Considerações históricas sobre o infinito e alguns de seus paradoxos

This research aims to elucidate some of the historical aspects of the idea of infinity during the creation of calculus and set theory. It also seeks to raise discussions about the nature of infinity: current infinite and potential infinite. For this, we conducted a survey with a qualitative approach in the form of exploratory study. This study was based on books of Mathematics' History and other scientific works such as articles, theses and dissertations on the subject. This work will bring the view of some philosophers and thinkers about the infinite, such as: Pythagoras, Plato, Aristotle, Galilei, Augustine, Cantor. The research will be presented according to chronological order. The objective of the research is to understand the infinite from ancient Greece with the paradoxes of Zeno, during the time which the conflict between the conceptions atomistic and continuity were dominant, and in this context that Zeno launches its paradoxes which contradict much a concept as another, until the theory Cantor set, bringing some paradoxes related to this theory, namely paradox of Russell and Hilbert's paradox. The study also presents these paradoxes mentioned under the mathematical point of view and the light of calculus and set theory

Considerações históricas sobre o infinito e alguns de seus paradoxos

This research aims to elucidate some of the historical aspects of the idea of infinity during the creation of calculus and set theory. It also seeks to raise discussions about the nature of infinity: current infinite and potential infinite. For this, we conducted a survey with a qualitative approach in the form of exploratory study. This study was based on books of Mathematics' History and other scientific works such as articles, theses and dissertations on the subject. This work will bring the view of some philosophers and thinkers about the infinite, such as: Pythagoras, Plato, Aristotle, Galilei, Augustine, Cantor. The research will be presented according to chronological order. The objective of the research is to understand the infinite from ancient Greece with the paradoxes of Zeno, during the time which the conflict between the conceptions atomistic and continuity were dominant, and in this context that Zeno launches its paradoxes which contradict much a concept as another, until the theory Cantor set, bringing some paradoxes related to this theory, namely paradox of Russell and Hilbert's paradox. The study also presents these paradoxes mentioned under the mathematical point of view and the light of calculus and set theory

An ecological economic interpretation of the Jevons effect

This article develops an ecological economic interpretation of the Jevons effect. Moreover, it is argued that under the neoclassical paradigm there are no elements with which to foresee the long-term existence of this phenomenon. The objective of these arguments is to demonstrate that the Jevons effect can be used to compare the ability of neoclassical and ecological economics describing the social appropriation of nature. This is elaborated in two steps. First, we show the importance of the thesis that the economy cannot be cut off from the biophysical materiality of what is produced to give consistency to the so-called Khazzoom-Brookes postulate. It is made clear that this supposition is exogenous to the neoclassical paradigm. Second, the supposition of the biophysical materiality of what is produced is utilized to make an ecological economic interpretation of the Jevons effect. Afterwards, a comparison is made between the neoclassical and the ecological economic perspectives. This comparison leads to the following conclusions: (i) the persistent presence of the Jevons effect in the long run is an anomaly in the neoclassical paradigm; (ii) the observation of the non-existence of the Jevons effect is a refutation of the supposition that economic growth and biophysical materiality are not separable, a central thesis defended by ecological economists. This situation makes possible to use the Jevons effect as a 'laboratory test' to compare the ability of neoclassical and ecological economic paradigms to describe the social appropriation of nature. (C) 20111 Elsevier B.V. All rights reserved.

The re-establishment of the normal blood lactate response to exercise in humans after prolonged acclimatization to altitude

