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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.
This paper examines the following question. If
and
are saturated formations then
is defined to be the class of all soluble groups whose
belong to
. In general
is a formation, but need not be a saturated formation. Here the smallest saturated formation containing
is studied. 相似文献
3.
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
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.
V. M. Petrogradsky 《Israel Journal of Mathematics》1999,113(1):323-339
Suppose that
% MathType!End!2!1! is a variety of Lie algebras, and letc
n(
% MathType!End!2!1!) be the dimension of the linear span of all multilinear words onn distinct letters in the free algebraF(
% MathType!End!2!1!,X) of the variety
% MathType!End!2!1!. We consider an exponential generating function
% MathType!End!2!1!, called the complexity function. The complexity function is an entire function of a complex variable provided
the variety of Lie algebras is nontrivial. In this paper we introduce the notion of complexity for Lie varieties in terms
of the growth of complexity functions; also we describe what the complexity means for the codimension growth of the variety.
Our main goal is to specify the complexity of a product of two Lie varieties in terms of the complexities of multiplicands.
The main observation here is thatC(
% MathType!End!2!1!),z) behaves like a composition of three functionsC(
% MathType!End!2!1!),z), exp(z), andC(
% MathType!End!2!1!),z).
Partially supported by grant RFFI 96-01-00146; the author is grateful to the University of Bielefeld for hospitality, where
he was DAAD-fellow. 相似文献
6.
Let F be a subfield of a commutative field extending ℝ. Let
We say thatf :
preserves distanced ≥ 0 if for eachx,y ∈ ℝ ∣x- y∣= d implies ϕ2(f(x),f(y)) = d2
. We prove that each unit-distance preserving mappingf :
has a formI o (ρ,ρ), where
is a field homomorphism and
is an affine mapping with orthogonal linear part. 相似文献
7.
Moshe Dubiner 《Journal d'Analyse Mathématique》1995,67(1):39-116
We consider the problem of polynomial approximation to a real valued functionf defined on a compact set
. An approximation theorem is proven in terms of the newly defined modulus of approximation. It is shown to imply a multidimensional
Jackson type theorem which is stronger than previously known results even for the interval [−1, 1]. A strong multidimensional
Bernstein type inverse theorem is also proven. We allow quite general approximation quasi-norms including
for 0<q≤∞.
We have found that the space of polynomials ℙ on a compact setX induces a semimetric
which encapsulates the local structure of ℙ. Any semimetric ρ equivalent to
suffices for the rough theory presented here. Many examples of sets
and their metrics are presented. 相似文献
8.
Peter Raith 《Journal d'Analyse Mathématique》1999,78(1):117-142
Assume thatX is a finite union of closed intervals and consider aC
1-mapX→ℝ for which {c∈X: T′c=0} is finite. Set
. Fix ann ∈ ℕ. For ε>0, theC
1-map
is called an ε-perturbation ofT if
is a piecewise monotonic map with at mostn intervals of monotonicity and
is ε-close toT in theC
1-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X → ℝ, the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for
every continuous functionf:X → ℝ. If (R(T),T) has positive topological entropy and a unique measure μ of maximal entropy, then every sufficiently small perturbation
ofT has a unique measure
of maximal entropy, and the map
is continuous atT in the weak star-topology. 相似文献
9.
L. I. Danilov 《Mathematical Notes》1997,61(1):48-57
We consider Stepanov almost periodic functions μ ∈
ranging in the metric space
of Borel probability measures on a complete separable metric space
is equipped with the Prokhorov metric). The main result is as follows: a function
, belongs to
if and only if for each bounded continuous function
, the function
is Stepanov almost periodic (of order 1) and
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 57–68, January, 1997.
Translated by I. P. Zvyagin 相似文献
10.
Lars Hörmander 《Israel Journal of Mathematics》1973,16(1):103-116
Two extensions of a classical theorem of Rellich are proved: (1) LetP=P(−iϖ/ϖx) be a partial differential operator with constant coefficients in
, let the manifolds contained in
have codimension ≧k>0, and denote by Γ an open cone in
intersecting each normal plane of every such manifold. If
,Pu=0 and
it follows thatu=0. (2) Assume in addition that each irreducibe lfactor ofP van shes on a real hypersurface and that Γ contains both normal directions at some such point. If
andP(D) u has compact support, the same condition withk=1 implies thatu has compact support. In both results the hypotheses on the cone Γ and on the operatorP are minimal. 相似文献
11.
Ilijas Farah 《Israel Journal of Mathematics》2006,154(1):235-246
We prove two results about the quotient over the asymptotic density zero ideal. First, it is forcing equivalent to
% MathType!End!2!1!, where
% MathType!End!2!1! is the homogeneous probability measure algebra of characterc. Second, if it has analytic Hausdorff gaps, then they look considerably different from proviously known gaps of this form.
Partially supported by NSERC. 相似文献
12.
