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Table of Content

      
    20 August 2017
    Volume 52 Issue 8
    Representation of Choquet integral of the set-valued functions with respect to fuzzy measures and the characteristic of its primitive
    GONG Zeng-tai, KOU Xu-yang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  1-9.  doi:10.6040/j.issn.1671-9352.0.2016.450
    Abstract ( 424 )   PDF (780KB) ( 324 )   Save
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    The analytic properties of the Choquet integral of set-valued functions with respect to fuzzy measures are discussed, such as the characteristics of the primitive, representation of integral, differentiability of the primitive, and so on. Firstly, based on the previous results, the calculation of Choquet integral of set-valued function is investigated, and a representation theorem of Choquet integral for set-valued function is obtained as a Radon-Nikodym property in some sense. In addition, the characteristics of the primitive of the Choquet integral for set valued functions are given. Finally, the definition of the Choquet integral of set-valued functions with respect to fuzzy measures is improved, and the concepts of the above functions and below function of the set-valued functions are proposed, which achieved the domination of the Choquet integral of set-valued functions with respect to fuzzy measures.
    Approximation of lagrange interpolation polynomials based on the fourth Chebyshev nodes
    ZHANG Yan-yan, YAN Chao
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  10-16.  doi:10.6040/j.issn.1671-9352.0.2016.315
    Abstract ( 403 )   PDF (588KB) ( 231 )   Save
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    This paper first provides the exact approximation errors for an analytic function class under the maximum norm based on the Lagrange interpolation polynomials with the fourth Chebyshev nodes in the worst setting. As for the norm of Lp(p>1), the corresponding strong asymptotic order for that kind of analytic function class is obtained.
    Existence and stability for multiple gabor frames
    SONG Liang, FENG Jin-shun, CHENG Zheng-xing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  17-24.  doi:10.6040/j.issn.1671-9352.0.2016.189
    Abstract ( 356 )   PDF (678KB) ( 206 )   Save
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    Since redundant frames are play very important role in signal processing and image processing, existence and perturbation for multiple Gabor frames are studied in this paper. The sufficient condition for the existence of multiple Gabor frames is proposed. It is shown that a function which is the generator of Gabor frames is also a generator of Gabor frames after it is perturbed. According to the frame stability criterion, we prove that a class of irregular Gabor frames are stable frames as well.
    Expanded mixed finite element method for compressible miscible displacement in heterogeneous porous media
    YU Jin-biao, REN Yong-qiang, CAO Wei-dong, LU Tong-chao, CHENG Ai-jie, DAI tao
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  25-34.  doi:10.6040/j.issn.1671-9352.0.2017.040
    Abstract ( 395 )   PDF (630KB) ( 224 )   Save
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    We consider the numerical methods for the mathematical model describing the transport and diffusion process of porous media flow. There are two kinds of fluids, one is displaced by another, which are compressible and miscible. The media is supposed to be heterogeneous, so the permeability is of full tensor form. For the pressure equation, an expanded mixed finite element method is introduced to solve the variables of pressure, gradient, and velocity. For the concentration equation, a Galerkin finite element formulation is constructed to solve the variable of concentration. This approach aims at obtaining more reliable numerical solutions for porous media flow with heterogenous permeability. By means of theoretical analysis, optimal error estimates in L2-norm for pressure and in H1-norm for concentration are derived.
    Convergence analysis for inverse problems in a degenerate parabolic equation
    ZHANG Tai-nian, LI Zhao-xing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  35-42.  doi:10.6040/j.issn.1671-9352.0.2017.005
    Abstract ( 337 )   PDF (598KB) ( 196 )   Save
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    This paper consider an inverse problem of reconstructing the principal coefficient in a second order degenerate parabolic equation of non-divergence form by using some additional observation data. It is transformed into an optimal control problem. The major problem is that the principal coefficient is unknown, but the degenerate degree of equation is determined, in general, by the principal coefficient. By introducing some weighted Sobolev spaces and some new source conditions, and adding a strong regularity condition to the admissible function set of the principal term, we prove the convergence of the optimal solution.
