An elementary geometric nonstandard proof of the Jordan curve theorem

We give an elementary proof, using nonstandard analysis, of the Jordan curve theorem. We also give a nonstandard generalization of the theorem. The proof is purely geometrical in character, without any use of topological concepts and is based on a discrete finite form of the Jordan theorem, whose proof is purely combinatorial.Some familiarity with nonstandard analysis is assumed. The rest of the paper is self-contained except for the proof a discrete standard form of the Jordan theorem. The proof is based on hyperfinite approximations to regions on the plane.Research of the first author partially supported by FONDECYT Grant # 91-1208 and of the second author, by FONDECYT Grant # 90-0647.     

Free radical chemistry of flavan-3-ols: determination of thermodynamic parameters and of kinetic reactivity from short (ns) to long (ms) time scale

The physical chemistry and the free radical chemistry of the most abundant polyphenolic flavan-3-ols in food, catechin, its methylated metabolites, and several methylated analogues, have been investigated by laser flash photolysis and cyclic voltammetry studies. Two independent phenoxyl radicals formed upon oxidation of flavan-3-ols have been characterized and identified unambiguously: a short-lived resorcinol-like radical characterized by an absorption band at lambda = 495 nm and a long-lived catechol-like transient absorbing at lambda = 380 nm. The determination of all the thermodynamic constants of each phenolic function of flavan-3-ols, namely, redox potential (E degrees (3') = 0.13(5) V/SCE, E degrees (4') = 0.11(0) V/SCE, E degrees (5) = 0.28(5) V/SCE) and microscopic dissociation constants (pK(a3') = 9.02, pK(a4') = 9.12, pK(a5) = 9.43, pK(a7) = 9.58) were performed. These values are discussed and compared to the prediction of the density functional theory calculations made on the different species catechin, catechin phenoxyl, and catechin phenolate for each phenolic site.     

On semigroups admitting ring structure

The set of elements of an (associative) ring under multiplication form a semigroup, but not every semigroup is isomorphic to the multiplicative structure of a ring. The class of all multiplicative semigroups of all rings can not be described axiomatically. Nevertheless for unique-addition rings, for finite rings and other special cases interesting characterizations can be given. An abbreviated version was presented at the Symposium on Semigroups and the Multiplicative Structure of Rings held at the University of Puerto Rico-Mayaguez, March 9–13, 1970.     

α - Benzenesulfonyl free radicals

Allylic α-halosulfones give, on reduction with tri n-butyl tin hydride, sizeable amounts of dimers. It so appears that free radicals can indeed be formed α to an arenesulfonyl group and coupling can occur during tin hydride reduction of halides.     

Mathematical treatment of polarographic reversible adsorption waves and considerations on their origin

Polarographic current-potential characteristics and current-time curves for a Nernstian charge transfer O+neR with Langmuir or Frumkin adsorption of reactant and/or product are derived via a mathematical procedure based on the diffusion-layer approximation. It is shown that all features of reversible adsorption waves can be explained by the effect of adsorption of reactant and product upon the only rate-determining stage, namely the diffusion stage. Conversely, no conclusion can be drawn as to whether charge transfer takes place in the adsorbed or else in the non-adsorbed state from a comparison between theoretical predictions and experimental behaviour. The origin of adsorption prewaves and post-waves is justified by the concept of entropy production, which can also be used to explain the origin of the so-called adsorption pseudo-prewaves.     

Evaluating radiation risks and resource opportunities associated with phosphogypsum in the Philippines

Journal of Radioanalytical and Nuclear Chemistry - Phosphogypsum (PG) accumulates during wet-phosphoric acid production for fertilizers. In the Philippines, PG is partly (40%) utilized to produce...     

Pure bending problem for a vibrating elastic plate with non-uniform temperature

This work was performed in the University of Delaware Center for Composite Materials under the auspices of the University/Industry Research Program Application of Composite Materials to Industrial Products. The author(s) acknowledge the support of the University of Delaware/Rutgers University National Engineering Research Center for Composites Manufacturing Science and Engineering. The Center is a National Science Foundation cross-disciplinary research program.