共查询到20条相似文献,搜索用时 46 毫秒
1.
M. A. Nalbandyan 《Russian Mathematics (Iz VUZ)》2009,53(10):45-56
For any sequence {ω(n)}
n∈ℕ tending to infinity we construct a “quasiquadratic” representation spectrum Λ = {n
2 + o(ω(n))}
n∈ℕ: for any almost everywhere (a. e.) finite measurable function f(x) there exists a series in the form $
\mathop \sum \limits_{k \in \Lambda }
$
\mathop \sum \limits_{k \in \Lambda }
α
k
ω
k
(x) that converges a. e. to this function, where {w
k
(x)}
k∈ℕ is the Walsh system. We find representation spectra in the form {n
l
+ o(n
l
)}
n∈ℕ, where l ∈ {2
k
}
k∈ℕ. 相似文献
2.
Stephen Dias Barreto 《Proceedings Mathematical Sciences》2000,110(4):347-356
We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of
evolution groups {τt(ω)}ω∈/Ω of the spin system. The notion of ergodicity of a measure preserving group of automorphisms of the probability space Ω, is
used to prove the almost sure independence of the Arveson spectrum Sp(τ(ω)) of τt(ε). As a consequence, for any family of (τ(ω),β) — KMS states {ρ(ω)}, the spectrum of the generator of the group of unitaries
which implement τ(ω) in the GNS representation is also almost surely independent of ω. 相似文献
3.
We consider an infinite tandem queueing network consisting of ·/GI/1/∞ stations with i.i.d. service times. We investigate the asymptotic behavior of t(n, k), the inter-arrival times between customers n and n + 1 at station k, and that of w(n, k), the waiting time of customer n at station k. We establish a duality property by which w(n, k) and the “idle times”y(n, k) play symmetrical roles. This duality structure, interesting by itself, is also instrumental in proving some of the ergodic
results. We consider two versions of the model: the quadrant and the half-plane. In the quadrant version, the sequences of
boundary conditions {w(0,k), k∈ℕ} and {t(n, 0), n∈ℕ}, are given. In the half-plane version, the sequence {t(n, 0), n∈ℕ} is given. Under appropriate assumptions on the boundary conditions and on the services, we obtain ergodic results for
both versions of the model. For the quadrant version, we prove the existence of temporally ergodic evolutions and of spatially
ergodic ones. Furthermore, the process {t(n, k), n∈ℕ} converges weakly with k to a limiting distribution, which is invariant for the queueing operator. In the more difficult half plane problem, the aim
is to obtain evolutions which are both temporally and spatially ergodic. We prove that 1/n∑
k=1
n
w(0, k) converges almost surely and in L
1 to a finite constant. This constitutes a first step in trying to prove that {t(n,k), n∈ℤ} converges weakly with k to an invariant limiting distribution.
Received: 23 March 1999 / Revised version: 5 January 2000 / Published online: 12 October 2000 相似文献
4.
A. I. Pavlov 《Mathematical Notes》2000,68(3):370-377
The main result of this paper is the following theorem. Suppose thatτ(n) = ∑
d|n
l and the arithmetical functionF satisfies the following conditions:
Then there exist constantsA
1,A
2, andA
3 such that for any fixed \g3\s>0 the following relation holds:
. Moreover, if for any primep the inequality \vbf(p)\vb\s<1 holds and the functionF is strongly multiplicative, thenA
1\s>0.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 429–438, September, 2000. 相似文献
1) | the functionF is multiplicative; |
2) | ifF(n) = ∑ d|n f(d), then there exists an α>0 such that the relationf(n)=O(n −α) holds asn→∞. |
5.
Let F ì PG \mathcal{F} \subset {\mathcal{P}_G} be a left-invariant lower family of subsets of a group G. A subset A ⊂ G is called F \mathcal{F} -thin if xA ?yA ? F xA \cap yA \in \mathcal{F} for any distinct elements x, y ∈ G. The family of all F \mathcal{F} -thin subsets of G is denoted by t( F ) \tau \left( \mathcal{F} \right) . If t( F ) = F \tau \left( \mathcal{F} \right) = \mathcal{F} , then F \mathcal{F} is called thin-complete. The thin-completion t*( F ) {\tau^*}\left( \mathcal{F} \right) of F \mathcal{F} is the smallest thin-complete subfamily of PG {\mathcal{P}_G} that contains F \mathcal{F} . Answering questions of Lutsenko and Protasov, we prove that a set A ⊂ G belongs to τ*(G) if and only if, for any sequence (g
n
)
n∈ω
of nonzero elements of G, there is n ∈ ω such that
?i0, ?, in ? { 0, 1 } g0i0 ?gninA ? F . \bigcap\limits_{{i_0}, \ldots, {i_n} \in \left\{ {0,\;1} \right\}} {g_0^{{i_0}} \ldots g_n^{{i_n}}A \in \mathcal{F}} . 相似文献
6.
