Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.     

Synthesis and characterization of flavylium salts having three types color depending on recrystallization conditions

Three types of flavylium salts (FVs, yellow, green and red) have been synthesized and the colors depended on recrystallization conditions. The existence of these color states was confirmed by diffuse reflectance spectra. The spectra were almost the same as the absorption spectra in ethanol solution. The molecular state of FVs in crystals will be the same as that in solutions. The crystal colors of the FVs are controlled by the recrystallization conditions.     

Carrier generation process on photoconductive polymer films as studied by magnetic field effects on the charge-transfer fluorescence and photocurrent

We have studied the magnetic field effects (MFEs) on the charge-transfer fluorescence and transient photocurrent of a 1,2,4,5-tetracyanobenzene-doped poly(N-vinylcarbazole) film, which reflect the recombination and escape yields of the carriers, respectively. The recombination yield dependence of the external magnetic field (B) clearly shows two types of the MFEs, growth with increasing B due to the hyperfine mechanism (HFM) and a negative dip due to the level-crossing mechanism (LCM). On the other hand, the escape yield indicates complementary MFEs with a sharp decrease in yield with increasing B and then a positive dip. Simultaneous observation of the HFM- and LCM-MFEs proves the stepwise hole-hopping mechanism rather the long-range hole-jumping one. The quantitative analysis of the recombination and escape MFEs is performed using the stochastic Liouville equations (SLE) for a one-dimensional lattice model in which the stepwise hole hops take place between the nearest neighbor carbazole units with spin conservation. The SLE analysis provides the recombination and hole transfer rate constants of 7.0 x 10(7) and 4.5 x 10(8) s(-1), respectively. The boundary site number for the ion pairs in the one-dimensional model is estimated by the best fit to the experimental results. The interionic distance of the boundary ion pair in the one-dimensional model including eight sites agrees with the thermalization distance in the Onsager model. Hence, it is concluded that the elementary processes in the Onsager model applied to molecular amorphous solids are the stepwise hole hops rather than a long-range hole jump.     

Effect of labile hydrogens on measurement of tritium preserved in hydrogens of cellulose

Various f-elements are separated as anionic complexes from both acidic and alkaline solutions by precipitation with alkylpyridinium salts. The precipitates are also cationic surfactants where the simple counter-ion (e.g. nitrate or chloride) is replaced by the negatively charged complex anion of an actinide or lanthanide. The low solubility of these precipitates is explained by a strong affinity of divalent complex counter-ions of f-elements to the quaternary nitrogen. Precipitations in solutions of nitric acid allow to separate tetravalent f-elements from other metals, in alkaline carbonate solutions tetravalent and hexavalent actinides are precipitated simultaneously. The last procedure yields precipitates, which are very intimate mixtures of hexavalent and tetravalent actinides. This allows to prepare mixed oxides in a simple way.     

X-ray scattering by water molecules studied by using synchrotron radiation

The energy spectra of free water molecules were measured at scattering angles 2θ ranging from 10.5° to 75.7°, using an angle-dispersive-type diffractometer and synchrotron radiation as an X-ray source. A silicon (111) monochrometer was used to obtain incident X-rays with the wavelengths of (1.543/n) Å (n = 1,3,4,5). Observed inelastic scattering peaks are clearly separated from eleastic ones at s values [s = (4π/λ) sin Å] larger than 8 Å^?1. The increase of the separation with an increasing s value was consistent with the classical theory of the Compton shift. The total (elastic plus inelastic) intensities were obtained over a range of s = 0.74–5.0 Å^?1. Experimental difference intensities Δσ_ee and Δσ_ne were obtained separately by combining the X-ray and high-energy electron scattering data. The experimental results are in reasonable agreement with the theoretical intensities calculated from SCF and CI molecular wave functions with a basis set of double-zeta plus polarization functions. © 1994 John Wiley & Sons, Inc.     

One-step furan ring formation: Synthesis of furo[3,2-h]quinolones

The one-pot reaction of ethyl 1-cyclopropyl-6,7,8-trifluoro-1,4-dihydro-4-oxoquinoline-3-carboxylate ( 6 ) with tert-butyl acetoacetate gave 3-tert-butyl 7-ethyl 9-cyclopropyl-4-fluoro-6,9-dihydro-2-methyl-6-oxofuro[3,2-h]quinoline-3,7-dicarboxylate ( 5 ). This regioselective cyclization was rationalized by the Hard and Soft Acids and Bases principle. By use of a similar furan-forming reaction, we prepared 2-(amino-methyl)furo[3,2-h]quinoline-7-carboxylic acid 4 . Compound 4 showed weak antibacterial activity.     

