Low-density polyethylene (LDPE) waste generates an environmental impact. To achieve the most suitable option for their degradation, it is necessary to implement chemical, physical and biological treatments, as well as combining procedures. Best treatment was prognosticated by Plackett-Burman Experimental Design (PB), evaluating five factors with two levels (0.25 mM or 1.0 gL-1 glucose, 1.0 or 2.0 mM CuSO4, 0.1 or 0.2 mM ABTS [2, 20-azino-bis(3-ethylbenzothiazoline-6-sulphonic acid)], pH 4.5 ± 0.2 or 7.0 ± 0.2 and 30 or 90 day incubation), which was reproduced for 150 days. Therefore, PB identified a sequential treatment (plasma followed by fungus) for partial LDPE biodeterioration. Sheets were pretreated with glow discharge plasma (O2, 3.0 x 10−2 mbar, 600 V, 6 min.), followed by Pleurotus ostreatus biodeterioration. Fungus growth, colonization percentage, and pigment generation followed. Laccase (Lac), manganese peroxidase (MnP) and lignin peroxidase (LiP) activities were appraised. Additionally, contact angle (CA), functional group presence and changes and carbonyl and vinyl indices (Fourier transformed infrared spectroscopy) were evaluated. LDPE surface changes were assessed by Young’s modulus, yield strength, scanning electronic microscopy (SEM), Fourier transformed infrared spectroscopy (FTIR) and atomic force microscopy (AFM). Plasma discharge increased hydrophilicity, decreasing CA by 76.57% and increasing surface roughness by 99.81%. P. ostreatus colonization was 88.72% in 150 days in comparison with untreated LDPE (45.55%). After this treatment carbonyl groups (C = O), C = C insaturations, high hydrophilicity CA (16 ± 4) °, and low surface roughness (7 ± 2) nm were observed. However, the highest Lac and LiP activities were detected after 30 days (Lac: 2.817 U Lac g-1 and LiP: 70.755 U LiP g-1). In addition, highest MnP activity was observed at day 120 (1.097 U MnP g-1) only for P. ostreatus treated LDPE. Plasma favored P. ostreatus adsorption, adherence, growth and colonization (88.72%), as well as partial LDPE biodeterioration, supported by increased hydrophilicity and presence of specific functional chemical groups. The approximate 27% changes in LDPE physical properties support its biodeterioration.

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The collective behavior of the singular values of large Toeplitz matrices is described by the Avram-Parter theorem. In the case of Hermitian matrices, the Avram-Parter theorem is equivalent to Szegő's theorem on the eigenvalues. The Avram-Parter theorem in conjunction with an improvement made by Trench implies estimates in the mean between the singular values and the appropriately ordered absolute values of the symbol. The purpose of this paper is twofold. Under natural hypotheses, we first strengthen the known estimates in the mean to estimates in the maximum norm, thus turning from collective results on the singular values to results on individual singular values. Secondly, we want to emphasize that the use of the quantile function eases the proofs and statements of results significantly and provides a promising language for forthcoming research into higher order asymptotics for individual singular values. (J.M. Bogoya), aboettch@mathematik.tu-chemnitz.de (A. Böttcher), grudsky@math.cinvestav.mx (S.M. Grudsky), maximenko@esfm.ipn.mx (E.A. Maximenko).

The paper is devoted to the structure and the asymptotics of the eigenvector matrix of Hermitian Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the real line. The results extend existing results on banded Toeplitz matrices to full Toeplitz matrices with temperate decay of the entries in the first row and column. We establish formulas for both the exact and the asymptotic computation of arbitrarily prescribed individual components of arbitrarily prescribed individual eigenvectors. These formulas are in terms of the Wiener-Hopf factorization of a function which depends solely on the symbol and the corresponding eigenvalue or even only on an approximation to this eigenvalue. The paper does not aim at providing numerical algorithms. Its main purpose is rather to reveal the structure underneath the eigenvectors, which are shown to be the sum of two harmonics and certain edge corrections. (J.M. Bogoya), aboettch@mathematik.tu-chemnitz.de (A. Böttcher), grudsky@math.cinvestav.mx (S.M. Grudsky), maximenko@esfm.ipn.mx (E.A. Maximenko).