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1.
Stefan Eilertsen 《Arkiv f?r Matematik》2000,38(1):53-75
A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (− Δ)μ inR
n
,n≥1, is obtained, for μ∈(0,1/2n)/(1,1/2n−1). This extends some results for the polyharmonic operator obtained by Maz'ya and Maz'ya-Donchev.
As in the polyharmonic case, the proof is based on a weighted positivity property of (− Δ)μ, where the weight is a fundamental solution of this operator. It is shown that this property holds for μ as above while there
is an interval [A
n
, 1/2n−A
n
], whereA
n
→1, asn→∞, with μ-values for which the property does not hold. This interval is non-empty forn≥8. 相似文献
2.
A set U of vertices of a graph G is called a geodetic set if the union of all the geodesics joining pairs of points of U is the whole graph G. One result in this paper is a tight lower bound on the minimum number of vertices in a geodetic set. In order to obtain
that result, the following extremal set problem is solved. Find the minimum cardinality of a collection 𝒮 of subsets of [n]={1,2,…,n} such that, for any two distinct elements x,y∈[n], there exists disjoint subsets A
x
,A
y
∈𝒮 such that x∈A
x
and y∈A
y
. This separating set problem can be generalized, and some bounds can be obtained from known results on families of hash functions.
Received: May 19, 2000 Final version received: July 5, 2001 相似文献
3.
Xu Bing 《高校应用数学学报(英文版)》1995,10(1):45-48
STRONGLAWSFORα-MIXINGSEQUENCEPROCESSESINDEXEDBYSETS¥XUBINGAbstract:LetJ={1,2,...}dandlet{Xj,j∈J}beana-mixingsequencewhichisno... 相似文献
4.
巫世权 《高校应用数学学报(英文版)》1993,8(2):175-181
Let Cdenote the set of all k-subests of an n-set.Assume Alohtain in Ca,and A lohtain in (A,B) is called a cross-2-intersecting family if |A B≥2 for and A∈A,B∈B.In this paper,the best upper bounds of the cardinalities for non-empty cross-2-intersecting familles of a-and b-subsets are obtained for some a and b,A new proof for a Frankl-Tokushige theorem[6] is also given. 相似文献
5.
Andreas Fr?hlich 《Annali dell'Universita di Ferrara》2000,46(1):11-19
We consider weights of Muckenhoupt classA
q, 1<q<∞. For a bounded Lipschitz domain Ω⊂ℝn we prove a compact embedding and a Poincaré inequality in weighted Sobolev spaces. These technical tools allow us to solve
the weak Neumann problem for the Laplace equation in weighted spaces on ℝn, ℝn
+, on bounded and on exterior domains Ω with boundary of classC
1, which will yield the Helmholtz decomposition ofL
ω
q(Ω)n for general ω∈A
q. This is done by transferring the method of Simader and Sohr [4] to the weighted case. Our result generalizes a result of
Farwig and Sohr [2] where the Helmholtz decomposition ofL
ω
p(Ω)n is proved for an exterior domain and weights of Muckenhoupt class without singularities or degeneracies in a neighbourhood
of ϖΩ.
Sunto In questo lavoro consideriamo dei pesi della classe di MuckenhouptA q, 1<q<∞. Per un dominio limitato lipschitziano Ω⊂ℝn, dimostriamo una immersione compatta ed una disuguaglianza di Poincaré in spazi di Sobolev con peso. Questa tecnica ci consente di risolvere il problema debole di Neumann per l’equazione di Laplace in spazi pesati in ℝn, ℝn + in domini limitati ed in domini esterni con frontiera di classeC 1, che conduce alla decomposizione di Helmholtz diL ω q(Ω)n per un qualsiasi ω∈A q. Il risultato è ottenuto trasferendo il metodo di Simader e Sohr [4] al caso pesato. Quello qui presente estende un risultato di Farwig e Sohr [2] dove la decomposizione di Helmholtz diL ω q(Ω)n è dimostrata per domini esterni e pesi della classe di Muckenhoupt privi di singolarità in un intorno di ϖΩ.相似文献
6.
Russell Merris 《Israel Journal of Mathematics》1983,46(4):301-304
Denote byH
n the set ofn byn, positive definite hermitian matrices. Hadamard proved thath(A)≧det(A) for allA∈H
n, whereh(A) is the product of the main diagonal elements ofA. Subsequently, M. Marcus showed that per(A)≧h(A) for allA∈H
n. This article contains a result for all generalized matrix functions from which it follows thath(A)≧(per(A1/n
))
n
,A∈H
n. 相似文献
7.
