Logarithmic Potential Theory on Riemann Surfaces

We develop a logarithmic potential theory on Riemann surfaces which generalizes logarithmic potential theory on the complex plane. We show the existence of an equilibrium measure and examine its structure. This leads to a formula for the structure of the equilibrium measure which is new even in the plane. We then use our results to study quadrature domains, Laplacian growth, and Coulomb gas ensembles on Riemann surfaces. We prove that the complement of the support of the equilibrium measure satisfies a quadrature identity. Furthermore, our setup allows us to naturally realize weak solutions of Laplacian growth (for a general time-dependent source) as an evolution of the support of equilibrium measures. When applied to the Riemann sphere this approach unifies the known methods for generating interior and exterior Laplacian growth. We later narrow our focus to a special class of quadrature domains which we call Algebraic Quadrature Domains. We show that many of the properties of quadrature domains generalize to this setting. In particular, the boundary of an Algebraic Quadrature Domain is the inverse image of a planar algebraic curve under a meromorphic function. This makes the study of the topology of Algebraic Quadrature Domains an interesting problem. We briefly investigate this problem and then narrow our focus to the study of the topology of classical quadrature domains. We extend the results of Lee and Makarov and prove (for n ≥ 3) c ≤ 5n-5, where c and n denote the connectivity and degree of a (classical) quadrature domain. At the same time we obtain a new upper bound on the number of isolated points of the algebraic curve corresponding to the boundary and thus a new upper bound on the number of special points. In the final chapter we study Coulomb gas ensembles on Riemann surfaces.

Quantum Mechanics Studies of Fuel Cell Catalysts and Proton Conducting Ceramics with Validation by Experiment

We carried out quantum mechanics (QM) studies aimed at improving the performance of hydrogen fuel cells. This led to predictions of improved materials, some of which were subsequently validated with experiments by our collaborators.

In part I, the challenge was to find a replacement for the Pt cathode that would lead to improved performance for the Oxygen Reduction Reaction (ORR) while remaining stable under operational conditions and decreasing cost. Our design strategy was to find an alloy with composition Pt3M that would lead to surface segregation such that the top layer would be pure Pt, with the second and subsequent layers richer in M. Under operating conditions we expect the surface to have significant O and/or OH chemisorbed on the surface, and hence we searched for M that would remain segregated under these conditions. Using QM we examined surface segregation for 28 Pt₃M alloys, where M is a transition metal. We found that only Pt₃Os and Pt₃Ir showed significant surface segregation when O and OH are chemisorbed on the catalyst surfaces. This result indicates that Pt₃Os and Pt3Ir favor formation of a Pt-skin surface layer structure that would resist the acidic electrolyte corrosion during fuel cell operation environments. We chose to focus on Os because the phase diagram for Pt-Ir indicated that Pt-Ir could not form a homogeneous alloy at lower temperature. To determine the performance for ORR, we used QM to examine all intermediates, reaction pathways, and reaction barriers involved in the processes for which protons from the anode reactions react with O₂ to form H₂O. These QM calculations used our Poisson-Boltzmann implicit solvation model include the effects of the solvent (water with dielectric constant 78 with pH 7 at 298K). We found that the rate determination step (RDS) was the O_ad hydration reaction (O_ad + H₂O_ad -> OH_ad + OH_ad) in both cases, but that the barrier for pure Pt of 0.50 eV is reduced to 0.48 eV for Pt₃Os, which at 80 degrees C would increase the rate by 218%. We collaborated with the Pu-Wei Wu’s group to carry out experiments, where we found that the dealloying process-treated Pt2Os catalyst showed two-fold higher activity at 25 degrees C than pure Pt and that the alloy had 272% improved stability, validating our theoretical predictions.

