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 .

On spectral invariance of single scattering albedo for water droplets and ice crystals at weakly absorbing wavelengths

The single scattering albedo w_0l in atmospheric radiative transfer is the ratio of the scattering coefficient to the extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, thus the single scattering albedo, are functions of wavelength l and droplet size r. This note shows that for water droplets at weakly absorbing wavelengths, the ratio w_0l(r)/w_0l(r0) of two single scattering albedo spectra is a linear function of w_0l(r). The slope and intercept of the linear function are wavelength independent and sum to unity. This relationship allows for a representation of any single scattering albedo spectrum w_0l(r) via one known spectrum w_0l(r0). We provide a simple physical explanation of the discovered relationship. Similar linear relationships were found for the single scattering albedo spectra of non-spherical ice crystals.

Physical interpretation of the spectral radiative signature in the transition zone between cloud-free and cloudy regions

One-second-resolution zenith radiance measure- ments from the Atmospheric Radiation Measurement pro- gram’s new shortwave spectrometer (SWS) provide a unique opportunity to analyze the transition zone between cloudy and cloud-free air, which has considerable bearing on the aerosol indirect effect. In the transition zone, we find a re- markable linear relationship between the sum and difference of radiances at 870 and 1640 nm wavelengths. The intercept of the relationship is determined primarily by aerosol prop- erties, and the slope by cloud properties. We then show that this linearity can be predicted from simple theoretical con- siderations and furthermore that it supports the hypothesis of inhomogeneous mixing, whereby optical depth increases as a cloud is approached but the effective drop size remains un- changed.

Comparison of MODIS broadband albedo over an agricultural site with ground measurements and values derived from Earth observation data at a range of spatial scales

Land surface albedo is dependent on atmospheric state and hence is difficult to validate. Over the UK persistent cloud cover and land cover heterogeneity at moderate (km-scale) spatial resolution can also complicate comparison of field-measured albedo with that derived from instruments such as the Moderate Resolution Imaging Spectrometer (MODIS). A practical method of comparing moderate resolution satellite-derived albedo with ground-based measurements over an agricultural site in the UK is presented. Point measurements of albedo made on the ground are scaled up to the MODIS resolution (1 km) through reflectance data obtained at a range of spatial scales. The point measurements of albedo agreed in magnitude with MODIS values over the test site to within a few per cent, despite problems such as persistent cloud cover and the difficulties of comparing measurements made during different years. Albedo values derived from airborne and field-measured data were generally lower than the corresponding satellite-derived values. This is thought to be due to assumptions made regarding the ratio of direct to diffuse illumination used when calculating albedo from reflectance. Measurements of albedo calculated for specific times fitted closely to the trajectories of temporal albedo derived from both Systeme pour l'Observation de la Terre (SPOT) Vegetation (VGT) and MODIS instruments.

Can we measure terrestrial photosynthesis from space directly, using spectral reflectance and fluorescence?

Attempts to estimate photosynthetic rate or gross primary productivity from remotely sensed absorbed solar radiation depend on knowledge of the light use efficiency (LUE). Early models assumed LUE to be constant, but now most researchers try to adjust it for variations in temperature and moisture stress. However, more exact methods are now required. Hyperspectral remote sensing offers the possibility of sensing the changes in the xanthophyll cycle, which is closely coupled to photosynthesis. Several studies have shown that an index (the photochemical reflectance index) based on the reflectance at 531 nm is strongly correlated with the LUE over hours, days and months. A second hyperspectral approach relies on the remote detection of fluorescence, which is a directly related to the efficiency of photosynthesis. We discuss the state of the art of the two approaches. Both have been demonstrated to be effective, but we specify seven conditions required before the methods can become operational.

Stratospheric water vapor and climate: sensitivity to the representation in radiation codes

There has been considerable interest in the climate impact of trends in stratospheric water vapor (SWV). However, the representation of the radiative properties of water vapor under stratospheric conditions remains poorly constrained across different radiation codes. This study examines the sensitivity of a detailed line-by-line (LBL) code, a Malkmus narrow-band model and two broadband GCM radiation codes to a uniform perturbation in SWV in the longwave spectral region. The choice of sampling rate in wave number space (Δν) in the LBL code is shown to be important for calculations of the instantaneous change in heating rate (ΔQ) and the instantaneous longwave radiative forcing (ΔFtrop). ΔQ varies by up to 50% for values of Δν spanning 5 orders of magnitude, and ΔFtrop varies by up to 10%. In the three less detailed codes, ΔQ differs by up to 45% at 100 hPa and 50% at 1 hPa compared to a LBL calculation. This causes differences of up to 70% in the equilibrium fixed dynamical heating temperature change due to the SWV perturbation. The stratosphere-adjusted radiative forcing differs by up to 96% across the less detailed codes. The results highlight an important source of uncertainty in quantifying and modeling the links between SWV trends and climate.

Spectral analysis of diffusions with jump boundary

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.

On the spectral gap of Brownian motion with jump boundary

In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are dierent and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap from the jump distribution in a multi-dimensional setting.

