共查询到20条相似文献,搜索用时 812 毫秒
1.
Dorothee Schueth 《Commentarii Mathematici Helvetici》1995,70(1):434-454
It is known that ifH
m is the classical (2m+1)-dimensional Heisenberg group, Γ a cocompact discrete subgroup ofH
m andg a left invariant metric, then (Γ/H
m, g) is infinitesimally spectrally rigid within the family of left invariant metrics. The purpose of this paper is to show that
for everym≥2 and for a certain choice of Γ andg, there is a deformation (Γ/H
m, g
α) withg=g
1 such that for every α≠1, (Γ/H
m, g
α)does admit a nontrivial isospectral deformation. For α≠1 the metricsg
α will not beH
m-left invariant, and the (Γ/H
m, gxα) will not be nilmanifolds, but still solvmanifolds. 相似文献
2.
In accordance with the demands of the so-called local approach to inverse problems, the set of “waves” uf (·, T) is studied, where uf (x,t) is the solution of the initial boundary-value problem utt−Δu=0 in Ω×(0,T), u|t<0=0, u|∂Ω×(0,T)=f, and the (singular) control f runs over the class L2((0,T); H−m (∂Ω)) (m>0). The following result is established. Let ΩT={x ∈ Ω : dist(x, ∂Ω)<T)} be a subdomain of Ω ⊂ ℝn (diam Ω<∞) filled with waves by a final instant of time t=T, let T*=inf{T : ΩT=Ω} be the time of filling the whole domain Ω. We introduce the notation Dm=Dom((−Δ)m/2), where (−Δ) is the Laplace operator, Dom(−Δ)=H2(Ω)∩H
0
1
(Ω);D−m=(Dm)′;D−m(ΩT)={y∈D−m:supp y ⋐ ΩT. If T<T., then the reachable set R
m
T
={ut(·, T): f ∈ L2((0,T), H−m (∂Ω))} (∀m>0), which is dense in D−m(ΩT), does not contain the class C
0
∞
(ΩT). Examples of a ∈ C
0
∞
, a ∈ R
m
T
, are presented.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 7–21.
Translated by T. N. Surkova. 相似文献
3.
If G and H are vertex-transitive graphs, then the framing number fr(G,H) of G and H is defined as the minimum order of a graph every vertex of which belongs to an induced G and an induced H. This paper investigates fr(C
m,C
n) for m<n. We show first that fr(C
m,C
n)≥n+2 and determine when equality occurs. Thereafter we establish general lower and upper bounds which show that fr(C
m,C
n) is approximately the minimum of and n+n/m.
Received: June 12, 1996 / Revised: June 2, 1997 相似文献
4.
George Purdy 《Israel Journal of Mathematics》1978,30(1-2):54-56
If ann-dimensional polytope has facets of areaA
1,A
2, …,A
m, then 2A
i <A
1+…+A
m fori=1,…,m. We show here that conversely these inequalities also ensure the existence of a polytope having these areas. 相似文献
5.
We study self adjoint operators of the form?H
ω = H
0 + ∑λω(n) <δ
n
,·>δ
n
,?where the δ
n
’s are a family of orthonormal vectors and the λω(n)’s are independently distributed random variables with absolutely continuous probability distributions. We prove a general
structural theorem saying that for each pair (n,m), if the cyclic subspaces corresponding to the vectors δ
n
and δ
m
are not completely orthogonal, then the restrictions of H
ω to these subspaces are unitarily equivalent (with probability one). This has some consequences for the spectral theory of
such operators. In particular, we show that “well behaved” absolutely continuous spectrum of Anderson type Hamiltonians must
be pure, and use this to prove the purity of absolutely continuous spectrum in some concrete cases.
Oblatum 27-V-1999 & 6-I-2000?Published online: 8 May 2000 相似文献
6.
Based on a new regularization-renormalization method, the λφ4 model used in standard model (SM) is studied both perturbatively and nonperturbatively by Gaussian effective potential (GEP).
The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling
with theSU(2) ×U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated to bem
H≈138 GeV. The critical temperature (T
c
) for restoration of symmetry of Higgs field, the critical energy scale (μmax, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale (μmax, at which the symmetry of the Higgs field is restored) in the SM areT
c
≈476 GeV, μc≈0.547 × 1015 and μmax≈0.873 × 1015, respectively.
