Problems and results on additive properties of general sequences,V

A very special case of one of the theorems of the authors states as follows: Let 1a ₁a ₂... be an infinite sequence of integers for which all the sumsa _i +a _j , 1ij, are distinct. Then there are infinitely many integersk for which 2k can be represented in the forma _i +a _j but 2k+1 cannot be represented in this form. Several unsolved problems are stated.Dedicated to our friend Professor E. Hlawka on the occasion of his seventieth birthday     

Additive functions

1<q<2 L:= _n=1 1/q ⁿ=1/q–1. [0,1] _n()=1, A _n:= _i=1 ^n–1 _i(x)/q^i+1/n x _n(x)=0, _n>. , = _{n=1 n}(x)/qⁿ. F: [0,L]R , F(x)= _{n=1 n}(x)a_n, _n=1 ¦a _n¦<. [0,L]. q(1,2), . , q(1, 2), . .     

Separation and determination of volatile compounds in synthetic wine samples by gas chromatography using UV-visible molecular absorption spectrometry as detector

This paper shows the separation and determination of eight compounds containing the OH group (ethanol, pentanol, 3-methyl-1-butanol, hexanol, phenol, benzyl-alcohol, phenylethanol and geraniol) in synthetic wine by gas chromatography using UV-Vis molecular absorption spectrometry as detection system. All the parameters affecting the separation and determination were optimised using some methods of experiment design. The analytical characteristics of each compound were calculated and detection limits ranging from 2.3 to 74 mg l(-1) have been obtained.     

Thermodynamic properties of ternary semiconducting alloys

Using the new information supplied by extended-x-ray-absorption-fine-structure measurements and the results of our structural model, we compute the bond probability of a few ternary semiconducting III–V and II–VI alloys as a function of temperature and composition in the framework of a modified quasi-chemical approximation. We derive the thermodynamic functions of mixing, considering both elastic and chemical contributions to the bond energies. We examine how the deviation from the full randomness affects the ordering of such alloys and we construct the phase diagrams in the region of phase separation. Possible formation of ordered compounds at low temperatures is predicted.     

Determination of lithium in human serum by electrothermal atomic absorption spectrometry

An efficient method was developed for the determination of nanogram levels of lithium in biological samples. Serum samples from human subjects from southeastern Spain, treated or not treated with lithium carbonate, were analyzed by electrothermal atomic absorption spectrometry. The samples were previously treated with a matrix modifier consisting of 0.1% Triton X-100 and injected through a graphite tube with L'vov platform. The Li concentrations measured by the procedure described for the 3 certified reference samples used were not significantly different (p > 0.05) than certified levels. Sample recoveries and variability during several days, with coefficients of variation from 4.00 to 14.8%, demonstrated the reliability and accuracy of this technique. Mean Li concentration determined in the serum of individuals with psychiatric disorders treated with Li (n = 117, 5.077 +/- 1.795 microg Li/mL) was significantly higher (p < 0.001) than that in individuals not treated with Li (n = 24, 1.902 +/- 2.054 ng Li/mL).     

Intramolecular "Aryl-metal chelate ring" pi,pi-interactions as structural evidence for metalloaromaticity in (aromatic alpha,alpha'-diimine)-copper(II) chelates: molecular and crystal structure of aqua(1,10-phenanthroline)(2-benzylmalonato)copper(II) three-hydrate

By reaction of Cu(2)CO(3)(OH)(2), 2-benzylmalonic acid (H(2)Bzmal), and 1,10-phenanthroline (phen), [Cu(Bzmal)(phen)(H(2)O)] x 3H(2)O (compound 1) has been obtained and characterized by thermal, spectral, magnetic, and X-ray diffraction methods. The molecular structure of 1 is remarkably similar to that of [Cu(Bzmal)(bipy)(H(2)O)] x 2H(2)O (compound 2, bipy = 2,2'-bipyridine). In both complexes, the aryl(Bzmal) ring produces an unexpected pi,pi-stacking interaction with the Cu(II)-(aromatic alpha,alpha'-diimine) chelate ring, at an average distance d(pi)(-)(pi) of 3.40 A, involving roughly parallel and smoothly slipped rings. This insight is discussed as new structural evidence for metalloaromaticity of Cu(II)-(aromatic alpha,alpha'-diimine) chelate rings. Interestingly, 1 recognizes itself by a weak intermolecular pi,pi-stacking interaction between aryl(Bzmal) ligands to give pairs of complex molecules. In contrast, there is an intermolecular pyridyl-pyridyl pi,pi-stacking interaction also forming pairs of complex molecules in 2.     

Automation of the gas analysis of14C-labelled compounds utilizing a piston-type counter tube

In this paper an automatic apparatus designed for the radioactivity measurement of¹⁴C-labelled organic compounds in the gaseous phase is described. The labelled organic compounds are combusted in a mixture of argon and oxygen. After combustion the oxygen content of the gas is eliminated by passing it through a copper packing. The water and heteroelements present are also removed and the radioactive carbon dioxide gas is swept by argon carrier gas into a piston-type counter tube. In the counter tube the piston forming a dividing wall moves forward in accordance with the rate of combustion and sweeping, and thus sucks the gases leaving the combustion tube into the effective tube volume. The anode wire is carried by a reel located in the piston and a spring device ensures its stretched state. At the end of the sweeping period methane is fed into the counter tube and the activity of the argon—methane—carbon dioxide mixture is measured in the limited proportional region. Manual and automatic operation is possible. The piston-type counter tube provides possibility for strandardization by means of extrapolation and for measurement of absolute activities.     

Synthesis and characterization of new di- and tri-nuclear cyano-bridged bis(dioximato)cobalt(III) complexes

Summary Several new neutral and cationic di- and tri-nuclear cyano-bridged bis(dioximato)cobalt(III) complexes have been synthesized and characterized (dioximato = dimethylglyoximato or diphenylglyoximato). These compounds are obtained through substitution of labile axial ligands by the nitrogen of the cyano-group in [Co(dioximato)₂(CN)₂]^– or [LCo(dioximato)₂(CN)] (L = H₂O, NH₃, or py). In the first case, the existence of only one band in the CN-stretching region of the i.r. spectrum at 2190–2200 cm^–1 is indicative of a trinuclear compound, while the presence of a second band at 2140 cm^–1 attributable to a terminal cyano-group indicates a dinuclear structure. In the presence of water, aquation of axial positions may take place at the same time as bridge formation, whereas the use of a non-aqueous solvent allows the preparation of complexes with pyridine or NH₃.     

A field theoretical approach to calculate electronic Born-Oppenheimer coupling terms

In this paper we suggest to consider the spatial distribution of the Born-Oppenheimer nonadiabatic coupling terms as fields which are created by sources, located at degeneracy points, and which can be derived using the ordinary mathematical tools of field theory. It is shown that the curl-divergence equations as formed within a given Hilbert space [M. Baer, Chem. Phys. Lett. 35, 112 (1975)] can be converted into a set of inhomogeneous coupled Poisson equations which are solved for a given set of boundary conditions. The method is applied to the three-state Hilbert subspace of the H(3) system. The numerical results are compared with ab initio calculations for which a very encouraging fit is found.