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25 September 2007, Volume 2007 Issue 5 Previous Issue    Next Issue

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Some Remarks on the Weighted Entropy(English) WANG Lin-feng; 2007, 2007 (5):  1-11.  Abstract ( 3368 )   PDF (188KB) ( 362 )   Save This paper gave the monotonicity of weighted entropy, studied the short time behavior of the weighted heat kernel, showed the entropy can be regarded as an isoperimetric constant, and used it to discuss some geometric properties of the manifold. Related Articles | Metrics

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Criterion for Elliptic Curves with the Lowest 3-Power in L(1)(Chinese) SUN Nai-zhe 2007, 2007 (5):  12-19.  Abstract ( 3130 )   PDF (265KB) ( 442 )   Save 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. Related Articles | Metrics

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Positive Solutions for an nth-Order Delay Differential Equation(English) LU Qiu-ying;ZHU De-ming 2007, 2007 (5):  20-33.  Abstract ( 3040 )   PDF (218KB) ( 456 )   Save 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. Related Articles | Metrics

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Oscillation Theorems for Certain Second-Order Nonlinear Matrix Differential Equations(English) XU Yan-cong;MENG Fan-wei 2007, 2007 (5):  34-38.  Abstract ( 3599 )   PDF (174KB) ( 407 )   Save 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. Related Articles | Metrics

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onditionally Stable Dirichlet Problem for Nonlinear Singulary Perturbed Systems(Chinese) WANG Ai-feng;WANG Xun-yang;NI Ming-kang 2007, 2007 (5):  39-46.  Abstract ( 3018 )   PDF (306KB) ( 348 )   Save 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. Related Articles | Metrics

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Parallel Computation of the Moore-Penrose Inverse of a Bidiagonal Matrix(English) FANG Mao-zhong 2007, 2007 (5):  47-53.  Abstract ( 3072 )   PDF (165KB) ( 363 )   Save 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. Related Articles | Metrics

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3×3 Matrix Spectral Problem and Its Darboux Transformation(Chinese) ZHOU Zhen-chuan;ZHOU Zhen-jiang; 2007, 2007 (5):  54-61.  Abstract ( 2948 )   PDF (316KB) ( 392 )   Save 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. Related Articles | Metrics

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Image Restoration Combining the Total Variation Minimization and a SecondOrder Functional(English) LI Fang 2007, 2007 (5):  62-69.  Abstract ( 3051 )   PDF (772KB) ( 505 )   Save 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 secondorder 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. Related Articles | Metrics

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Intrinsic Image Segmentation on a Riemannian Manifold(Chinese) FAN Jin-song;PI Ling;LI Fang;SHEN Chao-min 2007, 2007 (5):  70-77.  Abstract ( 3510 )   PDF (654KB) ( 364 )   Save 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. Related Articles | Metrics

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Second and Third Largest Spectral Radii of 2-Trees with n Vertices(English) YU Hai-xin;;YUAN Jin-song;HONG Yuan;Shu Jin-long 2007, 2007 (5):  78-84.  Abstract ( 3281 )   PDF (526KB) ( 530 )   Save 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. Related Articles | Metrics

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On the 3-Colorable Planar Graph(Chinese) ZHANG Xue-yuan;CHEN Cang;MIAO Lian-ying 2007, 2007 (5):  85-88.  Abstract ( 3579 )   PDF (185KB) ( 590 )   Save By using the discharging method, it was proved that every planar graph is 3-colorable, provided that it has not any 4-, 5-cycles, and the distance between any two triangles is at least 2. Related Articles | Metrics

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Newly Designed Option and Its Application in Risk Management(Chinese) XIA Xiao-hui;ZHOU Bin 2007, 2007 (5):  89-91.  Abstract ( 2730 )   PDF (146KB) ( 511 )   Save Related Articles | Metrics

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Selection of Top Quality Portfolio under H-Value Rule(Chinese) LIANG Yi-kong;CHAI Jun 2007, 2007 (5):  92-97.  Abstract ( 2711 )   PDF (265KB) ( 468 )   Save 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 shortsailing 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.  Related Articles | Metrics

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Decentralized Adaptive Control for Uncertain Large-Scale Systems with Time-Varying Delays in the Interconnections(English) XU Jian-qiang;;CHEN Shu-zhong 2007, 2007 (5):  98-106.  Abstract ( 3063 )   PDF (254KB) ( 407 )   Save 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. Related Articles | Metrics

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Domain OntologyBased Document Automatic Summarization(Chinese) WANG Qi;JIANG Kai-zhong;YANG Jing;GU Jun-zhong 2007, 2007 (5):  107-112.  Abstract ( 3569 )   PDF (417KB) ( 1535 )   Save 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 keysentences were used, which are proved to improve the quality of automatic summarization arithmetic by experiment. Related Articles | Metrics

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NLMSBased AEDA Algorithm for Sound Source Localization(Chinese) LU Jing-yan;ZHU Shou-zheng 2007, 2007 (5):  113-117.  Abstract ( 3128 )   PDF (390KB) ( 306 )   Save To speed conventional Adaptive Eigenvalue Deposition Algorithm (AEDA), an NLMSbased optimized AEDA algorithm was proposed.It gives better performance for convergence,which makes it possible for realtime applications.Experimental results showed that this method can work well in sound source localization. Related Articles | Metrics

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Dynamic Characterization of an Innovative RF MEMS Switch(Chinese) ZHANG Yong-hua;LIU Lei;DING Gui-fu; CAI Bing-chu;LAI Zong-sheng 2007, 2007 (5):  118-122.  Abstract ( 2966 )   PDF (333KB) ( 457 )   Save Due to the use of permanent magnet in structure,a bistable electromagnetic radio frequency microelectromechanical systems (RF MEMS) switch based on UVLIGA 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. Related Articles | Metrics

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Enhancement of Giant MagnetoImpedance Effect Using LC Resonance(Chinese) WU Zhiming;ZHAO Zhen-jie;LIU Long-ping;YANG Xie-long 2007, 2007 (5):  123-127.  Abstract ( 3353 )   PDF (239KB) ( 449 )   Save In this study, resonance enhancement of Giant MagnetoImpedance effect in Febased glasscoated microwires was investigated. A new method was adopted by sputtering a copper layer in the outside of the Febased glasscoated 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. Related Articles | Metrics

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Scalar Field Perturbation and PhaseTransition of Black Holes (English) LU Ji-zong;JIANG Yuan-fang 2007, 2007 (5):  128-133.  Abstract ( 2997 )   PDF (236KB) ( 416 )   Save 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 nonrotating BTZ black hole background. This special property reflects that the massless BTZ black hole is a different phase from that of the generic nonrotating BTZ hole.  Related Articles | Metrics

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Preparation and Surface Study of Titanium Dioxide Films with Different Crystalline Structures (Chinese) HU Shi-qiong;WANG Xiang-hui;LIU En-qing;SHI Qin;YU Wen-juan 2007, 2007 (5):  134-140.  Abstract ( 3085 )   PDF (404KB) ( 381 )   Save Titanium dioxide (TiO2) films with different crystalline structures were prepared via solgel dip coating method. The influences of humidity, substrate and catalyst acid on the film quality such as integrality and crystallization were investigated. Pure anatasetyped and rutiletyped TiO2 films with homogeneous and compact nanostructure were prepared under the optimized conditions. The surface characters of both types of TiO2 films were studied by surface energy test and infrared spectrum analysis. The results showed that bothtyped films are able to capture OH radicle, but anatasetyped TiO2 film shows a stronger capability, which leads to a higher surface energy and better hydrophilicity. Related Articles | Metrics