Smoothing properties for a coupled system of nonlinear evolution dispersive equations

We study the smoothness properties of solutions to the coupled system of equations of Korteweg—de Vries type. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data (u₀, v₀ possesses certain regularity and sufficient decay as x → ∞, then the solution (u(t). v(t)) will be smoother than (u0, v0) for 0 < t ≤ T where T is the existence time of the solution.     

A relax-and-cut algorithm for the prize-collecting Steiner problem in graphs

Given an undirected graph G with penalties associated with its vertices and costs associated with its edges, a Prize Collecting Steiner (PCS) tree is either an isolated vertex of G or else any tree of G, be it spanning or not. The weight of a PCS tree equals the sum of the costs for its edges plus the sum of the penalties for the vertices of G not spanned by the PCS tree. Accordingly, the Prize Collecting Steiner Problem in Graphs (PCSPG) is to find a PCS tree with the lowest weight. In this paper, after reformulating and re-interpreting a given PCSPG formulation, we use a Lagrangian Non Delayed Relax and Cut (NDRC) algorithm to generate primal and dual bounds to the problem. The algorithm is capable of adequately dealing with the exponentially many candidate inequalities to dualize. It incorporates ingredients such as a new PCSPG reduction test, an effective Lagrangian heuristic and a modification in the NDRC framework that allows duality gaps to be further reduced. The Lagrangian heuristic suggested here dominates their PCSPG counterparts in the literature. The NDRC PCSPG lower bounds, most of the time, nearly matched the corresponding Linear Programming relaxation bounds.     

Automata and logics over finitely varying functions

We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or “signals”. In particular, we introduce a natural class of automata for generating finitely varying functions called ’s, and show that it coincides in terms of language definability with a natural monadic second-order logic interpreted over finitely varying functions Rabinovich (2002) [15]. We also identify a “counter-free” subclass of ’s which characterise the first-order definable languages of finitely varying functions. Our proofs mainly factor through the classical results for word languages. These results have applications in automata characterisations for continuously interpreted real-time logics like Metric Temporal Logic (MTL) Chevalier et al. (2006, 2007) [6] and [7].     

The number of faces of the tridiagonal Birkhoff polytope

Counting basic objects as the vertices of polyhedra is a demanding problem in general, even for the most basic structured polytope. In this paper, we determine the number of q-faces for some q ≥ 1 of the polytope of tridiagonal doubly stochastic matrices.     

GRASP with hybrid heuristic-subproblem optimization for the multi-level capacitated minimum spanning tree problem

We propose a GRASP using an hybrid heuristic-subproblem optimization approach for the Multi-Level Capacitated Minimum Spanning Tree (MLCMST) problem. The motivation behind such approach is that to evaluate moves rearranging the configuration of a subset of nodes may require to solve a smaller-sized MLCMST instance. We thus use heuristic rules to define, in both the construction and the local search phases, subproblems which are in turn solved exactly by employing an integer programming model. We report numerical results obtained on benchmark instances from the literature, showing the approach to be competitive in terms of solution quality. The proposed GRASP have in fact improved the best known upper bounds for almost all of the considered instances.     

Surfactant design for the 1,1,1,2-tetrafluoroethane-water interface: ab initio calculations and in situ high-pressure tensiometry

