On reconstruction theorems in noncommutative Riemannian geometry

We present a novel account of the theory of commutative spectral triples and their two closest noncommutative generalisations, almost-commutative spectral triples and toric noncommutative manifolds, with a focus on reconstruction theorems, viz, abstract, functional-analytic characterisations of global-analytically defined classes of spectral triples. We begin by reinterpreting Connes's reconstruction theorem for commutative spectral triples as a complete noncommutative-geometric characterisation of Dirac-type operators on compact oriented Riemannian manifolds, and in the process clarify folklore concerning stability of properties of spectral triples under suitable perturbation of the Dirac operator. Next, we apply this reinterpretation of the commutative reconstruction theorem to obtain a reconstruction theorem for almost-commutative spectral triples. In particular, we propose a revised, manifestly global-analytic definition of almost-commutative spectral triple, and, as an application of this global-analytic perspective, obtain a general result relating the spectral action on the total space of a finite normal compact oriented Riemannian cover to that on the base space. Throughout, we discuss the relevant refinements of these definitions and results to the case of real commutative and almost-commutative spectral triples. Finally, we outline progess towards a reconstruction theorem for toric noncommutative manifolds.

Seismic reflection experiments imaging the physical nature of crustal structures in southern California

Seismic reflection methods have been extensively used to probe the Earth's crust and suggest the nature of its formative processes. The analysis of multi-offset seismic reflection data extends the technique from a reconnaissance method to a powerful scientific tool that can be applied to test specific hypotheses. The treatment of reflections at multiple offsets becomes tractable if the assumptions of high-frequency rays are valid for the problem being considered. Their validity can be tested by applying the methods of analysis to full wave synthetics.

Three studies illustrate the application of these principles to investigations of the nature of the crust in southern California. A survey shot by the COCORP consortium in 1977 across the San Andreas fault near Parkfield revealed events in the record sections whose arrival time decreased with offset. The reflectors generating these events are imaged using a multi-offset three-dimensional Kirchhoff migration. Migrations of full wave acoustic synthetics having the same limitations in geometric coverage as the field survey demonstrate the utility of this back projection process for imaging. The migrated depth sections show the locations of the major physical boundaries of the San Andreas fault zone. The zone is bounded on the southwest by a near-vertical fault juxtaposing a Tertiary sedimentary section against uplifted crystalline rocks of the fault zone block. On the northeast, the fault zone is bounded by a fault dipping into the San Andreas, which includes slices of serpentinized ultramafics, intersecting it at 3 km depth. These interpretations can be made despite complications introduced by lateral heterogeneities.

In 1985 the Calcrust consortium designed a survey in the eastern Mojave desert to image structures in both the shallow and the deep crust. Preliminary field experiments showed that the major geophysical acquisition problem to be solved was the poor penetration of seismic energy through a low-velocity surface layer. Its effects could be mitigated through special acquisition and processing techniques. Data obtained from industry showed that quality data could be obtained from areas having a deeper, older sedimentary cover, causing a re-definition of the geologic objectives. Long offset stationary arrays were designed to provide reversed, wider angle coverage of the deep crust over parts of the survey. The preliminary field tests and constant monitoring of data quality and parameter adjustment allowed 108 km of excellent crustal data to be obtained.

