共查询到20条相似文献,搜索用时 187 毫秒
1.
Huang-jia Tian 《高校应用数学学报(英文版)》2014,29(2):217-229
In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold. 相似文献
2.
We prove that any C1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity. 相似文献
3.
席南华 《数学物理学报(B辑英文版)》2009,29(3):515-526
Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper. 相似文献
4.
Poincaré and Sobolev Inequalities for Vector Fields Satisfying Hrmander's Condition in Variable Exponent Sobolev Spaces
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In this paper,we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces.The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type.We obtain the first order Poincare inequalities for vector fields satisfying Hrmander's condition in variable non-isotropic Sobolev spaces.We also set up the higher order Poincare inequalities with variable exponents on stratified Lie groups.Moreover,we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups.These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p(x)-subLaplacian.Our results are only stated and proved for vector fields satisfying Hrmander's condition,but they also hold for Grushin vector fields as well with obvious modifications. 相似文献
5.
In this paper we study normal forms for a class of germs of 1-resonant vector fields on R^n with mutually different eigenvalues which may admit extraneous resonance relations. We give an estimation on the index of finite determinacy from above as well as the essentially simplified polynomial normal forms for such vector fields. In the case that a vector field has a zero eigenvalue, the result leads to an interesting corollary, a linear dependence of the derivatives of the hyperbolic variables on the central variable. 相似文献
6.
Da Wei YANG 《数学学报(英文版)》2022,(1):225-248
We give a brief survey on the dynamics of vector fields with singularities. The aim of this survey is not to list all results in this field, but only to introduce some results from several viewpoints and some technics. 相似文献
7.
Zhen-yueZhang Tiang-weiQuyang 《计算数学(英文版)》2003,21(5):657-670
It is well-known that if we have an approximate eigenvalue λ- of a normal matrix A of order n,a good approximation to the corresponding eigenvector u can be computed by one inverse iteration provided the position,say kmax,of the largest component of u is known.In this paper we give a detailed theoretical analysis to show relations between the eigenvecor u and vector xk,k=1,…,n,obtained by simple inverse iteration,i.e.,the solution to the system(A-λI)x=ek with ek the kth column of the identity matrix I.We prove that under some weak conditions,the index kmax is of some optimal properties related to the smallest residual and smallest approximation error to u in spectral norm and Frobenius norm.We also prove that the normalized absolute vector v=|u|/||u||∞ of u can be approximated by the normalized vector of (||x1||2,…||xn||2)^T,We also give some upper bounds of |u(k)| for those “optimal“ indexeds such as Fernando‘s heuristic for kmax without any assumptions,A stable double orthogonal factorization method and a simpler but may less stable approach are proposed for locating the largest component of u. 相似文献
8.
JavierCHAVARRIGA IsaacA.GARCIA 《数学学报(英文版)》2005,21(1):185-192
In this work we study Lie symmetries of planar quasihomogeneous polynomial vector fields from different points of view, showing its integrability. Additionally, we show that certain perturbations of such vector fields which generalize the so-called degenerate infinity vector fields are also integrable. 相似文献
9.
We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr¨obner basis of the ideal. Further we give a projective analogue for the so-called footprint bound, and a version of it that is suitable for estimating the number of rational points of projective algebraic varieties over finite fields. An application to Serre's inequality for the number of points of projective hypersurfaces over finite fields is included. 相似文献
10.
A Note on the Stability of Geodesics on Diffeomorphism Groups with One-side Invariant Metric
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Li Juan ZHOU 《数学学报(英文版)》2020,36(5):620-630
In this note,we consider the stability of geodesics on volume-preserving diffeomorphism groups with one-side invariant metric.We showed that for non-Beltrami fields on a three-dimensional compact manifold,there does not exist Eulerian stable flow which is Lagrangian exponential unstable.We noticed that a stationary flow corresponding to the KdV equation can be Eulerian stable while the corresponding motion of the fluid is at most exponentially unstable. 相似文献
11.
Let Ω be a bounded domain of the complex plane whose boundary is a closed Jordan curve and (F
n
)
n≥0 the sequence of Faber polynomials of Ω. We say that a bounded linear operator T on a separable Banach space X is Ω-hypercyclic if there exists a vector x of X such that {F
n
(T)x: n ≥ 0} is dense in X. We show that many of the results in the spectral theory of hypercyclic operators involving the unit disk or its boundary
have Ω-hypercyclic counterparts which involve the domain Ω or its boundary. The influence of the geometry of Ω or the smoothness
of its boundary on Faber-hypercyclicity is also discussed. 相似文献
12.
Zhen-long Chen San-yang Liu 《应用数学学报(英文版)》2005,21(4):623-636
Let φ be a Hausdorff measure function and A be an infinite increasing sequence of positive integers. The Hausdorff-type measure φ - mA associated to φ and A is studied. Let X(t)(t ∈ R^N) be certain Gaussian random fields in R^d. We give the exact Hausdorff measure of the graph set GrX([0, 1]N), and evaluate the exact φ - mA measure of the image and graph set of X(t). A necessary and sufficient condition on the sequence A is given so that the usual Hausdorff measure function for X([0, 1] ^N) and GrX([0, 1]^N) are still the correct measure functions. If the sequence A increases faster, then some smaller measure functions will give positive and finite ( φ A)-Hausdorff measure for X([0, 1]^N) and GrX([0, 1]N). 相似文献
13.
