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.      

Theory and simulation in heterogeneous gold catalysis

This critical review covers the application of quantum chemistry to the burgeoning area of the heterogeneous oxidation by Au. We focus on the most established reaction, the oxidation of CO at low temperature. The review begins with an overview of the methods available comparing the treatment of the electron-electron interaction and relativistic effects. The structure of Au particles and their interaction with oxide reviews is then discussed in detail. Calculations of the adsorption and reaction of CO and O(2) are then considered and results from isolated and supported Au clusters compared (155 references).     

Blue-LED Synthesis of Pummerer's Ketones by Peroxidase-Lignin-Catalyzed Oxidative Coupling of Substituted Phenols

Pummerer's ketones resembling the tricyclic scaffold of bioactive natural substances were synthesized by blue-LED driven Horseradish Peroxidase oxidative coupling of substituted phenols in 2-methyltetrahydrofuran by using meso-tetraphenylporphyrin as photosensitizer and dioxygen as primary oxidant. The application of functionalized lignin nanoparticles as a renewable and efficient platform for the immobilization of the enzyme extended the effectiveness of the overall process to heterogeneous catalysis under buffer limiting conditions.     

Synthesis, molecular structure, spectroscopic studies and second-order nonlinear optical behaviour of N,N'-(2-hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II)

N,N'-(2-Hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II) has been synthesized. The crystal structure has been determined by X-ray diffraction analysis, and linear optical characterization has been determined by UV-vis spectroscopy. It was found that the molecule under investigation has solvatochromic behaviour in the UV region, implying non-zero microscopic first hyperpolarizability. To reveal the microscopic nonlinear optical (NLO) properties, the static first hyperpolarizabilities (beta) and the electric dipole moments (mu) were evaluated by using the ab initio finite field (FF) method. According to the results of the FF calculations, the synthesized compound exhibits non-zero beta values, and it might have microscopic NLO behaviour.     

Structures and solution dynamics of pseudorotaxanes mediated by alkali-metal cations

Kinetic stability studies of a series of pseudorotaxanes formed from electron-rich crown ethers (hosts and ) and naphthalene diimide (guest ) in the presence of alkali salt templates MX (where M(+) = Li(+) and Na(+), and X(-) = Cl(-), Br(-), I(-), NO(3)(-) and CF(3)SO(3)(-)) were performed by (1)H NMR. The switching between the (bound) host and its linkage isomer host (free) was monitored in solution in the presence and absence of alkali salts, to establish the relative thermodynamic stabilities in the series. We also report here six new crystal structures, for pseudorotaxanes of type: [.], [M(2)..](2+) and [M(2)..](2+). Their solution-phase structures are in good agreement with the solid-state structures determined by X-ray crystallography.     

Designing Zn(II) and Cu(II) derivatives as probes for in vitro fluorescence imaging

New M(II) bis(thiosemicarbazonato) complexes (M = Ni(II), Cu(II) and Zn(II)) featuring allyl groups at the exocyclic nitrogens have been synthesised. The complexes were characterised in solution by spectroscopic methods and their solid state structures determined by single crystal X-ray diffraction using synchrotron radiation. The Zn(II) complex was found to be intrinsically fluorescent and soluble in biocompatible media. The uptake of this Zn(II) complex in HeLa, MCF-7 and IGROV cancer cells was monitored by fluorescence microscopies (epi- and confocal fluorescence imaging). The radiolabelling to (64)Cu(II) bis(thiosemicarbazonato) complex was performed cleanly by transmetallation from the corresponding Zn(II) species using (64)Cu(OAc)(2).     

OH, HO2, and ozone gaseous diffusion coefficients

The diffusion of OH, HO2, and O3 in He, and of OH in air, has been investigated using a coated-wall flow tube reactor coupled to a chemical ionization mass spectrometry. The diffusion coefficients were determined from measurements of the loss of the reactive species to the flow tube wall as a function of pressure. On the basis of the experimental results, D(OH-He) = 662 +/- 33 Torr cm2 s-1, D(OH-air) = 165 +/- 20 Torr cm2 s-1, D(HO2-He) = 430 +/- 30 Torr cm2 s-1, and D(O3-He) = 410 +/- 25 Torr cm2 s-1 at 296 K. We show that the measured values for OH and HO2 are in better agreement with measured values of their polar analogues (H2O and H2O2) compared with measured values of their nonpolar analogues (O and O2). The measured value for OH in air is 25% smaller than that for O (the nonpolar analogue). The difference between the measured value for HO2 and O2 (the nonpolar analogue) in air is expected to be even larger. Also we show that calculations of the diffusion coefficients based on Lennard-Jones potentials are in excellent agreement with the measurements. This gives further confidence that these calculations can be used to estimate accurate diffusion coefficients for conditions where laboratory data currently do not exist.     

Specific heat and frequency shifts for the translational modes in ammonia solid I close to phase transition

The specific heat C(p) is correlated to the frequency shifts (1/nu)( partial differentialnu/ partial differentialT)(p) in ammonia solid I close to the melting point. Our calculated Raman frequencies for the translational modes of nu(T) (100 cm(-1)) and nu(T) (130 cm(-1)), are used for this correlation for the pressures of 0, 1.93 and 3.07 kbar in this crystalline system. We obtain that the specific heat varied linearly with the frequency shifts for those pressures studied and values of the slope dP(m)/dT were extracted. The observed behaviour of the ammonia solid I near the melting point is explained on the basis of our spectroscopic modification of the first Pippard relation.