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25 January 2009, Volume 2009 Issue 1 Previous Issue    Next Issue

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Properties of a new class of transformation graphs (Chinese) LIU Rui-fang;SHU Jin-long 2009, 2009 (1):  1-6.  Abstract ( 3040 )   PDF (252KB) ( 1540 )   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 $G$. Related Articles | Metrics

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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 ( 3380 )   PDF (329KB) ( 1527 )   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. Related Articles | Metrics

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On dissection of unicyclic graphs(English) WANG Xiao;DUAN Fang 2009, 2009 (1):  13-21.  Abstract ( 3423 )   PDF (201KB) ( 1644 )   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. Related Articles | Metrics

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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 ( 3337 )   PDF (227KB) ( 1588 )   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 $\{f_i\}_{i=1}^{M}$. Related Articles | Metrics

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Perturbations about eigenspaces (Chinese) CHEN Jian-xin; 2009, 2009 (1):  28-31.  Abstract ( 3237 )   PDF (202KB) ( 1570 )   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 $[2]$. Related Articles | Metrics

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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 ( 3535 )   PDF (214KB) ( 1450 )   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 $\mathop {\lim }\limits_{u \to + \infty } f(t,u) / u$. Related Articles | Metrics

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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 ( 3685 )   PDF (228KB) ( 1540 )   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. Related Articles | Metrics

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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 ( 3366 )   PDF (150KB) ( 2442 )   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$(0, 0, 0)$. Related Articles | Metrics

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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 ( 3532 )   PDF (243KB) ( 1556 )   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. Related Articles | Metrics

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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 ( 2819 )   PDF (255KB) ( 1358 )   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. Related Articles | Metrics

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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 ( 2998 )   PDF (358KB) ( 1418 )   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. Related Articles | Metrics

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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 ( 2935 )   PDF (485KB) ( 1446 )   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. Related Articles | Metrics

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Gould-Hsu inversions and Hagen-Rothe type convolutions(Chinese) WEI Chuan-an 2009, 2009 (1):  78-83.  Abstract ( 2855 )   PDF (178KB) ( 1559 )   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. Related Articles | Metrics

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Liouville theorem about the variable exponent Laplacian(Chinese) Wang Lin-feng 2009, 2009 (1):  84-93.  Abstract ( 3098 )   PDF (256KB) ( 1572 )   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. Related Articles | Metrics

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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 ( 2716 )   PDF (193KB) ( 1530 )   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. Related Articles | Metrics

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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 ( 3536 )   PDF (608KB) ( 1720 )   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. Related Articles | Metrics

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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 ( 3040 )   PDF (604KB) ( 1498 )   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. Related Articles | Metrics

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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 ( 3125 )   PDF (1151KB) ( 1897 )   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. Related Articles | Metrics

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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 ( 3690 )   PDF (845KB) ( 2399 )   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.  Related Articles | Metrics

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Twist-4 effect in polarized structure function(Chinese) YANG Dong-yan;RUAN Jian-hong 2009, 2009 (1):  128-136.  Abstract ( 2882 )   PDF (1012KB) ( 1633 )   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. Related Articles | Metrics

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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 ( 3014 )   PDF (459KB) ( 1602 )   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. Related Articles | Metrics