Sobre o Teorema da Função Inversa

Pós-graduação em Matemática em Rede Nacional - IBILCE

Class Notes for Math 921/922: Real Analysis, Instructor Mikil Foss

Topics include: Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon- Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration, Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon-Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration.

Relationship between eggplant seed morphology and germination

Structural differences such as abnormalities, damage and free spaces in seeds may affect germination. The aim of this study was to study the relationship between eggplant seed morphology and seed germination. Ten seed lots of the eggplant cultivar Embu were evaluated by X-ray image analysis and the germination test. Seed image analysis was performed by Image Pro Plus® software and the whole seed area and free space between the embryo and endosperm were measured. The internal seed area filled by the embryo and endosperm was calculated from the difference between the whole seed and free space areas. Based on these results and visual seed analysis, seeds were classified into three categories and information on germination was obtained for each one. X-ray image analysis provides a perfect view of the internal seed parts and for seed morphology studies. An increase in seed area filled by the endosperm and embryo does not improve seed germination. Mechanical seed damage and deteriorated tissues can adversely affect seed germination.

Harnack inequalities in sub-Riemannian settings

In the present thesis, we discuss the main notions of an axiomatic approach for an invariant Harnack inequality. This procedure, originated from techniques for fully nonlinear elliptic operators, has been developed by Di Fazio, Gutiérrez, and Lanconelli in the general settings of doubling Hölder quasi-metric spaces. The main tools of the approach are the so-called double ball property and critical density property: the validity of these properties implies an invariant Harnack inequality. We are mainly interested in the horizontally elliptic operators, i.e. some second order linear degenerate-elliptic operators which are elliptic with respect to the horizontal directions of a Carnot group. An invariant Harnack inequality of Krylov-Safonov type is still an open problem in this context. In the thesis we show how the double ball property is related to the solvability of a kind of exterior Dirichlet problem for these operators. More precisely, it is a consequence of the existence of some suitable interior barrier functions of Bouligand-type. By following these ideas, we prove the double ball property for a generic step two Carnot group. Regarding the critical density, we generalize to the setting of H-type groups some arguments by Gutiérrez and Tournier for the Heisenberg group. We recognize that the critical density holds true in these peculiar contexts by assuming a Cordes-Landis type condition for the coefficient matrix of the operator. By the axiomatic approach, we thus prove an invariant Harnack inequality in H-type groups which is uniform in the class of the coefficient matrices with prescribed bounds for the eigenvalues and satisfying such a Cordes-Landis condition.

Taylor formula for Kolmogorov equations

After briefly discuss the natural homogeneous Lie group structure induced by Kolmogorov equations in chapter one, we define an intrinsic version of Taylor polynomials and Holder spaces in chapter two. We also compare our definition with others yet known in literature. In chapter three we prove an analogue of Taylor formula, that is an estimate of the remainder in terms of the homogeneous metric.

A Divided City in a Common Market: EU Citizenship and Everyday Instrumentalities on the Polish-German Border

Based on an ethnographic case study in the border cities of Frankfurt (Oder), Germany and Słubice, Poland, this article explores the construction and maintenance of ethnic difference within the transnational economic and social spaces created by the European Union's common market. Through an examination of three domains of cross-border citizenship practice - shopping and consumption, housing and work - this article argues that even as the European Union deploys policies aimed at creating de-territorialised and supranational forms of identity and citizenship, economic asymmetries and hierarchies of value embedded within these policies grant rights differentially in ways that continue to be linked to ethnicity and nationality.

Fluids and barriers of the CNS establish immune privilege by confining immune surveillance to a two-walled castle moat surrounding the CNS castle

