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We examine a result of Basor and Ehrhardt concerning Hankel and Toeplitz plus Hankel matrices, within the context of the Riordan group of lower-triangular matrices. This allows us to determine the LDU decomposition of certain symmetric Toeplitz plus Hankel matrices. We also determine the generating functions and Hankel transforms of associated sequences.

This study investigated how repeated applications of different types of anaerobic digestates and undigested cattle slurry affected the growth responses and nutritional aspects of ryegrass swards (Lolium perenne L.) and soil nutrient concentrations, in a twoseason field trial. The treatments included four different types of anaerobic digestate, undigested cattle slurry, nitrogen control (Ncontrol) with calcium ammonium nitrate (CAN) and a no fertiliser control, distributed in a randomised block design with three replicates. The different types of biofertilisers drove a comparable average forage daily growth rate varying between 65 and 79 kg ha −1 day −1 (p > 0.05). Crude protein and neutral or acid detergent fibre of the forage were not influenced by any type of biofertiliser (p > 0.05). Most of the anaerobic digestates led to increases in the level of soil available P and K (p < 0.05). Despite the detectable influence of the levels of NPK in the biofertilisers on the plant growth responses, different anaerobic digestates when applied using the same dry matter amounts can drive comparable forage grass growth responses with low influence over the nutritional quality of the ryegrass forage. Repeated applications of anaerobic digestates can help to increase or reduce the losses of the soil available P and K. The application of anaerobic digestate, cattle slurry and calcium ammonium nitrate led to increases in the N content of the soil; however, there were no differences between them, despite their considerable differences in terms of N inputs. This might be linked to the volatility and losses of the readily available N from the biofertilisers applied.

We present properties of the group structure of Riordan arrays. We examine similar properties among known Riordan subgroups, and from this, we define H [r , s, p], a family of Riordan arrays. We generalize conditions for involutions, and pseudoinvolutions of H [r , s, p], and we present stabilizers of this family. We find abelian subgroups as intersections of Riordan subgroups and show some alternative semidirect products of the Riordan group.

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