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On nulls of perturbed Fredholm operators and degenerate homoclinic bifurcations

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Science china mathematics 2004年第4期47卷 617-627页

作者： ZHANG WeinianDepartment of mathematics, sichuan university, chengdu 610064, china Department of mathematics Sichuan University Chengdu China

It is known that small perturbations of a Fredholm operatorL have nulls of dimension not larger than dimN(L). In this paper for any given positive integer κ ? dimN(L) we prove that there is a perturbation ofL which has an exactly κ-dimensional null. Actually, our proof gives a construction of the perturbation. We further apply our result to concrete examples of differential equations with degenerate homoclinic orbits, showing how many independent homoclinic orbits can be bifurcated from a perturbation.

关键词： Fredholm operator, perturbation, dimension, decomposition, degenerate homoclinic bifurcation.

ON THE SPACES OF THE MAXIMAL POINTS

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Chinese Annals of mathematics,Series B 2003年第3期24卷 303-308页

作者： LIANG JIHUA LIU YINGMING Institute of mathematics, sichuan university, chengdu 610064, china. Institute of mathematics, sichuan university, chengdu 610064, china. Institute of mathematics Sichuan University Chengdu 610064 China

For a continuous domain D, some characterization that the convex powerdomain CD is adomain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it isproved that the set of the maximal points Max(CD) of CD with the relative Scott topology ishomeomorphic to the set of all Scott compact subsets of Max(D) with the topology induced bythe Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.

关键词： Convex powerdomain Maximal points Hausdorff metric

APPLICATIONS OF THE THEORY OF CAMINA GROUPS

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Chinese Annals of mathematics,Series B 1999年第1期20卷 39-50页

作者： REN YONGCAI(Department of mathematics,sichuan Union university,chengdu 610064,china) Department of mathematics Sichuan Union University Chengdu 610064 China

In this papert the author first gives a conjugacy-class version of Camina hypotheses andthen applys the Camina group theory to discussing two classes of finite groups.

关键词： Camina groups Applications Characters

TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES

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Chinese Annals of mathematics,Series B 2002年第3期23卷 385-396页

作者： CAO GUANGFU Department of mathematics, sichuan university, chengdu 610064, china. Department of mathematics Sichuan University Chengdu 610064 China

The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are computed. In addition, the author proves that the spectra of Toeplitz operators with C^1-symbols are always connected, and discusses the algebraic prop-erties of Toeplitz *** particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and Tψ^* = Tψ^- if and only if Tψ is a scalar operator.

关键词： Dirichlet space Toeplitz operator Toeplitz algebra

Uniform asymptotic stability in functional differential equations with infinite delay

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Chinese Science Bulletin 1998年第12期43卷 1000-1003页

作者： XU Anshi Department of mathematics, sichuan university, chengdu 610064, china Department of mathematics Sichuan University Chengdu China

The fading memory space is used as phace space, and Liapunov methods are used to give conditions ensuring that the zero solution of functional differential equations with infinite delay is uniformly asymptotically sta... 详细信息

关键词： functional differential equation integral-differential equation fading memory space uniform asymptotic stalility.

Additive characters and orthogonal systems of polynomials in several indeterminates over residue class rings

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Chinese Science Bulletin 1998年第4期43卷 275-277页

作者： HONG Shaofang Department of mathematics, sichuan university, chengdu 610064, china Department of Matherrratics Sichuan University Chcngdu China

Let m, n and k be positive integers, m>1 and k≤n . Let Z m =Z/ m Z denote the residue class ring modulo m . Let Z denote the group of additive characters of ring Z m , x 0 denote the identity of Z . A necessary and sufficient condition for the system f\-1, ..., f\-k∈ Z m [ x\-1, ..., x\-n ] to be orthogonal is given: for all additive characters ψ 1, ..., ψ k ∈Z with ψ i≠x 0 for some i, 1≤i≤k, ∑(c\-1, ..., c\-n)∈ Z n m ψ(f\-1(c\-1, ..., c\-n))...ψ k(f\-k(c\-1, ..., c\-n))=0. As corollaries, the result of Shiue_Sun_Zhang and the result of Sun are obtained.

关键词： orthogonal system additive character permutation polynomial Jacobi matrix.

Variational minimizing parabolic and hyperbolic orbits for the restricted 3-body problems Dedicated to my Teacher Professor Yang Wannian on the Occasion of his 75th Birthday

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Science china mathematics 2012年第4期55卷 721-725页

作者： ZHANG ShiQing Department of mathematics and Yangtze Center of mathematics,sichuan university,chengdu 610064,china Department of mathematics and Yangtze Center of mathematics Sichuan University Chengdu China

Using variational minimizing methods,we prove the existence of the odd symmetric parabolic or hyperbolic orbit for the restricted 3-body problems with weak forces.

关键词： restricted 3-body problems variational minimizers odd parabolic orbits odd hyperbolic orbits

Cardinal invariants associated with Fubini product of ideals

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Science china mathematics 2010年第2期53卷 425-430页

作者： HONG JianYong & ZHANG ShuGuo College of mathematics, sichuan university, chengdu 610064, china College of mathematics Sichuan University Chengdu China

We prove some results displaying the relationship between Fubini product of ideals and its factor ideals, and study a partial order using the cardinal invariant of the continuum. The relationships among transitive car... 详细信息

关键词： cardinal invariant continuum Fubini product

Completely regular paracompact reflection of locales

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Science china mathematics 2006年第6期49卷 820-826页

作者： HE Wei & LUO Maokang Department of mathematics, Nanjing Normal university, Nanjing 210097, china Department of mathematics, sichuan university, chengdu 610064, china Department of mathematics Nanjing Normal University Nanjing China Department of mathematics Sichuan University Chengdu China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.