Two-dimensional integrable generalization of the Camassa-Holm equation

In this letter we discuss the (2 + 1)-dimensional generalization of the Camassa-Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa-Holm equation. First, we find the equation in a perturbative calculation in shallow-water theory. We then demonstrate its integrability and find several particular solutions describing (2 + 1) solitary-wave like solutions. © 1999 Published by Elsevier Science B.V. All rights reserved.

On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Democrazia e cattolicesimo negli Stati Uniti. La libertà di religione e il pensiero di John Courtney Murray

L'elaborato affronta il pensiero di John Courtney Murray dal punto di vista teologico e politico, sottolineandone le influenze esterne ai circoli intellettuali cattolici e la particolare rilevanza per l'integrazione della comunità cattolica nella società statunitense.

Lydia Holm, Rollenbild

Signatur des Originals: S 36/F08853

Geometric Integrability of the Camassa-Holm Equation. II

It is known that the Camassa–Holm (CH) equation describes pseudo-spherical surfaces and that therefore its integrability properties can be studied by geometrical means. In particular, the CH equation admits nonlocal symmetries of “pseudo-potential type”: the standard quadratic pseudo-potential associated with the geodesics of the pseudo-spherical surfaces determined by (generic) solutions to CH, allows us to construct a covering π of the equation manifold of CH on which nonlocal symmetries can be explicitly calculated. In this article, we present the Lie algebra of (first-order) nonlocal π-symmetries for the CH equation, and we show that this algebra contains a semidirect sum of the loop algebra over sl(2,R) and the centerless Virasoro algebra. As applications, we compute explicit solutions, we construct a Darboux transformation for the CH equation, and we recover its recursion operator. We also extend our results to the associated Camassa–Holm equation introduced by J. Schiff.

Promoting mixed stands through conversion treatments. Effect of holm oak coppices thinning on black pine regeneration

The effects of conversion treatments, depending on ecological factors and silvicultural parameters (thinning intensity, thinning type and rotation, among others) have been studied during the last fifteen years in an experimental trial in Central Spain. The general climate is continental Mediterranean; soils are low depth and limy; vegetation is an homogeneous dense coppices of Quercus ilex with isolated Pinus nigra trees. The experimental design (three locations) includes different thinning intensities (from 0 to 100% of extracted basal area). Inventories have been carried out in 1994 and 2010; thinning treatments were done in 1995 and 2011. Analysis of the effects of the conversion treatment show the increment of diameter and height growth rates, the canopy recovery and the stand resprouting, finding differences in these effects between thinning treatments. Besides the induced changes at holm oak stand, the application of conversion treatment clearly changed the woodland dynamics. Fifteen years after the thinnings, floristic composition varied and an abundant pine regeneration was installed in the woodland. In this work we describe the changes between inventories in tree species composition and diameter distribution, specially in the case of black pine. The conversion treatment caused changes in forest dynamics in the short term, increasing biodiversity and diversifying the forest structure. The fast installation of Pinus regeneration suggests the potential of the zone for the establishment of multipurpose mixed Quercus-Pinus stands in wide areas where Quercus species were favoured by human populations for firewood production. Conversion treatment of coppices, with the creation of mixed stands, constitutes a good management alternative for extensive areas and an interesting technique to adaptation to global change.

Implementation of a module for risk of ozone impacts assessment to vegetation in the integrated assessment modelling system for the Iberian peninsula. Evaluation for wheat and holm oak

A module to estimate risks of ozone damage to vegetation has been implemented in the Integrated Assessment Modelling system for the Iberian Peninsula. It was applied to compute three different indexes for wheat and Holm oak; daylight AOT40 (cumulative ozone concentration over 40 ppb), cumulative ozone exposure index according to the Directive 2008/50/EC (AOT40-D) and PODY (Phytotoxic Ozone Dose over a given threshold of Y nmol m−2 s−1). The use of these indexes led to remarkable differences in spatial patterns of relative ozone risks on vegetation. Ozone critical levels were exceeded in most of the modelling domain and soil moisture content was found to have a significant impact on the results. According to the outputs of the model, daylight AOT40 constitutes a more conservative index than the AOT40-D. Additionally, flux-based estimations indicate high risk areas in Portugal for both wheat and Holm oak that are not identified by AOT-based methods.

