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 .

Towards the main sequence: detailed analysis of weak line and post-T Tauri stars

A detailed study was performed for a sample of low-mass pre-main-sequence (PMS) stars, previously identified as weak-line T Tauri stars, which are compared to members of the Tucanae and Horologium Associations. Aiming to verify if there is any pattern of abundances when comparing the young stars at different phases, we selected objects in the range from 1 to 100 Myr, which covers most of PMS evolution. High-resolution optical spectra were acquired at European Southern Observatory and Observatorio do Pico dos Dias. The stellar fundamental parameters effective temperature and gravity were calculated by excitation and ionization equilibria of iron absorption lines. Chemical abundances were obtained via equivalent width calculations and spectral synthesis for 44 per cent of the sample, which shows metallicities within 0.5 dex solar. A classification was developed based on equivalent width of Li I 6708 angstrom and Ha lines and spectral types of the studied stars. This classification allowed a separation of the sample into categories that correspond to different evolutive stages in the PMS. The position of these stars in the Hertzsprung-Russell diagram was also inspected in order to estimate their ages and masses. Among the studied objects, it was verified that our sample actually contains seven weak-line T Tauri stars, three are Classical T Tauri, 12 are Fe/Ge PMS stars and 21 are post-T Tauri or young main-sequence stars. An estimation of circumstellar luminosity was obtained using a disc model to reproduce the observed spectral energy distribution. Most of the stars show low levels of circumstellar emission, corresponding to less than 30 per cent of the total emission.

New palladium(II) complexes with pyrazole ligands Part II. Synthesis, spectral and thermal studies, and antitumor evaluation

This study describes the synthesis, IR, (1)H, and (13)C{(1)H} NMR spectroscopic as well the thermal characterization of the new palladium(II) pyrazolyl complexes [PdCl(2)(HmPz)(2)] 1, [PdBr(2)(HmPz)(2)] 2, [PdI(2)(HmPz)(2)] 3, [Pd(SCN)(2)(HmPz)(2)] 4 {HmPz = 4-methylpyrazole}. The residues of the thermal decomposition were identified as Pd(0) by X-ray powder diffraction. From the initial decomposition temperatures, the thermal stability of the complexes can be ordered in the sequence: 1 > 2 > 4 a parts per thousand 3. The cytotoxic activities of the complexes and the ligand were investigated against two murine cancer cell lines: mammary adenocarcinoma (LM3) and lung adenocarcinoma (LP07) and compared to cisplatin under the same experimental conditions.

A new firefly luciferase with bimodal spectrum: Identification of structural determinants of spectral pH-sensitivity in firefly luciferases

Fireflies emit flashes in the green-yellow region of the spectrum for the purpose of sexual attraction. The bioluminescence color is determined by the luciferases. It is well known that the in vitro bioluminescence color of firefly luciferases can be shifted toward the red by lower pH and higher temperature; for this reason they are classified as pH-sensitive luciferases. However, the mechanism and structural origin of pH sensitivity in fireflies remains unknown. Here we report the cloning of a new luciferase from the Brazilian twilight active firefly Macrolampis sp2, which displays an unusual bimodal spectrum. The recombinant luciferase displays a sensitive spectrum with the peak at 569 nm and a shoulder in the red region. Comparison of the bioluminescence spectra of Macrolampis, Photinus and Cratomorphus firefly luciferases shows that the distinct colors are determined by the ratio between green and red emitters under luciferase influence. Comparison of Macrolampis luciferase with the highly similar North American Photinus pyralis luciferase (91%) showed few substitutions potentially involved with the higher spectral sensitivity in Macrolampis luciferase. Site-directed mutagenesis showed that the natural substitution E354N determines the appearance of the shoulder in the red region of Macrolampis luciferase bioluminescence spectrum, helping to identify important interactions and residues involved in the pH-sensing mechanism in firefly luciferases. © 2005 American Society for Photobiology.

Probing the anomalous extinction of four young star clusters: the use of colour-excess, main-sequence fitting and fractal analysis

Aims. We studied four young star clusters to characterise their anomalous extinction or variable reddening and asses whether they could be due to contamination by either dense clouds or circumstellar effects. Methods. We evaluated the extinction law (R-V) by adopting two methods: (i) the use of theoretical expressions based on the colour-excess of stars with known spectral type; and (ii) the analysis of two-colour diagrams, where the slope of the observed colour distribution was compared to the normal distribution. An algorithm to reproduce the zero-age main-sequence (ZAMS) reddened colours was developed to derive the average visual extinction (A(V)) that provides the closest fit to the observational data. The structure of the clouds was evaluated by means of a statistical fractal analysis, designed to compare their geometric structure with the spatial distribution of the cluster members. Results. The cluster NGC 6530 is the only object of our sample affected by anomalous extinction. On average, the other clusters suffer normal extinction, but several of their members, mainly in NGC 2264, seem to have high R-V, probably because of circumstellar effects. The ZAMS fitting provides A(V) values that are in good agreement with those found in the literature. The fractal analysis shows that NGC 6530 has a centrally concentrated distribution of stars that differs from the substructures found in the density distribution of the cloud projected in the A(V) map, suggesting that the original cloud was changed by the cluster formation. However, the fractal dimension and statistical parameters of Berkeley 86, NGC 2244, and NGC 2264 indicate that there is a good cloud-cluster correlation, when compared to other works based on an artificial distribution of points.

