Chiu, C. H., Wang, Y. T., Walther, B. A. & Chao, A. An improved nonparametric lower bound of species richness via a modified good-turing frequency formula.
Furthermore, we improve the best known solutions on 60 out of 100 and improve the lower bound on all 100 instances from the literature.
In this paper we improve the lower bound of α to lower the condition of C1 linearization for planar contractions.
In addition, we give an example for three players that improves the lower bound on the (unrestricted) price of stability to 1.571.
(1999) provided a small table of lower bounds for the maximum number of mutually orthogonal frequency squares of type F(n;λ) (HSS Table), and posed the following research problem: Improve the lower bound for the entries in HSS Table.
In this article we improve the lower bound on the maximum nonlinearity of 1-resilient Boolean functions, for n even, by proposing a method of constructing this class of functions attaining the best nonlinearity currently known.
These observations lead to the problem of improving the lower bound for (Gamma_{3}), in comparison with (1), so that it can supplement Theorem 2.
One can easily see that the value of in Table 1 does not improve the lower bound in (1.35) due to Hall, but the the approach that we used is simple and depends only on a well-known Wirtinger-type inequality and the asymptotic formulas of the moments.
