On the Discrete Hardy Inequality

Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given.     

Development of Molecular Mechanics Torsion Parameters for alpha,beta-Cyclopropyl Ketones and Conformational Analysis of Bicyclo[m.1.0]alkan-2-ones

Conformations of cyclopropyl methyl ketone have been studied using ab initio methods in an effort to quantify the effects of conjugative overlap between the cyclopropane ring and an adjacent ketone carbonyl. Results were comparable with previous experimental and theoretical studies. Cyclopropyl methyl ketone exhibits a global energy minimum in the s-cis conformer and a local energy minimum near the s-trans conformer. The potential energy curve obtained was used to derive torsion parameters which were employed in molecular mechanics studies of the conformations of the set of bicyclo[m.1.0]alkan-2-ones having larger ring sizes from five- to 16-membered. Similar conformations for the cyclopropyl ketone substructure are observed for all the medium and large ring systems examined. Possible synthetic ramifications of local conformational anchoring by this functional group array are discussed.     

Newton's method and periodic solutions of nonlinear wave equations

We prove the existence of periodic solutions of the nonlinear wave equation satisfying either Dirichlet or periodic boundary conditions on the interval [O, π]. The coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation. Using a version of Newton's method, we show that this equation has solutions provided the nonlinearity g(x, u) satisfies certain generic conditions of nonresonance and genuine nonlinearity. © 1993 John Wiley & Sons, Inc.     

Mechanism studies of the conversion of 13C-labeled n-butane on zeolite H-ZSM-5 by using 13C magic angle spinning NMR spectroscopy and GC-MS analysis

By using 13C MAS NMR spectroscopy (MAS = magic angle spinning), the conversion of selectively 13C-labeled n-butane on zeolite H-ZSM-5 at 430-470 K has been demonstrated to proceed through two pathways: 1) scrambling of the selective 13C-label in the n-butane molecule, and 2) oligomerization-cracking and conjunct polymerization. The latter processes (2) produce isobutane and propane simultaneously with alkyl-substituted cyclopentenyl cations and condensed aromatic compounds. In situ 13C MAS NMR and complementary ex situ GC-MS data provided evidence for a monomolecular mechanism of the 13C-label scrambling, whereas both isobutane and propane are formed through intermolecular pathways. According to 13C MAS NMR kinetic measurements, both pathways proceed with nearly the same activation energies (E(a) = 75 kJ mol(-1) for the scrambling and 71 kJ mol(-1) for isobutane and propane formation). This can be rationalized by considering the intermolecular hydride transfer between a primarily initiated carbenium ion and n-butane as being the rate-determining stage of the n-butane conversion on zeolite H-ZSM-5.     

Surface Energy of Low-Index Faces of Single-Crystal Gold in Molten Sodium,Potassium, and Cesium Chlorides

The free energies of formation of gold faces (111) and (100) in molten sodium, potassium, and cesium chlorides are measured by the meniscus weighing method. The effect of the cation size, temperature, and electric potential on the electrocapillary curve and PZC is considered. A mechanism for the anion adsorption at a charged metal surface, based on the participation of valence orbitals of the electrode metal in the formation of surface compounds, is suggested.     

Atomic force microscopy study for supermolecular microstructures in side-chain liquid crystalline polymer films

Atomic force microscopy (AFM) is employed to study the supermolecular microstructures of disclinations and inversion walls in thin films of a smectic side-chain liquid crystalline polymer. Two-dimensional nanostripes are formed in thin films when the material enters the smectic phase. A possible mechanism for their formation is also suggested. The stripes run parallel to the local director and thus decorate the overall patterns of nematic director around the disclinations and inversion walls. Three patterns involving radial, spiral, and circular supermolecular microstructures of a positive disclination with s = +1 and one hyperbolic pattern of a negative disclination with s = -1 are observed. The cores of all these microstructures exhibit circular dark centers in AFM height images. It is found that the specific configurations of a pair of (+1, -1) disclinations form during the late stage of annihilation and inversion walls always separate a pair of (+1, +1) disclinations. The analysis on the director fields around disclinations and inversion walls shows that the bend and splay elastic constants are of the same order of magnitude in the side-chain liquid crystalline polymer.     

Decarbonylation of N-carbazolylacetyl chloride in the friedel-crafts acylation reaction

Reaction products of N-carbazolylacetyl chloride under Friedel-Crafts reaction conditions include carbon monoxide, the reaction product from carbazole and formaldehyde (CF condensate), and carbazole. It is postulated that decarbonylation of N-carbazolylacetyl chloride involves intermediate formation of a N-carbazolylmethyl cation.     

Derivatives of 2,4-diamino-6-methylpteridine

Eighteen derivatives of 2,4-diamino-6-methylpteridine related to methotrexate and aminopterin have been prepared from 6-(bromomethyl)-2,4-pteridinediamine by nucleophilic displacement reactions. None of these compounds showed any antileukemic acitivity.