Harnack estimates for quasi-linear degenerate parabolic differential equations

We establish the intrinsic Harnack inequality for non-negative solutions of a class of degenerate, quasilinear, parabolic equations, including equations of the p-Laplacian and porous medium type. It is shown that the classical Harnack estimate, while failing for degenerate parabolic equations, it continues to hold in a space-time geometry intrinsic to the degeneracy. The proof uses only measure-theoretical arguments, it reproduces the classical Moser theory, for non-degenerate equations, and it is novel even in that context. Hölder estimates are derived as a consequence of the Harnack inequality. The results solve a long standing problem in the theory of degenerate parabolic equations.     

Arylation of β-methallyl alcohol catalyzed by Pd(OAc)2 in combination with P(t-Bu)3: application to fragrance synthesis

Pd(OAc)₂ in combination with P(t-Bu)₃ catalyzes the coupling of β-methallyl alcohol with 1-bromo-3,4-(methylenedioxy)benzene (1a), 1-bromo-4-methoxybenzene (1b), or 1-bromo-4-tert-butylbenzene (1c). The reaction affords the corresponding 2-methyl-3-aryl-propanals, which are valuable floral fragrances. With 1a or 1b high reaction rates are obtained at 130 °C using NMP/water mixtures and an inorganic base such as Na₂CO₃. The chemoselectivity of the reaction is almost complete, so that the process appears practically feasible. In contrast, the coupling of β-methallyl alcohol with 1c proceeds with low reaction rates.     

Monitoring the Light-induced Isomerisation of the Prototypical Polycyclic Aromatic Hydrocarbons C10H8+ through Ion-Molecule Reactions

Structural rearrangements in ions are essential for understanding the composition and evolution of energetic and chemically active environments. This study explores the interconversion routes for simple polycyclic aromatic hydrocarbons, namely naphthalene and azulene radical cations (C₁₀H₈⁺), by combining mass spectrometry and vacuum ultraviolet tunable synchrotron radiation through the chemical monitoring technique. Products of ion-molecule reactions are used to probe C₁₀H₈⁺ structures that are formed as a function of their internal energies. Isomerisation from azulene radical cation towards naphthalene radical cation in a timescale faster than 80 μs was monitored, whereas no reverse isomerisation was observed in the same time window. When energising C₁₀H₈⁺ with more than 6 eV, the reactivity of C₁₀H₈⁺ unveils the formation of a new isomeric group with a contrasted reactivity compared with naphthalene and azulene cations. We tentatively assigned these structures to phenylvinylacetylene cations.     

Polyfunctional inorganic-organic hybrid materials: an unusual kind of NLO active layered mixed metal oxalates with tunable magnetic properties and very large second harmonic generation

Mixed M(II)/M(III) metal oxalates, as "stripes" connected through strong hydrogen bonding by para-dimethylaminobenzaldeide (DAMBA) and water, form an organic-inorganic 2D network that enables segregation in layers of the cationic organic NLO-phore trans-4-(4-dimethylaminostyryl)-1-methylpyridinium, [DAMS+]. The crystalline hybrid materials obtained have the general formula [DAMS]4[M2M'(C2O4)6].2DAMBA.2H2O (M = Rh, Fe, Cr; M' = Mn, Zn), and their overall three-dimensional packing is non-centrosymmetric and polar, therefore suitable for second harmonic generation (SHG). All the compounds investigated are characterized by an exceptional SHG activity, due both to the large molecular quadratic hyperpolarizability of [DAMS+] and to the efficiency of the crystalline network which organizes [DAMS+] into head-to-tail arranged J-type aggregates. The tunability of the pairs of metal ions allows exploiting also the magnetic functionality of the materials. Examples containing antiferro-, ferro-, and ferri-magnetic interactions (mediated by oxalato bridges) are obtained by coupling proper M(III) ions (Fe, Cr, Rh) with M(II) (Mn, Zn). This shed light on the role of weak next-nearest-neighbor interactions and main nearest-neighbor couplings along "stripes" of mixed M(II)/M(III) metal oxalates of the organic-inorganic 2D network, thus suggesting that these hybrid materials may display isotropic 1D magnetic properties along the mixed M(II)/M(III) metal oxalates "stripes".     

