Equality cases in matrix norm inequalities of golden-thompson type

The equality cases in several matrix norm (trace) inequalities are characterized. Norm inequalities of Golden-Thompson type and of its complement type are treated as well as a logarithmic trace inequality and norm inequalities for matrix exponentials.     

Synthesis and chiroptical properties of optically active poly(ethynylcarbazole) derivatives: Substituent effect on the helix formation

Novel chiral acetylene monomers containing carbazole, 2‐ethynyl‐9‐[(S)‐2‐methylbutoxycarbonyl]carbazole ( 1 ), 3‐ethynyl‐9‐[(S)‐2‐methylbutoxycarbonyl]carbazole ( 2 ), 2‐ethynyl‐9‐[(S)‐2‐methylbutyl]carbazole ( 3 ), and 2‐ethynyl‐9‐[(S)‐4‐methylhexyl]carbazole ( 4 ) were synthesized and polymerized with [(nbd)RhCl]₂? Et₃N. The corresponding polyacetylenes with number‐average molecular weights ranging from 68,700 to 310,000 were obtained in good yields. Poly( 1 ) exhibited a large specific rotation and an intense Cotton effect in toluene, indicating that it formed a helix with predominantly one‐handed screw sense, while the other three polymers showed no evidence for taking a helical structure. Poly( 1 ) largely decreased the CD intensity upon heating from ?10 to 60 °C. Poly( 1 ) showed a Cotton effect in film state in a manner similar to solution state. No chiral amplification was observed in the copolymerization of 1 with achiral 2‐ethynyl‐9‐tert‐butoxycarbonylcarbazole ( 5 ). © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4450–4458, 2007     

Synthesis and properties of poly(phenylacetylenes) having two polar groups or one cyclic polar group on the phenyl ring

Phenylacetylene (PA) derivatives having two polar groups (ester, 2a – d ; amide, 4) or one cyclic polar group (imide, 5a – c ) were polymerized using (nbd)Rh⁺[(η⁶‐C₆H₅)B^?(C₆H₅)₃] catalyst to afford high molecular weight polymers (～1 × 10⁶ – 4 × 10⁶). The hydrolysis of ester‐containing poly(PA), poly( 2a) , provided poly(3,4‐dicarboxyPA) [poly ( 3 )], which could not be obtained directly by the polymerization of the corresponding monomer. The solubility properties of the present polymers were different from those of poly(PA) having no polar group; that is, poly( 2a )–poly( 2d ) dissolved in ethyl acetate and poly( 4 ) dissolved in N,N‐dimethylformamide, while poly(PA) was insoluble in such solvents. Ester‐group‐containing polymers [poly( 2a )–poly( 2d )] afforded free‐standing membranes by casting from THF solutions. The membrane of poly( 2a ) showed high carbon dioxide permselectivity against nitrogen (PCO₂/PN₂ = 62). © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5943–5953, 2006     

Formation Thermodynamics of Binary and Ternary Lanthanide(III) Complexes with 1,10-Phenanthroline and Chloride in N,N-Dimethylformamide

Formation thermodynamics of binary and ternary lanthanide(III) (Ln = La, Ce, Nd, Eu, Gd, Dy, Tm, Lu) complexes with 1,10-phenanthroline (phen) and the chloride ion have been studied by titration calorimetry and spectrophotometry in N,N-dimethyl-formamide (DMF) containing 0.2 mol-dm^–3 (C₂H₅)₄NClO₄ as a constant ionic medium at 25°C. In the binary system with 1,10-phenanthroline, the Ln(phen)³⁺ complex is formed for all the lanthanide(III) ions examined. The reaction enthalpy and entropy values for the formation of Ln(phen)³⁺ decrease in the order La > Ce > Nd, then increase in the order Nd < Eu < Gd < Dy, and again decrease in the order Dy > Tm > Lu. The variation is explained in terms of the coordination structure of Ln(phen)³⁺ that changes from eight to seven coordination with decreasing ionic radius of the metal ion. In the ternary Ln³⁺-Cl^–-phen system, the formation of LnCl(phen)²⁺, LnCl₂(phen)⁺, and LnCl₃(phen) was established for cerium(III), neodymium(III), and thulium(III), and their formation constants, enthalpies, and entropies were obtained. The enthalpy and entropy values are also discussed from the structural point of view.     

