A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion

A functional limit theorem for the empirical measure-valued process of eigenvalues of a matrix fractional Brownian motion is obtained. It is shown that the limiting measure-valued process is the non-commutative fractional Brownian motion recently introduced by Nourdin and Taqqu (J Theor Probab 27:220–248, 2014). Young and Skorohod stochastic integral techniques and fractional calculus are the main tools used.     

Preliminary results on sol-gel processing of 〈100〉 oriented Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript>-PbTiO<Subscript>3</Subscript> thin films using diol-based solutions

A novel sol-gel method is used here for the synthesis of air-stable and precipitate-free diol-based sols of 0.7Pb(Mg_1/3Nb_2/3)O₃-0.3PbTiO₃ (PMN-PT). Sols containing a 15 mol% lead excess have been used for the preparation of PMN-PT thin films. The films were deposited onto (111)Pt/TiO₂/SiO₂/(100)Si substrates, and crystallised in oxygen by Rapid Thermal Processing (RTP), using different temperatures and soaking times. Single perovskite films are obtained when treated at temperatures between 600 and 700°C for 6 s. Those crystallised at other temperatures contain a secondary pyrochlore phase. This phase also appears in the films treated at 650°C with soaking times longer than 6 s. PMN-PT films with a 〈100〉 preferred orientation were prepared by using a PbTiO₃ seeding layer onto the substrate. These PMN-PT films present relaxor-type electrical properties. Dielectric permittivity, , shows significant dispersion. Its temperature dependence presents a broad maximum at 110–130°C, which position shifts towards higher temperatures with frequency. Ferroelectric hysteresis loops show high values of saturation polarisation but very low remanence. The piezoelectric activity of the films has been tested by the measurement of their local piezoelectric hysteresis loops.     

Molecular-programmed self-assembly of homo- and heterometallic penta- and hexanuclear coordination compounds: synthesis, crystal structures, and magnetic properties of ladder-type CuII2MIIx (M=Cu, Ni; x=3, 4) oxamato complexes with CuII2 metallacyclophane cores

New homo- and heterometallic, hexa- and pentanuclear complexes of formula {[Cu2(mpba)2(H2O)F][Cu(Me5dien)]4}(PF6)(3).5H2O (1), {[Cu2(Me3mpba)2(H2O)2][Cu(Me5dien)]4}(ClO4)(4).12H2O (2), {[Cu2(ppba)2][Cu(Me5dien)]4}(ClO4)4 (3), and [Ni(cyclam)]{[Cu2(mpba)2][Ni(cyclam)]3}(ClO4)(4).6H2O (4) [mpba=1,3-phenylenebis(oxamate), Me3mpba=2,4,6-trimethyl-1,3-phenylenebis(oxamate), ppba=1,4-phenylenebis(oxamate), Me5dien=N,N,N'N' ',N' '-pentamethyldiethylenetriamine, and cyclam=1,4,8,11-tetraazacyclotetradecane] have been synthesized through the use of the "complex-as-ligand/complex-as-metal" strategy. The structures of 1-3 consist of cationic CuII6 entities with an overall [2x2] ladder-type architecture which is made up of two oxamato-bridged CuII3 linear units connected through two m- or p-phenylenediamidate bridges between the two central copper atoms to give a binuclear metallacyclic core of the cyclophane-type. Complex 4 consists of cationic CuII2NiII3 entities with an incomplete [2x2] ladder-type architecture which is made up of oxamato-bridged CuIINiII and CuIINiII2 linear units connected through two m-phenylenediamidate bridges between the two copper atoms to give a binuclear metallacyclophane core. The magnetic properties of 1-3 and 4 have been interpreted according to their distinct "dimer-of-trimers" and "dimer-plus-trimer" structures, respectively, (H=-J(S1A.S3A+S1A.S4A+S2B.S5B+S2B.S6B)-J'S1A.S2B). Complexes 1-4 exhibit moderate to strong antiferromagnetic coupling through the oxamate bridges (-JCu-Cu=81.3-105.9 cm-1; -JCu-Ni=111.6 cm-1) in the trinuclear and/or binuclear units. Within the binuclear metallacyclophane core, a weak to moderate ferromagnetic coupling (J'Cu-Cu=1.7-9.0 cm-1) operates through the double m-phenylenediamidate bridge, while a strong antiferromagnetic coupling (J'Cu-Cu=-120.6 cm-1) is mediated by the double p-phenylenediamidate bridge.     

