Models with commutative orthogonal block structure: a general condition for commutativity.

A linear mixed model whose variance-covariance matrix is a linear combination of known pairwise orthogonal projection matrices that add to the identity matrix, is a model with orthogonal block structure (OBS). OBS have estimators with good behavior for estimable vectors and variance components, moreover it may be interesting that the least squares estimators give the best linear unbiased estimators, for estimable vectors. We can achieve it, requiring commutativity between the orthogonal projection matrix, on the space spanned by the mean vector, and the orthogonal projection matrices involved in the expression of the variance-covariance matrix. This commutativity condition defines a more restrict class of OBS, named COBS (model with commutative orthogonal block structure). With this work we aim to present a commutativity condition, resorting to a special class of matrices, named U-matrices.

Assessing the diurnal variability of pharmaceutical and personal care products in a full-scale activated sludge plant.

An intensive sampling campaign has been carried out in a municipal wastewater treatment plant (WWTP) to assess the dynamics of the influent pharmaceutical active compounds (PhAC) and musks. The mass loadings of these compounds in wastewater influents displayed contrasting diurnal variations depending on the compound. The musks and some groups of PhACs tended to follow a similar diurnal trend as compared to macropollutants, while the majority of PhACs followed either the opposite trend or no repeatable trend. The total musk loading to the WWTP was 0.74 ± 0.25 g d(-1), whereas the total PhAC mass loading was 84.7 ± 63.8 g d(-1). Unlike the PhACs, the musks displayed a high repeatability from one sampling day to the next. The range of PhAC loadings in the influent to WWTPs can vary several orders of magnitude from one day or week to the next, representing a challenge in obtaining data for steady-state modelling purposes.

Heavy metal migration during electroremediation of fly ash from different wastes--modelling.

Fly ash is an airborne material which is considered hazardous waste due to its enrichment on heavy metals. Depending on the waste from which they are originated, fly ash may be further valorised, e.g. as soil amendment or concrete and ceramics adjuvant, or landfilled, when defined as hazardous material. In any case, heavy metal content has to be decreased either for fly ash valorisation or for complying with landfill criteria. The electrodialytic (EDR) process is a remediation technique based on the principle of electrokinetics and dialysis, having the aim to remove heavy metals from contaminated solid media. EDR was here applied to fly ashes from the combustion of straw (ST), from the incineration of municipal solid waste (DK and PT) and from the co-combustion of wood (CW). A statistical study, using F tests, Bonferroni multiple comparison method and a categorical regression, was carried out to determine which variables ("Ash type", "Duration", "Initial pH", "Final pH", "Acidification" and "Dissolution") were the most significant for EDR efficiency. After establishing these, the selected variables were then used to characterize some kinetic parameters, from metals migration during EDR, using a biregressional design. Cd, Cr, Cu, Ca and Zn migration velocity and acceleration to the electrodes (anode and cathode) were then considered. Cd and Cu migration to the cathode were found to be significantly influenced by "Ash type", "Duration", "Final pH" and "Dissolution".

Trimmed joint regression: a new approach to the joint regression analysis for cultivar relative-performance evaluation.

A new approach to joint regression analysis, entitled Trimmed Joint Regression (TJR), is proposed in which the adjustment of the linear relative-yield pattern of the cultivars is trimmed from the residues which can be attributed to a "specific interaction". The ranking of the residues to the joint regressions for each cultivar, within each trial, is analysed by the Friedman test to ascertain if they belong to the same parental distribution of the population of residues, for the different genotypes. The rejection of the null hypothesis is envisaged as the result of an organized pattern of the residues, due to a "specific interaction", and the genotypes responsible for such interactions are identified. The trimming method consists of the assessment of the linear regressions, after a reassessment of data related with "specific interactions". The increased accuracy which can be achieved is shown in a numerical example where the high repeatability of the method is illustrated by means of a comparison of the estimated yields for 1- and 2-year trials.