共查询到20条相似文献,搜索用时 46 毫秒
1.
Fuqing Gao 《Journal of Theoretical Probability》2003,16(2):401-418
Let f
n
be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in
d
. It is proved that if the kernel function is an integrable function with bounded variation, and the common density function f of the random variables is continuous and f(x) 0 as |x| , then the moderate deviation principle and large deviation principle for
hold. 相似文献
2.
Let Θ be a bounded open set in ℝ
n
, n ⩾ 2. In a well-known paper Indiana Univ. Math. J., 20, 1077–1092 (1971) Moser found the smallest value of K such that
$
\sup \left\{ {\int_\Omega {\exp \left( {\left( {\frac{{\left| {f(x)} \right|}}
{K}} \right)^{{n \mathord{\left/
{\vphantom {n {(n - 1)}}} \right.
\kern-\nulldelimiterspace} {(n - 1)}}} } \right):f \in W_0^{1,n} (\Omega ),\left\| {\nabla f} \right\|_{L^n } \leqslant 1} } \right\} < \infty
$
\sup \left\{ {\int_\Omega {\exp \left( {\left( {\frac{{\left| {f(x)} \right|}}
{K}} \right)^{{n \mathord{\left/
{\vphantom {n {(n - 1)}}} \right.
\kern-\nulldelimiterspace} {(n - 1)}}} } \right):f \in W_0^{1,n} (\Omega ),\left\| {\nabla f} \right\|_{L^n } \leqslant 1} } \right\} < \infty
相似文献
3.
Approximation to the function |x| plays an important role in approximation theory. This paper studies the approximation to the function xαsgn x, which equals |x| if α = 1. We construct a Newman Type Operator rn(x) and prove max |x|≤1|xαsgn x-rn(x)|~Cn1/4e-π1/2(1/2)αn. 相似文献
4.
In the study of two-dimensional compact toric varieties, there naturally appears a set of coordinate planes of codimension
two $
Z = {*{20}c}
\cup \\
{1 < \left| {i - j} \right| < d - 1} \\
\{ z_i = z_j = 0\}
$
Z = \begin{array}{*{20}c}
\cup \\
{1 < \left| {i - j} \right| < d - 1} \\
\end{array} \{ z_i = z_j = 0\}
in ℂ
d
. Based on the Alexander-Pontryagin duality theory, we construct a cycle that is dual to the generator of the highest dimensional
nontrivial homology group of the complement in ℂ
d
of the set of planes Z. We explicitly describe cycles that generate groups H
d+2(ℂ
d
\ Z) and H
d−3($
\bar Z
$
\bar Z
), where $
\bar Z
$
\bar Z
= Z ∪ {∞}. 相似文献
5.
Suppose that X is a complex Banach space with the norm ‖·‖ and n is a positive integer with dim X ⩾ n ⩾ 2. In this paper, we consider the generalized Roper-Suffridge extension operator $
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
on the domain $
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
$
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
defined by
|