Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Iron-rich spinels from Brazilian soils

Tropical soils often contain high amounts of iron oxides. Hematite (αFe₂O₃) and goethite (αFeOOH) are the most widespread iron oxides, but magnetite (Fe₃O₄) and maghemite (γFe₂O₃) occur in magnetic pedons. A wide range of spinel compositions in the Fe₃O₄-γFe₂O₃ series has been identified in magnetic Brazilian soils. Isomorphic substitution of mainly Ti⁴⁺, Al³⁺ and Mg²⁺, but also of Cr³⁺ and Mn²⁺ and other minor elements for iron are related to changes in their structural stability and magnetic properties. Magnetic iron oxides of selected Brazilian pedodomains are discussed, distinguishing those produced from mafic rocks (tuffite, basalt), where primary magnetite transforms to maghemite, from those produced in non-mafic lithologies (such as steatite), where inherited magnetite may be exceptionally stable in the soil. This revised version was published online in August 2006 with corrections to the Cover Date.     

Vortex states in soft magnets in two and three dimensions

The magnetization curves of arrays of near-spherical soft ferromagnetic particles are compared with those of quasi-two-dimensional dots with similar radius prepared by a rapid e-beam lithographic technique. Curves for the three-dimensional particles are anhysteretic and fit a M(H)/M_s=tanh(cμ₀H) law, whereas the two-dimensional arrays show irreversible segments in the first and third quadrants where the planar vortex state transforms to a collinear state by discontinuous rotation of magnetization about an axis perpendicular to the vortex axis. The additional symmetry of the spherical particle allows this rotation to occur continuously, without energy barriers due to the demagnetizing field.     

Simultaneous sensing of L-tyrosine and epinephrine using a glassy carbon electrode modified with nafion and CeO2 nanoparticles

An electrochemical sensor was developed and tested for detection of L-tyrosine in the presence of epinephrine by surface modification of a glassy carbon electrode (GCE) with Nafion and cerium dioxide nanoparticles. Fabrication parameters of a surfactant-assisted precipitation method were optimized to produce 2–3 nm CeO₂ nanoparticles with very high surface-to-volume ratio. The resulting nanocrystals were characterized structurally and morphologically by X-ray diffractometery (XRD), scanning and high resolution transmission electron microscopy (SEM and HR-TEM). The nanopowder is sonochemically dispersed in a Nafion solution which is then used to modify the surface of a GCE electrode. The electrochemical activity of L-tyrosine and epinephrine was investigated using both a Nafion-CeO₂ coated and a bare GCE. The modified electrode exhibits a significant electrochemical oxidation effect of L-tyrosine in a 0.2 M Britton-Robinson (B-R) buffer solution of pH 2. The electro-oxidation peak current increases linearly with the L-tyrosine concentration in the molar concentration range of 2 to 160 μM. By employing differential pulse voltammetry (DPV) for simultaneous measurements, we detected two reproducible peaks for L-tyrosine and epinephrine in the same solution with a peak separation of about 443 mV. The detection limit of the sensor (signal to noise ratio of 3) for L-tyrosine is ~90 nM and the sensitivity is 0.20 μA μM⁻¹, while for epinephrine these values are ~60 nM and 0.19 μA μM⁻¹. The sensor exhibited excellent selectivity, sensitivity, reproducibility and stability as well as a very good recovery time in real human blood serum samples.

Simultaneous electrochemical determination of L-tyrosine and epinephrine in blood plasma with Nafion-CeO₂/GCE modified electrode showing a 443 mV peak-to-peak potential difference between species oxidation peak currents.

     

Differential non-destructive image current detection in a fourier transform quadrupole ion trap

Dual-detector differential non-destructive Fourier transform detection in a quadrupole ion trap is shown to improve signal intensity and reduce noise compared with spectra recorded using a single detector. A larger area detector in each end-cap electrode is machined to fit its hyperbolic shape and so minimize field imperfections on the z-axis. Argon, acetophenone and bromobenzene spectra were recorded to allow a comparison between single- and dual-detector (differential) modes of detection and to demonstrate the improvement achieved with differential detection. Copyright 1999 John Wiley & Sons, Ltd.     

An octahedral random network

Construction, topology and radial distribution functions of a 2064-atom continuous random network of AB₃ stoichiometry are described. It is composed of corner-sharing AB₆ octahedra, with no broken bonds. Odd-membered A rings predominate. Density is 11% greater than for the ideal AIF₃ structure.     

Quantitative Mössbauer analysis of maghemite-hematite mixtures in external applied field

Mixtures of synthetic maghemite and hematite have been studied by Mössbauer spectroscopy at room temperature with an applied magnetic field of 0.2 T. The results show that the relative area of each subspectrum reproduces very satisfactorily the weighted quantities, whereas the agreement is poor in absence of the external field, particularly for higher fractions of hematite.