2010 No. 1
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2010, (1): 1-5.
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Abstract:
By the method of boundary layer function the formal asymptotic solution for the problem was constructed, and its uniformly validity was proved using the theory of differential inequalities. An example was given.
By the method of boundary layer function the formal asymptotic solution for the problem was constructed, and its uniformly validity was proved using the theory of differential inequalities. An example was given.
2010, (1): 6-9.
Abstract:
The Laplacian spread of a graph is defined to be the difference between the largest and the second-smallest Laplacian eigenvalues of the graph. Using properties of polynomial, we characterized the graphs with the maximal Laplacian spread among all bicyclic graphs.
The Laplacian spread of a graph is defined to be the difference between the largest and the second-smallest Laplacian eigenvalues of the graph. Using properties of polynomial, we characterized the graphs with the maximal Laplacian spread among all bicyclic graphs.
2010, (1): 10-16.
Abstract:
This paper studied the relation between the Lapacian energy with the singular values of the Laplacian matrix and obtain some results on the bound of the Laplacian energy on a graph. Changes of the energy caused by deletion of edges and vertices of a graph were also studied. The results may help to have a better understanding of pi-electron energy in a molecule in theoretical chemistry.
This paper studied the relation between the Lapacian energy with the singular values of the Laplacian matrix and obtain some results on the bound of the Laplacian energy on a graph. Changes of the energy caused by deletion of edges and vertices of a graph were also studied. The results may help to have a better understanding of pi-electron energy in a molecule in theoretical chemistry.
2010, (1): 17-23.
Abstract:
This paper extended the ZTP regression model to Zero-truncated generalized Poisson regression model. An algorithm for estimating parameters was obtained and two score tests were presented for testing the ZTP regression model against the ZTGP regression model, and for testing the significance of regression coefficients. A numerical example was given to illustrate our method and the power of score tests was investigated by Monte Carlo simulation.
This paper extended the ZTP regression model to Zero-truncated generalized Poisson regression model. An algorithm for estimating parameters was obtained and two score tests were presented for testing the ZTP regression model against the ZTGP regression model, and for testing the significance of regression coefficients. A numerical example was given to illustrate our method and the power of score tests was investigated by Monte Carlo simulation.
2010, (1): 24-33.
Abstract:
Based on Wu’s elimination method and “divide-and-conquer” strategy, the undetermined coefficient method for constructing polynomial conservation laws of nonlinear differential-difference equations was improved. Furthermore, a Maple package CLawDDEs was developed to automatically derive conserved densities and associated fluxes of polynomial differential-difference equations. For parameterized nonlinear differential-difference equations, CLawDDEs can also filter out the compatibility conditions which admit the existence of infinitely conservation laws. So CLawDDEs can be used as an effective tool to test the integrability of nonlinear differential-difference equations.
Based on Wu’s elimination method and “divide-and-conquer” strategy, the undetermined coefficient method for constructing polynomial conservation laws of nonlinear differential-difference equations was improved. Furthermore, a Maple package CLawDDEs was developed to automatically derive conserved densities and associated fluxes of polynomial differential-difference equations. For parameterized nonlinear differential-difference equations, CLawDDEs can also filter out the compatibility conditions which admit the existence of infinitely conservation laws. So CLawDDEs can be used as an effective tool to test the integrability of nonlinear differential-difference equations.
2010, (1): 34-38.
Abstract:
Based on modified quasi-Newton equation, a new limited memory quasi-Newton method with two-loop recursion was proposed. Comparing to the classical limited memory BFGS method, the new method uses more function value and gradient informations to construct the quasi-Newton update mectrix, and does not need more computational efforts. The theory analysis and numerical results show the efficiency of the proposed method.
Based on modified quasi-Newton equation, a new limited memory quasi-Newton method with two-loop recursion was proposed. Comparing to the classical limited memory BFGS method, the new method uses more function value and gradient informations to construct the quasi-Newton update mectrix, and does not need more computational efforts. The theory analysis and numerical results show the efficiency of the proposed method.
2010, (1): 39-43.
Abstract:
In this paper, A problem about an equality of the generalized inverses of matrices, proposed by CHEN Xiao-juan and GUO Wen-bin, was solved. In the end, a simpler supplemental proof was also given.
