2007 No. 5
Display Method:
2007, (5): 1-11.
Abstract(
PDF 188KB
Abstract:
This paper gave the monotonicity of weighted entropy,studied the short time behavior of the weighted heat kernel, showedthe entropy can be regarded as an isoperimetric constant,and used it to discuss some geometric properties of the manifold.
This paper gave the monotonicity of weighted entropy,studied the short time behavior of the weighted heat kernel, showedthe entropy can be regarded as an isoperimetric constant,and used it to discuss some geometric properties of the manifold.
2007, (5): 12-19.
Abstract:
Let K be the 3rd cyclotomic field, E D[lambda] :y2=x3-24 3 3 D[lambda]] be an elliptic curve defined over K, where D\in K is a square-free algebraic integer and [[lambda]] in Z . Qiu Derong found a rather complicated function as the criterion for the value of the Hecke L-function attached to the curve E D[lambda]([lambda]=2,4) at s=1 divided by the period [OMEGA] to be exactly divisible by 3 n/2 -1 . This paper reduced Qiu’s criterion to a simpler version in terms of weighted graphs.
Let K be the 3rd cyclotomic field, E D[lambda] :y2=x3-24 3 3 D[lambda]] be an elliptic curve defined over K, where D\in K is a square-free algebraic integer and [[lambda]] in Z . Qiu Derong found a rather complicated function as the criterion for the value of the Hecke L-function attached to the curve E D[lambda]([lambda]=2,4) at s=1 divided by the period [OMEGA] to be exactly divisible by 3 n/2 -1 . This paper reduced Qiu’s criterion to a simpler version in terms of weighted graphs.
2007, (5): 20-33.
Abstract:
This paper dealt with the existence of positive solutions for the nonlinear eigenvalue problem and the superlinear semipositone problem of an $n$th-order delay differential equation. The main results in this paper generalize some of the existing results in the literature. The proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.
This paper dealt with the existence of positive solutions for the nonlinear eigenvalue problem and the superlinear semipositone problem of an $n$th-order delay differential equation. The main results in this paper generalize some of the existing results in the literature. The proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.
2007, (5): 34-38.
Abstract:
Some new oscillation criteria were established for the second order nonlinear matrix differential system $ (a(t)\X’(t))’+b(t)\X’(t)+\Q(t)f(\X(t))= 0,t\geqslant t_ 0 0,$ where $\Q(t),$ $f’(\X(t))$ are $n \times n$ matrices with $f’(\X(t))$ positive definite, and $a(t),$ $b(t)$ are real-valued functions. The criteria were presented in the form of $\lim \sup\lambda_ 1 const $ by using a particular function $\phi(t,s,r)$ defined as $\phi(t,s,r)=(t-s)^ \alpha (s-r)^ \beta $, where $\alpha,\ \beta \frac 1 2 $ are constants and $r \geqslant t_0.$ Our results improve many known oscillation results.
Some new oscillation criteria were established for the second order nonlinear matrix differential system $ (a(t)\X’(t))’+b(t)\X’(t)+\Q(t)f(\X(t))= 0,t\geqslant t_ 0 0,$ where $\Q(t),$ $f’(\X(t))$ are $n \times n$ matrices with $f’(\X(t))$ positive definite, and $a(t),$ $b(t)$ are real-valued functions. The criteria were presented in the form of $\lim \sup\lambda_ 1 const $ by using a particular function $\phi(t,s,r)$ defined as $\phi(t,s,r)=(t-s)^ \alpha (s-r)^ \beta $, where $\alpha,\ \beta \frac 1 2 $ are constants and $r \geqslant t_0.$ Our results improve many known oscillation results.
2007, (5): 39-46.
Abstract:
Using the boundary function method, this paper studied a conditionally stable Dirichlet problem for a kind of nonlinear perturbed systems.The asymptotic solution of the problem was given and proved to be uniformly effective. And the existence and uniqueness of the solution for the systems were proved.
