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Acta Mathematica Sinica,Chinese Series
2019, Vol.35 Num.5
Online: 2019-05-15

583 Robert PARKER, Andrew ROSALSKY
Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements
For a double array {Vm,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 {bm,n, m≥1,n ≥ 1} of positive constants, the limit law max1≤km,1≤ln||Σ i=1k||Σ j=1l Vi,j||/bm,n → 0 a.c. and in Lp as mn → ∞ is shown to hold if Σm=1 Σn=1 E||Vm,n||p/bm,np < ∞. 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): 583-596 [Abstract] ( 0 ) [HTML 1KB] [PDF 228KB] ( 17 )
597 Hua Zhong KE
On Duality in Filtered Cohomologies
For a symplectic manifold (M2n, 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+dΛ)-and ddΛ-cohomologies.
2019 Vol. 35 (5): 597-608 [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 Grauert-Riemenschneider 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 ∂√ωl=for all l, i.e., if T is a closed positive current on X such that ſX Tacn>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 ſX Tacn>0, then the class {T} is big and X is Kähler.
2019 Vol. 35 (5): 609-618 [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 re-parameterized 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): 619-631 [Abstract] ( 0 ) [HTML 1KB] [PDF 537KB] ( 8 )
632 Yu Feng GAO, Yan Xun CHANG, Tao FENG
Simple Minimum (K4-e)-coverings of Complete Multipartite Graphs
A decomposition of Kn(g) ∪Γ, the complete n-partite equipartite graph over gn vertices union a graph Γ (called the excess) that is a subgraph of Kn(g), into edge disjoint copies of a graph G is called a simple minimum group divisible covering of type gn with G if Γ contains as few edges as possible. We examine all possible excesses for simple minimum group divisible (K4-e)-coverings. Necessary and sufficient conditions are established for their existence.
2019 Vol. 35 (5): 632-648 [Abstract] ( 1 ) [HTML 1KB] [PDF 248KB] ( 12 )
649 Yu Zhe LIU, Chao ZHANG
On Derived Unique Gentle Algebras
An algebra A is called derived-unique provided that any algebra which is derived equivalent to A is necessarily Morita equivalent to A. We classify derived-unique gentle algebras with at most one cycle using the combinatorial invariant introduced by Avella-Alaminos and Geiss.
2019 Vol. 35 (5): 649-661 [Abstract] ( 0 ) [HTML 1KB] [PDF 239KB] ( 11 )
662 Nattiwut MAUGMAI, Teerapat SRICHAN
The Mean-value of Meromorphic Functions with Respect to a Generalized Boolean Transformation
A formula for the mean-value 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): 662-670 [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 Roper-Suffridge 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, SΩ* (β, A, B), almost starlike mapping of complex order λ on ΩN under different conditions, and thus we get the corresponding results on the unit ball Bn in Cn. The conclusions lead to some known results.
2019 Vol. 35 (5): 671-689 [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 pq.
2019 Vol. 35 (5): 690-702 [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): 703-720 [Abstract] ( 0 ) [HTML 1KB] [PDF 234KB] ( 11 )
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