Sliding in a piecewise-smooth dynamical system with a hold-on effect

In this paper, we study a piecewise-smooth dynamical system of a Filippov type that has a specific discontinuity in the form of a hold-on term. The system resembles a driven dry-friction oscillator with the difference that the magnitude of the friction depends on the value of a local maximum of the oscillator displacement. Due to the hold-on term, the definition of the sliding region is not trivial. Along with a sliding region that is found analytically and is valid for any orbits, there exists a sliding region that we name ‘virtual’ because it is specific for each particular orbit. The existence of the virtual sliding region is explained by the specific discontinuity — the hold-on term — and the behavior associated with the sliding region and its boundaries can be considered as a new type of sliding-associated behavior.     

Efficacy of End-Only-Functionalized Oligo(arylene-ethynylene)s in Killing Bacterial Biofilms

Cationic end-only-functionalized oligo(arylene-ethynylene)s (EO-OPEs) have recently been found to be broad-spectrum and effective antimicrobial agents because of their unique structure and optical properties. In this study, we investigated their potential use for preventing and reducing Escherichia coli (E. coli) biofilms. The Calgary biofilm device (CBD) was used to form bacterial biofilms of E. coli; in these studies, the minimum inhibitory concentration (MIC) and the minimum biofilm eradication concentration (MBEC) were determined. E. coli biofilms uniformly grow on pegs of the CBD device lid. The MIC values determined for EO-OPEs are comparable to those found for standard antibiotics such as kanamycin (MIC = 11.2 μg/mL). About 10-30 times the concentration of EO-OPEs was required to eradicate E. coli biofilms and prevent regrowth in the dark. Near-UV irradiation of EO-OPEs enhanced their efficacy in killing biofilms.     

Quantum gray solitons in confining potentials

We define and study holelike excitations (the Lieb II mode) in a weakly interacting Bose liquid subject to external confinement. These excitations are obtained by semiclassical quantization of gray solitons propagating on top of a Thomas-Fermi background. Radiation of phonons by an accelerated gray soliton leads to a finite lifetime of these excitations. It is shown that, for a large number of trapped atoms, most of the Lieb II levels can be experimentally resolved.     

Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations

We have implemented the sweep algorithm for the variational optimization of SU(2) U(1) (spin and particle number) invariant matrix product states (MPS) for general spin and particle number invariant fermionic Hamiltonians. This class includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are presented. This allows to assess the performance of other quantum chemical methods. For small basis sets, MPS calculations in the saturation regime of the optical response properties can be performed. These results are extrapolated to the thermodynamic limit.     

Absence of localization in a class of Schrödinger operators with quasiperiodic potential

We prove that a class of discrete Schrödinger operators with a quasiperiodic potential taking only a finite number of values, exhibits purely continuous spectrum; in particular they cannot have localized eigenvectors.Groupe de Recherche 048 of C.N.R.S.     

Thermodynamics for the zero-level set of the Brownian bridge

The random set of instants where the Brownian bridge vanishes is constructed in terms of a random branching process. The Hausdorff measure supported by this set is shown to be equivalent to the partition function of a special class of disordered systems. This similarity is used to show rigorously the existence of a phase transition for this particular class of disordered systems. Moreover, it is shown that at high temperature the specific free energy has the strong self-averaging property and that at low temperature it has no self-averaging property. The unicity at high-temperature and the existence of many limits at low temperature are established almost surely in the disorder.Work supported by the Swiss National Science Foundation     

Robust prediction and interpolation for vector stationary processes

Summary Robust multivariate prediction and interpolation problems for statistically contaminated vector valued second order stationary processes are considered. The statistical contamination is modeled by requiring that the spectral density matrices of the processes lie within certain nonparametric classes. Both prediction and interpolation are then formalized as games whose saddle point solutions are sought. Finally, such solutions are found and analyzed, for two specific multivariate spectral classes.Research supported by the Air Force Office of Scientific Research under Grants AFOSR-83-0229 and AFOSR-82-0030     

On the Distribution of Activity Time in PERT

In PERT analysis the activity-time distribution is assumed to be a beta distribution, and the mean and variance of the activity time are estimated on the basis of the ‘pessimistic’, ‘most likely’ and ‘optimistic’ completion times, which are subjectively determined by an analyst. In this paper, on the basis of the study of the PERT assumptions, we present an improvement of these estimates. It is also shown that, by means of additional reasonable assumptions, the activity-time distribution in PERT analysis may be essentially simplified.     