Project supported in part by the National Natural Science Foundation of China. 相似文献
7.
P. Penner 《Algebra Universalis》1981,13(1):307-314
Following W. Taylor we define a hyperidentity ∈ to be formally the same as an identity (e.g.,F(G(x, y, z), G(x, y, z))=G(x, y, z)). However, a varietyV is said to satisfy a hyperidentity ∈, if whenever the operation symbols of ∈ are replaced by any choice of polynomials (appropriate
forV) of the same arity as the corresponding operation symbols of ∈, then the resulting identity holds inV in the usual sense. For example, if a varietyV of type <2,2> with operation symbols ∨ and ∧ satisfies the hyperidentity given above, then substituting the polynomial (x∨y)∨z
for the symbolG, and the polynomialx∧y forF, we see thatV must in particular satisfy the identity ((x∨y)∨z)∧((x∨y)∨z)=((x∨y)∨z). The set of all hyperidentities satisfied by a varietyV, will be denoted byH(V). We shall letH
m
(V) be the set of all hyperidentities hoiding inV with operation symbols of arity at mostm, andH
n
(V) will denote the set of all hyperidentities ofV with at mostn distinct variables. In this paper we shall show that ifV is a nontrivial variety of lattices or the variety of all semilattices, then for any integersm andn, there exists a hyperidentity ∈ such that ∈ holds inV, and ∈ is not a consequence ofH
m
(V)∪H
n
(V). From this it is deduced that the hyperidentities ofV are not finitely based, partly soling a problem of Taylor [7, Problem 3].
The research of the author was supported by NSERC of Canada.
Presented by W. Taylor. 相似文献
8.
Let K be a field of characteristics 0 or a field of characteristic 2 and of transcendence degree ≥1, and let G=GL(n, K) be
the general linear group of degree n≥2 over K. Further, let
. It is proved that in G there exist chains of subgroups {Hm:m ∈ {, infinite in both directions, such that Hm<Hm−1, Hm−1 coincides with the normalizer NG(Hm), and every quotient group Hm−1/Hm is an elementary Abelian group of type (2,2,...,2) and of rank p. Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 30–66.
Translated by V. V. Ishkhanov. 相似文献
9.
Jacob Feldman 《Israel Journal of Mathematics》1980,36(3-4):321-345
A new approach is given to the entropy of a probability-preserving group action (in the context ofZ and ofR
n
), by defining an approximate “r-entropy”, 0<r<1, and lettingr → 0. If the usual entropy may be described as the growth rate of the number of essential names, then ther-entropy is the growth rate of the number of essential “groups of names” of width≦r, in an appropriate sense. The approach is especially useful for actions of continuous groups. We apply these techniques to
state and prove a “second order” equipartition theorem forZ
m
×R
n
and to give a “natural” proof of Ornstein’s isomorphism theorem for Bernoulli actions ofZ
m
×R
n
, as well as a characterization of such actions which seems to be the appropriate generalization of “finitely determined”. 相似文献
10.
It is well known that if m is an L
p
-multiplier for the Fourier transform on
\mathbbRn{\mathbb{R}^n} , (1 < p < ∞) then there exists a pseudomeasure σ such that T
m
f = σ * f . A similar problem is discussed for the L
p
−Fourier multipliers for H{\mathcal{H}} -valued functions on the Heisenberg group, where H{\mathcal{H}} is a separable Hilbert space. 相似文献
11.
Yong Ding Senhua Lan 《分析论及其应用》2006,22(4):339-352
Let A be a symmetric expansive matrix and Hp(Rn) be the anisotropic Hardy space associated with A. For a function m in L∞(Rn), an appropriately chosen function η in Cc∞(Rn) and j ∈ Z define mj(ξ) = m(Ajξ)η(ξ). The authors show that if 0 < p < 1 and (m)j belongs to the anisotropic nonhomogeneous Herz space K11/p-1,p(Rn), then m is a Fourier multiplier from Hp(Rn) to Lp(Rn). For p = 1, a similar result is obtained if the space K10,1(Rn) is replaced by a slightly smaller space K(w).Moreover, the authors show that if 0 < p ≤ 1 and if the sequence {(mj)V} belongs to a certain mixednorm space, depending on p, then m is also a Fourier multiplier from Hp(Rn) to Lp(Rn). 相似文献
12.
