A sharp inequality for the variance with respect to the Ewens sampling formula

Lithuanian Mathematical Journal - We examine the variance of a linear statistic defined on the symmetric group endowed with the Ewens probability. Despite the dependence of the summands, it can be...     

The Kendrick analysis for polymer mass spectrometry

The mass spectrum of a polymer often displays repetitive patterns with peak series spaced by the repeating unit(s) of the polymeric backbones, sometimes complexified with different adducts, chain terminations, or charge states. Exploring the complex mass spectral data or filtering the unwanted signal is tedious whether performed manually or automatically. In contrast, the now 60‐year‐old Kendrick (mass defect) analysis, when adapted to polymer ions, produces visual two‐dimensional maps with intuitive alignments of the repetitive patterns and favourable deconvolution of features overlaid in the one‐dimensional mass spectrum. This special feature article reports on an up‐to‐date and theoretically sound use of Kendrick plots as a data processing tool. The approach requires no prior knowledge of the sample but offers promising dynamic capabilities for visualizing, filtering, and sometimes assigning congested mass spectra. Examples of applications of the approach to polymers are discussed throughout the text, but the same tools can be readily extended to other applications, including the analysis of polymers present as pollutants/contaminants, and to other analytes incorporating a repetitive moiety, for example, oils or lipids. In each of these instances, data processing can benefit from the application of an updated and interactive Kendrick analysis.     

Numerical study of two-airfoil arrangements by a discrete vortex method

Theoretical and Computational Fluid Dynamics - The aerodynamic characteristics of two neighboring airfoils are greatly different from those of a single airfoil, for both attached and detached flow...     

Ultrasmall Superparamagnetic Iron Oxide Nanoparticles with Europium(III) DO3A as a Bimodal Imaging Probe

A new prototype consisting of ultrasmall superparamagnetic iron oxide (USPIO) nanoparticles decorated with europium(III) ions encapsulated in a DO3A organic scaffold was designed as a platform for further development of bimodal contrast agents for MRI and optical imaging. The USPIO nanoparticles act as negative MRI contrast agents, whereas the europium(III) ion is a luminophore that is suitable for use in optical imaging detection. The functionalized USPIO nanoparticles were characterized by TEM, DLS, XRD, FTIR, and TXRF analysis, and a full investigation of the relaxometric and optical properties was conducted. The typical luminescence emission of europium(III) was observed and the main red emission wavelength was found at 614 nm. The relaxometric study of these ultrasmall nanoparticles showed r₂ values of 114.8 mm ^?1_Fes^?1 at 60 MHz, which is nearly double the r₂ relaxivity of Sinerem^®.     

Highly Axial Magnetic Anisotropy in a N3O5 Dysprosium(III) Coordination Environment Generated by a Merocyanine Ligand

A spiropyran‐based switchable ligand isomerizes upon reaction with lanthanide(III) precursors to generate complexes with an unusual N₃O₅ coordination sphere. The air‐stable dysprosium(III) complex shows a hysteresis loop at 2 K and a very strong axial magnetic anisotropy generated by the merocyanine phenolate donor.     

Hyperpositive non-linear effects: enantiodivergence and modelling

The chiral ligand N-methylephedrine (NME) was found to catalyse the addition of dimethylzinc to benzaldehyde in an enantiodivergent way, with a monomeric and a homochiral dimeric complex both catalysing the reaction at a steady state and giving opposite product enantiomers. A change in the sign of the enantiomeric product was thus possible by simply varying the catalyst loading or the ligand ee, giving rise to an enantiodivergent non-linear effect. Simulations using a mathematical model confirmed the possibility of such behaviour and showed that this can lead to situations where a reaction gives racemic products, although the system is composed only of highly enantioselective individual catalysts. Furthermore, depending on the dimer''s degree of participation in the catalytic conversion, enantiodivergence may or may not be observed experimentally, which raises questions about the possibility of enantiodivergence in other monomer/dimer-catalysed systems. Simulations of the reaction kinetics showed that the observed kinetic constant k_obs is highly dependent on user-controlled parameters, such as the catalyst concentration and the ligand ee, and may thus vary in a distinct way from one experimental setup to another. This unusual dependency of k_obs allowed us to confirm that a previously observed U-shaped catalyst order vs. catalyst loading-plot is linked to the simultaneous catalytic activity of both monomeric and dimeric complexes.

An asymmetric reaction consisting of competing monomeric and dimeric catalysts may explain enantiodivergent non-linear effects.