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 average) It can be used to study the weighted average of the form $(T^\alpha (\hbox {ln }T)^\beta)^{-1}\int _0^T h(t) \, dt.$ Finally, every frame can be written as a (multiple of a) average of two orthonormal bases for a larger Hilbert space. represents an average over rotations, of the Stein-Tomas restriction phenomenon. Convolution, Average Sampling, and a Calderon Resolution of the Identity for Shift-Invariant Spaces In previous work, under some assumptions, we specified a replacement rule which minimizes the long-run (expected) average cost per unit time and possesses control limit property. Fur-thermore, the limiting distribution of average cost of a portfolio of increasing life insurance for multiple-life status is studied. Rate of convergence for multiple change-points estimation of moving-average processes Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. Assuming Hull and White model for the interest rates, a closed-form formula for geometric-average options is derived. The average particle sizes and the silica contents of the nanocomposite particles were in the ranges from 120-330 nm and 15%-20%, respectively. the average relative error was only 4.73%, and the reaction constants were determined as Km = 0.0748 g/L, Ks = 7.961 g/L, kd = 9.358/min, k2 = 38.439/min, Ea = 64.826 kJ/mol, Ed = 80.031 kJ/mol in accordance with the proposed kinetic mode. The average particle size of Fe3O4 was 7.4 nm, and magnetic particles were well-dispersed. The relationship between the process parameters and the average diameter of polysulfone nanofibers was investigated. The average diameter and the diameter distribution of electrospinning nanofibers were measured experimentally by using scanning electron microscopy. The average particle sizes were 40-50 nm, and the size distributions were narrow. PS nanoparticles with smaller diameter such as a number-average diameter of 18.7 nm and better monodispersity were obtained since the dropped styrene amount was suitable under 20wt-% emulsifier amount and 3wt-% initiator amount based on the monomer. The number-average molecular weight of the soluble copolyimides measured by GPC was larger than 4.0 × 104, and the polydispersity index was higher than 1.5. The average apparent rate constants of the three antioxidants at 25°C are (1.34 ± 0.03) × 10-3 at pH 6.8, (1.20 ± 0.02) × 10-3 at pH 4.0 and (6.58 ± 0.02) × 10-3 mol·L-1·h-1 at pH 9.2, respectively. For the PEO samples with average molecular weights (Mn) ranging from 1.0 × 103 g/mol to 1.0 × 104 g/mol, the lateral perturbation from the AFM tip in the hard-tapping or nanoscratch modes could not induce the growth of the flat-on lamellae. The resulting average value of the Avrami exponent at n = 3.34 suggests that primary crystallization may correspond to a three-dimensional spherulitic growth.

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