Spatial distribution of the soil carbon pool in a Holm oak dehesa in Spain

Aims Dehesas are agroforestry systems characterized by scattered trees among pastures, crops and/or fallows. A study at a Spanish dehesa has been carried out to estimate the spatial distribution of the soil organic carbon stock and to assess the influence of the tree cover. Methods The soil organic carbon stock was estimated from the five uppermost cm of themineral soil with high spatial resolution at two plots with different grazing intensities. The Universal Kriging technique was used to assess the spatial distribution of the soil organic carbon stocks, using tree coverage within a buffering area as an auxiliary variable. Results A significant positive correlation between tree presence and soil organic carbon stocks up to distances of around 8 m from the trees was found. The tree crown cover within a buffer up to a distance similar to the crown radius around the point absorbed 30 % of the variance in the model for both grazing intensities, but residual variance showed stronger spatial autocorrelation under regular grazing conditions. Conclusions Tree cover increases soil organic carbon stocks, and can be satisfactorily estimated by means of crown parameters. However, other factors are involved in the spatial pattern of the soil organic carbon distribution. Livestock plays an interactive role together with tree presence in soil organic carbon distribution.

Development of somatic embryogenesis for cloning and conservation of mature holm oak trees (Quercus ilex L.)

La encina (Quercus ilex L.) es una de las especies forestales mediterráneas más importantes. Constituye gran parte del estrato arbóreo de dehesas o montados, produce bellota como alimento del ganado y establece simbiosis con hongos micorrizógenos de gran valor económico. La encina está considerada como una especie recalcitrante en términos de conservación de semillas y capacidad morfogénica, lo que dificulta los programas de conservación de recursos genéticos y la mejora de la especie. La propagación vegetativa es una potente herramienta de los programas de mejora, por lo que es preciso desarrollar protocolos de regeneración somática en encina. La embriogénesis somática está considerada como la modalidad más adecuada de regeneración basada en técnicas de cultivo de tejidos vegetales utilizada en biotecnología forestal. Este trabajo se centra en el estudio de determinados aspectos de la embriogénesis somática para la regeneración clonal de encinas adultas. La memoria de esta tesis se ha dividido en capítulos que se corresponden con diferentes aspectos del sistema embriogénico. La embriogénesis somática se indujo en tegumentos maternos de óvulos en desarrollo procedentes de bellotas inmaduras de encinas adultas. A pesar de las bajas frecuencias de inducción, las líneas embriogénicas generadas se amplificaron mediante embriogénesis secundaria observándose cierta pérdida de la capacidad de diferenciación con el tiempo. Tanto el genotipo como la formulación del medio de cultivo influyeron en la respuesta embriogénica, concluyendo que la formulación de macronutrientes de Schenk y Hildebrant del medio sin reguladores de crecimiento fue la combinación más efectiva en la inducción. Los resultados sugirieron la existencia de una ventana en el desarrollo del óvulo más sensible a la inducción. El genotipo in[luyó en la capacidad proliferativa de los cultivos y en la conversión de los embriones somáticos, que se incrementó suplementando el medio con ácido indol-3-butírico y 6-benciladenina. El cultivo en medio líquido de líneas embriogénicas en condiciones de inmersión transitoria incrementó el crecimiento, dependiendo del genotipo, con respecto al cultivo en medio semisólido. Sin embargo, no mejoró la capacidad de diferenciar embriones cotiledonares aislados. Se estableció un protocolo de inicio y mantenimiento de cultivos en suspensión para varias líneas embriogénicas mediante inoculación en alta densidad de agregados embrionarios procedentes del medio semisólido. Para evitar la pérdida de vigor y la capacidad morfogénica debida al cultivo prolongado se desarrolló un protocolo de crioconservación de líneas embriogénicas mediante vitrificación. Al determinar la influencia de los agentes crioprotectores antes y después de su inmersión en nitrógeno líquido se concluyó que las respuestas de capacidad de crecimiento y de diferenciación del material embriogénico son independientes, además de estar bajo influencia del genotipo y el tipo de material crioconservado. La combinación de sacarosa y PVS2 previa a la inmersión en nitrógeno líquido proporcionó la mayor tasa de recuperación. Cuando las líneas fueron crioconservadas 30 días la capacidad de diferenciación se