A cutting plane algorithm for a clustering problem

In this paper we consider a clustering problem that arises in qualitative data analysis. This problem can be transformed to a combinatorial optimization problem, the clique partitioning problem. We have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope. These theoretical results are utilized in this paper. We describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before. We discuss some details of the implementation of our code and present our computational results. We mention applications from, e.g., zoology, economics, and the political sciences.     

A Simplex-Type Algorithm for General Transportation Problems: An Alternative to Stepping-Stone

This paper re-examines use of the linear programming (LP) formulation to solve the transportation problem (TP). The proposed method is a general-purpose algorithm which uses only one operation, the Gauss Jordan pivoting used in the simplex method. The final tableau can be used for post-optimality analysis of TP. This algorithm appears to be faster than simplex, more general than stepping-stone and simpler than both in solving general TP. A numerical example illustrates the methodology. It is assumed the reader is familiar with simplex terminology.     

High-pressure effect on the crystal and magnetic structure of LuMnO3: Correlation between a distortion of the triangular lattice and the symmetry of the magnetic state in hexagonal frustrated manganites

The effect of a high pressure (up to 6 GPa) on the crystal and magnetic structure of the hexagonal manganite LuMnO₃ is studied by neutron diffraction in the temperature range 10–295 K. It is found that, as the pressure increases, the ordered magnetic moment of Mn ions at T = 10 K decreases noticeably from 2.48 (0 GPa) to 1.98 μ_B (6 GPa). This decrease is due to an enhancement of the geometrical frustration effects on the triangular lattice. At the same time, the symmetry of the triangular antiferromagnetic state (the irreducible representation Γ₂) remains unchanged. A correlation is revealed between the distortion parameter of the triangular lattice formed by Mn ions and the symmetry of the antiferromagnetic state of hexagonal manganites RMnO₃. Based on this correlation, a generalized magnetic phase diagram of these compounds is constructed. The obtained phase diagram provides an explanation for the changes observed in the magnetic state of hexagonal manganites caused by high pressure and chemical substitution.     

Approximation of Matrices and a Family of Gander Methods for Polar Decomposition

Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank approximants. Properties of Gander methods are investigated in details. AMS subject classification (2000) 65F30, 15A18     

The measurement of beta asymmetries at UNISOR/NOF using external plastic scintillator detectors

The performance of two external plastic scintillator detectors has been tested in an off-line mode using a source of¹⁰⁶RuFe at UNISOR/NOF. The measurement of beta asymmetries at various temperatures has resulted in the reproduction of the previously-determined magnetic dipole moment for the 1⁺ ground state of¹⁰⁶Rh and in addition the conclusion that the sign of this moment is positive.     

Charge transfer states in GeO2-doped silicate fiber-optic waveguides and their role in second-harmonic generation

The concentration dependence of the broad-band luminescence arising in GeO₂-doped silicate fiber-optic waveguides is measured and interpreted. The spectra obtained show that electronic excitations of a new type that are absent in pure silicate glass — charge transfer excitons — arise in the doped system. Under the action of light an electron can be transferred both from a Ge center into the host and between Ge centers. Self-organization of these excitations in the field of a light wave (orientational ordering of their dipole moments) results in the appearance of a macroscopic electric field that destroys the initial centrosymmetry of the system and allows second-harmonic generation. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 737–740 (25 November 1998)     

Paraelectric resonance of centers with icosahedral symmetry

The paraelectric resonance spectrum of non-central impurity ions situated in crystal fields of icosahedral symmetry is predicted. A multiwell potential is considered that corresponds to the displacement of the ions from the center of symmetry toward the vertices of the icosahedron, the faces of a dodecahedron, and the pentagonal faces of a fullerene molecule. The effective Hamiltonian of endohedral complexes in external electric fields with arbitrary orientation is obtained, its eigenvalues are found, and the line intensities of different transitions between the tunnelling levels are calculated. Fiz. Tverd. Tela (St. Petersburg) 39, 1693–1698 (September 1997)     

Flow in a waterfall with large Froude number

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes.     

Mutual coupling of elements in finite microstrip antennas

The mutual coupling of the radiating elements in microstrip antennas is studied using a rigorous electrodynamic approach in which the field singularities at the radiator edges are taken into account with analytic accuracy. A spectral method is employed in combination with a method of semi-inversion by extraction of the Green-function singularity. The degree of interaction of the elements of microstrip structures at the fundamental and higher current harmonicsis determined, and the applicability of various approximations is assessed.Radio-Astronomy Institute, Academy of Sciences of Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 8, pp. 688–701, August, 1992.     

Infrared ellipsometry study of the oxidation mechanisms of hydrogenated amorphous silicon

A detailed study of the oxidation of plasma deposited amorphous silicon (a-Si : H) using infrared phase modulated ellipsometry (IRPME) is presented. a-Si : H is found to be resistant against air oxidation confirming previous measurements. A 5–6 Å thick oxide layer at the surface of a-Si : H is observed after a few months of exposure to air. The extreme sensitivity of IRPME is emphasized. In particular Si-O-Si and (O_n)Si-H stretching vibrations are identified at the film surface at the submonolayer level. The oxidation mechanisms are discussed. The weak reactivity of a-Si : H with atmosphere is correlated with the presence of a hydrogen rich thin layer at the top surface.