甘肃省数学会2017学术年会议程

主办单位：甘肃省数学会

承办单位：陇南师范高等专科学校

2017年5月12-15日

开幕式及理事会议议程

1、学会副理事长罗彦锋教授介绍参加会议的嘉宾

2、陇南师范高等专科学校校长刘先春教授致欢迎词

3、学会理事长李万同教授讲话并介绍2016年甘肃省数学优秀博士论文评审情况

5、颁发2016年甘肃省数学优秀博士论文证书

6、开幕式结束

7、学会副理事长刘仲奎教授主持第十一届理事会第三次会议

甘肃省数学会2017学术年会

（5月12日-15日）

5月12日	全天报到（陇南成县蓝天大酒店一楼大厅）
5月12日	20:00-20:40	预备会议（学术委员会、组织委员会、会务组成员）	主持人：李万同

5月 13日 上午	地点：陇南师专南校区餐饮综合楼5楼（学生活动中心）多功能报告厅
	08:00-08:30		开幕式		主持人：罗彦锋
	08:30-09:00		照相 地点：南校区体育馆前
	09:00-09:40		第十一届理事会第三次会议（全体理事，其余人员列席）		主持人：刘仲奎
	大会报告
	地点：陇南师专南校区餐饮综合楼5楼（学生活动中心）多功能报告厅
	时间	报告题目		报告人及单位		主持人
	10:00-10:40	Periodic Homogenization of Parabolic Problems		耿 俊兰州大学		李万同
	10:40-11:20	Bernoulli空间上的场算子在数学物理中的若干应用		王才士西北师大		马如云
	11:20-12:00	Optimal control for age-dependentpopulation hybrid systemin a polluted environment.		雒志学兰州交大		褚衍东

5月13日下午	分组报告 14:10-18:10
	学术一组第一阶段 14:10-16:10 地点：餐饮综合楼5楼多功能报告厅
	主持人：赵有益 王三福
	时间	报告题目	报告人及单位
	14:10-14:50	Least Area Surfaces in 3-manifolds.	陈立志兰州大学
	14:30-14:50	给定平均曲率问题正解的全局结构	高红亮兰州交大
	14:50-15:10	Cartan-Eilenberg FP-injective complexes	卢 博西北民大
	15:10-15:30	Optimal bilinear control of Gross-Pitaevskii equations with Coulombian potentials	冯斌华西北师大
	15:30-15:50	鞍点问题的局部循环剩余分裂迭代法	朱睦正河西学院
	15:50-16:10	旋转对称空间中的平均曲率型流	郭芳承陇东学院
	学术一组第二阶段 16:30-18:10 地点：餐饮综合楼5楼多功能报告厅
	主持人：韩金仓 马统一
	时间	报告题目	报告人及单位
	16:30-16:50	On fractional non-autonomous evolution equation of mixed type with nonlocal initial conditions	陈鹏玉西北师大
	16:50-17:10	Dynamics of reaction-diffusion epidemic models with nonlocal effect	张 亮兰州大学
	17:10-17:30	适应性动力系统与进化分支	张 锋 甘肃农大
	17:30-17:50	半线性分数阶脉冲积分-微分方程解的一些新的存在性和唯一性结果	周文学兰州交大
	17:50-18:10	图的电阻距离和基尔霍夫指标	刘 群 河西学院
	学术二组第一阶段 14:10-16:10 地点：餐饮综合楼5楼 505教室
	主持人：欧志英 许万银
	时间	报告题目	报告人及单位
	14:10-14:30	Tilting subcategories with respect to cotorsion triples in abelian categories	狄振兴西北师大
	14:30-14:50	Threshold changeable secret sharing scheme based on Chinese Remainder Theorem	贾星星兰州大学
	14:50-15:10	On the degree sequence determined by the Laplacian spectrumof the corresponding graph	文 飞 兰州交大
	15:10-15:30	Equitable vertex arboricity of graphs	高毓平 兰州大学
	15:30-15:50	Two knight Pascal's triangles	冯积社 陇东学院
	15:50-16:10	关于Lebesgue-Nagell方程整数解的讨论	冉银霞 陇南师专

