Coincidences in generalized Lucas sequences

For an integer $k\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized Lucas sequence which starts with $0,\ldots,0,2,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all the integers that appear in different generalized Lucas sequences; i.e., we study the Diophantine equation $L_n^{(k)}=L_m^{(\ell)}$ in nonnegative integers $n,k,m,\ell$ with $k, \ell\geq 2$. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method. This paper is a continuation of the earlier work [4].Comment: 14 page

Some arithmetic functions of factorials in Lucas sequences

We prove that if {un}n≥ 0 is a nondegenerate Lucas sequence, then there are only finitely many effectively computable positive integers n such that |un|=f(m!), where f is either the sum-of-divisors function, or the sum-of-proper-divisors function, or the Euler phi function. We also give a theorem that holds for a more general class of integer sequences and illustrate our results through a few specific examples. This paper is motivated by a previous work of Iannucci and Luca who addressed the above problem with Catalan numbers and the sum-of-proper-divisors function

Here we find the Padovan and Perrin numbers that are concatenations of two terms of the other sequence. We also find the intersection between these ternary sequences.

Here we find the Padovan and Perrin numbers that are concatenations of two terms of the other sequence. We also find the intersection between these ternary sequences. AMS subject classifications: 11B39, 11D61, 11J8

Here we find the Padovan and Perrin numbers that are concatenations of two terms of the other sequence. We also find the intersection between these ternary sequences.

Here we find the Padovan and Perrin numbers that are concatenations of two terms of the other sequence. We also find the intersection between these ternary sequences. AMS subject classifications: 11B39, 11D61, 11J8

Reconstructing the narrative A literary antidote to the meaning crisis

Treballs Finals del Grau d'Estudis Anglesos, Facultat de Filologia, Universitat de Barcelona, Curs: 2018-2019, Tutor: Rodrigo Andrés[eng]The Meaning Crisis is the state we are currently living in, a time of great disagreement, confusion, and suffering, where the mechanisms we used to employ in order to properly extract meaning and progress towards wisdom are failing us. This project aims to be a literary response (and, hopefully, antidote) to the Meaning Crisis. In order to do so, I explore how the Meaning Crisis expresses itself in the stories we read through a historical analysis of the development of narratological models. Firstly, I delve into the teleological narrative and how it was transformed by the Enlightenment. Secondly, I analyze how the cyclical narrative of Modernism and Postmodernism was a critical response to the pitfalls of the teleological narrative. Finally, taking into account the strong and weak points of both the teleological and the cyclical narrative, I propose my own narratological model, called the narrative of traditional cosmology, which aims to be a bridge between the two, combining them together into a single model of production, analysis and consumption of literature. To conclude, I suggest that a model like the narrative of traditional cosmology could be a potentially successful antidote to the Meaning Crisis in the realm of literature, while also stressing the importance of practice and communion with the art of the word.[spa] La Crisis de significado es el estado en el que vivimos actualmente, una era de gran desacuerdo, confusión y sufrimiento, en la que los mecanismos que empleábamos para extraer adecuadamente significado y progresar hacia la sabiduría nos están fallando. Este proyecto pretende ser una respuesta literaria (y posiblemente un antídoto) a la Crisis de significado. Con ese objetivo en mente, exploro cómo la Crisis de significado se expresa en los relatos que leemos hoy en día a través de un análisis histórico del desarrollo de varios modelos narratológicos. En primer lugar, profundizo acerca de la narrativa teleológica y cómo esta fue transformada por la Ilustración. En segundo lugar, analizo cómo la narrativa cíclica del modernismo y el posmodernismo fue una respuesta crítica a los inconvenientes de la narrativa teleológica. Finalmente, teniendo en cuenta los puntos fuertes y débiles tanto de la narrativa teleológica como de la cíclica, propongo mi propio modelo narratológico, denominado narrativa de la cosmología tradicional, que pretende ser un puente entre ambas, combinándolas en un único modelo de producción, análisis y consumo literario. Para concluir, sugiero que un modelo como la narrativa de la cosmología tradicional podría ser un antídoto potencialmente exitoso contra la Crisis de significado en el ámbito literario, a la vez que enfatizo la importancia de la práctica y la comunión con el arte de la palabra

