Optimal control and admissible relaxation for subdifferential evolution inclusions

In this paper we study the relaxation of optimal control problems monitored by subdifferential evolution inclusions. First under appropriate convexity conditions, we establish an existence result. Then we introduce the relaxed problem and show that it always has a solution under fairly general hypotheses on the data. Subsequently we examine when the relaxation is admissible. So we show that every relaxed trajectory can be approximated by extremal original ones (i.e. original trajectories generated by bang-bang controls) and that the values of the original and relaxed problems are equal. Some examples are also presented.     

Enhancing the accuracy of virtual screening: molecular dynamics with quantum-refined force fields

Summary A methodology aimed at improving the accuracy of current docking–scoring procedures is proposed, and validated through detailed tests of its performance in predicting the activity of HIV-1 protease inhibitors. This methodology is based on molecular dynamics simulations using a force field whose effective charges are refined by means of a novel procedure that relies on quantum-mechanical calculations and preserves the internal consistency of the parameterization scheme.     

Surface reactions kinetics between nanocrystalline magnetite and uranyl

Magnetite is the most important end member of iron corrosion products under reducing environment, which is the condition expected in a deep geological high level radioactive waste disposal. Nanocrystalline magnetite was synthesized in the laboratory and its physicochemical properties were analyzed in detail. The kinetics of the adsorption of U(VI) and the kinetics of the actinide reduction to a lower oxidation state, in presence of the oxide, were studied by means of batch sorption techniques and X-ray photoelectron spectroscopy (XPS) analysis. The results showed that the uranium sorption and reduction processes on the magnetite surface have very fast kinetics (hours), the reduction process being triggered by sorption. XPS measurements showed that the speciation of uranium at the surface does not show significant changes with time (from 1 day to 3 months), as well as the quantity of uranium detected at the surface. The surface speciation depended on the initial pH of the contact solution. Considering that the Eh of equilibrium between magnetite and the solution, under our experimental conditions, is slightly positive (50-100 mV), the uranium reduction would also be thermodynamically possible within the liquid phase. However, the kinetics of reduction in the liquid occur at a much slower rate which, in turn, has to depend on the attainment of the magnetite/solution equilibrium. The decrease of uranium in solution, observed after the uranyl adsorption stage, and particularly at acidic pH, is most probably due to the precipitation of U(IV) formed in the solution.     

Symbolic Computation of Newton Sum Rules for the Zeros of Polynomial Eigenfunctions of Linear Differential Operators

A symbolic algorithm based on the generalized Lucas polynomials of first kind is used in order to compute the Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators with polynomial coefficients.     

Bounds and monotonicity for the generalized Robin problem

We consider the principal eigenvalue λ ₁^Ω(α) corresponding to Δu = λ (α) u in W, \frac?u?v = au \Omega, \frac{\partial u}{\partial v} = \alpha u on ∂Ω, with α a fixed real, and W ì Rⁿ\Omega \subset {\mathcal{R}}^n a C ^0,1 bounded domain. If α > 0 and small, we derive bounds for λ ₁^Ω(α) in terms of a Stekloff-type eigenvalue; while for α > 0 large we study the behavior of its growth in terms of maximum curvature. We analyze how domain monotonicity of the principal eigenvalue depends on the geometry of the domain, and prove that domains which exhibit domain monotonicity for every α are calibrable. We conjecture that a domain has the domain monotonicity property for some α if and only if it is calibrable.     

Photo-induced pyridine substitution in cis-[Ru(bpy)(2)(py)(2)]Cl(2): a snapshot by time-resolved X-ray solution scattering

Determination of transient structures in light-induced processes is a challenging goal for time-resolved techniques. Such techniques are becoming successful in detecting ultrafast structural changes in molecules and do not require the presence of probe-like groups. Here, we demonstrate that TR-WAXS (Time-Resolved Wide Angle X-ray Scattering) can be successfully employed to study the photochemistry of cis-[Ru(bpy)(2)(py)(2)]Cl(2), a mononuclear ruthenium complex of interest in the field of photoactivatable anticancer agents. TR-WAXS is able to detect the release of a pyridine ligand and the coordination of a solvent molecule on a faster timescale than 800 ns of laser excitation. The direct measurement of the photodissociation of pyridine is a major advance in the field of time-resolved techniques allowing detection, for the first time, of the release of a multiatomic ligand formed by low Z atoms. These data demonstrate that TR-WAXS is a powerful technique for studying rapid ligand substitution processes involving photoactive metal complexes of biological interest.     