We also carried out similar QM studies followed by experimental validation for the Os/Pt core-shell catalyst fabricated by the underpotential deposition (UPD) method. The QM results indicated that the RDS for ORR is a compromise between the OOH formation step (0.37 eV for Pt, 0.23 eV for Pt_2ML/Os core-shell) and H₂O formation steps (0.32 eV for Pt, 0.22 eV for Pt_2ML/Os core-shell). We found that Pt_2ML/Os has the highest activity (compared to pure Pt and to the Pt₃Os alloy) because the 0.37 eV barrier decreases to 0.23 eV. To understand what aspects of the core shell structure lead to this improved performance, we considered the effect on ORR of compressing the alloy slab to the dimensions of pure Pt. However this had little effect, with the same RDS barrier 0.37 eV. This shows that the ligand effect (the electronic structure modification resulting from the Os substrate) plays a more important role than the strain effect, and is responsible for the improved activity of the core- shell catalyst. Experimental materials characterization proves the core-shell feature of our catalyst. The electrochemical experiment for Pt_2ML/Os/C showed 3.5 to 5 times better ORR activity at 0.9V (vs. NHE) in 0.1M HClO₄ solution at 25 degrees C as compared to those of commercially available Pt/C. The excellent correlation between experimental half potential and the OH binding energies and RDS barriers validate the feasibility of predicting catalyst activity using QM calculation and a simple Langmuir–Hinshelwood model.

In part II, we used QM calculations to study methane stream reforming on a Ni-alloy catalyst surfaces for solid oxide fuel cell (SOFC) application. SOFC has wide fuel adaptability but the coking and sulfur poisoning will reduce its stability. Experimental results suggested that the Ni4Fe alloy improves both its activity and stability compared to pure Ni. To understand the atomistic origin of this, we carried out QM calculations on surface segregation and found that the most stable configuration for Ni₄Fe has a Fe atom distribution of (0%, 50%, 25%, 25%, 0%) starting at the bottom layer. We calculated that the binding of C atoms on the Ni4Fe surface is 142.9 Kcal/mol, which is about 10 Kcal/mol weaker compared to the pure Ni surface. This weaker C binding energy is expected to make coke formation less favorable, explaining why Ni₄Fe has better coking resistance. This result confirms the experimental observation. The reaction energy barriers for CHx decomposition and C binding on various alloy surface, Ni₄X (X=Fe, Co, Mn, and Mo), showed Ni₄Fe, Ni₄Co, and Fe₄Mn all have better coking resistance than pure Ni, but that only Ni₄Fe and Fe₄Mn have (slightly) improved activity compared to pure Ni.

In part III, we used QM to examine the proton transport in doped perovskite-ceramics. Here we used a 2x2x2 supercell of perovskite with composition Ba₈X₇M₁(OH)₁O₂₃ where X=Ce or Zr and M=Y, Gd, or Dy. Thus in each case a 4⁺ X is replace by a 3⁺ M plus a proton on one O. Here we predicted the barriers for proton diffusion allowing both includes intra-octahedron and inter-octahedra proton transfer. Without any restriction, we only observed the inter-octahedra proton transfer with similar energy barrier as previous computational work but 0.2 eV higher than experimental result for Y doped zirconate. For one restriction in our calculations is that the O_donor-O_acceptor atoms were kept at fixed distances, we found that the barrier difference between cerates/zirconates with various dopants are only 0.02~0.03 eV. To fully address performance one would need to examine proton transfer at grain boundaries, which will require larger scale ReaxFF reactive dynamics for systems with millions of atoms. The QM calculations used here will be used to train the ReaxFF force field.

Radioautographic method of determination of number of bacteria in water-bodies [Translation from: Informatsionnyi Byulleten Biologiya Vnutrennikh Vod No.26, 65-67, 1975]

The radioautographic method of determination of the number of autotrophic microorganisms was initially suggested for counting methane-oxidizing bacteria. With the help of this method colonies of hydrogen-oxidizing bacteria are differentiated even more clearly from heterotrophic. Under laboratory conditions it was shown that colonies grown on membrane filters from a pure culture of thionic bacteria on a nutrient medium with radio- active carbonate, give better prints on film. This method was tested by the authors for determining the number of these bacteria in the meromictic Lake Vae de San Juan during the expedition to Cuba in the summer of 1973. The study showed that that the thionic bacteria are found throughout the pelagial. It proved that the thionic bacteria can be well considered in water-bodies by the radioautographic method.

