Synthesis and excited state properties of a [60]fullerene derivative bearing a star-shaped multi-photon absorption chromophore

The synthesis and excited state properties of a compound assembling C60 with a new multi-photon absorption chromophore are reported.     

A time discretization scheme of a characteristics method for a fluid–rigid system with discontinuous density

We propose a new characteristics method for the time discretization of a fluid–rigid system in the case when the densities of the fluid and the solid are different. This method is based on a global weak formulation involving only terms defined on the whole fluid–rigid domain. The main idea is to construct a characteristic function which preserves the rigidity of the solid at the discrete time levels. A convergence result for this semi-discrete scheme is then given.     

Contractually stable networks

We consider situations where players are part of a network and belong to coalitions in a given coalition structure. We propose the concept of contractual stability to predict the networks that are going to emerge at equilibrium when the consent of coalition partners is needed for adding or deleting links. Two different decision rules for consent are analyzed: simple majority and unanimity. We characterize the coalition structures that make the strongly efficient network contractually stable under the unanimity decision rule and the coalition structures that sustain some critical network as contractually stable under the simple majority decision rule and under any decision rule requiring the consent of any proportion of coalition partners. Requiring the consent of coalition members may help to reconcile stability and efficiency in some classical models of network formation.     

Counting Function of Characteristic Values and Magnetic Resonances

We consider the meromorphic operator-valued function I ? K(z) = I ? A(z)/z where A is holomorphic on the domain 𝒟 ? ?, and has values in the class of compact operators acting in a given Hilbert space. Under the assumption that A(0) is a selfadjoint operator which can be of infinite rank, we study the distribution near the origin of the characteristic values of I ? K, i.e. the complex numbers w ≠ 0 for which the operator I ? K(w) is not invertible, and we show that generically the characteristic values of I ? K converge to 0 with the same rate as the eigenvalues of A(0).

We apply our abstract results to the investigation of the resonances of the operator H = H ₀ + V where H ₀ is the shifted 3D Schrödinger operator with constant magnetic field of scalar intensity b > 0, and V: ?³ → ? is the electric potential which admits a suitable decay at infinity. It is well known that the spectrum σ(H ₀) of H ₀ is purely absolutely continuous, coincides with [0, + ∞[, and the so-called Landau levels 2bq with integer q ≥ 0, play the role of thresholds in σ(H ₀). We study the asymptotic distribution of the resonances near any given Landau level, and under generic assumptions obtain the main asymptotic term of the corresponding resonance counting function, written explicitly in the terms of appropriate Toeplitz operators.     

Fluorescent Microcrystals Obtained from Coumarin 6 Using the Reprecipitation Method

The reprecipitation method was applied to Coumarin 6. A concentrated solution of the dye in acetone was mixed at room temperature with a large volume of water, and microcrystals rapidly appeared in the medium. Their size and shape were visualized by fluorescence microscopy, as well as by transmission electron microscopy. The absorption and fluorescence properties were studied on the suspensions and compared with those of the dissolved dye. This study is aimed at clarifying the influence of the reprecipitation process upon the fluorescence properties of the dye in the solid state.     

Electrochemical and photochemical approaches for the synthesis of the C28–C38 fragment of okadaic acid

Okadaic acid, a potent and selective inhibitor of Protein Phosphatases 1 and 2A (PP1 and PP2A), is widely used as a probe for various biochemical processes. We describe herein two innovative methods for the synthesis of the terminal C28–C38 fragment of the natural polyether. Suárez photochemical oxidative cyclization and electrochemical oxidation of malonates to their ketals equivalents have been successfully applied for the assembly of the key spiroketal core.     

Toward Transition-Metal-Templated Construction of Arylated B4 Chains by Dihydroborane Dehydrocoupling

The reactivity of a diruthenium tetrahydride complex towards three selected dihydroboranes was investigated. The use of [DurBH₂] (Dur=2,3,5,6-Me₄C₆H) and [(Me₃Si)₂NBH₂] led to the formation of bridging borylene complexes of the form [(Cp*RuH)₂BR] (Cp*=C₅Me₅; 1 a : R=Dur; 1 b : R=N(SiMe₃)₂) through oxidative addition of the B−H bonds with concomitant hydrogen liberation. Employing the more electron-deficient dihydroborane [3,5-(CF₃)₂-C₆H₃BH₂] led to the formation of an anionic complex bearing a tetraarylated chain of four boron atoms, namely Li(THF)₄[(Cp*Ru)₂B₄H₅(3,5-(CF₃)₂C₆H₃)₄] ( 4 ), through an unusual, incomplete threefold dehydrocoupling process. A comparative theoretical investigation of the bonding in a simplified model of 4 and the analogous complex nido-[1,2(Cp*Ru)₂(μ-H)B₄H₉] ( I ) indicates that there appear to be no classical σ-bonds between the boron atoms in complex I , whereas in the case of 4 the B₄ chain better resembles a network of three B−B σ bonds, the central bond being significantly weaker than the other two.     

High-Field Detection of Biomarkers with Fast Field-Cycling MRI: The Example of Zinc Sensing

Many smart magnetic resonance imaging (MRI) probes provide response to a biomarker based on modulation of their rotational correlation time. The magnitude of such MRI signal changes is highly dependent on the magnetic field and the response decreases dramatically at high fields (>2 T). To overcome the loss of efficiency of responsive probes at high field, with fast-field cycling magnetic resonance imaging (FFC-MRI) we exploit field-dependent information rather than the absolute difference in the relaxation rate measured in the absence and in the presence of the biomarker at a given imaging field. We report here the application of fast field-cycling techniques combined with the use of a molecular probe for the detection of Zn²⁺ to achieve 166 % MRI signal enhancement at 3 T, whereas the same agent provides no detectable response using conventional MRI. This approach can be generalized to any biomarker provided the detection is based on variation of the rotational motion of the probe.     

Transient adaptivity applied to two-phase incompressible flows

An anisotropic adaptation process is applied to a three-dimensional incompressible two-phase flow solver. The solver uses a level set/finite element method on unstructured tetrahedral meshes. We show how the level set function can be used to build an anisotropic mesh with good properties. Some computations with a strong transient character and large densities ratios (1/1000) are presented. We show that the efficiency of the computations can be deeply enhanced by mesh adaptations.