[EN] 1. One to five weeks of chronic exposure to hypoxia has been shown to reduce peak blood lactate concentration compared to acute exposure to hypoxia during exercise, the high altitude 'lactate paradox'. However, we hypothesize that a sufficiently long exposure to hypoxia would result in a blood lactate and net lactate release from the active leg to an extent similar to that observed in acute hypoxia, independent of work intensity. 2. Six Danish lowlanders (25-26 years) were studied during graded incremental bicycle exercise under four conditions: at sea level breathing either ambient air (0 m normoxia) or a low-oxygen gas mixture (10 % O(2) in N(2), 0 m acute hypoxia) and after 9 weeks of acclimatization to 5260 m breathing either ambient air (5260 m chronic hypoxia) or a normoxic gas mixture (47 % O(2) in N(2), 5260 m acute normoxia). In addition, one-leg knee-extensor exercise was performed during 5260 m chronic hypoxia and 5260 m acute normoxia. 3. During incremental bicycle exercise, the arterial lactate concentrations were similar at sub-maximal work at 0 m acute hypoxia and 5260 m chronic hypoxia but higher compared to both 0 m normoxia and 5260 m acute normoxia. However, peak lactate concentration was similar under all conditions (10.0 +/- 1.3, 10.7 +/- 2.0, 10.9 +/- 2.3 and 11.0 +/- 1.0 mmol l(-1)) at 0 m normoxia, 0 m acute hypoxia, 5260 m chronic hypoxia and 5260 m acute normoxia, respectively. Despite a similar lactate concentration at sub-maximal and maximal workload, the net lactate release from the leg was lower during 0 m acute hypoxia (peak 8.4 +/- 1.6 mmol min(-1)) than at 5260 m chronic hypoxia (peak 12.8 +/- 2.2 mmol min(-1)). The same was observed for 0 m normoxia (peak 8.9 +/- 2.0 mmol min(-1)) compared to 5260 m acute normoxia (peak 12.6 +/- 3.6 mmol min(-1)). Exercise after acclimatization with a small muscle mass (one-leg knee-extensor) elicited similar lactate concentrations (peak 4.4 +/- 0.2 vs. 3.9 +/- 0.3 mmol l(-1)) and net lactate release (peak 16.4 +/- 1.8 vs. 14.3 mmol l(-1)) from the active leg at 5260 m chronic hypoxia and 5260 m acute normoxia. 4. In conclusion, in lowlanders acclimatized for 9 weeks to an altitude of 5260 m, the arterial lactate concentration was similar at 0 m acute hypoxia and 5260 m chronic hypoxia. The net lactate release from the active leg was higher at 5260 m chronic hypoxia compared to 0 m acute hypoxia, implying an enhanced lactate utilization with prolonged acclimatization to altitude. The present study clearly shows the absence of a lactate paradox in lowlanders sufficiently acclimatized to altitude.

The structure of planktonic communities under variable coastal upwelling conditions off Cape Ghir (31ºN), in the Canary Current System (NW Africa)

Universidad de Las Palmas de Gran Canaria. Facultad de Ciencias del Mar. Programa de doctorado en Oceanografía. Diploma de Estudios Avanzados

Longitudinal bar buckling behavior

Reinforced concrete columns might fail because of buckling of the longitudinal reinforcing bar when exposed to earthquake motions. Depending on the hoop stiffness and the length-over-diameter ratio, the instability can be local (in between two subsequent hoops) or global (the buckling length comprises several hoop spacings). To get insight into the topic, an extensive literary research of 19 existing models has been carried out including different approaches and assumptions which yield different results. Finite element fiberanalysis was carried out to study the local buckling behavior with varying length-over-diameter and initial imperfection-over-diameter ratios. The comparison of the analytical results with some experimental results shows good agreement before the post buckling behavior undergoes large deformation. Furthermore, different global buckling analysis cases were run considering the influence of different parameters; for certain hoop stiffnesses and length-over-diameter ratios local buckling was encountered. A parametric study yields an adimensional critical stress in function of a stiffness ratio characterized by the reinforcement configuration. Colonne in cemento armato possono collassare per via dell’instabilità dell’armatura longitudinale se sottoposte all’azione di un sisma. In funzione della rigidezza dei ferri trasversali e del rapporto lunghezza d’inflessione-diametro, l’instabilità può essere locale (fra due staffe adiacenti) o globale (la lunghezza d’instabilità comprende alcune staffe). Per introdurre alla materia, è proposta un’esauriente ricerca bibliografica di 19 modelli esistenti che include approcci e ipotesi differenti che portano a risultati distinti. Tramite un’analisi a fibre e elementi finiti si è studiata l’instabilità locale con vari rapporti lunghezza d’inflessione-diametro e imperfezione iniziale-diametro. Il confronto dei risultati analitici con quelli sperimentali mostra una buona coincidenza fino al raggiungimento di grandi spostamenti. Inoltre, il caso d’instabilità globale è stato simulato valutando l’influenza di vari parametri; per certe configurazioni di rigidezza delle staffe e lunghezza d’inflessione-diametro si hanno ottenuto casi di instabilità locale. Uno studio parametrico ha permesso di ottenere un carico critico adimensionale in funzione del rapporto di rigidezza dato dalle caratteristiche dell’armatura.

