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 Chinese Annals of Mathematics, Series B   [SJR: 0.445]   [H-I: 25]   [0 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 0252-9599 - ISSN (Online) 1860-6261    Published by Springer-Verlag  [2355 journals]
• A nontrivial homotopy element of order p 2 detected by the classical Adams
spectral sequence
• Authors: Hao Zhao; Linan Zhong
Pages: 1 - 8
Abstract: Abstract Let p be an odd prime. The authors detect a nontrivial element ã p of order p2 in the stable homotopy groups of spheres by the classical Adams spectral sequence. It is represented by $$a_0^{p - 2} h_1 \in Ext_A^{p - 1,pq + p - 2} (\mathbb{Z}/p,\mathbb{Z}/p)$$ in the E2-term of the ASS and meanwhile p · ã p is the first periodic element α p .
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1046-8
Issue No: Vol. 39, No. 1 (2018)

• A boundary Schwarz lemma for holomorphic mappings on the polydisc
• Authors: Yang Liu; Zhihua Chen; Yifei Pan
Pages: 9 - 16
Abstract: Abstract The authors prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions. For the special case of one complex variable, the obtained results give the classic boundary Schwarz lemma.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1047-7
Issue No: Vol. 39, No. 1 (2018)

• The iteration formulae of the Maslov-type index theory in weak symplectic
Hilbert space
• Authors: Li Wu; Chaofeng Zhu
Pages: 17 - 32
Abstract: Abstract The authors prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space. Then a direct proof of the iteration formulae for the Maslov-type indices of symplectic paths is given.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1048-6
Issue No: Vol. 39, No. 1 (2018)

• On a vector version of a fundamental Lemma of J. L. Lions
• Authors: Philippe G. Ciarlet; Maria Malin; Cristinel Mardare
Pages: 33 - 46
Abstract: Abstract Let Ω be a bounded and connected open subset of ℝ N with a Lipschitz-continuous boundary, the set Ω being locally on the same side of ∂Ω. A vector version of a fundamental lemma of J. L. Lions, due to C. Amrouche, the first author, L. Gratie and S. Kesavan, asserts that any vector field v = (ui) ∈ (D′(Ω)) N , such that all the components $$\frac{1}{2}({\partial _j}{v_i} + {\partial _i}{v_j})$$ , 1 ≤ i, j ≤ N, of its symmetrized gradient matrix field are in the space H−1(Ω), is in effect in the space (L2(Ω)) N . The objective of this paper is to show that this vector version of J. L. Lions lemma is equivalent to a certain number of other properties of interest by themselves. These include in particular a vector version of a well-known inequality due to J. Nečas, weak versions of the classical Donati and Saint-Venant compatibility conditions for a matrix field to be the symmetrized gradient matrix field of a vector field, or a natural vector version of a fundamental surjectivity property of the divergence operator.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1049-5
Issue No: Vol. 39, No. 1 (2018)

• Homological epimorphisms, compactly generated t -structures and
Gorenstein-projective modules
• Authors: Nan Gao; Xiaojing Xu
Pages: 47 - 58
Abstract: Abstract The aim of this paper is two-fold. Given a recollement (T′, T, T″, i*, i*, i!, j!, j*, j*), where T′, T, T″ are triangulated categories with small coproducts and T is compactly generated. First, the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i* preserves compact objects. As a con-sequence, given a ladder (T′, T, T″, T, T′) of height 2, then the certain BBD-induction of compactly generated t-structures is compactly generated. The authors apply them to the recollements induced by homological ring epimorphisms. This is the first part of their work. Given a recollement (D(B-Mod),D(A-Mod),D(C-Mod), i*, i*, i!, j!, j*, j*) induced by a homological ring epimorphism, the last aim of this work is to show that if A is Gorenstein, A B has finite projective dimension and j! restricts to D b (C-mod), then this recollement induces an unbounded ladder (B-Gproj,A-Gproj, C-Gproj) of stable categories of finitely generated Gorenstein-projective modules. Some examples are described.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1050-z
Issue No: Vol. 39, No. 1 (2018)

• Finite p -groups with few non-major k -maximal subgroups
• Authors: Boyan Wei; Haipeng Qu; Yanfeng Luo
Pages: 59 - 68
Abstract: Abstract A subgroup of index p k of a finite p-group G is called a k-maximal subgroup of G. Denote by d(G) the number of elements in a minimal generator-system of G and by δ k (G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G. In this paper, the authors classify the finite p-groups with δd(G)(G) ≤ p2 and δd(G)−1(G) = 0, respectively.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1051-y
Issue No: Vol. 39, No. 1 (2018)

• Exponential convergence to time-periodic viscosity solutions in
time-periodic Hamilton-Jacobi equations
• Authors: Kaizhi Wang
Pages: 69 - 82
Abstract: Abstract Consider the Cauchy problem of a time-periodic Hamilton-Jacobi equation on a closed manifold, where the Hamiltonian satisfies the condition: The Aubry set of the corresponding Hamiltonian system consists of one hyperbolic 1-periodic orbit. It is proved that the unique viscosity solution of Cauchy problem converges exponentially fast to a 1-periodic viscosity solution of the Hamilton-Jacobi equation as the time tends to infinity.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1052-x
Issue No: Vol. 39, No. 1 (2018)

