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1.
Let κ be a cardinal which is measurable after generically adding many Cohen subsets to κ and let be the κ-Rado graph. We prove, for 2 ≤ m < ω, that there is a finite value such that the set [κ]
m
can be partitioned into classes such that for any coloring of any of the classes C
i
in fewer than κ colors, there is a copy of in such that is monochromatic. It follows that , that is, for any coloring of with fewer than κ colors there is a copy of such that has at most colors. On the other hand, we show that there are colorings of such that if is any copy of then for all , and hence . We characterize as the cardinality of a certain finite set of types and obtain an upper and a lower bound on its value. In particular, and for m > 2 we have where r
m
is the corresponding number of types for the countable Rado graph.
Research of M. Džamonja and J. A. Larson were partially supported by Engineering and Physical Sciences Research Council and
research of W. J. Mitchell was partly supported by grant number DMS 0400954 from the United States National Science Foundation. 相似文献
2.
Valentina S. Harizanov Carl G. JockuschJr. Julia F. Knight 《Archive for Mathematical Logic》2009,48(1):39-53
We study the complexity of infinite chains and antichains in computable partial orderings. We show that there is a computable
partial ordering which has an infinite chain but none that is or , and also obtain the analogous result for antichains. On the other hand, we show that every computable partial ordering
which has an infinite chain must have an infinite chain that is the difference of two sets. Our main result is that there is a computably axiomatizable theory K of partial orderings such that K has a computable model with arbitrarily long finite chains but no computable model with an infinite chain. We also prove
the corresponding result for antichains. Finally, we prove that if a computable partial ordering has the feature that for every , there is an infinite chain or antichain that is relative to , then we have uniform dichotomy: either for all copies of , there is an infinite chain that is relative to , or for all copies of , there is an infinite antichain that is relative to . 相似文献
3.
Kenley Jung 《Mathematische Annalen》2007,338(1):241-248
Suppose M is a tracial von Neumann algebra embeddable into (the ultraproduct of the hyperfinite II1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k ,γ). We say that X is tubular if for any ε > 0 there exist and γ > 0 such that if then there exists a k × k unitary u satisfying for each 1 ≤ i ≤ n. We show that the following conditions are equivalent:
Research supported in part by the NSF.
Dedicated to Ed Effros on the occasion of his 70th birthday. 相似文献
• | M is amenable (i.e., injective). |
• | X is tubular. |
• | Any two embeddings of M into are conjugate by a unitary . |
4.
In this article we extend Milnor’s fibration theorem to the case of functions of the form with f, g holomorphic, defined on a complex analytic (possibly singular) germ (X, 0). We further refine this fibration theorem by looking not only at the link of , but also at its multi-link structure, which is more subtle. We mostly focus on the case when X has complex dimension two. Our main result (Theorem 4.4) gives in this case the equivalence of the following three statements:
Moreover one has that if these conditions hold, then the Milnor-Lê fibration of is a fibration of the multilink . We also give a combinatorial criterium to decide whether or not the multilink is fibered. If the meromorphic germ f/g is semitame, then we show that the Milnor-Lê fibration given by is equivalent to the usual Milnor fibration given by . We finish this article by discussing several realization problems.
Research partially supported by CONACYT and DGAPA-UNAM, Mexico, and by CNRS and ECOS, France. 相似文献
(i) | The real analytic germ has 0 as an isolated critical value; |
(ii) | the multilink is fibered; and |
(iii) | if is a resolution of the holomorphic germ , then for each rupture vertex (j) of the decorated dual graph of π one has that the corresponding multiplicities of f, g satisfy: . |
5.
Ahmed Ainouche 《Graphs and Combinatorics》2009,25(2):129-137
Let G = (V, E) be a any simple, undirected graph on n ≥ 3 vertices with the degree sequence . We consider the class of graphs satisfying the condition where , is a positive integer. It is known that is hamiltonian if θ ≤ δ. In this paper,
相似文献
(i) | we give a necessary and sufficient condition, easy to check, ensuring that is nonhamiltonian and we characterize all the exceptional sub-classes. |
(ii) | we prove that is either bipartite or contains cycles of all lengths from 3 to c(G), the length of a longest cycle in G. |
6.
