A modulus gradient model for an axially loaded inhomogeneous elastic rod

A new gradient elasticity formulation is proposed for a one-dimensional linear elastic inhomogeneous rod. In the new formulation, similar to the differential relation between the local strain and the gradient enhanced strain in the classical models of gradient elasticity, a differential relation is proposed for the Young’s modulus. Analytical and finite element solutions of the proposed formulation are derived. Results of the proposed model are compared with a classical model of gradient elasticity for a model problem of carbon nanotube reinforced polymer composite.     

The São Paulo School of Advanced Sciences (ESPCA) on Recent Developments in Synchrotron Radiation

The São Paulo School of Advanced Sciences (ESPCA) on Recent Developments in Synchrotron Radiation was held July 13–24, 2015, at the Brazilian Synchrotron Light Laboratory (LNLS) in Campinas, Brazil. The school was attended by 96 students, 48 from Brazil and 48 from 17 different countries. A total of 27 different nationalities were represented in this 12-day school. In addition, 22 lecturers presented 34 talks.     

Complexation of metal ions with double-armed diazadithia lariat ether carrying anthracene moieties in acetonitrile–dioxane

A new 14-membered crown ether with nitrogen–sulfur donor atom carrying two anthryl groups was designed and synthesized by the reaction of the corresponding macrocyclic compound and 9-(chloromethyl) anthracene. The influence of metal cations such as Al³⁺, Zn²⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺, Mn²⁺, Cu²⁺, Cd²⁺, Hg²⁺ and Pb²⁺ on the spectroscopic properties of the ligand was investigated in acetonitrile–dioxane solution (1/1) by means of absorption and emission spectrometry. The results of spectrophotometric titration experiments disclosed the complexation stoichiometry and complex stability constant of the novel ligand with Fe²⁺, Fe³⁺, Al³⁺, Cd²⁺, Cu²⁺, Zn²⁺, Pb²⁺ and Hg²⁺ cations. Absorption spectra show isobestic points in the spectrophotometric titration of these cations. The presence of excess of Al³⁺, Zn²⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺, Mn²⁺, Cu²⁺, Cd²⁺, Hg²⁺ and Pb²⁺ cations caused an enhancement of anthryl fluorescence. Especially, the enhancement in case of the interaction of Hg²⁺ and Al³⁺ cations with the ligand was pronounced.     

Complexation of metal ions with the novel diazadithia crown ether carrying two anthryl pendants in acetonitrile–tetrahydrofuran

A new crown ether carrying two anthryl groups with nitrogen–sulfur donor atom was designed and synthesized by the reaction of the corresponding macrocyclic compound and 9-chloromethyl anthracene. The influence of metal cations such as Al³⁺, Zn²⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺, Mn²⁺, Cu²⁺, Cd²⁺, Hg²⁺ and Pb²⁺ on the spectroscopic properties of the ligand was investigated in acetonitrile–tetrahydofuran solution (1/1) by means of absorption and emission spectrometry. Absorption spectra show isosbestic points in the spectrophotometric titration of Fe²⁺, Fe³⁺, Al³⁺, Cu²⁺ and Hg²⁺. The results of spectrophotometric titration experiments disclosed the complexation stoichiometry and complex stability constant of the novel ligand with Fe²⁺, Fe³⁺, Al³⁺, Cu²⁺and Hg²⁺cations. The presence of excess amounts of Al³⁺, Zn²⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺, Mn²⁺, Cu²⁺, Cd²⁺, Hg²⁺ and Pb²⁺ cations caused an enhancement of anthryl fluorescence. The ligand showed good sensitivity for Zn²⁺ with respect to other metal cations with linear range and detection limit of 1.4 × 10^?7 to 4.1 × 10^?6 M and 1.0 × 10^?8 M respectively.     

Sobolev regularity for first order mean field games

In this paper we obtain Sobolev estimates for weak solutions of first order variational Mean Field Game systems with coupling terms that are local functions of the density variable. Under some coercivity conditions on the coupling, we obtain first order Sobolev estimates for the density variable, while under similar coercivity conditions on the Hamiltonian we obtain second order Sobolev estimates for the value function. These results are valid both for stationary and time-dependent problems. In the latter case the estimates are fully global in time, thus we resolve a question which was left open in [23]. Our methods apply to a large class of Hamiltonians and coupling functions.     

A generalisation of a theorem of Koldunov with an elementary proof

We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.     

Bioconjugation of D‐glucuronic acid sodium salt to well‐defined primary amine‐containing homopolymers and block copolymers

The synthesis of well‐defined carboxylic acid‐functionalized glycopolymers prepared via one‐step postpolymerization modification of poly(N‐[3‐aminopropyl] methacrylamide) (PAPMA), a water‐soluble primary amine methacrylamide, in aqueous medium is demonstrated. PAPMA was first polymerized via aqueous reversible addition‐fragmentation chain transfer polymerization in aqueous buffer using 4‐cyanopentanoic acid dithiobenzoate as the chain transfer agent and 4,4′‐azobis(4‐cyanovaleric acid) (V‐501) as the initiator at 70 °C. The resulting well‐defined PAPMA was then conjugated with D ‐glucuronic acid sodium salt through reductive amination in alkaline medium (pH 8.5) at 45 °C. The successful bioconjugation was proven through proton (¹H) and carbon (¹³C) nuclear magnetic resonance spectroscopy and matrix‐assisted laser desorption/ionization time of flight mass spectrometry analysis, which indicated near quantitative conversion. A similar bioconjugation reaction was conducted with poly(2‐aminoethyl methacrylate) (PAEMA) and poly(2‐aminoethyl methacrylate‐b‐poly(N‐[2‐hydroxypropyl]methacrylamide) (PAEMA‐b‐PHPMA). For the PAEMA homopolymers and block copolymers, however, lower conversion was obtained, most likely because of degradation reactions of PAEMA in alkaline medium. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3052–3061, 2010     

Synthesis and metal-ion binding properties of new N2S4- and N2S5-donor macrocycles

Synthetic procedures for new N₂S₄- and N₂S₅-donor macrocycles (2 and 4) were given. The ligands were prepared by the reaction of NaBH₄ with the appropriate macrocyclic diamide in the presence of boron trifluoride ethyl etherate in dry tetrahydrofuran (THF). Solvent extraction method was used to evaluate metal-ion binding properties of the new ligands. The solvent extraction experiments suggested that the reduced macrocycles have Ag⁺ and Hg²⁺ selectivities compared to Pb²⁺, Co²⁺, Zn²⁺, Ni²⁺, Cu²⁺, Mn²⁺ and Cd²⁺ ions. The extraction constants (log K _ex) and complex compositions were determined for Ag⁺ and Hg²⁺ complex of compound (4).