Enrichment of surfactant from its aqueous solution using ultrasonic atomization

Dilute aqueous solutions of dodecyl-benzenesulfonic acid sodium salt (DBS-Na) and polyoxyethylenenonylphenyl ethers (PONPEs) were ultrasonically atomized. The surfactants were concentrated in collected mist droplets. The enrichment ratio increased with decreasing surfactant concentration. Depending on the surfactant’s molecular weight and affinity to water, different enrichment ratio was observed in the range of low feed concentrations. For anionic surfactant, DBS-Na, the enrichment ratio was significantly improved by KCl addition and a peak appeared on the plot of the ratio against KCl concentration. Addition of NaCl or CaCl₂ · 2H₂O to the surfactant solution also enhanced the enrichment ratio; however, the effect was relatively small. Such behaviors of the ratio were interpreted as enhanced interfacial adsorption of the surfactant and a lack of supply of surfactant monomers from liquid bulk because of slow breaking of surfactant micelles. Time required for collecting an amount of mist was also observed. Among the three salt systems, the time for KCl system was twice as long as others. This fact suggested that the formation of smaller droplets in KCl system.     

Studies on vocal fold injection and changes in pitch associated with alcohol intake

The current study was carried out with particular emphasis on the association between phonetic function tests and alterations in the appearance of the hypopharyngeal and laryngeal mucosa, such as capillary dilatation, edema, and vocal fold injection after alcohol intake. The results demonstrated the occurrence of previously unrecognized pathophysiological changes associated with synchronous phonetic functions in the vocal pathway after alcohol intake. Serum ethanol and aldehyde concentration levels were evaluated hourly for 2.5 h after ingestion of alcohol. When an electronystagmogram showed the typical pattern of alcohol intake, the study was initiated. Occasionally, rhinography was performed on subjects complaining of a stuffy nose after alcohol intake.     

Curved Ferroelectric Liquid Crystal Matrix Displays Driven by Field-Sequential-Color and Active-Matrix Techniques

This paper describes a curved field-sequential-color matrix display using fast-response ferroelectric liquid crystal. Black matrix and transparent electrode patterns were formed on a thin plastic substrate by a transfer method from a glass substrate. While a composite film of liquid crystal and micro-polymers of walls and fibers was formed between the flexible substrates by printing, laminating and curing processes of a solution of monomers and liquid crystal, the mechanical stability was enhanced by use of multi-functional monomers to form large display panels. The image pixels of the matrix panel were driven by an active matrix scheme using an external switch transistor array at a frequency of 180 Hz for intermittent three-primary-color backlight illumination. The flexible A4-paper-sized color display with 24 × 16 pixels and 60 Hz field frequency was demonstrated by illuminating it with sequential three-primary-color lights from light-emitting diodes of the backlight. Our display system is useful in various information displays because of its freedom of setting and location.     

Density matrix and eigenstates for an excess electron in water

We extend the molecular theory of the solvated electrons [Chandler, Singh and Richardson, J. Chem. Phys. 81, 1975 (1984)] to calculate the density matrix for an excess electron in water. Using this density matrix, the numerically obtained solvent induced interaction [Miura and Hirata, J. Phys. Chem. 98, 9649 (1994)] and our developed method [Sethia, Sanyal and Singh, J. Chem. Phys. 93, 7268 (1990)], we have calculated the eigenstates of the electron in water. These results show that the excees electron in water behaves almost like a free particle with effective mass m* in a constant potential well.     

Measurement on Spot Size Dependence of Dense WDM Dielectric Multilayer Filters

We present the spot size dependence of dielectric multilayer filters for use in dense WDM systems. We found large dependences of filter performances on the spot size and the incident angle of input light, which should be important for miniaturizing multi-channel add/drop filters.     

Light Diffraction of Aligned Polymer Fibers Periodically Dispersed by Phase Separation of Liquid Crystal and Polymer

We have confirmed light diffraction of aligned polymer fibers obtained by a phase separation of an anisotropic-phase solution of liquid crystal and polymer. He—Ne laser light passing through the polymer fibers was scattered in the axis vertical to the fibers, and had two peaks of light intensity symmetrical to the center of the transmitting laser spot. The two peaks were found to be caused by light diffraction due to the periodic polymer-fiber dispersion because the peaks corresponded to values calculated by intervals between the fibers. The periodical fiber networks are considered to be formed by anisotropic spinodal decomposition. This effect can be used to measure the dispersion order of the polymer fibers. © 2004 The Optical Society of Japan