Authors:Pei-Sen Li Pages: 1021 - 1038 Abstract: Abstract 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. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6472-0 Issue No:Vol. 33, No. 8 (2017)
Authors:Yongming Zhang Pages: 1039 - 1047 Abstract: Abstract Let Y be a smooth projective surface defined over an algebraically closed field k with char k ≠ 2, and let τ: X → Y be a double covering branched along a smooth divisor. We show that I X is stable with respect to τ*H if the tangent bundle I Y is semi-stable with respect to some ample line bundle H on Y. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6190-7 Issue No:Vol. 33, No. 8 (2017)
Authors:Jie Zhou; Jun Zhu; Liu Quan Sun Pages: 1048 - 1060 Abstract: Abstract 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. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6221-4 Issue No:Vol. 33, No. 8 (2017)
Authors:Tomasz Rybicki Pages: 1061 - 1072 Abstract: Abstract 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 C r -bisections of a Lie groupoid Γ of class C r , where 1 ≤ r ≤ ω, 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. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6125-3 Issue No:Vol. 33, No. 8 (2017)
Authors:Jerzy Jezierski Pages: 1073 - 1082 Abstract: Abstract We show for which (d, n) ∈ ℤ × ℕ there exists a smooth self-map f: S 2 → S 2 so that deg(f) = d and Fix(f n ) is a point. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6120-8 Issue No:Vol. 33, No. 8 (2017)
Authors:Jiao Chen Pages: 1083 - 1106 Abstract: Abstract 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 multi-parameter 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: $${T_m}f\left( {{x_1},{x_2},{x_3}} \right) = \frac{1}{{{{\left( {2\pi } \right)}^{{n_1} + {n_2} + {n_3}}}}}\int_{{\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}} {m\left( \xi \right)\widehat f} {e^{2\pi ix \cdot \xi }}d\xi $$ where \(x = \left( {{x_1},{x_2},{x_3}} \right) \in {\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}\) and \(\xi = \left( {{\xi _1},{\xi _2},{\xi _3}} \right) \in {\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}\) . One of our main results is the following: Assume that m(ξ) is a function on \({\mathbb{R}^{{n_1} + {n_2} + {n_3}}}\) satisfying \(\mathop {\sup }\limits_{j,k,l \in \mathbb{Z}} {\left\ {{m_{j,k,l}}} \right\ _{{W^{\left( {{s_1},{s_2},{s_3}} \right)}}}} < \infty \) with \(s_{i} > n_{i}(\frac{1}{p}-\frac{1}{2})\) for 1 ≤ i ≤ 3. Then T m is bounded from \({H^p}\left( {{\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}} \right)\) to \({H^p}\left( {{\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}} \right)\) for all 0 < p ≤ 1 and \(\left\ {{T_m}} \right\ {}_{{H^P} \to {H^P}} \lesssim \mathop {\sup }\limits_{j,k,l \in \mathbb{Z}} {\left\ {{m_{j,k,l}}} \right\ _{{W^{\left( {{s_1},{s_{2,}}{s_3}} \right)}}}}\) . Moreover, the smoothness assumption on s i for 1 ≤ i ≤ 3 is optimal. Here we have used the notations m j,k,l (ξ) = m(2 j ξ 1, 2 k ξ 2, 2 l ξ 3)Ψ(ξ 1)Ψ(ξ 2)Ψ(ξ 3) and Ψ(ξ i ) is a suitable cut-off function on \({\mathbb{R}^{{n_i}}}\) for 1 ≤ i ≤ 3, and \({W^{\left( {{s_1},{s_2},{s_3}} \right)}}\) is a three-parameter Sobolev space on \({\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}\) . Because the Fefferman criterion breaks down in three parameters or more, we consider the L p boundedness of the Littlewood–Paley square function of T m f to establish its boundedness on the multi-parameter Hardy spaces. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6526-3 Issue No:Vol. 33, No. 8 (2017)
Authors:Saber Omidi; Bijan Davvaz; Jian Ming Zhan Pages: 1107 - 1124 Abstract: Abstract 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. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6093-7 Issue No:Vol. 33, No. 8 (2017)
Authors:Tai Xiang Sun; Guang Wang Su; Hong Jian Xi; Xin Kong Pages: 1125 - 1130 Abstract: Abstract 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 x k ∈ T and a sequence of positive integers n 1 < n 2 < ··· such that lim k→∞ x k = x and lim k→∞ \(f^{n_{k}}\) (x k ) = 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 x ∈ T. (3) ∩ n=1 ∞ f n (T) = P(f), and ω(x, f) is a periodic orbit for every x ∈ T and map h: x → ω(x, f) (x ∈ T) is continuous. (4) Ω(x, f) is a periodic orbit for any x ∈ T. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6289-x Issue No:Vol. 33, No. 8 (2017)
