A New Technique for Translating Discrete Hybrid Automata into Piecewise Affine Systems

The paper proposes a new translation algorithm that translates a hybrid system described as a discrete hybrid automaton (DHA) into an equivalent piecewise affine (PWA) system. The translation algorithm exploits, among others, a new technique for cell enumeration in hyperplane arrangement, all proposed in this paper. The new translation technique enables the transfer of several analysis and synthesis tools developed for PWA systems to a DHA class of hybrid systems.     

Injective colorings of planar graphs with few colors

An injective coloring of a graph is a vertex coloring where two vertices have distinct colors if a path of length two exists between them. In this paper some results on injective colorings of planar graphs with few colors are presented. We show that all planar graphs of girth ≥ 19 and maximum degree Δ are injectively Δ-colorable. We also show that all planar graphs of girth ≥ 10 are injectively (Δ+1)-colorable, that Δ+4 colors are sufficient for planar graphs of girth ≥ 5 if Δ is large enough, and that subcubic planar graphs of girth ≥ 7 are injectively 5-colorable.     

Determination of the relative sputtering yield of carbon to tantalum by means of Auger electron spectroscopy depth profiling

The relative sputtering yield of carbon with respect to tantalum was determined for 1 keV Ar⁺ ion bombardment in the angular range of 70°–82° (measured from surface normal) by means of Auger electron spectroscopy depth profiling of C/Ta and Ta/C bilayers. The ion bombardment‐induced interface broadening was strongly different for the C/Ta and Ta/C, whereas the C/Ta interface was found to be rather sharp, the Ta/C interface was unusually broad. Still the relative sputtering yields (Y_C/Y_Ta) derived from the Auger electron spectroscopy depth profiles of the two specimens agreed well. The relative sputtering yields obtained were different from those determined earlier on thick layers, calculated by simulation of SRIM2006 and by the fitting equation of Eckstein. The difference increases with increase of angle of incidence. Copyright © 2009 John Wiley & Sons, Ltd.     

Field cooled and zero field cooled 207Pb NMR of the relaxor ferroelectric PMN

A 2.8 kV/cm electric field has been applied parallel to the external magnetic field along the [111] direction of a PMN single crystal and the 207Pb NMR spectra were measured at 9.1 T. Whereas the zero field cooled (ZFC) spectrum exhibits a Gaussian-like line shape, the FC spectrum clearly shows a two peak structure. One of the two peaks coincides with the ZFC spectrum. The other peak is shifted by about 100 kHz towards lower frequencies with respect to the ZFC peak and seems to be characteristic for the ferroelectric state. The ferroelectric shift agrees with the predictions of the spherical random bond-random field model.     

Torsion and related concepts: An introductory overview

The aim of this paper is to provide an overview of all the basic aspects of the torsion of a manifold, with particular stress on the expressions in an anholonomic basis. After a brief review of anholonomic bases and Koszul covariant derivative, we show how the expressions for the torsion and the Riemann tensors in a general (anholonomic) basis arise from their expressions in a coordinate basis. We further derive the expression for the contortion tensor, which arises from the requirement that an affine connection with torsion be metric (preserving). The latter requirement is related to the equivalence principle, whose mathematical aspects in a manifold with torsion are discussed next. Finally, we derive the expression for the distortion tensor, which is an analog of the curvature tensor but arising from the torsion rather than the metric tensor.     

Evidence of supercritical behavior in liquid single crystal elastomers

Temperature profiles of the first and the second moment of the nematic order parameter distribution function, as determined from the deuteron nuclear magnetic resonance line shapes, as well as heat capacity response, provide support for the supercritical scenario of the nematic-paranematic phase transition in liquid single crystal elastomers. The relative strength of the locked-in internal mechanical field with respect to the critical field can be decreased by swelling the elastomer samples with low molecular mass nematogen. By increasing the concentration of the dopant, critical and below-critical behavior is promoted.     

Radiative seesaw mechanism and degenerate neutrinos

The radiative seesaw mechanism of Witten generates the right-handed neutrino masses in SO(10) with the spinorial 16(H) Higgs field. We study here analytically the 2nd and 3rd generations for the minimal Yukawa structure containing and Higgs representations. In the approximation of small 2nd generation masses and gauge loop domination we find the following results: (1) beta-tau unification, (2) natural coexistence between large theta(l) and small theta(q), and (3) degenerate neutrinos.     

Slater ice rules and H-bond dynamics in KDP-type systems

We report on the first observation of the dynamics of correlated hydrogen switching among the six Slater D2PO4 configurations, induced by unpaired D3PO4 and DPO4 Takagi group diffusion in a deuteron glass Rb0.5(ND4)0.5D2PO4. The results obtained by two-dimensional (2D) 31P exchange NMR prove the validity of the Slater-Takagi ice rules and allow for the direct determination of the correlation time for the unpaired Takagi group visits to a given D2PO4 group.     

Analytical radiochemistry of neutron activated samples in practice

Analytical radiochemistry of neutron-activated samples, as practiced during past decades at the Jo?ef Stefan Institute Ljubljana, is outlined. The paper reviews achievements made in both elemental analysis and analyses of long-lived radionuclides, in variety of sample types. The presented analytical procedures include application of diverse chemical separations, multiple irradiations of samples, use of various nuclear reactions and detection modes for particular measurands, and determination of elements that are difficult to be determined by neutron activation analysis (NAA). Useful practical applications of neutron-activated tracers for chemical yield determinations, as unique feature of radiochemical NAA in comparison with non-nuclear analytical methods, are also addressed.     

Some results of investigations into relationships between a few elements of nodular graphite cast iron and nodular graphite

Summary Some Results of Investigations Into Relationship Between a Few Elements of Nodular Graphite Cast Iron and Nodular Graphite An investigation of the fractured surfaces of pins, having a diameter of 1.5 mm, obtained during the production of commercial nodular cast irons of Meehanite types is reported. The investigation was performed using a scanning electron microsopec (SEM) with an attachment for energy dispersive analysis and scanning Auger microprobe (SAM), where the principal attention was given to SAM. Point analysis, Auger images and Auger line scans were performed on the fractured surfaces and also approximately 200 Å and 1m below the surface. The nodule/metal and intercrystalline graphite interfaces in the investigated iron were free of foreign elements.The paper has been presented at 12th Colloquium on Materials Analysis, Institute for Analytical Chemistry, Technical University in Vienna, May 13–15, 1985.