Material selection summation

For the calculations of the optical properties of polymer films with embedded nanoparticles, two routes can be selected. In the exact route, the extinction cross sections Cact(v) of single particles are calculated. The calculated extinction spectra for single particles—or, better, a summation of various excitation spectra for a particle assembly—can be compared with the experimental spectra of the embedded nanoparticles. In the statistic route, an effective dielectric function e(v) is calculated from the dielectric function of the metal e(T) and of the polymer material po(v) by using a mixing formula, the so-called effective medium theory. The optical extinction spectra calculated from the effective dielectric functions by using the Fresnel formulas can be compared with the experimental spectra. 

Consider an industrial plant manufacturing a variety of products. The items are registered on a list under certain conventional names. Let L be this list, I (e L) be the name (address) of a product. In selected intervals, the production is balanced in money units let m, be the corresponding item for the /-th product. As negative product we can regard a raw material the corresponding nti is then negative. The summary production of product / in two subsequent intervals (m, and m]) is obtained by summation, thus m, + the increase in production per... 

Let a cylindrical bar, of a not necessarily circular cross-section, be fixed at one end, x = 0, and loaded at the other, x = 5,, by a distribution of external tractions that reduces to a single transverse force P (P, P2). The bar whose material is elastic, isotropic, homogeneous, and of a diatomic structure is referred to a rectangular coordinate system, x X2, Xo, with the x -axis coinciding with the axis of the bar (as the locus of the centroids of the cross-sections), and the plane x-j X2 selected as the plane of fixing. We wish to apply the numerals 1 and 2 in parentheses, (1) and (2), placed as superscripts, to denote the constituent media of the material of the bar the repeated indices, placed primarily as subscripts, indicate Einstein summation (e.g., e + 022 + 33) Within the framework... 

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