ZETA DETERMINANT FOR DOUBLE SEQUENCES OF SPECTRAL TYPE

We study the spectral functions, and in particular the zeta function, associated to a class of sequences of complex numbers, called of spectral type. We investigate the decomposability of the zeta function associated to a double sequence with respect to some simple sequence, and we provide a technique for obtaining the first terms in the Laurent expansion at zero of the zeta function associated to a double sequence.

Registration of Sub-Sequence and Multi-Camera Reconstructions for Camera Motion Estimation

This paper presents different application scenarios for which the registration of sub-sequence reconstructions or multi-camera reconstructions is essential for successful camera motion estimation and 3D reconstruction from video. The registration is achieved by merging unconnected feature point tracks between the reconstructions. One application is drift removal for sequential camera motion estimation of long sequences. The state-of-the-art in drift removal is to apply a RANSAC approach to find unconnected feature point tracks. In this paper an alternative spectral algorithm for pairwise matching of unconnected feature point tracks is used. It is then shown that the algorithms can be combined and applied to novel scenarios where independent camera motion estimations must be registered into a common global coordinate system. In the first scenario multiple moving cameras, which capture the same scene simultaneously, are registered. A second new scenario occurs in situations where the tracking of feature points during sequential camera motion estimation fails completely, e.g., due to large occluding objects in the foreground, and the unconnected tracks of the independent reconstructions must be merged. In the third scenario image sequences of the same scene, which are captured under different illuminations, are registered. Several experiments with challenging real video sequences demonstrate that the presented techniques work in practice.

Analyses of a Holocene soil/loess sequence in Southern Siberia

We conducted a high-resolution study of a unique Holocene sequence of wind-blown sediments and buried soils in Southern Siberia, far from marine environment influences. This was accomplished in order to assess the difference between North Atlantic marine and in-land climate variations. Relative wind strength was determined by grain size analyses of different stratigraphic units. Petromagnetic measurements were performed to provide a proxy for the relative extent of pedogenesis. An age model for the sections was built using the radiocarbon dating method. The windy periods are associated with the absence of soil formation and relatively low values of frequency dependence of magnetic susceptibility (FD), which appeared to be a valuable quantitative marker of pedogenic activity. These events correspond to colder intervals which registered reduced solar modulation and sun spot number. Events, where wind strength was lower, are characterized by soil formation with high FD values. Spectral analysis of our results demonstrates periodic changes of 1500, 1000 and 500 years of relatively warm and cold intervals during the Holocene of Siberia. We presume that the 1000 and 500 year climatic cycles are driven by increased solar insolation reaching the Earth surface and amplified by other still controversial mechanisms. The 1500 year cycle associated with the North Atlantic circulation appears only in the Late Holocene. Three time periods - 8400-9300 years BP, 3600-5100 years BP, and the last ~250 years BP - correspond to both the highest sun spot number and the most developed soil horizons in the studied sections

Spectral reflectance of ODP Leg 178 holes

The routine use of spectrophotometry on the sediment surfaces of archive halves of each section during the onboard sedimentological core description process is a great stride toward development of real-time noninvasive characterization of deep-sea sediments. Spectral reflectance data have been used so far for mineral composition studies as well as for lithostratigraphic correlation between sites (Balsam and Deaton, 1991; Balsam et al., 1997; Mix et al., 1995; Ortiz et al., 1999). Their results demonstrate that spectrophotometry can estimate CaCO3 content by using the 4.65-, 5.25-, and 5.55-µm wavelength spectrums. A detailed overview of various other noninvasive methods is given in Ortiz and Rack (1999). The purpose of this study is to test whether spectrophotometry in the visible band can be used as a tool to gather further information about grain-size variation, sorting, compaction, and porosity, which are directly linked to the sedimentation process. From remote sensing data analyses, it is known that diffuse spectral reflectance data in the visible band in the wavelength window of 7.0-6.5 µm are sensitive to grain-size variations. It appears that a relationship between grain size and signal absorption exists only in this wavelength window. (e.g., Clark, 1999; Gaffey, 1986; Gaffey et al., 1993). Variations in grain size during a sedimentation process are linked to depositional energy, which affects sorting, compaction, and porosity of sediment deposits. As an example, we study here the spectrophotometric data of the sedimentary sequence of Hole 1098C, which was deposited under widely varying environmental conditions. Alternating turbidite and finely laminated sediments were recovered from Hole 1098C. The turbidites are related to a high depositional energy environment; the finely laminated sediments are related to a low depositional energy environment. Data from Hole 1098C were therefore used to test whether the spectral reflectance data can provide a proxy for these different depositional environments.

