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15 February 2018, Volume 35 Issue 1    Next Issue

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A Game between Two Insurance Companies with Jump-diffusion Risk Model KONG Xiang-yu, RONG Xi-min 2018, 35 (1):  1-15.  doi: 10.3969/j.issn.1005-3085.2018.01.001 Abstract ( 209 )   PDF (1058KB) ( 264 )   Save In this paper, we combine a jump-diffusion model and the game theory, considering a non-zero reinsurance game between two insurance companies under a jump-diffusion model. We assume that there are one risk-free assets (such as bonds) and one kind of risky assets (such as stock) available for insurance companies to invest. At the same time, this paper considers the optimal reinsurance problem with proportional reinsurance which is assumed to be calculated via the expected premium principle. We establish the Hamilton-Jacobi-Bellman equations under the goal of maximizing the utility of the difference between the two insurance companies' terminal surplus, which is modeled by jump-diffusion risk process. We also prove the existence of Nash equilibrium between the two companies by applying the method of game theory and the stochastic dynamic programming principle, and give a Nash equilibrium strategy. In some special cases, the influences of economic variables on our optimal strategies are demonstrated and some economic explanations are given accordingly. Related Articles | Metrics

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The GI/Geo/1 Queue with Threshold and Multiple Working Vacations MA Shuang-feng, XU Xiu-li, JING Xin, SONG Xiao-feng 2018, 35 (1):  16-24.  doi: 10.3969/j.issn.1005-3085.2018.01.002 Abstract ( 167 )   PDF (231KB) ( 224 )   Save In a random service system, people focus on decreasing system's cost and improving service rates. Based on the above purpose, this paper introduces the threshold and vacation interruption strategies into a discrete time GI/Geo/1 working vacation queue. Firstly, the two-dimensional embedded Markov chain before customers arrival instant is established, its transition probability matrix of GI/M/1-type is obtained. Secondly, the stationary queue length distribution is derived by the matrix analysis method, and the expected queue length and mean sojourn time are expressed. Finally, numerical analysis for the performance indices of the system are presented using the Matlab software, which shows that the expected queue length and sojourn time are both increasing with the increase of a threshold but decreasing with the increase of working vacation rates. It is expected that the results obtained here would provide some useful information for the research of SVC systems and wireless networks. Related Articles | Metrics

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A Note on the Impact of the Convex Combination Factor of a Convex Combination Projection Algorithm YAN Xi-hong, WANG Chuan-long 2018, 35 (1):  25-32.  doi: 10.3969/j.issn.1005-3085.2018.01.003 Abstract ( 195 )   PDF (174KB) ( 230 )   Save Many algorithms have been developed to solve optimization models which have wide-spread real-world applications. Among them, the gradient projection method for solving convex programs is one of the most noteworthy methodologies and has received much attention. In this paper, we consider a convex combination projection algorithm for solving convex programs. In the process of the convex combination projection algorithm, the new iterative point is updated based on the convex combination of the previous point and the point generated by the gradient projection method. Furthermore, we numerically analyze the efficiency and effectiveness of the convex combination projection algorithm and the impact of the convex combination factor on the algorithm. The numerical results show that the convex combination projection algorithm performs more stably than the gradient projection method and outperforms the gradient projection method when an appropriate convex combination factor is given. Related Articles | Metrics

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Comparative Test of Two Groups for Concentration-time Curves ZHAO Li-ping, XIA Zhi-ming 2018, 35 (1):  33-44.  doi: 10.3969/j.issn.1005-3085.2018.01.004 Abstract ( 268 )   PDF (217KB) ( 341 )   Save Aiming at two groups of samples from different populations in the pharmacokinetics, we developed a comparative test of two groups. Firstly, we provided the likelihood function when the null hypothesis and the alternative hypothesis are given. Then the likelihood ratio statistic is constructed, and we proved that the limit distribution of the statistic is $\chi^{2}(3)$ when null hypothesis is true. Lastly the numerical simulation is conducted to confirm the truth of the theory through data verification. The results show that for the two groups with the same parameters, the empirical distribution and the limit distribution fitting well when the sample size is large.  On the contrary, the more differences  parameters with the smaller values of the $p$-value, and the evidence to refuse the null hypothesis will be more sufficient. Related Articles | Metrics

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The Problem of Stability of Fractional Degenerate Differential System with Delay ZHANG Zhi-xin, ZHANG Yu-feng, JIANG Wei 2018, 35 (1):  45-54.  doi: 10.3969/j.issn.1005-3085.2018.01.005 Abstract ( 232 )   PDF (160KB) ( 474 )   Save The stability of a fractional degenerate differential system with delay is considered. Firstly, according to the Laplace transform method for the Caputo fractional derivatives, the stability conditions for the degenerate differential system with multiple-delays under different Caputo derivatives are derived and the corresponding criterions are given in different cases. Secondly, by using the roots of the characteristic equation, the all-delays stability of fractional degenerate differential systems are analyzed and some sufficient conditions are obtained. Some results generalize the corresponding results of the fractional differential system. Finally, some examples are presented to illustrate the validity of theorems. Related Articles | Metrics

