree with Albertson index equal to every even positive integer but 4. The existence of a unicyclic graph with irregularity index equal to m is shown for every even positive integer m except 4. It is also shown that the Albertson index of a cyclic graph can attain any even positive integer.Publisher's Versio

Inverse problem for Albertson irregularity index

Graph indices have attracted great interest as they give us numerical clues for several properties of molecules. Some indices give valuable information on the molecules under consideration using mathematical calculations only. For these reasons, the calculation and properties of graph indices have been in the center of research. Naturally, the values taken by a graph index is an important problem called the inverse problem. It requires knowledge about the existence of a graph having index equal to a given number. The inverse problem is studied here for Albertson irregularity index as a part of investigation on irregularity indices. A class of graphs is constructed to Show that the Albertson index takes all positive even integers. It has been proven that there exists at least one tree with Albertson index equal to every even positive integer but 4. The existence of a unicyclic graph with irregularity index equal to m is shown for every even positive integer m except 4. It is also shown that the Albertson index of a cyclic graph can attain any even positive integer.Publisher's Versio

Experimentally induced puromycine aminonucleoside nephrosis (PAN) in rats: evaluation of angiogenic protein platelet-derived endothelial cell growth factor (PD-ECGF) expression in glomeruli

<p>Abstract</p> <p>Background</p> <p>In experimentally induced puromycine aminonucleoside nephrosis (PAN) animal models, nephrotic syndrome with minimal change disease and focal and segmental sclerosis-like nephritis similar to that in human is demonstrated; however, the real mechanism of PAN is not yet elucidated. Platelet derived endothelial cell growth factor (PD-ECGF), an endothelial mitogen protein, is believed to take part in microvessel formation and in stimulation of angiogenesis and its expression has not been totally demonstrated in PAN rats yet. In this study, we aimed to examine PD-ECGF expression in acute and chronic PAN induced in rats and find out the association between its expression and the stages of angiogenesis in kidney.</p> <p>Methods</p> <p>For the experiment, twenty-four Male Wistar Albino rats were used and divided into four groups; control group (n = 6), pre-proteinuria group (n = 6), acute group (n = 6) and chronic group (n = 6). We compared statistically all data by One-way ANOVA Test followed by Dunn Multiple Comparison Test.</p> <p>Results</p> <p>Proteinurea levels in control and pre-proteinuria groups were not statistically different; however, it was remarkably higher in the acute nephrosis group and significantly greater in the chronic nephrosis group than control group (<it>p </it>< 0.0025). In pre-proteinuria group, the serum albumin and creatinine clearances also did not significantly differ from the control group. On the other hand, in the acute and chronic nephrosis groups, serum albumin and creatinine clearances progressively decreased (<it>p </it>< 0.05). In our immunohistochemical studies, we showed elevated PD-ECGF expression in glomeruli of acute and chronic PAN rats. Microscopic and ultrastructural appearances of the glomeruli of acute and chronic PAN showed various sequential steps of angiogenesis, macrophages and immature capillaries with primitive lumens and apoptotic endothelial cells in the increased mesangial matrix.</p> <p>Conclusions</p> <p>It is reported that acute and chronic PAN progressively increase PD-ECGF expression and following induction of angiogenesis in the affected glomeruli.</p

Synthesis, antimicrobial and antioxidant activities of pyridyl substituted thiazolyl triazole derivatives

In this present study, 63 different 5-[4-methyl-2-(pyridin-3/4-yl)thiazole-5-yl]-4-substituted-3-substituted benzylthio-4H-1,2,4-triazole derivatives were synthesized, and evaluated for their in vitro antimicrobial activity against various human pathogenic microorganisms and antioxidant activity. The derivatives were synthesized in a multi-step synthesis procedure including triazole and thiazole ring closure reactions, respectively. The synthesized derivatives (A1-24; B1-39) were screened for their antibacterial, antifungal, and antioxidant activities compared to standard agents. The derivatives possessing 3-pyridyl moiety particularly exhibited relatively high antibacterial activity (MIC= < 3.09-500 µg/mL) against Gram-positive bacteria, and compounds possessing 4-pyridyl moiety showed remarkable antioxidant activity.Eskisehir Osmangazi Universit