共查询到20条相似文献,搜索用时 31 毫秒
1.
Let ℤ2N={0, ..., 2N-1} denote the group of integers modulo 2N, and let L be the space of all real functions of ℤ2N which are supported on {0,...N−1}. The spectral phase of a function f:ℤ2N→ℝ is given by φf(k)=arg
for k ∈ ℤ2N, where
denotes the discrete Fourier transforms of f.
For a fixed s∈L let Ks denote the cone of all f:ℤ2N→ℝ which satisfy φf ≡ φs and let Ms be its linear span. The angle αs between Ms and L determines the convergence rate of the signal restoration from phase algorithm of Levi and Stark [3]. Here we prove
the following conjectures of Urieli et al. [7] who verified them for the N≤3 case:
Acknowledgments and Notes. Nir Cohen-Supported by CNPq grant 300019/96-3. Roy Meshulam-Research supported by the Fund for the Promotion of Research
at the Technion. 相似文献
1. | α (Ms, L)≤π/4 for a generic s∈L. |
2. | If s∈L is geometric, i.e., s(j)=qj for 0≤j≤N−1 where ±1≠q∈ℝ, then α(Ms, L)=π/4. |
2.
Zhi-Wei Sun 《Israel Journal of Mathematics》1992,77(3):345-348
In this paper it is shown that if every integer is covered bya
1+n
1ℤ,…,a
k
+n
k
ℤ exactlym times then for eachn=1,…,m there exist at least (
n
m
) subsetsI of {1,…k} such that ∑
i
∈
I
1/n
i
equalsn. The bound (
n
m
) is best possible.
Research supported by the National Nature Science Foundation of P.R. of China. 相似文献
3.
A k-dimensional hypertree X is a k-dimensional complex on n vertices with a full (k−1)-dimensional skeleton and
\binomn-1k\binom{n-1}{k} facets such that H
k
(X;ℚ)=0. Here we introduce the following family of simplicial complexes. Let n,k be integers with k+1 and n relatively prime, and let A be a (k+1)-element subset of the cyclic group ℤ
n
. The sum complex
X
A
is the pure k-dimensional complex on the vertex set ℤ
n
whose facets are σ⊂ℤ
n
such that |σ|=k+1 and ∑
x∈σ
x∈A. It is shown that if n is prime, then the complex X
A
is a k-hypertree for every choice of A. On the other hand, for n prime, X
A
is k-collapsible iff A is an arithmetic progression in ℤ
n
. 相似文献
4.
Solving a problem of Erdős and Heilbronn, in 1994 Dias da Silva and Hamidoune proved that ifA is a set ofk residues modulo a primep,p≥2k−3, then the number of different elements of ℤ/pℤ that can be written in the forma+a′ wherea, a′ ∈A,a∈a′, is at least 2k−3. Here we extend this result to arbitrary Abelian groups in which the order of any nonzero element is at least 2k−3.
Visiting the Rényi Institute of the Hungarian Academy of Sciences. Research partially supported by Hungarian Scientific Research
Grants OTKA T043623 and T043631 and the CRM, University of Montreal. 相似文献
5.
A. Borel 《Proceedings Mathematical Sciences》1987,97(1-3):45-52
In this noteG is a locally compact group which is the product of finitely many groups Gs(ks)(s∈S), where ks is a local field of characteristic zero and Gs an absolutely almost simplek
s-group, ofk
s-rank ≥1. We assume that the sum of the rs is ≥2 and fix a Haar measure onG. Then, given a constantc > 0, it is shown that, up to conjugacy,G contains only finitely many irreducible discrete subgroupsL of covolume ≥c (4.2). This generalizes a theorem of H C Wang for real groups. His argument extends to the present case, once it is shown
thatL is finitely presented (2.4) and locally rigid (3.2). 相似文献
6.
