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1.
Given a permutation ω of {1, …, n}, let R(ω) be the root degree of ω, i.e. the smallest (prime) integer r such that there is a permutation σ with ω = σ
r
. We show that, for ω chosen uniformly at random, R(ω) = (lnlnn − 3lnlnln n + O
p
(1))−1 lnn, and find the limiting distribution of the remainder term.
Research supported in part by NSF grants CCR-0225610, DMS-0505550 and ARO grant W911NF-06-1-0076.
Research supported by NSF grant DMS-0406024. 相似文献
2.
Teresa Bermúdez Isabel Marrero Antonio Martinón 《Integral Equations and Operator Theory》2009,64(4):487-494
A bounded linear operator T on a Hilbert space H is called an m-isometry for a positive integer m if . We prove some properties concerning the behaviour of the orbit of an m-isometry. For example, every orbit of an m-isometry is eventually norm increasing and some m-isometries can not be N-supercyclic, that is, there does not exist an N-dimensional subspace EN such that the orbit of T at EN is dense in H.
To Professor José Rodríguez Expósito on his 60th birthday 相似文献
3.
We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − ε)n vertices, in terms of the expansion properties of G. As a result we show that for fixed d ≥ 2 and 0 < ε < 1, there exists a constant c = c(d, ε) such that a random graph G(n, c/n) contains almost surely a copy of every tree T on (1 − ε)n vertices with maximum degree at most d. We also prove that if an (n, D, λ)-graph G (i.e., a D-regular graph on n vertices all of whose eigenvalues, except the first one, are at most λ in their absolute values) has large enough spectral gap D/λ as a function of d and ε, then G has a copy of every tree T as above.
Research supported in part by a USA-Israeli BSF grant, by NSF grant CCR-0324906, by a Wolfensohn fund and by the State of
New Jersey.
Research supported in part by USA-Israel BSF Grant 2002-133, and by grants 64/01 and 526/05 from the Israel Science Foundation.
Research supported in part by NSF CAREER award DMS-0546523, NSF grant DMS-0355497, USA-Israeli BSF grant, and by an Alfred
P. Sloan fellowship. 相似文献
4.
Danilo Bazzanella 《Archiv der Mathematik》2008,91(2):131-135
This paper is concerned with the number of primes in short intervals. We prove that , for θ > 1/2, with the assumption of an heuristic hypothesis weaker than the Lindel?f hypothesis.
Received: 8 October 2007, Revised: 14 April 2008 相似文献
5.
Piotr Jucha 《Archiv der Mathematik》2008,90(6):559-571
We discuss the properties of the Wu pseudometric and present counterexamples for its upper semicontinuity that answers the
question posed by Jarnicki and Pflug. We also give formulae for the Wu pseudometric in elementary Reinhardt domains.
Received: 12 September 2007 相似文献
6.
Zineb Mimouni René Limage 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):569-574
Within the framework of the study of the fibrillation mechanism in an electrorheological (ER) suspension, this work presents
a comparison between the self similar solutions when the kernel is Ki,j ~ (i−1 + j−1) and the behaviour of the chains growth. Till now, the field induced chains formation has only been studied by numerical
or experimental methods. The work of Fournier and Lauren?ot (Communications in Mathematical Physics 256 2005) on the Smoluchowski’s
equation allows us to present an analytical solution for the field induced pearl chains in a colloidal ER suspension.
René Limage: Chercheur indépendant, dipl?mé de l’Université de Liége. 相似文献
7.
Massimo Grossi 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(2):227-241
Let Ω be a smooth bounded domain of
with N ≥ 5. In this paper we prove, for ɛ > 0 small, the nondegeneracy of the solution of the problem
under a nondegeneracy condition on the critical points of the Robin function. Our proof uses different techniques with respect
to other known papers on this topic. 相似文献
8.
A simple and rigorous derivation of the maximum recoverable work is presented. In contrast to previous derivations it is based
on simple and rigorous projectional methods. The principle holds if the stress has a non-trivial Newtonian component.
相似文献
9.
In this paper, we compute certain invariants of extension algebras of the torus algebra by , where is the C*-algebra of compact operators on an infinite dimensional separable Hilbert space H. These extension algebras are also constructed up to isomorphism.
Received: 5 July 2007, Revised: 14 February 2008 相似文献
10.
For 30 years the Lempel–Ziv factorization LZ
x
of a string x = x[1..n] has been a fundamental data structure of string processing, especially valuable for string compression and for computing
all the repetitions (runs) in x. Traditionally the standard method for computing LZ
x
was based on Θ(n)-time (or, depending on the measure used, O(n log n)-time) processing of the suffix tree ST
x
of x. Recently Abouelhoda et al. proposed an efficient Lempel–Ziv factorization algorithm based on an “enhanced” suffix array – that is, a suffix array SA
x
together with supporting data structures, principally an “interval tree”. In this paper we introduce a collection of fast
space-efficient algorithms for LZ factorization, also based on suffix arrays, that in theory as well as in many practical
circumstances are superior to those previously proposed; one family out of this collection achieves true Θ(n)-time alphabet-independent processing in the worst case by avoiding tree structures altogether.
