The colorings of homeomorphisms on connected graphs

In this paper, we decide the exact value of the color number of a fixed point free homeomorphism on a connected locally finite graph. We prove that for every fixed-point free homeomorphism from a connected locally finite graph into itself, the greatest common divisor of all period for its map is equal to one or three if and only if its color number is 4.     

Comparison between sonodynamic effect and photodynamic effect with photosensitizers on free radical formation and cell killing

Although enhancement of ultrasound-induced cell killing by photodynamic reagents has been shown, the sonochemical mechanism in detail is still not clear. Here, comparison between sonodynamic effect and photodynamic effect with photosensitizers at a concentration of 10 μM on free radical formation and cell killing was made. When electron paramagnetic-resonance spectroscopy (EPR) was used to detect 2,2,6,6-tetramethyl-4-piperidone-N-oxyl (TAN) after photo-irradiation or sonication with 2,2,6,6-tetramethyl-4-piperidone (TMPD), the order of TAN formation in the photo-irradiated samples was as follows: rhodamine 6G (R6) > sulforhodamine B (SR) > hematoporphyrin (Hp) > rhodamine 123 (R123) > rose bengal (RB) > erythrosine B (Er) = 0; although there was time-dependent TAN formation when the samples were sonicated, no significant difference among these agents were observed. All these agents suppressed ultrasound-induced OH radical formation detected by EPR-spin trapping. Sensitizer-derived free radicals were markedly observed in SR, RB and Er, while trace level of radicals derived from R6 and R123 were observed. Enhancement of ultrasound-induced decrease of survival in human lymphoma U937 cells was observed at 1.5 W/cm² (less than inertial cavitation threshold) for R6, R123, SR and Er, and at 2.3 W/cm² for R6, R123, Er, RB and SR. On the other hand, photo-induced decrease of survival was observed for R6, Hp and RB at the same concentration (10 μM). These comparative results suggest that (1) ¹O₂ is not involved in the enhancement of ultrasound-induced loss of cell survival, (2) OH radicals and sensitizer-derived free radicals do not take part in the enhancement, and (3) the mechanism is mainly due to certain mechanical stress such as augmentation of physical disruption of cellular membrane by sensitizers in the close vicinity of cells and/or cavitation bubbles.     

Pressure effect on bulk weak ferromagnets: (BDH-TTP)[M(isoq)2(NCS)4] (M = Cr(III), Fe(III); isoq = Isoquinoline)

The pressure dependence of the magnetic properties of weak ferromagnets (BDH-TTP)[M(isoq)2(NCS)4] [BDH-TTP = 2,5-bis(1',3'-dithiolan-2'-ylidene)-1,3,4,6-tetrathiapentalene; M = Cr, Fe; isoq = isoquinoline] is discussed. These salts form two-dimensional magnetic sheets, where ferrimagnetic chains of donor cation radical (S = 1/2) and anion [S = 3/2 (Cr), 5/2 (Fe)] are antiferromagnetically connected by weak donor-donor and anion-anion interchain S...S contacts. Under ambient pressure, both the Cr and Fe salts undergo a weak ferromagnetic transition at Tc = 7.6 K, below which a spontaneous magnetization emerges along the direction perpendicular to the sheets. The application of the pressure elevates the transition temperatures up to 16.6 and 11.6 K at 9 kbar for M = Cr and Fe, respectively. As the pressure increases, the remanent magnetization M(r) decreases, whose pressure dependence for the Cr salt is larger than that for the Fe salt. This difference indicates that the spin-canting angle of the Cr salt is reduced because of the increase of antiferromagnetic interaction by applied pressure, in contrast to the Fe salt, where single-ion anisotropy contributes less. The quantitative analysis of the magnetization curves of the Cr salt using the mean-field approximation reveals that the intermolecular exchange interaction increases as the pressure increases, among which the interchain anion-anion interaction has the highest pressure sensitivity. This result is consistent with the temperature dependence of the crystal structure showing that the thermal contraction in the distances of interchain anion-anion S...S contacts is the most remarkable in intrachain S...S contacts. The large pressure dependence of the transition temperature of these salts is therefore explained as a result of the fact that the interchain interactions, the anion-anion interaction in particular, are strengthened by applied pressure.     

