共查询到20条相似文献,搜索用时 328 毫秒
1.
袁荣 《应用数学学报(英文版)》1998,14(1):68-73
Itiswellknownthattheexistenceofalmostperiodicsolutionsiscloselyrelatedtothestabilityofsolutions.Forfunctionaldifferentialequationswithinfinitedelay,Y.Hin.[5'6]studiedtheproblemsontheexistenceofalmostperiodicsolutionsandthestability.However,therearefewpapersll2]dealingwithneutralfunctionaldifferentialequationswithinfinitedelay.Inthepresentpaper,forneutralfunctionaldifferentialequationswithinfinitedelay,weprovetheinherencetheoremfortheuniformlystableoperatorD(t),definethestabilitywithrespecttot… 相似文献
2.
Franc Forstneric 《Journal of Geometric Analysis》1999,9(1):93-117
Let n > 1 and let
C
n
denote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire
mappings F:C
n →C
n
and for holomorphic automorphisms of
C
n
on discrete subsets of
C
n.We also prove an interpolation theorem for proper holomorphic embeddings of Stein manifolds into
C
n.For each closed complex submanifold (or subvariety) M ⊂
C
n
of complex dimension m < n we construct a domain Ω ⊂C
n
containing M and a biholomorphic map F: Ω →
C
n
onto
C
n
with J F ≡ 1such that F(M) intersects the image of any nondegenerate entire map G:C
n−m →C
n
at infinitely many points. If m = n − 1, we construct F as above such that
C
n ∖F(M) is hyperbolic. In particular, for each m ≥ 1we construct proper holomorphic embeddings F:C
m →C
m−1
such that the complement
C
m+1 ∖F(C
m
)is hyperbolic. 相似文献
3.
Pavel Shvartsman 《Journal of Geometric Analysis》2002,12(2):289-324
We prove a Helly-type theorem for the family of all m-dimensional convex compact subsets of a Banach space X. The result is
formulated in terms of Lipschitz selections of set-valued mappings from a metric space (M, ρ) into this family.
Let M be finite and let F be such a mapping satisfying the following condition: for every subset M′ ⊂ M consisting of at most
2m+1 points, the restriction F|M′ of F to M′ has a selection fM′ (i. e., fM′(x) ∈ F(x) for all x ∈ M′) satisfying the Lipschitz condition ‖ƒM′(x) − ƒM′(y)‖X ≤ ρ(x, y), x, y ∈ M′. Then F has a Lipschitz selection ƒ: M → X such that ‖ƒ(x) − ƒ(y)‖X ≤ γρ(x,y), x, y ∈ M where γ is a constant depending only on m and the cardinality of M. We prove that in general, the upper
bound of the number of points in M′, 2m+1, is sharp.
If dim X = 2, then the result is true for arbitrary (not necessarily finite) metric space. We apply this result to Whitney’s
extension problem for spaces of smooth functions. In particular, we obtain a constructive necessary and sufficient condition
for a function defined on a closed subset of
R
2
to be the restriction of a function from the Sobolev space W
∞
2
(R
2).A similar result is proved for the space of functions on
R
2
satisfying the Zygmund condition. 相似文献
4.
Thierry De Pauw 《Journal of Geometric Analysis》2002,12(1):29-61
A concentrated (ξ, m) almost monotone measure inR
n
is a Radon measure Φ satisfying the two following conditions: (1) Θ
m
(Φ,x)≥1 for every x ∈spt (Φ) and (2) for everyx ∈R
n
the ratioexp [ξ(r)]r−mΦ(B(x,r)) is increasing as a function of r>0. Here ξ is an increasing function such thatlim
r→0-ξ(r)=0. We prove that there is a relatively open dense setReg (Φ) ∋spt (Φ) such that at each x∈Reg(Φ) the support of Φ has the following regularity property: given ε>0 and λ>0 there is an m dimensional spaceW ⊂R
n
and a λ-Lipschitz function f from x+W into x+W‖ so that (100-ε)% ofspt(Φ) ∩B (x, r) coincides with the graph of f, at some scale r>0 depending on x, ε, and λ. 相似文献
5.