V. N. Konovalov 《Ukrainian Mathematical Journal》2005,57(12):1911-1936
Let s ∈ ℕ and let Δ
+
s
be the set of functions x: I ↦ ℝ on a finite interval I such that the divided differences [x; t
0, ..., t
s
] of order s of these functions are nonnegative for all collections of s + 1 different points t
0, ..., t
s
∈ I. For the classes Δ
+
s
B
p
: = Δ
+
s
∩ B
p
, where B
p
is the unit ball in L
p
, we determine the orders of Kolmogorov and linear widths in the spaces Lq
for 1 ≤ q > p ≤ ∞.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1633–1652, December, 2005. 相似文献
7.
We prove that there exists an absolute constant c>0 such that if A is a set of n monic polynomials, and if the product set A.A has at most n
1+c
elements, then |A+A|≫n2. This can be thought of as step towards proving the Erdős–Szemerédi sum-product conjecture for polynomial rings. We also
show that under a suitable generalization of Fermat’s Last Theorem, the same result holds for the integers. The methods we
use to prove are a mixture of algebraic (e.g. Mason’s theorem) and combinatorial (e.g. the Ruzsa–Plunnecke inequality) techniques. 相似文献
8.
In this paper, we present the conditions on dilation parameter {s
j}j that ensure a discrete irregular wavelet system {s
j
n/2ψ(s
j
·−bk)}
j∈ℤ,k∈ℤ
n
to be a frame on L2(ℝn), and for the wavelet frame we consider the perturbations of translation parameter b and frame function ψ respectively. 相似文献
9.
We consider the random variable ζ = ξ1ρ+ξ2ρ2+…, where ξ1, ξ2, … are independent identically distibuted random variables taking the values 0 and 1 with probabilities P(ξi = 0) = p0, P(ξi = 1) = p1, 0 < p0 < 1. Let β = 1/ρ be the golden number.
The Fibonacci expansion for a random point ρζ from [0, 1] is of the form η1ρ + η2ρ2 + … where the random variables ηk are {0, 1}-valued and ηkηk+1 = 0. The infinite random word η = η1η2 … ηn … takes values in the Fibonacci compactum and determines the so-called Erdős measure μ(A) = P(η ∈ A) on it. The invariant
Erdős measure is the shift-invariant measure with respect to which the Erdős measure is absolutely continuous.
We show that the Erdős measures are sofic. Recall that a sofic system is a symbolic system that is a continuous factor of
a topological Markov chain. A sofic measure is a one-block (or symbol-to-symbol) factor of the measure corresponding to a
homogeneous Markov chain. For the Erdős measures, the corresponding regular Markov chain has 5 states. This gives ergodic
properties of the invariant Erdős measure.
We give a new ergodic theory proof of the singularity of the distribution of the random variable ζ. Our method is also applicable
when ξ1, ξ2, … is a stationary Markov chain with values 0, 1. In particular, we prove that the distribution of ζ is singular and that
the Erdős measures appear as the result of gluing together states in a regular Markov chain with 7 states. Bibliography: 3
titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 28–47. 相似文献
10.
G. A. Noskov 《Algebra and Logic》1997,36(2):117-132
A group Γ has type F Pn if a trivial ℤΓ-module ℤ has a projective resolution P:…Pn → … → P1 → P0 → ℤ in which ℤΓ-module Pn,…P1, P0 are finitely generated. Let the finitely generated group Γ be a split extension of the Abelian group M by an Abelian group
Q, suppose M is torsion free, and assume Γ∈F Pm, m≥2. Then the invariant ∑
c
M
is m-tame.
Translated fromAlgebra i Logika, Vol. 36, No. 2, pp. 194–218, March–April, 1997. 相似文献
11.
Jianqiang Zhao 《数学学报(英文版)》2008,24(10):1593-1616
In this paper, we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζq (s1,..., Sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (Renormalization of Multiple Zeta Values, arxiv: math/0606076v3). We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζq(S1,..., sd) (i.e., s1 ≤ 1). Moreover, when q ↑ 1 our renormalizations agree with those of Guo and Zhang. 相似文献
12.
