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Additively Indecomposable Positive Definite Integral Lattices
《Acta Mathematica Sinica,English Series》2025年第3期908-924,共17页Ruiqing Wang 
In this paper, we obtain some sufficient and necessary conditions for indecomposable positive definite integral lattices with discriminants 2, 3, 4 and 5 over Z being additively indecomposable lattices. Using these re...
关键词：Indecomposable lattice additively indecomposable lattice unimodular lattice adjacent lattice GENUS 
Kaiser Criterion in Factor Models
《Acta Mathematica Sinica,English Series》2025年第2期547-552,共6页Changhu Wang Jianhua Guo Yanyuan Ma Shurong Zheng 
Supported by NSFC (Grant Nos. 11631003, 11690012)。
Despite of the wide use of the factor models, the issue of determining the number of factors has not been resolved in the statistics literature. An ad hoc approach is to set the number of factors to be the number of e...
关键词：Factor model Kaiser criterion positive definite 
Non-Gaussian Random Bi-matrix Models for Bi-free Central Limit Distributions with Positive Definite Covariance Matrices
《Acta Mathematica Sinica,English Series》2019年第12期1891-1905,共15页Ming Chu GAO 
In this paper,we construct random two-faced families of matrices with non-Gaussian entries to approximate a bi-free central limit distribution with a positive definite covariance matrix.We prove that,under modest cond...
关键词：Bi-free CENTRAL limit distributions NON-GAUSSIAN RANDOM matrices asymptotic bi-freeness 
The α-Geometric Structures on Manifold of Positive Definite Hermite Matrices被引量：2
《Acta Mathematica Sinica,English Series》2014年第12期2137-2145,共9页Xiao Min DUAN Hua Fei SUN Lin Yu PENG 
Supported by Natural Science Foundations of China(Grant No.61179031 and 61401058)
Geometric structures of a manifold of positive definite Hermite matrices are considered from the viewpoint of information geometry.A Riemannian metric is defined and dual α-connections are introduced.Then the fact th...
关键词：Positive definite Hermite matrices information geometry optimal approximation 
On Conditionally Positive Definite Dot Product Kernels
《Acta Mathematica Sinica,English Series》2008年第7期1127-1138,共12页V.A.MENEGATTO C.P.OLIVEIRA Ana P.PERON 
PROCAD-CAPES,Grant # 0092/01-0
Let m and n be fixed, positive integers and P a space composed of real polynomials in m variables. The authors study functions f ： R →R which map Gram matrices, based upon n points of R^m, into matrices, which are n...
关键词：conditionally positive definite kernels dot product kernels Gram matrices CONVEXITY convexity in the sense of Jensen 
A Problem about the Weak Hilbert Property
《Acta Mathematica Sinica,English Series》1998年第4期481-486,共6页Zeng Guangxing, Departement of Mathematics and Systems Science, Nanchang University, Nanchang 330047, China 
Project supported by National Natural Science Foundation of China
In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilb...
关键词：Ordered field Preordered field The weak Hilbert property Positive definite polynomial 
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