Pressure effect on the electrical conductivity and superconductivity of beta-(BDA-TTP)2I3

The pressure-induced electrical conductivity properties of beta-(BDA-TTP)2I3 have been investigated; the salt exhibits a dramatic change in the conductivity behaviour above ca. 10 kbar and undergoes a superconducting transition with an onset near 10 K.     

A granularity-based framework of deduction, induction, and abduction

In this paper, we propose a granularity-based framework of deduction, induction, and abduction using variable precision rough set models proposed by Ziarko and measure-based semantics for modal logic proposed by Murai et al. The proposed framework is based on α-level fuzzy measure models on the basis of background knowledge, as described in the paper. In the proposed framework, deduction, induction, and abduction are characterized as reasoning processes based on typical situations about the facts and rules used in these processes. Using variable precision rough set models, we consider β-lower approximation of truth sets of nonmodal sentences as typical situations of the given facts and rules, instead of the truth sets of the sentences as correct representations of the facts and rules. Moreover, we represent deduction, induction, and abduction as relationships between typical situations.     

Skeletal Rearrangement of O‐Propargylic Formaldoximes by a Gold‐Catalyzed Cyclization/Intermolecular Methylene Transfer Sequence

Skeletal rearrangement of O‐propargylic formaldoximes, in the presence of gold catalysts, afforded 4‐methylene‐2‐isoxazolines in good to excellent yields by an intermolecular methylene transfer. In addition, the cascade reaction with maleimide in the presence of a gold catalyst afforded isoxazole derivatives by cyclization/methylene transfer and a subsequent ene reaction, whereas that using a copper catalyst gave oxazepines through a 2,3‐rearrangement.     

Electrochemical decomposition of layer-by-layer thin films composed of TEMPO-modified poly(acrylic acid) and poly(ethyleneimine)

The decomposition of layer-by-layer (LbL) thin films composed of 2,2,6,6-tetramethylpiperidine-1-oxyl free radical-appended poly(acrylic acid) (TEMPO-PAA) and poly(ethylenimine) (PEI) was studied by using a quartz crystal microbalance (QCM) and cyclic voltammetry. The electrode potential of the (PEI/TEMPO-PAA)₄/PEI film-coated Au resonator was scanned from +0.2 to +0.8 V vs Ag/AgCl. The CV showed that the oxidation peak current decreased as the number of scans increased. The change in the resonance frequency of the QCM increased after electrolysis, indicating that the film was decomposed by electrolysis. The positive charges originating from the oxoammonium ions probably destabilized the (PEI/TEMPO-PAA)₄/PEI film. Furthermore, the release of 5,10,15,20-tetraphenyl-21H,23H-porphine tetrasulfonic acid (TPPS) from TPPS-loaded (PEI/TEMPO-PAA)₄/PEI-coated ITO electrodes was investigated. TPPS was released at electrode potentials greater than +0.6 V by the decomposition of the film. The results suggest that TEMPO-PAA/PEI LbL films are suitable for electrochemically controlled drug delivery systems.     

Catalytic reactions of oxetanes with protonic reagents and aprotic reagents leading to novel polymers

This paper reports new addition reactions of oxetanes with certain protonic reagents such as carboxylic acid, phenol, and thiol, and with certain aprotic reagents such as acyl chloride, thioester, phosphonyl dichloride, silyl chloride, and chloroformate using quaternary onium salts as catalysts. The kinetic study of the addition reactions of oxetanes was also investigated. These new addition reactions were applicable to the synthesis of new polymers. These polyaddition systems could also construct both polymer main chains and reactive side chains. The alternating copolymerization of oxetanes with carboxylic anhydride was performed. Furthermore, it was found that anionic ring‐opening polymerization of oxetanes containing hydroxy groups proceeded to afford the hyperbranched polymer (HBP) with an oxetanyl group and many hydroxy groups at the ends of the polymer chains. Alkali developable photofunctional HBPs were synthesized by the polyaddition of bis(oxetane)s or tris(oxetane)s, and their patterning properties were examined, too. The photo‐induced cationic polymerization of the polymers with pendant oxetanyl groups and the thermal curing reactions of polyfunctional oxetanes (oxetane resins) were also examined to give the crosslinking materials quantitatively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 709–726, 2007