共查询到20条相似文献,搜索用时 15 毫秒
1.
Digen Zhang 《manuscripta mathematica》2001,106(4):405-409
Let A⊂R be an extension of commutative rings with 1. We show that A is totally real (i.e. all maximal ideals of A are real) and A⊂R is a Prüfer extension if and only if R is totally real and the holomorphy ring H(R/A) of R over A is A.
Received: 2 January 2001 / Revised version: 23 April 2001 相似文献
2.
Lower and upper estimates are given on the size of a family of subsets of an n-element set containing no three distinct sets satisfying A ∩ B ⊂ C, A ⊄ B. This is a sharpening of an earlier result where the same question was solved under the condition that there are no three
distinct sets such that A ∩ B ⊂ C.
The second author was supported by the Hungarian National Foundation for Scientific Research grant numbers NK062321, AT048826,
the Bulgarian National Science Fund under Grant IO-03/2005 and the projects of the European Community: INTAS 04-77-7171, FIST–MTKD-CT-2004-003006. 相似文献
3.
Elbieta Wagner-Bojakowska Wadysaw Wilczyski 《Rendiconti del Circolo Matematico di Palermo》2000,49(1):5-26
We prove that for an arbitrary setA ⊂ ℝ its interior in aψ-density topology equalsA ∩ φβ(B), whereB is a measurable kernel ofA andβ is some countable ordinal. Moreover, eachβ, 1≤β<Ω, realizes the interior ofA for someA εS. 相似文献
4.
David E. Dobbs 《Rendiconti del Circolo Matematico di Palermo》2001,50(2):259-270
Résumé Une extensionA⊂B des anneaux (commutatifs) satisfait à la propriété si tout arbre dans Spec(B) couvre un arbre dans Spec(A). Il est possible qu'une extension entière d'un anneau Noethérien ne satisfait pas à . SiA⊂B soit unei-extension satisfaisante à soit “going-up” soit “going-down”, alorsA⊂B satisfait à . Cependant, une extension d'anneaux satisfaisante à “going-up”, “going-down”, et peut être nonunibranche dans
hauteur >1. Un anneau intègreA a le spectre d'un arbre si et seulement siA⊂B satisfait àP pour tout anneau intègreB contenantA (resp., suranneau de BézoutB deA). De plus, si un anneau intègreA n'ait pas de spectre d'un arbre mais soit localement de dimension finie, (par exemple, tout anneau intègre Noethérien de
dimension au moins 2), alors il existe un suranneau de BézoutB deA et un arbre saturé dans Spec(B) de sorte que card=4 et l'image de à l'égard de la flèche canonique Spec(B)→Spec(A) est un ensemble saturé tel que card =3 mais n'est pas d'arbre. On donne également des caractérisations associées des classes
desi-domaines et des ai-domaines.
相似文献
5.
Eero Hyry 《manuscripta mathematica》1999,98(3):377-390
Let A be a normal local ring which is essentially finite type over a field of characteristic zero. Let I⊂A be an ideal such that the Rees algebra R
A
(I) is Cohen–Macaulay and normal. In this paper we address the question: “When does R
A
(I) have rational singularities?” In particular, we study the connection between rational singularities of R
A
(I) and the adjoint ideals of the powers I
n
(n∋ℕ).
Received: 25 May 1998 / Revised version: 20 August 1998 相似文献
6.
V. V. Makeev 《Journal of Mathematical Sciences》2011,175(5):572-573
Let X be an affine cross-polytope, i.e., the convex hull of n segments A
1
B
1,…, A
n
B
n
in
\mathbbRn {\mathbb{R}^n} that have a common midpoint O and do not lie in a hyperplane. The affine flag F(X) of X is the chain O ∈ L
1 ⊂⋯ ⊂ L
n
=
\mathbbRn {\mathbb{R}^n} , where L
k
is the k-dimensional affine hull of the segments A
1
B
1,…, A
k
B
k
, k ≤ n. It is proved that each convex body K ⊂
\mathbbRn {\mathbb{R}^n} is circumscribed about an affine cross-polytope X such that the flag F(X) satisfies the following condition for each k ∈{2,…, n}:the (k−1)-planes of support at A
k
and B
k
to the body L
k
∩ K in the k-plane L
k
are parallel to L
k
−1.Each such X has volume at least V(K)/2
n(n−1)/2. Bibliography: 5 titles. 相似文献
7.
