Bilateral polynomial matrix equations in two indeterminates

Two special cases of the bilateral 2-D polynomial matrix equationDU +VN=C whenC=I andC=I with being a -stable 2-D polynomial, which are related respectively to deadbeat and asymptotic control problems of 2-D systems, are first considered. By generalizing the concepts of factor coprimeness, zero coprimeness and zero skew primeness in the 2-D polynomial ring to the ring of causal -stable 2-D rational functions, a constructive solution of these two problems mentioned is proposed. Based on these results, we derive a solvability condition for the bilateral equiation whereC is a general 2-D polynomial matrix. The general solutions are investigated as well.     

Preparation of rod-shaped BaTiO3 powder

Rod-shaped BaTiO₃ powder particles have been prepared from rod-shaped TiO₂ ·nH₂O and BaCO₃ in molten chloride. The morphology of BaTiO₃ particles was studied referring to the effects of the chemical species of the starting titanium compound, amount of chloride, particle size of the titanium compound and reaction conditions, and the preparation condition of rod-shaped BaTiO₃ has been determined: i.e., large TiO₂ ·nH₂O particles were heated at 700°C in molten salt with an equal amount of BaTiO₃. This condition was effective in suppressing the formation of BaTiO₃ by a solution-precipitation process as well as the deformation of either TiO₂ ·nH₂O or BaTiO₃, which are responsible for the formation of equiaxed BaTiO₃ particles. The obtained rod-shaped BaTiO₃ particles had a cubic symmetry. Electron diffraction analysis showed that the following topotactic relation is retained; 0 1 0_{potassium tetratitanate} 0 1 0_{hydrated titania} 1 0 0_anatase 1 0 0_{barium titanate}     

Formation of monodispersed Ta2O5 powders

The Ta₂O₅ powders synthesized by the hydrolysis of tantalum pentaethoxide, Ta(OC₂H₅)₅ in alcoholic solution were monodispersed fine oxide particles, which were a uniform, spherical shape, non-agglomerate, and had a narrow size distribution. They grew to 1.2m after ageing for 1 h after hydrolysis. Powder X-ray diffraction and differential thermal analysisthermogravimetric analysis showed the particles were amorphous and hydrated. These particles lost the water at 290° C and gave well-crystalline Ta₂O at 740° C. Throughout these thermal processes, the particle morphology was kept almost the same.     

Growth of Al2O3 whiskers by vapour-phase reactions

Needle-like or wool-like Al₂O₃ whiskers can be grown on a substrate by the hydrolysis of aluminium fluoride vapour. Effects of the growth conditions on the morphology of the crystals and growth processes of the whisker were investigated, and the optimum growth condition of whiskers was examined. Adequate vapour pressure conditions of the reactant gases for the growth of the wool-like whisker were found to be . Aluminium oxyfluoride was assumed to be the most probable intermediate species for the growth of Al₂O₃ whiskers. A variety of crystal morphologies are also shown and described with respect to the experimental conditions.     

Radiation grafting of α,β,β-trifluoroethylenesulfonyl fluoride onto low-density polyethylene film by simultaneous irradiation method. I. Kinetic study of simultaneous-irradiation grafting

α,β,β-Trifluoroethylenesulfonyl fluoride (TFESF) was grafted onto polyethylene (PE) film by a simultaneous-irradiation method. The influences of the grafting conditions were analyzed kinetically. The dependencies of the grafting rate on the dose rates and monomer concentrations ranging from 10 to 75% were found to be of 1 and 0 order, respectively. The overall activation energy for the graft polymerization was 2.05 × 10⁴ J/mol. The grafting rate was found to be independent of the film thicknesses ranging from 25 to 100 μm.     

Fast computation of computer-generated hologram using Xeon Phi coprocessor

We report fast computation of computer-generated holograms (CGHs) using Xeon Phi coprocessors, which have massively x86-based processors on one chip, recently released by Intel. CGHs can generate arbitrary light wavefronts, and therefore, are promising technology for many applications: for example, three-dimensional displays, diffractive optical elements, and the generation of arbitrary beams. CGHs incur enormous computational cost. In this paper, we describe the implementations of several CGH generating algorithms on the Xeon Phi, and the comparisons in terms of the performance and the ease of programming between the Xeon Phi, a CPU and graphics processing unit (GPU).     

Influence of Metal Ions on the Order-Disorder Transition Temperature of the Ba-M-O (M: La, Y, In, or Ga) System

Preparation of BaLa₂O₄, B_a3,Y₄O₉, B_a,In₂O₅, and Ba₃Ga₂O₆ powders and their sintering were investigated in Ar or air. These sintered bodies with perovskite-related structure were synthesized by reaction sintering, using mixed powders in the atomic ratios of Ba/La = 1, Ba/Y = 0.75, Ba/In = 1, and Ba/Ga = 1.5. The order-disorder transition temperatures of the BaLa₂O₄, Ba₃Y₄O₉, Ba₂In₂O₅, and Ba₃Ga₂O₆ sintered bodies were 270°, 350°, 880°, and 123O^oC, respectively. It was found that the temperatures were influenced by the ionic radius of cations in B sites, and the transition temperatures decreased with increasing ionic radius.     

Improvement in Thermoelectric Characteristics of n-type Iron Disilicide by Local Composition Modification

High thermoelectric figure of merit semiconducting ceramics of n -type iron disilicide with modified local compositions have been developed. Sintering and annealing of the composite powder composed of iron disilicide and precipitated cobalt (II) hydroxide resulted in the dissolution of excess Co and oxygen into the iron disilicide phase. Excess Co segregated to the grain boundary region, while interstitially incorporated oxygen was distributed homogeneously in the microstructure. The maximum figure of merit achieved was 5.2 × 10⁻⁴/K at 673 K.     

Prostaglandin-like substances formed during autoxidation of methyl linolenate

Prostaglandin-like substances other than 3-(2-ethyl-5-hydroxy-3-oxo)-cyclopentanyl-2-propenal (compound I), which upon reacting with amino acids form reddish pigments, were purified, and their chemical structures were determined. Three red pigment-forming substances (RPS) in autoxidized methyl linolenate were purified successively by gel chromatography on Sephadex LH-20, column chromatography and thin layer chromatography on Silica Gel 60, and by high performance liquid chromatography on μ-Porasil. IR spectra of the RPS showed the absorption of an ester group (νC=O 1730 cm⁻¹ in CHCl₃) and of a longer branched chain (νC-H 2800–3100 cm⁻¹), in addition to the absorption bands observed in compound I. Electron impact mass spectra of the trimethylsilyl ethers obtained after reduction with NaBH₄ and NaBD₄ were analyzed in detail and compared with those of compound I. The structures of the RPS were identified as stereoisomeric methyl 8-[2-(2-formylvinyl)-3-hydroxy-5-oxo-cyclopentanyl]-octanoates derived from methyl 12-hydroperoxy-linolenate. Presented at the general meeting of the Japanese Society of Scientific Fisheries, held at Tohoku University, Sendai, Japan, October 1984.