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1.
For a positive integer n and R>0, we set
. Given R>1 and n≥4 we construct a sequence of analytic perturbations (H
j
) of the completely integrable Hamiltonian
on
, with unstable orbits for which we can estimate the time of drift in the action space. These functions H
j
are analytic on a fixed complex neighborhood V of
, and setting
the time of drift of these orbits is smaller than (C(1/ɛ
j
)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly resonant surface, the result is therefore almost optimal since the stability
exponent for such orbits is 1/2(n−2). An analogous result for Hamiltonian diffeomorphisms is also proved. Two main ingredients are used in order to deal with
the analytic setting: a version of Sternberg's conjugacy theorem in a neighborhood of a normally hyperbolic manifold in a
symplectic system, for which we give a complete (and seemingly new) proof; and Easton windowing method that allow us to approximately
localize the wandering orbits and estimate their speed of drift. 相似文献
2.
W. A. Al-Salam 《Annali di Matematica Pura ed Applicata》1965,67(1):75-94
Summary In this paper we determine all orthogonal polynomials Un(x) such that Un(x)=x−1/2
F
2n+1
(x
1/2
) and
where f(t), u(t) have Taylor series expansions.
Supported in part by N. S. F. grant GP-1593. 相似文献
3.
LetX be a complex manifold with finitely many ends such that each end is eitherq-concave or (n−q)-convex. If
, then we prove thatH
pn−q
(X) is Hausdorff for allp. This is not true in general if
(Rossi’s example withn=2 andq=1). If all ends areq-concave, then this is the classical Andreotti-Vesentini separation theorem (and holds also for
). Moreover the result was already known in the case when theq-concave ends can be ‘filled in’ (again also for
). To prove the result we first have to study Serre duality for the case of more general families of supports (instead of
the family of all closed sets and the family of all compact sets) which is the main part of the paper. At the end we give
an application to the extensibility of CR-forms of bidegree (p, q) from (n−q)-convex boundaries,
.
This research was partially supported by TMR Research Network ERBFMRXCT 98063. 相似文献
4.
Xiugui LIU 《数学年刊B辑(英文版)》2008,29(3):291-316
Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π*S is one of the central problems in homotopy theory. This paper constructs a new nontrivial family of homotopy elements in the stable homotopy groups of spheres πp^nq+2pq+q-3S which isof order p and is represented by kohn ∈ ExtA^3,P^nq+2pq+q(Zp,Zp) in the Adams spectral sequence, wherep 〉 5 is an odd prime, n ≥3 and q = 2(p-1). In the course of the proof, a new family of homotopy elements in πp^nq+(p+1)q-1V(1) which is represented by β*i'*i*(hn) ∈ ExtA^2,pnq+(p+1)q+1 (H^*V(1), Zp) in the Adams sequence is detected. 相似文献
5.
A. V. Demyanov 《Journal of Mathematical Sciences》2006,136(2):3706-3717
The problem of establishing necessary and sufficient conditions for l.s.c. under PDE constraints is studied for a special
class of functionals:
with respect to the convergence un → u in measure, vn ⇀ v in Lp(Ω;ℝd)
in W−1,p(Ω), and χn ⇀ χ in Lp(Ω), where χn ∈ Z:= {χ ∈ L∞(Ω): 0 ≤ χ(x) ≤ 1 for a.e. x}. Here
is a constant-rank partial differential operator. The main result is that if the characteristic cone of
has the full dimension, then the l.s.c. is equivalent to the fact that the F± are both
-quasiconvex and
for a.e. x ∈ Ω and for all u ∈ ℝd. As a corollary, we obtain several results for the functional
with respect to the same convergence. We show that this functional is l.s.c. iff
Bibliography: 14 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 100–119. 相似文献
6.
Let V
n
be an open manifold of non-negative sectional curvature with a soul Σ of co-dimension two. The universal cover of the unit normal bundle N of the soul in such a manifold is isometric to the direct product M
n-2 × R. In the study of the metric structure of V
n
an important role plays the vector field X which belongs to the projection of the vertical planes distribution of the Riemannian submersion on the factor M in this metric splitting . The case n = 4 was considered in [Gromoll, D., Tapp, K.: Geom. Dedicata 99, 127–136 (2003)] where the authors prove that X is a Killing vector field while the manifold V
4 is isometric to the quotient of by the flow along the corresponding Killing field. Following an approach of [Gromoll, D., Tapp, K.: Geom. Dedicata 99, 127–136 (2003)] we consider the next case n = 5 and obtain the same result under the assumption that the set of zeros of X is not empty. Under this assumption we prove that both M
3 and Σ3 admit an open-book decomposition with a bending which is a closed geodesic and pages which are totally geodesic two-spheres,
the vector field X is Killing, while the whole manifold V
5 is isometric to the quotient of by the flow along corresponding Killing field.
