Differentiation of species of the Baccharis genus by HPLC and chemometric methods.

Phytochemical investigation of the aerial parts of three Baccharis species (Asteraceae family) was performed using HPLC and chemometric methods, with the objective of distinguishing between three morphologically very similar species: Baccharis genistelloides Persoon var. trimera (Less.) DC, B. milleflora (Less.) DC and B. articulata (Lam.) Persoon. With the help of Principal Component Analysis (PCA) and variance weights, it was possible to characterize the chromatographic profiles of the alcoholic extracts of the three species. Application of Soft Independent Modeling of Class Analogy (SIMCA) and K-Nearest Neighbor (KNN) methods on a training set of 74 extracts resulted in models that correctly classified all eight samples in an independent test set.     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007     

Detection of hepatocarcinoma in rats by integration of the fluorescence spectrum: Experimental model

The incorporation of spectroscopic techniques into diagnostic procedures may greatly improve the chances for precise diagnostics. One promising technique is fluorescence spectroscopy, which has recently been used to detect many different types of diseases. In this work, we use laser-induced tissue fluorescence to detect hepatocarcinoma in rats using excitation light at wavelengths of 443 and 532 nm. Hepatocarcinoma was induced chemically in Wistar rats. The collected fluorescence spectrum ranges from the excitation wavelength up to 850 nm. A mathematical procedure carried out on the spectrum determines a figure of merit value, which allows the detection of hepatocarcinoma. The figure of merit involves a procedure which evaluates the ratio between the backscattered excitation wavelength and the broad emission fluorescence band. We demonstrate that a normalization allowed by integration of the fluorescence spectra is a simple operation that may allow the detection of hepatocarcinoma.     

Asymptotic expansions of the Hurwitz-Lerch zeta function

The Hurwitz-Lerch zeta function Φ(z,s,a) is considered for large and small values of a∈C, and for large values of z∈C, with |Arg(a)|<π, z∉[1,∞) and s∈C. This function is originally defined as a power series in z, convergent for |z|<1, s∈C and 1−a∉N. An integral representation is obtained for Φ(z,s,a) which define the analytical continuation of the Hurwitz-Lerch zeta function to the cut complex z-plane C?[1,∞). From this integral we derive three complete asymptotic expansions for either large or small a and large z. These expansions are accompanied by error bounds at any order of the approximation. Numerical experiments show that these bounds are very accurate for real values of the asymptotic variables.     

Calculation of the dynamic temperature characteristics of a heated graphite tube used in electrothermal atomic absorption measurements

A method and computer program were developed for calculating the temperature of any part of a graphite furnace tube at any instant of time after onset of the heating cycle. Results for tubes of the Massman design show large differences in spatial temperature distributions during and at the end of the heating cycle when equilibrium is reached. When constant current is applied to contoured tubes, greater heating rates at the tube centres are obtained than with standard tubes.     

Cantor exchange systems and renormalization

We prove a one-to-one correspondence between (i) C¹⁺ conjugacy classes of C^1+H Cantor exchange systems that are C^1+H fixed points of renormalization and (ii) C¹⁺ conjugacy classes of C^1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, we prove that there is no C^1+α Cantor exchange system, with bounded geometry, that is a C^1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set.     

Solving multiple-objective problems in the objective space

Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and Ollero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.This work was partially sponsored by grants from CNP_q and FAPESP, Brazil. The authors are indebted to the anonymous reviewers for their valuable comments.