The initial value problem for some hyperbolic‐dispersive system

We consider the initial value problem for some nonlinear hyperbolic‐dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well‐posedness for this system. We also discuss the extension of our results to more general hyperbolic‐dispersive system. Copyright © 2011 John Wiley & Sons, Ltd.     

Molecular weight between entanglements for linear d-glucans

Dynamic viscoelasticity measurements were carried out for concentrated solutions of linear d-glucans in BmimCl to examine the effect of the linkage between repeating units of glucose on the rheological properties. The values of molecular weight between entanglements (M _e) were determined for four d-glucans: curdlan, pullulan, cellulose, and amylose. From the concentration dependence of M _e, the value of M _e in the molten state (M _e,melt) for each d-glucan was estimated as a material constant. The order of M _e,melt became cellulose?<?pullulan?<?curdlan?<?amylose, indicating that the linkage is actually influential in M _e,melt for the linear d-glucans. The relationship between M _e,melt and the molecular structure of the d-glucans were discussed assuming that the values of M _e,melt for the d-glucans primarily reflect the chain stiffness such as the characteristic ratio C _∞ on the analogy of synthetic polymers. Although the trend was not so clear, it was shown that N _unit is a decreasing function of C _∞ .     

Coordination of methyl coenzyme M and coenzyme M at divalent and trivalent nickel cyclams: model studies of methyl coenzyme M reductase active site

Divalent and trivalent nickel complexes of 1,4,8,11-tetraazacyclotetradecane, denoted as cyclam hereafter, coordinated by methyl coenzyme M (MeSCoM(-)) and coenzyme M (HSCoM(-)) have been synthesized in the course our model studies of methyl coenzyme M reductase (MCR). The divalent nickel complexes Ni(cyclam)(RSCoM)(2) (R = Me, H) have two trans-disposed RSCoM(-) ligands at the nickel(II) center as sulfonates, and thus, the nickels have an octahedral coordination. The SCoM(2-) adduct Ni(cyclam)(SCoM) was also synthesized, in which the SCoM(2-) ligand chelates the nickel via the thiolate sulfur and a sulfonate oxygen. The trivalent MeSCoM adduct [Ni(cyclam)(MeSCoM)(2)](OTf) was synthesized by treatment of [Ni(cyclam)(NCCH(3))(2)](OTf)(3) with ((n)Bu(4)N)[MeSCoM]. A similar reaction with ((n)Bu(4)N)[HSCoM] did not afford the corresponding trivalent HSCoM(-) adduct, but rather the divalent nickel complex polymer [-Ni(II)(cyclam)(CoMSSCoM)-](n) was obtained, in which the terminal thiol of HSCoM(-) was oxidized to the disulfide (CoMSSCoM)(2-) by the Ni(III) center.     

Indium(III) triflate-catalyzed reaction of 2-carbomethoxycyclobutanone with nitrones

2-Carbomethoxycyclobutanone reacted with N-phenyl-C-arylnitrones to afford methyl 5-oxo-2-[aryl(phenylamino)methyl]tetrahydrofuran-2-carboxylates by the catalysis of indium(III) triflate in the presence of magnesium sulfate.     

Intramolecular [2+2] cycloaddition of homoallylketenes to bicyclo[2.1.1]hexan-5-ones

Intramolecular [2+2] cycloaddition of γ,δ-unsaturated ketenes derived from hex-5-enoyl chloride derivatives gave bicyclo[2.1.1]hexan-5-ones with complete regioselectivity.     

Titanium(IV) chloride-mediated ring cleavage and Michael addition of 3,3-dialkylcyclobutanones and 3-[(trimethylsilyl)methyl]-cyclobutanones

β'-Chloro and β',γ'-unsaturated trichlorotitanium enolates, which were formed in situ by titanium(IV) chloride-mediated ring cleavage of 3,3-dialkylcyclobutanones and 3-[(trimethylsilyl)methyl]cyclobutanones, reacted with enones to give Michael adducts with keeping a labile β'-chloro or β',γ'-unsaturated group.     

