Subshifts with slow complexity and simple groups with the Liouville property

We study random walk on topological full groups of subshifts, and show the existence of infinite, finitely generated, simple groups with the Liouville property. Results by Matui and Juschenko-Monod have shown that the derived subgroups of topological full groups of minimal subshifts provide the first examples of finitely generated, simple amenable groups. We show that if the (not necessarily minimal) subshift has a complexity function that grows slowly enough (e.g. linearly), then every symmetric and finitely supported probability measure on the topological full group has trivial Poisson–Furstenberg boundary. We also get explicit upper bounds for the growth of Følner sets.     

The Mass Shell in the Semi-Relativistic Pauli–Fierz Model

We consider the semi-relativistic Pauli–Fierz model for a single free electron interacting with the quantized radiation field. Employing a variant of Pizzo’s iterative analytic perturbation theory we construct a sequence of ground state eigenprojections of infra-red cutoff, dressing transformed fiber Hamiltonians and prove its convergence, as the cutoff goes to zero. Its limit is the ground state eigenprojection of a certain renormalized fiber Hamiltonian. The ground state energy is an exactly twofold degenerate eigenvalue of the renormalized Hamiltonian, while it is not an eigenvalue of the original fiber Hamiltonian unless the total momentum is zero. These results hold true, for total momenta inside a ball about zero of arbitrary radius ${\mathfrak{p} > 0}$ , provided that the coupling constant is sufficiently small depending on ${\mathfrak{p}}$ and the ultra-violet cutoff. Along the way we prove twice continuous differentiability and strict convexity of the ground state energy as a function of the total momentum inside that ball.     

On the role of reachability and observability in NMR experimentation

It is shown that the system theoretic concepts of reachability and observability are relevant to the analysis of NMR experiments. Moreover, the sets of reachable states are examined and Lie theoretic criteria are given for the reachability of the system. The question is investigated how the set of reachable states depends on the class of input functions that are allowed. Both one‐dimensional and multi‐dimensional NMR experiments are considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

BF3·Et2O and trifluoroacetic acid/triethyl amine-mediated synthesis of functionalized piperidines

A two-step short and efficient strategy for the synthesis of substituted piperidones and piperidines in high diastereoselectivity (only trans-configuration), by employing cascade type reaction using BF₃·Et₂O or by carrying out one pot deprotection of ^tBoc group followed by intramolecular aza-Michael addition of α,β-unsaturated beta keto esters has been developed. Using a similar strategy a short access to hydroxy pipecolic acid is also described. Very simple and rapid experimental procedures involving mild conditions and only one or two chromatographic purifications are the main features of the process.     

Kinetics of dissociation of tris-2,2′-bipyridyl-iron(II) cation in aqueous acetic acid solutions

The kinetics of dissociation of tris-2,2′-bipyridyl-iron(II) complex ion have been examined in aqueous acetic acid solutions. The reaction is first order in the complex ion; the dependence of rate on H⁺ is somewhat like that observed in aqueous solutions approaching a limiting value at higher H⁺ concentrations. The influence of solvent composition on the reaction rate under acid-dependent and acid-independent conditions shows an initial retardation by acetic acid. The argument of ion-pair formation based on decrease of dielectric constant proposed to explain the kinetics in other aqueous solvent media was found useless to explain the behavior in acetic acid solutions. Other solvent parameters also did not provide satisfactory correlation with the kinetic results, thus, indicating the operation of more complex microscopic solute-solvent and solvent-solvent interactions. While solvent effects play some part in the rate process, the rate of reaction would tend to zero in the absence of H₂O and H⁺. This interesting observation proved useful in proposing a reaction mechanism that is consistent with the rate behavior over the entire range of solvent composition. The activity of water in the reaction medium is controlled by the content of acetic acid which can effect the structure of water through operation of hydrophobic forces and formation of hydrates. While acetic acid cannot possibly fulfill the role of water in occupying the vacated coordination position, the anomalous rise in rate even under some water deficient conditions seems to be related to the coordinating ability of HSO₄^? derived from H₂SO₄ present in the solution.     

Dynamical signatures of ‘phase transitions’: Chaos in finite clusters

Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition, surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state. The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These and related applications are reviewed in the present article.     

