Blaschke, Privaloff, Reade and Saks Theorems for Diffusion Equations on Lie Groups

We prove some asymptotic characterizations for the subsolutions to a class of diffusion equations on homogeneous Lie groups. These results are the diffusion counterpart of the classical Blaschke, Privaloff, Reade and Saks Theorems for harmonic functions.     

On some notions of good reduction for endomorphisms of the projective line

Let Φ be an endomorphism of ${\mathbb{P}^1_{\overline{\mathbb{Q}}}}$ , the projective line over the algebraic closure of ${\mathbb{Q}}$ , of degree ≥ 2 defined over a number field K. Let v be a non-archimedean valuation of K. We say that Φ has critically good reduction at v if any pair of distinct ramification points of Φ do not collide under reduction modulo v and the same holds also for any pair of branch points. We say that Φ has simple good reduction at v if the map Φ _v , the reduction of Φ modulo v, has the same degree of Φ. We prove that if Φ has critically good reduction at v and the reduction map Φ _v is separable, then Φ has simple good reduction at v.     

Poset embeddings of Hilbert functions

For a standard graded algebra $R$ , we consider embeddings of the poset of Hilbert functions of $R$ -ideals into the poset of $R$ -ideals, as a way of classification of Hilbert functions. There are examples of rings for which such embeddings do not exist. We describe how the embedding can be lifted to certain ring extensions, which is then used in the case of polarization and distraction. A version of a theorem of Clements–Lindström is proved. We exhibit a condition on the embedding that ensures that the classification of Hilbert functions is obtained with images of lexicographic segment ideals.     

Reproducibility experiments on measuring acoustical properties of rigid-frame porous media (round-robin tests)

This paper reports the results of reproducibility experiments on the interlaboratory characterization of the acoustical properties of three types of consolidated porous media: granulated porous rubber, reticulated foam, and fiberglass. The measurements are conducted in several independent laboratories in Europe and North America. The studied acoustical characteristics are the surface complex acoustic impedance at normal incidence and plane wave absorption coefficient which are determined using the standard impedance tube method. The paper provides detailed procedures related to sample preparation and installation and it discusses the dispersion in the acoustical material property observed between individual material samples and laboratories. The importance of the boundary conditions, homogeneity of the porous material structure, and stability of the adopted signal processing method are highlighted.     

Magnetically induced thermal rectification

We consider far from equilibrium heat transport in chaotic billiard chains with noninteracting charged particles in the presence of nonuniform transverse magnetic field. If half of the chain is placed in a strong magnetic field, or if the strength of the magnetic field has a large gradient along the chain, heat current is shown to be asymmetric with respect to exchange of the temperatures of the heat baths. Thermal rectification factor can be arbitrarily large for sufficiently small temperature of one of the baths.     

The beneficial influence of ultrasound in the polymerization of epsilon-caprolactam to polyamide-6 (Nylon 6). Part II: additional experiment to understand the "pre-sonication effect"

Ultrasound (US) “pre-sonication effect” is the beneficial effect of US in the hydrolytic polymerization of ε-caprolactam (CL) mixtures with very low water concentrations (about 0.1–1 wt%). It appears after a mild initial treatment of the mixtures with US [17.5–20 kHz, short times (5–15 min), low temperatures (70–110 °C)] followed by heating at 220–260 °C. An explanation is proposed on the basis of the formation in mild conditions (100 °C) of low concentrations of cyclic oligomers never detected in the literature at those conditions. These, under US irradiation, produce linear amino acid oligomers, which are strong activators of polymerization when the mixture of CL and water, after US irradiation, is heated at the suitable polymerization temperature indicated above.     

Thermodynamics of mechanical transduction of surface confined receptor/ligand reactions

Chemomechanics of surface stress is discussed in terms of interfacial thermodynamics. In the first section the paper shows how to quantitatively describe the chemical equilibrium of a receptor/ligand binding reaction confined at a solid-liquid interface and how the overall work of the reaction splits into chemical and surface work, that appears as a surface pressure. In the second section this thermodynamic model is applied to describe the experimental results of microcantilever bending induced by DNA hybridization occurring onto one of its faces.     

The use of cation exchange matrix separation coupled with ICP-MS to directly determine platinum group element (PGE) and other trace element emissions from passenger cars equipped with diesel particulate filters (DPF)

Inductively coupled plasma-mass spectrometry coupled with cation exchange matrix separation has been optimised for the direct determination of platinum group element (PGE) and trace element emissions from a diesel engine car. After matrix separation method detection limits of 1.6 ng g(-1) for Pd, 0.4 ng g(-1) for Rh and 4.3 ng g(-1) for Pt were achieved, the method was validated against the certified reference material BCR 723, urban road dust. The test vehicle was fitted with new and aged catalytic converters with and without diesel particulate filters (DPF). Samples were collected after three consecutive New European Driving Cycle (NEDC) of the particulate and "soluble" phases using a home-made sampler optimised for trace element analysis. Emission factors for the PGEs ranged from 0.021 ng km(-1) for Rh to 70.5 ng km(-1) for Pt; when a DPF was fitted, the emission factors for the PGEs actually used in the catalysts dropped by up to 97% (for Pt). Trace element emission factors were found to drop by a maximum of 92% for Ni to a minimum of 18% for Y when a DPF was fitted; a new DPF was also found to cause a reduction of up to 86% in the emission of particulate matter.     

Evolution of the protein corona of lipid gene vectors as a function of plasma concentration

The concept that the effective unit of interest in the cell-nanomaterial interaction is the particle and its corona of associated proteins is emerging. Here we investigate the compositional evolution of the protein corona of 1,2-dioleoyl-3-trimethylammonium propane (DOTAP) cationic liposomes (CLs) and DOTAP/DNA lipoplexes over a wide range of plasma concentrations (2.5-80%). The composition of the hard corona of lipoplexes is quite stable, but that of CLs does evolve considerably. We show that the protein corona of CLs is made of both low-affinity and competitive-binding proteins whose relative abundance changes with the plasma concentration. This result may have deep biological implications for the application of lipid-based gene vectors both in vitro and in vivo.