In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension ...In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations.展开更多
In this study,the fractal dimensions of velocity fluctuations and the Reynolds shear stresses propagation for flow around a circular bridge pier are presented.In the study reported herein,the fractal dimension of velo...In this study,the fractal dimensions of velocity fluctuations and the Reynolds shear stresses propagation for flow around a circular bridge pier are presented.In the study reported herein,the fractal dimension of velocity fluctuations（u′,v′,w′） and the Reynolds shear stresses（u′v′ and u′w′） of flow around a bridge pier were computed using a Fractal Interpolation Function（FIF） algorithm.The velocity fluctuations of flow along a horizontal plane above the bed were measured using Acoustic Doppler Velocity meter（ADV）and Particle Image Velocimetry（P1V）.The PIV is a powerful technique which enables us to attain high resolution spatial and temporal information of turbulent flow using instantaneous time snapshots.In this study,PIV was used for detection of high resolution fractal scaling around a bridge pier.The results showed that the fractal dimension of flow fluctuated significantly in the longitudinal and transverse directions in the vicinity of the pier.It was also found that the fractal dimension of velocity fluctuations and shear stresses increased rapidly at vicinity of pier at downstream whereas it remained approximately unchanged far downstream of the pier.The higher value of fractal dimension was found at a distance equal to one times of the pier diameter in the back of the pier.Furthermore,the average fractal dimension for the streamwise and transverse velocity fluctuations decreased from the centreline to the side wall of the flume.Finally,the results from ADV measurement were consistent with the result from PIV,therefore,the ADV enables to detect turbulent characteristics of flow around a circular bridge pier.展开更多
This paper first suggests the use of the Fourier frequency transmission method of two dimensions function （ 2D FFT） to analyze radial rotating errors that occurred in a rotor. Based on this method a magnetic rotor i...This paper first suggests the use of the Fourier frequency transmission method of two dimensions function （ 2D FFT） to analyze radial rotating errors that occurred in a rotor. Based on this method a magnetic rotor is measured. The authors point out that the main cause to affect radial rotating accuracy of the rotating shaft at a high speed is the dynamic imbalance of the shaft itself. Finally the feedforward control scheme is suggested to improve the accuracy of the shaft in an active magnetic bearing （ AMB ） system.展开更多
The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further...The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.展开更多
The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Wei...The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function.展开更多
基金supported by NSFC (11201152)supported by NSFC(11371148)+4 种基金STCSM(13dz2260400)FDPHEC(20120076120001)Fundamental Research Funds for the central Universities,scut(2012zz0073)Fundamental Research Funds for the Central Universities SCUT(D2154240)Guangdong Natural Science Foundation(2014A030313230)
文摘In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations.
文摘In this study,the fractal dimensions of velocity fluctuations and the Reynolds shear stresses propagation for flow around a circular bridge pier are presented.In the study reported herein,the fractal dimension of velocity fluctuations（u′,v′,w′） and the Reynolds shear stresses（u′v′ and u′w′） of flow around a bridge pier were computed using a Fractal Interpolation Function（FIF） algorithm.The velocity fluctuations of flow along a horizontal plane above the bed were measured using Acoustic Doppler Velocity meter（ADV）and Particle Image Velocimetry（P1V）.The PIV is a powerful technique which enables us to attain high resolution spatial and temporal information of turbulent flow using instantaneous time snapshots.In this study,PIV was used for detection of high resolution fractal scaling around a bridge pier.The results showed that the fractal dimension of flow fluctuated significantly in the longitudinal and transverse directions in the vicinity of the pier.It was also found that the fractal dimension of velocity fluctuations and shear stresses increased rapidly at vicinity of pier at downstream whereas it remained approximately unchanged far downstream of the pier.The higher value of fractal dimension was found at a distance equal to one times of the pier diameter in the back of the pier.Furthermore,the average fractal dimension for the streamwise and transverse velocity fluctuations decreased from the centreline to the side wall of the flume.Finally,the results from ADV measurement were consistent with the result from PIV,therefore,the ADV enables to detect turbulent characteristics of flow around a circular bridge pier.
文摘This paper first suggests the use of the Fourier frequency transmission method of two dimensions function （ 2D FFT） to analyze radial rotating errors that occurred in a rotor. Based on this method a magnetic rotor is measured. The authors point out that the main cause to affect radial rotating accuracy of the rotating shaft at a high speed is the dynamic imbalance of the shaft itself. Finally the feedforward control scheme is suggested to improve the accuracy of the shaft in an active magnetic bearing （ AMB ） system.
基金Project supported by the National Natural Science Foundation of China (No.10071088, No.10171098).
文摘The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.
文摘The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function.
