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    25 January 2009, Volume 2009 Issue 1 Previous Issue    Next Issue
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    Article
    Properties of a new class of transformation graphs (Chinese)
    LIU Rui-fang;SHU Jin-long
    2009, 2009 (1):  1-6. 
    Abstract ( 3010 )   PDF (252KB) ( 1518 )   Save

    This paper defined a new class of transformation graphs by
    introducing symbol“0”, and for a simple nonempty undirected graph
    $G$, investigated the connectedness and regularity of ten new
    transformation graphs of $G$. When $G$ is a regular graph, the
    spectra of transformation graphs of $G$ were determined in terms of
    the spectrum of $G$.

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    Crossing number of simultaneous embedding of two planar graphs with restriction (Chinsese)
    LU Jun-jie;REN Han
    2009, 2009 (1):  7-12. 
    Abstract ( 3352 )   PDF (329KB) ( 1512 )   Save
    Consider a red planar graph and a green planar graph
    simutaneously $2$-cell embedded on a surface. With some restriction,
    a red edge can cross a green edge. This paper studied the minimum
    number of these red-green crosses by using technique of integer
    programming, and some results are obtained.
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    On dissection of unicyclic graphs(English)
    WANG Xiao;DUAN Fang
    2009, 2009 (1):  13-21. 
    Abstract ( 3386 )   PDF (201KB) ( 1608 )   Save
    By the principle of mathematical induction and classified
    discussion, the sharp bounds for dissection of unicyclic graphs of a
    fixed order were given. Among all unicyclic graphs of order
    $n(n\geqslant 6)$, the graph $\Delta_{n-3}$ has the minimum $a(G)$
    and $b(G)$, and the graph $K_{1,n-1}^{+}$ has maximum $a(G)$ and
    $b(G)$, where $\Delta_{n-3}$ denotes the graph obtained from $K_{3}$
    and $P_{n-3}$ by joining a vertex of $K_{3}$ to one endvertex of
    $P_{n-3}$, and $K_{1,n-1}^{+}$ denotes the graph obtained from
    $K_{1,n-1}$ by joining its two vertices of degree one.
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    Algorithm of optimal constructing unit-norm tight frame (Chinese)
    XIN You-ming;CHENG Zun-shui;XING Jian-min
    2009, 2009 (1):  22-27. 
    Abstract ( 3305 )   PDF (227KB) ( 1574 )   Save
    Let $\{f_i\}_{i=1}^{M}$ be unit-norm vectors in $\CN$.
    This paper introduces an algorithm to construct a unit-norm tight
    frame by adding minimum vectors $\{g_i\}_{i=1}^{K}$ to
    $\{f_i\}_{i=1}^{M}$.
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    Perturbations about eigenspaces (Chinese)
    CHEN Jian-xin;
    2009, 2009 (1):  28-31. 
    Abstract ( 3209 )   PDF (202KB) ( 1551 )   Save
    By using the method of matrix equation equivalent
    transformation, combined the properties of $2$-norm and $F$-norm and
    their relationship with eigenvalue, this paper dealt with the upper
    bound for perturbation of diagonalized non-singular matrix
    eigenspaces. Upper bound was obtained for matrix
    eigenspace $\|{\rm sin}\Theta\|_{F}$ conditioned by $\eta_{2}=\|{\bm A}^{-\frac{1}{2}}{\bm E}{\bm A}^{-\frac{1}{2}}\|_{2}<1$.
    The final theorem is the extension of theorem $4. 1$ in $[2]$.
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    Existence theorem of positive solution to a nonlinear Sturm-Liouville problem (Chinese)
    YAO Qing-liu
    2009, 2009 (1):  32-36. 
    Abstract ( 3502 )   PDF (214KB) ( 1426 )   Save

    The existence of positive solution was studied for the
    nonlinear Sturm-Liouville boundary value problem, where the
    nonlinear term $f(t,u)$ may be singular at $t = 0,\,t = 1$. By
    introducing the integrations of height functions of nonlinear term
    on bounded set the growths of nonlinear term were described. By
    applying the Krasnoselskii fixed point theorem in degree theory and
    the dominated convergence theorems in real variable, an existence
    theorem of positive solution was proved when there are limit
    functions $\mathop {\lim }\limits_{u \to + 0} f(t,u) / u$ and
    $\mathop {\lim }\limits_{u \to + \infty } f(t,u) / u$.

