Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients

The Ramanujan Journal - In this paper we evaluate quadratic sums of Gaussian q-binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of...     

An adaptive large neighborhood search heuristic for the Pollution-Routing Problem

The Pollution-Routing Problem (PRP) is a recently introduced extension of the classical Vehicle Routing Problem with Time Windows which consists of routing a number of vehicles to serve a set of customers, and determining their speed on each route segment so as to minimize a function comprising fuel, emission and driver costs. This paper presents an adaptive large neighborhood search for the PRP. Results of extensive computational experimentation confirm the efficiency of the algorithm.     

The exponentiated generalized power Lindley distribution: Properties and applications

In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of the density and hazard rate functions, the quantile function, moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived.Moreover, we discuss the parameter estimation of the new distribution using the maximum likelihood and diagonally weighted least squares methods. A simulation study is performed to evaluate the estimators. We use two real data sets to illustrate the applicability of the new model. Empirical findings show that the proposed model provides better fits than some other well-known extensions of Lindley distributions.     

Determination of the hydroxyl radical by its adduct formation with phenol and liquid chromatography/electrochemical detection

An HPLC-ECD method is described for the indirect determination of the hydroxyl (OH) radical. Fenton's reaction is used to produce OH, which simultaneously attacks phenols (phenol or pyrocatechol) to form the adducts, pyrocatechol or pyrogallic acid. Thus, [OH] quantification is based on the separation and detection of pyrogallic acid and/or pyrocatechol by an isocratic HPLC-ECD method. The quantification of OH is also performed alternatively by a chronoamperometric detection in an electrochemical cell, where simultaneously formed Fe^III (Fenton's reaction) combines [Fe^II(CN)₆]⁴⁻ to produce the Prussian blue (PB) molecules (Fe₄^III[Fe^II(CN)₆]₃). Newly formed PB molecules are then immediately converted to colorless Everitts salt (K₄Fe₄^II[Fe^II(CN)₆]₃) with the reduction of the high-spin Fe^III to Fe^II at the surface of a glassy carbon electrode at +0.150 V (versus Ag/AgCl). The calculated concentration of OH during incubation (0.626 ppm) can be detected with negative errors by the HPLC-ECD (0.595 and 0.615 ppm with the errors −5.2 and −1.8%, respectively) and by the chronoamperometric method (0.552 and 0.607 ppm with the errors −11.8 and −3.0%, respectively). For the comparison of the two sets of data, HPLC-ECD method is much more promising.