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.     

The [Ru(CN)5(pyS)](4-) complex, an efficient self-assembled monolayer for the cytochrome c heterogeneous electron transfer studies

The organothiol 4-mercaptopyridine (pyS) has been used extensively as facilitator for the assessment of heterogeneous electron transfer reaction of cytochrome c (cyt c). Its efficiency, however, is strongly affected by the instability of the adlayer due to the C-S bond cleavage. The K(4)[Ru(CN)(5)(pyS)].3H(2)O complex was synthesized and characterized aiming its utilization as an inorganic self-assembled monolayer (SAM) that would enhance the gold adlayer stability. The SAM formed by this complex onto gold (RupySAu) was characterized by spectroscopic (FTIRRAS and SERS) and electrochemical (LSV) techniques. The ex situ vibrational SERS and FTIRRAS spectra data of this SAM formed onto gold suggest a sigma interaction between the gold and sulfur atoms of the complex, inducing a perpendicular arrangement in relation to the surface normal. Additionally, SERS and FTIRRAS spectra performed for freshly prepared RupySAu adlayer and for large immersion times in the precursor solution have not shown any significant change that would reflect the degradation of the adlayer. The LSV desorption curves of this SAM indicate an enhancement in the C-S bond strength of the pyS ligand when coordinated to the [Ru(CN)(5)](3-) moiety. Comparatively to the data obtained for the desorption process of the pyS monolayer, the reductive desorption potential, E(rd), of the RupySAu presents a shift of -17 mV. This bond strength intensification leads to an increase in the stability of the monolayer. The voltammetric curves of cyt c carried out with the RupySAu electrode showed electrochemical parameters consistent with those reported for the native protein, as well as the maintenance of the electrochemical kinetic data after repetitive cycles. The results all together suggest that the pi back-bonding effect from the [Ru(CN)(5)](3-) metal center plays an important role in the stability of the RupySAu adlayer, improving the assessment of the cyt c heterogeneous electron transfer reaction.     

Electrophilic Fluorination of Organoplatinum(II) Iodides: Iodine and Platinum Atoms as Competing Fluorination Sites

A series of diphosphine Pt(II) aryl iodo complexes were reacted with XeF(2) to cleanly produce the corresponding Pt(II) difluoro complexes and free iodoarenes. However, when aryl ligands bearing fluoro substituents in the ortho positions were used, the formation of the corresponding Pt(II) aryl fluoro complexes was observed in the reaction with XeF(2). In the case of the Pt-C(6)F(5) complex, the products of the fluoride-for-iodide exchange were the only products observed by means of (31)P and (19)F NMR spectroscopy. The experimental and theoretical studies suggest that the formation of iodine-fluorine bond may accompany this transformation. The plausible "I-F" species could be trapped by electron-richer organoplatinum complexes to give a Pt(IV) transient which subsequently eliminates the corresponding aryl iodide. Hence, in some cases a pathway involving an attack of XeF(2) at the iodo ligand of Pt(II) aryl iodo complexes to generate I-F species can be operative in addition to or instead of the XeF(2) attack at the metal center. Our DFT studies demonstrate that the electrophilic attacks of XeF(2) at both sites, platinum and iodide, can be competitive.     

Investigations into beam monitors at the AEg ̄ IS experiment

Detailed diagnostic of antiproton beams at low energies is required for essentially all experiments at the Antiproton Decelerator (AD), but will be particularly important for the future Extra Low ENergy Antiproton ring (ELENA) and its keV beam lines to the different experiments. Many monitors have been successfully developed and operated at the AD, but in particular beam profile monitoring remains a challenge. A dedicated beam instrumentation and detector test stand has recently been setup at the AE \(\bar {g}\) IS experiment (Antimatter Experiment: Gravity, Interferometry, Spectroscopy). Located behind the actual experiment, it allows for parasitic use of the antiproton beam at different energies for testing and calibration. With the aim to explore and validate different candidate technologies for future low energy beam lines, as well as the downstream antihydrogen detector in AE \(\bar {g}\) IS, measurements have been carried out using Silicon strip and pixel detectors, a purpose-built secondary emission monitor and emulsions. Here, results from measurements and characterization of the different detector types with regard to their future use at the AD complex are presented.