On fencing problems

Fencing problems regard the bisection of a convex body in a way that some geometric measures are optimized. We introduce the notion of relative diameter and study bisections of centrally symmetric planar convex bodies, bisections by straight line cuts in general planar convex bodies and also bisections by hyperplane cuts for convex bodies in higher dimensions. In the planar case we obtain the best possible lower bound for the ratio between the relative diameter and the area.     

Extractive fluorimetric determination of ultratraces of lead with cryptand 2.2.2 and eosin

A new speetrofluorimetric method for determination of ultratraces of lead is based on solvent extraction into chloroform of the ion-pair formed between the positively-charged cryptate of lead with cryptand 2.2.2 and the eosinate anion. The detection limit for lead is 1 ng ml , and the linear working range is from the detection limit to 250 ng ml . The relative standard deviation is 3.7% at the 100 ng ml level. The method is highly selective for the extraction and determination of lead in the presence of other cations, and has been tested for direct determination of lead contamination in soft drinks. Aggregation of the extracted ion-pair in the organic phase has been demonstrated in fundamental extraction studies.     

Multiple Stable Conformations Account for Reversible Concentration‐Dependent Oligomerization and Autoinhibition of a Metamorphic Metallopeptidase

Molecular plasticity controls enzymatic activity: the native fold of a protein in a given environment is normally unique and at a global free‐energy minimum. Some proteins, however, spontaneously undergo substantial fold switching to reversibly transit between defined conformers, the “metamorphic” proteins. Here, we present a minimal metamorphic, selective, and specific caseinolytic metallopeptidase, selecase, which reversibly transits between several different states of defined three‐dimensional structure, which are associated with loss of enzymatic activity due to autoinhibition. The latter is triggered by sequestering the competent conformation in incompetent but structured dimers, tetramers, and octamers. This system, which is compatible with a discrete multifunnel energy landscape, affords a switch that provides a reversible mechanism of control of catalytic activity unique in nature.     

From the Galilei to the Lorentz group in a general light-cone frame

The most general coordinate system in which the Galilean symmetries of the ordinary and the Bell and Ruegg light-cone frames appear is found. With a modification of this general coordinate system it is possible to go from the Galilei group in two space dimensions to the Lorentz group, a process inverse to the contraction of the Lorentz group with respect to the subgroup of rotations. As an example of the applicability of this modified general light-cone frame, the two-dimensional Schrödinger-Pauli equation is obtained to all orders.     

X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

Determination of amino acids in apple extracts by high performance liquid chromatography

Summary A rapid and sensitive method for the simultaneous determination of primary amino acids in apple is described. After sample preparation, amino acids were derivatized with o-phthaldialdehyde/2-mercaptoethanol and separated on a reversed phase column with a gradient of phosphate buffer-tetrahydrofuran-methanol as the mobile phase. Detection was carried out with a fluorescence detector at excitation and emission wavelengths of 340 nm and 425 nm respectively. Recovery studies showed good results for all substances (91–109%) (with coefficients of variation ranging, from 0.1 to 9.0%). This method was applied to the monitoring of amino acids during the ripening of apples.     

Volume approximation of smooth convex bodies by three-polytopes of restricted number of edges

For a given convex body K in \Bbb R³{\Bbb R}^3 with C ² boundary, let P ^c _n be the circumscribed polytope of minimal volume with at most n edges, and let P ⁱ _n be the inscribed polytope of maximal volume with at most n edges. Besides presenting an asymptotic formula for the volume difference as n tends to infinity in both cases, we prove that the typical faces of P ^c _n and P ⁱ _n are asymptotically regular triangles and squares, respectively, in a suitable sense.     

Sequential extraction--spectrofluorometric determination of lead and cadmium using cryptands.

A spectrofluorimetric method for the determination of ultratrace amounts of lead and cadmium is described based on the sequential extraction of the ternary ion-association complexes formed between the cation, a cryptand as the ligand and eosin as a counter ion. A linear working range from the detection limit (0.5 ng ml(-1) to 250 ng ml(-1) of lead and to 1 50 ng ml(-1) of cadmium was obtained. The relative standard deviation was 2-4%. The proposed method has been applied successfully to the determination of lead and cadmium in zinc metals and soft drinks.