The Integrated European Project "GEHA - GEnetics of Healthy Aging": recruitment, health status assessment and survival of the Italian 90+ sibpairs

The present study is part of the EU Integrated Project “GEHA – Genetics of Healthy Aging” (Franceschi C et al., Ann N Y Acad Sci. 1100: 21-45, 2007), whose aim is to identify genes involved in healthy aging and longevity, which allow individuals to survive to advanced age in good cognitive and physical function and in the absence of major age-related diseases. Aims The major aims of this thesis were the following: 1. to outline the recruitment procedure of 90+ Italian siblings performed by the recruiting units of the University of Bologna (UNIBO) and Rome (ISS). The procedures related to the following items necessary to perform the study were described and commented: identification of the eligible area for recruitment, demographic aspects related to the need of getting census lists of 90+siblings, mail and phone contact with 90+ subjects and their families, bioethics aspects of the whole procedure, standardization of the recruitment methodology and set-up of a detailed flow chart to be followed by the European recruitment centres (obtainment of the informed consent form, anonimization of data by using a special code, how to perform the interview, how to collect the blood, how to enter data in the GEHA Phenotypic Data Base hosted at Odense). 2. to provide an overview of the phenotypic characteristics of 90+ Italian siblings recruited by the recruiting units of the University of Bologna (UNIBO) and Rome (ISS). The following items were addressed: socio-demographic characteristics, health status, cognitive assessment, physical conditions (handgrip strength test, chair-stand test, physical ability including ADL, vision and hearing ability, movement ability and doing light housework), life-style information (smoking and drinking habits) and subjective well-being (attitude towards life). Moreover, haematological parameters collected in the 90+ sibpairs as optional parameters by the Bologna and Rome recruiting units were used for a more comprehensive evaluation of the results obtained using the above mentioned phenotypic characteristics reported in the GEHA questionnaire. 3. to assess 90+ Italian siblings as far as their health/functional status is concerned on the basis of three classification methods proposed in previous studies on centenarians, which are based on: • actual functional capabilities (ADL, SMMSE, visual and hearing abilities) (Gondo et al., J Gerontol. 61A (3): 305-310, 2006); • actual functional capabilities and morbidity (ADL, ability to walk, SMMSE, presence of cancer, ictus, renal failure, anaemia, and liver diseases) (Franceschi et al., Aging Clin Exp Res, 12:77-84, 2000); • retrospectively collected data about past history of morbidity and age of disease onset (hypertension, heart disease, diabetes, stroke, cancer, osteopororis, neurological diseases, chronic obstructive pulmonary disease and ocular diseases) (Evert et al., J Gerontol A Biol Sci Med Sci. 58A (3): 232-237, 2003). Firstly these available models to define the health status of long-living subjects were applied to the sample and, since the classifications by Gondo and Franceschi are both based on the present functional status, they were compared in order to better recognize the healthy aging phenotype and to identify the best group of 90+ subjects out of the entire studied population. 4. to investigate the concordance of health and functional status among 90+ siblings in order to divide sibpairs in three categories: the best (both sibs are in good shape), the worst (both sibs are in bad shape) and an intermediate group (one sib is in good shape and the other is in bad shape). Moreover, the evaluation wanted to discover which variables are concordant among siblings; thus, concordant variables could be considered as familiar variables (determined by the environment or by genetics). 5. to perform a survival analysis by using mortality data at 1st January 2009 from the follow-up as the main outcome and selected functional and clinical parameters as explanatory variables. Methods A total of 765 90+ Italian subjects recruited by UNIBO (549 90+ siblings, belonging to 258 families) and ISS (216 90+ siblings, belonging to 106 families) recruiting units are included in the analysis. Each subject was interviewed according to a standardized questionnaire, comprising extensively utilized questions that have been validated in previous European studies on elderly subjects and covering demographic information, life style, living conditions, cognitive status (SMMSE), mood, health status and anthropometric measurements. Moreover, subjects were asked to perform some physical tests (Hand Grip Strength test and Chair Standing test) and a sample of about 24 mL of blood was collected and then processed according to a common protocol for the preparation and storage of DNA aliquots. Results From the analysis the main findings are the following: - a standardized protocol to assess cognitive status, physical performances and health status of European nonagenarian subjects was set up, in respect to ethical requirements, and it is available as a reference for other studies in this field; - GEHA families are enriched in long-living members and extreme survival, and represent an appropriate model for the identification of genes involved in healthy aging and longevity; - two simplified sets of criteria to classify 90+ sibling according to their health status were proposed, as operational tools for distinguishing healthy from non healthy subjects; - cognitive and functional parameters have a major role in categorizing 90+ siblings for the health status; - parameters such as education and good physical abilities (500 metres walking ability, going up and down the stairs ability, high scores at hand grip and chair stand tests) are associated with a good health status (defined as “cognitive unimpairment and absence of disability”); - male nonagenarians show a more homogeneous phenotype than females, and, though far fewer in number, tend to be healthier than females; - in males the good health status is not protective for survival, confirming the male-female health survival paradox; - survival after age 90 was dependent mainly on intact cognitive status and absence of functional disabilities; - haemoglobin and creatinine levels are both associated with longevity; - the most concordant items among 90+ siblings are related to the functional status, indicating that they contain a familiar component. It is still to be investigated at what level this familiar component is determined by genetics or by environment or by the interaction between genetics, environment and chance (and at what level). Conclusions In conclusion, we could state that this study, in accordance with the main objectives of the whole GEHA project, represents one of the first attempt to identify the biological and non biological determinants of successful/unsuccessful aging and longevity. Here, the analysis was performed on 90+ siblings recruited in Northern and Central Italy and it could be used as a reference for others studies in this field on Italian population. Moreover, it contributed to the definition of “successful” and “unsuccessful” aging and categorising a very large cohort of our most elderly subjects into “successful” and “unsuccessful” groups provided an unrivalled opportunity to detect some of the basic genetic/molecular mechanisms which underpin good health as opposed to chronic disability. Discoveries in the topic of the biological determinants of healthy aging represent a real possibility to identify new markers to be utilized for the identification of subgroups of old European citizens having a higher risk to develop age-related diseases and disabilities and to direct major preventive medicine strategies for the new epidemic of chronic disease in the 21st century.

