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1.
Let Λ be an isolated non-trivial transitive set of a C 1 generic diffeomorphism f ∈ Diff (M ). We show that the space of invariant measures supported on Λ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ (which implies that the set of irregular+ points is also residual in Λ). As an application, we show that the non-uniform hyperbolicity of irregular+ points in Λ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in Λ) determines the uniform hyperbolicity of Λ. 相似文献
2.
Jrgen Bang-Jensen 《Journal of Graph Theory》1995,20(2):255-265
In this paper we study those digraphs D for which every pair of internally disjoint (X, Y)-paths P1, P2 can be merged into one (X, Y)-path P* such that V(P1) ∪ V(P2), for every choice of vertices X, Y ? V(D). We call this property the path-merging property and we call a graph path-mergeable if it has the path-merging property. We show that each such digraph has a directed hamiltonian cycle whenever it can possibly have one, i.e., it is strong and the underlying graph has no cutvertex. We show that path-mergeable digraphs can be recognized in polynomial time and we give examples of large classes of such digraphs which are not contained in any previously studied class of digraphs. We also discuss which undirected graphs have path-mergeable digraph orientations. © 1995, John Wiley & Sons, Inc. 相似文献
3.
Cyril Houdayer 《Mathematische Annalen》2010,346(4):969-989
We give examples of non-amenable infinite conjugacy classes groups Γ with the Haagerup property, weakly amenable with constant
Λcb(Γ) = 1, for which we show that the associated II1 factors L(Γ) are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra P ì L(G){P \subset L(\Gamma)} generates an amenable von Neumann algebra. Nevertheless, for these examples of groups Γ, L(Γ) is not isomorphic to any interpolated free group factor L(F
t
), for 1 < t ≤ ∞. 相似文献
4.
We deal with (n−1)-generated modules of smooth (analytic, holomorphic) vector fieldsV=(X
1,..., Xn−1) (codimension 1 differential systems) defined locally on ℝ
n
or ℂ
n
, and extend the standard duality(X
1,..., Xn−1)↦(ω), ω=Ω(X1,...,Xn−1,.,) (Ω−a volume form) betweenV′s and 1-generated modules of differential 1-forms (Pfaffian equations)—when the generatorsX
i are linearly independent—onto substantially wider classes of codimension 1 differential systems. We prove that two codimension
1 differential systemsV and
are equivalent if and only if so are the corresponding Pfaffian equations (ω) and
provided that ω has1-division property: ωΛμ=0, μ—any 1-form ⇒ μ=fω for certain function germf. The 1-division property of ω turns out to be equivalent to the following properties ofV: (a)fX∈V, f—not a 0-divisor function germ ⇒X∈V (thedivision property); (b) (V
⊥)⊥=V; (c)V
⊥=(ω); (d) (ω)⊥=V, where ⊥ denotes the passing from a module (of vector fields or differential 1-forms) to its annihilator.
Supported by Polish KBN grant No 2 1090 91 01.
Partially supported by the fund for the promotion of research at the Technion, 100–942. 相似文献
5.
E. I. Berezhnoi 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(3):163-171
Under the assumptions that Δ(f, h)(t) = |f(t + h) − f(t)|, X is a symmetric space of functions in [0, 1], α ∈ (0, 1) and p ∈ [1, ∞) are any fixed number, by the triple (X, α, p) a Besov type space Λ
X,p
α
is constructed, where the norm is given by the equality
For any α
0 ∈ (0, 1), it is shown that there exists an infinite-dimensional, closed subspace of Λ
X,p
α0, such that any non-identically zero function does not belong to the subspace Λ
X,p
α
with α > α
0.
The work is done under the financial support of RFFI, Project Cod 08-01-00669 相似文献
6.
Let Λ be a finite-dimensional algebra over an algebraically closed field k. We denote by mod Λ the category of finitely generated left Λ-modules. Consider the family ℱ(u) of the indecomposables M∈mod Λ such that
, where
is the subspace of morphisms which factorize through semisimple modules. If P,Q are projectives in mod Λ, ℱ(u)(P,Q) is the family of those modules M∈ℱ(u) such that a minimal projective presentation is of the formfM: P→Q. We prove that if Λ is of tame representation type then each ℱ(P,Q) has only a finite number of isomorphism classes or is parametrized by μ(u,P,Q) one-parameter families. We give an upper bound for this number in terms of u,P and Q. Then we give some sufficient conditions for tame of polynomial growth type. For the proof we consider similar results for
bocses.
Presented by Y. Drozd
Mathematics Subject Classifications (2000) 16G60, 16G70, 16G20. 相似文献
7.