This dataset, along with two others from the central and western Mojave, was used to constrain rock properties and the physical condition of the crust. The multi-offset analysis proceeded in two steps. First, an increase in reflection peak frequency with offset is indicative of a thinly layered reflector. The thickness and velocity contrast of the layering can be calculated from the spectral dispersion, to discriminate between structures resulting from broad scale or local effects. Second, the amplitude effects at different offsets of P-P scattering from weak elastic heterogeneities indicate whether the signs of the changes in density, rigidity, and Lame's parameter at the reflector agree or are opposed. The effects of reflection generation and propagation in a heterogeneous, anisotropic crust were contained by the design of the experiment and the simplicity of the observed amplitude and frequency trends. Multi-offset spectra and amplitude trend stacks of the three Mojave Desert datasets suggest that the most reflective structures in the middle crust are strong Poisson's ratio (σ) contrasts. Porous zones or the juxtaposition of units of mutually distant origin are indicated. Heterogeneities in σ increase towards the top of a basal crustal zone at ~22 km depth. The transition to the basal zone and to the mantle include increases in σ. The Moho itself includes ~400 m layering having a velocity higher than that of the uppermost mantle. The Moho maintains the same configuration across the Mojave despite 5 km of crustal thinning near the Colorado River. This indicates that Miocene extension there either thinned just the basal zone, or that the basal zone developed regionally after the extensional event.

Violence in the Medieval Church before the First Crusade

The attitude of the medieval church towards violence before the First Crusade in 1095 underwent a significant institutional evolution, from the peaceful tradition of the New Testament and the Roman persecution, through the prelate-led military campaigns of the Carolingian period and the Peace of God era. It would be superficially easy to characterize this transformation as the pragmatic and entirely secular response of a growing power to the changing world. However, such a simplification does not fully do justice to the underlying theology. While church leaders from the 5th Century to the 11th had vastly different motivations and circumstances under which to develop their responses to a variety of violent activities, the teachings of Augustine of Hippo provided a unifying theme. Augustine’s just war theology, in establishing which conflicts are acceptable in the eyes of God, focused on determining whether a proper causa belli or basis for war exists, and then whether a legitimate authority declares and leads the war. Augustine masterfully integrated aspects of the Old and New Testaments to create a lasting and compelling case for his definition of justified violence. Although at different times and places his theology has been used to support a variety of different attitudes, the profound influence of his work on the medieval church’s evolving position on violence is clear.

Theory of s-d exchange scattering in dilute magnetic alloys

The problem of s-d exchange scattering of conduction electrons off localized magnetic moments in dilute magnetic alloys is considered employing formal methods of quantum field theoretical scattering. It is shown that such a treatment not only allows for the first time, the inclusion of multiparticle intermediate states in single particle scattering equations but also results in extremely simple and straight forward mathematical analysis. These equations are proved to be exact in the thermodynamic limit. A self-consistent integral equation for electron self energy is derived and approximately solved. The ground state and physical parameters of dilute magnetic alloys are discussed in terms of the theoretical results. Within the approximation of single particle intermediate states our results reduce to earlier versions. The following additional features are found as a consequence of the inclusion of multiparticle intermediate states;

(i) A non analytic binding energy is pre sent for both, antiferromagnetic (J < o) and ferromagnetic (J > o) couplings of the electron plus impurity system.

(ii) The correct behavior of the energy difference of the conduction electron plus impurity system and the free electron system is found which is free of unphysical singularities present in earlier versions of the theories.

(iii) The ground state of the conduction electron plus impurity system is shown to be a many-body condensate state for J < o and J > o, both. However, a distinction is made between the usual terminology of "Singlet" and "Triplet" ground states and nature of our ground state.

(iv) It is shown that a long range ordering, leading to an ordering of the magnetic moments can result from a contact interaction such as the s-d exchange interaction.

(v) The explicit dependence of the excess specific heat of the Kondo systems is obtained and found to be linear in temperatures as T→ o and T ℓnT for 0.3 T_K ≤ T ≤ 0.6 T_K. A rise in (ΔC/T) for temperatures in the region 0 < T ≤ 0.1 T_K is predicted. These results are found to be in excellent agreement with experiments.

(vi) The existence of a critical temperature for Ferromagnetic coupling (J > o) is shown. On the basis of this the apparent contradiction of the simultaneous existence of giant moments and Kondo effect is resolved.

Temporal and spatial variations in the quality of water in El Gergal Reservior, Seville, Spain

It is often difficult to define ‘water quality’ with any degree of precision. One approach is that suggested by Battarbee (1997) and is based on the extent to which individual lakes have changed compared with their natural ‘baseline’ status. Defining the base-line status of artificial lakes and reservoirs however, is, very difficult. In ecological terms, the definition of quality must include some consideration of their functional characteristics and the extent to which these characteristics are self-sustaining. The challenge of managing lakes in a sustainable way is particularly acute in semi-arid, Mediterranean countries. Here the quality of the water is strongly influenced by the unpredictability of the rainfall as well as year-to-year variations in the seasonal averages. Wise management requires profound knowledge of how these systems function. Thus a holistic approach must be adopted and the factors influencing the seasonal dynamics of the lakes quantified over a range of spatial and temporal scales. In this article, the authors describe some of the ways in which both long-term and short-term changes in the weather have influenced the seasonal and spatial dynamics of phytoplankton in El Gergal, a water supply reservoir situated in the south of Spain. The quality of the water stored in this reservoir is typically very good but surface blooms of algae commonly appear during warm, calm periods when the water level is low. El Gergal reservoir is managed by the Empresa Municipal de Abastecimiento y Saneamiento (EMASESA) and supplies water for domestic, commercial and industrial use to an area which includes the city of Seville and twelve of its surrounding towns (ca. 1.3 million inhabitants). El Gergal is the last of two reservoirs in a chain of four situated in the Rivera de Huelva basin, a tributary of the Guadalquivir river. It was commissioned by EMASESA in 1979 and since then the company has monitored its main limnological parameters on, at least, a monthly basis and used this information to improve the management of the reservoir. As a consequence of these intensive studies the physical, chemical and biological information acquired during this period makes the El Gergal database one of the most complete in Spain. In this article the authors focus on three ‘weather-related’ effects that have had a significant impact on the composition and distribution of phytoplankton in El Gergal: (i) the changes associated with severe droughts; (ii) the spatial variations produced by short-term changes in the weather; (iii) the impact of water transfers on the seasonal dynamics of the dinoflagellate Ceratium.

Cointegration analysis of money demand in the Euro Area

The analysis of the evolution of the M3 money aggregate is an important element in the definition and implementation of monetary policy for the ECB. A well-defined and stable long run demand function is an essential requisite for M3 to be a valid monetary tool. Therefore, this paper analyzes based in cointegration techniques the existence of a long run money demand, estimating it and testing its stability for the Euro Area and for ten of its member countries. Specifically, bearing in mind the high degree of monetary instability that the current economic crisis has created in the Euro Area, we also test whether this has had a noticeable impact in the cointegration among real money demand and its determinants. The analysis gives evidence of the existence of a long run relationship when the aggregated Euro Area and six of the ten countries are considered. However, these relationships are highly instable since the outbreak of the financial crisis, leading in some cases to even rejecting cointegration. All this suggests that the ECB’s strategy of focusing in the M3 monetary aggregates could not be a convenient approach under the current circumstances

Formal methods in the foundations of science

The intent of this study is to provide formal apparatus which facilitates the investigation of problems in the methodology of science. The introduction contains several examples of such problems and motivates the subsequent formalism.

A general definition of a formal language is presented, and this definition is used to characterize an individual’s view of the world around him. A notion of empirical observation is developed which is independent of language. The interplay of formal language and observation is taken as the central theme. The process of science is conceived as the finding of that formal language that best expresses the available experimental evidence.

To characterize the manner in which a formal language imposes structure on its universe of discourse, the fundamental concepts of elements and states of a formal language are introduced. Using these, the notion of a basis for a formal language is developed as a collection of minimal states distinguishable within the language. The relation of these concepts to those of model theory is discussed.

An a priori probability defined on sets of observations is postulated as a reflection of an individual’s ontology. This probability, in conjunction with a formal language and a basis for that language, induces a subjective probability describing an individual’s conceptual view of admissible configurations of the universe. As a function of this subjective probability, and consequently of language, a measure of the informativeness of empirical observations is introduced and is shown to be intuitively plausible – particularly in the case of scientific experimentation.

The developed formalism is then systematically applied to the general problems presented in the introduction. The relationship of scientific theories to empirical observations is discussed and the need for certain tacit, unstatable knowledge is shown to be necessary to fully comprehend the meaning of realistic theories. The idea that many common concepts can be specified only by drawing on knowledge obtained from an infinite number of observations is presented, and the problems of reductionism are examined in this context.

A definition of when one formal language can be considered to be more expressive than another is presented, and the change in the informativeness of an observation as language changes is investigated. In this regard it is shown that the information inherent in an observation may decrease for a more expressive language.

The general problem of induction and its relation to the scientific method are discussed. Two hypotheses concerning an individual’s selection of an optimal language for a particular domain of discourse are presented and specific examples from the introduction are examined.

I. A study of the dynamics of triplet excitons in molecular crystals. II. An investigation of delayed light emission from Chlorella pyrenoidosa

I. PREAMBLE AND SCOPE

Brief introductory remarks, together with a definition of the scope of the material discussed in the thesis, are given.

II. A STUDY OF THE DYNAMICS OF TRIPLET EXCITONS IN MOLECULAR CRYSTALS

Phosphorescence spectra of pure crystalline naphthalene at room temperature and at 77˚ K are presented. The lifetime of the lowest triplet ³B_1u state of the crystal is determined from measurements of the time-dependence of the phosphorescence decay after termination of the excitation light. The fact that this lifetime is considerably shorter in the pure crystal at room temperature than in isotopic mixed crystals at 4.2˚ K is discussed, with special importance being attached to the mobility of triplet excitons in the pure crystal.

Excitation spectra of the delayed fluorescence and phosphorescence from crystalline naphthalene and anthracene are also presented. The equation governing the time- and spatial-dependence of the triplet exciton concentration in the crystal is discussed, along with several approximate equations obtained from the general equation under certain simplifying assumptions. The influence of triplet exciton diffusion on the observed excitation spectra and the possibility of using the latter to investigate the former is also considered. Calculations of the delayed fluorescence and phosphorescence excitation spectra of crystalline naphthalene are described.

A search for absorption of additional light quanta by triplet excitons in naphthalene and anthracene crystals failed to produce any evidence for the phenomenon. This apparent absence of triplet-triplet absorption in pure crystals is attributed to a low steady-state triplet concentration, due to processes like triplet-triplet annihilation, resulting in an absorption too weak to be detected with the apparatus used in the experiments. A comparison of triplet-triplet absorption by naphthalene in a glass at 77˚ K with that by naphthalene-h₈ in naphthalene-d₈ at 4.2˚ K is given. A broad absorption in the isotopic mixed crystal triplet-triplet spectrum has been tentatively interpreted in terms of coupling between the guest ³B_1u state and the conduction band and charge-transfer states of the host crystal.

III. AN INVESTIGATION OF DELAYED LIGHT EMISSION FROM Chlorella Pyrenoidosa

An apparatus capable of measuring emission lifetimes in the range 5 X 10^-9 sec to 6 X 10^-3 sec is described in detail. A cw argon ion laser beam, interrupted periodically by means of an electro-optic shutter, serves as the excitation source. Rapid sampling techniques coupled with signal averaging and digital data acquisition comprise the sensitive detection and readout portion of the apparatus. The capabilities of the equipment are adequately demonstrated by the results of a determination of the fluorescence lifetime of 5, 6, 11, 12-tetraphenyl-naphthacene in benzene solution at room temperature. Details of numerical methods used in the final data reduction are also described.

The results of preliminary measurements of delayed light emission from Chlorella Pyrenoidosa in the range 10^-3 sec to 1 sec are presented. Effects on the emission of an inhibitor and of variations in the excitation light intensity have been investigated. Kinetic analysis of the emission decay curves obtained under these various experimental conditions indicate that in the millisecond-to-second time interval the decay is adequately described by the sum of two first-order decay processes. The values of the time constants of these processes appear to be sensitive both to added inhibitor and to excitation light intensity.