Soulaymane Korry 《Israel Journal of Mathematics》2003,133(1):357-367
Letp∈(1, +∞) ands ∈ (0, +∞) be two real numbers, and letH
p
s
(ℝ
n
) denote the Sobolev space defined with Bessel potentials. We give a classA of operators, such thatB
s,p
-almost all points ℝ
n
are Lebesgue points ofT(f), for allf ∈H
p
s
(ℝ
n
) and allT ∈A (B
s,p
denotes the Bessel capacity); this extends the result of Bagby and Ziemer (cf. [2], [15]) and Bojarski-Hajlasz [4], valid
wheneverT is the identity operator. Furthermore, we describe an interesting special subclassC ofA (C contains the Hardy-Littlewood maximal operator, Littlewood-Paley square functions and the absolute value operatorT: f→|f|) such that, for everyf ∈H
p
s
(ℝ
n
) and everyT ∈C, T(f) is quasiuniformly continuous in ℝ
n
; this yields an improvement of the Meyers result [10] which asserts that everyf ∈H
p
s
(ℝ
n
) is quasicontinuous. However,T (f) does not belong, in general, toH
p
s
(ℝ
n
) wheneverT ∈C ands≥1+1/p (cf. Bourdaud-Kateb [5] or Korry [7]). 相似文献
8.
Then-th commutator for a,b in a ringR is defined inductively as follows: [a,b]1=[a,b]=ab−ba and[a,b]
n=[[a,b]−1,b]. We characterize the ringsR without non-zero nil right ideals in which[a,b]
nis nilpotent or regular for alla,b∈R. We also examine the case whereR is a semiprime ring with involution in which[t
1, t2]nis nilpotent or regular for all tracest
1,t2∈R. 相似文献
9.
Soon-Mo Jung Byungbae Kim 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):293-308
A result of Skof and Terracini will be generalized; More precisely, we will prove that if a functionf : [-t, t]n →E satisfies the inequality (1) for some δ > 0 and for allx, y ∈ [-t, t]n withx + y, x - y ∈ [-t, t]n, then there exists a quadratic functionq: ℝn →E such that ∥f(x) -q(x)∥ < (2912n2 + 1872n + 334)δ for anyx ∈ [-t, t]
n
. 相似文献
10.
Given a subgroup G of the symmetric group S
n
on n letters, a semigroup S of transformations of X
n
is G-normal if G
S
=G, where G
S
consists of all permutations h∈S
n
such that h
−1
fh∈S for all f∈S. A semigroup S is G-normax if it is a maximal semigroup in the set of all G-normal semigroups.
In 1996, I. Levi showed that the alternating group A
n
can not serve as the group G
S
for any semigroup of total transformations of X
n
. In 2000 and 2001, I. Levi, D.B. McAlister and R.B. McFadden described all A
n
-normal semigroups of partial transformations of X
n
. Also, in 1994, I. Levi and R.B. McFadden described all S
n
-normal semigroups.
In this paper, we show that the dihedral group D
n
may serve as the group G
S
for semigroups of transformations of X
n
. We characterize a large class of D
n
-normax semigroups and describe certain D
n
-normal semigroups. 相似文献
11.
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
12.
Paul-Jean Cahen 《manuscripta mathematica》1990,67(1):333-343
Let A be a commutative domain with quotient field K and AS the ring of integer-valued polynomials thus AS={f∈K[X]; f(A)⊂A}; we show that the Krull dimension of AS is such that dim AS≥dim A[X]-1 and give examples where dim AS=dim A[X]-1. Considering chains of primes of AS above a maximal idealm of finite residue field, we give also examples where the length of such a chain can arbitrarily be prescribed (whereas in
A[X] the length of such chains is always 1). To provide such examples we consider a pair of domains A⊂B sharing an ideal I
such that A/I is finite; we give sufficient conditients to have AS⊂B[X] and show that in this case dim AS=dim B[X]. At last, as a generalisation of Noetherian rings of dimension 1, we consider domains with an ideal I such that
A/I is finite and a power In of I is contained in a proper principal ideal of A; for such domains we show that every prime of AS above a primem containing I is maximal.
相似文献
13.
We raise the following problem. For natural numbers m, n ≥ 2, determine pairs d′, d″ (both depending on m and n only) with the property that in every pair of set systems A, B with |A| ≤ m, |B| ≤ n, and A ∩ B ≠ 0 for all A ∈ A, B ∈ B, there exists an element contained in at least d′ |A| members of A and d″ |B| members of B. Generalizing a previous result of Kyureghyan, we prove that all the extremal pairs of (d′, d″) lie on or above the line (n − 1) x + (m − 1) y = 1. Constructions show that the pair (1 + ɛ / 2n − 2, 1 + ɛ / 2m − 2) is infeasible in general, for all m, n ≥ 2 and all ɛ > 0. Moreover, for m = 2, the pair (d′, d″) = (1 / n, 1 / 2) is feasible if and only if 2 ≤ n ≤ 4.