In this paper, A problem about an equality of the generalized inverses of matrices, proposed by CHEN Xiao-juan and GUO Wen-bin, was solved. In the end, a simpler supplemental proof was also given.
2010, (1): 44-51.
Abstract:
In this paper, a modified conjugate gradient formula beta _k^MLSbased on the formula of the Liu-Storey(LS) nonlinear conjugate gradient method was proposed. It was proved that under the Wolfe-Powell line search and even under the strong Wolfe-Powell line search, with parameter sigma in bigg(0,frac12bigg), the new method has sufficient descent and global convergence properties. Preliminary numerical results show that the method is very promising.
In this paper, a modified conjugate gradient formula beta _k^MLSbased on the formula of the Liu-Storey(LS) nonlinear conjugate gradient method was proposed. It was proved that under the Wolfe-Powell line search and even under the strong Wolfe-Powell line search, with parameter sigma in bigg(0,frac12bigg), the new method has sufficient descent and global convergence properties. Preliminary numerical results show that the method is very promising.
2010, (1): 52-61.
Abstract:
By using the backstepping design method we formulated a simple controller to control the system to its unstable equilibrium (0,0,0), any point of the form (0,0,1+b+p(1-p))(0p1) in phase space, and forced the first state variable to trace arbitrary given function r(t). Suppose one parameter was unknown, we proposed a unidirectional coupled scheme and a parameter update role to assure the new Lorenz-like system to globally synchronize with a copy of itself. We presented a rigorous proof of our design by constructing proper Lyapunov function. Numerical simulations using Matlab were presented to show the feasibility of our design.
By using the backstepping design method we formulated a simple controller to control the system to its unstable equilibrium (0,0,0), any point of the form (0,0,1+b+p(1-p))(0p1) in phase space, and forced the first state variable to trace arbitrary given function r(t). Suppose one parameter was unknown, we proposed a unidirectional coupled scheme and a parameter update role to assure the new Lorenz-like system to globally synchronize with a copy of itself. We presented a rigorous proof of our design by constructing proper Lyapunov function. Numerical simulations using Matlab were presented to show the feasibility of our design.
2010, (1): 62-68，7.
Abstract:
The globally exponentially attractive set and synchronization problem of the brushless dc motor (BLDCM) chaotic system were researched. Firstly, based on the definition of globally exponentially attractive set and Lyapunov stability theory, a sufficient condition for the globally exponentially attractive was given. Secondly, nonlinear feedback control was used to realize the synchronization of two chaotic systems. Finally, numerical simulations were presented to show the effectiveness of the proposed chaos synchronization scheme.
The globally exponentially attractive set and synchronization problem of the brushless dc motor (BLDCM) chaotic system were researched. Firstly, based on the definition of globally exponentially attractive set and Lyapunov stability theory, a sufficient condition for the globally exponentially attractive was given. Secondly, nonlinear feedback control was used to realize the synchronization of two chaotic systems. Finally, numerical simulations were presented to show the effectiveness of the proposed chaos synchronization scheme.
2010, (1): 69-78.
Abstract:
The paper considered a call center with interacting voice response (IVR) by using Markov model. By constructing a two-state and a three-state MC, stationary probability was given using flow conservation equation and Q-matrix respectively. Furthermore, other performance indexes was deduced, too.
The paper considered a call center with interacting voice response (IVR) by using Markov model. By constructing a two-state and a three-state MC, stationary probability was given using flow conservation equation and Q-matrix respectively. Furthermore, other performance indexes was deduced, too.
2010, (1): 79-84.
Abstract:
This paper proposed a model to analyze the licensing schemes when the patentee had private information about its technology value. In this model, the patentee was considered as an insider in Homogenous Stackelberg Market instead of an independent RD institute. Based on this model, this paper presented the patentee’s optimal licensing option for maximizing its profit under the condition that the licensee may accept the contract. In the same way, this paper analyzed the fixed fee, royalty and the profit of the patentee in the model, respectively. This paper aims at proposing an idea for the participants to advance the efficiency of licensing.
