Download Advances in Mathematics Research, Volume 20 PDF

ISBN-10: 1634827422

ISBN-13: 9781634827423

Advances in arithmetic study

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30] V. A. Luchnikov, M. L. Gavrilova, N. N. Medvedev, and V. P. Voloshin. The Voronoi– Delaunay approach for the free volume analysis of a packing of balls in a cylindrical container. Future Generation Computer Systems, V. 18 (2002), 673-679. [31] J. Mościński, M. Bargiel, Z. A. Rycerz, and P. W. M. Jacobs, The Force-Biased Algorithm for the Irregular Close Packing of Equal Hard Spheres, Molecular Simulation, V. 3 (1989), no. 4, 201-212. [32] R. Y. Yang, R. P. Zou, and A. B. Yu, Voronoi tessellation of the packing of fine uniform spheres, Physical Review E, V.

5 for different pore size variation coefficients. 5, the Laguerre–Voronoi approach gave results, which are closer to the real ones. , [38] was the estimation of the variations in the mechanical behavior of Voronoi closed-cell foams of low relative density as functions of their microstructure. The authors employed intermediate cases between regular structures and random structures using a finite perturbation. New laws were proposed in order to approximate the macroscopic mechanical behavior of Voronoi closed-cell foams under uniaxial tension and compression.

Relation with Laplace’s Transform Preliminary Background The relation between Z-transform and Laplace’s transform is provided by the identity z  e sT , as a result of the equality (  (t ) denotes the Dirac delta distribution or generalized function and holds for Laplace’s transform) 44 Jumarie Guy  L (t  nT )  e  st  (t  nT )dt  e nsT . 0 We then have the equality T F (e sT )   e  snT f (nT )T , k 0 therefore, on setting and (n  1)T  nT  dt , lim TF (e sT )  L f (t ) . T 0 Application to Fractional Difference For small T , one has the approximation (1  z 1 )  s  T  , z  e sT therefore the expected equality  F( ) (e sT )    lim   T  T 0   s  L f (t ) .

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