Concerning the current conditions and transport of sand in the shallow water areas off the coast of the south-eastern North Sea [Translation from: Hamburger Kustenforschung 29 [pages 41-43 only], 1974]

With the aid of the German Research Association in the central programme 'Sand movements in the German coastal region', an investigation into the current conditions in the shallow water areas of the coasts of the south-eastern North Sea between Sylt and the Weser estuary was carried out by the author. Foundations of the work are 19 continuous current recordings in five profiles normal to the coast from years 1971 to 1973. Off the coasts of the south-eastern North Sea varying tidal currents impinge; they are currents whose directions may vary periodically through all points of the compass. They are caused by the circulating tides in the North Sea (Amphidromien). The turning flow movement experiences a deformation in the very shallow coastal waters, and as it happens the flow turning movement in the case of high tide continues right up onto the outer flats, while here and in the fore-lying shallow water areas around the time of low water (on account of the small depths of waters), there prevails a more variable current. A result of this hydrodynamical procedure is the development of counter currents. This partial translation of the original paper provides the summary of this study of of the mudflat areas between the Elbe and Weser.

On the set of eigenvalues of a class of equimodular matrices

The structure of the set ϐ(A) of all eigenvalues of all complex matrices (elementwise) equimodular with a given n x n non-negative matrix A is studied. The problem was suggested by O. Taussky and some aspects have been studied by R. S. Varga and B.W. Levinger.

If every matrix equimodular with A is non-singular, then A is called regular. A new proof of the P. Camion-A.J. Hoffman characterization of regular matrices is given.

The set ϐ(A) consists of m ≤ n closed annuli centered at the origin. Each gap, ɤ, in this set can be associated with a class of regular matrices with a (unique) permutation, π(ɤ). The association depends on both the combinatorial structure of A and the size of the a_ii. Let A be associated with the set of r permutations, π₁, π₂,…, π_r, where each gap in ϐ(A) is associated with one of the π_k. Then r ≤ n, even when the complement of ϐ(A) has n+1 components. Further, if π(ɤ) is the identity, the real boundary points of ɤ are eigenvalues of real matrices equimodular with A. In particular, if A is essentially diagonally dominant, every real boundary point of ϐ(A) is an eigenvalues of a real matrix equimodular with A.

Several conjectures based on these results are made which if verified would constitute an extension of the Perron-Frobenius Theorem, and an algebraic method is introduced which unites the study of regular matrices with that of ϐ(A).

Reform of Spain's profesional services market: Implementation of the EU Services Directive

The implementation of the European Commission Services Directive initiated the modernization process of services markets within the European Union. The objective was to guarantee the creation of a single market by ensuring the freedom of establishment and circulation. The transposition of the Directive in Spain triggered an initial wave of reforms in the Spanish legal system. A second package of reforms is currently underway, following recommendations by the EC, IMF and OECD, which highlight the relative lack of competition in Spain’s services as one of the major imbalances in its economy, alongside the public deficit and unemployment. Both the implemented and planned reforms represent a major step forward. Nevertheless, the government has recently announced modifications to the draft bill of the Professional Services and Associations Law, which is expected to soon be submitted for parliamentary debate and approval. Taking into consideration modifications already introduced, together with anticipated further changes, it will be important to maintain the main points of the draft bill and to introduce a deeper review of the legal framework for professional services, of the professional associations themselves, and for the activities that are subject to compulsory membership within a professional association. Spain’s territorial map of professional associations must too be redrawn.

Extension theorems for functions of vanishing mean oscillation

A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in R^d converges to zero with the volume of the cubes. We establish necessary and sufficient conditions for a locally integrable function defined on a bounded measurable set of positive measure to be the restriction to that set of a VMO function.

We consider the similar extension problem pertaining to BMO(ρ) functions; that is, those VMO functions whose mean oscillation over any cube is O(ρ(l(Q))) where l(Q) is the length of Q and ρ is a positive, non-decreasing function with ρ(0⁺) = 0.

We apply these results to obtain sufficient conditions for a Blaschke sequence to be the zeros of an analytic BMO(ρ) function on the unit disc.

