Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

Existence and uniqueness of optimal dynamic pricing and advertising controls without concavity

We consider a pricing and advertising dynamic-optimization problem where the goodwill dynamics evolve à la Nerlove–Arrow. The firm maximizes its profit over a finite-planning horizon corresponding to the product’s lifespan, and it turns out that the Hamiltonian is non-concave. We show the existence and uniqueness of an optimal solution under some mild conditions.     

Synthesis and structure–property relationship of carbazole‐alt‐benzothiadiazole copolymers

A series of four π‐conjugated carbazole‐alt‐benzothiadiazole copolymers (PCBT) were prepared by Suzuki cross‐coupling reaction between synthesized dibromocarbazoles as electron‐rich subunits and 4,7‐bis(4,4,5,5‐tetramethyl‐1,3,2‐dioxaborolan‐2‐yl)?2,1,3‐benzothiadiazole as electron‐deficient subunits. The subunits were directly linked through 2,7‐ or 3,6‐ positions of the carbazole. In addition, the carbazole monomers have been N‐substituted by a branched or a linear side‐chain. The chemical structure of the copolymers and their precursors was confirmed by NMR and IR spectroscopies, and their molar masses were estimated by SEC. Thermal analysis under N₂ atmosphere showed no weight loss below 329°C, and no glass transition was observed in between 0 and 250°C. The band gaps of all PCBTs evaluated by optical spectroscopies and by cyclic voltammetry analysis were consistent with expectations and ranged between 2.2 and 2.3 eV. Finally, 2,7 and 3,6 linkages were shown to influence optical properties of PCBTs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2059–2068     

Intra‐ and inter‐supramolecular complexation of poly(butyl methacrylate)‐co‐2‐(1,2,3‐triazol‐4‐yl)pyridine copolymers induced by CoII,FeII, and EuIII ions monitored by molecular hydrodynamics methods

Poly(butyl methacrylate) copolymers embedding bidentate 2‐(1,2,3‐triazol‐4‐yl)pyridine (trzpy) chelating units as comonomer in the side chains were synthesized by controlled radical addition‐fragmentation transfer (RAFT) polymerization. Intracomplexation and intercomplexation of the macromolecules of the poly(butyl methacrylate) copolymers containing 20 % mol of trzpy units induced by Co^II, Fe^II, and Eu^III ions were studied in the solutions by macromolecular hydrodynamics methods. The sedimentation velocity of extremely diluted copolymer solutions and the dynamic viscosity of moderately diluted solutions were studied in a wide range of the salts concentrations. Differences were observed with respect to the copolymer behavior in the presence of the Co²⁺, Fe²⁺, Eu³⁺ ions. These differences are namely due to the differences in the number of coordination bonds required for complex formation and not explicitly to the nature of the corresponding anions. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2632–2639     

Formation of Long,Multicenter π‐[TCNE]22− Dimers in Solution: Solvation and Stability Assessed through Molecular Dynamics Simulations

Purely organic radical ions dimerize in solution at low temperature, forming long, multicenter bonds, despite the metastability of the isolated dimers. Here, we present the first computational study of these π‐dimers in solution, with explicit consideration of solvent molecules and finite temperature effects. By means of force‐field and ab initio molecular dynamics and free energy simulations, the structure and stability of π‐[TCNE]₂^2? (TCNE=tetracyanoethylene) dimers in dichloromethane have been evaluated. Although the dimers dissociate at room temperature, they are stable at 175 K and their structure is similar to the one in the solid state, with a cofacial arrangement of the radicals at an interplanar separation of approximately 3.0 Å. The π‐[TCNE]₂^2? dimers form dissociated ion pairs with the NBu₄⁺ counterions, and their first solvation shell comprises approximately 20 CH₂Cl₂ molecules. Among them, the eight molecules distributed along the equatorial plane of the dimer play a key role in stabilizing the dimer through bridging C?H???N contacts. The calculated free energy of dimerization of TCNE ^{. ?} in solution at 175 K is ?5.5 kcal mol^?1. These results provide the first quantitative model describing the pairing of radical ions in solution, and demonstrate the key role of solvation forces on the dimerization process.     

The measurement of the magnetic susceptibility of some elements (Fe,Co, Ni,Ge, Sn,Te) in the liquid state

A magnetic balance was used for measuring the susceptibility of metals and alloys, in an atmosphere of purified argon, up to 1800°c.

Comparison of the susceptibilities of liquid Fe, Co and Ni gives information on the liquid state. The changes in the susceptibilities of Ge, Sn and Te on melting are typical of semi-metallic elements and semiconductors, but their behaviour differs according to the degree of symmetry in the solid state.     

Hubble Law: Measure and Interpretation

We have had the chance to live through a fascinating revolution in measuring the fundamental empirical cosmological Hubble law. The key progress is analysed: (1) improvement of observational means (ground-based radio and optical observations, space missions); (2) understanding of the biases that affect both distant and local determinations of the Hubble constant; (3) new theoretical and observational results. These circumstances encourage us to take a critical look at some facts and ideas related to the cosmological red-shift. This is important because we are probably on the eve of a new understanding of our Universe, heralded by the need to interpret some cosmological key observations in terms of unknown processes and substances.