Sensitivity of rough differential equations: An approach through the Omega lemma

The Itô map gives the solution of a Rough Differential Equation, a generalization of an Ordinary Differential Equation driven by an irregular path, when existence and uniqueness hold. By studying how a path is transformed through the vector field which is integrated, we prove that the Itô map is Hölder or Lipschitz continuous with respect to all its parameters. This result unifies and weakens the hypotheses of the regularity results already established in the literature.     

Precipitate assemblies formed on dislocation loops in aluminium-silver-copper alloys

The precipitation microstructure of the γ′ (AlAg₂) intermetallic phase has been examined in aluminium-silver-copper alloys. The microstructure developed in an Al-0.90at.%Ag-90at.Cu alloy was significantly different from that reported for binary Al-Ag alloys. The orientation relationship between the matrix and precipitate was unchanged; however, the γ′ phase formed assemblies with a two-dimensional, open arrangement of precipitates. Each such assembly contained two variants of the γ′ phase alternately arranged to form a faceted elliptical unit. The θ′ (Al₂Cu) phase formed on these assemblies after further ageing. Each assembly was formed via repeated precipitation of the γ′ phase on dissociated segments of a single dislocation loop. This faceted elliptical assembly has not been previously reported for the γ′ precipitate. The difference between the precipitation behaviour of the γ′ phase in Al-Ag and Al-Ag-Cu alloys was attributed to copper modifying the as-quenched defect structure of the matrix. The formation of faceted elliptical γ′ phase assemblies clarifies earlier observations on the precipitate number density and mechanical properties of aluminium-silver-copper alloys.     

Comparative Study of Alkali-Cation-Based (Li+, Na+, K+) Electrolytes in Acetonitrile and Alkylcarbonates

The development of a suitable functional electrolyte is urgently required for fast-charging and high-voltage alkali-ion (Li, Na, K) batteries as well as next-generation hybrids supercapacitors. Many recent works focused on an optimal selection of electrolytes for alkali-ion based systems and their electrochemical performance but the understanding of the fundamental aspect that explains their different behaviour is rare. Herein, we report a comparative study of transport properties for LiPF₆, NaPF₆, KPF₆ in acetonitrile (AN) and a binary mixture of ethylene carbonate (EC), dimethyl carbonate (DMC): (EC/DMC : 1/1, weigh) through conductivities, densities and viscosities measurements in wide temperature domain. By application of the Stokes-Einstein, Nernst-Einstein, and Jones Dole equations, the effective ionic solvated radius of cation (r_eff), the ionic dissociation coefficient (α_D) and structuring Jones Dole's parameters (A, B) for salt are calculated and discussed according to solvent or cation nature as a function of temperature. From the results, we demonstrate that better mobility of potassium can be explained by the nature of the ion-ion and ion-solvent interactions due to its polarizability. In the same time, the predominance of triple ions in the case of K⁺, is a disadvantage at high concentration.     

Fluorescent P-Hydroxyphosphole for Peptide Labeling through P-N Bond Formation

Synthesis of fluorescent P-hydroxybinaphtylphosphole-oxide or -sulfide was achieved by trapping a binaphtyl dianion with methyl dichlorophosphite or P-(N,N-diethylamino)dichlorophosphine, followed by oxidation or sulfuration of the P-center. After saponification or acid hydrolysis, the P-hydroxyphospholes were coupled to peptides using the coupling agent BOP, under the conditions required for the synthesis in solution or on a solid support. This new method was illustrated by the labeling of the JMV2959, a potent antagonist of the Growth Hormone Secretagogue Receptor type 1a (GHS−R1a). The labeled conjugates were used to characterize GHSR ligands by competition assays, based on Fluorescence Resonance Energy Transfer (FRET). Such P-hydroxyphosphole-oxide or -sulfide constitute a promising new class of compact fluorophores with large Stokes shift, for labeling biomolecules by grafting through the phosphorus atom.     

Crystal structure and magnetic properties of bis(2,2′-bipyridine) azido copper(II) perchlorate

The title compound has been synthesized and its crystal structure has been solved at room temperature. It crystallizes in the triclinic system, space groupP, witha=7.853(1) Å,b=10.177(1) Å,c=13.651(4) Å,=74.57(1)°,=88.49(1)°, =80.675(4)°, andZ=2. The structure consists of isolated [Cu(bipy)₂N₃]⁺ cations (bipy=2,2-bipyridine) and perchlorate anions. The metallic cation environment has a distorted trigonal-bipyramidal geometry. The EPR spectrum is rhombic, which indicates that the distortion with respect to the perfect trigonal bipyramid is sufficiently pronounced to mixz ²- andx ²–y ²-type orbitals in the ground state. The temperature dependence of the molar magnetic susceptibility has been investigated in the 300-2.2 K temperature range.     

Structural and luminescent properties of micro- and nanosized particles of lanthanide terephthalate coordination polymers

Reaction in water between rare earth ions (Ln = Y, La-Tm, except Pm) and the sodium salt of terephthalic acid leads to a family of lanthanide-based coordination polymers of general formula [Ln2(C8H4O4)3(H2O)4] n with Ln = La-Tm or Y. The isostructurality of the compounds with the previously reported Tb-containing polymer is ascertained on the basis of their X-ray powder diffraction diagrams. The coordination water molecules can be reversibly removed without destroying the crystal structure for compounds involving one of the lighter lanthanide ions (La-Eu). For compounds involving one of the heavier lanthanide ions (Tb-Tm) or yttrium, a structural change occurs during the drying process. X-ray diffraction data show this new anhydrous phase corresponding to the linking of pairs of Er(III) ions through mu-carboxylate bridges. Porosity profiles calculated for the anhydrous phases of Tb(III) and Er(III) show the presence of channels with very small sections. The luminescent properties of all the compounds have been recorded and the two most luminescent polymers, namely, the europium- and the terbium-containing ones, have been studied in more detail. Tb(III)-containing compounds display large quantum yields, up to 43%. Polyvinylpyrrolidone nanoparticles doped with [Ln2(C8H4O4)3(H2O)4] n (Ln = Eu, Tb, Er) have also been synthesized and characterized. The encapsulation of the coordination polymers results in somewhat reduced luminescence intensities and lifetime, but the nanoparticles can be dispersed in water and remain unchanged in this medium for more than 20 h.