Morris and Saxton used the method of containers to bound number n-vertex graphs with m edges containing no ℓ-cycles, hence girth more than ℓ. We consider a generalization r-uniform hypergraphs. The hypergraph H is minimum ℓ ≥ 2 such that there exist distinct vertices v 1 , … hyperedges e i + ∈ for all ≤ Letting N r ( n ) denote hypergraphs larger defining λ = ⌈ − ∕ ⌉ we show which tight when di...

In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of non-linear Hunter–Saxton equation. Firstly, operational matrices integration associated with are constructed by following strategy Chen Hsiao. The merged used to convert given problem into system algebraic equations that can be solved any classical method, such as Newt...

In the conventional weighted Gerchberg-Saxton (GS) algorithm, feedback is used to accelerate convergence. However, it will lead iteration divergence. To solve this issue, an adaptive GS algorithm proposed in paper. By replacing with our designed feedback, convergence can be ensured method. Compared traditional method, method improves peak signal-noise ratio of reconstructed image 4.8 dB on aver...