Uniaxial elongational viscosity of PS/a small amount of UHMW-PS blends

A series of polystyrene (PS) and a small amount of ultra high molecular weight (UHMW) PS blends have been prepared by using tetrahydrofuran (THF). Matrix PS has an M_w of 423,000 (M_w/M_n= 2.36) and UHMW-PS has either an M_w of 3,220,000 (M_w/M_n= 1.05) or 15,400,000 (M_w/M_n=1.30) in the range of concentration from 0 wt% to 1.5 wt%. The influence of a small amount of UHMW on dynamic viscoelasticity was investigated. At the frequency lower than 0.001 rad/s, the enhancement of G′ was observed by the incorporation of a small amount of UHMW. And the degree of enhancement was in the order of M_w of UHMW and its concentration. The measurement of uniaxial elongational viscosity for the blends was performed and the effects of UHMW on strain-hardening properties were analyzed at equal strain-rate conditions. The concentration of UHMW where the strain-hardening becomes substantially stronger was determined. To get more insight into the cause of enhancement of strain-hardening at a certain concentration, the damping function from step-shear stress relaxation was measured. The influence of a small amount of UHMW on the damping function was found to be small. It was interpreted, from time- and strain-dependency points, that the enhancement of strain-hardening by a small amount of UHMW was governed by the long relaxation time. Received: 6 September 2000 Accepted: 11 January 2001     

Surface contouring by phase-shifting digital holography

Surface contouring by phase-shifting digital holography is proposed that provides surface height from a change of reconstructed object phases due to the tilt of object illumination. Surface height from a reference plane is directly obtained from the phase change. Its sensitivity depends on the tilt angle as well as on the initial incident angle. By proper selection of the angles we can derive surface height without phase unwrapping. The sensitivity can be enhanced by increasing the tilt angle. Then we need phase unwrapping that is sensitive to noise due to laser speckles in the reconstructed images. This noise could be suppressed by selecting phase values at points of the maximum product of amplitudes before and after the illumination change in the course of data reduction from 1024×1024 to 512×512 and by selecting paths for phase unwrapping by looking for the intensity maximum. The observed height resolution is 20 μm. Effects of numerical focusing have also been investigated. The present method has the same sensitivity as the fringe projection method, but it has larger measurement depth and is also applicable to the deformation measurement with the same arrangement.     

Zwitterionic Mixed Valence: Internalizing Counteranions into a Biferrocenium Framework toward Molecular Expression of Half-Cells in Quantum Cellular Automata

Realization of molecular quantum cellular automata (QCA), a promising architecture for molecular computing through current-free processes, requires improved understanding and application of mixed-valence (MV) molecules. In this report, we present an electrostatic approach to creating MV subspecies through internalizing opposite charges in close proximity to MV ionic moieties. This approach is demonstrated by unsymmetrically attaching a charge-responsive boron substituent to a well-known organometallic MV complex, biferrocenium. Guest anions (CN⁻ and F⁻) bind to the Lewis acidic boron center, leading to unusual blue-shifts of the intervalence charge-transfer (IVCT) bands. To the best of our knowledge, this is the first reported example of a zwitterionic MV series in which the degree of positive charge delocalization can be varied by changing the bound anions, and serves to clarify the interplay between IVCT parameters. The key underlying factor is the variable zero-level energy difference in the MV states. This work provides new insight into imbuing MV molecules with external charge-responsiveness, a prerequisite of molecular QCA techniques.     

Real-time surface shape measurement by an active interferometer

We have succeeded in video rate analysis of fringes stabilized by an active interferometer placed outside optical benches. The interferometer uses the closed loop control of injection current of a laser diode to compensate for fringe movement that is detected by a spatial filtering detector. A video image of the locked fringes with tilt is supplied to the real-time fringe analyzer that delivers unwrapped phase distribution from the three phase shifted fringes generated by the electronic moiré method. For a concave mirror of 130 mm diameter placed on a wooden desk we observed the repeatability of λ/60 for P-V surface error of λ/5.