Michael Kallay 《Israel Journal of Mathematics》1974,17(2):149-161
Let
denote the class of plane convex bodies having a width functionw, wherew′ is absolutely continuous. It is proved that a body in
is determined (up to translation) by the radius of curvature function of its boundary. This result is then used for a characterization
of the extreme (indecomposable) bodies in
and for a density theorem for Reuleaux polygons in
.
The content of this paper is a revised version of a part of the Master of Science thesis written by the author under the supervision
of Professor Micha A. Perles at the Hebrew University of Jerusalem and submitted in October, 1971. 相似文献
13.
Wolfgang Lusky 《Israel Journal of Mathematics》2004,143(1):239-251
LetX be a Banach space with a sequence of linear, bounded finite rank operatorsR
n:X→X such thatR
nRm=Rmin(n,m) ifn≠m and lim
n→∞
R
n
x=x for allx∈X. We prove that, ifR
n−Rn
−1 factors uniformly through somel
p and satisfies a certain additional symmetry condition, thenX has an unconditional basis. As an application, we study conditions on Λ ⊂ ℤ such thatL
Λ=closed span
, where
, has an unconditional basis. Examples include the Hardy space
. 相似文献
14.
P. Pych-Taberska 《分析论及其应用》1994,10(4):25-36
For measurable functions f of two real variables there are considered the Boolean sums
of parametric extensions of certain univariate Durmeyer-type operators
and
. The weighted mixed moduli of continuity of
are estimated and the degrees of approximation of f by
in some weighted norms are investigated. 相似文献
15.
Volker Turau 《Israel Journal of Mathematics》1988,62(2):206-212
For a finite groupG and some prime powerp
n
, the
-subgroup
is defined by
. Meixner proved that ifG is a finite solvable group and
for somen≧1, then the Fitting length of
is bounded by 4n. In the following note it is shown that the 2-length of
is at mostn. This result cannot be derived from Meixner’s paper, since his result implies only that the 2-length is bounded by 2n. 相似文献
16.
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
17.
Yongjin Song 《Israel Journal of Mathematics》1995,90(1-3):189-197
LetR* be a simplicial involutive ring. According to certain involutions onK(R*) and
ε
L
R
∗, there are 1/2-local splittings
and
. It is known [2] that
ε
L
\ga
α
R
∗, the Wall-Witt group. SupposeI→R
S is a split extension of discrete involutive rings withI
2=0, andI is a freeS-bimodule. Then we have
and
. The trace map Tr: Prim
n
∧*M(I ⊗ ℚ)→
0
ρ
n
;I ⊗ ℚ) is an isomorphism. We prove in Lemma 1 that the trace map Tr is ℤ/2-equivariant. In Theorem 2 we show that under a certain
assumption the rational relative Wall-Witt group vanishes. Theorem 2 can be extended to a more general case (Theorem 3) by
employing Goodwillie’s reduction technique [3].
This work was partially supported by KOSEF under Grant 923-0100-010-1. 相似文献
18.
Let Ω be a domain in
with three or more boundary points in
andR(w, Ω) the conformal, resp. hyperbolic radius of Ω at the pointw ε Ω/{∞}. We give a unified proof and some generalizations of a number of known theorems that are concerned with the geometry
of the surface
in the case that the Jacobian of ∇R(w, Ω), the gradient ofR, is nonegative on Ω. We discuss the function ∇R(w, Ω) in some detail, since it plays a central role in our considerations. In particular, we prove that ∇R(w, Ω) is a diffeomorphism of Ω for four different types of domains.
This work was supported by a grant of the Deutsche Forschungsgemeinschaft for F. G. Avkhadiev. 相似文献
19.
Summary Continuing the program initiated in the first paper of this series, representations of the Lie algebra
of the Poincaré group
are constructed by forming suitable direct integrals of representations of SL(2, C) and extending them to
by means of four additional momentum operators whose matrix elements are derived in a basis adapted to the direct integral
structure. The representations obtained here include Wigner’s representations with positive mass and spin
and Wigner’s representations with zero mass, spin
and helicity ±
.
Lavoro eseguito con contributo del C.N.R. nell’ambito dell’attività di ricerca del Gruppo Nazionale per la Fisica Matematica
e per le applicazioni della Matematica alla Fisica ed all’Ingegneria.
Entrata in Redazione il 12 marzo 1972. 相似文献
20.
Summary Quaternion generalized fiber bundles
are studied, both isomorphic to global tensorial product
ordinary quaternion fiber bundles right and left respectively) and quite general ones. A cohomology class
is considered which represents the obstruction in order the fiber bundle be a tensorial product. Several properties and a
splitting principle are proved for bundles
. On this ground and founding on a convenient bundle BE → X associated to jaz (that we call Bonan's bundle and for which ɛ(
=ɛ(BE)) relations are stated among Stiefel-Whitney classes of
, BE and the class ɛ.
Entrata in Redazione il 14 agosto 1974.
Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni. 相似文献
Entrata in Redazione il 14 agosto 1974.
Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni. 相似文献