A note on the weighted norm inequality for the one-sided maximal operator

Let be the one-sided maximal function. In this note we obtain some necessary and sufficient conditions in order that the weighted weak type inequality holds for . Meanwhile, some necessary or sufficient conditions for the weighted inequality for are given.

     

Polarographic Studies of Dithiodiacetic Acid and the Uranyl-Dithiodiacetic Acid Complex

The polarographic behaviour of dithiodiacetic acid and that of U(VI) in a solution containing dithiodiacetic acid as complexing agent have been investigated. For the dithiodiacetic acid system, two waves appear over the pH range studied. The prewave is kinetic in nature and the mainwave is diffusion-controlled. However, as U(VI) is added into the dithiodiacetic acid system, the polarogram changes due to the existence of a complex. The current-potential curve of the first wave is not the normal S shape. This is due to the superposition of the first wave of the ligand and the wave due to the reduction of the U(VI) in the complex to U(V). The second wave is due to the reduction of the complex The first wave is an adsorption-controlled current and the second wave is partly diffusion-controlled and partly adsorption-controlled. We propose an electrode reaction mechanism for both systems and the complex species. The dissociation constant of the complex HASSAUO⁺₂ is found to be of the order of 10^?4.     

Solid-phase synthesis of pyrazolines and isoxazolines with sodium benzenesulfinate as a traceless linker

[reaction: see text] The preparation of pyrazoline and isoxazoline derivatives with traceless solid-phase sulfone linker strategy is described. Key steps involved in the solid-phase synthetic procedure include (i) sulfinate S-alkylation, (ii) sulfone anion alkylation, (iii) gamma-hydroxy sulfone --> gamma-ketosulfone oxidation, and (iv) traceless product release via elimination-cyclization. A library of 12 pyrazolines and isoxazolines was synthesized.     

Detailed analysis of α,ω-bis(4-hydroxybutyl) poly(dimethylsiloxane) using GPC-MALDI TOF mass spectrometry

In this study the prepolymer alpha,omega-bis(4-hydroxybutyl) poly(dimethylsiloxane), used in the formulation of oxygen permeable films, is evaluated by gel permeation chromatography (GPC) combined with matrix assisted laser desorption ionization (MALDI) time of flight (TOF) mass spectrometry (MS). Two unexpected mass distributions are observed in the mass spectra. Reaction schemes for the formation of these distributions are proposed. A solution phase trimethylsilane end group modification was performed on the prepolymer to determine whether the unexpected mass distributions occur as impurities from synthesis or as artifacts from the MS process. Evaluation of the TMS modified prepolymer indicates the unexpected mass distributions indeed occur as impurities from the synthetic procedure. Average molecular weight values are determined by traditional GPC, direct MALDI-TOF MS, and GPC-MALDI-TOF MS methods and the results are compared.     

Studies on the thermotropic liquid crystalline polymer. XII. Synthesis and properties of crosslinkable thermotropic liquid crystalline homo- and copoly(ether-ester)s

A series of crosslinkable thermotropic liquid crystalline poly(ether-ester)s and copoly(ether-ester)s was prepared. All of the polymers were crosslinked by thermal treatment or photo-irradiation upon heating. The thermal stability and thermal crosslinking reaction of these polymers were investigated. These polymers also could be crosslinked by copolymerization with vinyl monomers, such as styrene or methyl methacrylate. The crosslinked polymers exhibited thermotropic liquid crystalline behavior after softening by heating. The phase behavior of linear polymers and crosslinked polymers was studied by differential scanning calorimetry (DSC) and an optical polarizing microscope equipped with a heating stage. © 1995 John Wiley & Sons, Inc.