Using the boundary function method, this paper studied a conditionally stable Dirichlet problem for a kind of nonlinear perturbed systems.The asymptotic solution of the problem was given and proved to be uniformly effective. And the existence and uniqueness of the solution for the systems were proved.
2007, (5): 47-53.
Abstract:
This paper dealt with parallel computation of the Moore-Penrose inverse of a bidiagonal matrix. A divide and conquer algorithm was given. A numerical example and a theorem about parallel efficiency were presented.
This paper dealt with parallel computation of the Moore-Penrose inverse of a bidiagonal matrix. A divide and conquer algorithm was given. A numerical example and a theorem about parallel efficiency were presented.
2007, (5): 54-61.
Abstract:
The Lax pair of a 3×3 matrix spectral problem was constructed and the hierarchy corresponding to this Lax pair was also obtained. This hierarchy includes not only KdV and mKdV equations but also high-order NLS equation. Besides, with the help of the gauge transformation of spectral problem, the Darboux transformation of this $3\times3$ matrix spectral problem was deduced and its explicit solutions were given.
The Lax pair of a 3×3 matrix spectral problem was constructed and the hierarchy corresponding to this Lax pair was also obtained. This hierarchy includes not only KdV and mKdV equations but also high-order NLS equation. Besides, with the help of the gauge transformation of spectral problem, the Darboux transformation of this $3\times3$ matrix spectral problem was deduced and its explicit solutions were given.
2007, (5): 62-69.
Abstract:
A new variational model for noise removal was proposed. It combines the total variational (TV) functional with a second order functional,and the corresponding negative gradient flow is a fourth order PDE.The proposed model combines the benefits of the total variation model and the secondorder model,being able to preserve edges while at the same time avoid the staircase effect in smooth regions. Experimental results illustracted advantages of the proposed model.
A new variational model for noise removal was proposed. It combines the total variational (TV) functional with a second order functional,and the corresponding negative gradient flow is a fourth order PDE.The proposed model combines the benefits of the total variation model and the secondorder model,being able to preserve edges while at the same time avoid the staircase effect in smooth regions. Experimental results illustracted advantages of the proposed model.
2007, (5): 70-77.
Abstract:
An image segmentation model based on the view of Riemannian Geometry was proposed. Endowed with a Riemannian metric derived from the gray scale information of a given image, the image space became a Riemannian manifold. On this Riemannian manifold, we evolved a curve by the mean curvature flow using the level set methods. Because the gray scale information had been embedded into the Riemannian manifold, the evolution was intrinsic. Calculations show that the method is an extension of existing models; furthermore, finer controls for the evolution can be achieved. Numerical experiments show the effectivity and some good features of the proposed method.
An image segmentation model based on the view of Riemannian Geometry was proposed. Endowed with a Riemannian metric derived from the gray scale information of a given image, the image space became a Riemannian manifold. On this Riemannian manifold, we evolved a curve by the mean curvature flow using the level set methods. Because the gray scale information had been embedded into the Riemannian manifold, the evolution was intrinsic. Calculations show that the method is an extension of existing models; furthermore, finer controls for the evolution can be achieved. Numerical experiments show the effectivity and some good features of the proposed method.
2007, (5): 78-84.
Abstract:
By using the concept of Perron vector, this paper characterized the extremal graphs of all 2-trees with $n$ vertices ($n$ fixed) which have the second and the third largest spectral radius, respectively. Particularly, for $n=6$, five 2-trees with 6 vertices were found whose spectral radii are strictly descent.
By using the concept of Perron vector, this paper characterized the extremal graphs of all 2-trees with $n$ vertices ($n$ fixed) which have the second and the third largest spectral radius, respectively. Particularly, for $n=6$, five 2-trees with 6 vertices were found whose spectral radii are strictly descent.
2007, (5): 85-88.
Abstract:
By using the discharging method, it was proved that everyplanar graph is 3-colorable, provided that it has not any 4-,5-cycles, and the distance between any two triangles is at least 2.
