We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or,...We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.展开更多
Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructio...Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.展开更多
Recently,the field of rural vitalization has received extensive research attention.However,only few studies have proposed an approach to rural vitalization from the coupling perspective of township construction and th...Recently,the field of rural vitalization has received extensive research attention.However,only few studies have proposed an approach to rural vitalization from the coupling perspective of township construction and the resource environment.Taking Jiangsu Province of China as the study area,we constructed index systems of township construction function types and resource environments.Based on 875 township study units in Jiangsu,we characterized the township construction function type and resource environment and analyzed the dynamic process of their coupling from 2005 to 2017.The results are as follows:1)the townships of planting and breeding types in Jiangsu were mainly distributed in northern and central Jiangsu;the townships of business travel,industry,and integrated types were mainly distributed in southern Jiangsu;and the townships of ecological type were irregularly distributed throughout Jiangsu.2)Resource environment factors and township construction function types in Jiangsu clustered based on their location with some overlap.3)Spatial variability in the degree of coupling level between township construction and the resource environment in Jiangsu was not apparent,and low coupling levels accounted for most of the study units.The sum of the number of medium and high coupling townships in southern,central,and northern Jiangsu was roughly equal,and the coupling level between township construction and the resource environment in southern Jiangsu evolved remained unchanged,whereas that in the central and northern Jiangsu became imbalanced.4)In Jiangsu,township construction was mainly constrained by water resources,and the constraint parameters gradually increase.Large variability in resource environment constraint was observed in northern,central,and southern Jiangsu for different township construction function types.Based on these findings,we proposed the implementation of targeted rural vitalization strategies.展开更多
文摘We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.
文摘Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.
基金Under the auspices of National Key R&D Program of China(No.2018YFD1100100)。
文摘Recently,the field of rural vitalization has received extensive research attention.However,only few studies have proposed an approach to rural vitalization from the coupling perspective of township construction and the resource environment.Taking Jiangsu Province of China as the study area,we constructed index systems of township construction function types and resource environments.Based on 875 township study units in Jiangsu,we characterized the township construction function type and resource environment and analyzed the dynamic process of their coupling from 2005 to 2017.The results are as follows:1)the townships of planting and breeding types in Jiangsu were mainly distributed in northern and central Jiangsu;the townships of business travel,industry,and integrated types were mainly distributed in southern Jiangsu;and the townships of ecological type were irregularly distributed throughout Jiangsu.2)Resource environment factors and township construction function types in Jiangsu clustered based on their location with some overlap.3)Spatial variability in the degree of coupling level between township construction and the resource environment in Jiangsu was not apparent,and low coupling levels accounted for most of the study units.The sum of the number of medium and high coupling townships in southern,central,and northern Jiangsu was roughly equal,and the coupling level between township construction and the resource environment in southern Jiangsu evolved remained unchanged,whereas that in the central and northern Jiangsu became imbalanced.4)In Jiangsu,township construction was mainly constrained by water resources,and the constraint parameters gradually increase.Large variability in resource environment constraint was observed in northern,central,and southern Jiangsu for different township construction function types.Based on these findings,we proposed the implementation of targeted rural vitalization strategies.
