We prove that the distribution of the Borel radii (indirect Borel points) and that of Borel radii (indirect Borel points) concerning the small functions of a meromorphic function are the same. Furthermore, some equivalent conclusions on the Borel radii (indirect Borel points) of meromorphic functions of order $0<\rho<\infty$ are established. This is a continuous work of Tsuji [4,5].

For a general one-dimensional random walk with state-dependent transition probabilities, we present weak limits of the empirical moments of conductance along the path of the random walk. In particular we obtain remarkably simple quenched convergences under random conductance model.

We prove that every projective kawamata log terminal pair with maximal Albanese dimension has a good minimal model. We also give an affirmative answer to Ueno’s problem on subvarieties of Abelian varieties.

In this paper, we establish some differential Harnack inequalities for positive solutions to the nonlinear heat equations with potentials evolving by the Bernhard List’s flow. Our theorems generalize Cao and Zhang’s results [1].

A complex hyperbolic triangle group is a group generated by three complex involutions fixing complex lines in complex hyperbolic space. In a previous paper~[3] we discussed complex hyperbolic triangle groups of type $(n,n,\infty;k)$ and proved that for $n \geq 29$ these groups are not discrete. In this paper we show that if $n \geq 22$, then complex hyperbolic triangle groups of type $(n,n,\infty;k)$ are not discrete and give a new list of non-discrete groups of type $(n,n,\infty;k)$.