The aim of this note is to prove the following theorem. Let
where P(ix) is a nonnegative homogeneous elliptic polynomial on R
d
and V is a nonnegative polynomial potential. Then for every 1 < p < ∞ and every α > 0 there exist constants C
1, C
2 > 0 such that
and
for f in the Schwartz class . We take advantage of the Christ inversion theorem for singular integral operators with a small amount of smoothness on
nilpotent Lie groups, the maximal subelliptic L
2-estimates for the generators of stable semi-groups of measures, and the principle of transference of Coifman–Weiss.
In memory of Tadek Pytlik, our teacher and friend.
Research supported by the European Commission Marie Curie Host Fellowship for the Transfer of Knowledge “Harmonic Analysis,
Nonlinear Analysis and Probability” MTKD-CT-2004-013389 and by Polish funds for science in years 2005–2008 (research project
1P03A03029). 相似文献
6.
Klaus Langmann 《manuscripta mathematica》1994,84(1):389-400
For a homogenous polynomP ∈ℤ[X, Y] of degreed and forh ∈ ℕ letL(P, h) be the number of coprime solutions of the equation |P(x,y)|=h. Ift(h) is the number of distinct primefactors ofh, a theorem of Bombieri-Schmidt [1] givesL(P, h)≤Md
t(h)
+1 in the cased≥3. We prove for a finite collection of polynomialsP
w
∈ℤ[X, Y] under some conditions, that
for almost allh ∈ℤ (Satz 1; “almost all” in the sense “except finitely many cases”). As a corollary (Folgerung 3/4) we get for sufficiently
large primesp, that the equation |x
d
−c
z
y
d
|=p has at mostd+1 many solutions (x, y, z) ∈ ℕ
3 withc∤y. Ford=2 we get an analogon to a theorem of Mao-Hua (Folgerung 5).
相似文献
7.
8.
M.-C. Arnaud 《Publications Mathématiques de L'IHéS》2009,109(1):1-17
A theorem due to G. D. Birkhoff states that every essential curve which is invariant under a symplectic twist map of the annulus
is the graph of a Lipschitz map. We prove: if the graph of a Lipschitz map h:T→R is invariant under a symplectic twist map, then h is a little bit more regular than simply Lipschitz (Theorem 1); we deduce that there exists a Lipschitz map h:T→R whose graph is invariant under no symplectic twist map (Corollary 2).
Assuming that the dynamic of a twist map restricted to a Lipschitz graph is bi-Lipschitz conjugate to a rotation, we obtain
that the graph is even C
1 (Theorem 3).
Then we consider the case of the C
0 integrable symplectic twist maps and we prove that for such a map, there exists a dense G
δ
subset of the set of its invariant curves such that every curve of this G
δ
subset is C
1 (Theorem 4). 相似文献
9.
Min-Chun Hong 《manuscripta mathematica》1992,75(1):49-63
We define a negative exponential harmonic map from the ballB
n
of ℝn into the sphereS
n
of ℝ
n+1
. We prove that the equator map
is a negative exponential harmonic map, but not stable for the negative exponential functional whenn≥2. Moreover, we consider maps from a ballB
n
into the unit sphereS
m
of ℝm+1 wherem≥2, and prove that no nonconstant, non surjective map can reach either the minimum or the maximum of the negative exponential
functional. 相似文献
10.
M. A. Stepanova 《Journal of Mathematical Sciences》2005,131(1):5428-5437
Let f:S
2 ↬ R
3 be a generic smooth immersion. The skeleton of f is the following triple (Γ, D, p): Γ ⊂ R
3 is the 1-polyhedron of singular points of f, D = f−1(Γ) ⊂ S
2 is also a 1-polyhedron, and p : D → Γ, x ↦ f(x), is the projection. For triples of the form (D,Γ,p), where Γ has at most
four vertices, we give an iff-condition under which the triple is the skeleton of a smooth immersion f : S
2 ↬ R
3. Bibliography: 4 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 300–313. 相似文献
11.
