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Mathematical Theory and Applications 2018 Vol.38 Please wait a minute... For Selected: Download Citations EndNote Ris BibTeX Toggle Thumbnails Select Existence of Solutions to Class of p-Laplace Fractional Mathematical Theory and Applications    2018, 38 (1-2): 1-11.   Abstract （1279）      PDF（pc） （421KB）（177）       Knowledge map    In this paper we investigate the existence of solutions to a class of p-Laplace fractional impulsive ordinary differential system.By using the mountain pass theorem, we show that the system has at least one nontrivial solution if its nonlinear term possesses a super-p-growth rate. Related Articles | Metrics Select Finite Classical Group and Primitive Flag-transitive Symmetric(v,k,5)Designs Zhu Yan Mathematical Theory and Applications    2018, 38 (1-2): 12-23.   Abstract （1299）      PDF（pc） （450KB）（261）       Knowledge map    Let D=(P,B)be a symmetric(v,k,5)design with a flag-transitive point-primitive automor-phism group G. In this paper we show that if G is almost simple then the socle of G cannot be a finite classical group.  Related Articles | Metrics Select High Precision Quadrature Formulae for Singular Integrals with Cauchy Kernel Chen Chuanxi, Jin Guoxiang Mathematical Theory and Applications    2018, 38 (1-2): 24-32.   Abstract （1328）      PDF（pc） （733KB）（302）       Knowledge map    We establish a high accuracy Gauss-Kronrod quadrature formula for singular integrals with Cauchy kernel by using the separating singularity method. The new method for computing the coefficients and the remainder term of the formula are derived. Numerical experimental results with Matlab are consistent with our theoretical analysis. Related Articles | Metrics Select The Meromorphic Solution to Fermat Type Functional Equations Duan Jiangmei Mathematical Theory and Applications    2018, 38 (1-2): 33-37.   Abstract （1239）      PDF（pc） （205KB）（247）       Knowledge map    In this paper,the meromorphic solution to Fermat type functional equations is investigated.We prove that there do not exist non-constant meromorphic functions f(z),f(s)(z)and h(z)with order less than one that satisfy the functional equation f(z)7+f(s)(z)7+h(z)7 =1. Related Articles | Metrics Select Some New Lower Bounds for the Minimum Eigenvalue of M-matrices  Chen Fubin Mathematical Theory and Applications    2018, 38 (1-2): 38-47.   Abstract （1273）      PDF（pc） （358KB）（222）       Knowledge map    In this paper some new lower bounds for the minimum eigenvalue of M-matrix are given.Theoret-ical analysis and numerical example show that the new results improve the other existing results in some cases. Related Articles | Metrics Select Blow-up of Solutions to Multi-dimensional Wave Equations with Non-linear Mixed Terms Wang Husheng, Sun Haixia Mathematical Theory and Applications    2018, 38 (1-2): 48-53.   Abstract （1190）      PDF（pc） （242KB）（189）       Knowledge map    This paper studies the lifespan of the classical solution about wave equation with parameters. Based on the discussion of the parameters, we get an upper bound of the lifespan to the solution which improves the known results.  Related Articles | Metrics Select Passage Times to a Weighed Average-Exponential Jump Diffusion Model Yang Yunxia Mathematical Theory and Applications    2018, 38 (1-2): 54-64.   Abstract （1284）      PDF（pc） （405KB）（279）       Knowledge map    We employ a jump-diffusion model for asset prices whose assets jump sizes have a weighed average -exponential distribution.Under this model, to study the option pricing, we need to study the first passage time. In this paper the first passage time is derived, and the joint distribution of first passage time and the overshoot and the joint distribution of first passage time and return process are obtained by solving the equation with martingale method.  Related Articles | Metrics Select A Study on Pricing of Stock-linked Financial Products Based on Jump-diffusion Models Gao Mengyao , Zhao Dianli Mathematical Theory and Applications    2018, 38 (1-2): 65-75.   