K. G. Chetyrkin J. H. Kühn A. Maier P. Maierhöfer P. Marquard M. Steinhauser C. Sturm 《Theoretical and Mathematical Physics》2012,170(2):217-228
We consider recent theoretical and experimental improvements in determining charm- and bottom-quark masses. We present a new,
improved evaluation of the contribution of the gluon condensate 〈α
s
G
2
/π〉 to the charm mass determination and a detailed study of potential uncertainties in the continuum cross section for b[`(b)]b\bar b production, together with a study of the parametric uncertainty from the α
s
-dependence of our results. The final results, mc(3 GeV) = 986(13) MeV and mb(mb) = 4163(16) MeV, together with the closely related lattice determination mc(3 GeV) = 986(6) MeV, currently represent the most precise determinations of these two fundamental standard-model parameters.
We critically analyze the theoretical and experimental uncertainties. 相似文献
13.
A graph is called H-free if it contains no copy of H. Denote by f
n
(H) the number of (labeled) H-free graphs on n vertices. Erdős conjectured that f
n
(H) ≤ 2(1+o(1))ex(n,H). This was first shown to be true for cliques; then, Erdős, Frankl, and R?dl proved it for all graphs H with χ(H)≥3. For most bipartite H, the question is still wide open, and even the correct order of magnitude of log2
f
n
(H) is not known. We prove that f
n
(K
m,m
) ≤ 2
O
(n
2−1/m
) for every m, extending the result of Kleitman and Winston and answering a question of Erdős. This bound is asymptotically sharp for m∈{2,3}, and possibly for all other values of m, for which the order of ex(n,K
m,m
) is conjectured to be Θ(n
2−1/m
). Our method also yields a bound on the number of K
m,m
-free graphs with fixed order and size, extending the result of Füredi. Using this bound, we prove a relaxed version of a
conjecture due to Haxell, Kohayakawa, and Łuczak and show that almost all K
3,3-free graphs of order n have more than 1/20·ex(n,K
3,3) edges. 相似文献
14.
J. Wu 《Israel Journal of Mathematics》2010,178(1):349-391
Let X be a co-H-space of (p − 1)-cell complex with all cells in even dimensions. Then the loop space ΩX admits a retract Ā
min(X) that is the evaluation of the functor Ā
min on X. In this paper, we determine the homology H
*(Ā
min(X)) and give the EHP sequence for the spaces Ā
min(X). 相似文献
15.
Steven W. Klein 《Annals of the Institute of Statistical Mathematics》1982,34(1):559-577
Summary LetX
1,...,X
m andY
t,...,Y be independent, random samples from populations which are N(θ,σ
x
2
) and N(θ,σ
y
2
), respectively, with all parameters unknown. In testingH
0:θ=0 againstH
1:θ≠0, thet-test based upon either sample is known to be admissible in the two-sample setting. If, however, one testsH
0 againstH
1:|θ|≧ε>0, with ε arbitrary, our main results show: (i) the construction of a test which is better than the particulart-test chosen, (ii) eacht-test is admissible under the invariance principle with respect to the group of scale changes, and (iii) there does not exist
a test which simultaneously is better than botht-tests. 相似文献
16.
Let G be a locally compact group and μ a probability measure on G, which is not assumed to be absolutely continuous with respect to Haar measure. Given a unitary representation $\pi ,\mathcal{H}Let G be a locally compact group and μ a probability measure on G, which is not assumed to be absolutely continuous with respect to Haar measure. Given a unitary representation
p,H\pi ,\mathcal{H} of G, we study spectral properties of the operator π(μ) acting on
H\mathcal{H} Assume that μ is adapted and that the trivial representation 1
G
is not weakly contained in the tensor product
p?[`(p)]\pi\otimes \overline\pi We show that π(μ) has a spectral gap, that is, for the spectral radius
rspec(p(m))r_{\rm spec}(\pi(\mu)) of π(μ), we have
rspec(p(m)) < 1.r_{\rm spec}(\pi(\mu))< 1. This provides a common generalization of several previously known results. Another consequence is that, if G has Kazhdan’s Property (T), then
rspec(p(m)) < 1r_{\rm spec}(\pi(\mu))< 1 for every unitary representation π of G without finite dimensional subrepresentations. Moreover, we give new examples of so-called identity excluding groups. 相似文献
17.