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1

Towards effective water reuse: drivers, challenges and strategies shaping the organisational management of reclaimed water in Jordan

Treated wastewater or reclaimed water is gaining recognition as a valuable water resource around the world. To assess why, where and how water reuse takes place in Jordan, semi-structured interviews were conducted with representatives of 29 key organisations in 2008. The analysis reveals that water scarcity is a key driver for water reuse. However, despite such recognition, reuse was described positively by only a small proportion of the interviewees (n = 6). Negative and neutral perceptions regarding reuse dominated and the research found that this was related to two underlying challenges: (i) the requirement for more intensive management when using reclaimed water compared with freshwater and (ii) concern over societal acceptance of water reuse. These factors were found to be associated with the risks posed to humans and their environments, combined with negative emotional and cultural responses to human waste and its applications. Numerous strategies are identified that are employed by organisations to overcome these challenges. Wastewater treatment, regulation, monitoring, the mixing of treated effluent with freshwater and limited public discussion of water reuse are all employed to achieve maximum use of reclaimed water. Each strategy presents benefits of sort, but some may paradoxically also inhibit optimal use of reclaimed water. Careful modifications to the existing strategies of Jordanian agencies, such as more open discussion of reuse, could lead to greater social, economic and environmental gains.

N-(Aryl)picolinamide complexes of rhodium : synthesis, structure and, spectral and electrochemical properties

Reaction of a series of N-(aryl)picolinamide ligands (HL-R, where II denotes the acidic proton and R (R = OCH3, CH3, H, Cl and NO2) is the para substituent in the aryl fragment) with RhCl3 center dot 3H(2)O in refluxing ethanal in the presence of a base (NEt3) affords two groups of yellow complexes of type [Rh(H-R)(L-R)Cl-2] and [Rh(L-R)(2)(H2O)Cl]. In [Rh(HL-R)(L-R)Cl-2], HL-R is coordinated as neutral N,O-donor and L-R as monoanionic N,N-donor, and the two chlorides are mutually trans. In [Rh(L-R)(2)(H2O)CI] both the amide ligands are coordinated as monoanionic N,N-donor, and the chloro and aquo ligands are mutually cis. Structures of the [Rh(HL-OCH3)(L-CH3)Cl-2] and [Rh(L-Cl)(2)(H2O)CI] complexes have been determined by X-ray crystallography. All the complexes show characteristic H-1 NMR signals and intense LLCT transitions in the ultraviolet region. Cyclic voltammetry on the complexes shows an oxidation of the coordinated amide ligand within 0.78-1.80 V vs SCE and a reductive response within -0.20 to -0.75 V vs SCE. DFT calculations have been done to explain the electronic spectral and electrochemical properties.

Complexes of palladium using di-2-pyridyl ketone as ligand: synthesis, structure and, spectral and catalytic properties

During the reaction of di-2-pyridyl ketone (dpk) with Na(2)[PdCl(4)] in alcoholic media, the C=O fragment of dpk undergoes facile solvolysis and the transformed di-2-pyridyl ketone (dpk(ROH), R = Me or H) binds to palladium as NN-donor. When the reaction is carried out in refluxing methanol, a mono-complex of type [Pd(dpk(MeOH))Cl(2)] is obtained. A similar reaction in ethanol affords a bis-complex of type [Pd(dpk(ROH))(2)]Cl(2). Structure of both the complexes have been determined by X-ray crystallography. In acetonitrile solution the [pd(dpk(MeOH))Cl(2)] and [pd(dpk(ROH))(2)]Cl(2) complexes show intense absorptions in the visible and ultraviolet region, origin of which has been probed through uvr calculations. These two palladium complexes are found to be efficient catalysts for Suzuki cross-coupling reactions.

Ruthenium mediated C–H activation of benzaldehyde thiosemicarbazones: Synthesis, structure and, spectral and electrochemical properties of the resulting complexes

Reaction of five 4R-benzaldehyde thiosemicarbazones (R = OCH3, CH3, H, Cl and NO2) with [ Ru(PPh3)(3)(-CO)(H) Cl] in refluxing methanol in the presence of a base (NEt3) affords complexes of two different types, viz. 1-R and 2-R. In the 1-R complexes the thiosemicarbazone is coordinated to ruthenium as a dianionic tridentate C,N,S-donor via C-H bond activation. Two triphenylphosphines and a carbonyl are also coordinated to ruthenium. The tricoordinated thiosemicarbazone ligand is sharing the same equatorial plane with ruthenium and the carbonyl, and the PPh3 ligands are mutually trans. In the 2-R complexes the thiosemicarbazone ligand is coordinated to ruthenium as a monoanionic bidentate N, S-donor forming a four-membered chelate ring with a bite angle of 63.91(11)degrees. Two triphenylphosphines, a carbonyl and a hydride are also coordinated to ruthenium. The coordinated thiosemicarbazone ligand, carbonyl and hydride constitute one equatorial plane with the metal at the center, where the carbonyl is trans to the coordinated nitrogen of the thiosemicarbazone and the hydride is trans to the sulfur. The two triphenylphosphines are trans. Structures of the 1-CH3 and 2-CH3 complexes have been determined by X-ray crystallography. All the complexes show intense transitions in the visible region, which are assigned, based on DFT calculations, to transitions within orbitals of the thiosemicarbazone ligand. Cyclic voltammetry on the complexes shows two oxidations of the coordinated thiosemicarbazone on the positive side of SCE and a reduction of the same ligand on the negative side.

System identification algorithms for the analysis of dielectric responses from broadband spectroscopies

We discuss the modeling of dielectric responses for an electromagnetically excited network of capacitors and resistors using a systems identification framework. Standard models that assume integral order dynamics are augmented to incorporate fractional order dynamics. This enables us to relate more faithfully the modeled responses to those reported in the Dielectrics literature.