Neuronal activity within the central nervous system (CNS) strictly depends on homeostasis and therefore does not tolerate uncontrolled entry of blood components. It has been generally believed that under normal conditions, the endothelial blood-brain barrier (BBB) and the epithelial blood-cerebrospinal fluid barrier (BCSFB) prevent immune cell entry into the CNS. This view has recently changed when it was realized that activated T cells are able to breach the BBB and the BCSFB to perform immune surveillance of the CNS. Here we propose that the immune privilege of the CNS is established by the specific morphological architecture of its borders resembling that of a medieval castle. The BBB and the BCSFB serve as the outer walls of the castle, which can be breached by activated immune cells serving as messengers for outside dangers. Having crossed the BBB or the BCSFB they reach the castle moat, namely the cerebrospinal fluid (CSF)-drained leptomeningeal and perivascular spaces of the CNS. Next to the CNS parenchyma, the castle moat is bordered by a second wall, the glia limitans, composed of astrocytic foot processes and a parenchymal basement membrane. Inside the castle, that is the CNS parenchyma proper, the royal family of sensitive neurons resides with their servants, the glial cells. Within the CSF-drained castle moat, macrophages serve as guards collecting all the information from within the castle, which they can present to the immune-surveying T cells. If in their communication with the castle moat macrophages, T cells recognize their specific antigen and see that the royal family is in danger, they will become activated and by opening doors in the outer wall of the castle allow the entry of additional immune cells into the castle moat. From there, immune cells may breach the inner castle wall with the aim to defend the castle inhabitants by eliminating the invading enemy. If the immune response by unknown mechanisms turns against self, that is the castle inhabitants, this may allow for continuous entry of immune cells into the castle and lead to the death of the castle inhabitants, and finally members of the royal family, the neurons. This review will summarize the molecular traffic signals known to allow immune cells to breach the outer and inner walls of the CNS castle moat and will highlight the importance of the CSF-drained castle moat in maintaining immune surveillance and in mounting immune responses in the CNS.

Effects of Landscape Segregation on Livelihood Vulnerability: Moving From Extensive Shifting Cultivation to Rotational Agriculture and Natural Forests in Northern Laos

This study investigates four decades of socio-economic and environmental change in a shifting cultivation landscape in the northern uplands of Laos. Historical changes in land cover and land use were analyzed using a chronological series of remote sensing data. Impacts of landscape change on local livelihoods were investigated in seven villages through interviews with various stakeholders. The study reveals that the complex mosaics of agriculture and forest patches observed in the study area have long constituted key assets for the resilience of local livelihood systems in the face of environmental and socio-economic risks. However, over the past 20 years, a process of segregating agricultural and forest spaces has increased the vulnerability of local land users. This process is a direct outcome of policies aimed at increasing national forest cover, eradicating shifting cultivation and fostering the emergence of more intensive and commercial agricultural practices. We argue that agriculture-forest segregation should be buffered in such a way that a diversity of livelihood opportunities and economic development pathways can be maintained.

Differential optical densities of intraretinal spaces

PURPOSE: To test the hypothesis that hyporeflective spaces in the neuroretina found on optical coherence tomography (OCT) examination have different optical reflectivities according to whether they are associated with exudation or degeneration. METHODS: Retrospective analysis of eyes with idiopathic perifoveal telangiectasia (IPT), diabetic macular edema (DME), idiopathic central serous chorioretinopathy (CSC), retinitis pigmentosa (RP), or cone dystrophy (CD) and eyes of healthy control subjects. OCT scans were performed. Raw scan data were exported and used to calculate light reflectivity profiles. Reflectivity data were acquired by projecting three rectangular boxes, each 50 pixels long and 5 pixels wide, into the intraretinal cystoid spaces, centrally onto unaffected peripheral RPE, and onto the prefoveolar vitreous. Light reflectivity in the retinal pigment epithelium (RPE), vitreous, and intraretinal spaces for the different retinal conditions and control subjects were compared. RESULTS: Reflectivities of the vitreous and the RPE were similar among the groups. Hyporeflective spaces in eyes with exudation (DME, RP, and CSC) had higher reflectivity compared with the mean reflectivity of the vitreous, whereas the cystoid spaces in the maculae of the eyes without exudation (CD and IPT) had a lower reflectivity than did the normal vitreous. CONCLUSIONS: Analysis of the light reflectivity profiles may be a tool to determine whether the density of hyporeflective spaces in the macula is greater or less than that of the vitreous, and may be a way to differentiate degenerative from exudative macular disease.

Transnational Migration and Cross-border Mobility in the Serbian-Hungarian Border Region

The study is aiming to present migrant groups in the Serbian-Hungarian border region which are playing a role in forming transnational migration, ransnational networks and transnational spaces. Transnational migrants are using material, cultural, social and symbolical capital in various forms. The everyday activities of the people as well as their mobility, emotional attachments, and economic relationships have contributed to a transnational region the cross-border contacts in the last century were always present, even in spite of political and historical changes, only their intensity, political charge and tension has been changing. The asymmetries defining the border region has been reflected in different directions, places, time and in different volume. In this specially built and constantly reorganising scope, people who were living their everyday life have tried to use the differences for their benefit, and to improve their possibilities. With their transnational lifestyles and cross-border networks, they substantially contribute to the stability and prosperity of the cross-border region.

Global Cultural Law and Policy in the Age of Ubiquitous Internet

Digital technologies and the Internet in particular have transformed the ways we create, distribute, use, reuse and consume cultural content; have impacted on the workings of the cultural industries, and more generally on the processes of making, experiencing and remembering culture in local and global spaces. Yet, few of these, often profound, transformations have found reflection in law and institutional design. Cultural policy toolkits, in particular at the international level, are still very much offline/analogue and conceive of culture as static property linked to national sovereignty and state boundaries. The article describes this state of affairs and asks the key question of whether there is a need to reform global cultural law and policy and if yes, what the essential elements of such a reform should be.

Heisenberg symmetry and hypermultiplet manifolds

We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry – as opposed to Heisenberg U (1). We finally discuss the realization of the latter by gauging appropriate Sp(2, 4) generators in N = 2 conformal supergravity.

Exploring the association of children's engagement in nature and outdoor activity with physical activity: A systematic review

The natural environment and green spaces are settings that may facilitate physical activity and, as a result, combat childhood obesity and benefit children's physical health. A systematic review was conducted to assess the effect of children's engagement in outdoor activity on children's physical activity levels. A total of 169 articles were initially identified, of which 11 were eligible for inclusion in the systematic review. Studies were heterogeneous: cross-sectional, RCT, cohort, and direct observation. Study participants were between the ages of 3-15 years, and physical activity was measured by accelerometers, pedometers, direct observation or surveys. A majority of the studies (9/11) found a positive association between time spent outdoors and physical activity in children and adolescents. Of these 9 studies, 5 found this association specifically between time spent outdoors in greenspace and physical activity. Despite limitations, the findings of this review support the positive association between time spent outdoors and physical activity in children and adolescents, and the notion that children and adolescents who spend more time outdoors are more physically active. This demonstrates the need to use outdoor environments as settings for children's and adolescents' physical activity.^

Comments and conclusions on the I International Seminary “Interdiscipline in Territorial Management "

El objetivo principal del I Seminario Internacional “ La Interdisciplina en el Ordenamiento Territorial, fue debatir sobre el aporte de las diversas disciplinas que confluyen en el Ordenamiento Territorial. Las ponencias presentadas fueron de un alto nivel científico y a partir de los casos analizados se demuestra que en la realidad coexisten espacios fragmentados social y económicamente, ya que se verifica la existencia de espacios globalizados con fuertes inversiones frente a otros que quedan marginados. Esta situación se manifiesta a través de la presencia de nuevos procesos de expansión y suburbanización, espacios rurales que se desvalorizan y se abandonan, ecosistemas naturales que deben ser protegidos para evitar un mayor deterioro medioambiental. Entre las conclusiones de los trabajos presentados se destacan: • La necesidad del mejoramiento de la capacidad de gestión a través de propuestas de nuevas metodológicas de trabajo, • la búsqueda de soluciones a las grandes disparidades socioeconómicas y al progresivo deterioro ambiental a partir del consenso de los agentes que intervienen, • la formulación de nuevas normativas acordes a las exigencias que impone la economía de mercado, entre otros.

Desarrollo de un modelo de predimensionado de costes de construcción en el proyecto arquitectónico

