Avoiding breakdown in Van der Vorst's method

Van der Vorst's method is a development of Lanczos' iterative method for the solution of a large sparse system of linear equations. Both methods can suffer from Lanczos breakdown. The usual cure for this problem is a look-ahead method. Recently, the look-around method has been proposed, which tracks the edges of blocks in degenerate cases instead of jumping across them. Here we show how Van der Vorst's minimal residual principle can be built into the look-around method. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the role of dissipation on the Casimir-Polder potential between molecules in dielectric media

An expression for the Casimir-Polder potential between molecules in a homogeneous dispersive and absorptive dielectric medium is derived. The effect of retardation on the interaction energy is discussed by examining the wave-zone and nonretarded limits of the potential. Unlike Lifshitz theory, the interaction energy is not derived from the potential between macroscopic bodies. In this work, a Green function that explicitly accounts for absorption in the medium is obtained. This function leads to possible dissipation effects and presents a near-zone form that vanishes in the limit of nonabsorptive medium. Employing a two-level model, it is shown that the retarded van der Waals dispersion potential in a medium may become repulsive as a consequence of absorption by the medium. It is suggested that the repulsive dispersion force may delay precipitation of nonpolar molecules from a dielectric solvent or even inhibit chemical reaction between them.     

Small-span bending test for determination of elastic-plastic properties of ultrathin Pt wires

A mechanical testing methodology for determination of elastic-plastic properties of very thin metallic wires using small-span bending under lateral load is described. Sufficient strain is locally developed in the tested section of wire by unsymmetrical bending with two opposite probes where one end of the wire is fixed on a substrate with rigid joint by Joule heat welding. From the load-displacement relationships obtained experimentally, Young’s modulus is determined by analytical formulation. Moreover, yield stress and hardening modulus of the wire are identified using an optimization strategy with finite-element analyses. The thin Pt wires with a nominal diameter of about 625 nm are examined by the testing scheme and the wires are found to have higher yield stress compared to bulk Pt.     

Equivalence between modified symplectic Gram-Schmidt and Householder SR algorithms

The SR factorization for a given matrix A is a QR-like factorization A=SR, where the matrix S is symplectic and R is J-upper triangular. This factorization is fundamental for some important structure-preserving methods in linear algebra and is usually implemented via the symplectic Gram-Schmidt algorithm (SGS). There exist two versions of SGS, the classical (CSGS) and the modified (MSGS). Both are equivalent in exact arithmetic, but have very different numerical behaviors. The MSGS is more stable. Recently, the symplectic Householder SR algorithm has been introduced, for computing efficiently the SR factorization. In this paper, we show two new and important results. The first is that the SR factorization of a matrix A via the MSGS is mathematically equivalent to the SR factorization via Householder SR algorithm of an embedded matrix. The later is obtained from A by adding two blocks of zeros in the top of the first half and in the top of the second half of the matrix A. The second result is that MSGS is also numerically equivalent to Householder SR algorithm applied to the mentioned embedded matrix.     

Book reviews

Die Fernrohre und Entfevnungsmesser. By A. Konig and H. Kohler. 3rd Edition. (Berlin: Springer-Verlag, 1959.) [Pp. 475 +viii.] 88 dm.

Electronic Contacts Handbook. By Ragnar Holm, aided by Else Holm. 3rd Edition. (Berlin: Springer-Verlag, 1958.) [Pp. 522.] 52 dm.

From Nucleus to Universe. A Course of Selected Lectures in Physics and Astronomy in the University of Sydney, January 11-22,1960. Edited by Prof. S. T. Butler and Prof. H. Messel. (Sydney : Shakespeare Head Press Pty. Ltd., 1960.) [Pp. 335.] 84s.

Gus Calorimetry. By C . G. Hyde and M. W. Jones. (2nd Edition.) (London : Ernest Benn Ltd., 1960.) [Pp. 456.] 105s.

The Theory and Design of Inductance Coils. By V. G. Welsby. 2nd Edition. (London: Macdonald, 1960.) [Pp. 232+xviii.] 30s.

Report of the Research Council of the Department of Scientific and Industrial Research for the year, 1958-59. (Cmnd. 1049, H.M.S.O., May 1960.) 4s. 6d.

Mechanical Radiation. By R. B. Lindsay. (New York: McGraw Hill Book Co.) 77s. 6d.

A French Course for Technologists and Scientists. By H. Sheldon Jackson and J. Standing. (London: Harrap.) 16s.

Optics (Vol. 3 of A Degree Physics). By C. J. Smith. (Arnold, Jan. 1960.) [Pp. vii + 736.] 63s.

The Hollow Universe. By Charles de Koninck. (Oxford University Press, 1960.) [Pp. 127.] 12s. 6d.     

SU(2N f) ⊗O(3) light diquark symmetry and current-induced heavy baryon transition form factors

We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit asm _q→∞. Our discussion involvess-wave tos-wave as well ass-wave top-wave transitions. Using a constituent quark model picture for the light diquark system with an underlyingSU(2N _f)?O(3) symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.     

SU (2N f) ⊗ O(3) light diquark symmetry and current-induced heavy baryon transition form factors

We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit as m_q → ∞. Our discussion involves s-wave to s-wave as well as s-wave to p-wave transitions. Using a constituent quark model picture for the light diquark system with an underlying SU (2N_f) ? O(3) symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.     

On Kaluza-Klein theory

Assuming the compactification of 4 + K-dimensional space-time implied in Kaluza-Kleintype theories, we consider the case in which the internal manifold is a quotient space, $\text{G}\text{H}$. We develop normal mode expansions on the internal manifold and show that the conventional gravitational plus Yang-Mills theory (realizing local G symmetry) is obtained in the leading approximation. The higher terms in the expansions give rise to field theories of massive particles. In particular, for the original Kaluza-Klein 4 + 1-dimensional theory, the higher excitations describe massive, charged, purely spin-2 particles. These belong to infinite dimensional representations of an O(1,2).     

A spectrum-generating algebra for particles of spin 1/2

Spectrum-generating algebra techniques developed in previous works to deal with the problem of one particle in a potential are extended to deal with particles of spin 1/2. The method is illustrated considering the Pauli and Dirac equations with a Coulomb potential. The way to deal with some other potentials is indicated. In the Pauli euqation an intrinsic electric dipole moment term is included. It is particularly remarkable the simplicity with which the solutions are obtained.