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.     

Modification of the Falkenhagen equation to fit conductimetric data for concentrated electrolyte solutions

A modification of the Falkenhagen equation is proposed, which fits correctly data of 29 different 1:1 aqueous electrolyte solutions up to very high concentrations. The concept of activity is used to account for deviations from ideality appearing at higher concentrations. A discussion about trends in the value of the ‘distance of closest approach between two ions’, a, and novel conductivity data for several concentrated electrolyte solutions estimated by the proposed model are also provided.     

Potentiometric study of the protonation equilibrium of Tris(Hydroxymethyl) aminomethane in aqueous sodium perchlorate solutions at 25 degrees C: construction of a thermodynamic model

The protonation equilibrium of the Tris(Hydroxymethyl)aminomethane (TRIS) has been studied using an automated potentiometric system. The temperature was kept constant at 25 degrees C and the ionic strength was 0.1, 0.5, 1.0, 2.0 and 3.0 mol dm(-3) in NaClO(4). The experimental constants, obtained at different ionic strengths, were correlated by means of the modified Bromley methodology (MBM) and the thermodynamic protonation constant found to be log (0)beta = 8.07 +/- 0.01 . Those values together with some others for NaCl medium were used to construct a thermodynamic model on both molal and molar scales for the protonation equilibrium of TRIS.     

Analysis of bulk and inorganic degradation products of stones,mortars and wall paintings by portable Raman microprobe spectroscopy

This work reports the use of a portable Raman microprobe spectrometer for the analysis of bulk and decaying compounds in carbonaceous materials such as stones, mortars and wall paintings. The analysed stones include limestone, dolomite and carbonaceous sandstone, gypsum and calcium oxalate, both mono- and dihydrated, being the main inorganic degradation products detected. Mortars include bulk phases with pure gypsum, calcite and mixtures of both or with sand, soluble salts being the most important degradation products. The pigments detected in several wall paintings include Prussian blue, iron oxide red, iron oxide yellow, vermilion, carbon black and lead white. Three different decaying processes have been characterised in the mortars of the wall paintings: (a) a massive absorption of nitrates that reacted with calcium carbonate and promoted the unbinding of pigment grains, (b) the formation of black crusts in the vault of the presbytery and (c) the thermodecomposition of pigments due to a fire.     

Interactions of metal extractant reagents. V: The aggregation of tri-n-dodecylammonium hydrogenchromate and hydrogensulphate dissolved in toluene at 40°C

The aggregation equilibria of tri-n-dodecylammonium hydrogensulphate (TLAH ₂ SO ₄ ) and hydrogenchromate (TLAH ₂ CrO ₄ ) dissolved in toluene have been studied by vapor pressure osmometry at 40°C. The experimental data can be best fit by the formation of the species (TLAH ₂ SO ₄ ) ₄ (log ₄ = 6.3 ± 0.2) and (TLAH ₂ SO ₄ ) ₅ (log ₅ = 8.0 ± 0.2) in the acid sulphate system and (TLAH ₂ CrO ₄ ) ₂ (log ₂ = 0.75 ± 0.07) in the acid chromate one.     

An Electron Diffraction and XRPD Study of Superlattice Ordering in the Elpasolite-Related Oxyfluoride K3MoO3F3

A detailed electron diffraction and XRPD study has been made of the room-temperature α polymorph of K₃MoO₃F₃. It is shown that the true symmetry of this polymorph is neither tetragonal, trigonal, nor triclinic as previously reported but rather monoclinic I1a1, a=2a_p−c_p, b=4b_p, c=a_p+2c_p when expressed in terms of the underlying elpasolite (ordered perovskite) parent structure type. A highly structured, three-dimensional, continuous diffuse intensity distribution (presumably arising from local O/F ordering and associated structural relaxation) is shown to coexist with the sharp satellite reflections characteristic of the monoclinic supercell.     

Analytical methodology to evaluate the Terrestrial Weathering of Libyan Desert Glasses and Darwin Glasses after their formation

Analytical and Bioanalytical Chemistry - Libyan Desert Glasses (LDGs) and Darwin Glasses (DGs) are impact glasses produced by the impact of an extraterrestrial body into the Earth million years...     

Multispectroscopic Characterization of Oil on Copper Painting

A small plate of oil on copper painting from the Italian Renaissance period was characterized by means of noninvasive spectroscopic methods. The study was conducted by the use of energy-dispersive X-ray fluorescence, X-ray diffraction, and Raman and diffuse reflectance infrared Fourier transform spectroscopies to determine the technology production process in such kinds of artworks. Results allowed us to characterize the copper alloy of the support media; the preparation layer, which is composed by white lead; and the pictorial layer of variable composition (green copper sulphate compounds, red lead, carbon black, brown earth pigments, gold, vermilion, and white lead). The complementarity of the techniques used in this study has proven to be highly effective.