It is shown that ifT is a measure preserving automorphism on a probability space (Ω,B, m) which admits a random variable X0 with mean zero such that the stochastic sequence X0 o Tn,n ε ℤ is orthonormal and spans L0
2(Ω,B,m), then for any integerk ≠ 0, the random variablesX o Tnk,n ε ℤ generateB modulom. 相似文献
14.
Bálint Farkas 《Czechoslovak Mathematical Journal》2011,61(2):309-322
For a given bi-continuous semigroup (T(t))
t⩾0 on a Banach space X we define its adjoint on an appropriate closed subspace X° of the norm dual X′. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology σ(X°,X). We give the following application: For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions (endowed with the compact-open topology) and on the space M(Ω) of bounded Baire measures
(endowed with the weak*-topology). We show that bi-continuous semigroups on M(Ω) are precisely those that are adjoints of
bi-continuous semigroups on Cb(Ω). We also prove that the class of bi-continuous semigroups on Cb(ω) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict
topology. In general, if is not a Polish space this is not the case. 相似文献
15.
Sigmund Selberg Achenef Tesfahun 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(4):453-465
In recent work, the authors extended the local and global well-posedness theory for the 1D Dirac–Klein–Gordon equations, but
the uniqueness of the solutions was only known in the contraction spaces (of Bourgain–Klainerman–Machedon type). Here we prove
some unconditional uniqueness results [that is, uniqueness in the larger space C([0,T];X
0), where X
0 denotes the data space]. We also prove a result about persistence of higher regularity, which is stronger than the standard
version obtained from the contraction argument, since our result allows to independently increase the regularity of the spinor
and scalar fields, whereas in the standard result they must be increased by the same amount. 相似文献
16.
Amir Dembo Nina Gantert Yuval Peres Ofer Zeitouni 《Probability Theory and Related Fields》2002,122(2):241-288
In the study of large deviations for random walks in random environment, a key distinction has emerged between quenched asymptotics, conditional on the environment, and annealed asymptotics, obtained from averaging over environments. In this paper we consider a simple random walk {X
n
} on a Galton–Watson tree T, i.e., on the family tree arising from a supercritical branching process. Denote by |X
n
| the distance between the node X
n
and the root of T. Our main result is the almost sure equality of the large deviation rate function for |X
n
|/n under the “quenched measure” (conditional upon T), and the rate function for the same ratio under the “annealed measure” (averaging on T according to the Galton–Watson distribution). This equality hinges on a concentration of measure phenomenon for the momentum of the walk. (The momentum at level n, for a specific tree T, is the average, over random walk paths, of the forward drift at the hitting point of that level). This concentration, or
certainty, is a consequence of the uncertainty in the location of the hitting point. We also obtain similar results when {X
n
} is a λ-biased walk on a Galton–Watson tree, even though in that case there is no known formula for the asymptotic speed.
Our arguments rely at several points on a “ubiquity” lemma for Galton–Watson trees, due to Grimmett and Kesten (1984).
Received: 15 November 2000 / Revised version: 27 February 2001 / Published online: 19 December 2001 相似文献
17.
B. K. Driver 《Applied Mathematics and Optimization》1999,39(2):179-210
Let W(M) be the based (at o∈ M) path space of a compact Riemannian manifold M equipped with Wiener measure ν . This paper is devoted to considering vector fields on W(M) of the form X
s
h
(
σ
)=P
s
(
σ
)h
s
(
σ ) where P
s
(
σ ) denotes stochastic parallel translation up to time s along a Wiener path σ
∈ W(M) and {h
s
}
s∈ [0,1]
is an adapted T
o
M -valued process on W(M). It is shown that there is a large class of processes h (called adapted vector fields) for which we may view X
h
as first-order differential operators acting on functions on W(M) . Moreover, if h and k are two such processes, then the commutator of X
h
with X
k
is again a vector field on W(M) of the same form.
Accepted 5 May 1997 相似文献
18.
A. Rosenthal 《Israel Journal of Mathematics》1988,64(1):57-72
We generalize a result of R. Jewett [J]: IfT is an ergodic measure preserving transformation on (X, Ω,λ),T not necessarily invertible, there exists a strictly ergodicS acting on (Y, Θ,ν), whereY is compact, such that (X, Ω,λ, T) is measure theoretically isomorphic to (Y, Θ,ν, S). 相似文献
19.
M. Schmuckenschläger 《Potential Analysis》2011,35(3):287-300
This first result of this paper is about the Laplace transform of u(X
T
) where u is harmonic on some bounded domain Ω, X
t
is Brownian motion and T is the exit time from Ω. The following results focus on exit times from balls and Faber–Krahn and reverse Faber–Krahn type
inequalities for balls. We also study the behaviour of the first Dirichlet eigenvalue for complex balls under complex interpolation.
The method of proof heavily relays on the log-concavity of gaussian measures. 相似文献
20.
Amos Nevo 《Israel Journal of Mathematics》1991,75(1):1-19
We prove a structure theorem for locally finite connected graphsX with infinitely many ends admitting a non-compact group of automorphisms which is transitive in its action on the space of
ends, Ω
X
. For such a graphX, there is a uniquely determined biregular treeT (with both valencies finite), a continuous representationφ : Aut(X) → Aut(T) with compact kernel, an equivariant homeomorphism λ : Ω
X
→ Ω
T
, and an equivariant map τ : Vert(X) → Vert(T) with finite fibers. Boundary-transitive trees are described, and some methods of constructing boundary-transitive graphs
are discussed, as well as some examples. 相似文献