Structure and properties of Na-magadiite dependent on temperature

The mechanism of the thermal behaviour of Na-magadiite at a temperature range from 293–573 K was developed based on X-ray diffraction, DTA, DTL, Q-TG, and gravimetric measurements. A structure model (BRANDT et al.) previously proposed was additionally used. It is possible to show that there probably is a connection between the typical modifications of basal spacing and significant shiftings of silicate sheets. Different steps of dehydration, decrystallization and structure variations can be ascribed to the several thermal transitions. The results depend on sample treatment such as the existent or not existent solid-water vapour interaction and the establishment of equilibrium. It seems that there is a predominance of the first mentioned influence.     

Current status of biodiesel development in Brazil

In recent years, the concept of producing biodiesel from renewable lipid sources has regained international attention. In Brazil, a national program was launched in 2002 to evaluate the technical, economic, and environmental competitiveness of biodiesel in relation to the commercially available diesel oil. Several research projects were initiated nationwide to investigate and/or optimize biodiesel production from renewable lipid sources and ethanol derived from sugarcane (ethyl esters). Once implemented, this program will not only decrease our dependence on petroleum derivatives but also create new market opportunities for agribusiness, opening new jobs in the countryside, improving the sustainability of our energy matrix, and helping the Brazilian government to support important actions against poverty. This article discusses the efforts to develop the Brazilian biodiesel program in the context of technical specifications as well as potential oilseed sources.     

On the solution of singular linear systems of algebraic equations by semiiterative methods

Summary For a square matrixT ^n,n , where (I–T) is possibly singular, we investigate the solution of the linear fixed point problemx=T x+c by applying semiiterative methods (SIM's) to the basic iterationx ₀ ⁿ ,x _k T c _k–1+c(k1). Such problems arise if one splits the coefficient matrix of a linear systemA x=b of algebraic equations according toA=M–N (M nonsingular) which leads tox=M ^–1 N x+M ^–1 bT x+c. Even ifx=T x+c is consistent there are cases where the basic iteration fails to converge, namely ifT possesses eigenvalues 1 with ||1, or if =1 is an eigenvalue ofT with nonlinear elementary divisors. In these cases — and also ifx=T x+c is incompatible — we derive necessary and sufficient conditions implying that a SIM tends to a vector which can be described in terms of the Drazin inverse of (I–T). We further give conditions under which is a solution or a least squares solution of (I–T)x=c.Research supported in part by the Alexander von Humboldt-Stiftung     

Zur Bewegungsgeometrie auf der Kugel

Ohne Zusammenfassung     

In vivo 31P echo-planar spectroscopic imaging of human calf muscle

Localized phosphorus-31 NMR spectra of human calf muscle in vivo were obtained by means of echo-planar spectroscopic imaging (EPSI) with a 1.5-T whole-body scanner. The technique permits the measurement of two-dimensional 31P SI data at a minimum acquisition time of 2.4 s (8x8 voxels, TR=300 ms). With 9.4 min measurement time (TR=1100 ms, 64 averages) and 25x25x40 mm spatial resolution in vivo the 31P NMR signal-to-noise ratio (S/N) of the phosphocreatine (PCr) resonance was about 45; the multiplets of nucleoside 5'-triphosphates were resolved. Spectral quality permits quantitative assessment of the PCr signal in a measurement time that is shorter by a factor of 2 or more than the minimum measurement time feasible with chemical-shift imaging. In a functional EPSI study with a time resolution of 20.5 s on the calf muscle of volunteers, spectra showed a 40% decrease of the PCr signal intensity (at rest: S/N congruent with12) upon exertion of the muscle.     

Characterisation of the acoustic cavitation cloud by two laser techniques

An experimental investigation of the size and volumetric concentration of acoustic cavitation bubbles is presented. The cavitation bubble cloud is generated at 20 kHz by an immersed horn in a rectangular glass vessel containing bi-distilled water. Two laser techniques, laser diffraction and phase Doppler interferometry, are implemented and compared. These two techniques are based on different measuring principles. The laser diffraction technique analyses the light pattern scattered by the bubbles along a line-of-sight of the experimental vessel (spatial average). The phase Doppler technique is based on the analysis of the light scattered from single bubbles passing through a set of interference fringes formed by the intersection of two laser beams: bubble size and velocity distributions are extracted from a great number of single-bubble events (local and temporal average) but only size distributions are discussed here. Difficulties arising in the application of the laser diffraction technique are discussed: in particular, the fact that the acoustic wave disturbs the light scattering patterns even when there are no cavitation bubbles along the measurement volume. As a consequence, a procedure has been developed to correct the raw data in order to get a significant bubble size distribution. After this data treatment has been applied the results from the two measurement techniques show good agreement. Under the emitter surface, the Sauter mean diameter D(3, 2) is approximately 10 microm by phase Doppler measurement and 7.5 microm by laser diffraction measurement at 179 W. Note that the mean measured diameter is much smaller than the resonance diameter predicted by the linear theory (about 280 microm). The influence of the acoustic power is investigated. Axial and radial profiles of mean bubble diameters and void fraction are also presented.     

Numerical application of Euler's series transformation and its generalizations

Summary A nonlinear generalizationÊ _z of Euler's series transformation is compared with the (linear) Euler-Knopp transformationE _z and a twoparametric methodE . It is shown how to applyE orE _, to compute the valuef(z_o) of a functionf from the power series at 0 iff is holomorphic in a half plane or in the cut plane. BothE andE _, are superior toÊ _z . A compact recursive algorithm is given for computingE andE _,.