This paper proposed a model to analyze the licensing schemes when the patentee had private information about its technology value. In this model, the patentee was considered as an insider in Homogenous Stackelberg Market instead of an independent RD institute. Based on this model, this paper presented the patentee’s optimal licensing option for maximizing its profit under the condition that the licensee may accept the contract. In the same way, this paper analyzed the fixed fee, royalty and the profit of the patentee in the model, respectively. This paper aims at proposing an idea for the participants to advance the efficiency of licensing.
2010, (1): 85-90.
Abstract:
This paper computed the Jacobian of transformation textbfemphX=textbfemphBYB^mathrm T of singular quaternion matrices by using of the singular value decomposition of quaternion matrix and the density function of singular quaternion Wishart matrix. Then we defined the Beta and F distributions of quaternion matrix argument,and gave the density functions of the Beta and F distribution and the joint density functions of the nonzero eigenvalues of the singular quaternion matrices which satisfy the Beta or F distribution.
This paper computed the Jacobian of transformation textbfemphX=textbfemphBYB^mathrm T of singular quaternion matrices by using of the singular value decomposition of quaternion matrix and the density function of singular quaternion Wishart matrix. Then we defined the Beta and F distributions of quaternion matrix argument,and gave the density functions of the Beta and F distribution and the joint density functions of the nonzero eigenvalues of the singular quaternion matrices which satisfy the Beta or F distribution.
2010, (1): 91-98.
Abstract:
Let M be an n-dimensional complete noncompact Riemannian manifold with metric g, triangle_p(1pleqslant 2) the p-Laplace operator, by using the classical method of Li-Yau, a gradient estimate of the positive solution to equation triangle_pu=-lambda |u|^p-2u was proved under suitable curvature condition, in which lambdageqslant 0 is a constant; the upper bound estimate of lambda was a byproduct; one also showed that this estimate is sharp. This result generalizes the gradient estimate of the positive solution to elliptic equation triangle u=-lambda u.
Let M be an n-dimensional complete noncompact Riemannian manifold with metric g, triangle_p(1pleqslant 2) the p-Laplace operator, by using the classical method of Li-Yau, a gradient estimate of the positive solution to equation triangle_pu=-lambda |u|^p-2u was proved under suitable curvature condition, in which lambdageqslant 0 is a constant; the upper bound estimate of lambda was a byproduct; one also showed that this estimate is sharp. This result generalizes the gradient estimate of the positive solution to elliptic equation triangle u=-lambda u.
2010, (1): 99-102.
Abstract:
Let Abe a mathrm C^*-algebra. If A is Abelian, then each hereditary mathrm C^*-subalgebra (or one-sided closed ideal) of A is a closed ideal in A. Conversely, in terms of the correspondence between the pure state and the maximal left idea, we get that if each hereditary mathrm C^*-subalgebra (or one-sided closed ideal) of A is a closed ideal in A, then A must be Abelian. So in a noncommutative mathrm C^*-algebra, there must exist a hereditarymathrm C^*-subalgebra which is not a closed ideal. Using the main result, we also obtain a simple criterion to check if a given mathrm C^*-algebra A is Abelian, that is, A is Abelian if and only for any two positive elements a, bin A, there is a’in A such that ab=ba’.
Let Abe a mathrm C^*-algebra. If A is Abelian, then each hereditary mathrm C^*-subalgebra (or one-sided closed ideal) of A is a closed ideal in A. Conversely, in terms of the correspondence between the pure state and the maximal left idea, we get that if each hereditary mathrm C^*-subalgebra (or one-sided closed ideal) of A is a closed ideal in A, then A must be Abelian. So in a noncommutative mathrm C^*-algebra, there must exist a hereditarymathrm C^*-subalgebra which is not a closed ideal. Using the main result, we also obtain a simple criterion to check if a given mathrm C^*-algebra A is Abelian, that is, A is Abelian if and only for any two positive elements a, bin A, there is a’in A such that ab=ba’.
2010, (1): 103-107.
Abstract:
In this paper, we discussed a kind of comparison theory introduced by Lin Huaxin. We first used operator theory to discuss hiding information in the original definition and then obtain an equivalent definition of this comparison theory. Also, some useful properties and results are presented. In addition, we gave an interesting property about projections that it does not have and a characterization of simple C*-algebras.
In this paper, we discussed a kind of comparison theory introduced by Lin Huaxin. We first used operator theory to discuss hiding information in the original definition and then obtain an equivalent definition of this comparison theory. Also, some useful properties and results are presented. In addition, we gave an interesting property about projections that it does not have and a characterization of simple C*-algebras.