perdió en todas ellas. El análisis de SSR detectó variación somaclonal en el material crioconservado a corto plazo. SSR y RAPD mostraron importantes diferencias genéticas entre los árboles donantes y el material embriogénico que dependieron del genotipo. El grado de detección dependió del marcador empleado. Ambos marcadores revelaron baja inestabilidad intraclonal. Los RAPD revelaron variación genética intra-individuo en las encinas donantes. Se discuten la variación genética pre-existente en encina, su aparición durante las primeras fases de la inducción de embriogénesis, y la presencia de tejidos provenientes de la fertilización en el explanto materno. Esto hace preciso definir la identidad genética del material donante y acometer ensayos de detección precoz de variación somaclonal. ABSTRACT Holm oak (Quercus ilex L.) is one of the most important Mediterranean forest species. It conforms the tree layer of dehesas or montados, it produces acorns to feed the livestock and it establishes symbiosis with profitable mycorrhizal fungi. Holm oak is considered as recalcitrant species in terms of seed conservation and morphogenic capacities, which complicates the development of genetic conservation and improvement programs. Vegetative propagation is one of the mightiest tools for breeding programs therefore; developing protocols for clonal regeneration of holm oak is essential. Somatic embryogenesis is considered the best tissue culture-based way of plant regeneration in forest biotechnology. The present study is focused on the study of certain aspects of somatic embryogenesis for clonal regeneration of mature holm oak. This thesis manuscript is divided into several chapters that match with different aspects of the embryogenic system. Somatic embryogenesis induction was achieved on maternal teguments of developing ovules from immature acorns of adult holm oak trees. Despite the low induction frequencies, the generated embryogenic lines were amplified by secondary embryogenesis. A decline in the differentiation capacity over time was also observed. It was concluded that both genotype and culture media formulation influenced the embryogenic response, being the Schenk and Hildebrandt´s macronutrients formulation from culture medium and the lack of plant growth regulators the most effective combination for the induction of the embryogenic response. It has been suggested the existence of a developmental window in which ovules are prone to induction. Genotype influenced the proliferation capacity and the plant conversion of somatic embryos, which was also favoured by the presence of indol-3-butyric acid and 6-bencyladenine. The use of temporary immersion systems as proliferation in liquid culture of the embryogenic lines increased the growth depending on genotype, when compared to semisolid cultures. However, it did not improve the differentiation of single cotyledonary embryos. A protocol for the initiation and maintenance of embryogenic suspension cultures was established for several embryogenic lines with highly dense inoculi of embryogenic clusters from proliferating semisolid cultures. In order to avoid the loss of vigour and morphogenic ability of embryogenic lines due to prolonged cultures, a cryopreservation protocol for embryogenic lines of holm oak has been developed. During the determination of the influence of cryoprotective agents on the growth and differentiation capacities before and after liquid nitrogen immersion, it was concluded that both responses were independent from each other and also under the influence of genotype and the type of cryopreserved material. The combination of sucrose and PVS2 prior liquid nitrogen immersion provided higher recovery rates. When the same embryogenic lines were cryopreserved for 30 days, none was able to differentiate. The SSRs analysis of the short-term cryopreserved material detected somaclonal variation. Both SSR and RAPD markers showed high sensitivity to detect genetic differences between the donor trees and the generated embryogenic material. Nevertheless, the degree of instability detection depended on the marker. The SSR analysis indicated a relationship between genotype, the studied loci and the located polymorphisms. Also, both markers revealed low intraclonal genetic variation. The RAPD detected genetic variation within the donor trees. The presence of pre-existent genetic variation within mature trees, in addition to its occurrence during the early stages of the embryogenic induction, and the presence of tissues of fertilisation origin within the maternal explants are all discussed. Nonetheless, the determination of the genetic identity of donor material is required, in addition to early detection methods of somaclonal variation.