M. Laurent 《Journal of Mathematical Sciences》2012,180(5):592-598
Let Γ = Z
A + Z
n
⊂ R
n
be a dense subgroup of rank n + 1 and let [^(w)] \hat{w} (A) denote the exponent of uniform simultaneous rational approximation to the generating point A. For any real number v ≥
[^(w)] \hat{w} (A), the Hausdorff dimension of the set B
v
of points in R
n
that are v-approximable with respect to Γ is shown to be equal to 1/v. 相似文献
8.
W. Ishizuka C. Y. Wang 《Calculus of Variations and Partial Differential Equations》2008,32(3):387-405
For a bounded domain Ω ⊂ R
n
endowed with L
∞-metric g, and a C
5-Riemannian manifold (N, h) ⊂ R
k
without boundary, let u ∈ W
1,2(Ω, N) be a weakly harmonic map, we prove that (1) u ∈ C
α (Ω, N) for n = 2, and (2) for n ≥ 3, if, in additions, g ∈ VMO(Ω) and u satisfies the quasi-monotonicity inequality (1.5), then there exists a closed set Σ ⊂ Ω, with H
n-2(Σ) = 0, such that for some α ∈ (0, 1).
C. Y. Wang Partially supported by NSF. 相似文献
9.
Dragan Djurčić Rale M. Nikolić Aleksandar Torgašev 《Lithuanian Mathematical Journal》2011,51(4):472-476
We discuss the relationship between the weak and strong asymptotic equivalence relations and the generalized inverse in the
class A \mathcal {A} of all nondecreasing unbounded positive functions on a half-axis [a,+∞) (a > 0). As a main result, we prove a proper characterization of the functional class R
∞
∩
A \mathcal {A} , where R
∞
is the class of all rapidly varying functions. Also, we prove a characterization of the functional class PI
*
∩
A \mathcal {A} . 相似文献
10.
A. H. Forrest 《Israel Journal of Mathematics》1991,76(1-2):215-228
This paper deals with two possible definitions of recurrence in measure preserving systems. A set of integersR is said to be a set of (Poincaré) recurrence if, for all measure preserving systems (X, B, μ, T) and any measurable setA of positive measure, there is anr εR such thatμ(T
r
A∩A)>0.R is said to be a set of strong recurrence if, for all measure preserving systems (X, B, μ, T) and any measurable setA of positive measure, there is ane>0 and an infinite number of elementsr ofR such thatμ(T
r
A∩A)≥e (see Bergelson’s 1985 paper). This paper constructs a set of recurrenceR, an example of a measure preserving system (X, B, μ, T) and a measurable setA of measure 1/2, such that lim
r→∞:rεRμ
(A∩T
r
A)=0. In particularR is a set of recurrence but not a set of strong recurrence, giving a negative answer to a question of Bergelson posed in 1985.
Further, it also constructs a set of recurrence which does not force the continuity of positive measures and so reproves a
result of Bourgain published in 1987.
This paper forms a part of the author’s Ph.D. Thesis at the Ohio State University.
The author wishes to thank his advisor, Professor Bergelson, for suggesting the problem of this paper and for his guidance. 相似文献
11.
The question of which r.e. setsA possess major subsetsB which are alsor-maximal inA (A⊂rm
B) arose in attempts to extend Lachlan’s decision procedure for the αε-theory of ℰ*, the lattice of r.e. sets modulo finite sets, and Soare’s theorem thatA andB are automorphic if their lattice of supersets ℒ*(A) and ℒ*(B) are isomorphic finite Boolean algebras. We characterize the r.e. setsA with someB⊂rm
A as those with a Δ3 function that for each recursiveR
i
specifiesR
i
or
as infinite on
and to be preferred in the construction ofB. There are r.e.A andB with ℒ*(A) and ℒ*(B) isomorphic to the atomless Boolean algebra such thatA has anrm subset andB does not. Thus 〈ℰ*,A〉 and 〈ℰ*,B〉 are not even elementarily equivalent. In every non-zero r.e. degree there are r.e. sets with and withoutrm subsets. However the classF of degrees of simple sets with norm subsets satisfies
.
The authors were partially supported by NSF Grants MCS 76-07258, MCS 77-04013 and MCS 77-01965 respectively. 相似文献
12.