A generalized Hausdorff dimension for functions and sets

Let E be a compact subset of the n-dimensional unit cube, 1_n, and let C be a collection of convex bodies, all of positive n-dimensional Lebesgue measure, such that C contains bodies with arbitrarily small measure. The dimension of E with respect to the covering class C is defined to be the number

d_C(E) = sup(β:H_{β, C}(E) > 0),

where H_{β, C} is the outer measure

inf(Ʃm(C_i)^β:UC_i Ↄ E, C_i ϵ C) .

Only the one and two-dimensional cases are studied. Moreover, the covering classes considered are those consisting of intervals and rectangles, parallel to the coordinate axes, and those closed under translations. A covering class is identified with a set of points in the left-open portion, 1’_n, of 1_n, whose closure intersects 1_n - 1’_n. For n = 2, the outer measure H_{β, C} is adopted in place of the usual:

Inf(Ʃ(diam. (C_i))^β: UC_i Ↄ E, C_i ϵ C),

for the purpose of studying the influence of the shape of the covering sets on the dimension d_C(E).

If E is a closed set in 1₁, let M(E) be the class of all non-decreasing functions μ(x), supported on E with μ(x) = 0, x ≤ 0 and μ(x) = 1, x ≥ 1. Define for each μ ϵ M(E),

d_C(μ) = lim/c → inf/0 log ∆μ(c)/log c , (c ϵ C)

where ∆μ(c) = v/x (μ(x+c) – μ(x)). It is shown that

d_C(E) = sup (d_C(μ):μ ϵ M(E)).

This notion of dimension is extended to a certain class Ӻ of sub-additive functions, and the problem of studying the behavior of d_C(E) as a function of the covering class C is reduced to the study of d_C(f) where f ϵ Ӻ. Specifically, the set of points in 1₁,

(*) {d_B(F), d_C(f)): f ϵ Ӻ}

is characterized by a comparison of the relative positions of the points of B and C. A region of the form (*) is always closed and doubly-starred with respect to the points (0, 0) and (1, 1). Conversely, given any closed region in 1₂, doubly-starred with respect to (0, 0) and (1, 1), there are covering classes B and C such that (*) is exactly that region. All of the results are shown to apply to the dimension of closed sets E. Similar results can be obtained when a finite number of covering classes are considered.

In two dimensions, the notion of dimension is extended to the class M, of functions f(x, y), non-decreasing in x and y, supported on 1₂ with f(x, y) = 0 for x · y = 0 and f(1, 1) = 1, by the formula

d_C(f) = lim/s · t → inf/0 log ∆f(s, t)/log s · t , (s, t) ϵ C

where

∆f(s, t) = V/x, y (f(x+s, y+t) – f(x+s, y) – f(x, y+t) + f(x, t)).

A characterization of the equivalence d_C1(f) = d_C2(f) for all f ϵ M, is given by comparison of the gaps in the sets of products s · t and quotients s/t, (s, t) ϵ C_i (I = 1, 2).

Two and Three Finger Caging of Polygons and Polyhedra

Multi-finger caging offers a rigorous and robust approach to robot grasping. This thesis provides several novel algorithms for caging polygons and polyhedra in two and three dimensions. Caging refers to a robotic grasp that does not necessarily immobilize an object, but prevents it from escaping to infinity. The first algorithm considers caging a polygon in two dimensions using two point fingers. The second algorithm extends the first to three dimensions. The third algorithm considers caging a convex polygon in two dimensions using three point fingers, and considers robustness of this cage to variations in the relative positions of the fingers.

This thesis describes an algorithm for finding all two-finger cage formations of planar polygonal objects based on a contact-space formulation. It shows that two-finger cages have several useful properties in contact space. First, the critical points of the cage representation in the hand’s configuration space appear as critical points of the inter-finger distance function in contact space. Second, these critical points can be graphically characterized directly on the object’s boundary. Third, contact space admits a natural rectangular decomposition such that all critical points lie on the rectangle boundaries, and the sublevel sets of contact space and free space are topologically equivalent. These properties lead to a caging graph that can be readily constructed in contact space. Starting from a desired immobilizing grasp of a polygonal object, the caging graph is searched for the minimal, intermediate, and maximal caging regions surrounding the immobilizing grasp. An example constructed from real-world data illustrates and validates the method.