5月13日下午	学术二组第二阶段 16:30-18:10 地点：餐饮综合楼5楼 505教室
	主持人：王素云 何万生
	时间	报告题目	报告人及单位
	16:30-16:50	Multiplicative noise and blur removal used some convex optimaization model	汪 帆兰州大学
	16:50-17:10	数学在碳管理和气候变化中的应用	张美玲甘肃农大
	17:10-17:30	Eigenvalues of Discrete Sturm-Liouville Problems with Eigenparameter Dependent Boundary Conditions	高承华西北师大
	17:30-17:50	Analysis of a Special Predator-Prey Model with Two Delays, Herd Behavior and Prey Harvesting	孟新友兰州理工大
	17:50-18:10	Robust portfolio choice for a DC pension plan with stochastic income and interest rate	孙景云兰州城市学院
	学术三组 14:10-16:10 地点：校本部1号教学楼111教室
	主持人：陈京荣 彭康靑
	14:10-14:30	Global Well-posedness for the GNSC equations with highly oscillating initial data	孙小春 西北师大
	14:30-14:50	分数阶时滞和T-S模糊复杂网络的同步	马维元 西北民大
	14:50-15:10	复模糊线性系统	郭晓斌西北师大
	15:10-15:30	Choquet模糊积分分类器中模糊测度的学习	陈 莉 兰州城市学院
	15:30-15:50	完全模糊线性系统解的扰动分析	刘 坤 陇东学院
	15:50-16:10	实数序列的通项公式是初等函数	东洪平 陇南师专
	数学建模竞赛和数学竞赛组 16:30-18:10 地点：校本部1号教学楼111教室
	主持人：王海明 颜荣芳
	中学数学教育组第一阶段 14:30-16:10 地点：校本部1号教学楼107教室
	主持人：缑小锋 傅龙骧
	中学组第二阶段 16:30-18:10 地点：校本部1号教学楼107教室
	主持人：郑新英 董小平

5月 14日 上午	大会报告 第一阶段 8:00-10:00 地点：餐饮综合楼5楼多功能报告厅
	时间	报告题目	报告人及单位	主持人
	8:00-8:40	Klein-Gordon-Schrodinger型系统在能量空间的适定性	石启宏兰州理工大	霍海峰
	8.40-9.20	Statistical Inference Based on Jackknife Empirical Likelihood	李周平兰州大学	张国凤
	9:20-10:00	梯度流方法在反问题中的若干应用	熊向团西北师大	李永祥
	10:00-10:20	休 息
	大会报告 第二阶段 10:20-12:00 地点：餐饮综合楼5楼多功能报告厅
	时间	报告题目	报告人及单位	主持人
	10:20-11:00	Monotonicity of solutions to degenerate elliptic problems in half-spaces	黄水波西北民大	马少仙
	11:00-11:40	Periodic Principal Eigenvalues and Applications	孙建文兰州大学	赵 敦
	11:40－12:00 闭幕式 主持人：马如云 地点：餐饮综合楼5楼多功能报告厅
5月 14日 下午	14：30－17：40 自由交流

部分学术报告摘要

大会报告

Bernoulli空间上的场算子在数学物理中的若干应用

王才士西北师范大学

摘要：Bernoulli空间上的场算子包括湮灭算子和增生算子，满足典则反交换关系，因而可以解释为一种量子噪声。在此报告中，我们介绍上述算子在量子Markov半群构造、无穷自由度量子游荡、Dirichlet型与扩散过程等数学物理问题中的若干应用。

Optimal control for age-dependent population hybrid system in a polluted environment

Luo Zhixue (Lanzhou Jiaotong University)

Abstract: In this talk, we study an optimal control problem for an age-dependent population hybrid system in a polluted environment. Namely, we establish a new toxicant-population model with age-dependence in a small content of the environment.

