Resolution of the wavefront set via discrete sets

We introduce discrete wave-front sets of sup type and prove that they coincide with the Hörmander wave-front set of a distribution. To that end we recall the notion of admissible lattice pairs and wave-front sets in Fourier-Lebesgue spaces. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of substituted fused pyridines, pyrazines and pyrimidines by sequential Ugi/inverse electron demand Diels–Alder transformations

The synthesis of all four regioisomers of fused pyrrolidino-pyridines in a one-pot two-step sequential Ugi-inverse electron demand Diels–Alder reaction is described. Fused pyrrolidino-pyrazines, pyrrolidino-pyrimidines and azepinone pyridines can also be obtained in consecutive synthetic sequences.     

The Quasiasymptotic Expansion at the Origin. Abelian-Type Results for Laplace and Stieltjes Transforms

The notion of quasiasymptotic expansion at the origin of tempered distributions supported by [0, α] and the structural theorem for such distributions that have the quasiasymptotic expansion at the origin are given. As applications, the Abelian-type results for the distributional Stieltjes and Laplace transforms are obtained.     

On the Quasiasymptotic of Schwartz Distributions

The quasiasymptotic of distributions with the supports in (0, ∞) was studied by the Soviet mathematicians Vladimirov, Dro?inov and Zavialov in several papers. Some essential questions on the quasiasymptotic behaviour of Schwartz distributions defined on R are posed and answered in this paper.     

Paper chromatography of metal complexes : Realtionship between the rf and the stabiliiy of metal complexes

It is shown that the R_F values can be related to the stability constants of the corresponding metalligand coördination compounds. The relationship has been applied to prove graphically the stoichiometric identity of two or more complexes formed by paper chromatrography in a given system.     

Synthesis of fused imidazole rings by sequential van Leusen/C-H bond activation

A concise route to access fused imidazole rings employing the van Leusen three-component reaction followed by a Pd/Cu catalyzed intramolecular C-arylation is reported. The reaction was found to be general and the products were formed in moderate to excellent yields using the two-step reaction sequence.     

Synthesis of fused bicyclic imidazoles by sequential van Leusen/ring-closing metathesis reactions

[reaction: see text]. A new strategy employing the van Leusen three-component reaction and the ring-closing metathesis reaction in a sequential fashion to access fused bicyclic imidazole rings is reported. The two-step sequence generated compounds of significant molecular complexity from simple starting materials in an expedient fashion with excellent yields.     

Rapid and efficient synthesis of 1,2,4-oxadiazoles utilizing polymer-supported reagents under microwave heating

1,2,4-Oxadiazoles can be rapidly and efficiently synthesized from a variety of readily available carboxylic acids and amidoximes using either method A or method B. The use of commercially available polymer-supported reagents combined with microwave heating resulted in high yields and purities of the product 1,2,4-oxadiazoles in an expeditious manner. [structure: see text]