A second algorithm is developed for finding caging formations of a 3D polyhedron for two point fingers using a lower dimensional contact-space formulation. Results from the two-dimensional algorithm are extended to three dimension. Critical points of the inter-finger distance function are shown to be identical to the critical points of the cage. A decomposition of contact space into 4D regions having useful properties is demonstrated. A geometric analysis of the critical points of the inter-finger distance function results in a catalog of grasps in which the cages change topology, leading to a simple test to classify critical points. With these properties established, the search algorithm from the two-dimensional case may be applied to the three-dimensional problem. An implemented example demonstrates the method.

This thesis also presents a study of cages of convex polygonal objects using three point fingers. It considers a three-parameter model of the relative position of the fingers, which gives complete generality for three point fingers in the plane. It analyzes robustness of caging grasps to variations in the relative position of the fingers without breaking the cage. Using a simple decomposition of free space around the polygon, we present an algorithm which gives all caging placements of the fingers and a characterization of the robustness of these cages.

Tipperary, by Frank Delaney: a reading of the rewriting of history of Ireland

O objetivo da presente pesquisa é o de discutir a reescrita da história da Irlanda, mais especificamente aspectos relacionados à construção da identidade nacional e de marcas da tradição, a partir da leitura do romance Tipperary, de Frank Delaney. Publicada em 2007, essa obra aborda de forma singular as querelas sobre identidade nacional, nacionalismo, passado, memória, e seus personagens principais e a trama estão significativamente ligados ao contexto político-social da história da Irlanda. Nessa reconstrução da história, o passado é revisitado através de diferentes pontos de vista. Nossa atenção estará voltada para a seleção de elementos/momentos da história do país que ganham foco na narrativa, e as possíveis repercussões deste processo. Além disso, nos concentraremos na questão das tênues fronteiras entre história e ficção, ou seja, as fronteiras pouco delimitadas entre o discurso histórico e o discurso ficcional. Na escrita da história em Tipperary, Delaney aborda questões relativas a mitos, lendas e tradições como importantes fatores de identidade nacional em uma Irlanda que emerge como uma nação independente. No romance em questão, podemos observar como história e memória se unem na jornada do protagonista, em sua empreitada de narrar a história de sua vida e de seu país

Origin of Chinese ancient glasses;study on the earliest Chinese ancient glasses

The earliest Chinese ancient glasses before the West Han Dynasty (200 BC) from different regions are studied. The glass samples were unearthed from Hunan, Hubei, Yunnan, Sichuan, Guizhou, Guangdong and Xinjiang of China. The chemical composition of these glasses samples is analyzed by proton induced X-ray emission (PIXE) technique, energy dispersive X-ray fluorescence (EDXRF) method and inductively coupled plasma atomic emission spectrometry (ICP-AES). It is shown that the glass chemical compositions belong to barium-lead silicate BaO-PbO-SiO2, potash soda lime silicate K2O (Na2O)-CaO-SiO2 (K2O/Na2O > 1), soda potash lime silicate Na2O (K2O)-CaO-SiO2 (K2O/Na2O < 1) and potash silicate K2O-SiO2 glass systems, respectively. The origins of the earliest Chinese ancient glasses are discussed from the archaeological and historical points of view. These four types of Chinese ancient glasses were all made in Chinese territory using local raw materials. The glass preparation technology was related to the Chinese ancient bronze metallurgy and proto-porcelain glaze technology. The glass technology relationship between the East and the West is analyzed at the same time.

Holding mirrors up to Hamlet: what Franco Zeffirellis and Michael Almereydas filmic adaptations of the play tell us about it

