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EN
The present work investigates the propagation of harmonic plane waves in an isotropic and homogeneous elastic medium that is rotating with uniform angular velocity by employing the two-temperature generalized thermoelasticity, recently introduced by Youssef (IMA Journal of Applied Mathematics, 71, 383-390, 2006). Dispersion relation solutions for longitudinal as well as transverse plane waves are obtained analytically. Asymptotic expressions of several important characterizations of the wave fields, such as phase velocity, specific loss, penetration depth, amplitude coefficient factor and phase shift of thermodynamic temperature are obtained for high frequency as well as low frequency values. A critical value of the two-temperature parameter for the low frequency case is obtained. Using Mathematica, numerical values of the wave fields at intermediate values of frequency and for various values of the twotemperature parameter are computed. A detailed analysis of the effects of rotation on the plane wave is presented on the basis of analytical and numerical results. An in-depth comparative analysis of our results with the corresponding results of the special cases of absence of rotation of the body and with the case of generalized thermoelasticity is also presented. The most significant points are highlighted.
EN
A kinetic investigation of the slurry phase epoxidation of styrene with hydrogen peroxide has been carried out, for the first time, over nanoporous Au doped TS-1 catalyst, in a batch reactor, in the temperature range of 313-333 K. It was found that product selectivity and the rate of reaction are greatly influenced by concentrations of styrene and hydrogen peroxide. Kinetics studies reveal that the mechanism of the reaction is of the "Redox" type. The rate equation, r = k 1k2POPH/ (k1PO+ k2PH) deduced, assuming a steady state involving two stage oxidation-reduction process, represent the data most satisfactorily for the conversion of styrene to styrene oxide. A tentative mechanism of the process has also been suggested.
3
Content available remote A note on transversal hypersurfaces of Lorentzian almost paracontact manifolds
EN
Transversal hypersurfaces of Lorentzian almost paracontact manifolds are studied. It is proved that transversal hypersurfaces of Lorentzian almost paracontact manifolds admit an almost product structure and almost product Lorentzian metric structure. We shall also derive a formula which gives the relation between the connection with respect to the Lorentzian metric g and that with respect to induced Lorentzian metric G. Some properties of Lorentzian (f, g, u, v, lambda)-structure, transversal hypersurfaces of Lorentzian cosymplectic manifolds and Lorentzian paracontact Sasakian manifolds are also studied.
EN
The continued fraction expansions (CFE) approach coupled with several powerful stable reduction methods is proposed for the reduction of high order z-transfer functions. These methods include the advantages of stability preservation methods (SPM), such as Routh approximation, Routh Hurwitz array and stability equation method etc., with those of the method based on continued fraction expansions. The high order z-transfer functions are transformed in w-domain using bilinear transformation and the denominator of the reduced models are found in w-domain. The numerators of reduced order models are determined by matching the quotients of continued fraction expansions in w-domain. Finally, the reduced z-transfer functions are determined using reverse bilinear transformation. In this paper, combined features of SPM and CFE have been utilised to reduce the linear discrete time systems. To match the initial value of the original step response the bilinear transformation is applied in the high order z transfer function in such a way that the numerator and denominator polynomials of original system are separately expressed in w domain. And, to remove any steady error between the system and model responses, steady state values of original, and reduced systems are matched. The method proposed preserves the time domain and frequency domain characteristics and gives stable models for stable systems. An example illustrates the method.
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