Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

Band broadening evaluation by back-and-forth capillary electrophoresis

The purpose of this study is to develop a method for precise evaluation of band broadening in capillary electrophoresis. A capillary electrophoresis system with on-column twin detectors is constructed. Back-and-forth electrophoresis permits zones to make a round trip between the twin detectors placed at distant positions on the capillary. The system is capable of eliminating extra-column effects and discriminating between reversible and irreversible band-broadening mechanisms.     

A quantum chemical study of interchain hopping model of negatively charged solitons in polyacetylene

Phonon-assisted interchain hopping of negatively charged solitons in polyacetylene has been studied using a local chemical reaction model CH + CH₄ → CH₄ + CH. Quantum chemical characteristics of the electron transfer process have been analyzed in terms of the dynamic electron density and the mutual polarization moment. The CH stretching vibrational motion of CH₄, which is a local model of the sp³ defect, has been found to play a significant role for the electron transfer. The excitation of the corresponding vibrational mode of the sp³ defect would promote the interchain hopping of the charged soliton. The electron transfer process has also been studied in terms of the “regional” density functional theory. It has been shown that the driving force of the electron transfer is represented by the regional chemical potentials.     

One electron transfer mechanism in the enzymatic oxygenation of sulfoxide to sulfone promoted by a reconstituted system with purified cytochrome p-450

A kinetic study on enzymatic S-oxygenation of sulfoxides to sulfones was carried out by a reconstited system with purified cytochrome P-450. A linear correlation observed between log(Vmax)'s and the one-electron oxidation potentials of sulfoxides suggests that the oxygenation of sulfoxides proceeds via one electron transfer process to the active “oxenoid” intermediate of the enzyme.     

Analysis of flexural wave velocity and vibration mode in thin cylindrical shell

The relationship between the flexural wave velocity and the excited vibration mode of a thin cylindrical shell is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, all of these vibration modes are not excited actually. To estimate the excited vibration mode, the concept of "modified bending stiffness" is introduced, and the influence of each stress component upon the modified bending stiffness is analyzed. The excited mode is theoretically discriminated from the nonexcited mode based on the smallness of this modified bending stiffness. The validity of our theory is confirmed by an excellent agreement between theoretical and experimental results on flexural wave velocity.     

Statistical analysis of fluctuations of froth pressure on perforated plates without downcomers

Statistical properties of fluctuations of pressure drop across the gas–liquid dispersions on the tray were analyzed using a 215 mm dia. three plates column with different trays. Hydrodynamic regimes of the froth were characterized in terms of the statistical properties evaluated. It was proved that the on-line estimation of the flow behavior of the froth was possible on the basis of the pattern recognition of the power spectral density function of the pressure fluctuations. The time-domain stochastic models for fluctuations of the pressure drop were identified so as to be available for its forecast and simulation.     

Quantum Mechanics of the Composite System and Its Subsystems

We revisit the EPR problem and make clear what is a correct comprehension of its problem. When one applies the quantum mechanics correctly, it will be shown that there is no paradox. According to these lines of thought, a quantum teleportation scheme without resort to the von Neumann projection postulate is presented.     

Image reconstruction by using the propagation law of mutual intensity

An imaging method for partially coherent objects is proposed by the aid of the propagation law of mutual intensity, and it can be reduced to principles used in holography and radio astronomy if the coherence reaches the both extremes, i.e., perfect coherence and complete incoherence, respectively.