Identification of active oxalotrophic bacteria by Bromodeoxyuridine DNA labeling in a microcosm soil experiments

The oxalate-carbonate pathway (OCP) leads to a potential carbon sink in terrestrial environments. This process is linked to the activity of oxalotrophic bacteria. Although isolation and molecular characterizations are used to study oxalotrophic bacteria, these approaches do not give information on the active oxalotrophs present in soil undergoing the OCP. The aim of this study was to assess the diversity of active oxalotrophic bacteria in soil microcosms using the Bromodeoxyuridine (BrdU) DNA labeling technique. Soil was collected near an oxalogenic tree (Milicia excelsa). Different concentrations of calcium oxalate (0.5%, 1%, and 4% w/w) were added to the soil microcosms and compared with an untreated control. After 12 days of incubation, a maximal pH of 7.7 was measured for microcosms with oxalate (initial pH 6.4). At this time point, a DGGE profile of the frc gene was performed from BrdU-labeled soil DNA and unlabeled soil DNA. Actinobacteria (Streptomyces- and Kribbella-like sequences), Gammaproteobacteria and Betaproteobacteria were found as the main active oxalotrophic bacterial groups. This study highlights the relevance of Actinobacteria as members of the active bacterial community and the identification of novel uncultured oxalotrophic groups (i.e. Kribbella) active in soil

Isolation of oxalotrophic bacteria able to disperse on fungal mycelium

A technique based on an inverted Petri dish system was developed for the growth and isolation of soil oxalotrophic bacteria able to disperse on fungal mycelia. The method is related to the ‘fungal highways' dispersion theory in which mycelial fungal networks allow active movement of bacteria in soil. Quantification of this phenomenon showed that bacterial dispersal occurs preferentially in upper soil horizons. Eight bacteria and one fungal strain were isolated by this method. The oxalotrophic activity of the isolated bacteria was confirmed through calcium oxalate dissolution in solid selective medium. After separation of the bacteria-fungus couple, partial sequencing of the 16S and the ITS1 and ITS2 sequences of the ribosomal RNA genes were used for the identification of bacteria and the associated fungus. The isolated oxalotrophic bacteria included strains related to Stenotrophomonas, Achromobacter, Lysobacter, Pseudomonas, Agrobacterium, Cohnella, and Variovorax. The recovered fungus corresponded to Trichoderma sp. A test carried out to verify bacterial transport in an unsaturated medium showed that all the isolated bacteria were able to migrate on Trichoderma hyphae or glass fibers to re-colonize an oxalate-rich medium. The results highlight the importance of fungus-driven bacterial dispersal to understand the functional role of oxalotrophic bacteria and fungi in soil

Use of an isothermal microcalorimetry assay to characterize microbial oxalotrophic activity

Isothermal microcalorimetry (IMC) has been used in the past to monitor metabolic activities in living systems. A few studies have used it on ecological research. In this study, IMC was used to monitor oxalotrophic activity, a widespread bacterial metabolism found in the environment, and particularly in soils. Six model strains were inoculated in solid angle media with K-oxalate as the sole carbon source.Cupriavidus oxalaticus,Cupriavidus necator, andStreptomyces violaceoruber presented the highest activity (91, 40, and 55 μW, respectively) and a maximum growth rate (μmax h−1) of 0.264, 0.185, and 0.199, respectively, among the strains tested. These three strains were selected to test the incidence of different oxalate sources (Ca, Cu, and Fe-oxalate salts) in the metabolic activity. The highest activity was obtained in Ca-oxalate forC. oxalaticus. Similar experiments were carried out with a model soil to test whether this approach can be used to measure oxalotrophic activity in field samples. Although measuring oxalotrophic activity in a soil was challenging, there was a clear effect of the amendment with oxalate on the metabolic activity measured in soil. The correlation between heat flow and growth suggests that IMC analysis is a powerful method to monitor bacterial oxalotrophic activit