Linkage Isomerism and Spin Frustration in Heterometallic Rings: Synthesis,Structural Characterization,and Magnetic and EPR Spectroscopic Studies of Cr7Ni,Cr6Ni2, and Cr7Ni2 Rings Templated About Imidazolium Cations

The synthesis and structural characterization of three heterometallic rings templated about imidazolium cations is reported. The compounds are [2,4‐DiMe‐ImidH][Cr₇Ni^IIF₈(O₂CtBu)₁₆] 1 (2,4‐DiMe‐ImidH=the cation of 2,4‐dimethylimidazole), [ImidH]₂[Cr₆Ni^II₂F₈(O₂CCtBu)₁₆] 2 (ImidH=the cation of imidazole), and [1‐Bz‐ImidH]₂ [Cr₇Ni^II₂F₉(O₂CtBu)₁₈] 3 (1‐Bz‐ImidH=the cation of 1‐benzylimidazole). The structures show the formation of octagonal arrays of metals for 1 and 2 and a nonagon of metal centers for 3 . In all cases the edges of the polygon are bridged by a single fluoride and two pivalate ligands, and the position of the divalent metal centers cannot be distinguished by X‐ray diffraction. Magnetic studies combined with EPR spectroscopy allow the characterization of the magnetic states of the compounds. In each case the exchange is antiferromagnetic with a magnetic exchange parameter J≈?5.8 cm^?1, and it is not possible to differentiate the exchange between two Cr^III centers (J_CrCr) from the exchange between a Cr^III and a Ni^II center (J_CrNi). For 2 there is evidence for the presence of at least two, possibly four, linkage isomers of the heterometallic ring, caused by the presence of two divalent metal centers in the ring. The EPR spectroscopy of 3 suggests an S=1/2 ground state of the ring and that it is likely that only one linkage isomer is present.     

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.     

Generalized derivations as Jordan homomorphisms on lie ideals and right ideals

Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g（x） = x for all x ∈ R, or char（R） = 2, R satisfies the standard identity s4（x1, x2, x3, x4）, L is commutative and u2 ∈ Z（R）, for any u C L. We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set [I, I], where I is a non-zero right ideal of R.     

可换环上Abel李代数的全形的导子和自同构(英文)

决定了可换环上Abel李代数的全形的导子代数和自同构群.     

Practical synthesis of bicyclic pyrazol-5-one derivatives

This communication describes a convenient synthesis of fused bicyclic pyrazolones in a one-pot reaction procedure. Modified protocols are also developed to access 5,5-bicyclic and bulky pyrazolones in good yields. The method reported herein represents a practical approach to structurally diversified bicyclic pyrazolones.     

Interband photoconductivity of Ge/Si structures with self-organized quantum rings

At low temperatures a lateral photoconductivity (PC) of Ge/Si (1 0 0) self-organized quantum rings (QRs) structures as a function of interband light intensity has been investigated for different values of lateral voltage and temperature. In contrast to self-organized Ge/Si quantum dots (QDs) structures (grown at the same conditions) where the stepped PC was registered, for QRs structures essential smoothing of PC steps was observed. Such behavior is determined by decreasing of strain potential around QRs in conductive Si matrix due to a transfer of Ge atoms from the center of QDs to its periphery accompanied by Ge/Si intermixing.     

Negishi cross-coupling of organotellurium compounds: synthesis of biaryls, aryl-, and diaryl acetylenes

A functional group tolerant palladium-catalyzed Negishi coupling of diaryl tellurides with organozinc has been developed. This methodology permits efficient preparation of biaryls, aryl acetylenes and diaryl acetylenes in moderate to good yields. A preliminary study to gain further insight into the reaction was performed using in situ ReactIR technology.     

A Regularity Criterion for Semigroup Rings

An analogue of the Kunz–Frobenius criterion for the regularity of a local ring in a positive characteristic is established for general commutative semigroup rings.