In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.
In accordance with the terms global minerogenic series, regional metallogenic series and ore depositsystem which are put forward here, metallogenic environments at different levels are discussed for theporphyry copper...In accordance with the terms global minerogenic series, regional metallogenic series and ore depositsystem which are put forward here, metallogenic environments at different levels are discussed for theporphyry copper deposit series in China. It is considered that the porphyry copper deposits in China arecontrolled not only by the boundaries of convergent plates but, more importantly, by the boundaries ofintraplate divergent mobile belts and those between continental blocks. Besides, the emplacement ofhypabyssal and supper-hypabyssal calc-alkaline magmas and the temporal-spatial distribution of China'sporphyry copper deposits are governed by the superimposition of fracture systems of the pre-Alpine base-ments. Meso-Cenozoic cover and continental-margin new-born crust. Such a superimposition has also re-sulted in the polycyclicity of the mineralization.展开更多
A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..
In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition (OSC). As applications, we discuss a self-simila...In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition (OSC). As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.展开更多
In this paper, we introduce the concept of (4/3)? bandwidth interval based forecasting. The historical enrollments of the university of Alabama are used to illustrate the proposed method. In this paper we use the new ...In this paper, we introduce the concept of (4/3)? bandwidth interval based forecasting. The historical enrollments of the university of Alabama are used to illustrate the proposed method. In this paper we use the new simplified technique to find the fuzzy logical relations.展开更多
The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} ...The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.展开更多
We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statist...We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours.展开更多
Many forecasting models based on the concepts of Fuzzy time series have been proposed in the past decades. These models have been widely applied to various problem domains, especially in dealing with forecasting probl...Many forecasting models based on the concepts of Fuzzy time series have been proposed in the past decades. These models have been widely applied to various problem domains, especially in dealing with forecasting problems in which historical data are linguistic values. In this paper, we present a new fuzzy time series forecasting model, which uses the historical data as the universe of discourse and uses the K-means clustering algorithm to cluster the universe of discourse, then adjust the clusters into intervals. The proposed method is applied for forecasting University enrollment of Alabama. It is shown that the proposed model achieves a significant improvement in forecasting accuracy as compared to other fuzzy time series forecasting models.展开更多
In order to effectively analyse the multivariate time series data of complex process,a generic reconstruction technology based on reduction theory of rough sets was proposed,Firstly,the phase space of multivariate tim...In order to effectively analyse the multivariate time series data of complex process,a generic reconstruction technology based on reduction theory of rough sets was proposed,Firstly,the phase space of multivariate time series was originally reconstructed by a classical reconstruction technology.Then,the original decision-table of rough set theory was set up according to the embedding dimensions and time-delays of the original reconstruction phase space,and the rough set reduction was used to delete the redundant dimensions and irrelevant variables and to reconstruct the generic phase space,Finally,the input vectors for the prediction of multivariate time series were extracted according to generic reconstruction results to identify the parameters of prediction model.Verification results show that the developed reconstruction method leads to better generalization ability for the prediction model and it is feasible and worthwhile for application.展开更多
To enhance the accuracy of intuitionistic fuzzy time series forecasting model, this paper analyses the influence of universe of discourse partition and compares with relevant literature. Traditional models usually par...To enhance the accuracy of intuitionistic fuzzy time series forecasting model, this paper analyses the influence of universe of discourse partition and compares with relevant literature. Traditional models usually partition the global universe of discourse, which is not appropriate for all objectives. For example, the universe of the secular trend model is continuously variational. In addition, most forecasting methods rely on prior information, i.e., fuzzy relationship groups (FRG). Numerous relationship groups lead to the explosive growth of relationship library in a linear model and increase the computational complexity. To overcome problems above and ascertain an appropriate order, an intuitionistic fuzzy time series forecasting model based on order decision and adaptive partition algorithm is proposed. By forecasting the vector operator matrix, the proposed model can adjust partitions and intervals adaptively. The proposed model is tested on student enrollments of Alabama dataset, typical seasonal dataset Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and a secular trend dataset of total retail sales for social consumer goods in China. Experimental results illustrate the validity and applicability of the proposed method for different patterns of dataset.展开更多
In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.
Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi(x) =λix + bi, i = 1,2, 3, x =(x1, x2), b1=(0, 0), b3=(1-λ3 /2,√3...Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi(x) =λix + bi, i = 1,2, 3, x =(x1, x2), b1=(0, 0), b3=(1-λ3 /2,√3/2 (1-λ3)) This paper determines the exact Hausdorff measure, centred covering measure and packing measure of S under some conditions relating to the contraction parameter.展开更多
We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s(E∩B(x,r))≤(2r)^sfor all x ∈ E and r〉 0, where Cs ...We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s(E∩B(x,r))≤(2r)^sfor all x ∈ E and r〉 0, where Cs denotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure.展开更多
In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same p...In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some weU-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket, the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.展开更多
In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets a...In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.展开更多
In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite (p.c.f.) self-similar sets.
In this paper, we present a more simple and much shorter proof for the main result in the paper " An negative answer to a conjecture on the self-similar sets satisfy- ing the open set condition", which was published...In this paper, we present a more simple and much shorter proof for the main result in the paper " An negative answer to a conjecture on the self-similar sets satisfy- ing the open set condition", which was published in the journal Analysis in Theory and Applications in 2009.展开更多
文摘In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.
