Graphs G for which both G and G¯ are Contraction Critically k-Connected

 An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is called contraction critically k-connected. For k≥4, we prove that if both G and its complement Gˉ are contraction critically k-connected, then |V(G)|<k ^5/3+4k ^3/2. Received: October, 2001 Final version received: September 18, 2002 AMS Classification: 05C40     

Path chromatic numbers of graphs

Let the finite, simple, undirected graph G = (V(G), E(G)) be vertex-colored. Denote the distinct colors by 1,2,…,c. Let V_i be the set of all vertices colored j and let <V_i be the subgraph of G induced by V_i. The k-path chromatic number of G, denoted by χ(G; P_k), is the least number c of distinct colors with which V(G) can be colored such that each connected component of V_i is a path of order at most k, 1 ? i ? c. We obtain upper bounds for χ(G; P_k) and χ(G; P_∞) for regular, planar, and outerplanar graphs.     

Free radical copolymerization of sulfur dioxide with phenylacetylene

Free radical copolymerization of sulfur dioxide with phenylacetylene (PA) in o-dichlorobenzene was studied in a range of temperatures from 30 to 80^oC as a function of total monomer concentration ([SO₂] + [PA]). PA content in the copolymers increases with decreasing total monomer concentration and increasing temperature. M _w/M _n becomes sharper with decreasing the total monomer concentration, but does not depend upon feed compositions which are changed keeping total monomer concentration constant at 2, 4, and 6 mol/L, respectively. These results strongly indicate the existence of depropagation. Thermal decomposition of the copolymers happens more easily than PA homopolymer and the carbon-centered free radicals are detected during the decomposition. Reactivity of ～ CH??(Ph) free radical (～ PA · ) is also discussed.     

Evaluation of pyrimido[5,4-d]pyrimidine derivatives as peroxyoxalate chemiluminescence reagents using a flow injection system

Eighteen kinds of pyrimido[5,4-d]pyrimidines together with several commercially available fluorescent compounds such as perylene, Rhodamine B, etc., were evaluated as the reagents for a peroxyoxalate chemiluminescence (CL) detection system by using a flow injection method. The peroxyoxalate CL reaction employed consists of bis(2,4,6-trichlorophenyl)oxalate, hydrogen peroxide, triethylamine, and a fluorophore. Under the conditions used, 2,6-bis[di-(2-hydroxyethyl)amino]-4,8- dipiperidinopyrimido[5,4-d]pyrimidine (Dipyridamole) and 2,4,6,8-tetrathiomorpholinopyrimido[5,4-d]pyrimidine (1i) gave very intense chemiluminescence intensities which were larger than those of any other commercially available fluorescent compounds tested (e.g., 10 times larger than that of perylene).     

Hartree–Fock and density functional theory calculations for the reaction mechanism of nitric oxide reductase cytochrome P450nor from Fusarium oxysporum

A reaction mechanism of a nitric oxide reductase, cytochrome P450nor (P450nor) from Fusarium oxysporum, was clarified by using Density functional theory and Hartree–Fock calculations. In this reaction mechanism, molecular orbital (MO) analysis revealed that the NO ligand dissociates from the heme iron immediately after one-electron reduction by NADH, and MO energy analysis revealed that NADH acts as a one-electron reducer, not as a two-electron reducer, and that NADH has a pivotal role different from other one-electron reducers. The role of NADH is to act as a double one-electron donor (i.e. one-electron transfer occurring twice) and to combine with the NO⁻ molecule by charge recombination reaction. Our quantum chemical calculations indicated that all reactions occurring in the heme pocket are too fast to become rate-limiting. Therefore, the rate-limiting steps in the proposed reaction mechanism are the process of capturing NO and NADH into the heme pocket and the process of expelling a product generated in the heme pocket. Kinetics of these processes was discussed based on large-amplitude vibration, which helps capturing and expelling processes in a widely opened heme pocket of P450nor. The reaction mechanism proposed here well explains published experimental data.     