Erdős estimated the maximal number of integers selected from {1,2,…,N}, so that none of them divides the product of two others. In this paper, Erdős’ problem is extended to sets of integers such that none of them divides the product of k others. The proofs use combinatorial results. 相似文献
13.
Yu Miao 《Acta Appl Math》2009,106(2):177-184
Let X
k
=∑
i=−∞∞
a
i
ξ
k−i
,k≥1, be the moving average processes, where (ξ
i
)
i∈ℤ is a sequence of real stationary random variables. Under the assumptions that the large deviation principle (LDP) for real
stationary sequence holds, LDP for the moving average processes of real stationary sequence is established.
相似文献
14.
Paul Hill 《Czechoslovak Mathematical Journal》2008,58(4):1069-1081
Torsion-free covers are considered for objects in the category q
2. Objects in the category q
2 are just maps in R-Mod. For R = ℤ, we find necessary and sufficient conditions for the coGalois group G(A → B), associated to a torsion-free cover, to be trivial for an object A → B in q
2. Our results generalize those of E. Enochs and J. Rado for abelian groups. 相似文献
15.
Abdelmalek Azizi 《Rendiconti del Circolo Matematico di Palermo》1999,48(1):71-92
Let ℕ,i=√−1,k=ℚ(√d,i) andC
2 the 2-part of the class group ofk. Our goal is to determine alld such thatC
2⋍ℤ/2ℤ×ℤ/2ℤ.
Soientd∈ℕ,i=√−1,k=ℚ(√d,i), etC
2 la 2-partie du groupe de classes dek. On s'intéresse à déterminer tous lesd tel queC
2⋍ℤ/2ℤ×ℤ/2ℤ.
相似文献
16.
Let ℤ denote the set of all integers and ℕ the set of all positive integers. Let A be a set of integers. For every integer u, we denote by d
A
(u) and s
A
(u) the number of solutions of u=a − a′ with a,a′ ∈ A and u=a+a′ with a,a′ ∈ A and a≤a′, respectively. 相似文献
17.
József Beck 《Combinatorica》2002,22(2):169-216
Dedicated to the memory of Paul Erdős
We study the fair Maker–Breaker graph Ramsey game MB(n;q). The board is , the players alternately occupy one edge a move, and Maker wants a clique of his own. We show that Maker has a winning strategy in MB(n;q) if , which is exactly the clique number of the random graph on n vertices with edge-probability 1/2. Due to an old theorem of Erdős and Selfridge this is best possible apart from an additive
constant.
Received March 28, 2000 相似文献
18.
Dedicated to the memory of Paul Erdős
In [9] Thomassen proved that a -connected graph either contains k vertex disjoint odd cycles or an odd cycle cover containing at most 2k-2 vertices, i.e. he showed that the Erdős–Pósa property holds for odd cycles in highly connected graphs. In this paper, we
will show that the above statement is still valid for 576k-connected graphs which is essentially best possible.
Received November 17, 1999
RID="*"
ID="*" This work was supported by a post-doctoral DONET grant.
RID="†"
ID="†" This work was supported by an NSF-CNRS collaborative research grant.
RID="‡"
ID="‡" This work was performed while both authors were visiting the LIRMM, Université de Montpellier II, France. 相似文献
19.
We obtain a sufficient condition for a subsetH of positive integers to satisfy that the equidistribution (mod 1) of the sequences (u
n+h
− u
n; n=1, 2, ···) for allh ∈H implies the equidistribution of (u
n). Our condition is satisfied, for example, for the following sets: (1)H={n − m; n ∈ I, m ∈ I, n>m}, whereI is any infinite subset of integers; (2)H={| ψ (n)|; ψ(n)≠0,n ∈ Z}, where ψ is a nonconstant polynomial with integral coefficients having at least one integral zero (modq) for allq=2, 3, ···; (3)H={p+1;p is a prime} andH={p − 1;p is a prime}. 相似文献
20.
L. Pyber 《Combinatorica》1985,5(4):347-349
Every graph onn vertices, with at leastc
k
n logn edges contains ak-regular subgraph. This answers a question of Erdős and Sauer. 相似文献