Decomposition of ideals into pseudo-irreducible ideals

A proper ideal of a commutative ring is called pseudo-irreducible if it cannot be written as a product of two comaximal proper ideals. In this paper, we give a necessary and su?cient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal pseudo-irreducible ideals. Examples of such rings include Laskerian rings, or more generally J-Noetherian rings and ZD-rings. We study when certain classes of rings satisfy this condition.     

A new approach to fused furan ring systems and benzofurans: Intramolecular cyclization reactions of unsaturated acyloxy sulfone derivatives

Unsaturated acyloxy sulfones 3 undergo intramolecular cyclization upon deprotonation with LHMDS in THF. Dehydration and double bond isomerization of the products upon exposure to acid, gave the fused ring furans, 4, in good yields. This strategy could be readily adapted to prepare substituted benzofurans 12 from the cyclization reactions of acyloxy sulfones 11 prepared from phenols. Finally, this approach could be successfully modified to access dihydropyrans and benzopyrans.     

A study of aromatic three membered rings

The resonance energies (REs) of neutral three membered ring analogs of the cyclopropenyl cation, computed using block localized wave function (BLW) methods, reveal considerable variations. The RE's of cyclopropenes substituted with exocyclic double bonded groups C?X, (X = O, NH, CH₂, S, PH, SiH₂) increase with the electronegativity of X in the same row (SiH₂ < PH < S and CH₂ < NH < O). The extra cyclic resonance energies (ECREs) (an energetic measure of aromaticity based on comparisons with the RE's of acyclic models) of these derivatives range from +10.5 kcal/mol for cyclopropenone (X = O) (somewhat aromatic; the benzene ECRE is 29.3 kcal/mol) to ?2.4 kcal/mol (slightly antiaromatic) for X = SiH₂. Additional disubstitution of the C?C double bond by X′ groups (X′ = CH₃, NH₂, OH, SiH₃, PH₂, SH) increases the REs considerably, but has only small effects on the ECREs. Even the ECRE of deltic acid (X = O, X′ = OH) is only increased to +13.3 kcal/mol. The conclusion based on ECRE's, that all 12 of the three membered rings are only marginally aromatic/antiaromatic, is supported by the satisfactorily plot (R² = 0.92) of ECRE against values of NICS(0)_πzz (a superior nucleus chemical independent shift magnetic index of aromaticity), which range only from ?6.1 ppm (diatropic) for deltic acid (cf., ?35.5 ppm for benzene and ?14.2 ppm for the parent cyclopropenium ion) to +8.9 ppm (paratropic) for the silicon derivative, X = SiH₂, X′ = SiH₃. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Adaptive panel representation for oblique collision of two vortex rings

In this article, we use a hierarchical panel method for representing vortex sheet surface motion in 3D flow to investigate the oblique collision of two vortex rings. The particles representing the sheet are advected by a regularized Biot-Savart integral with smoothed Rosenhead-Moore kernel. The particle velocities are evaluated by an adaptive treecode algorithm based on Taylor expansions in Cartesian coordinates. The method allowed us to consider late stages of a vortex rings collision, producing a funnel region. Vorticity iso-surfaces evolution is also investigated.     

Some commutativity criteria for prime rings with differential identities on Jordan ideals

In this article, we present some commutativity theorems for a ring R equipped with a generalized derivation satisfying certain differential identities on Jordan ideals of R. Some related results for prime rings are also discussed. Finally; we provide examples to show that the assumed restrictions are not superfluous.     

Many associated primes of powers of primes

We construct families of prime ideals in polynomial rings for which the number of associated primes of the second power (or higher powers) is exponential in the number of variables in the ring.     

Weakly $I$-Semiregular Rings and $I$-Semiregular Rings

Let $I$ be an ideal of a ring $R$. We call $R$ weakly $I$-semiregular if $R$/$I$ is a von Neumann regular ring. This definition generalizes $I$-semiregular rings. We give a series of characterizations and properties of this class of rings. Moreover, we also give some properties of $I$-semiregular rings.     

