Table of Content

15 February 2017, Volume 34 Issue 1    Next Issue

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Direct Product Design for Mixture Models with Heteroscedastic Errors and its Optimalities YAN Fei, ZHANG Chong-qi 2017, 34 (1):  1-12.  doi: 10.3969/j.issn.1005-3085.2017.01.001 Abstract ( 112 )   PDF (176KB) ( 221 )   Save Mixture experimental designs have been widely used in industrial and agricultural production, scientific experiment and daily life. The traditional mixture experimental designs are generally implemented under the assumption that the experimental errors are homosce-dastic, but heteroscedastic errors are relatively more accordant with practical circumstances. In this paper, we mainly study the $D$-, $A$- and linear optimality of direct product designs for mixture product models under the assumption of heteroscedastic errors. It is shown that the $D$-, $A$- or linear optimal designs for mixture product models can be constructed from the corresponding optimal designs for their homogeneous sub-mixture models under given conditions. Related Articles | Metrics

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Study of Transfers System for Femtosecond Pulse Laser to Nano Metal Film FENG Yi-hu, SHI Lan-fang, MO Jia-qi 2017, 34 (1):  13-20.  doi: 10.3969/j.issn.1005-3085.2017.01.002 Abstract ( 167 )   PDF (548KB) ( 359 )   Save The solution to a class of nonlinear disturbed transfers system for the femtosecond pulse laser to Nano metal film is obtained by using the asymptotic method. The asymptotic behaviors of corresponding solution to this nonlinear system are discussed. Firstly, the outer solution to the reduced problem is solved. Next, a functional is constructed and its generalized variational is calculated, with its variational equivalent to zero. Thus the Lagrange multiplicator is found. Then, a generalized varitational iteration expansion is constructed by using the varitational principle. Therefore, arbitrary times of iteration expansions for the corresponding system can be solved successively. At the same time, the uniform convergence to the related expansion is accounted by using the variational theory of functional analytic. An example is enumerated, and by using the simulation method, the graphs of surface for its solution are given. From the results obtained in this study, it is validated that the solving method for nonlinear disturbed transfers system to Nano metal film can be provided in a simple and valid manner by using the generalized variational iteration. And it also has a general theoretical value and a wide application potential. Related Articles | Metrics

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Portfolio Model Based on Hybrid Quantum Particle Swarm Optimization with Empirical Research GAO Yue-lin, YU Ya-ping 2017, 34 (1):  21-30.  doi: 10.3969/j.issn.1005-3085.2017.01.003 Abstract ( 76 )   PDF (569KB) ( 483 )   Save In this paper, the portfolio model with the constraints of a number of assets and the proportion of investment is established on the basis of the Markowitz mean-variance model. For solving the model and the simulated actual investment, a quantum particle swarm hybrid algorithm is constructed by differential evolution and chaotic search. Numerical experiments show that the proposed algorithm is effective, and that the proposed hybrid algorithm performs better than other improved particle swarm optimization algorithm, differential evolution algorithm, genetic algorithm, simulated annealing algorithm and tabu search algorithm. Besides, the empirical results show that the proposed algorithm is a good solution to the portfolio model, and the simulation results show that the proposed model is effective. Related Articles | Metrics

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A Type of Complex Non-linear Difference Equation with Exponential Coefficients ZHOU Yan-ping, ZHENG Xiu-min 2017, 34 (1):  31-37.  doi: 10.3969/j.issn.1005-3085.2017.01.004 Abstract ( 92 )   PDF (145KB) ( 278 )   Save It is well known that the non-linear equations of Malmquist type are more general than the Painlev\'{e} equations and the Riccati equations in the field of complex differential equations and complex difference equations. In this paper, by using the difference analogues of Nevanlinna theory and the differential field theory, we investigate one type of complex difference equation of Malmquist type with exponential coefficients. We prove that for any transcendental meromorphic solution to the above complex difference equation of Malmquist type, if it is of finite order and has few zeros and poles, its growth should be of the same rate as that of the exponential function ${\rm e}^z$. The obtained result generalizes and complements the complex differential Malmquist Theorem and the complex difference Malmquist Theorem. Related Articles | Metrics

