2-microlocal analysis of martingales and stochastic integrals

Recently, a new approach in the fine analysis of sample paths of stochastic processes has been developed to predict the evolution of the local regularity under (pseudo-)differential operators. In this paper, we study the sample paths of continuous martingales and stochastic integrals. We proved that the almost sure 2-microlocal frontier of a martingale can be obtained through the local regularity of its quadratic variation. It allows to link the Hölder regularity of a stochastic integral to the regularity of the integrand and integrator processes. These results provide a methodology to predict the local regularity of diffusions from the fine analysis of its coefficients. We illustrate our work with examples of martingales with unusual complex regularity behaviour and square of Bessel processes.     

Experimental and numerical investigations on the pure material instability of an Oldroyd's 3-constant model

Received March 25, 2001 / Published online November 15, 2001     

Inverse problem for the reaction diffusion system by optimization method

In this paper, we study an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final measurement. First the given problem is transformed into an optimization problem by using optimal control framework and the existence of the minimizer for the control functional is established. Then we prove the stability estimate for two coefficients with the upper bound given by some Sobolev norms of the final measurement.     

Understanding guest and pressure‐induced porosity through structural transition in flexible interpenetrated MOF by Raman spectroscopy

Interpenetrating metal organic frameworks are interesting functional materials exhibiting exceptional framework properties. Uptake or exclusion of guest molecules can induce sliding in the framework making it porous or non‐porous. To understand this dynamic nature and how framework interaction changes during sliding, metal organic framework (MOF) 508 {Zn(BDC)( 4,4′‐Bipy)_0.5 · DMF(H₂O)_0.5} was selected for study. We have investigated structural transformation in MOF‐508 under variable conditions of temperature, pressure and gas loading using Raman spectroscopy and substantiated it with IR studies and density functional theory (DFT) calculations. Conformational changes in the organic linkers leading to the sliding of the framework result in changes in Raman spectra. These changes in the organic linkers are measured as a function of high pressure and low temperature, suggesting that the dynamism in MOF‐508 framework is driven by ligand conformation change and inter‐linker interactions. The presence of Raman signatures of adsorbed CO₂ and its librational mode at 149 cm⁻¹ suggests cooperative adsorption of CO₂ in the MOF‐508 framework, which is also confirmed from DFT calculations that give a binding energy of 34 kJ/mol. Copyright © 2015 John Wiley & Sons, Ltd.     

Lyotropic self-assembly of high-aspect-ratio semiconductor nanowires of single-crystal ZnO

Lyotropic nanowire dispersions are attractive precursors for semiconductor device fabrication because they permit the alignment control of active nanomaterials. The reliable production of nanowire-based mesophases, however, is very challenging in practice. We show that appropriately functionalized high-aspect-ratio nanowires of single-crystal ZnO spontaneously form nematic phases in organic and aqueous media. These systems show isotropic, biphasic, and nematic phases on increasing concentration, in reasonable agreement with Onsager's theory for rigid rods interacting via excluded volume. Suspensions were readily processed to produce films with large-area monodomains of aligned nanowires. Imprints of the director field in quiescently dried films display a propensity for bend deformation in the organic mesophase versus splay deformation in the aqueous case, suggesting that system elasticity may be tuned via surface functionalization. These results provide critical insight for the utilization of semiconductor nanowires as novel mesogens and further enable the use of solution-based routes for fabricating optoelectronic devices.     

A palladium-catalyzed three-component cross-coupling of conjugated dienes or terminal alkenes with vinyl triflates and boronic acids

A three-component coupling of vinyl triflates and boronic acids to alkenes catalyzed by palladium is reported. Using 1,3-dienes, selective 1,2-alkene difunction-alization is observed, whereas the use of terminal alkenes results in 1,1-alkene difunctionalization. The reaction outcome is attributed to the formation of stabilized, cationic Pd-π-allyl intermediates to regulate β-hydride elimination.     

A new identity for Parseval frames

In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.

     

Simple one‐pot conversion of organic compounds by hydrogen peroxide activated by ruthenium(III) chloride: organic conversions by hydrogen peroxide in the presence of ruthenium(III)

The aromatic compounds p‐nitrobenzaldehyde, p‐hydroxybenzaldehyde, naphthalene, toluene, catechol, quinol, aniline and toluidine dissolved in aqueous acetic acid or aqueous medium were oxidized in quantitative to good yields by 50% H₂O₂ in the presence of traces of RuCl₃ (～10^?8 mol; substrate/catalyst ratio 1488:1 to 341 250:1). Conditions for highest yields, in the most economical way, were obtained. Higher catalyst concentrations decrease the yield. Oxidation in aromatic aldehydes is selective at the aldehydic group only. In the case of hydrocarbons, oxidation results in the introduction of a hydroxyl group with >85% (in the case of toluene) selectivity for the ortho position. Formation of low‐molecular‐weight polyaniline was reduced to 10%, along with 90% formation of higher molecular weight polyaniline. In this new, simple and economical method, which is environmentally safe and requires less time, oxo‐centered carboxylate species of ruthenium(III) in acetic acid medium and hydrated ruthenium(III) chloride in aqueous medium probably catalyze the oxidation. Copyright © 2005 John Wiley & Sons, Ltd.     

Calculation and extrapolation of oscillator strengths in Rb-like,multiply charged ions

The oscillator strengths of dipole transitions between energy levels of the lowest configurations of ions of the Rb I isoelectronic sequence with nuclear charge Z=41–46 are calculated on the basis of the model potential method using an energy approach. For certain ions the reported data are published here for the first time. It is shown that the contribution of core polarization to the oscillator strength attains 15% for some transitions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 89–92, January, 1996.