Geochemistry of lipids in lacustrine sediments

An explanation of the basic premises of the subject and its terminology is given. The article then outlines aspects of research on the organic material found in lacustrine sediments, and the analytical methods involved.

Studies of chemical speciation in naturally anoxic basins

The chemical speciation of both metals and non-metals, the use of polarographic techniques, and application to the study of the chemistry of anoxic waters are considered. In the first part of the paper unfamiliar terminology is explained and then an example of simple lake chemistry is presented to illustrate why the concept of speciation is necessary.

On the Cesari fixed point method in a Banach space

In a paper published in 1961, L. Cesari [1] introduces a method which extends certain earlier existence theorems of Cesari and Hale ([2] to [6]) for perturbation problems to strictly nonlinear problems. Various authors ([1], [7] to [15]) have now applied this method to nonlinear ordinary and partial differential equations. The basic idea of the method is to use the contraction principle to reduce an infinite-dimensional fixed point problem to a finite-dimensional problem which may be attacked using the methods of fixed point indexes.

The following is my formulation of the Cesari fixed point method:

Let B be a Banach space and let S be a finite-dimensional linear subspace of B. Let P be a projection of B onto S and suppose Г≤B such that pГ is compact and such that for every x in PГ, P^-1x∩Г is closed. Let W be a continuous mapping from Г into B. The Cesari method gives sufficient conditions for the existence of a fixed point of W in Г.

Let I denote the identity mapping in B. Clearly y = Wy for some y in Г if and only if both of the following conditions hold:

(i) Py = PWy.

(ii) y = (P + (I - P)W)y.

Definition. The Cesari fixed paint method applies to (Г, W, P) if and only if the following three conditions are satisfied:

(1) For each x in PГ, P + (I - P)W is a contraction from P^-1x∩Г into itself. Let y(x) be that element (uniqueness follows from the contraction principle) of P^-1x∩Г which satisfies the equation y(x) = Py(x) + (I-P)Wy(x).

(2) The function y just defined is continuous from PГ into B.

(3) There are no fixed points of PWy on the boundary of PГ, so that the (finite- dimensional) fixed point index i(PWy, int PГ) is defined.

Definition. If the Cesari fixed point method applies to (Г, W, P) then define i(Г, W, P) to be the index i(PWy, int PГ).

The three theorems of this thesis can now be easily stated.

Theorem 1 (Cesari). If i(Г, W, P) is defined and i(Г, W, P) ≠0, then there is a fixed point of W in Г.

Theorem 2. Let the Cesari fixed point method apply to both (Г, W, P₁) and (Г, W, P₂). Assume that P₂P₁=P₁P₂=P₁ and assume that either of the following two conditions holds:

(1) For every b in B and every z in the range of P₂, we have that ‖b=P₂b‖ ≤ ‖b-z‖

(2)P₂Г is convex.

Then i(Г, W, P₁) = i(Г, W, P₂).

Theorem 3. If Ω is a bounded open set and W is a compact operator defined on Ω so that the (infinite-dimensional) Leray-Schauder index i_LS(W, Ω) is defined, and if the Cesari fixed point method applies to (Ω, W, P), then i(Ω, W, P) = i_LS(W, Ω).

Theorems 2 and 3 are proved using mainly a homotopy theorem and a reduction theorem for the finite-dimensional and the Leray-Schauder indexes. These and other properties of indexes will be listed before the theorem in which they are used.

Evaluating boundary dependent errors in QM/MM simulations.

