Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Low-Temperature Electronic Properties of the Lan+1NinO3n+1 (n = 2, 3, and ∞) System: Evidence for a Crossover from Fluctuating-Valence to Fermi-Liquid-like Behavior

Measurements of the temperature dependence of the electrical resistivity ρ(T), magnetic susceptibility χ(T), and Seebeck coefficient S(T) have been carried out on the n = 2, 3, and ∞ members of the homologous lanthanum nickel oxide systems La_n+1Ni_nO_3n+1 that were annealed in air. With increasing n, a progressive decrease in the electrical resistivity and a gradual change from insulating to metallic behavior are observed. La₃Ni₂O₇ is nonmetallic, showing a gradual increase in ρ when T decreases (dp/dT < 0) from 300 to 4.2 K, whereas La₄Ni₃O₁₀ and LaNiO₃ exhibit metallic resistivity (dp/dT > 0). A minimum in ρ(T) near 140 K is observed for La₄Ni₃O₁₀, while LaNiO₃ exhibits a T² dependence for ρ(T) below 50 K. The magnetic susceptibility of LaNiO₃ is Pauli-like, but the χ(T) data for La₃Ni₂O₇ and La₄Ni₃O₁₀ below 350 K show a decrease with decreasing temperature. The Seebeck coefficient of all these compounds is negative at high temperatures; La₃Ni₂O₇ and La₄Ni₃O₁₀ exhibit a sign change in S at low temperatures. These results suggest a crossover from a fluctuating-valence to a Fermi-liquid-like behavior with increasing n.     

A rapid finite difference algorithm,utilizing successive over-relaxation to solve the Poisson–Boltzmann equation

An efficient algorithm is presented for the numerical solution of the Poisson–Boltzmann equation by the finite difference method of successive over-relaxation. Improvements include the rapid estimation of the optimum relaxation parameter, reduction in number of operations per iteration, and vector-oriented array mapping. The algorithm has been incorporated into the electrostatic program DelPhi, reducing the required computing time by between one and two orders of magnitude. As a result the estimation of electrostatic effects such as solvent screening, ion distributions, and solvation energies of small solutes and biological macromolecules in solution, can be performed rapidly, and with minimal computing facilities.     

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Ohne Zusammenfassung     

Differential non-destructive image current detection in a fourier transform quadrupole ion trap

Dual-detector differential non-destructive Fourier transform detection in a quadrupole ion trap is shown to improve signal intensity and reduce noise compared with spectra recorded using a single detector. A larger area detector in each end-cap electrode is machined to fit its hyperbolic shape and so minimize field imperfections on the z-axis. Argon, acetophenone and bromobenzene spectra were recorded to allow a comparison between single- and dual-detector (differential) modes of detection and to demonstrate the improvement achieved with differential detection. Copyright 1999 John Wiley & Sons, Ltd.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.