Synthetic studies on the DEF-rings of FR182877 and hexacyclinic acid

A synthesis of model DEF-rings of the polyketide anti tumor natural products FR182877 and hexacyclinic acid has been achieved. The key steps in the synthesis are an intramolecular Pd(0) catalyzed allylic substitution reaction, which was used to generate a 9-membered carbocycle, and a novel transannular iodocyclization reaction which furnished the DF-rings of both natural products.     

on submicron rings and their application for coherent nanoelectronic devices

Electron-phase modulation in magnetic and electric fields will be presented in In_0.75Ga_0.25As Aharonov–Bohm (AB) rings. The zero Schottky barrier of this material made it possible to nanofabricate devices with radii down to below 200 nm without carrier depletion. We shall present a fabrication scheme based on wet and dry etching that yielded excellent reproducibility, very high contrast of the oscillations and good electrical gating. The operation of these structures is compatible with closed-cycle refrigeration and suggests that this process can yield coherent electronic circuits that do not require cryogenic liquids. The InGaAs/AlInAs heterostructure was grown by MBE on a GaAs substrate [F. Capotondi, G. Biasiol, D. Ercolani, V. Grillo, E. Carlino, F. Romanato, L. Sorba, Thin Solid Films 484 (2005) 400], and in light of the large effective g-factor and the absence of the Schottky barrier is a material system of interest for the investigation of spin-related effects [W. Desrat, F. Giazotto, V. Pellegrini, F. Beltram, F. Capotondi, G. Biasiol, L. Sorba, D.K. Maude, Phys. Rev. B 69 (2004) 245324; W. Desrat, F. Giazotto, V. Pellegrini, M. Governale, F. Beltram, F. Capotondi, G. Biasiol, L. Sorba, Phys. Rev. B 71 (2005) 153314; J. Nitta, T. Akazaki, H. Takayanagi, T. Enoki, Phys. Rev. Lett. 78 (1997) 1335] and the realization of hybrid superconductor/semiconductor devices [Th. Schäpers, A. Kaluza, K. Neurohr, J. Malindretos, G. Crecelius, A. van der Hart, H. Hardtdegen, H. Lüth, Appl. Phys. Lett. 71 (1997) 3575].     

Thiosemicarbazone complexes of the platinum metals. A story of variable coordination modes

Salicylaldehyde thiosemicarbazone (H₂saltsc) reacts with [M(PPh₃)₃X₂] (M = Ru, Os; X = Cl, Br) to afford complexes of type [M(PPh₃)₂(Hsaltsc)₂], in which the salicylaldehyde thiosemicarbazone ligand is coordinated to the metal as a bidentate N,S-donor forming a four-membered chelate ring. Reaction of benzaldehyde thiosemicarbazones (Hbztsc-R) with [M(PPh₃)₃X₂] also affords complexes of similar type, viz. [M(PPh₃)₂(bztsc-R)₂], in which the benzaldehyde thiosemicarbazones have also been found to coordinate the metal as a bidentate N,S-donor forming a four-membered chelate ring as before. Reaction of the Hbztsc-R ligands has also been carried out with [M(bpy)₂X₂] (M = Ru, Os; X = Cl, Br), which has afforded complexes of type [M(bpy)₂(bztsc-R)]⁺, which have been isolated as perchlorate salts. Coordination mode of bztsc-R has been found to be the same as before. Structure of the Hbztsc-OMe ligand has been determined and some molecular modelling studies have been carried out determine the reason for the observed mode of coordination. Reaction of acetone thiosemicarbazone (Hactsc) has then been carried out with [M(bpy)₂X₂] to afford the [M(bpy)₂(actsc)]ClO₄ complexes, in which the actsc ligand coordinates the metal as a bidentate N,S-donorformingafive-membered chelate ring. Reaction of H₂saltsc has been carried out with [Ru(bpy)₂Cl₂] to prepare the [Ru(bpy)₂(Hsaltsc)]ClO₄ complex, which has then been reacted with one equivalent of nickel perchlorate to afford an octanuclear complex of type [Ru(bpy)₂(saltsc-H)₄Ni₄](ClO₄)₄.