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Acta Mathematica Sinica,Chinese Series
2017, Vol.33 Num.8
Online: 2017-08-15

1021 Pei-Sen LI
Nonlinear Branching Processes with Immigration
The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established.
2017 Vol. 33 (8): 1021-1038 [Abstract] ( 4 ) [HTML 1KB] [PDF 252KB] ( 24 )
1039 Yongming ZHANG
On the Stability of Tangent Bundle on Double Coverings
Let Y be a smooth projective surface defined over an algebraically closed field k with char k≠2, and let π:X → Y be a double covering branched along a smooth divisor. We show that TX is stable with respect to π*H if the tangent bundle TX is semi-stable with respect to some ample line bundle H on Y.
2017 Vol. 33 (8): 1039-1047 [Abstract] ( 2 ) [HTML 0KB] [PDF 211KB] ( 6 )
1048 Jie ZHOU, Jun ZHU, Liu Quan SUN
A Class of Box-Cox Transformation Models for Recurrent Event Data with a Terminal Event
In this article, we study a class of Box-Cox transformation models for recurrent event data in the presence of terminal event, which includes the proportional means models as special cases. Estimating equation approaches and the inverse probability weighting technique are used for estimation of the regression parameters. The asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed methods is examined through simulation studies, and an application to a heart failure study is presented to illustrate the proposed method.
2017 Vol. 33 (8): 1048-1060 [Abstract] ( 4 ) [HTML 0KB] [PDF 251KB] ( 8 )
1061 Tomasz RYBICKI
n-transitivity of Bisection Groups of a Lie Groupoid
The notion of n-transitivity can be carried over from groups of diffeomorphisms on a manifold M to groups of bisections of a Lie groupoid over M. The main theorem states that the n-transitivity is fulfilled for all n ∈ N by an arbitrary group of Cr-bisections of a Lie groupoid Γ of class Cr, where 1 ≤ rω, under mild conditions. For instance, the group of all bisections of any Lie groupoid and the group of all Lagrangian bisections of any symplectic groupoid are n-transitive in the sense of this theorem. In particular, if Γ is source connected for any arrow γ ∈ Γ, there is a bisection passing through γ.
2017 Vol. 33 (8): 1061-1072 [Abstract] ( 2 ) [HTML 0KB] [PDF 266KB] ( 7 )
1073 Jerzy JEZIERSKI
Self-maps of S2 Homotopic to a Smooth Map with a Single n-periodic Point
We show for which (d,n) ∈ Z×N there exists a smooth self-map f:S2S2 so that deg(f)=d and Fix(fn) is a point.
2017 Vol. 33 (8): 1073-1082 [Abstract] ( 2 ) [HTML 0KB] [PDF 220KB] ( 8 )
1083 Jiao CHEN
Hörmander Type Theorem for Fourier Multipliers with Optimal Smoothness on Hardy Spaces of Arbitrary Number of Parameters

The main purpose of this paper is to establish the Hörmander-Mihlin type theorem for Fourier multipliers with optimal smoothness on k-parameter Hardy spaces for k ≥ 3 using the multiparameter Littlewood-Paley theory. For the sake of convenience and simplicity, we only consider the case k=3, and the method works for all the cases k ≥ 3:
Tmf(x1, x2, x3)=(1)/((2π)n1+n2+n3)∫Rn1×Rn2×Rn3 m(ξ)f(ξ)e2πix·ξ
where x=(x1, x2, x3) ∈ Rn1×Rn2×Rn3 and ξ=(ξ1, ξ2, ξ3) ∈ Rn1×Rn2×Rn3. One of our main results is the following:
Assume that m(ξ) is a function on Rn1×Rn2×Rn3 satisfying
||mj,k,l||W (s1,s2,s3) < ∞
with si > ni(1/p -1/2) for 1 ≤ i ≤ 3. Then Tm is bounded from Hp(Rn1×Rn2×Rn3) to Hp(Rn1×Rn2×Rn3) for all 0 < p ≤ 1 and
||Tm HpHp ≤ ||mj,k,l||W (s1,s2,s3)
Moreover, the smoothness assumption on si for 1 ≤ i ≤ 3 is optimal. Here we have used the notations mj,k,l(ξ)=m(2jξ1, 2kξ2, 2lξ3)Ψ(ξ1)Ψ(ξ2)Ψ(ξ3) and Ψ(ξi) is a suitable cut-off function on Rni for 1 ≤ i ≤ 3, and W(s1,s2,s3) is a three-parameter Sobolev space on Rn1×Rn2×Rn3.
Because the Fefferman criterion breaks down in three parameters or more, we consider the Lp boundedness of the Littlewood-Paley square function of Tmf to establish its boundedness on the multi-parameter Hardy spaces.

2017 Vol. 33 (8): 1083-1106 [Abstract] ( 5 ) [HTML 1KB] [PDF 352KB] ( 11 )
1107 Saber OMIDI, Bijan DAVVAZ, Jian Ming ZHAN
An Investigation on Ordered Algebraic Hyperstructures
In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.
2017 Vol. 33 (8): 1107-1124 [Abstract] ( 2 ) [HTML 0KB] [PDF 237KB] ( 7 )
1125 Tai Xiang, SUN Guang Wang SU, Hong Jian XI, Xin KONG
Equicontinuity of Maps on a Dendrite with Finite Branch Points
Let (T,d) be a dendrite with finite branch points and f be a continuous map from T to T.Denote by ω(x,f) and P (f) the ω-limit set of x under f and the set of periodic points of f,respectively.Write Ω(x,f)={y|there exist a sequence of points xkT and a sequence of positive integers n1 < n2 < … such that limk→∞xk=x and limk→∞ fnk (xk)=y}.In this paper,we show that the following statements are equivalent:(1) f is equicontinuous.(2)ω(x,f)=Ω(x,f) for any xT.(3)∩ n=1 f n (T)=P (f),and ω(x,f) is a periodic orbit for every xT and map h:xω(x,f)(xT) is continuous.(4)Ω(x,f) is a periodic orbit for any xT.
2017 Vol. 33 (8): 1125-1130 [Abstract] ( 3 ) [HTML 0KB] [PDF 183KB] ( 5 )
1131 Jian Hua YIN, Xiang Yu DAI
Solution to an Extremal Problem on Bigraphic Pairs with a Z3-connected Realization
Let S=(a1,...,am; b1,...,bn), where a1,...,am and b1,...,bn are two nonincreasing sequences of nonnegative integers. The pair S=(a1,...,am; b1,...,bn) is said to be a bigraphic pair if there is a simple bipartite graph G=(XY, E) such that a1,...,am and b1,...,bn are the degrees of the vertices in X and Y, respectively. Let Z3 be the cyclic group of order 3. Define σ(Z3, m, n) to be the minimum integer k such that every bigraphic pair S=(a1,...,am; b1,...,bn) with am, bn ≥ 2 and σ(S)=a1 +... + amk has a Z3-connected realization. For n=m, Yin[Discrete Math., 339, 2018-2026 (2016)] recently determined the values of σ(Z3, m, m) for m ≥ 4. In this paper, we completely determine the values of σ(Z3, m, n) for m n ≥ 4.
2017 Vol. 33 (8): 1131-1153 [Abstract] ( 2 ) [HTML 0KB] [PDF 380KB] ( 7 )
1154 Bing Mao DENG, De Gui YANG, Ming Liang FANG
Normality Concerning the Sequence of Functions

Let{fn} be a sequence of functions meromorphic in a domain D, let {hn} be a sequence of holomorphic functions in D, such that hn(z)h(z), where h(z)≠ 0 is holomorphic in D, and let k be a positive integer. If for each n ∈ N+, fn(z)≠0 and fn(k)(z)-hn(z) has at most k distinct zeros (ignoring multiplicity) in D, then {fn} is normal in D.

2017 Vol. 33 (8): 1154-1162 [Abstract] ( 3 ) [HTML 1KB] [PDF 200KB] ( 15 )
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