Identities of symmetry for Euler polynomials arising from quotients of fermionic integrals invariant under S_3

In this paper, we derive eight basic identities of symmetry in three variables related to Euler polynomials and alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interesting ones. The derivations of identities are based on the $p$-adic integral expression of the generating function for the Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating power sums.Comment: No comment

The Impact of Body Mass Index on Pancreatic Fistula After Pancreaticoduodenectomy in Asian Patients on the Basis of Asia-Pacific Perspective of Body Mass Index

 Context Several surgical complications are related to obesity. Objective This study evaluated the impact of obesity on pancreatic fistula after pancreaticoduodenectomy. Design We retrospectively reviewed the medical records of 159 patients who underwent pancreaticoduodenectomy between October 2002 and December 2008. Setting The patients were divided according to the body mass index as obese (body mass index equal to, or greater than, 25 kg/m2), or normal (body mass index less than 25 kg/m2). Methods Univariate and multivariate analyses were applied. Two-tailed P values less than 0.05 were considered as significant. Results Forty-six patients (28.9%) were obese and 113 patients (71.1%) were normal-weight. Obese group had a significantly higher incidence of pancreatic fistula and a greater amount of intraoperative blood loss. Other surgical complications were not significantly different between the two groups. Multivariate analysis found obesity, small pancreatic duct size (less than, or equal to, 3 mm), intraoperative blood loss, and combined resection as significant factors affecting pancreatic fistula. Conclusions Obese patients have an increased risk for pancreatic fistula after pancreaticoduodenectomy.

Correlation of the Rates of Solvolysis of i-Butyl Fluoroformate and a Consideration of Leaving-Group Effects

The specific rates of solvolysis of isobutyl fluoroformate (1) have been measured at 40.0 °C in 22 pure and binary solvents. These results correlated well with the extended Grunwald-Winstein (G-W) equation, which incorporated the NT solvent nucleophilicity scale and the YCl solvent ionizing power scale. The sensitivities (l and m-values) to changes in solvent nucleophilicity and solvent ionizing power, and the kF/kCl values are very similar to those observed previously for solvolyses of n-octyl fluoroformate, consistent with the additional step of an addition-elimination pathway being rate-determining. The solvent deuterium isotope effect value (kMeOH/kMeOD) for methanolysis of 1 was determined, and for solvolyses in ethanol, methanol, 80% ethanol, and 70% TFE, the values of the enthalpy and the entropy of activation for the solvolysis of 1 were also determined. The results are compared with those reported earlier for isobutyl chloroformate (2) and other alkyl haloformate esters and mechanistic conclusions are drawn