Burkholder theorem in Riesz spaces

The main purpose of this paper is to give a vector lattice version of a Theorem by Burkholder about convergence of martingales. The proof is based on a vector lattice analogue of Austin’s sample function theorem, proved recently by Grobler, Labuschagne and Marraffa and on a new characterization of elements of the sup-completion of a universally complete vector lattice do not belong to the space.

     

Efficient Solution Phase Synthesis of PPII Helix Mimicking Ena/VASP EVH1 Inhibitors from Proline-Derived Modules (ProMs)

In the search for efficient inhibitors for the enabled/vasodilator-stimulated phosphoprotein homology 1 (EVH1) domain to reduce cell motility in metastatic cancer, we previously developed a toolkit of proline-derived modules (ProMs), which mimic the PPII helix found in the natural −FPPPP− binding motif of EVH1. In this work, we describe the modular assembly of these ProM-based pentapeptidic EVH1 ligands through liquid phase peptide synthesis. We initially used pentafluorophenyl (Pfp) active esters for amide bond formation and built up the growing peptide chain from the C- to the N-terminus. Switching to HATU/DIPEA coupling conditions and changing the directionality of the synthesis from the N- to the C-terminus afforded the target ligands with improved overall yields and purity. Employing a Fmoc-protected (instead of the N-acetylated) phenylalanine derivative as N-terminal building block significantly reduced epimerization. In contrast to the originally used solid phase peptide synthesis (SPPS), the developed solution phase method allowed for a facile alteration of the C-terminal ProM unit and the production of various pentapeptidic ligands in an efficient fashion even on a multigram scale.     

Atomic force microscopy of model lipid membranes

Supported lipid bilayers (SLBs) are biomimetic model systems that are now widely used to address the biophysical and biochemical properties of biological membranes. Two main methods are usually employed to form SLBs: the transfer of two successive monolayers by Langmuir–Blodgett or Langmuir–Schaefer techniques, and the fusion of preformed lipid vesicles. The transfer of lipid films on flat solid substrates offers the possibility to apply a wide range of surface analytical techniques that are very sensitive. Among them, atomic force microscopy (AFM) has opened new opportunities for determining the nanoscale organization of SLBs under physiological conditions. In this review, we first focus on the different protocols generally employed to prepare SLBs. Then, we describe AFM studies on the nanoscale lateral organization and mechanical properties of SLBs. Lastly, we survey recent developments in the AFM monitoring of bilayer alteration, remodeling, or digestion, by incubation with exogenous agents such as drugs, proteins, peptides, and nanoparticles.

An Efficient Algorithm for the Knapsack Sharing Problem

The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in numerous real world applications. In the KSP, we have a knapsack of capacity c and a set of n objects, namely N, where each object j, j = 1,...,n, is associated with a profit p _j and a weight w _j. The set of objects N is composed of m different classes of objects J _i, i = 1,...,m, and N = ^m _i=1 J _i. The aim is to determine a subset of objects to be included in the knapsack that realizes a max-min value over all classes.In this article, we solve the KSP using an approximate solution method based upon tabu search. First, we describe a simple local search in which a depthparameter and a tabu list are used. Next, we enhance the algorithm by introducing some intensifying and diversifying strategies. The two versions of the algorithm yield satisfactory results within reasonable computational time. Extensive computational testing on problem instances taken from the literature shows the effectiveness of the proposed approach.     

Stabilité de l'écoulement de Hartmann chauffé par le basStability of the Hartmann flow heated from below

A numerical study is conducted in order to determine the influence of a vertical magnetic field, the Reynolds number and a temperature stratification on the instabilities occurring in the Hartmann flow heated from below. For $\mathit{Pr}=0.001$ and $\mathit{Ha}?2.5$, the results show that the vertical magnetic field has a stabilizing effect on both transverse oscillatory travelling waves $(T)$ and longitudinal stationary rolls $(L)$. The temperature stratification is responsible of a destabilization of the transverse $(T)$ modes and the appearance of longitudinal $(L)$ modes non-existent for the isothermal Hartmann flow. Moreover, the extent of the domains of Re where the transverse modes $(T)$ prevail is found to narrow when Ha increases and to widen when Ra increases for a given value of Ha. On the other hand, for the $(L)$ modes, the extent of the domains of Re where they prevail increases when Ha grows. To cite this article: W. Fakhfakh et al., C. R. Mecanique 334 (2006).     

