A note on shape and stability calculations in heavy and superheavy nuclei

Attention is focused onto the spurious state contributions inherent in existing equilibrium shape and fission half-life assessments of heavy and superheavy nuclei. The results indicate that compensation for such effects is essential if these calculations are to be considered reliable.     

A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table

Let G be a graph consisting of powers of disjoint cycles and let A be an intersecting family of independent r-sets of vertices. Provided that G satisfies a further condition related to the clique numbers of the powers of the cycles, then |A| will be as large as possible if it consists of all independent r-sets containing one vertex from a specified cycle. Here r can take any value, 1?r?α(G), where α(G) is the independence number of G. This generalizes a theorem of Talbot dealing with the case when G consists of a cycle of order n raised to the power k. Talbot showed that .     

Pairings from down-sets and up-sets in distributive lattices

If D is a set of subsets of a finite set such that a?D,b ? a ? b?D, then D is called a down-set. Berge proved that any down-set D is the disjoint union of pairs {a, b} such that a ∩ b = /b/ together with the singleton {?} if |D| is odd. A proof is given of the corresponding result for finite distributive lattices, together with a number of generalizations and analogues of it; when specialized to the lattice of all subsets of a finite set, this proof is rather simpler than was Berge's.     

Approaches to the liquid chromatographic determination of carboxylic acids using potentiometric detection with a metallic copper electrode

Summary A metallic copper electrode is evaluated as a potentiometric detector for carboxylic acids. The application of this device to ion-exchange chromatography is illustrated by the determination of oxalate in urine. Oxalate was selectively detected in the presence of a 100-fold excess of sulphate after separation on a low-capacity methacrylate anion-exchange column using 0.7mM potassium hydrogen phthalate at pH 7.1 as eluent. Calibration plots were linear up to 50ppm of oxalate. Potentiometric detection has also been applied to ion-exclusion chromatography using 0.005% phosphoric acid as eluent. With this method detection limits of 0.2, 2.1, 5.0 and 5.3μg were obtained for formic, acetic, propionic and iso-butyric acids, respectively.