Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. IV

Part IV of this series consists of two complementary subparts devoted to attain the following two goals: (i) By shifting from the previous setting of the Banach algebra B (ℬ︁)= B (ℬ︁, ℬ︁) to a broader setting of the space B (X, ℬ︁) of all bounded linear operators from a normed space X to a Banach space ℬ︁, we extend our previous theoretical framework to incorporate part of the theory of additive correlation involving the Asymptotic Linearity Theorems, which have been developed for a study of correlation between structure and properties in molecules having many identical moieties, especially in macromolecules having repeating units. (ii) By reverting our focus to the special algebra B (ℋ︁) with ℋ︁ being a Hilbert space, we develop a theorem which is useful for a structural analysis of spectral symmetry of linear operators representing physico-chemical network systems. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67 : 57–69, 1998     

Cyclotron resonance in (GaAs)n/(AlAs)n superlattices under ultra-high magnetic fields

We present a review on recent study of the type I to type II transition in short-period superlattices (SLs) of GaAs/AlAs by means of cyclotron resonance (CR) in pulsed high magnetic fields. The behavior of CR varies depending on the thickness of the GaAs and AlAs layers. In CR of (GaAs)_n/(AlAs)_n, the resonance peak at the X minima was observed in the type II regime for n smaller than 14, whereas the resonance at the Γ point was observed for n>15. We estimated electron masses on X and Γ point in the SLs by using the empirical sp³ tight-binding method including second-nearest-neighbor interaction. These calculations have shown good agreement with the experimental results. Moreover, it was found that the angular dependence of the CR peak position does not obey the simple cosine dependence due to the subband mixing in high magnetic fields. From the angular dependence in the SLs, the longitudinal and transverses electron masses of AlAs at the X point were deduced to be m_t=0.21m₀ and m_l=1.04m₀, respectively.     

Monte Carlo Simulation of Near Infrared Reflectance Spectroscopy in the Wavelength Range from 1000 nm to 1900 nm

We have calculated the characteristics of reflected near infrared light, which is incident on the skin surface, scattered in the skin tissue and detected, in the wavelength range from 1000 nm to 1900 nm. We have used a Monte Carlo method to calculate the propagation path, the average photon visit depth, the average photon path length, etc. for the cases of short source-detector distances, to which the isotropic scattering approximation cannot be applied. An experiment to validate the simulation results was also conducted using a liquid phantom.     

Nonexistence theorem except the out-of-phase and in-phase solutions in the coupled van der Pol equation system

We consider a coupled van der Pol equation system. Our coupled system consists of two van der Pol equations that are connected with each other by linear terms. We assume that two distinctive solutions (out-of-phase and in-phase solutions) exist in the dynamical system of coupled equations and give answers to some problems.     

Preliminary considerations towards a theoretical foundation of the zero point energy additivity rules

A new method is presented for the analysis of zero point energies of linear chains and their generalized analogues. The aspect of form and topological considerations play a fundamental role in the method.     

Polycyclic N-heterocyclic compounds. XLIV. Synthesis of the novel B,D-Dihomo-11,13,15-triazasteroidal skeleton and their effect on reserpine-induced hypothermia and inhibitory activity on platelet aggregation

Synthesis of benzo[3,4]cyclohepta[1,2-e]pyrimido[1,2-c]pyrimidines, corresponding to the B,D-dihomo-11,13,15-triazasteroidal skeleton as a novel ring system is described. Their effects on reserpine-induced hypothermia in mice and inhibitory activity against collagen-induced platelet aggregation were also investigated.     

Asymmetric oxidation of 1,2-diols using N-bromosuccinimide in the presence of chiral copper catalyst

Asymmetric oxidation of 1,2-diols using N-bromosuccinimide (NBS) in the presence of copper(II) triflate and (R,R)-Ph-BOX has been exploited. This oxidation was applicable to asymmetric desymmetrization of meso-hydrobenzoin and kinetic resolution of dl-hydrobenzoin and racemic-cycloalkane-cis-1,2-diols to afford optically active α-ketoalcohols with good to high enantiomeric excess.     

The Asymptotic Linearity Theorem for the study of additivity problems of the zero-point vibrational energy of hydrocarbons and the total pi-electron energy of alternant hydrocarbons

By using the approach via the aspect of form and general topology, as well as basic notions of abstract algebra, a theoretical framework has been developed which elucidates the mechanism of the additivity relationships between structure and properties in molecules having many identical moieties. The main theorem, the Asymptotic Linearity Theorem (ALT), together with an auxiliary theorem, the a Independence Theorem, implies that the zero-point vibrational energy (or total pi-electron energy for the case of alternant hydrocarbons)E _n of a linearly extended system B-A _n -B having n repeating identical moieties has the asymptotic expansionE _n = n + +o(1) as n , where is independent of the choice of the end moieties B and B. The theorem being formulated in a general context, the actual implication of the ALT is much broader than the above two applications would indicate.On leave from: Institute for Fundamental Chemistry, 34-4 Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 606, Japan.     

Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution VII

The present Part VII of this series of articles is a direct extension of Part VI, where (1) fundamental methodology in the repeat space theory (RST) and (2) frontier electron theory of reactivity indices were theoretically linked. This part presents an estimate of the size of the regular index set, which was a central notion in Part VI, and two new theorems that are simpler and more powerful than the main theorem in Part VI. The main theorem in this part enables one to globally contextualize the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in Part V) and the μ Existence Theorem (derived from the main theorem in Part VI) into the star algebra structure of the generalized repeat space ??_r(q, d). © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004