• Equivalent conditions of complete convergence and complete moment
convergence for END random variables
• Authors: Aiting Shen; Mei Yao; Benqiong Xiao
Pages: 83 - 96
Abstract: Abstract In this paper, the complete convergence and the complete moment convergence for extended negatively dependent (END, in short) random variables without identical distribution are investigated. Under some suitable conditions, the equivalence between the moment of random variables and the complete convergence is established. In addition, the equivalence between the moment of random variables and the complete moment convergence is also proved. As applications, the Marcinkiewicz-Zygmund-type strong law of large numbers and the Baum-Katz-type result for END random variables are established. The results obtained in this paper extend the corresponding ones for independent random variables and some dependent random variables.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1053-9
Issue No: Vol. 39, No. 1 (2018)

• New homogeneous Einstein metrics on SO(7)/ T
• Authors: Yu Wang; Tianzeng Li; Guosong Zhao
Pages: 97 - 110
Abstract: Abstract The authors compute non-zero structure constants of the full flag manifold M = SO(7)/T with nine isotropy summands, then construct the Einstein equations. With the help of computer they get all the forty-eight positive solutions (up to a scale ) for SO(7)/T, up to isometry there are only five G-invariant Einstein metrics, of which one is Kähler Einstein metric and four are non-Kähler Einstein metrics.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1054-8
Issue No: Vol. 39, No. 1 (2018)

• Nongeneric bifurcations near a nontransversal heterodimensional cycle
• Authors: Xingbo Liu; Xiaofei Wang; Ting Wang
Pages: 111 - 128
Abstract: Abstract In this paper bifurcations of heterodimensional cycles with highly degenerate conditions are studied in three dimensional vector fields, where a nontransversal intersection between the two-dimensional manifolds of the saddle equilibria occurs. By setting up local moving frame systems in some tubular neighborhood of unperturbed heterodimensional cycles, the authors construct a Poincaré return map under the nongeneric conditions and further obtain the bifurcation equations. By means of the bifurcation equations, the authors show that different bifurcation surfaces exhibit variety and complexity of the bifurcation of degenerate heterodimensional cycles. Moreover, an example is given to show the existence of a nontransversal heterodimensional cycle with one orbit flip in three dimensional system.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1055-7
Issue No: Vol. 39, No. 1 (2018)

• Quenching phenomenon for a parabolic MEMS equation
• Authors: Qi Wang
Pages: 129 - 144
Abstract: Abstract This paper deals with the electrostatic MEMS-device parabolic equation $${u_t} - \Delta u = \frac{{\lambda f(x)}}{{{{(1 - u)}^p}}}$$ in a bounded domain Ω of ℝ N , with Dirichlet boundary condition, an initial condition u0(x) ∈ [0, 1) and a nonnegative profile f, where λ > 0, p > 1. The study is motivated by a simplified micro-electromechanical system (MEMS for short) device model. In this paper, the author first gives an asymptotic behavior of the quenching time T* for the solution u to the parabolic problem with zero initial data. Secondly, the author investigates when the solution u will quench, with general λ, u0(x). Finally, a global existence in the MEMS modeling is shown.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1056-6
Issue No: Vol. 39, No. 1 (2018)

• Approximate solution of the Kuramoto-Shivashinsky equation on an unbounded
domain
• Authors: Wael W. Mohammed
Pages: 145 - 162
Abstract: Abstract The main goal of this paper is to approximate the Kuramoto-Shivashinsky (K-S for short) equation on an unbounded domain near a change of bifurcation, where a band of dominant pattern is changing stability. This leads to a slow modulation of the dominant pattern. Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation, which is called the Ginzburg-Landau (G-L for short) equation, for the amplitudes of the dominating modes.
PubDate: 2018-01-01
DOI: 10.1007/s11401-018-1057-5
Issue No: Vol. 39, No. 1 (2018)

• Embedded surfaces for symplectic circle actions
• Authors: Yunhyung Cho; Min Kyu Kim; Dong Youp Suh
Pages: 1197 - 1212
Abstract: Abstract The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precisely, it is shown that (1) if (M, ω) admits a Hamiltonian S 1-action, then there exists a two-sphere S in M with positive symplectic area satisfying ‹c 1(M, ω), [S]› > 0, and (2) if the action is non-Hamiltonian, then there exists an S 1-invariant symplectic 2-torus T in (M, ω) such that ‹c 1(M, ω), [T]› = 0. As applications, the authors give a very simple proof of the following well-known theorem which was proved by Atiyah-Bott, Lupton-Oprea, and Ono: Suppose that (M, ω) is a smooth closed symplectic manifold satisfying c 1(M, ω) = λ·[ω] for some λ ∈ R and G is a compact connected Lie group acting effectively on M preserving ω. Then (1) if λ < 0, then G must be trivial, (2) if λ = 0, then the G-action is non-Hamiltonian, and (3) if λ > 0, then the G-action is Hamiltonian.
PubDate: 2017-11-01
DOI: 10.1007/s11401-017-1031-7
Issue No: Vol. 38, No. 6 (2017)

