The Fixed Point of a Generalization of the Renormalization Group Maps for Self-Avoiding Paths on Gaskets

Let W(x,y) = ax ³+ bx ⁴+ f ₅ x ⁵+ f ₆ x ⁶+ (3 ax ²)² y+ g ₅ x ⁵ y + h ₃ x ³ y ² + h ₄ x ⁴ y ² + n ₃ x ³ y ³+a ₂₄ x ² y ⁴+a ₀₅ y ⁵+a ₁₅ xy ⁵+a ₀₆ y ⁶, and X = , , where the coefficients are non-negative constants, with a > 0, such that X ²(x,x ²)−Y(x,x ²) is a polynomial of x with non-negative coefficients. Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding paths on the 3 and 4 dimensional pre-gaskets. We prove that there exists a unique fixed point (x _f ,y _f ) of Φ in the invariant set . 2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41.     

Structure, thermal and transport properties of PVAc-LiClO4 solid polymer electrolytes

The lithium ion conducting solid polymer electrolytes (SPE) based on PVAc-LiClO₄ of various compositions were prepared by solution casting technique. Structure and surface morphology characterization were studied by X-ray diffraction (XRD) analysis and scanning electron microscopy (SEM) measurements, respectively. Thermal and conductivity behavior of polymer-salt complexes were studied by employing differential scanning calorimetry (DSC) and ac impedance measurements, respectively. XRD and SEM analyses indicate the amorphous nature of the polymer-salt complexes. DSC measurements show decrease in T_g with the increase in LiClO₄ concentrations. The bulk conductivity of the PVAc:LiClO₄ polymer electrolytes was found to vary between 7.6×10⁻⁷ and 6.2×10⁻⁵ S cm⁻¹ at 303 K with the increase in salt concentration. The temperature dependence of the polymer electrolyte complexes appear to obey Arrhenius law.     

Cyclization from Higher Excited States of Diarylethenes Having a Substituted Azulene Ring

The cyclization reaction of diarylethenes having an azulene ring occurs only via higher excited states. Novel diarylethenes having an azulene ring with a strong donor or acceptor were synthesized and examined in these reactions. A derivative having an electron-donating 1,3-benzodithiol-2-ylidenemethyl group at the 1-position of the azulene ring showed photochromism, whereas neither a derivative having a π-conjugated electron-donating group at the 3-position of the azulene ring nor derivatives having a π-conjugated electron-withdrawing group at the 1- or 3-position of the azulene ring showed any photochromism. The photoreactivities of these compounds were explained by calculating forces and bond orders on the excited states using density functional theory (DFT) and time-dependent (TD)-DFT.     

Detection of N-nitroso-bile acids at 285 nm in reverse-phase HPLC

In the present study, we developed a novel, simple, and specific detection method using an RP-HPLC at UV 285 nm for the separation and quantification of N-nitroso-bile acids. First, we found that N-nitroso-bile acids have a specific spectrophotometric absorbance at 285 nm. Using this 285 nm detection system, we could especially measure N-nitroso-bile acids, even in co-existence of non-N-nitroso-bile acids. Next, we observed the decomposition of N-nitroso-glychocholate under alkaline, acidic, and neutral conditions. N-nitroso-glychocholate rapidly decomposed under alkaline conditions (pH 9) (t(1/2) = 0.96 h), but remained fairly stable under acidic (pH 2) (t(1/2) = 12.8 h) and neutral (pH 7) (t(1/2) = 7.8 h) conditions. This study is the first report, which simply and specifically analyzes N-nitroso-bile acids using an RP-HPLC system.     

Sputtering angle effects by Kr mixing in N+ ion beam on the lifetime of nitrided carbon stripper foils

Nitrided carbon stripper (NCS) foils with high nitrogen content were produced by ion beam sputtering of reactive nitrogen gas. Such foils seem to be very useful as strippers in high-intensity heavy ion accelerators. We have conducted comprehensive research, development, and production of such foils with high reproducibility. Krypton, a heavy noble gas, was mixed with the reaction nitrogen gas (IBSRN) in the ion beam sputtering process to produce stripper foils with short sputtering deposition time and long lifetimes in the high intensity ion beam irradiation. With the (N₂ + Kr) mixed gas ions we investigated the influence of different sputtering angles (α) on the lifetime of the NCS-foils in case of poly-graphite material. The lifetime measurement of these foils of 20 ± 5 μg/cm² was performed with a 3.2 MeV Ne⁺ ion beam as usual. The foils made at a sputtering angle of 15° showed a maximum of 11.0 and 7.5  C/cm² average charge density, respectively, which corresponded to about 275 and 187 times the lifetime of the best commercially available foils.     