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Some Limit Theorems for Pairwise NQD Random Sequences SONG Ming-zhu, WU Yong-feng 2017, 34 (1):  38-46.  doi: 10.3969/j.issn.1005-3085.2017.01.005 Abstract ( 135 )   PDF (142KB) ( 223 )   Save In this paper, we study the complete convergence properties and strong laws of large numbers for pairwise NQD random sequences. We present the definition of pairwise NQD random sequences and the Kolmogorov inequality to the case of pairwise NQD random sequences. Based on the Kolmogorov inequality, we obtain complete convergence properties of pairwise NQD random sequences. We construct two non-increasing functions based on the properties of non-increasing function, and obtain some strong laws of large number for pairwise NQD random sequences, which is similar to independent random variable sequences. The theorem obtained in this paper thus inclines to extend the related results presented in previous literatures. Related Articles | Metrics

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An Enumeration Result in the Alignment Space LU Guo-xiang 2017, 34 (1):  47-58.  doi: 10.3969/j.issn.1005-3085.2017.01.006 Abstract ( 90 )   PDF (163KB) ( 174 )   Save Alignment space is a metric space which is generated by the generalized error. The sequence structure analysis among the space plays a more and more important role in practice. In this paper, the structures of the sequences between which the Alignment distance is 2 in Alignment space ${F_2}^*$ are studied. Alignment distance distribution is also proposed. And the analytic expression for the sequences pairs between which the length is $n$ and the Alignment distance is 2 is obtained. Related Articles | Metrics

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$(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-Fuzzy Subinclines CHEN Liu-hong, LIAO Zu-hua, TONG Juan, LU Teng, LI Yong, ZHAO Yan-cai 2017, 34 (1):  59-72.  doi: 10.3969/j.issn.1005-3085.2017.01.007 Abstract ( 72 )   PDF (194KB) ( 313 )   Save Incline algebra plays an important role in the field of automaton theory, logic of binary relations, medical diagnosis and Markov chains, etc.. In this paper, we firstly introduce the concept of $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subinclines and discuss its equivalent characterizations. Then we prove an important property that the union of $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subinclines is also an $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subincline. We also obtain the properties of homomorphic image and homomorphic preimage based on the anti-extension principle. Besides, after introducing the concept of anti-direct product of fuzzy sets, we prove the anti-direct product of $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subinclines is still an $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subincline. Finally, we introduce the new concepts of Noetherian subinclines and Artinian subinclines and discuss the relationships between Noetherian subinclines, Artinian subinclines and $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subinclines. Related Articles | Metrics

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On Bicriteria Scheduling of Due Date Assignment and Weighted Number of Tardy Jobs LIN Hao, HE Cheng 2017, 34 (1):  73-86.  doi: 10.3969/j.issn.1005-3085.2017.01.008 Abstract ( 148 )   PDF (127KB) ( 177 )   Save The due date assignment in the scheduling problems is concerned with the benefit balance between the assignment cost and the performance criterion. This arises the bicriteria scheduling problems of due date assignment. In single machine bicriteria scheduling of due date assignment with weighted number of tardy jobs, only the linear combination version has been studied in the literature. This paper further studies more models, namely, the constraint version and the Pareto optimization version. The main contribution of this study is the related results on the NP-hardness, polynomially solvable cases, and the polynomial time approximation scheme. By using the proposed manner, the features of a multicriteria optimization problem can be effectively characterized. Related Articles | Metrics

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Generalized Eigenvalue Problems and Computation of Angles between Two Linear Manifolds ZHANG Sheng-gui 2017, 34 (1):  87-99.  doi: 10.3969/j.issn.1005-3085.2017.01.009 Abstract ( 152 )   PDF (122KB) ( 212 )   Save The angle between two nontrivial linear manifolds in the high dimensional Euclidean space can be characterized as a quadratic programming with quadratic equation constraints (QP-QEC). The computing of such angles has many important applications in statistics and data analysis, such as the canonical correlation analysis and the kernel correlation analysis between two multivariate random vectors. This paper explores the relationship between a more general QP-QEC and its corresponding generalized eigenvalue problem in terms of the KKT conditions. On this basis, we design an algorithm for computing such an angle by means of the solution method of the generalized eigenvalue problem. Related Articles | Metrics

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On Periodic Boundary Problem for $p$-Laplacian Fractional Differential Equations ZHOU Hui, ZHOU Zong-fu, WANG Li-ping 2017, 34 (1):  100-110.  doi: 10.3969/j.issn.1005-3085.2017.01.010 Abstract ( 87 )   PDF (122KB) ( 440 )   Save In this paper, by using the coincidence degree theory, the existence of solutions for the $p$-Laplacian fractional differential equations with periodic boundary conditions is studied. The result obtained in this paper extends some known results. Related Articles | Metrics