El objetivo de la presente investigación es el desarrollo de un modelo de cálculo rápido, eficiente y preciso, para la estimación de los costes finales de construcción, en las fases preliminares del proyecto arquitectónico. Se trata de una herramienta a utilizar durante el proceso de elaboración de estudios previos, anteproyecto y proyecto básico, no siendo por tanto preciso para calcular el “predimensionado de costes” disponer de la total definición grafica y literal del proyecto. Se parte de la hipótesis de que en la aplicación práctica del modelo no se producirán desviaciones superiores al 10 % sobre el coste final de la obra proyectada. Para ello se formulan en el modelo de predimensionado cinco niveles de estimación de costes, de menor a mayor definición conceptual y gráfica del proyecto arquitectónico. Los cinco niveles de cálculo son: dos que toman como referencia los valores “exógenos” de venta de las viviendas (promoción inicial y promoción básica) y tres basados en cálculos de costes “endógenos” de la obra proyectada (estudios previos, anteproyecto y proyecto básico). El primer nivel de estimación de carácter “exógeno” (nivel .1), se calcula en base a la valoración de mercado de la promoción inmobiliaria y a su porcentaje de repercusión de suelo sobre el valor de venta de las viviendas. El quinto nivel de valoración, también de carácter “exógeno” (nivel .5), se calcula a partir del contraste entre el valor externo básico de mercado, los costes de construcción y los gastos de promoción estimados de la obra proyectada. Este contraste entre la “repercusión del coste de construcción” y el valor de mercado, supone una innovación respecto a los modelos de predimensionado de costes existentes, como proceso metodológico de verificación y validación extrínseca, de la precisión y validez de las estimaciones resultantes de la aplicación práctica del modelo, que se denomina Pcr.5n (Predimensionado costes de referencia con .5niveles de cálculo según fase de definición proyectual / ideación arquitectónica). Los otros tres niveles de predimensionado de costes de construcción “endógenos”, se estiman mediante cálculos analíticos internos por unidades de obra y cálculos sintéticos por sistemas constructivos y espacios funcionales, lo que se lleva a cabo en las etapas iniciales del proyecto correspondientes a estudios previos (nivel .2), anteproyecto (nivel .3) y proyecto básico (nivel .4). Estos cálculos teóricos internos son finalmente evaluados y validados mediante la aplicación práctica del modelo en obras de edificación residencial, de las que se conocen sus costes reales de liquidación final de obra. Según va evolucionando y se incrementa el nivel de definición y desarrollo del proyecto, desde los estudios previos hasta el proyecto básico, el cálculo se va perfeccionando en su nivel de eficiencia y precisión de la estimación, según la metodología aplicada: [aproximaciones sucesivas en intervalos finitos], siendo la hipótesis básica como anteriormente se ha avanzado, lograr una desviación máxima de una décima parte en el cálculo estimativo del predimensionado del coste real de obra. El cálculo del coste de ejecución material de la obra, se desarrolla en base a parámetros cúbicos funcionales “tridimensionales” del espacio proyectado y parámetros métricos constructivos “bidimensionales” de la envolvente exterior de cubierta/fachada y de la huella del edificio sobre el terreno. Los costes funcionales y constructivos se ponderan en cada fase del proceso de cálculo con sus parámetros “temáticos/específicos” de gestión (Pg), proyecto (Pp) y ejecución (Pe) de la concreta obra presupuestada, para finalmente estimar el coste de construcción por contrata, como resultado de incrementar al coste de ejecución material el porcentaje correspondiente al parámetro temático/especifico de la obra proyectada. El modelo de predimensionado de costes de construcción Pcr.5n, será una herramienta de gran interés y utilidad en el ámbito profesional, para la estimación del coste correspondiente al Proyecto Básico previsto en el marco técnico y legal de aplicación. Según el Anejo I del Código Técnico de la Edificación (CTE), es de obligado cumplimiento que el proyecto básico contenga una “Valoración aproximada de la ejecución material de la obra proyectada por capítulos”, es decir , que el Proyecto Básico ha de contener al menos un “presupuesto aproximado”, por capítulos, oficios ó tecnologías. El referido cálculo aproximado del presupuesto en el Proyecto Básico, necesariamente se ha de realizar mediante la técnica del predimensionado de costes, dado que en esta fase del proyecto arquitectónico aún no se dispone de cálculos de estructura, planos de acondicionamiento e instalaciones, ni de la resolución constructiva de la envolvente, por cuanto no se han desarrollado las especificaciones propias del posterior proyecto de ejecución. Esta estimación aproximada del coste de la obra, es sencilla de calcular mediante la aplicación práctica del modelo desarrollado, y ello tanto para estudiantes como para profesionales del sector de la construcción. Como se contiene y justifica en el presente trabajo, la aplicación práctica del modelo para el cálculo de costes en las fases preliminares del proyecto, es rápida y certera, siendo de sencilla aplicación tanto en vivienda unifamiliar (aisladas y pareadas), como en viviendas colectivas (bloques y manzanas). También, el modelo es de aplicación en el ámbito de la valoración inmobiliaria, tasaciones, análisis de viabilidad económica de promociones inmobiliarias, estimación de costes de obras terminadas y en general, cuando no se dispone del proyecto de ejecución y sea preciso calcular los costes de construcción de las obras proyectadas. Además, el modelo puede ser de aplicación para el chequeo de presupuestos calculados por el método analítico tradicional (estado de mediciones pormenorizadas por sus precios unitarios y costes descompuestos), tanto en obras de iniciativa privada como en obras promovidas por las Administraciones Públicas. Por último, como líneas abiertas a futuras investigaciones, el modelo de “predimensionado costes de referencia 5 niveles de cálculo”, se podría adaptar y aplicar para otros usos y tipologías diferentes a la residencial, como edificios de equipamientos y dotaciones públicas, valoración de edificios históricos, obras de urbanización interior y exterior de