Authors:Jian Hua Yin; Xiang Yu Dai Pages: 1131 - 1153 Abstract: Abstract Let S = (a 1, …, a m ; b 1, …, b n ), where a 1, …, a m and b 1, …, b n are two nonincreasing sequences of nonnegative integers. The pair S = (a 1, …, a m ; b 1, …, b n ) is said to be a bigraphic pair if there is a simple bipartite graph G = (X ∪ Y, E) such that a 1, …, a m and b 1, …, b n are the degrees of the vertices in X and Y, respectively. Let Z 3 be the cyclic group of order 3. Define σ(Z 3, m, n) to be the minimum integer k such that every bigraphic pair S = (a 1, …, a m ; b 1, …, b n ) with a m , b n ≥ 2 and σ(S) = a 1 + ⋯ + a m ≥ k has a Z 3-connected realization. For n = m, Yin [Discrete Math., 339, 2018—2026 (2016)] recently determined the values of σ(Z 3, m, m) for m ≥ 4. In this paper, we completely determine the values of σ(Z 3, m, n) for m ≥ n ≥ 4. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6380-3 Issue No:Vol. 33, No. 8 (2017)
Authors:Bing Mao Deng; De Gui Yang; Ming Liang Fang Pages: 1154 - 1162 Abstract: Abstract Let {f n } be a sequence of functions meromorphic in a domain D, let {h n } be a sequence of holomorphic functions in D, such that \({h_n}\left( z \right)\mathop \Rightarrow \limits^\chi h\left( z \right)\) , where h(z) ≢ 0 is holomorphic in D, and let k be a positive integer. If for each n ∈ ℕ+, f n (z) ≠ 0 and f n (k) − h n (z) has at most k distinct zeros (ignoring multiplicity) in D, then {f n } is normal in D. PubDate: 2017-08-01 DOI: 10.1007/s10114-017-6234-z Issue No:Vol. 33, No. 8 (2017)
Authors:Xia Zhang; Ming Liu Pages: 899 - 910 Abstract: Abstract In this paper, we first study the mean ergodicity of random linear operators using some techniques of measure theory and L 0-convex analysis. Then, based on this, we give a characterization for a complete random normed module to be mean ergodic. PubDate: 2017-07-01 DOI: 10.1007/s10114-017-6444-4 Issue No:Vol. 33, No. 7 (2017)
Authors:Ali Ben Amor; Tarek Kenzizi Pages: 981 - 995 Abstract: Abstract We establish conditions ensuring either existence or blow-up of nonnegative solutions for the heat equation generated by the Dirichlet fractional Laplacian perturbed by negative potentials on bounded sets. The elaborated theory is supplied by some examples. PubDate: 2017-07-01 DOI: 10.1007/s10114-017-6246-8 Issue No:Vol. 33, No. 7 (2017)
Authors:Hong Hai Liu Pages: 1011 - 1020 Abstract: Abstract In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H 1 to L 1, and prove variation, oscillation and λ-jump operators related to smooth truncations are bounded from H 1 to L 1. PubDate: 2017-07-01 DOI: 10.1007/s10114-017-5788-0 Issue No:Vol. 33, No. 7 (2017)
Authors:Rui Dong Wang; Xu Jian Huang Abstract: Abstract In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres. PubDate: 2017-07-20 DOI: 10.1007/s10114-017-6589-1
Authors:Jian Ping Zhang; Yun Zhang Li Abstract: Abstract For refinable function-based affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame (WNABF). Under the setting of reducing subspaces of L 2(ℝ d ), we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions. PubDate: 2017-07-20 DOI: 10.1007/s10114-017-6445-3
Authors:Pei Ma; Feng Quan Li; Yan Li Abstract: Abstract In this paper, we study the Pohozaev identity associated with a Hénon–Lane–Emden system involving the fractional Laplacian: $$\left\{ {\begin{array}{*{20}c} {( - \Delta )^s u = \left x \right ^a v^p ,} & {x \in \Omega ,} \\ {( - \Delta )^s v = \left x \right ^b u^q ,} & {x \in \Omega ,} \\ {u = v = 0,} & {x \in \mathbb{R}^n \backslash \Omega ,} \\ \end{array} } \right.$$ in a star-shaped and bounded domain Ω for s ∈ (0, 1). As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases. PubDate: 2017-07-20 DOI: 10.1007/s10114-017-6556-x
Authors:János Kollár; Johannes Nicaise; Chen Yang Xu Abstract: Abstract Given a family of Calabi–Yau varieties over the punctured disc or over the field of Laurent series, we show that, after a finite base change, the family can be extended across the origin while keeping the canonical class trivial. More generally, we prove similar extension results for families whose log-canonical class is semi-ample. We use these to show that the Berkovich and essential skeleta agree for smooth varieties over ℂ((t)) with semi-ample canonical class. PubDate: 2017-07-15 DOI: 10.1007/s10114-017-7048-8
Authors:Xin Ma; Ti Wei Zhao; Zhao Yong Huang Abstract: Abstract We introduce and study (pre)resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories. PubDate: 2017-07-15 DOI: 10.1007/s10114-017-6416-8
Authors:Youngsoo Seol Abstract: Abstract We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31, 433–451 (2015)]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes. PubDate: 2017-07-15 DOI: 10.1007/s10114-017-6433-7
Authors:Xing Xiao Li; Hong Ru Song Abstract: Abstract In this paper, we give a complete conformal classification of the regular space-like hypersurfaces in the de Sitter Space S 1 m+1 with parallel para-Blaschke tensors. PubDate: 2017-07-15 DOI: 10.1007/s10114-017-6208-1
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