2009 No. 4
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2009, (4): 1-9.
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Abstract:
This paper gave a review of recent developments in the study of nullities of undirected simple graphs. The problem on nullity is very interesting in characterizing all kinds of properties of graphs as well as in determination of the stability of a molecule in chemistry. The results on bipartite graphs, trees, unicyclic graphs, bicyclic graphs, line graphs of trees were introduced. And thegraphs with large nullities were discussed.
This paper gave a review of recent developments in the study of nullities of undirected simple graphs. The problem on nullity is very interesting in characterizing all kinds of properties of graphs as well as in determination of the stability of a molecule in chemistry. The results on bipartite graphs, trees, unicyclic graphs, bicyclic graphs, line graphs of trees were introduced. And thegraphs with large nullities were discussed.
2009, (4): 10-15.
Abstract:
The energy $\mathcal{E}(G)$ of a graph $G$ is the sum of the absolute values of all the eigenvalues of the adjacency matrix of $G$. It is used in chemistry to approximate the total $\pi$-electron energy of a molecule. This paper presented some new lower bounds for $\mathcal{E}(G)$, and characterized those graphs for which these bounds were attained.
The energy $\mathcal{E}(G)$ of a graph $G$ is the sum of the absolute values of all the eigenvalues of the adjacency matrix of $G$. It is used in chemistry to approximate the total $\pi$-electron energy of a molecule. This paper presented some new lower bounds for $\mathcal{E}(G)$, and characterized those graphs for which these bounds were attained.
2009, (4): 16-20.
Abstract:
he minimum number of colors required to give a graph $G$ an adjacent vertex-distinguishing edge partition was studied. Based on the classification of the degree of a graph, this paper proved that every graph without $K_{2}$ of minimum degree at least 188 permits an adjacent vertex-distinguishing 3-edge partition. The result is more superior than previous ones.
he minimum number of colors required to give a graph $G$ an adjacent vertex-distinguishing edge partition was studied. Based on the classification of the degree of a graph, this paper proved that every graph without $K_{2}$ of minimum degree at least 188 permits an adjacent vertex-distinguishing 3-edge partition. The result is more superior than previous ones.
2009, (4): 21-25.
Abstract:
In this paper, the generalized inverse form solution of Davis, Kahan and Weinberger’s norm-preserving extension theorem was given. Consequently, Zheng’s result (1996) was proved in a more simple way.
In this paper, the generalized inverse form solution of Davis, Kahan and Weinberger’s norm-preserving extension theorem was given. Consequently, Zheng’s result (1996) was proved in a more simple way.
2009, (4): 26-34.
Abstract:
This paper analyzed the convergence of preconditioned AOR and 2PPJ iterative methods when the coefficient matrix is an $\emph{\textbf{M}}$-matrix, and pointed out some errors of known results and established correct convergence theorems. Meanwhile, by the $\emph{\textbf{H}}$-splitting theory, the convergence of the preconditioned AOR iterative method for the case of the coefficient matrix being an $\emph{\textbf{H}}$-matrix was discussed and the convergence interval of parameters was
This paper analyzed the convergence of preconditioned AOR and 2PPJ iterative methods when the coefficient matrix is an $\emph{\textbf{M}}$-matrix, and pointed out some errors of known results and established correct convergence theorems. Meanwhile, by the $\emph{\textbf{H}}$-splitting theory, the convergence of the preconditioned AOR iterative method for the case of the coefficient matrix being an $\emph{\textbf{H}}$-matrix was discussed and the convergence interval of parameters was
2009, (4): 35-38.
Abstract:
For any given complex number $\lambda$, this paper proved that there exists a 3 by 3 nonnegative matrix \textbf{\emph{A}} with at least 4 zero entries such that $\lambda$ is an eigenvalue of \textbf{\emph{A}}. The number 4 of zero entries here is the largest possible.
For any given complex number $\lambda$, this paper proved that there exists a 3 by 3 nonnegative matrix \textbf{\emph{A}} with at least 4 zero entries such that $\lambda$ is an eigenvalue of \textbf{\emph{A}}. The number 4 of zero entries here is the largest possible.
2009, (4): 39-46.
Abstract:
This paper introduced concepts of norms of quaternion matrices by means of complex representation of a quaternion matrix, studied the quaternionic least squares (QLS) problem and derived an algebraic method of finding solutions of the QLS problem in quaternionic quantum theory. A numerical example verified the efficiency of the algorithm.
This paper introduced concepts of norms of quaternion matrices by means of complex representation of a quaternion matrix, studied the quaternionic least squares (QLS) problem and derived an algebraic method of finding solutions of the QLS problem in quaternionic quantum theory. A numerical example verified the efficiency of the algorithm.
