Small perturbations of an indefinite elliptic equation

We investigate a perturbed semilinear indefinite elliptic equation and show that the results known for the unperturbed equation still hold if the perturbation is sufficiently small. To this end, we use a continuity argument that allows us to establish the existence of two positive solutions even in the case where the strong maximum principle does not apply.     

Discrepancy of random graphs and hypergraphs

Answering in a strong form a question posed by Bollobás and Scott, in this paper we determine the discrepancy between two random k‐uniform hypergraphs, up to a constant factor depending solely on k. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 47, 147–162, 2015     

Theoretical study in gas phase of linear and nonlinear optical properties of the ortho-, meta- and para-nitrophenol isomers

The linear (α), and nonlinear (β, γ) optical NLO properties of ortho-, meta- and para-nitrophenol (ONP, MNP and PNP) isomers have been calculated in gas phase by using ab initio (HF, MP2 and MP4) and density functional theory (DFT) (B3LYP, CAM-B3LYP) methods, with the 6-31+G(d,p) and 6-311+G(3d,3p) standard and the Sadlej specialized basis sets. These properties were evaluated both at static and at dynamic regime within the finite field FF numerical techniques and the time-dependent-Hartree–Fock approach at 1,910 nm, respectively. Additional calculations were performed for the β static hyperpolarizability of these isomers in presence of p-dioxane solvent with the Onsager Model and the SCRF-PCM approach, using B3LYP/6-31+G(d,p) and MP2/6-31+G(d,p) levels of theory. Additionally, CCSD/6-31+G(d,p) calculations were performed for the α, β and γ properties of PNP isomer. The B3LYP and MP2 α _ave results of the nitrophenol isomers are comparable to the experimental α _ave reports; while the tendency for the β _v calculated values (β _v PNP > β _v MNP > β _v ONP), that can be explained in terms of the O _x atomic charge of the –NO₂ group, does not follow exactly the experimental ones. The B3LYP γ _ave results are in correspondence to the experimental measurements, the correlation of which is r ² = 0.99. The use of FF methodology in conjunction with the B3LYP and MP2 methods and the 6-31+G(d,p) basis set show to be appropriate approaches to predict qualitative optical properties of Push–Pull like organic molecules, provided are considered the solvent effects or frequency dependence. However, to have a clear picture of the NLO properties of an isolated molecule, higher order correlation effects combined with specialized basis sets, frequency and solvent effects should be employed. We have demonstrated that MP4/Sadlej level of theory is able to reproduce NLO properties that can be considered equivalent to those from more sophisticated approaches, such as CCSD together with extended basis sets.     

On the selection of the most adequate radial basis function

Radial basis function (RBF) methods can provide excellent interpolants for a large number of poorly distributed data points. For any finite data set in any Euclidean space, one can construct an interpolation of the data by using RBFs. However, RBF interpolant trends between and beyond the data points depend on the RBF used and may exhibit undesirable trends using some RBFs while the trends may be desirable using other RBFs. The fact that a certain RBF is commonly used for the class of problems at hand, previous good behavior in that (or other) class of problems, and bibliography, are just some of the many valid reasons given to justify a priori selection of RBF. Even assuming that the justified choice of the RBF is most likely the correct choice, one should nonetheless confirm numerically that, in fact, the most adequate RBF for the problem at hand is the RBF chosen a priori. The main goal of this paper is to alert the analyst as to the danger of a priori selection of RBF and to present a strategy to numerically choose the most adequate RBF that better captures the trends of the given data set. The wing weight data fitting problem is used to illustrate the benefits of an adequate choice of RBF for each given data set.     