Development of somatic embryogenesis for cloning and conservation of mature holm oak trees (Quercus ilex L.)

La encina (Quercus ilex L.) es una de las especies forestales mediterráneas más importantes. Constituye gran parte del estrato arbóreo de dehesas o montados, produce bellota como alimento del ganado y establece simbiosis con hongos micorrizógenos de gran valor económico. La encina está considerada como una especie recalcitrante en términos de conservación de semillas y capacidad morfogénica, lo que dificulta los programas de conservación de recursos genéticos y la mejora de la especie. La propagación vegetativa es una potente herramienta de los programas de mejora, por lo que es preciso desarrollar protocolos de regeneración somática en encina. La embriogénesis somática está considerada como la modalidad más adecuada de regeneración basada en técnicas de cultivo de tejidos vegetales utilizada en biotecnología forestal. Este trabajo se centra en el estudio de determinados aspectos de la embriogénesis somática para la regeneración clonal de encinas adultas. La memoria de esta tesis se ha dividido en capítulos que se corresponden con diferentes aspectos del sistema embriogénico. La embriogénesis somática se indujo en tegumentos maternos de óvulos en desarrollo procedentes de bellotas inmaduras de encinas adultas. A pesar de las bajas frecuencias de inducción, las líneas embriogénicas generadas se amplificaron mediante embriogénesis secundaria observándose cierta pérdida de la capacidad de diferenciación con el tiempo. Tanto el genotipo como la formulación del medio de cultivo influyeron en la respuesta embriogénica, concluyendo que la formulación de macronutrientes de Schenk y Hildebrant del medio sin reguladores de crecimiento fue la combinación más efectiva en la inducción. Los resultados sugirieron la existencia de una ventana en el desarrollo del óvulo más sensible a la inducción. El genotipo in[luyó en la capacidad proliferativa de los cultivos y en la conversión de los embriones somáticos, que se incrementó suplementando el medio con ácido indol-3-butírico y 6-benciladenina. El cultivo en medio líquido de líneas embriogénicas en condiciones de inmersión transitoria incrementó el crecimiento, dependiendo del genotipo, con respecto al cultivo en medio semisólido. Sin embargo, no mejoró la capacidad de diferenciar embriones cotiledonares aislados. Se estableció un protocolo de inicio y mantenimiento de cultivos en suspensión para varias líneas embriogénicas mediante inoculación en alta densidad de agregados embrionarios procedentes del medio semisólido. Para evitar la pérdida de vigor y la capacidad morfogénica debida al cultivo prolongado se desarrolló un protocolo de crioconservación de líneas embriogénicas mediante vitrificación. Al determinar la influencia de los agentes crioprotectores antes y después de su inmersión en nitrógeno líquido se concluyó que las respuestas de capacidad de crecimiento y de diferenciación del material embriogénico son independientes, además de estar bajo influencia del genotipo y el tipo de material crioconservado. La combinación de sacarosa y PVS2 previa a la inmersión en nitrógeno líquido proporcionó la mayor tasa de recuperación. Cuando las líneas fueron crioconservadas 30 días la capacidad de diferenciación se perdió en todas ellas. El análisis de SSR detectó variación somaclonal en el material crioconservado a corto plazo. SSR y RAPD mostraron importantes diferencias genéticas entre los árboles donantes y el material embriogénico que dependieron del genotipo. El grado de detección dependió del marcador empleado. Ambos marcadores revelaron baja inestabilidad intraclonal. Los RAPD revelaron variación genética intra-individuo en las encinas donantes. Se discuten la variación genética pre-existente en encina, su aparición durante las primeras fases de la inducción de embriogénesis, y la presencia de tejidos provenientes de la fertilización en el explanto materno. Esto hace preciso definir la identidad genética del material donante y acometer ensayos de detección precoz de variación somaclonal. ABSTRACT Holm oak (Quercus ilex L.) is one of the most important Mediterranean forest species. It conforms the tree layer of dehesas or montados, it produces acorns to feed the livestock and it establishes symbiosis with profitable mycorrhizal fungi. Holm oak is considered as recalcitrant species in terms of seed conservation and morphogenic capacities, which complicates the development of genetic conservation and improvement programs. Vegetative propagation is one of the mightiest tools for breeding programs therefore; developing protocols for clonal regeneration of holm oak is essential. Somatic embryogenesis is considered the best tissue culture-based way of plant regeneration in forest biotechnology. The present study is focused on the study of certain aspects of somatic embryogenesis for clonal regeneration of mature holm oak. This thesis manuscript is divided into several chapters that match with different aspects of the embryogenic system. Somatic embryogenesis induction was achieved on maternal teguments of developing ovules from immature acorns of adult holm oak trees. Despite the low induction frequencies, the generated embryogenic lines were amplified by secondary embryogenesis. A decline in the differentiation capacity over time was also observed. It was concluded that both genotype and culture media formulation influenced the embryogenic response, being the Schenk and Hildebrandt´s macronutrients formulation from culture medium and the lack of plant growth regulators the most effective combination for the induction of the embryogenic response. It has been suggested the existence of a developmental window in which ovules are prone to induction. Genotype influenced the proliferation capacity and the plant conversion of somatic embryos, which was also favoured by the presence of indol-3-butyric acid and 6-bencyladenine. The use of temporary immersion systems as proliferation in liquid culture of the embryogenic lines increased the growth depending on genotype, when compared to semisolid cultures. However, it did not improve the differentiation of single cotyledonary embryos. A protocol for the initiation and maintenance of embryogenic suspension cultures was established for several embryogenic lines with highly dense inoculi of embryogenic clusters from proliferating semisolid cultures. In order to avoid the loss of vigour and morphogenic ability of embryogenic lines due to prolonged cultures, a cryopreservation protocol for embryogenic lines of holm oak has been developed. During the determination of the influence of cryoprotective agents on the growth and differentiation capacities before and after liquid nitrogen immersion, it was concluded that both responses were independent from each other and also under the influence of genotype and the type of cryopreserved material. The combination of sucrose and PVS2 prior liquid nitrogen immersion provided higher recovery rates. When the same embryogenic lines were cryopreserved for 30 days, none was able to differentiate. The SSRs analysis of the short-term cryopreserved material detected somaclonal variation. Both SSR and RAPD markers showed high sensitivity to detect genetic differences between the donor trees and the generated embryogenic material. Nevertheless, the degree of instability detection depended on the marker. The SSR analysis indicated a relationship between genotype, the studied loci and the located polymorphisms. Also, both markers revealed low intraclonal genetic variation. The RAPD detected genetic variation within the donor trees. The presence of pre-existent genetic variation within mature trees, in addition to its occurrence during the early stages of the embryogenic induction, and the presence of tissues of fertilisation origin within the maternal explants are all discussed. Nonetheless, the determination of the genetic identity of donor material is required, in addition to early detection methods of somaclonal variation.