Bivariate second--order linear partial differential equations and orthogonal polynomial solutions

In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially self--adjoint and of hypergeometric type. General formulae for all these properties are obtained explicitly in terms of the polynomial coefficients of the partial differential equation, using vector matrix notation. Moreover, Rodrigues representations for the polynomial eigensolutions and for their partial derivatives of any order are given. Finally, as illustration, these results are applied to specific Appell and Koornwinder orthogonal polynomials, solutions of the same partial differential equation.Comment: 27 page

Fourth-order differential equations satisfied by the generalized co-recursive of all classical orthogonal polynomials. A study of their distribution of zeros

AbstractThe unique fourth-order differential equation satisfied by the generalized co-recursive of all classical orthogonal polynomials is given for any (but fixed) level of recursivity. Up to now, these differential equations were known only for each classical family separately and also for a specific recursivity level. Moreover, we use this unique fourth-order differential equation in order to study the distribution of zeros of these polynomials via their Newton sum rules (i.e., the sums of powers of their zeros) which are closely related with the moments of such distribution. Both results are obtained with the help of two programs built in Mathematica symbolic language

Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Discrete case

AbstractWe present a simple approach in order to compute recursively the connection coefficients between two families of classical (discrete) orthogonal polynomials (Charlier, Meixner, Kravchuk, Hahn), i.e., the coefficients Cm(n) in the expression Pn(X)=∑nm=0Cm(n)Qm(x), where Pn(x) and Qm(x) belong to the aforementioned class of polynomials. This is SCV2 done by adapting a general and systematic algorithm, recently developed by the authors, to the discrete classical situation. Moreover, extensions of this method allow to give new addition formulae and to estimate Cm(n)-asymptotics in limit relations between some families

Connection problems for polynomial solutions of nonhomogeneous differential and difference equations

AbstractWe consider nonhomogeneous hypergeometric-type differential, difference and q-difference equations whose nonhomogeneity is a polynomial qn(x). The polynomial solution of these problems is expanded in the ∗ Qn(x)∗ basis, and also in a basis ∗Pn(x)∗, related in a natural way with the homogeneous hypergeometric equation. We give an algorithm building a recurrence relation for the expansion coefficients in both bases that we solve explicitly in many cases involving classical orthogonal polynomials. Finally, some concrete applications and extensions are given

Characterisation of thermo-hygrometric conditions of an archaeological site affected by unlike boundary weather conditions

This paper applies statistical techniques to analyse microclimatic data (temperature and relative humidity) recorded at the archaeological site of Plaza de l'Almoina (Valencia, Spain). This study has allowed us to quantify the effect of certain measures that were adopted for preventive conservation. The first monitoring campaign took place in 2010 at this archaeological site, showing harmful effects on the conservation state of the remains due to the presence of a skylight that partly covers the remains and causes a greenhouse effect. This skylight was covered with a water layer to prevent overheating of this archaeological site. However, this layer was removed in 2013 due to water leaks, and the indoor conditions changed. Over the summer, a temporary canvas was installed over the skylight to avoid heating of the archaeological site below by preventing the incidence of direct sunlight. The main importance of this work was to characterise the effect of unlike boundary weather conditions of different years in the indoor microclimate of the archaeological site, and to study the effect of the new boundary situation. This paper shows that the removal of water from the skylight caused a temperature increase inside the museum; meanwhile, the subsequent installation of the canvas cover allows appropriate daily cycles of temperature and relative humidity, especially in areas under the skylight. This work also shows that the replacement of a water ditch near the archaeological site by a PVC pipe was also detected by the sensors due to the difference in water vapour pressure.This work was partially supported by the Spanish Government (Ministerio de Ciencia e Innovacion) with grants numbers HAR2010-21944-C02-01 and HAR2010-21944-C02-02. The authors thank the personal collaboration of the archaeologist Albert Ribera and Carmen Perez.Merello Gimenez, P.; Fernández Navajas, A.; Curiel Esparza, J.; Zarzo Castelló, M.; García Diego, FJ. (2014). Characterisation of thermo-hygrometric conditions of an archaeological site affected by unlike boundary weather conditions. Building and Environment. 76:125-133. doi:10.1016/j.buildenv.2014.03.009S1251337