Integration questions related to fractional Brownian motion 总被引:1,自引:0,他引:1
Let {B
H
(u)}
u
∈ℝ be a fractional Brownian motion (fBm) with index H∈(0, 1) and (B
H
) be the closure in L
2(Ω) of the span Sp(B
H
) of the increments of fBm B
H
. It is well-known that, when B
H
= B
1/2 is the usual Brownian motion (Bm), an element X∈(B
1/2) can be characterized by a unique function f
X
∈L
2(ℝ), in which case one writes X in an integral form as X = ∫ℝ
f
X
(u)dB
1/2(u). From a different, though equivalent, perspective, the space L
2(ℝ) forms a class of integrands for the integral on the real line with respect to Bm B
1/2. In this work we explore whether a similar characterization of elements of (B
H
) can be obtained when H∈ (0, 1/2) or H∈ (1/2, 1). Since it is natural to define the integral of an elementary function f = ∑
k
=1
n
f
k
1
[uk,uk+1)
by ∑
k
=1
n
f
k
(B
H
(u
k
+1) −B
H
(u
k
)), we want the spaces of integrands to contain elementary functions. These classes of integrands are inner product spaces.
If the space of integrands is not complete, then it characterizes only a strict subset of (B
H
). When 0<H<1/2, by using the moving average representation of fBm B
H
, we construct a complete space of integrands. When 1/2<H<1, however, an analogous construction leads to a space of integrands which is not complete. When 0<H<1/2 or 1/2<H<1, we also consider a number of other spaces of integrands. While smaller and henceincomplete, they form a natural choice
and are convenient to workwith. We compare these spaces of integrands to the reproducing kernel Hilbert space of fBm.
Received: 9 August 1999 / Revised version: 10 January 2000 / Published online: 18 September 2000 相似文献
18.
Multiderivations of Coxeter arrangements 总被引:3,自引:0,他引:3
Hiroaki Terao 《Inventiones Mathematicae》2002,148(3):659-674
Let V be an ℓ-dimensional Euclidean space. Let G⊂O(V) be a finite irreducible orthogonal reflection group. Let ? be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H∈? choose α
H
∈V
* such that H=ker(α
H
). For each nonnegative integer m, define the derivation module D
(m)
(?)={θ∈Der
S
|θ(α
H
)∈Sα
m
H
}. The module is known to be a free S-module of rank ℓ by K. Saito (1975) for m=1 and L. Solomon-H. Terao (1998) for m=2. The main result of this paper is that this is the case for all m. Moreover we explicitly construct a basis for D
(m)
(?). Their degrees are all equal to mh/2 (when m is even) or are equal to ((m−1)h/2)+m
i
(1≤i≤ℓ) (when m is odd). Here m
1≤···≤m
ℓ are the exponents of G and h=m
ℓ+1 is the Coxeter number. The construction heavily uses the primitive derivation D which plays a central role in the theory of flat generators by K. Saito (or equivalently the Frobenius manifold structure
for the orbit space of G). Some new results concerning the primitive derivation D are obtained in the course of proof of the main result.
Oblatum 27-XI-2001 & 4-XII-2001?Published online: 18 February 2002 相似文献
19.
The multicolor Ramsey number Rr(H) is defined to be the smallest integer n=n(r) with the property that any r-coloring of the edges of the complete graph Kn must result in a monochromatic subgraph of Kn isomorphic to H. It is well known that 2rm<Rr(C2m+1)<2(r+2)!m and Rr(C2m)≥(r−1)(m−1)+1. In this paper, we prove that Rr(C2m)≥2(r−1)(m−1)+2.
This research is supported by NSFC(60373096, 60573022) and SRFDP(20030141003) 相似文献
20.
Assuming m − 1 < kp < m, we prove that the space C
∞(M, N) of smooth mappings between compact Riemannian manifolds M, N (m = dim M) is dense in the Sobolev space W
k,p
(M, N) if and only if π
m−1(N) = {0}. If π
m−1(N) ≠ {0}, then every mapping in W
k,p
(M, N) can still be approximated by mappings M → N which are smooth except in finitely many points. 相似文献