On the stability of liquid droplets with line tension

Prompted by recent works on line tension effects upon the stability of liquid droplets laid on a rigid substrate, we prove existence and stability of equilibrium configurations when the substrate is either planar or spherical. For positive line tension our argument involves only set symmetrization, while for negative line tension a stability criterion is proposed which makes variational problems well-posed in the framework of sets with finite perimeter. Several applications illustrate the role of the criterion in providing a natural cutoff length that selects destabilizing modes. The work of M. Negri has been partially supported by INdAM through the grant “Mathematical challenges in nanomechanics at the interface between atomistic and continuum models”.     

Study of the reactivity of α‐acylenaminoketones. Synthesis of pyrazoles

The reactions of 4‐(methylamino)‐3‐penten‐2‐one with diazoketones yielded the α‐acylenaminoketones 1–3 in good yields. Preparation of the α‐acylenaminoketone 4 was carried out by treatment of 4‐(t‐butyl‐amino)‐3‐penten‐2‐one with benzoyl chloride being followed by reaction of transamination with methyl‐amine. The reactions were carried out in five different solvents and were submitted to gas chromatogra‐phy/mass spectrometry analysis, with the goal of obtaining substituted pyrazoles and determining which of the carbonyls would preferentially be attacked by the nucleophile. The reactions of compounds 1–4 with hydrazine reagents led to the formation of the pyrazoles 5–7a‐q . Small amounts of 4‐methylamino‐2‐pentenones 10a‐q , amides 11a‐q and pyrazoles 12a‐q were also obtained in these reactions. The unexpected formation of pyrazoles 15d,h,q was detected when methanol and N,N‐dimethylformamide were used as solvents in the reactions of α‐acylenaminoketone 4 with hydrazine reagents.     

Optimal rigid inclusion shapes in elastic bodies with cracks

The paper concerns the control of rigid inclusion shapes in elastic bodies with cracks. Cracks are located on the boundary of rigid inclusions and in the bulk. Inequality type boundary conditions are imposed at the crack faces to guarantee mutual non-penetration. Inclusion shapes are considered as control functions. First we provide the problem formulation and analyze the shape sensitivity with respect to geometrical perturbations of the inclusion. Then, based on Griffith criterion, we introduce the cost functional, which measures the shape sensitivity of the problem with respect to the geometry of the inclusion, provided by the energy release rate. We prove existence of optimal shapes for the problem considered.     

High energy resolution Auger spectroscopy on a CMA instrument

An experimental method that increases the analyzer resolution of cylindrical mirror analyzer CMA‐based Auger spectrometers is described. By means of electrically biasing the sample, the effective energy resolution obtainable from the CMA instrument is improved from the native 0.5 to 0.1% or even better for higher kinetic energy Auger transitions. In addition, the maximum kinetic energy Auger transition observable by the CMA Auger instrument is increased from 3200 to 5700 eV, in the current realization. It is also shown that the sensitivity of the energy scale calibration to sample working distance with respect to the analyzer is simultaneously reduced, making the method suitable for chemical surface analysis. The biasing is accomplished using a special sample holder with electronics and software that can be added to an existing instrument. The overall capability of the Auger instrument for chemical analysis is, therefore, increased, while preserving all the analytical functionality and features of the CMA. Copyright © 2011 John Wiley & Sons, Ltd.     

Siderophore-Mediated Iron Uptake Promotes Yeast–Bacterial Symbiosis

In the present study, siderophore produced by the marine yeast Aureobasidium pullulans was characterized as hydroxamate by chemical and bioassays. The hydroxamate assignment was supported by the appearance of peaks at 1,647.21?C1,625.99?cm^?1 and at 1,435.04?cm^?1 in the infrared spectrum. The purified siderophore exhibited specific growth-promoting activity under iron-limited conditions for siderophore auxotrophic probiotic bacteria. Cross-utilization of siderophore indicates a symbiotic relationship between the yeast A. pullulans and the selected probiotic bacterial strains. Statistical optimization of medium components for improved siderophore production in A. pullulans was depicted by response surface methodology. The shift in UV?CVis spectroscopy indicates the photoreactive property and subsequent oxidative cleavage of purified siderophore on exposure to sunlight.     