Sedimentary data from the Semlac loess-paleosol sequence

The volumetric magnetic susceptibility was measured at frequencies of 300 and 3000 Hz in a static field of 300 mA/m using a Magnon International VSFM in the Laboratory for Environmental- and Palaeomagnetism at the University of Bayreuth. The magnetic susceptibility was mass-normalised. The frequency dependence was calculated as MSfd = (MSlf - MShf) / MSlf *100 [%]. A spectrophotometer (Konica Minolta CM-5) was used to determine the colour of dried and homogenised sediment samples by detecting the diffused reflected light under standardised observation conditions (2° Standard Observer, Illuminant C). Colour spectra were obtained in the visible range (360 to 740 nm), in 10 nm increments, and the spectral data was converted into the Munsell colour system and the CIELAB Colour Space (L*a*b*, CIE 1976) using the Software SpectraMagic NX (Konica Minolta). The measurement of the particle size was conducted by using a Laser Diffraction Particle Size Analyzer (Beckman Coulter LS 13 320 PIDS) and by calculating the mean diameters of the particles within a size range of 0.04 - 2000 µm. Each sample was measured two times in two different concentrations to increase accuracy. Finally all measurements with reliable obscuration (8 - 12 %) were averaged.

Coral reef habitat maps derived from a high-spatial-resolution multi-spectral satellite image using object based image analysis

Coral reef maps at various spatial scales and extents are needed for mapping, monitoring, modelling, and management of these environments. High spatial resolution satellite imagery, pixel <10 m, integrated with field survey data and processed with various mapping approaches, can provide these maps. These approaches have been accurately applied to single reefs (10-100 km**2), covering one high spatial resolution scene from which a single thematic layer (e.g. benthic community) is mapped. This article demonstrates how a hierarchical mapping approach can be applied to coral reefs from individual reef to reef-system scales (10-1000 km**2) using object-based image classification of high spatial resolution images guided by ecological and geomorphological principles. The approach is demonstrated for three individual reefs (10-35 km**2) in Australia, Fiji, and Palau; and for three complex reef systems (300-600 km**2) one in the Solomon Islands and two in Fiji. Archived high spatial resolution images were pre-processed and mosaics were created for the reef systems. Georeferenced benthic photo transect surveys were used to acquire cover information. Field and image data were integrated using an object-based image analysis approach that resulted in a hierarchically structured classification. Objects were assigned class labels based on the dominant benthic cover type, or location-relevant ecological and geomorphological principles, or a combination thereof. This generated a hierarchical sequence of reef maps with an increasing complexity in benthic thematic information that included: 'reef', 'reef type', 'geomorphic zone', and 'benthic community'. The overall accuracy of the 'geomorphic zone' classification for each of the six study sites was 76-82% using 6-10 mapping categories. For 'benthic community' classification, the overall accuracy was 52-75% with individual reefs having 14-17 categories and reef systems 20-30 categories. We show that an object-based classification of high spatial resolution imagery, guided by field data and ecological and geomorphological principles, can produce consistent, accurate benthic maps at four hierarchical spatial scales for coral reefs of various sizes and complexities.

Effects of bubbles, cracks, and volcanic tephra on the spectral albedo of bare ice near the Transantarctic Mountains: Implications for sea glaciers on Snowball Earth

Spectral albedo was measured along a 6 km transect near the Allan Hills in East Antarctica. The transect traversed the sequence from new snow through old snow, firn, and white ice, to blue ice, showing a systematic progression of decreasing albedo at all wavelengths, as well as decreasing specific surface area (SSA) and increasing density. Broadband albedos under clear-sky range from 0.80 for snow to 0.57 for blue ice, and from 0.87 to 0.65 under cloud. Both air bubbles and cracks scatter sunlight; their contributions to SSA were determined by microcomputed tomography on core samples of the ice. Although albedo is governed primarily by the SSA (and secondarily by the shape) of bubbles or snow grains, albedo also correlates highly with porosity, which, as a proxy variable, would be easier for ice sheet models to predict than bubble sizes. Albedo parameterizations are therefore developed as a function of density for three broad wavelength bands commonly used in general circulation models: visible, near-infrared, and total solar. Relevance to Snowball Earth events derives from the likelihood that sublimation of equatorward-flowing sea glaciers during those events progressively exposed the same sequence of surface materials that we measured at Allan Hills, with our short 6 km transect representing a transect across many degrees of latitude on the Snowball ocean. At the equator of Snowball Earth, climate models predict thick ice, or thin ice, or open water, depending largely on their albedo parameterizations; our measured albedos appear to be within the range that favors ice hundreds of meters thick. Citation: