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Table of Content

      
    20 September 2019
    Volume 54 Issue 9
     
    Fuzzing sample optimization method for software vulnerability detection
    Jing ZHANG,Cheng CHEN,Huan-ke ZHENG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  1-8, 35.  doi:10.6040/j.issn.1671-9352.0.2019.205
    Abstract ( 336 )   HTML ( 6 )   PDF (681KB) ( 160 )   Save
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    Software vulnerability detection Fuzzy testing techniques are commonly used in information physical fusion systems.But there are a large number of redundant test samples in Fuzzing technology, and the sample detection anomaly is less effective. Therefore, this paper proposes a Fuzzing sample optimization method for software vulnerability detection. Firstly, the samples that are not accepted by the software in the random sample are filtered out, and the improved dynamic programming algorithm is used to calculate the sample reduced set, and the number of initial samples is reduced. Then track the stain propagation path during the test, use the improved algorithm of Simhash and Hamming distance to solve the similarity of the sample propagation path, and further reduce the sample redundancy by deleting the samples with higher similarity. Finally, the genetic variation of the sample that triggers the abnormality is constructed. New test samples will increase the validity of the sample. It can be seen from the experimental results that compared with the method based on greedy algorithm and based on abnormal distribution orientation, the proposed method effectively reduces the test sample redundancy and improves the validity of the test sample.

    Quantitative characteristics and applications of P-information hidden mining
    Xiu-mei HAO,Ning-ning LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  9-14.  doi:10.6040/j.issn.1671-9352.0.2019.189
    Abstract ( 243 )   HTML ( 4 )   PDF (410KB) ( 113 )   Save
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    The classical set has static characteristics. With the rapid development of science and technology, massive data updates very quickly. Therefore using the classical set to study data mining problems has been limited. It is necessary to involve dynamic characteristics into ordinary set and replace "static" by "dynamic". Thus P-set has the above characteristics. By using P-set and its attribute migration, the granularity and mining degree of internal and external k-order P-information are proposed; also the quantitative relationship between attribute migration and information mining is discussed. The migration information chain theorem and the minimum and maximum mining degree theorem are given. P-information is a new theory and method for dynamic information system knowledge mining. Finally, the application of P-information in data mining is given.

    The relationship between abnormal information system and inverse P-augmented matrices
    Ling ZHANG,Xue-fang REN
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  15-21.  doi:10.6040/j.issn.1671-9352.0.2018.382
    Abstract ( 243 )   HTML ( 3 )   PDF (410KB) ( 110 )   Save
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    Inverse P-sets are models with dynamic characteristics, inverse P-augmented matrices are the new mathematical concepts obtained by using inverse P-sets to improve general augmented matrix. For convenience of discussion, the general augmented matrix A is defined as system's normal state, internal inverse P-augmented matrix AF and outer inverse P-augmented matrix AF are all defined as system's abnormal states, then the concept of matrix content, its measurement and its correlation theorems are proposed. Based on the above concepts, the relation theorem between system's abnormal state and internal inverse P-augmented matrix, the relation theorem between system's abnormal state and outer inverse P-augmented matrix, and the matrix content recognition criterion of system's abnormal state are given. Finally, an application and its experimental verification are shown.

    Intelligent fusion of information and reasoning generation of its P-augmented matrix
    Feng-sheng XU,Xiu-qing YU,Li-hua ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  22-28.  doi:10.6040/j.issn.1671-9352.0.2018.579
    Abstract ( 275 )   HTML ( 3 )   PDF (400KB) ( 100 )   Save
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    Packet sets is a dynamic mathematics model, which introduces dynamic characteristics into common set X and improve it. Packet augmented matrix is obtained by common augmented matrix using packet sets. Based on the dynamic characteristics of Packet sets and structure of packet augmented matrix, the paper provides the reasoning generation of its P-augmented matrix, intelligent fusion of information and the relationship between intelligent fusion of information and packet augmented matrix. Furthermore, the separation of information intelligent fusion and its attribute intelligent characteristics are given. At the end, an application to the above theory results is shown.

    Lattice of bipolar fuzzy ideals in negative non-involutive residuated lattices
    LIU Chun-hui, ZHANG Hai-yan, LI Yu-mao
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  29-35.  doi:10.6040/j.issn.1671-9352.0.2019.131
    Abstract ( 267 )   PDF (423KB) ( 99 )   Save
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    In this paper, the problem of bipolar fuzzy ideals is further studied in negative non-involutive residuated lattices. The definition of bipolar fuzzy ideal which is generated by a bipolar fuzzy set is given and its two representation theorems are established. It is proved that the set BFI(L)which containing of all bipolar fuzzy ideals in a negative non-involutive residuated lattice L, under the partial order, forms a complete Heyting algebra. This work further expands the way for revealing the structural characteristics of negative non-involutive residuated lattices.
    Distributivity of fuzzy implications over additively generated overlap and grouping functions
    ZHANG Ting-hai, QIN Feng
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  36-42.  doi:10.6040/j.issn.1671-9352.0.2018.560
    Abstract ( 266 )   PDF (411KB) ( 60 )   Save
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    Among the researches of the fuzzy system, the distributivity between fuzzy implications and some special aggregation functions(e.g. t-norms, t-conorms, uninorms, t-operators, semi-uninorms and semi-t-operators)has been studied by many authors. Overlap functions and grouping functions have been followed with interest for their applications in image processing, classification problems and decision making based on fuzzy preference relations. In this paper, we give necessary and sufficient conditions for two distributivity equations I(O(x,y),z)=G(I(x,z),I(y,z)) and I(x,G1(y,z))=G2(I(x,y),I(x,z)), where O is an additively generated overlap function, G1 and G2 are additively generated grouping functions and I is a binary function satisfying boundary conditions.
    Information measures of interval valued Pythagorean fuzzy sets and their applications
    SUN Qian-qian, LI Xiao-nan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  43-53.  doi:10.6040/j.issn.1671-9352.0.2019.038
    Abstract ( 345 )   PDF (507KB) ( 116 )   Save
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    Entropy, distance and similarity are important information measurement tools in fuzzy sets and their generalization theories. The information metrics research based on interval valued Pythagorean fuzzy sets mostly involves the distance formula of interval valued Pythagorean fuzzy numbers, and rarely involves metrics of ambiguity and similarity. In view of this situation, firstly, the axiomatization definition of entropy, distance and similarity of interval valued Pythagorean fuzzy sets is first proposed. Then study the relationship between entropy, distance and similarity. Finally, the entropy and similarity of the interval valued Pythagorean fuzzy set are applied to the field of pattern recognition. Comparative analysis shows the flexibility and effectiveness of the proposed measures.
    Qualitative analysis of a diffusive predator-prey model with density dependence
    LI Hai-xia
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  54-61.  doi:10.6040/j.issn.1671-9352.0.2018.667
    Abstract ( 295 )   PDF (1828KB) ( 182 )   Save
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    The uniqueness of coexistence solutions and asymptotic behavior for a diffusive predator-prey model with density dependence are studied. The sufficient conditions of the existence of coexistence solutions are given by means of the fixed point index theory. Then, by making use of the perturbation theory for linear operators, we discuss the stability and uniqueness of coexistence solutions. Finally, the conditions of the extinction and permanence for the system by the comparison principle for parabolic equations, and the theoretical results of asymptotic behavior for the system are verified by some numerical simulations. The results show that the two species can coexist and the system has a unique coexistence solution under certain conditions.
    Analysis of a stochastic single population system with age-dependent and diffusion in a polluted environment
    HU Yong-liang, LUO Zhi-xue, LIANG Li-yu, FENG Yu-xing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  62-68.  doi:10.6040/j.issn.1671-9352.0.2019.124
    Abstract ( 323 )   PDF (419KB) ( 127 )   Save
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    A new stochastic single population system with age-dependent and diffusion in a polluted environment is formulated and investigated. The existence and uniqueness of the solution of this stochastic system is obtained via It(^overo)s formula in Hilbert space. The general stochastic biological population model with age structure and diffusion is extended by adding toxicant to the population.
    Optimal control of a size-structured system with two species in periodic environments
    LIANG Li-yu, LUO Zhi-xue
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  69-75.  doi:10.6040/j.issn.1671-9352.0.2018.721
    Abstract ( 291 )   PDF (391KB) ( 200 )   Save
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    The optimal control of a prey-predator population system with size-structure in periodic environments is studied. First of all, the existence of the optimal solution of optimal control is proved by applying Mazur theorem in functional analysis. Then, the adjoint system is derived and the necessary conditions for optimal control are obtained by means of tangent and normal cones in nonlinear analysis.
    Research of an epidemic model on adaptive networks
    CHEN Lu, ZHANG Xiao-guang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  76-82.  doi:10.6040/j.issn.1671-9352.0.2018.729
    Abstract ( 310 )   PDF (448KB) ( 98 )   Save
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    By using the triple approximation formula under multinomial distributions, the SIS moment closure infectious disease model in the adaptive network is closed, the effects of adaptive behavior on the spread of infectious diseases under multinomial distributions is studied. Through the theory of qualitative and stability, the basic reproduction number R0 of the model is obtained and the stability of the equilibrium points are analyzed. Adaptive behavior of rewiring has multiple effects on infectious disease transmission are obtained: When the relative infection rate is small enough, the model has a standard forward bifurcation and when R0<1, the disease tends to be extinct; on the contrary, mathematically, it is rigorously proved that the rewiring can lead to the occurrence of complex dynamic behaviors such as the backward bifurcation and saddle-node bifurcation, ect. Therefore R0<1 is not enough to control the spread of infectious diseases.
    Reconstruction of unknown surface heat flux from an internal temperature history
    REN Jian-long
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  83-90.  doi:10.6040/j.issn.1671-9352.0.2019.010
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    An inverse heat conduction problem is discussed by using the temperature observed at a certain point in the interior of the heater to recover the surface heat flux of heater wall. The forward problem is solved with the method of variable separation, then the original problem is transformed into Volterra integral equation of the second kind and the uniqueness of the solution of integral equation is proved. Numerical simulation is conducted with the direct solving method. The numerical results are carried out to confirm the feasible and effective of the aforementioned method,and the heat flux is recovered very well.
    Hidden attractor with two memristors and Hamilton energy control
    MU Na-na, AN Xin-lei, XU Hao-nan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  91-97.  doi:10.6040/j.issn.1671-9352.0.2018.708
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    Based on the Kirchhoffs law, a nonlinear chaotic circuit model is designed by including a flux-controlled memristor and a charge-controlled memristor. The hidden attractor is found through analyzing characteristics of the equilibrium points. And then, simulation and comparison studies of bifurcation diagram and phase trajectory and Poincaré map of parameter are carried out by simulation software. The Hamiltonian energy function of the memristor system is calculated according to Helmholtz theorem, and the relationships between the current and the energy are discussed. Based on this, the new Hamilton energy control method is proposed to control the memristor system to the desired states by choosing different control parameter.
    Cyclic controlled quantum teleportation by using a ten-qubit entangled state as the channel
    PENG Jia-yin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  98-104.  doi:10.6040/j.issn.1671-9352.0.2019.093
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    The paper proposes a protocol of cyclic controlled teleportation for three unknown two-qubit states by using a ten-qubit maximally entangled state as the quantum channel. In this protocol, Alice can teleport her two-qubit state of qubits a and a' to Bob, Bob can transfer his two-qubit state of qubits b and b' to Charlie, and Charlie can also transmit his two-qubit state of qubits c and c' to Alice. It is shown that only if the senders Alice, Bob, Charlie and the controller David collaborate with each other, the cyclic controlled quantum teleportation can be realized successfully.
    Social network user identity linkage model based on comprehensive information
    YANG Ya-ru, WANG Yong-qing, ZHANG Zhi-bin, LIU Yue, CHENG Xue-qi
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  105-113.  doi:10.6040/j.issn.1671-9352.1.2018.115
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    With the increasing popularity of social media sites, users prefer to join multiple online social networks, how to associate multiple user identities in a social network as a new job in social media is of great significance. This paper studies a representative user identity linkage model and proposes a user identity linkage model based on comprehensive information(BiALP). The model learns the internal structure information, attribute information and content information of the network through the node expression method. It is characterized by the node representation of the source network and the target network, and is based on the associated user pairs. With tagged data, the relationship between the source network and the target network is learned through a binary supervised learning manner. A large number of experiments have shown that the BiALP model has a significant improvement(35%)compared to other representative user identity linkage models.
    Construction of the cubic λμ-α-DP curve with two kinds of shape parameters
    ZHANG Di, ZHA Dong-dong, LIU Hua-yong
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(9):  114-126.  doi:10.6040/j.issn.1671-9352.0.2019.005
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    This paper constructs a type of cubic λμ-α-DP basic function with two kinds of shape parameters. It can effectively global or locally modify its shape. The properties of the cubic λμ-α-DP basis function and curve are analyzed. Moreover, the effect and modification ability of the basis function and the curve with different parameter values are illustrated through graphics. Smooth continuous conditions of the curve are deduced: they can meet with G2 continuous when certain conditions are met. G1 continuous rotating surfaces are also given. Furthermore, using the singular blending technique, the singular blending cubic λμ-α-DP interpolation curve with shape parameters is constructed. The properties of the curve and the influences of the curve with multiple parameters are presented. By changing the blending parameters, the approximation degree between the singular blending interpolation curve and its control polygon can be adjusted, thus enhancing the shape-control capability of the cubic λμ-α-DP interpolation curves.