On differences of perfect powers and prime powers

Given a prime number $q$ and a squarefree integer $C_1$, we develop a method to explicitly determine the tuples $(y, n, \alpha)$ for which the difference $y^n-q^\alpha$ has squarefree part equal to $C_1$. Our techniques include the combination of the local information provided by Galois representations of Frey-Hellegouarch curves with the effective resolution of Thue-Mahler equations, as well as the use of improved lower bounds for $q-$adic and complex logarithms. As an application of this methodology, we will completely resolve the case when $1 \le C_1 \le 20$ and 2 \le q < 25

Reseña de libros

ES] Barros da Costa, Hugo. NYC relatos gráficos (por Pablo Rodríguez-Navarro) pp82.--Barros da Costa, Hugo. On the path of Louis Kahn ( por Pedro Molina-Siles) pp.83.-- Cabodevilla Artieda, Ignacio. Análisis comparativo de la arquitectura gótica en los reinos de Aragón y Nápoles (S. XIII-XV) (por Noelia Cervero Sánchez). pp. 84--Salvador García, Elena. Protocolo HBIM para la gestión eficiente del uso público del patrimonio arquitectónico (por María José Viñals Blasco & Jorge Luis García-Valldecabres) pp. 85.-- Sánchez de la Guía, Lucía. Modelos y métodos de participación del usuario en el diseño de productos y servicios (por Marina Puyuelo Cazorla) pp 86.Rodríguez Navarro, P.; Molina Siles, PJ.; Cervero Sánchez, N.; Viñals Blasco, MJ.; García Valldecabres, JL.; Puyuelo Cazorla, M. (2020). Reseña de libros. EGE Revista de Expresión Gráfica en la Edificación. 0(12):82-86. https://doi.org/10.4995/ege.2020.14077OJS828601

Asymptotic Fermat's Last Theorem for a family of equations of signature (2, 2n, n)

In this paper, we study the integer solutions of a family of Fermat-type equations of signature (2, 2n, n), Cx2 + qky2n = zn. We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant BC, q such that if n &gt; BC, q, there are no solutions (x, y, z, n) of the equation. Our methods use the modular method for Diophantine equations, along with level lowering and Galois theory

Conservation analysis of the <i>Pseudomonas syringae</i> pv. syringae UMAF0158 chromosome.

<p>From the outside in, the outermost circle (black) shows the scale line. Circles 2 to 4 display similarity (<i>E</i>-value ≤ 1×10⁻¹⁰) among UMAF0158 and the three <i>P</i>. <i>syringae</i> with complete genome sequences: DC3000 (grey), 1448A (orange) and B728a (red). Circles 5 to 7 display similarity (<i>E</i>-value ≤ 1×10⁻¹⁰) among UMAF0158 and the draft genomes of the three phylogenetically closest <i>P</i>. <i>syringae</i> strains among the 25 selected in this study: 642 (purple), BRIP39023 (green) and Cit 7 (blue). Circles 8 and 9 display putative horizontally transferred regions (red) and prophages (purple), respectively; circle 10 shows G+C in relation to the mean G+C in 2 kb windows (red); circle 11 shows trinucleotide composition (black).</p

Genomic organization of putative <i>Pseudomonas syringae</i> pv. syringae UMAF0158 secretion systems involved in effector translocation.

<p><b>A,</b> T6SS-1. <b>B,</b> T6SS-2. <b>C,</b> T3SS-1 (<i>hrc</i>-1). <b>D,</b> T3SS-2 (<i>rhc</i>). Genes presumably involved in secretion are shown in red. Components of the T6SS with no consensual name are labelled with their corresponding NCBI-annotated locus tags. Numbers below the arrows refer to bp positions in the chromosome.</p

Phylogenetic analyses of <i>Pseudomonas syringae</i> pv. syringae UMAF0158 and 25 selected strains of the <i>P</i>. <i>syringae</i> complex (see S1 Table).

<p>Multilocus sequence analysis were performed using a concatenated dataset for <i>gapA</i>, <i>gltA</i>, <i>recA</i>, <i>rpoA</i> and <i>rpoB</i>. The evolutionary history was inferred using the Maximum Likelihood method based on the JTT matrix-based model. The percentage of trees in which the associated taxa clustered in the bootstrap test (1000 replicates) is shown next to the branches. <i>P</i>. <i>fluorescens</i> strain Pf-5 was used as an outgroup. <b>A,</b> Phylogeny based on protein products. <b>B,</b> Phylogeny based on DNA sequences. Some strains were labelled with the corresponding phylotype of pv. syringae [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0136101#pone.0136101.ref021" target="_blank">21</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0136101#pone.0136101.ref022" target="_blank">22</a>] and clade of phylogroup 2 of <i>P</i>. <i>syringae</i> complex [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0136101#pone.0136101.ref006" target="_blank">6</a>]. The alignments used to generate this figure have been included as supporting information (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0136101#pone.0136101.s005" target="_blank">S2 File</a>).</p

Summary of putative virulence-associated genes in <i>Pseudomonas syringae</i> pv. syringae UMAF0158.

