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1.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
2.
Wojciech Jaworski 《Israel Journal of Mathematics》1996,94(1):201-219
Let μ be a probability measure on a locally compact second countable groupG defining a recurrent (but not necessarily Harris) random walk. Denote byG
∞ the space of paths and byB
(a)the asymptotic σ-algebra. Let the starting measure be equivalent to the Haar measure and writeQ for the corresponding Markov measure onG
∞. We prove thatL
∞(G∞, B(a), Q) is in a canonical way isomorphic toL
∞(G/N) whereN is the smallest closed normal subgroup ofG such that μ(zN)=1 for somez∈G. The groupG/N is either a finite cyclic group with generatorzN or a compact abelian group having the cyclic group
as a dense subgroup. As a corollary we obtain that the set of all φ∈L
1(G) such that
coincides with the kernel of the canonical mapping ofL
1(G)ontoL
1(G/N). In particular, when μ is aperiodic, i.e.,G=N, then the random walk is mixing:
for every φ∈L
1(G) with ∝ φ=0. 相似文献
3.
We prove that for almost allσ ∈G ℚ the field
has the following property: For each absolutely irreducible affine varietyV of dimensionr and each dominating separable rational mapϕ:V→
there exists a point a ∈
such thatϕ(a) ∈ ℤr. We then say that
is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields
other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ. 相似文献
4.
Götz Brunner 《Israel Journal of Mathematics》1972,12(3):306-313
In the definition ofCW-complexes, the one-point spaceP, respectively the spaceP∪* with basepoint *, play the roll of the only “building-stone”. Let
be a family of compact spaces. Then the definition of a generalizedCW-complex over
is obtained from the definition of aCW-complex by replacingP by the spaces of
and formation of the mapping cone by a slightly modified construction. LetCW
* denote the category of all pointed spaces which have the homotopy type of a generalizedCW-complex over
. If
, thenCW
* is the category of all pointedCW-spaces.CW
* is closed under the formation of direct sums and of mapping cones, cylinders and tori, and is formally characterized as
the smallest such subcategory of Top * containing the spaces W∪*,
. Following the methods of E. H. Brown, it is proved, that any half exact homotopy functor onCW
* is representable, and any cohomology theory onCW
is naturally equivalent to the cohomology theory of an Ω-spectrum; for example, the singular cohomo logy is representable
onCW
for any family
of compact spaces.
相似文献
5.
Zoé Chatzidakis 《Israel Journal of Mathematics》1986,55(2):173-183
LetK be a hilbertian field,G(K) its absolute Galois group. IfK is countable, then for a.a.
inG(K)
e
,
and there is no intermediate field
with
. Let
∈G(K)
e
. Then for a.a.
in
. 相似文献
6.
Let
be a (not necessarily semi-finite) σ-finite von Neumann algebra. We prove that there exists a finite von Neumann algebra
so that for every 1 < p < 2, the Haagerup L
p
-space associated with
embeds isomorphically into
. We also provide a proof of the following non-commutative generalization of a classical result of Rosenthal: if
is a semi-finite von Neumann algebra then every reflexive subspace of
embeds isomorphically into L
r
(
) for some r > 1.
Dedicated to Professor H. P. Rosenthal on the occasion of his sixty-fifth birthday
Research partially supported by NSF grant DMS-0456781. 相似文献
7.
For a given centred convex bodyK of ℝ,n≥3, let
be the class of all convex bodies with the same projection body asK. The question whetherK can be expressed as a Blaschke average of two non-homothetic bodies from
is considered. Necessary and sufficient conditions onK to be Blaschke decomposable in
are given.
The paper provides also a characterization of the bodiesK such that the Blaschke indecomposable bodies in
are dense in
itself. 相似文献
8.
Let
be the Heisenberg group and μ
r
be the normalized surface measure on the sphere of radiusr in ℂ
n
. Let
. We prove an optimalL
p-boundedness result for the spherical maximal functionMf, namely we prove thatM is bounded onL
p(I
n
) if and only ifp>2n/2n−1. 相似文献
9.
