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We present a unified description of the position-space wave functions, the momentum-space wave functions, and the phase-space Wigner functions for the bound states of a Morse oscillator. By comparing with the functions for the harmonic oscillator the effects of anharmonicity are visualized. Analytical expressions for the wave functions and the phase space functions are given, and it is demonstrated how a numerical problem arising from the summation of an alternating series in evaluating Laguerre functions can be circumvented. The method is applicable also for other problems where Laguerre functions are to be calculated. The wave and phase space functions are displayed in a series of curves and contour diagrams. An Appendix discusses the calculation of the modified Bessel functions of real, positive argument and complex order, which is required for calculating the phase space functions for the Morse oscillator.

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This paper describes new algorithms and related software for total variation (TV) image reconstruction, more specifically: denoising, inpainting, and deblurring. The algorithms are based on one of Nesterov's first-order methods, tailored to the image processing applications in such a way that, except for the mandatory regularization parameter, the user needs not specify any parameters in the algorithms. The software is written in C with interface to Matlab (version 7.5 or later), and we demonstrate its performance and use with examples.

Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse matrices with the same pattern that have a positive semidefinite completion. Efficient large-scale algorithms for evaluating these barriers and their derivatives are important in interior-point methods for nonsymmetric conic formulations of sparse semidefinite programs. The algorithms are based on the multifrontal method for sparse Cholesky factorization

In high-elevation streams of western Colorado, mayflies (Baetis bicaudatus) develop faster, but mature at a smaller size where trout are present compared to streams where fish are absent. These life history traits reduce the time of larval exposure to trout predation, but cost reduced fecundity. We designed a field experiment involving manipulation of whole streams to determine whether these changes were caused by the presence of brook trout, and specifically, whether they could be triggered by trout chemical cues. In 1999 and 2000, we introduced water from containers with brook trout (Salvelinus fontinalis) into five naturally fishless streams, and fishless stream water into five adjacent control streams, to determine whether these cues alone could induce the mayfly life history traits we have observed in natural trout streams. As in previous small-scale experiments, the size at which mayflies matured declined significantly in streams with added trout chemicals but did not change in streams with fishless water only. Thus, life history traits similar to those observed in the field were induced within the natural variability inherent in streams. These results demonstrate the strength of this predator-prey interaction and indicate that brook trout are an important agent of natural selection on mayfly life history traits.