Sören Kierkegaard als Kommunikationsanalytiker und Sozialkritiker

Kierkegaard gilt weitgehend als Interpret des einsamen, auf sich selbst zurückgeworfenen Individuums. Aber: Er beschreibt auch einen Existenz-Typus, der eine intensive Kommunikation mit seinen Mitmenschen unterhält, und zwar eine destruktive: den Dämonischen. Diese Kommunikation ist in sich widersprüchlich und paradox. Die gleiche Kommunikationsform entdeckt er bei Massenmedien, Massenorganisationen und Ideologien. Kierkegaard ist damit auch ein Deuter unserer gegenwärtigen Gesellschaft.

Substratversorgung von NO-Synthasen

Resultate dieser Arbeit zeigen, dass endotheliale und neuronale NO-Synthasen (eNOS und nNOS) ihr Substrat Arginin nicht ausschließlich aus extrazellulären, sondern auch aus intrazellulären Quellen beziehen. Das Substrat aus den intrazellulären Quellen scheint nicht über Membrantransporter in den Extrazellulärraum gelangen zu können. Dies deutet darauf hin, dass eine enge Assoziation der Arginin-bereitstellenden Enzyme mit eNOS bzw. nNOS vorliegen könnte. Dadurch würde das durch diese Enzyme generierte Arginin direkt an die NOS weitergereicht und nicht über Transporter gegen andere basische Aminosäuren (AS) im Extrazellulärraum ausgetauscht werden. Eine intrazelluläre Substrat-Quelle besteht aus dem so genannten „Recycling“, der Umwandlung des bei der NO-Synthese entstehenden Citrullins in Arginin. Eine Kopplung von Arginin-bereitstellenden „Recycling“-Enzymen mit NOS wird in Endothelzellen und teilweise auch in TGW-nu-I Neuroblastomzellen beobachtet, nicht jedoch in A673 Neuroepitheliomzellen. Die Kopplung scheint daher vom Zelltyp abhängig zu sein. Das zur Arginin-Regeneration benötigte Citrullin kann allen untersuchten Zellen durch den Austausch mit spezifischen neutralen AS, die ausschließlich zum Substratprofil des System N Transporters SN1 passen, entzogen werden. Die Anwesenheit von SN1-Substraten im Extrazellulärraum führt daher indirekt zu einer Depletion der Recycling-Quelle. SN1 mRNA ist in allen untersuchten Zellen nachweisbar. Aus Protein-Abbau stammendes Arginin stellt den zweiten Teil der intrazellulären Arginin-Quelle dar. Dieser ist in allen untersuchten eNOS- oder nNOS exprimierenden Zellen vorhanden. Das Arginin stammt dabei sowohl aus lysosomalem als auch proteasomalen Proteinabbau, wie der Einsatz spezifischer Inhibitoren zeigt. Extrazelluläres Histidin (aber keine andere Aminosäure) kann diese Arginin-Quelle depletieren. Wir vermuten deshalb, dass Histidin über den Peptid-Histidin-Transporter PHT1, der in allen untersuchten Zellen stark exprimiert ist, gegen die durch lysosomalen und proteasomalen Proteinabbau entstehenden Arginin-haltigen Di- und Tripeptide ausgetauscht wird. Der wichtigste endogene NOS-Inhibitor, asymmetrisches Dimethylarginin (ADMA), ein Marker für endotheliale Dysfunktion und Risikofaktor für kardiovaskuläre Erkrankungen, stammt ebenfalls aus Proteinabbau. Die Verfügbarkeit dieser intrazellulären Arginin-Quelle wird deshalb stark vom Methylierungsgrad des Arginins in den abgebauten Proteinen abhängen. Eine lokale ADMA-Anreicherung könnte eine Erklärung für das Arginin-Paradox sein, der unter pathophysiologischen Bedingungen beobachteten Verminderung der endothelialen NO-Synthese bei anscheinend ausreichenden intrazellulären Argininkonzentrationen. Da auch in neurodegenerativen Erkrankungen, wie Morbus Alzheimer, ADMA eine Rolle zu spielen scheint, könnte das Arginin-Paradox auch für die nNOS-vermittelte NO-Synthese von Bedeutung sein. Die Resultate demonstrieren, dass die Substratversorgung der beiden NOS-Isoformen nicht ausschließlich von kationischen Aminosäuretransportern abhängig ist, sondern auch von Transportern für neutrale Aminosäuren und Peptide, und außerdem von Arginin-bereitstellenden Enzymen. Der jeweilige Beitrag der verschiedenen Arginin-Quellen zur Substratversorgung der NOS ist daher abhängig vom Anteil der jeweiligen Aminosäuren und Peptide in der extrazellulären Flüssigkeit.

