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15 August 2016, Volume 33 Issue 4 Previous Issue    Next Issue

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A Study on Impact of Introducing of CSI300F to CSI300 Stock from Statistical and Fractal Characteristics ZHENG Feng, ZHAO Wen-yao 2016, 33 (4):  331-338.  doi: 10.3969/j.issn.1005-3085.2016.04.001 Abstract ( 39 )   PDF (238KB) ( 10 )   Save Due to the dramatic fluctuation of China's stock market, CSI300F has been strictly limited. The study of CSI300 futures and spot market has become one of the main issues which are most concerned in the financial markets. In this paper, we study the impact of the introduction of CSI300F to CSI300 from the perspectives of statistical and multi-fractal characteristics. The statistical analysis shows that, the distribution of the CSI300 return series becomes less asymmetric, and the heavy tail phenomenon is more obvious after the introduction of CSI300F, which shows the introduction of CSI300F decreases the return volatility of CSI300. Through the analysis of MF-DFA (multi-fractal detrending fluctuation analysis), we find that the characteristics of the general hurst index and the multi-fractal spectrum both show the complexity of the market has decreased, which reveals that the CSI300 market becomes more efficient. The analysis of MF-DXA (multi-fractal detrended cross-correlation analysis) method shows that the fractal degree of the correlation between the two markets has increased, clarifying that the volatility of CSI300 market has increased. Therefore, the introduction of the CSI300F makes the spot market become more efficient, and the restrictions on trading CSI300F make both CSI300F and CSI300 market less efficient. Related Articles | Metrics

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Mean First-passage Time of a Piecewise Nonlinear Model Driven by Multiplicative Non-Gaussian Noise and Additive White Noise GUO Yong-feng, SHEN Ya-jun 2016, 33 (4):  339-348.  doi: 10.3969/j.issn.1005-3085.2016.04.002 Abstract ( 28 )   PDF (576KB) ( 9 )   Save The noise-induced escape problem in stochastic systems has appeared in many fields. In most of the existing theoretical studies on this topic, the mean first-passage time (MFPT) is introduced to quantify the characteristic quantity of escape process. It has been applied to many problems, such as the switching time problem of electronic devices and the life of bistable devices problem. In this paper, we study the MFPT in a piecewise nonlinear model driven by correlated noises for the cases of multiplicative non-Gaussian noise and an additive Gaussian white noise. By using the path integral method, the unified colored noise approximation and the steepest-descent approximation method, the expression of the MFPT is derived. Numerical computation results show that, under the effect of non-Gaussian noise deviating from the Gaussian distribution, correlation time of the non-Gaussian noise and cross-correlation strength, increasing the intensity of non-Gaussian noise leads to the appearance of a one-peak structure in the MFPT. However, the MFPT of the system decreases with the increase of the additive white noise intensity. This shows that MFPT corresponding to the non-Gaussian noise and Gaussian white noise exhibits very different behavior. In addition, we also discuss the effect of the degree of non-Gaussian noise deviating from the Gaussian distribution, correlation time of the non-Gaussian noise and cross-correlation strength on MFPT. Related Articles | Metrics

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Solving Multiple Problems of Hyperbolic Diffusion with Dissipative Terms Based on Multiple Integral Finite Volume Method ZHANG Li-jian, LUO Yue-sheng, GAO Yang 2016, 33 (4):  349-368.  doi: 10.3969/j.issn.1005-3085.2016.04.003 Abstract ( 41 )   PDF (439KB) ( 14 )   Save Hyperbolic diffusion equation is a class of important partial differential equation in mathematics, and has been widely used in many engineering fields. It is usually used to describe the propagation of acoustic waves and currently in potential field, and also used to simulate the models of convection diffusion and heat conduction in computational fluid dynamics. In this paper, we propose a multiple integral finite volume method to solve the multiple problems of hyperbolic diffusion with dissipative terms. It is difficult to improve accuracy for solving this problem with classical finite volume method. Therefore, we propose a new finite volume format based on the variable limit integral, which improves the capability of traditional methods. We use the Fourier analysis method to analyze the stability of the discrete format, and provide the priori estimation as well as convergence. Finally, numerical experiments confirm the correctness of the proposed theoretical results. Related Articles | Metrics

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Departure Process of $M/G/1$ Queueing System under Min$(N,D)$-policy WEI Ying-yuan, TANG Ying-hui, GU Jian-xiong, YU Miao-miao 2016, 33 (4):  369-381.  doi: 10.3969/j.issn.1005-3085.2016.04.004 Abstract ( 31 )   PDF (197KB) ( 10 )   Save This paper considers the departure process of the $M/G/1$ queue with Min$(N,D)$-policy. Using the total probability decomposition technique and the renewal process theory, we discuss the expected number of departures occurring in finite time interval from an arbitrary initial state. Both the transient expression and the steady state expression of the expected departure number are obtained. The important relation among departure process, server state process and renewal process of service during server busy period is discovered. The relation displays the stochastic decomposition characteristic of the departure process, i.e., the expected departure number is decomposed into two parts: one is the server busy probability, and the other is the expected departure number during server busy period, which simplifies the discussion on the departure process. Furthermore, the approximate expansion for convenient calculation of the expected departure number is obtained. Finally, we derive the corresponding results for some special cases. Since the departure process also often corresponds to an arrival process in downstream queues in queueing network, it is expected that the results obtained in this paper would provide useful information for queueing network. Related Articles | Metrics

