In this paper, we study the fractal properties of the hyperbolic curve introduced by J. Belair ([Be]). We obtain some conditions of nowhere-differentiability of this kind of curves and its Bouligand dimension, and fin...In this paper, we study the fractal properties of the hyperbolic curve introduced by J. Belair ([Be]). We obtain some conditions of nowhere-differentiability of this kind of curves and its Bouligand dimension, and find a class of curves which are almost everywhere differertiable and have Bouligand dimensions being greater than one simultaneously.展开更多
In this paper, by using fractal curves, a family of fractal surfaces are defined. Each fractal surface of this family is called Star Product Fractal Surface (SPFS). A theorem of the dimensions of the SPFS is strictly ...In this paper, by using fractal curves, a family of fractal surfaces are defined. Each fractal surface of this family is called Star Product Fractal Surface (SPFS). A theorem of the dimensions of the SPFS is strictly proved. The relationship between the dimensions of the SPFS and the dimensions of the fractal curves constructing the SPFS is obtained.展开更多
A flexible or planar eddy current probe with a differential structure can suppress the lift-off noise during the inspection of defects.However,the extent of the lift-off effect on differential probes,including differe...A flexible or planar eddy current probe with a differential structure can suppress the lift-off noise during the inspection of defects.However,the extent of the lift-off effect on differential probes,including different coil structures,varies.In this study,two planar eddy current probes with differential pickup structures and the same size,Koch and circular probes,were used to compare lift-off effects.The eddy current distributions of the probes perturbed by 0°and 90°cracks were obtained by finite element analysis.The analysis results show that the 90°crack can impede the eddy current induced by the Koch probe even further at relatively low lift-off distance.The peak-to-peak values of the signal output from the two probes were compared at different lift-off distances using finite element analysis and experimental methods.In addition,the effects of different frequencies on the lift-off were studied experimentally.The results show that the signal peak-to-peak value of the Koch probe for the inspection of cracks in 90°orientation is larger than that of the circular probe when the lift-off distance is smaller than 1.2 mm.In addition,the influence of the lift-off distance on the peak-to-peak signal value of the two probes was studied via normalization.This indicates that the influence becomes more evident with an increase in excitation frequency.This research discloses the lift-off effect of differential planar eddy current probes with different coil shapes and proves the detection merit of the Koch probe for 90°cracks at low lift-off distances.展开更多
A novel approach of printed circuit board(PCB)image locating is presented Based on the rectangle mark image edge of PCB,the featur es is used to describe the image edge and the fractal properby of image edge is anal...A novel approach of printed circuit board(PCB)image locating is presented Based on the rectangle mark image edge of PCB,the featur es is used to describe the image edge and the fractal properby of image edge is analyzed It is proved that the rectangle mark image edge of PCB has some fractal features A method of deleting unordinary curve noise and compensating the length of the fractal curve is put forward,which can get the fractal dimension value from one complex edge fractal property curve The relation between the dim ension of the fractal curve and the turning angle of image can be acquired from an equation,as a result,the angle value of the PCB image is got exactly A real image edge analysis result confirms that the method based on the fractal theory is a new powerful tool for angle locating on PCB and related image area.展开更多
Assuming that plasma particles are moving on continuous and non-differentiable curves, some dynamic properties in plasma ablation are analyzed via scale-relativity theory: the splitting of plasma plume, multi-peak str...Assuming that plasma particles are moving on continuous and non-differentiable curves, some dynamic properties in plasma ablation are analyzed via scale-relativity theory: the splitting of plasma plume, multi-peak structures, at various distances from the target surface and plasma oscillations through self-similarity. Our theoretical results are in good agreement with the experimental ones.展开更多
A novel asymmetrical Pi-shaped defected ground structure （DGS） with 3-interations Koch fractal curves is proposed to design a microstrip low-pass filter （LPF） with uhra-wide stop-band （SB）. The proposed LPFs wit...A novel asymmetrical Pi-shaped defected ground structure （DGS） with 3-interations Koch fractal curves is proposed to design a microstrip low-pass filter （LPF） with uhra-wide stop-band （SB）. The proposed LPFs with a single resonator and two cascaded resonators are both designed, simulated, manufactured and measured. Simulation and experiment results demonstrate that the designed LPF has a very sharp transition band （TB） and an ultra-wide SB performance compared with the existed similar symmetrical and asymmetrical DGS. The proposed LPF with two cascaded resonators is with a compact size of 36. 8 mm x 24.0 mm, a very low insertion loss of less than 0.7 dB under 1.9 GHz, and a wide SB from 2.2 GHz to 8 GHz with rejection of larger than 30 dB.展开更多
文摘In this paper, we study the fractal properties of the hyperbolic curve introduced by J. Belair ([Be]). We obtain some conditions of nowhere-differentiability of this kind of curves and its Bouligand dimension, and find a class of curves which are almost everywhere differertiable and have Bouligand dimensions being greater than one simultaneously.
