共查询到20条相似文献,搜索用时 31 毫秒
1.
Zhiqing Han 《数学学报(英文版)》2000,16(2):349-360
Abstract
In this paper we prove a very general result concerning solvability of the resonant problem: Δu + λκ
u + g(x, u) = h (x); u = 0, x ∈∂Ω, which immediately gives three generalized Landesman-Lazer conditions. The most interesting application of the general
result is concerned with the problem when λκ = λ1, in which case we prove solvability results for it under conditions which are not the standard Landesman-Lazer condition
or only partly enjoy it. Furthermore, we propose a new sign condition and give a comprehensive extension of a main result
of Figueiredo and Ni. 相似文献
2.
We characterize cardinalsκ such that 2λ = 2κ wheneverκ ≦λ < 2κ using ideals in small algebras of sets satisfying certain completeness and saturation conditions.
Research of this author was supported by an NSF Grant. 相似文献
3.
Guohua Wu 《Archive for Mathematical Logic》2003,42(2):201-204
We give a characterization of strongly compact cardinals in terms of Q
κ
λ. We also prove that weakly normal Q-measures on Q
κ
λ are ⊂κ-normal.
Received: 29 September 2000 / Revised version: March 2002 Published online: 5 November 2002
This project is supported by the New Zealand Marsden Fund. The author wishes to thank the referee for numerous comments and
suggestions which have been incorporated into this version of the paper. 相似文献
4.
We investigate closed surfaces in Euclidean 3-space satisfying certain functional relations κ = F(λ) between the principal curvatures κ, λ. In particular we find analytic closed surfaces of genus zero where F is a quadratic polynomial or F(λ) = cλ2n+1. This generalizes results by H. Hopf on the case where F is linear and the case of ellipsoids of revolution where F(λ) = cλ3. 相似文献
5.
We investigate closed surfaces in Euclidean 3-space satisfying certain functional relations κ = F(λ) between the principal curvatures κ, λ. In particular we find analytic closed surfaces of genus zero where F is a quadratic polynomial or F(λ) = cλ2n+1. This generalizes results by H. Hopf on the case where F is linear and the case of ellipsoids of revolution where F(λ) = cλ3. 相似文献
6.
The concept of enlargement of a generalized topology was introduced by á. Császár [4]. He also introduced the concepts of
(κ,λ)-continuity and (κ
μ
,λ
ν)-continuity on enlargements. In this paper, we characterize the (κ,λ)-continuity and introduce the concept of strong (κ,λ)-continuity on enlargements. In particular, we study characterizations for the strong (κ,λ)-continuity and the relationships among (μ,ν)-continuity, (κ,λ)-continuity, strong (κ,λ)-continuity and (κ
μ
,λ
ν)-continuity. 相似文献
7.
Assaf Rinot 《Archive for Mathematical Logic》2007,46(5-6):457-464
In their paper from 1981, Milner and Sauer conjectured that for any poset , if , then P must contain an antichain of size κ. We prove that for λ > cf(λ) = κ, if there exists a cardinal μ < λ such that cov(λ, μ, κ, 2) = λ, then any poset of cofinality λ contains λ
κ
antichains of size κ. The hypothesis of our theorem is very weak and is a consequence of many well-known axioms such as GCH, SSH and PFA. The
consistency of the negation of this hypothesis is unknown.
相似文献
8.
We deal with the question of existence of a universal object in the category of universal locally finite groups; the answer
is negative for many uncountable cardinalities; for example, for 2ℵ
0, and assuming G.C.H. for every cardinal whose confinality is >ℵ0. However, if λ>κ when κ is strongly compact and of λ=ℵ0, then there exists a universal locally finite group of cardinality λ. The idea is to use the failure of the amalgamation
property in a strong sense. We shall also prove the failure of the amalgamation property for universal locally finite groups
by transferring the kind of failure of the amalgamation property from LF into ULF.
