Search

Structural priors incorporated with the discrete cosine transformation (DCT) based electrical impedance tomography (EIT) algorithm improves the interpretability of EIT results in a clinical setting. However, a false prior will produce a misleading result compromising clinical decisions. Detection of false priors is crucial. In our investigation, a redistribution index (RI) is proposed to quantify the potential error introduced by a false structural prior. Simulations in terms of different scales of atelectasis were conducted to evaluate the plausibility of the RI. The behaviour of RI makes it possible to detect a false prior with a defined threshold, which must be determined according to the requirements and tolerance of an application. The redistribution index depends also on the reconstruction method and different parameters like the regularization hyperparameter. Therefore, we investigated as well the sensitivity of the RI on the choice of the hyperparameter. From the evaluation, it seems plausible that the RI can be further developed into an indicator for false priors in EIT reconstruction. [ABSTRACT FROM AUTHOR]

A modified version of the single Lanczos propagation method is proposed, which allows both energies and overlaps between multiple target functions and all eigenfunctions to be computed from a single Lanczos recursion with no explicit construction of the eigenfunctions. This method is employed to help assigning some highly excited bending levels of acetylene (HCCH) using a six-dimensional exact quantum Hamiltonian and target functions designed to extract information about the shape of the eigenfunctions. In the special case of the Ã-state vibrational eigenfunctions being the target functions, the Ã→&Xtilde; resonance emission spectra are obtained. The assignments on the Bramley et al. [J. Mol. Spectrosc. 157, 301 (1993)] potential energy surface show a strong resemblance to the experimentally observed normal-to-local mode transition in the bending overtones, while that of Halonen et al. [Mol. Phys. 47, 1097 (1982)] supports no such transition in the same energy range. [ABSTRACT FROM AUTHOR]

We report accurate calculations of vibrational energy levels of HOOH, DOOD, and HOOD up to 10 000 cm-1 above the zero-point energy levels on a high-quality ab initio potential energy surface. These energies were determined by the Lanczos algorithm based on repetitive matrix-vector multiplication. The six-dimensional vibrational Hamiltonian in the diatom-diatom Jacobi coordinate system was discretized in a mixed basis/grid representation. A direct product potential optimized discrete variable representation was used for the radial coordinates, while nondirect product spherical harmonics were employed for the angular degrees of freedom. The calculation and storage of the potential matrix in the angular finite basis representation were avoided by using a series of one-dimensional pseudo-spectral transformations to a direct product angular coordinate grid. The diatom-diatom exchange symmetry, when applicable, was incorporated into the basis, which significantly enhanced the efficiency for symmetric isotopomers. A few hundred low-lying vibrational levels of each isotopomer were assigned and compared with experimental data. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Discusses a method using a single Lanczos eigenvalue algorithm to determine multiple transition amplitudes without the explicit calculation of the eigenstates. Usefulness of the method for large dimensional problems; Numerical behaviors of the Lanczos algorithm.

A cosine transform between the order and angle of the Chebyshev operator is identified. Because the order and angle form a conjugate pair similar to energy and time, the Chebyshev state can be considered as a cosine-type evolution state in the order domain, analogous to a time-dependent wave packet. The order/angle formulation is analytically equivalent to the time/energy formulation, but the former may have some numerical advantages in certain applications. This is illustrated by examining the spectral method and the filter-diagonalization method in both formulations. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A general and efficient filter-diagonalization method is proposed to solve the quantum mechanical eigenvalue/eigenstate problem in a pre-specified energy range. This method is in similar spirit to the original filter-diagonalization approach, but it eliminates the time propagation by expanding the filter operator directly in the energy space in terms of Chebychev polynomials. Our approach is more efficient than the existing methods because neither time propagation nor time-to-energy transformation is needed. It also allows the choice of the most efficient filter operator for the system of interest. This method is tested for a one-dimensional Morse oscillator and for the two-dimensional Henon–Heiles system. The results show excellent convergence and accuracy. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this Note, we discuss the convergence scaling law of the filter-diagonalization method based on the Chebyshev recursion, as applied to molecular spectroscopic problems. Comparison with the scaling law observed earlier for the Lanczos algorithm indicates that the two recursive methods have very similar convergence behaviors. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]