Nonlinear second-order equations with functional implicit impulses and nonlinear functional boundary conditions

In this paper we deal with nonlinear second-order boundary value problems with impulses. The impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear. In both cases functional dependence on the solution is allowed. The existence results follow from the existence of a pair of well-ordered lower and upper solutions.     

Shadowing with multidimensional time in Banach spaces

We study linear dynamical systems with multidimensional time in Banach spaces. Using Taylor functional calculus we prove that under additional assumptions hyperbolic systems have shadowing property.     

A Fubini theorem

Let I₀ be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I₀ and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Ros?anowski-Shelah stating that I₀ on N² strongly violates the countable chain condition.     

Elastic instability of the nano-structured state as an intrinsic probe to study the early formation stages of sol–gel derived (Pb<Subscript>1-x</Subscript>Ca<Subscript>x</Subscript>)TiO<Subscript>3</Subscript> thin films

A novel method to investigate the early formation stages of polycrystalline (Pb_1-xCa_x)TiO₃ (PCT) perovskite films by means of traditional Brillouin and micro-Brillouin spectroscopy (BS, mBS) is described in the present work. The films were prepared by chemical solution deposition (CSD) onto oxidized (100)Si substrates and treated at temperatures between 350–650 °C by rapid thermal processing (RTP). The elastic instability observed by Brillouin spectroscopy at the nano-structured state of the PCT films was used here to determine their crystallization temperatures. Coexistence of different nanocrystalline phases (e.g., pyrochlore, perovskite) in the films could also be detected by this technique. The reliability of these results is demonstrated by complementary information obtained by X-ray diffraction (XRD) and scanning force microscopy (SFM). The effects of the annealing temperature and of the Ca²⁺ content on the crystallization process of these films are also discussed. PACS 78.35.+c; 77.84.-s; 61.82.Rx     

Silicon etching in Cl2 environment

The ion-beam-assisted etching of silicon in Cl₂ environment is considered. The theoretically calculated dependences of silicon etching rate on the flux of Cl₂ molecules at different ion current densities are compared with experimentally measured. The composition of the adsorbed layer is determined. It is found that SiCl₂ molecules prevail in the adsorbed layer. The reciprocal of relative concentration of SiCl₂ molecules in the adsorbed layer linearly depends on the ion-to-neutral flux ratio.     

Practical aspects associated with location planning for maternal and perinatal assistance in Brazil

A study has been carried out aimed at reducing perinatal mortality in the municipality of Rio de Janeiro through a better distribution of health care facilities. The algorithmic aspects are detailed elsewhere and here the emphasis is on practical issues and difficulties encountered. A 3-level hierarchical model was developed. Both uncapacitated and capacitated versions are briefly described together with some results based on actual data. The project brought to light many contradictions between OR theory and practice in developing countries and, unfortunately, the models developed were not implemented by the municipality health authorities. Possible reasons for this outcome are analysed.     

Cauchy-Born Rule and the Stability of Crystalline Solids： Dynamic Problems

We study continuum and atomistic models for the elastodynamics of crystalline solids at zerotemperature.We establish sharp criterion for the regime of validity of the nonlinear elastic wave equationsderived from the well-known Cauchy-Born rule.     

Trace element concentrations from São Francisco River - PR analyzed with PIXE technique

Summary Kulcsszavak (angolul, ha nem azonos az elozovel)     

A new approach towards peptidosulfonamides: synthesis of potential inhibitors of bacterial peptidoglycan biosynthesis enzymes MurD and MurE

Peptidosulfonamides are an emerging group of peptidomimetics with a variety of applications in medicinal chemistry. We present a novel approach to the synthesis of peptidosulfonamides, and apply it to a series of new potential inhibitors of the bacterial peptidoglycan biosynthesis enzymes MurD and MurE. The synthesis was conducted via N-phthalimido β-aminoethanesulfonyl chlorides, which are new building blocks for the synthesis of peptidosulfonamides. In the most crucial step, sulfonic acids or their sodium salts were converted into the corresponding sulfonyl chlorides using an excess of either SOCl₂ or SOCl₂/DMF, and then coupled to the C-protected amino acid. None of the compounds significantly inhibited MurD, however, some inhibited MurE; one had an IC₅₀ below 200 μM, which constitutes a promising starting point for further development. Molecular modelling simulations were performed on two analogues to investigate the absence of inhibitory activity of the sulfonamide compounds on MurD.