The work of the first and third authors was supported in part by grants from the Natural Sciences & Engineering Research Council
of Canada. 相似文献
11.
Olympia Talelli 《Archiv der Mathematik》2007,89(1):24-32
We define a group G to be of type Φ if it has the property that for every
-module G, proj.
G < ∞ iff proj.
H G < ∞ for every finite subgroup H of G. We conjecture that the type Φ is an algebraic characterization of those groups G which admit a finite dimensional model for
, the classifying space for the family of the finite subgroups of G. We also conjecture that the type Φ is equivalent to spli being finite, where spli
is the supremum of the projective lengths of the injective
-modules. Here we prove certain parts of these conjectures.
The project is cofounded by the European Social Fund and National Resources–EPEAK II–Pythagoras.
Received: 21 June 2006 相似文献
12.
Gerd Faltings 《Milan Journal of Mathematics》2008,76(1):93-123
We show that formal groups can be used to simplify the construction of Néron models. Also we give a new proof of the stable
reduction theorem for abelian varieties.
Received: September 2007 相似文献
13.
Masao Tsugaki 《Combinatorica》2009,29(1):127-129
A tree T is called a k-tree, if the maximum degree of T is at most k. In this paper, we prove that if G is an n-connected graph with independence number at most n + m + 1 (n≥1,n≥m≥0), then G has a spanning 3-tree T with at most m vertices of degree 3. 相似文献
14.
We prove that the so-called Smoluchowski-Kramers approximation holds for a class of partial differential equations perturbed
by a non-Gaussian noisy term. Namely, we show that the solution of the one-dimensional semi-linear stochastic damped wave
equations
, u(0) = u0, ut (0) = v0, endowed with Dirichlet boundary conditions, converges as the parameter μ goes to zero to the solution of the semi-linear
stochastic heat equation
, u(0) = u0, endowed with Dirichlet boundary conditions.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
15.
Adimurthi Jacques Giacomoni 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(1):1-20
This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem
We consider a function h which is smooth and changes sign. 相似文献
16.
Niamh O’Sullivan 《Archiv der Mathematik》2007,88(1):1-11
In this paper we prove that rational indecomposability is a genus property for finitely generated torsion-free nilpotent groups
of class 2. We use this result to determine the genus of finitely generated torsion-free nilpotent groups of class 2 which
decompose as a direct product of rationally indecomposable groups.
Received: 3 November 2005 相似文献
17.
Bertrand Toën 《Selecta Mathematica, New Series》2006,12(1):39-134
The purpose of this work is to introduce a notion of affine stacks, which is a homotopy version of the notion of affine schemes, and to give several applications in the context of algebraic
topology and algebraic geometry.
As a first application we show how affine stacks can be used in order to give a new point of view (and new proofs) on rational
and p-adic homotopy theory. This gives a first solution to A. Grothendieck’s schematization problem described in [18].
We also use affine stacks in order to introduce a notion of schematic homotopy types. We show that schematic homotopy types give a second solution to the schematization problem, which also allows us to go beyond
rational and p-adic homotopy theory for spaces with arbitrary fundamental groups. The notion of schematic homotopy types is also used in
order to construct various homotopy types of algebraic varieties corresponding to various co-homology theories (Betti, de
Rham, l-adic, ...), extending the well known constructions of the various fundamental groups.
Finally, just as algebraic stacks are obtained by gluing affine schemes we define
$$ \infty $$-geometric stacks as a certain gluing of affine stacks. Examples of
$$ \infty $$-geometric stacks in the context of algebraic topology (moduli spaces of dga structures up to quasi-isomorphisms)
and Hodge theory (non-abelian periods) are given. 相似文献
18.
We study eigenvalues of positive definite kernels of L2 integral operators on unbounded real intervals. Under the assumptions of integrability and uniform continuity of the kernel
on the diagonal the operator is compact and trace class. We establish sharp results which determine the eigenvalue distribution
as a function of the smoothness of the kernel and its decay rate at infinity along the diagonal. The main result deals at
once with all possible orders of differentiability and all possible rates of decay of the kernel. The known optimal results
for eigenvalue distribution of positive definite kernels in compact intervals are particular cases. These results depend critically
on a 2-parameter differential family of inequalities for the kernel which is a consequence of positivity and is a differential
generalization of diagonal dominance. 相似文献
19.
Joseph Lehec 《Archiv der Mathematik》2009,92(4):366-376
The Yao-Yao partition theorem states that for any probability measure μ on having a density which is continuous and bounded away from 0, it is possible to partition into 2n regions of equal measure for μ in such a way that every affine hyperplane of avoids at least one of the regions. We give a constructive proof of this result and extend it to slightly more general measures.
Received: 21 August 2008 相似文献
20.
Christine Bessenrodt 《Archiv der Mathematik》2007,89(1):1-9
Starting from the question when all irreducible p-Brauer characters for a symmetric or an alternating group are of p-power degree, we classify the p-modular irreducible representations of p-power dimension in some families of representations for these groups. In particular, this then allows to confirm a conjecture
by W. Willems for the alternating groups.
Received: 14 June 2006 相似文献