Supported by the Faculty of Natural Sciences of the Hogskolan i Kalmar (Sweden). 相似文献
7.
Abstract A classical result of A. D. Alexandrov states that a connected compact smooth n-dimensional manifold without boundary, embedded in ℝn+1, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane Xn+1 =constant in case M satisfies: for any two points (X′,Xn+1),
on M, with
, the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper,
we establish it under some additional conditions. Some variations of the Hopf Lemma are also presented. Several open problems
are described. Part I dealt with corresponding one dimensional problems.
(Dedicated to the memory of Shiing-Shen Chern)
* Partially supported by NSF grant DMS-0401118. 相似文献
8.
A monotone structure (
;μ) consists of a structure
and a monotone systemμ over the domain of
.L(Q
n
) is
, enlarged by a newn-ary quantifierQ
n
.
says in (
;μ) that there isU ∈μ such thatϕ[ā] is valid in (
;μ) for allā ∈U
n
. If
is a class of monotone structures,
means thatϕ is valid in all expansions of monotone structures in
. We show for the class
of all ultrafilters that interpolation with respect to
holds forL(Q
n
) exactly in casen=1. Then we prove for a large class of
(e.g. the class of topological groups) thatL(Q
n
) satisfies interpolation with respect to
for alln ≧ 1. Counterexamples indicate that the class of
is sharp in some sense. Finally the results are carried over to certain topological structures and the interior quantifiersI
n
instead ofQ
n
, thereby generalizing results of Makowsky/Ziegler and Sgro, and to a multidimensional type of monotone structures including
uniform spaces. 相似文献
9.
For multiplicative functions ƒ(n), let the following conditions be satisfied: ƒ(n)≥0 ƒ(p
r)≤A
r,A>0, and for anyε>0 there exist constants
,α>0 such that
and Σ
p≤x
ƒ(p) lnp≥αx. For such functions, the following relation is proved:
. Hereτ(n) is the number of divisors ofn andC(ƒ) is a constant.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 443–456, September, 1998.
The work of the first author was supported by the Russian Foundation for Basic Research. 相似文献
10.
This paper considers empirical Bayes estimation of the mean θ of the univariate normal densityf
0 with known variance where the sample sizesm(n) may vary with the component problems but remain bounded by
<∞. Let {(θ
n
,X
n
=(X
n,1,...,X
n, m(n)
))} be a sequence of independent random vectors where theθ
n
are unobservable and iidG and, givenθ
n
=θ has densityf
θ
m(n)
. The first part of the paper exhibits estimators for the density of
and its derivative whose mean-squared errors go to zero with rates
and
respectively. LetR
m(n+1)(G) denote the Bayes risk in the squared-error loss estimation ofθ
n+1 usingX
n+1. For given 0<a<1, we exhibitt
n
(X1,...,X
n
;X
n+1) such that
.
forn>1 under the assumption that the support ofG is in [0, 1]. Under the weaker condition that E[|θ|2+γ]<∞ for some γ>0, we exhibitt
n
*
(X
1,...,X
n
;X
n+1) such that
forn>1. 相似文献
11.
Given a sequence x of points in the unit interval, we associate with it a virtual permutation w=w(x) (that is, a sequence
w of permutationsw
n
such that for all n=1,2,..., wn−1=w′n is obtained from wn by removing the last element n from its cycle). We introduce a detailed version of the well-known stick breaking process
generating a random sequence x. It is proved that the associated random virtual permutation w(x) has a Ewens distribution.
Up to subsets of zero measure, the space
of virtual permutations is identified with the cube [0, 1]∞. Bibliography: 8 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 223, 1995, pp. 162–180. 相似文献
12.