The main result of this work is a Dancer-type bifurcation result for the quasilinear elliptic problem
Here, Ω is a bounded domain in denotes the Dirichlet p-Laplacian on , and is a spectral parameter. Let μ1 denote the first (smallest) eigenvalue of −Δ
p
. Under some natural hypotheses on the perturbation function , we show that the trivial solution is a bifurcation point for problem (P) and, moreover, there are two distinct continua, and , consisting of nontrivial solutions to problem (P) which bifurcate from the set of trivial solutions at the bifurcation point (0, μ1). The continua and are either both unbounded in E, or else their intersection contains also a point other than (0, μ1). For the semilinear problem (P) (i.e., for p = 2) this is a classical result due to E. N. Dancer from 1974. We also provide an example of how the union looks like (for p > 2) in an interesting particular case.
Our proofs are based on very precise, local asymptotic analysis for λ near μ1 (for any 1 < p < ∞) which is combined with standard topological degree arguments from global bifurcation theory used in Dancer’s original
work.
Submitted: July 28, 2007. Accepted: November 8, 2007. 相似文献
((P)) |
7.
8.
In this paper, we prove that if is a radially symmetric, sign-changing stationary solution of the nonlinear heat equation
in the unit ball of , N ≥ 3, with Dirichlet boundary conditions, then the solution of (NLH) with initial value blows up in finite time if |λ − 1| > 0 is sufficiently small and if α is subcritical and sufficiently close to 4/(N − 2).
F. Dickstein was partially supported by CNPq (Brazil). 相似文献
9.
Anna Maria Micheletti Angela Pistoia 《Calculus of Variations and Partial Differential Equations》2009,34(2):233-265
Given (M, g) a smooth compact Riemannian N-manifold, N ≥ 2, we show that positive solutions to the problem
are generated by stable critical points of the scalar curvature of g, provided is small enough. Here p > 2 if N = 2 and if N ≥ 3.
The authors are supported by Mi.U.R. project “Metodi variazionali e topologici nello studio di fenomeni non lineari”. 相似文献
10.
Asher M. Kach 《Archive for Mathematical Logic》2008,47(3):211-219
The main result is that for sets , the following are equivalent:
Other results discuss the relationship between these sets and the sets.
The author’s research was partially supported by a VIGRE grant fellowship. The author thanks Denis Hirschfeldt and Steffen
Lempp for an insightful conversation about LIMINF sets; Christopher Alfeld and Robert Owen for numerous comments and suggestions; and his thesis advisor Steffen Lempp for
his guidance. 相似文献
(1) | The shuffle sum σ(S) is computable. |
(2) | The set S is a limit infimum set, i.e., there is a total computable function g(x, t) such that enumerates S. |
(3) | The set S is a limitwise monotonic set relative to 0′, i.e., there is a total 0′-computable function satisfying such that enumerates S. |
11.
Stevo Stević 《Mediterranean Journal of Mathematics》2008,5(1):61-76
In this paper we investigate harmonic Hardy-Orlicz and Bergman-Orlicz b
φ,α
(B) spaces, using an identity of Hardy-Stein type. We also extend the notion of the Lusin property by introducing (φ, α)-Lusin property with respect to a Stoltz domain. The main result in the paper is as follows: Let be a nonnegative increasing convex function twice differentiable on (0, ∞), and u a harmonic function on the unit ball B in . Then the following statements are equivalent:
相似文献
(a) | . |
(b) | . |
(c) | u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for any . |
(d) | u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for some . |
12.
Robert J. Taggart 《Mathematische Zeitschrift》2009,261(4):933-949
Suppose that {T
t
: t ≥ 0} is a symmetric diffusion semigroup on L
2(X) and denote by its tensor product extension to the Bochner space , where belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf–Dunford–Schwartz ergodic theorem
and show that this extends to a maximal theorem for analytic continuations of on . As an application, we show that such continuations exhibit pointwise convergence. 相似文献
13.
We consider the following Liouville equation in
For each fixed and a
j
> 0 for 1 ≤ j ≤ k, we construct a solution to the above equation with the following asymptotic behavior:
相似文献
14.
