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2018, Vol. 38 No. 1-2   Published date: 30 June 2018
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• Existence of Solutions to Class of p-Laplace Fractional

  2018, 38(1-2): 1-11. doi:

  Abstract ( 1279 )   PDF (421KB) ( 177 )   　　

  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.

• Finite Classical Group and Primitive Flag-transitive Symmetric(v,k,5)Designs

  Zhu Yan

  2018, 38(1-2): 12-23. doi:

  Abstract ( 1299 )   PDF (450KB) ( 261 )   　　

  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. 

• High Precision Quadrature Formulae for Singular Integrals with Cauchy Kernel

  Chen Chuanxi, Jin Guoxiang

  2018, 38(1-2): 24-32. doi:

  Abstract ( 1328 )   PDF (733KB) ( 302 )   　　

  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.
  

  
  

• The Meromorphic Solution to Fermat Type Functional Equations

  Duan Jiangmei

  2018, 38(1-2): 33-37. doi:

  Abstract ( 1239 )   PDF (205KB) ( 247 )   　　

  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.

• Some New Lower Bounds for the Minimum Eigenvalue of M-matrices 

  Chen Fubin

  2018, 38(1-2): 38-47. doi:

  Abstract ( 1273 )   PDF (358KB) ( 222 )   　　

  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.

• Blow-up of Solutions to Multi-dimensional Wave Equations with Non-linear Mixed Terms

  Wang Husheng, Sun Haixia

  2018, 38(1-2): 48-53. doi:

  Abstract ( 1190 )   PDF (242KB) ( 189 )   　　

  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. 

• Passage Times to a Weighed Average-Exponential Jump Diffusion Model

  Yang Yunxia

  2018, 38(1-2): 54-64. doi:

  Abstract ( 1284 )   PDF (405KB) ( 279 )   　　

  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. 

• A Study on Pricing of Stock-linked Financial Products Based on Jump-diffusion Models

  Gao Mengyao , Zhao Dianli

  2018, 38(1-2): 65-75. doi:

  Abstract ( 1207 )   PDF (392KB) ( 306 )   　　

  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.
  

  
  

• Auxiliary Function Method in Proof of Integral Inequality#br#

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  Liu Xinge, Tang Meilan

  2018, 38(1-2): 76-79. doi:

  Abstract ( 1301 )   PDF (174KB) ( 338 )   　　

  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. 

• New Group Decision Making Method in Interval-triangular Fuzzy Setting Based on TOPSIS

  Li Min, Su Bianping , Zhang Qiangqiang

  2018, 38(1-2): 80-95. doi:

  Abstract ( 1267 )   PDF (536KB) ( 307 )   　　

  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. 

• Fuzzy Portfolio Model Based on the Mean of Preference Possibility and Empirical Analysis

  Sun Kunjie

  2018, 38(1-2): 96-103. doi:

  Abstract ( 1185 )   PDF (736KB) ( 211 )   　　

  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.

• The Long and Short Relationship between CPI and PPI under Cointegration Theory

  Shi Kai , Tan Xuemei

  2018, 38(1-2): 104-110. doi:

  Abstract ( 1314 )   PDF (402KB) ( 408 )   　　

  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. 

• The Optimal Order Quantity for Two-Level Suppliers on the Fresh Products under Freshness function

  Zhou Xin , Zhang Huizhen

  2018, 38(1-2): 111-117. doi:

  Abstract ( 1295 )   PDF (420KB) ( 207 )   　　

  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.

• Analysis on Gray Relevance of Scientific and Technological Input and Economic Growth of Hainan Province

  Li Zhaoming, Kuang Qiaojuan, Huang Hao, Wang Haohua

  2018, 38(1-2): 118-128. doi:

  Abstract ( 1185 )   PDF (623KB) ( 225 )   　　

  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.