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    Spike-like solutions of nonlinear singularly perturbed equations (Chinese)
    ZHU Zhen-bo;LIN Wu-zhong;
    2009, 2009 (1):  37-42. 
    Abstract ( 3651 )   PDF (228KB) ( 1526 )   Save
    The existence of spike-like solutions of a class of
    Sturm-Liouville singularly perturbed problem was investigated and
    its sufficient condition was given. Meanwhile, the uniformly valid
    asymptotic solutions were constructed by the method of boundary
    layer functions and remainder estimation was presented. Finally, an
    example was given to illustrate the obtained results.
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    Boundedness of the solutions of the T-system and its control(English)
    SHU Yong-lu;WANG Meng
    2009, 2009 (1):  43-47. 
    Abstract ( 3345 )   PDF (150KB) ( 2413 )   Save
    The boundedness of solutions of a chaotic T-system was
    proved by constructing a new Lyapunov function. Furthermore, the
    theoretical results of the boundedness of a T-system can be used for
    chaos control and synchronization. Effective linear feedback
    controller was proposed for stabilizing chaos to unstable
    equilibrium$(0, 0, 0)$.
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    Perturbation analysis for the minimal norm solution of the consistent operator equation in Banach spaces(Chinese)
    WANG Jing-jing;LI Zhi-hua;XUE Yi-feng
    2009, 2009 (1):  48-52. 
    Abstract ( 3499 )   PDF (243KB) ( 1532 )   Save
    Let~$X, Y$~ be Banach spaces and let $T$ be a
    densely--defined closed linear operator from $\mathcal{D}(T)\subset$
    to $Y$ with closed range. Suppose the non-consistent perturbation
    of the consistent equation $Tx=b$ is $ \|(T+\delta T)x-\bar
    b\|=\min\limits_{z\in\mathcal{D}(T)}\|(T+\delta T)z-\bar b\|, $
    where $\delta T$ is a bounded linear operator from $X$ to $Y$. Under
    certain conditions (e. g. $X$ and $Y$ are reflexive Banach spaces),
    let $\bar x_m$ be the minimal norm solution of above equation and
    let $x_m$ be minimal norm solution of the set $S(T,
    b)=\{x\in\mathcal{D}(T)\vert\, Tx=b\}$. In this paper, we give an
    estimation of the upper bound of $\dfrac{\dist(\bar x_m, S(T,
    b))}{\|x_m\|}$ when $\delta(\Ker T, \Ker(T+\delta T))$ is small
    enough.
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    Extreme points and strongly extreme points in Orlicz sequence spaces equipped with the generalized Orlicz norm(Chinese)
    DUAN Li-fen;CUI Yun-an
    2009, 2009 (1):  53-60. 
    Abstract ( 2783 )   PDF (255KB) ( 1335 )   Save
    For the Orlicz sequence spaces generated by a $N$-function
    and equipped with the generalized Orlicz norm, criteria of extreme
    points and strongly extreme points were presented. Based on the
    criterias, both sufficient and necessary conditions were derived to
    make these spaces be convex and mid-point locally uniform convex.
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    Stability of homoclinic loops to saddle-focus with higher dimensions (Chinese)
    HUANG Xuan;WANG Li-ying
    2009, 2009 (1):  61-67. 
    Abstract ( 2919 )   PDF (358KB) ( 1381 )   Save
    By establishing a new stability definition suitable for
    the orbit homoclinic to a saddle-focus in a space with dimensions
    larger than 3, the stability criterion was given for the homoclinic
    orbit to a hyperbolic saddle-focus in a class of higher dimensional
    systems.
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    Traveling wave solutions of equation K(n,-n,2n) (Chinese)
    BI Ping;QIU Zhao-cheng
    2009, 2009 (1):  68-77. 
    Abstract ( 2900 )   PDF (485KB) ( 1429 )   Save
    The traveling wave solutions and the dynamical properties
    of Equation $K(n,-n,2n)$ were studied in terms of the bifurcation
    theory of dynamic systems and of the qualitative theory. Based on
    the characters of an integrable system, the solitary traveling wave
    solutions, uncountably infinite many smooth periodic wave solutions
    and non-smooth periodic traveling wave solutions of the system were
    obtained. According to the relationship between traveling waves and
    phase orbits, that changes of parameters led to the transitions of
    traveling wave solutions of different types were revealed.
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    Gould-Hsu inversions and Hagen-Rothe type convolutions(Chinese)
    WEI Chuan-an
    2009, 2009 (1):  78-83. 
    Abstract ( 2804 )   PDF (178KB) ( 1538 )   Save

    Four kinds of Hagen-Rothe type convolutions were defined
    by introducing denominator factors. They have no closed expressions
    themselves. Two identities due to Andrews and Burge produced other
    four convolution formulas by means of reversals and linear
    combinations. Starting from these four formulae and using Gould-Hsu
    inversions, four pairs of reciprocal formulas with respect to
    Hagen-Rothe type convolutions were established.

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    Liouville theorem about the variable exponent Laplacian(Chinese)
    Wang Lin-feng
    2009, 2009 (1):  84-93. 
    Abstract ( 3062 )   PDF (256KB) ( 1537 )   Save

    A weak maximum principle for the variable exponent Laplace
    on a complete noncompact Riemannian manifold under suitable
    conditions about the growth of the volume was established, by which
    a Liouville type theorem for the variable exponent Laplace was
    proved.