The influence of road networks on brown bear spatial distribution and habitat suitability in a human-modified landscape

Roads are human infrastructure that heavily affect wildlife, often with marked impacts on carnivores, including brown bears Ursus arctos. Here, we assessed the potential impact of road networks on the distribution of brown bears in the small, isolated and endangered Cantabrian population of north-western Spain. To ascertain whether local road networks affect brown bear spatial distribution, we first assessed potential influences on the distance of bear locations to roads using candidate models which included topographic variables, landcover types, bear age and reproductive status, traffic volume and road visibility. Then, we built two sets of habitat suitability models, both with and without roads, to discern the possible loss of habitat suitability caused by roads. The mean distance of bear locations to the nearest road was 968 804 m and the closest road was a low traffic road in 72.5% of cases. Candidate models showed little influence of our variables on bear distance to the nearest road, with the exception of elevation. Habitat suitability models revealed that road networks in our study area seem to have almost no effect on brown bear habitat suitability, except for females with yearlings during the denning season. However, this result may also be a consequence of the fact that only a small proportion (16.5%) of the cells classified as suitable bear habitats were crossed by roads, that is, most of the roads are primarily located in unsuitable bear habitats in the Cantabrian Mountains. Compared to previous studies conducted in other populations, mainly North American ones, our findings might suggest a different response of Eurasian brown bears to roads due to a longer bear-human coexistence in Europe versus North America. However, the indirect approach used in our study does not exclude other detrimental effects, for example, road mortality, increased stress and movement pattern disruption, only detectable by more direct approaches such as telemetry

The influence of road networks on brown bear spatial distribution and habitat suitability in a human-modified landscape

Roads are human infrastructure that heavily affect wildlife, often with marked impacts on carnivores, including brown bears Ursus arctos. Here, we assessed the potential impact of road networks on the distribution of brown bears in the small, isolated and endangered Cantabrian population of north-western Spain. To ascertain whether local road networks affect brown bear spatial distribution, we first assessed potential influences on the distance of bear locations to roads using candidate models which included topographic variables, landcover types, bear age and reproductive status, traffic volume and road visibility. Then, we built two sets of habitat suitability models, both with and without roads, to discern the possible loss of habitat suitability caused by roads. The mean distance of bear locations to the nearest road was 968 ± 804 m and the closest road was a low traffic road in 72.5% of cases. Candidate models showed little influence of our variables on bear distance to the nearest road, with the exception of elevation. Habitat suitability models revealed that road networks in our study area seem to have almost no effect on brown bear habitat suitability, except for females with yearlings during the denning season. However, this result may also be a consequence of the fact that only a small proportion (16.5%) of the cells classified as suitable bear habitats were crossed by roads, that is, most of the roads are primarily located in unsuitable bear habitats in the Cantabrian Mountains. Compared to previous studies conducted in other populations, mainly North American ones, our findings might suggest a different response of Eurasian brown bears to roads due to a longer bear-human coexistence in Europe versus North America. However, the indirect approach used in our study does not exclude other detrimental effects, for example, road mortality, increased stress and movement pattern disruption, only detectable by more direct approaches such as telemetry.During this research, EG-B was financially supported by a FPU grant (FPU15-03429) from the Spanish Ministry of Science, Innovation and Universities. VP, EG-B, AMG and HRV were financially supported by the I + D + I Project PID2020-114181GB-I00 financed by the Spanish Ministry of Science and Innovation, the Agencia Estatal de Investigación (AEI) and the Fondo Europeo de Desarrollo Regional (FEDER, EU). AMG was supported by the Predoctoral Fellowship PRE2018-086102. AZA was financially supported by a Margarita Salas contract financed by the European Union-NextGenerationEU, Ministerio de Universidades y Plan de Recuperación, Transformación y Resiliencia, through the call of the Universidad de Oviedo (Asturias).Peer reviewe

Rubbing behavior of European brown bears: factors affecting rub tree selectivity and density