Poly[(N-isopropylacrylamide-co-acrylamide-co-(hydroxyethylmethacrylate))] thermoresponsive microspheres: An accurate method based on solute exclusion technique to determine the volume phase transition temperature

Poly[(N-isopropylacrylamide-co-acrylamide-co-(hydroxyethylmethacrylate))] [poly(NIPAAm-co-AAm-co-HEMA)] copolymer was synthesized as a new thermoresponsive material possessing a lower critical solution temperature (LCST) around 37 °C in phosphate buffer, pH 7.4, at a solution concentration of 1%, w/v. The influence of polymer concentration on LCST was determined by cloud point measurements and by microcalorimetric analysis. The copolymer was transformed in hydrogel microspheres by suspension reticulation of OH groups with glutaraldehyde. The volume phase transition temperature (VPTT) of microspheres was determined by a new approach, which involves measurement of the increase in concentration of a blue dextran (BD) solution at different temperatures in the presence of dry microspheres. The minimum BD concentration that gives reliable and reproducible results was determined to be 1 mg/ml. However, the higher is the concentration of BD in solution the smaller is the error. Contrary to solution of the linear polymer which displays a sharp phase transition temperature, the dependence of water regain of the hydrogel with temperature lasts from 4 °C to 50 °C.     

Relatively Stable Bundles over Elliptic Fibrations

We consider a relative Fourier‐Mukai transform de.ned on elliptic fibrations over an arbitrary base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah and Tu's results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree.     

Direct metalation of methoxymethyl arylmethyl ethers: A tin-free approach to the generation of α-alkoxyalkoxy-substituted aryllithiums

The generation of a series of α-methoxymethoxy-substituted arylmethyllithiums was achieved by direct metalation of the corresponding arylmethyl methoxymethyl ethers. While the effect of substituents at the benzylic position is straightforward, substituents located on the aromatic ring promote the set up of a competition between lateral and aromatic metalation, strongly affected by the position and relative ortho directing properties of the new substituent. The proposed methodology allows a simple approach to the generation of a wide array of functionalized organolithium reagents.     

Photoinduced processes in dipyrrolyl-perfluoro-cyclopentenes

The photobehavior of five photochromic dipyrrolyl-perfluoro-cyclopentenes was studied by steady state and time-resolved absorption spectroscopy. The quantum yields of the UV-photoinduced ring-closing reaction (coloration) and the visible-stimulated cycloreversion reaction (bleaching) were measured. Kinetic and thermodynamic parameters of thermal bleaching were also determined. Nanosecond time-resolved experiments showed formation of a transient, which was not a precursor of the reaction photoproduct. This transient was tentatively assigned to a radical cation formed by direct photoionization through a short-lived triplet state. The nature of the transient species was supported by photoinduced electron transfer to electron acceptors.     

LES-based Study of the Roughness Effects on the Wake of a Circular Cylinder from Subcritical to Transcritical Reynolds Numbers

This paper investigates the effects of surface roughness on the flow past a circular cylinder at subcritical to transcritical Reynolds numbers. Large eddy simulations of the flow for sand grain roughness of size k/D = 0.02 are performed (D is the cylinder diameter). Results show that surface roughness triggers the transition to turbulence in the boundary layer at all Reynolds numbers, thus leading to an early separation caused by the increased momentum deficit, especially at transcritical Reynolds numbers. Even at subcritical Reynolds numbers, boundary layer instabilities are triggered in the roughness sublayer and eventually lead to the transition to turbulence. The early separation at transcritical Reynolds numbers leads to a wake topology similar to that of the subcritical regime, resulting in an increased drag coefficient and lower Strouhal number. Turbulent statistics in the wake are also affected by roughness; the Reynolds stresses are larger due to the increased turbulent kinetic energy production in the boundary layer and separated shear layers close to the cylinder shoulders.     

NIR emitting ytterbium chelates for colourless luminescent solar concentrators

A new oxyiminopyrazole-based ytterbium chelate enables NIR emission upon UV excitation in colorless single layer luminescent solar concentrators for building integrated photovoltaics.