Quality Circles: A Practical Guide

Journal of the Operational Research Society -     

A Class of Incomplete Orthogonal Factorization Methods. I: Methods and Theories

We present a class of incomplete orthogonal factorization methods based on Givens rotations for large sparse unsymmetric matrices. These methods include: Incomplete Givens Orthogonalization (IGO-method) and its generalisation (GIGO-method), which drop entries from the incomplete orthogonal and upper triangular factors by position; Threshold Incomplete Givens Orthogonalization (TIGO()-method), which drops entries dynamically by their magnitudes; and its generalisation (GTIGO(,p)-method), which drops entries dynamically by both their magnitudes and positions. Theoretical analyses show that these methods can produce a nonsingular sparse incomplete upper triangular factor and either a complete orthogonal factor or a sparse nonsingular incomplete orthogonal factor for a general nonsingular matrix. Therefore, these methods can potentially generate efficient preconditioners for Krylov subspace methods for solving large sparse systems of linear equations. Moreover, the upper triangular factor is an incomplete Cholesky factorization preconditioner for the normal equations matrix from least-squares problems.     

Ethyl 1,2,3,4-tetra-O-acetyl-β-D-glucopyranuronate

The crystal structure, at 120 K, and solution ¹H and ¹³C NMR spectra of ethyl 1,2,3,4-tetra-O-acetyl--D-glucopyranuronate, (8) have been determined. Compound 8 crystallizes in the triclinic space group, P1 (Z = 1) with a = 6.0209(3) Å, b = 8.9698(5) Å, c = 9.9818(8) Å, = 104.965(2)°, = 98.522(3)°, = 106.790(5)°. The Cremer and Pople puckering parameters [Q = 0.602(4) Å, = 7.1(4)°, = 325(3)°] for the pyranose ring in the solid state indicate a near ideal ⁴C₁ chair conformation with a slight distortion in the direction towards ⁰H₅. A number of weak, soft intermolecular C–H O hydrogen bonds set up a 3D array. NMR spectra and FAB and EIMS data have been obtained. Solution NMR parameters suggest that the solid state conformation is maintained in solution in chloroform.     

Arithmetic of Finite Ordered Sets: Cancellation of Exponents, I

Garrett Birkhoff conjectured in 1942 that when A, B, P are finite posets satisfying A ^P B ^P , then A B. We show that this is true in case P is dismantlable to each of its points, or P is connected and each of A and B is dismantlable to each of its covering pairs.     

X-ray scattering study of thin films of poly(2,5-bis(3-alkylthiophen-2-yl)thieno[3,2-b]thiophene)

Poly(2,5-bis(3-alkylthiophen-2-yl)thieno[3,2-b]thiophene), PBTTT, is a semiconducting polymer that forms thin film transistors (TFTs) with high field effect mobility on silicon dioxide dielectrics that are treated with alkyltrichlorosilanes ( approximately 0.2 to 0.5 cm2/V s) but forms TFTs with poor mobility on bare silicon dioxide (<0.005 cm2/V s). The microstructure of spin-coated thin films of PBTTT on these surfaces was studied using synchrotron X-ray diffraction and atomic force microscopy. PBTTT crystallizes with lamellae of pi-stacked polymer chains on both surfaces. The crystalline domains are well-oriented relative to the substrate in the as-spun state and become highly oriented and more ordered with thermal annealing in the liquid crystalline mesophase. Although the X-ray scattering from PBTTT is nearly identical on both surfaces, atomic force microscopy showed that the domain size of the crystalline regions depends on the substrate surface. These results suggest that electrical transport in PBTTT films is strongly affected by the domain size of the crystalline regions and the disordered regions between them.     

Single P and As dopants in the Si(001) surface

Using first-principles density functional theory, we discuss doping of the Si(001) surface by a single substitutional phosphorus or arsenic atom. We show that there are two competing atomic structures for isolated Si-P and Si-As heterodimers, and that the donor electron is delocalized over the surface. We also show that the Si atom dangling bond of one of these heterodimer structures can be progressively charged by additional electrons. It is predicted that surface charge accumulation as a result of tip-induced band bending leads to structural and electronic changes of the Si-P and Si-As heterodimers which could be observed experimentally. Scanning tunneling microscopy (STM) measurements of the Si-P heterodimer on a n-type Si(001) surface reveal structural characteristics and a bias-voltage dependent appearance, consistent with these predictions. STM measurements for the As:Si(001) system are predicted to exhibit similar behavior to P:Si(001).     

ELDONET--a decade of monitoring solar radiation on five continents

The European light dosimeter network (ELDONET) comprises more than 40 stations in 24 countries on 5 continents. The present report compares solar radiation data in the photosynthetic active radiation, UV-A (315-400 nm) and UV-B (280-315 nm) wavelength ranges for 17 stations at different latitudes on the northern and southern hemispheres for up to 10 years of monitoring. While the maximal irradiances on clear days follow a latitudinal gradient due to the cosine dependence on the solar angle, the total doses strongly depend on the local climate and atmospheric conditions as well as the day-length distribution over the year. UV-B irradiances and doses are strongly influenced by the total column ozone, which is recorded for all covered stations.