Hari Bercovici 《Complex Analysis and Operator Theory》2007,1(3):335-339
Consider a domain
, and two analytic matrix-valued functions functions
. Consider also points
and positive integers n
1, n
2, . . . , n
N
. We are interested in the existence of an analytic function
such that X(ω) is invertible, and G(ω) coincides with X(ω)F(ω)X(ω)−1 up to order n
j
at the point ω
j
. We will see that such a function exists provided that F(ω
j
),G(ω
j
) have cyclic vectors, and the characteristic polynomials of F,G coincide up to order n
j
at ω
j
. This allows one to give a short proof to a result of Huang, Marcantognini and Young concerning spectral interpolation in
the unit disk.
The author was partially supported by a grant from the National Science Foundation.
Received: September 8, 2006. Accepted: January 11, 2007. 相似文献
7.
V. V. Rimatskii 《Algebra and Logic》1996,35(5):344-349
In the present article, we prove the theorem which states that every table modal logic λ of depth 2 over S4 has a finite basis
of admissible inference rules. In addition, it is established that a finite algebra ℒ belongs to Fω(λ)Q iff there exist numbers n1…, nk such that
(Lemma 5). Let F be a λ-frame of depth 2 and b a cluster of the second layer in F. We show that for any n1,…,nk, there exist no p-morphisms from (Fn1⊔…⊔Fnk)+ a local component K (b) such that, for any n, there is no p-morphism from any local component of Fn onto K (b) (Lemma 6).
Translated fromAlgebra i Logika, Vol. 35, pp. 612–622, September–October, 1996. 相似文献
8.
Let (Ω,f,P) be a probability space and letT be a measure-preserving weak mixing transformation. We define a large class of sequences of integers calledp-sequences, such that iff∈L
1 there exists a set Ω′⊂Ω of probability one and for ω∈Ω′ we have
for everyp-sequence {kn}. 相似文献
9.
Zheng Zukang 《数学学报(英文版)》1994,10(4):337-347
LetX
1,X
2, ...,X
n
be a sequence of nonnegative independent random variables with a common continuous distribution functionF. LetY
1,Y
2, ...,Y
n
be another sequence of nonnegative independent random variables with a common continuous distribution functionG, also independent of {X
i
}. We can only observeZ
i
=min(X
i
,Y
i
), and
. LetH=1−(1−F)(1−G) be the distribution function ofZ. In this paper, the limit theorems for the ratio of the Kaplan-Meier estimator
or the Altshuler estimator
to the true survival functionS(t) are given. It is shown that (1)P(δ(n)=1 i.o.)=0 ifF(τ
H
) < 1 andP(δ
n
=0 i.o. )=0 ifG(τH) > 1 where δ(n) is the corresponding indicator function of
and
have the same order
a.s., where {T
n
} is a sequence of constants such that 1−H(T
n
)=n
−α(logn)β(log logn)γ. 相似文献
10.
Nariankadu D. Shyamalkumar Kasturi Varadarajan 《Discrete and Computational Geometry》2012,47(1):44-63
We consider the problem of fitting a subspace of a specified dimension k to a set P of n points in ℝ
d
. The fit of a subspace F is measured by the L
τ
norm, that is, it is defined as the τ-root of the sum of the τth powers of the Euclidean distances of the points in P from F, for some τ≥1. Our main result is a randomized algorithm that takes as input P, k, and a parameter 0<ε<1; runs in
nd ·2O(\fractk2e log2 \frac ke)nd \cdot2^{O(\frac{\tau k^{2}}{\varepsilon} \log^{2} \frac {k}{\varepsilon})} time, and returns a k-subspace that with probability at least 1/2 has a fit that is at most (1+ε) times that of the optimal k-subspace. 相似文献
11.
Yasushi Taga 《Annals of the Institute of Statistical Mathematics》1971,23(1):355-363
Summary Let {X
n
},n=1,2,..., be a sequence of independent random variables distributed according to a distribution functionF(x) with finite variance,F
n
(x) be the empiric distribution function ofX
1,...,X
n
for eachn, andφ
(n)
*
andφ
* be optimum stratifications corresponding toF
n
(x) andF(x) respectively.