Abstract （1207）      PDF（pc） （392KB）（306）       Knowledge map    Based on the assumption that the stock price obeys jump-diffusion models, this paper studies the asset pricing problem of two stock-linked financial products. Firstly,the parameters of the jump-diffusion model are estimated based on outlier detection, and the parameters of the geometric Brownian motion model are estimated by the moment estimation method. Then, according to the results of parameter estimation, the capital preserving financial products and the threshold financial products are priced separately, and the impacts of jump on the price of two products are analyzed. For the capital preserving financial products and the thresh-old financial products,the numerical simulation indicates that the model with jump process is closer to the original stock price. And when the stock price obeys the jump-diffusion model, both two products’price are higher than that of the stock price obeying geometric Brownian motion, which shows that the significant events described by the jump process will affect the stock price and have a major impact on the price of financial products. Therefore, this paper has some practical significance to research the pricing of stock-linked financial  products with jump process. Related Articles | Metrics Select Auxiliary Function Method in Proof of Integral Inequality#br# #br# Liu Xinge, Tang Meilan Mathematical Theory and Applications    2018, 38 (1-2): 76-79.   Abstract （1301）      PDF（pc） （174KB）（338）       Knowledge map    Inequalities are widely used in mathematical research and practice.This paper analyses the problems of proving inequalities in the Undergraduate’s Mathematical Contest.Based on the method of constructing auxiliary functions and Cauchy’s mean value theorem,more general integral inequalities are established,which generalize the inequalities appearing in Undergraduate’s Mathematical Contest and the inequalities in the existing literature.  Related Articles | Metrics Select New Group Decision Making Method in Interval-triangular Fuzzy Setting Based on TOPSIS Li Min, Su Bianping , Zhang Qiangqiang Mathematical Theory and Applications    2018, 38 (1-2): 80-95.   Abstract （1267）      PDF（pc） （536KB）（307）       Knowledge map    In multiple attribute group decision making, because every expert has his own knowledge and expertise, different experts have different weights for different attributes. A new method to determine the Expert’s weights is put forward based on the TOPSIS method in interval-triangular fuzzy setting. If the evaluation value is close to the positive idea evaluation value and far away from the negative ideal evaluation value it will be given a large weight; Otherwise, the evaluation value will be given a small weight. Experience shows that the weight of experts determined by this method has a significant effect on solving practical decision-making problems. A new method of multiple attribute interval-valued intuitionistic fuzzy group decision making is presented in this paper, including the attribute weights are completely known, partly known and completely unknown. Finally, the feasibility and validity of this method are proved by our examples.  Related Articles | Metrics Select Fuzzy Portfolio Model Based on the Mean of Preference Possibility and Empirical Analysis Sun Kunjie Mathematical Theory and Applications    2018, 38 (1-2): 96-103.   Abstract （1185）      PDF（pc） （736KB）（211）       Knowledge map    In this paper, by means of objective fuzzy frequency statistics, the uncertain returns of securities investment are expressed by fuzzy numbers, and the fuzzy returns are clarified by the possibility mean of fuzzy numbers, and the semi-absolute deviation function is used to measure the risk of securities investment. Considering the constraint of securities turnover rate, a portfolio model based on preference possibility mean-semi-absolute deviation is constructed, and the empirical analysis of the model is carried out. Related Articles | Metrics Select The Long and Short Relationship between CPI and PPI under Cointegration Theory Shi Kai , Tan Xuemei Mathematical Theory and Applications    2018, 38 (1-2): 104-110.   