2009, (4): 47-53.
Abstract:
A new kind of weighted generalized inverse was defined to study indefinite least squares (ILS) problem and equality constrained indefinite least squares (ILSE) problem. By applying hyperbolic-QR factorization, the solutions to the two problems were obtained. Also the perturbation bounds of the solutions were derived.
A new kind of weighted generalized inverse was defined to study indefinite least squares (ILS) problem and equality constrained indefinite least squares (ILSE) problem. By applying hyperbolic-QR factorization, the solutions to the two problems were obtained. Also the perturbation bounds of the solutions were derived.
Tests for functional-coefficient parts on semiparametric varying-coefficient partially linear models
2009, (4): 54-61.
Abstract:
Based on the quasi-likelihood estimates obtained by the local linear method,~the generalized likelihood ratio tests for the models were established.~Under the null hypothesis the test statistic followed asymptotically the $\chi^{2}$-distribution with the scale constants and the degree of freedom being independent of the nuisance parameters and the nuisance functions,~which was called the Wilks phenomenon.~A simulated example was presented to illustrate the proposed methods.
Based on the quasi-likelihood estimates obtained by the local linear method,~the generalized likelihood ratio tests for the models were established.~Under the null hypothesis the test statistic followed asymptotically the $\chi^{2}$-distribution with the scale constants and the degree of freedom being independent of the nuisance parameters and the nuisance functions,~which was called the Wilks phenomenon.~A simulated example was presented to illustrate the proposed methods.
2009, (4): 62-68.
Abstract:
By using the characterization of heavy-tailed random variables in $\mathcal{D}\cap\mathcal{L}$, precise large deviations for sums (nonrandom sums and random sums) of negatively associated heavy-tailed random variables in $\mathcal{D}\cap\mathcal{L}$ were obtained, where the subclass $\mathcal{D}\cap\mathcal{L}$ strictly contains $\mathcal{C}$. Therefore, it firstly extends some existed precise large deviation results to some larger subclasses of heavy tailed distributions.
By using the characterization of heavy-tailed random variables in $\mathcal{D}\cap\mathcal{L}$, precise large deviations for sums (nonrandom sums and random sums) of negatively associated heavy-tailed random variables in $\mathcal{D}\cap\mathcal{L}$ were obtained, where the subclass $\mathcal{D}\cap\mathcal{L}$ strictly contains $\mathcal{C}$. Therefore, it firstly extends some existed precise large deviation results to some larger subclasses of heavy tailed distributions.
2009, (4): 69-77.
Abstract:
The method of boundary function was used to construct uniformly valid asymptotic solutions of the Robin problem of a class of semilinear singularly perturbed equations, which are often used as models for chemical reactions. At the same time the existence and uniqueness of the solution and the estimation of the remainder for the problem were given.
The method of boundary function was used to construct uniformly valid asymptotic solutions of the Robin problem of a class of semilinear singularly perturbed equations, which are often used as models for chemical reactions. At the same time the existence and uniqueness of the solution and the estimation of the remainder for the problem were given.
2009, (4): 78-81.
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This paper was concerned with a one-dimensional linear wave equation associated with nonlinear boundary conditions. The unique local solution to the wave equation was proved to exist. The result is that the nonlinearity at the boundary causes a finite time blow up of the solution, even for small initial data. And the upper bound to the blow up time is given in the paper
This paper was concerned with a one-dimensional linear wave equation associated with nonlinear boundary conditions. The unique local solution to the wave equation was proved to exist. The result is that the nonlinearity at the boundary causes a finite time blow up of the solution, even for small initial data. And the upper bound to the blow up time is given in the paper
2009, (4): 82-91.
Abstract:
A result on vanishing cohomology for finite-dimensional modular Lie superalgebras was obtained, with aid of the approach provided by Dzhumadil’daev for modular Lie algebras. Some examples are given as demonstration of the vanishing result, as well as its applications.
A result on vanishing cohomology for finite-dimensional modular Lie superalgebras was obtained, with aid of the approach provided by Dzhumadil’daev for modular Lie algebras. Some examples are given as demonstration of the vanishing result, as well as its applications.
2009, (4): 92-97.
Abstract:
This paper established an improved KMPalgorithm for pattern matching in string. Tests proved that the algorithm has less comparison times and higher efficiency under the circumstances that the pattern first appears in the bottom half of a text string.
This paper established an improved KMPalgorithm for pattern matching in string. Tests proved that the algorithm has less comparison times and higher efficiency under the circumstances that the pattern first appears in the bottom half of a text string.
2009, (4): 98-106.