2010, (1): 108-110.
Abstract:
By weak c-supplement we investigated the possibility that a finite group is in a saturated formation containing all supersoluble groups. It was showed that for a saturated formation mathcalF containing all supersoluble groups, if there exists a group G such that G contins a normal subgroup N and G/N is supersoluble and if maximal subgroups of Sylow subgroups of N are c-supplemented in G, then Gin mathcalF. Some results are extended.
By weak c-supplement we investigated the possibility that a finite group is in a saturated formation containing all supersoluble groups. It was showed that for a saturated formation mathcalF containing all supersoluble groups, if there exists a group G such that G contins a normal subgroup N and G/N is supersoluble and if maximal subgroups of Sylow subgroups of N are c-supplemented in G, then Gin mathcalF. Some results are extended.
2010, (1): 111-117.
Abstract:
Based on an analysis of the characteristics of P2P network and related security issues, this paper proposed a global trust model which has a high resistance to malicious acts and free riders. Specifically, if the malicious nodes or free riders try to reregister into the system to white wash their low credibility and trust, the model can quickly trace and isolate them, showing high white washing resistance. The results of simulation showed that this model can easily isolate malicious behaviors, especially has high resistance to white washing.
Based on an analysis of the characteristics of P2P network and related security issues, this paper proposed a global trust model which has a high resistance to malicious acts and free riders. Specifically, if the malicious nodes or free riders try to reregister into the system to white wash their low credibility and trust, the model can quickly trace and isolate them, showing high white washing resistance. The results of simulation showed that this model can easily isolate malicious behaviors, especially has high resistance to white washing.
2010, (1): 118-126.
Abstract:
A scalable authentication protocol based on bilinear paring was proposed. There are several advantages of the new protocol: (1) By using the bilinear group, the length of public parameter and keys decreases with the same security level, hence we reduce bandwidth needed in communication, thus the protocol is more suitable for the huge internet system. (2) It incorporates a 3-factor authentication mechanism for detecting compromise. (3) The password can be canceled by user’s requirement. (4) The protocol has great efficiency and scalable implement.
A scalable authentication protocol based on bilinear paring was proposed. There are several advantages of the new protocol: (1) By using the bilinear group, the length of public parameter and keys decreases with the same security level, hence we reduce bandwidth needed in communication, thus the protocol is more suitable for the huge internet system. (2) It incorporates a 3-factor authentication mechanism for detecting compromise. (3) The password can be canceled by user’s requirement. (4) The protocol has great efficiency and scalable implement.
2010, (1): 127-134.
Abstract:
A new allocation algorithm based on Ant Colony Optimization (ACO) was established to satisfy the property of cloud computing. When start, this algorithm first prognosticated the capability of the potential available resource nodes, then analyzed some factors such as network qualities or response times to acquire a set of optimal compute resources. This algorithm met the needs of cloud computing more than others for grid environment with shorter response time and better performance, which were proved by the simulation results in the Gridsim environment.
A new allocation algorithm based on Ant Colony Optimization (ACO) was established to satisfy the property of cloud computing. When start, this algorithm first prognosticated the capability of the potential available resource nodes, then analyzed some factors such as network qualities or response times to acquire a set of optimal compute resources. This algorithm met the needs of cloud computing more than others for grid environment with shorter response time and better performance, which were proved by the simulation results in the Gridsim environment.
2010, (1): 135-141.
Abstract:
In order to simplify the computation complexity for traditional single integral equation in electromagnetic scattering from dielectric objects, a new single integral equation was proposed. The numerical results of RCS (radar cross section) obtained from several dielectric objects with large permittivity are in agreement with the exact results. Furthermore, the calculation amount is reduced apparently and the singularity of the integral core is weakened. The validity of the new single integral equation was also discussed.
In order to simplify the computation complexity for traditional single integral equation in electromagnetic scattering from dielectric objects, a new single integral equation was proposed. The numerical results of RCS (radar cross section) obtained from several dielectric objects with large permittivity are in agreement with the exact results. Furthermore, the calculation amount is reduced apparently and the singularity of the integral core is weakened. The validity of the new single integral equation was also discussed.