Peripherally Monomial-Preserving Maps between Uniform Algebras

Let and be uniform algebras and p(z,w) = z^mwⁿ a twovariable monomial. We characterize maps T from certain subsets of into such that holds for all f and g in the domain of T; peripherally monomial-preserving maps. Furthermore and are proved to be isometrical isomorphic as Banach algebras. If the greatest common divisor of m and n is 1, then T is extended to an isometrical linear isomorphism; a weighted composition operator. An example of peripherally monomial-preserving surjections between uniform algebras which is not linear, nor multiplicative, nor injective is given when the greatest common divisor is strictly greater than 1. The first, third and fourth authors were partly supported by the Grantsin-Aid for Scientific Research, The Ministry of Education, Science, Sports and Culture, Japan.     

Measurement of the group refractive index of air by two-wavelength interferometry

The group refractive index of air at 3.44 μm is directly measured with an accuracy of 2 × 10^-7 using two-wavelength simultaneous interferometry with a 3.51- and 3.37-μm simultaneous operation He-Xe laser.     

Elastic-constant measurements in solid argon at the melting point

The velocities of ultrasonic waves have been measured in solidified argon in the pressure range up to 6 kb (600 MPa). Shear wave velocities could be measured to temperatures very close to the melting point, such that both liquid and solid phases coexisted, $\text{(T?T}{}_{\mathrm{<mtext>m</mtext>}}\text{)}\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{<10}{}^{-5}$. The measurements show that neither the shear velocity tends to zero nor its derivative with temperature tends to -8 as T→T_m.     

Selective oxidation of hydroxy groups of phenylthio and phenylseleno alcohols

Various kinds of alcohols bearing phenylthio or phenylseleno moiety were converted into the corresponding carbonyl compounds in good to excellent yields by treating with dimesityl diselenide and $\text{tert}$-butyl hydroperoxide.     

Entire Solutions with Merging Fronts to Reaction–Diffusion Equations

We deal with a reaction–diffusion equation u _t = u _xx + f(u) which has two stable constant equilibria, u = 0, 1 and a monotone increasing traveling front solution u = φ(x + ct) (c > 0) connecting those equilibria. Suppose that u = a (0 < a < 1) is an unstable equilibrium and that the equation allows monotone increasing traveling front solutions u = ψ₁(x + c ₁ t) (c ₁ < 0) and ψ₂(x + c ₂ t) (c ₂ > 0) connecting u = 0 with u = a and u = a with u = 1, respectively. We call by an entire solution a classical solution which is defined for all . We prove that there exists an entire solution such that for t≈ − ∞ it behaves as two fronts ψ₁(x + c ₁ t) and ψ₂(x + c ₂ t) on the left and right x-axes, respectively, while it converges to φ(x + ct) as t→∞. In addition, if c > − c ₁, we show the existence of an entire solution which behaves as ψ₁( − x + c ₁ t) in and φ(x + ct) in for t≈ − ∞.     

Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Multiatomic step formation on GaAs(001) vicinal surfaces during thermal treatment

We observed the surface morphology of vicinal GaAs(001) after thermal treatment in AsH₃/H₂ atmosphere by atomic force microscopy (AFM). Clear multiatomic steps were formed under the high temperature thermal treatment. Next, we investigated the mechanism of step bunching during thermal treatment by two experiments from the view point of Ga atom evaporation. One is the selective thermal treatment using a partially masked GaAs wafer, and the evaporation amount of Ga atoms was estimated by AFM. The other is the investigation of photoluminescence (PL) peak energy shifts for AlGaAs/GaAs single quantum wells with a thermal treatment process at the top of the GaAs quantum well layer, compared to those without thermal treatment. These results indicate that the evaporation hardly occurs during the thermal treatment process. Therefore, step bunching phenomena on GaAs(001) vicinal surfaces during thermal treatment are probably caused by migration of the atoms detached from upside steps and their re-incorporation to downside steps.     

Rheological properties of poly(vinyl chloride)/plasticizer systems—relation between sol–gel transition and elongational viscosity

Poly(vinyl chloride) (PVC)/di-isononyl phthalate systems with PVC content of 45.5 (PVC8) and 70.4 wt% (PVC6) were prepared by a hot roller at 150 °C and press molded at 180 °C. The dynamic viscoelasticity and elongational viscosity of PVC8 and PVC6 were measured in the temperature range from 150 to 220 °C. We have found that the storage and loss shear moduli, G′ and G″, of PVC8 and PVC6 exhibited the power-law dependence on the angular frequency ω at 190 and 210 °C, respectively. Correspondingly, the tan δ values did not depend on ω. These temperatures indicate the critical gel temperature T _gel of each system. The critical relaxation exponent n obtained from these data was 0.75 irrespective of PVC content, which was in agreement with the n values reported previously for the low PVC concentration samples. These results suggest that the PVC gels of different plasticizer content have a similar fractal structure. Below T _gel, the gradual melting of the PVC crystallites takes place with elevating temperature, and above T _gel, a densely connected network throughout the whole system disappears. Correspondingly, the elongational viscosity behavior of PVC8 and PVC6 exhibited strong strain hardening below T _gel, although it did not show any strain hardening above T _gel. These changes in rheological behavior are attributed to the gradual melting of the PVC crystallites worked as the cross-linking domains in this physical gel, thereby inapplicability of the of time–temperature superposition for PVC/plasticizer systems.