A novel class of periodically changing features hidden in radar pulse sequence environment,named G features,is proposed.Combining fractal theory and Hilbert-Huang transform,the features are extracted using changing ch...A novel class of periodically changing features hidden in radar pulse sequence environment,named G features,is proposed.Combining fractal theory and Hilbert-Huang transform,the features are extracted using changing characteristics of pulse parameters in radar emitter signals.The features can be applied in modern complex electronic warfare environment to address the issue of signal sorting when radar emitter pulse signal parameters severely or even completely overlap.Experiment results show that the proposed feature class and feature extraction method can discriminate periodically changing pulse sequence signal sorting features from radar pulse signal flow with complex variant features,therefore provide a new methodology for signal sorting.展开更多
The sandwich structure of cushioning packaging has an important influence on the cushioning performance.Mathematical fractal theory is an important graphic expression.Based on Hilbert fractal theory,a new sandwich str...The sandwich structure of cushioning packaging has an important influence on the cushioning performance.Mathematical fractal theory is an important graphic expression.Based on Hilbert fractal theory,a new sandwich structure was designed.The generation mechanism and recurrence formula of theHilbert fractal were expressed by Lin’s language,and the second-orderHilbert sandwich structure was constructed fromthermoplastic polyurethane.The constitutive model of the hyperelastic body was established by using the finite element method.With the unit mass energy absorption as the optimization goal,the fractal sandwich structure was optimized,and the best result was obtained when the order was 2.5 and the unit layer thickness was 0.75 mm.TheHilbert sandwich structure was compared with the rice-shaped sandwich structure commonly used in industry,and the Hilbert fractal structure had better energy absorption.This has practical significance for the development and application of newcushioning packaging structures.展开更多
A Hilbert transform for H61der continuous circulant （2 × 2） matrix functions, on the d- summable （or fractal） boundary F of a Jordan domain Ω in R2n, has recently been introduced within the framework of Herm...A Hilbert transform for H61der continuous circulant （2 × 2） matrix functions, on the d- summable （or fractal） boundary F of a Jordan domain Ω in R2n, has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the HSlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the HSlder exponents, the diameter of F and a specific d-sum （d 〉 d） of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.展开更多
基金supported by the National Natural Science Foundation of China (60872108)the Postdoctoral Science Foundation of China(200902411+3 种基金20080430903)Heilongjiang Postdoctoral Financial Assistance (LBH-Z08129)the Scientific and Technological Creative Talents Special Research Foundation of Harbin Municipality (2008RFQXG030)Central University Basic Research Professional Expenses Special Fund Project
文摘A novel class of periodically changing features hidden in radar pulse sequence environment,named G features,is proposed.Combining fractal theory and Hilbert-Huang transform,the features are extracted using changing characteristics of pulse parameters in radar emitter signals.The features can be applied in modern complex electronic warfare environment to address the issue of signal sorting when radar emitter pulse signal parameters severely or even completely overlap.Experiment results show that the proposed feature class and feature extraction method can discriminate periodically changing pulse sequence signal sorting features from radar pulse signal flow with complex variant features,therefore provide a new methodology for signal sorting.
基金supported by the Natural Science Foundation of Tianjin Munici-pality[21YDTPJC00480]the Science and Technology Project of Tianjin[20YDTPJC00830].
文摘The sandwich structure of cushioning packaging has an important influence on the cushioning performance.Mathematical fractal theory is an important graphic expression.Based on Hilbert fractal theory,a new sandwich structure was designed.The generation mechanism and recurrence formula of theHilbert fractal were expressed by Lin’s language,and the second-orderHilbert sandwich structure was constructed fromthermoplastic polyurethane.The constitutive model of the hyperelastic body was established by using the finite element method.With the unit mass energy absorption as the optimization goal,the fractal sandwich structure was optimized,and the best result was obtained when the order was 2.5 and the unit layer thickness was 0.75 mm.TheHilbert sandwich structure was compared with the rice-shaped sandwich structure commonly used in industry,and the Hilbert fractal structure had better energy absorption.This has practical significance for the development and application of newcushioning packaging structures.
文摘A Hilbert transform for H61der continuous circulant （2 × 2） matrix functions, on the d- summable （or fractal） boundary F of a Jordan domain Ω in R2n, has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the HSlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the HSlder exponents, the diameter of F and a specific d-sum （d 〉 d） of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.
