共查询到20条相似文献,搜索用时 15 毫秒
1.
R. I. McLachlan H. Z. Munthe-Kaas G. R. W. Quispel A. Zanna 《Foundations of Computational Mathematics》2008,8(3):335-355
We present new explicit volume-preserving methods based on splitting for polynomial divergence-free vector fields. The methods
can be divided in two classes: methods that distinguish between the diagonal part and the off-diagonal part and methods that
do not. For the methods in the first class it is possible to combine different treatments of the diagonal and off-diagonal
parts, giving rise to a number of possible combinations.
This paper is dedicated to Arieh Iserles on the occasion of his 60th anniversary. 相似文献
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Jun-Muk Hwang 《Compositio Mathematica》2001,125(3):255-262
We show that the vanishing order of a non-zero vector field at a generic point of a smooth Fano variety of Picard number 1 cannot exceed the dimension of the Fano variety. Furthermore, if there exist only finitely many rational curves of minimal degree through a generic point of the Fano variety, we show that a non-zero vector field cannot vanish at a generic point of the Fano variety. 相似文献
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A formula of Poisson summation type is established for sumsinvolving relative norms in an extension of number fields. 相似文献
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Higher-order variational sets are proposed for set-valued mappings, which are shown to be more convenient than generalized
derivatives in approximating mappings at a considered point. Both higher-order necessary and sufficient conditions for local
Henig-proper efficiency, local strong Henig-proper efficiency and local λ-proper efficiency in set-valued nonsmooth vector optimization are established using these sets. The technique is simple and
the results help to unify first and higher-order conditions. As consequences, recent existing results are derived. Examples
are provided to show some advantages of our notions and results.
This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam. 相似文献
7.
Le Anh Vinh 《Graphs and Combinatorics》2013,29(6):1943-1949
We study a finite analog of a problem of Erd?s, Hickerson and Pach on the maximum number of occurrences of a fixed angle among n directions in three-dimensional spaces. 相似文献
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主要研究循环数域的导子公式.利用Kronecker-Weber定理及整体域的分歧理论,对于给定除子分歧个数的素数次循环扩域,明确给出了这类数域的导子公式及其个数. 相似文献
9.
V. V. Kornyak 《Journal of Mathematical Sciences》2002,108(6):1004-1014
The cohomology of Lie (super)algebras has many important applications in mathematics and physics. At present, since the required algebraic computations are very tedious, the cohomology is explicitly computed only in a few cases for different classes of Lie (super)algebras. That is why application of computer algebra methods is important for this problem. We describe an algorithm (and its C implementation) for computing the cohomology of Lie algebras and superalgebras. In elaborating the algorithm, we focused mainly on the cohomology with coefficients in trivial, adjoint, and coadjoint modules for Lie (super)algebras of the formal vector fields. These algebras have many applications to modern supersymmetric models of theoretical and mathematical physics. As an example, we consider the cohomology of the Poisson algebra Po(2) with coefficients in the trivial module and present 3- and 5-cocycles found by a computer. Bibliography: 6 titles. 相似文献
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Qin Yue 《K-Theory》2005,35(1-2):69-91
Let
and
, d1 and d2 squarefree integers, be an imaginary field and a biquadratic field, respectively. Let S be the set consisting of all infinite primes, all dyadic primes and all finite primes which ramify in E. Suppose the 4-rank of the class group of F is zero and the S-ideal class group of F has odd order, we give the forms of all elements of order ⩽ 2 in K2OE and use the Hurrelbrink and Kolster’s method [Hurrelbrink, J. and Kolster, M.: J. reine angew. Math. 499 (1998), 145–188] to obtain the forms of all elements of order 4 in K2OE.
Received: September 2004 相似文献
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We show that any nondegenerate vector field u in \begin{align*}L^{\infty}(\Omega, \mathbb{R}^N)\end{align*}, where Ω is a bounded domain in \begin{align*}\mathbb{R}^N\end{align*}, can be written as \begin{align*}u(x)= \nabla_1 H(S(x), x)\quad {\text for a.e.\ x \in \Omega}\end{align*}}, where S is a measure‐preserving point transformation on Ω such that \begin{align*}S^2=I\end{align*} a.e. (an involution), and \begin{align*}H: \mathbb{R}^N \times \mathbb{R}^N \to \mathbb{R}\end{align*} is a globally Lipschitz antisymmetric convex‐concave Hamiltonian. Moreover, u is a monotone map if and only if S can be taken to be the identity, which suggests that our result is a self‐dual version of Brenier's polar decomposition for the vector field as \begin{align*}u(x)=\nabla \phi (S(x))\end{align*}, where ? is convex and S is a measure‐preserving transformation. We also describe how our polar decomposition can be reformulated as a (self‐dual) mass transport problem. © 2012 Wiley Periodicals, Inc. 相似文献
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应用F_q[t]上的Pell方程这一初等方法重新证明一个已知的结果:实二次函数域F_q(t)(D~(1/2))理想类数为1时,D只能为P或QR,其中P,Q,R是F_q[t]中的首一不可约多项式且Q,R次数为奇数. 相似文献
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de Oliveira Fabiana R. Oliveira Fabrícia R. 《Journal of Optimization Theory and Applications》2021,190(1):259-273
Journal of Optimization Theory and Applications - This paper proposes and analyzes a globalized version of the Newton method for finding a singularity of the nonsmooth vector fields. Basically, the... 相似文献
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This paper treats the problem of minimizing the norm of vectorfields in L1 with prescribed divergence. The ridge of . playsan important role in the analysis, and in the case where R2is a polygonal domain, the ridge is thoroughly analysed andsome examples are presented. In the case where Rn is a Lipschitzdomain and the divergence is a finite positive Borel measure,the infimum is calculated, and it is shown that if an extremalexists, then it is of the form 1 = Fd, where F is a nonnegativefunction and d(x) is the distance from x to the boundary .Finally, if R2 is a polygonal domain and the measure is representedby a nonnegative continuous function, then an explicit expressionfor the extremal is given, and it is proven that this extremalis unique. 相似文献
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Ukrainian Mathematical Journal - Let (M,g) be a Riemannian manifold and let TM be its tangent bundle equipped with a Riemannian (or pseudo-Riemannian) lift metric derived from g. We give a... 相似文献
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Let R
3 be a bounded domain,
0$$
" align="middle" border="0">
, a family of extending subdomains, and =(x) a positive function in
be a space of -solenoidal vector fields,
0$$
" align="middle" border="0">
, a family of subspaces, G orthogonal projectors in
onto
. A unitary transformation that diagonalizes the family of projectors {G} is constructed: it takes
to the operator of multiplication by the independent variable. The isometry of this transformation is proved with the help of the operator Riccati equation for the NeumanntoDirichlet mapping. Bibliography: 8 titles. 相似文献
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A unifying approach for proving certain commutator estimates involving smooth, not-necessarily divergence-free vector fields is introduced and implemented in the scales of weighted Triebel–Lizorkin and Besov spaces and certain variable exponent Triebel–Lizorkin and Besov spaces. Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fluid mechanics. 相似文献
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Guoting Chen 《Numerical Algorithms》2001,27(1):1-33
We study Lie's method in the way of Ushiki for further reduction of normal forms for vector fields with singularity at the origin. We give further reduction of normal forms in two typical cases for vector fields in dimension 2: one with a rotation as its linear part and the other with a nilpotent linear part. 相似文献