Spin 3/2 Field Equation: Separation and Solution in a Class of Lema?tre–Tolman–Bondi Cosmologies

The spin 3/2 field equation is studied in the general Lema?tre–Tolman–Bondi (LTB) space-time. The equation is separated by variable separation. The angular dependence factors out at the level of the general LTB metric. Due to spherical symmetry the separated angular equations coincide with those, previously integrated, relative to the Robertson–Walker and Schwarzschild metric. Separation of time and radial dependence is possible within a class of LTB cosmological models for which the physical radius is a product of a time and a radial function, the last one being further selected by the consistency condition of the radial equations. The separated time dependence, that can be integrated by series, results essentially unique. Instead the radial dependence can be reduced to two independent second order ordinary differential equations that still depend on an arbitrary radial function that is an integration function of the cosmological model. The generalization of the scheme to arbitrary spin field equation is suggested.     

Extreme statistics in Raman fiber amplifiers: From analytical description to experiments

In this work, we investigate the emergence of rare and intense events during the Raman fiber amplification of a continuous wave. We highlight how dispersive properties and pump depletion can strongly influence the statistical properties of the amplified signal and its optical spectrum. Under certain conditions, the probability density functions of the amplified signal are calculated analytically and compared with the results of the numerical simulations. The conclusions are qualitatively validated by experiments carried out at telecommunication wavelengths.     

The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed.     

Changes in cerebral activity after decreased upper-limb hypertonus: an EMG-fMRI study

Objective

Whereas several studies have used functional magnetic resonance imaging (fMRI) to investigate motor recovery, whether therapy to decrease post-stroke hypertonus alters central motor patterns remains unclear. In this study, we used continuous electromyography (EMG)-fMRI to investigate possible changes in movement-related brain activation in patients receiving Botulinum toxin (BoNT-A) for hand-muscle hypertonus after chronic stroke.

Methods

We studied eight stroke patients all of whom had hemiparesis and associated upper-limb hypertonus. All patients underwent an fMRI-EMG recording and clinical-neurological assessment before BoNT-A and 5 weeks thereafter. The handgrip motor task during imaging was fixed across both patients and controls. The movements were metronome paced, movement amplitude and force were controlled with a plastic orthosis, dynamometer and EMG recording. An age-matched control group was recruited from among healthy volunteers underwent the same fMRI-EMG recording.

Results

Before BoNT-A, while patients moved the paretic hand, fMRI detected wide bilateral activation in the sensorymotor areas (SM1), in the supplementary motor area (SMA) and cerebellum. After BoNT-A blood oxygenation level-dependent (BOLD) activation decreased in ipsilateral and contralateral motor areas and became more lateralized. BOLD activation decreased also in ipsilateral cerebellar regions and in the SMA.

Conclusion

Changes in peripheral upper-limb hypertonus after BoNT-A were associated to an improvement in active movements and more lateralized and focalized activation of motor areas. The clinical and EMG-fMRI coregistration technique we used to study hand-muscle hypertonus in patients receiving BoNT-A after chronic stroke should be useful in future studies seeking improved strategies for post-stroke neurorehabilitation.     

Observation of the V2O5(001) surface using ambient atomic force microscopy

Constant force images of the V₂O₅(001) surface were recorded in ambient conditions with atomic force microscopy. All images exhibit the 11.5 Å × 3.5 Å. periodicity expected for a bulk terminated surface. However, images reveal differences from the ideal structure. The experimental results are interpreted in terms of preferential adsorption sites for water molecules. Because these sites are thought to influence the catalytic properties of the surface, their characterization is an important step towards understanding how the atomic-scale structure of a surface influences its properties.     

Empirical consequences of the scientific construction: The program of local hidden-variables theories in quantum mechanics

We claim that physics has been constructed because three “philosophical” principles have been respected, namely, realism, locality, and consistency. These principles lead to an interpretation of quantum mechanics (QM) in terms of local hidden-variables theories (LHV). In order to prove that LHV have not been refuted, we analyze the empirical proofs of Bell's inequalities and we argue that none is loophole-free. Then we propose a restricted QM that does not contain measurement postulates and that does not claim that all state vectors (self-adjoint operators) are states (observables). The contradiction of such restricted QM with Bell's inequality cannot be shown as a theorem, but only by the design of a loophole-free experiment. Finally, we argue that noise has been underestimated in quantum theory. It does not appear in QM, but it is essential in quantum field theory. We conjecture that noise will prevent the violation of Bell's inequality.