Almost-regular factorization of graphs

For integers a and b, 0 ? a ? a ? b, an [a, b]-graph G satisties a ? deg(x, G) ? b for every vertex x of G, and an [a, b]-factor is a spanning subgraph F such that a ? deg(x, F) ? b for every vertex x of F. An [a, b]-factor is almost-regular if b = a + 1. A graph is [a, b]-factorable if its edges can be decomposed into [a, b]-factors. When both K and t are positive integers and s is a nonnegative integer, we prove that every [(12K + 2)t + 2ks, (12k + 4)t + 2ks]-graph is [2k,2k + 1]-factorable. As its corollary, we prove that every [r.r + 1]-graph with r ? 12k² + 2k is [2k + 1]-factorable, which is a partial extension of the two results, one by Thomassen and the other by Era.     

Kinetics of phase separation in polymer blends. Calculations based on nonlinear theory

Suzuki's scaling theory for transient phenomena is applied to the calculation of the kinetics of phase separation in the early-to-intermediate stage based on a nonlinear theory proposed by Langer, Bar-on, and Miller (LBM). Calculated results are compared with experimental data on light scattering from a polymer blend system. Deviations from predictions of Cahn's linearized theory in the early time range of phase separation can be explained well by the proposed method of calculation. Nonlinear effects are found to play an essential role in characterizing the light scattering behavior of phase separation in the intermediate stage. Time evolutions of the single-point distribution function of composition are calculated, and the results are in good agreement with those reported in digital imaging analysis experiments and computer simulations of the time-dependent Ginzburg-Landau equation. The influence of asymmetry of free-energy on the single-point distribution function is also investigated in this study. © 1993 John Wiley & Sons, Inc.     

Iron-Chloranilate Intercalation Compounds: Synthesis,Crystal Structures,and Thermal Properties

Abstract

Hydrogen bond supported new iron-chloranilate assemblies, {(Hpy)[Fe(CA)₂(H₂O)₂](H₂O)}_n (py = pyridine, H₂CA = chloranilic acid, C₆H₂O₄Cl₂) (1), and [(phz)₂[Fe(CA)₂(H₂O)₂](H₂O)₂]_n (phz = phenazine, C₁₂H₈N₂) (2) have been synthesized and characterized. Compound 2 crystallizes in the monoclinic, space group C2/m (#12), with a= 29.135(6) Å, b= 16.886(6) Å, c = 15.017(5) Å, ß = 165.907(1)°, V= 1798(2) ų, Z = 2. In both the compounds two chloranilate dianions and two water molecules are coordinated to the iron ion making anionic monomers [Fe(CA)₂(H₂O)₂]^?, which are the building blocks of the compounds. The coordination environment around the iron ion in the building block is a distorted octahedron, where two water molecules sit on the trans position to each other. [Fe(CA)₂(H₂O)₂]^? anions form common layer structures, supported by hydrogen bonds. Hpy⁺ are intercalated in between the layers of 1 by electrostatic and hydrogen bonding interactions and phz are intercalated in that of 2 by electrostatic interactions. DSC traces of 1 show anomaly at 174 K, indicating phase transition in the compound.     

Photochemistry of 3-aryl-2-isoxazoline1

3-Phenyl-2-isoxazoline (1) was irradiated to give 4-phenyl-2-oxazoline (3), β-aminoaldehyde (14) and benzonitrile from its π-π^* singlet excited state. Several related derivatives afforded similar photoproducts on irradiation. The quantum yields of the photoreactions were dependent on the magnitudes of the singlet energies of the 2-isoxazolines. p-Cyanophenyl-2-isoxazoline (1c) formed a one-to-one photoadduct (22) with benzene.     

Syntheses and thermal reactions of 2-alkyl(or aryl)-1-benzoyl-3,4-dihydro-2-thianaphthalenes

1-Benzoyl-2-methy1-3,4-dihydro-2-thianaphthalene ($\text{4a}$) underwent novel intermolecular 1,4-rearrangement in refluxing toluene to give an enol ether $\text{5a}$, while rearrangement of 2-phenyl derivative $\text{4e}$ proceeded intramolecularly in refluxing xylene to afford a 1,4-rearranged enol ether $\text{5b}$. On the other hand, ylides $\text{4a–e}$ were refluxed in alcohols to afford some ring-opened products $\text{10–12}$.     

Monochromatic and Heterochromatic Subgraphs in Edge-Colored Graphs - A Survey

Nowadays the term monochromatic and heterochromatic (or rainbow, multicolored) subgraphs of an edge-colored graph appeared frequently in literature, and many results on this topic have been obtained. In this paper, we survey results on this subject. We classify the results into the following categories: vertex-partitions by monochromatic subgraphs, such as cycles, paths, trees; vertex partition by some kinds of heterochromatic subgraphs; the computational complexity of these partition problems; some kinds of large monochromatic and heterochromatic subgraphs. We have to point out that there are a lot of results on Ramsey type problem of monochromatic and heterochromatic subgraphs. However, it is not our purpose to include them in this survey because this is slightly different from our topics and also contains too large amount of results to deal with together. There are also some interesting results on vertex-colored graphs, but we do not include them, either. Supported by NSFC, PCSIRT and the “973” program.     

Application of extraction chromatography to the separation of thorium and uranium dissolved in a solution of high salt concentration

Extraction chromatography with commercially available UTEVA resin (for uranium and tetravalent actinide) was applied for the separation of Th and U from control solutions prepared from a multi-element control solution and from sample solutions of solidified simulated waste. Thorium and U in control solutions with 1-5mol/dm(3) HNO(3) were extracted with UTEVA resin and recovered with a solution containing 0.1mol/dm(3) HNO(3) and 0.05mol/dm(3) oxalic acid to be separated from the other metallic elements. Extraction behavior of U in the sample solutions was similar to that in the control solutions, but extraction of Th was dependent on the concentration of HNO(3). Thorium was extracted from 5mol/dm(3) HNO(3) sample solutions but not from 1mol/dm(3) HNO(3) sample solutions. We conjecture that thorium fluoride formation interferes with extraction of Th. Addition of Al(NO(3))(3) and Fe(NO(3))(3), which have higher stability constant with fluoride ion than Th, does improve extractability of Th from 1mol/dm(3) HNO(3) sample solution.     

Transmission electron microscopy study of an AlN nucleation layer for the growth of GaN on a 7-degree off-oriented (0 0 1) Si substrate by metalorganic vapor phase epitaxy

We have investigated the morphology of the high-temperature-grown AlN nucleation layer and its role in the early stage of GaN growth, by means of transmission electron microscopy. The nitride was selectively grown on a 7-degree off-oriented (0 0 1) patterned Si substrate by metalorganic vapor phase epitaxy. AlN was deposited on the inclined unmasked (1 1 1) facet in the form of islands. The size of the islands varied along the slope, which is attributable to the diffusion of the growth species in the vapor phase. The GaN nucleation occurred at the region where rounded AlN islands formed densely. The threading dislocations were observed to generate in the GaN nucleated region.