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三维Plumbed流形的不变量 总被引:3,自引:0,他引:3
本文给出了三维plumbed流形的由Blanchet,Habegger,Masbaum和Vogel给出的Witten型不变量的公式.作为特例对所有透镜空间和Poincare同调球给出了这些不变量的更具体的公式. 相似文献
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一类纽结的Conway多项式不变量 总被引:1,自引:0,他引:1
本文研究了一类特殊纽结,证明了存在无限多个仅具有两个负交叉点的纽结,而其Conway多项式非正.事实上,也给出了此类纽结的Conway多项式一个一般公式. 相似文献
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Thecalcualtionof〈zk1,zk2,…,zkn〉LofthispaperwillbeintermoftheKauffmanbracket-polynomial[1,2,3].TheKauffmanbracketpolynomialofaplanardiagramofanunorientedlinkisanelement〈D〉∈Z[A,A-1]definedbythefollowingprocess.AstateofDisdefinedtobeamapsfromthecrossing… 相似文献
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线性常微分方程的不变量及其应用 总被引:2,自引:0,他引:2
在这篇文章里,我们证明了n阶线性常微分方程在变换T=(t)与交换x=u(t)y下分别有n—1个不变量,并对后一情形给出了不变量的具体表述式.最后,我们还利用这些不变量研究了(1)的解的非振动性等问题. 相似文献
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研究了所谓广义树状链环的Kauffman括号多项式,给出了更一般三维流形的由Blanchet等得到的Witten型不变量的计算方法. 相似文献
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《数学的实践与认识》2013,(15)
主要利用Galaktionov提出的符号不变量的方法来研究非线性反应扩散方程组的精确解,首先引入Hamilton-Jacobi算子作为方程组的符号不变量,通过对称约化找到方程组容许的超定方程组系统并对其求解,进而得到了允许符号不变量的方程组的具体形式、约束条件和其变量分离解,最后给出某些例子. 相似文献
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关于一类矩阵的一个不变量 总被引:3,自引:0,他引:3
王章雄 《数学的实践与认识》1999,29(3):29-32
本文讨论满足关联方程的实数矩阵A,得到关于A的行(列)和的一个不变量。 相似文献
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The paper is for a general audience and may serve as a preliminary introduction to the theory of finite-type invariants. 相似文献
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Raphaël Rebelo Francis Valiquette 《Journal of Difference Equations and Applications》2013,19(4):285-318
This paper is concerned with the invariant discretization of differential equations admitting infinite-dimensional symmetry groups. By way of example, we first show that there are differential equations with infinite-dimensional symmetry groups that do not admit enough joint invariants preventing the construction of invariant finite difference approximations. To solve this shortage of joint invariants we propose to discretize the pseudo-group action. Computer simulations indicate that the numerical schemes constructed from the joint invariants of discretized pseudo-group can produce better numerical results than standard schemes. 相似文献
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We show that Toda lattices with the Cartan matrices A
n
, B
n
, C
n
, and D
n
are Liouville-type systems. For these systems of equations, we obtain explicit formulas for the invariants and generalized Laplace invariants. We show how they can be used to construct conservation laws (x and y integrals) and higher symmetries. 相似文献
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Peter J. Olver 《Foundations of Computational Mathematics》2001,1(1):3-68
A new, algorithmic theory of moving frames is applied to classify joint invariants and joint differential invariants of transformation
groups. Equivalence and symmetry properties of submanifolds are completely determined by their joint signatures, which are
parametrized by a suitable collection of joint invariants and/or joint differential invariants. A variety of fundamental geometric
examples are developed in detail. Applications to object recognition problems in computer vision and the design of invariant
numerical approximations are indicated.
August 25, 1999. Final version received: May 3, 2000. Online publication: xxxx. 相似文献
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We study the filling invariants at infinity div
k
for Hadamard manifolds defined by Brady and Farb [ Trans. Am. Math. Soc. 350(8) (1998), 3393–3405]. Among other results, we give a positive answer to the question they posed: whether these invariants
can be used to detect the rank of a symmetric space of noncompact type. 相似文献
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Vladimir Tchernov 《Compositio Mathematica》2003,135(1):103-122
The study of the Vassiliev invariants of Legendrian knots was started by D. Fuchs and S. Tabachnikov who showed that the groups of C-valued Vassiliev invariants of Legendrian and of framed knots in the standard contact R3 are canonically isomorphic. Recently we constructed the first examples of contact 3-manifolds where Vassiliev invariants of Legendrian and of framed knots are different. Moreover in these examples Vassiliev invariants of Legendrian knots distinguish Legendrian knots that are isotopic as framed knots and homotopic as Legendrian immersions. This raised the question what information about Legendrian knots can be captured using Vassiliev invariants. Here we answer this question by showing that for any contact 3-manifold with a cooriented contact structure the groups of Vassiliev invariants of Legendrian knots and of knots that are nowhere tangent to a vector field that coorients the contact structure are canonically isomorphic. 相似文献
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Xiaolei LIU 《数学年刊B辑(英文版)》2016,37(6):875-890
The modular invariants of a family of curves are the degrees of the
pullback of the corresponding divisors by the moduli map. The
singularity indices were introduced by Xiao (1991) to classify
singular fibers of hyperelliptic fibrations and to compute global
invariants locally. In semistable case, the author shows that the
modular invariants corresponding to the boundary divisor classes are
just the singularity indices. As an application, the author shows
that the formula of Xiao for relative Chern numbers is the same as
that of Cornalba-Harris in semistable case. 相似文献
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本文利用Poincare形式研究了一个保守完整动力系统的积分不变量,对异步变分引入了新的参数,给出了Poincare和Poincare-Cartan积分不变量的一个推广。 相似文献
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Damjan Kobal 《K-Theory》1999,17(2):141-150
By the use of the Karoubi Tower diagram we generalize the classical invariants of quadratic forms. Similar to Quillen's higher K-theory generalization of the classical K-theory groups, these invariants are an extension of the classical invariants by the use of homotopy theory. The iterated forgetful maps in the Karoubi Tower are KR valued and yield a generalization of the standard (rank, discriminant and total Hasse–Witt) invariants of quadratic forms in two directions. First, we get invariants of all degrees. Second, these invariants are defined for every Hermitian ring. They yield and generalize the Clifford invariant in the case of a field of characteristic different from 2, or in the case of an arithmetic Dedekind domain containing
. 相似文献
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L. Katzarkov 《Acta Appl Math》2003,75(1-3):85-103
Recently, together with Auroux and Donaldson, we have introduced some new invariants of four-dimensional symplectic manifolds. Building on the Moishezon–Teicher braid factorization techniques, we show how to compute fundamental groups of compliments to a ramification curve of generic projection. We also show that these fundamental groups are only homology invariants and outline the computations in some examples.Demonstrating the ubiquity of algebra, we go further and, using Braid factorization, we compute invariants of a derived category of representations of the quiver associated with the Fukaya–Seidel category of the vanishing cycles of a Lefschetz pencil and a structure of a symplectic four-dimensional manifold. This idea is suggested by the homological mirror symmetry conjecture of Kontsevich. We do not use it in our computations, although everything is explicit. We outline a procedure for finding homeomorphic, nonsymplectomorphic, four-dimensional symplectic manifolds with the same Saiberg–Witten invariants. This procedure defines invariants in the smooth category as well. 相似文献