Courbes nodales et ramification sauvage virtuelle

Let S be the spectrum of a discrete valuation ring of residue characteristic p>0. Let Z be a scheme separated and of finite type over S, and denote by K_c(Z,) (l≠p) the Grothendieck group of -constructible sheaves on the etale site of Z. In this article, we introduce the subgroup of virtual sheaves with virtual wild ramification zero, and we prove that this subgroup is preserved by the formalism of six operations “à la Grothendieck”.     

Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group

It was proved by Bahouri et al. [9] that the Schrödinger equation on the Heisenberg group $\mathbb{H}^d,$ involving the sublaplacian, is an example of a totally non-dispersive evolution equation: for this reason global dispersive estimates cannot hold. This paper aims at establishing local dispersive estimates on $\mathbb{H}^d$ for the linear Schrödinger equation, by a refined study of the Schrödinger kernel $S_t$ on $\mathbb{H}^d.$ The sharpness of these estimates is discussed through several examples. Our approach, based on the explicit formula of the heat kernel on $\mathbb{H}^d$ derived by Gaveau [19], is achieved by combining complex analysis and Fourier-Heisenberg tools. As a by-product of our results we establish local Strichartz estimates and prove that the kernel $S_t$ concentrates on quantized horizontal hyperplanes of $\mathbb{H}^d.$     

Nash constructible functions

Nash constructible functions on a real algebraic set V are defined as linear combinations, with integer coefficients, of Euler characteristic of fibres of proper regular morphisms restricted to connected components of algebraic sets. We prove that if V is compact, these functions are sums of signs of semialgebraic arc-analytic functions (i.e. functions which become analytic when composed with any analytic arc). We also give a sharp upper bound to the number of semialgebraic arc-analytic functions which are necessary to define any given Nash constructible functions.     

Infrared and visible emission of Er in combustion-synthesized CaAl2O4 phosphors

New near-infrared luminescent, monoclinic CaAl₂O₄:Er³⁺ phosphor was prepared by using the combustion route at furnace temperatures as low as 500 °C in a few minutes. Combustion synthesized phosphor has been well characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy-dispersive analysis of X-ray (EDAX) mapping studies. The luminescence spectra of Er³⁺-doped calcium aluminate were studied at UV (380 nm), vis (488 nm) and IR (980 nm) excitation. Upon UV and vis excitation, the CaAl₂O₄:Er³⁺ phosphor exhibits emission bands at ~523 nm and at ~547 nm, corresponding to transitions from the ²H_11/2 and ⁴S_3/2 erbium levels to the ⁴I_15/2 ground state. A strong luminescence at 1.55 μm in the infrared (IR) region due to ⁴I_13/2→⁴I_15/2 transition has been observed in CaAl₂O₄:Er³⁺ phosphor upon 980 nm CW pumping. In the spectrum of IR-excited up-conversion luminescence, green (~523 and ~547 nm) and red (662 nm) luminescence bands were present, the latter associated with the ⁴F_9/2→⁴I_15/2 transitions of Er³⁺ ions. Both excited state absorption and energy transfer may be proposed as processes responsible for the population of the ⁴S_3/2 and ⁴F_9/2 erbium levels upon IR excitation. The mechanisms responsible for the up-conversion luminescence are discussed.     

Infrared emission and defect centres in Er and Yb codoped Y3Al5O12 phosphors

YAG phosphor powders doped/codoped with Er³⁺/(Er³⁺ + Yb³⁺) have been synthesised by using the solution combustion method. The effect of direct pumping into the ⁴I_11/2 level under 980 nm excitation of doped/codoped Er³⁺/Yb³⁺−Er³⁺ in Y₃Al₅O₁₂ (YAG) phosphor responsible for an infrared (IR) emission peaking at ∼1.53 μm corresponding to the ⁴I_13/2→⁴I_15/2 transition has been studied. YAG exhibits three thermally-stimulated luminescence (TSL) peaks at around 140°C, 210°C and 445°C. Electron spin resonance (ESR) studies were carried out to identify the centres responsible for the TSL peaks. The room temperature ESR spectrum of irradiated phosphor appears to be a superposition of two distinct centres. One of the centres (centre I) with principal g-value 2.0176 is identified as O⁻ ion, while centre II with an isotropic g-factor 2.0020 is assigned to an F⁺ centre (singly ionised oxygen vacancy). An additional defect centre is observed during thermal-annealing experiments and this centre (assigned to F⁺ centre) seems to originate from an F-centre (oxygen vacancy with two electrons) and these two centres appear to correlate with the observed high-temperature TSL peak in YAG phosphor.     