Heterogeneous molecular distribution in supported multicomponent lipid bilayers

Membrane domains contribute important structural and functional attributes to biological membranes. We describe the heterogeneous nanoscale distribution of lipid molecules within microscale membrane domains in multicomponent lipid bilayers composed of dipalmitoylphosphatidylcholine (DPPC), dilauroylphosphatidylcholine (DLPC), and cholesterol (chol). The lipids were labeled with the fluorescent lipid analogues Bodipy-PC and DiI-C20:0 to identify the distribution of individual membrane components. We used a near-field scanning optical microscope (NSOM) at room temperature to identify the nanoscale structures in the membrane. Simultaneous multicolor NSOM imaging at the emission maxima of the fluorescent analogues revealed a patchy distribution of Bodipy-PC and DiI-C20:0 indicative of phase separations in the bilayer. In a cholesterol-free system (DPPC/DLPC = 1:1), NSOM images proved that the two phosphatidylcholine molecules can coexist in domains at the micrometer level but form nanoscopic patches within the domains; DPPC occurs at the edge of the domains, whereas DLPC is present throughout the domains. In the presence of cholesterol (DPPC/DLPC = 7:3, chol = 18.9%), the two lipid molecules were more miscible but incomplete phase separations also occurred. The average domain sizes were 140-200 nm, well below the resolution capabilities of diffraction-limited light microscopy techniques; the domains were unresolvable by confocal microscopy. Our high-resolution NSOM studies of membrane domain behavior provide a better understanding of complex membrane phase phenomena in multicomponent biological membranes.     

A new-type photoreaction of a carbonyl compound: Part 2. Photoinduced ω-bond dissociation in p-halomethylbenzophenone studied by time-resolved EPR technique and laser flash photolysis

Photodissociation of the carbon-X (X = Br and Cl) bonds in p-bromo- and p-chloromethylbenzophenone (BMBP and CMBP) in solution were investigated by time-resolved EPR and laser flash photolysis techniques. BMBP and CMBP were found to undergo ω-bond cleavage to yield the p-benzoylbenzyl radical (BBR) at 295 K, and the quantum yields (Φ_BBR) were determined. The CIDEP signal originated from BBR formed upon decomposition of CMBP was obtained while that for BMBP was absent. By using triplet sensitization of acetone, the efficiencies (_BBR) of the CX bond fission in the triplet states of BMBP and CMBP were determined. The agreement between the Φ_BBR and _BBR values for CMBP indicates that the CCl bond dissociation occurs only in the triplet state. In contrast to CMBP, the cleavage of the CBr bond in BMBP upon direct excitation was concluded to be the event only in the excited singlet state without triplet formation, whereas the triplet state was also reactive for ω-bond dissociation. The rate of CBr bond dissociation seemed to be greater than that of intersystem crossing from the S₁ to the T₁ state. Schematic energy diagrams of the excited states of BMBP and CMBP were shown, and the reaction profiles were discussed from the viewpoint of the CX bond enthalpies.     

Photocrosslinking of poly(2,3-epithiopropyl methacrylate) by the oxidation of pendant episulfide groups

In the photocrosslinking of poly(2,3-epithiopropyl methacrylate) (PETMA) films the effect of the pendant episulfide group's oxidation on the crosslinking of PETMA was investigated. Thermal crosslinking of PETMA is promoted by peroxides such as benzoyl peroxide and hydrogen peroxide. IR spectrum of the crosslinked PETMA showed that the reaction proceeded through the oxidation of episulfide groups by the peroxides. The anthracene (An) sensitized photocrosslinking of PETMA films also proceeded via the oxidation of episulfide groups by singlet oxygen. It was found that residual tetrahydrofuran (THF) in the films remarkably increased the rate of the photocrosslinking and/or reduced the induction period. From the further investigation concerning casting solvents it was found that residual CS₂, CCl₄, and CHCl₃ in films increased the rate of the photocrosslinking and/or reduced the induction period of the photocrosslinking. The disappearance rate of An in the films was also increased by the presence of residual CS₂, CCl₄, and CHCl₃, differring from the result of THF. These results were explained by a difference in lifetime of singlet oxygen in the films. From the results were explained by a difference in lifetime of singlet oxygen in the films. From the results concerning the effects of hydroperoxides such as THF hydroperoxide and t-butyl hydroperoxide on the photocrosslinking of PETMA films the acceleration effect of the residual THF was deduced to be due to the promotion of singlet oxygen-oxidation of sulfide groups by protic compounds such as THF hydroperoxide and H₂O in the THF.     

A mixed version of Menger's theorem

An(a, b)-n-fan means a union ofn internally disjoint paths. Menger's theorem states that a graphG has an(a, b)-n-fan if and only ifG isn-connected betweena andb. We show thatG contains edge-disjoint(a, b)-n-fans if and only if for anyk withk0min{n–1, |V(G)|–2} and for any subsetX ofV(G)-{a, b} with cardinalityk, G-X is (n-k)-edge-connected betweena andb.