Majorantes para a ordem de subgrafos induzidos k-regulares

Muitos dos problemas de otimização em grafos reduzem-se à determinação de um subconjunto de vértices de cardinalidade máxima que induza um subgrafo k-regular. Uma vez que a determinação da ordem de um subgrafo induzido k-regular de maior ordem é, em geral, um problema NP-difícil, são deduzidos novos majorantes, a determinar em tempo polinomial, que em muitos casos constituam boas aproximações das respetivas soluções ótimas. Introduzem-se majorantes espetrais usando uma abordagem baseada em técnicas de programação convexa e estabelecem-se condições necessárias e suficientes para que sejam atingidos. Adicionalmente, introduzem-se majorantes baseados no espetro das matrizes de adjacência, laplaciana e laplaciana sem sinal. É ainda apresentado um algoritmo não polinomial para a determinação de umsubconjunto de vértices de umgrafo que induz umsubgrafo k-regular de ordem máxima para uma classe particular de grafos. Finalmente, faz-se um estudo computacional comparativo com vários majorantes e apresentam-se algumas conclusões.

Spectral characterization of families of split graphs

An upper bound for the sum of the squares of the entries of the principal eigenvector corresponding to a vertex subset inducing a k-regular subgraph is introduced and applied to the determination of an upper bound on the order of such induced subgraphs. Furthermore, for some connected graphs we establish a lower bound for the sum of squares of the entries of the principal eigenvector corresponding to the vertices of an independent set. Moreover, a spectral characterization of families of split graphs, involving its index and the entries of the principal eigenvector corresponding to the vertices of the maximum independent set is given. In particular, the complete split graph case is highlighted.

Materiais à base de óxidos com estrutura do tipo perovskite e compósitos como ânodos de PCES

This work was focused on the analysis of transport, thermomechanical and electrochemical properties of a series of perovskite-like oxide materials and composites for potential applications as anodes of intermediate-temperature solid oxide fuel cells (SOFCs) with lanthanum gallate and silicate solid electrolytes. The primary attention was centered on A(Mn,Nb)O3-δ (A = Sr, Ca) and (La,Sr)(Mn,Ti)O3-based systems, lanthanum chromite substituted with acceptor-type and variable-valence cations, and various Ni-containing cermets. Emphasis was given to phase stability of the materials, their crystal structure, microstructure of porous electrode layers and dense ceramics, electronic conductivity, Seebeck coefficient, oxygen permeability, thermal and chemical induced expansion, and anodic overpotentials of the electrodes deposited onto (La,Sr)(Ga,Mg)O3- and La10(Si,Al)6O27- based electrolyte membranes. In selected cases, roles of oxygen diffusivity, states of the transition metal cations relevant for the electronic transport, catalytically active additives and doped ceria protective interlayers introduced in the model electrochemical cells were assessed. The correlations between transport properties of the electrode materials and electrochemical behavior of porous electrodes showed that the principal factors governing anode performance include, in particular, electronic conduction of the anode compositions and cation interdiffusion between the electrodes and solid electrolytes. The latter is critically important for the silicatebased electrolyte membranes, leading to substantially worse anode properties compared to the electrochemical cells with lanthanum gallate solid electrolyte. The results made it possible to select several anode compositions exhibiting lower area-specific electrode resistivity compared to known analogues, such as (La,Sr)(Cr,Mn)O3-δ.