B. A. Khudaigulyev 《Differential Equations》2012,48(2):255-263
We study the behavior of nonnegative solutions of the Dirichlet problem for a linear elliptic equation with a singular potential
in the ball B = B(0,R) ⊂ R
n
(n ≥ 3), R ≤ 1. We find an exact condition on the potential ensuring the existence or absence of a nonnegative solution of that problem. 相似文献
13.
Hans Schoutens 《manuscripta mathematica》2003,111(3):379-412
In this paper, non-standard tight closure is proposed as an alternative for classical tight closure on finitely generated
algebras over ℂ. It has the advantage that it admits a functional definition, similar to the characteristic p definition of tight closure, where instead of the characteristic p Frobenius, its ultraproduct, the non-standard Frobenius, is used. This new closure operation cl(⋅) has the same properties as classical tight closure, to wit, (1) if A is regular, then 𝔞=cl(𝔞); (2) if A⊂B is an integral extension of domains, then cl(𝔞 B)∩A⊂cl(𝔞); (3) if A is local and is a system of parameters, then (Colon-Capturing); (4) if 𝔞 is generated by m elements, then cl𝔞 contains the integral closure of 𝔞
m
and is contained in the integral closure of 𝔞 (Brian?on-Skoda).
Received: 25 June 2002 / Revised version: 14 February 2003
Published online: 19 May 2003
Partially supported by a grant from the National Science Foundation. 相似文献
14.
David E. Dobbs 《Rendiconti del Circolo Matematico di Palermo》2000,49(2):319-324
Résumé SoitR ⊂T une extension des anneaux commutatifs et soit {P
α :α ∈I} une cha?ne croissante des idéaux premiers deR (I étant un ensemble totalement ordonné, peut-être infini). Alors il existe un anneau de paravaluationV deT et une cha?ne {Q
α} des idéaux premiers deV de sorte queR ⊂V etQ
α ∩R =P
α pour toutα ∈I. Tout d’abord, on établit le cas spécial dans lequelT est un corps; dans ce cas, on trouve en effet un tel anneau de valuationV deT. Ensuite, l’assertion ci-dessus pour le cas général découle comme conséquence. Dans le cas général, on peut aussi remplacer
le mot “paravaluation” avec le mot “valuation” siR est un anneau de Marot etT est son anneau total de fractions.
相似文献
15.
Robert L. BRYANT 《数学年刊B辑(英文版)》2006,27(1):95-112
Abstract Let SO(n) act in the standard way on ℂn and extend this action in the usual way to ℂn+1 = ℂ ⊕ ℂn.
It is shown that a nonsingular special Lagrangian submanifold L ⊂ ℂn+1 that is invariant under this SO(n)-action intersects the fixed ℂ ⊂ ℂn+1 in a nonsingular real-analytic arc A (which may be empty). If n > 2, then A has no compact component.
Conversely, an embedded, noncompact nonsingular real-analytic arc A ⊂ ℂ lies in an embedded nonsingular special Lagrangian submanifold that is SO(n)-invariant. The same existence result holds for compact A if n = 2. If A is connected, there exist n distinct nonsingular SO(n)-invariant special Lagrangian extensions of A such that any embedded nonsingular SO(n)-invariant special Lagrangian extension of A agrees with one of these n extensions in some open neighborhood of A.
The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gérard and Tahara to prove the existence of the extension.
* Project supported by Duke University via a research grant, the NSF via DMS-0103884, the Mathematical Sciences Research Institute,
and Columbia University.
(Dedicated to the memory of Shiing-Shen Chern, whose beautiful works and gentle encouragement have had the most profound influence
on my own research) 相似文献
16.
Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces
S. Takahashi W. Takahashi M. Toyoda 《Journal of Optimization Theory and Applications》2010,147(1):27-41
Let C be a closed and convex subset of a real Hilbert space H. Let T be a nonexpansive mapping of C into itself, A be an α-inverse strongly-monotone mapping of C into H and let B be a maximal monotone operator on H, such that the domain of B is included in C. We introduce an iteration scheme of finding a point of F (T)∩(A+B)−10, where F (T) is the set of fixed points of T and (A+B)−10 is the set of zero points of A+B. Then, we prove a strong convergence theorem, which is different from the results of Halpern’s type. Using this result, we
get a strong convergence theorem for finding a common fixed point of two nonexpansive mappings in a Hilbert space. Further,
we consider the problem for finding a common element of the set of solutions of a mathematical model related to equilibrium
problems and the set of fixed points of a nonexpansive mapping. 相似文献
17.
