Maximal L p – L q -Estimates for the Stokes Equation: a Short Proof of Solonnikov’s Theorem

Introducing a new localization method involving Bogovskiĭ's operator we give a short and new proof for maximal L^p – L^q-estimates for the solution of the Stokes equation. Moreover, it is shown that, up to constants, the Stokes operator is an R{\mathcal{R}}-sectorial operator in L^p_s(W)L^{p}_{\sigma}(\Omega), 1 < p < ￥1 < p < \infty, of R{\mathcal{R}}-angle 0, for bounded or exterior domains of Ω.     

AC-conductivity and Raman spectra of polyiodide inclusion compounds (β-cyclodextrin)2·KI7·16H2O and (β-cyclodextrin)2·LiI7·14H2O during the dehydration process

The frequency and temperature dependence of ac-conductivity and phase shift of polycrystalline inclusion compounds (β-CD)₂·KI₇·16H₂O and (β-CD)₂·LiI₇·14H₂O (β-CD=β-cyclodextrin) has been investigated over the frequency and temperature ranges of 0-100 kHz and 240-420 K. A Raman spectroscopic study and calorimetric measurements are also accomplished. The Arrhenius exponential behaviour of the ac-conductivity for T>275 K is caused by the contribution of the metal cations K⁺, Li⁺. This contribution is facilitated by the water-net via the Grotthuss mechanism. The ac conductivity starts deviating from the exponential behaviour with lower increasing rate, at 347 K for β-K and at 353 K for β-Li reaching a maximum value at 371.1 and 361.8 K, respectively, and then decreases rapidly due to the gradual removal of all the water molecules. The values 371.1 and 361.8 K are characterized as semiconductor to metal transition temperatures. The shift of the initial Raman peak at 179 cm⁻¹ to the final value 165 cm⁻¹ as the temperature increases reveals the lengthening of I₂ units via a charge transfer interaction in I⁻₇ units. A second topical maximum value of conductivity appears at 399.7 K for β-K and 403 K for β-Li, attributed to the sublimation of I₂.     

Disordered lattice solitons

We study the properties of a nonlinear Schr?dinger equation in the presence of a disordered potential modeling a waveguide array. We find that, for both signs of the nonlinearity, there is a large number of soliton families each one possessing different quantitative properties. However, all these families can be categorized to only a few classes with the same qualitative properties. Highly confined solitons exist in each waveguide of the lattice. In addition, solitons families originate from each Anderson mode. Resonant interactions between a soliton and an Anderson mode can take place, leading to broadening of the soliton profile.     

Antiferromagnetic behaviour of germanium monoselenide connected with the negative magnetoresistance effect

The transport properties of GeSe indicate an antiferromagnetic character up to the temperature of 376 K. Above that temperature a metallic behaviour is materialized. Magnetic measurements confirm these findings indicating a Néel temperature at 381 K above which GeSe becomes paramagnetic. The magnetic moment is to be attributed to spin only angular momentum processes.     

Monolayer binary active phase (Mo-V) and (Cr-V) supported on titania catalysts for the selective catalytic reduction (SCR) of NO by NH3

Monolayer catalysts containing binary active phases (VOx-CrOx, VOx-MoOx) were prepared by simultaneous deposition of the corresponding transition metal-oxo species on the TiO2 (anatase) surface using the equilibrium deposition filtration technique. The prepared samples contained various amounts of each transition metal but almost the same total metal loading. They were characterized by atomic absorption spectroscopy, N2 adsorption, UV-vis diffuse reflectance spectroscopy, X-ray photoelectron spectroscopy, and tested for the selective catalytic reduction of NO by NH3 in the temperature range 250-450 degrees C. It was found that the transition-metal ionic species used for the preparation of these catalysts compete for the same surface sites of the TiO2 carrier upon co-deposition. Small amounts of the second phase (Mo- or Cr-oxo phase) are sufficient in order to promote the catalytic activity at relatively high temperatures, in contrast to what happens in the corresponding industrial catalysts prepared by conventional methods. An electronic interaction between V- and Cr-oxo species favored at a V/Cr atomic ratio around 3 is probably responsible for the relatively high catalytic performance of the corresponding TiCrV catalyst. The activity of the studied catalysts is well correlated with the intensity of a DRS absorption band that appeared at ca. 400 nm, which is considered as a measure of the magnitude of interactions exerted between the monolayer transition metal-oxo species and the TiO2 carrier. This correlation is independent of the transition metals combination used and follows the same linear relationship found previously for single-active-phase catalysts.     

Three-dimensional vortex solitons in self-defocusing media

We demonstrate that families of vortex solitons are possible in a bidispersive three-dimensional nonlinear Schr?dinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity.     

Discrete X-wave formation in nonlinear waveguide arrays

We present experimental evidence for the spontaneous formation of discrete X waves in AlGaAs waveguide arrays. This new family of optical waves has been excited, for the first time, by using the interplay between discrete diffraction and normal temporal dispersion, in the presence of Kerr nonlinearity. Our experimental results are in good agreement with theoretical predictions.     

On Countable Products of Finite Hausdorff Spaces

We investigate in ZF (i.e., Zermelo‐Fraenke set theory without the axiom of choice) conditions that are necessary and sufficient for countable products ∏_m∈ℕX_m of (a) finite Hausdorff spaces X_m resp. (b) Hausdorff spaces X_m with at most n points to be compact resp. Baire. Typica results: (i) Countable products of finite Hausdorff spaces are compact (resp. Baire) if and only if countable products of non‐empty finite sets are non‐empty. (ii) Countable products of discrete spaces with at most n + 1 points are compact (resp. Baire) if and only if countable products of non‐empty sets with at most n points are non‐empty.     

Non‐constructive Properties of the Real Numbers

We study the relationship between various properties of the real numbers and weak choice principles.