Lower ligand denticity leading to improved thermodynamic and kinetic stability of the Gd3+ complex: the strange case of OBETA

OBETA, OBETA, you bet: Thermodynamic and kinetic measurements show an apparent paradox. The stability of complexes of lanthanide trivalent ions is higher with the heptadentate ligand OBETA (ethylene glycol-bis(2-aminoethyl ether)-N,N,N',N'-tetraacetic acid) than with its octadentate homologue EGTA (2,2'-oxybis(ethylamine)-N,N,N',N'-tetraacetic acid). The unusual properties of Gd(OBETA)(-) (see structure), combined with the presence of two fast exchanging coordinated water molecules, candidates this complex as an MRI contrast agent.     

The effect of titanium dioxide exposure on the thermal properties of Zebrafish (<Emphasis Type="Italic">Danio rerio</Emphasis>) bones

This article presents the changes in the thermal properties of the control and titanium dioxide (TiO₂), both nano and bulk exposed Zebrafish bones by using thermo analytical techniques. The result shows that the mass loss due to the thermal decomposition occurs in three distinct steps due to loss of water, organic and inorganic materials. The titanium dioxide exposed bones present a different thermal behaviour compared to the control bones. The residue masses are found to be increased due to titanium dioxide exposure. In particular, nano titanium dioxide exposure increases the residue mass level significantly (three fold) when compared to titanium dioxide bulk exposure. These thermal characteristics can be used as a qualitative method to check the metal oxide intoxication in biological samples.     

On compound Poisson processes arising in change-point type statistical models as limiting likelihood ratios

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these likelihood ratios, which is an exponential functional of a two-sided Poisson process driven by some parameter, can be approximated (for sufficiently small values of the parameter) by another one, which is an exponential functional of a two-sided Brownian motion. In this paper we consider yet another likelihood ratio, which is the exponent of a two-sided compound Poisson process driven by some parameter. We establish, that similarly to the Poisson type one, the compound Poisson type likelihood ratio can be approximated by the Brownian type one for sufficiently small values of the parameter. We equally discuss the asymptotics for large values of the parameter and illustrate the results by numerical simulations.     

Target Visualization by MRI Using the Avidin/Biotin Amplification Route: Synthesis and Testing of a Biotin–Gd‐DOTA Monoamide Trimer

To design efficient targeting strategies in magnetic resonance (MR) molecular imaging applications, the formation of supramolecular adducts between (strept)avidin ((S)Av) and tribiotinylated Gd‐DOTA‐monoamide complexes (DOTA=1,4,7,10‐tetraazacyclododecane‐N,N′,N′′,N′′′‐tetraacetic acid) was explored. Two compounds based on the trivalent core of tris(2‐aminoethyl)amine each containing three biotin molecules and one ( L1 ) or three ( L2 ) DOTA‐monoamide (DOTAMA) ligands were synthesized. In these tribiotinylated derivatives the biotins are spaced far enough apart to allow the formation of the supramolecular adduct with the protein and to host the chelating units in between the (S)Av layers. Size exclusion HPLC analyses indicated complete formation of very high molecular weight polymers (>2 MDa) with (S)Av in solution. A ¹H NMR spectroscopy relaxometric study on the obtained polymeric adducts showed a marked increase of the relaxivity at 35–40 MHz as a consequence of the lengthening of the tumbling time due to the formation of Gd‐chelates/(S)Av polymers. The most efficient Gd₃ L2 /(S)Av polymeric system was used for a test in cell cultures. The target is represented by a neural cell adhesion molecule (NCAM), which is overexpressed in Kaposi’s sarcoma cells and tumor endothelial cells (TEC) and that is efficiently recognized by a biotinylated tetrameric peptide (C3d‐Bio). In vitro experiments showed that only cells incubated with both C3d‐Bio and Gd₃ L2 /SAv polymer were hyperintense with respect to the control. Relaxation rates of cell pellets incubated with Gd₃ L2 /SAv alone were not significantly different from the untreated cells demonstrating the absence of a specific binding.     

The anisotropy introduced by the mesh in the finite element approximation of the mumford-shah functional

We compute explicitly the anisotropy effect in the H ¹ term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations.