6 papers
Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation
Yubin He
The classical Khintchine--JarnÃk Theorem provides elegant criteria for determining the Lebesgue measure and Hausdorff measure of sets of points approximated by rational points, wh…
A dimensional mass transference principle from balls to open sets and applications to dynamical Diophantine approximation
Yubin He
The mass transference principle of Beresnevich and Velani is a powerful mechanism for determining the Hausdorff dimension/measure of sets that arise naturally in Diophant…
Evaluating Hydro-Science and Engineering Knowledge of Large Language Models
Shiruo Hu, Wenbo Shan, Yingjia Li +16
Hydro-Science and Engineering (Hydro-SE) is a critical and irreplaceable domain that secures human water supply, generates clean hydropower energy, and mitigates flood and drought…
Shrinking Targets versus Recurrence: a brief survey
Yubin He, Bing Li, Sanju Velani
Let be a compact metric space and a measure preserving dynamical system. Furthermore, given a real, positive function , let and $ R(T,…
Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights
Yubin He
Under a reasonable decay assumption on the approximating function, we establish a zero-full law for the Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine f…
A unified approach to mass transference principle and large intersection property
Yubin He
The mass transference principle, discovered by Beresnevich and Velani [Ann Math (2), 2006], is a landmark result in Diophantine approximation that allows us to obtain the Hausdorff…