Development and validation of a liquid chromatographic/tandem mass spectrometric assay for the quantitation of nucleoside HIV reverse transcriptase inhibitors in biological matrices

Besides liquid chromatographic (LC)/UV methods adapted to therapeutic drug monitoring, there is still a need for more powerful techniques that can be used for pharmacological research and clinical purposes. We developed an LC method coupled with tandem mass spectrometry (MS/MS) to separate, detect and quantify with high sensitivity the nucleoside analogues used in multitherapies (zidovudine, stavudine, zalcitabine, didanosine, lamivudine and abacavir) in plasma and in the intracellular medium. We worked on two essential issues: (i) the need to use two ionization modes in order to achieve the best sensitivity, which leads to the optimization of the chromatographic separation of drugs detected in the positive ionization mode and drugs detected in the negative ionization mode, and (ii) the need to optimize the extraction step in order to enhance sample recovery. The peripheral blood mononuclear cells were lysed in Tris buffer-MeOH. A clean-up procedure was performed by solid-phase extraction only for plasma samples. The LC separation was carried out on a Zorbax Stable Bond C(18) column followed by MS/MS analysis after electrospray ionization in either the negative or positive mode. The positive ionization mode was applied at the beginning of the run to detect zalcitabine and lamivudine, then the ionization mode was changed to negative for the detection of didanosine, stavudine, internal standard and zidovudine. The calibration range for all the analytes was 0.5-200 ng ml(-1). The recoveries were between 64 and 90%, with coefficients of variation (CVs) lower than 15%. The inaccuracy (bias) was +/-15% with CVs always lower than 12%. The analytes were stable at room temperature and in the extraction solvent for at least 24 h, after storage at -80 degrees C for 3 months, after three freeze-thaw cycles and in the injection solvent after 48 h at 4 degrees C. Together with the measurement of intracellular triphosphorylated metabolites thanks to the powerful plasma and intracellular assay method for intact drugs, it is possible to describe the behaviour of nucleoside analogues against HIV through plasma pharmacokinetics, cell membrane diffusion including drug transport involvement, and also the intracellular metabolism.     

Quinobis(imidazolylidene): Synthesis and Study of an Electron‐Configurable Bis(N‐Heterocyclic Carbene) and Its Bimetallic Complexes

Reaction of bromanil with N,N′‐dimesitylformamidine followed by deprotonation with NaN(SiMe₃)₂ afforded 1,1′,3,3′‐tetramesitylquinobis(imidazolylidene) ( 1 ), a bis(N‐heterocyclic carbene) (NHC) with two NHC moieties connected by a redox active p‐quinone residue, in 72 % yield of isolated compound. Bimetallic complexes of 1 were prepared by coupling to FcN₃ ( 2 ) or FcNCS ( 3 ; Fc=ferrocenyl) or coordination to [M(cod)Cl] ( 4 a or 4 b , where M=Rh or Ir, respectively; cod=1,5‐cyclooctadiene). Treatment of 4 a and 4 b with excess CO(g) afforded the corresponding [M(CO)₂Cl] complexes 5 a and 5 b , respectively. Analysis of 2 – 5 by NMR spectroscopy and X‐ray diffraction indicated that the electron‐deficient quinone did not significantly affect the inherent spectral properties or coordination chemistry of the flanking imidazolylidene units, as compared to analogous NHCs. Infrared spectroscopy and cyclic voltammetry revealed that decreasing the electron density at ML_n afforded an increase in the stretching energy and a decrease in the reduction potential of the quinone, indicative of metal–quinone electronic interaction. Differential pulse voltammetry and chronoamperometry of the metal‐centered oxidations in 2 – 4 revealed two single, one‐electron peaks. Thus, the metal atoms bound to 1 are oxidized at indistinguishable potentials and do not appear electronically coupled. However, the metal–quinone interaction was used to increase the electron density at coordinated metal atoms. Infrared spectroelectrochemistry revealed that the average ν_CO values for 5 a and 5 b decreased by 14 and 15 cm^?1, respectively, upon reduction of the quinone embedded within 1 . These shifts correspond to 10 and 12 cm^?1 decreases in the Tolman electronic parameter of this ditopic ligand.