For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind o...For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.展开更多
FMS is a sort of highly automatic machining system, how to ensure partquality is master key to system highly active running. At first, series of machining dimension andprocess capability of flexible manufacturing syst...FMS is a sort of highly automatic machining system, how to ensure partquality is master key to system highly active running. At first, series of machining dimension andprocess capability of flexible manufacturing system(FMS), is analyzed. Result of its, strongself-correlation of data series shows that time series analysis is applicable to data seriesanalyzed. Based on-line modeling and forecasting for data series, principle and method of feedbackcompensation control is proposed. On a foundation of the virtual instrument platform, Labview ofnational instrument (NI), FMS dimension and process capability monitoring system(monitoring system)is developed. In practice, it is proved that part quality and process capability of FMS are greatlyimproved.展开更多
Properties of fractional Brownian motions （fBms） have been investigated by researchers in different fields, e.g. statistics, hydrology, biology, finance, and public transportation, which has helped us better underst...Properties of fractional Brownian motions （fBms） have been investigated by researchers in different fields, e.g. statistics, hydrology, biology, finance, and public transportation, which has helped us better understand many complex time series observed in nature [1-4]. The Hurst exponent H （0 〈 H 〈 1） is the most important parameter characterizing any given time series F（t）, where t represents the time steps, and the fractal dimension D is determined via the relation D = 2 - H.展开更多
Let E be a Moran fractal and Hs(E) denote the s-dimensional Hausdorff measure of E. In this paper, we define a orthonormal and complete system. of functions in the Hilbert space L2(E,Hs) and prove that partial sums of...Let E be a Moran fractal and Hs(E) denote the s-dimensional Hausdorff measure of E. In this paper, we define a orthonormal and complete system. of functions in the Hilbert space L2(E,Hs) and prove that partial sums of the Fourier series,with respect to Φ, of each function f(x)∈L1(E,Hs) converge to f(x) at Hs-a.e. x∈E. Moreover, the Fourier series of f, for f∈Lp(E,Hs), p≥1, converges to f in Lp-norm. When Moran fractals degenerate into self-similar fractals, our results well agree with M. Reyes's results.展开更多
文摘For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.
基金This project is supported by Weaponry Advanced Fund Item of China (No.2000JS38.5.1 OT2001)
文摘FMS is a sort of highly automatic machining system, how to ensure partquality is master key to system highly active running. At first, series of machining dimension andprocess capability of flexible manufacturing system(FMS), is analyzed. Result of its, strongself-correlation of data series shows that time series analysis is applicable to data seriesanalyzed. Based on-line modeling and forecasting for data series, principle and method of feedbackcompensation control is proposed. On a foundation of the virtual instrument platform, Labview ofnational instrument (NI), FMS dimension and process capability monitoring system(monitoring system)is developed. In practice, it is proved that part quality and process capability of FMS are greatlyimproved.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.11173064,11233001,11233008,and U1531131)the Strategic Priority Research Program,the Emergence of Cosmological Structures of the Chinese Academy of Sciences(Grant No.XDB09000000)
文摘Properties of fractional Brownian motions （fBms） have been investigated by researchers in different fields, e.g. statistics, hydrology, biology, finance, and public transportation, which has helped us better understand many complex time series observed in nature [1-4]. The Hurst exponent H （0 〈 H 〈 1） is the most important parameter characterizing any given time series F（t）, where t represents the time steps, and the fractal dimension D is determined via the relation D = 2 - H.
文摘Let E be a Moran fractal and Hs(E) denote the s-dimensional Hausdorff measure of E. In this paper, we define a orthonormal and complete system. of functions in the Hilbert space L2(E,Hs) and prove that partial sums of the Fourier series,with respect to Φ, of each function f(x)∈L1(E,Hs) converge to f(x) at Hs-a.e. x∈E. Moreover, the Fourier series of f, for f∈Lp(E,Hs), p≥1, converges to f in Lp-norm. When Moran fractals degenerate into self-similar fractals, our results well agree with M. Reyes's results.
