Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

Modular organization of intrinsic connections associated with spectral tuning in cat auditory cortex

Many response properties in primary auditory cortex (AI) are segregated spatially and organized topographically as those in primary visual cortex. Intensive study has not revealed an intrinsic, anatomical organizing principle related to an AI functional topography. We used retrograde anatomic tracing and topographic physiologic mapping of acoustic response properties to reveal long-range (≥1.5 mm) convergent intrinsic horizontal connections between AI subregions with similar bandwidth and characteristic frequency selectivity. This suggests a modular organization for processing spectral bandwidth in AI.

Electroretinogram analysis of relative spectral sensitivity in genetically identified dichromatic macaques

The retinas of macaque monkeys usually contain three types of photopigment, providing them with trichromatic color vision homologous to that of humans. However, we recently used molecular genetic analysis to identify several macaques with a dichromatic genotype. The affected X chromosome of these animals contains a hybrid gene of long-wavelength-sensitive (L) and middle-wavelength-sensitive (M) photopigments instead of separate genes encoding L and M photopigments. The product of the hybrid gene exhibits a spectral sensitivity close to that of M photopigment; consequently, male monkeys carrying the hybrid gene are genetic protanopes, effectively lacking L photopigment. In the present study, we assessed retinal expression of L photopigment in monkeys carrying the hybrid gene. The relative sensitivities to middle-wavelength (green) and long-wavelength (red) light were measured by electroretinogram flicker photometry. We found the sensitivity to red light to be extremely low in protanopic male monkeys compared with monkeys with the normal genotype. In female heterozygotes, sensitivity to red light was intermediate between the genetic protanopes and normal monkeys. Decreased sensitivity to long wavelengths was thus consistent with genetic loss of L photopigment.

Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups.

We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We also compare those results with the well-known characterizations for classical Besov spaces Bp,qs.

Spectral features in isolated neutron stars induced by inhomogeneous surface temperatures

The thermal X-ray spectra of several isolated neutron stars display deviations from a pure blackbody. The accurate physical interpretation of these spectral features bears profound implications for our understanding of the atmospheric composition, magnetic field strength and topology, and equation of state of dense matter. With specific details varying from source to source, common explanations for the features have ranged from atomic transitions in the magnetized atmospheres or condensed surface, to cyclotron lines generated in a hot ionized layer near the surface. Here, we quantitatively evaluate the X-ray spectral distortions induced by inhomogeneous temperature distributions of the neutron star surface. To this aim, we explore several surface temperature distributions, we simulate their corresponding general relativistic X-ray spectra (assuming an isotropic, blackbody emission), and fit the latter with a single blackbody model. We find that, in some cases, the presence of a spurious ‘spectral line’ is required at a high significance level in order to obtain statistically acceptable fits, with central energy and equivalent width similar to the values typically observed. We also perform a fit to a specific object, RX J0806.4−4123, finding several surface temperature distributions able to model the observed spectrum. The explored effect is unlikely to work in all sources with detected lines, but in some cases it can indeed be responsible for the appearance of such lines. Our results enforce the idea that surface temperature anisotropy can be an important factor that should be considered and explored also in combination with more sophisticated emission models like atmospheres.

Autonomy in the global era: Euro-regionalism and new policy spaces in education. ACES Working Papers, August 2010

Framed by a critical discussion of methodological nationalism, this paper explores the intersection of new and evolving regional, central state, and supranational education policy spaces through examples drawn from post-Franco Spain. This work is situated within the broader literature on the development of a European Education Policy Space, which aims to understand changing governance structures in European education (cf. Grek et al., 2009; Lawn & Lingard,2002; N6voa & Lawn, 2002). Using policy documents since 2000 and interview data, the paper first examines Spanish and regional (Catalan) education policy related to devolution, namely Catalonia's recently revised Statute of Autonomy. The paper then places devolution in Spain and Catalonia in a broader context of Euro-regionalism, which has deepened and legitimized regional autonomy. Together these shifts in educational governance and the development of new education policy spaces have promoted a concept of the multi-scalar, European "ideal citizen" (Engel & Ortloff, 2009). The last section presents an overview of the recent influx of immigrants into Catalonia and Spain, exploring whether and to what extent recent education policy promoting the "ideal citizen" has taken non-European immigrants into account.

Outline studies in arithmetic, algebra and geometry,

Cover-title.

Vorlesungen zur Einführung in die Algebra der linearen Transformationen

Mode of access: Internet.

Solar radio emission; spectral observations in the decameter range, 24 July 1959-28 February 1961.

Cover title.

First course in modern algebra

Mode of access: Internet.

Ergebnisse der Spectral-Analyse in Anwendung auf die Himmelskörper /

Mode of access: Internet.

Lectures in abstract algebra.

v. 1. Basic concepts.--v. 2. Linear algebra.--v. 3. Theory of fields and Galois theory.