It is shown in this paper thatφ
(a)
*
tends almost surely toφ
* under a suitable criterion.
Institute of Statistical Mathematics 相似文献
12.
A. G. Babenko 《Mathematical Notes》1996,60(3):248-263
In this paper we prove the Jackson-Stechkin inequalityE
n−1(f)<ω
n
(f, 2τ
n
,λ),n≥1,m≥5,r≥1, f ∈L2(
),f ≢ const, which is sharp for eachn=2, 3, ...; hereE
n−1
(f) is the best approximation of a functionf by spherical polynomials of degree ≤n−1, ω
n
(f, τ) is theτth modulus of continuity off based on the translations
,t ∈ ℝ,x ∈
,
,
is the measure of the unit Euclidean sphere
,
, andτ
n
,λ is the first positive zero of the Gegenbauer cosine polynomial
(cost).
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 333–355, September, 1996.
The present paper was discussed at Ural State University in a seminar headed by Professor Arestov. The author is grateful
to Professor Arestov and Associate Professor Popov for useful conversations.
This research was supported by the State Commission for Higher Education of the Russian Federation under grant No. 2-16-5-31
and by the Russian Foundation for Basic Research under grant No. 93-011-196. 相似文献
13.
Yair Glasner 《Transformation Groups》2009,14(4):787-800
Let A be a locally compact group topologically generated by d elements and let k > d. Consider the action, by precomposition, of Γ = Aut(F k ) on the set of marked, k-generated, dense subgroups $ {D_{k,A}}: = \left\{ {\eta \in {\text{Hom}}\left( {{F_k},A} \right)\left| {\overline {\left\langle {\phi \left( {{F_k}} \right)} \right\rangle } = A} \right.} \right\}
14.
We give a characterization of the class Co(F)\mathbf{Co}(\mathcal{F}) [Co(Fn)\mathrm{\mathbf{Co}}(\mathcal{F}_n), n < ω, respectively] of lattices isomorphic to convexity lattices of posets which are forests [forests of length at most n, respectively], as well as of the class Co(L)\mathbf{Co}(\mathcal{L}) of lattices isomorphic to convexity lattices of linearly ordered posets. This characterization yields that the class of finite
members from Co(F)\mathbf{Co}(\mathcal{F}) [from Co(Fn)\mathbf{Co}(\mathcal{F}_n), n < ω, or from Co(L)\mathbf{Co}(\mathcal{L})] is finitely axiomatizable within the class of finite lattices. 相似文献
15.
Yu. F. Korobeinik 《Mathematical Notes》2000,67(4):448-458
LetF ⊂ ℂ be a dense-in-itself set that has a nonempty connected interior and contains the origin, and let
be the space of infinitely differentiable complex-valued functions onF. For some classes of such setsF, we prove that for an arbitrary sequence
of complex numbers there exists a functionf ε
withf
(n)(0)=d
n,n=0, 1, 2, ..., and study the analyticity properties off. The functionf is constructed in the form of various function series, namely, a power series, a series of simple fractions, and an exponential
series. Analytic solutions of the multidimensional Borel problem are also considered.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 525–538, April, 2000. 相似文献
16.
Y. C. Wang 《Acta Mathematica Hungarica》2012,135(3):248-269
Let Hk\mathcal{H}_{k} denote the set {n∣2|n,
n\not o 1 (mod p)n\not\equiv 1\ (\mathrm{mod}\ p) ∀ p>2 with p−1|k}. We prove that when
X\frac1120(1-\frac12k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{2k}\right) +\varepsilon}\leqq H\leqq X, almost all integers
n ? \allowbreak Hk ?(X, X+H]n\in\allowbreak {\mathcal{H}_{k} \cap (X, X+H]} can be represented as the sum of a prime and a k-th power of prime for k≧3. Moreover, when
X\frac1120(1-\frac1k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{k}\right) +\varepsilon}\leqq H\leqq X, almost all integers n∈(X,X+H] can be represented as the sum of a prime and a k-th power of integer for k≧3. 相似文献
17.
A. V. Harutyunyan W. Lusky 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(3):128-135
Let U
n
be the unit polydisk in C
n
and S be the space of functions of regular variation. Let 1 ≤ p < ∞, ω = (ω
1, ..., ω
n
), ω
j
∈ S(1 ≤ j ≤ n) and f ∈ H(U
n
). The function f is said to be in holomorphic Besov space B
p
(ω) if
|