Klein-Gordon-Schrodinger型系统在能量空间的适定性

石启宏兰州理工大学理学院

摘要：由于耦合了两个不同类型的方程，尤其是Schrodinger算子估计时正则性的不可降性，导致Klein-Gordon-Schrodinger(KGS)系统研究有很大的难度。本报告主要介绍在能量空间中KGS型系统的适定性理论。我们用粘性消失方法结合L^p-L^q估计得到了能量空间中弱解的存在性，进一步通过解差分析和研究摄动Schrodinger方程的Strichartz估计证明了不同物理效应下该弱解的唯一性，最后我们展示一个证明KGS型系统适定性的更一般化方法。

Statistical Inference Based on Jackknife Empirical Likelihood

LI Zhouping(Lanzhou University)

Abstract:Empirical likelihood (EL) has been found very useful in many various fields. However, when dealing with nonlinear statistical functionals/constraints, there have been serious computational difficulties. The jackknife empirical likelihood (JEL) introduced by Jing, Yuan and Zhou (2009) with focus on U-statistics, isa quite simple and promising method, and can largely release the heavy computational burden of ordinary EL method for nonlinear constraints.In this talk, we will discuss the recent advances in JEL methodology, and introduce some of our recent works in this direction.

梯度流方法在反问题中的若干应用

熊向团西北师范大学

摘要：梯度流方法是计算几何中的一个基本方法，本报告试图引入该方法到反问题的正则化方法的设计。首先通过这一方法设计出一般反问题的修改Landweber迭代方法，理论上给出误差估计，并应用到具体的反问题。最后应用梯度流的思想求解一个多个系数的反演问题。

Monotonicity of solutions to degenerate elliptic problems in half-spaces

Shuibo Huang

School ofMathematics and Computer,Northwest Minzu University,

In this paper, we consider the monotonicity properties of positive weak solutions to quasilinear elliptic problems with first-order term

\begin{align*}

\left\{\begin{array}{llll}

-\text{div}\mathcal {A}(x,u,\nabla u)+b(x,u)|\nabla u|^q=f(x,u), &x\in \mathbb{R}^N_+,\\

u(x',y)>0, &x\in \mathbb{R}^N_+,\\

u(x',0)=0, &x\in \partial\mathbb{R}^N_+,

\end{array}

\right.

\end{align*}

where $N\geq2$, $1<p <2$ and $1<q\leq p$ and the

function $\mathcal {A}(x,s,\xi)$ defines a generalized Leray–Lions operator. The main novelty of the present paper is that the function $\mathcal {A}(x,s,\xi)$, depending also on $\xi$, is local Lipschitz continuous with respect to $s$ and the underlying domain $\mathbb{R}^N_+$ is unbounded. The results of this paper extends earlier results of A. Farina et.al.(2015)\cite{FMRS2015} for $\text{div}\mathcal {A}(x,u,\nabla u)=\Delta_p u$.

分组报告

给定平均曲率问题正解的全局结构

高红亮 兰州交通大学数理学院

摘要：本报告考虑Minkowski空间中平均曲率问题正解的全局结构。首先，运用单边全局分歧理论和连通分支取极限的思想建立了球域上给定平均曲率问题径向正解的全局结构。其次，运用时间映像的方法研究了一维Minkowski-曲率方程Dirichlet问题正解的精确个数。

Cartan-Eilenberg FP-injective complexes

Lu Bo

College of Mathematics and Computer Science, Northwest University for Nationalities

Abstract In this article, we extend the notion of FP-injective modules to that of Cartan-Eilenberg complexes. We show that a complexCis Cartan-Eilenberg FP-injective if and only ifCand Z(C) are complexes consisting of FP-injective modules over right coherent rings. As an application, coherent rings are char-acterized in various ways, using Cartan-Eilenberg FP-injective and Cartan-

Eilenberg at complexes.

Optimal bilinear control of Gross-Pitaevskii equations with Coulombian potentials

冯斌华西北师范大学

摘要：In this paper, we consider an optimal bilinear control problem for the Gross–Pitaevskii equations with Coulombian potentials. We show the well-posedness of the problem and the existence of an optimal control. In addition, the first order optimality system is rigorously derived. In particular, we prove the Fréchet-differentiability of the unconstrained functional. We extend the study of Hintermüller et al. (SIAM J. Control Optim. 51: 2509-2543, 2013) to more general power nonlinearities and unbounded potentials.