Scent-mediated communication is considered the principal communication channel in many mammal species. Compared with visual and vocal communication, odors persist for a longer time, enabling individuals to interact without being in the same place at the same time. The brown bear (Ursus arctos), like other mammals, carries out chemical communication, for example, by means of scents deposited on marking (or rub) trees. In this study, we assessed rub tree selectivity of the brown bear in the predominantly deciduous forests of the Cantabrian Mountains (NW Spain). We first compared the characteristics of 101 brown bear rub trees with 263 control trees. We then analyzed the potential factors affecting the density of rub trees along 35 survey routes along footpaths. We hypothesized that: (1) bears would select particular trees, or tree species, with characteristics that make them more conspicuous; and (2) that bears would select trees located in areas with the highest presence of conspecifics, depending on the population density or the position of the trees within the species’ range. We used linear models and generalized additive models to test these hypotheses. Our results showed that brown bears generally selected more conspicuous trees with a preference for birches (Betula spp.). This choice may facilitate the marking and/ or detection of chemical signals and, therefore, the effectiveness of intraspecific communication. Conversely, the abundance of rub trees along footpaths did not seem to depend on the density of bear observations or their relative position within the population center or its border. Our results suggest that Cantabrian brown bears select trees based on their individual characteristics and their location, with no influence of characteristics of the bear population itself. Our findings can be used to locate target trees that could help in population monitoring

Evaluation of corrective measures implemented for the preventive conservation of fresco paintings in Ariadne s house (Pompeii, Italy)

BACKGROUND: A microclimate monitoring study was conducted in 2008 aimed at assessing the conservation risks affecting the valuable wall paintings decorating Ariadne s House (Pompeii, Italy). It was found that thermohygrometric conditions were very unfavorable for the conservation of frescoes. As a result, it was decided to implement corrective measures, and the transparent polycarbonate sheets covering three rooms (one of them delimited by four walls and the others composed of three walls) were replaced by opaque roofs. In order to examine the effectiveness of this measure, the same monitoring system comprised by 26 thermohygrometric probes was installed again in summer 2010. Data recorded in 2008 and 2010 were compared. RESULTS: Microclimate conditions were also monitored in a control room with the same roof in both years. The average temperature in this room was lower in 2010, and it was decided to consider a time frame of 18 summer days with the same mean temperature in both years. In the rooms with three walls, the statistical analysis revealed that the diurnal maximum temperature decreased about 3.5 ºC due to the roof change, and the minimum temperature increased 0.5 ºC. As a result, the daily thermohygrometric variations resulted less pronounced in 2010, with a reduction of approximately 4 ºC, which is favorable for the preservation of mural paintings. In the room with four walls, the daily fluctuations also decreased about 4 ºC. Based on the results, other alternative actions are discussed aimed at improving the conservation conditions of wall paintings. CONCLUSIONS: The roof change has reduced the most unfavorable thermohygrometric conditions affecting the mural paintings, but additional actions should be adopted for a long term preservation of Pompeian frescoes.This work was partially supported by the Spanish Government (Ministerio de Ciencia e Innovacion) under projects HAR2010-21944-C02-01 and HAR2010-21944-C02-02.Merello Giménez, P.; García Diego, FJ.; Zarzo Castelló, M. (2013). Evaluation of corrective measures implemented for the preventive conservation of fresco paintings in Ariadne s house (Pompeii, Italy). Chemistry Central Journal. 7(1):87-87. doi:10.1186/1752-153X-7-87S878771DELOSRIOS, A., CAMARA, B., GARCIADELCURA, M., RICO, V., GALVAN, V., & ASCASO, C. (2009). Deteriorating effects of lichen and microbial colonization of carbonate building rocks in the Romanesque churches of Segovia (Spain). Science of The Total Environment, 407(3), 1123-1134. doi:10.1016/j.scitotenv.2008.09.042Nava, S., Becherini, F., Bernardi, A., Bonazza, A., Chiari, M., García-Orellana, I., … Vecchi, R. (2010). An integrated approach to assess air pollution threats to cultural heritage in a semi-confined environment: The case study of Michelozzo’s Courtyard in Florence (Italy). Science of The Total Environment, 408(6), 1403-1413. doi:10.1016/j.scitotenv.2009.07.03

Microclimate monitoring of Ariadne's house (Pompeii, Italy) for preventive conservation of fresco paintings

