Mathematical Problems in Engineering

Research Article

Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization

Table 4

Relationship between vertices, slopes, and prevertices.
Polygon vertices (Figure 12)Slopes 𝛼 𝑛 Prevertices (Genetic Algorithm)
𝑤 1 = − 0 . 4 4 + 7 . 9 6 𝑖 𝛼 1 = − 0 . 0 9 3 9 𝑥 1 = 5 . 9 0 8 0 2 4
𝑤 2 = − 1 . 2 8 + 7 . 7 1 𝑖 𝛼 2 = − 0 . 0 9 3 9 𝑥 2 = 5 . 9 1 1 5 7 1
𝑤 3 = − 2 . 0 0 + 7 . 2 2 𝑖 𝛼 3 = − 0 . 0 9 3 9 𝑥 3 = 5 . 9 1 5 3 8 7
𝑤 4 = − 2 . 5 7 + 6 . 5 4 𝑖 𝛼 4 = − 0 . 0 9 3 9 𝑥 4 = 5 . 9 1 9 6 8 2
𝑤 5 = − 2 . 9 1 + 5 . 7 2 𝑖 𝛼 5 = − 0 . 0 9 3 9 𝑥 5 = 5 . 9 2 4 8 6 1
𝑤 6 = − 2 . 9 9 + 4 . 8 5 𝑖 𝛼 6 = − 0 . 0 9 3 9 𝑥 6 = 5 . 9 3 1 5 3 5
𝑤 7 = − 2 . 8 2 + 3 . 9 9 𝑖 𝛼 7 = − 0 . 0 9 3 9 𝑥 7 = 5 . 9 4 1 1 6 3
𝑤 8 = − 2 . 4 0 + 3 . 2 1 𝑖 𝛼 8 = − 0 . 0 2 3 3 𝑥 8 = 5 . 9 5 8 8 0 1
𝑤 9 = − 1 . 0 7 + 1 . 1 1 𝑖 𝛼 9 = 0 . 6 8 0 5 𝑥 9 = 6 . 5 1 9 1 7 7
𝑤 1 0 = − 5 . 9 7 + 1 . 1 1 𝑖 𝛼 1 0 = − 0 . 5 0 0 0 𝑥 1 0 = 6 . 8 6 6 0 8 1
𝑤 1 1 = − 5 . 9 7 + 0 . 0 0 𝑖 𝛼 1 1 = − 0 . 5 0 0 0 𝑥 1 1 = 6 . 8 6 6 0 8 2
𝑤 1 2 = 6 . 0 0 + 0 . 0 0 𝑖 𝛼 1 2 = − 0 . 5 0 0 0 𝑥 1 2 = 4 . 8 5 6 3 1 5
𝑤 1 3 = 6 . 0 0 + 4 . 0 0 𝑖 𝛼 1 3 = − 0 . 6 7 2 0 𝑥 1 3 = 4 . 8 5 6 6 9 3
𝑤 1 4 = 0 . 9 9 + 0 . 9 9 𝑖 𝛼 1 4 = 0 . 8 5 2 5 𝑥 1 4 = 5 . 1 6 6 3 9 9
𝑤 1 5 = 2 . 4 0 + 3 . 2 0 𝑖 𝛼 1 5 = − 0 . 0 2 3 3 𝑥 1 5 = 5 . 8 5 3 8 1 2
𝑤 1 6 = 2 . 8 1 + 3 . 9 8 𝑖 𝛼 1 6 = − 0 . 0 9 3 9 𝑥 1 6 = 5 . 8 7 1 3 3 2
𝑤 1 7 = 2 . 9 9 + 4 . 8 4 𝑖 𝛼 1 7 = − 0 . 0 9 3 9 𝑥 1 7 = 5 . 8 8 1 0 1 4
𝑤 1 8 = 2 . 9 0 + 5 . 7 2 𝑖 𝛼 1 8 = − 0 . 0 9 3 9 𝑥 1 8 = 5 . 8 8 7 7 0 4
𝑤 1 9 = 2 . 5 7 + 6 . 5 4 𝑖 𝛼 1 9 = − 0 . 0 9 3 9 𝑥 1 9 = 5 . 8 9 2 8 9 5
𝑤 2 0 = 2 . 0 1 + 7 . 2 2 𝑖 𝛼 2 0 = − 0 . 0 9 3 9 𝑥 2 0 = 5 . 8 9 7 1 9 8
𝑤 2 1 = 1 . 2 8 + 7 . 7 1 𝑖 𝛼 2 1 = − 0 . 0 9 3 9 𝑥 2 1 = 5 . 9 0 1 0 1 2
𝑤 2 2 = 0 . 4 3 + 7 . 9 6 𝑖 𝛼 2 2 = − 0 . 0 9 3 9 𝑥 2 2 = 5 . 9 0 4 5 5 9