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.     

Novel silicon-containing drugs derived from the indomethacin scaffold: Synthesis, characterization and evaluation of biological activity

Synthesis, spectroscopic characterization and in vitro pharmacological and cancer cell growth inhibitory activity studies of new silicon-containing compounds based on the indomethacin scaffold are now reported. Amidation of the indomethacin carboxylate group using amino-functional silanes generated a series of novel lipophilic derivatives of indomethacin. The pharmacological activity of these derivatives tested against human recombinant cyclooxygenase-1 and 2 demonstrated that the silicon-containing derivatives are cyclooxygenase-2 (COX-2) selective. The silicon-containing amides of indomethacin demonstrated in vitro growth inhibitory activity against human MiaPaCa-2 pancreatic carcinoma cells at low μM concentrations. The 3a and 3c derivatives exhibited the most potent in vitro antiproliferative activity, with IC₅₀ <6.0 μM, compared to unmodified indomethacin having an IC₅₀100 μM. We dedicate this paper to Prof. Mitsuo Kira, outstanding organosilicon chemist and valued friend.     

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.     

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.     

Synthesis of a silene from 1,1-dilithiosilole and 2-adamantanone

Reaction of 1,1-dilithio-1-sila-2,3,4,5-tetraphenylsilole with 2-adamantanone produces a 5-silafulvene. This represents a new method for synthesis of silenes, leading to the first example of a silapentafulvene.     

A disilapentalene and a stable diradical from the reaction of a dilithiosilole with a dichlorocyclopropene

The reaction of 1,1-dilithio-2,3,4,5-tetraphenylsilole (1) with 1,1-dichloro-2,3-diphenylcyclopropene (2) leads to the novel 1,4-disila-1,4-dihydropentalene (4), as well as an exceptionally stable diradical for which the structure 3 is suggested. The diradical is unreactive toward water, methanol, and chloroform; upon heating it transforms into 4. Structure 3 for the paramagnetic species is proposed on the basis of EPR data and theoretical calculations. The trans-trans isomer of diradical 3 was calculated to be more stable than its cis-cis isomer. The strong and stable EPR signal in the reaction mixture is probably due to the trans-trans isomer of diradical 3 in the triplet state. A reaction scheme describing the formation of 3 and 4 is presented.