The band spectrum of the periodic airy-schrodinger operator on the real line

We introduce the periodic Airy-Schr\"odinger operator and we study its band spectrum. This is an example of an explicitly solvable model with a periodic potential which is not differentiable at its minima and maxima. We define a semiclassical regime in which the results are stated for a fixed value of the semiclassical parameter and are thus estimates instead of asymptotic results. We prove that there exists a sequence of explicit constants, which are zeroes of classical functions, giving upper bounds of the semiclassical parameter for which the spectral bands are in the semiclassical regime. We completely determine the behaviour of the edges of the first spectral band with respect to the semiclassical parameter. Then, we investigate the spectral bands and gaps situated in the range of the potential. We prove precise estimates on the widths of these spectral bands and these spectral gaps and we determine an upper bound on the integrated spectral density in this range. Finally, in the semiclassical regime, we get estimates of the edges of every spectral bands and thus of the widths of every spectral bands and spectral gaps

Estimating spectral irradiance from measurements in seven spectral bands

Accurate measurement and characterisation of fluctuations in the irradiance environment is important for many areas of optical remote sensing. This paper reports a method of estimating spectral irradiance over the VNIR region (400 - 1100nm) from the radiance of a calibrated reference panel, measured in seven narrow (10nm) spectral bands. Earlier work established the potential for estimating spectral irradiance from multi-band data using a neural network technique (Milton et al., 2000). The approach described here uses linear regression analysis to regenerate the irradiance spectrum from data in seven reference wavelengths. The method was tested using data from a specially designed multiband radiometer – the INdependent SPectral IRradiance Estimator (INSPIRE). The irradiance spectrum was partitioned into a number of distinct regions within each of which the spectral irradiance was estimated from irradiance measured at one of the reference wavelengths. The precision of the method was found to be better than ±5% over most wavelengths from 400nm to 1100nm. Furthermore, the slope coefficients of the individual regression models were found to be sensitive to the sky radiance conditions, especially over the region 600-760nm, and improvement in the precision of the predicted spectrum (to within ±3%) was obtained by taking the diffuse-to-global (D:G) irradiance ratio at the time of measurement into account

Optimum thermal infrared bands for mapping general rock type and temperature from space

A study was carried out to determine quantitatively the number and locations of spectral bands required to perform general rock-type discrimination from spaceborne imaging sensors using only thermal infrared measurements. Beginning with laboratory spectra collected under idealized conditions from relatively well characterized, homogeneous samples, a radiative transfer model was employed to transform ground exitance values into the corresponding spectral radiance at the top of the atmosphere. Taking sensor noise into account analysis of these data revealed that three 1 micrometer wide spectral bands would permit independent estimators of rock-type and sample temperature from a satellite infrared multispectral scanner. This study, indicates that the location of three spectral bands at 8.1-9.1 micrometers, 9.5-10.5 micrometers and 11.0-12.0 micrometers, and the employment of appropriate preprocessing to minimize atmospheric effects makes it possible to predict general rock-type and temperature for a variety of atmospheric states and temperatures

Hyperspectral classification of Cyperus esculentus clones and morphologically similar weeds

Cyperus esculentus (yellow nutsedge) is one of the world's worst weeds as it can cause great damage to crops and crop production. To eradicate C. esculentus, early detection is key-a challenging task as it is often confused with other Cyperaceae and displays wide genetic variability. In this study, the objective was to classify C. esculentus clones and morphologically similar weeds. Hyperspectral reflectance between 500 and 800 nm was tested as a measure to discriminate between (I) C. esculentus and morphologically similar Cyperaceae weeds, and between (II) different clonal populations of C. esculentus using three classification models: random forest (RF), regularized logistic regression (RLR) and partial least squares-discriminant analysis (PLS-DA). RLR performed better than RF and PLS-DA, and was able to adequately classify the samples. The possibility of creating an affordable multispectral sensing tool, for precise in-field recognition of C. esculentus plants based on fewer spectral bands, was tested. Results of this study were compared against simulated results from a commercially available multispectral camera with four spectral bands. The model created with customized bands performed almost equally well as the original PLS-DA or RLR model, and much better than the model describing multispectral image data from a commercially available camera. These results open up the opportunity to develop a dedicated robust tool for C. esculentus recognition based on four spectral bands and an appropriate classification model

Using high resolution optical imagery to detect earthquake-induced liquefaction: the 2011 Christchurch earthquake

Using automated supervised methods with satellite and aerial imageries for liquefaction mapping is a promising step in providing detailed and region-scale maps of liquefaction extent immediately after an earthquake. The accuracy of these methods depends on the quantity and quality of training samples and the number of available spectral bands. Digitizing a large number of high-quality training samples from an event may not be feasible in the desired timeframe for rapid response as the training pixels for each class should be typical and accurately represent the spectral diversity of that specific class. To perform automated classification for liquefaction detection, we need to understand how to build the optimal and accurate training dataset. Using multispectral optical imagery from the 22 February, 2011 Christchurch earthquake, we investigate the effects of quantity of high-quality training pixel samples as well as the number of spectral bands on the performance of a pixel-based parametric supervised maximum likelihood classifier for liquefaction detection. We find that the liquefaction surface effects are bimodal in terms of spectral signature and therefore, should be classified as either wet liquefaction or dry liquefaction. This is due to the difference in water content between these two modes. Using 5-fold cross-validation method, we evaluate performance of the classifier on datasets with different pixel sizes of 50, 100, 500, 2000, and 4000. Also, the effect of adding spectral information was investigated by adding once only the near infrared (NIR) band to the visible red, green, and blue (RGB) bands and the other time using all available 8 spectral bands of the World-View 2 satellite imagery. We find that the classifier has high accuracies (75%–95%) when using the 2000 pixels-size dataset that includes the RGB+NIR spectral bands and therefore, increasing to 4000 pixels-size dataset and/or eight spectral bands may not be worth the required time and cost. We also investigate accuracies of the classifier when using aerial imagery with same number of training pixels and either RGB or RGB+NIR bands and find that the classifier accuracies are higher when using satellite imagery with same number of training pixels and spectral information. The classifier identifies dry liquefaction with higher user accuracy than wet liquefaction across all evaluated scenarios. To improve classification performance for wet liquefaction detection, we also investigate adding geospatial information of building footprints to improve classification performance. We find that using a building footprint mask to remove them from the classification process, increases wet liquefaction user accuracy by roughly 10%.Published versio

On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations

We solve the Cauchy problem for the Korteweg-de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finite-gap potentials under the assumption that the respective spectral bands either coincide or are disjoint.Comment: 29 page