In this paper we prove that, ifK is a closed subset ofW
0
1,p
(Ω,R
m
) with 1<p<+∞ andm≥1, thenK is stable under convex combinations withC
1 coefficients if and only if there exists a closed and convex valued multifunction from Ω toR
m
such that
The casem=1 has already been studied by using truncation arguments which rely on the order structure ofR (see [2]). In the casem>1 a different approach is needed, and new techniques involving suitable Lipschitz projections onto convex sets are developed.
Our results are used to prove the stability, with respect to the convergence in the sense of Mosco, of the class of convex
sets of the form (*); this property may be useful in the study of the limit behaviour of a sequence of variational problems
of obstacle type.
This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990 相似文献
12.
Let M
m
be a m-dimensional submanifold in the n-dimensional unit sphere S
n
without umbilic point. Two basic invariants of M
m
under the M?bius transformation group of S
n
are a 1-form Φ called M?bius form and a symmetric (0,2) tensor A called Blaschke tensor. In this paper, we prove the following rigidity theorem: Let M
m
be a m-dimensional (m≥3) submanifold with vanishing M?bius form and with constant M?bius scalar curvature R in S
n
, denote the trace-free Blaschke tensor by . If , then either ||?||≡0 and M
m
is M?bius equivalent to a minimal submanifold with constant scalar curvature in S
n
; or and M
m
is M?bius equivalent to in for some c≥0 and .
Received: 15 May 2002 / Revised version: 3 February 2003
Published online: 19 May 2003
RID="*"
ID="*" Partially supported by grants of CSC, NSFC and Outstanding Youth Foundation of Henan, China.
RID="†"
ID="†" Partially supported by the Alexander Humboldt von Stiftung and Zhongdian grant of NSFC.
Mathematics Subject Classification (2000): Primary 53A30; Secondary 53B25 相似文献
13.
Remco van der Hofstad Frank den Hollander Gordon Slade 《Probability Theory and Related Fields》1998,111(2):253-286
Summary. We introduce a new inductive approach to the lace expansion, and apply it to prove Gaussian behaviour for the weakly self-avoiding
walk on ℤ
d
where loops of length m are penalised by a factor e
−β/m p
(0<β≪1) when: (1) d>4, p≥0; (2) d≤4, . In particular, we derive results first obtained by Brydges and Spencer (and revisited by other authors) for the case d>4, p=0. In addition, we prove a local central limit theorem, with the exception of the case d>4, p=0.
Received: 29 October 1997 / In revised form: 15 January 1998 相似文献
14.
C. Hamburger 《Applied Mathematics and Optimization》1999,40(2):183-190
Finsler's theorem asserts the equivalence of (i) and (ii) for pairs of real quadratic forms f and g on R
n
: (i) f( ξ ) >0 for all ξ≠ 0 with g( ξ ) =0; (ii) f-λ g>0 for some λ∈
R. We prove two extensions: 1. We admit a vector-valued quadratic form g:
R
n
→
R
k
, for which we show that (i) implies that f-λ . . . g>0 on an ( n-k+1 ) -dimensional subspace Y
R
n
for some λ∈
R
k
. 2. In the nonstrict version of Finsler's theorem for indefinite g we replace R
n
by a real
vector
space
X .
Accepted 22 February 1998 相似文献
15.