Peter Müller 《Israel Journal of Mathematics》1999,109(1):319-337
Letf (X, t)εℚ[X, t] be an irreducible polynomial. Hilbert’s irreducibility theorem asserts that there are infinitely manyt
0εℤ such thatf (X, t
0) is still irreducible. We say thatf (X, t) isgeneral if the Galois group off (X, t) over ℚ(t) is the symmetric group in its natural action. We show that if the degree off with respect toX is a prime ≠ 5 or iff is general of degree ≠ 5, thenf (X, t
0) is irreducible for all but finitely manyt
0εℤ unless the curve given byf (X, t)=0 has infinitely many points (x
0,t
0) withx
0εℚ,t
0εℤ. The proof makes use of Siegel’s theorem about integral points on algebraic curves, and classical results about finite
groups, going back to Burnside, Schur, Wielandt, and others.
Supported by the DFG. 相似文献
8.
Robert S. Strichartz 《Journal d'Analyse Mathématique》2006,99(1):333-353
For certain Cantor measures μ on ℝn, it was shown by Jorgensen and Pedersen that there exists an orthonormal basis of exponentialse
2πiγ·x for λεΛ. a discrete subset of ℝn called aspectrum for μ. For anyL
1 functionf, we define coefficientsc
γ(f)=∝f(y)e
−2πiγiy
dμ(y) and form the Mock Fourier series ∑λ∈Λcλ(f)e
2πiλ·x
. There is a natural sequence of finite subsets Λn increasing to Λ asn→∞, and we define the partial sums of the Mock Fourier series by
We prove, under mild technical assumptions on μ and Λ, thats
n(f) converges uniformly tof for any continuous functionf and obtain the rate of convergence in terms of the modulus of continuity off. We also show, under somewhat stronger hypotheses, almost everywhere convergence forfεL
1.
Research supported in part by the National Science Foundation, Grant DMS-0140194. 相似文献
9.
We prove that ifX is a Polish space andF a face ofP(X) with the Baire property, thenF is either a meager or a co-meager subset ofP(X). As a consequence we show that for every abelian Polish groupX and every analytic Haar-null set Λ⊆X, the set of test measuresT(Λ) of Λ is either meager or co-meager. We characterize the non-locally-compact groups as the ones for which there exists
a closed Haar-null setF⊆X withT(F) meager, Moreover, we answer negatively a question of J. Mycielski by showing that for every non-locally-compact abelian Polish
group and every σ-compact subgroupG ofX there exists aG-invariantF
σ subset ofX which is neither prevalent nor Haar-null.
Research supported by a grant of EPEAEK program “Pythagoras”. 相似文献
10.
In this article we introduce the paranormed sequence spaces(f,Λ,△m,p),c0(f,Λ,△m,p) and ■∞(f,Λ,△m,p),associated with the multiplier sequence Λ =(λk),defined by a modulus function f.We study their different properties like solidness,symmetricity,completeness etc.and prove some inclusion results. 相似文献
11.
Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E | arbieary f ∈ E, S(f , e) loheain in w(e)} isomorphic to E° by θ:Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J(E∪ S°) satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J(S°), called the weakly inverse hull of a weakly inverse system (S°, E, θ, φ) with I(∑) ≌ S°, E(∑) ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given. 相似文献
12.
Jindřich Zapletal 《Israel Journal of Mathematics》1997,97(1):101-111
Two total functionsf, g fromω
1 toω are called strongly almost disjoint if {α<ω
1:f(α)=g(α)} is finite. We show that it is consistent with ZFC to have families of pairwise strongly almost disjoint functions of arbitrary
prescribed size. 相似文献
13.
Daciberg L. Gonçalves Elena Kudryavtseva Heiner Zieschang 《manuscripta mathematica》2002,107(3):311-341
Let f:M
1→M
2 be a continuous map and c:M
1→M
2 a constant map between closed (not necessarily orientable) surfaces. By definition the pair (f,c) has the Wecken property if f can be deformed into a map f' such that the number of coincidence points of (f',c) is the same as the number of essential coincidence classes of (f,c) and, hence, every essential coincidence class consists of exactly one point. When both surfaces are orientable the problem
to determine all maps which have the Wecken property was solved in [14]. Let A(f) denote the absolute degree as defined in [6] or [15] and . Here we show that a map f has the Wecken property iff either the Euler characteristic or . In free groups there are solved certain quadratic equations closely related to the root problem.
Received: Received: 18 January 2001 / Revised version: 27 November 2001 相似文献
14.
