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.

A brief but comprehensive review of the averaged Hausdorff distances that have recently been introduced as quality indicators in multi-objective optimization problems (MOPs) is presented. First, we introduce all the necessary preliminaries, definitions, and known properties of these distances in order to provide a stat-of-the-art overview of their behavior from a theoretical point of view. The presentation treats separately the definitions of the $(p,q)$ -distances ${GD}_{p,q}$ , ${IGD}_{p,q}$ , and ${\Delta }_{p,q}$ for finite sets and their generalization for arbitrary measurable sets that covers as an important example the case of continuous sets. Among the presented results, we highlight the rigorous consideration of metric properties of these definitions, including a proof of the triangle inequality for distances between disjoint subsets when $p,q⩾1$ , and the study of the behavior of associated indicators with respect to the notion of compliance to Pareto optimality. Illustration of these results in particular situations are also provided. Finally, we discuss a collection of examples and numerical results obtained for the discrete and continuous incarnations of these distances that allow for an evaluation of their usefulness in concrete situations and for some interesting conclusions at the end, justifying their use and further study.

The paper is concerned with finite Hermitian Toeplitz matrices whose entries in the first row grow like a polynomial. Such matrices cannot be viewed as truncations of an infinite Toeplitz matrix which is generated by an integrable function or a nice measure. The main results describe the first-order asymptotics of the extreme eigenvalues as the matrix dimension goes to infinity and also deliver unexpected barriers for the eigenvalues. One purpose of the paper is to popularize once more that questions on the eigenvalues of matrices can be answered in a very elegant way by passing to integral operators. This idea was introduced by Harold Widom about fifty years ago. In this way one can also give an alternative proof to results by William F. Trench on Hermitian Toeplitz matrices with increasing entries.