Superstructure in the Metastable Intermediate‐Phase Li2/3FePO4 Accelerating the Lithium Battery Cathode Reaction

LiFePO₄ is an important cathode material for lithium‐ion batteries. Regardless of the biphasic reaction between the insulating end members, Li_xFePO₄, x≈0 and x≈1, optimization of the nanostructured architecture has substantially improved the power density of positive LiFePO₄ electrode. The charge transport that occurs in the interphase region across the biphasic boundary is the primary stage of solid‐state electrochemical reactions in which the Li concentrations and the valence state of Fe deviate significantly from the equilibrium end members. Complex interactions among Li ions and charges at the Fe sites have made understanding stability and transport properties of the intermediate domains difficult. Long‐range ordering at metastable intermediate eutectic composition of Li_2/3FePO₄ has now been discovered and its superstructure determined, which reflected predominant polaron crystallization at the Fe sites followed by Li⁺ redistribution to optimize the Li? Fe interactions.     

Vibronic Structures in Absorption and Fluorescence Spectra of Firefly Oxyluciferin in Aqueous Solutions

To elucidate the factors determining the spectral shapes and widths of the absorption and fluorescence spectra for keto and enol oxyluciferin and their conjugate bases in aqueous solutions, the intensities of vibronic transitions between their ground and first electronic excited states were calculated for the first time via estimation of the vibrational Franck–Condon factors. The major normal modes, overtones and combination tones in absorption and fluorescence spectra are similar for all species. The theoretical full widths at half maximum of absorption spectra are 0.4–0.7 eV and those for the fluorescence spectra are 0.4–0.5 eV, except for phenolate‐keto that exhibits exceptionally sharp peak widths due to the dominance of the 0–0′ or 0′–0 band. These spectral shapes and widths explain many relevant features of the experimentally observed spectra.     

Quantum yields and quantitative spectra of firefly bioluminescence with various bivalent metal ions

We measured quantitative spectra of firefly (Photinus pyralis) bioluminescence in the presence of Zn²⁺ and other bivalent metal ions to investigate the effects of these metal ions on luciferin‐luciferase reaction. We studied the dependence of the quantum yield and spectrum on quantity and kind of bivalent metal ions. Adding various amounts of Mg²⁺, Mn²⁺ and Ca²⁺ produced virtually no change in the quantum yields or the spectra of bioluminescence. In contrast, increasing amounts of ions such as Zn²⁺ and Cd²⁺ decreased quantum yields and changed the bioluminescence color from yellow‐green to red. Quantitative analysis showed that the sensitivities of the quantum yield and color to various metal ions were in the order of Hg²⁺>Zn²⁺, Cd²⁺>Ni²⁺, Co²⁺, Fe²⁺≫Mg²⁺, Mn²⁺, Ca²⁺. We propose that the changes in quantum yield and spectrum caused by the metal ions are due to their effect on luciferase that surrounds oxyluciferin during its radioactive decay. We also found that having more metal ions accelerated bioluminescence reactions. The sensitivity of the reaction rate had no correlation with those of the quantum yield and spectrum.     

Interlaboratory study of DNA extraction from multiple ground samples, multiplex real-time PCR, and multiplex qualitative PCR for individual kernel detection system of genetically modified maize

In many countries, the labeling of grains, feed, and foodstuff is mandatory if the genetically modified (GM) organism content exceeds a certain level of approved GM varieties. We previously developed an individual kernel detection system consisting of grinding individual kernels, DNA extraction from the individually ground kernels, GM detection using multiplex real-time PCR, and GM event detection using multiplex qualitative PCR to analyze the precise commingling level and varieties of GM maize in real sample grains. We performed the interlaboratory study of the DNA extraction with multiple ground samples, multiplex real-time PCR detection, and multiplex qualitative PCR detection to evaluate its applicability, practicality, and ruggedness for the individual kernel detection system of GM maize. DNA extraction with multiple ground samples, multiplex real-time PCR, and multiplex qualitative PCR were evaluated by five laboratories in Japan, and all results from these laboratories were consistent with the expected results in terms of the commingling level and event analysis. Thus, the DNA extraction with multiple ground samples, multiplex real-time PCR, and multiplex qualitative PCR for the individual kernel detection system is applicable and practicable in a laboratory to regulate the commingling level of GM maize grain for GM samples, including stacked GM maize.