n/a

Let \(\alpha,\beta\in(0,1)\) and
\[
K^{\alpha,\beta}:=\left\{a\in L^\infty(\mathbb{T}):\
\sum_{k=1}^\infty |\widehat{a}(-k)|^2 k^{2\alpha}<\infty,\
\sum_{k=1}^\infty |\widehat{a}(k)|^2 k^{2\beta}<\infty
\right\}.
\]
Mark Krein proved in 1966 that \(K^{1/2,1/2}\) forms a Banach algebra. He also observed that this algebra is important in the asymptotic theory of finite Toeplitz matrices. Ten years later, Harold Widom extended
earlier results of Gabor Szegö for scalar symbols and established the asymptotic trace formula
\[
\operatorname{trace}f(T_n(a))=(n+1)G_f(a)+E_f(a)+o(1)
\quad\text{as}\ n\to\infty
\]
for finite Toeplitz matrices \(T_n(a)\) with matrix symbols \(a\in K^{1/2,1/2}_{N\times N}\). We show that if \(\alpha+\beta\ge 1\) and \(a\in K^{\alpha,\beta}_{N\times N}\), then the Szegö-Widom asymptotic trace formula holds with \(o(1)\) replaced by \(o(n^{1-\alpha-\beta})\).

Fiber reinforced polymers (FRP) are often used to strengthen RC structures.
Despite intense research, durability of reinforced concrete (RC) retrofitted with FRP remains insufficiently known. Long time behavior of the bond laminate-concrete, in flexural strengthening, under environmental action is not well known, conditioning Codes and engineers. An experimental program that subjected RC beams, externally reinforced with Glass FRP (GFRP) strips, to temperature and salt water cycles, for up to 10000h is reported.
At selected intermediate times, the RC beams were loaded to failure in bending. Rupture took place, normally, by tensile failure of concrete at a short distance from the interface with GFRP. The results showed that freeze-thaw cycles were the most severe of the environmental
conditions. The study also generated also non-linear bond-slip relationships from the experimental data. Numerical modeling has been undertaken, based on a commercial code.
The model is based on smeared cracking. Parameters needed for the characterization, namely cohesion and friction angle, were obtained from shear tests conceived for the effect.

Analisa-se e caracteriza-se por via experimental a ligação entre elementos de betão armado e materiais compósitos, nomeadamente com base nas fibras de vidro. Fabricaram-se vigas de betão armado que foram exteriormente reforçadas com GFRP. Os resultados obtidos experimentalmente foram comparados com os resultados conseguidos por intermédio de modelação computacional, recorrendo-se ao programa de cálculo ATENA 2D. Para melhor modelação de elementos de interface, foram realizados ensaios de corte tendo-se obtido valores que permitiram caracterizar a lei de rotura de Mohr-Coulomb. Os parâmetros estudados foram a evolução das forças máximas absorvidas pelo reforço; as tensões de aderência máximas; a distribuição das tensões de aderência.

A mixture of 70% (w/w) pine biomass and 30% (w/w) plastics (mixture of polypropylene, polyethylene, and polystyrene) was subjected to pyrolysis at 400 °C, for 15 min, with an initial pressure of 40 MPa. Part of the solid residue produced was subjected to extraction with dichloromethane (DCM). The extracted residue (residue A) and raw residue (residue B) were analyzed by weight loss combustion and submitted to the leaching test ISO/TS 21268-2 using two different leachants: DCM (0.2%, v/v) and calcium chloride (0.001 mol/L). The concentrations of the heavy metals Cd, Cr, Ni, Zn, Pb and Cu were determined in the eluates and in the two residues. The eluates were further characterized by determining their pH and the concentrations of benzene, toluene, ethylbenzene and xylenes (BTEX). The presence of other organic contaminants in the eluates was qualitatively evaluated by gas chromatography, coupled with mass spectrometry. An ecotoxicological characterization was also performed by using the bio-indicator Vibrio fischeri. The chemical and ecotoxicological results were analyzed according to the French proposal of Criteria on the Evaluation Methods of Waste Ecotoxicity (CEMWE). Residue A was not considered to be ecotoxic by the ecotoxicological criterion (EC50 (30 min) ≥10%), but it was considered to be ecotoxic by the chemical criterion (Ni ≥ 0.5 mg/L). Residue B was considered to be ecotoxic by the ecotoxicological criterion: EC50 (30 min) ≤ 10%. Besides that, residue B was considered to be hazardous according the European legislation (BTEX concentrations higher than 100 ppb). The results indicate that volatile organic contaminants can be present in sufficient amounts in these residues and their eluates to induce ecotoxicity levels. The extraction of the pyrolysis residue with DCM was an efficient method for removing lighter organic contaminants.