Square-free class sizes in products of groups

We obtain some structural properties of a factorised group $G = AB$, given that the conjugacy class sizes of certain elements in $A\cup B$ are not divisible by $p^2$, for some prime $p$. The case when $G = AB$ is a mutually permutable product is especially considered

Matrices similar to centrosymmetric matrices

In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices. Furthermore, we give conditions for a matrix to be similar to a matrix which has a centrosymmetric principal submatrix, and conditions under which a matrix can be dilated to a matrix similar to a centrosymmetric matrix.Comment: 15 page

The numerical range of some periodic tridiagonal operators is the convex hull of the numerical ranges of two finite matrices

In this paper we prove a conjecture stated by the first two authors in \cite{IM} establishing the closure of the numerical range of a certain class of $n+1$-periodic tridiagonal operators as the convex hull of the numerical ranges of two tridiagonal $(n+1) \times (n+1)$ matrices. Furthermore, when $n+1$ is odd, we show that the size of such matrices simplifies to $\frac{n}{2}+1$

The numerical range of periodic banded Toeplitz operators

We prove that the closure of the numerical range of a $(n+1)$-periodic and $(2m+1)$-banded Toeplitz operator can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. In contrast to the periodic $3$-banded (or tridiagonal) case, we show an example of a $2$-periodic and $5$-banded Toeplitz operator such that the closure of its numerical range is not equal to the numerical range of a single finite matrix.Comment: 17 pages, 1 figur

Projection based ensemble learning for ordinal regression

The classification of patterns into naturally ordered labels is referred to as ordinal regression. This paper proposes an ensemble methodology specifically adapted to this type of problems, which is based on computing different classification tasks through the formulation of different order hypotheses. Every single model is trained in order to distinguish between one given class (k) and all the remaining ones, but grouping them in those classes with a rank lower than k, and those with a rank higher than k. Therefore, it can be considered as a reformulation of the well-known one-versus-all scheme. The base algorithm for the ensemble could be any threshold (or even probabilistic) method, such as the ones selected in this paper: kernel discriminant analysis, support vector machines and logistic regression (all reformulated to deal with ordinal regression problems). The method is seen to be competitive when compared with other state-of-the-art methodologies (both ordinal and nominal), by using six measures and a total of fifteen ordinal datasets. Furthermore, an additional set of experiments is used to study the potential scalability and interpretability of the proposed method when using logistic regression as base methodology for the ensemble

Evaluation of Citriculture Mechanisation Level in Valencia Region (Spain): Poll Results

[EN] The increase of the technology level of citrus production operations is required to improve production profitability and reduce production costs. In the framework of the project CITRUSTECH ("Technological advances for modernisation and sustainability in citrus production"), three different poll questionnaires were developed and conducted in the Valencia region to assess the citriculture mechanisation level. In total, 142 questionaries for small and medium-size plantations, 32 for cooperative technicians and 16 for large-size plantations were conducted. From a socioeconomic point of view, clear age and sex inequalities were found. From the technological point of view, relevant differences were found between plantation sizes. The role of the cooperative mechanisation services (custom cost) and other customer services was revealed, with a higher percentage of the area under cultivation at the expense of the small-size plantations. The use of some manual tools was confirmed in pruning, even in large-size orchards. In small-size orchards, the use of backpack sprayers was verified. Regarding farm machinery, besides tractors, hydro-pneumatic sprayers and agricultural shredders were employed. No farm machinery was used during harvesting operations, apart from transport equipment, due to the reduced plantation frames.This research has been funded by the European Agricultural Fund for Rural Development and cofounded by the Ministerio de Agricultura, Pesca y Alimentacion (project GO "Avances tecnologicos para la modernizacion y la sostenibilidad en la produccion de citricos CITRUSTECH").Ortiz Sánchez, MC.; Torregrosa, A.; Martínez, JM. (2022). Evaluation of Citriculture Mechanisation Level in Valencia Region (Spain): Poll Results. Agronomy. 12(6):1-6. https://doi.org/10.3390/agronomy120613661612