Quasilinear and singular elliptic systems

In this paper, we investigate a general quasilinear elliptic and singular system. By monotonicity methods, we give some existence and uniqueness results. Next, we give some applications to biological models

Graph morphisms and exhaustion of curve graphs of low-genus surfaces

This work is the extension of the results by the author in [7] and [6] for low-genus surfaces. Let $S$ be an orientable, connected surface of finite topological type, with genus $g \leq 2$, empty boundary, and complexity at least $2$; as a complement of the results of [6], we prove that any graph endomorphism of the curve graph of $S$ is actually an automorphism. Also, as a complement of the results in [6] we prove that under mild conditions on the complexity of the underlying surfaces any graph morphism between curve graphs is induced by a homeomorphism of the surfaces. To prove these results, we construct a finite subgraph whose union of iterated rigid expansions is the curve graph $\mathcal{C}(S)$. The sets constructed, and the method of rigid expansion, are closely related to Aramayona and Leiniger's finite rigid sets in [2]. Similarly to [7], a consequence of our proof is that Aramayona and Leininger's rigid set also exhausts the curve graph via rigid expansions, and the combinatorial rigidity results follow as an immediate consequence, based on the results in [6].Comment: 47 pages, 52 figures. All comments are welcome

INDICATORS OF URBAN SUSTAINABILITY IN MEXICO

The principal objective of this project is to summarize the characteristics that define urban sustainability in Mexican cities; its basic principles and the advantages of their application in the development of future cities, as well as the description of the indicators of urban sustainability that directly affect the development of communities, from households, colonies or neighbourhoods to cities or regions. The project’s method is based on the analysis of bibliographical information and the revision of some practical cases that refer to the development of sustainable indicators in urban environment.Indicators, sustainability, urbanism, development, cities.

Beyond the classical strong maximum principle: forcing changing sign near the boundary and flat solutions

We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain $\Omega$ can be extended, under suitable conditions, to the case in which the forcing term $f(x)$ is changing sign. In addition, in the case of solutions, the normal derivative on the boundary may also vanish on the boundary (definition of flat solutions). This leads to examples in which the unique continuation property fails. As a first application, we show the existence of positive solutions for a sublinear semilinear elliptic problem of indefinite sign. A second application, concerning the positivity of solutions of the linear heat equation, for some large values of time, with forcing and/or initial datum changing sign is also given.Comment: 20 pages 2 Figure

Automorphisms groups of simplicial complexes of infinite type surfaces

Let S be an orientable surface of innite genus with a nite numberof boundary components. In this work we consider the curve complex C(S), the nonseparating curve complex N(S), and the Schmutz graph G(S) of S. When all topological ends of S carry genus, we show that all elements in the automorphismgroups Aut(C(S)), Aut(N(S)), and Aut(G(S)) are geometric, i.e. these groups are naturally isomorphic to the extended mapping class group MCG(S) of the innite surface S. Finally, we study rigidity phenomena within Aut(C(S)) and Aut(N(S))

Monitoring resistance of Cydia pomonella (L.) Spanish field populations to new chemical insecticides and the mechanisms involved

BACKGROUND: A widespread resistance of Cydia pomonella to organophosphates was demonstrated in populations from the Spanish Ebro Valley area that showed high levels of enzymatic detoxification. To determine the efficacy of new insecticides, neonate larvae bioassays were carried out on twenty field codling moth populations collected from three different Spanish apple production areas. Synergist bioassays were performed to detect the enzymatic mechanisms involved. RESULTS: The least active ingredients were methoxyfenozide, with 100% of the populations showing significantly lower mortality than the susceptible strain, and lambda-cyhalothrin, with very high resistant ratios (872.0 for the most resistant field population). Approximately 50% of the populations were resistant or tolerant to thiacloprid. By contrast, tebufenozide was very effective in all the field populations, as was chlorpyrifos-ethyl despite its widespread use during the last few years. Indoxacarb, spinosad and chlorantraniliprole also provided high efficacy, as did emamectin and spinetoram, which are not yet registered in Spain. CONCLUSION: The resistant Spanish codling moth populations can be controlled using new reduced-risk insecticides. The use of synergists showed the importance of the concentration applied and the difficulty of interpreting the results in field populations that show multiple resistance to different active ingredients.The authors would like to express their sincere thanks to the fruit growers who gave us access to their orchards and to the grower advisors of the areas (plant defense area technicians), who helped identify the best orchards for the assays, and Mònica Pérez for her technical help. This study was partially supported by grants AGL2013-49164 and AGL2016-77373 of the Spanish Ministry for Science and Innovation and by the CERCA Programme / Generalitat de Catalunya

Kant : "l'única prova possible per a una demostració de l'existència de Déu"

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