• The Betti numbers of real toric varieties associated to Weyl chambers of
type B
• Authors: Suyoung Choi; Boram Park; Hanchul Park
Pages: 1213 - 1222
Abstract: Abstract The authors compute the (rational) Betti number of real toric varieties associated to Weyl chambers of type B, and furthermore show that their integral cohomology is p-torsion free for all odd primes p.
PubDate: 2017-11-01
DOI: 10.1007/s11401-017-1032-6
Issue No: Vol. 38, No. 6 (2017)

• Torsion in the cohomology of torus orbifolds
• Authors: Hideya Kuwata; Mikiya Masuda; Haozhi Zeng
Pages: 1247 - 1268
Abstract: Abstract The authors study torsion in the integral cohomology of a certain family of 2n-dimensional orbifolds X with actions of the n-dimensional compact torus. Compact simplicial toric varieties are in our family. For a prime number p, the authors find a necessary condition for the integral cohomology of X to have no p-torsion. Then it is proved that the necessary condition is sufficient in some cases. The authors also give an example of X which shows that the necessary condition is not sufficient in general.
PubDate: 2017-11-01
DOI: 10.1007/s11401-017-1034-4
Issue No: Vol. 38, No. 6 (2017)

• Virtual braids, virtual Temperley-Lieb algebra and f -polynomial
• Authors: Zhiguo Li; Fengchun Lei; Jingyan Li
Pages: 1275 - 1286
Abstract: Abstract The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra, which is an approach similar to Jones’s original construction.
PubDate: 2017-11-01
DOI: 10.1007/s11401-017-1036-2
Issue No: Vol. 38, No. 6 (2017)

• Topology of moment-angle manifolds arising from flag nestohedra
• Authors: Ivan Limonchenko
Pages: 1287 - 1302
Abstract: Abstract The author constructs a family of manifolds, one for each n ≥ 2, having a nontrivial Massey n-product in their cohomology for any given n. These manifolds turn out to be smooth closed 2-connected manifolds with a compact torus Tm-action called moment-angle manifolds Z P , whose orbit spaces are simple n-dimensional polytopes P obtained from an n-cube by a sequence of truncations of faces of codimension 2 only (2-truncated cubes). Moreover, the polytopes P are flag nestohedra but not graph-associahedra. The author also describes the numbers β −i,2(i+1)(Q) for an associahedron Q in terms of its graph structure and relates it to the structure of the loop homology (Pontryagin algebra) H *(ΩZ Q ), and then studies higher Massey products in H *(Z Q ) for a graph-associahedron Q.
PubDate: 2017-11-01
DOI: 10.1007/s11401-017-1037-1
Issue No: Vol. 38, No. 6 (2017)

• Buchstaber invariants of universal complexes
• Authors: Yi Sun
Pages: 1335 - 1344
Abstract: Abstract Davis and Januszkiewicz introduced (real and complex) universal complexes to give an equivalent definition of characteristic maps of simple polytopes, which now can be seen as “colorings”. The author derives an equivalent definition of Buchstaber invariants of a simplicial complex K, then interprets the difference of the real and complex Buchstaber invariants of K as the obstruction to liftings of nondegenerate simplicial maps from K to the real universal complex or the complex universal complex. It was proved by Ayzenberg that real universal complexes can not be nondegenerately mapped into complex universal complexes when dimension is 3. This paper presents that there is a nondegenerate map from 3-dimensional real universal complex to 4-dimensional complex universal complex.
PubDate: 2017-11-01
DOI: 10.1007/s11401-017-1041-5
Issue No: Vol. 38, No. 6 (2017)

• On the equivalence of integral T k -cohomology Chern numbers and T k - K
-theoretic Chern numbers
• Authors: Wei Wang
Pages: 1353 - 1364
Abstract: Abstract This paper mainly deals with the question of equivalence between equivariant cohomology Chern numbers and equivariant K-theoretic Chern numbers when the transformation group is a torus. By using the equivariant Riemann-Roch relation of Atiyah-Hirzebruch type, it is proved that the vanishing of equivariant cohomology Chern numbers is equivalent to the vanishing of equivariant K-theoretic Chern numbers.
PubDate: 2017-11-01
DOI: 10.1007/s11401-017-1043-3
Issue No: Vol. 38, No. 6 (2017)

• Difference cochains and Reidemeister traces
• Authors: Baoqun Zhang; Xuezhi Zhao
Pages: 1365 - 1372
Abstract: Abstract The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps, and find out a relation involving these two invariants. As an application, an inductive formula of the Reidemeister traces for self-maps on a kind of CW-complex, including spherical manifolds is obtained.
PubDate: 2017-11-01
DOI: 10.1007/s11401-017-1044-2
Issue No: Vol. 38, No. 6 (2017)

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