2009 No. 1
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2009, (1): 1-6.
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Abstract:
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 $G$.
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 $G$.
2009, (1): 7-12.
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Consider a red planar graph and a green planar graphsimutaneously $2$-cell embedded on a surface. With some restriction,a red edge can cross a green edge. This paper studied the minimumnumber of these red-green crosses by using technique of integerprogramming, and some results are obtained.
Consider a red planar graph and a green planar graphsimutaneously $2$-cell embedded on a surface. With some restriction,a red edge can cross a green edge. This paper studied the minimumnumber of these red-green crosses by using technique of integerprogramming, and some results are obtained.
2009, (1): 13-21.
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By the principle of mathematical induction and classifieddiscussion, the sharp bounds for dissection of unicyclic graphs of afixed 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.
By the principle of mathematical induction and classifieddiscussion, the sharp bounds for dissection of unicyclic graphs of afixed 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.
2009, (1): 22-27.
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Let $\{f_i\}_{i=1}^{M}$ be unit-norm vectors in $\CN$.This paper introduces an algorithm to construct a unit-norm tightframe by adding minimum vectors $\{g_i\}_{i=1}^{K}$ to$\{f_i\}_{i=1}^{M}$.
Let $\{f_i\}_{i=1}^{M}$ be unit-norm vectors in $\CN$.This paper introduces an algorithm to construct a unit-norm tightframe by adding minimum vectors $\{g_i\}_{i=1}^{K}$ to$\{f_i\}_{i=1}^{M}$.
2009, (1): 28-31.
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By using the method of matrix equation equivalenttransformation, combined the properties of $2$-norm and $F$-norm andtheir relationship with eigenvalue, this paper dealt with the upperbound for perturbation of diagonalized non-singular matrixeigenspaces. 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 $[2]$.
By using the method of matrix equation equivalenttransformation, combined the properties of $2$-norm and $F$-norm andtheir relationship with eigenvalue, this paper dealt with the upperbound for perturbation of diagonalized non-singular matrixeigenspaces. 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 $[2]$.
2009, (1): 32-36.
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The existence of positive solution was studied for thenonlinear Sturm-Liouville boundary value problem, where thenonlinear term $f(t,u)$ may be singular at $t = 0,\,t = 1$. Byintroducing the integrations of height functions of nonlinear termon bounded set the growths of nonlinear term were described. Byapplying the Krasnoselskii fixed point theorem in degree theory andthe dominated convergence theorems in real variable, an existencetheorem of positive solution was proved when there are limitfunctions $\mathop {\lim }\limits_{u \to + 0} f(t,u) / u$ and$\mathop {\lim }\limits_{u \to + \infty } f(t,u) / u$.
The existence of positive solution was studied for thenonlinear Sturm-Liouville boundary value problem, where thenonlinear term $f(t,u)$ may be singular at $t = 0,\,t = 1$. Byintroducing the integrations of height functions of nonlinear termon bounded set the growths of nonlinear term were described. Byapplying the Krasnoselskii fixed point theorem in degree theory andthe dominated convergence theorems in real variable, an existencetheorem of positive solution was proved when there are limitfunctions $\mathop {\lim }\limits_{u \to + 0} f(t,u) / u$ and$\mathop {\lim }\limits_{u \to + \infty } f(t,u) / u$.
2009, (1): 37-42.
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The existence of spike-like solutions of a class ofSturm-Liouville singularly perturbed problem was investigated andits sufficient condition was given. Meanwhile, the uniformly validasymptotic solutions were constructed by the method of boundarylayer functions and remainder estimation was presented. Finally, anexample was given to illustrate the obtained results.
The existence of spike-like solutions of a class ofSturm-Liouville singularly perturbed problem was investigated andits sufficient condition was given. Meanwhile, the uniformly validasymptotic solutions were constructed by the method of boundarylayer functions and remainder estimation was presented. Finally, anexample was given to illustrate the obtained results.
2009, (1): 43-47.
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The boundedness of solutions of a chaotic T-system wasproved by constructing a new Lyapunov function. Furthermore, thetheoretical results of the boundedness of a T-system can be used forchaos control and synchronization. Effective linear feedbackcontroller was proposed for stabilizing chaos to unstableequilibrium$(0, 0, 0)$.
The boundedness of solutions of a chaotic T-system wasproved by constructing a new Lyapunov function. Furthermore, thetheoretical results of the boundedness of a T-system can be used forchaos control and synchronization. Effective linear feedbackcontroller was proposed for stabilizing chaos to unstableequilibrium$(0, 0, 0)$.
2009, (1): 48-52.
