A <Emphasis Type="Italic">V</Emphasis>-cycle Multigrid for multilevel matrix algebras: proof of optimality

We analyze the convergence rate of a multigrid method for multilevel linear systems whose coefficient matrices are generated by a real and nonnegative multivariate polynomial f and belong to multilevel matrix algebras like circulant, tau, Hartley, or are of Toeplitz type. In the case of matrix algebra linear systems, we prove that the convergence rate is independent of the system dimension even in presence of asymptotical ill-conditioning (this happens iff f takes the zero value). More precisely, if the d-level coefficient matrix has partial dimension n _r at level r, with , then the size of the system is , , and O(N(n)) operations are required by the considered V-cycle Multigrid in order to compute the solution within a fixed accuracy. Since the total arithmetic cost is asymptotically equivalent to the one of a matrix-vector product, the proposed method is optimal. Some numerical experiments concerning linear systems arising in 2D and 3D applications are considered and discussed.     

An investigation on the nature of the peptide at m/z 904, overexpressed in plasma of patients with colorectal cancer and familial adenomatous polyposis

In an investigation devoted to the search for plasma markers for colorectal cancer (CRC), carried out by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry, a series of overexpressed peptides were identified in the plasma of patients. Among them the peptide with molecular weight 903 Da was the most abundant one, with a mean +/- (SD) relative abundance of 37 +/- 17% and a frequency over 60%. Interestingly, also in plasma samples of ten subjects affected by familial adenomatous polyposis (FAP), the peptide with molecular weight 903 was overexpressed. In this investigation, MALDI/MS/MS experiments were carried out on the ion at m/z 904 detected in the MALDI mass spectra of CRC and FAP patients. The data analysis by SwissProt.2007.01.09 indicates that this peptide is due to the sequence RPPGFSPF, found in the kininogen-1 precursor, which is an alpha-2-thiol proteinase inhibitor. In the case of subjects affected by a particular FAP syndrome, the MALDI/MS/MS spectra were quite different from those obtained from CRC and FAP patients. In fact, two sequences have been evidenced: RPPGFSPF belonging to kininogen-1 precursor, and PRKSSSSR belonging to Forkhead box protein 01A.     

Enzyme sensor for the electrochemical detection of the marine toxin okadaic acid

An enzyme sensor for the electrochemical detection of the marine toxin okadaic acid (OA) has been developed. The strategy was based on the inhibition of immobilised protein phosphatase (PP2A) by this toxin and the electrochemical measurement of the enzyme activity by the use of appropriate enzyme substrates, electrochemically active after dephosphorylation by the enzyme. Colorimetric inhibition assays have demonstrated the PP2A from human red blood cells to be more sensitive and to provide a wider linear range than the one produced by genetic engineering. Catechyl monophosphate (CMP) and p-aminophenyl phosphate (p-APP) have been tested as enzyme substrates, the former providing higher electrochemical currents at convenient working potentials (+450 mV vs. Ag/AgCl). Biosensors with 19.1 and 5.0 U of immobilised enzyme have been applied to the OA detection. Whereas the 19.1-U biosensor has provided higher electrochemical currents and more reliable determinations, the 5.0-U one has attained a lower 50% inhibition coefficient (IC₅₀) value (22.19 in front of 154.84 μg L⁻¹) and a larger working range (2.69-171.87 in front of 42.97-171.87 μg L⁻¹). The analysis of toxicogenic dinoflagellate extracts with both biosensors and the comparison with the colorimetric assay and liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS) have demonstrated the applicability of the developed electrochemical devices as screening biotools for the assessment of the toxicity of a sample.     

Geometry and Conformation of Thietanium Ions from Diffraction Data and Ab Initio Calculations

Four‐membered ring thiosulfonium ions may be obtained quantitatively and under mild conditions by anionotropic rearrangement of C‐(tert‐butyl)‐substituted thiiranium ion precursors. Thus, t‐4‐(tert‐butyl)‐r‐1,2,2,c‐3‐tetramethylthietanium tetrafluoroborate or hexachloroantimonate ( 2a or 2b , resp.) were formed from thiiranium ion 1 . The thietanium salts 2a and 2b were characterized by X‐ray crystal‐structure analysis. Their cation geometry was also optimized by ab initio calculations at the RHF/6‐31G*//RHF/6‐31G* level, as were those of its stereoisomer 3 and of the unsubstituted S‐methylthietanium ion 5 . Comparison of 2 , 3 , and 5 with 4 – the only other thietanium ion studied by XRD, where the C‐atoms of the thioniacyclobutane ring are part of a trinorbornane skeleton – indicates that, in these systems, relief from substituent overcrowding is easily achieved by a folding of the four‐membered ring along the line connecting the two opposite C‐atoms. The corresponding ring‐deformation normal mode has a calculated frequency as low as 109 cm⁻¹ in ion 5 , to be compared with a frequency of 138 cm⁻¹ in methylcyclobutane. For thietanium ion 2 , the frequencies of the two normal modes involving such ring deformation have calculated values of 61 and 85 cm⁻¹.     

Solvent Trapping during Large Volume Injection with an Early Vapor Exit,Part 2: Chromatographic Results and Conclusions

Solvent trapping reconcentrates volatile components after injection or on-line transfer of large volumes. When an early vapor exit is used, typically after a 5–10 m × 0.53 mm i.d. uncoated precolumn, the solvent trapping process differs from that described previously. The visual experiments and the conclusions drawn therefrom, as described in a previous paper, are supplemented with chromatographic results. They show that even hexane can be quantitatively analyzed in 250 μl of a pentane solution. Injection of a volume of 250 μl by vaporizer/precolumn solvent splitting was used in the analysis of gasoline in drinking water. Conditions for the transfer of a 1000 μl volume can easily be adjusted through detection of the front end of the flooded zone by a thermocouple mounted on the outer wall of the precolumn.     

The reaction-annihilator distribution and the nonholonomic Noether theorem for lifted actions

We consider nonholonomic systems with linear, time-independent constraints subject to positional conservative active forces. We identify a distribution on the configuration manifold, that we call the reaction-annihilator distribution ℜ°, the fibers of which are the annihilators of the set of all values taken by the reaction forces on the fibers of the constraint distribution. We show that this distribution, which can be effectively computed in specific cases, plays a central role in the study of first integrals linear in the velocities of this class of nonholonomic systems. In particular we prove that, if the Lagrangian is invariant under (the lift of) a group action in the configuration manifold, then an infinitesimal generator of this action has a conserved momentum if and only if it is a section of the distribution ℜ°. Since the fibers of ℜ° contain those of the constraint distribution, this version of the nonholonomic Noether theorem accounts for more conserved momenta than what was known so far. Some examples are given.      

Ab initio and DFT Study on 2H-Isoxazol-5-one: Consequences of Strong Intermolecular Hydrogen-Bond Formation in Supramolecular Structures

Ab initio and density-functional-theory (DFT) calculations on 2H-isoxazol-5-one (A), its linear dimer (LD), cyclic dimer (CD), and cyclic trimer (CT), have been performed with several basis sets in the gas phase, including electron correlation by second-order Møller-Plesset perturbation theory. The calculated complexation energy for the intermolecular H-bonded trimer as well as the corresponding geometric changes are in good agreement with the notion of resonance-assisted intermolecular H-bond formation. Bond distances and angles of the optimized geometry of CT are in accordance with the X-ray-diffraction data found on a trimeric supramolecular complex of parent compound 4-(2-methoxybenzyl)-3-phenyl-4H-isoxazol-5-one. Ab initio and DFT geometry optimizations are also reproducing exactly the large asymmetry in bond angles around the CO group that is systematically present in all literature available X-ray data for analogous heterocyclic penta-atomic compounds.     

Surface-controlled spatially heterogeneous physical properties of a supramolecular gel with homogeneous chemical composition

Controlling supramolecular self-assembly across multiple length scales to prepare gels with localised properties is challenging. Most strategies concentrate on fabricating gels with heterogeneous components, where localised properties are generated by the stimuli-responsive component. Here, as an alternative approach, we use a spiropyran-modified surface that can be patterned with light. We show that light-induced differences in surface chemistry can direct the bulk assembly of a low molecular weight gelator, 2-NapAV, meaning that mechanical gel properties can be controlled by the surface on which the gel is grown. Using grazing incidence X-ray diffraction and grazing incidence small angle X-ray scattering, we demonstrate that the origin of the different gel properties relates to differences in the architectures of the gels. This provides a new method to prepare a single domain (i.e., chemically homogeneous) hydrogel with locally controlled (i.e., mechanically heterogeneous) properties.

A mechanical pattern is created in a hydrogel film by pre-patterning the underlying surface chemistry. This allows spatial variation of the viscous component of the gel, controlling dissipative forces in the gel film without altering gel chemistry.