数学季刊

曹蕾, 陈守信,

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.

循环图的距离能量

周后卿

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.

混合跳-扩散模型下美式浮动履约回望期权的临界实施价格

杨朝强

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.

幺半群上的强α-自反环

彭宅铭 , 谷勤勤 , 张蕊蕊

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.

有界正则零函数的导数估计

郭怡冰, 王平安

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.

关于s-凸函数的Hermite-Hadamard型积分不等式的推广

连铁艳, 汤伟

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.

Yetter-Drinfeld Hopf代数的Maschke型定理

史美华, 贾玲

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].

具有多个单项式的分数阶微分系统的李雅普诺夫型不等式的研究

漆勇方, 韩丽涛, 魏胥婷

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.

正交Cauchy函数方程的模糊稳定性

闭吕庆, , 戴松松, 胡波,

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.

一类具马尔科夫链中立型随机神经网络的动力学性质

马鹏宇, 杜波

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)-开集与γ-(α,β)-T_i空间

吴耀强

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.

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