Mehmet Cenkci

Multiple two-variable p-adic q-L-function and its behavior at s = 0

The objective of this paper is to construct a multiple p-adic q-L-function of two variables which interpolates multiple generalized q-Bernoulli polynomials. By using this function, we solve a question of Kim and Cho. We also define a multiple partial q-zeta function which is related to the multiple q-L-function of two variables. Finally, we give a finite-sum representation of the multiple p-adic q-L-function of two variables and prove a multiple q-extension of the generalized formula of Diamond and Ferrero-Greenberg.

Comparison of glomerular filtration rate measurements with the two plasma sample and single plasma sample, gamma camera Gates, creatinine clearance, and prediction equation methods in potential kidney donors with normal renal function.

ObjectiveTo compare measured glomerular filtration rate (GFR) by single plasma sample methods (SPSMs), gamma camera Gates, 24-h endogenous creatinine clearance, and prediction equations (Cockcroft–Gault and modification of renal disease (MDRD)) with the two plasma sample method (TPSM) considered as the reference in potential kidney donors with normal renal function. MethodsOne hundred and fifteen subjects (50 male, 65 female; mean age 41.9±12.2 years) with normal renal function were prospectively included in this study. GFR was calculated by TPSM (120-min and 240-min samples) and SPSM (180-min sample). ResultsWhile there was strong statistically significant correlation between the TPSM and all SPSMs, low correlation was found in Gates, creatinine clearance, Cockcroft–Gault and MDRD. In all SPSMs, 95% limits of agreements were consistent with each other and within clinically acceptable limits. The lowest bias, median absolute difference, mean percentage error, and the best precision were found for Christensen and Groths method as modified by Watson (CGmW). ConclusionsAmong the SPSMs, CGmW can reflect GFR more accurately than the other methods. Neither the gamma camera Gates method nor the creatinine clearance method nor the prediction equations (Cockcroft–Gault and MDRD) could calculate GFR accurately. All these techniques could result in mistakes in the management of potential kidney donors.

Congruences for Generalized -Bernoulli Polynomials

In this paper, we give some further properties of -adic --function of two variables, which is recently constructed by Kim (2005) and Cenkci (2006). One of the applications of these properties yields general classes of congruences for generalized -Bernoulli polynomials, which are -extensions of the classes for generalized Bernoulli numbers and polynomials given by Fox (2000), Gunaratne (1995), and Young (1999, 2001).

A NEW APPROACH TO q-GENOCCHI NUMBERS AND POLYNOMIALS

In this paper, new q-analogs of Genocchi numbers and poly- nomials are defined. Some important arithmetic and combinatoric rela- tions are given, in particular, connections with q-Bernoulli numbers and polynomials are obtained.