    Some research about Wigner-Yanase-Dyson skew information
    WANG Li-li, CHEN Zheng-li
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  43-47.  doi:10.6040/j.issn.1671-9352.0.2017.036
    Abstract ( 306 )   PDF (674KB) ( 203 )   Save
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    Based on the study of some properties of the Wigner-Yanase-Dyson skew information and the Wigner-Yanase correlation, the Wigner-Yanase-Dyson skew information is given for different quantum channels. Finally, the concavity with the Wigner-Yanase-Dyson skew information is proven.
    Characterizations of n-fold positive implicative filter in residuated lattice
    LIU Li-jun
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  48-52.  doi:10.6040/j.issn.1671-9352.0.2016.491
    Abstract ( 345 )   PDF (643KB) ( 147 )   Save
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    The concept of n-fold implicative filter and n-fold positive implicative filter are introduced in residuated lattice. By studying their properties, a series of characterization theorems are given. On this basis, the sufficient and necessary condition that non-empty subsets of residuated lattice become n-fold(positive)implicative filter are proposed. And the relation between n-fold implicative filter and n-fold positive implicative filter is discussed. The results of the study further extend the filter theory of the residuated lattice. It is important theoretical foundation for the application of algebraic logic and computer information processing.
    Parametric estimations for renewal-geometric process
    LIANG Xiao-lin, GUO Min, LI Jing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  53-57.  doi:10.6040/j.issn.1671-9352.0.2016.576
    Abstract ( 302 )   PDF (1193KB) ( 206 )   Save
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    According to the definition and the properties of renewal-geometric process, we get the parametric estimation of renewal-geometric process by Change-points detection via cross-validation and the improved least-squares method. Some simulation experiments are performed, and the simulation results show that the proposed method is effective.
    A graded hard thresholding pursuit algorithm
    SHI Zhang-lei, LI Wei-guo
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  58-64.  doi:10.6040/j.issn.1671-9352.0.2016.474
    Abstract ( 313 )   PDF (3381KB) ( 215 )   Save
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    Inspired by hard thresholding pursuit algorithm(HTP). A graded hard thresholding pursuit algorithm(APGHTP)was proposed for solving compressive sensing problems. The theoretical guarantees of the new algorithm were given under restricted isometry property(RIP)condition.In the numerical experiment, regardless of whether the measured value contains error, APGHTP performance is better, which proves the sparse recovery ability of the algorithm.When recovering sparse vectors, the number of iterations required for APGHTP is the same as that of sparse vectors.
    A class of minimal inequalities for demimartingales
    FENG De-cheng, ZHANG Xiao, ZHOU Lin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  65-69.  doi:10.6040/j.issn.1671-9352.0.2016.532
    Abstract ( 313 )   PDF (576KB) ( 192 )   Save
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    In the background of the demimartingale sequence {Sn, n≥1}, a class of minimal inequalities for the sequence {cnSn, n≥1} and {cng(Sn), n≥1} are given in this paper. These results generalize the corresponding results in recent papers.
    On the mean value of a hybrid arithmetic function
    LI Ting-ting, LAO Hui-xue
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  70-74.  doi:10.6040/j.issn.1671-9352.0.2016.505
    Abstract ( 325 )   PDF (567KB) ( 208 )   Save
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    Let λf(n) be the Fourier coefficients of cusp forms of the normalized Hecke operator Tn, σ(n) be the sum-of-divisors function, and φ(n) be the Eulers function. The average order estimation of hybrid arithmetic functions of the form λf(n)σb(n)φc(n) is investigated by using analytic methods, and the upper bound estimate ∑n≤xλf(n)σb(n)φc(n)≪xb+c+1/2+ε,for any ε>0 is obtained.
    Relative torsionless modules
    XU Hui, ZHAO Zhi-bing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  75-80.  doi:10.6040/j.issn.1671-9352.0.2016.458
    Abstract ( 364 )   PDF (1428KB) ( 186 )   Save
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    Some elementary properties of relative torsionless modules with respect to a faithful and balanced bimodule are studied. Some equivalent conditions for a left or right Noether ring is a QF-ring is gotten. It is proved that a finitely generated module is an ω-torsionless module if and only if it is an ω-1-syzygy module if and only if it is an ω-1-torsionfree module when ω is a generalized tilting bimodule. Moreover, the extension closure of the class of ω-torsionless modules is investigated, and some classical results are generalized to the relative case.