Environmental factors, clipping and fire: effects on cerrado (Brazilian savanna) native and invasive grasses

The Brazilian Cerrado houses a hugely diverse biota and is considered a conservation hotspot. One of the greatest threats to the integrity of this ecosystem is introduced African grasses, which can competitively exclude native grasses and cause changes in the microclimate and other disturbances. The Cerrado is a mosaic vegetation that provides different combinations, both spatially and temporally, of conditions that can become natural stressors to the herbaceous vegetation (water, nutrient and light availability). These mosaics are reflected in differences in relationships among native and invasive species, affecting competition and creating situations (place/season) that are more, or less, susceptible to invasion. The present study aimed to identify the different biological responses of native (Aristida recurvata, Aristida setifolia, Axonopus barbigerus, Echinolaena inflexa, Gymnopogon spicatus, Paspalum gardnerianum, Paspalum stellatum, Schizachyrium microstachyum, Schizachyrium sanguineum) and invasive (Melinis minutiflora and Andropogon gayanus) grasses to variations in natural stressors and to disturbance (fire and clipping), in order to understand changes in ecosystem functioning and competition processes between the grasses, and to understand invasion dynamics in this ecosystem. The presence of invasive species proved to affect the ecosystem functioning by increasing soil feeding activity. These differences were no longer observed in the dry season or when fires were frequent, showing that water availability and fire are more detrimental to soil feeding activity than is the vegetation. Laboratory experiments showed that both drought and flood simulated scenarios damaged both species, although the invasive species performed better under all watering conditions and responded better to fertilization. Underlying mechanisms such as the efficiency of photosynthesis and antioxidant mechanisms helped to explain this behavior. The invasive species grew faster and showed less cellular damage and a healthier photosystem, reflected in higher assimilation rates under stress. These differences between the native and invasive species were reduced with clipping, especially in dry soil with no fertilization, where the native species recovered better in relation to the pre-clipping levels. Flooding was as stressful as drought, but the invasive species can bypass this issue by growing an extensive root system, especially in the better-drained soils. Fire is more detrimental than clipping, with a slower recovery, while post-fire temperatures affect the germination of both invasive and native seeds and may be an important factor influencing the persistence of a diverse biota. This approach will finally contribute to the choice of the appropriate management techniques to preserve the Cerrado’s biodiversity.

Enquadramento cartográfico do Complexo de Granja (NW Ceará, Brasil) e avaliação de sistemas de referenciação geográfica

Este estudo destaca os benefícios da análise metódica da cartografia de base que suporta a produção de Cartografia Geológica. Em certas regiões, as cartas base publicadas estão ainda associadas a redes geodésicas clássicas e, com frequência, são introduzidos erros quando se desconsideram parâmetros essenciais como a Projecção Cartográfica e o Datum Geodésico. Com o uso sistemático dos dispositivos de GPS e dos Sistemas de Informação Geográfica para a elaboração das cartas geológicas, é imprescindível o conhecimento prévio do Sistema de Coordenadas ao qual devem estar ajustados os dados geo-espaciais. Neste estudo de caso, as diferenças e os erros associados à aquisição de coordenadas entre os Data geocêntricos WGS84 e SIRGAS2000 são residuais, atendendo aos parâmetros das cartas base, à região do globo, o campo de acção e a escala, minimizando assim a propagação de erros de posicionamento e georreferenciação subsequentes.

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

The Riemann sphere in GeoGebra

The stereographic projection is a bijective smooth map which allows us to think the sphere as the extended complex plane. Among its properties it should be emphasized the remarkable property of being angle conformal that is, it is an angle measure preserving map. Unfortunately, this projection map does not preserve areas. Besides being conformal it has also the property of projecting spherical circles in either circles or straight lines in the plane This type of projection maps seems to have been known since ancient times by Hipparchus (150 BC), being Ptolemy (AD 140) who, in his work entitled "The Planisphaerium", provided a detailed description of such a map. Nonetheless, it is worthwhile to mention that the property of the invariance of angle measure has only been established much later, in the seventeenth century, by Thomas Harriot. In fact, it was exactly in that century that the Jesuit François d’Aguilon introduced the terminology "stereographic projection" for this type of maps, which remained up to our days. Here, we shall show how we create in GeoGebra, the PRiemannz tool and its potential concerning the visualization and analysis of the properties of the stereographic projection, in addition to the viewing of the amazing relations between Möbius Transformations and stereographic projections.