Table of Content

30 December 2017, Volume 32 Issue 4

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Local Existence of Solution to the Incompressible Oldroyd Model Equations

LIU Yun, YUAN Bao-quan

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

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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. 

A Finite Volume Unstructured Mesh Method for Fractional-in-space Allen-Cahn Equation

CHEN Ai-min, , LIU Fa-wang

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

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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. 

General Integral Formulas of (0; q)(q > 0) Differential Forms on the Analytic Varieties

CHEN Shu-jin

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

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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. 

The 1-Good-neighbor Connectivity and Diagnosability of Locally Twisted Cubes

REN Yun-xia, WANG Shi-ying

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

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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. 

Adjacent Vertex Distinguishing I-total Coloring of Outerplanar Graphs

GUO Jing, CHEN Xiang-en

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

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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.

Recover Implied Volatility in Short-term Interest Rate Model

ZHAO Fang-fang, XU Zuo-liang

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

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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. 

Convergence Rate of Estimator for Nonparametric Regression Model under \widetide{p}-mixing Errors

HU Qi, HUANG Qian, YANG Wen-zhi, LI Xiao-qin

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

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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. 

A Kind of Identities Involving Complete Bell Polynomials

YANG Ji-zhen, WANG Yun-peng

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

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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. 

Global Stability of A Stochastic Predator-prey Model with Stage-structure

BAI Hong-fang, XU Rui

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

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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. 

Fekete-SzegÄo Problem for Certain Subclass of p-Valent Analytic Functions using Quasi-Subordination

AO En, LI Shu-hai, TANG Huo, Siqinqimuge

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.