HAC estimation and strong linearity testing in weak ARMA models

In the framework of ARMA models, we consider testing the reliability of the standard asymptotic covariance matrix (ACM) of the least-squares estimator. The standard formula for this ACM is derived under the assumption that the errors are independent and identically distributed, and is in general invalid when the errors are only uncorrelated. The test statistic is based on the difference between a conventional estimator of the ACM of the least-squares estimator of the ARMA coefficients and its robust HAC-type version. The asymptotic distribution of the HAC estimator is established under the null hypothesis of independence, and under a large class of alternatives. The asymptotic distribution of the proposed statistic is shown to be a standard χ² under the null, and a noncentral χ² under the alternatives. The choice of the HAC estimator is discussed through asymptotic power comparisons. The finite sample properties of the test are analyzed via Monte Carlo simulation.     

Towards the synthesis of MAX-phase functional coatings by pulsed laser deposition

Pulsed laser deposition with a Nd:YAG laser was used to grow thin films from a pre-synthesized Ti₃SiC₂ MAX-phase formulated ablation target on oxidized Si(1 0 0) and MgO(1 0 0) substrates. The depositions were carried out in a substrate temperature range from 300 to 900 K, and the pressure in the deposition chamber ranged from vacuum (10⁻⁵ Pa) to 0.05 Pa Argon background pressure. The properties of the films have been investigated by Rutherford backscattering spectrometry for film thickness and stoichiometric composition and X-ray diffraction for the crystallinity of the films. The silicon content of the films varied with the energy density of the laser beam. To suppress especially the silicon re-sputtering from the substrate, the energy of the incoming particles must be below a threshold of 20 eV. Therefore, the energy density of the laser beam must not be too high. At constant deposition energy density the film thickness depends strongly on the background pressure. The X-ray diffraction measurements show patterns that are typical of amorphous films, i.e. no Ti₃SiC₂ related reflections were found. Only a very weak TiC(2 0 0) reflection was seen, indicating the presence of a small amount of crystalline TiC.     

Partitioning Balls into Topologically Equivalent Pieces

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Partitioning Balls into Topologically Equivalent Pieces

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U(2, 2) Symmetry as a Common Basis for Quantum Theory and Geometrodynamics

We formulated some criticisms of the Diracequation and its Clifford-algebraic philosophy; inparticular, we show that, within a general-relativisticcontext, they seem to contain hidden action-at-distance concepts. We suggest a new model based on thefour-component Klein-Gordon equation locally invariantunder the U(2,2) gauge group. The usual Dirac equationis then obtained as a certain approximation. The geometrodynamical sector shows reasonablecorrespondence with general relativity.     

Relevance of Reflection in Static and Dynamic Light Scattering Experiments

Using a monodisperse PMMA dispersion, it was shown that light reflection at the sample cuvette walls may greatly influence the results of both static (SLS) and dynamic (DLS) light scattering experiments. Considering SLS, this reflection phenomenon mostly causes an overestimation of the scattered intensity at high scattering angles, which may give rise to the emergence of an additional, artificial peak in the lower region of the particle size distribution. On the other hand, the influcence of reflection on DLS measurements was shown to be particularly important in the upper region of the particle size distribution. The experimentally observed phenomena were explained from the basic principles of both particle sizing methods. Finally, it was shown that the disturbing effect of reflection could be avoided by modifying either the hardware or the software of the static and dynamic light scattering technique.     

Invariants of Conformai and Projective Structures

While in Euclidean, equiaffine or centroaffine differential geometry there exists a unique, distinguished normalization of a regular hypersurface immersion x: M ⁿ → Aⁿ⁺¹, in the geometry of the general affine transformation group, there only exists a distinguished class of such normalizations, the class of relative normalizations. Thus, the appropriate invariants for speaking about affine hypersurfaces are invariants of the induced classes, e.g. the conformai class of induced metrics and the projective class of induced conormal connections. The aim of this paper is to study such invariants. As an application, we reformulate the fundamental theorem of affine differential geometry.     

Zeeman transitions in deuterium atoms induced by ultra-relativistic electrons

We present data showing hyperfine transitions in an atomic deuterium beam induced by the (476 MHz) radio-frequency field of a 704 MeV electron beam in a storage ring. A polarized deuterium beam, produced in an atomic beam source, was crossed with a stored electron beam and analyzed with a Breit--Rabi polarimeter. Electron-beam induced transitions were singled out by injecting different combinations of hyperfine states. Transition probabilities as high as 70% were measured at large currents (~ 100 mA). All possible deuterium transitions for a radio-frequency of 476 MHz were observed. In addition, a 1--6 transition resulting from the first harmonic (952 MHz) was observed. The effects of these transitions are of general importance for the polarized internal target technique applied in nuclear and particle physics experiments. The data are reasonably described by numerical estimates. The observed mechanism can be exploited to create nuclear polarized atoms when injecting electron polarized atoms with no net nuclear polarization into a storage cell. However, when nuclear polarized atoms are injected, care should be taken to avoid this mechanism, since it would result in depolarization of the atoms. The studies enabled us to choose the magnetic guide field during our spin-dependent electron--deuteron scattering experiments, such that electron-beam induced depolarizing effects were avoided. This revised version was published online in July 2006 with corrections to the Cover Date.