Boundary Data Maps for Schrodinger Operators on a Compact Interval

We provide a systematic study of boundary data maps, that is, 2 \times 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrodinger operators on a compact interval [0,R] with separated boundary conditions at 0 and R. Most of our results are formulated in the non-self-adjoint context. Our principal results include explicit representations of these boundary data maps in terms of the resolvent of the underlying Schrodinger operator and the associated boundary trace maps, Krein-type resolvent formulas relating Schrodinger operators corresponding to different (separated) boundary conditions, and a derivation of the Herglotz property of boundary data maps (up to right multiplication by an appropriate diagonal matrix) in the special self-adjoint case.Comment: 40 page

Principal Solutions Revisited

The main objective of this paper is to identify principal solutions associated with Sturm-Liouville operators on arbitrary open intervals $(a,b) \subseteq \mathbb{R}$, as introduced by Leighton and Morse in the scalar context in 1936 and by Hartman in the matrix-valued situation in 1957, with Weyl-Titchmarsh solutions, as long as the underlying Sturm-Liouville differential expression is nonoscillatory (resp., disconjugate or bounded from below near an endpoint) and in the limit point case at the endpoint in question. In addition, we derive an explicit formula for Weyl-Titchmarsh functions in this case (the latter appears to be new in the matrix-valued context).Comment: 27 pages, expanded Sect. 2, added reference

Minimal Rank Decoupling of Full-Lattice CMV Operators with Scalar- and Matrix-Valued Verblunsky Coefficients

Relations between half- and full-lattice CMV operators with scalar- and matrix-valued Verblunsky coefficients are investigated. In particular, the decoupling of full-lattice CMV operators into a direct sum of two half-lattice CMV operators by a perturbation of minimal rank is studied. Contrary to the Jacobi case, decoupling a full-lattice CMV matrix by changing one of the Verblunsky coefficients results in a perturbation of twice the minimal rank. The explicit form for the minimal rank perturbation and the resulting two half-lattice CMV matrices are obtained. In addition, formulas relating the Weyl--Titchmarsh $m$-functions (resp., matrices) associated with the involved CMV operators and their Green's functions (resp., matrices) are derived.Comment: 30 page

On Self-Adjoint and J-Self-Adjoint Dirac-Type Operators: A Case Study

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl-Titchmarsh half-line m-coefficients (and 2 × 2 matrix-valued M-matrices) in the non-self-adjoint context and derive some of their basic properties. We conclude with an illustrative example showing that crossing spectral arcs in the non-self-adjoint context imply the blowup of the norm of spectral projections in the limit where the crossing point is approached

A Comparison and Evaluation of Performances among Crop Yield Forecasting Models Based on Remote Sensing: Results from Tte Geoland Observatory of Food Monitoring

In the context of the GEOLAND EC FP6 project the comparison of different remote sensing based approaches for yield forecasting over large areas in Europe are tested and results inter-compared. In particular the methods tested include the ones in use within the MARS-Crop Yield Forecasting System as the results from the Crop Growth Monitoring System model and vegetation indicators derived from Low Resolution SPOT-VGT and NOAA Images, METEOSAT based yield forecasting and ERS-Scatterometer Crop Performance Index. Performances of the different models were tested in Spain, Belgium and Poland. The inter-comparisons of the crop yield forecasts were mainly based on the forecasting error obtained from the different approaches based on the Root Mean Square Forecast Error (RMSFE). This error was derived by comparing the predicted yields of the different models with the official yield as from official statistics (EUROSTAT). The comparison of the RMSFE was used to verify the convergence of results from the different models, the reliability of the information, i.e. precision and bias, and its precocity compared to the crop cycle. The results showed that the indicators are able to give reliable information with some differences: remote sensing indicators are more precise and accurate in southern areas (less cloud cover) while in northern areas good results are obtained under the use of better local calibrations of traditional crop yield forecasting systems and/or the use of additional information for instance remote sensing data as inputs into advanced crop modelling systems. Furthermore, in order to take care of the different time series length available, a qualitative indicator called Performance Score (Ps) was introduced. The analysis of the Ps showed that when a long time series of observation is available greater advantages are obtained from RS rather than from more advanced crop models.JRC.DDG.H.4-Monitoring agricultural resource

The effect of prior alcohol consumption on the ataxic response to alcohol in high-alcohol preferring mice

We have previously shown that ethanol-naïve high-alcohol preferring (HAP) mice, genetically predisposed to consume large quantities of alcohol, exhibited heightened sensitivity and more rapid acute functional tolerance (AFT) to alcohol-induced ataxia compared to low-alcohol preferring mice. The goal of the present study was to evaluate the effect of prior alcohol self-administration on these responses in HAP mice. Naïve male and female adult HAP mice from the second replicate of selection (HAP2) underwent 18 days of 24-h, 2-bottle choice drinking for 10% ethanol vs. water, or water only. After 18 days of fluid access, mice were tested for ataxic sensitivity and rapid AFT following a 1.75 g/kg injection of ethanol on a static dowel apparatus in Experiment 1. In Experiment 2, a separate group of mice was tested for more protracted AFT development using a dual-injection approach where a second, larger (2.0 g/kg) injection of ethanol was given following the initial recovery of performance on the task. HAP2 mice that had prior access to alcohol exhibited a blunted ataxic response to the acute alcohol challenge, but this pre-exposure did not alter rapid within-session AFT capacity in Experiment 1 or more protracted AFT capacity in Experiment 2. These findings suggest that the typically observed increase in alcohol consumption in these mice may be influenced by ataxic functional tolerance development, but is not mediated by a greater capacity for ethanol exposure to positively influence within-session ataxic tolerance

Differential Parental Care by Adult Mountain Plovers, Charadrius montanus

We studied chick survival of the Mountain Plover (Charadrius montanus) in Montana and found that chicks tended by females had higher survival rates than chicks tended by males, and that chick survival generally increased during the nesting season. Differences in chick survival were most pronounced early in the nesting season, and may be related to a larger sample of nests during this period. When compared to information about the nest survival of male- and female-tended plover nests, our chick data suggest a trade-off for adult plovers between the egg and chick phases of reproduction. Because Mountain Plover pairs have clutches at two nests at two different locations and show differential success between the sexes during the egg and chick phases, we offer that the Mountain Plover breeding system favours optimizing annual recruitment in a dynamic ecologic setting driven by annually unpredictable drought, grazing, and predation pressures

Borg-Marchenko-type Uniqueness Results for CMV Operators

We prove local and global versions of Borg–Marchenko-type uniqueness theorems for half-lattice and full-lattice CMV operators (CMV for Cantero, Moral, and Velázquez [15]). While our half-lattice results are formulated in terms of Weyl–Titchmarsh functions, our full-lattice results involve the diagonal and main off-diagonal Green’s functions