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations provide a powerful tool for studying chemical reactions, especially in complex biochemical systems. In most works to date, the quantum region is kept fixed throughout the simulation and is defined in an ad hoc way based on chemical intuition and available computational resources. The simulation errors associated with a given choice of the quantum region are, however, rarely assessed in a systematic manner. Here we study the dependence of two relevant quantities on the QM region size: the force error at the center of the QM region and the free energy of a proton transfer reaction. Taking lysozyme as our model system, we find that in an apolar region the average force error rapidly decreases with increasing QM region size. In contrast, the average force error at the polar active site is considerably higher, exhibits large oscillations and decreases more slowly, and may not fall below acceptable limits even for a quantum region radius of 9.0 A. Although computation of free energies could only be afforded until 6.0 A, results were found to change considerably within these limits. These errors demonstrate that the results of QM/MM calculations are heavily affected by the definition of the QM region (not only its size), and a convergence test is proposed to be a part of setting up QM/MM simulations.

A reforma curricular de Psicologia na Universidade Estadual da Paraíba: as recontextualizações institucionais

A análise em tela investiga a construção do projeto político pedagógico do Departamento de Psicologia da Universidade Estadual da Paraíba (2011), tendo como parâmetros o projeto político pedagógico inicial do curso (1999) e a produção de textos, discursos e documentos no cenário nacional que versam sobre a reforma curricular da graduação em Psicologia no Brasil. A abordagem do ciclo contínuo de políticas, proposta por Stephen Ball e a vertente analítica das comunidades epistêmicas são a base teórico-metodológica escolhida. Também há uma interlocução com o campo da Psicologia da Educação, em uma perspectiva multidisciplinar, apoiada nas contribuições de Michel Foucault sobre discurso e poder. Compreendemos, a partir desta perspectiva, que as políticas curriculares são pensadas e produzidas num processo complexo que envolve diversas ações nos contextos da influência, produção e da prática (BALL e BOWE, 1992). Ainda que o foco de nossa pesquisa seja no contexto da prática (reforma curricular do curso de Psicologia), a análise considera os outros contextos pelas relações de interdependência que há entre eles. O intervalo cronológico definido para compreensão das políticas curriculares para a formação em Psicologia (1999-2011) foi atento às definições ocorridas, neste período, as quais permitem a análise mais precisa do nosso objeto: as recontextualizações institucionais na reforma curricular da Psicologia da UEPB. Elas são analisadas a partir da identificação de dois projetos de formação em disputa no cenário nacional: um projeto generalista e outro especialista. O primeiro tem como características principais a defesa de um curso com denominação única (Curso de Psicologia), formação focada na profissionalização, substituição das antigas áreas de habilitação para ênfases curriculares, dissociação entre formação profissional e formação do professor e, por fim, extinção da terminologia de bacharel. Já o segundo defende dois aspectos que dizem respeito a reivindicação da formação do bacharel e a formação do professor. Identificamos que o projeto de formação generalista que tem como maior representante o CFP, tornou-se vencedor, no cenário nacional, tendo repercussões no contexto da prática na UEPB. Há algumas sintonias entre as diretrizes curriculares construídas para a Psicologia na universidade e as diretrizes do CFP que defendem a inclusão das práticas emergentes ao currículo da graduação em Psicologia no país. Esta constatação atesta a ação de uma comunidade epistêmica que defendeu um projeto de formação focado na profissionalização na área clínica. Assim, concluímos que, ainda que haja a definição da profissionalização como meta do curso de Psicologia da UEPB, é a área/ênfase de Psicologia Organizacional e do Trabalho que aparece como dominante; a área/ênfase de Psicologia Clínica tem suas horas diminuídas; as ênfases curriculares são correlatas das áreas de formação do PPPI (1999) e a formação do professor de Psicologia é excluída do NPPP (2011), ficando para o futuro a construção de um projeto específico para esta formação. Portanto, a reforma curricular de Psicologia da Universidade Estadual da Paraíba, apesar de pretender uma formação generalista, reproduz uma lógica especialista e o perfil do curso foca na profissionalização, mas com uma ascensão da área/ênfase Psicologia Organizacional e do Trabalho.