Two‐factors each component of which contains a specified vertex

It is shown that if G is a graph of order n with minimum degree δ(G), then for any set of k specified vertices {v₁,v₂,…,v_k} ? V(G), there is a 2‐factor of G with precisely k cycles {C₁,C₂,…,C_k} such that v_i ∈ V(C_i) for (1 ≤ i ≤ k) if or 3k + 1 ≤ n ≤ 4k, or 4k ≤ n ≤ 6k ? 3,δ(G) ≥ 3k ? 1 or n ≥ 6k ? 3, . Examples are described that indicate this result is sharp. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 188–198, 2003     

Preparation of macroreticular chelating resins containing mercapto groups from 2,3-epithiopropyl methacrylate/divinylbenzene copolymer beads and their adsorption capacity

Macroreticular chelating resins containing mercapto groups were prepared by the reaction of 2,3-epithiopropyl methacrylate/divinylbenzene macroreticular copolymer beads with ethanolic potassium hydrogensulfide solution for 1 h at 50°C. The adsorption capacities of this resin for Ag⁺, Hg²⁺, Pb²⁺ and Cd²⁺ were determined at various pH values. In the acidic region, the resin shows a high affinity for Ag⁺ and Hg²⁺ and high resistance against air oxidation. Cadmium is readily eluted with 1 mol dm^?3 hydrochloric acid; silver, mercury and copper ions can be eluted with 1 mol dm^?3 hydrochloric acid containing 5% (w/v) thiourea. The proposed resin appears to be useful for the removal of As³⁺ from aqueous solutions.     

Spin dynamic study on the electric field dependence of carrier generation

Using an acceptor-doped poly(N-vinylcarbazole) film, the magnetic field effect (MFE) on the generation efficiency of photoinduced charge was measured under various electric fields in order to clarify how the applied electric field affects the elementary processes in the photocarrier generation in photoconductive polymeric molecular solids. The external magnetic field influenced the electron spin dynamics among the geminate electron-hole pairs within a scale of a few nanometers and decreased the photocarrier generation efficiency. The observed MFE due to a hyperfine mechanism was almost independent of the electric field. By employing the stochastic Liouville equations based on a one-dimensional lattice model, we performed some model calculations for the dissociation, hopping, and recombination rate dependence of MFE on the generation efficiency. From a comparison between the observed and calculated MFE, it was concluded that the electric field affects the dissociation more than the hopping and the recombination. This coincides with the concepts in the Onsager model that is used to analyze the electric field dependence of carrier generation efficiency so far. The one-dimensional lattice model is a proper model for the carrier generation in polymeric molecular solids, which is qualitatively consistent with the Onsager model except for the long-range hole jump.     

Hydrolysis and Condensation Processes of Titanium iso-Propoxide Modified with Catechol: An NMR Study

The hydrolysis and condensation processes of titanium iso-propoxide modified with catechol (C₆H₄(OH)₂; H₂cat) have been investigated by ¹H, ¹³C and ¹⁷O nuclear magnetic resonance spectroscopy. The hydrolysis reactions of the modified titanium iso-propoxide in the system with Ti:tetrahydrofuran (THF):H₂O = 1:20:x (x = 1, 2 and 5 in a molar ratio) are essentially completed in the initial stage (<1 h), and the condensation reactions also proceed significantly during this stage. Upon hydrolysis with H₂O/Ti = 1, the iso-propoxy groups are selectively hydrolyzed and the catecholate groups remain bound to titanium. With H₂O/Ti = 2 and 5, both the iso-propoxy and catecholate groups are hydrolyzed, and the hydrolysis of the iso-propoxy groups is relatively preferential. Approximately half the catecholate groups are stably bound to titanium, even after hydrolysis with H₂O/Ti = 5.     

