Numerical differentiation on scattered data through multivariate polynomial interpolation

BIT Numerical Mathematics - We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja...     

Mild Microfluidic Approaches to Oxide Nanoparticles Synthesis

Oxide nanoparticles (oxide NPs) are advanced materials with a wide variety of applications in different fields. The use of continuous flow methods is particularly appealing for their synthesis due to the high control achieved over the reaction conditions and the easy process scalability. The present review focuses on the preparation of oxide NPs using microfluidic setups at low temperature (≤80 °C), since the employment of mild reaction conditions is crucial for developing sustainable and cost-effective processes. A particular emphasis will be put on the improvement over the final product features (e. g., size, shape, and size distribution) given by flow methods with respect to conventional batch procedures. The main issues that arise by treating NPs suspensions in microfluidic systems are product deposition or channel clogging; mitigation strategies to overcome these drawbacks will also be presented and discussed.     

Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure ${\mu }_{\chi }$ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces $L_{\alpha }^p({\mu }_{\chi })$ adapted to X and ${\mu }_{\chi }$ ($1<p<\infty$, $\alpha \ge 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.     

Temporal evolution of DMS and DMSP in Antarctic Coastal Sea water

The temporal evolution of concentrations of dimethylsulphide (DMS), its precursor dimethylsulphoniopropionate (DMSP) and chlorophyll a is surveyed weekly in the water column and in a landfast ice core at a coastal station of Gerlache Inlet (Terra Nova Bay, Antarctica) from 27 November 2000 to 14 February 2001. The DMS and DMSP profile concentrations in the water column are similar and show a clear temporal trend, with minimum values (<0.7?nM) at all depths occurring on 27 November 2000 and maximum values (4.8 × 10²?nM for DMS and 1.8 × 10²?nM for DMSP) in surface water on 27 December 2000 for DMS and on 19 December 2000 for DMSP. When the sea-ice cover is present, the temporal evolution of DMSP closely follows that of chlorophyll a in the water column, supporting the idea that DMSP, and therefore DMS, has a phytoplanktonic origin. However, when the ice cover breaks up during the late austral summer, a second phytoplankton bloom occurs, while the DMSP concentration in the sea-water column remains very low. In the ice core, the results show higher concentrations of DMSP than those of the underlying sea water, highlighting the important role of sea ice in the sulphur cycle of the Antarctic ecosystem.     

Birationally rigid hypersurfaces

We prove that for N≥4, all smooth hypersurfaces of degree N in ? ^N are birationally superrigid. First discovered in the case N=4 by Iskovskikh and Manin in a work that started this whole direction of research, this property was later conjectured to hold in general by Pukhlikov. The proof relies on the method of maximal singularities in combination with a formula on restrictions of multiplier ideals.     

Isopropenyl acetate: A cheap and general acylating agent of alcohols under metal-free conditions

Functionalized primary, secondary and tertiary alcohols are efficiently acetylated by isopropenyl acetate and catalytic p-TsOH.