Marie-Hélène Mourgues 《Archive for Mathematical Logic》2002,41(7):631-642
We extend the notion of absolute convergence for real series in several variables to a notion of convergence for series in
a power series field ℝ((t
Γ)) with coefficients in ℝ. Subsequently, we define a natural notion of analytic function at a point of ℝ((t
Γ))m. Then, given a real function f analytic on a open box I of ℝ
m
, we extend f to a function f
★ which is analytic on a subset of ℝ((t
Γ))
m
containing I. We prove that the functions f
★ share with real analytic functions certain basic properties: they are , they have usual Taylor development, they satisfy the inverse function theorem and the implicit function theorem.
Received: 5 October 2000 / Revised version: 19 June 2001 / Published online: 12 July 2002 相似文献
16.
If ψ ∈ L2(R), Λ is a discrete subset of the affine groupA =R
+ ×R, and w: Λ →R
+ is a weight function, then the weighted wavelet system generated by ψ, Λ, and w is
. In this article we define lower and upper weighted densities D
w
−
(Λ) and D
w
+
(Λ) of Λ with respect to the geometry of the affine group, and prove that there exist necessary conditions on a weighted wavelet
system in order that it possesses frame bounds. Specifically, we prove that if W(ψ, Λ, w) possesses an upper frame bound,
then the upper weighted density is finite. Furthermore, for the unweighted case w = 1, we prove that if W(ψ, Λ, 1) possesses
a lower frame bound and D
w
+
(Λ−1) < ∞, then the lower density is strictly positive. We apply these results to oversampled affine systems (which include the
classical affine and the quasi-affine systems as special cases), to co-affine wavelet systems, and to systems consisting only
of dilations, obtaining some new results relating density to the frame properties of these systems. 相似文献
17.
ZHANG Fubao 《中国科学A辑(英文版)》2001,44(5):631-644
In this paper, we consider the higher dimensional second order differential equations of the formẍ + ∇F(x,t) = 0,x ∈R
n
with a class of weakly coupled potentials F( x, t ), periodically depending on t. We prove the existence of infinitely many
quasi-periodic solutions for such equations via the KAM theorem. 相似文献
18.
We consider an Abel equation (*)y’=p(x)y
2 +q(x)y
3 withp(x), q(x) polynomials inx. A center condition for (*) (closely related to the classical center condition for polynomial vector fields on the plane)
is thaty
0=y(0)≡y(1) for any solutiony(x) of (*).
Folowing [7], we consider a parametric version of this condition: an equation (**)y’=p(x)y
2 +εq(x)y
3
p, q as above, ε ∈ ℂ, is said to have a parametric center, if for any ɛ and for any solutiony(ɛ,x) of (**)y(ɛ, 0)≡y(ɛ, 1)..
We give another proof of the fact, shown in [6], that the parametric center condition implies vanishing of all the momentsm
k
(1), wherem
k
(x)=∫
0
x
pk
(t)q(t)(dt),P(x)=∫
0
x
p(t)dt. We investigate the structure of zeroes ofm
k
(x) and generalize a “canonical representation” ofm
k
(x) given in [7]. On this base we prove in some additional cases a composition conjecture, stated in [6, 7] for a parametric
center problem.
The research of the first and the third author was supported by the Israel Science Foundation, Grant No. 101/95-1 and by the
Minerva Foundation. 相似文献
19.
Jia Chaohua 《数学学报(英文版)》1993,9(3):321-336
LetP(x) denote the greatest prime factor of IIz<n≤x+x1/2
n. In this paper, we prove thatP(x)>x
0.723 holds true for a sufficiently largex.
Project supported by the Tian Yuan Itam in the National Natural Science Foundation of China. 相似文献
20.
《Quaestiones Mathematicae》2013,36(4):265-269
Abstract We prove the following theorem in answer to a question raised by P Nowosad and R Tovar in [3]. If K is a kernel operator on L2(x,u) with kernel K(x, y) if P(x): = UX |K(x, y)|2 d μ(y))½ and Q(x): = (UX |K (y, x)|2 d μ(y))½ and if x PQdμ < ∞, then σ|λi|2 < ∫X PQd μ where (λi) is the se = zuence of eigenvalues of K. 相似文献