Benzolactams. II. Synthesis of tetrahydrobenz[d]indeno-[1,2-b]azepines and their 12-Oxo derivatives

Aromatic methoxy and/or methylenedioxy substituted 7-methyltetrahydrobenz[d]indeno[1,2-b]-azepines 7 and their 12-oxo derivatives 8 were efficiently synthesized by the general method consisting of two types of intramolecular dehydrative cyclizations, as follows. N-Methyl-N-β-phenethylacetamides 1 were cyanomethylated in the two-step process of chloromethylation and treatment of the resultant benzyl chlorides with sodium cyanide. The condensation of the benzyl cyanides 2 with the appropriate benzaldehydes, followed by reduction of the benzylidene function, gave α,β-diphenylpropionitriles 3 . Successively, hydrolysis to the amino acids 4 and the thermal cyclization converted 3 to the benzylbenzazepinones 5 , which were also prepared by benzylation of the benzazepinones 6 smoothly by heating of 5 with phosphoryl chloride to afford the title azepines 7 . Further, these tetracyclic enamines 7 underwent autoxidation to the corresponding 12-oxo derivatives 8 , on exposure to oxygen in the presence of Triton B.     

A finiteness theorem of harmonic maps from compact lie groups toO HS(H)

In this article we study the behavior of harmonic maps from compact connected Lie groups with bi-invariant metrics into a Hilbert orthogonal group. In particular, we will demonstrate that any such harmonic map always has image contained within someO(n),n<∞. Since homomorphisms are a special subset of the harmonic maps we get as a corollary an extension of the Peter-Weyl theorem, namely, that every representation of a connected compact Lie group is finite dimensional. This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.     

Direct observations of the behavior of single silicon atoms on a metal surface

The behavior of single silicon adatoms on the W {110} plane has been successfully studied for the first time. Single atom diffusion parameters are found to be E_d = 0.70 ± 0.07 eV, and $\text{d}{}_0\text{= 3.08 × 10}{}^{\mathrm{?4}}\text{× 10}{}^{\mathrm{\pm 1.28}}\text{solcm}{}^2\text{s}$. The field desorption behavior of Si atoms is similar to that of metal adatoms. SiSi adatom-adatom interaction shows nonmonotonic distance dependence, but the repulsive region around 3.2 Å is much weaker than those found in metal adatom interactions.     

Synthesis and characterisation of Gd2O3 nanocrystals functionalised by organic acids

Nanocrystals of Gd2O3 have been prepared by various methods, using, e.g., trioctylphosphine oxide (TOPO), diethylene glycol (DEG) or glycine. The crystalline particles were of sizes 5 to 15 nm. Different carboxylic acids, e.g., oleic acid or citric acid, were adsorbed onto the surface of the particles made with DEG. IR measurements show that the molecules coordinate to the Gd2O3 surface via the carboxylate group in a bidentate or bridging manner. The organic-acid/particle complexes were characterised by XRPD, TEM, FTIR, Raman, and XPS.     

Lack of natural weighted estimates for some singular integral operators

We show that the classical Hörmander condition, or analogously the -Hörmander condition, for singular integral operators is not sufficient to derive Coifman's inequality

where , is the Hardy-Littlewood maximal operator, is any weight and is a constant depending upon and the constant of . This estimate is well known to hold when is a Calderón-Zygmund operator.

As a consequence we deduce that the following estimate does not hold:

where and where is an arbitrary weight. However, by a recent result due to A. Lerner, this inequality is satisfied whenever is a Calderón-Zygmund operator.

One of the main ingredients of the proof is a very general extrapolation theorem for weights.

     

A New Partition Identity Coming from Complex Dynamics

We present a new identity involving compositions (i.e., ordered partitions of natural numbers). The formula has its origin in complex dynamical systems and appears when counting, in the polynomial family periodic critical orbits with equivalent itineraries. We give two different proofs of the identity; one following the original approach in dynamics and another with purely combinatorial methods. Received October 1, 2004     

The time dependent susceptibility of spin glasses

A relation is found between the time-dependent susceptibility of the Edwards-Anderson spin glass model and the spin self-correlation. The relation is explicitly proved to hold for Monte Carlo simulations of the model. The susceptibility peaks found in Monte Carlo calculations are discussed.     

Tetrapyrrole singlet excited state quenching by carotenoids in an artificial photosynthetic antenna

Two artificial photosynthetic antenna models consisting of a Si phthalocyanine (Pc) bearing two axially attached carotenoid moieties having either 9 or 10 conjugated double bonds are used to illustrate some of the function of carotenoids in photosynthetic membranes. Both models studied in toluene, methyltetrahydrofuran, and benzonitrile exhibited charge separated states of the type C*+-Pc*- confirming that the quenching of the Pc S1 state is due to photoinduced electron transfer. In hexane, the Pc S1 state of the 10 double bond carotenoid-Pc model was slightly quenched but the C*+-Pc*- transient was not spectroscopically detected. A semiclassical analysis of the data in hexane at temperatures ranging from 180 to 320 K was used to demonstrate that photoinduced electron transfer could occur. The model bearing the 10 double bond carotenoids exhibits biexponential fluorescence decay in toluene and in hexane, which is interpreted in terms of an equilibrium mixture of two isomers comprising s-cis and s-trans conformers of the carotenoid. The shorter fluorescence lifetime is associated with an s-cis carotenoid conformer where the close approach between the donor and acceptor moieties provides through-space electronic coupling in addition to the through-bond component.     

Phase Transition in Ferromagnetic Ising Models with Non-uniform External Magnetic Fields

In this article we study the phase transition phenomenon for the Ising model under the action of a non-uniform external magnetic field. We show that the Ising model on the hypercubic lattice with a summable magnetic field has a first-order phase transition and, for any positive (resp. negative) and bounded magnetic field, the model does not present the phase transition phenomenon whenever lim?inf?h _i >0, where \(\mathbf{h}=(h_{i})_{i\in \mathbb{Z}^{d}}\) is the external magnetic field.     

Effective radiating area and beam non-uniformity ratio of ultrasound transducers at 5 MHz, according to IEC 61689:2007

This paper discloses results of measuring the effective radiating area (A_ER) and the beam non-uniformity ratio (R_BN) for US transducers at 5.0 MHz. Measurements were carried out at Laboratory of Ultrasound of the Brazilian National Institute of Metrology, Standardization, and Industrial Quality. As reliability proof of system’s adequacy, uncertainties were assessed. The calculation protocol was developed based on standard IEC 61689:2007. Type A uncertainty was estimated after four repetitions of the full procedure for the determination of A_ER and R_BN, and Type B uncertainty was estimated from the mathematical model for both calculations, obtained from IEC 61689:2007 and the guide to the expression of uncertainty in measurement. The procedure presented herein represents the state of the art regarding metrology for testing therapeutic ultrasound devices, and its application results in fundamental aspects to support their evaluation regarding quality assurance, for instance, for a certification process due safety and performance.