Carbon-13 NMR studies of the biologically active nor-diterpenoid dilactones from Podocarpus plants

Carbon-13 NMR signals of the biologically active norditerpenoid dilactones from Podocarpus plants were fully assigned by using selective ¹H decoupling, coupling constants (²J_CH), spin-lattice relaxation times (T₁) and correlation of the spectra of more than thirty dilactone congeners. The spectra of five nagilactones, B, C, D, E and F, which constitute representative members of three major structural types of the dilactones: (A) 8:14, 9:11-dienolide (α-pyrone) type, (B) 7α:8α-epoxy-9:11-enolide type, and (C) 7:8,9:11-dienolide type, were extensively analysed. Some characteristic steric interactions for the substituents on the ring system can be demonstrated from the spectral properties.     

Hierarchy of the Selberg Zeta Functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Mathematics Subject Classifications (2000). Primary 11M36, Secondary 33B15     

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.     

Bright band gap photoluminescence from unprocessed single-walled carbon nanotubes

Unprocessed single-walled carbon nanotubes suspended in air at room temperature emit bright, sharply peaked band gap photoluminescence. This is in contrast with measurements taken from nanotubes lying on the flat surface for which no luminescence was detected. Each individual nanotube has a luminescence peak of similar linewidth ( approximately 13 meV), with different species emitting at various different wavelengths spanning at least 1.0 to 1.6 microm. A strong enhancement of photoluminescence intensity is observed when the excitation wavelength is resonant with the second Van Hove singularity, unambiguously confirming the origin of the photoluminescence.     

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.