Scaling laws of complex band random matrices

We study a model of complex band random matrices capable of describing the transitions between three different ensembles of Hermitian matrices: Gaussian orthogonal, Gaussian unitary and Poissonian. Analyzing numerical data we observe new scaling relations based on the generalized localization length of eigenvectors. We show that during transitions between canonical ensembles of random matrices the changes of statistical properties of eigenvalues and eigenvectors are correlated.     

BOUNDS IN THE TURING REDUCIBILITY OF FUNCTIONS

A hierarchy of functions with respect to their role as bounds in the Turing reducibility of functions is introduced and studied. This hierarchy leads to a certain notion of incompressibility of sets which is also investigated.     

Copper(II) and oxovanadium(IV) complexes of α-hydroxymethylserine

Summary Potentiometric and spectroscopic measurements were used to characterize the binding ability of -hydroxy-methylserine (Hms) with copper(II) and oxovanadium(IV) ions. The ligand was found to be generally a more efficient chelating agent than serine. Both of the deprotonated hydroxyl groups of Hms can be involved in coordination to vanadyl ions, whereas copper(II) binds in the same way as with serine.     

An investigation of the reliability of the Galerkin-Petrov method with a special study of the helium atom ground state

A convergence characterization of the Galerkin-Petrov method by means of quantities characterizing pairs of subspaces is presented. The usefulness of our approach for setting up reliable computational schemes is demonstrated for the He atom ground state. Several methods of constructing pairs of subspaces for use in quantum chemistry are suggested.     

Vibrational frequencies and force constants of N2O4 in complexes with molecules of different solvents determined by Raman spectra andAb initio calculation

The Raman spectra of N₂O₄ solutions in organic solvents have been recorded. The frequencies ofv ₁,v ₂, andv ₃ bands of N₂O₄ increase with increasing solvent electron-donor properties. Especially large changes ofv ₃ N-N stretching band have been observed (254.5 cm^–1 in n-hexane, 276.5 cm^–1 in 1,4-dioxane). The ab initio calculations have shown that the interaction between N₂O₄ and electron-donor molecules causes an increase of N-N and N-O stretching and O-N-O bending force constants of N₂O₄ in agreement with the results of Raman study.     

Comonomer effects with high-activity titanium- and vanadium-based catalysts for ethylene polymerization

High-activity titanium- and vanadium-based catalysts for ethylene polymerization frequently show an increase in reaction rate in the presence of an α-olefin. The magnitude of this increase depends on the specific α-olefin. The results show propylene > 1-butene > 1-hexene in increasing initial reaction rates. Addition of certain electron-donor compounds to these catalysts can lower the magnitude of the comonomer effect and, in some cases, totally eliminate such an effect. Among the classes of electron-donor compounds examined were ether-alcohols, ether-esters, amino-alcohols, alkoxysilanes, siloxanes, and phosphine oxides. Reaction kinetics show that the presence of a comonomer can influence the kinetic order of the reaction. These results can be interpreted using a mechanistic model involving two vacant coordination positions at the active sites. In this model electron donors and comonomers are viewed as Lewis-base ligands which influence features of chain propagation and chain termination. As Lewis-base ligands, the comonomers can also increase the number of active sites available for polymerization. Catalyst deactivation following the initial comonomer rate increase is believed to be caused by reaction with the Lewis bases (α-olefin included) in the system and by possible reduction in the oxidation state of the metal centers. The most acidic metal centers activated by the comonomer are most reactive to Lewis bases and deactivate most rapidly. Veratrole (1,2-dimethoxybenzene) can be employed as a probe for estimating the number of bis-vacant coordination sites in vanadium-based catalysts. Addition of low levels of veratrole led to significant deactivation of the vanadium-based catalyst. © 1993 John Wiley & Sons, Inc.     

Long-range tin-tin coupling constants: II. Two-bond coupling via carbon

Tin-119 and carbon-13 NMR data for a total of 34 compounds containing the grouping Sn-C-Sn (C is either sp³- or sp²-hybridised) are presented and discussed. In organotin derivatives of alkanes, ²J(Sn-C-Sn) can only be correlated with ¹J(Sn-C₂) if a sign change for the former coupling is assumed. In most of the compounds of this type studied, ¹J(Sn-CH₃) is, due to rehybridisation and in contrast to the usual situation, larger than ¹J(Sn-C²); the same is true in some cases for distannylakenes, the behaviour of which is complicated by changes in the torsional angle about the carbon-carbon double bond. Thus correlation of ²J(Sn-C-Sn) with other spectral parameters is not possible in these cases. The total tin chemical shift range for compounds MeⁿSn(CH₂MME₃)_4-n (M  C, Si, Ge, Sn; n  0–4) is 140 ppm. Incorporation of a ditin fragment in a six-membered ring causes a downfield tin shift of 30 ppm.     

Comparison of the evaporation processes of classical spectrography and optical spectrometry tandem technique for the determination of the relevant environmental elements

The evaporation as a part of the spectrochemical excitation process is a complicated procedure during which different thermo-chemical reactions connected mainly to the formation of carbides are overshot. This one is accelerated namely at the 4000 K on the top of the carrier electrode. The carbide creation markedly affects the evaporation process of single elements of the given matrix and modifies this process. In spite of this it is evident that the intensity of the DC arc has a significant impact on the evaporation of all elements. The evaporation capability of two optical methods, the classical non-controlled direct current (DC) arc spectrography and the PC controlled DC arc optical emission spectrometry, have been compared for the determination of some environmental important elements (Al, Cr, Ni, and V). The experiments were carried out using grating spectrograph PGS-2 and simultaneous multi-channel LECO 750 spectrometer which is connected to a separated evaporation cell and adjusted to the Marinković plasma source. Standardized evaporation curves were designed and the half-time (t_50%) values and the total (t_100%) evaporation time values were calculated. The basic statistical evaluation was done and the main figures of the merit were calculated.