Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a(0) + a(1)x(1) + ... + a(n)x(n) subject to certain constraints to solve the problem of minimizing a rational function of the form (a(0) + a(1)x(1) + ... + a(n)x(n))/(b(0) + b(1)x(1) + ... + b(n)x(n)) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo`s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo`s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an alpha-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an alpha-approximation (1 1/alpha-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.

The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

Prevalence of untreated caries in deciduous teeth in urban and rural areas in the state of Sao Paulo, Brazil

Objectives. To describe the prevalence of dental caries in children with deciduous teeth in urban and rural areas in the state of Sao Paulo, Brazil, and to identify associated factors. Methods. The study included 24 744 children ( 5 - 7 years of age) examined as part of an epidemiological survey on oral health carried out in the state of Sao Paulo ( Levan-tamento Epidemiologico de Sa de Bucal do Estado de Sao Paulo). Multilevel analysis was used to investigate whether the prevalence of untreated caries was associated with the sociodemographic characteristics of the children examined or with the socioeconomic aspects of the participating cities. Results. Being black or brown ( adjusted odds ratio ( OR) = 1.27), attending school in rural areas ( adjusted OR = 1.88), and attending public school ( adjusted OR = 3.41) were identified as determinants for an increased probability of presenting deciduous teeth with untreated caries. Being a female ( adjusted OR = 0.83) was identified as a protective factor. The negative coefficients obtained for second- level independent variables indicate that the oral health profile of the cities included in the study were positively impacted by a higher municipal human development index ( beta = - 0.47) and fluoridated drinking water ( beta = - 0.32). Conclusions. The prevalence of untreated caries is influenced by individual and sociodemographic factors. The present study provides epidemiological information concerning the rural areas in the state of Sao Paulo. This information is useful for strategic planning and for establishing guidelines for oral health actions in local health systems, thereby contributing to oral health equity.

Comparative bioavailability of cefuroxime axetil suspension formulations administered with food in healthy subjects

Objective: To assess the comparative bioavailability of two formulations (250 mg/5 mL suspension) of cefuroxime axetil (CAS 64544-07-6), administered with food, in healthy volunteers of both sexes. Methods: The study was conducted using an open, randomized, two-period crossover design with a 1-week washout interval. Plasma samples were obtained for up to 12 h post dose. Plasma cefuroxime axetil concentrations were analyzed by liquid chromatography coupled with tandem mass spectrometry (LC-MS-MS) with negative ion electrospray ionization using multiple reactions monitoring (MRM). From the cefuroxime axetil plasma concentration vs. time curves, the following pharmacokinetic parameters were obtained: AUC(last) and C(max). Results: The limit of quantification was 0.1 mu g/mL for plasma cefuroxime axetil analysis. The geometric mean and 90% confidence interval CI of test/reference product percent ratios were: 106.1% (100.8%-111.8%) for C(max), 109.4% (104.8%-114.2%) for AUC(last). Conclusion: Since the 90% Cl for AUC(last) and C(max) ratios were within the 80-125 % interval proposed by the US FDA, it was concluded that cefuroxime axetil (test formulation, 250 mg/5 mL suspension) was bioequivalent to a reference formulation under fed conditions, for both the rate and extent of absorption.

Reaction functions for weakly bound systems

We propose a new technique to analyze total reaction cross sections. In this technique, which has been previously applied to fusion reactions, the experimental data are used to build a dimensionless reaction function, which does not depend oil the system size or details of the optical potential. In this way, total reaction cross sections for different systems can be directly compared. We employ this technique to perform a systematic study of reaction cross sections of weakly bound systems in different mass ranges, and compare their reaction functions with the ones of tightly bound systems with similar masses. We show that breakup reactions and neutron transfers in halo systems lead to large reaction functions, well above the ones of typical tightly or weakly bound stable systems. (C) 2009 Elsevier B.V. All rights reserved.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Analytical Assessment of a Home Made Capillary Electrophoresis Equipment with Linear Charge Coupled Device for Visible Light Absorption Detection in the Determination of Food Dyes

The performance of modular home made capillary electrophoresis equipment with spectrophotometric detection, at a visible region by means of a miniaturized linear charge coupled device, was evaluated for the determination of four food dyes. This system presents a simple but efficient home made cell detection scheme. A computer program that converts the spectral data after each run into the electropherograms was developed to evaluate the analytical parameters. The dyes selected for analytical evaluation of the system were Brilliant Blue FCF, Fast Green FCF, Sunset Yellow FCF, and Amaranth. Separation was carried out in a 29cm length and 75 mu m I.D fused silica capillary, using 10mmolL-1 borate buffer at pH 9, with separation voltage of 7.5kV. The detection limits for the dyes were between 0.3 and 1.5mgL-1 and the method presented adequate linearity over the ranges studied, with correlation coefficients greater than 0.99. The method was applied for determination and quantification of these dyes in fruit juices and candies.