Abstract （1314）      PDF（pc） （402KB）（408）       Knowledge map    The CPI and the PPI are important indexes of our country. In order to study the relationship between PPI and CPI, this paper analyzed the month data from January 2006to July 2017.First,this paper used seasonal adjustment to eliminate the influence of seasonal factors, then established the error correction model based on the cointegration test. The results show that there is a long-term equilibrium between CPI and PPI, and the short-term fluctuation of PPI would also have a significant effect on the CPI.  Related Articles | Metrics Select The Optimal Order Quantity for Two-Level Suppliers on the Fresh Products under Freshness function Zhou Xin , Zhang Huizhen Mathematical Theory and Applications    2018, 38 (1-2): 111-117.   Abstract （1295）      PDF（pc） （420KB）（207）       Knowledge map    With the development of cold-chain logistics technology, the market demands of fresh products are also growing. This paper introduces the freshness function and studies the decision-making has impact of demand uncertainty on a fresh product supply chain with two-tier suppliers ,in which the downstream supplier observes market demand information and sends an order to the upstream suppliers; while the upstream supplier provides fresh products. This paper finds that the downstream supplier has an optimal order quantity, which can maximize his expected profit. In addition, it is found that the higher the freshness, the greater the optimal order quantity. There is an optimal production time, which will maximize his expected profit. Finally, the correctness and rationality of the conclusions of this paper are verified by numerical examples. Related Articles | Metrics Select Analysis on Gray Relevance of Scientific and Technological Input and Economic Growth of Hainan Province Li Zhaoming, Kuang Qiaojuan, Huang Hao, Wang Haohua Mathematical Theory and Applications    2018, 38 (1-2): 118-128.   Abstract （1185）      PDF（pc） （623KB）（225）       Knowledge map    Considering the geometric similarity and relative change rate of sequences, this paper gives a way to improve the insufficiency on T’s correlation degree and calculate the absolute correlation degree and the relative correlation degree to obtain more accurate results. The calculated results and relevance analysis on Hainan province＇s R&D expenses by the improved T’s correlation degree show that Hainan province＇s R&D Planning has some drawbacks, such as funding imbalance and instability, slight and unreasonable planning, which would weaken the economic development by the investments of R&D. Some suggestions are given for reference at the end.  Related Articles | Metrics Select Clustering Analysis for the Delayed Flocking Model with Multi-topology Structures Huang Yao , Liu Yicheng Mathematical Theory and Applications    2018, 38 (3-4): 1-11.   Abstract （1314）      PDF（pc） （552KB）（301）       Knowledge map    Flocking behavior is a common phenomenon in nature. The research of flocking theory has been widely applied in economy, military and management. This paper studies the group behavior of two models with time delays under different topology structures, and obtains necessary and sufficient conditions. For the Cucker-Smale type model with directed graphs, we get the necessary and sufficient conditions of time delay .For another model with competitive relationship between individuals under bipartite graph, we also explore the influence of time delay on group behavior, and get the necessary and sufficient conditions. Finally, we verify the correctness of the conclusion by numerical simulation.  Related Articles | Metrics Select Strongly M-α-symmetric Rings and Their Extensions Geng Yanli, Geng Daohong Mathematical Theory and Applications    2018, 38 (3-4): 12-17.   Abstract （1270）      PDF（pc） （248KB）（223）       Knowledge map    Let M be a monoid andα an endomorphism of a ring R. We investigate the properties of M-symmetric rings with endomorphisms on R by introducing the concept of strongly M-α-symmetric ring. Using the classical method in ring theory, we prove that(1)R is a strongly right M-α-symmetric ring if and only if R is a strongly left M-α-symmetric ring;(2)Letαbe an automorphism of R. If R is a right Ore ring, hen R is a strongly M-α-symmetric ring if and only if Q is a strongly M-a-symmetric ring, where Q is the classical right quotient ring of the R. Related Articles | Metrics Select Improvement and Application of Shortest Path Algorithm Based on Point Cut Set Wu Man , Bai Mingli , Zeng Yongxin, Jiang Feng , Li Yebin Mathematical Theory and Applications    2018, 38 (3-4): 18-32.   