By using the discharging method, it was proved that everyplanar graph is 3-colorable, provided that it has not any 4-,5-cycles, and the distance between any two triangles is at least 2.
2007, (5): 89-91.
Abstract:
2007, (5): 92-97.
Abstract:
This paper studied how to select several top quality stocks from thousands of stocks in the security market to get a better portfolio.Firstly,H-value rule which can evaluate quality of portfolio was given under the condition of permitting shortsailing for the first time. Then,how to select the better portfolio under H-value rule was studied.Secondly,A simplified theorem of H-value was introduced under the market index model. It showed the efficiency of the selection.
This paper studied how to select several top quality stocks from thousands of stocks in the security market to get a better portfolio.Firstly,H-value rule which can evaluate quality of portfolio was given under the condition of permitting shortsailing for the first time. Then,how to select the better portfolio under H-value rule was studied.Secondly,A simplified theorem of H-value was introduced under the market index model. It showed the efficiency of the selection.
2007, (5): 98-106.
Abstract:
The problem of decentralized adaptive control was considered for a class of uncertain large-scale time-varying delays systems in the presence of mismatched and matched uncertainties. The interconnections were assumed to satisfy the match condition and be bounded by a linear function of delayed states with unknown gains. The upper bounds of the matching uncertainties and perturbations were also assumed to be unknown. The adaptation laws were proposed to estimate such unknown bounds, and by making use of the LMI method, a class of decentralized robust adaptive controllers was constructed. Based on the Lyapunov stability theory and Lyapunov-Krasovskii functional, it was shown that the state trajectories of the large-scale systems were uniformly asymptotically to zero. Finally, a numerical example was given to demonstrate the validity of the results.
The problem of decentralized adaptive control was considered for a class of uncertain large-scale time-varying delays systems in the presence of mismatched and matched uncertainties. The interconnections were assumed to satisfy the match condition and be bounded by a linear function of delayed states with unknown gains. The upper bounds of the matching uncertainties and perturbations were also assumed to be unknown. The adaptation laws were proposed to estimate such unknown bounds, and by making use of the LMI method, a class of decentralized robust adaptive controllers was constructed. Based on the Lyapunov stability theory and Lyapunov-Krasovskii functional, it was shown that the state trajectories of the large-scale systems were uniformly asymptotically to zero. Finally, a numerical example was given to demonstrate the validity of the results.
2007, (5): 107-112.
Abstract:
A new arithmetic based on Latent Semantic Analysis Model and domain ontology was proposed to summarize the document. Based on the traditional statistic arithmetic,recognition of document theme and computation of concept similarity were imposed by using domain ontology,which described the main content of documents better. In the guide of document theme and concept similarity, statistical approaches and heuristic rules to extract keysentences were used, which are proved to improve the quality of automatic summarization arithmetic by experiment.
A new arithmetic based on Latent Semantic Analysis Model and domain ontology was proposed to summarize the document. Based on the traditional statistic arithmetic,recognition of document theme and computation of concept similarity were imposed by using domain ontology,which described the main content of documents better. In the guide of document theme and concept similarity, statistical approaches and heuristic rules to extract keysentences were used, which are proved to improve the quality of automatic summarization arithmetic by experiment.
2007, (5): 113-117.
Abstract:
To speed conventional Adaptive Eigenvalue Deposition Algorithm (AEDA), an NLMSbased optimized AEDA algorithm was proposed.It gives better performance for convergence,which makes it possible for realtime applications.Experimental results showed that this method can work well in sound source localization.
To speed conventional Adaptive Eigenvalue Deposition Algorithm (AEDA), an NLMSbased optimized AEDA algorithm was proposed.It gives better performance for convergence,which makes it possible for realtime applications.Experimental results showed that this method can work well in sound source localization.
2007, (5): 118-122.
