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.     

Infraglottic aspect of canine vocal fold vibration: Effect of increase of mean airflow rate and lengthening of vocal fold

The mucosal upheaval (MU), where the mucosal wave starts and propagates upward, appears only when the vocal fold vibrates. The location of the MU histologically and the effect of changes in mean air flow rate (MFR) and vocal fold length on occurrence of the MU were studied in twelve excised canine larynges. The lower surface of the vocal fold was marked to serve as a landmark for subsequent study. Cricothyroid approximation was performed to lengthen the vocal fold. After taking high-speed pictures or recording stroboscopic images from the tracheal side, a small cut wound was made at the mark. This wound served to compare the position of the MU with the histologically identified location of the mark. The larynx was then sectioned in the frontal plane. Before lengthening the vocal fold, the MU occurred on the area where the lamina propria became thinner and where the muscular layer neared the epithelial layer. After lengthening the vocal fold, the MU actually shifted medially compared with its original position. The subglottic area surrounded by the bilateral MUs became longer and thinner. Whether or not complete glottal closure during a vibratory cycle was achieved did not alter these findings. In contrast, with a fixed vocal fold length the MU appeared more laterally as MFR increased, but, based on the relation with the mark, its location on the vocal fold did not change from its original position before increase of MFR.     

Probing for electrical inclusions with complex spherical waves

Let a physical body Ω in ?² or ?³ be given. Assume that the electric conductivity distribution inside Ω consists of conductive inclusions in a known smooth background. Further, assume that a subset Γ ? ?Ω is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on Γ. More precisely: given a ball B with center outside the convex hull of Ω and satisfying (B? ∩ ?Ω) ? Γ, boundary measurements on Γ with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion‐free domain near Γ and is robust against measurement noise. © 2007 Wiley Periodicals, Inc.     

A perfect one-factorization ofK 36

In this paper, a perfect one-factorization ofK ₃₆ is given, which is factor-1-rotational.     

Crystallographic report: Bis{µ‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]1κ:S,2κ:S‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]‐1κ2S,S′}dicadmium(II)

The centrosymmetric title compound, [Cd₂{CH₃OC₆H₄P(OC₅H₉)S₂}₄], features an eight‐membered [? Cd? S? P? S? ]₂ ring owing to the presence of bridging dithiolate ligands. Tetrahedral coordination geometries for cadmium are completed by chelating ligands. Copyright © 2004 John Wiley & Sons, Ltd.     

Preparation and condensation reactions of a new light-fluorous Mukaiyama reagent: reliable purification with fluorous solid phase extraction for esters and amides

A modified light-fluorous Mukaiyama reagent bearing a C₈F₁₇ tag was prepared and examined in ester and amide forming condensation reactions. Following the reactions, the desired product was effectively separated from the fluorous pyridone by-product using a simple fluorous solid phase extraction.     

SUPER TOUGH GELS WITH A DOUBLE NETWORK STRUCTURE

 Living tissues work with fantastic functions in soft and wet gel-like state. Thus, hydrogels have attracted much attention as excellent soft & wet materials, suitable for making artificial organs for medical treatments.However, conventional hydrogels are mechanically too weak for practical uses. We have created double network (DN) hydrogels with extremely high mechanical strength in order to overcome this problem. DN gels are interpenetrating network (IPN) hydrogels consisting of rigid polyelectrolyte and soft neutral polymer. Their excellent mechanical properties cannot be explained by the standard fracture theories. In this paper, we discuss about the toughening mechanism of DN gels in accordance with their characteristic behavior, such as large hysteresis and necking phenomenon. We also describe the results on tissue engineering application of DN gels.     

