Three-dimensional vibration analysis of a torus with circular cross section

The free vibration characteristics of a torus with a circular cross section are studied by using the three-dimensional, small-strain, elasticity theory. A set of three-dimensional orthogonal coordinates system, comprising the polar coordinate (r, theta) at each circular cross section and the circumferential coordinate phi around the ring, is developed. Each of the displacement components u(r), v(theta), and w(phi) in the r, theta, and phi directions, respectively, is taken as a product of the Chebyshev polynomials in the r direction and the trigonometric functions in the theta and phi directions. Eigenfrequencies and vibration mode shapes have been obtained via a three-dimensional displacement-based extremum energy principle. Upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions. The eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross-sectional radius are investigated in detail. Very accurate eigenfrequencies and deformed mode shapes of the three-dimensional vibration are presented. All major modes such as flexural thickness-shear modes, in-plane stretching modes, and torsional modes are included in the analysis. The results may serve as a benchmark reference for validating other computational techniques for the problem.     

Trimethoxysilylpolymethacrylate as new material for stone conservation. Porosimetric and colorimetric investigations

Aimed to obtain new materials for the conservation of stone substrates, we report here on the synthesis of a polymer which has been obtained by inducing polymerization on a methacrylate monomer functionalized by alchoxysilane groups. Two lithotypes, the Comiso calcarenite and Mistretta quartzite, stones largely used in artworks of north-eastern Sicily, were treated with the above polymer and its conserving efficacy evaluated in terms of porosimetric features, hydric properties and appearance. The collected data were compared to those provided, under the same experimental conditions, by an ethylmethacrylate/methylmethacrylate copolymer and an alkylalchoxysilane, products widely employed in the protection of stones. Experiments aimed to test the durability of the above polymer against UV artificial ageing are also reported.     

Tracer studies on f-actin fluctuations

We present a study on the fluctuations of semiflexible actin filaments using fluorescence videomicroscopy, focusing on the end-to-end fluctuations of single filaments. In order to specifically measure the position of the polymer's ends, we developed a novel noninvasive method that consists of annealing short end tags to the filaments. This allows us to probe polymer fluctuations to a very high accuracy. We compared the distribution of the end-to-end distance with recent theoretical results, and found excellent agreement. We also studied the dynamics of the mean-square end-to-end distance deltaR2(t) and orientation of the ends, deltaTheta(2)(t), finding power laws t(3/4) and t(1/4), respectively. Scaling behavior for deltaR2(t) is observed over several decades in relaxation time in agreement with theoretical results.     

Quasi-solitonic behavior of self-written waveguides created by photopolymerization

We investigated the condition of unique self-written channel and multichannel propagation inside bulk photopolymerizable materials. Light was introduced in the medium by a single-mode optical fiber. At a very low beam power of 5 muW , a unique uniform-channel waveguide without any broadening was obtained by polymerization. When the input power is increased to 100 muW , the guide becomes chaotic and multichannel. We connected two fibers separated by a 1-cm distance. The results open the door to studies of the optical and electro-optical properties of photopolymerized guides doped by nonlinear optical chromophores and to possible applications in integrated optical devices.     

Synthesis and application of planar-chiral phosphaferrocene-oxazolines, a new class of P,N-ligands

The synthesis of several phosphaferrocene-oxazolines, members of a new family of planar-chiral ligands, is described. These bidentate P, N-ligands are applied to enantioselective palladium-catalyzed allylic alkylations, for which it is shown that the planar-chirality of the phosphaferrocene, not the chirality of the oxazoline, determines the stereochemical outcome of the reaction.     

Correspondence between generalized binomial field states and coherent atomic states

We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.     

On list primitive recursion and the complexity of computinginf

We present a primitive recursive programinf_with_lists computing the minimum of two natural numbersn andp (written in unary notation) and using primitive recursion on lists. This program has at first sight the required property of visiting simultaneously its inputs, so it is a counterexample to a theorem showing that such a program cannot be written in the language of primitive recursion on natural numbers, in the more general framework of primitive recursion on term algebras. However, its complexity is at leastinf(n,p)² so it does not implement the algorithm we have in mind to computeinf(n,p).     

119Sn mössbauer,IR, 1H NMR spectroscopic and thermal decomposition studies on organotin(IV) adducts with glycylglycine

The complexes R₂SnCl₂·(H₂glygly), (H₂glygly = glycylglycine) (R = Me, Buⁿ, Octⁿ, Ph) and RSnCl₃·(H₂glygly)