Canonical and Noncanonical Recursion Operators in Multidimensions

The hierarchies of evolution equations associated with the spectral operators ?_x?_y ? R?_y ? Q and ?_x?_y ? Q in the plane are considered. In both cases a recursion operator Ф₁₂, which is nonlocal and generates the hierarchy, is obtained. It is shown that only in the first case does the recursion operator satisfy the canonical geometrical scheme in 2 + 1 dimensions proposed by Fokas and Santini. The general procedure proposed allows one to derive, at the same time, the evolution equations associated with a given linear spectral problem and their Backlund transformations (if they exist), with no need to verify by long and tedious computations the algebraic properties of Ф₁₂. Two equations in the first hierarchy can be considered as two different integrable generalizations in the plane of the dispersive long wave equation. All equations in this hierarchy are shown to be both a dimensional reduction of bi-Hamiltonian n × n matrix evolution equations in multidimensions and a generalization in the plane of bi-Hamiltonian n × n matrix evolution equations on the line.     

Linear programming solutions and distance functions under α-returns to scale

This note generalizes analytical relationships among activity variables of Dataenvelopment analysis models previously derived in a previous article by theauthors of this note. We relax the assumption of constant returns to scale byshowing that the key results hold under a weaker assumption of homogeneity. Weuse the notion of α-returns to scale to extend the analysis tostrictly increasing and decreasing returns, covering now the whole range ofreturns to scale for multi-output homogenous technologies.     

Scattering of acoustic waves by macroscopically inhomogeneous poroelastic tubes

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. For planar configurations, the wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently: first in the case of rigid frame inhomogeneous porous materials and then in the case of inhomogeneous poroelastic materials in the framework of Biot's theory. This paper focuses on the solution of the full wave equation in cylindrical coordinates for poroelastic tubes in which the acoustic and elastic properties of the poroelastic tube vary in the radial direction. The reflection coefficient is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method in the case of a two-layer poroelastic tube. As an example, a long bone excited in the sagittal plane is considered. Finally, a discussion is given of ultrasonic time domain scattered field for various inhomogeneity profiles, which could lead to the prospect of long bone characterization.     

Surface modifications of illite in concentrated lime solutions investigated by pyridine adsorption

The surface properties and functionality of an illite-containing clay mineral in alkaline solutions containing increasing quantities of calcium hydroxide were investigated using FTIR monitored pyridine adsorption at various temperatures. Results showed that the binding behavior of electron donor pyridine molecules to illite platelets is mostly governed by electron acceptor sites located at the edges of the clay particles. The binding of bulky hydrated calcium ions at the surface of the illite platelets decreases the surface area of illite. Moderate thermal treatments up to 450 °C do not affect the structure of the clay mineral but strongly decrease the number of Lewis and Brönsted sites available at the edges of the clay platelets.     

TAT peptide internalization: seeking the mechanism of entry

During the last decade several peptides have been extensively studied for their ability to translocate across the plasma membrane. These peptides have been called "cell penetrating peptides" (CPP) or "protein transduction domains" (PTD). These peptides also promote the cellular uptake of various cargo molecules. Their mechanism of cellular entry appeared very intriguing since most publications in the field highlighted an energy-independent process. Indeed, cellular uptake of these peptides was still observed by fluorescence microscopy at low temperature or in the presence of several drugs known to inhibit active transport. In addition, internalization was reported to be much faster than known endocytic processes. However the involvement of a specific cellular component responsible for this uptake process appeared unlikely following intensive structure activity relationship studies using a wide panel of Tat analogues. Several reports about a possible artefactual redistribution of CPPs, and their associated cargos, during the cell fixation step commonly used for fluorescence microscopy have recently emerged in the literature. Moreover strong ionic interactions of CPPs with the cell surface also led to an overestimation of the recorded cell-associated fluorescent signal. It now seems well established that arginine-rich peptides are internalized by an energy dependent process involving endocytosis. Whatever the case, however, an increasing number of data indicate that the conjugation of non-permeant molecules to these CPPs allows their cellular uptake and leads to the expected biological responses, thus pointing to the interest of this delivery strategy. However, initial structure activity relationship studies of these CPPs will have to be reconsidered and the relative potency of each peptide (and their analogues) to vectorize the cargos to their most appropriate subcellular compartment will require careful re-evaluation.     