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Let~$X, Y$~ be Banach spaces and let $T$ be adensely--defined closed linear operator from $\mathcal{D}(T)\subset$to $Y$ with closed range. Suppose the non-consistent perturbationof the consistent equation $Tx=b$ is $ \|(T+\delta T)x-\barb\|=\min\limits_{z\in\mathcal{D}(T)}\|(T+\delta T)z-\bar b\|, $where $\delta T$ is a bounded linear operator from $X$ to $Y$. Undercertain conditions (e. g. $X$ and $Y$ are reflexive Banach spaces),let $\bar x_m$ be the minimal norm solution of above equation andlet $x_m$ be minimal norm solution of the set $S(T,b)=\{x\in\mathcal{D}(T)\vert\, Tx=b\}$. In this paper, we give anestimation of the upper bound of $\dfrac{\dist(\bar x_m, S(T,b))}{\|x_m\|}$ when $\delta(\Ker T, \Ker(T+\delta T))$ is smallenough.
Let~$X, Y$~ be Banach spaces and let $T$ be adensely--defined closed linear operator from $\mathcal{D}(T)\subset$to $Y$ with closed range. Suppose the non-consistent perturbationof the consistent equation $Tx=b$ is $ \|(T+\delta T)x-\barb\|=\min\limits_{z\in\mathcal{D}(T)}\|(T+\delta T)z-\bar b\|, $where $\delta T$ is a bounded linear operator from $X$ to $Y$. Undercertain conditions (e. g. $X$ and $Y$ are reflexive Banach spaces),let $\bar x_m$ be the minimal norm solution of above equation andlet $x_m$ be minimal norm solution of the set $S(T,b)=\{x\in\mathcal{D}(T)\vert\, Tx=b\}$. In this paper, we give anestimation of the upper bound of $\dfrac{\dist(\bar x_m, S(T,b))}{\|x_m\|}$ when $\delta(\Ker T, \Ker(T+\delta T))$ is smallenough.
2009, (1): 53-60.
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For the Orlicz sequence spaces generated by a $N$-functionand equipped with the generalized Orlicz norm, criteria of extremepoints and strongly extreme points were presented. Based on thecriterias, both sufficient and necessary conditions were derived tomake these spaces be convex and mid-point locally uniform convex.
For the Orlicz sequence spaces generated by a $N$-functionand equipped with the generalized Orlicz norm, criteria of extremepoints and strongly extreme points were presented. Based on thecriterias, both sufficient and necessary conditions were derived tomake these spaces be convex and mid-point locally uniform convex.
2009, (1): 61-67.
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By establishing a new stability definition suitable forthe orbit homoclinic to a saddle-focus in a space with dimensionslarger than 3, the stability criterion was given for the homoclinicorbit to a hyperbolic saddle-focus in a class of higher dimensionalsystems.
By establishing a new stability definition suitable forthe orbit homoclinic to a saddle-focus in a space with dimensionslarger than 3, the stability criterion was given for the homoclinicorbit to a hyperbolic saddle-focus in a class of higher dimensionalsystems.
2009, (1): 68-77.
Abstract:
The traveling wave solutions and the dynamical propertiesof Equation $K(n,-n,2n)$ were studied in terms of the bifurcationtheory of dynamic systems and of the qualitative theory. Based onthe characters of an integrable system, the solitary traveling wavesolutions, uncountably infinite many smooth periodic wave solutionsand non-smooth periodic traveling wave solutions of the system wereobtained. According to the relationship between traveling waves andphase orbits, that changes of parameters led to the transitions oftraveling wave solutions of different types were revealed.
The traveling wave solutions and the dynamical propertiesof Equation $K(n,-n,2n)$ were studied in terms of the bifurcationtheory of dynamic systems and of the qualitative theory. Based onthe characters of an integrable system, the solitary traveling wavesolutions, uncountably infinite many smooth periodic wave solutionsand non-smooth periodic traveling wave solutions of the system wereobtained. According to the relationship between traveling waves andphase orbits, that changes of parameters led to the transitions oftraveling wave solutions of different types were revealed.
2009, (1): 78-83.
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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.
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.
2009, (1): 84-93.
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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.
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.
2009, (1): 94-103.
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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.
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.
2009, (1): 104-110.
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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.
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.
2009, (1): 111-116.
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A new algorithm for resource scheduling in grid environment based on multiQoS 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.
A new algorithm for resource scheduling in grid environment based on multiQoS 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.
2009, (1): 117-123.
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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.
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.
2009, (1): 124-127.
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With solution blending process, PZT/PVDF composite thin films was formed. Dielectric constant and loss factor was measured through shortended 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.
With solution blending process, PZT/PVDF composite thin films was formed. Dielectric constant and loss factor was measured through shortended 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.
2009, (1): 128-136.
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This paper calculated the proton and neutron spin structure functiong1 and the asymmetryA1 with modified DGLAP equations which considered twist-4 effect. With the HERMES experiment data, we discussed twist-4 effect in polarized structure function.
This paper calculated the proton and neutron spin structure functiong1 and the asymmetryA1 with modified DGLAP equations which considered twist-4 effect. With the HERMES experiment data, we discussed twist-4 effect in polarized structure function.
2009, (1): 137-140.
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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.
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.