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1.
S. A. Antonyan 《Mathematical Notes》1999,65(2):135-143
It is proved that a based-free action α of a given compact Lie groupG on the Hilbert cubeQ is equivalent to the standard based-free action σ if and only if the orbit spaceQ
0/α of the free partQ
0=Q* is aQ-manifold having the proper homotopy type of the orbit spaceQ
0/σ. The existence of an equivariant retraction (Q
0, σ)→(Q
0, α) is established. It is proved that for any TikhonovG-spaceX the family of all equivariant mapsX→ conG separates the points and the closed sets inX.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 163–174, February, 1999. 相似文献
2.
We analyze the structure of a continuous (or Borel) action of a connected semi-simple Lie group G with finite center and real rank at least 2 on a compact metric (or Borel) space X, using the existence of a stationary measure as the basic tool. The main result has the following corollary: Let P be a minimal parabolic subgroup of G, and K a maximal compact subgroup. Let λ be a P-invariant probability measure on X, and assume the P-action on (X,λ) is mixing. Then either λ is invariant under G, or there exists a proper parabolic subgroup Q⊂G, and a measurable G-equivariant factor map ϕ:(X,ν)→(G/Q,m), where ν=∫
K
kλdk and m is the K-invariant measure on G/Q. Furthermore, The extension has relatively G-invariant measure, namely (X,ν) is induced from a (mixing) probability measure preserving action of Q.
Oblatum 14-X-1997 & 18-XI-1998 / Published online: 20 August 1999 相似文献
3.
Rong-mao ZHANG & Zheng-yan LIN Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2007,50(1):35-46
Let {W(t),t∈R}, {B(t),t∈R } be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (Xi(t),... ,Xd(t)) and X1(t),... ,Xd(t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q (?) (0,∞), the exact Hausdorff measures of the image X(Q) = {X(t) : t∈Q} and the graph GrX(Q) = {(t, X(t)) :t∈Q}are established. 相似文献
4.
A. I. Perov 《Functional Analysis and Its Applications》2010,44(1):69-72
Let M be a complete K-metric space with n-dimensional metric ρ(x, y): M × M → R
n
, where K is the cone of nonnegative vectors in R
n
. A mapping F: M → M is called a Q-contraction if ρ (Fx,Fy) ⩽ Qρ (x,y), where Q: K → K is a semi-additive absolutely stable mapping. A Q-contraction always has a unique fixed point x* in M, and ρ(x*,a) ⩽ (I - Q)-1 ρ(Fa, a) for every point a in M. The point x* can be obtained by the successive approximation method x
k
= Fx
k-1, k = 1, 2,..., starting from an arbitrary point x
0 in M, and the following error estimates hold: ρ (x*, x
k
) ⩽ Q
k
(I - Q)-1ρ(x
1, x
0) ⩽ (I - Q)-1
Q
k
ρ(x
1, x
0), k = 1, 2,.... Generally the mappings (I - Q)-1 and Q
k
do not commute. For n = 1, the result is close to M. A. Krasnosel’skii’s generalized contraction principle. 相似文献
5.
6.
John Wermer 《Arkiv f?r Matematik》2008,46(1):183-196
Let X be a rationally convex compact subset of the unit sphere S in ?2, of three-dimensional measure zero. Denote by R(X) the uniform closure on X of the space of functions P/Q, where P and Q are polynomials and Q≠0 on X. When does R(X)=C(X)? Our work makes use of the kernel function for the $\bar{\delta}_{b}Let X be a rationally convex compact subset of the unit sphere S in ℂ2, of three-dimensional measure zero. Denote by R(X) the uniform closure on X of the space of functions P/Q, where P and Q are polynomials and Q≠0 on X. When does R(X)=C(X)?
Our work makes use of the kernel function for the operator on S, introduced by Henkin in [5] and builds on results obtained in Anderson–Izzo–Wermer [3].
We define a real-valued function ε
X
on the open unit ball intB, with ε
X
(z,w) tending to 0 as (z,w) tends to X. We give a growth condition on ε
X
(z,w) as (z,w) approaches X, and show that this condition is sufficient for R(X)=C(X) (Theorem 1.1).
In Section 4, we consider a class of sets X which are limits of a family of Levi-flat hypersurfaces in intB.
For each compact set Y in ℂ2, we denote the rationally convex hull of Y by . A general reference is Rudin [8] or Aleksandrov [1]. 相似文献
7.
