Dimension polynomials of difference local algebras

We extend the concept of the difference dimension polynomial of a difference field extension to difference local algebras. The main theorem of the paper establishes the existence and form of the dimension polynomial associated with the localization of a finitely generated well-mixed difference algebra at a prime reflexive difference ideal.     

A complicated path of salicylaldehyde through the Biginelli reaction: a case of unexpected spiroketalization

Cyclocondensation of salicylaldehydes with alkyl acetoacetates and 2-aminobenzothiazoles or 2-amino-5-methylthiazole under classical Biginelli reaction conditions gives rare hetarylamino substituted 2,2′-spirobischromanecarboxylate derivatives. The mechanism and observed stereoselectivity of the unexpected pseudo-four-component process are discussed.     

Bombieri's Theorem in Short Intervals

Under the assumption of sixth power large sieve mean-value of Dirichlet L-function,we improve Bombieri's theorem in short intervals by virtue of the large sieve method and Heath-Brown's identity.     

Synthesis of 2,2′-bipyrrole-5-carboxaldehydes and their application in the synthesis of B-ring functionalized prodiginines and tambjamines

Facile, versatile, and cost-effective synthetic routes for the preparation of a range of new 3-alkyl-, 4-alkyl-, 3,4-dialkyl-, and 3-halo-4-alkyl-2,2′-bipyrrole-5-carboxaldehydes have been developed. These 2,2′-bipyrrole-5-carboxaldehydes offer interesting potential as building blocks for making bioactive natural and unnatural products, as demonstrated by the synthesis of B-ring functionalized prodiginines (PGs) and tambjamines.     

Platanus acerifolia’s buds: additional non-polar metabolites and structure revision of two previous dihydrochalcone-like metabolites

In addition to the methylated and prenylated flavonoids previously reported from Platanus acerifolia, the multistep chromatographic processing of the n-hexane extract of the fresh unripe buds resulted in the isolation of 11 metabolites. Besides six common wax constituents, the n-hexane portion led to the isolation of four gem-dimethylpyrano flavanones. They corresponded to two pairs of angular and linear isomers derived only from pinocembrin (5,7-dihydroxyflavanone). Additionally, a novel β-decadione was split into the major keto-enol tautomer as shown by the detailed NMR and EIMS analyses. Moreover, the structures of grenoblone and 4-hydroxygrenoblone, two previously reported dihydrochalcone-like metabolites, were revised according to the EIMS spectra.     

Integral closure,basically full closure,and duals of nonresidual closure operations

We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [5], extending our previous results to the expanded context. We apply this duality in particular to integral and basically full closures and their respective cores to obtain integral and basically empty interiors and their respective hulls. We also dualize some of the known formulas for the core of an ideal to obtain formulas for the hull of a submodule of the injective hull of the residue field. The article concludes with illustrative examples in a numerical semigroup ring.     

Cohen and multiple Cohen strongly summing multilinear operators

Considering the successful theory of multiple summing multilinear operators as a prototype, we introduce the classes of multiple Cohen strongly p-summing multilinear operators and polynomials. The adequacy of these classes under the viewpoint of the theory of multilinear and polynomial ideals and holomorphy types is discussed in detail.     

On noncommutative piecewise Noetherian rings

We extend the definition of a piecewise Noetherian ring to the noncommutative case, and investigate various properties of such rings. In particular, we show that a ring with Krull dimension is piecewise Noetherian. Certain fully bounded piecewise Noetherian rings have Gabriel dimension and exhibit the Gabriel correspondence between prime ideals and indecomposable injective modules.     

An efficient synthesis of highly functionalized dinucleotide cap analogs

An efficient synthesis of new cap analogs containing aminoallyl linkers such as m⁷G[5′]pppp[5′]U-aminoallyl and m₂^7,3′OG[5′]pppp[5′]U-aminoallyl is reported. The final cap analog has been isolated with high purity (>99.8%) after ion-exchange column purification.     

A convenient approach towards boron cluster modifications with adenosine and 2′-deoxyadenosine

New 2′-deoxyadenosine and adenosoine modifications: 8-[(2-dimethylaminoethyl)amino]-2′-deoxyadenosine and 8-[(2-dimethylaminoethyl)amino]adenosine were prepared and their reactivity towards cyclic oxonium adducts of closo-dodecaborate and cobalt-bis-dicarbollide was studied. The cleavage reactions of clusters oxonium rings by N,N-dimethylanio group of modified nucleosides led to the first [B₁₂H₁₂]²⁻ and new [Co(C₂B₉H₁₁)₂]⁻ conjugates with adenosine and 2′-deoxyadenosine respectively. The proposed methodology provides a convenient route for the synthesis of libraries of boron cluster modified adenosine and 2′-deoxyadenosine derivatives for biological screening.