旋转对称空间中的平均曲率型流

陇东学院 郭芳承

Guan Pengfei和Li Junfang于2015年对空间形式中的星形闭曲面定义了一种新的平均曲率型流，报告将介绍该流的几何性质，并将该流与其它类型的平均曲率型流做简单比较。其次将详细介绍我们针对该流所做的一个进一步的结果，即旋转对称空间中星形闭曲面的平均曲率型流理论。

On fractional non-autonomous evolution equation of mixed type with nonlocal initial conditions

陈鹏玉西北师范大学

摘要：In this talk, we deals with the following nonlinear time fractional non- autonomous integro-differential evolution equation of mixed type with nonlocal initial conditions and measure of noncompactness

in infinite-dimensional Banach space, whereis the standard Caputo's fractional time derivative of order,is a family of closed linear operators defined on a dense domainin Banach spaceintosuch thatis independent of, is a constant,is a Caratheodory type function, is a nonlocal function to be specified later,andare Volterra and Fredholm integral operators, respectively. Combining the theory of fractional calculus and evolution families, the fixed point theorem with respect to convex-power

condensing operator and a new estimation technique of the measure of noncompact ness, we obtained the existence of mild solutions under the situation that the nonlinear term and nonlocal function satisfy some appropriate local growth conditions and a noncompactness measure condition. Our results generalize and improve some previous results on this topic, since the condition of uniformly continuity of the nonlinearity is not required, and also the strong restriction on the constants in the condition of noncompactness measure is completely deleted. As samples of applications, we consider a time fractional non-autonomous partial differential equation with homogeneous Dirichlet boundary condition and nonlocal initial condition.

Some new existence and uniqueness results of solutions to semilinear impulsive fractional integro-differential equations

周文学兰州交通大学

Abstract：We consider the existence and uniqueness of solutions for the boundary value problem of semilinear impulsive integro-differential equations of fractional order q∈(1, 2]. Our results are based on the Altman fixed point theorem and a standard fixed point theorem. Two examples are presented to illustrate the main results.

Tilting subcategories with respect to cotorsion triples in abelian categories

狄振兴西北师范大学

摘要：Given a non-negative integernand a complete hereditary cotorsion triple (X,Z,Y), the notion ofn-X-tilting subcategories in an abelian categoryAis introduced. It is proved that a virtually Gorenstein ringRisn-Gorenstein if and only if the subcategoryGIof Gorenstein injectiveR-modules isn-GP-tilting with respect to the cotorsion triple (GP，GP^⊥=^⊥GI，GI), whereGPstands for the subcategory of Gorenstein projectives. In case a subcategoryMofAis closed under direct summands such that each object inM^⊥admits a rightM-approximation, a Bazzoni's characterization is given forMto ben-X-tilting. Finally, an Auslander-Reiten correspondence is established between the class ofn-X-tilting subcategories and that of certain subcategories ofA, which areX-coresolving covariantly finite and closed under direct summands. This talk is based on a joint work with Jiaqun Wei, Xiaoxiang Zhang and Jianlong Chen.

Equitable vertex arboricity of graphs

Yuping Gao

School of Mathematics and Statistics, Lanzhou University

AbstractWu, Zhang and Li [Discrete Math, 313(2013): 2696-2701] conjectured that the vertex set of any simple graphGcan be equitably partitioned intomsubsets so that each subset induces a forest, whereΔ(G)is the maximum degree ofGandmis an integer withm>=⌈(Δ(G)+1）/2⌉. In this talk, we will list some results related to this conjecture.

On the degree sequence determined by the Laplacian spectrumof the corresponding graph

FeiWen

School ofMathematics and Physics, Lanzhou Jiaotong University

Abstract.LetG(ΔxΔ, . . . ,2x2 ,1x1 ) be the set of connected graph with degree sequence

