Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

UPWIND FINITE VOLUME SCHEMES FOR SEMICONDUCTOR DEVICE

The mathematical model of semiconductor devices is described by the initial boundary value problem of a system of three nonlinear partial differential equations. One equation in elliptic form is for the electrostatic potential; two equations of convection-dominated diffusion type are for the electron and hole concentrations. Finite volume element procedure are put forward for the electrostatic potential, while upwind     

Observability Inequalities by Internal Observation and Their Applications

By means of a Carleman estimate, we obtain several observability inequalities by internal observation for hyperbolic equations with lower-order terms. Also, we apply our observability results to an exact controllability problem and an inverse wave source problem.     

Asymptotic distribution of maximal autoregressive process with weight tending to 1

The maximal operator plays the similar role as the summation operator in the sense of stability of operation. So, we could discussARMA processes in the maximal operation by the same way as in the summation operation. However, many papers already treated with moving order statistics. In this paper, we discuss asymptotic behaviors of maximal autoregressive (MAR) processes with the weight tending to 1.     

Numerical calculation of invariant manifolds for maps

Many processes in the sciences and in engineering are modelled by dynamical systems and—in discretized version—by nonlinear maps. To understand the often complicated dynamical behaviour it is a well established tool to use the concept of invariant manifolds of the system. In this way it is often possible to reduce the dimension of the system considerably. In this paper we propose a new method to calculate numerically invariant manifolds near fixed points of maps. We prove convergence of our procedure and provide an error estimation. Finally, the application of the method is illustrated by examples.     

Molar extinction coefficients of solutions of some organic compounds

Molar extinction coefficients of aqueous solutions of some organic compounds, viz. formamide (CH₃NO),N-methylformamide (C₂H₅NO),NN-dimethylformamide (C₃H₇NO),NN-dimethylacetamide (C₄H₉NO), 1,4-dioxane (C₄H₈O₂₄), succinimide (C₄H₅NO₂) and solutions of acetamide (C₂H₅NO) and benzoic acid (C₇H₆O₂) in 1,4-dioxane (C₄H₈O₂) have been determined by narrow beam γ-ray transmission method at 81, 356, 511, 662, 1173 and 1332 keV. The experimental values of mass attenuation coefficients of these compounds have been used to calculate effective atomic numbers and electron densities. The additivity rule earlier used for aqueous solution has been extended to non-aqueous (1,4-dioxane) solutions.     

Measurements and calculations of H2-broadening and shift parameters of water vapour transitions of the ν1 + ν2 + ν3 band

The water vapour line broadening and shifting for 97 lines in the ν₁ + ν₂ + ν₃ band induced by hydrogen pressure are measured with Bruker IFS 125 HR FTIR spectrometer. The measurements were performed at room temperature, at the spectral resolution of 0.01 cm^?1 and in a wide pressure range of H₂. The calculations of the broadening γ and shift δ coefficients were performed in the semi-classical method framework with use of an effective vibrationally depended interaction potential. Two potential parameters were optimised to improve the quality of calculations. Good agreements with measured broadening coefficients were achieved. The comparison of calculated broadening coefficients γ with the previous measurements is discussed. The analytical expressions that reproduce these coefficients for rotational, ν₂, ν₁, and ν₃ vibrational bands are presented.     

X-ray attenuation coefficients of Fe compounds in the K-edge region at different energies and the validity of the mixture rule

The total mass attenuation coefficients for element Fe and compounds FeF₃, Fe₂O₃, FeCl₂·4H₂O, FeCl₃2NH₄Cl·H₂O were measured at different energies between 4.508-17.443 keV range by using secondary excitation method. Ti, V, Cr, Ni, Cu, Zn, As, Se, Br, Rb, Sr, Y, Zr, Nb, Mo were chosen as secondary exciter. 59.5 keV gamma rays emitted from an ²⁴¹Am annular source were used to excite secondary exciter and K_α(K-L₃, L₂) lines emitted of secondary exciter were counted by a Si(Li) detector with a resolution of 160 eV at 5.9 keV. It was observed that mixture rule method is not a suitable method for determination of the mass attenuation coefficients of compounds, especially at energy that is near the absorption edge. Obtained values were compared with theoretical values.     

Geometric visualization of the Brewster angle from dielectric-magnetic interface

A geometric visualization is presented for the Brewster angle for a plane wave reflecting from an interface. The surface is assumed to be isotropic but it is allowed to display both dielectric and magnetic susceptibility, and hence the Brewster (polarizing) angle can attain any value between 0 and 90^°, and can exist for both parallel and perpendicular polarizations. The geometric construction (a tetrahedron) is spanned by the basic material parameters of the surface. The Brewster angle appears in one of the faces of the tetrahedron.     

A comment on “Ab initio study: the potential energy curves and ro-vibrational spectrum of low-lying excited states of HCl+ cation”

Since the ²Π state in HCl⁺ is an inverted doublet, the energy of the ²Π_1/2 state is higher than the ²Π_3/2. Therefore, the larger value of intensity correspond to the transition of ²Π_3/2. We calculated the Einstein A coefficients and radiation lifetimes for the A²Σ⁺-X²Π transition. Our results are in good agreement with the experimental data and theoretical values. Then the ro-vibrational line intensities of the 1-0 band were calculated for the ²Π_3/2 and ²Π_1/2 states of HCl⁺. Employing the RKR potential, the predicted band origins for Δν=1-0 are 2569.3 and 2568.55 cm-1 for ²Π_3/2 and ²Π_1/2, respectively.