A characterization of some families of Cohen--Macaulay, Gorenstein and/or Buchsbaum rings

We provide algorithmic methods to check the Cohen--Macaulayness, Buchsbaumness and/or Gorensteiness of some families of semigroup rings that are constructed from the dilation of bounded convex polyhedrons of $\R^3_{\geq}$. Some families of semigroup rings are given satifying these properties

Union of Sets of Lengths of Numerical Semigroups

Let S = be a numerical semigroup, let s is an element of S and let Z(s) be its set of factorizations. The set of lengths is denoted by L(s) = {L(x(1), ... , x(p)) vertical bar (x(1), ... , x(p)) is an element of Z(s)}, where L(x(1), ... , x(p)) = x(1) + ... + x(p). The following sets can then be defined: W(n) = {s is an element of S vertical bar there exists x is an element of Z(s) such that L(x) = n}, nu(n) = boolean OR(s is an element of W(n)) L(s) = {l(1) P(N) is almost periodic with period lcm(a(1), a(p))

An extension of Wilf's conjecture to affine semigroups

Producción CientíficaLet C ⊂ Qp be a rational cone. An affine semigroup S ⊂ C is a C-semigroup whenever (C \ S) ∩ Np has only a finite number of elements. In this work, we study the tree of C-semigroups, give a method to generate it and study their subsemigroups with minimal embedding dimension. We extend Wilf’s conjecture for numerical semigroups to C- semigroups and give some families of C-semigroups fulfilling the extended conjecture. We also check that other conjectures on numerical semigroups seem to be also satisfied by C-semigroups

Tourist activity on the coast of the Region of Murcia (Southeast of Spain): brief considerations on its recent evolution and current state

La fachada mediterránea ha constituido, históricamente, un espacio de referencia turística a escala nacional e internacional. Entre las delimitaciones administrativas localizadas en esta franja litoral, la Región de Murcia ha quedado estancada respecto al resto. Este estudio pretende analizar el proceso, evolución y causas que han llevado a esta región a quedar descolgada del desarrollo turístico llevado a cabo por las comunidades y provincias litorales mediterráneas. Asimismo, se analiza el contraste entre las diferentes áreas turísticas regionales, intentando conocer los espacios de mayor pujanza y las razones que han llevado a dicha situación. La metodología empleada es de tipo cuantitativa, utilizando los datos estadísticos oficiales aportados por la Comunidad Autónoma de la Región de Murcia y el Instituto Nacional de Estadística (INE). Los principales resultados de la investigación evidencian el atraso turístico de la Región de Murcia, así como las dilatadas desigualdades existentes entre los municipios costeros que la integran.The Mediterranean coastal front has traditionally been a focus of tourism on a national and inter‐ national scale. With regards to the administrative delimitations of the coastline, the situation in the Region of Murcia has been long stagnant, resulting in slower and more unequal processes of modernisation than in other similar regions of Spain. This study is directed at analysing the processes, evolution and causes for this relative divorce between Murcia and the rest of the Mediterranean coastal communities and provinces. A comparison and contrast is made of the various different regional tourist areas in an attempt to ascertain areas of greater strength and the reasons that have led to these being so. The methodology used is quantitative, using the of‐ ficial statistics provided by the Autonomous Community of the Region of Murcia and the National Institute of Statistics. The main results of this research underline how the Region of Murcia lags behind the rest in terms of tourism, as well as the broad‐ranging inequalities existing between the Murcian coastal municipalities

The Buchweitz Set of a Numerical Semigroup

Let A subset of Z be a finite subset. We denote by B(A) the set of all integers n >= 2 such that |nA|>(2n-1)(|A|-1), where nA=A+middotmiddotmiddot+A denotes the n-fold sumset of A. The motivation to consider B(A)stems from Buchweitz's discovery in 1980 that if a numerical semigroup S subset of N is a Weierstrass semigroup, then B(N\S)= empty set . By constructing instances where this condition fails, Buchweitz disproved a longstanding conjecture by Hurwitz (Math Ann 41:403-442, 1893). In this paper, we prove that for any numerical semigroup S subset of N of genus g >= 2, the set B(N\S) is finite, of unbounded cardinality as S varies

On reducible non-Weierstrass semigroups

Weierstrass semigroups are well known along the literature. We present a new family of non- Weierstrass semigroups which can be written as an intersection of Weierstrass semigroups. In addition, we provide methods for computing non-Weierstrass semigroups with genus as large as desired.Funding information: Part of this paper was written during a visit of Fernando Torres to the Universidad de Cadiz (Spain) ; his visit was partially supported by Ayudas para Estancias Cortas de Investigadores (EST2018-R0, Programa de Fomento e Impulso de la Investigacion y la Transferencia en la Universidad de Cadiz) . Fernando Torres was partially supported by CNPq/Brazil (Grant 310623/2017-0) . Juan Ignacio Garcia-Garcia, Daniel Marin-Aragon, and Alberto Vigneron-Tenorio were partially supported by Junta de Andalucia research groups FQM-343 and FQM-366, and by the project MTM2017-84890-P (MINECO/FEDER, UE)