Abstract （1355）      PDF（pc） （2595KB）（397）       Knowledge map    By introducing the concept of cut point and point cut set, which are the important part of graph theory, this paper combines the algorithm of finding cut point and point cut set with the classical Dijkstra algorithm to form an improved parallel algorithm. The application of the improved parallel algorithm is also given. It provides a theoretical basis for finding the shortest path of undirected graph, and improves the routing algorithm in the routing protocol OSPF, which reduces the time complexity of the algorithm. Related Articles | Metrics Select Existence of Traveling Wave Solutions for a Class of Cooperative Lotka-Volterra System Liu Hui , Hu Haijun Mathematical Theory and Applications    2018, 38 (3-4): 33-42.   Abstract （1285）      PDF（pc） （370KB）（356）       Knowledge map    Focusing on the effect of global climate change on species persistence,we consider a cooperative  Lotka-Volterra system with intrinsic growth rate,which depends on climate change.By constructing the appropriate upper and lower solutions,and combining the method of monotone iteration,we prove that when  two species are weakly cooperative,there exist a pair of monotone traveling wave solutions in the reaction-diffusion system.  Related Articles | Metrics Select General Solution to the Two Species Lotka—Volterra Equation with Constant Coefficients Zhu Shuyang, Zhu Yan Mathematical Theory and Applications    2018, 38 (3-4): 43-49.   Abstract （1515）      PDF（pc） （270KB）（383）       Knowledge map    The two species Lotka—Volterra equation has important applications. The analytical solution of the  equation can be obtained by using the integral method and the adjustment coefficient method. First ,a linear  transform is carried out and unknown parameters are embedded in the transform. Then the first equation is substituted into the second equation. The analytic solutions of the new equation is obtained by integrating method and parameter adjustment method. Finally, the general solution of the population of two species Lotka—Volterra equation is derived.  Related Articles | Metrics Select A New Preconditioning Technique for Hermitian Toeplitz Systems Liu Zhongyun, Xu Weijin, Chen Siheng, Zhang Yulin Mathematical Theory and Applications    2018, 38 (3-4): 50-58.   Abstract （1342）      PDF（pc） （341KB）（370）       Knowledge map    In this paper we give a preconditioned conjugate gradient method(PCG)to solve the Hermitian To-eplitz system Ax=b.Based on the fact that an Hermitian Toeplitz matrix Acan be reduced into a real Toeplitzmatrix plus a Hankel matrix(i.e.,UAU*=T+H)by a unitary similarity transformation(this unitary matrix  is U=(I-iJ)/ √2),we first reduce the system Ax=b to a real linear systems(T+H)[x1,x2]=[b1,b2]. Then we propose a new preconditioner for solving those two systems.In particular,our solver only involveseal arithmetics when the discrete sine transform(DST)and discrete cosine transform(DCT)are used.The  spectral properties of the preconditioned matrix are analyzed,and the computational complexity is discussed. Numerical experiments show that our preconditioner performs well for solving the Hermitian Toeplitz systems. Related Articles | Metrics Select On the Norms of r-circulant Matrices with Jacobsthal and Jacobsthal-Lucas Numbers Mathematical Theory and Applications    2018, 38 (3-4): 59-68.   Abstract （1369）      PDF（pc） （366KB）（280）       Knowledge map    In this paper we study the norms of r-circulant matricesA = Cr(J0,J1, …,Jn-1) and B =Cr(D0,D1,…,Dn-1)where Jnand Dnare Jacobsthal and Jacobsthal-Lucas numbers,and give some boundsfor the spectral norms of Kronecker and Hadamard products ofthe r-matrices Aand B.  Related Articles | Metrics Select A Kind of Generalized Inverse Eigen-pairs Problem for Fixed-Free Mass-Spring System Huang Xiantong Mathematical Theory and Applications    2018, 38 (3-4): 69-84.   