The covariety of perfect numerical semigroups with fixed Frobenius number

Let $S$ be a numerical semigroup. We will say that $h\in {\mathbb{N}} \backslash S$ is an {\it isolated gap }of $S$ if $\{h-1,h+1\}\subseteq S.$ A numerical semigroup without isolated gaps is called perfect numerical semigroup. Denote by ${\mathrm m}(S)$ the multiplicity of a numerical semigroup $S$. A covariety is a nonempty family ${\mathscr{C}}$ of numerical semigroups that fulfills the following conditions: there is the minimum of ${\mathscr{C}},$ the intersection of two elements of ${\mathscr{C}}$ is again an element of ${\mathscr{C}}$ and $S\backslash \{{\mathrm m}(S)\}\in {\mathscr{C}}$ for all $S\in {\mathscr{C}}$ such that $S\neq \min({\mathscr{C}}).$ In this work we prove that the set {\mathscr{P}}(F)=\{S\mid S \mbox{ is a perfect numerical}\ \mbox{semigroup with Frobenius number }F\} is a covariety. Also, we describe three algorithms which compute: the set ${\mathscr{P}}(F),$ the maximal elements of ${\mathscr{P}}(F)$ and the elements of ${\mathscr{P}}(F)$ with a given genus. A ${\mathrm{Parf}}$-semigroup (respectively, ${\mathrm{Psat}}$-semigroup) is a perfect numerical semigroup that in addition is an Arf numerical semigroup (respectively, saturated numerical semigroup). We will prove that the sets: {\mathrm{Parf}}(F)=\{S\mid S \mbox{ is a {\mathrm{Parf}}-numerical semigroup with Frobenius number} F\} and {\mathrm{Psat}}(F)=\{S\mid S \mbox{ is a {\mathrm{Psat}}-numerical semigroup with Frobenius number } F\} are covarieties. As a consequence we present some algorithms to compute ${\mathrm{Parf}}(F)$ and ${\mathrm{Psat}}(F)$.Comment: arXiv admin note: text overlap with arXiv:2302.09121, arXiv:2303.12470, arXiv:2305.02070, arXiv:2305.1388

Design Aspects of a Broadband Beam-Reconfigurable Leaky-Wave Antenna

Design aspects of a novel beam-reconfigurable pla-nar series-fed array are addressed to achieve beam steering with frequency tunability over a relatively broad bandwidth. The design is possible thanks to the use of the complementary strip-slot, which is an innovative broadly matched microstrip radiator, and the careful selection of the phase shifter parameters.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A Method for a Fast Evaluation of the Biostimulant Potential of Different Natural Extracts for Promoting Growth or Tolerance against Abiotic Stress

[EN] Under adverse environmental conditions, biostimulants can help crops withstand abiotic stress while increasing productivity. We have designed a sequential system based on two different biological model organisms¿the baker¿s yeast Saccharomyces cerevisiae and the plant Arabidopsis thaliana¿to evaluate the potential as biostimulants of a battery of 11 different natural extracts on a blind-test basis. Firstly, yeast assays consist in a drop test in solid medium, and a BioScreen® test with liquid cultures. The method is completed with two plant assays to assess effects on germination and growth. The designed method provided relevant data on the ability of each extract to promote biomass accumulation under normal conditions and in the presence of abiotic stresses, such as drought, salinity, or cold. Besides, this laboratory-based method allowed to assess the potential toxicity or unsuspected deleterious effect of each extract in a short period of time (six months) with low budget and space requirements. We could also test the effects of the biostimulants during germination, vegetative, and reproductive growth, under normal and stressed conditions. As each product is tested on different organisms at different developmental stages, we could get some preliminary information on the mode of action. This method enables a fast screen of many different products, in order to select potential candidates to be marketed as biostimulants, avoiding long and expensive field tests with previously uncharacterized productsThis study is a part of the research agreement: Estudio de estimulación del crecimiento y protector frente al estrés abiótico de diferentes formulaciones en levadura, Arabidopsis y tomate funded by Agrométodos SA.Saporta Bon, R.; Bou, C.; Frías, V.; Mulet, JM. (2019). A Method for a Fast Evaluation of the Biostimulant Potential of Different Natural Extracts for Promoting Growth or Tolerance against Abiotic Stress. Agronomy. 9(3):1-16. https://doi.org/10.3390/agronomy9030143S1169

Diseño de nuevas matrices cementantes basadas en residuos de construcción y demolición

En este trabajo se va a estudiar la posible reutilización de los residuos de construcción y demolición (RCD) centrando especial atención en su empleo como adición activa al cemento. Los residuos son recogidos de diversas plantas de gestión españolas de distintas localizaciones. Es importante conocer las características de estos residuos y de esta manera conocer su comportamiento como adición en el cemento. Estas características van a depender del material original, del tratamiento en la planta de gestión y también de la posibilidad de que contenga productos indeseables como pintura, mortero, grasa u otros. Este estudio muestra la caracterización de los residuos recogidos, desde el punto de vista químico, mineralógico y su actividad puzolánica, así como la caracterización de las mezclas obtenidas por la sustitución del cemento por el residuo en porcentajes determinados. Los resultados revelan un buen comportamiento y una composición similar a otros residuos que normalmente son usados como adiciones activas en los cementos

Recursos fitogenéticos: bases para un futuro resiliente al clima y libre de hambre en el Caribe

En toda la región Caribe, el cambio climático no solamente planteará desafíos sino también una amplia gama de oportunidades, que ofrecen mayor importancia a la riqueza de recursos fitogenéticos de la región. Materializar el potencial de estos recursos para contribuir a garantizar la seguridad alimentaria y crear sistemas agrícolas más resilientes frente al cambio climático requerirá de una mayor cooperación regional. Los objetivos centrales de esta cooperación deberán ser: desarrollar intervenciones oportunas en las fronteras nacionales que mejoren la colecta, conservación y el intercambio de los recursos fitogenéticos