Table of Content

30 September 2018, Volume 33 Issue 3

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The Existence of Domain Wall Solutions in Ambj?rn--Nielsen-Olesen Theory

CAO Lei, CHEN Shou-xin,

2018, 33(3):  221-232.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.001

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The Ambj?rn-Nielsen-Olesen(ANO) model arises from field theory, in the limiting BPS state, the ANO model is actually a domain wall model which is a basic construct describing a phase transition between two phases. In this paper, we derive a coupled second-order ordinary differential equations of the domain wall model. Then we establish the existence and uniqueness theorem for the domain solutions by using a dynamical shooting method for the parameter γ = 1, and variational method for the parameter γ > 0 and γ = 1. 

The Distance Energy of Circulant Graphs

ZHOU Hou-qing

2018, 33(3):  233-239.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.002

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For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph. 

Critical Exercise Price for American Floating Strike Lookback Option in a Mixed Jump-Diffusion Model

YANG Zhao-qiang

2018, 33(3):  240-259.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.003

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This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using Itö formula and Wick-Itö-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model.

Strongly α-Refexive Rings Relative to a Monoid

PENG Zhai-ming, GU Qin-qin, ZHANG Rui-rui

2018, 33(3):  260-271.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.004

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For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring Q, we prove that R is strongly M-α-reflexive if and only if Q is strongly M-α-reflexive, where R is α-rigid, α is an epimorphism of R. The relationship between some special subrings of upper triangular matrix rings and strongly M-α-reflexive rings is also investigated. Several known results similar to strongly M-α-reversible rings are obtained. 

Estimation of Derivatives for Bounded Regular Vanishing Functions

GUO Yi-bing, WANG Ping-an

2018, 33(3):  272-277.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.005

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In this paper, we mainly discuss the problem of estimating the n-th derivative for bounded regular vanishing functions. The estimation of the n-th derivative for the function is deduced by the 1-th and 2-th derivative. 

Generalizations of Hermite-Hadamard Type Inequalities Involving S-convex Functions

LIAN Tie-yan , TANG Wei

2018, 33(3):  278-286.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.006

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Some new Hermite-Hadamard type’s integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard’s integral inequality are generalized. 

The Maschke-type Theorems of Yetter-Drinfeld Hopf Algebras

SHI Mei-hua, JIA Ling

2018, 33(3):  287-292.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.007

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In this paper, we give the Maschke-type theorem for a Yetter-Drinfeld Hopf algebra which extends the famous results for a usual Hopf algebra[3]. 

Lyapunov-type inequalities for fractional differential systems with more than three monomials

QI Yong-fang, HAN Li-tao, WEI Xu-ting

2018, 33(3):  293-301.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.008

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This paper presents Lyapunov-type inequalities for fractional differential systems with more than three monomials by using the Gronwall-Inequality and the Greens function.The results of this paper extend the research methods of similar problems and generalize some early conclusions on this topic.In addition,with the help of the results,we can analyze the solution of differential systems. 

Fuzzy Stability of the Orthogonal Cauchy Functional equations

BI Lv-qing , DAI Song-song, HU Bo,

2018, 33(3):  302-312.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.009

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In this paper, we establish fuzzy stability of the orthogonal Cauchy functional equations f(x + y) = f(x) + f(y), x ⊥ y and the orthogonal Cauchy functional of P exider type f(x + y) = g(x) + h(y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rtz. 

Dynamic Properties of Neutral Stochastic Differential Equations with Markovian Switching

MA Peng-yu, DU Bo

2018, 33(3):  313-323.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.010

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A generalized neutral stochastic functional differential equation(NSFDE) with Markovian switching is studied. We will discuss some important properties of the solutions including boundedness and exponential stability by using Lyapunov-Krasovskii functional,Matrix inequality and some analysis techniques. Finally, an numerical example for neutral stochastic neural networks with Markovian switching is given to show the effectiveness of the results in this paper. 

γ-(α,β)-Open Sets and γ-(α,β)-T_i Spaces

WU Yao-qiang

2018, 33(3):  324-330.  doi:10.13371/j.cnki.chin.q.j.m.2018.03.011

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We introduce the concept of γ-(α, β)-open sets and the concepts of γ-(α, β)-T_i spaces(i = 0, 1, 2, 3, 4) based on the concept of

(α, β)-open sets. We obtain some properties of γ-(α, β)-Tispaces. Furthermore, we study their essential characterization in topological space.