Validation of an ELISA method for the serological diagnosis of canine brucellosis due to Brucella canis

In the present study, the validation of an enzyme-linked immunosorbent assay (ELISA) for serodiagnosis of canine brucellosis is described. Two different antigenic extracts, obtained by heat or ultrasonic homogenization of microbial antigens from a wild isolate of Brucella canis bacteria, were compared by ELISA and Western blot (WB). A total of 145 canine sera were used to define sensitivity, specificity and accuracy of the ELISA as follows: (1) sera from 34 animals with natural B. canis infection, confirmed by blood culture and PCR, as well as 51 sera samples from healthy dogs with negative results by the agar-gel immunodiffusion (ACID) test for canine brucellosis, were used as the control panel for B. cants infection; and (2) to scrutinize the possibility of cross reactions with other common dog infections in the same geographical area in Brazil, 60 sera samples from dogs harboring known infections by Leptospira sp., Ehrlichia canis, canine distemper virus (CDV), Neospora caninum, Babesia canis and Leishmania chagasi (10 in each group) were included in the study. The ELISA using heat soluble bacterial extract (HE-antigen) as antigen showed the best values of sensitivity (91.18%), specificity (100%) and accuracy (96.47%). In the WB analyses, the HE-antigen showed no cross-reactivity with sera from dogs with different infections, while the B. canis sonicate had various protein bands identified by those sera. The performance of the ELISA standardized with the heat soluble B. canis antigen indicates that this assay can be used as a reliable and practical method to confirm infection by this microorganism, as well as a tool for seroepidemiological studies. (C) 2010 Elsevier Ltd. All rights reserved.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Hyperfunctions and (analytic) hypoellipticity

In this work we discuss the problem of smooth and analytic regularity for hyperfunction solutions to linear partial differential equations with analytic coefficients. In particular we show that some well known ""sum of squares"" operators, which satisfy Hormander`s condition and consequently are hypoelliptic, admit hyperfunction solutions that are not smooth (in particular they are not distributions).

Comparative bioavailability of three ibuprofen formulations in healthy human volunteers

Objective: To assess the bioequivalence of three ibuprofen formulations (Test formulation: ibuprofen (400 mg capsule) manufactured by Cardinal Health Brasil 402 Ltda. (Sorocaba, Brazil) and licensed to Boehringer Ingelheim do Brasil Quim. e Farm. Ltda. (Sao Paulo, Brazil); Reference formulation (1): ibuprofen (Advil (R); 2 x 200 mg coated tablet) from Wyeth-Whitehall Ltda. (Itapevi, Brazil); Reference formulation (2): ibuprofen (Alivium (R); 8 ml x 50 mg/ml solution) from Schering Plough S.A. (Rio de Janeiro, Brazil)) in 24 healthy volunteers of both sexes. Methods: The study was conducted using an open, randomized, three-period crossover design with at least 5-day washout interval. Plasma samples were obtained over a 24-h period. Plasma ibuprofen concentrations were analyzed by liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS) with negative ion electrospray ionization using multiple reaction monitoring (MRM). The following pharmacokinetic parameters were obtained from the ibuprofen plasma concentration vs. time curves: AUC(last), AUC(trunctmax) AUC(inf) and C-max. Results: The limit of quantification for ibuprofen was 0.1 mu g x ml(-1). The geometric mean with corresponding 90% confidence interval (CI) for Test/Reference (1) percent ratios were 114.24% (90% CI = 105.67, 123.50%) for C-max, 98.97% (90% CI = 94.69, 103.44%) for AUC(last) and 99.40% (90% CI = 95.21, 103.78%) for AUCinf. The geometric mean and respective 90% confidence interval (CI) for Test/Reference (2) percent ratios were 108.38% (90% Cl = 100.195, 117.25%) for C-max, 100.79% (90% CI = 96.39, 105.40%) for AUC(last) and 101.26% (90% CI = 96.94, 105.77%) for AUC(inf); t(max) for the 400 mg Test capsule was shorter than that for the 2 x 200 mg Reference (1) tablets (p < 0.002). Conclusion: Since the 90% CI for AUC(last), AUC(inf) and C-max ratios were within the 80 - 125% interval proposed by the US FDA, it was concluded that ibuprofen formulation manufactured by Cardinal Health Brasil 402 Ltda. and licensed to Boehringer Ingelheim do Brasil Quim. e Farm. Ltda. is bioequivalent to the Advil (R) and Alivium (R) formulations with regard to both the rate and the extent of absorption.