In situ high-pressure tensiometry and ab initio calculations were used to rationally design surfactants for the 1,1,1,2-tetrafluoroethane-water (HFA134a|W) interface. Nonbonded pair interaction (binding) energies (E(b)) of the complexes between HFA134a and candidate surfactant tails were used to quantify the HFA-philicity of selected moieties. The interaction between HFA134a and an ether-based tail was shown to be predominantly electrostatic in nature and much more favorable than that between HFA134a and a methyl-based fragment. The interfacial activity of (i) amphiphiles typically found in FDA-approved pressurized metered-dose inhaler (pMDI) formulations, (ii) a series of nonionic surfactants with methylene-based tails, and (iii) a series of nonionic surfactants with ether-based tails was investigated at the HFA134a|W interface using in situ tensiometry. This is the first time that the tension of the surfactant-modified HFA134a|W interface has been reported in the literature. The ether-based surfactants were shown to be very interfacially active, with tension decreasing by as much as 27 mN.m(-)(1). However, the methyl-based surfactants, including those from FDA-approved formulations, did not exhibit high activity at the HFA134a|W interface. These results are in direct agreement with the E(b) calculations. Significant differences in interfacial activity are noted for surfactants at the 2H,3H-perfluoropentane (HPFP)|water and HFA134a|W interfaces. Care should be taken, therefore, when results from the mimicking solvent (HPFP) are extrapolated to HFA134a-based systems. The results shown here are of relevance in the selection of surfactants capable of forming and stabilizing reverse aqueous aggregates in HFA-based pMDIs, which are promising formulations for the systemic delivery of biomolecules to and through the lungs.     

Development and in-house validation of a microbiological assay for determination of cefepime in injectable preparations

Cefepime is a new parenteral cephalosporin that has been described as a fourth-generation, broad-spectrum antibiotic. This paper reports the development and in-house validation of an agar diffusion bioassay using a cylinder-plate method for the determination of cefepime in powder for injection. The validation performed yielded good results in terms of linearity, precision, accuracy, and robustness. The assay is based on the inhibitory effect of cefepime upon the strain of Micrococcus luteus ATCC 10240 used as the test microorganism. The results of assays were treated statistically by analysis of variance (ANOVA) and were found to be linear (r = 0.99993) in the selected range of 8.0-32.0 microg/mL; precise [repeatability: relative standard deviation (RSD) = 1.39%, intermediate precision: between-day RSD = 1.77%, and between-analyst RSD = 1.97%] and accurate. Comparison of bioassay and liquid chromatography by ANOVA showed no significant difference between methodologies. The results demonstrated the validity of the proposed bioassay, which is a simple and useful alternative methodology for cefepime determination in routine quality control.     

Determination of diclofenac in pharmaceutical preparations by diffuse reflectance photometry

A quantitative analytical method for the determination of diclofenac in pharmaceutical preparations by diffuse reflectance in the visible region of the spectrum is presented. The color reaction is done directly in the measuring cell immediately after mixing, using small volumes of the analyte solution, of the reagent and of the buffer solutions. All reflectance measurements were carried out in a home made reflectometer equipped with a red LED as light source and a LDR as detector. The calibration curves were constructed from 1.0 to 18 mg mL⁻¹ (about 3.0 × 10⁻³ to 5.5 × 10⁻² mol L⁻¹) of sodium diclofenac or of potassium diclofenac in the analytical solution, with typical correlation coefficients equal to 0.999. The detection limit was estimated to be about 0.7 mg mL⁻¹ (2 × 10⁻³ mol L⁻¹). The method was applied to determine diclofenac in solid and liquid pharmaceutical preparations. The R.S.D. varied from 2% to 4% depending of the sample. The results were compared with those obtained with the HPLC procedure recommended by the United States Pharmacopoeia using the statistical Student's t-test procedure.     

The venom gland of queens of Apis mellifera (Hymenoptera, Apidae): morphology and secretory cycle

The venom gland of queens of Apis mellifera was examined through light and transmission electron microscopy and subjected to electrophoretic analyses. Virgin queens exhibited prismatic secretory cells containing large amounts of rough endoplasmic reticulum with dilated cisternae, open secretory spaces, numerous vacuoles and granules scattered in the cytoplasm, and spherical nuclei with numerous nucleoli. The secretion produced was non-refringent under polarized light and the electrophoretic analysis of glandular extracts revealed five main protein bands. In mated queens, the venom gland exhibited a high degree of degeneration. Its secretion was refringent under polarized light and one of the main bands was absent in the electrophoretic pattern obtained. The morphological aspects observed are in agreement with the function of this gland in queens, given that virgin queens use venom in battles for the dominance of the colony, a situation that occurs as soon as they emerge, while fertilized queens rarely use venom.