Left-divisibility and word problems in single relation monoids

LetM be a monoid presented by <Σ;u=v> whereu andv are words on the finite alphabet Σ./ Deciding the world problem forM is still an open question, though it seems decidable and partial results exist. The remaining cases to solve are presentations of the form <a, b; bva=aua>,u, v∈{a, b}^⋆ The word problem is then closely related to the left-divisibility problem, as shown by S.I. Adjan who introduced a procedure that “almost” allows to decide the problem. The main contribution, due to Adjan and Oganesjan, states that ifbva is an unbordered factor ofaua then the word problem is deciable. We restrict Adjan's procedure to study the case whenbva is unbordered, which allows us to extend Adjan and Oganesjan's theorem. More specifically, we show (Proposition 4.24) that the word problem is decidable for presentations <a, b; bva=aua> with the only following condition: Inbva, the leftmost train ofb is strictly longer than the others. The following corollary naturally holds: The word problem is decidable for presentations of the form <a, b; b ^m a ⁿ =aua>,u∈{a, b}^⋆,m, n>0     

Phonon replica of excited level of free exciton in CdS

We report here the first experimental observation of the flourescence of a LO phonon replica from the A_n=2 excitonic level in cadmium sulfide. A very simple theoretical interpretation is given. We present also experimental data about phonon replicas in the case of forbidden transitions.     

Gamma-ray spectra and sensitivities for 2.8 MeV neutron activation analysis

The use of 2.8 MeV neutrons produced by the D(d, n)³He reaction should be taken into consideration in some applications of radioactivation analysis. The low number of elements activable by these neutrons makes possible to minimize the matrix interference and the background below the characteristic photopeaks. The very low dead-time of the spectrometric measurements permits the use of the maximum neutron flux available now and in the future. The purpose of this paper is to define experimentally the sensitivity of determination for the 16 main elements activable with a 400 keV Van de Graaff accelerator at a 2.8 MeV neutron flux of 2·10⁶ n·cm⁻²·sec⁻¹ on the sample.     

Étude de la déformation d'un liquide magnétique

Sans résumé     

Correlations between acidity, surface structure, and catalytic activity of niobium oxide supported on zirconia

The development of the acidity and the relationship between acidity, catalytic activity, and the surface structure for niobium oxide supported on zirconia were investigated for a series of solids. The catalysts were active for 2-propanol dehydration only above a threshold in Nb loading. The acidity was studied by infrared spectroscopy of adsorbed 2,6-dimethylpyridine as a probe molecule, and the onset of activity was correlated with that of the formation of relatively strong Br?nsted acid sites. The variation in the abundance of these sites also correlated with the catalytic activity. Raman, IR, and UV spectroscopy results indicated that the active sites were related to polymeric Nb surface species. These results were compared to those previously reported for the WO(x)/ZrO(2) catalysts.     

Dynamics of traveling waves in the transverse section of a laser

We analyze the general features of the formation and interaction of transverse traveling waves and the appearance of filamentation in broad area semiconductor lasers with current profiling. For small apertures, the emitted profile is symmetric consisting of two counterpropagating transverse traveling waves, both emanating from the center of the device. For larger apertures, the emission becomes asymmetric as one of the traveling waves expands to occupy an increased area while the other occupies the remaining, smaller spatial region. In both devices, the pattern becomes unstable at higher injection currents due to optical filamentation, although an intermediate state is present in the wider device whereby the dominant wave undergoes a Hopf bifurcation before filamentation occurs.     

Optical spin hall effect

A remarkable analogy is established between the well-known spin Hall effect and the polarization dependence of Rayleigh scattering of light in microcavities. This dependence results from the strong spin effect in elastic scattering of exciton polaritons: if the initial polariton state has a zero spin and is characterized by some linear polarization, the scattered polaritons become strongly spin polarized. The polarization in the scattered state can be positive or negative dependent on the orientation of the linear polarization of the initial state and on the direction of scattering. Very surprisingly, spin polarizations of the polaritons scattered clockwise and anticlockwise have different signs. The optical spin Hall effect is possible due to strong longitudinal-transverse splitting and finite lifetime of exciton polaritons in microcavities.     

Three-dimensional recomposition of the absorption field inside a nonbuoyant sooting flame

A remote scanning retrieval method was developed to investigate the soot layer produced by a laminar diffusion flame established over a flat plate burner in microgravity. Experiments were conducted during parabolic flights. This original application of an inverse problem leads to the three-dimensional recomposition by layers of the absorption field inside the flame. This technique provides a well-defined flame length that substitutes for other subjective definitions associated with emissions.     

Detection of acoustic waves by NMR using a radiofrequency field gradient

A B(1) field gradient-based method previously described for the detection of mechanical vibrations has been applied to detect oscillatory motions in condensed matter originated from acoustic waves. A ladder-shaped coil generating a quasi-constant RF-field gradient was associated with a motion-encoding NMR sequence consisting in a repetitive binomial 13;31; RF pulse train (stroboscopic acquisition). The NMR response of a gel phantom subject to acoustic wave excitation in the 20-200 Hz range was investigated. Results showed a linear relationship between the NMR signal and the wave amplitude and a spectroscopic selectivity of the NMR sequence with respect to the input acoustic frequency. Spin displacements as short as a few tens of nanometers were able to be detected with this method.     

Concentration of sodium ion as the determining factor for the association of dansyl amino acids with the teicoplanin molecule in reversed-phase liquid chromatography

The mechanism of the binding of D,L dansyl amino acids to teicoplanin was investigated. Na+ was used as an indicator of the interactions between the solutes and teicoplanin. The number (n) of sodium ions, Na+, excluded from the solute-teicoplanin interface when analyte transfer occurred was determined. A thermodynamic study and enthalpy-entropy compensation were performed to further explore the interaction mechanism. From these results, it was shown that teicoplanin was balanced between 2 conformational states characterized by distinct enantioselective properties. This approach indicates that liquid chromatography (LC) is a useful tool to extract physicochemical and molecular information from retention data. Thus, LC can be used as a complementary technique with the conventional techniques of molecular interaction analysis.