Abstract （1187）      PDF（pc） （589KB）（205）       Knowledge map    This paper discusses the problem for constructing a kind of fixed-free mass-spring system by solving a kind of generalized inverse eigen-pairs problem. The conditions of solvability and the expression of solution are derived. The numerical algorithms and some numerical examples are given. Related Articles | Metrics Select The Perturbed BFGS Method for the Unconstrained Optimization with the Armijo Line Search Yan Jiaojiao Mathematical Theory and Applications    2018, 38 (3-4): 85-92.   Abstract （1247）      PDF（pc） （310KB）（239）       Knowledge map    A perturbed BFGS method was proposed in[3]to solve the unconstrained optimization and was proved to be globally convergent when the Wolfe line search is used.In this paper,we show that the perturbed BFGS method also possesses global convergence for nonconvex problems with the relatively weaker Armijo line search.Numerical results show that this method with the Armijo search is also promising.  Related Articles | Metrics Select A New Perturbed BFGS Method for Unconstrained Optimization Problems Chen Fei Mathematical Theory and Applications    2018, 38 (3-4): 93-100.   Abstract （1178）      PDF（pc） （299KB）（225）       Knowledge map     Based on the idea of constrained optimization and the BFGS method in unconstrained optimization,this paper presents a new perturbed BFGS method for the unconstrained optimization.We prove that the proposed method has global convergence for nonconvex optimization problems.Numerical results show that this method is efficient.  Related Articles | Metrics Select Combined Forecasting of Improved Multidimensional Grey Model and Support Vector Machine Liang Zhixun, Yuan Quan, Zeng Xiangyan Mathematical Theory and Applications    2018, 38 (3-4): 101-110.   Abstract （1263）      PDF（pc） （562KB）（350）       Knowledge map    Support vector machine improves the generalization ability through the principle of structural risk  minimization.It is mostly used to solve the classification problem and regression problem of small samples.However,when used for prediction,a single model has certain limitations.In this paper,an improved multi-dimensional gray model and a support vector machine combined forecasting model are proposed.The combined forecasting model realizes the complementary advantages of different models,and can avoid the limitations of  the single model,increase the stability of the model.The experimental simulation results show that the proposed combined forecast.The prediction effect of the model is significantly better than the support vector machine and the innovation-based prioritization method,the prediction accuracy of the combined prediction  model is higher than that of the single prediction model.  Related Articles | Metrics Select A Note on the Harmonic Mean Limit Theorem of Stochastic Transition Probability of Finite Nonhomogeneous Markov Chains Li Shilin, Yang Weiguo Mathematical Theory and Applications    2018, 38 (3-4): 111-113.   Abstract （1267）      PDF（pc） （151KB）（256）       Knowledge map    This note points out that the result about the harmonic mean limit of stochastic transition probability of finite non-homogeneous Markov chain is a corollary of the strong limit theorem for any random adaptive  sequence.  Related Articles | Metrics Select The Evaluation Model of Football Striker Athletes in Higher Vocational Colleges Based on Analytic Hierarchy Process Duan Zhenhua, Hu Peiyong , Dai Liutong Mathematical Theory and Applications    2018, 38 (3-4): 114-122.   Abstract （1195）      PDF（pc） （620KB）（478）       Knowledge map    The evaluation model of selecting football striker athletes in higher vocational colleges is established  by using document literature,expert consultation and other methods to screen out the evaluation indicators of  excellent striker athletes by combining the specific data under the indicators of football striker athletes.Analytic Hierarchy Process(AHP)is also used to evaluate athletes comprehensively so that the selection of football athletes is more scientific and operable.  Related Articles | Metrics Select A Theorem Related to Matrix Exponential Function and Its Teaching Method Zheng Yan Mathematical Theory and Applications    2018, 38 (3-4): 123-128.   Abstract （1364）      PDF（pc） （226KB）（506）       Knowledge map    This paper introduces a very useful theorem for calculating matrix exponential function,and discusses its introduction and treatment in teaching.  Related Articles | Metrics