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By direct computing, we have (M hat{x},hat{y})={-1,0}), (hat {N}(hat{x},operatorname{dom}G)=N hat{x},operatorname{dom}G)={0}), hat{D}^G(hat{x},hat{y}) bigl y^ bigr)= left { textstylebegin{array}l@{quad}l} 0, & y^=0; emptyset, & mbox{else}, end{array}displaystyle right.
By direct computing, we have (hat{N}(hat{x},K =N hat{x},K =mathbb {R}_) and hat{D}^N hat{x},hat{y}) bigl y^ bigr)=D^N hat{x},hat{y}) bigl y^ bigr)= bigl{ x^in mathbb{R}mid x^leq y^ bigr}.
Therefore, the sum of two-hop influence propagation for every node in V′ is no more than n Δ 2 ( nΔ ) 4 = 1 n 3 Δ 2. By direct computing, we have the sum of (r+1 -hop influence pr+1 -hopon influencehan the sum of r-hopropagation propagatisn for any node i.
Conceptually, the simplest approach to the optimization problem described above is to solve it jointly at a central location by direct computing p C ≡ p C, 1 p C, 2 ⋯ p C, N ≡ arg min p ∑ i = 1 N M i p A i, (2).
Different from direct computing instantaneous frequencies ω p (t), p = 1,..., k, from the purely frequency modulated s pq (q is the iteration number of the p th times decomposition) like Equations (27) to (29), we can also have the following HT, for each PF component PF i (t), just as Equation (14): H ̃ i ( t ) = P π ∫ - ∞ ∞ P F i ( t ′ ) t - t ′ d t ′ (34).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com