A Six-Vertex Theorem for Bounding Normal Planar Curves

We prove that the number of vertices of a smooth normal planarcurve is at least 6, if it bounds a surface other than the disk.     

Radiotracer studies of the antitumor metallocene molybdocene dichloride with biomolecules

Neutron irradiation of Cp₂MoCl₂ for 24 h afforded the radiotracer Cp₂⁹⁹MoCl₂ which was characterised by UV–Vis spectroscopy and thin layer chromatography. Binding experiments with the thiol containing protein human serum albumin (HSA) or calf thymus DNA, were monitored for ⁹⁹Mo using a gamma counter. Under the conditions investigated, molar ratios of binding of 0.2:1 (Cp₂MoCl₂:DNA) and 9.4:1 (Cp₂MoCl₂:HSA) were calculated. The results are consistent with in vitro coordination studies that have shown strong preferential interaction of Cp₂MoCl₂ with thiols versus other donor sites in biomolecules including DNA.     

An Enumerative Geometry for Magic and Magilatin Labellings

A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without the diagonals). A magilatin labelling is like a magic labelling but the values need be distinct only within each set. We show that the number of n × n magic or magilatin labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in the square. Our results differ from previous ones because we require that the entries in the square all be different from each other, and because we derive our results not by ad hoc reasoning but from a general theory of counting lattice points in rational inside-out polytopes. We also generalize from set systems to rational linear forms. Dedicated to the memory of Claudia Zaslavsky, 1917–2006 Received August 10, 2005     

Nonaqueous diazotization of 4-amino-3-arylisothiazole-5-carboxylate esters

4-Amino-3-arylisothiazole-5-carboxylate esters are converted to the corresponding desamino, chloro, bromo, and iodo esters by processes involving nonaqueous diazotization. These related procedures open up the possibility for the conversion of readily available heterocyclic ortho-amino esters and nitriles to related heterocyclic derivatives, which are not easily obtained by alternate routes.     

The neutral weak current of the nucleon

A brief review of the structure of the nucleon as determined through parity-violating electron scattering is presented. The relationship between the electromagnetic and neutral weak currents is developed in a pedagogical introduction. Recent results and present measurements are discussed.     

The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

Separation of non UV-absorbing cations by capillary electrophoresis

Summary A new buffer system for the separation of cations with capillary electrophoresis using indirect UV-detection is described. p-Aminopyridine can be used in the wide pH-range between 3 and 10. High-speed separations of positively charged non-UV absorbing ions are possible. Separation of ions with similar mobilities can be achieved by the addition of complexation reagents. The separation of potassium and ammonium is possible either with the addition of crown ether or at high pH-values. Transition metals can be separated by adding 2-hydroxybutyric acid to the buffer.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Anomalous capacitance of quantum well double-barrier diodes

The S-parameters of several different quantum well double barrier diodes have been measured. A technique has been developed for measuring whisker contacted diodes with and HP 8510B automatic network analyzer. Special coaxial mounts using K-connectors were designed to enable measurements up to 20 GHz. The voltage-dependent conductance and capacitance were derived from the measured reflection coefficient of each device. The C/V characteristics were observed to exhibit an anomalous increase at voltages corresponding the the negative differential resistance region (NDR). These are the first reported S-parameter measurements in the negative differential resistance region of quantum well double barrier diodes. A theory is presented that explains, in part, the observed results.     

Topochemically Controlled Redox Reactions in the System In/Sn/Cl

The difference in reactivity of the two modifications of InCl in solid state reactions with SnCl₂ is discussed. It is explained on the basis of semi‐empirical and ab initio calculations giving the density of states diagrams of InCl and the energies of possible disproportionation reactions. Their general features are discussed on the basis of a simple bonding picture for open‐packed structures involving inert pair elements. A detailed analysis of the DOS distribution allows to pinpoint the observed redox instability to a specific structural feature of α‐InCl.