文摘In this paper, by using fractal curves, a family of fractal surfaces are defined. Each fractal surface of this family is called Star Product Fractal Surface (SPFS). A theorem of the dimensions of the SPFS is strictly proved. The relationship between the dimensions of the SPFS and the dimensions of the fractal curves constructing the SPFS is obtained.
基金Supported by Gansu Provincial Natural Science Foundation of China(Grant No.22JR5RA229)National Natural Science Foundation of China(Grant Nos.51807086,12162021)Hongliu Youth Found of Lanzhou University of Technology and Gansu Provincial Outstanding Graduate Student Innovation Star of China(Grant No.2021CXZX-453).
文摘A flexible or planar eddy current probe with a differential structure can suppress the lift-off noise during the inspection of defects.However,the extent of the lift-off effect on differential probes,including different coil structures,varies.In this study,two planar eddy current probes with differential pickup structures and the same size,Koch and circular probes,were used to compare lift-off effects.The eddy current distributions of the probes perturbed by 0°and 90°cracks were obtained by finite element analysis.The analysis results show that the 90°crack can impede the eddy current induced by the Koch probe even further at relatively low lift-off distance.The peak-to-peak values of the signal output from the two probes were compared at different lift-off distances using finite element analysis and experimental methods.In addition,the effects of different frequencies on the lift-off were studied experimentally.The results show that the signal peak-to-peak value of the Koch probe for the inspection of cracks in 90°orientation is larger than that of the circular probe when the lift-off distance is smaller than 1.2 mm.In addition,the influence of the lift-off distance on the peak-to-peak signal value of the two probes was studied via normalization.This indicates that the influence becomes more evident with an increase in excitation frequency.This research discloses the lift-off effect of differential planar eddy current probes with different coil shapes and proves the detection merit of the Koch probe for 90°cracks at low lift-off distances.
文摘A novel approach of printed circuit board(PCB)image locating is presented Based on the rectangle mark image edge of PCB,the featur es is used to describe the image edge and the fractal properby of image edge is analyzed It is proved that the rectangle mark image edge of PCB has some fractal features A method of deleting unordinary curve noise and compensating the length of the fractal curve is put forward,which can get the fractal dimension value from one complex edge fractal property curve The relation between the dim ension of the fractal curve and the turning angle of image can be acquired from an equation,as a result,the angle value of the PCB image is got exactly A real image edge analysis result confirms that the method based on the fractal theory is a new powerful tool for angle locating on PCB and related image area.
基金support of Posdru Cuantumdoc“Doctoral Studies for European Performances in Research and Inovation”ID79407 project funded by the European Social Found and Romanian Government.
文摘Assuming that plasma particles are moving on continuous and non-differentiable curves, some dynamic properties in plasma ablation are analyzed via scale-relativity theory: the splitting of plasma plume, multi-peak structures, at various distances from the target surface and plasma oscillations through self-similarity. Our theoretical results are in good agreement with the experimental ones.
基金supported by the National Natural Science Foundation of China (21656001)
文摘A novel asymmetrical Pi-shaped defected ground structure （DGS） with 3-interations Koch fractal curves is proposed to design a microstrip low-pass filter （LPF） with uhra-wide stop-band （SB）. The proposed LPFs with a single resonator and two cascaded resonators are both designed, simulated, manufactured and measured. Simulation and experiment results demonstrate that the designed LPF has a very sharp transition band （TB） and an ultra-wide SB performance compared with the existed similar symmetrical and asymmetrical DGS. The proposed LPF with two cascaded resonators is with a compact size of 36. 8 mm x 24.0 mm, a very low insertion loss of less than 0.7 dB under 1.9 GHz, and a wide SB from 2.2 GHz to 8 GHz with rejection of larger than 30 dB.