On representations of Ψ* andC
*-algebras ofb-pseudo-differential operators on manifolds with corners
R. Lauter 《Journal of Mathematical Sciences》2000,98(6):684-705
The author computes the Jacobson topology and the corresponding Borel structure on the spectrum of
. Here
denotes the C*-algebra generated by the algebra
of b-pseudo-differential operators of orderO on a compact manifold with corners (in the sense of Melrose). The author also reduces the problem of classification of representations
to the problem of classification of positive Borel measures on certain well-known Borel spaces. Bibliography:29 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 18, 1998, pp. 85–117. 相似文献
13.
Y. Nishimura 《Proceedings of the Steklov Institute of Mathematics》2006,252(1):212-224
For a simple complete multipolytope
in ℝn, Hattori and Masuda defined a locally constant function
on ℝn minus the union of hyperplanes associated with
, which agrees with the density function of an equivariant complex line bundle over a Duistermaat-Heckman measure when
arises from a moment map of a torus manifold. We improve the definition of
and construct a convex chain
on ℝn. The well-definiteness of this convex chain is equivalent to the semicompleteness of the multipolytope
. Generalizations of the Pukhlikov-Khovanskii formula and an Ehrhart polynomial for a simple lattice multipolytope are given
as corollaries. The constructed correspondence ⨑ub;simple semicomplete multipolytopes⫂ub; →; ⨑ub;convex chains⫂ub; is surjective
but not injective. We will study its “kernel.” 相似文献
14.
M. B. Khripunova 《Mathematical Notes》1998,64(3):394-400
It is proved that if ƒ(n) is a multiplicative function taking a valueζ on the set of primes such thatζ
3 = 1,ζ ≠ 1 andƒ
3(p
r)=1 forr≥2, then there exists aθ ∈ (0, 1), for which
, where
.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 457–464, September, 1998.
The author wishes to thank Professor N. M. Timofeev for useful discussions.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00502. 相似文献
15.
16.
We consider hypercyclic composition operators on
which can be obtained from the translation operator using polynomial automorphisms of
. In particular we show that if C
S
is a hypercyclic operator for an affine automorphism S on
, then
for some polynomial automorphism Θ and vectors a and b, where I is the identity operator. Finally, we prove the hypercyclicity of “symmetric translations” on a space of symmetric analytic
functions on ℓ1.
Received: 8 June 2006 Revised: 26 September 2006 相似文献
17.
I. M. Guseinov 《Mathematical Notes》1997,62(2):172-180
We prove the existence of a transformation operator that takes the solution of the equationy″=λ2n
y to the solution of the equation
with a condition at infinity. Some properties of the kernel of this operator are studied.
Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 206–215, August, 1997.
Translated by M. A. Shishkova 相似文献
18.
Summary Let Mm,
m be two m-dimensional compact oriented hypersurfaces of class C3 immersed in a Riemannian manifold Rm+1 of constant sectional curvature. Suppose that Rm+1 admits a one-parameter continuous group G of conformal transformations satisfying a certain condition (which holds automatically
when G is a group of isometric transformations). Suppose further that there is a1 − 1 transformation Tτ ∈ G between Mm and
m such that
for each P ∈ Mm and each
m. If the r-th mean curvature for any r, 1 ⩽ r ⩽ m, of Mm at each point P ∈ Mm is equal to that of
m at the corresponding point
, together with other conditions, then Mm and
m are congruent mod G. This is a generalization of a joint theorem ofH. Hopf andY. Katsurada [5] in which G is a group of isometric transformations.
Entrata in Redazione il 13 Giugno 1975.
The first author was partially supported by the National Science Foundation grant GP-33944. 相似文献
19.
A. L. Gladkov 《Mathematical Notes》1996,60(3):264-268
We study the Cauchy problem in the layer Π
T
=ℝ
n
×[0,T] for the equationu
t
=cGΔu
t
+Δϕ(u), wherec is a positive constant and the functionϕ(p) belongs toC
1(ℝ+) and has a nonnegative monotone non-decreasing derivative. The unique solvability of this Cauchy problem is established for
the class of nonnegative functionsu(x,t) ∈C
x,t
2,1
(Π
T
) with the properties:
,
.
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 356–362, September, 1996.
This research was partially supported by the International Science Foundation under grant No. MX6000. 相似文献
20.
Let A be a Banach algebra which does not contain any nonzero idempotent element, let γ > 0, and let
. We show that if
then
. We also show, assuming a suitable spectral condition on x, that if
, then
Received: 12 July 2006 Revised: 31 January 2007 相似文献