Numerical solution of random differential models

This paper deals with the construction of a numerical solution of random initial value problems by means of a random improved Euler method. Conditions for the mean square convergence of the proposed method are established. Finally, an illustrative example is included in which the main statistics properties such as the mean and the variance of the stochastic approximation solution process are given. © 2011 Elsevier Ltd.This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universidad Politecnica de Valencia grant PAID06-09-2588 and Mexican Conacyt.Cortés López, JC.; Jódar Sánchez, LA.; Villafuerte Altuzar, L.; Company Rossi, R. (2011). Numerical solution of random differential models. Mathematical and Computer Modelling. 54(7):1846-1851. https://doi.org/10.1016/j.mcm.2010.12.037S1846185154

Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling

The objective of this paper is to complete certain issues from our recent contribution [J. Calatayud, J.-C. Cort\'es, M. Jornet, L. Villafuerte, Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties, Advances in Difference Equations, 2018:392, 1--29 (2018)]. We restate the main theorem therein that deals with the homogeneous case, so that the hypotheses are clearer and also easier to check in applications. Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example. We also prove the uniqueness of mean square solution via an habitual Lipschitz condition that extends the classical Picard Theorem to mean square calculus. In this manner, the study on general random non-autonomous second order linear differential equations with analytic data processes is completely resolved. Finally, we relate our exposition based on random power series with polynomial chaos expansions and the random differential transform method, being the latter a reformulation of our random Fr\"obenius method.Comment: 15 pages, 0 figures, 2 table

Local Scale Genetic Diversity and its Role in Coping with Changing Climate

Climate change is thought to alter the patterns of genetic diversity within species and populations. Yet, it is not well-understood how genetic diversity influences organism’s adaptation to changing climate. In this chapter, I explore how within-population genetic diversity may be affected by local environmental heterogeneity and to what extent this variation may promote adaption. I focus on mountain ecosystems since they are heterogeneous environments at a fine scale that offer a unique mosaic of highly localized environmental conditions. I start summarizing the drivers of genetic isolation at a local scale and the diversification and adaptation patterns that result from it. I continue discussing these processes in terms of populations\u27 reactions to changing conditions using my own long-term ecological genomic studies. This allows me to demonstrate that local-scale variation, in the long term, may offer safe places for species in a warming world due to their fine-scale topographic variability, which may provide suitable habitats within only a few meters of species’ current locations. Yet, such fine-scale habitat variability can also lead to locally genetically adapted populations, so that individuals and populations adapted to a narrow range of conditions may respond poorly to future environments

Interacción entre vulcanismo, tectónica y sedimentación en una plataforma carbonatada somera: Ejemplo en el Tethys occidental (Jurásico Medio, sureste de la Cordillera Ibérica)

In the southeastern Iberian Range, several mainly volcaniclastic rocks resulting from submarine eruptions can be found interbedded in the Lower‒Middle Jurassic carbonate succession. The geological mapping of the outcrop­ping volcanic rocks reveals that they follow three well marked lineaments of cortical weakness (Teruel, Caudiel and Alcublas Fault Zones), probably caused by the faulting related to the opening and sea‒floor spreading of the Ligurian and Alpine Tethys oceans. The present work introduces the results of the study, which aims to evaluate the tectonosedimentary evolution of a shallow submarine setting affected by volcanism during the Aalenian‒Bajocian boundary (Middle Jurassic). This site, known as “Caudiel volcanic outcrop”, is located at the southeastern part of the Caudiel Fault Zone. The presence of positive subaqueous volcaniclastic reliefs, added to shallow marine plat­forms, strongly affects the depth‒dependent carbonate sedimentation: it induces substantial changes in lithofacies compared to other neighboring areas, or even directly prevents the sedimentation. Moreover, episodic normal fault activity generated a dynamic topography over time, with variable rates of both subsidence and uplifting throughout different areas. The Caudiel outcrop represents a good ancient example of interaction between multiple factors (volcanism, tectonism and sedimentation) in shallow carbonate platforms, where the accommodation changes and the sedimentation rates seem to be subordinate to the local tectonic disturbances.En el sureste de la Cordillera Ibérica (España) existen una serie de afloramientos de rocas volcánicas origi­nadas por erupciones submarinas, principalmente de tipo volcanoclástico, interestratificadas en las sucesiones carbonatadas del Jurásico Inferior y Medio. La cartografía geológica de los afloramientos de rocas volcánicas revela que se encuentran alineados a lo largo de tres elementos de debilidad cortical bien definidos (zonas de falla de Teruel, de Caudiel y de Alcublas), originados probablemente por fracturas relacionadas con la apertura y expansión del Tethys Ligur y del Tethys Alpino. En este trabajo se presentan los resultados del estudio de la evolución tectonosedimentaria de un ambiente submarino somero afectado por la presencia de una acumulación volcánica que tuvo lugar en el Jurásico Medio (límite Aaleniense‒Bajociense). Se trata del afloramiento volcánico de Caudiel, que es el más suroriental de todos los afloramientos localizados en uno de los tres elementos de debilidad estructural mencionados: la Zona de Falla de Caudiel. La presencia de un relieve positivo en el fondo de la plataforma, ya de por sí bastante somera, condiciona la sedimentación carbonatada, muy sensible a la pro­fundidad, hasta el punto de llegar a inducir cambios significativos de facies con respecto a otras áreas cercanas o de impedir la sedimentación. Los movimientos episódicos del substrato generaron una topografía irregular y cambiante a lo largo del tiempo, con tasas variables de hundimiento y levantamiento en diferentes áreas. El aflo­ramiento de Caudiel constituye un buen ejemplo fósil de interacción entre varios factores (vulcanismo, tectónica y sedimentación) en plataformas carbonatadas someras, en las que los cambios de acomodación y las tasas de sedimentación parecen estar subordinadas a perturbaciones tectónicas de carácter local

