A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable...A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable Hausdorff topological gyrogroup has a suitable set;moreover,it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.展开更多
In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannia...In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.展开更多
基金supported by Fujian Provincial Natural Science Foundation of China(2024J02022)the NSFC(11571158)+1 种基金supported by the NSFC(12071199)supported by the Young and middle-aged project in Fujian Province(JAT190397)。
文摘A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable Hausdorff topological gyrogroup has a suitable set;moreover,it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.
文摘In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.
基金Supported by National Science Foundation of China(30970090)China Postdoctoral Science Foundation Funded Project (20090450136)+2 种基金Innovation Foundation of Harbin Science and Technology Bureau(2010RFQXS043)the Research Program of Heilongjiang Education Bureau(11551377)Outstanding Young Scientist Foundation of Heilongjiang University
