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.     

Hochschild cohomology and “smoothness” in monoidal categories

We introduce and investigate the properties of Hochschild cohomology of algebras in an abelian monoidal category M. We show that the second Hochschild cohomology group of an algebra in M classifies extensions of A up to an equivalence. We characterize algebras of Hochschild dimension 0 (separable algebras), and of Hochschild dimension ≤1 (formally smooth algebras). Several particular cases and applications are included in the last section of the paper.     

Partitioning Balls into Topologically Equivalent Pieces

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Partitioning Balls into Topologically Equivalent Pieces

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Simulated cosmic strings in a “big bang” in superfluid3He at 100 μK

During studies of the impact of single neutrons on superfluid³He at around 100μK we have measured the thermal energy released in the superfluid following the nuclear reaction, n+³He→p+³H+764keV. However, we find that the measured energy deposited in the quasiparticle system shortly after this reaction is substantially less than what we expect. We believe that this energy deficit represents that energy which has gone into the creation of vortices, in analogy to the creation of cosmic strings in the early universe via the Kibble mechanism. Furthermore, from the magnitude of the deficit, we can infer the vortex density which compares favorably with that predicted in Zurek’s scenairo.     

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.     

Intramolecular hemiacetals. The acid-base-catalyzed ring-chain interconversion of 2-substituted 2-hydroxy-4,4-dimethylmorpholinium cations in aqueous solution.

The ring-chain tautomerism in aqueous solution of some aryl-substituted morpholinium salts (bromides), has been studied and equilibrium constants are reported. In the crystals the substrates exist entirely in their cyclic forms as hemiacetals, but in aqueous solution NMR measurements reveal that an equilibrium is established between the cyclic (hemiacetal) and the noncyclic (ketone) form, the degree of ring-opening being more pronounced with electron-donating aryl substituents at the carbonyl carbon. The kinetics of the ring-chain interconversion in water has been investigated spectrophotometrically by a 'pH jump' stopped-flow technique. General base catalysis is observed with a Br?nsted beta value apparently independent of substituent and equal to 0.60. The Hammett rho values for various base catalysts are close to those for very similar intermolecular reactions involving hemiacetal breakdown, leading to the suggestion of a 'normal' class n mechanism for base catalysis. For acid catalysis, however, a quite different situation is encountered, since no general acid but only (weak) catalysis by the hydronium ion can be detected. We believe this deviation from 'normal' general acid catalysis is caused by an electrostatic interaction, and we suggest that it might result from a change in the usual class e mechanism for general acid catalysis by a situation in which rate-limiting concerted proton transfer is replaced by rate-limiting preprotonation. This is supported by the observed drastic change in Hammett rho value for catalysis by the hydronium ion, compared with the 'normal' case. An interesting case is encountered for the 4-aminophenyl-substituted substrate, in which the amino group becomes protonated in acid solution, thus representing a new substituent. Despite this complication, the various equilibrium and rate constants may also be evaluated experimentally for this substrate.     

Monitoring genomic alterations with a panel of oligonucleotide probes specific for various simple repeat motifs

Germline and somatic instability of the human genome was studied, using synthetic oligonucleotides specific for simple repeat motifs. The following probes were used: (GTG)5, (GACA)4, (GATA)4, (CT)8, (TTAGGG)3, (GT)8, (GAA)6 and (GGAT)4. Each of them is unique with respect to the target regions recognized in the genome. Thus compilation of the various fingerprint data provides a complex map of the genome (and its deviations). While the fingerprints of differentiated somatic tissues never showed any alterations, in tumor tissues (namely gliomas) many changes could be detected. Most of the latter reflect secondary karyological aberrations. In nearly one third of the gliomas, drastically amplified and apparently monomorphic DNA fragments were identified. This marker should make it possible to deal with causal pathogenetic mechanisms as well as novel diagnostic strategies.