Phase Measurement Algorithm in Wavelength Scanned Fizeau Interferometer

Wavelength scanned interferometry allows the simultaneous measurement of top surface shape and optical thickness variation of a transparent object consisting of several parallel surfaces. Interference signals from these surfaces can be separated in frequency space, and their phases are detected by discrete Fourier analysis. However, these signal frequencies are shifted from the detection frequency by the refractive index dispersion of the object and a nonlinearity of the wavelength scanning. The Fourier analysis is sensitive to the detuning of the signal frequency and suffers from the multiple-beam interference noise. Conventional error-compensating algorithms cannot be applied to an object consisting of more than three reflecting surfaces. We derive a new 2N-1 sample error-compensating algorithm, which allows the phase detection of any order of harmonic frequency among the interference signals. The new algorithm suppresses the effect of signal frequency detuning as well as the multiple-beam interference noise and can be applied to the measurement of complex objects consisting of more than three reflecting surfaces.     

Synthesis of spherical and hemispherical sugar‐containing poly(ornithine) dendrimers

A novel sugar‐containing poly(ornithine) dendrimer is synthesized for possible antigen delivery and related applications. The dendrimer contains an ornithine dendron as interior scaffolding and oligosaccharides on the periphery, which provide an attachment site for a peptide antigen. Maltose or lactose is bound to both hemispherical and spherical poly(ornithine) dendrimer generation 3 (G3) by reductive amination between its reducing end and the peripheral amino group of the dendrimer using a borane‐pyridine complex in a buffer solution at 50 °C. The degree of substitution of sugar is changed by varying the molar ratio of sugar to dendrimer. When the surface of spherical poly(ornithine) dendrimer G3 is modified by binding β‐alanine to the 16 amino groups, highly substituted maltose‐ or lactose‐β‐alanine‐poly(ornithine) dendrimer G3 is obtained in high yield after 7 days of reaction. The structures of these sugar‐containing dendrimers are characterized by NMR and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry analyses. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1400–1414, 2004     

A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

Macromolecular synthesis from saccharic lactones. Ring-opening polyaddition of D-glucaro- and D-mannaro-1,4:6,3-dilactones with alkylenediamines

Ring-opening polyaddition of a saccharic acid dilactone prepared from D-glucose, D-glucaro-1,4 : 6,3-dilactone, with several alkylenediamines proceeded at room temperature with no catalyst. The resulting new polyamides carrying many pendant hydroxyl groups, poly(alkylene D-glucaramide)s, were more amorphous and hydrophilic than the corresponding nylons having no hydroxyl groups, and were hydrolyzed more easily than the latter in an acidic condition. The ring-opening ability of D-mannaro-1,4:6,3-dilactone, which was another saccharic acid dilactone obtained from D-mannitol, was found to be lower than that of the D-glucaric analogue. © 1993 John Wiley & Sons, Inc.     

Intrinsic field theory of chemical reactions

An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

Pressure response of Raman spectra of water and its implication to the change in hydrogen bond interaction

In situ Raman spectroscopic measurements of water in the region of OH vibration were conducted up to 0.4 GPa at 23 and 52 degrees C. The frequencies of the decomposed OH stretching bands initially decreased with increasing pressure, reached a minimum at 0.15 GPa and increased up to 0.3 GPa and then decreased, which corresponds to the variations of the strength of hydrogen bonding. This variation was observed at 23 degrees C, but not at 52 degrees C, which suggests a change in pressure dependence on the hydrogen bond interaction between these two temperatures. Based on the equilibration model between hydrogen-bonded and nonhydrogen-bonded molecules, the present experimental results indicate that the pressure variation of the viscosity depends on the ratio of hydrogen-bonded molecules, rather than the strength of hydrogen bonding between molecules.     

Complexation of a hydrophobic thiazorylazophenol with Ni2+ at sodium dodecylsulfate micellar surface

Complexation of thiazorylazododecylphenol (TADP) with Ni2+ at the surface of sodium dodecylsulfate (SDS) micelles has been spectrophotometrically studied. Complicated spectral changes are analyzed by a factor and multivariate analysis, which implies the formation of [TDAP(OH-)Ni]0 as well as a simple 1:1 complex of Ni2+ with TDAP at the micellar interface. All of the equilibrium constants required to describe this system are substantially affected by electrolyte concentrations. Coexistent electrolytes vary the surface potential of the micelle, and in turn influence the equilibria taking place on the micellar surface. The electrostatic potential estimated based on the equilibrium shifts is more negative than that calculated according to Poisson-Boltzmann theory, which simply involves electrostatic effects. This disagreement is possibly caused by different aqueous environments around the micelle from bulk solution, which also facilitate the formation of unusual complex such as [TDAP(OH-)Ni]0.