(ΔxΔ, . . . ,2x2 ,1x1 ). In this talk,we show that the degree sequences ofG(3n3 ,2n2 ,1n1 ) andG(4n4 ,2n2 ,1n1 ) are determined by Laplacian spectrum with some restrictions. By those results we obtain thatsun graph,Cn◦2K1 andG(41,2n−3,12) are determined by their Laplacian spectra. Furthermore, we prove that any graphG∈G(Δ1,2n2 ,1n1 ) (Δ≥3), whose degree sequence is determined by Laplacian spectrum except thatGis a bicyclic graph withΔ=4. Moreover, ifGis a bicyclic graph withΔ=4, thenGmay beL-cospectral to a graph with degree sequence (33,2n2−3,1n1+1). Applying this result we conclude that some graphs such asstarlike trees,unicyclic

graph Un,p,friendship graphandbutterfly graphet al. are determined by their Laplacian spectra. Moreover, we first give a Laplacian spectral characterization of the degree sequence ofp-rose graph which supports Liu’s conjecture.

Two knight Pascal's triangles

冯积社陇东学院

摘要：In the combinatorics, the problem of the enumeration lattice paths is a hot research topic. We give two kinds of Pascal integer triangular, which is the number of knight walk paths, and give the explicit formulas to evaluate it.

关于Lebesgue-Nagell方程整数解的讨论

冉银霞 陇南师范高等专科学校

摘要：本文讨论了著名的Lebesgue-Nagell方程当的整数解。利用初等方法得到了如下结论：当x为偶数时，找到了方程的所有整数解，实际上，对n不是质数的情况利用文中的方法都可以给出它们的全部整数解；遗憾的是，当x为奇数时，只找到了方程有解的必要条件。但是值得庆幸的是，当p=7,11,13等这些较小数值时，文中的方法可以彻底解决这些方程的求解问题。

Analysis of a Special Predator-Prey Model with Two Delays, Herd Behavior and Prey Harvesting

孟新友兰州理工大学

摘要：In this paper, we propose a predator-prey system with square root functional response, two delays and prey harvesting, in which an equation is given to investigate the economic interest of the yield of the harvest effort. The local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the distribution of roots of the corresponding characteristic equation and taking two delays as bifurcation parameters. Further, some explicit formulas determining the properties of Hopf bifurcation are gained by applying the normal form method and center manifold theory. Finally, simulations are given to check the theoretical results.

Multiplicative noise and blur removal used some convex optimaization model

汪帆兰州大学

摘要：我们提出了一种新的凸优化模型对带模糊的乘性噪音图像进行图像恢复。其中主要的想法是将带模糊项的乘性噪音模型方程中的图像变量和噪音变量分开，修改后的目标方程中包含一个原噪音的逆的项，一个对观测图像、噪音和图像变量的数据拟合项以及一个TV的正则化项或者Framelet-based的正则化项。我们可以使用ADM算法对模型进行处理，数据实验表明我们的模型能够有效的，快速的应对带模糊的乘性噪音问题（Gamma噪音，Gaussian噪音，Rayleigh分布），实验结果优于现在已发表的其他方法。

Robust portfolio choice for a DC pension plan with stochastic income and interest rate

孙景云兰州城市学院数学学院

Abstract：This paper considers a robust portfolio choice problem for a defined contribution (DC) pension plan with stochastic income and stochastic interest rate. The investment objective of the pension plan is to maximize the expected utility of the wealth at the retirement time. We assume that the financial market consists of a stock, a zero-coupon bond and a risk-free asset. And the member of DC pension plan is ambiguity-averse, which means that the member is uncertain about the expected return rate of the bond and stock. Meanwhile, the member’s ambiguity-aversion level toward these two financial assets is quite different. The closed-form expressions of the robust optimal investment strategy and the corresponding value function are derived by adopting the stochastic dynamic programming approach. Furthermore, the sensitive analysis of model parameters on the optimal investment strategy are presented. We find that the member’s aversion on model ambiguity increases her hedging demand and has remarkable impact on the optimal investment strategy. Moreover, we demonstrate that ignoring model uncertainty will lead to significant utility loss for the ambiguity-averse member (AAM), and the model uncertainty about the stock dynamics implies greater effect on the outcome of the investment than the bond.

Eigenvalues of Discrete Sturm-Liouville Problems with Eigenparameter Dependent

Boundary Conditions

高承华西北师范大学

摘要：We Consider the discrete right definite Sturm-Liouville problems

where for, for i=1,2. We obtain the existence of the eigenvalues, the sign-changing times of the eigenfunctions and the interlacing results of the eigenvalues of the above problem, the Dirichlet problem and the Neumann problem.

