Almost Resolvable Maximum Packings of Complete Graphs with 4-Cycles

If the complete graph K _n has vertex set X, a maximum packing of K _n with 4-cycles, (X, C, L), is an edge-disjoint decomposition of K _n into a collection C of 4-cycles so that the unused edges (the set L) is as small a set as possible. Maximum packings of K _n with 4-cycles were shown to exist by Sch?nheim and Bialostocki (Can. Math. Bull. 18:703–708, 1975). An almost parallel class of a maximum packing (X, C, L) of K _n with 4-cycles is a largest possible collection of vertex disjoint 4-cycles (so with ?/4?{\lfloor/4\rfloor} 4-cycles in it). In this paper, for all orders n, except 9, which does not exist, and possibly 23, 41 and 57, we exhibit a maximum packing of K _n with 4-cycles so that the 4-cycles in the packing are resolvable into almost parallel classes, with any remaining 4-cycles being vertex disjoint. [Note: The three missing orders have now been found, and appear in Billington et al. (to appear).]     

A Theory for Quantum Accelerator Modes in Atom Optics

Unexpected accelerator modes were recently observed experimentally for cold cesium atoms when driven in the presence of gravity. A detailed theoretical explanation of this quantum effect is presented here. The theory makes use of invariance properties of the system, that are similar to the ones of solids, leading to a separation into independent kicked rotor problems. The analytical solution makes use of an asymptotic approximation very similar to the semiclassical one, except that the small parameter is not Planck's constant, but rather the detuning from the frequency that is resonant in absence of gravity.     

Stress dependence of sapphire cathodoluminescence from optically active oxygen defects as a function of crystallographic orientation

The cathodoluminescence (CL) spectrum of the synthetic sapphire single crystal has been studied with respect to the different crystallographic planes of the crystal in order to describe the tensorial stress dependence of the band related to oxygen defects. Experiments provide the link between CL spectral shift and stress, which is referred to as the piezo-spectroscopic (PS) relationship. Using the biaxial stress field developed at the tip of cracks generated from the corners of a Vickers indentation, we clearly detected stress dependence for the cumulative band arising from the F+-center transition of optically active oxygen vacancies. The matrix of PS coefficients along different crystallographic axes of single-crystal sapphire could be precisely determined. The shallow nature of the electron probe may enable the characterization of surface stress fields with a spatial resolution that may not be easily available by conventional laser probes. The PS calibration results collected on oxygen-defect bands allow the direct determination of unknown surface residual stress fields stored in sapphire substrates for electronics applications.     

Analysis of residual stresses in ternary electroconductive composites

Residual stresses in ceramic particle electroconductive composites were investigated by Raman microprobe spectroscopy and X-ray diffraction. The composites were ternary electroconductive ceramics in the system AlN+SiC+(ZrB₂,MoSi₂). Due to the poor definition of the reinforcing phase peaks, only the matrix residual stress could be evaluated by Raman spectroscopy, whilst the residual stress in the reinforcing phase was calculated by the equilibrium conditions. These calculated values were compared with those experimentally obtained by X-ray diffraction. The agreement between Raman and X-ray results was quite satisfactory. The values of residual stress calculated by the composite theory were in good agreement with those measured by Raman and X-ray diffraction for the MoSi₂-containing composite. For the ZrB₂-containing composite, the value calculated by the composite theory falls between the values measured by Raman and X-ray diffraction. PACS 81.05.Je; 87.64.Je; 87.64.Bx     

Characterization of nanosized TiO2 synthesized inside a porous glass-ceramic monolith by metallo-organic decomposition process

This work reports the preparation of TiO₂ by decomposition of a metallo-organic precursor (MOD process) in the pores of an α-NbPO₅ glass-ceramic monolith (PGC-NbP) and the study of the TiO₂ anatase-rutile transition phase. The impregnation of titanium di-(propoxy)-di-(2-ethylhexanoate) in the PGC-NbP was confirmed by diffuse reflectance infrared spectroscopy. In the restrictive porous environment the decomposition of the metallo-organic compound exhibits a lower initial decomposition temperature but a higher final decomposition temperature, in comparison to the free precursor. The pure TiO₂ rutile phase is formed only above 700 °C when the titanium precursor is decomposed outside the pores. The TiO₂ anatase obtained inside the PGC-NbP was stabilized up to 750 °C and exhibits a smaller average crystallite size in comparison with the MOD process performed without PGC-NbP. Furthemore, the temperature of the TiO₂ anatase-rutile transformation depends on crystallite size, which was provided by XRD and Raman spectroscopy. The precursor impregnation-decomposition cycle revealed a linear mass increment inside PGC-NbP. Micro-Raman spectroscopy shows the presence of a gradient concentration of the TiO₂ inside the PGC-NbP. The use of the MOD process in the PGC-NbP pores has several advantages: control of the amount and the nature of the phase formed and preservation of the pore structure of PGC-NbP for subsequent treatments and reactions.     

Determination of Judd-Ofelt intensity parameters of pure samarium(III) complexes

This work reports an alternative aproach to obtain the Judd-Ofelt intensity parameters of Sm(III) complexes with the general formula: [Sm(tta)₃(L)_n], with L = H₂O, triphenylphosphine oxide (tppo), 2,2′-bipyridine (bipy) and 1,10-phenantroline (phen); n = 2 for H₂O and tppo and n = 1 for phen and bipy, using the absorption spectra of rare earth complexes where the powders are dispersed in KBr pellets. This approach can be applied to other complexes of rare earth ions that have spin allowed transitions and it is validated by comparing the emission spectra of the complexes with those dispersed in KBr pellets.     

Addition reactions of azoesters with 2-thioquinazolinones

Reaction between diethyl azodicarboxylate (I) and 1,2,3,4-tetrahydro-2-thioquinazolin-4-one (II), as a cyclic model of thiourea, both in alcoholic medium and in inert solvents has been investigated. By carrying out the reaction in an inert solvent, it was possible to isolate an intermediate. Evidence is presented that the intermediate, in turn, was converted into the final products. Structures were unequivocally assigned by mass spectrometry.     

Non-recurrent behaviour in quantum dynamics

We study the motion of a quantum rotator under an external periodic perturbation. For the resonant case, i.e. when the frequency of driving pulses is rationally connected with the frequencies of the free rotator, the quasi-energy spectrum is known to be continuous. We prove that for a generic choice of the potential there is a non-empty set of non-resonant values of the external frequency such that the quasi-energy spectrum still has a continuous component.     

Micromechanics of fracture in a ceramic/metal composite studied by in situ fluorescence spectroscopy II: fracture mechanics analysis

Fluorescence microprobe spectroscopy was used in [1] to determine in situ microstress fields that develop during fracture in a model ceramic/metal composite. In particular, experimental and theoretical procedures were described in order to relate the experimental peak-shift to the various stress components and combinations thereof. Based on suitable micromechanical concepts, these stress maps are now used to predict quantities related to the fracture mechanics, such as (critical) stress intensity factors, R-curves, and crack-opening displacements. All predictions are compared with direct measurements of these quantities to demonstrate the feasibility and soundness of the micromechanics approach.Received: 10 September 2003, Accepted: 1 November 2003, Published online: 3 February 2004PACS: 68.37.Uv, 62.60.Mk Correspondence to: W.H. Müller