Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity q > 1 and with natural growth

In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second-order discontinuous elliptic systems with nonlinearity q > 1 and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension n = q without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets $\Omega_0 \subset \OmegaIn this paper we deal with the H?lder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second-order discontinuous elliptic systems with nonlinearity q > 1 and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global H?lder continuous in the case of the dimension n = q without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets , are always empty for n = q. Moreover we show that also for 1 < q < 2, but q close enough to 2, the solutions are global H?lder continuous for n = 2.      

Water-soluble, electroactive, and photoluminescent quaterthiophene-dinucleotide conjugates

Quaterthiophene-dinucleotide conjugates 5'TA3'-t4-3'AT5', 5'AA3'-t4-3'AA5', and 5'TT3'-t4-3'TT5' (TA: thymidine-adenosine, AA: adenosine-adenosine, TT: thymidine-thymidine) were synthesized and analyzed by a combination of spectroscopy and microscopy, electrical characterization, and theoretical calculations. Circular dichroism (CD) experiments demonstrated a transfer of chirality from the dinucleotides to quaterthiophene at high ionic strength and in cast films. The films were photoluminescent and electroactive. CD and photoluminescence spectra and current density/voltage plots (measured under dynamic vacuum) displayed significant variation on changing the dinucleotide scaffold. Molecular mechanics and molecular dynamics calculations indicated that the conformation and packing modes of the conjugates are the result of a balance between intra- and intermolecular nucleobase-thiophene stacking interactions and intramolecular hydrogen bonding between the nucleobases.     

FT-IR study of the nature and stability of NOx surface species on ZrO2, VOx/ZrO2 and MoOx/ZrO2 catalysts

The adsorption of NO, NO/O₂ mixtures and NO₂ on pure ZrO₂ and on two series of catalysts supported on ZrO₂, one containing vanadia and the other molybdena (ZV and ZMo, respectively), has been investigated. The V and Mo surface contents of the latter were ≤3 atoms nm⁻² and ≤5 atoms nm⁻², respectively. All samples had been previously submitted to a standard oxidation treatment. On all samples, only extremely minor amounts of NO_x surface species are formed by NO interaction at room temperature (RT). NO_x surface species are formed in greater amounts on pure ZrO₂ when NO and O₂ are coadsorbed at RT; they are mainly nitrites, small amounts of nitrates, and small amounts of (O₂NO−H)^δ− species; when ZrO₂ is warmed to 623 K in the NO/O₂ mixture, nitrites decrease, nitrates and (O₂NO−H)^δ− species increase. The same NO_x species as on the ZrO₂ surface free from V (or Mo) are formed on ZV (or ZMo) samples with surface V (or Mo) density <1.5 atoms nm⁻²; however, they occur in decreased amount with increasing V (or Mo) coverage. On ZV samples with a surface V density of 1.5–3 atoms nm⁻² (or ZMo samples with a surface Mo density of 1.5–5 atoms nm⁻²) when NO and O₂ are coadsorbed at RT, there is formation of small amounts of nitrites, nitrates (both on ZrO₂ surface free from V (or Mo) and at the edges of V- or Mo-polyoxoanions) and NO₂ ^δ+ species, associated with V⁵⁺ (or Mo⁶⁺) of very strong Lewis acidity; when samples are warmed up 623 K in the NO/O₂ mixture, nitrites disappear, nitrates increase, NO₂ ^δ+ species remain constant or slightly decrease. When NO₂ is allowed into contact at RT with oxidized samples, surface situations almost identical to those obtained for each sample warmed to 623 K in NO/O₂ mixture is reached. The NO_x surface species stable at 623 K, the temperature at which catalysts show the best performance in the selective catalytic reduction (SCR) of NO by NH₃, are nitrates, both on ZrO₂ and on polyvanadates or polymolybdates at high nuclearity. On the contrary, nitrites and NO₂ ^δ+ species are unstable at 623 K.