Direct fail-proof triangularization algorithms for AX + XB = C with Error-Free and parallel implementations

Two 0(mn³) inversion-free direct algorithms to compute a solution of the linear system AX +XB = C by triangularizing a Hessenberg matrix are presented. Without any loss of generality the matrix A is assumed upper Hessenberg and the order m of A the order n of B. The algorithms have an in-built consistency check, are capable of pruning redundant rows and converting the resulting matrix into a full row rank matrix, and permit A and —B to be any square matrices with common or distinct eigenvalues. In addition, these algorithms can also solve the homogeneous system AX +XB = 0 (null matrix C). An error-free implementation of the solution X using multiple modulus residue arithmetic as well as a parallelization of the algorithms is discussed.     

Structural changes upon reduction of dipyrido[2,3-a:3',2'-c]phenazine probed by vibrational spectroscopy, ab initio calculations, and deuteration studies

A series of bridging ligands, dipyrido[2,3-a:3',2'-c]phenazine (ppb), dipyrido[2,3-a:3',2'-c]-6,7-dichlorophenazine (ppbCl2), and dipyrido[2,3-a:3',2'-c]-6,7-dimethylphenazine (ppbMe2), and their binuclear copper(I) complexes have been synthesized, and their spectral properties were measured. The single-crystal structure of the complex, [(PPh3)2Cu(mu-ppbCl2)Cu(PPh3)2](BF4)2 in the monoclinic space group P21/c, 18.2590(1), 21.1833(3), 23.2960(3) A with Z = 4 is reported. The copper(I) complexes are deeply colored through MLCT transitions in the visible region. The vibrational spectra of the ligands have been modeled using ab initio hybrid density functional theory (DFT) methods (B3LYP/6-31G(d)) and compared to experimental FT-Raman and IR data. The DFT calculations are used to interpret the resonance Raman spectra, and thus the electronic spectra, of the complexes. The preferential enhancement of modes associated with the phenanthroline section of the ligands with blue excitation (lambda(exc) = 457.9 nm) over phenazine-based modes with redder excitation (lambda(exc) = 514.5 and 632.8 nm) suggests the 2 MLCT transitions terminated on different unoccupied MOs are present under the visible absorption envelope. The radical anion species of the ligands are prepared by the electrochemical reduction of the binuclear copper(I) complexes; no evidence of dechelation prevalent in other copper(I) complexes is observed. The resonance Raman spectra of the reduced complexes are dramatically different from those of the parent species. Across the series common bands are observed at about 1590 and 1570 cm(-1) which do not shift with reduction but are altered in intensity. The normal-mode analysis of the radical anion species suggests that these normal modes primarily involve bond length distortions that are unaffected by reduction.     

AB-initio studies of N-O-F compounds. Internal rotation in hydroxylamine and its fluorinated derivatives

Ab-initio molecular orbital theory at both the minimal and extended basis set levels have been applied to the study of internal rotation in hydroxylamine and its fluorinated derivatives. The computed energies are analyzed in terms of a Fourier-type expansion of the potential function. The total potential function V(φ)can be dissected into onefold (V₁), twofold (V₂) and threefold (V₃) components and plots of these components together with V(φ) are given for each of the molecules studied herein. Additionally geometry optimizations have been carried out as a function of the internal rotation angle φ (φ = : NOX dihedral angle) for H₂NOH and F₂NOF. For H₂NOH geometry optimizations are found to be less important than for F₂NOF. In general the fluorinated hydroxylamines prefer a $\text{trans}$-conformation (φ = 180°) while hydroxylamine itself adopts the $\text{cis}$-conformation (φ = 0°) largely as a result of a lower dipole interaction (V₁ term) in the $\text{cis}$-conformation.     