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Multi-symplectic Euler-box Scheme for a High-order Wave Equation of KdV Type WANG Jun-jie, LI Sheng-ping 2018, 35 (1):  55-68.  doi: 10.3969/j.issn.1005-3085.2018.01.006 Abstract ( 180 )   PDF (251KB) ( 310 )   Save The high order KdV equation, an important nonlinear wave equation, has a broad application prospect. In the paper, a multi-symplectic Euler-box scheme is presented for the high order KdV equation. First, we give the multi-symplectic structure of the high-order KdV equation by canonical transformation, and obtain an associated multi-symplectic conservation law, the local energy and momentum conservation laws. Then, we apply the Euler-box scheme to obtain a discrete scheme of the high order KdV equation, and study the scheme based on a Hamilton-space system. Moreover, we prove that the scheme preserves a dispersed multi-symplectic conservation law, and give the backward error analysis of the scheme. Finally, the numerical experiments of the solitary wave are given, and results show that the numerical scheme is an efficient method with excellent long-time numerical behaviors. Related Articles | Metrics

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The $b$-continuity of Some Special Corona Graphs LV Chuang, WANG Ke-lun, ZHANG Ruo-dong, PAN Shu-xia 2018, 35 (1):  69-78.  doi: 10.3969/j.issn.1005-3085.2018.01.007 Abstract ( 148 )   PDF (148KB) ( 288 )   Save The $b$-coloring of a graph $G$ is a proper vertex coloring, in which every two color classes exists at least one edge. The $b$-chromatic number of a graph $G$ is the largest integer $k$ such that $G$ admits a $b$-coloring with $k$ colors. A graph $G$ is said to be $b$-continuity if and only if for every integer $k$, $\chi(G) \leq k \leq b(G)$, there exists a $b$-coloring with $k$ colors. In this paper, the $b$-continuity of some special Corona graphs is proved by designing the specific coloring scheme according to the structural properties of Corona graphs. Related Articles | Metrics

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Research of Numerical Methods for Solving Fractional-order Telegraph Equations Based on Chebyshev Polynomials NIU Bian-ling, LI Deng-ao, ZHAO Fu-qiang, XIE Jia-quan 2018, 35 (1):  79-87.  doi: 10.3969/j.issn.1005-3085.2018.01.008 Abstract ( 179 )   PDF (267KB) ( 281 )   Save Fractional-order telegraph equation is regarded as one of most important equations in communication engineering, which is hard to obtain the analytical solution, so it is crucial to study the numerical methods. In order to obtain the numerical solutions of fractional-order telegraph equations, this study derives the corresponding differential operational matrix through Chebyshev polynomials. Furthermore, the nonlinear telegraph equation is transformed into the system of algebra equations with known coefficients. Then, the numerical solutions can be obtained by solving the system. Lastly, the numerical example is proposed to verify the feasibility and effectiveness. Related Articles | Metrics

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Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations LUO Shuang-hua, WANG Song, ZHANG Cheng-yi, LIU Qing-bing 2018, 35 (1):  88-100.  doi: 10.3969/j.issn.1005-3085.2018.01.009 Abstract ( 125 )   PDF (152KB) ( 320 )   Save The local polynomial smoother (LPS) method is proposed in this paper to derive the numerical solution of the Bagley-Torvik fractional-order differential equations. Firstly, the local polynomial smoother method is well constructed and its main thinking is emphasized. Then this method is employed to solve the Bagley-Torvik FDEs. Finally, some numerical comparison experiments with some other methods are made to demonstrate that the LPS method proposed is more efficient and more accurate than Legendre operational matrix method and pseudo-spectral method. Related Articles | Metrics

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The Generalized Shock Layer Solution to Singular Perturbation Equation FENG Yi-hu, MO Jia-qi 2018, 35 (1):  101-109.  doi: 10.3969/j.issn.1005-3085.2018.01.010 Abstract ( 154 )   PDF (115KB) ( 458 )   Save A class of generalized singular perturbation initial boundary value problem for the reaction diffusion equation is studied. Firstly, the outer solution to original problem is obtained. Next, the initial layer and interior shock layer corrective terms for the generalized asymptotic solutions to original problem are constructed by using the theory of generalized functions. Finally, used the fixed point theorem of functional analytic, the uniformly validity of the generalized asymptotic solution is proved. In this paper, the shock wave asymptotic solution possess simple, valid and higher accuracy peculiarity. Related Articles | Metrics

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Limiting Behavior of the Bisexual Galton-Watson  Branching Process with Immigration and Population-size-dependent Mating in Random Environments SONG Ming-zhu, XIANG Ya-yun 2018, 35 (1):  110-122.  doi: 10.3969/j.issn.1005-3085.2018.01.011 Abstract ( 160 )   PDF (125KB) ( 216 )   Save Firstly, this paper introduces the development of bisexual Galton-Watson branching process. On the basis of past achievements, a model with population size dependent mating and immigration (BIPSDM) is established in random environments, that is more conform to the fact about bisexual biological reproduction. Then, applying some classical results on superadditive functions, the limit of mean growth rate per mating unit is obtained. Through discussing extinct probability of BIPSDM, a necessary and sufficient condition for BIPSDM to become extinct with probability one was found under certain conditions. Some properties known are enlarged in this article. Related Articles | Metrics