Abstract:
Due to the use of permanent magnet in structure,a bistable electromagnetic radio frequency microelectromechanical systems (RF MEMS) switch based on UVLIGA technology requires no energy to remain at “on” or “off” state. And the electromagnetic actuation with low power consumption can be achieved.The dynamic characterization of the switch was successfully measured using DMEMS dynamic measurement system attached to wyko NT1 100 optical profiling system supplied by Veeco instruments Co.,Ltd.The results of test showed that the bistable electromagnetic actuation is achieved, and the switching time is less than 20 μs.
Due to the use of permanent magnet in structure,a bistable electromagnetic radio frequency microelectromechanical systems (RF MEMS) switch based on UVLIGA technology requires no energy to remain at “on” or “off” state. And the electromagnetic actuation with low power consumption can be achieved.The dynamic characterization of the switch was successfully measured using DMEMS dynamic measurement system attached to wyko NT1 100 optical profiling system supplied by Veeco instruments Co.,Ltd.The results of test showed that the bistable electromagnetic actuation is achieved, and the switching time is less than 20 μs.
2007, (5): 123-127.
Abstract:
In this study, resonance enhancement of Giant MagnetoImpedance effect in Febased glasscoated microwires was investigated. A new method was adopted by sputtering a copper layer in the outside of the Febased glasscoated wires. A capacitance was formed between the ferromagnetic core and outer copper layer, where the glass insulator works as dielectric layer. Therefore, the composite wire constructs a LC resonance circuit by itself, resulting in an increase of GMI ratio from 250% to 330%. Meanwhile, the influence of resonance frequency on the GMI effect was discussed.
In this study, resonance enhancement of Giant MagnetoImpedance effect in Febased glasscoated microwires was investigated. A new method was adopted by sputtering a copper layer in the outside of the Febased glasscoated wires. A capacitance was formed between the ferromagnetic core and outer copper layer, where the glass insulator works as dielectric layer. Therefore, the composite wire constructs a LC resonance circuit by itself, resulting in an increase of GMI ratio from 250% to 330%. Meanwhile, the influence of resonance frequency on the GMI effect was discussed.
2007, (5): 128-133.
Abstract:
In this paper, the scalar field perturbations in the background of the massless BTZ black holes was discussed. We found that the massless BTZ hole contains only normal modes in the perturbations. This is different from the perturbation results in the generic nonrotating BTZ black hole background. This special property reflects that the massless BTZ black hole is a different phase from that of the generic nonrotating BTZ hole.
In this paper, the scalar field perturbations in the background of the massless BTZ black holes was discussed. We found that the massless BTZ hole contains only normal modes in the perturbations. This is different from the perturbation results in the generic nonrotating BTZ black hole background. This special property reflects that the massless BTZ black hole is a different phase from that of the generic nonrotating BTZ hole.
2007, (5): 134-140.
Abstract:
Titanium dioxide (TiO2) films with different crystalline structures were prepared via solgel dip coating method. The influences of humidity, substrate and catalyst acid on the film quality such as integrality and crystallization were investigated. Pure anatasetyped and rutiletyped TiO2 films with homogeneous and compact nanostructure were prepared under the optimized conditions. The surface characters of both types of TiO2 films were studied by surface energy test and infrared spectrum analysis. The results showed that bothtyped films are able to capture OH radicle, but anatasetyped TiO2 film shows a stronger capability, which leads to a higher surface energy and better hydrophilicity.
Titanium dioxide (TiO2) films with different crystalline structures were prepared via solgel dip coating method. The influences of humidity, substrate and catalyst acid on the film quality such as integrality and crystallization were investigated. Pure anatasetyped and rutiletyped TiO2 films with homogeneous and compact nanostructure were prepared under the optimized conditions. The surface characters of both types of TiO2 films were studied by surface energy test and infrared spectrum analysis. The results showed that bothtyped films are able to capture OH radicle, but anatasetyped TiO2 film shows a stronger capability, which leads to a higher surface energy and better hydrophilicity.