Background: Ariadne's house, located at the city center of ancient Pompeii, is of great archaeological value due to the fresco paintings decorating several rooms. In order to assess the risks for long-term conservation affecting the valuable mural paintings, 26 temperature data-loggers and 26 relative humidity data-loggers were located in four rooms of the house for the monitoring of ambient conditions. Results: Data recorded during 372 days were analyzed by means of graphical descriptive methods and analysis of variance (ANOVA). Results revealed an effect of the roof type and number of walls of the room. Excessive temperatures were observed during the summer in rooms covered with transparent roofs, and corrective actions were taken. Moreover, higher humidity values were recorded by sensors on the floor level. Conclusions: The present work provides guidelines about the type, number, calibration and position of thermohygrometric sensors recommended for the microclimate monitoring of mural paintings in outdoor or semi-confined environments. © 2012 Merello et al.; licensee Chemistry Central Ltd.This work was partially supported by the Spanish Government (Ministerio de Ciencia e Innovacion) under projects HAR2010-21944-C02-01 and HAR2010-21944-C02-02.Merello Giménez, P.; García Diego, FJ.; Zarzo Castelló, M. (2012). Microclimate monitoring of Ariadne's house (Pompeii, Italy) for preventive conservation of fresco paintings. Chemistry Central Journal. 6:145-161. https://doi.org/10.1186/1752-153X-6-145S1451616Ribera A, Olcina M, Ballester C: Pompeya Bajo Pompeya, las Excavaciones en la Casa de Ariadna. Valencia: Fundación MARQ; 2007.World Monuments Fund: World Monuments Watch: 100 Most Endangered Sites. New York: World Monuments Fund; 1996.Anter KF: Colours in Pompeiian cityscape: Adding pieces to the puzzle. Color Res Appl 2006,31(4):331–340.Harris J: Protecting Pompeii and the Italian heritage in 2012. http://www.i-italy.org/bloggers/18935/protecting-pompeii-and-italian-heritage-2012Augusti S: La Tecnica Dell’antica Pittura Parietale Pompeiana. Napoli: Gaetano Macchiaroli Editore; 1950.Miriello D, Barca D, Bloise A, Ciarallo A, Crisci GM, De Rose T, Gattuso C, Gazineo F, La Russa MF: Characterisation of archaeological mortars from Pompeii (Campania, Italy) and identification of construction phases by compositional data analysis. J Arch Sci 2010, 37:2207–2223.Castriota M, Cosco V, Barone T, De Santo G, Carafa P, Cazzanelli E: Micro-Raman characterizations of Pompei’s mortars. J Raman Spectrosc 2008,39(2):295–301.Maguregui M, Knuutinen U, Castro K, Madariaga JM: Raman spectroscopy as a tool to diagnose the impact and conservation state of Pompeian second and fourth style wall paintings exposed to diverse environments (House of Marcus Lucretius). J Raman Spectrosc 2010,41(11):1400–1409.Genestar C, Pons C, Más A: Analytical characterisation of ancient mortars from the archaeological Roman city of Pollentia (Balearic Islands, Spain). Anal Chim Acta 2006, 557:373–379.Duran A, Perez-Maqueda LA, Poyato J, Perez-Rodriguez JL: A thermal study approach to roman age wall painting mortars. J Therm Anal Calorim 2010,99(3):803–809.Pérez MC, García Diego F-J, Merello P, D’Antoni P, Fernández Navajas A, Ribera Lacomba A, Ferrazza L, Pérez Miralles J, Baró JL, Merce P, D’Antoni H, Curiel Esparza J: Ariadne’s house (Pompeii, Italy) wall paintings: a multidisciplinary study of its present state focused on a future restoration and preventive conservation. Mater Constr in pressBernardi A: Microclimate in the British Museum. London. Museum Manag Curat 1990, 9:169–182.Bernardi A, Camuffo D: Microclimate in the Chiericati Palace Municipal Museum. Vicenza. Museum Manag Curat 1995, 14:5–18.Camuffo