Nicola Garofalo 《manuscripta mathematica》2008,126(3):353-373
We prove some new a priori estimates for H
2-convex functions which are zero on the boundary of a bounded smooth domain Ω in a Carnot group . Such estimates are global and are geometric in nature as they involve the horizontal mean curvature of ∂Ω. As a consequence of our bounds we show that if has step two, then for any smooth H
2-convex function in vanishing on ∂Ω one has
.
Supported in part by NSF Grant DMS-07010001. 相似文献
15.
16.
Besides other things we prove that if , , locally minimizes the energy
, with N-functions a ≤ b having the Δ2-property, then . Moreover, the condition
for all large values of t implies . If n = 2, then these results can be improved up to for all s < ∞ without the hypothesis . If n ≥ 3 together with M = 1, then higher integrability for any exponent holds under more restrictive assumptions than .
相似文献
17.
Yonutz V. Stanchescu 《Combinatorica》2008,28(3):343-355
We describe the structure of three dimensional sets of lattice points, having a small doubling property. Let be a finite subset of ℤ3 such that dim = 3. If and , then lies on three parallel lines. Moreover, for every three dimensional finite set that lies on three parallel lines, if , then is contained in three arithmetic progressions with the same common difference, having together no more than terms. These best possible results confirm a recent conjecture of Freiman and cannot be sharpened by reducing the quantity
υ or by increasing the upper bounds for . 相似文献
18.
Résumé. Soit A une algèbre réelle sans diviseurs de zéro. On suppose que l’espace vectoriel A est muni d’une norme ∥.∥ préhilbertienne vérifiant ∥a
2∥ ≤ ∥a∥2 pour tout . Alors A est de dimension finie dans chacun des quatre cas suivants :
A est isomorphe à ou dans les deux premiers cas et isomorphe à ou dans les deux derniers cas.
1. | A est commutative contenant un élément non nul a tel que ∥ax∥ = ∥a∥ ∥x∥ pour tout , |
2. | A est commutative algébrique et ∥a 2∥ = ∥a∥2 pour tout , |
3. | A est alternative contenant un élément unité e tel que ∥e∥ = 1, |
4. | A est alternative contenant un élément central non nul a tel que ∥ax∥ = ∥a∥ ∥x∥ pour tout . |
Let A be a real algebra without divisor of zero. Assuming that a vector space A is endowed with a pre-Hilbert norm ∥.∥ satisfying ∥a 2∥ ≤ ∥a∥2 for all . Then A is finite dimensional in the four following cases :A is isomorphic to or in the two first cases and isomorphic to or in the two last cases.
1. A is a commutative containing a nonzero element a such that ∥ax∥ = ∥a∥∥x∥ for all , 2. A is a commutative algebraic and ∥a 2∥ = ∥a∥2 for all , 3. A is an alternative containing a unit element e such that ∥e∥ = 1, 4. A is an alternative containing a nonzero central element a such that ∥ax∥ = ∥ a∥∥x∥ for all .
相似文献
19.
Let X1 and X2 be subspaces of quotients of R
OH and C
OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor
product into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our
result produces a completely isomorphic embedding of (equipped with its natural operator space structure) into with a QWEP von Neumann algebra.
Received: June 2006, Revision: June 2007, Accepted: September 2007 相似文献
20.
Mean-value theorems and extensions of the Elliott-Daboussi theorem on additive arithmetic semigroups
Wen-Bin Zhang 《The Ramanujan Journal》2008,15(1):47-75
We present more general forms of the mean-value theorems established before for multiplicative functions on additive arithmetic
semigroups and prove, on the basis of these new theorems, extensions of the Elliott-Daboussi theorem. Let
be an additive arithmetic semigroup with a generating set ℘ of primes p. Assume that the number G(m) of elements a in
with “degree” ∂(a)=m satisfies
with constants q>1, ρ
1<ρ
2<⋅⋅⋅<ρ
r
=ρ, ρ≥1, γ>1+ρ. For the main result, let α,τ,η be positive constants such that α>1,τ
ρ≥1, and τ
α
ρ≥1. Then for a multiplicative function f(a) on
the following two conditions (A) and (B) are equivalent. These are (A) All four series
converge and
and (B) The order τ
ρ mean-value
exists with m
f
≠0 and the limit
exists with M
v
(α)>0.
相似文献