Complexation of poly(vinyl alcohol)–congo red aqueous solutions. 3. Dynamic light scattering study

Mesoscopic structures of poly(vinyl alcohol)(SINGLEBOND)Congo red (PVA(SINGLEBOND) CR) complexes in aqueous solutions were investigated in terms of dynamic light scattering (DLS) technique. The intensity-intensity time correlation function, g⁽²⁾(t), was analyzed with an equation including a single and a stretched exponential function. Two diffusion coefficients, D_f (fast) and D_s (slow) were evaluated. D_f was converted to the apparent correlation length, ξ_app, via the mode-mode coupling hypothesis. The estimated ξ_app was insensitive to the sol(SINGLEBOND)to(SINGLEBOND)gel transition but decreased with CR concentration. This change may be related to the electrostatic screening effect. On the other hand, D_s oscillates with increasing CR concentration at a specific PVA concentration range. This explains well the reentrant sol(SINGLEBOND)gel(SINGLEBOND)sol(SINGLEBOND)gel transition behavior observed in the PVA(SINGLEBOND)CR systems. D_s seems to represent the mobility of the PVA(SINGLEBOND)CR complexes, which annihilates at the gel point. © 1996 John Wiley & Sons, Inc.     

Module-based assembly of copper(II) chloranilate compounds: syntheses, crystal structures, and magnetic properties of [[Cu(2)(CA)(terpy)(2)][Cu(CA)(2)]](n)() and [[Cu(2)(CA)(terpy)(2)(dmso)(2)][Cu(CA)(2)(dmso)(2)](EtOH)](n)(H(2)CA = chloranilic acid, terpy = 2,2':6',2' '-terpyridine, dmso = dimethyl sulfoxide)

Two new copper(II) compounds of chloranilate and 2,2':6',2' '-terpyridine have been synthesized, and the structures have been solved by the single-crystal X-ray diffraction method. The crystal structure of [[Cu(2)(CA)(terpy)(2)][Cu(CA)(2)]](n)(1), where H(2)CA = chloranilic acid and terpy = 2,2':6',2' '-terpyridine, consists of two modules, the dimer unit [Cu(2)(CA)(terpy)(2)](2+) and the anionic mononuclear unit [Cu(CA)(2)](2)(-), forming an alternated chain. The chain is stabilized by semicoordinating and additional but efficient secondary bonding interactions. The crystal structure of [[Cu(2)(CA)(terpy)(2)(dmso)(2)][Cu(CA)(2)(dmso)(2)](EtOH)](n)(2), where dmso = dimethyl sulfoxide, consists of solvent molecules and two discrete modules, the dimer unit [Cu(2)(CA)(terpy)(2)(dmso)(2)](2+) and the anionic mononuclear unit [Cu(CA)(2)(dmso)(2)](2)(-). The dimer units form a layer by secondary bonding interactions, and the monomer units and ethanol molecules are introduced between the layers. The magnetic properties of 1 and 2 have been investigated in the temperature range 2.0-300 K. A weak ferromagnetic interaction was observed in 1, J(a) = 2.36 cm(-)(1) and zJ(b) = -0.68 cm(-)(1) while no exchange coupling was observed in 2.     

Numerical Verification Methods for Solutions of the Free Boundary Problem

We propose two methods to enclose the solution of an ordinary free boundary problem. The problem is reformulated as a nonlinear boundary value problem on a fixed interval including an unknown parameter. By appropriately setting a functional space that depends on the finite element approximation, the solution is represented as a fixed point of a compact map. Then, by using the finite element projection with constructive error estimates, a Newton-type verification procedure is derived. In addition, numerical examples confirming the effectiveness of current methods are given.     

Dependence of tracking error characteristics on objective lens shift for in-line-type differential push-pull methods using segmented gratings

In this paper, we present the validity of in-line-type differential push-pull methods using segmented gratings with respect to the radial shift of an objective lens by numerical calculation for the first time. In these differential push-pull methods, the segmented gratings for generating sub spots are divided into two to four regions each with a specific phase value and a width. Tracking error signals are calculated with respect to the objective lens shift under parameter conditions of the widths of the segmented regions. The obtained results show that the grating of the simpler configuration with two regions reveals good compatibility between DVD-R and DVD-RAM compared with those with three or four regions     

Hodge algebra structures on certain rings of invariants and applications

Let B be a commutative ring with identity, m, n, and r be positive integers such that r ≤ min{m, n}, a ₁, …, a _r (resp. b ₁, … b _r ) be integers such that 1 ≤ a ₁< … < a _r ≤ m (resp. 1 ≤ b ₁ < … < b _r < n) and U (resp. V) be the most general m × r (resp. r × n) matrix such that s-minors of first a _s ? 1 rows (resp. b _s ? 1 columns) of U (resp. V) are all zero for s = 1, …, r. We investigate the B-algebra C generated by all the entries of UV and all the r-minors of U and V. We introduce a Hodge algebra structure, to which the discrete Hodge algebra associate is Cohen Macaulay, on C and prove that C is Cohen-Macaulay if so is B. Using this Hodge algebra structure, we show that C is the ring of absolute invariants of a certain group action, compute the divisor class group and the canonical class of C, and give a criterion of Gorenstein property of C in terms of a ₁ ,…, a _r and b ₁…, b _r .     

Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.     

On the sampling conditions for reconstruction of an acoustic field from a finite sound source

A simple and accurate method for the estimation of ultrasonic transducer fields is developed. In the method, the angular spectrum is employed to evaluate the three-dimensional propagation from a measured plane to an arbitrary parallel plane. The implementation uses a discrete convolution that is described in detail. Relative to conventional spatial-frequency representations, the implementation of the angular spectrum method in this paper has the advantage of being free from artifacts, enabling sample spacing to be greater than one half wavelength, using memory efficiently, and interpolating the measured data. The loosened sampling requirement and natural interpolation of the method permit efficient reconstruction of the full three-dimensional acoustic field from a coarse sound pressure measurement on single plane.     

Existence of global decaying solutions to the exterior problem for the Klein–Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity

We prove the existence of global decaying solutions to the exterior problem for the Klein–Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity. To derive the required estimates of solutions we employ a ‘loan’ method.     

Ammonium chiral borate salt catalyzed asymmetric Friedel-Crafts alkylation of indoles with α,β-disubstituted enals

In the presence of a catalytic amount of ammonium chiral borate salt, asymmetric Friedel-Crafts alkylation of indoles with α,β-disubstituted enals proceeded to give the corresponding 1,4-addition products with moderate enantioselectivities.     

Effect of nitriding on grain oriented silicon steel bearing aluminum (the second study)

All kinds of high-permeability GO are manufactured using AlN as the main inhibitor. From a purely metallurgical viewpoint, three types of inhibitor preparation for high-permeability GO have been shown. They include a complete solution without nitriding, a complete precipitation with nitriding and a partial precipitation with nitriding. In this study, another possibility, i.e., a complete solution method with nitriding, was investigated to avoid the extra high-temperature slab reheating and to examine the effect of nitriding on GO bearing Al. This method can also provide the sharp Goss texture, and nitriding is shown to be very useful for changing the inhibitor intensity, depending on the primary grain size.