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Inexact Newton-MCG Algorithm for Reflexive Solution of Nonlinear Algebraic Equations LIANG Zhi-yan, ZHANG Kai-yuan, NING Qian-zhi 2016, 33 (4):  382-390.  doi: 10.3969/j.issn.1005-3085.2016.04.005 Abstract ( 30 )   PDF (162KB) ( 10 )   Save Nonlinear algebraic equations have wide applications in scientific computation and engineering application. In this paper, the inexact Newton-MCG algorithm for computing the reflexive solution of the nonlinear algebraic equation is proposed. The algorithm is constructed based on the Newton method for calculating the reflexive solution of the nonlinear algebraic equations and the modified conjugate gradient method for the approximate reflexive solution or the approximate reflexive least-square solution of the linear algebraic equation derived from each Newton step. Moreover, the proposed algorithm only requires the nonlinear algebraic equation to have the reflexive solution and the solution may not be unique, owing to the wide scope of applications and the finite-step convergent property of the MCG method. Finally, some numerical experiments illustrate the efficiency of the new algorithm. Related Articles | Metrics

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Fuzzy $LI$-ideals in Bounded Heyting Algebras LIU Chun-hui 2016, 33 (4):  391-401.  doi: 10.3969/j.issn.1005-3085.2016.04.006 Abstract ( 27 )   PDF (167KB) ( 6 )   Save Ideals is one of the important tools for studying the structure characteristics of logical algebras. In this paper, by using methods and principles of algebra and fuzzy sets, we introduce the notion of fuzzy $LI$-ideals and investigate their properties in bounded Heyting algebras. Relation between fuzzy $LI$-ideals and fuzzy lattice ideals is also discussed. Representation theorem of fuzzy $LI$-ideal generated by a fuzzy set is provided. Furthermore, we prove that the set consisting of all fuzzy $LI$-ideals in a given bounded Heyting algebra, under fuzzy set-inclusion order, forms a complete Heyting algebra. Related Articles | Metrics

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Oscillation Criteria for Second-order Neutral Dynamic Equations with Mixed Nonlinearities on Time Scales HUANG Xian-yong, YANG Qi-gui, CAO Jun-fei 2016, 33 (4):  402-418.  doi: 10.3969/j.issn.1005-3085.2016.04.007 Abstract ( 31 )   PDF (160KB) ( 7 )   Save The oscillation of neutral dynamic equations on time scales has important implications in both theory and application. This paper considers the oscillation of a class of second-order neutral dynamic equations with mixed nonlinearities. Firstly, the neutral coefficient function $\pi(t)$ is defined. By means of the generalized Riccati transformation technique and the averaging technique, we establish some new oscillation criteria for the second-order neutral dynamic equations under the case $\pi(t_{0})=\infty$. Then, when $\pi(t_{0})<\infty$, by strengthening the assumptions and using some inequalities and some analytic techniques, we also obtain several oscillation criteria for the equations. Our work generalizes and improves some known results in the literature for oscillation of second-order neutral dynamic equations. Finally, two examples are presented to illustrate the importance of our results. Related Articles | Metrics

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The Singularly Perturbed Problems for Nonlinear Nonlocal Disturbed Evolution Equations with Two Parameters FENG Yi-hu, WU Qin-kuan, XU Yong-hong, MO Jia-qi 2016, 33 (4):  419-427.  doi: 10.3969/j.issn.1005-3085.2016.04.008 Abstract ( 23 )   PDF (123KB) ( 7 )   Save The nonlinear nonlocal singularly perturbed problems for the disturbed evolution equations are studied. Using the singular perturbation method, the structure of solution to the problem is discussed in the cases of two small parameters. Under the suitable conditions, firstly, the outer solution to the boundary value problem is given. Secondly, the variables of multiple scales are introduced to obtain the boundary layer corrective terms for the solution. Then the stretched variable is applied to the boundary neighborhood to get the initial layer correction term. Finally, using the fix point theorem, the uniformly valid asymptotic expansion of the solution to the problem is proved. The proposed method possesses the advantages of convenient use and high accuracy. Related Articles | Metrics

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The Fractional Super Broer-Kaup-Kupershmidt Hierarchy and its Nonlinear Integrable Couplings WEI Han-yu, LUO Lin, XIA Tie-cheng 2016, 33 (4):  428-440.  doi: 10.3969/j.issn.1005-3085.2016.04.009 Abstract ( 19 )   PDF (136KB) ( 5 )   Save Based on the fractional supertrace identity on superalgebras, we derive the fractional super Broer-Kaup-Kupershmidt hierarchy and its super Hamiltonian structures. Then, we present a nonlinear super integrable Hamiltonian couplings for the fractional super Broer-Kaup-Kupershmidt hierarchy. The proposed method can be generalized to other fractional super hierarchies. Related Articles | Metrics