parcela, proyectos de parques y jardines, etc….. Estas lineas de investigación suponen trabajos paralelos al aquí desarrollado, y que a modo de avance parcial se recogen en las comunicaciones presentadas en los Congresos internacionales Scieconf/Junio 2013, Rics‐Cobra/Septiembre 2013 y en el IV Congreso nacional de patología en la edificación‐Ucam/Abril 2014. ABSTRACT The aim of this research is to develop a fast, efficient and accurate calculation model to estimate the final costs of construction, during the preliminary stages of the architectural project. It is a tool to be used during the preliminary study process, drafting and basic project. It is not therefore necessary to have the exact, graphic definition of the project in order to be able to calculate the cost‐scaling. It is assumed that no deviation 10% higher than the final cost of the projected work will occur during the implementation. To that purpose five levels of cost estimation are formulated in the scaling model, from a lower to a higher conceptual and graphic definition of the architectural project. The five calculation levels are: two that take as point of reference the ”exogenous” values of house sales (initial development and basic development), and three based on calculation of endogenous costs (preliminary study, drafting and basic project). The first ”exogenous” estimation level (level.1) is calculated over the market valuation of real estate development and the proportion the cost of land has over the value of the houses. The fifth level of valuation, also an ”exogenous” one (level.5) is calculated from the contrast between the basic external market value, the construction costs, and the estimated development costs of the projected work. This contrast between the ”repercussions of construction costs” and the market value is an innovation regarding the existing cost‐scaling models, as a methodological process of extrinsic verification and validation, of the accuracy and validity of the estimations obtained from the implementation of the model, which is called Pcr.5n (reference cost‐scaling with .5calculation levels according to the stage of project definition/ architectural conceptualization) The other three levels of “endogenous” construction cost‐scaling are estimated from internal analytical calculations by project units and synthetic calculations by construction systems and functional spaces. This is performed during the initial stages of the project corresponding to preliminary study process (level.2), drafting (level.3) and basic project (level.4). These theoretical internal calculations are finally evaluated and validated via implementation of the model in residential buildings, whose real costs on final payment of the works are known. As the level of definition and development of the project evolves, from preliminary study to basic project, the calculation improves in its level of efficiency and estimation accuracy, following the applied methodology: [successive approximations at finite intervals]. The basic hypothesis as above has been made, achieving a maximum deviation of one tenth, in the estimated calculation of the true cost of predimensioning work. The cost calculation for material execution of the works is developed from functional “three‐dimensional” cubic parameters for the planned space and constructive “two dimensional” metric parameters for the surface that envelopes around the facade and the building’s footprint on the plot. The functional and building costs are analyzed at every stage of the process of calculation with “thematic/specific” parameters of management (Pg), project (Pp) and execution (Pe) of the estimated work in question, and finally the cost of contractual construction is estimated, as a consequence of increasing the cost of material execution with the percentage pertaining to the thematic/specific parameter of the projected work. The construction cost‐scaling Pcr.5n model will be a useful tool of great interest in the professional field to estimate the cost of the Basic Project as prescribed in the technical and legal framework of application. According to the appendix of the Technical Building Code (CTE), it is compulsory that the basic project contains an “approximate valuation of the material execution of the work, projected by chapters”, that is, that the basic project must contain at least an “approximate estimate” by chapter, trade or technology. This approximate estimate in the Basic Project is to be performed through the cost‐scaling technique, given that structural calculations, reconditioning plans and definitive contruction details of the envelope are still not available at this stage of the architectural project, insofar as specifications pertaining to the later project have not yet been developed. This approximate estimate of the cost of the works is easy to calculate through the implementation of the given model, both for students and professionals of the building sector. As explained and justified in this work, the implementation of the model for cost‐scaling during the preliminary stage is fast and accurate, as well as easy to apply both in single‐family houses (detached and semi‐detached) and collective housing (blocks). The model can also be applied in the field of the real‐estate valuation, official appraisal, analysis of the economic viability of real estate developments, estimate of the cost of finished projects and, generally, when an implementation project is not available and it is necessary to calculate the building costs of the projected works. The model can also be applied to check estimates calculated by the traditional analytical method (state of measurements broken down into price per unit cost details), both in private works and those promoted by Public Authorities. Finally, as potential lines for future research, the “five levels of calculation cost‐scaling model”, could be adapted and applied to purposes and typologies other than the residential one, such as service buildings and public facilities, valuation of historical buildings, interior and exterior development works, park and garden planning, etc… These lines of investigation are parallel to this one and, by way of a preview, can be found in the dissertations given in the International Congresses Scieconf/June 2013, Rics‐Cobra/September 2013 and in the IV Congress on building pathology ‐Ucam/April 2014.