Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh–Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram–Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.     

A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

The CeCl3·7H2O-NaI system as promoter in the synthesis of functionalized trisubstituted alkenes via Knoevenagel condensation

The arylidene malonates with two different geminal carboxylate functions, a suitable class of substrates of several synthetic and pharmacological studies, are easily available through Knoevenagel condensation of ethyl tert-butyl malonate and different aromatic aldehydes. The results have increased the potentialities of CeCl₃·7H₂O-NaI system as a type of water-tolerant green Lewis acid promoter for carbon-carbon bond forming procedures.     

Immunological and biochemical evidence that blepharismin is not a prosthetic group

A polyclonal, multispecific antiserum was raised against a whole 3[(3-cholamidopropyl)-dimethylammonio]-1-propanesulfonate-extract of nonirradiated Blepharisma japonicum cells. It was used to reveal the composition of solutions that were hypothesized to contain the photoreceptor of the ciliate. A Bio-Gel A 1.5 m fine column chromatography of the extract allowed recovery of a single elution peak isolated by recording the 580 nm light absorbance. Fused-rocket immunoelectrophoresis of this material revealed a large number of > 300 kDa coeluted proteins. Blepharismin-rich material with a molecular mass of approximately 50 kDa, consisting of at least nine proteins was obtained when the same extract underwent preparative isoelectric focusing before column chromatography separation. Purification of the pigment obtained from light-exposed cells gave blepharismin-rich material with a molecular weight of approximately 200 kDa. Comparison of the materials obtained under the same conditions, either from the dark-kept or light-irradiated cells, by means of pore-gradient electrophoresis confirmed that proteins present in the two preparations were different. It revealed only a very small amount, if any, of proteins in the chromatography fractions with the highest absorbance at 600 nm. Results are discussed on the basis of the hypothesis that a specific blepharismin-binding protein does not exist in the protozoan.