Abstract:
A new idea to bring broadband service to vehicles by WOBAN (hybrid WirelessOptical BroadbandAccess Network) was presented and a working model of an urban road WOBAN was given. Considering traffic flow as a key factor for the optimal ONU (Optical Network Unit) placement in urban road WOBAN, a scheme to characterize urban road features based on traffic flow was proposed and four examined spot types were defined. Furthermore, we compared two place evaluation strategies.
A new idea to bring broadband service to vehicles by WOBAN (hybrid WirelessOptical BroadbandAccess Network) was presented and a working model of an urban road WOBAN was given. Considering traffic flow as a key factor for the optimal ONU (Optical Network Unit) placement in urban road WOBAN, a scheme to characterize urban road features based on traffic flow was proposed and four examined spot types were defined. Furthermore, we compared two place evaluation strategies.
2009, (4): 107-114.
Abstract:
TCP employs delaybased congestion avoidance (DCA) algorithms to improve the throughput of network system. However, there are many factors to affect the DCA algorithm efficiency. In order to solve these problems, a fuzzy control based DCA algorithms (FDCA) was proposed to reduce the influences of the factors. The simulations show that the algorithm provides more accurate and timely indication of network congestion, and increases network throughput.
TCP employs delaybased congestion avoidance (DCA) algorithms to improve the throughput of network system. However, there are many factors to affect the DCA algorithm efficiency. In order to solve these problems, a fuzzy control based DCA algorithms (FDCA) was proposed to reduce the influences of the factors. The simulations show that the algorithm provides more accurate and timely indication of network congestion, and increases network throughput.
2009, (4): 115-123.
Abstract:
By analysis of existed proposals for true 3D volumetric displays based on rotation, the visual voxel display technology was explained. In order to overcome limitations and shortcomings of current rotation proposals, a new highspeed display interface based on ARMCortexM3 was raised. Using its high speed bandwidth, equality of voxel volume and voxel brightness was realized. Finally horizontal 360°,vertical visual 180° visual angle range and high brightness display effect is obtained.
By analysis of existed proposals for true 3D volumetric displays based on rotation, the visual voxel display technology was explained. In order to overcome limitations and shortcomings of current rotation proposals, a new highspeed display interface based on ARMCortexM3 was raised. Using its high speed bandwidth, equality of voxel volume and voxel brightness was realized. Finally horizontal 360°,vertical visual 180° visual angle range and high brightness display effect is obtained.
2009, (4): 124-130.
Abstract:
Through absorption of bromine vapor, the electrical conductivity of Polyphenylacetylene (PPA) enhanced by 1012 times. After pressing the bromine doped powder sample into pellet, we found that the conductivity of the samples increased with time. UVVis spectra, IR, and XPS spectra indicated that strong conjugation effect exists between PPA and bromine, and Charge Transfer Complex (CTC) is formed in PPA after doping; bromine doping increases the conjugation of PPA and improves its conductivity; the pressure can promote the doping effect of bromine on PPA.
Through absorption of bromine vapor, the electrical conductivity of Polyphenylacetylene (PPA) enhanced by 1012 times. After pressing the bromine doped powder sample into pellet, we found that the conductivity of the samples increased with time. UVVis spectra, IR, and XPS spectra indicated that strong conjugation effect exists between PPA and bromine, and Charge Transfer Complex (CTC) is formed in PPA after doping; bromine doping increases the conjugation of PPA and improves its conductivity; the pressure can promote the doping effect of bromine on PPA.
2009, (4): 131-136.
Abstract:
The structural and magnetic properties of the antiperovskite (Fe1-x Nx)4N compounds were investigated by employing a full potential linearized augmented plane wave method (FPLAPW)．The dependence of lattice constants on the content of Ni was calculated．The calculated results of total energy imply that Ni prefers to occupy the corner sites rather than the facecenter sites．The investigation of the dependence of the binding energy of (Fe1-x Nx)4N on the Ni content indicates that the stabilization of ( (Fe1-x Nx)4N increases firstly and then decreases. The compound reaches the most stabilization at x=0.25．After x0.75, it becomes unstable, which is agreed with the result of experiment very well．The effects of different exchange correlation potentials on the magnetic moment were discussed.
The structural and magnetic properties of the antiperovskite (Fe1-x Nx)4N compounds were investigated by employing a full potential linearized augmented plane wave method (FPLAPW)．The dependence of lattice constants on the content of Ni was calculated．The calculated results of total energy imply that Ni prefers to occupy the corner sites rather than the facecenter sites．The investigation of the dependence of the binding energy of (Fe1-x Nx)4N on the Ni content indicates that the stabilization of ( (Fe1-x Nx)4N increases firstly and then decreases. The compound reaches the most stabilization at x=0.25．After x0.75, it becomes unstable, which is agreed with the result of experiment very well．The effects of different exchange correlation potentials on the magnetic moment were discussed.