For a Tychonoff space X,we use ↓USC F(X) and ↓C F(X) to denote the families of the hypographs of all semi-continuous maps and of all continuous maps from X to I = [0,1] with the subspace topologies of the hyperspace Cld F(X × I) consisting of all non-empty closed sets in X × I endowed with the Fell topology.In this paper,we shall show that there exists a homeomorphism h:↓USC F(X) → Q = [1,1] ω such that h(↓CF(X))=c0 = {(xn)∈Q| lim n→∞ x n = 0} if and only if X is a locally compact separable metrizable space and the set of isolated points is not dense in X. 相似文献
8.
Idealization of a decomposition theorem 总被引:1,自引:1,他引:0
In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A
I-sets and A
I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A
I-continuous.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
David E. Dobbs 《Rendiconti del Circolo Matematico di Palermo》2009,58(3):327-336
If T is a (commutative unital) ring extension of a ring R, then Λ(T /R) is defined to be the supremum of the lengths of chains of intermediate fields between R
P
/P R
P
and T
Q
/QT
Q
, where Q varies over Spec(T) and P:= Q ∩ R. The invariant σ(R):= sup Λ(T/R), where T varies over all the overrings of R. It is proved that if Λ(S/R)< ∞ for all rings S between R and T, then (R, T) is an INC-pair; and that if (R, T) is an INC-pair such that T is a finite-type R-algebra, then Λ(T/R)< ∞. Consequently, if R is a domain with σ(R) < ∞, then the integral closure of R is a Prüfer domain; and if R is a Noetherian G-domain, then σ(R) < ∞, with examples showing that σ(R) can be any given non-negative integer. Other examples include that of a onedimensional Noetherian locally pseudo-valuation
domain R with σ(R)=∞. 相似文献
10.
Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0, 1], respectively. With the Hausdorff-metric, they are topological spaces. In this paper, we prove that, if X is an infinite compact metric space with a dense set of isolated points, then (↓USCC(X), ↓CC(X)) ≈ (Q, c0 ∪ (Q \ Σ)), i.e., there is a homeomorphism h :↓USCC(X) → Q such that h(↓CC(X)) = c0 ∪ (Q \ Σ... 相似文献
11.
We will consider global problems in the ringK[X
1, …,X
n] on the polynomials with coefficients in a subfieldK ofC.
LetP=(P
1, …,P
n):K
n
→K
n be a polynomial map such that (P
1,…,P
n) is a quasi-regular sequence generating a proper ideal, the main thing we do is to use the algebraic residues theory (as
described in [5]) as a computational tool to give some result to test when a map (P
1, …,P
n) is a proper map by computing a finite number of residue symbols. 相似文献
12.
S. L. Berlov 《Journal of Mathematical Sciences》1998,89(2):1082-1086
Let R=P1⊕P2⊕…⊕Pn be a decomposition of a ring into a direct sum of indecomposable left ideals. Assume that these ideals possess the following
properties: (1) any nonzero homomorphisms ϕ: Pi→Pj is a monomorphism; (2) if subideals Q1, Q2 of the ideal Pj are isomorphic to the ideal Pi, then there exists a subideal Q3⊆Q1⊎Q2, which is also isomorphic to Pi. It is proved that, under these asumptions, a left quotient ring of the ring R exists. This left quotient ring inherits properties(1), (2) and satisfies condition (3): any nonzero homomorphism ϕ: Pi→Pi is an automorphism of the ideal Pi. Bibliography: 2 titles.
Translated fromZapiski Nauchnyk Seminarov POMI, Vol. 227, 1995, pp. 9–14. 相似文献
13.
Let X(t) be an N parameter generalized Lévy sheet taking values in ℝd with a lower index α, ℜ = {(s, t] = ∏
i=1
N
(s
i, t
i], s
i < t
i}, E(x, Q) = {t ∈ Q: X(t) = x}, Q ∈ ℜ be the level set of X at x and X(Q) = {x: ∃t ∈ Q such that X(t) = x} be the image of X on Q. In this paper, the problems of the existence and increment size of the local times for X(t) are studied. In addition, the Hausdorff dimension of E(x, Q) and the upper bound of a uniform dimension for X(Q) are also established. 相似文献
14.
