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and Applied Analysis 3 If ‖N(x) − N(y)‖ ≤ k ‖x − y‖, 0 < k < 1, then e 0 = f, 󵄩 󵄩 󵄩 󵄩 e 1 󵄩 󵄩 󵄩 󵄩 = 󵄩 󵄩 󵄩 󵄩 N (e 0 ) 󵄩 󵄩 󵄩 󵄩 ≤ k 󵄩 󵄩 󵄩 󵄩 e 0 󵄩 󵄩 󵄩 󵄩 , 󵄩 󵄩 󵄩 󵄩 e 2 󵄩 󵄩 󵄩 󵄩 = 󵄩 󵄩 󵄩 󵄩 N (e 0 + e 1 ) − N (e 0 ) 󵄩 󵄩 󵄩 󵄩 ≤ k 󵄩 󵄩 󵄩 󵄩 e 1 󵄩 󵄩 󵄩 󵄩 ≤ k 2 󵄩 󵄩 󵄩 󵄩 e 0 󵄩 󵄩 󵄩 󵄩 , 󵄩 󵄩 󵄩 󵄩 e 3 󵄩 󵄩 󵄩 󵄩 = 󵄩 󵄩(More)
Superhydrophobicity can arise from the ability of a submerged rough hydrophobic surface to trap air in its surface pores, and thereby reduce the contact area between the water and the frictional solid walls. A submerged surface can only remain superhydrophobic (SHP) as long as it retains the air in its pores. SHP surfaces have a short underwater life, and(More)
Superhydrophobic (SHP) surfaces are known for their drag-reducing attributes thanks to their ability to trap air in their surface pores and thereby reduce the contact between water and the frictional solid area. SHP surfaces are prone to failure under elevated pressures or because of air-layer dissolution into the surrounding water. Slippery liquid-infused(More)
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