Zeta functions of<Emphasis Type="Italic">q</Emphasis>-perfect numbers

We introduce a notion ofq-analogue of the perfect numbers. We also define a new zeta function which we call a zeta function ofq-perfect numbers. In this paper, the properties of theq-perfect numbers and the zeta functions are studied. Especially, we determine theq-perfect numbers whenq is a root of unity.     

Radical deoxygenation of hydroxyl groups via phosphites

A highly efficient, two-step sequence method for the deoxygenation of hydroxyl groups has been developed. The method involves the preparation of the 2-(2-iodophenyl)ethyl methyl phosphite derivative of an alcohol using methyl dichlorophosphite and 2-(2-iodophenyl)ethanol. Treatment of the phosphite intermediate with (n-Bu)3SnH/AIBN in refluxing benzene cleanly produces the deoxygenation product of the original alcohol.     

Remote asymmetric induction with vinylketene silyl n,o-acetal

A highly regio- and diastereoselective TiCl4-mediated vinylogous Mukaiyama aldol reaction using the chiral vinylketene silyl N,O-acetal has been developed. The present vinylogous Mukaiyama aldol reaction provides a unique and effective means of controlling remote asymmetric induction. The methyl group at the alpha-position is important in achieving a high level of stereoselectivity. From a synthetic point of view, this methodology can provide a one-step construction of delta-hydroxy-alpha,gamma-dimethyl-alpha,beta-unsaturated carbonyl unit that is seen in many natural polyketide products.     

Template polymerization of columnar architectures based on the salts of a carboxylic acid and 2-amino alcohols: application to the molecular recognition of 2-amino alcohols

The salts of trialkoxybenzoic acids and 2-amino alcohols showed a columnar liquid crystalline phase; in the case of the salt of a polymerizable acid and norephedrine, the photopolymerization proceeded efficiently in the liquid crystalline state, and the resultant solid adsorbed 2-amino alcohols size, regio-, and enantio-selectively.     

On a p-Local Geometry Associated with a Complex of Non-Trivial p-Subgroups

Let D be a complex of non-trivial p-subgroups of a finite groupG, closed under G-conjugation. In this paper, a p-local geometry^p(G; D) is introduced for G associated with the complex D. Thehomotopy equivalence between ^p(G; D) and D is also studied.2000 Mathematics Subject Classification 20E15, 51E24.     

Double-Modulation Submillimeter-Wave Spectroscopy of HOC(+) in the nu(2) Excited Vibrational State

The submillimeter-wave rotational transitions of HOC(+) in the nu(2) excited state are first detected using the double-modulation method, and the precise transition frequencies and the much improved molecular constants are obtained. The measurements of the ground state HOC(+) and DOC(+) submillimeter-wave lines are extended up to the 840-GHz region. It is found that the higher order centrifugal distortion constant, H, is necessary to fit the observed transition frequencies to the experimental accuracy. Copyright 2000 Academic Press.     

Exciton localization behaviour in different well width undoped GaN/Al0.07Ga0.93N nanostructures

We report results from optical spectroscopy such as photoluminescence (PL) and time resolved photo-luminescence (TRPL) techniques from different well width MOCVD grown GaN/Al_0.07Ga_0.93N MQW samples. There is evidence of localization at low temperature in all samples. The decay time of all samples becomes non-exponential when the detection energy is increased with respect to the peak of the emission. Localization of carriers (excitons) is demonstrated by the “S-shape” dependences of the PL peak energies on the temperature. The time-resolved PL spectra of the 3-nm well multi quantum wells reveal that the spectral peak position shifts toward lower energies as the decay time increases and becomes red-shifted at longer decay times. There is a gradient in the PL decay time across the emission peak profile, so that the PL process at low temperatures is a free electron-localized hole transition.