Soluções quase automórficas para equações diferenciais abstratas de segunda ordem

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Representando disputas, disputando representações: cientistas sociais e campo acadêmico no ensino de sociologia

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Significados de atividade na terapia ocupacional na área de saúde mental: um olhar sobre a prática da atividade

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Alto estrutural na região de Laranjal Paulista/SP: caracterização gravimétrica e geológica

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Vanishing of Ext and Tor over complete intersections

Let (R,m) be a local complete intersection, that is, a local ring whose m-adic completion is the quotient of a complete regular local ring by a regular sequence. Let M and N be finitely generated R-modules. This dissertation concerns the vanishing of Tor(M, N) and Ext(M, N). In this context, M satisfies Serre's condition (S_{n}) if and only if M is an nth syzygy. The complexity of M is the least nonnegative integer r such that the nth Betti number of M is bounded by a polynomial of degree r-1 for all sufficiently large n. We use this notion of Serre's condition and complexity to study the vanishing of Tor_{i}(M, N). In particular, building on results of C. Huneke, D. Jorgensen and R. Wiegand [32], and H. Dao [21], we obtain new results showing that good depth properties on the R-modules M, N and MtensorN force the vanishing of Tor_{i}(M, N) for all i>0. We give examples showing that our results are sharp. We also show that if R is a one-dimensional domain and M and MtensorHom(M,R) are torsion-free, then M is free if and only if M has complexity at most one. If R is a hypersurface and Ext^{i}(M, N) has finite length for all i>>0, then the Herbrand difference [18] is defined as length(Ext^{2n}(M, N))-(Ext^{2n-1}(M, N)) for some (equivalently, every) sufficiently large integer n. In joint work with Hailong Dao, we generalize and study the Herbrand difference. Using the Grothendieck group of finitely generated R-modules, we also examined the number of consecutive vanishing of Ext^{i}(M, N) needed to ensure that Ext^{i}(M, N) = 0 for all i>>0. Our results recover and improve on most of the known bounds in the literature, especially when R has dimension two.

Class Notes for Math 918: Cohen Macaulay Modules, Instructor Roger Wiegand

Topics covered are: Cohen Macaulay modules, zero-dimensional rings, one-dimensional rings, hypersurfaces of finite Cohen-Macaulay type, complete and henselian rings, Krull-Remak-Schmidt, Canonical modules and duality, AR sequences and quivers, two-dimensional rings, ascent and descent of finite Cohen Macaulay type, bounded Cohen Macaulay type.

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Significados de atividade na terapia ocupacional na área de saúde mental: um olhar sobre a prática da atividade

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Alto estrutural na região de Laranjal Paulista/SP: caracterização gravimétrica e geológica

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Oligocene-Neogene deep-sea Columbia Channel system in the South Brazilian Basin: Seismic stratigraphy and environmental changes

The Columbia Channel (CCS) system is a depositional system located in the South Brazilian Basin, south of the Vitoria-Trindade volcanic chain. It lies in a WNW-ESE direction on the continental rise and abyssal plain, at a depth of between 4200 and 5200 m. It is formed by two depocenters elongated respectively south and north of the channel that show different sediment patterns. The area is swept by a deep western boundary current formed by AABW. The system has been previously interpreted has a mixed turbidite-contourite system. More detailed study of seismic data permits a more precise definition of the modern channel morphology, the system stratigraphy as well as the sedimentary processes and control. The modern CCS presents active erosion and/or transport along the channel. The ancient Oligo-Neogene system overlies a ""upper Cretaceous-Paleogene"" sedimentary substratum (Unit U1) bounded at the top by a major erosive ""late Eocene-early Oligocene"" discordance (D2). This ancient system is subdivided into 2 seismic units (U2 and U3). The thick basal U2 unit constitutes the larger part of the system. It consists of three subunits bounded by unconformities: D3 (""Oligocene-Miocene boundary""), D4 (""late Miocene"") and D5 (""late Pliocene""). The subunits have a fairly tabular geometry in the shallow NW depocenter associated with predominant turbidite deposits. They present a mounded shape in the deep NE depocenter, and are interpreted as forming a contourite drift. South of the channel, the deposits are interpreted as a contourite sheet drift. The surficial U3 unit forms a thin carpet of deposits. The beginning of the channel occurs at the end of U1 and during the formation of D2. Its location seems to have been determined by active faults. The channel has been active throughout the late Oligocene and Neogene and its depth increased continuously as a consequence of erosion of the channel floor and deposit aggradation along its margins. Such a mixed turbidite-contourite system (or fan drift) is characterized by frequent, rapid lateral facies variations and by unconformities that cross the whole system and are associated with increased AABW circulation. (C) 2009 Elsevier B.V. All rights reserved.

Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Ordovician klippen structures of the Sierra de Umango: New insights on Tectonic evolution of the Western Sierras Pampeanas, Argentina

The basement rock of the Pampean flat-slab (Sierras Pampeanas) in the Central Andes was uplifted and rotated in the Cenozoic era. The Western Sierras Pampeanas are characterised by meta-igneous rocks of Grenvillian Mesoproterozoic age and metasedimentary units metamorphosed in the Ordovician period. These rocks, known as the northern Cuyania composite terrane, were derived from Laurentia and accreted toward Western Gondwana during the Early Paleozoic. The Sierra de Umango is the westernmost range of the Western Sierras Pampeanas.This range is bounded by the Devonian sedimentary rocks of the Precordillera on the western side and Tertiary rocks from the Sierra de Maz and Sierra del Espinal on the eastern side and contains igneous and sedimentary rocks outcroppings from the Famatina System on the far eastern side. The Sierra de Umango evolved during a period of polyphase tectonic activity, including an Ordovician collisional event, a Devonian compressional deformation, Late Paleozoic and Mesozoic extensional faulting and sedimentation (Paganzo and Ischigualasto basins) and compressional deformation of the Andean foreland during the Cenozoic. A Nappe System and an important shear zone, La Puntilla-La Falda Shear Zone (PFSZ), characterise the Ordovician collisional event, which was related to the accretion of Cuyania Terrane to the proto-Andean margin of Gondwana. Three continuous deformational phases are recognised for this event: the D1 phase is distinguished by relics of 51 preserved as internal foliation within interkinematic staurolite por-phyroblasts and likely represents the progressive metamorphic stage; the D2 phase exhibits P-T conditions close to the metamorphic peak that were recorded in an 52 transposition or a mylonitic foliation and determine the main structure of Umango; and the D3 phase is described as a set of tight to recumbent folds with S3 axial plane foliation, often related to thrust faults, indicating the retrogressive metamorphic stage. The Nappe System shows a top-to-the S/SW sense direction of movement, and the PFSZ served as a right lateral ramp in the exhumation process. This structural pattern is indicative of an oblique collision, with the Cuyania Terrane subducting under the proto-Andean margin of Gondwana in the NE direction. This continental subduction and exhumation lasted at least 30 million years, nearly the entire Ordovician period, and produced metamorphic conditions of upper amphibolite-to-granulite facies in medium- to high-pressure regimes. At least two later events deformed the earlier structures: D4 and D5 deformational phases. The D4 deformational phase corresponds to upright folding, with wavelengths of approximately 10 km and a general N-S orientation. These folds modified the S2 surface in an approximately cylindrical manner and are associated with exposed, discrete shear zones in the Silurian Guandacolinos Granite. The cylindrical pattern and subhorizontal axis of the D4 folds indicates that the S2 surface was originally flat-lying. The D4 folds are responsible for preserving the basement unit Juchi Orthogneiss synformal klippen. This deformation corresponds to the Chanica Tectonic during the interval between the Devonian and Carboniferous periods. The D5 deformational phase comprehends cuspate-lobate shaped open plunging folds with E W high-angle axes (D5 folds) and sub-vertical spaced cleavage. The D5 folds and related spaced cleavage deformed the previous structures and could be associated with uplifting during the Andean Cycle. (C) 2012 Elsevier Ltd. All rights reserved.

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2D

A direct reconstruction algorithm for complex conductivities in W-2,W-infinity(Omega), where Omega is a bounded, simply connected Lipschitz domain in R-2, is presented. The framework is based on the uniqueness proof by Francini (2000 Inverse Problems 6 107-19), but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.