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Abstract:We focus on the nonhomogeneous backward heat problem of finding the initial temperature θ = θ(x, y) = u(x, y, ) such thatwhere Ω = ( , π) × ( , π). In the problem, the source f = f(x, y, t) and the final data h = h(x, y) are determined through random noise data g ij (t) and d ij satisfying the regression modelswhere (X i , Y j ) are grid points of Ω. The problem is severely ill-posed. To regularize the instable solution of the problem, we use the trigonometric least squares method in nonparametric regression associated with the projection method. In addition, convergence rate is also investigated numerically.

The aim of this study was to investigate the effects of Equistasi®, a wearable device, on the relationship between muscular activity and postural control changes in a sample of 25 Parkinson’s disease (PD) subjects. Gait analysis was carried out through a six-cameras stereophotogrammetric system synchronized with two force plates, an eight-channel surface electromyographic system, recording the activity of four muscles bilaterally: Rectus femoris, tibialis anterior (TA), biceps femoris, and gastrocnemius lateralis (GL). The peak of the envelope (PoE) and its occurrence within the gait cycle (position of the peak of the envelope, PPoE) were calculated. Frequency-domain posturographic parameters were extracted while standing still on a force plate in eyes open and closed conditions for 60 s. After the treatment with Equistasi®, the mid-low (0.5–0.75) Hz and mid-high (0.75–1 Hz) components associated with the vestibular and somatosensory systems, PoE and PPoE, displayed a shift toward the values registered on the controls. Furthermore, a correlation was found between changes in proprioception (power spectrum frequencies during the Romberg Test) and the activity of GL, BF (PoE), and TA (PPoE). Results of this study could provide a quantitative estimation of the effects of a neurorehabilitation device on the peripheral and central nervous system in PD.

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The reaction between allene and hydrogen over pumice-supported metals of the eighth group has been investigated in a constant volume reactor for a wide range of temperature and reactant ratios. The shape of the pressure-time curves were found to be dependent upon the reactant ratios and their order of admission. The reaction over nickel-pumice is principally a selective formation of propylene with small yields of propane and reduced polymers of allene. The orders of hydrogenation reaction are first, or slightly higher, and zero with respect to hydrogen and allene respectively. The apparent activation energies for Pd, Pt, Co, Fe, Ni, Rh, Tr, Ru, and 0 s are 13, 17.4, 10.8, 9.4, 7.8, 9.6, 5.3, 3.0, and 4.6 kcal/n~ole respectively. The catalytic activities of the metals are in the sequence While selectivity was found to decrease with increasing initial hydrogen pressures, it increased with increasing temperaturcs, IntroductionThough several papers have appeared in the last 30 years describing tlie kinetics of catalytic liydrogenation of olefins and alkynes, very little work has been reported about the kinetics of tlie hydrogenation of allene over metal catalysts. Bond and Sheridan (1) studied the hydrogenation of allene over pumice-supported nickel, palladiun~, and platinum catalysts. Tlie order of rcactioiis were found to be one and about zero with respect to hydrogen and allene respectively. Kistiakowsky and co-workers (2) hydrogenated allene with a large excess of hydrogen. They did not specify the catalyst used. Recently Bond and co-workers (3) have reported about tlie selectivities observed in the first stage of the reaction, for alumina-supported ruthenium, rhodium, osmiu~n, iridium, and platinum catalysts. No mention has been made about tlie effect of reactant ratios and temperature on the selectivity. This paper describes a detailed study of tlie kinetics of allene liydrogenation over pumicesupported metals of the eighth group and the effect of the various experimental variables upon tlie selectivity of the reaction in presence of nickel-pumice catalyst.