Tracking poles and representing Hankel operators directly from data

Summary We propose and analyse a method of estimating the poles near the unit circleT of a functionG whose values are given at a grid of points onT: we give an algorithm for performing this estimation and prove a convergence theorem. The method is to identify the phase for an estimate by considering the peaks of the absolute value ofG onT, and then to estimate the modulus by seeking a bestL ² fit toG over a small arc by a first order rational function. These pole estimates lead to the construction of a basis ofL ² which is well suited to the numerical representation of the Hankel operator with symbolG and thereby to the numerical solution of the Nehari problem (computing the bestH , analytic, approximation toG relative to theL norm), as analysed in [HY]. We present the results of numerical tests of these algorithms.Partially supported by grants from the AFOSR and NSF     

The synthesis of 1,4-diazacycl[3,2,2]azine

The diazaanalog of “cycl[3,2,2]azine”, “1,4-diazacycl[3,2,2]azine” (1,4,7b-triazacyclopent-[cd]indene) and its 2-methyl derivative were prepared. These compounds are subject to facile acid-catalyzed hydrolysis affording substituted imidazo[1,2-a]pyridines.     

Nucleophilic substitution in 5,6,7,8-tetrafluoro- and 6,7-difluoro-1,2,3,4-tetrahydro-9-alkenyl-1,4-methanonaphthalenes and related compounds. A search for homoallylic conjugation

The second-order rate constants for the nucleophilic replacement of fluorine by isopropoxide in 5,6,7,8-tetrafluoro- and 6,7,-difluoro-1,2,3,4-tetrahydro-9-alkenyl-1,4-methanonaphthalenes and related 9-alkyl systems have been measured. A factor of 6 - 7 separates the most reactive compounds [the 9- (4′-trifluoromethylbenzylidene) derivatives] from the least reactive compounds [the syn-9-isopropyl derivatives] in both the tetrafluoro- and difluoro-series. It is concluded for these small reactivity differences.     

Submanifolds of complex space forms admitting an almost contact metric compound structure

Summary Real hypersurfaces of an almost Hermitian manifold naturally admit an almost contact metric structure and the (f, g, u, v, w, , , )-structure is defined on submanifolds of codimension 3 of an almost Hermitian manifold. We study the so-called semi-invariant submanifolds of a complex space form with almost contact metric compound structure which is a general notion of (f, g, u, v, w, , , )-structure.Dedicated to professor Eulyong Pak on his 60th birthdayThis research was partially supported by Korean Science and Engineering Foundation Grant.     

Fabrication of hollow palladium spheres and their successful application to the recyclable heterogeneous catalyst for suzuki coupling reactions

Novel palladium hollow spheres were synthesized using silica spheres as a template, and they were successfully applied as recyclable heterogeneous catalysts for Suzuki cross coupling reactions.     

The reaction of 2-picoline N-Oxide with o-substituled benzoates and lsatoic anhydrides

The reaction of 2-picoline N-Oxide anion with o-substituted henzoates and isatoic anhydrides to give synthetically useful l-(2-methoxyphenyl)-2-(2-pyridinyl)ethanone N-oxides, I-(2-hydroxy-phenyJ)-2-(2-pyridinyl)ethanone N-oxides and I -(2-arninopheny])-2-(2-pyridinyl)ethanone N-oxides is described.