On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier Inc. All rights reserved.

Interacting model for the cosmological dark sector

We discuss a new interacting model for the cosmological dark sector in which the attenuated dilution of cold dark matter scales as a(-3)f(a), where f(a) is an arbitrary function of the cosmic scale factor a. From thermodynamic arguments, we show that f(a) is proportional to the entropy source of the particle creation process. In order to investigate the cosmological consequences of this kind of interacting models, we expand f(a) in a power series, and viable cosmological solutions are obtained. Finally, we use current observational data to place constraints on the interacting function f(a).

Comparing non-stationary and irregularly spaced time series

In this paper, we present approximate distributions for the ratio of the cumulative wavelet periodograms considering stationary and non-stationary time series generated from independent Gaussian processes. We also adapt an existing procedure to use this statistic and its approximate distribution in order to test if two regularly or irregularly spaced time series are realizations of the same generating process. Simulation studies show good size and power properties for the test statistic. An application with financial microdata illustrates the test usefulness. We conclude advocating the use of these approximate distributions instead of the ones obtained through randomizations, mainly in the case of irregular time series. (C) 2012 Elsevier B.V. All rights reserved.

Structure- and Ligand-Based Structure-Activity Relationships for a Series of Inhibitors of Aldolase

Aldolase has emerged as a promising molecular target for the treatment of human African trypanosomiasis. Over the last years, due to the increasing number of patients infected with Trypanosoma brucei, there is an urgent need for new drugs to treat this neglected disease. In the present study, two-dimensional fragment-based quantitative-structure activity relationship (QSAR) models were generated for a series of inhibitors of aldolase. Through the application of leave-one-out and leave-many-out cross-validation procedures, significant correlation coefficients were obtained (r(2) = 0.98 and q(2) = 0.77) as an indication of the statistical internal and external consistency of the models. The best model was employed to predict pK(i) values for a series of test set compounds, and the predicted values were in good agreement with the experimental results, showing the power of the model for untested compounds. Moreover, structure-based molecular modeling studies were performed to investigate the binding mode of the inhibitors in the active site of the parasitic target enzyme. The structural and QSAR results provided useful molecular information for the design of new aldolase inhibitors within this structural class.