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
Reverse logistics are playing more and more important role with the development of competition and the social responsibility of enterprises.It could be divided into commission acceptance,recycling and returned goods h...Reverse logistics are playing more and more important role with the development of competition and the social responsibility of enterprises.It could be divided into commission acceptance,recycling and returned goods handling.Reverse logistics information system consists of the database establishment,network structure and logic structure design.The collection,storage,processing,transmission and output functions of the reverse logistics information system were discussed in the thesis.Eventually,it established seven modules for the reverse logistics information system including the system management module,oriented module,returning goods processing module,reverse transportation management module,information sharing module,statistical analysis module and cost control module.展开更多
The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;&...The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate survival functions for arbitrary <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2, 3, <span style="font-family:;" "=""><span style="font-family:Verdana;">...<span style="font-family:Verdana;">, given all the univariate marginal survival functions. This universal form of <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2 and the main results for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:;" "=""><span style="font-family:Verdana;"> = 3 and <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the <span style="font-family:Verdana;"><span style="font-family:Verdana;">copula<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.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Course Construction of Customs Practice,China(No.z201308003)
文摘Reverse logistics are playing more and more important role with the development of competition and the social responsibility of enterprises.It could be divided into commission acceptance,recycling and returned goods handling.Reverse logistics information system consists of the database establishment,network structure and logic structure design.The collection,storage,processing,transmission and output functions of the reverse logistics information system were discussed in the thesis.Eventually,it established seven modules for the reverse logistics information system including the system management module,oriented module,returning goods processing module,reverse transportation management module,information sharing module,statistical analysis module and cost control module.
文摘The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate survival functions for arbitrary <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2, 3, <span style="font-family:;" "=""><span style="font-family:Verdana;">...<span style="font-family:Verdana;">, given all the univariate marginal survival functions. This universal form of <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2 and the main results for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:;" "=""><span style="font-family:Verdana;"> = 3 and <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the <span style="font-family:Verdana;"><span style="font-family:Verdana;">copula<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.