D, Bernardi A, Sturaro G, Valentino A: The microclimate inside the Pollaiolo and Botticelli rooms in the Uffizi Gallery. Florence. J Cult Herit 2002, 3:155–161.La Gennusa M, Rizzo G, Scaccianoce G, Nicoletti F: Control of indoor environments in heritage buildings: Experimental measurements in an old Italian museum and proposal of a methodology. J Cult Herit 2005,6(2):147–155.Camuffo D, Sturaro G, Valentino A: Thermodynamic exchanges between the external boundary layer and the indoor microclimate at the Basilica of Santa Maria Maggiore, Rome, Italy: the problem of conservation of ancient works of art. Bound Lay Meteorol 1999, 92:243–262.Tabunschikov Y, Brodatch M: Indoor air climate requirements for Russian churches and cathedrals. Indoor Air 2004,14(Suppl 7):168–174.Loupa G, Charpantidou E, Kioutsioukis I, Rapsomanikis S: Indoor microclimate, ozone and nitrogen oxides in two medieval churches in Cyprus. Atmos Environ 2006, 40:7457–7466.Vuerich E, Malaspina F, Barazutti M, Georgiadis T, Nardino M: Indoor measurements of microclimate variables and ozone in the church of San Vincenzo (Monastery of Bassano Romano – Italy): a pilot study. Microchem J 2008, 88:218–223.García-Diego F-J, Zarzo M: Microclimate monitoring by multivariate statistical control: the renaissance frescoes of the cathedral of valencia (Spain). J Cult Herit 2010,11(3):339–344.Zarzo M, Fernández-Navajas A, García-Diego F-J: Long-term monitoring of fresco paintings in the Cathedral of Valencia (Spain) through humidity and temperature sensors in various locations for preventive conservation. Sensors 2011,11(9):8685–8710.Maekawa S, Lambert F, Meyer J: Environmental monitoring at Tiwanaku. Mater Res Soc Symp Proc 1995, 352:885–892.Lillie M, Smith R, Reed J, Inglis R: Southwest Scottish Crannogs: using in situ studies to assess preservation in wetland archaeological contexts. J Archaeol Sci 2008,35(7):1886–1900.Verdecchia F, Zoccatelli C, Norelli E, Miandro R: Integrated monitoring network for surface deformation in Capo Colonna archaeological area, Crotone. Italy. IAHS-AISH P 2010, 339:345–351.Nava S, Becherini F, Bernardi A, Bonazza A, Chiari M, García-Orellana I, Lucarelli F, Ludwig N, Migliori A, Sabbioni C, Udisti R, Valli G, Vecchi R: An integrated approach to assess air pollution threats to cultural heritage in a semi-confined environment: the case study of Michelozzo’s Courtyard in Florence (Italy). Sci Total Environ 2010,408(6):1403–1413.Hygrochron Temperature/Humidity Logger iButton with 8KB Data-Log Memory. Maxim Integrated Products. http://datasheets.maxim-ic.com/en/ds/DS1923.pdfTemperature Logger iButton with 8KB Data-Log Memory. Maxim Integrated Products. http://datasheets.maxim-ic.com/en/ds/DS1922L-DS1922T.pdfVisco G, Plattner SH, Fortini P, Di Giovanni S, Sammartino MP: Microclimate monitoring in the Carcer Tullianum: temporal and spatial correlation and gradients evidenced by multivariate analysis; first campaign. Chem Cent J 2012,6(Suppl 2):S11.UNI 10829: Works of Art of Historical Importance. Ambient Conditions for the Conservation. Measurement and Analysis. Milano: UNI Ente Nazionale Italiano di Unificazione; 1999.DM 10/2001: Atto di Indirizzo sui Criteri Tecnico-scientifici e Sugli Standard di Funzionamento e Sviluppo dei Musei. Ministero per i Beni e le Attività Culturali. Gazzeta Ufficiale della Repubblica Italiana (Official Bulletin of Italian Republica), Rome (Italy); 2001. DL 112/1998 art. 150 comma 6Camuffo D: Microclimate for Cultural Heritage. Amsterdam: Elsevier Science; 1998.ASTM E 104–02: Standard Practice for Maintaining Constant Relative Humidity by Means of Aqueous Solutions. West Conshohocken, PA: ASTM Intl; 2012.Statgraphics Software. http://www.statgraphics.ne