Multiple-scattering-theory analysis of XANES spectra of SO2 adsorbed on Cu(100)

The sulphur K-edge x-ray absorption spectra of SO₂ multilayer and of SO₂ submonolayer adsorbed on Cu(100) are analysed. It is found that the dominant spectral features are of a molecular origin. The results support earlier findings that the SO₂ molecule stands perpendicular to the surface. Use of non-selfconsistent potentials does not lead to a good quantitative agreement between theory and experiment.     

Lagrangian Duality in Set-Valued Optimization

In this paper, we study optimization problems where the objective function and the binding constraints are set-valued maps and the solutions are defined by means of set-relations among all the images sets (Kuroiwa, D. in Takahashi, W., Tanaka, T. (eds.) Nonlinear analysis and convex analysis, pp. 221–228, 1999). We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type under convexity assumptions. A necessary condition and a sufficient condition for the existence of saddle points are given. The authors thank the two referees for valuable comments and suggestions on early versions of the paper. The research of the first author was partially supported by Ministerio de Educación y Ciencia (Spain) Project MTM2006-02629 and by Junta de Castilla y León (Spain) Project VA027B06.     

Temperature modulated DSC study of the kinetics of free radical isothermal network polymerization

Temperature modulated differential scanning calorimetry (TMDSC) is used to study the kinetics of the free radical isothermal polymerization of triethyleneglycol dimethacrylate (TEGDMA). Azo-bis-isobutironitrile was used as initiator. The polymerization’s temperature is lower than the final glass transition temperature of the polymer network. The measurement of the average heat flow released and the heat capacity during the reaction allows identifying the different stages of the reaction. The presence of double peaks in the heat flow is ascribed to the autoacceleration. The influence of temperature, measuring conditions and oxygen are described. Vitrification is detected by the drop in heat capacity. It occurs at increasing conversion rates for increasing temperatures. After vitrification, the diffusion-controlled reaction continues.     

Inferring mixed-culture growth from total biomass data in a wavelet approach

It is shown that the presence of mixed-culture growth in batch fermentation processes can be very accurately inferred from total biomass data by means of the wavelet analysis for singularity detection. This is accomplished by considering simple phenomenological models for the mixed growth and the more complicated case of mixed growth on a mixture of substrates. The main quantity provided by the wavelet analysis is the Hölder exponent of the singularity that we determine for our illustrative examples. The numerical results point to the possibility that Hölder exponents can be used to characterize the nature of the mixed-culture growth in batch fermentation processes with potential industrial applications. Moreover, the analysis of the same data affected by the common additive Gaussian noise still lead to the wavelet detection of the singularities although the Hölder exponent is no longer a useful parameter.     

On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

Mössbauer studies of the re-entrant spin-glass behaviour of Fe–Al alloys

Fe–Al alloys around the concentration of 30 at. % Al present re-entrant spin-glass behaviour at low temperatures. This behaviour is not completely understood and Mössbauer spectroscopy, combined with other experimental techniques, is useful to describe and explain this behaviour. Results show that the Mössbauer spectra coincide with the magnetic behaviour showed in literature and they can be explained as a magnetic cluster system whose magnetic clusters are getting smaller when the temperature is decreasing. When the temperature is reaching to the spin-glass transition at 92 K the spins in the paramagnetic matrix are moving slower and below this transition the spins are completely frozen.     

A real time method for surface cleanliness measurement

The measurement of surface cleanliness is a significant problem in many industrial and technological processes. Existing methods are based on laboratory procedures, that are not performed in real time, can not be automated, and usually are restricted to a small portion of the sample. In this study we describe a new method for real time measurement of the amount of surface dirt or contamination deposited on a surface. It relies on the ablation of the surface dirt film by means of a short laser pulse, and the subsequent measurement of the emitted sound. The intensity of the sound is proportional to the amount of surface dirt and provides a direct measurement of the cleanliness of the surface. We also developed a reference sample for calibration, based on a uniform distribution of dots printed on white paper. The density and the dot size can be easily modified providing a homogeneous, uniform and reproducible standard for the measurement. Based on this method, we designed, developed and patented the first industrial instrument for on-line determination of the degree of cleanliness of manufactured cold rolled steel plate bobbins. PACS 79.20.D; 81.70.C; 42.62.     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.