An acetic anhydride pyridine mixture acetylates hydroxyl groups in tissue sections. The acetyl groups can be removed from tissue sections by weak alkali. Sections acetylated by acetic anhydride pyridine no longer produce aldehydes after oxidation by periodic acid. Acetylated sections subjected to weak alkali regain the ability to produce aldehydes after oxidation by periodic acid. Acetylation o...

Periodic patterns are observed when supported lipid monolayers doped with low concentrations of fluorescent lipid probes are observed with epi-fluorescence microscopy. Monolayers of dipalmitoyl phosphatidylcholine were examined on air-water interfaces and also on alkylated glass coverslips. The patterns are formed by periodic arrays of solid-phase lipid domains in equilibrium with fluid-phase l...

We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, ...

Since the extension principles of constructing wavelet frames were presented, a lot of symmetric and compactly supported wavelet frames with high vanishing moments have been constructed. However the problem of constructing periodic wavelet frames with the help of extension principles is open. In this paper, we will construct tight periodic wavelet frames using the unitary extension principle an...

Wavelet transforms for discrete-time periodic signals are developed. In this nite-dimensional context, key ideas from the continuous-time papers of Daubechies and of Cohen, Daubechies, and Feauveau are isolated to give a concise, rigorous derivation of the discrete-time periodic analogs of orthonormal and symmetric biorthogonal bases of compactly supported wavelets. These discrete-time periodic...

para-aminobenzoic acid is supported on silica gel via reaction of activated silica gel and p-aminobenzoic acid which is then converted to its manganese and cobalt salts. a mixture of the manganese and cobalt salts of the acid is used to catalyze allylic and benzylic alcohols to their corresponding carbonyl compounds in reasonable yields using oxygen or air. reactions are clean and the catalysts...