<p>Summary of putative virulence-associated genes in <i>Pseudomonas syringae</i> pv. syringae UMAF0158.</p

Bioinformatics Analysis of the Complete Genome Sequence of the Mango Tree Pathogen <i>Pseudomonas syringae</i> pv. syringae UMAF0158 Reveals Traits Relevant to Virulence and Epiphytic Lifestyle

<div><p>The genome sequence of more than 100 <i>Pseudomonas syringae</i> strains has been sequenced to date; however only few of them have been fully assembled, including <i>P</i>. <i>syringae</i> pv. syringae B728a. Different strains of pv. syringae cause different diseases and have different host specificities; so, UMAF0158 is a <i>P</i>. <i>syringae</i> pv. syringae strain related to B728a but instead of being a bean pathogen it causes apical necrosis of mango trees, and the two strains belong to different phylotypes of pv.syringae and clades of <i>P</i>. <i>syringae</i>. In this study we report the complete sequence and annotation of <i>P</i>. <i>syringae</i> pv. syringae UMAF0158 chromosome and plasmid pPSS158. A comparative analysis with the available sequenced genomes of other 25 <i>P</i>. <i>syringae</i> strains, both closed (the reference genomes DC3000, 1448A and B728a) and draft genomes was performed. The 5.8 Mb UMAF0158 chromosome has 59.3% GC content and comprises 5017 predicted protein-coding genes. Bioinformatics analysis revealed the presence of genes potentially implicated in the virulence and epiphytic fitness of this strain. We identified several genetic features, which are absent in B728a, that may explain the ability of UMAF0158 to colonize and infect mango trees: the mangotoxin biosynthetic operon <i>mbo</i>, a gene cluster for cellulose production, two different type III and two type VI secretion systems, and a particular T3SS effector repertoire. A mutant strain defective in the rhizobial-like T3SS Rhc showed no differences compared to wild-type during its interaction with host and non-host plants and worms. Here we report the first complete sequence of the chromosome of a pv. syringae strain pathogenic to a woody plant host. Our data also shed light on the genetic factors that possibly determine the pathogenic and epiphytic lifestyle of UMAF0158. This work provides the basis for further analysis on specific mechanisms that enable this strain to infect woody plants and for the functional analysis of host specificity in the <i>P</i>. <i>syringae</i> complex.</p></div

Effects of Ozone Treatment on Personal Protective Equipment Contaminated with SARS-CoV-2

Background: Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is causing profound health, economic, and social problems worldwide. Management of personal protective equipment (PPE) and its potential limited availability have created concerns about the increased risks for healthcare professionals at hospitals and nursing homes. Ozone is a powerful oxidant agent. The objectives of this study were to examine the effects of ozone treatment on PPE contaminated with SARS-CoV-2, and to explore whether relative humidity could modify those effects. Methods: PPE contaminated by heat-inactivated SARS-CoV-2 were treated with different ozone concentrations, exposure times, and relative humidity conditions. SARS-CoV-2 gene amplification was assessed by real-time polymerase chain reaction. Results: There was no amplification of SARS-CoV-2 in PPE after the following ozone exposures: 30 s at 10,000 ppm (20 g/m3), 5 min at 4000 ppm, and 10 min at 2000 ppm. At lower ozone concentrations, 4&ndash;12 ppm (0.008&ndash;0.024 g/m3), the effects were highly dependent on the relative humidity conditions. Conclusions: Oxidative stress induced by ozone exposure eliminated heat-inactivated SARS-CoV-2 in different PPE components under appropriate exposure times, ozone concentrations, and relative humidity conditions. These findings could have implications in decreasing the risk of contamination associated with personal protective equipment management and in increasing its availability. Further research in the original SARS-CoV-2 strain is guaranteed

General features of the <i>Pseudomonas syringae</i> pv. syringae UMAF0158 genome and comparison with <i>P</i>. <i>syringae</i> pv. syringae B728a, <i>P</i>. <i>syringae</i> pv. phaseolicola 1448A and <i>P</i>. <i>syringae</i> pv. tomato DC3000.

<p>^a The number of predicted CDSs corresponds to those indicated at NCBI for the corresponding genome sequences (March 1st, 2015).</p><p>General features of the <i>Pseudomonas syringae</i> pv. syringae UMAF0158 genome and comparison with <i>P</i>. <i>syringae</i> pv. syringae B728a, <i>P</i>. <i>syringae</i> pv. phaseolicola 1448A and <i>P</i>. <i>syringae</i> pv. tomato DC3000.</p