Stability of vinylidene chloride copolymers containing 4-vinylpyridine units

Vinylidene chloride copolymers are prominent in the barrier plastic packaging industry. These materials display excellent barrier to the transport of oxygen (and other small molecules) as well as flavor and aroma molecules. However, they suffer from a propensity to undergo degradative dehydrochlorination at process temperatures. To scavenge hydrogen chloride formed and prevent its interaction with the metallic components of process equipment, a passive base is usually included as an additive prior to processing. The base is most often an inorganic oxide or salt. These may negatively impact the properties of the polymer, particularly as a film. An organic base that could be covalently incorporated into the copolymer might display better behavior. Accordingly, a series of copolymers containing low levels of 4-vinylpyridine (0.05–3 mole%) have been prepared, characterized, and examined by thermogravimetry to assess thermal stability. In all cases, polymers containing 4-vinylpyridine units are less stable than the polymer containing none of this comonomer. Clearly, the pyridine moiety is a sufficiently strong base to promote E2 elimination of hydrogen chloride to generate dichlormethylene units in the mainchain from which thermal degradation may be initiated.     

Degradation of vinylidene chloride/methyl acrylate/phenylacetylene (VDC/MA/PA) terpolymers. Effect of internal unsaturation on the stability of Saran copolymers

The thermal degradation of vinylidene chloride/methyl acrylate/phenylacetylene (VDC/MA/PA) terpolymers containing a constant 9 wt % methyl acrylate and small but varying amounts of phenylacetylene has been examined in the solid phase and in bibenzyl solution. Thermally promoted degradative dehydrochlorination, largely uncomplicated by methyl chloride formation, readily occurs at temperatures approaching 200°C. Incorporation of phenylacetylene into the polymer structure greatly facilitates degradative dehydrochlorination. Indeed, the presence of phenylacetylene induces the formation of polyene segments during the polymerization so that all the terpolymers, even at very low phenylacetylene loading, are tan in color. The decreased stability of polymers containing internal unsaturation arises from an increased rate of initiation for the degradation reaction. The propagation rate is largely unaffected by the level of unsaturation initially present in the polymer. Thus random double bonds have been identified as the principal defect sites responsible for the facile degradation of Saran copolymers. Species which promote the degradation of Saran polymers probably do so by facilitating the introduction of double bonds into the structure. The ratio of hydrogen chloride to stilbene formed for degradation of the terpolymers in bibenzyl solution is ca. 35:1. This is strongly reminiscent of PVDC degradation and suggests that for degradation of either the homopolymer or Saran copolymers the chain-carrying allylic radical pair does not dissociate to any appreciable extent as dehydrochlorination occurs.     

The behavior of amides of N-acylamino acids toward aniline and substituted anilines under papain catalysis

Resolution of z-dl-alanine amide has been achieved through papain-catalyzed reactions with aniline, the three anisidines, the three aminophenols and the three fluoroanilines. Most of the resultant anilides displayed better than a 95% resolution of the racemic amide. The four methyl esters of hippuric acid, z-glycine, z-l-alanine and z-dl-alanine were prepared by means of a recently reported catalytic dehydrator in the presence of excess dry methanol. Subsequent treatment with ammonia produced the amides. Three N-acylaminomalonic amides were synthesized by a different route than previously used, from ethyl aminomalonate hydrochloride. Trial asymmetric syntheses were unsuccessful for papain catalysis of such achiral amides with aniline. A few organic solutes were tested for their effects on the activity of papain during anilide synthesis. The pH dependence of yield was studied for papain catalysis of reactions between aniline and hippuric amide and then aniline and z-glycine amide.     

The Geographical Allocation of Community Care Resources — A Case Study

The paper presents a case study of methods of allocating a given amount of home help resource between a number of geographical areas within a County Social Services Department. Questionnaires were completed for a sample of clients covering such information as:

1. i)
   the type of client,
    
2. ii)
   the amount of home help actually received, and
    
3. iii)
   the "ideal" amount of help judged necessary.
    

Various allocations were presented to the decision makers, ranging from the simple assumption that the number of hours provided to each type of client should be the same throughout the County, to more "sophisticated" allocations which took account of such geographical differences as the level of provision of other support services and the current and forecast population structure.Although developed within the context of the home help service, the approach is general enough to be applicable to the allocation of other such services to clients, e.g. home nursing.