A characterization of projective subspaces of codimension two as quasi-symmetric designs with good blocks

Consider an incidence structure whose points are the points of a PG_n(n+2,q) and whose block are the subspaces of codimension two, where n?2. Since every two subspaces of codimension two intersect in a subspace of codimension three or codimension four, it is easily seen that this incidence structure is a quasi-symmetric design. The aim of this paper is to prove a characterization of such designs (that are constructed using projective geometries) among the class of all the quasi-symmetric designs with correct parameters and with every block a good block. The paper also improves an earlier result for the special case of n=2 and obtains a Dembowski-Wagner-type result for the class of all such quasi-symmetric designs.     

New standing solitary waves in water

By means of the parametric excitation of water waves in a Hele-Shaw cell, we report the existence of two new types of highly localized, standing surface waves of large amplitude. They are, respectively, of odd and even symmetry. Both standing waves oscillate subharmonically with the forcing frequency. The two-dimensional even pattern presents a certain similarity in the shape with the 3D axisymmetric oscillon originally recognized at the surface of a vertically vibrated layer of brass beads. The stable, 2D odd standing wave has never been observed before in any media.     

Broad band acousto-optic deflector for holographic memories

A practical inexpensive mechanism for effecting improved Rayleigh resolution in a random access deflector without sacrificing its performance has been constructed. It comprises an acousto-optic deflector in the form of a flat transducer grating, made from a single piezoelectric platelet. The deflector steers the acoustic column to track the Bragg angle as the acoustic frequency changes.     

Estimation of a Stieltjes function expanded to Taylor series at complex conjugate points

Taylor series expansions of a Stieltjes function f in various complex conjugate points are used to construct the so called unified continued fractions (UCF) terminated on P-th step by a remainder named tail of f. We prove that, if f is a Stieltjes function then its tail is also a Stieltjes function. The estimations of f are obtained in what follows. Numerical calculations of the new complex bounds on f generated by complex conjugate input data are carried out.     

Rhodium-catalyzed stereoselective formation of Z-enamines from allylaziridines

Rhodium (I)-catalyzed isomerization of N-allylaziridines affords isolable Z-enamines in excellent yields and with high stereoselectivity. Cationic [Rh(BINAP)(COD)]OTf and RhH(CO)(PPh3)3 follow the same selectivity toward the Z-isomers. This selectivity is not observed with other N-allylamines which give the thermodynamically more stable E-isomers. These unexpected results suggest a possible deviation from the commonly accepted mechanism of isomerization. Preliminary results show that the Z-enamines undergo cycloaddition with DMAD to form highly strained N-cyclobutenyl aziridines.     

Ruthenium-catalyzed intramolecular homo-diels-alder reaction of alkyne-tethered norbornadienes. An entry to fused angular triquinanes

2-(pent-4-ynyl)norbornadienes undergo an intramolecular [2+2+2] cycloaddition in the presence of (nbd)RuCl2(PPh3)2 as a catalyst affording annelated deltacyclenes in good to excellent yields. The usefulness of the reaction is illustrated by the straighforward conversion of pentacyclene 2a into the angularly fused triquinane 19.     

C-Silylation de composes a fonction nitrile. Synthese de nitriles α-silicies

The direct silylation by Me₃SiCl/Li/THF of saturated nitriles having a hydrogen atom in the α position with respect to the function leads, according to a simple and rapid process, to the corresponding α-silylated nitriles in yields that are moderate but much higher than those given by the comparable previously known routes. α, β-Unsaturated nitriles give the derivatives resulting from the disilylation of the double bond. Allyl or benzyl cyanide and diphenyl acetonitrile first undergo the elimination of the nitrile group (which behaves as a halogen atom) whereas cyanamid affords bis(trimethylsilyl)carbodiimide giving after further silylation the unexpected tris(trimethylsilyl)amine.     

Cobalt(I)-catalyzed [6+2] cycloadditions of cyclooctatetra(tri)ene with alkynes

The cobalt-catalyzed [6+2] cycloaddition of cyclooctatetraene 1 with alkynes 3 affords monosubstituted bicyclo[4.2.2]deca-2,4,7,9-tetraenes 4 in fair to good yields. Due to the valence tautomerism, 1,3,5-cyclooctatriene 2, in equilibrium with bicyclo[4.2.0]octa-2,4-diene A, and alkynes 3 are converted to 10 and 11 according to [6+2] and [4+2] cycloadditions, respectively.