Synthesis of mono- and 1,3-diaminocalix[4]arenes via Ullmann-type amination and amidation of 1,3-bistriflate esters of calix[4]arenes

Practical methods are described for the preparation of monoamines 4 and 1,3-diamines 5, bearing one or two amino group(s) instead of the hydroxy group(s) at the 28-position or at both the 26- and 28-positions of p-tert-butylcalix[4]arene (1a) and p-tert-butylthiacalix[4]arene (1b), via the Ullmann-type amination or amidation. Thus, the copper-catalyzed or mediated amination of the 1,3-bistriflate ester (2a) of 1a with benzylamine affords either mono(benzylamino) triflate 7a or 1,3-bis(benzylamine) 8 in a high yield, depending on the reaction conditions. On the other hand, the 1,3-bistriflate ester (2b) of 1b resists disubstitution and produces, under stoichiometric conditions, mono(benzylamino) triflate 7b. The disubstitution of 2b is achieved by amidation with tosylamide, giving 1,3-bis(tosylamide) 17b. The hydrogenolysis of the benzylamino moiety of 7a, followed by the hydrolysis of the Tf moiety, affords monoamine 4a, while the hydrogenolysis of 8 affords 1,3-diamine 5a. The amino moiety of 7b can be deprotected under acidic conditions to give, after hydrolysis, monoamine 4b. The hydrolysis of 17b affords 1,3-diamine 5b. The overall yields of compounds 4a, 4b, 5a, and 5b are 72%, 45%, 78%, and 24%, respectively, based on commercially available compounds 1 and are much higher than the ones previously reported in the literature.     

Protective Effect of Ferulic Acid against Hydrogen Peroxide Induced Apoptosis in PC12 Cells

Ferulic Acid (FA) is a highly abundant phenolic phytochemical which is present in plant tissues. FA has biological effects on physiological and pathological processes due to its anti-apoptotic and anti-oxidative properties, however, the detailed mechanism(s) of function is poorly understood. We have identified FA as a molecule that inhibits apoptosis induced by hydrogen peroxide (H₂O₂) or actinomycin D (ActD) in rat pheochromocytoma, PC12 cell. We also found that FA reduces H₂O₂-induced reactive oxygen species (ROS) production in PC12 cell, thereby acting as an anti-oxidant. Then, we analyzed FA-mediated signaling responses in rat pheochromocytoma, PC12 cells using antibody arrays for phosphokinase and apoptosis related proteins. This FA signaling pathway in PC12 cells includes inactivation of pro-apoptotic proteins, SMAC/Diablo and Bad. In addition, FA attenuates the cell injury by H₂O₂ through the inhibition of phosphorylation of the extracellular signal-regulated kinase (ERK). Importantly, we find that FA restores expression levels of brain-derived neurotrophic factor (BDNF), a key neuroprotective effector, in H₂O₂-treated PC12 cells. As a possible mechanism, FA increases BDNF by regulating microRNA-10b expression following H₂O₂ stimulation. Taken together, FA has broad biological effects as a neuroprotective modulator to regulate the expression of phosphokinases, apoptosis-related proteins and microRNAs against oxidative stress in PC12 cells.     

Two-dimensional network formation of cardiac myocytes in agar microculture chip with 1480 nm infrared laser photo-thermal etching

We have developed a new method that enables agar microstructures to be used to cultivate cells and that allows cell network patterns to be controlled. The method makes use of non-contact three-dimensional photo-thermal etching with a 1480 nm infrared focused laser beam, which is strongly absorbed by water and agar gel, to form the shapes of agar microstructures. It allows microstructures to be easily formed in an agar layer within a few minutes, with cell-culture holes formed by the spot heating of a 100 mW laser and tunnels by the tracing of a 100 microm s(-1), 40 mW laser. We cultivated rat cardiac myocytes in adjacent microstructures and observed synchronized beating in them 90 min after they had made physical contact. Our results indicate that the system can make and use microstructures for cell-network cultivation in a minimal amount of time without any expensive microfabrication facilities or complicated procedures.     

A new monitoring system of cultured myocardial cell motion: effect of pilose antler extract and cardioactive agents on spontaneous beating of myocardial cell sheets

Effects of various cardioactive agents and a water extract of the pilose antler of Cervus nippon var. mantchuricus on periodic beating of cultured myocardial cell sheets were examined by using an image analyzing system. Norepinephrine increased the beating rate and the beating amplitude, whereas digoxin and forskolin enlarged only the beating amplitude. Verapamil and propranolol decreased both the beating rate and the beating amplitude. The water extract of the pilose antler showed no remarkable effects in a standard medium (2.1 mM Ca2+). However, it significantly increased the beating amplitude when the beating was suppressed by replacement with a low calcium medium (0.5 mM Ca2+). A similar effect was found for 70% ethanol-soluble and -insoluble fractions of the extract.     

13C- and 1H-NMR and FTIR spectroscopic evidence for aggregate formation of organosilanes in toluene

 Changes in the ¹³C and ¹H NMR chemical shifts of the silane coupling agent (3-aminopropyltri-ethoxysilane, APTS) in toluene, which were detected as the concentration of APTS increased, have been interpreted in terms of the formation of micelles and the presence of a critical micelle concentration (CMC) equal to ca. 0.47 mol 1^-1. For the protons of the n-propyl segment, ¹H NMR splitting patterns have been analyzed and conformations of the propyl segment have been discussed. Plots of relative absorbance of the two NH₂ stretch IR bands at 3324 and 3384 cm^-1 against concentration provided an inflection point (corresponding to the CMC) at a value equal to 0.46 mol 1^-1. Thus, consideration of the interaction of APTS with a surface must take into account the presence of both APTS aggregates as well as APTS monomers. Received: 16 August 1996 Accepted: 26 September 1996