    Characterizations of rings relative to an ideal
    WANG Yong-duo, HE Jian
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  81-84.  doi:10.6040/j.issn.1671-9352.0.2016.432
    Abstract ( 342 )   PDF (625KB) ( 244 )   Save
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    Let I be an ideal of a ring R. The concept of pseudo semiprojective I-covers is introduced. It is shown that every left R-module has a pseudo semiprojective I-cover if and only if every left R-module has a proj-ective I-cover. It is also proved that the class of all pseudo semiprojective modules is a projectivity class, and then some well known results are generalized.
    Homological dimensions with respect to semidualizing modules and excellent extensions
    CHEN Xiu-li, CHEN Jian-long
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  85-89.  doi:10.6040/j.issn.1671-9352.0.2016.386
    Abstract ( 428 )   PDF (745KB) ( 230 )   Save
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    Let C be a semidualizing R-module with R being a commutative ring. It is investigated the transfer properties of C-homological dimensions under(almost)excellent extensions, and it is discussed that the precovering and preenveloping properties of the C-projectives, C-injectives, and C-flats. As applications, it is proved that if S≥R is an excellent extension, then R is Noetherian if and only if S is Noetherian, and R is coherent if and only if S is coherent.
    Prehomomorphisms and restricted products of regular semigroups with a multiplicative inverse transversal
    WANG Shou-feng
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  90-93.  doi:10.6040/j.issn.1671-9352.0.2016.507
    Abstract ( 278 )   PDF (588KB) ( 186 )   Save
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    Prehomomorphisms and restricted products of regular semigroups with a multiplicative inverse transversal are introduced. It is proved that the class of regular semigroups with a multiplicative inverse transversal together with prehomomorphisms form a category, by using restricted products some characterizations of prehomomorphisms between two regular semigroups with a multiplicative inverse transversal are obtained.
    Neighbor sum distinguishing index of a kind of sparse graphs
    PAN Wen-hua, XU Chang-qing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  94-99.  doi:10.6040/j.issn.1671-9352.0.2016.326
    Abstract ( 290 )   PDF (901KB) ( 168 )   Save
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    Let φ be a proper k-edge coloring of G. For each vertex v∈V(G), set fφ(v)=∑uv∈E(G)φ(uv). φ is called a k-neighbor sum distinguishing edge coloring of G if fφ(u)≠fφ(v) for each edge uv∈E(G). The smallest k such that G has a k-neighbor sum distinguishing edge coloring is called the neighbor sum distinguishing index, denoted by χ'Σ(G). The neighbor sum distinguishing index of a kind of sparse graphs is determined. It is proved that if G is a graph without isolated edges, Δ≥6 and mad(G)≤5/2, then χ'Σ(G)=Δ if and only if G has no adjacent vertices of maximum degree.
    Total coloring of planar graphs with maximum degree seven
    WANG Xiao-li, WANG Hui-juan, LIU Bin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  100-106.  doi:10.6040/j.issn.1671-9352.0.2016.363
    Abstract ( 303 )   PDF (1002KB) ( 231 )   Save
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    Let G be a planar graph with maximum degree Δ≥7. It is proved that if chordal 5-cycles of G are not adjacent to chordal 6-cycles, then its total chromatic number is Δ+1 by the discharging method.
    The fundamental theorem forAMHH in Yetter-Drinfeld module categories
    CHEN Hua-xi, XU Qing-bing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(8):  107-110.  doi:10.6040/j.issn.1671-9352.0.2016.582
    Abstract ( 356 )   PDF (562KB) ( 354 )   Save
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    The definitions of weak Hopf algebra and weak comodule algebras in Yetter-Drinfeld module categories are introduced, and the fundamental theorem forAMHH in Yetter-Drinfeld module categories is obtained.