Análise de estabilidade de sistemas dinâmicos híbridos e descontínuos modelados por semigrupos:

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A model of road effect using line integrals and a test of the performance of two new road indices using the distribution of small mammals in an Atlantic Forest landscape

Effects of roads on wildlife and its habitat have been measured using metrics, such as the nearest road distance, road density, and effective mesh size. In this work we introduce two new indices: (1) Integral Road Effect (IRE), which measured the sum effects of points in a road at a fixed point in the forest; and (2) Average Value of the Infinitesimal Road Effect (AVIRE), which measured the average of the effects of roads at this point. IRE is formally defined as the line integral of a special function (the infinitesimal road effect) along the curves that model the roads, whereas AVIRE is the quotient of IRE by the length of the roads. Combining tools of ArcGIS software with a numerical algorithm, we calculated these and other road and habitat cover indices in a sample of points in a human-modified landscape in the Brazilian Atlantic Forest, where data on the abundance of two groups of small mammals (forest specialists and habitat generalists) were collected in the field. We then compared through the Akaike Information Criterion (AIC) a set of candidate regression models to explain the variation in small mammal abundance, including models with our two new road indices (AVIRE and IRE) or models with other road effect indices (nearest road distance, mesh size, and road density), and reference models (containing only habitat indices, or only the intercept without the effect of any variable). Compared to other road effect indices, AVIRE showed the best performance to explain abundance of forest specialist species, whereas the nearest road distance obtained the best performance to generalist species. AVIRE and habitat together were included in the best model for both small mammal groups, that is, higher abundance of specialist and generalist small mammals occurred where there is lower average road effect (less AVIRE) and more habitat. Moreover, AVIRE was not significantly correlated with habitat cover of specialists and generalists differing from the other road effect indices, except mesh size, which allows for separating the effect of roads from the effect of habitat on small mammal communities. We suggest that the proposed indices and GIS procedures could also be useful to describe other spatial ecological phenomena, such as edge effect in habitat fragments. (C) 2012 Elsevier B.V. All rights reserved.

Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier Inc. All rights reserved.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Visual complaints and visual hallucinations in Parkinson's disease

Background Visual symptoms are common in Parkinson's disease (PD) and are frequently under-diagnosed. The detection of visual symptoms is important for differential diagnosis and patient management. Aim To establish the prevalence of recurrent visual complaints (RVC) and recurrent visual hallucinations (RVH) and to investigate their interaction in PD patients and controls. Methods This cross-sectional study included 88 PD patients and 90 controls. RVC and RVH were assessed with a visual symptom questionnaire and the North-East-Visual-Hallucinations-Interview (NEVHI). Results Double vision (PD vs. Controls: 18.2% vs. 1.3%; p < 0.001), misjudging objects when walking (PD vs. Controls: 12.5% vs. 1.3%; p < 0.01), words moving whilst reading (PD vs. Controls: 17.0% vs. 1.3%; p < 0.001) and freezing in narrow spaces (PD vs. Controls: 30.7% vs. 0%; p < 0.001) were almost exclusively found in PD patients. The same was true for recurrent complex visual hallucinations and illusions (PD vs. Controls: both 17.0% vs. 0%; p < 0.001). Multiple RVC (43.2% vs. 15.8%) and multiple RVH (29.5% vs. 5.6%) were also more common in PD patients (both p < 0.001). RVC did not predict recurrent complex visual hallucinations; but double vision (p = 0.018, R2 = 0.302) and misjudging objects (p = 0.002, R2 = 0.302) predicted passage hallucinations. Misjudging objects also predicted the feeling of presence (p = 0.010, R2 = 0.321). Conclusions Multiple and recurrent visual symptoms are common in PD. RVC emerged as risk factors predictive of the minor forms of hallucinations, but not recurrent complex visual hallucinations.

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Consideration of Multi-Phase Criterion in the Differential Protection Algorithm for High-Impedance Grounded Synchronous Generators

The generator differential protection is one of the most important electrical protections of synchronous generator stator windings. Its operation principle is based on the comparison of the input current and output current at each phase winding. Unwanted trip commands are usually caused by CT saturation, wrong CT selection, or the fact that they may come from different manufacturers. In generators grounded through high impedance, only phase-to-phase or three-phase faults can be detected by the differential protection. This kind of fault causes differential current to flow in, at least, two phases of the winding. Several cases of unwanted trip commands caused by the appearance of differential current in only one phase of the generator have been reported. In this paper multi-phase criterion is proposed for generator differential protection algorithm when applied to high impedance grounded generators.

Regulation of Oleoresinosis in Grand Fir (Abies grandis)1 : Differential Transcriptional Control of Monoterpene, Sesquiterpene, and Diterpene Synthase Genes in Response to Wounding

Grand fir (Abies grandis Lindl.) has been developed as a model system for the study of wound-induced oleoresinosis in conifers as a response to insect attack. Oleoresin is a roughly equal mixture of turpentine (85% monoterpenes [C10] and 15% sesquiterpenes [C15]) and rosin (diterpene [C20] resin acids) that acts to seal wounds and is toxic to both invading insects and their pathogenic fungal symbionts. The dynamic regulation of wound-induced oleoresin formation was studied over 29 d at the enzyme level by in vitro assay of the three classes of synthases directly responsible for the formation of monoterpenes, sesquiterpenes, and diterpenes from the corresponding C10, C15, and C20 prenyl diphosphate precursors, and at the gene level by RNA-blot hybridization using terpene synthase class-directed DNA probes. In overall appearance, the shapes of the time-course curves for all classes of synthase activities are similar, suggesting coordinate formation of all of the terpenoid types. However, closer inspection indicates that the monoterpene synthases arise earlier, as shown by an abbreviated time course over 6 to 48 h. RNA-blot analyses indicated that the genes for all three classes of enzymes are transcriptionally activated in response to wounding, with the monoterpene synthases up-regulated first (transcripts detectable 2 h after wounding), in agreement with the results of cell-free assays of monoterpene synthase activity, followed by the coordinately regulated sesquiterpene synthases and diterpene synthases (transcription beginning on d 3–4). The differential timing in the production of oleoresin components of this defense response is consistent with the immediate formation of monoterpenes to act as insect toxins and their later generation at solvent levels for the mobilization of resin acids responsible for wound sealing.

Topics in differential geometry.

Based on lectures given in the spring of 1949; a few of the latest results of work done since that time have been included.

Beispiele über die Lehren des Differential-, Integral- und Variations-Kalkul's und Aufgaben über deren Anwendung /

No more published?

Notes on intrinsic calculus /

Mode of access: Internet.

Concepts from tensor analysis and differential geometry.

Mode of access: Internet.

L.A. Sohncke's Sammlung von aufgaben aus der differential- und integralrechnung /

th. 1. Differentialrechnung.--th. 2. Integralrechnung.

Integral calculus,

Mode of access: Internet.

The JNR Property and the Borel Structure of a Banach Space

Research partially supported by a grant of Caja de Ahorros del Mediterraneo.