Transfer functions of US transducers for harmonic imaging and bubble responses

Current medical diagnostic echo systems are mostly using harmonic imaging. This means that a fundamental frequency (e.g., 2 MHz) is transmitted and the reflected and scattered higher harmonics (e.g., 4 and 6 MHz), produced by nonlinear propagation, are recorded. The signal level of these harmonics is usually low and a well-defined transfer function of the receiving transducer is required. Studying the acoustic response of a single contrast bubble, which has an amplitude in the order of a few Pascal, is another area where an optimal receive transfer function is important.

We have developed three methods to determine the absolute transfer function of a transducer. The first is based on a well-defined wave generated by a calibrated source in the far field. The receiving transducer receives the calibrated wave and from this the transfer functions can be calculated. The second and third methods are based on the reciprocity of the transducer. The second utilizes a calibrated hydrophone to measure the transmitted field. In the third method, a pulse is transmitted by the transducer, which impinges on a reflector and is received again by the same transducer. In both methods, the response combined with the transducer impedance and beam profiles enables the calculation of the transfer function.

The proposed methods are useful to select the optimal piezoelectric material (PZT, single crystal) for transducers used in reception only, such as in certain 3D scanning designs and superharmonic imaging, and for selected experiments like single bubble behavior.

We tested and compared these methods on two unfocused single element transducers, one commercially available (radius 6.35 mm, centre frequency 2.25 MHz) the other custom built (radius 0.75 mm, centre frequency 4.3 MHz). The methods were accurate to within 15%.     

Catalytic Reduction of p‐Nitrophenol and Hexacyanoferrate (III) by Borohydride Using Green Synthesized Gold Nanoparticles

A simple and green approach for the synthesis of well‐stabilized gold nanoparticles (AuNPs) using gum Acacia (GA) is presented here. The gum acacia acts as the reductant and stabilizer. The synthesized gold nanoparticles were characterized by using ultraviolet visible (UV‐Vis), fourier transform infrared spectroscopy (FTIR), x‐ray diffraction (XRD), dynamic light scattering (DLS) and transmission electron microscopy (TEM) techniques. The UV‐Vis study revealed a distinct surface plasmon resonance at 520 – 550 nm, due to the formation of AuNPs. FTIR analysis showed the evidence that –OH groups present in the gum matrix were responsible in reducing the tetra chloroauric acid into AuNPs. XRD studies confirmed the formation of well crystalline nanoparticles with fcc structure and the particle size ranges from 4 – 29 nm, as indicated by TEM analysis. The synthesized gold nanoparticles exhibited homogeneous catalytic activity. The two model reactions studied were the reduction of p‐nitro phenol and the reduction of hexacyanoferrate (III) by borohydride ions. Both the reactions were monitored by UV‐Vis spectroscopy. The kinetic investigations were carried out for the AuNPs‐catalyzed reactions at different temperatures and different amount of catalyst.     

A facile and convenient synthesis of novel imidazo[1,2-b] isoxazoles and their Mannich bases as potential biodynamic agents

A series of novel imidazo[1,2-b]isoxazoles 3 and their Mannich bases 4–6 were synthesized via convenient reactions. The reaction of 3-aminoisoxazole 1 with substituted phenacyl bromides 2 in dry ethanol afforded the corresponding 6-methyl-3-aryl imidazo[1,2-b]isoxazoles 3 in good yields.Compounds 3 on treatment with 37% formaline and secondary amines furnished the corresponding novel Mannich bases viz., 6-methyl-3-aryl-2-(morpholine/pyrrolidin-1-yl/piperidin-1-yl)-methyl-imidazo[1,2-b]isoxazoles 4–6.     

The Latin-American network of human genetics

The Latin-American Network of Human Genetics (RELAGH) is an internet-based federation of human and medical genetic societies of Latin America constituted in 2001. Member societies include the Mexican Association of Human Genetics, the Brazilian Society of Clinical Genetics, the Human Genetics Section of the Argentinean Society of Genetics, the Colombian Society of Human Genetics and the Panamanian Human Genetics Society. RELAGH is a full member of the steering committee of the International Federation of Human Genetics Societies. A core activity of RELAGH is to become a platform for the integration and collaboration of human geneticists across Latin America regarding training, services and research in medical genetics in the region.