A double microbeam MEMS ohmic switch for RF-applications with low actuation voltage

In this paper, we propose the design of an ohmic contact RF microswitch with low voltage actuation, where the upper and lower microplates are displaceable. We develop a mathematical model for the RF microswitch made up of two electrostatically actuated microplates; each microplate is attached to the end of a microcantilever. We assume that the microbeams are flexible and that the microplates are rigid. The electrostatic force applied between the two microplates is a nonlinear function of the displacements and applied voltage. We formulate and solve the static and eigenvalue problems associated with the proposed microsystem. We also examine the dynamic behavior of the microswitch by calculating the limit-cycle solutions. We discretize the equations of motion by considering the first few dominant modes in the microsystem dynamics. We show that only two modes are sufficient to accurately simulate the response of the microsystem under DC and harmonic AC voltages. We demonstrate that the resulting static pull-in voltage and switching time are reduced by 30 and 45%, respectively, as compared to those of a single microbeam-microplate RF-microswitch. Finally, we investigate the global stability of the microswitch using different excitation conditions.     

Optimal distributed-control of vortices in Navier–Stokes flows

Optimal control of time-dependent fluid-flow governed by the incompressible Navier–Stokes model is considered. A cost functional based on a local dynamical systems characterization of vortices is investigated. The resulting functional is a non-convex function of the velocity gradient tensor. The optimality systems based on a Lagrangian formulation and adjoint equations describing first order necessary optimality conditions is provided. The first and the second derivative of the cost functional with respect to the control are derived. To cite this article: S. Chaabane et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Crystal structure,Hirshfeld surface analysis,vibrational properties,and electrical and dielectric studies of the bis (4-benzylpyridinium) tetrachlorocuprate (II)

The present paper undertakes the study of (C₁₂H₁₂N)₂CuCl₄, which is a new hybrid compound. It is synthesized and characterized by single-crystal X-ray diffraction, Hirshfeld surface analysis, and FT-IR, FT-Raman, and impedance spectroscopies. It is crystallized in the monoclinic system with C2/c space group. Its crystal structure was determined and refined down to an R value of 0.05 and a wR value of 0.14. The structure can be described by the alternation of two different, cationic–anionic layers parallel to (110) plan. This complex is assembled into 3D supramolecular architecture by hydrogen bonds (N–H…Cl, C–H…Cl) and π–π interactions. Hirshfeld surface analyses and fingerprint plots are used for decoding intermolecular interactions in the crystal network and contribution of component units for the construction of the 3D architecture. The presence of different functional groups and the nature of their vibrations were identified by FT-IR and FT-Raman spectroscopies. The material is characterized by impedance spectroscopy technique measured in 209–500 MHz frequency and 296–390 K temperature ranges. In addition, the Cole–Cole (Z? versus Z?) plots were well fitted to an equivalent circuit built up by a parallel combination of resistance (R) and constant phase elements (CPEs). The close values of activation energies obtained from the analysis of equivalent circuit data confirm that the transport is through ion hopping mechanism in the bis (4-benzylpyridinium) tetrachlorocuprate.     

Synthesis and structural study of copolymers of l-lactic acid and bis(2-hydroxyethyl terephthalate)

Poly(ethylene terephthalate)-poly(lactic acid) (PET-PLLA) copolyesters were synthesized by the melt reaction of bis(2-hydroxyethyl terephthalate) (BHET) with l-lactic acid oligomers (OLLA) in the presence of SnCl₂, H₂O-p-toluene sulfonic acid, H₂O catalytic system. The ¹H and ¹³C NMR studies confirm the incorporation of lactate units in PET chains after reaction. Copolyesters containing nearly equimolar terephthalate/lactate ratio are not completely random and present some block-copolymer character, while the microstructure of PET-rich copolyesters is a random one. Due to a longer PET sequence length, the latter exhibit a melting point close to 210 °C while the other ones are amorphous. SEC/MALDI-TOF MS off-line coupling was used to obtain the absolute average molar masses of the copolyesters. The results indicate that the conventional polystyrene calibration method leads to a strong overestimation of PET-PLLA molar masses, while the determined by NMR is much closer to the SEC/MALDI value.     

Magnetic control of natural convection in the horizontal Bridgman configuration using a spectral method: transversal plan

The present study investigates the electromagnetic braking of buoyancy convective flows occurring in differentially heated cavities, filled with low Prandtl, dilute, incompressible and electrically conducting alloys, and subjected to a constant horizontal temperature gradient. In practice, such flows known as ‘Hadley circulation’ are relevant in material processing technologies, such as the horizontal Bridgman configuration. A collocation spectral numerical method is developed to solve the two-dimensional Navier–Stokes equations, modelling the flow phenomena occurring in such configurations, using a vorticity–stream function formulation. The two components of the velocity are deduced from the stream function and the temperature distribution is obtained through the resolution of the energy conservation equation. The results in terms of velocity and temperature distributions for a given Grashof number are obtained for various Hartmann numbers and show that as the Hartmann number increases, the electromagnetic braking of the flow is observed. Moreover, the results illustrate the changes affecting the flow structure which becomes quasi-parallel in the core region of the cavity for sufficiently high values of Ha and the onset of the Hartmann and parallel layers along the boundaries. Also, with increasing Ha, the isotherms are less affected by the convective flow and become parallel to the vertical walls indicating that heat transfer is mainly achieved by conduction.