We would like to thank Simon Thomas for reading carefully a preliminary version of this paper, proving Lemma 20 and making
valuable remarks. Also we thank the United States—Israel Binational Science Foundation for partially supporting this work. 相似文献
9.
Bronius Grigelionis 《Lithuanian Mathematical Journal》2011,51(2):194-206
We prove that the Thorin class $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 , is the minimal class of probability distributions on
\mathbbR+ {\mathbb{R}_{+} } that is closed under convolutions and weak limits and contains the Tweedie distributions Tw(κ+1)/κ
(μ, λ), μ > 0, λ > 0. 相似文献
10.
M. Vanninathan 《Proceedings Mathematical Sciences》1981,90(3):239-271
In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of
the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic
expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we
denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet:
λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).
Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in
the case of Neumann eigenvalue problem. 相似文献
11.
Tokuzo Shiga 《Probability Theory and Related Fields》1997,108(3):417-439
Summary. We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf;
d
in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate
the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ↘0.
Received: 21 May 1996 / In revised form: 2 February 1997 相似文献
12.
I. Juhász 《Israel Journal of Mathematics》1993,81(3):369-379
The weight-spectrumSp(w, X) of a spaceX is the set of weights of all infinite closed subspaces ofX. We prove that ifκ>ω is regular andX is compactT
2 withω(X)≥κ then some λ withκ≤λ≤2<κ is inSp(ω, X). Under CH this implies that the weight spectrum of a compact space can not omitω
1, and thus solves problem 22 of [M]. Also, it is consistent with 2ω=c being anything it can be that every countable closed setT of cardinals less thanc withω ∈ T satisfiesSp(w, X)=T for some separable compact LOTSX. This shows the independence from ZFC of a conjecture made in [AT].
Research supported by OTKA grant no. 1908. 相似文献
13.
We introduce an extension, indexed by a partially ordered set P and cardinal numbers κ,λ, denoted by (κ,<λ)⇝P, of the classical relation (κ,n,λ)→ρ in infinite combinatorics. By definition, (κ,n,λ)→ρ holds if every map F: [κ]
n
→[κ]<λ
has a ρ-element free set. For example, Kuratowski’s Free Set Theorem states that (κ,n,λ)→n+1 holds iff κ ≥ λ
+n
, where λ
+n
denotes the n-th cardinal successor of an infinite cardinal λ. By using the (κ,<λ)⇝P framework, we present a self-contained proof of the first author’s result that (λ
+n
,n,λ)→n+2, for each infinite cardinal λ and each positive integer n, which solves a problem stated in the 1985 monograph of Erdős, Hajnal, Máté, and Rado. Furthermore, by using an order-dimension
estimate established in 1971 by Hajnal and Spencer, we prove the relation $(\lambda ^{ + (n - 1)} ,r,\lambda ) \to 2^{\left\lfloor {\tfrac{1}
{2}(1 - 2^{ - r} )^{ - n/r} } \right\rfloor }
$(\lambda ^{ + (n - 1)} ,r,\lambda ) \to 2^{\left\lfloor {\tfrac{1}
{2}(1 - 2^{ - r} )^{ - n/r} } \right\rfloor }
, for every infinite cardinal λ and all positive integers n and r with 2≤r<n. For example, (ℵ210,4,ℵ0)→32,768. Other order-dimension estimates yield relations such as (ℵ109,4,ℵ0) → 257 (using an estimate by Füredi and Kahn) and (ℵ7,4,ℵ0)→10 (using an exact estimate by Dushnik). 相似文献
14.
Saharon Shelah 《Israel Journal of Mathematics》1996,95(1):61-114
We continue the investigations in the author’s book on cardinal arithmetic, assuming some knowledge of it. We deal with the
cofinality of (S
≤ℵ
0(κ), ⊆) for κ real valued measurable (Section 3), densities of box products (Section 5,3), prove the equality cov(λ,λ,θ+,2) in more cases even when cf(λ)=ℵ0 (Section 1), deal with bounds of pp(λ) for λ limit of inaccessible (Section 4) and give proofs to various claims I was sure
I had already written but did not find (Section 6).
