Free Groups from Fields

In the nineteenth century, field theory brilliantly resolveda number of questions that had taxed mathematicians for centuries;for example, ‘The circle cannot be squared’ by straightedge and compass, and solving polynomial equations by radicalsis not always possible. These successes have continued to beheld up as superb examples of the power of mathematical thought,and are demonstrated at an undergraduate level. The purposeof this article is to provide another such natural example whichleads to a concrete realisation of the free group on 2 generators.     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

Über die Magnetischen Eigenschaften der Cobaltate Na6CoS4, Na6CoSe4 und K6CoS4

Magnetic Properties of the Cobaltates Na₆CoS₄, Na₆CoSe₄, and K₆CoS₄ The alkali metal cobalt chalcogenides Na₆CoS₄, Na₆CoSe₄, and K₆CoS₄ crystallize in the space group P6₃mc with Z = 4. The structure is characterized by isolated [CoX₄]-tetrahedra. The magnetic susceptibilities show Curie-Weiss behaviour. The deviations at low temperatures are caused by antiferromagnetic interactions. The magnetic moments are discussed with regard to ligand-field parameters.     

Monte Carlo determinations of the beta dose rate to tooth enamel

The results of Monte Carlo simulations of the beta dose rate to enamel are presented. The dose rates are the most comprehensive to date, incorporating the beta spectrum from 21 different radionuclides, all internal conversion and Auger electrons, the majority of the bremsstrahlung radiation, effects due to radon loss in the uranium series, and variations in the moisture content of the sediment. Applications to a new dating technique in archaeology using electron spin resonance and beta-gradient isochrons are discussed.     

Aspects of alpha-particle scattering and structure of the nuclear surface

The interaction of α particles above 5 MeV with a 2s-1d target is dominated by resonances. It cannot be described only in terms of a mean-field one-body potential. An analysis of the elastic α-particle scattering by ²⁸Si encourages the comprehension of the resonance states to be mainly fragments of a mixed-parity band. In the present article, the angular distributions of particles scattered by ³²S are analyzed in terms of such bands. The analysis of new data from an experiment made at Florida State University reveals the existence of states that do not belong to the above bands. This follows from a coupled-channel analysis of the elastic and inelastic (2⁺) cross sections. An α-particle structure at the nuclear surface is suggested.     

Dirac-Hestenes spinor fields on Riemann-Cartan manifolds

In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named the spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to Geroch's theorem concerning the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle, CB) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.     

Directed metalation/ligand coupling approach to the enantioselective synthesis of 1,1′-binaphthyls

Introduction of a 2-isopropoxycarbonyl or 2-NN-dimethylcarbamoyl group into homochiral 1-p-tolyl- or 1-t-butyl-sulfinylnaphthalenes, via directed metalation reaction, followed by ligand coupling reaction with 1-naphthylmagnesium bromide, furnished atropisomeric 1,1′-binaphthyls in 82–95% enantiomeric excess (e.e.).     

Topological Simplicity of a Certain LF-Algebra

We show that the LF-algebra considered by Akkar and Nacir in [1] is topologically simple.     

Maximum-entropy data analysis

The reconstruction of physical quantities from (computer-) experimental data is very often hampered by the presence of noise, insufficient information and above all by the ill-posed nature of the underlying inversion problem. It will be demonstrated that the maximum entropy concepts is particularly suited for this type of data-analysis problems. It is based on Bayesian statistics and provides a consistent probabilistic theory to obtain unbiased results, independent of any model assumptions. This is particularly desirable if there is no additional information to justify these hypotheses. If, on the other hand, additional prior knowledge is available, it can be effectively incorporated into the computation, leading to more stringent confidence intervals.