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    Derivations and 2-Cocycles of the Algebra of (r,s)-Differential Operators(English)
    CHEN Ru;LIN Lei;LIU Dong
    2009, 2009 (1):  94-103. 
    Abstract ( 2694 )   PDF (193KB) ( 1507 )   Save

    This paper defined the $(r,s)$-differential operator of the
    algebra of Laurent polynomials over the complex numbers field. Let
    $\mathcal{D}_{r,s}$ be the associative algebra generated by $\{
    t^{\pm 1} \}$ and the $(r,s)$-differential operator, which is called
    ($r,s$)-differential operators algebra. In this paper, the
    derivation algebra of $\mathcal{D}_{r,s}$ and its Lie algebra
    $\mathcal{D}_{r,s}^-$ were described and all the non-trivial
    2-cocycles were determined.

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    X charts with asymmetric sample sizes fordefecting asymmetric Losses(Chinese)
    GUO Bao-cai;SUN Li-rong
    2009, 2009 (1):  104-110. 
    Abstract ( 3493 )   PDF (608KB) ( 1634 )   Save
    In some production systems, upward and downward shifts of processes may cause different losses. To meet the need of quality control in these situations,this paper proposed two X〖DD(-*3〗〖KG*3〗—〖DD)〗 charts with asymmetric sample sizes. A Markov chain method was used to obtain their statistical properties. Numerical results indicate, for the shifts of less than 1.5 process standard deriation from the mean, that using asymmetric sample sizes is more efficient in detecting the shifts in one direction, while without missing the shifts in the other direction. Using the warning limit may speed up in detecting the shifts in one direction.
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    Algorithm for resource scheduling based on multiQoS constraints(Chinese)
    CHEN Yu-lan;ZHENG Jun;HU Wen-xin
    2009, 2009 (1):  111-116. 
    Abstract ( 3001 )   PDF (604KB) ( 1480 )   Save
    A new algorithm for resource scheduling in grid environment based on multiQoS constraints and greedy method was proposed. It takes a driver function which is determined by parameters“deadline”, “budget”, “time weight” and “cost weight” which the user provided as the greedy criterion. The performance of this new scheduling algorithm, choosing a most economic resource for scheduling each time and achieving the maximum of customer′s satisfaction, is demonstrated by its implementation on Gridsim.
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    Improved boundary tracing automaton in8neigthorhood digital image(Chinese)
    LIU Yan;GAO Wei-nan;WANG Zhi-qing;JU Zhi-yong
    2009, 2009 (1):  117-123. 
    Abstract ( 3084 )   PDF (1151KB) ( 1814 )   Save
    Based on the boundary tracing algorithm, this study presented an improved automaton with a simplified state transition set. A comparison showed that the modified automaton greatly reduces the computational time and memory space.
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    PZT/PVDF flexible composites applied on ISM antenna(Chinese)
    ZHENG Zheng-qi;YUE Peng;WANG Lian-wei;ZHANG Jie
    2009, 2009 (1):  124-127. 
    Abstract ( 3662 )   PDF (845KB) ( 2392 )   Save
    With solution blending process, PZT/PVDF composite thin films was formed. Dielectric constant and loss factor was measured through shortended waveguide test line. As the composite has the advantage of high dielectric constant, low loss factor and flexibility, a miniaturized ISM band composite microstrip antenna was designed for ETC system of freeway. 
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    Twist-4 effect in polarized structure function(Chinese)
    YANG Dong-yan;RUAN Jian-hong
    2009, 2009 (1):  128-136. 
    Abstract ( 2838 )   PDF (1012KB) ( 1621 )   Save
    This paper calculated the proton and neutron spin structure functiong1 and the asymmetryA1 with modified DGLAP equations which considered twist-4 effect. With the HERMES experiment data, we discussed twist-4 effect in polarized structure function.
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    Effect on vibrational levels of H+2 by its approximateanalytic wave function for the ground state(Chinese)
    QIN Ai-li;WANG Ya-ling;GUO Ying-chun;CHEN Yang-qin
    2009, 2009 (1):  137-140. 
    Abstract ( 2975 )   PDF (459KB) ( 1542 )   Save
    This paper studied the effect of approximate analytic wave function of the ground state of φH+2=1/2(1+S)1/2φH(z,ra)+φH(z,rb)) on its vibrational levels. Potential energy as a function of internuclear distance and z was calculated, and vibrational energy levels of the ground state were also worked out. By comparing them with experimental vibrational energy levels, it was found that this wave function with z=1.23 works very well for ground vibrational level of H+2 But for higher vibrational levels, z=1.13 is better.
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