Time-Resolved Fourier Transform Emission Spectroscopy of CF<Subscript>3</Subscript>Br and CF<Subscript>3</Subscript>CFHCF<Subscript>3</Subscript> in a Pulsed Electrical Discharge

The environmentally important decomposition of halogenated species CF₃Br and CF₃CHFCF₃ in helium discharge plasma was investigated by time-resolved high-resolution Fourier transform infrared emission spectroscopy. Contrary to classical pyrolysis, a deeper fragmentation of precursors up to atoms and lower molecular species was observed. Excited molecular products CF, CF₂ and CF₄ achieved the maximal concentration in the afterglow. The high concentration of all these species is in agreement with a kinetic model based on radical chemistry. The non-detectable concentration of CF₃ can be connected to its high reactivity and the formation of more stable products, CF₄ and CF₂, by addition or release of a fluorine atom, respectively. Other products included HF, HBr, CO and cyano compounds that were produced by secondary reactions with traces of water vapor, atmospheric oxygen and nitrogen present in original industrial samples as impurities.     

Oxygen-isotope labeled titania: Ti(18)O2

(18)O-isotope labelled titania (anatase, rutile) was synthesized. The products were characterized by Raman spectra together with their quantum chemical modelling. The interaction with carbon dioxide was investigated using high-resolution FTIR spectroscopy, and the oxygen isotope exchange at the Ti(18)O(2)/C(16)O(2) interface was elucidated.     

A spectral approach to bandwidth and separator problems in graphs

Lower bounds on the bandwidth, the size of a vertex separator of general undirected graphs, and the largest common subgraph of two undirected (weighted) graphs are obtained. The bounds are based on a projection technique developed for the quadratic assignment problem, and once more demonstrate the importance of the extreme eigenvalues of the Laplacian. They will be shown to be strict for certain classes of graphs and compare favourably to bounds already known in literature. further improvement is gained by applying nonlinear optimization methods.     

The cut cone III: On the role of triangle facets

The cut polytopeP _n is the convex hull of the incidence vectors of the cuts (i.e. complete bipartite subgraphs) of the complete graph onn nodes. A well known class of facets ofP _n arises from the triangle inequalities:x _ij +x _ik +x _jk ≤ 2 andx _ij -x _ik -x _jk ≤ 0 for 1 ≤i,j, k ≤n. Hence, the metric polytope M_n, defined as the solution set of the triangle inequalities, is a relaxation ofP _n . We consider several properties of geometric type for P_n, in particular, concerning its position withinM _n . Strengthening the known fact ([3]) thatP _n has diameter 1, we show that any set ofk cuts,k ≤ log₂ n, satisfying some additional assumption, determines a simplicial face ofM _n and thus, also, ofP _n . In particular, the collection of low dimension faces ofP _n is contained in that ofM _n . Among a large subclass of the facets ofP _n , the triangle facets are the closest ones to the barycentrum of P_n and we conjecture that this result holds in general. The lattice generated by all even cuts (corresponding to bipartitions of the nodes into sets of even cardinality) is characterized and some additional questions on the links between general facets ofP _n and its triangle facets are mentioned.     

Bi(Pb)–Sr–Ca–Cu–O layers prepared by a new method of laser ablation in air

Bi(Pb)–Sr–Ca–Cu–O layers were prepared by laser ablation in air, that is without using a vacuum chamber. At this method a much higher density of pulse energy of laser beam is required (10–30 J cm^–2) in comparison with the standard method (1–3 J cm^–2). The mentioned condition has specific effects on the nature of the transport of material from the target. As follows from the electron microprobe analysis of the layers, the starting composition of the transported material is identical with that of the superconducting phase sintered in the target; one exception represents Pb, the content of which in the transported material is lower. The image of the process is complemented by UV/VIS spectroscopy scans of the plasma plume.     

The distribution of ions and their valencies in manganese ferrites I. MnFe2O4+γ ferrites

A model for the distribution of cations in the spinel lattice of manganese ferrites MnFe₂O₄₊ was elaborated on the basis of the experimental studies of the basic magnetic quantities, electrical conductivity and magnetic relaxation of the given ferrites, taking into consideration their crystallographic properties. The conclusions following from this model are in good agreement with the experimental results obtained by us and by other authors both for stoichiometric manganese ferrite and for a ferrite where 0.

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I. MnFe₂O₄₊

, MnFe₂O₄₊ . , , , , , 0.

     

On periodical behaviour in societies with symmetric influences

We propose a simple model of society with a symmetric functionw(u, v) measuring the influence of the opinion of memberv on that of memberu. The opinions are chosen from a finite set. At each step everyone accepts the majority opinion (with respect tow) of the other members. The behaviour of such a society is clearly periodic after some initial time. We prove that the length of the period is either one or two.     

Nonlinear equations with expansive nonlinearities

Summary We prove existence and multiplicity theorems for nonlinear equations at resonance with expansive nonlinearities.

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Riassunto Si provano teoremi di esistenza e molteplicità per equazioni nonlineari in risonanza con nonlinearità espansiva.

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These results were obtained while the second author was visiting the University of Ferrara through a grant of C.N.R.

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Supported by C.N.R., G.N.A.F.A.     

The distribution of ions and their valencies in manganese ferrites II. Mn1+xFe2-xO4+y ferrites

The influence of the oxygen content on the saturation magnetic moment and the Curie temperature was studied experimentally on non-stoichiometric manganese ferrites having a varying excess of manganese. Taking into consideration the results of studying the electrical conductivity and magnetic relaxation effects, a model was elaborated for the distribution of ions in these ferrites, which starts out from the distribution of ions in stoichiometric manganese ferrite. The experimental results obtained by us and those of other authors confirm the justification of this model.

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II. Mn_1+xFe_2-xO_4+y

. , . .

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In conclusion the authors thank members of their technological department for preparing the samples and M. Mikulá for carefully carrying out the chemical analyses.