Chinese Quarterly Journal of Mathematics

Statistical Analysis for Constant-stress Partially Accelerated Life Test with Interval Censored Data

LONG Bing, ZHANG Zhong-zhan

2019, 34(1): 1-13. doi:10.13371/j.cnki.chin.q.j.m.2019.01.001

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In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.

On Intersection Multiplicity of Algebraic Curves

LIANG Hong-Chang

2019, 34(1): 14-20. doi:10.13371/j.cnki.chin.q.j.m.2019.01.002

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In this paper, we study the intersection multiplicity of algebraic curves at a point both in R~2 and in real projective plane P~2. We introduce the fold point of curves and provide conditions for the relations between the intersection multiplicity of curves at a point and the folds of the point.

When Exchange Rings are Von Neumann Regular

HUANG Chao-ling

2019, 34(1): 21-28. doi:10.13371/j.cnki.chin.q.j.m.2019.01.003

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We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.

The Properties of The Rational Maps With Buried Components

ZHUANG Wei

2019, 34(1): 29-42. doi:10.13371/j.cnki.chin.q.j.m.2019.01.004

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Let R（z） be an NCP map with buried components of degree d = degf ≥ 2 on the complex sphere ■, and HD denotes the Hausdorff dimension. In this paper we prove that if R_n→ R algebraically, and Rn and R topologically conjugate for all n >> 0, then R_n is an NCP map with buried components for all n >> 0, and for some C > 0,d_H（J（R）,J（R_n）） ≤ C（dist（R, R_n)^1/d,where dH denotes the Hausdorff distance, and HD（J（R_n）） → HD（J（R））.In this paper we also prove that if the Julia set J（R） of an NCP map R（z） with buried components is locally connected, then any component J_i（R） is either a real-analytic curve or HD（J_i（R）） > 1.

An Improvement in Ordered Cone b-metric Spaces Over Banach Algebras

HAN Yan, XU Shao-yuan, DONG Yan-shou

2019, 34(1): 43-51. doi:10.13371/j.cnki.chin.q.j.m.2019.01.005

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The purpose of this paper is to improve some famous theorems for contractive mapping from ρ(α + β) ∈ [0,1/s) to ρ(α + β) ∈ [0, 1) in ordered cone b-metric spaces over Banach algebras with coefficient s ≥ 1(ρ(x) is the spectral radius of the generalized Lipschitz constant x). Moreover, some similar improvements in ordered cone b-metric spaces are also obtained, which from α + β∈ [0,1/s) to α + β∈ [0, 1). Some examples are given to support that our new results are genuine improvements and generalizations.

Some Results on H-cordial Graphs and Semi-H-cordial Graphs

CHEN Li-na, XIE Yan-tao

2019, 34(1): 52-56. doi:10.13371/j.cnki.chin.q.j.m.2019.01.006

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I. Cahit calls a graph H-cordial if it is possible to label the edges with the numbers from the set{1,-1} in such a way that, for some k, at each vertex v the sum of the labels on the edges incident with v is either k or-k and the inequalities |v(k)-v(-k)| ≤ 1 and|e(1)-e(-1)| ≤ 1 are also satisfied. A graph G is called to be semi-H-cordial, if there exists a labeling f, such that for each vertex v, |f(v)| ≤ 1, and the inequalities |e_f(1)-e_f(-1)| ≤ 1 and |v_f(1)-v_f(-1)| ≤ 1 are also satisfied. An odd-degree(even-degree) graph is a graph that all of the vertex is odd(even) vertex. Three conclusions were proved:(1) An H-cordial graph G is either odd-degree graph or even-degree graph;(2) If G is an odd-degree graph, then G is H-cordial if and only if |E(G)| is even;(3) A graph G is semi-H-cordial if and only if |E(G)| is even and G has no Euler component with odd edges.

Study On the Impact of Open Residential Block on Urban Traffic Congestion Based on Dynamic Com-prehensive Evaluation Model

MA Fang-fang, LI Han

2019, 34(1): 57-65. doi:10.13371/j.cnki.chin.q.j.m.2019.01.007

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The growing use of vehicles with the development of China brings greater pressure on the existing road traffic network. Based on the domestic and international research experiences and the domestic congestion situations, this paper selected six indicators that affect the traffic conditions. As each single indicator cannot reflect the detailed traffic quality separately, the dynamic comprehensive evaluation principle is adopted.Then we used the principle of "Variation Driven" to determine the weight vector of each sub-indicator, and established a multi-indicator comprehensive evaluation system through the dynamic weight of each sub-indicator. Finally, the rationality and feasibility of the system is demonstrated by case analysis. This provides a strong theoretical foundation and basis to mitigate traffic congestion.

The Cohomology Structures of Partial Entwining Structures

JIA Ling

2019, 34(1): 66-74. doi:10.13371/j.cnki.chin.q.j.m.2019.01.008

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In this paper we mainly reveal the rich cohomology theories for partial entwining structures.

Analysis On an SEIRS Epidemic Model with Pulse Vaccination and Two Time Delays

GAO Jian-zhong, ZHANG Tai-lei

2019, 34(1): 75-87. doi:10.13371/j.cnki.chin.q.j.m.2019.01.009

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In this paper, an SEIRS epidemic model with pulse vaccination and two time delays is proposed. By using stroboscopic map and comparison principle, the disease-free periodic solution(DFPS for short) is obtained and the global asymptotic stability of the DFPS is proved. The sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.

Lyapunov-type Inequalities For A System of Nonlinear Difference Equations

WEI Geng-ping

2019, 34(1): 88-98. doi:10.13371/j.cnki.chin.q.j.m.2019.01.010

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This paper establishes several new Lyapunov-type inequalities for the system of nonlinear difference equations■,which extend/supplement and improve some related existing ones.

A Remark on Double Ore Extensions

LI Qi-Ning

2019, 34(1): 99-110. doi:10.13371/j.cnki.chin.q.j.m.2019.01.011

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The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of A which can not be presented as iterated Ore extensions.

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