Wan, Xin
Published in
Acta Mathematica Sinica, English Series

We prove an anticyclotomic Iwasawa main conjecture proposed by Perrin-Riou for Heegner points for semi-stable elliptic curves E over a quadratic imaginary field K satisfying a certain generalized Heegner hypothesis, at an ordinary prime p. It states that the square of the index of the anticyclotomic family of Heegner points in E equals the characte...

Wei, Da Sheng
Published in
Acta Mathematica Sinica, English Series

Let X be a toric variety over a number field k with k̅[X]× = k̅×. Let W ⊂ X be a closed subset of codimension at least 2. We prove that X \ W satisfies strong approximation with algebraic Brauer-Manin obstruction.

Abreu-Blaya, Ricardo Bory-Reyes, Juan Herrera-Peláez, Marcos Antonio Sigarreta-Almira, José María
Published in
Acta Mathematica Sinica, English Series

The paper provides integral representations for solutions to a certain first order partial differential equation natural arising in the factorization of the Lamé—Navier system with the help of Clifford analysis techniques. These representations look like in spirit to the Borel—Pompeiu and Cauchy integral formulas both in three and higher dimensiona...

Zhang, Dong Han Lu, You Zhang, Sheng Gui
Published in
Acta Mathematica Sinica, English Series

Pilsniak and Woźniak put forward the concept of neighbor sum distinguishing (NSD) total coloring and conjectured that any graph with maximum degree Δ admits an NSD total (Δ + 3)-coloring in 2015. In 2016, Qu et al. showed that the list version of the conjecture holds for any planar graph with Δ ≥ 13. In this paper, we prove that any planar graph wi...

Charak, Kuldeep Singh Laine, Ilpo
Published in
Acta Mathematica Sinica, English Series

This is a corrigendum to our paper, “On a class of prime entire functions”, published in Acta Math. Sin., Engl. Ser., 25, 1647–1652 (2009).

Yin, Hong Yan Zhou, Da Zhang, Xing An
Published in
Acta Mathematica Sinica, English Series

In this paper, we investigate the isolated closed orbits of two types of cubic vector fields in ℝ3 by using the idea of central projection transformation, which sets up a bridge connecting the vector field X (x) in ℝ3 with the planar vector fields. We have proved that the cubic vector field in ℝ3 can have two isolated closed orbits or one closed or...

Liao, Gui Li Liu, Qi Meng Zhang, Rong Mao
Published in
Acta Mathematica Sinica, English Series

A self-weighted quantile procedure is proposed to study the inference for a spatial unilateral autoregressive model with independent and identically distributed innovations belonging to the domain of attraction of a stable law with index of stability α, α ∈ (0, 2]. It is shown that when the model is stationary, the self-weighted quantile estimate o...

Doumas, Aristides V. Papanicolaou, Vassilis G.
Published in
Acta Mathematica Sinica, English Series

A collector samples coupons with replacement from a pool containing g uniform groups of coupons, where “uniform group ” means that all coupons in the group are equally likely to occur (while coupons of different groups have different probabilities to occur). For each j = 1,…, g, let Tj be the number of trials needed to detect Group j, namely to col...

Liao, Jun Liu, He Guo Xu, Xing Zhong Zhang, Ji Ping
Published in
Acta Mathematica Sinica, English Series

The aim of this paper is to determine the structure and to establish the isomorphic invariant of the finitely generated nilpotent group G of infinite cyclic commutator subgroup. Using the structure and invariant of the group which is the central extension of a cyclic group by a free abelian group of finite rank of infinite cyclic center, we provide...

Luo, Xiao Fang Nie, Xiao Xiao Yin, Jian Dong
Published in
Acta Mathematica Sinica, English Series

In this article, the authors introduce the concept of shadowable points for set-valued dynamical systems, the pointwise version of the shadowing property, and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable; every chain transitive set-valued dynamical system has either the shadowi...