Topological Excitations in the Thirring model

The quantization of the massless Thirring model in the light-cone using functional methods is considered. The need to compactify the coordinate $x^-$ in the light-cone spacetime implies that the quantum effective action for left-handed fermions contains excitations similar to abelian instantons produced by composite of left-handed fermions. Right-handed fermions don't have a similar effective action. Thus, quantum mechanically, chiral symmetry must be broken as a result of the topological excitations. The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling.Comment: title changed, one reference added, accepted in Phys. Lett.

Aportes del pensamiento de Gabriel Marcel a una reflexión filosófica de lo educacional

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Contribució a l'estudi dels fongs de Sant Joan de l'Erm i la Vall de Santa Magdalena (I)

En aquesta zona dels Pirineus, a les comarques del nord de Lleida (Alt Urgell-Pallars Sobir á), els autors han identitificat 100 especies de fongs (2 mixomicets , 13 ascomicets , 1 teliomicet , 6 fragmobasidiomicets i 78 basidiomicets). Remarquem entre elles: Dumontinia tuberosa , Rhytisma salicinum, Agaricus crocodilinus, Bankera fuligineoalba, Clitocybula lacerata , Lactariu s hysginus , L. rufus, Myxomphalia maura, Pholiota highlandensis i Tricholoma fulvum. De totes les especies es conserven diapositiva i material d'herbarioOne hundred species of fungi (two myxomycetes, 13 ascomycetes , one teliomycete, six phragmobasidiomycetes and 78 basidiomycetes) are recorded from the above-mentioned area, in the north of the Pyrenees , between the regions of Alt Urgell and Pallars Sobir á. Sorne species are highlighted: Dumontinia tuberosa, Rhytisma salicinum, Agaricus crocodilinus, Bankera fuligineoalba, Clitocybula lacerala, Lactariu s hysginus, L. rufus, Myxomphalia maura, Pholiota highlandensis and Tricholomafulvum. All have been photographed and exciccata properly depositedEn esta zona de los Pirineos, situada en las comarcas del norte de la provincia de Lleida (Alt Urgell-Pallars Sobirá), los autores han identificado 100 especies de hongos, (2 Mixomicetes, 13 Ascomicetes, 1 Teliomicete , 56 Fragmobasidiomicetes y 78 Basidiomicetes). Destacamos entre ellas: Dumontinia tuberosa, Rhytisma salicinum, Aga ricus crocodilinus, Bankera fuligineoalba, Clitocybula lacerata, Lactariu s hysginus, L. rufus, Myxomphalia maura, Pholiota highlandensis y Tricholoma fulvum. De todas las especies se conservan diapositiva y material de herbario

Solving Riccati time-dependent models with random quadratic coefficient

This paper deals with the construction of approximate solutions of a random logistic differential equation whose nonlinear coefficient is assumed to be an analytic stochastic process and the initial condition is a random variable. Applying p-mean stochastic calculus, the nonlinear equation is transformed into a random linear equation whose coefficients keep analyticity. Next, an approximate solution of the nonlinear problem is constructed in terms of a random power series solution of the associate linear problem. Approximations of the average and variance of the solution are provided. The proposed technique is illustrated through an example where comparisons with respect to Monte Carlo simulations are shown. © 2011 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universitat Politecnica de Valencia grant PAID06-09-2588 and Mexican Conacyt.Cortés López, JC.; Jódar Sánchez, LA.; Company Rossi, R.; Villafuerte Altuzar, L. (2011). Solving Riccati time-dependent models with random quadratic coefficient. Applied Mathematics Letters. 24(12):2193-2196. https://doi.org/10.1016/j.aml.2011.06.024S21932196241