Global Well-posedness for the GNSC equations with highly oscillating initial data

孙小春西北师范大学

摘要：We prove the global well-posedness for the generalized Navier-Stokes-Coriolis equations with small data in critical hybrid-Besov spaces. This result also holds for a class of highly oscillating initial data. This is a joint work with prof. Y. Ding.

分数阶时滞和T-S模糊复杂网络的同步

马维元西北民族大学

摘要：主要针对分数阶时滞复杂网络和分数阶T-S模糊复杂网络的同步问题进行了研究。首先考虑了带有时滞、非线性耦合、外部扰动分数阶复杂动力网络的外部牵制同步.建立了一般的分数阶时滞系统的渐近稳定性定理，提出了一组新的控制器，结合分数阶导数理论和矩阵不等式，实现了分数阶复杂网络所有节点的完全同步.在上述的框架下，耦合配置矩阵和内部耦合矩阵可以是对称的或非对称的，网络可以是时滞的或非时滞的，节点内部耦合可以是线性的或非线性的.数值仿真结果证实了该控制方法的有效性.其次，围绕着分数阶T-S模糊复杂网络的脉冲同步.建立了分数阶脉冲系统比较原理，可用于一般的分数阶脉冲问题解的大小比较.采用分数阶T-S模糊系统作为复杂网络动力系统，具有局部线性等优点. 基于比较原理和分数阶Gronwall-Bellman 不等式，得到了在脉冲控制作用下分数阶T-S 模糊复杂网络的同步标准. 最后，通过相应的数值例子来验证所提出标准的准确性和有效性.

复模糊线性系统

郭晓斌西北师范大学

摘要:对基于不同模糊数的复模糊线性系统Ax=b和复模糊矩阵XA=B基本理论和方法进行了研究，取得一些结果。内容前沿，方法创新，结果丰富和发展了模糊线性系统理论。

Choquet模糊积分分类器中模糊测度的学习

陈莉兰州城市学院数学学院

摘要：分类问题是模式识别系统的重要组成部分,也是机器学习的重要研究领域。在应用模糊积分进行融合时，一个关键性的问题就是如何确定模糊测度的值来更好的描述各个分类器自身在融合系统中具有的重要程度及分类器之间的交互作用，以提高分类器系统性能。模糊测度除了由领域专家给定，还有很多从已有数据中学习获得的方法。许多学者在这方面做了大量工作，提出了各种确定模糊测度的方法，主要有启发式方法，优化方法，随机搜索等。

本文结合离散集上Choque积分的计算法则,将模糊测度的确定、模糊数值函数的数值计算作为整体转化为一个优化模型，利用遗传算法从具体的数据信息中得到使问题最优的模糊测度，进而计算得到离散集上模糊数值函数的Choquet积分。并对如何从经典实值数据、区间值模糊数据、模糊数值数据中确定模糊测度,计算相应的Choquet积分,给出了算例和结果分析。

完全模糊线性系统解的扰动分析

刘坤陇东学院

摘要：借助特定的-水平截集和LR-模糊数的近似乘法，利用模糊集的分解定理和扩张原理将完全模糊线性系统转化成三个同阶分明线性系统，使用矩阵的谱范数估计不同扰动情形下分明线性系统的相对误差界，通过取最大值方法给出完全模糊线性系统的相对误差界，据此分析一个完全模糊线性系统解的稳定性。

实数序列的通项公式是初等函数

东洪平 陇南师范高等专科学校

摘要：在探讨数列的通项公式的过程中，提出了一个十分基础性的问题：任给一个实数序列，能否给出其通项公式？答案是肯定的。进一步提出了一个更有意思的问题：实数序列的通项公式是初等函数吗？非常遗憾的是，至今我们既举不出反例，也不能给出肯定的答复。但对于有穷实数序列可以用幂级数函数给出其通项公式，而对于无穷实数序列只能在某些特殊的情形才可以用幂级数函数给出其通项公式。