A pair of orthogonal frames

We start with a characterization of a pair of frames to be orthogonal in a shift-invariant space and then give a simple construction of a pair of orthogonal shift-invariant frames. This is applied to obtain a construction of a pair of Gabor orthogonal frames as an example. This is also developed further to obtain constructions of a pair of orthogonal wavelet frames.     

Hyperfunctional Weights for Orthogonal Polynomials

The Chebychev polynomials associated to any given moments μ_{n ∞} ⁰ are formally orthogonal with respect to the formal δ-series $$w(x)= {\sum^\infty_0}(- 1)^{n}\mu_{{n}}\delta^{(n)}(x)/n!.$$ We show that this formal weight can be a true hyperfunctional weight if its Fourier transform is a slowly increasing holomorphic function in some tubular neighborhood of the real line. It provides a unifying treatment of real and complex orthogonality of Chebychev polynomials including all classical examples and characterizes Chebychev polynomials having Bessel type orthogonality.     

A new caffeoyl quinic acid from aster scaber and its inhibitory activity against human immunodeficiency virus-1 (HIV-1) integrase

The phytochemical study of the aerial parts of Aster scaber Thunb. (Asteraceae) yielded a new caffeoyl quinic acid, (-) 3,5-dicaffeoyl-muco-quinic acid (2) and three known compounds, (-) 3,5-dicaffeoyl quinic acid (1), (-) 4,5-dicaffeoyl quinic acid (3), (-) 5-caffeoyl quinic acid (4). The structures were established by high resolution spectroscopic methods. The antiviral effects against HIV-1 integrase of the compounds was evaluated. (-) 3,5-Dicaffeoyl-muco-quinic acid (2) exhibited potent antiviral activity with an IC50 value of 7.0 +/- 1.3 microg/ml.     

Cyano-bridged CuII-MV (M = Mo, W) bimetallic layered complexes exhibiting novel honeycomblike structures

Self-assembly of a new precursor [Cu(L)](ClO4)2 (1) (L = macrocyclic ligand) with octacyanometalates [M(CN)8]3- (M = Mo, W) produced two-dimensional cyano-bridged Cu(II)-M(V) bimetallic assemblies [Cu(L)]3n[M(CN)8]2n.6nH2O [M = Mo (2), W (3)] with novel honeycomblike structures, characterized by spectroscopic data, single-crystal X-ray diffraction studies, and magnetic measurements. The crystallographic determination reveals that compounds 2 and 3 are isostructural and crystallize in the triclinic system (P). The Cu atom in a distorted octahedral environment experiences a tetragonal elongation of apical nitrogen atoms exhibiting average Cu-Nax lengths of 2.566 Angstroms for 2 and 2.593 Angstroms for 3, which accounts for the Jahn-Teller effect of a Cu(II) ion. The Cu-NC angles are magnetically important, ranging from 135.7 to 159.2 degrees. Three types of L in the crystal lattice are observed, which are dependent on the relative positions of the pendant hydroxyl groups with respect to the CuN4 basal plane. The positions are correlated with hydrogen bonding of OH groups to neighboring atoms. The magnetic data indicate that ferromagnetic and antiferromagnetic interactions between Cu(II) and M(V) through the CN linkage coexist.     

Suppressed beta-hydride elimination in palladium-catalyzed cascade cyclization-coupling reactions: an efficient synthesis of 3-arylmethylpyrrolidines

[formula: see text] A novel type of palladium-catalyzed cascade cyclization-coupling reaction that proceeds with suppressed beta-hydride elimination has been found. One of the N-sulfonyl oxygens is suggested to coordinatively stabilize an alkylpalladium intermediate, thus preventing the intermediate from the usual beta-elimination. This is the first sequential palladium-catalyzed coupling reaction where the Suzuki and Heck reactions can compete. The reaction provides an efficient synthetic route to 4-methylene-3-arylmethylpyrrolidines, which are not readily available by other routes.     

Pore size distributions in low‐k dielectric thin films from X‐ray porosimetry

X‐ray reflectivity has been used to determine the mass uptake of probe molecules in porous thin films supported on thick silicon wafers. The adsorption occurs by capillary condensation when the films are exposed to probe vapor at controlled partial vapor pressures. The probe solvent partial pressure was varied by mixing saturated air and dry air at constant temperature or by changing sample temperature at a constant vapor concentration. Pore size distribution in the films can be calculated from the probe uptake with typical porosimetric approaches such as the application of the Kelvin equation to convert partial pressure into pore size. For illustration, the pore size distribution of three different nanoporous thin films, the primary candidate of ultra‐low‐k interlevel dielectrics in the next generation of integrated circuit chips, was determined with this technique. These samples represent different generations of low‐k dielectrics developed by industry. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2170–2177, 2002