Robert M. Burton 《Israel Journal of Mathematics》1980,35(4):339-348
LetT: Y→Y be the Bernoulli two shift with independent generatorQ={Q
0,Q
1} and letS: X→X be a measure preserving bijection. If (S, X) is ergodic then the skew product onX×Y defined by {fx339-1} is aK-automorphism. IfŜ is also Bernoulli we sayS is pre-Bernoulli. J. Feldman showed that ifS is pre-Bernoulli thenS must be loosely Bernoulli. We construct an example to show the converse is false, i.e. anS that is loosely Bernoulli but not pre-Bernoulli. 相似文献
15.
We construct the Chow ringCH*(X) =CH
0
(X)⊕CH
1
(X)⊕CH
2
(X) of a reduced, quasi-projective surfaceX, together with Chern class mapsc
i
:K
0
(X) → CH
i
(X), with the usual properties. As a consequence, we show that the cycle mapCH
2
(X)→ F
0
K
0
(X) is an isomorphism. Our treatment is greatly influenced by an unpublished 1983 preprint of Levine’s, but is much simpler,
since we deal only with surfaces. 相似文献
16.
Paul Arne ?stv?r 《K-Theory》2004,31(4):345-355
Let X be a connected based space and p be a two-regular prime number. If the fundamental group of X has order p, we compute the two-primary homotopy groups of the homotopy fiber of the trace map A(X) → TC(X) relating algebraic K-theory of spaces to topological cyclic homology. The proof uses a theorem of Dundas and an explicit calculation of the cyclotomic
trace map K(ℤ[Cp])→ TC(ℤ[Cp]). 相似文献
17.
Let X be a non-singular complex projective curve of genus ≥3. Choose a point x ∈ X. Let Mx be the moduli space of stable bundles of rank 2 with determinant We prove that the Chow group CHQ1(Mx) of 1-cycles on Mx with rational coefficients is isomorphic to CHQ0(X). By studying the rational curves on Mx, it is not difficult to see that there exits a natural homomorphism CH0(J)→CH1(Mx) where J denotes the Jacobian of X. The crucial point is to show that this homomorphism induces a homomorphism CH0(X)→CH1(Mx), namely, to go from the infinite dimensional object CH0(J) to the finite dimensional object CH0(X). This is proved by relating the degeneration of Hecke curves on Mx to the second term I*2 of Bloch's filtration on CH0(J).
Insong Choe was supported by KOSEF (R01-2003-000-11634-0). 相似文献
18.
We define and study a class of summable processes, called additive summable processes, that is larger than the class used
by Dinculeanu and Brooks [D-B].
We relax the definition of a summable processesX:Ω×ℝ+→E⊂L(F, G) by asking for the associated measureI
X to have just an additive extension to the predictableσ-algebra ℘, such that each of the measures (I
X)
z
, forz∈(L
G
p
)*, beingσ-additive, rather than having aσ-additive extension. We define a stochastic integral with respect to such a process and we prove several properties of the
integral. After that we show that this class of summable processes contains all processesX:Ω×ℝ+→E⊂L(F, G) with integrable semivariation ifc
0 ∋G. 相似文献
19.
Yu. È. Linke 《Siberian Mathematical Journal》2011,52(3):501-511
Given a continuous sublinear operator P: V → C(X) from a Hausdorff separable locally convex space V to the Banach space C(X) of continuous functions on a compact set X we prove that the subdifferential ∂P at zero is operator-affinely homeomorphic to the compact subdifferential ∂
c
Q, i.e., the subdifferential consisting only of compact linear operators, of some compact sublinear operator Q: ł2 → C(X) from a separable Hilbert space ł2, where the spaces of operators are endowed with the pointwise convergence topology. From the topological viewpoint, this
means that the space L
c
(ł2, C(X)) of compact linear operators with the pointwise convergence topology is universal with respect to the embedding of the subdifferentials
of sublinear operators of the class under consideration. 相似文献
20.
E. Ballico 《Annali dell'Universita di Ferrara》1999,45(1):123-125
Fix integersg, k andt witht>0,k≥3 andtk<g/2−1. LetX be a generalk-gonal curve of genusg andR∈Pic
k
(X) the uniqueg
k
1
onX. SetL:=K
X⊗(R
*)⊗t.L is very ample. Leth
L:X→P(H
0(X, L)*) be the associated embedding. Here we prove thath
L(X) is projectively normal. Ifk≥4 andtk<g/2−2 the curveh
L(X) is scheme-theoretically cut out by quadrics.
The author was partially supported by MURST and GNSAGA of CNR (Italy). 相似文献