Formal planning rationality in public sector professional work: between discourse and practice

Although rational models of formal planning have been seriously criticized by strategy literature, they not only remain a widely used organizational practice in private firms, but they have increasingly been entering public, professional organizations too, as part of public sector managerial reforms. This research addresses this apparent paradox, exploring the meaning of formal planning in public sector professional work. Curiously, this is an issue that remains under-investigated in the literature: the long debate on formal planning in strategy research devoted scant attention to its diffusion in the public sector, and public sector studies have scrutinized the introduction of other management tools in professional work, but very limitedly formal planning itself. In fact, little is known on the actual meaning of formal planning in public, professional services. This research is based upon a case of adoption of formal planning tools in a public hospital. Embracing a discourse analytical lens, it examines which formal planning discourse entered professional work, to what extent, and how professionals interpret it and engage with it in their practice. The analysis uncovers dynamics of social construction of meaning where, eventually, a formal planning discourse both shapes and is shaped by professional practice. In particular, it is found that formal planning rationality largely penetrated professional work, but not to the detriment of professional values. Morevover, formal planning ‘fails’ as a tool for rational decision making, but it takes up a knowledge work and a social value in professional work, as a tool for explicitation of action courses and for dialogue between otherwise more disconnected parts of the organization.

Determinants of child undernutrition in India. A micro-case study to operationalize the Capability Approach

The present research aims at shedding light on the demanding puzzle characterizing the issue of child undernutrition in India. Indeed, the so called ‘Indian development paradox’ identifies the phenomenon according to which higher level of income per capita is recorded alongside a lethargic reduction in the proportion of underweight children aged below three years. Thus, in the time period occurring from 2000 to 2005, real Gross Domestic Production per capita has annually grown at 5.4%, whereas the proportion of children who are underweight has declined from 47% to 46%, a mere one point percent. Such trend opens up the space for discussing the traditionally assumed linkage between income-poverty and undernutrition as well as food intervention as the main focus of policies designed to fight child hunger. Also, it unlocks doors for evaluating the role of an alternative economic approach aiming at explaining undernutrition, such as the Capability Approach. The Capability Approach argues for widening the informational basis to account not only for resources, but also for variables related to liberties, opportunities and autonomy in pursuing what individuals value.The econometric analysis highlights the relevance of including behavioral factors when explaining child undernutrition. In particular, the ability of the mother to move freely in the community without the need of asking permission to her husband or mother-in-law is statistically significant when included in the model, which accounts also for confounding traditional variables, such as economic wealth and food security. Also, focusing on agency, results indicates the necessity of measuring autonomy in different domains and the need of improving the measurement scale for agency data, especially with regards the domain of household duties. Finally, future research is required to investigate policy venues for increasing agency in women and in the communities they live in as viable strategy for reducing the plague of child undernutrition in India.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Three Essays in Spatial Economics

This work contributes to the field of spatial economics by embracing three distinct modelling approaches, belonging to different strands of the theoretical literature. In the first chapter I present a theoretical model in which the changes in urban system’s degree of functional specialisation are linked to (i) firms’ organisational choices and firms’ location decisions. The interplay between firms’ internal communication/managing costs (between headquarters and production plants) and the cost of communicating with distant business services providers leads the transition process from an “integrated” urban system where each city hosts every different functions to a “functionally specialised” urban system where each city is either a primary business center (hosting advanced business services providers, a secondary business center or a pure manufacturing city and all this city-types coexist in equilibrium.The second chapter investigates the impact of free trade on welfare in a two-country world modelled as an international Hotelling duopoly with quadratic transport costs and asymmetric countries, where a negative environmental externality is associated with the consumption of the good produced in the smaller country. Countries’ relative sizes as well as the intensity of negative environmental externality affect potential welfare gains of trade liberalisation. The third chapter focuses on the paradox, by which, contrary to theoretical predictions, empirical evidence shows that a decrease in international transport costs causes an increase in foreign direct investments (FDIs). Here we propose an explanation to this apparent puzzle by exploiting an approach which delivers a continuum of Bertrand- Nash equilibria ranging above marginal cost pricing. In our setting, two Bertrand firms, supplying a homogeneous good with a convex cost function, enter the market of a foreign country. We show that allowing for a softer price competition may indeed more than offset the standard effect generated by a decrease in trade costs, thereby restoring FDI incentives.

Black hole evaporation and stress tensor correlations

General Relativity is one of the greatest scientific achievementes of the 20th century along with quantum theory. These two theories are extremely beautiful and they are well verified by experiments, but they are apparently incompatible. Hints towards understanding these problems can be derived studying Black Holes, some the most puzzling solutions of General Relativity. The main topic of this Master Thesis is the study of Black Holes, in particular the Physics of Hawking Radiation. After a short review of General Relativity, I study in detail the Schwarzschild solution with particular emphasis on the coordinates systems used and the mathematical proof of the classical laws of Black Hole "Thermodynamics". Then I introduce the theory of Quantum Fields in Curved Spacetime, from Bogolubov transformations to the Schwinger-De Witt expansion, useful for the renormalization of the stress energy tensor. After that I introduce a 2D model of gravitational collapse to study the Hawking radiation phenomenon. Particular emphasis is given to the analysis of the quantum states, from correlations to the physical implication of this quantum effect (e.g. Information Paradox, Black Hole Thermodynamics). Then I introduce the renormalized stress energy tensor. Using the Schwinger-De Witt expansion I renormalize this object and I compute it analytically in the various quantum states of interest. Moreover, I study the correlations between these objects. They are interesting because they are linked to the Hawking radiation experimental search in acoustic Black Hole models. In particular I find that there is a characteristic peak in correlations between points inside and outside the Black Hole region, which correpsonds to entangled excitations inside and outside the Black Hole. These peaks hopefully will be measurable soon in supersonic BEC.

The Presence of Words in Visual Art from Surrealism to Conceptualism

Without a doubt, one of the biggest changes that affected XXth century art is the introduction of words into paintings and, in more recent years, in installations. For centuries, if words were part of a visual composition, they functioned as reference; strictly speaking, they were used as a guideline for a better perception of the subject represented. With the developments of the XXth century, words became a very important part of the visual composition, and sometimes embodied the composition itself. About this topic, American art critic and collector Russell Bowman wrote an interesting article called Words and images: A persistent paradox, in which he examines the American and the European art of the XXth century in almost its entirety, dividing it up in six “categories of intention”. The aforementioned categories are not based on the art history timeline, but on the role that language played for specific artists or movements. Taking inspiration from Bowman's article, this paper is structured in three chapters, respectively: words in juxtaposition and free association, words as means of exploration of language structures, and words as means for political and personal messages. The purpose of this paper is therefore to reflect on the role of language in contemporary art and on the way it has changed from artist to artist.