Hui Xue Lao 《数学学报(英文版)》2009,25(4):687-692
Let Af(n) be the coefficient of the logarithmic derivative for the Hecke L-function. In this paper we study the cancellation of the function Ay(n) twisted with an additive character e(α√n), α 〉0, i.e. Ef(x) = Σx〈n〈2x Af(n)e(α√n). 相似文献
15.
Ali Ghaffari 《Semigroup Forum》2008,76(1):95-106
Let S be a foundation locally compact topological semigroup. Two new topologies τ
c
and τ
w
are introduced on M
a
(S)*. We introduce τ
c
and τ
w
almost periodic functionals in M
a
(S)*. We study these classes and compare them with each other and with the norm almost periodic and weakly almost periodic functionals.
For f∈M
a
(S)*, it is proved that T
f
∈ℬ(M
a
(S),M
a
(S)*) is strong almost periodic if and only if f is τ
c
-almost periodic. Indeed, we have obtained a generalization of a well known result of Crombez for locally compact group to
a more general setting of foundation topological semigroups. Finally if P(S) (the set of all probability measures in M
a
(S)) has the semiright invariant isometry property, it is shown that the set of τ
w
-almost periodic functionals has a topological left invariant mean. 相似文献
16.
Incompleteness and minimality of complex exponential system 总被引:3,自引:0,他引:3
Guan-tie DENG School of Mathematical Sciences Beijing Normal University Beijing China 《中国科学A辑(英文版)》2007,50(10):1467-1476
A necessary and sufficient condition is obtained for the incompleteness of a complex exponential system E(A,M)in C_α,where C_αis the weighted Banach space consisting of all complex continuous functions f on the real axis R with f(t)exp(-α(t))vanishing at infinity,in the uniform norm‖f‖_α=sup{|f(t)e~(-α(t))|:t∈R}with respect to the weightα(t).If the incompleteness holds, then the complex exponential system E(?)is minimal and each function in the closure of the linear span of complex exponential system E(?)can be extended to an entire function represented by a Taylor-Dirichlet series. 相似文献
17.
LetP be a convexd-polytope without triangular 2-faces. Forj=0,…,d−1 denote byf
j(P) the number ofj-dimensional faces ofP. We prove the lower boundf
j(P)≥f
j(C
d) whereC
d is thed-cube, which has been conjectured by Y. Kupitz in 1980. We also show that for anyj equality is only attained for cubes. This result is a consequence of the far-reaching observation that such polytopes have
pairs of disjoint facets. As a further application we show that there exists only one combinatorial type of such polytopes
with exactly 2d+1 facets. 相似文献
18.
The propertyP
m
(directly analogous to Valentine’s propertyP
3) is used to prove several curious results concerning subsets of a topological linear space, among them the following: (a)
If a closed setS has propertyP
m
and containsk points of local nonconvexity no distinct pair of which can see each other viaS, thenS is the union ofm − k − 1 or fewer starshaped sets. (b) Any closed connected set with propertyP
m
is polygonally connected. (c) A closed connected setS with propertyP
m
is anL
m−1 set (each pair of points may be joined by a polygonal arc ofm − 1 of fewer sides inS). (d) A finite-dimensional set with propertyP
m
is anL
2m − 3 set. A new proof of Tietze’s theorem on locally convex sets is given, and various examples refute certain plausible conjectures. 相似文献
19.
Suppose that f(x) = (f
1(x),...,f
r
(x))
T
, x∈R
d
is a vector-valued function satisfying the refinement equation f(x) = ∑Λ
c
κ
f(2x−κ) with finite set Λ of Z
d
and some r×r matricex c
κ. The requirements for f to have accuracy p are given in terms of the symbol function m(ξ).
Supported by NSFC 相似文献
20.
Kenneth S. Alexander 《Probability Theory and Related Fields》1998,110(4):441-471
Summary. For lattice models on ℤ
d
, weak mixing is the property that the influence of the boundary condition on a finite decays exponentially with distance
from that region. For a wide class of models on ℤ2, including all finite range models, we show that weak mixing is a consequence of Gibbs uniqueness, exponential decay of an
appropriate form of connectivity, and a natural coupling property. In particular, on ℤ2, the Fortuin-Kasteleyn random cluster model is weak mixing whenever uniqueness holds and the connectivity decays exponentially,
and the q-state Potts model above the critical temperature is weak mixing whenever correlations decay exponentially, a hypothesis satisfied
if q is sufficiently large. Ratio weak mixing is the property that uniformly over events A and B occurring on subsets Λ and Γ, respectively, of the lattice, |P(A∩B)/P(A)P(B)−1| decreases exponentially in the distance between Λ and Γ. We show that under mild hypotheses, for example finite range,
weak mixing implies ratio weak mixing.
Received: 27 August 1996 / In revised form: 15 August 1997 相似文献