A birational construction of projective compactifications of ℂ3 with second Betti number equal to onewith second Betti number equal to one

We give an explicit construction of all projective compactifications of ℂ³ with second Betti number equal to one. Dedicated to K.-N. Hatsue Entrata in Redazione il 30 novembre 1998.     

Coupling of numerical Green''s matrix and boundary integral equations for the elastodynamic analysis of inhomogeneous bodies on an elastic half-space

A coupled system of integral equations (of the domain and boundary types) is formulated for the elastodynamic response analysis of a locally inhomogeneous body on a homogeneous elastic half-space. The method uses the fundamental solution for homogeneous elastostatics in the inhomogeneous domain owing to the lack of a fundamental solution in inhomogeneous elastodynamics.

The integral representation of displacements in the inhomogeneous domain is formulated with the help of this elastostatic fundamental solution by considering the term induced by the inhomogeneity of materials and the acceleration term as the body force term. Then the Green's matrix is obtained numerically from this integral representation and combined with the ordinary boundary integral equations, which are valid in the exterior homogeneous half-space.

Some numerical examples show the efficiency and the versatility of this coupled method.     

Singular Fano compactifications of (I)

In this paper we study the singular Fano compactifications of with small Gorenstein singularities and determine the structure of such a compactification in the case of the Fano index r 2.Mathematics Subject Classification (2000): 14J45 , 32J05     

High-speed wavelength-division multiplexing quantum key distribution system

A high-speed quantum key distribution system was developed with the wavelength-division multiplexing (WDM) technique and dedicated key distillation hardware engines. Two interferometers for encoding and decoding are shared over eight wavelengths to reduce the system's size, cost, and control complexity. The key distillation engines can process a huge amount of data from the WDM channels by using a 1 Mbit block in real time. We demonstrated a three-channel WDM system that simultaneously uses avalanche photodiodes and superconducting single-photon detectors. We achieved 12 h continuous key generation with a secure key rate of 208 kilobits per second through a 45 km field fiber with 14.5 dB loss.     

Laser Stark spectroscopy of the ν4 band of CH3C15N: Fermi resonance with 3ν83

Laser Stark spectra for the ν₄ band of CH₃C¹⁵N have been measured by using CO₂ and N₂O lasers. Almost 650 resonances have been assigned to about 140 ro-vibrational transitions with J′ ≤ 34 and K ≤ 11. An anomaly of the rotational structure around K = 7 has been proved to be due to a Fermi interaction by analyzing each K subband separately. Observed data have been fitted to a model which includes ν₄-3ν₈³ Fermi coupling by the method of least squares. The standard deviation of observed from calculated frequencies is 4.6 MHz. Molecular constants derived are also listed.     

Nuclear magnetic resonance spectra of carbanions—VI. Cumyl-, α-methylbenzyl- and benzyl carbanions

The proton magnetic resonance spectra of the three title carbanions have been observed in THF with potassium as a counter ion. The ortho-protons in the α-methylbenzyl carbanion are nonequivalent at room temperature. This shows that the α-carbon in this carbanion is in the near-sp² configuration. The aromatic proton chemical shifts of the benzylpotassium obtained here are at higher shielding than those of benzyllithium reported previously by Sandel and Freedman. This seems to arise from the different ionic nature of the bonds between carbon and metal in the carbanions.     

[a,b]-factorization of a graph

Let a and b be integers such that 0 ? a ? b. Then a graph G is called an [a, b]-graph if a ? d_G(x) ? b for every x ? V(G), and an [a, b]-factor of a graph is defined to be its spanning subgraph F such that a ? d_F(x) ? b for every vertex x, where d_G(x) and d_F(x) denote the degrees of x in G and F, respectively. If the edges of a graph can be decomposed into [a.b]-factors then we say that the graph is [2a, 2a]-factorable. We prove the following two theorems: (i) a graph G is [2a, 2b)-factorable if and only if G is a [2am,2bm]-graph for some integer m, and (ii) every [8m + 2k, 10m + 2k]-graph is [1,2]-factorable.     

Preparation of single-crystalline platinum nanowires with small diameters under mild conditions

We report a convenient method to synthesize single-crystalline platinum nanowires with high aspect ratio of ca. 2.0 nm diameter by sophisticated and precise control of Pt(0) nuclei and their growth.     

Aromaticity and π-bond covalency: prominent intermolecular covalent bonding interaction of a Kekulé hydrocarbon with very significant singlet biradical character

An anthracene-linked bisphenalenyl Kekulé molecule with very significant singlet biradical character has shown a prominent covalent bonding interaction between molecules in a molecular aggregate. High aromatic stabilization energy in the anthracene linker is responsible for the significant singlet biradical character.     

Diastereoselective synthesis of new psi[(E)-CH=CMe]- and psi[(Z)-CH=CMe]-type alkene dipeptide isosteres by organocopper reagents and application to conformationally restricted cyclic RGD peptidomimetics

Diastereoselective synthesis of new psi[(E)-CH=CMe]- and psi[(Z)-CH=CMe]-type alkene dipeptide isosteres corresponding to dipeptides having one N-methylamino acid, and application to bioactive peptides, are described. In a key reaction introducing the chiral alpha-alkyl group of the isosteres, organocopper-mediated alkylation of syn-beta-methylated gamma-mesyloxy-alpha,beta-enoate 26a afforded E- and Z-isomers of anti-S(N)2' products in a solvent-dependent manner. The resulting two isosteres, D-Phe-psi[(E)-CH=CMe]-L-Val 27a and D-Phe-psi[(Z)-CH=CMe]-L-Val 28b, which corresponded to trans- and cis-conformers of D-Phe-L-MeVal, respectively, were utilized in a structure-activity relationship study on cyclic RGD peptides 1 and 2, in company with a psi[(E)-CH=CH]-type alkene dipeptide isostere, D-Phe-psi[(E)-CH=CH]-L-Val. The cyclic isostere-containing pseudopeptides 3, 4, and 40 were synthesized and biological activity against integrin alpha(V)beta(3) and alpha(IIb)beta(3) receptors were also evaluated.