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Approximate expressions for the spatially homogeneous and spatially inhomogeneous corrections to the equilibrium reaction rates obtained within the renormalization technique developed in the previous papers have been derived. Arbitral set of the chemical reactions is considered. Obtained reaction rates depend on the heat capacities of the species participation in the chemical reactions. This reflects the quasi-stationary process of the exchange of the energy between the translational and internal degrees of freedom of the reacting species. [ABSTRACT FROM AUTHOR]

Free vibration with multiple degrees of freedom is considered. In such case the solution is described by an exact two-step formula involving matrix cosine. Since the corresponding matrix is symmetric then it is proper to use L∞ instead of Pade approximations to cos. Longer step sizes and smaller errors is the gain of this approach. [ABSTRACT FROM AUTHOR]

Segments of two given circular arcs can be blended to produce a segment of a new curve. The new curve that been produced which also known as blending curve is form in a C-shape. That's mean the two circular arcs are blend at the same endpoints. Bezier Curve refer to [1] is the main application in this construction of blending curve. As the two circular arcs are create using the Rational Bezier Curve for the shape refer to [2]. First degree of Bezier Curve is use in blending function along with function H(t). Blending can provide a smooth transition from one curve to another and can give various degrees of smoothness at the endpoints of the blend, where the smoothness is measured analogously to parametric continuity, Cn and geometric continuity, Gn. The accuracy of the approximation to a best blending curve obtained by different blending formulas is compared via analysis. Two types of blending formula introduced, which are Blend A and B. Blend A which involve only parametric continuity, C0, C1 and C2 Blend A. Next, new blending formula known as Blend B which actually a correction to the C0 Blend A. So, some correction term are added to the blending function in C0 Blend A for obtaining parametric continuity, C1 and C2 Blend B. Then, geometric continuity use for Blend B by increasing the smoothness of blending curve that result in parametric continuity. Some free parameter are added to the original blending function of G1 and G2 Blend B and secure to be C¹ and C² Blend B. Finally, the curvature which measures how quickly a tangent line turns on a curve is applied. So, appropriate result of blending curve can be obtained through the observation of the shape which lies within the convex hull of their control points and its curvature value at the start and end points equal to the curvature of the two circular arcs that are being blended. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical approximation of a fluid-structure interaction problem. The interaction of turbulent flow with flexibly supported airfoil with an aileron is considered, where the non-linearities due to the high deflection occuring for aeroelastic systems after the loss of their aeroelastic stability are involved. The motion of the airfoil is described with the aid of a system of ordinary differential equations for two or three degrees of freedom coupled with the Reynolds averaged Navier-Stokes system of equations completed by the k - ω turbulence model. Numerical results are shown. [ABSTRACT FROM AUTHOR]

The pseudo-median procedure is a technique for treatment group comparison which adopts the pseudo-median as a location parameter. The power of this procedure is estimated in various shapes of distributions and different degrees of variation. The bootstrap method is employed to generate the approximate sampling distribution of the statistic. The results show that the power of this procedure is not affected by the shape of the data. However, the power is affected somewhat by the heterogeneity of variances. [ABSTRACT FROM AUTHOR]

Antidata in Bayesian inference was claimed in [1]. The idea was that when an entropic 1-prior (as defined in [1]) encodes an estimate of the unknown distribution parameters (for example the parameters of a Gaussian), this estimate could reduce the degrees of freedom in the posterior pdf (probability density function) of the parameters, as if it annihilated information in the likelihood. This would be in contrast to the (natural conjugate) 0-prior, where typically the estimate with weight α>0 acts like an additional α data points combined with the actual n data samples, thus increasing the degrees of freedom in the posterior by α and making the 0-posterior more informative. I became skeptical of antidata when I failed to see it in plots that I produced. I found that antidata, in the clearest scenario (when the sample statistic coincides with the parameter estimate), does not occur with the Bernoulli, Exponential, or Gaussian (when only ν is unknown or when μ and ν are both unknown) models. This was measured in terms of the parametrization-neutral information gain of the posteriors relative to a Uniform prior (or virtual Uniform prior). We correct some computations of the 1-prior published in [1]. These computations were not the source of the appearance of antidata; rather, an approximation to the 1-posterior and possibly the choice of parametrization were what allowed that. It remains to find antidata in other probability models, or to prove it does not occur at all. Our computations and reasoning suggest that usually (but not always) the 1-prior is actually the more informative entropic prior for inference. [ABSTRACT FROM AUTHOR]

Charge transfer (CT) in molecular ion-neutral interactions can proceed through dynamically coupled electronic, vibrational, and rotational degrees of freedom. Using the upgraded Oak Ridge National Laboratory ion-atom merged-beams apparatus, absolute direct charge transfer is explored from keV/u collision energies where the collision is considered 'ro-vibrationally frozen' to sub-eV/u collision energies where collision times are long enough to sample vibrational and rotational modes. Our first molecular ion measurement with the merged-beams apparatus has been performed for D2++H and is used to benchmark high energy sudden approximation theory and vibrational specific adiabatic theory for the (H2-H)+ complex. CT measurements have also been performed for D3++H from 2 eV/u to 2 keV/u and CO++D from 20 eV/u to 2000 eV/u. With straightforward improvements to the apparatus, we plan to extend our measurements to key 'destructive' rate coefficients for H2+ and CH+ with H at temperatures relevant to the interstellar medium. [ABSTRACT FROM AUTHOR]

In this work we analyze the approximations of second order eigenvalue problems (EVPs). The nonconforming piecewise linear finite element with integral degrees of freedom is used. We prove that the eigenvalues computed by means of this element on convex domain are smaller than the exact ones if the mesh size is small enough. Some numerical results are also given. [ABSTRACT FROM AUTHOR]

We develop a quantal cumulant dynamics method for the quantum tunneling in dissipative environment. Reduced equations of motion of classical and quantal cumulant variables without bath degrees of freedom are derived. We observed suppression of the tunneling that depends on the sign of a friction constant for an Ohmic approximation and on the magnitude of a bath frequency for a single bath mode approximation. A possible mechanism of the suppression is explored by analyzing an effective quantal potential of the tunneling path. [ABSTRACT FROM AUTHOR]