Recursive differential equations of the raman-nath type: A general review

Summary In this paper we discuss the differential recursive equations of the Raman-Nath type and introduce a very general technique of analysis, valid for both exact and perturbed solutions.

---

Riassunto In questo lavoro si studiano equazioni differenziali alle ricorrenze di tipo Raman-Nath e s’introduce una tecnica di analisi valida per la ricerca di soluzioni esatte e perturbate.

---

Резюме В этой статье мы обсуждаем дифференциальные уравнения Рамана-Ната и вводим очень общую технику анализа, справедливую для точных и пертурбационных решений.

     

Synthesis of heterocyclic compounds IV1 pyrazol-1′-ylpyridines2

2-Pyrazol-1-ylpyridines were synthesized by condensation of pyridylhydrazines with 1,3-dicarbonyl compounds or by theUllmann arylation of pyrazoles with halopyridines.Taken in part from the Master's thesis ofA. A. A. Pinto, Instituto Militar de Engenharia, Rio de Janeiro, 1978.     

Quasiclassical dynamics simulation of the collision-induced dissociation of Cr(CO)6 + with Xe

Quasiclassical trajectory calculations are employed to investigate the dynamics of collision-induced dissociation (CID) of Cr(CO)6 + with Xe atoms at collision energies ranging from 1.3 to 5.0 eV. The trajectory simulations show that direct elimination of CO ligands, during the collision, becomes increasingly important as the collision energy increases. In a significant number of cases, this shattering mechanism is accompanied with a concomitant formation of a transient Xe-Cr(CO)x +(x<6) complex. The calculated results are in very good agreement with the experimental results presented previously [F. Muntean and P. B. Armentrout, J. Chem. Phys. 115, 1213 (2001)]. In particular, the computed cross sections and scattering maps for the product ions Cr(CO)x +(x=3-5) compare very favorably with the reported experimental data. However, in contrast with the conclusions of the previous study, the present calculations suggest that CID dynamics for this system exhibits a significant impulsive character rather than proceeding via a complex surviving more than a rotational period.     

Efficient synthesis of the glucosidase inhibitor blintol, the selenium analogue of the naturally occurring glycosidase inhibitor salacinol

An efficient synthesis of blintol, the selenium congener of the naturally occurring glycosidase inhibitor salacinol, and a potent glucosidase inhibitor itself, is described. Unlike our previously reported synthesis, this improved route makes use of p-methoxybenzyl ether protecting groups in the synthesis of one of the two key intermediates, 2,3,5-tri-O-p-methoxybenzyl-1,4-anhydro-4-seleno-D-arabinitol, from L-xylose. The other key intermediate, 2,4-O-benzylidene-L-erythritol-1,3-cyclic sulfate, was successfully prepared from D-glucose instead of the expensive L-glucose. All protecting groups in the resulting adducts were removed with trifluoroacetic acid to yield a mixture of stereoisomers, thereby obviating the problematic deprotection of benzyl ethers by hydrogenolysis. The major stereoisomer, blintol, was then obtained by fractional crystallization.     

An Almost Prime Element in a Commutative Radical Banach Algebra

Thomas conjectured that there is no such thing as an almostprime element in a commutative radical Banach algebra. Thispaper shows that there is such an element. However, it stillleaves open the question of whether there is an element thatis almost prime, but not prime. 2000 Mathematics Subject Classification46J40, 46J45.     

Isolation and structural determination of xerophytolic acid A, a 3-geranyl-4-hydroxybenzoate derivative from Xerophyta plicata

A novel compound of a rare class of secondary metabolites, 3-geranyl-4-hydroxybenzoic acid derivative, methyl xerophytolate A (2), was isolated from the crude extract of Xerophyta plicata (Velloziaceae) collected in Rio de Janeiro, Brazil. The structure of 2 was elucidated using spectroscopic methods.     

Mechanism for the elimination of aromatic molecules from polyenes in tandem mass spectrometry

We report here a general mechanism for the elimination of aromatic molecules from polyene containing natural products of several compound classes in tandem mass spectrometry.     

Linear attraction in quasi-linear difference systems

The equivalence and asymptotic equivalence between the solutions of a linear difference system and some families of quasi-linear ones are studied by using a Lipschitz component-wise condition combined with a spectrally small dichotomy, which is introduced. The equivalence is described by a homeomorphism and the results also include unbounded solutions. The results show the vectorial attractivity of the solutions of the linear part.