Potential of applying adaptive strategies in buildings to reduce the severity of fuel poverty according to the climate zone and climate change: The case of Andalusia

The reduction of fuel poverty is among the major challenges of countries, policymakers, stakeholders, and researchers. Many contributions have today emerged; however, two aspects should be widely considered. On the one hand, the use of strategies based on the reduction of energy consumption through the adaptive approach, and on the other hand, the impact of climate change on fuel poverty, particularly considering the recent representative concentration pathways (RCP). This paper addresses both issues in Andalusia, which is among the regions with the highest population ratio under poverty risk. For this purpose, 4 zones with possibilities of applying adaptive strategies were distinguished in the Andalusian geography, and 3 climate change scenarios (RCP 2.6, RCP 4.5, and RCP 8.5) were projected in each decade (from 2030 to 2100). A total of 6,528 cases of representative social housing, simulated in all scenarios, were parametrically studied. All data were assessed from the point of view of fuel poverty risk. The results showed that the adaptive strategies influence the reduction of fuel poverty, both in annual and monthly values. Moreover, the increase in fuel poverty cases because of global warming could be reduced by this approach in the four zones detected in Andalusia

Temperature Inversions due to warm air advections at low levels in the Vega Media del Segura river (Region of Murcia)

En el Sureste peninsular son frecuentes las situaciones anticiclónicas alimentadas en invierno por la dorsal subtropical marítima. Bajo estas condiciones, las cuencas y valles fluviales intrabéticos son bastante proclives al desarrollo de inversiones térmicas. Un claro ejemplo lo constituye la Vega Media del Segura en los meses de invierno, especialmente cuando el enfriamiento nocturno del suelo aparece acompañado por movimientos de aire anticiclónico subsidente, advecciones cálidas de componente SO a niveles bajos atmosféricos y flujos fríos catabáticos procedentes de la Sierra de Carrascoy. En el presente artículo se analizan tales factores y las situaciones de inversión térmica más importantes registradas en esta Vega durante el período 2000-2011. Para ello se han utilizado los datos de las estaciones meteorológicas y de los sondeos aerológicos disponibles en el área, en particular los relativos a régimen de temperaturas, estratificación térmica vertical e indicadores de estabilidad atmosférica.Anticyclonic situations fed by the maritime subtropical dorsal in winter are frequent in the South-east Spain. Under these conditions, the intrabaetic depressions and fluvial valleys are prone to thermal inversions. A clear example is the Middle Valley of the Segura River during winter months, especially when cooling at night appears to be accompanied by anticyclonic subsident air, warm advection SW flows at low atmospheric levels and cold katabatic winds proceeding from Sierra de Carrascoy. Such factors and the most temperature inversion situations registered in the study area during the period 2000-2011 are analyzed in this work. For this purpose data of meteorological stations and aerological soundings (e.g. temperature regime, vertical thermal stratification, indicators of atmospheric stability) were used

The extractive fishing activity in Murcia Region (Spain) 1987-2020

La pesca extractiva es una actividad con gran tradición en las zonas litorales de España desde que el ser humano las ha ido ocupando a lo largo de la historia. Desde la incorporación de España a la Comunidad Económica Europea, en 1986, este sector ha vivido transformaciones de gran relevancia. Este estudio tiene como objetivo analizar el sector pesquero de captura en la Región de Murcia desde 1987 hasta la actualidad. Para ello se ha recopilado y tratado la información estadística básica: censo de barcos, trabajadores empleados, o cantidad y valor de la pesca desembarcada. Los resultados reflejan una regresión en el número de embarcaciones y de empleados en el sector, mientras que el volumen y precio de las capturas presentan fluctuaciones interanuales, como consecuencia de la reestructuración de la flota pesquera, y una tendencia al alza del valor de las capturas. Conviene destacar la idoneidad de llevar a cabo análisis similares en otros territorios con el fin de conocer la situación actual de la pesca en España.Extractive fishing is an activity with a long tradition in the coastal areas of Spain dating back to the first human settlements that arose there. Since the incorporation of Spain into the European Economic Community in 1986, this sector has undergone highly relevant transformations. This study seeks to analyze the capture fisheries sector in the Region of Murcia from 1987 to the present day. To do this, basic statistical information has been compiled: census of boats, workers employed, or quantity and value of landed fish. The results reflect a regression in the number of boats and employees in the sector, while the volume and price of catches show year-on-year fluctuations, as a result of the restructuring of the fleet, and an upward trend in the value of catches. It is worth highlighting the advisability of carrying out similar analyses in other territories in order to determine the current situation of fishing in Spain