On the curvature of free boundaries with a Bernoulli-type condition

In this paper we study the classical external Bernoulli problem set in an annular domain Ω$\Omega$ of the plane.     

Electrochemical properties of monolayer-protected Au and Pd nanoparticles extracted from within dendrimer templates

The electrochemical properties of Au and Pd monolayer-protected clusters (MPCs), prepared by dendrimer-templating and subsequent extraction, are described. Differential pulse voltammetry was used to estimate the size of the MPCs, and the results were compared to microscopic data and calculated values. Purification of the extracted Au and Pd nanoparticles was not required to obtain well-defined differential pulse voltammetry peaks arising from quantized double-layer charging. The calculated sizes of the nanoparticles were essentially identical to those determined from the electrochemical data. The capacitance of the particles was independent of the composition of core metal. Transmission electron microscopy data overestimated the size of the smallest Pd nanoparticles because of inadequate point-to-point resolution.     

Electrostatic effect of specifically adsorbed electroinactive ions upon electrode processes: Part IV. Carbon Tetrachloride electroreduction in the presence of Cl−, Br−, SCN−, and N3−

The rate constant for CCl₄ electroreduction on mercury, once corrected for diffuselayer effects according to Frumkin, still depends on the charge density q_i due to specifically abdsorbed supporting ions. Thus, in the presence of the adsorbed anions Cl^?, Br^?, SCN^? and N₃^?, the logarithm Φ of the rate constant corrected for diffuse-layer effects decreases linearly with |q_i|. The slopes of the various Φ vs. q_i plots are in fairly good agreement with the theoretical treatment of ref. 9, which accounts for the electrostatic interactions between the activated complex for the electrode reaction and the neighbouring adsorbed electroinactive ions within the compact layer. An analogous behaviour is observed in the reduction of CBr₄.     

In situ analysis and imaging of aromatic amidine at varying ligand densities in solid phase

We report the development of a fast and accurate fluorescence-based assay for amidine linked to cellulose membranes and Sepharose gel. The assay is founded on the glyoxal reaction, which involves reaction of an amidine group with glyoxal and an aromatic aldehyde, leading to the formation of a fluorophore that can be analyzed and quantified by fluorescence spectroscopy and imaging. While the assay has been reported previously for aromatic amidine estimation in solution phase, here we describe its adaptation and application to amidine linked to diverse forms of solid matrices, particularly benzamidine Sepharose and benzamidine-linked cellulose membranes. These functionalized porous matrices find important application in purification of serine proteases. The efficacy of a protein separation device is determined by, among other factors, the ligand (amidine) density. Hence, a sensitive and reproducible method for amidine quantitation in solid phase is needed. The glyoxal reaction was carried out on microbead-sized Sepharose gel and cellulose membranes. Calibration curves were developed for each phase, which established linearity in the range of 0–0.45 μmol per mL amidine for free amidine in solution, 0–0.45 μmol amidine per mL Sepharose gel, and 0–0.48 μmol per mL cellulose membrane. The assay showed high accuracy (~ 3.4% error), precision (RSD < 2%), and reproducibility. Finally, we show how this fluorescent labeling (glyoxal) method can provide a tool for imaging membranes and ligand distribution through confocal laser scanning microscopy.

Graphical abstract

     

Kinetic Modeling of Non-Linear Polymerization

Recent developments of a method based upon population balances of generating functions of polymer chain length distributions (CLD) are presented. The calculation of the CLD and how to take into account chain length dependent reactivity are discussed. Prediction of polymer properties is also possible but only easily done for the average molecular radius of gyration; some results are presented for a radical polymerization including transfer to polymer and propagation with terminal double bonds.     

Tumour-host dynamics under radiotherapy

Tumour-host interaction is modelled by the Lotka-Volterra equations. Qualitative analysis and simulations show that this model reproduces all known states of development for tumours. Radiotherapy effect is introduced into the model by means of the linear-quadratic model and the periodic Dirac delta function. The evolution of the system under the action of radiotherapy is simulated and parameter space is obtained, from which certain threshold of effectiveness values for the frequency and applied doses are derived. A two-dimensional logistic map is derived from the modified Lotka-Volterra model and used to simulate the effectiveness of radiotherapy in different regimens of tumour development. The results show the possibility of achieving a successful treatment in each individual case by employing the correct therapeutic strategy.     

Regioselective Synthesis of the Spiro-benzofuran Unit,Present in Several Natral Products,by an Intramolecular Michael Cyclization

The regioselective construction of a spirocycle unit, common to several biologically active natural products, through an intramolecular Michael cyclization is described.