Hamlet (1601), de William Shakespeare, é, desde o Fólio de 1623, circundada por um enorme e variado volume de leituras, que abrangem desde textos críticos e teóricos até as mais diversas adaptações teatrais e cinematográficas. Desde o final do século 19, o cinema vem adaptando peças de Shakespeare, fornecendo novos pontos de vista e sugestões para a encenação dessa obra ao levá-la inúmeras vezes para as telas. Dentre uma longa lista de adaptações fílmicas de Hamlet, o Hamlet mainstream de Franco Zeffirelli (1990) e o Hamlet 2000 (2000), filme independente de Michael Almereyda, compõem o corpus eleito para análise nesta dissertação. Dialogando com noções de críticos e teóricos que desenvolveram estudos sobre o conceito de adaptação, tais como André Bazin, Robert Stam e Linda Hutcheon, sugiro uma desierarquização entre a peça shakespeariana e os filmes logo, entre literatura/teatro e cinema. O objetivo final deste trabalho encontra-se na proposta de uma reflexão sobre esses filmes enquanto potenciais materiais críticos elucidativos para o estudo da peça, úteis na discussão de alguns de seus mais importantes temas e/ou questões

Transgression in Carson McCullers The Ballad of the Sad Café

Este trabalho tem como objetivo principal discutir a obra The Ballad of the Sad Café, publicada em 1951, pela escritora norte-americana Carson McCullers, que abordou temas polêmicos, como a sexualidade, papéis sociais e suas respectivas e muitas vezes concomitantes transgressões. Em tal discussão serão analisadas as presenças do Gótico, do Grotesco e de outros elementos literários que se mostram eficazes ao lidarmos com a subversão dos valores patriarcais construídos socialmente. Como pontos cruciais deste trabalho, será traçado um paralelo entre a sociedade vitoriana e a sociedade do Sul norte-americano de meados do século XX, enfocando também a protagonista Miss Amelia Evans, que desafia o modelo da heroína gótica tradicional

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.

Da homeopatia à medicina chinesa: a trajetória dos pontos de Weihe

Esta dissertação de mestrado é um estudo de natureza sócio-histórico que constrói a trajetória do sistema de Pontos de Weihe, um sistema médico minoritário, cuja origem encontra-se na Homeopatia, porém, seu desenvolvimento o levou de encontro a Acupuntura. Esse estudo tem como objetivo inserir seu objeto de análise na discussão de questões pertinentes ao desenvolvimento conceitual da Homeopatia. Sendo um sistema médico complexo, a racionalidade médica homeopática possui seis dimensões, a saber: morfologia (ou anatomia), dinâmica vital (ou fisiologia), doutrina, diagnóstico, terapêutica e cosmologia. Destas, a dimensão da morfologia e o exame físico da dimensão diagnóstica são compartilhados com a biomedicina, enquanto, as demais, baseiam-se no para digma vitalista, ainda que nem todas tenham sido desenvolvidas conceitualmente e encontrem-se apenas implícitas. Tal situação conferiu à Homeopatia a denominação de racionalidade médica híbrida. Este estudo parte do pressuposto que a Homeopatia é um sistema médico ainda em construção e que deve caminhar para o desenvolvimento conceitual de suas dimensões tendo como elemento norteador sua natureza vitalista. Portanto, espera-se que, ao resgatar-se a história do sistema de Pontos de Weihe, crie-se a possibilidade de repensar a morfologia homeopática, de forma que, ela possa expressar o movimento da força vital na saúde e no adoecimento. Espera-se, também, que, ao revelar uma colaboração possível da Medicina Chinesa, racionalidade médica que compartilha com a Homeopatia o paradigma vitalista, abra-se a possibilidade de repensar a base conceitual da dinâmica vital homeopática. Buscar uma sistematização da dinâmica vital, ao mesmo tempo, compatível com o paradigma vitalista e agregadora dos elementos centrais do pensamento homeopático é passo importante no desenvolvimento desta racionalidade, pois, permite que se parta de um mesmo esquema conceitual, e portanto, de uma mesma base paradigmática, em direção a criação de outros sistemas diagnósticos que concorram com o diagnóstico medicamentoso e o confirmem. Utilizou-se, como fontes primárias e secundárias para a construção da trajetória dos Pontos de Weihe, artigos e livros de Weihe e seus discípulos que, sofreram uma tradução livre do idioma original, o alemão, para o português. O substrato conceitual empregado foram as reflexões de George Canguilhem a respeito da história que se desvia dos obstáculos que impedem sua linearidade, comprometendo a compreensão das descobertas científicas como determinadas por suas condições de aparecimento, transfigurando-as no aparecimento puro daquilo que deveria ser.