Structural and spectroscopic properties of the diazocarbene radical (CNN) and its ions CNN(+) and CNN(-): a high-level theoretical investigation

The diazocarbene radical, CNN, and the ions CNN(+) and CNN(-) were investigated at a high level of theory. Very accurate structural parameters for the states X(3)Sigma(-) and A(3)Pi of CNN, and X(2)Pi of both CNN(+) and CNN(-) were obtained with the UCCSD(T) method using correlated-consistent basis functions with extrapolations to the complete basis set limit, with valence only and also with all electrons correlated. Harmonic and anharmonic frequencies were obtained for all species and the Renner parameter and average frequencies evaluated for the Pi states. At the UCCSD(T)/CBS(T-5) level of theory, Delta(f)H(0 K) = 138.89 kcal/mol and Delta(f)H(298 K) = 139.65 kcal/mol were obtained for diazocarbene; for the ionization potential and the electron affinity of CNN, 10.969 eV (252.95 kcal/mol), and 1.743 eV (40.19 kcal/mol), respectively, are predicted. Geometry optimization was also carried out with the CASSCF/MRCI/CBS(T-5) approach for the states X(3)Sigma(-) A(3)Pi, and a(1)Delta of CNN, and with the CASSCF/MRSDCI/aug-cc-pVTZ approach for the states b(1)Sigma(+), c(1)Pi, d(1)Sigma(-), and B(3)Sigma(-), and excitation energies (T(e)) evaluated. Vertical energies were calculated for 15 electronic states, thus improving on the accuracy of the five transitions already described, and allowing for a reliable overview of a manifold of other states, which is expected to guide future spectroscopic experiments. This study corroborates the experimental assignment for the vertical transition X (3)Sigma(-) <- E (3)Pi.

Solvation in Pure Liquids: What Can Be Learned from the Use of Pairs of Indicators?

The solvation of six solvatochromic probes in a large number of solvents (33-68) was examined at 25 degrees C. The probes employed were the following: 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenyl pyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr(2), respectively. Of these, MePMBr is a novel compound. They can be grouped in three pairs, each with similar pK(a) in water but with different molecular properties, for example, lipophilicity and dipole moment. These pairs are formed by RB and MePM; QB and MePMBr; WB and MePMBr(2), respectively. Theoretical calculations were carried out in order to calculate their physicochemical properties including bond lengths, dihedral angles, dipole moments, and wavelength of absorption of the intramolecular charge-transfer band in four solvents, water, methanol, acetone, and DMSO, respectively. The data calculated were in excellent agreement with available experimental data, for example, bond length and dihedral angles. This gives credence to the use of the calculated properties in explaining the solvatochromic behaviors observed. The dependence of an empirical solvent polarity scale E(T)(probe) in kcal/mol on the physicochemical properties of the solvent (acidity, basicity, and dipolarity/polarizability) and those of the probes (pK(a), and dipole moment) was analyzed by using known multiparameter solvation equations. For each pair of probes, values of E(T)(probe) (for example, E(T)(MePM) versus E(T)(RB)) were found to be linearly correlated with correlation coefficients, r, between 0.9548 and 0.9860. For the mercyanine series, the values of E(T)(probe) also correlated linearly, with (r) of 0.9772 (MePMBr versus MePM) and 0.9919 (MePMBr(2) versus MePM). The response of each pair of probes (of similar pK(a)) to solvent acidity is the same, provided that solute-solvent hydrogen-bonding is not seriously affected by steric crowding (as in case of RB). We show, for the first time, that the response to solvent dipolarity/polarizability is linearly correlated to the dipole moment of the probes. The successive introduction of bromine atoms in MePM (to give MePMBr, then MePMBr(2)) leads to the following linear decrease: pK(a) in water, length of the phenolate oxygen-carbon bond, length of the central ethylenic bond, susceptibility to solvent acidity, and susceptibility to solvent dipolarity/polarizability. Thus studying the solvation of probes whose molecular structures are varied systematically produces a wealth of information on the effect of solute structure on its solvation. The results of solvation of the present probes were employed in order to test the goodness of fit of two independent sets of solvent solvatochromic parameters.