Matoušek 《Discrete and Computational Geometry》2002,28(1):45-48
Abstract. A finite set N ⊂ R
d
is a weak ε-net for an n -point set X ⊂ R
d
(with respect to convex sets) if it intersects each convex set K with |K ∩ X| ≥ ε n . It is shown that there are point sets X ⊂ R
d
for which every weak ε -net has at least const ⋅
points. This distinguishes the behavior of weak ε -nets with respect to convex sets from ε -nets with respect to classes of shapes like balls or ellipsoids in R
d
, where the size can be bounded from above by a polynomial function of d and ε . 相似文献
18.
András Máthé 《Israel Journal of Mathematics》2008,164(1):285-302
We show that Hausdorff measures of different dimensions are not Borel isomorphic; that is, the measure spaces (ℝ, B, H
s
) and (ℝ, B, H
t
) are not isomorphic if s ≠ t, s, t ∈ [0, 1], where B is the σ-algebra of Borel subsets of ℝ and H
d
is the d-dimensional Hausdorff measure. This answers a question of B. Weiss and D. Preiss.
To prove our result, we apply a random construction and show that for every Borel function ƒ: ℝ → ℝ and for every d ∈ [0, 1] there exists a compact set C of Hausdorff dimension d such that ƒ(C) has Hausdorff dimension ≤ d.
We also prove this statement in a more general form: If A ⊂ ℝn is Borel and ƒ: A → ℝm is Borel measurable, then for every d ∈ [0, 1] there exists a Borel set B ⊂ A such that dim B = d·dim A and dim ƒ(B) ≤ d·dim ƒ (A).
Partially supported by the Hungarian Scientific Research Fund grant no. T 49786. 相似文献
19.
Ekaterina Blagoveshchenskaya 《Journal of Mathematical Sciences》2008,149(2):1047-1062
Let X be a block-rigid almost completely decomposable group of ring type with regulator A and p-primary regulator quotient X/A such that p
l
= exp X/A with natural l > 1. From the well-known fact p
l
End A ⊂ End X ⊂ End A it follows that End X = End X ∪ End A and p
l
End A = End X ∪ p
l
End A. Generalizing these, we determine the chain End X = ɛ
A
(l)
⊂ ɛ
A
(l−1)
⊂ ɛ
A
(l−2)
⊂ ⋯ ⊂ ɛ
A
(1)
⊂ ɛ
A
(0)
= End A, satisfying p
l−k
ɛ
A
(k)
= End X ∪p
l−k
End A, and construct groups X
k
′
and
such that ɛ
A
(k)
= Hom
, where k = 1, 2,..., l − 1.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 17–38, 2006. 相似文献
20.
Byron L. Walden 《Journal d'Analyse Mathématique》1994,63(1):231-253
In 1981, Hayman and Wu proved that for any simply connected domain Ω and any Riemann mappingF: Ω →D,F′ ∈ L1 (L ∩ Ω), whereL is any line in the complex plane. Several years later, Fernández, Heinonen and Martio showed that there is anε > 0 such thatF′ ∈ L1+∈(L ∩ Ω). The question arises as to which curves other than lines satisfy such a statement. A curve Γ is said to be Ahlfors-David
regular if there is a constantA such that for any B(x, r) (the disk of radiusr centered atx), l(Γ ∩ B(x, r))≤ Ar. The major result of the paper is the following theorem: Let Γ be an Ahlfors-David regular curve with constantA. Then there exists an∈ > 0, depending only onA, such thatF′ ∈ L1+∈(Γ ∩ Ω). This result is the synthesis of the extension of Fernández, Heinonen and Martio, and the result of Bishop and Jones
showing thatF′ ∈ L1(Γ ∩ Ω). The proof of the results uses a stopping-time argument which seeks out places in the curve where small pieces may
be added in order to control the portions of the curve where |F′ | is large. This is accomplished with an estimate on the
vanishing of the harmonic measure of the curve in such places. The paper also includes simpler arguments for the special cases
where Γ = ∂Ω and Γ ⊂Ω. 相似文献