Chiral Resolution of the Enantiomers of New Aromatase Inhibitors by Liquid Chromatography on Amylose Stationary Phases

Analytical HPLC methods for derivatized amylose chiral stationary phases were developed for the direct enantioseparation of substituted [1-(imidazo-1-yl)-1-phenylmethyl)] benzothiazolinone and benzoxazolinone derivatives with one stereogenic center. These analogues of fadrozole constitute new potent nonsteroidal inhibitors of aromatase (P450 arom.). The separations were made using normal phase methodology with mobile phase consisting of n-hexane-alcohol (ethanol, 1-propanol or 2-propanol) in various proportions, and a silica-based amylose tris-3,5-dimethylphenylcarbamate (Chiralpak AD), or tris-(S)-1-phenylethylcarbamate (Chiralpak AS). The effects of concentration of various aliphatic alcohols in the mobile phase were studied. Baseline separation (R_s > 1.5) was easily obtained in all cases, ethanol being often the more interesting modifier. The effects of structural features of the solutes along with the temperature of the column on the discrimination between the enantiomers were examined for different mobile phase compositions.     

Wetting transitions of ionic solutions

Cahn's phenomenological theory of wetting of a solid substrate by a saturated vapor is generalized to the case where the substrate is charged and the wetting film contains counterions, with or without added salt. The electrostatic contribution to the grand potential associated with these ions is calculated within a nonlinear Poisson-Boltzmann theory. In the salt-free case, when the wetting film includes only counterions released by the substrate, the wetting transition is always first order, regardless of its nature in a neutral system. When salt is present, other wetting scenarios may arise, depending on the salt concentration and substrate surface charge. Over a restricted range of salt concentrations, a wetting scenario similar to that of prewetting, is predicted to occur along the liquid-vapor coexistence line. This scenario includes a discontinuous wetting transition between microscopic and mesoscopic film thicknesses, followed by a continuous divergence of the film thickness at higher temperatures.     

Electric field-controlled water permeation coupled to ion transport through a nanopore

We report molecular dynamics simulations of a generic hydrophobic nanopore connecting two reservoirs which are initially at different Na(+) concentrations, as in a biological cell. The nanopore is impermeable to water under equilibrium conditions, but the strong electric field caused by the ionic concentration gradient drives water molecules in. The density and structure of water in the pore are highly field dependent. In a typical simulation run, we observe a succession of cation passages through the pore, characterized by approximately bulk mobility. These ion passages reduce the electric field, until the pore empties of water and closes to further ion transport, thus providing a possible mechanism for biological ion channel gating.     

Molar heat capacities and volumes of transfer of cytosine,thymine, caffeine and 1,3-diethylthymine to aqueous solutions of glycyl-glycine and L-α-alanyl-L-α-alanine at 25°C

Densities and specific heat capacities of ternary aqueous systems containing dipeptides (glycyl-glycine or L--alanyl-L--alanine) and nucleic acid bases (cytosine or thymine) or their alkyl derivatives (1,3-diethylthymine or caffeine) were determined at 25°C by flow calorimetry and flow densimetry. The partial molar volumes and heat capacities of transfer at infinite dilution of the different nucleic acid bases from water to water+dipeptide solutions were obtained therefrom. Except for the case of the transfer of cytosine to aqueous glycyl-glycine solutions where a small positive dependence of the transfer quantities was observed with the dipeptide concentration, the values of the heat capacities of transfer were in general low, positive or negative, depending on the compensation of hydrophobic-hydrophilic interactions between the dipeptide and the base. The volumes of transfer of most of the bases are very small, within the limit of the experimental error.     

Investigation into the valence electronic structure of norbornene using electron momentum spectroscopy, Green's function, and density functional theories

Results of a study of the valence electronic structure of norbornene (C(7)H(10)), up to binding energies of 30 eV, are reported. Experimental electron momentum spectroscopy (EMS) and theoretical Green's function and density functional theory approaches were utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among the tested models, the combination of the Becke-Perdew functional and a polarized valence basis set of triple-zeta quality provides the best representation of the electron momentum distributions for all 19 valence orbitals of norbornene. This experimentally validated model was then used to extract other molecular properties of norbornene (geometry, infrared spectrum). When these calculated properties are compared to corresponding results from independent measurements, reasonable agreement is typically found. Due to the improved energy resolution, EMS is now at a stage to very finely image the effective topology of molecular orbitals at varying distances from the molecular center, and the way the individual atomic components interact with each other, often in excellent agreement with theory. This will be demonstrated here. Green's Function calculations employing the third-order algebraic diagrammatic construction scheme indicate that the orbital picture of ionization breaks down at binding energies larger than about 22 eV. Despite this complication, they enable insights within 0.2 eV accuracy into the available ultraviolet emission and newly presented (e,2e) ionization spectra. Finally, limitations inherent to calculations of momentum distributions based on Kohn-Sham orbitals and employing the vertical depiction of ionization processes are emphasized, in a formal discussion of EMS cross sections employing Dyson orbitals.