Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Unraveling the electronic structures of low-valent naphthalene and anthracene iron complexes: x-ray, spectroscopic, and density functional theory studies

Naphthalene and anthracene transition metalates are potent reagents, but their electronic structures have remained poorly explored. A study of four Cp*-substituted iron complexes (Cp* = pentamethylcyclopentadienyl) now gives rare insight into the bonding features of such species. The highly oxygen- and water-sensitive compounds [K(18-crown- 6){Cp*Fe(η4-C10H8)}] (K1), [K(18-crown-6){Cp*Fe(η4-C14H10)}] (K2), [Cp*Fe(η4-C10H8)] (1), and [Cp*Fe(η4-C14H10)] (2) were synthesized and characterized by NMR, UV−vis, and 57Fe Mössbauer spectroscopy. The paramagnetic complexes 1 and 2 were additionally characterized by electron paramagnetic resonance (EPR) spectroscopy and magnetic susceptibility measurements. The molecular structures of complexes K1, K2, and 2 were determined by single-crystal X-ray crystallography. Cyclic voltammetry of 1 and 2 and spectroelectrochemical experiments revealed the redox properties of these complexes, which are reversibly reduced to the monoanions [Cp*Fe(η4-C10H8)]− (1−) and [Cp*Fe(η4-C14H10)]− (2−) and reversibly oxidized to the cations [Cp*Fe(η6-C10H8)]+ (1+) and [Cp*Fe(η6-C14H10)]+ (2+). Reduced orbital charges and spin densities of the naphthalene complexes 1−/0/+ and the anthracene derivatives 2−/0/+ were obtained by density functional theory (DFT) methods. Analysis of these data suggests that the electronic structures of the anions 1− and 2− are best represented by low-spin FeII ions coordinated by anionic Cp* and dianionic naphthalene and anthracene ligands. The electronic structures of the neutral complexes 1 and 2 may be described by a superposition of two resonance configurations which, on the one hand, involve a low-spin FeI ion coordinated by the neutral naphthalene or anthracene ligand L, and, on the other hand, a low-spin FeII ion coordinated to a ligand radical L•−. Our study thus reveals the redox noninnocent character of the naphthalene and anthracene ligands, which effectively stabilize the iron atoms in a low formal, but significantly higher spectroscopic oxidation state.

Legal outlier, again? U.S. felon suffrage: comparative and international human rights perspectives

The judiciousness of American felon suffrage policies has long been the subject of scholarly debate, not least due to the large number of affected Americans: an estimated 5.3 million citizens are ineligible to vote as a result of a criminal conviction. This article offers comparative law and international human rights perspectives and aims to make two main contributions to the American and global discourse. After an introduction in Part I, Part II offers comparative law perspectives on challenges to disenfranchisement legislation, juxtaposing U.S. case law against recent judgments rendered by courts in Canada, South Africa, Australia, and by the European Court of Human Rights. The article submits that owing to its unique constitutional stipulations, as well as to a general reluctance to engage foreign legal sources, U.S. jurisprudence lags behind an emerging global jurisprudential trend that increasingly views convicts’ disenfranchisement as a suspect practice and subjects it to judicial review. This transnational judicial discourse follows a democratic paradigm and adopts a “residual liberty” approach to criminal justice that considers convicts to be rights-holders. The discourse rejects regulatory justifications for convicts’ disenfranchisement, and instead sees disenfranchisement as a penal measure. In order to determine its suitability as a punishment, the adverse effects of disenfranchisement are weighed against its purported social benefits, using balancing or proportionality review. Part III analyzes the international human rights treaty regime. It assesses, in particular, Article 25 of the International Covenant on Civil and Political Rights (“ICCPR”), which proclaims that “every citizen” has a right to vote without “unreasonable restrictions.” The analysis concludes that the phrase “unreasonable restrictions” is generally interpreted in a manner which tolerates certain forms of disenfranchisement, whereas other forms (such as life disenfranchisement) may be incompatible with treaty obligations. This article submits that disenfranchisement is a normatively flawed punishment. It fails to treat convicts as politically-equal community members, degrades them, and causes them grave harms both as individuals and as members of social groups. These adverse effects outweigh the purported social benefits of disenfranchisement. Furthermore, as a core component of the right to vote, voter eligibility should cease to be subjected to balancing or proportionality review. The presumed facilitative nature of the right to vote makes suffrage less susceptible to deference-based objections regarding the judicial review of legislation, as well as to cultural relativity objections to further the international standardization of human rights obligations. In view of this, this article proposes the adoption of a new optional protocol to the ICCPR proscribing convicts’ disenfranchisement. The article draws analogies between the proposed protocol and the ICCPR’s “Optional Protocol Aiming at the Abolition of the Death Penalty.” If adopted, the proposed protocol would strengthen the current trajectory towards expanding convicts’ suffrage that emanates from the invigorated transnational judicial discourse.