文摘In accordance with the terms global minerogenic series, regional metallogenic series and ore depositsystem which are put forward here, metallogenic environments at different levels are discussed for theporphyry copper deposit series in China. It is considered that the porphyry copper deposits in China arecontrolled not only by the boundaries of convergent plates but, more importantly, by the boundaries ofintraplate divergent mobile belts and those between continental blocks. Besides, the emplacement ofhypabyssal and supper-hypabyssal calc-alkaline magmas and the temporal-spatial distribution of China'sporphyry copper deposits are governed by the superimposition of fracture systems of the pre-Alpine base-ments. Meso-Cenozoic cover and continental-margin new-born crust. Such a superimposition has also re-sulted in the polycyclicity of the mineralization.
基金Supported in part by the Foundations of the National Natural Science Committee(No.10572154)Jiangxi Province Natural Science Committee(No.0611005)the Foundation of Education Ministry, Jiangxi Province(No.[2006]239), China
文摘A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..
基金Supported in part by Education Ministry, Anhui province, China (No. KJ2008A028)
文摘In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition (OSC). As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.
文摘In this paper, we introduce the concept of (4/3)? bandwidth interval based forecasting. The historical enrollments of the university of Alabama are used to illustrate the proposed method. In this paper we use the new simplified technique to find the fuzzy logical relations.
基金Supported by NNSF of China and the Foundation of Wuhan University
文摘The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.
基金the National Natural Science Foundation of China
文摘We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours.
文摘Many forecasting models based on the concepts of Fuzzy time series have been proposed in the past decades. These models have been widely applied to various problem domains, especially in dealing with forecasting problems in which historical data are linguistic values. In this paper, we present a new fuzzy time series forecasting model, which uses the historical data as the universe of discourse and uses the K-means clustering algorithm to cluster the universe of discourse, then adjust the clusters into intervals. The proposed method is applied for forecasting University enrollment of Alabama. It is shown that the proposed model achieves a significant improvement in forecasting accuracy as compared to other fuzzy time series forecasting models.
基金Project(61025015) supported by the National Natural Science Funds for Distinguished Young Scholars of ChinaProject(21106036) supported by the National Natural Science Foundation of China+2 种基金Project(200805331103) supported by Research Fund for the Doctoral Program of Higher Education of ChinaProject(NCET-08-0576) supported by Program for New Century Excellent Talents in Universities of ChinaProject(11B038) supported by Scientific Research Fund for the Excellent Youth Scholars of Hunan Provincial Education Department,China
文摘In order to effectively analyse the multivariate time series data of complex process,a generic reconstruction technology based on reduction theory of rough sets was proposed,Firstly,the phase space of multivariate time series was originally reconstructed by a classical reconstruction technology.Then,the original decision-table of rough set theory was set up according to the embedding dimensions and time-delays of the original reconstruction phase space,and the rough set reduction was used to delete the redundant dimensions and irrelevant variables and to reconstruct the generic phase space,Finally,the input vectors for the prediction of multivariate time series were extracted according to generic reconstruction results to identify the parameters of prediction model.Verification results show that the developed reconstruction method leads to better generalization ability for the prediction model and it is feasible and worthwhile for application.
基金supported by the National Natural Science Foundation of China(61309022)
文摘To enhance the accuracy of intuitionistic fuzzy time series forecasting model, this paper analyses the influence of universe of discourse partition and compares with relevant literature. Traditional models usually partition the global universe of discourse, which is not appropriate for all objectives. For example, the universe of the secular trend model is continuously variational. In addition, most forecasting methods rely on prior information, i.e., fuzzy relationship groups (FRG). Numerous relationship groups lead to the explosive growth of relationship library in a linear model and increase the computational complexity. To overcome problems above and ascertain an appropriate order, an intuitionistic fuzzy time series forecasting model based on order decision and adaptive partition algorithm is proposed. By forecasting the vector operator matrix, the proposed model can adjust partitions and intervals adaptively. The proposed model is tested on student enrollments of Alabama dataset, typical seasonal dataset Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and a secular trend dataset of total retail sales for social consumer goods in China. Experimental results illustrate the validity and applicability of the proposed method for different patterns of dataset.
文摘In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.
基金the Foundation of National Natural Science Committee of Chinathe Foundation of the Natural Science of Guangdong Provincethe Foundation of the Advanced Research Center of zhongshan University
文摘Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi(x) =λix + bi, i = 1,2, 3, x =(x1, x2), b1=(0, 0), b3=(1-λ3 /2,√3/2 (1-λ3)) This paper determines the exact Hausdorff measure, centred covering measure and packing measure of S under some conditions relating to the contraction parameter.
基金supported by the National Natural Science Foundation of China (No. 11371379)
文摘We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s(E∩B(x,r))≤(2r)^sfor all x ∈ E and r〉 0, where Cs denotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure.
基金supported by the grants NSFC11201232, 12KJB110008Qing Lan Project, 13KJB110015, 12YJAZH096the Project-sponsored by SRF for ROCS, SEM
文摘In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some weU-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket, the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.
基金partially supported by the foundation of the research item of Strong Department of Engineering Innovation, which is sponsored by the Strong School of Engineering Innovation of Hanshan Normal University, China, 2013partially supported by National Natural Science Foundation of China (No. 11371379)
文摘In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.
基金supported by the National Natural Science Foundation of China(No.11201232)Qing Lan Project of Jiangsu Province
文摘In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite (p.c.f.) self-similar sets.
基金Supported in part by National Natural Science Foundation of China (No.10961003)
文摘In this paper, we present a more simple and much shorter proof for the main result in the paper " An negative answer to a conjecture on the self-similar sets satisfy- ing the open set condition", which was published in the journal Analysis in Theory and Applications in 2009.