Plane curves whose singular points are cusps and triple coverings of ℙ2

We study a plane curve C whose singular points are cusps and the surface which is a triple covering of ² branched along C. As a result, especially we obtain an inequality for the sum of the Milnor numbers at the singularities of C and new surfaces of general type.     

Mesure invariante pour l’équation stochastique d’un modéle de compétition limitée entre des espéces avec une diffusion spatiale

On considére l’équation stochastique decrivant un systéme den espéces avec une perturbation stochastique du type environnemental et une diffusion dans un territoire de chaque espéce. On suppose la compétition avec un effet limité entre le espéces différentes, tandis que l’effet logistique pour chaque espéce est supposé quadratique. Sous une condition convenable pour les coefficients, on démontre l’existence d’une mesure invariante pour cette équation stochastique, oú la densité de population de chaque espéce est presque surement positive.      

Unicité de la solution de l'équation monodimensionnelle ou à symétrie sphérique d'un gaz visqueux et calorifère

In questo articolo dimostriamo l'unicità della soluzione (globale in tempo) dell'equazione monodimensionale o a simmetria sferica di un gas viscoso e termoconduttore con la superficie libera. In questo risultato il limite inferiore della densità ρ può essere uguale a 0. Assieme al teorema di esistenza dimostrato nei lavori precedenti, costituisce il teorema di esistenza e di unicità (globale in tempo) per questa equazione.     

Dynamical systems which realize given random bi-sequences of points on their orbits

A dynamical system consists of a phase space of possible states, together with an evolution rule that determines all future states and all past states given a state at any particular moment. In this paper, we show that for any countable random infinite bi-sequences of states of some phase space, there exists an evolution rule in C⁰-topology which realizes precisely the given sequences of states on their orbits and satisfies some regular conditions on the times to realize the states.     

Difference-frequency terahertz-wave generation from 4-dimethylamino-N-methyl-4-stilbazolium-tosylate by use of an electronically tuned Ti:sapphire laser

Among nonlinear materials, the organic ionic salt crystal 4-dimethylamino- N -methyl-4-stilbazolium-tosylate (DAST) is known for its large nonlinearity. We generated a coherent terahertz (THz) wave, using DAST, from the difference frequency between two oscillating wavelengths of an electronically tuned Ti:sapphire laser. In LiNbO(3), LiTaO(3), KTiOPO(4), and GaP crystals, THz-wave generation was not observed under the same experimental conditions. This result proves the high efficiency of DAST crystals for generation of difference-frequency THz waves.     

Unambiguous detection of target DNAs by excimer-monomer switching molecular beacons

A new class of molecular beacons were developed in which pyrene fluorophores were connected both at 3' and 5' ends of a single-stranded oligonucleotide. The two pyrene-based fluorophores were synthesized from the same starting material, so that the preparation of the beacons was simplified. The detection strategy of the beacons for target DNAs is based on "excimer-monomer emission switching" of the pyrene fluorophores: excimer emission of the pyrene moieties changed to monomer one when the beacons hybridized with the targets. This type of two-state mode of fluorescence allows unambiguous detection of the target DNAs because strict 1:1 correlation between the nonhybridized and the hybridized beacons can be monitored by the presence of isoemissive points of the fluorescence changes. The beacons can detect target 19-mer DNAs and can discriminate the targets from their single-nucleotide mismatches at 1 nM concentration. Advantages of the excimer-monomer switching molecular beacons were discussed in comparison with conventional ones.     

Ruthenium-catalyzed hydrophosphinylative cyclization of 1,6-diynes. Stereoselective synthesis of exocyclic 1,3-dienylphosphine oxides

The first catalytic synthesis of exocyclic 1,3-dienylphosphine oxides was achieved by the ruthenium-catalyzed selective hydrophosphinylative cyclization of 1,6-diynes. A plausible mechanism involving a ruthenacyclopentatriene intermediate is proposed on the basis of the DFT calculations of model ruthenium complexes.