共查询到20条相似文献,搜索用时 93 毫秒
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利用临界点理论研究了p-q-Laplace系统的周期边值问题.首先定义p-q-Laplace系统的弱周期解;其次给出一些引理;然后用临界点理论中的极小极大方法得到关于p-q-Laplace系统弱周期解的一个存在性定理;最后讨论了p-q-Laplace系统的相关问题.本文使用的主要方法是临界点理论中的环绕定理. 相似文献
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本文给出了一类加权的第二Borel-Cantelli引理.这是对以前该引理的两种推广的一个补充. 相似文献
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在结合环中,环的极小条件等价于极大条件的充要性定理,已由许永华在文献[1]、[2]中给出。本文利用(?)加群的一个易于证明的性质,获得许永华定理的比较简单的证明。引理1 A 为可换加群,A 的子群的极小条件等价于极大条件的充要条件是存在某一正整数 k,使得对所有的,α∈A,都有 kα=0. 相似文献
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引入Schwarz引理的一个最常见的推广定理,并且作出了详细的证明.同时以引理形式介绍了一个实用的复数性质,并且利用这两个引理,给出了开圆盘内解析函数的的实部,虚部以及模的估计式. 相似文献
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一族非线性约束条件下的摄动梯度投影法 总被引:9,自引:2,他引:7
对问题(P),堵丁柱改变了以往的做法,利用对约束切空间的摄动技巧,给出了一个收敛的梯度投影方法.本文推广了[1]中方法,给出了一个更一般的收敛算法,它无需[1]中对约束函数的凸性假设,也不须多次求投影梯度.本文中算法的收敛性证明是建立在[3]中引理10.2.6的简单推广得到的引理3的基础上的.本文引理3减弱了引理10.2.6中的条件3,因而更具实用性.可以简化许多算法的收敛性证明. 相似文献
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该文运用变分方法研究R~N上一类拟线性椭圆型方程,得到一定条件下这类问题的两个非负解的存在性.其中一个解是通过局部极小得到的,另一个是运用山路引理得到的. 相似文献
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本文我们给出关于靶流形为Heisenbcrg群的迷向映射的Luckhaus型引理,此结果对研究靶流形为Heisenberg群的能量极小映射的高阶正则性将发挥重要作用. 相似文献
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In this paper, we find by inverse technique two solutions of a system of linear equations which together serve as a sufficient
and necessary condition for well-poised Bailey chains. Using these two solutions, we establish a new well-poised Bailey chain,
two usual Bailey chains, and a well-poised extension of Bailey’s lemma. Their applications to q-series are also investigated.
X. Ma was supported by Natural Science Foundation of China (No. 10771156). 相似文献
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Professor William Parry 《Probability Theory and Related Fields》1969,13(2):95-113
Summary This paper introduces the notion of a free G extension of a dynamical system where G is a compact abelian group. The concept is closely allied to that of generalised discrete spectrum (which includes Abramov's quasi-discrete spectrum as a special case). We give necessary and sufficient conditions for a G extension of a minimal (uniquely ergodic) dynamical system to be minimal (uniquely ergodic) and show that in a certain sense a general G extension lifts these properties. Stable G-extensions always lift these properties if the underlying space is connected. This fact is then used to characterise all uniquely ergodic and minimal affine transformations of a certain three dimensional nilmanifold. The rest of the paper is devoted to the exhibition of group invariants for systems with generalised discrete spectrum. In particular it is shown that such systems always have a compact abelian group as underlying space. A lemma which facilitates this result gives necessary and sufficient conditions for a connected G-extension of a compact abelian group to be a compact abelian group. 相似文献
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非凸半定规划的广义Fakars引理及最优性条件 总被引:1,自引:0,他引:1
1引言在本文中,我们用(?),S~n,S_ ~n分别表示有限维向量空间,n阶对称矩阵空间及n阶半正定矩阵锥.我们考虑如下形式的非凸半定规划问题: 相似文献
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Richard Taylor 《Publications Mathématiques de L'IHéS》2008,108(1):183-239
We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy
of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), l-adic lifts of certain automorphic mod
l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which
is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara’s lemma. 相似文献
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We give a necessary and sufficient condition for a K?hler manifold of complex dimension n ≧ 2 to be a complex space form in terms of its sectional curvatures, which is an extension of Schur’s lemma. Our study is
related to a congruence theorem for circles in a complex space form
Received: 6 October 2006 相似文献
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Francisco Javier García-Pacheco 《Arkiv f?r Matematik》2011,49(2):325-333
In this paper we consider the problem of the non-empty intersection of exposed faces in a Banach space. We find a sufficient
condition to assure that the non-empty intersection of exposed faces is an exposed face. This condition involves the concept
of inner point. Finally, we also prove that every minimal face of the unit ball must be an extreme point and show that this is not the case
at all for minimal exposed faces since we prove that every Banach space with dimension greater than or equal to 2 can be equivalently
renormed to have a non-singleton, minimal exposed face. 相似文献
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In previous work arising from the study of Ramanujan's Lost Notebook, a new Abel type lemma was proved. In this paper, we
discuss extensions of this lemma and use it to prove many q-series identities.
The first author was partially supported by NSF grant DMS–0200047. The second author was partially supported by FCT, Portugal,
through program POCTI.
2000 Mathematics Subject Classification:Primary—33D15; Secondary—05A30 相似文献
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It is an intriguing open problem to give a combinatorial characterisation or polynomial algorithm for determining when a graph
is globally rigid in ℝ
d
. This means that any generic realisation is uniquely determined up to congruence when each edge represents a fixed length
constraint. Hendrickson gave two natural necessary conditions, one involving connectivity and the other redundant rigidity.
In general, these are not sufficient, but they do suffice in two dimensions, as shown by Jackson and Jordán. Our main result
is an analogue of the redundant rigidity condition for frameworks that have both direction and length constraints. For any
generic globally rigid direction-length framework in ℝ
d
with at least 2 length edges, we show that deleting any length edge results in a rigid framework. It seems harder to obtain
a corresponding result when a direction edge is deleted: we can do this in two dimensions, under an additional hypothesis
that we believe to be unnecessary. Our proofs use a lemma of independent interest, stating that a certain space parameterising
equivalent frameworks is a smooth manifold. We prove this lemma using arguments from differential topology and the Tarski–Seidenberg
theorem on semi-algebraic sets. 相似文献
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NotesonSmoothMapGermsYuLi(余立);ZhangGuobin(张国滨)(ZhanjiangTeachersCollege,China)Abstract:Inthispaper,westudythedeterminacyofrea... 相似文献