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ISBN-10: 1634827422

ISBN-13: 9781634827423

Advances in arithmetic examine

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Hence, the minimum distance satisfies the inequality was: , . Formulas for calculating some principal statistics were also given. Some procedures for the smoothing and optimization of the Delaunay triangles were proposed. ,n. where Ai is the i-cell area, and Si is the total length of the line segments forming the individual cell i. Hence, the objective was ∑ , where Kelvin‟s parameters Ki of the individual cells are weighted with the areas Ai of the corresponding cells normalized with the average cell area ARVE/n.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] F. Aurenhammer, Voronoi diagrams-A survey of a fundamental geometric data structure, ACM Computing Surveys, V. 23 (1991), no. 3, 345-405. K. Bagi, Discussion of the paper “Tensorial form definitions of discrete mechanical quantities for granular assemblies” [M. Satake, Int. J. Solids and Structures 2004, 41(21), pp. 5775–5791] 2006, International Journal of Solids and Structures, V. 43 (2006), 2840–2844. M. de Berg, O. Cheong, M van Kreveld, and M.

For a known tessellation and a cell C, the authors defined the dihedral angle θe at edge e as the angle between the two facets of C sharing e: θe =  - arccos (nm), where n and m are the outward unit vectors normal to the two facets in C adjacent to e and () is the scalar product. The other angles to measure were the ones between two edges on a facet, which were referred to as interior or bond angles. These angles can be measured via the scalar product of the direction vectors of the adjacent edges.

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Advances in Mathematics Research, Volume 20


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