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2017年 第32卷 第4期    刊出日期：2017-12-30

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不可压缩Oldroyd方程局部解的存在性

刘筠, 原保全

2017, 32(4):  331-344.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.001

摘要 ( 75 )   PDF (548KB) ( 116 )  

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This paper investigates the local-in-time existence and uniqueness of strong solutions in H^s for s >n/2 to the incompressible Oldroyd model equations in Rⁿ, n = 2, 3.The result reads: if u₀, F₀∈ H^s（Rⁿ） with s >n/2, then there exists a unique strong solution u, F ∈ C（[0, T]; H^s（Rⁿ））, where T = T（‖u₀‖H^s, ‖F₀‖H^s） is the local existence time. 

有限体积方法非结构网格方法解分数阶Allen-Cahn程

陈爱敏, 刘发旺

2017, 32(4):  345-354.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.002

摘要 ( 79 )   PDF (761KB) ( 250 )  

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Fractional-in-space Allen-Cahn equation containing a very strong nonlinear source term and small perturbation shows metastability and a quartic double well potential.Using a finite volume unstructured triangular mesh method, the present paper solves the twodimensional fractional-in-space Allen-Cahn equation with homogeneous Neumann boundary condition on different irregular domains. The efficiency of the method is presented through numerical computation of the two-dimensional fractional-in-space Allen-Cahn equation on different domains. 

在解析簇上(0,q),(q>0)微分形式的一般积分公式

陈叔瑾

2017, 32(4):  355-370.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.003

摘要 ( 90 )   PDF (602KB) ( 146 )  

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In this paper, firstly using different method and technique we derive the corresponding integral representation formulas of(0, q)(q > 0) differential forms for the two types of the bounded domains in complex submanifolds with codimension-m. Secondly we obtain the unified integral representation formulas of(0, q)(q > 0) differential forms for the general bounded domain in complex submanifold with codimension-m, which include Hatziafratis formula, i.e. Koppelman type integral formula for the bounded domain with smooth boundary in analytic varieties. In particular, when m = 0, we obtain the unified integral representation formulas of(0, q)(q > 0) differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula. 

局部扭立方的1好邻连通度和诊断度

任云霞, 王世英

2017, 32(4):  371-381.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.004

摘要 ( 111 )   PDF (481KB) ( 182 )  

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Diagnosability of a multiprocessor system is one important study topic. In 2012, Peng et al. proposed the g-good-neighbor diagnosability that restrains every fault-free node to contain at least g fault-free neighbors. The locally twisted cube LTQ_n has many good properties. In this paper, we show that the 1-good-neighbor connectivity κ~1(LTQ_n) = 2n-2 and the 1-good-neighbor diagnosability of LTQ_n is 2n-1 under the PMC model for n ≥ 4 and the MM~*model for n ≥ 5. 

外平面图的邻点可区别Ⅰ-全染色

郭靖, 陈祥恩

2017, 32(4):  382-394.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.005

摘要 ( 76 )   PDF (482KB) ( 111 )  

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Let G be a simple graph with no isolated edge. An Ⅰ-total coloring of a graph G is a mapping φ : V(G) ∪ E(G) → {1, 2, ···, k} such that no adjacent vertices receive the same color and no adjacent edges receive the same color. An Ⅰ-total coloring of a graph G is said to be adjacent vertex distinguishing if for any pair of adjacent vertices u and v of G, we have C_φ(u) = C_φ(v), where C_φ(u) denotes the set of colors of u and its incident edges. The minimum number of colors required for an adjacent vertex distinguishing Ⅰ-total coloring of G is called the adjacent vertex distinguishing Ⅰ-total chromatic number, denoted by χ_at~i(G).In this paper, we characterize the adjacent vertex distinguishing Ⅰ-total chromatic number of outerplanar graphs.

短期利率模型中隐含波动率的重构

赵芳芳, 许作良

2017, 32(4):  395-406.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.006

摘要 ( 65 )   PDF (519KB) ( 91 )  

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This paper concerns an inverse problem of recovering implied volatility in shortterm interest rate model from the market prices of zero-coupon bonds. Based on linearization, an analytic solution, which is given as a power series, is derived for the direct problem.By neglecting high order terms in the power series, an integral equation about the perturbation of volatility is formulated and the Tikhonov regularization method is applied to solve the integral equation. Finally numerical experiments are given and the results show that the method is effective. 

-混合误差下非参数回归模型估计量的收敛速度

胡琪, 黄倩, 杨文志, 李晓琴

2017, 32(4):  407-414.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.007

摘要 ( 70 )   PDF (371KB) ( 100 )  

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In this paper, we investigate the nonparametric regression model based on ?ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. We obtain the convergence rate for the weighted estimator of unknown function g(x) in pthmean, which yields the convergence rate in probability. Moreover, an example of the nearest neighbor estimator is also illustrated and the convergence rates of estimator are presented. 

一类包含有完全Bell多项式的恒等式

杨继真, 王云鹏

2017, 32(4):  415-424.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.008

摘要 ( 91 )   PDF (395KB) ( 129 )  

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The purpose of this paper is to establish a formula of higher derivative by Faà di Bruno formula, and apply it to some known results to get some identities involving complete Bell polynomials. 

一类具有阶段结构的随机捕食与被捕食模型的全局稳定性分析

白宏芳, 徐瑞

2017, 32(4):  425-431.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.009

摘要 ( 91 )   PDF (393KB) ( 196 )  

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In this paper, a stochastic predator-prey model with stage structure for predator and ratio-dependent functional response is concerned. Sufficient conditions for the global asymptotic stability of positive equilibrium are established. Some numerical simulations are carried out to illustrate the theoretical results. 

由拟从属关系定义的P叶解析函数子类的Fekete-Szeg?问题

敖恩, 李书海, 汤获, 斯琴其木格

2017, 32(4):  432-440.  doi:10.13371/j.cnki.chin.q.j.m.2017.04.010

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In this paper, a new certain class of р-valent analytic functions with quasisubordination is defined and the Fekete-Szeg? problems for functions belonging to the class are derived. The results presented here provide extensions of those given in some earlier works.