Laurdan and Prodan as Polarity-Sensitive Fluorescent Membrane Probes

The steady-state and dynamic fluorescence spectral properties of 2-dimethylamino-6-lauroylnaphthalene (LAURDAN) and several other naphthalene derivatives are summarized to illustrate their sensitivity to the polarity of the environment. Results obtained both in solvents of different polarity and in phospholipid vesicles in two phase states are presented. The emission red shift observed in polar solvents and in the phospholipid liquid–crystalline phase is explained on the basis of dipolar relaxation of solvent molecules surrounding the fluorescent naphthalene moiety of these probes. In phospholipid environments, experimental evidence is shown that excludes the intramolecular relative reorientation of the dimethylamino and carbonyl groups in the naphthalene and the reorientation of the entire fluorescent moiety. The solvent dipolar relaxation observed for LAURDAN and PRODAN in phospholipid bilayers has been attributed to a small number of water molecules present at the membrane interface. A comparison between LAURDAN emission in phospholipid vesicles prepared in D₂O and in H₂O is also presented. The definition and the derivation of the generalized polarization function are also discussed.     

Derivation of the Forchheimer Law Via Matched Asymptotic Expansions

Matched asymptotics are used formally in the linearized Navier–Stokes equations, the so-called Oseen approximation, to derive a nonlinear law for the flow of a single-phase, incompressible Newtonian fluid through a rigid porous medium. A suitable choice of the linear term gives, to order a Forchheimer-type law.     

Mechanism of Thyroxine Deiodination by Naphthyl‐Based Iodothyronine Deiodinase Mimics and the Halogen Bonding Role: A DFT Investigation

This paper deals with a systematic density functional theory (DFT) study aiming to unravel the mechanism of the thyroxine (T4) conversion into 3,3′,5‐triiodothyronine (rT3) by using different bio‐inspired naphthyl‐based models, which are able to reproduce the catalytic functions of the type‐3 deiodinase ID‐3. Such naphthalenes, having two selenols, two thiols, and a selenol–thiol pair in peri positions, which were previously synthesized and tested in their deiodinase activity, are able to remove iodine selectively from the inner ring of T4 to produce rT3. Calculations were performed including also an imidazole ring that, mimicking the role of the His residue, plays an essential role deprotonating the selenol/thiol moiety. For all the used complexes, the calculated potential energy surfaces show that the reaction proceeds via an intermediate, characterized by the presence of a X?I?C (X=Se, S) halogen bond, whose transformation into a subsequent intermediate in which the C?I bond is definitively cleaved and the incipient X?I bond is formed represents the rate‐determining step of the whole process. The calculated trend in the barrier heights of the corresponding transition states allows us to rationalize the experimentally observed superior deiodinase activity of the naphthyl‐based compound with two selenol groups. The role of the peri interactions between chalcogen atoms appears to be less prominent in determining the deiodination activity.     

Electrochemical, EPR and computational results on [Fe2Cp2(CO)2]-based complexes with a bridging hydrocarbyl ligand

The dimetallacyclopentenone complexes [Fe₂Cp₂(CO)(μ−CO){μ−η¹:η³−C_αHC_β(R)C(O)}] (R = CH₂OH, 1a; R = CMe₂OH, 1b; R = Ph, 1c) were prepared by photolytic reaction of [Fe₂Cp₂(CO)₄] with alkyne according to the literature procedure. The X-ray and the electrochemical characterization of 1c are presented. The μ-allenyl compound [Fe₂Cp₂(CO)₂(μ−CO){μ−η¹:η²_α,β−C_αHC_βCMe₂][BF₄] ([2][BF₄]), obtained by reaction of 1b with HBF₄, underwent monoelectron reduction to give a radical species which was detected by EPR at room temperature. The EPR signal has been assigned to [Fe₂Cp₂(CO)₂(μ−CO){μ−η¹:η²_α,β-C_αHC_βCMe₂}], [2]^•. The molecular structures of [2]⁺ and [2]^• were optimized by DFT calculations. The unpaired electron in [2]^• is localized mainly at the metal centers and, coherently, [2]^• does not undergo carbon-carbon dimerization, by contrast with what previously observed for the μ-vinyl radical complex [Fe₂Cp₂(CO)₂(μ−CO){μ−η¹:η²-CHCH(Ph)}]^•, [3]^•. Electron spin density distributions similar to the one of [2]^• were found for the μ-allenyl radical complexes [Fe₂Cp₂(CO)₂(μ-CO){μ-η¹:η²_α,β-C_αHC_βC(R¹)(R²)}]^• (R¹ = R² = H, [4]^•; R¹ = H, R² = Ph, [5]^•; R¹ = R² = Ph, [6]^•).