A weighted eigenvalue problem for the p-Laplacian plus a potential

Let Δ _p denote the p-Laplacian operator and Ω be a bounded domain in . We consider the eigenvalue problem

Titanium(III) trisamidotriazacyclononane: reactions with C60 and radicals

The reaction of titanium trisamidotriazacyclononane, [Ti{N(Ph)SiMe2}3tacn] (1), with C60 led to the synthesis of [Ti{N(Ph)SiMe2}3tacn]C60 (2) in high yield. Treatment of 2 with PhCH2Br led to the formation of [Ti{N(Ph)SiMe2}3tacn]Br and the radical PhCH2C60 (3). The reaction of CH3I with 1 gives two products. One is [Ti{N(Ph)SiMe2}3tacn]I (4), which results from the oxidation of 1 by an I radical. The other product, 5, resulting from a multistep reaction scheme that involves redox and nucleophilic reactions, presents an imido ligand formed by ligand rearrangement upon C-N bond cleavage. In solution, an exchange process that corresponds to a reversible 1,3-silyl shift between two Ti-bonded N atoms leads to isomers 5a and 5b. This equilibrium transforms an imido (TiNPh) into an amido ligand (Ti{NPh}SiMe2CH2Ph) with concomitant generation of an anionic moiety in the originally neutral triazacyclononane ring. In solution, either 5a or 5b displays additional fluxional processes that consist of its corresponding racemization processes.     

Effect of the polymeric coating over Fe<Subscript>3</Subscript>O<Subscript>4</Subscript> particles used for magnetic separation

In this work, the synthesis of magnetite nanoparticles by two variant chemical coprecipitation methods that involve reflux and aging conditions was investigated. The influence of the synthesis conditions on particle size, morphology, magnetic properties and protein adsorption were studied. The synthesized magnetite nanoparticles showed a spherical shape with an average particle size directly influenced by the synthesis technique. Particles of average size 27 nm and 200 nm were obtained. When the coprecipitation method was used without reflux and aging, the smallest particles were obtained. Magnetite nanoparticles obtained from both methods exhibited a superparamagnetic behavior and their saturation magnetization was particle size dependent. Values of 67 and 78 emu g⁻¹ were obtained for the 27 nm and 200 nm magnetite particles, respectively. The nanoparticles were coated with silica, aminosilane, and silica-aminosilane shell. The influence of the coating on protein absorption was studied using Bovine Serum Albumin (BSA) protein.      

Alternative positional FEM applied to thermomechanical impact of truss structures

This paper presents a formulation to deal with dynamic thermomechanical problems by the finite element method. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions, not displacements, to solve the mechanical problem. The thermal problem is solved by a regular finite element method. Such formulation has the advantage of being simple and accurate. As a solution strategy, it has been used as a natural split of the thermomechanical problem, usually called isothermal split or isothermal staggered algorithm. Usual internal variables and the additive decomposition of the strain tensor have been adopted to model the plastic behavior. Four examples are presented to show the applicability of the technique. The results are compared with other authors’ numerical solutions and experimental results.     

Three-pion resonances

We investigate the continuum three-pion problem within a relativistic three-body model that takes into account the S andP waves. The dynamical input of the two-body subsystem is given by separable potentials, which yield a good fit to the scattering data and resonance parameters up to a two-body invariant mass of 900MeV. We introduce a parameter expressing the ambiguity in the reduction of a fully relativistic theory to a three-dimensional one. The masses and widths of the ,a ₁(1260), and (1300) mesons, which decay predominantly into three pions, are reasonably well described by our model. Theh ₁(1170) meson, however, which also decays into three pions, cannot be explained as a three-pion resonance. Some Argand diagrams are shown in those channels where resonances exist.     

Localized states in polymeric molecules. IV. Polyacetylene beyond simple Hückel Model

We have used the transfer matrix technique to study the electronic structure of trans-polyacetylene, within a model Hamiltonian which includes second-neighbors interactions. The results show that the valence and conduction band widths and the energy of the localized state are dependent on the strength of the second neighbors couplings. However, for the physically reasonable range of parameters, the electronic structure of the material is only slightly modified, indicating that a simple Hückel treatment is quite accurate for this system.Work partially supported by the Brazilian Agencies FINEP and CNPq