Computation of Spatial Covariance Matrices

In an earlier article, Ghosh derived the density for the distance between two points uniformly and independently distributed in a rectangle. This article extends that work to include the case where the two points lie in two different rectangles in a lattice. This density allows one to find the expected value of certain functions of this distance between rectangles analytically or by one-dimensional numerical integration.

In the case of isotropic spatial models or spatial models with geometric anisotropy terms for agricultural experiments one can use these theoretical results to compute the covariance between the yields in different rectangular plots. As the numerical integration is one-dimensional these results are computed quickly and accurately. The types of covariance functions used come from the Matérn and power families of processes. Analytic results are derived for the de Wijs process, a member of both families and for the power models also.

Software in R is available. Examples of the code are given for fitting spatial models to the Fairfield Smith data. Other methods for the estimation of the covariance matrices are discussed and their pros and cons are outlined.     

A simple zero length surface-modification approach for preparing novel bifunctional supports for co-immobilisation studies

A straightforward method of creating a bifunctional support possessing pre-defined ratios of amine and chloromethyl groups based upon a controlled conversion of standard Merrifield resin is presented. It avoids the extensive optimisation of reactant concentrations and reaction conditions required by existing methods. Furthermore, it avoids increases in the spacer/linker length that lead to detrimental reductions in the rigidity of the grafted layer. The method will allow for efficient, predictable and reproducible co-immobilisation of molecular species.     

铈铝复合载体对钼基催化剂耐硫甲烷化催化性能的研究

采用共沉淀法、浸渍法和沉积沉淀法制备了CeO₂-Al₂O₃复合载体,比较了不同复合载体浸渍钴钼后的耐硫甲烷化催化性能,并优化了复合载体中CeO₂的含量。结合N₂物理吸附、XRD、H₂-TPR等表征手段对复合载体及其负载的钴钼催化剂进行物相和结构分析发现,在Al₂O₃中添加CeO₂可以明显提高合成气的耐硫甲烷化活性,其中,沉积沉淀法制备的25% CeO₂-Al₂O₃复合载体负载钴钼后具有最佳催化活性。     

Prediction of thermal conductivity of polymer-based composites by using support vector regression

Support vector regression (SVR) combined with particle swarm optimization (PSO) for its parameter optimization, was proposed to establish a model to predict the thermal conductivity of polymer-based composites under different mass fractions of fillers (mass fraction of polyethylene (PE) and mass fraction of polystyrene (PS)). The prediction performance of SVR was compared with those of other two theoretical models of spherical packing and flake packing. The result demonstrated that the estimated errors by l...     

Relations between the convexity of a set and the differentiability of its support function

It is known that, in finite dimensions, the support function of a compact convex set with nonempty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper, we realize a thorough study of the relations between the differentiability of the support function on the interior of its domain and the convexity of the set, mainly for unbounded sets. Then, we revisit some results related to the differentiability of the cost function associated to a production function.     

Investigating students' levels of engagement with mathematics: critical events,motivations, and influences on behaviour

Universities invest significant resources in the provision of mathematics tuition to first year students, through both traditional and non-traditional means. Research has shown that a significant minority of students do not engage with these resources appropriately. This paper presents findings from a study of two groups of students at Maynooth University. Both groups had similar mathematical backgrounds on entry to university. The first group consisted of seven students who had failed first year mathematics and had very low levels of engagement with available supports. The second group consisted of nine students who had passed first year mathematics and had engaged with the supports to a significant extent. It emerged that while both groups initially displayed similar tactics and encountered similar difficulties, their levels of reaction to a number of critical events in their mathematical education were key to their engagement levels and their subsequent progression. Further analysis revealed aspects of the students' behaviour which caused them to approach or avoid difficulties. The reasons behind the different student behaviours were investigated, and the main categories of influence on student behaviour which emerged from the interview data were fear, social factors, and motivation.     

Ultrasonically induced ZnO–biosilica nanocomposite for degradation of a textile dye in aqueous phase

In the present study, a porous clay-like support with unique characteristics was used for the synthesis and immobilization of ZnO nanostructures to be used as sonocatalyst for the sonocatalytic decolorization of methylene blue (MB) dye in the aqueous phase. As a result, the sonocatalytic activity of ZnO–biosilica nanocomposite (77.8%) was higher than that of pure ZnO nanostructures (53.6%). Increasing the initial pH from 3 to 10 led to increasing the color removal from 41.8% to 88.2%, respectively. Increasing the sonocatalyst dosage from 0.5 to 2.5 g/L resulted in increasing the color removal, while further increase up to 3 g/L caused an obvious drop in the color removal. The sonocatalysis of MB dye over ZnO–biosilica nanocomposite was temperature-dependent. The presence of methanol produced the most adverse effect on the sonocatalysis of MB dye. The addition of chloride and carbonate ions had a negligible effect on the sonocatalysis, while the addition of persulfate ion led to increasing the color removal from 77.8% to 99.4% during 90 min. The reusability test exhibited a 15% drop in the color removal (%) within three consecutive experimental runs. A mineralization efficiency of 63.2% was obtained within 4 h.     

An in silico expert system for the identification of eye irritants

This report describes development of an in silico, expert rule-based method for the classification of chemicals into irritants or non-irritants to eye, as defined by the Draize test. This method was developed to screen data-poor cosmetic ingredient chemicals for eye irritancy potential, which is based upon exclusion rules of five physicochemical properties – molecular weight (MW), hydrophobicity (log P), number of hydrogen bond donors (HBD), number of hydrogen bond acceptors (HBA) and polarizability (Pol). These rules were developed using the ADMET Predictor software and a dataset of 917 eye irritant chemicals. The dataset was divided into 826 (90%) chemicals used for training set and 91 (10%) chemicals used for external validation set (every 10th chemical sorted by molecular weight). The sensitivity of these rules for the training and validation sets was 72.3% and 71.4%, respectively. These rules were also validated for their specificity using an external validation set of 2011 non-irritant chemicals to the eye. The specificity for this validation set was revealed as 77.3%. This method facilitates rapid screening and prioritization of data poor chemicals that are unlikely to be tested for eye irritancy in the Draize test.