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1.
A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: $
\mathbb{I}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M there exists a map g′: $
\mathbb{I}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M such that g′ is ɛ-homotopic to g and dim g′ ({z} × $
\mathbb{I}
$
\mathbb{I}
n
) ≤ n for all z ∈ $
\mathbb{I}
$
\mathbb{I}
m
. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij
[11] and Tuncali-Valov [10]. 相似文献
2.
The set of all m × n Boolean matrices is denoted by $
\mathbb{M}
$
\mathbb{M}
m,n
. We call a matrix A ∈ $
\mathbb{M}
$
\mathbb{M}
m,n
regular if there is a matrix G ∈ $
\mathbb{M}
$
\mathbb{M}
n,m
such that AGA = A. In this paper, we study the problem of characterizing linear operators on $
\mathbb{M}
$
\mathbb{M}
m,n
that strongly preserve regular matrices. Consequently, we obtain that if min{m, n} ⩽ 2, then all operators on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserve regular matrices, and if min{m, n} ⩾ 3, then an operator T on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserves regular matrices if and only if there are invertible matrices U and V such that T(X) = UXV for all X ε $
\mathbb{M}
$
\mathbb{M}
m,n
, or m = n and T(X) = UX
T
V for all X ∈ $
\mathbb{M}
$
\mathbb{M}
n
. 相似文献
3.
Stevo Stević 《Siberian Mathematical Journal》2009,50(6):1098-1105
Let $
\mathbb{B}
$
\mathbb{B}
be the unit ball in ℂ
n
and let H($
\mathbb{B}
$
\mathbb{B}
) be the space of all holomorphic functions on $
\mathbb{B}
$
\mathbb{B}
. We introduce the following integral-type operator on H($
\mathbb{B}
$
\mathbb{B}
):
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
相似文献
4.
A. A. Mogul’skiĭ 《Siberian Advances in Mathematics》2010,20(3):191-200
Let X,X(1),X(2),... be independent identically distributed random variables with mean zero and a finite variance. Put S(n) = X(1) + ... + X(n), n = 1, 2,..., and define the Markov stopping time η
y
= inf {n ≥ 1: S(n) ≥ y} of the first crossing a level y ≥ 0 by the random walk S(n), n = 1, 2,.... In the case $
\mathbb{E}
$
\mathbb{E}
|X|3 < ∞, the following relation was obtained in [8]: $
\mathbb{P}\left( {\eta _0 = n} \right) = \frac{1}
{{n\sqrt n }}\left( {R + \nu _n + o\left( 1 \right)} \right)
$
\mathbb{P}\left( {\eta _0 = n} \right) = \frac{1}
{{n\sqrt n }}\left( {R + \nu _n + o\left( 1 \right)} \right)
as n → ∞, where the constant R and the bounded sequence ν
n
were calculated in an explicit form. Moreover, there were obtained necessary and sufficient conditions for the limit existence
$
H\left( y \right): = \mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _y = n} \right)
$
H\left( y \right): = \mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _y = n} \right)
for every fixed y ≥ 0, and there was found a representation for H(y). The present paper was motivated by the following reason. In [8], the authors unfortunately did not cite papers [1, 5] where
the above-mentioned relations were obtained under weaker restrictions. Namely, it was proved in [5] the existence of the limit
$
\mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _y = n} \right)
$
\mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _y = n} \right)
for every fixed y ≥ 0 under the condition
$
\mathbb{E}
$
\mathbb{E}
X
2 < ∞ only; In [1], an explicit form of the limit $
\mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _0 = n} \right)
$
\mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _0 = n} \right)
was found under the same condition
$
\mathbb{E}
$
\mathbb{E}
X
2 < ∞ in the case when the summand X has an arithmetic distribution. In the present paper, we prove that the main assertion in [5] fails and we correct the original proof. It worth noting that
this corrected version was formulated in [8] as a conjecture. 相似文献
5.
In this note we construct a function φ in L2(Bn,dμ) which is unbounded on any neighborhood of each boundary point of Bn such that Tφ is a trace class operator on weighted Bergman space Lα2(Bn,dμ) for several complex variables. 相似文献
6.
7.
Assume that no cardinal κ < 2
ω
is quasi-measurable (κ is quasi-measurable if there exists a κ-additive ideal
$
\mathbb{I}
$
\mathbb{I}
of X contains uncountably many pairwise disjoint subfamilies
$
\mathbb{I}
$
\mathbb{I}
-Bernstein unions ∪
$
\mathbb{I}
$
\mathbb{I}
-Bernstein if A and X \ A meet each Borel $
\mathbb{I}
$
\mathbb{I}
-positive subset B ⊆ X). This result is a generalization of the Four Poles Theorem (see [1]) and results from [2] and [4]. 相似文献
8.
I. E. Zuber 《Vestnik St. Petersburg University: Mathematics》2010,43(3):139-142
A control of an nth-order discrete system under an external perturbation is considered. The elements of the matrix of the system are functionals
of any nature. The observation matrix is constant and has arbitrary size m × n. A control ensuring the independence of the output σ
k
on the external perturbation ψ
k
is synthesized; moreover,
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