A mapT: X→X on a normed linear space is callednonexpansive if ‖Tx-Ty‖≤‖x-y‖∀x, y∈X. Let (Ω, Σ,P) be a probability space,
an increasing chain of σ-fields spanning Σ,X a Banach space, andT: X→X. A sequence (xn) of strongly
-measurable and stronglyP-integrable functions on Ω taking on values inX is called aT-martingale if
.
LetT: H→H be a nonexpansive mapping on a Hilbert spaceH and let (xn) be aT-martingale taking on values inH. If
then x
n
/n converges a.e.
LetT: X→X be a nonexpansive mapping on ap-uniformly smooth Banach spaceX, 1<p≤2, and let (xn) be aT-martingale (taking on values inX). If
then there exists a continuous linear functionalf∈X
* of norm 1 such that
If, in addition, the spaceX is strictly convex, x
n
/n converges weakly; and if the norm ofX
* is Fréchet differentiable (away from zero), x
n
/n converges strongly.
This work was supported by National Science Foundation Grant MCS-82-02093 相似文献
10.
Let
denote the class of ergodic probability preserving transformations which are disjoint from every weakly mixing system. Let
be the class of multipliers for
, i.e. ergodic transformations whose all ergodic joinings with any element of
are also in
. Fix an ergodic rotationT, a mildly mixing actionS of a locally compact second countable groupG and an ergodic cocycle ϕ forT with values inG. The main result of the paper is a sufficient (and also necessary by [LeP] whenG is countable Abelian andS is Bernoullian) condition for the skew product build fromT, ϕ andS to be an element of
. Moreover, the self-joinings of such extensions ofT are described with an application to study semisimple extensions of rotations.
Dedicated to Hillel Furstenberg on the occasion of his retirement
The first-named author was supported in part by CRDF, grant UM1-2546-KH-03.
The second-named author was supported in part by KBN grant 1P03A 03826. 相似文献
11.
Paweł Hitczenko 《Israel Journal of Mathematics》1993,84(1-2):161-178
Letf
n
= Σ
k=1
n
v
k
r
k
,n=1,…, be a martingale transform of a Rademacher sequence (r
n)and let (r
n
′
) be an independent copy of (r
n).The main result of this paper states that there exists an absolute constantK such that for allp, 1≤p<∞, the following inequality is true:
In order to prove this result, we obtain some inequalities which may be of independent interest. In particular, we show that
for every sequence of scalars (a
n)one has
where
is theK-interpolation norm between ℓ1 and ℓ2. We also derive a new exponential inequality for martingale transforms of a Rademacher sequence.
This research was supported in part by an NSF grant and an FRPD grant at NCSU. 相似文献
12.
A graphG is embeddable in its complement
ifG is isomorphic with a subgraph of
. A complete characterization is given of those (p,p−1) graphs which are embeddable in their complements. In particular, letG be a (p,p−1) graph wherep≧6 ifp is even andp≧9 ifp is odd; thenG is embeddable in
if and only ifG is neither the starK
1,p−1 norK
1,n
∪C
3 withn≧4. 相似文献
13.
Given ∈, we construct a sequence
, … of Borel sub-sigma-algebras on the unit interval with the following property. Suppose the identity functionf(x)=x is transformed by successive conditioning on
, then
, then
, Then the lim sup, with respect ton, will exceed (pointwise almost-everywhere) 1−∈ and its lim inf will be less than ∈.
The sequence of functions also will fail to converge in the
. This contrasts with the long-open conjecture that if all the
come from a finite set of sigma-algebras, then the resulting sequence of functions must converge in
.
J. L. King was partially supported by NSF grant DMS-9112595. 相似文献
14.
Johnson William B. Lindenstrauss Joram Schechtman Gideon 《Israel Journal of Mathematics》1986,54(2):129-138
It is proved that ifY ⊂X are metric spaces withY havingn≧2 points then any mapf fromY into a Banach spaceZ can be extended to a map
fromX intoZ so that
wherec is an absolute constant. A related result is obtained for the case whereX is assumed to be a finite-dimensional normed space andY is an arbitrary subset ofX.
Supported in part by US-Israel Binational Science Foundation and by NSF MCS-7903042.
Supported in part by NSF MCS-8102714. 相似文献
15.
In this paper we prove two (rather unrelated) theorems about projective sets. The first one asserts that subsets of ℵ1 which are
in the codes are constructible; thus it extends the familiar theorem of Shoenfield that
subsets of ω are constructible. The second is concerned with largest countable
sets and establishes their existence under the hypothesis of Projective Determinacy and the assumption that there exist only
countably many ordinal definable reals.
Y. N. Moschovakis is a Sloan Foundation Fellow. During the preparation of this paper, both authors were partially supported
by NSF Grant GP-27964. 相似文献
16.
Letα ∈R,ε=(α+o(1)))/n andp=1/2(1+ε). Denote by
a random subgraph of the directedn-dimensional hypercube
, where each of then2
n
directed edges is chosen independently with probabilityp. Then the probability that
is strong-connected tends to exp{−2exp{−α}}. The proof of this main result uses a double-randomization technique. Similar techniques may be employed to yield a simpler
proof of the known analogous result for undirected random graphs on the cube.
The main result is applied to the analysis of the dynamic behavior of asynchronous binary networks. It implies that for almost
all random binary networks with fixpoints, convergence to a fixpoint is guaranteed.
Partially supported by grant #438/89 of the Israel Academy of Sciences. 相似文献
17.
According to Grothendieck Duality Theory [RD], on each varietyV over a fieldk, there is a canonical complex of
-modules, theresidue complex
. These complexes satisfy (and are characterized by) functorial properties in the categoryV ofk-varieties. In [Ye] a complex
is constructed explicitly (when the fieldk is perfect). The main result of this paper is that the two families of complexes,
and
, which carry certain additional data (such as trace maps…), are uniquely isomorphic. As a corollary we recover Lipman’s canonical
dualizing sheaf of [Li], and we obtain formulas for residues of local cohomology classes of differential forms. 相似文献
18.
Let {X
k
,k=1,2,…} be a sequence of independent binomial variables, with
the Fourier transform of the distribution ofY. Finally denote lim [P
k
− 1/2] byδ. We haveTheorem.
Research supported by N.S.F. Grant GP-25736.
Research supported by N.S.F. Grant GP-12365. 相似文献
19.
For an idealJ on an infinite setX with add(J)=κ, let
be the smallest size of any subfamilyY ofJ with the property that any member ofJ can be covered by less than κ members ofY. We study the value of
forA in
, where
denotes the smallest [δ]<θ ideal onP
κ(λ). We also discuss the problem of whether there exists a setA such that
, or even
.
Some of the material in this paper originally appeared as part of the author's doctoral dissertation completed at the Université
de Caen, 1998.
Partially supported by the Israel Science Foundation. Publication 813. 相似文献
20.
Summary Let
a plane angle of opening α∈(π, 2π). LetP
D andP
N the Dirichlet and Neumann problems associated to the Poisson equation in
. ForP
D andP
N it is proved non existence of solution in L
p
(
) whenp=2/(1±π/α). In other words, the ranges of elliptic operators naturally associated toP
D andP
N are not-closed in L
p
(
) forp=2/(1±π/α).
Sunto Sia } un angolo piano di apertura α∈(π, 2π). SianoP D eP N i problemi di Dirichlet e di Neumann associati all'equazione di Poisson in . PerP D eP N si prova non esistenza di soluzioni in L p ( ) quandop=2/(1±π/α). Vale a dire i ranges degli operatori ellittici naturalmente associati aP D eP N sono non-chiusi in π--AgBrα K L p ( ) perp=2/(1±π/α).相似文献