Soluciones periódicas para un modelo de población celular sujeto a una radiación periódica general

En este trabajo consideramos modelos con tratamiento de radiaciónperiódico contra el cáncer que describen la dinámica de las poblaciones celulares en un tumor. Establecemos la existencia de órbitas periódicas, utilizandola teoría de los sistemas cooperativos. Damos condiciones suficientes parala unicidad de la solución periódica, también para que esta sea un atractorglobal. Realizamos simulaciones numéricas utilizando funciones de radiaciónespecíficas para ilustrar nuestros resultados analíticos.In this work, we considered models with periodic radiation can-cer treatment which describe the dynamics of cell populations in a tumor.This may also be used to consider dynamics of healthy tissue under periodic radiation exposure. We establish the existence of periodic orbits, byusing theory of cooperative systems. We give sufficient conditions for theuniqueness of the periodic solution which then becomes a global attractor.Numerical simulations are performed using specific radiation functions to illustrate our analytical findings

Existence of periodic solutions for seasonal epidemic models with quarantine

In this work, we establish the existence of periodic orbits for a seasonal saturated epidemiological model of a population consisting of susceptible, infectious and quarantined individuals (an SIQS model). To do so, we use Leray-Schauder degree theory. We also provide numerical examples of these solutions

Different types of backward bifurcations on account of an improvement in treatment efficiency

Understanding why there are multiple equilibrium points when R0 < 1 has been one of the main motivations to analyze existence of a backward bifurcation in epidemiological models. Existence of multiple endemic states is usually associated to branches of equilibrium points of the models, which could arise from either the disease-free equilibrium point if R0 = 1 or from an endemic equilibrium point if R0 > 1. In this work, an SIR model with a density-dependent treatment rate is analyzed. The nature of the point where backward bifurcation emerges is explained in function of the velocity of the per-capita treatment rate. Strategies for the control or eradication of the disease will be proposed in function of the efficiency of the treatment

Eutrophication and macroalgal blooms in temperate and tropical coastal waters: Nutrient enrichment experiments with Ulva spp.

Receiving coastal waters and estuaries are among the most nutrient-enriched environments on earth, and one of the symptoms of the resulting eutrophication is the proliferation of opportunistic, fast-growing marine seaweeds. Here, we used a widespread macroalga often involved in blooms, Ulva spp., to investigate how supply of nitrogen (N) and phosphorus (P), the two main potential growth-limiting nutrients, influence macroalgal growth in temperate and tropical coastal waters ranging from low- to high-nutrient supplies. We carried out N and P enrichment field experiments on Ulva spp. in seven coastal systems, with one of these systems represented by three different subestuaries, for a total of nine sites. We showed that rate of growth of Ulva spp. was directly correlated to annual dissolved inorganic nitrogen (DIN) concentrations, where growth increased with increasing DIN concentration. Internal N pools of macroalgal fronds were also linked to increased DIN supply, and algal growth rates were tightly coupled to these internal N pools. The increases in DIN appeared to be related to greater inputs of wastewater to these coastal waters as indicated by high δ15N signatures of the algae as DIN increased. N and P enrichment experiments showed that rate of macroalgal growth was controlled by supply of DIN where ambient DIN concentrations were low, and by P where DIN concentrations were higher, regardless of latitude or geographic setting. These results suggest that understanding the basis for macroalgal blooms, and management of these harmful phenomena, will require information as to nutrient sources, and actions to reduce supply of N and P in coastal waters concerned.Fil: Teichberg, Mirta. Leibniz Center For Tropical Marine Research; AlemaniaFil: Fox, Sophia E.. Marine Biological Laboratory; Estados UnidosFil: Olsen, Ylva S.. Bangor University; Reino UnidoFil: Valiela, Ivan. Marine Biological Laboratory; Estados UnidosFil: Martinetto, Paulina Maria del Rosario. Universidad Nacional de Mar del Plata; ArgentinaFil: Iribarne, Oscar Osvaldo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Marinas y Costeras; ArgentinaFil: Muto, Elizabeti Yuriko. Universidade de Sao Paulo; BrasilFil: Petti, Monica A.V.. Universidade de Sao Paulo; BrasilFil: Corbisier, Thaïs N.. Universidade de Sao Paulo; BrasilFil: Soto-Jiménez, Martín. Universidad Nacional Autónoma de México; MéxicoFil: Páez-Osuna, Federico. Universidad Nacional Autónoma de México; MéxicoFil: Castro, Paula. University Of Coimbra; BrasilFil: Freitas, Helena. University Of Coimbra; BrasilFil: Zitelli, Andreina. Università Iuav Di Venezia; ItaliaFil: Cardinaletti, Massimo. Gruppo Veritas; ItaliaFil: Tagliapietra, Davide. Consiglio Nazionale delle Ricerche; Itali

Surfaces in R4 with constant principal angles with respect to a plane

We study surfaces in R4 whose tangent spaces have constant principal angles with respect to a plane. Using a PDE we prove the existence of surfaces with arbitrary constant principal angles. The existence of such surfaces turns out to be equivalent to the existence of a special local symplectomorphism of $\R^2$. We classify all surfaces with one principal angle equal to $0$ and observe that they can be constructed as the union of normal holonomy tubes. We also classify the complete constant angles surfaces in R4 with respect to a plane. They turn out to be extrinsic products. We characterize which surfaces with constant principal angles are compositions in the sense of Dajczer-Do Carmo. Finally, we classify surfaces with constant principal angles contained in a sphere and those with parallel mean curvature vector fiel

Vértices de la función beta y órbitas periódicas para flujos magnéticos

En este trabajo de tesis M denotará una variedad conexa y cerrada