Structural studies of Cr-doped mullite derived from single-phase precursors

Cr-doped mullites were prepared from single-phase precursors containing up to 9.60 wt% Cr₂O₃ using a sol-gel technique followed by thermal treatment. Particle induced X-ray emission spectroscopy and X-ray powder diffraction were used to characterize the samples. Mullites were orthorhombic, space group Pbam. Cr doping caused the increase of unit-cell parameters. Strongest expansion was noticed along c-axis followed by a and b (Δc/c=0.089, Δa/a=0.061, Δb/b=0.045% per mole Cr₂O₃). A second phase, namely θ-(Al,Cr)₂O₃, was revealed by XRD in the sample containing 9.60 wt% Cr₂O₃. The structure of mullites was refined by the Rietveld method, location of Cr³⁺ was performed by the EPR spectroscopy. At low chromium doping level (Cr₂O₃ content less than ∼5 wt%) Cr³⁺ ions were substituted for Al³⁺ in the AlO₆ octahedra of the mullite structure (M1 site). For higher doping level, Cr³⁺ ions were additionally substituted for Al³⁺ in the AlO₆ octahedra of the second phase [θ-(Al,Cr)₂O₃ at 1400 °C, or α-(Al,Cr)₂O₃ at 1600 °C] which segregated in the system. Substitution of Cr³⁺ for Al³⁺ on M1 site in the mullite structure resulted in increase of average distances in (M1)O₆ octahedron and decrease of average distances in T*O₄ tetrahedron, while average distances in TO₄ tetrahedron stayed almost constant.     

A finite cutting plane method for facial disjunctive programs

This paper shows that any linear disjunctive program with a finite number of constraints can be transformed into an equivalent facial program. Based upon linear programming technique, a new, finite cutting plane method is presented for the facial programs.

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Zusammenfassung Die Arbeit zeigt, daß jedes lineare disjunktive Optimierungsproblem mit endlich vielen Restriktionen in ein äquivalentes Fazetten-Problem transformiert werden kann. Auf der Grundlage von linearer Optimierungstechnik wird für das Fazetten-Problem ein neues, endliches Schnittebenenverfahren vorgestellt.

     

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.     

Particle scattering in Euclidean Lattice Field Theories

A Haag-Ruelle Scattering Theory for Euclidean Lattice Field Theories is developed.Work supported by DAAD, Deutscher Akademischer Austauschdienst. Partially supported by CNPq     

Crossed products of groups on a category and Auslander-Reiten quivers

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 6, pp. 794–798, June, 1989.     

Thickness induced transversal percolation in Pt-Al2O3 nano-composites

Investigations of thickness induced percolation process in Pt_ξ-Al₂O₃ nano-composites were carried out using grazing angle X-ray scattering. It is shown that the morphological characteristics of the nano-scaled Pt particles change significantly within the growth transversal direction. The initially non percolated two phases Pt_ξ-Al₂O₃ nano-composites show a noteworthy tendency to a percolated morphology with a gradual transversal increase of Pt nano-particles' average diameter in addition to the increase of the Pt nano-particles' poly-dispersity. This transversal morphological evolution is followed by a percolation phenomenon of the Pt nano-particles for a thickness of about ∼119.5 nm. This transversal morphological evolution seems to corroborate far too much with a columnar growth process.     

Linear sorting withO(logn) processors

A file ofn records can be sorted in linear time givenO(log(n)) processors. Four such algorithms are presented and analyzed. All of them have reasonable hardware requirements; no memory access conflicts are generated; a constant number of communication lines per processor are needed (except for one case); and the space requirements areO(n) orO(n log(log(n))).     

A telescope illumination system for a wide-field endoscope

Endoscopic illumination systems conduct light down a built-in fibre-optic bundle to illuminate the object. Many modern endoscopes employ wide-field imaging optical systems and therefore require an illuminating beam of large divergence. This is commonly provided by placing a strong diverging lens at the far end of the fibre bundle, but it results in a poor uniformity of illumination in the object space. This paper describes the design of a telescopic illumination system to overcome this problem.