We define a closure operation for ideals in a commutative ring which has all the good properties of solid closure (at least in the case of equal characteristic) but such that also every ideal in a regular ring is closed. This gives in particular a kind of tight closure theory in characteristic zero without referring to positive characteristic.

A regioselective synthesis of oxepinones and azepinones in good to excellent yields from alkynylcyclopropanecarboxylic acid derivatives is described. This novel cycloisomerization cascade process consists of a nucleophilic addition followed by a cyclopropane ring-opening, where both donor and acceptor groups are required as substituents of the cyclopropane ring.

In the presence of allyl tri-n-butyltin--AIBN, cyclopropylmethyl bromides/xanthates undergo ring-opening reaction with concomitant formation of geminal diallyl derivatives in good yields. The ring closing metathesis reactions on geminal diallyl derivatives with Grubbs' catalyst provided spirocyclopentenyl products. Combination of these two methodologies has been applied to the synthesis of mono...

Transmission electron microscopic studies on CS2 hydrolase provide direct evidence for the existence of the hexadecameric catenane and octameric ring topologies. Reconstructions of both protein assemblies are in good agreement with crystallographic analyses of the catenane and ring forms of CS2 hydrolase.

The one-step cyclocondensation of substituted isoflavones with cyanothioacetamide in the presence of sodium hydroxide gave an array of 3-cyano-5,6-diaryl pyridine-2(1H)-thiones in good yields. The procedure involves base-mediated ring opening of the isoflavones and subsequent Knoevenagel condensation between the 1,3-dicarbonyl intermediate generated from the isoflavones and cyanothioacetamide, ...

gem-Difluoro-1,7-enyne amides are suitable building blocks for the synthesis of difluorodihydropyridinones via a ring-closing metathesis reaction, and of 4,4-difluoro-3-oxoisoquinolines through a ring-closing metathesis-enyne metathesis tandem reaction. These products, in turn, undergo a Diels-Alder reaction to yield heterotricyclic systems in moderate to good yields.

We investigate a class of vector ring spatial solitons that carry no net angular momentum. Specifically, we show analytically and numerically that the dominant low-frequency perturbations that typically disrupt ring solitons are suppressed for these solitons. By comparing our analytical and numerical results, we show that our simple analysis gives good qualitative predictions on the regions of ...

The ring expansion of cyclopropane derivatives provides a powerful method to construct synthetically useful four-membered carbocycles. Herein, a new type of gold(I)-catalyzed ring expansion of an unactivated alkynylcyclopropane/sulfonamide trapping strategy to (E)-2-alkylidenecyclobutanamines was described. The reaction tolerates a range of aryl and alkyl substituents with moderate to good yields.

The numerical analysis of a semiconductor ring laser (SRL) by using the basic two-mode model and parameter mismatch in backscattering coefficients is presented this paper to account for asymmetry along ring. operation SRL discovered be affected changing conservative fixed value dissipative parameter, bidirectional regime with alternating oscillation can suppressed. results experimental literatu...

The asymmetric ring-opening of meso-aziridines with primary alcohols is realized using an N,N'-dioxide-Mg(OTf)2 complex as the catalyst. The desired vicinal trans-β-amino ethers are afforded in good yields and enantioselectivities. Aniline and water could also be used as the nucleophiles for the ring-opening in an identical catalyst system.