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Acta Mathematica Sinica,Chinese Series
2019, Vol.35 Num.5
Online: 20190515
ARTICLES
ARTICLES
583
Robert PARKER, Andrew ROSALSKY
Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements
For a double array {
V
_{m,n,}
m
≥1,
n
≥1} of independent, mean 0 random elements in a real separable Rademacher type
p
(1≤
p
≤ 2) Banach space and an increasing double array {
b
_{m,n}
,
m
≥1,
n
≥ 1} of positive constants, the limit law max
_{1≤k≤m,1≤l≤n}
Σ
_{i}
_{=1}
^{k}
Σ
_{j}
_{=1}
^{l}
V
_{i,j}
/
b
_{m,n}
→ 0 a.c. and in
L
_{p}
as
m
∨
n
→ ∞ is shown to hold if Σ
_{m}
_{=1}
^{∞}
Σ
_{n}
_{=1}
^{∞}
E

V
_{m,n}

^{p}
/
b
_{m,n}
^{p}
< ∞. This strong law of large numbers provides a complete characterization of Rademacher type
p
Banach spaces. Results of this form are also established when 0<
p
≤1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space.
2019 Vol. 35 (5): 583596 [
Abstract
] (
0
) [
HTML
1KB] [
PDF
228KB] (
17
)
597
Hua Zhong KE
On Duality in Filtered Cohomologies
For a symplectic manifold (
M
^{2n}
,
ω
) without boundary (not necessarily compact), we prove Poincaré type duality in filtered cohomology rings of differential forms on
M
, and we use this result to obtain duality between (
d
+
d
^{Λ}
)and
dd
^{Λ}
cohomologies.
2019 Vol. 35 (5): 597608 [
Abstract
] (
0
) [
HTML
1KB] [
PDF
235KB] (
9
)
609
Zhi Wei WANG
On Grauert–Riemenschneider Type Criteria
Let (
X
,
ω
) be a compact Hermitian manifold of complex dimension
n
. In this article, we first survey recent progress towards GrauertRiemenschneider type criteria. Secondly, we give a simplified proof of Boucksom's conjecture given by the author under the assumption that the Hermitian metric
ω
satisfies ∂√
∂
ω
^{l}
=for all
l
, i.e., if
T
is a closed positive current on
X
such that ſ
_{X}
T
_{ac}
^{n}
>0, then the class {
T
} is big and
X
is Kähler. Finally, as an easy observation, we point out that Nguyen's result can be generalized as follows:if ∂√
∂
ω
=0, and
T
is a closed positive current with analytic singularities, such that
ſ
_{X}
T
_{ac}
^{n}
>0, then the class {
T
} is big and
X
is Kähler.
2019 Vol. 35 (5): 609618 [
Abstract
] (
1
) [
HTML
1KB] [
PDF
218KB] (
12
)
619
Fan Qun LI, Xin Sheng ZHANG
Bayesian Estimation of Large Precision Matrix Based on Cholesky Decomposition
In this paper, we consider the estimation of a high dimensional precision matrix of Gaussian graphical model. Based on the reparameterized likelihood, we obtain the full conditional distribution of all parameters in Cholesky factor. Furthermore, by imposing the prior information, we obtain the shrinkage Bayesian estimator of large precision matrix, and establish the asymptotic distribution of all parameters in the Cholesky factor. At last, we demonstrate our method through the simulation study and an application to telephone call center data.
2019 Vol. 35 (5): 619631 [
Abstract
] (
0
) [
HTML
1KB] [
PDF
537KB] (
8
)
632
Yu Feng GAO, Yan Xun CHANG, Tao FENG
Simple Minimum (
K
_{4}
e)coverings of Complete Multipartite Graphs
A decomposition of
K
_{n(g)}
∪Γ, the complete
n
partite equipartite graph over
gn
vertices union a graph Γ (called the
excess
) that is a subgraph of
K
_{n(g)}
, into edge disjoint copies of a graph
G
is called a
simple minimum group divisible covering
of type
g
^{n}
with
G
if Γ contains as few edges as possible. We examine all possible excesses for simple minimum group divisible (
K
_{4}

e
)coverings. Necessary and sufficient conditions are established for their existence.
2019 Vol. 35 (5): 632648 [
Abstract
] (
1
) [
HTML
1KB] [
PDF
248KB] (
12
)
649
Yu Zhe LIU, Chao ZHANG
On Derived Unique Gentle Algebras
An algebra
A
is called derivedunique provided that any algebra which is derived equivalent to
A
is necessarily Morita equivalent to
A
. We classify derivedunique gentle algebras with at most one cycle using the combinatorial invariant introduced by AvellaAlaminos and Geiss.
2019 Vol. 35 (5): 649661 [
Abstract
] (
0
) [
HTML
1KB] [
PDF
239KB] (
11
)
662
Nattiwut MAUGMAI, Teerapat SRICHAN
The Meanvalue of Meromorphic Functions with Respect to a Generalized Boolean Transformation
A formula for the meanvalue distribution of certain meromorphic functions on a vertical line
s
=
σ
+iR under a generalized Boolean transformation, called rational Boolean transformation from R into itself, is derived using Birkhoff's ergodic theorem. This formula is represented as a computable integral. Using the Cauchy's integral theorem, values of this integral corresponding to various possible cases are explicitly computed.
2019 Vol. 35 (5): 662670 [
Abstract
] (
1
) [
HTML
1KB] [
PDF
200KB] (
10
)
671
Yan Yan CUI, Chao Jun WANG, Hao LIU
Biholomorphic Mappings and the Extension Operators on New Hartogs Domains
In this paper, we generalize the RoperSuffridge operator on the extended Hartogs domains. By using the geometric properties and the growth theorems of subclasses of biholomorphic mappings, we obtain the generalized operators preserve the properties of parabolic and spirallike mappings of type
β
and order
ρ
,
S
_{Ω}
^{*}
(
β, A, B
), almost starlike mapping of complex order λ on Ω
_{N}
under different conditions, and thus we get the corresponding results on the unit ball
B
^{n}
in C
^{n}
. The conclusions lead to some known results.
2019 Vol. 35 (5): 671689 [
Abstract
] (
1
) [
HTML
1KB] [
PDF
296KB] (
15
)
690
Fu Rong WANG, Shao Fei DU
Möbius Regular Maps of Order
pq
Möbius regular maps are surface embeddings of graphs with doubled edges such that (i) the automorphism group of the embedding acts regularly on flags and (ii) each doubled edge is a center of a Möbius band on the surface. In this paper, we classify Möbius regular maps of order
pq
for any two primes
p
and
q
, where
p
≠
q
.
2019 Vol. 35 (5): 690702 [
Abstract
] (
0
) [
HTML
1KB] [
PDF
261KB] (
9
)
703
Yi WU, Xue Jun WANG
On Consistency of the Nearest Neighbor Estimator of the Density Function and Its Applications
In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency, strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.
2019 Vol. 35 (5): 703720 [
Abstract
] (
0
) [
HTML
1KB] [
PDF
234KB] (
11
)
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