Done mainly 1–4/1991. I thank Alice Leonhardt for typing and retyping so beautifully and accurately. Partially supported by
the Basic Research Fund, Israel Academy of Sciences. Publication number 430. 相似文献
15.
A uniform ultrafilterU on κ is said to be λ-separating if distinct elements of the ultrapower never projectU to the same uniform ultrafilterV on λ. It is shown that, in the presence of CH, an ω-separating ultrafilterU on κ>ω is non-(ω, ω1)-regular and, in fact, if κ < ℵω thenU is λ-separating for all λ. Several large cardinal consequences of the existence of such an ultrafilterU are derived. 相似文献
16.
Masahiro Shioya 《Israel Journal of Mathematics》1999,114(1):347-357
Letκ >ω be a regular cardinal and λ >κ a cardinal. Solovay’s classical result for κ[So] led Menas [Me] to conjecture that a stationary subset ofP
κλ would split into λ<κ stationary set of size κ+ (see[BT]), the conjecture implies that the size is (κ+)<κ as well.
Part of this work was done during the author’s stay at Boston University as one of the Japanese Overseas Research Fellows.
He gratefully acknowledge Professor Akihiro Kanamori’s hospitality. He also wishes to thank members of the set theory seminar
at Waseda University for their interest at the early stage. 相似文献
17.
Saharon Shelah 《Israel Journal of Mathematics》1990,70(1):69-81
We give a complete proof of the consistency of the existence of a universal graph of powerλ, whereκ =κ
<κ
<λ = cfλ < 2
κ
are arbitrary.
The author would like to thank the NSF for partially supporting this research, Alice Leonhardt for the beautiful typing, and
M. Kojman for proofreading. Publication No. 175A.
The proof in the second section of [9] is flawed. 相似文献
18.
The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the conneetivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ1(L) = 2λ1 (D), and that for a connected graph G and its line graph L, if one of κ1 (L) and λ(G) exists, then κ1(L) = λ2(G). This paper determines that κ1(B(d, n) is equal to 4d- 8 for n = 2 and d ≥ 4, and to 4d-4 for n ≥ 3 and d ≥ 3, and that κ1(K(d, n)) is equal to 4d- 4 for d 〉 2 and n ≥ 2 except K(2, 2). It then follows that B(d,n) and K(d, n) are both super connected for any d ≥ 2 and n ≥ 1. 相似文献
19.
Existence results for semilinear elliptic variational inequalities with changing sign nonlinearities
In this paper we present some existence results for a class of semilinear elliptic variational inequalities, depending on
a real parameter λ, with changing sign nonlinearities. The fundamental tool to prove the existence result is a penalization
method combined with the Mountain Pass Theorem and the Linking Theorem, respectively in the case λ < λ 1 and λ ≥ λ 1, where λ1 is the first eigenvalue of the uniformly elliptic operator A involved in the variational inequality. 相似文献
20.
Following [5], aT
3 spaceX is called good (splendid) if it is countably compact, locally countable (andω-fair).G(κ) (resp.S(κ)) denotes the statement that a good (resp. splendid) spaceX with |X|=κ exists. We prove here that (i) Con(ZF)→Con(ZFC+MA+2
ω
is big+S(κ) holds unlessω=cf(κ)<κ); (ii) a supercompact cardinal implies Con(ZFC+MA+2suω>ω+1+┐G(ωω+1); (iii) the “Chang conjecture” (ωω+1),→(ω
1,ω) implies ┐S(κ) for allκ≧k≧ωω; (iv) ifP addsω
1 dominating reals toV iteratively then, in
, we haveG(λω) for allλ.
Research supported by Hungarian National Foundation for Scientific Research grant no. 1805. 相似文献