Synthesis, chemical, electrochemical characterization of oxomolybdenum(V) complexes of 2-(3,5-dimethyl pyrazol-1-yl) benzothiazole ligand: crystal structure of ligand and oxomolybdenum(VI) complex and density functional theory (DFT) calculation

This work reports the ligational behavior of the neutral bidentate chelating molecule 2-(3,5-dimethyl pyrazol-1-yl) benzothiazole towards the oxomolybdenum(V) center. Both mononuclear complexes of the type (MoOX3L)-O-V and binuclear complexes of the formula (Mo2O4X2L2)-O-V (where X = Cl, Br) are isolated in the solid state. The complexes are characterized by elemental analyses, various spectroscopic techniques (UV-Vis IR), magnetic susceptibility measurement at room temperature, and cyclic voltammetry for their redox behavior at a platinum electrode in CH3CN. The mononuclear complexes (MoOX3L)-O-V are found to be paramagnetic while the binuclear complexes Mo2O4X2L2 are diamagnetic. Crystal and molecular structure of the ligand and the dioxomolybdenum complex (MoO2Br2L)-O-VI (obtained from the complex MoOBr3L during crystallization) have been solved by single crystal X-ray diffraction technique. Relevant DFT calculations of the ligand and the complex (MoO2Br2L)-O-VI are also carried out.

Correlation between Fourier series expansion and Hückel orbital theory

The Fourier series can be used to describe periodic phenomena such as the one-dimensional crystal wave function. By the trigonometric treatements in Hückel theory it is shown that Hückel theory is a special case of Fourier series theory. Thus, the conjugated π system is in fact a periodic system. Therefore, it can be explained why such a simple theorem as Hückel theory can be so powerful in organic chemistry. Although it only considers the immediate neighboring interactions, it implicitly takes account of the periodicity in the complete picture where all the interactions are considered. Furthermore, the success of the trigonometric methods in Hückel theory is not accidental, as it based on the fact that Hückel theory is a specific example of the more general method of Fourier series expansion. It is also important for education purposes to expand a specific approach such as Hückel theory into a more general method such as Fourier series expansion.

Model-measurement comparison of mesospheric temperature inversions, and a simple theory for their occurrence

Mesospheric temperature inversions are well established observed phenomena, yet their properties remain the subject of ongoing research. Comparisons between Rayleigh-scatter lidar temperature measurements obtained by the University of Western Ontario's Purple Crow Lidar (42.9°N, 81.4°W) and the Canadian Middle Atmosphere Model are used to quantify the statistics of inversions. In both model and measurements, inversions occur most frequently in the winter and exhibit an average amplitude of ∼10 K. The model exhibits virtually no inversions in the summer, while the measurements show a strongly reduced frequency of occurrence with an amplitude about half that in the winter. A simple theory of mesospheric inversions based on wave saturation is developed, with no adjustable parameters. It predicts that the environmental lapse rate must be less than half the adiabatic lapse rate for an inversion to form, and it predicts the ratio of the inversion amplitude and thickness as a function of environmental lapse rate. Comparison of this prediction to the actual amplitude/thickness ratio using the lidar measurements shows good agreement between theory and measurements.

Islamic mutual funds' financial performance and international investment style: evidence from 20 countries

We pursue the first large-scale investigation of a strongly growing mutual fund type: Islamic funds. Based on an unexplored, survivorship bias-adjusted data set, we analyse the financial performance and investment style of 265 Islamic equity funds from 20 countries. As Islamic funds often have diverse investment regions, we develop a (conditional) three-level Carhart model to simultaneously control for exposure to different national, regional and global equity markets and investment styles. Consistent with recent evidence for conventional funds, we find Islamic funds to display superior learning in more developed Islamic financial markets. While Islamic funds from these markets are competitive to international equity benchmarks, funds from especially Western nations with less Islamic assets tend to significantly underperform. Islamic funds’ investment style is somewhat tilted towards growth stocks. Funds from predominantly Muslim economies also show a clear small cap preference. These results are consistent over time and robust to time varying market exposures and capital market restrictions.

PRESENTATION. Experimental and behavioral economics. Theory, tools and topics

This note presents the special issue on Experimental and Behavioral Economics. The volume includes some recent contributions from these correlated disciplines –empirical the former and theoretical the latter– and their potential contribution to the intersection of Economics with Psychology and Sociology. The project “El papel de la comparación social en las decisiones económicas bajo incertidumbre” (Junta de Andalucía, P07-SEJ-03155)” provided us with inspiration and financial support to publish this volume.

Neural population models and cortical field theory: overview

The term neural population models (NPMs) is used here as catchall for a wide range of approaches that have been variously called neural mass models, mean field models, neural field models, bulk models, and so forth. All NPMs attempt to describe the collective action of neural assemblies directly. Some NPMs treat the densely populated tissue of cortex as an excitable medium, leading to spatially continuous cortical field theories (CFTs). An indirect approach would start by modelling individual cells and then would explain the collective action of a group of cells by coupling many individual models together. In contrast, NPMs employ collective state variables, typically defined as averages over the group of cells, in order to describe the population activity directly in a single model. The strength and the weakness of his approach are hence one and the same: simplification by bulk. Is this justified and indeed useful, or does it lead to oversimplification which fails to capture the pheno ...