In particular, if the dilation parameter is 21/3, and the lattice subgroup is sufficiently fine, then the "Mexican hat" wavelet, Le-L/2δ, generates a wavelet frame, for which the ratio of the optimal frame bounds is 1.0000 to four significant digits.
In this note it is shown that a necessary and sufficient condition for the existence of a P3-factorization of complete multipartite graph λKmn is (1) m≥3, (2) mn≡0 (mod 3) and (3) λ(m-1)n≡0(mod 4).
Given a simple graph G and a positive integer k, the induced matching k-partition problem asks whether there exists a k-partition (V1, V2, ..., Vk) of V(G) such that for each i(1≤i≤k), G[Vi] is 1-regular.
As the order is 1, the result here is simplified to that of first order differential equation.
The influence factors of the synthesis were discussed, and the best reaction conditions were found: the molar ratio of n-butyraldehyde to 1,2-propanediol is 1:1.5, the amount of catalyst used is 1.2% of feed stock, and the reaction time is 1.0 h.