The lowest scattering state of one-dimensional Bose gas with attractive interactions

We investigate the lowest scattering state of one-dimensional Bose gas with attractive interactions trapped in a hard wall trap. By solving the Bethe ansatz equation numerically we determine the full energy spectrum and the exact wave function for different attractive interaction parameters. The resultant density distribution, momentum distribution, reduced one body density matrix and two body correlation show that the decreased attractive interaction induces rich density profiles and specific correlation properties in the weakly attractive Bose gas.Comment: 6 pages, 6figure

Exact Weighted-FBP Algorithm for Three-Orthogonal-Circular Scanning Reconstruction

Recently, 3D image fusion reconstruction using a FDK algorithm along three-orthogonal circular isocentric orbits has been proposed. On the other hand, we know that 3D image reconstruction based on three-orthogonal circular isocentric orbits is sufficient in the sense of Tuy data sufficiency condition. Therefore the datum obtained from three-orthogonal circular isocentric orbits can derive an exact reconstruction algorithm. In this paper, an exact weighted-FBP algorithm with three-orthogonal circular isocentric orbits is derived by means of Katsevich's equations of filtering lines based on a circle trajectory and a modified weighted form of Tuy's reconstruction scheme

Vegetation Mapping of Mammoth Cave National Park using Multi-date Landsat-8 Imagery and Lidar data

Up-to-date and detailed vegetation map provides critical information for habitat management. In addition, a vegetation map is necessary for the Park’s Fire Management, for classification of fuel types, and for delineation of fire management units. There have been several attempts of vegetation mapping in 1934, 1975 and 1997. Recent advancements in mapping technology and the availability of high resolution Lidar data call for a new vegetation map for the Park’s management team. In this study, Landsat-8 Operational Land Imager (OLI) imagery, Lidar and geology dataset were applied to vegetation mapping. Habitat types are determined by a combination of geology, aspect and slope. Coniferous and deciduous trees are distinguished using multi-date Landsat-8 imagery through image classification and NDVI analysis. Habitat type and physical properties derived from Lidar data will be applied to identify specific vegetation species. The research will produce a new vegetation map and a habitat map for the Mammoth Cave National Park. The maps will provide critical information for habitat and fire management. The research method integrating Lidar and Landsat-8 data in digital vegetation and habitat mapping will be valuable for similar projects at other locations

The fundamental gap of a kind of two dimensional sub-elliptic operator

This paper is concerned at the minimization fundamental gap problem for a class of two-dimensional degenerate sub-elliptic operators. We establish existence results for weak solutions, Sobolev embedding theorem and spectral theory of sub-elliptic operators. We provide the existence and characterization theorems for extremizing potentials $V(x)$ when $V(x)$ is subject to $L^\infty$ norm constraint