The problem originates from Razborov and Vereshchagin’s work on decision tree complexity.
Research supported in part by the Hungarian Research Fund under grant OTKA T-032969. 相似文献
14.
S. N. Preobrazhenskii 《Moscow University Mathematics Bulletin》2010,65(4):166-171
It is shown that if a function determined on the segment [−1, 1] has a sufficiently good approximation by partial sums of
its expansion over Legendre polynomial, then, given the function’s Fourier coefficients c
n
for some subset of n ∈ [n
1, n
2], one can approximately recover them for all n ∈ [n
1, n
2]. A new approach to factorization of integer numbers is given as an application. 相似文献
15.
H. Gaifman 《Israel Journal of Mathematics》1974,19(4):359-368
We construct a sequence of transitive finite setsA
n
,n∈ω, such that, puttingA = U
n∈ω
A
n
,A is transitive of rank ω (without urelements) and, for every sentence Φ in the language of set theory,A ⊧φ if and only ifA
n
⊧φ, for all but finitely manyn’s. This implies the claim of the title. 相似文献
16.
Yosef Stein 《Israel Journal of Mathematics》1989,68(1):109-122
LetK be an algebraically closed field of characteristic zero. ForA ∈K[x, y] let σ(A) = {λ ∈K:A − λ is reducible}. For λ ∈ σ(A) letA − λ = ∏
i=1
n(λ)
A
iλ
k
μ whereA
iλ are distinct primes. Let ϱλ(A) =n(λ) − 1 and let ρ(A) = Σλɛσ(A)ϱλ(A). The main result is the following:
Theorem.If A ∈ K[x, y] is not a composite polynomial, then ρ(A) < degA. 相似文献
17.
Vitalij A. Chatyrko Venuste Nyagaharwa 《P-Adic Numbers, Ultrametric Analysis, and Applications》2011,3(2):100-107
Let A be the family of all meager sets of the real line ℝ, V be the family of all Vitali sets of ℝ, V
1 be the family of all finite unions of elements of V and V
2 = {(C \ A
1) ∪ A
2: C ∈ V
1; A
1, A
2 ∈ A}. We show that the families V, V
1, V
2 are invariant under translations of ℝ, and V
1, V
2 are abelian semigroups with the respect to the operation of union of sets. Moreover, V ⊂ V
1 ⊂ V
2 and V
2 consists of zero-dimensional sets without the Baire property. Then we extend the results above to the Euclidean spaces ℝ
n
, n ≥ 2, and their products with the finite powers of the Sorgenfrey line. 相似文献
18.
It is proved that all the equivalence relations of a universal algebra A are its congruences if and only if either |A| ≤ 2 or every operation f of the signature is a constant (i.e., f(a
1
, . . . , a
n
) = c for some c ∈ A and all the a
1
, . . . , a
n
∈ A) or a projection (i.e., f(a
1
, . . . , a
n
) = a
i
for some i and all the a
1
, . . . , a
n
∈ A). All the equivalence relations of a groupoid G are its right congruences if and only if either |G| ≤ 2 or every element a ∈ G is a right unit or a generalized right zero (i.e., x
a
= y
a
for all x, y ∈ G). All the equivalence relations of a semigroup S are right congruences if and only if either |S| ≤ 2 or S can be represented as S = A∪B, where A is an inflation of a right zero semigroup, and B is the empty set or a left zero semigroup, and ab = a, ba = a
2 for a ∈ A, b ∈ B. If G is a groupoid of 4 or more elements and all the equivalence relations of it are right or left congruences, then either all
the equivalence relations of the groupoid G are left congruences, or all of them are right congruences. A similar assertion for semigroups is valid without the restriction
on the number of elements. 相似文献
19.
Chmielinski has proved in the paper [4] the superstability of the generalized orthogonality equation |〈f(x), f(y)〉| = |〈x,y〉|. In this paper, we will extend the result of Chmielinski by proving a theorem: LetD
n be a suitable subset of ℝn. If a function f:D
n → ℝn satisfies the inequality ∥〈f(x), f(y)〉| |〈x,y〉∥ ≤ φ(x,y) for an appropriate control function φ(x, y) and for allx, y ∈ D
n, thenf satisfies the generalized orthogonality equation for anyx, y ∈ D
n. 相似文献
20.
Let X
1
, X
2
, ..., Xn be n independent identically distributed real random variables and Sn = Σ
n=1
n
Xi. We obtain precise asymptotics forP (Sn ∈ nA) for rather arbitrary Borel sets A1 in terms of the density of the dominating points in A. Our result extends classical theorems in the field of large deviations
for independent samples. We also obtain asymptotics forP (Sn ∈ γnA), with γn/n → ∞.
Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part I. 相似文献