Rare earth centers properties and electron trapping in SnO2 thin films produced by sol–gel route

Some very relevant optical, electrical, and structural properties of SnO₂ doped with rare-earth ions Er³⁺ and Eu³⁺ are presented. Films are produced by the sol–gel-dip coating process, and may be described as a combination of nanoscopic dimension crystallites (about 3–10 nm) with their respective intergrain potential barriers. The Er³⁺ and Eu³⁺ ions are expected to act as acceptors in SnO_2, which is a natural n-type conductor, inducing a high degree of charge compensation. Electron trapping and emission spectra data are presented and are rather distinct, depending on the location of the rare-earth impurity. This behavior allows the identification of two distinct centers: located either in the SnO₂ lattice or segregated at the particles surface. Based on a model for thermally activated cross-section defects, the difference between the capture energy of the photo-excited electron and the intergrain potential barrier is evaluated, leading to distinct values for high and low symmetry sites. A higher distortion in the lattice of undoped SnO₂ and SnO₂:Eu (1 at.%) was evaluated from Rietveld refinements of X-ray diffraction data. This was confirmed by Raman spectra, which are associated with the particles size and disorder. By comparing the samples with the same doping concentration, it was found that this disorder is higher in Eu-doped SnO₂ than in Er-doped SnO₂, which is in agreement with a higher energy for the lattice relaxation in the trapping process by Eu³⁺ centers.     

Topological entropy of continuous self-maps on closed surfaces

The objective of this work is to present sufficient conditions for having positive topological entropy for continuous self-maps defined on a closed surface by using the action of this map on the homological groups of the closed surface.     

A note on chain-based semi-Heyting algebras

We determine the number of non-isomorphic semi-Heyting algebras on an n-element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non-isomorphic semi-Heyting chains of a given size in some important subvarieties of the variety of semi-Heyting algebras that were introduced in [5]. We further exploit this recursive method to calculate the numbers $A(n,m)$ of non-isomorphic semi-Heyting chains with n elements such that removing the mth element ($1<m<n$) we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi-Heyting chain with $n-1$ elements can be extended to a n element semi-Heyting chain by adding a new element in the mth place. Finally we combine these results by finding a second way to calculate the numbers $A(n,m)$ that provides some extra information.     

New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

Consecutive Supramolecular Polymerization of a Rylene-Based Twistacene

The synthesis and self-assembling features of twistacene 1 are reported. The supramolecular polymerization of 1 displays a consecutive pathway to afford slipped ( AggI ) and rotationally displaced ( AggII ) aggregates conditioned by the formation of intramolecularly H-bonded pseudocycles. In methylcyclohexane, both AggI and AggII are highly stable and the interconversion of the kinetically controlled AggI into the thermodynamically controlled AggII takes several weeks to occur. The utilization of toluene as solvent changes the energetic level for both aggregates and favors a faster conversion of AggI into AggII within a period of minutes. This conversion can be accelerated by the addition of seeds. Furthermore, concentration dependent kinetic studies demonstrate the consecutive character of the supramolecular polymerization of 1 .     

Organic–inorganic bonding in chitosan–silica hybrid networks: Physical properties

Novel biomaterials are needed for bone tissue repair with improved mechanical performance compared to classical bioceramics. The objective of this work was to characterize a hybrid filler material, which is capable to coat as a thin film porous scaffolds improving their mechanical properties for bone tissue engineering. The hybrid filler material is a blend of chitosan and silica network formed through in situ sol–gel using tetraethylortosilicate and 3‐glycidoxypropyltrimethoxysilane (GPTMS) as silica precursors. The hypothesis was that the epoxy ring of GPTMS could react with the amino groups of chitosan in acidic media while it is also reacting the siloxane groups of hydrolyzed silica precursors. The formation of the hybrid organic–inorganic network was assessed by different physical techniques revealing changes in molecular mobility and hydrophilicity upon chemical reaction. Finally, the cytotoxicity of the samples was also evaluated by MTT assay. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1391–1400     

Connecting free volume with shape memory properties in noncytotoxic gamma‐irradiated polycyclooctene

The free volume holes of a shape memory polymer have been analyzed considering that the empty space between molecules is necessary for the molecular motion, and the shape memory response is based on polymer segments acting as molecular switches through variable flexibility with temperature or other stimuli. Therefore, thermomechanical analysis (TMA) and positron annihilation lifetime spectroscopy (PALS) have been applied to analyze shape recovery and free volume hole sizes in gamma‐irradiated polycyclooctene (PCO) samples, as a noncytotoxic alternative to more conventional PCO crosslinked via peroxide for future applications in medicine. Thus, a first approach relating structure, free volume holes and shape memory properties in gamma‐irradiated PCO is presented. The results suggest that free volume holes caused by gamma irradiation in PCO samples facilitate the recovery process by improving movement of polymer chains and open possibilities for the design and control of the macroscopic response. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1080–1088     

Deformation of Gabor systems

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames “without inequalities” from lattices to non-uniform sets.