Highly enantioselective synthesis of beta-amino alcohols: a catalytic version

Highly enantioselective rearrangement of beta-amino alcohols was realized by using a catalytic amount of trifluoroacetic anhydride.     

Transition metal binding properties of the redox-active 1,4,7,10,13,16-hexa(ferrocenylmethyl)-1,4,7,10,13,16-hexaazacyclooctadecane and its electrochemical behaviour in a non-aqueous solvent

Solution studies to elucidate the coordination behaviour and the electrochemical response of the ferrocene-functionalized polyazamacrocycle 1,4,7,10,13,16-hexa(ferrocenylmethyl)-1,4,7,10,13,16-hexaazacyclooctadecane (L¹) by potentiometric methods and electrochemical techniques have been carried out. Potentiometric methods in the presence of Cd²⁺, Hg²⁺, Pb²⁺ and Zn²⁺ were carried out in 1,4-dioxane/water (70:30 v/v, 25°C, 0.1 mol dm⁻³ KNO₃). Electrochemical studies were carried out in acetonitrile/dichloromethane (50:50 v/v, 25°C, 0.1 mol dm⁻³ TBAClO₄) in the presence of transition metal ions and anions.     

A novel five‐coordinate cadmium phenanthroline thiosulfate

The structure of the novel cadmium phenanthroline thio­sulfate poly­[[(1,10‐phenanthroline‐κ²N,N′)­cadmium(II)]‐μ₃‐thio­sulfato‐κ³S:S:O], [Cd(S₂O₃)(C₁₂H₈N₂)]_n, with a pentacoordinated Cd centre, is reported. It forms linear chains built up around a 2₁ axis and is isostructural with the known bi­pyridine homologue. The structure is also compared with a previously reported closely related mono­aqua monohydrated phase, where the Cd²⁺ cation is hexacoordinated. The incidence of weak C—H⋯O interactions in the determination of its general packing properties is discussed.     

Confidence sets and coverage probabilities based on preliminary estimators in logistic regression models

In this paper we present recentered confidence sets for the parameters of a logistic regression model based on preliminary minimum ?$?$-divergence estimators. Asymptotic coverage probabilities are given as well as a simulation study in order to analyze the coverage probabilities for small and moderate sample sizes.     

Structure-based secondary structure-independent approach to design protein ligands: Application to the design of Kv1.2 potassium channel blockers

We have developed a structure-based approach to the design of protein ligands. This approach is based on the transfer of a functional binding motif of amino acids, often referred as to the "hot spot", on a host protein able to reproduce the functional topology of these residues. The scaffolds were identified by a systematic in silico search in the Protein Data Bank for proteins possessing a group of residues in a topology similar to that adopted by the functional motif in a reference ligand of known 3D structure. In contrast to previously reported studies, this search is independent of the particular secondary structure supporting the functional motif. To take into account the global properties of the host protein, two additional criteria were taken into account in the selection process: (1) Only those scaffolds sterically compatible with the positioning of the functional motif as observed in a reference complex model were retained. (2) Host proteins displaying electrostatic potentials, in the region of the transferred functional motif, similar to that of the reference ligand were selected. This approach was applied to the development of protein ligands of the Kv1.2 channel using BgK, a small protein isolated from the sea anemone Bunodosoma granulifera, as the reference ligand. Four proteins obtained by this approach were produced for experimental evaluation. The X-ray structure of one of these proteins was determined to check for similarity of the transferred functional motif with the structure it adopts in the reference ligand. Three of these protein ligands bind the Kv1.2 channel with inhibition constants of 0.5, 1.5, and 1.6 microM. Several mutants of these designed protein ligands gave binding results consistent with the presumed binding mode. These results show that protein ligands can be designed by transferring a binding motif on a protein host selected to reproduce the functional topology of this motif, irrespective to the secondary structure supporting the functional motif, if the host protein possesses steric and electrostatic properties compatible with the binding to the target. This result opens the way to the design of protein ligands by taking advantage of the considerable structural repertoire of the Protein Data Bank.