Synthesis of the C8-C20 and C21-C30 segments of pectenotoxin 2

In this study, we synthesized the C8-C20 and C21-C30 segments of the diarrhetic shellfish toxin pectenotoxin 2. The C8-C20 segment was assembled from a phosphonate corresponding to the C8-C15 segment (prepared from l-malic acid in 19 steps) and an aldehyde corresponding to the C16-C20 segment (synthesized from 3-methyl-3-butenol in nine steps) by a twelve-step process including the Horner-Wadsworth-Emmons reaction, regio- and stereoselective reduction of the resulting enone, diastereoselective epoxidation, and 5-exo epoxide cleavage forming the C-ring. The C21-C30 segment was constructed in 13 steps from (S)-glycidol via a route involving E-ring formation by 5-exo epoxide cleavage and stereoselective methylation at C27 by the Evans method.     

Polymerization of vinyl monomers in the water–1,4-dioxane system containing peroxide and water-soluble polymer

Water-solube polymer (PST) containing triethylenetetramine side chain was prepared by the amination of chloromethylated polystyrene with triethylenetetramine in 1,4-dioxane. The polymerization of vinyl monomers was carried out in the water–organic solvent system containing PST and a very small amount of peroxide. The polymerization of methyl methacrylate proceeded smoothly in the presence of both peroxide and PST. It was found that the polymerization was initiated with the radicals generated by the interaction between hydroperoxide and amino groups of PST. 1,4-Dioxane hydroperoxide showed a high activity for the polymerization of methyl methacrylate. The maximum rate of the polymerization was observed at 60°C and in an approximately neutral solution. The addition of suitable amount of Cu(II) accelerated the polymerization of methyl methacrylate. The selective polymerization of vinyl monomers was observed in this system.     

Vertex-Disjoint Cycles Containing Specified Edges

Dirac and Ore-type degree conditions are given for a graph to contain vertex disjoint cycles each of which contains a previously specified edge. One set of conditions is given that imply vertex disjoint cycles of length at most 4, and another set of conditions are given that imply the existence of cycles that span all of the vertices of the graph (i.e. a 2-factor). The conditions are shown to be sharp and give positive answers to conjectures of Enomoto in [3] and Wang in [5]. Revised: July 28, 1999     

Reactions of N, N-dichloroalkylamines with solid base as studied by FTIR combined with DFT calculations

Products of vacuum gas–solid reactions of N, N-dichloroalkylamines with KOH have been identified by FTIR spectroscopy and DFT calculations. It has been found that the reactions consist of elimination of two Cl atoms accompanied with migration of an H atom, a ring carbon or a methyl group from the -carbon to the N atom and unstable imines with a C=N double bond are formed.     

Construction of positively-charged layered assemblies assisted by cyclodextrin complexation

A beta-cyclodextrin dimer is found to be effective in preparing a layer-by-layer architecture of positively charged ferrocene-appended poly(allylamine) presumably on the basis of strong beta-cyclodextrin-ferrocene host-guest interaction.     

Atomistic damage mechanisms during hypervelocity projectile impact on AlN: A large-scale parallel molecular dynamics simulation study

Atomistic mechanisms of damage initiation during hypervelocity (15 km/s) impact on an AlN coating is investigated using parallel molecular-dynamics simulations involving 209 million atoms. On impact a strong shock wave is generated, which then splits into an elastic precursor and a structural phase transformation (SPT) waves, the latter driving a wurtzite to rocksalt structural transition. During its development, the SPT wave induces plastic processes in the intact wurtzite material, which in turn facilitate the nucleation and growth of brittle cracks. Specifically, the interface between the transformed (rocksalt) and untransformed (wurtzite) regions acts as a source of nanocavities and kink bands. They further interact with stress release waves reflected from the back surface and create cracks in mode I, from the nanocavities, and in mode II, from the kink band superdislocation boundary. Stresses are evaluated using a stoichiometric-preserving formula for virial local averages on inhomogeneous binary systems. Defects are analyzed using shortest-path ring statistics.