You cannot fight the pressure: Structural rearrangements of active pharmaceutical ingredients under magic angle spinning

Although solid-state nuclear magnetic resonance (NMR) is a versatile analytical tool to study polymorphs and phase transitions of pharmaceutical molecules and products, this work summarizes examples of spontaneous and unexpected (and unwanted) structural rearrangements and phase transitions (amorphous-to-crystalline and crystalline-to-crystalline) under magic angle spinning (MAS) conditions, some of them clearly being due to the pressure experienced by the samples. It is widely known that such changes can often be detected by X-ray powder diffraction (XRPD); here, the capability of solid-state NMR experiments with a special focus on ¹H-¹³C frequency-switched Lee–Goldburg heteronuclear correlation (FSLG HETCOR)/MAS NMR experiments to detect even subtle changes on a molecular level not observable by conventional 1D NMR experiments or XRPD is presented. Furthermore, it is shown that a polymorphic impurity combined with MAS can induce a crystalline-to-crystalline phase transition. This showcases that solid-state NMR is not always noninvasive and such changes upon MAS should be considered in particular when compounds are studied over longer time spans.     

Remarkably efficient synthesis of 2H-indazole 1-oxides and 2H-indazoles via tandem carbon-carbon followed by nitrogen-nitrogen bond formation

Base-catalyzed tandem carbon-carbon followed by nitrogen-nitrogen bond formations quantitatively converted N-alkyl-2-nitro-N-(2-oxo-2-aryl-ethyl)-benzenesulfonamides to 2H-indazoles 1-oxides under mild conditions. Triphenylphosphine or mesyl chloride/triethylamine-mediated deoxygenation afforded 2H-indazoles.     

Photoinduced magnetization in copper octacyanomolybdate

This article describes the studies of a photomagnetic cyanide-bridged Cu-Mo bimetallic assembly, Cu(II)(2)[Mo(IV)(CN)(8)].8H(2)O (Cu(II), S = (1)/(2); Mo(IV), S = 0) (1), which has an intervalence transfer (IT) band from Mo(IV)-CN-Cu(II) to Mo(V)-CN-Cu(I) around 480 nm. Wide-angle X-ray scattering and X-ray spectroscopic studies provide precise information about the 3D connectivity and the local environment of the transition metal ions. Irradiating with blue light causes solid 1 to exhibit a spontaneous magnetization (Curie temperature = 25 K). The thermal reversibility is carefully studied and shows the long-time stability of the photoinduced state up to 100 K. Photoreversibility is also observed; i.e., the magnetization is induced by irradiation with light below 520 nm, while the magnetization is reduced by irradiation with light above 520 nm. The UV-vis absorption spectrum after irradiation shows a decrease of the IT band and the appearance of the reverse-IT band in the region of 600-900 nm (lambda(max) = 710 nm). This UV-vis absorption spectrum is recovered to the original spectrum by irradiation with 658-, 785-, and 840-nm light. In this photomagnetic effect, the excitation of the IT band causes an electron transfer from Mo(IV) to Cu(II), producing a ferromagnetic mixed-valence isomer of Cu(I)Cu(II)[Mo(V)(CN)(8)].8H(2)O (Cu(I), S = 0; Cu(II), S = (1)/(2); Mo(V), S = (1)/(2)) (1'). 1' returns to 1 by irradiation of the reverse-IT band, which obeys the scheme for the potential energy surface in mixed-valence class II compounds.     

Considerations on the possibilities and limitations of comprehensive normal phase-reversed phase liquid chromatography (NPLC x RPLC)

A comprehensive normal phase system LC-reversed phase LC (NPLC x RPLC) was evaluated for the separation of a pharmaceutical mixture and citrus oil extracts. NPLC was performed on a 25 cm x 1 mm ID x 5 microm dp diol phase. In the second dimension, an RP 18 monolithic column (10 cm L x 4.6 mm ID x 2 microm macropore size) and an octadecyl silicagel-packed column (5 cm L x 4.6 mm ID x 3.5 microm dp) were applied for the analyses of the pharmaceutical sample and the citrus oil extracts, respectively. A two-position/ten-port switching valve was used as interface. Under optimised LC conditions, the high degree of orthogonality between NP and RP resulted in peak capacities of 300 for the pharmaceutical sample and of 450 for the citrus oil extract composed of lemon and orange oil. Despite the features of NPLC x RPLC, several shortcomings related with the solvent incompatibility between the two LC modes were identified and the practical consequences were discussed.     

Design of original bioactive formulations based on sugar-surfactant/non-steroidal anti-inflammatory catanionic self-assemblies: a new way of dermal drug delivery

A new kind of catanionic assembly was developed that associates a sugar-based surfactant with a non-steroidal anti-inflammatory drug (NSAID). Three different assemblies using indomethacin, ibuprofen and ketoprofen as NSAIDs were easily obtained in water by an acid-base reaction. These assemblies formed new amphiphilic entities because of electrostatic and hydrophobic effects in water and led to the spontaneous formation of vesicles. These catanionic vesicles were then tested as potential NSAID delivery systems for dermatological application. The anti-inflammatory activity was evaluated in vivo, and this study clearly showed an improved therapeutic effect for NSAIDs that were formulated as catanionic vesicles. These vesicles ensured a slower diffusion of the NSAID through the skin. This release probably increased the time of retention of the NSAID in the targeted strata of the skin. Thus, the present study suggests that this catanionic bioactive formulation could be a promising dermal delivery system for NSAIDs in the course of skin inflammation treatment.