Elucidation of the Role of the Complex in Hydride Transfer Reaction between Methylene Blue and 1-Benzyl-1,4-dihydronictinamide by Effect of γ-Cyclodextrin

The kinetics of the hydride transfer reaction between Methylene Blue (MB⁺) and 1-benzyl-1,4-dihydronicotinamide (BNAH) were studied in 10% ethanol-90% water mixed solvents containing β- and γ-cyclodextrins (β-CD and γ-CD). The pseudo-first order rate constant shows kinetic saturation at high initial concentration of BNAH. This indicates the formation of a complex between MB⁺ and BNAH. The reaction was suppressed by addition of β-CD, but enhanced by addition of γ-CD. MB⁺ and BNAH were separately accommodated within the β-CD cavity and the cavity walls may protect the activity site of the reactants. On the other hand, in the MB⁺-BNAH-γ-CD system, the inclusion of the complex between MB⁺ and BNAH with γ-CD occurred. This effect of γ-CD can distinguish between the productive and non-productive nature of the complex.     

A characteristic effect of pressure on inclusion complexation of phenothiazine dyes with p-sulfonatocalix[6]arene in a room-temperature ionic liquid

The inclusion complexation of p-sulfonatocalix[6]arene (Calix-S6) with three kinds of phenothiazine dyes was studied spectrophotometrically in a mixture of a room-temperature ionic liquid [bmim]BF₄ (1-butyl-3-methylimidazolium tetrafluoroborate) and ethanol. We have determined the association constants of Calix-S6 with phenothiazine dyes under external static pressure up to 767 bar in the [bmim]BF₄-ethanol and alcohol-water mixtures. With increasing external pressure, the inclusion equilibrium in the alcohol-water mixtures was shifted to the dissociation side. Conversely, the inclusion equilibrium of methylene blue (MB) and azure A (AA) in the ionic liquid mixture was shifted to the association side. From the analysis of the pressure effects, the reaction volumes ΔV for inclusion complexation were estimated as −7 to 9 cm³ mol⁻¹ in the [bmim]BF₄-ethanol mixture and 20–32 cm³ mol⁻¹ in the alcohol-water mixtures. Based on the results, we have suggested that there is a competing complexation between the included dye and [bmim]BF₄ molecules in the ionic liquid.     

Solvent Effects on the Absorption Spectrum of the Product and the Equilibrium Constant for the Proton Transfer Reaction from 1-Phenacylquinolinium Bromide to Amines

The equilibrium constants, K ₂, have been determined for the proton-transfer reactions of 1-phenacylquinolinium ion, PHQ⁺, with several amines {triethylamine (TEA), N,N,N′,N′-tetramethylethylenediamine (ED), N,N,N′, N′-tetramethylpropanediamine (PD), N,N,N′,N′-tetramethylbutanediamine (BD), and 1,8-bis(dimethylamino-naphthalene (DMAN)} in acetonitrile (AN), AN-tetrahydrofuran (THF) and AN-ethanol (EtOH) mixtures. The reaction was followed spectrophotometrically using a stopped-flow technique. The K ₂ value decreased for DMAN and increased for TEA with increasing vol-% of THF in AN-THF mixtures. The changes in the K ₂ value for ED, PD and BD changed in the order: ED, PD and BD from a pattern similar to TEA to a pattern similar to DMAN. The change in the K ₂ value for DMAN with increasing vol-% of THF in AN-THF mixtures was explained by the effect of polarity on the stability of P⁻Q⁺ (the deprotonated product of PHQ⁺). The effect of THF on the K ₂ value is consistent with that of the peak wavelength of the absorption spectrum of P⁻Q⁺. The change in the K ₂ value for TEA, ED, PD and BD depended on the structures of the protonated bases, one of the products for this reaction. The effect of EtOH on the K ₂ value for DMAN was examined in ternary EtOH-THF-AN mixtures that contain different amounts of EtOH and whose relative permittivities were adjusted to that of EtOH. The K ₂ value increased with increasing vol-% of EtOH because of the stabilization of P⁻Q⁺ upon the formation of the hydrogen-bonded complex with EtOH. The absorption spectrum of P⁻Q⁺ demonstrated a blue shift as the vol-% of EtOH increased.