Let M({nk}k≥1,{ck}k≥1) be the collection of homogeneous Moran sets determined by {nk}k≥1and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. Then the maximal ...Let M({nk}k≥1,{ck}k≥1) be the collection of homogeneous Moran sets determined by {nk}k≥1and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. Then the maximal and minimal values of Hausdorff dimensions for elements in M are determined. The result is proved that for any value s between the maximal and minimal values, there exists an element in M{nk}k≥1, {ck}k≥1) such that its Hausdorff dimension is equal to s. The same results hold for packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.展开更多
The authors mainly study the Hausdorff operators on Euclidean space Rn. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and H...The authors mainly study the Hausdorff operators on Euclidean space Rn. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and Herz type spaces. The results reveal that the Hausdorff operators have better performance on the Herz type Hardy spaces HKP（Rn） than their performance on the Hardy spaces Hv（Rn） when 0 〈 p 〈 1. Also, the authors obtain some new results and reprove or generalize some known results for the high dimensional Hardy operator and adjoint Hardy operator.展开更多
The self similar sets satisfying the open condition have been studied. An estimation of fractal, by the definition can only give the upper limit of its Hausdorff measure. So to judge if such an upper limit is its exac...The self similar sets satisfying the open condition have been studied. An estimation of fractal, by the definition can only give the upper limit of its Hausdorff measure. So to judge if such an upper limit is its exact value or not is important. A negative criterion has been given. As a consequence, the Marion’s conjecture on the Hausdorff meas\| ure of the Koch curve has been proved invalid.展开更多
In this paper, we propose a novel method for finger-vein recognition. We extract the features of the vein patterns for recognition. Then, the minutiae features included bifurcation points and ending points are extract...In this paper, we propose a novel method for finger-vein recognition. We extract the features of the vein patterns for recognition. Then, the minutiae features included bifurcation points and ending points are extracted from these vein patterns. These feature points are used as a geometric representation of the vein patterns shape. Finally, the modified Hausdorff distance algorithm is provided to evaluate the identifica-tion ability among all possible relative positions of the vein patterns shape. This algorithm has been widely used for comparing point sets or edge maps since it does not require point cor-respondence. Experimental results show these minutiae feature points can be used to perform personal verification tasks as a geometric rep-resentation of the vein patterns shape. Fur-thermore, in this developed method. we can achieve robust image matching under different lighting conditions.展开更多
We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function ...We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.展开更多
In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results a...In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results are substantial extensions of some known results on Multilinear high dimensional Hardy operator.展开更多
In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness o...In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.展开更多
In this paper, we study certain Hausdorff operators in the high-dimensional product spaces. We obtain their power weighted boundedness from Lp to Lq and characterize the necessary and sufficient conditions for their b...In this paper, we study certain Hausdorff operators in the high-dimensional product spaces. We obtain their power weighted boundedness from Lp to Lq and characterize the necessary and sufficient conditions for their boundedness on the power weighted Lp spaces. Moreover, in the case p = q, we obtain the sharp bound constants.展开更多
With the development of global position system（GPS）,wireless technology and location aware services,it is possible to collect a large quantity of trajectory data.In the field of data mining for moving objects,the pr...With the development of global position system（GPS）,wireless technology and location aware services,it is possible to collect a large quantity of trajectory data.In the field of data mining for moving objects,the problem of anomaly detection is a hot topic.Based on the development of anomalous trajectory detection of moving objects,this paper introduces the classical trajectory outlier detection（TRAOD） algorithm,and then proposes a density-based trajectory outlier detection（DBTOD） algorithm,which compensates the disadvantages of the TRAOD algorithm that it is unable to detect anomalous defects when the trajectory is local and dense.The results of employing the proposed algorithm to Elk1993 and Deer1995 datasets are also presented,which show the effectiveness of the algorithm.展开更多
Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, r...Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, respectively. Existence of intersections of the sample paths of XH and XK is studied. More generally, let E1 R^N1, E2 R^N2 and F R^d be Borel sets. A necessary condition and a sufficient condition for P{（X^H（E1） ∩ X^K（E2）） ∩ F ≠ Ф} 〉 0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 x E2 x F in the metric space （R^N1＋N2＋d, ρ） are proved, whereρ is a metric defined in terms of H and K. These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.展开更多
A spectral method is used to derive a series of equations for axisymmetric Couette-Taylor flow. A three-modes system, which is similar to the Lorenz systems, is obtained by a suitable three-modes truncation of the Nav...A spectral method is used to derive a series of equations for axisymmetric Couette-Taylor flow. A three-modes system, which is similar to the Lorenz systems, is obtained by a suitable three-modes truncation of the Navier-Stokes equations for the incompressible flow between two concentric rotating cylinders. The stability of the three-modes systems is discussed. Moreover, the existence of its attractor and the estimation of Hausdorff dimension are given.展开更多
Let 0<A≤1/3 ,K(λ) be the attractor of an iterated function system {ψ1,ψ2} on the line, where 1(x)= AT, ψ1(x) = 1-λ+λx, x∈[0,1]. We call K(λ) the symmetry Cantor sets. In this paper, we obtained the exact H...Let 0<A≤1/3 ,K(λ) be the attractor of an iterated function system {ψ1,ψ2} on the line, where 1(x)= AT, ψ1(x) = 1-λ+λx, x∈[0,1]. We call K(λ) the symmetry Cantor sets. In this paper, we obtained the exact Hausdorff Centred measure of K(λ).展开更多
In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, t...In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.展开更多
基金Project supported by the National Climbing Project"Nonlinear Science"and the Scientific Foundation of the State Education Commission of China.
文摘Let M({nk}k≥1,{ck}k≥1) be the collection of homogeneous Moran sets determined by {nk}k≥1and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. Then the maximal and minimal values of Hausdorff dimensions for elements in M are determined. The result is proved that for any value s between the maximal and minimal values, there exists an element in M{nk}k≥1, {ck}k≥1) such that its Hausdorff dimension is equal to s. The same results hold for packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.
基金supported by the National Natural Science Foundation of China (Nos. 10931001, 10871173)
文摘The authors mainly study the Hausdorff operators on Euclidean space Rn. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and Herz type spaces. The results reveal that the Hausdorff operators have better performance on the Herz type Hardy spaces HKP（Rn） than their performance on the Hardy spaces Hv（Rn） when 0 〈 p 〈 1. Also, the authors obtain some new results and reprove or generalize some known results for the high dimensional Hardy operator and adjoint Hardy operator.
文摘The self similar sets satisfying the open condition have been studied. An estimation of fractal, by the definition can only give the upper limit of its Hausdorff measure. So to judge if such an upper limit is its exact value or not is important. A negative criterion has been given. As a consequence, the Marion’s conjecture on the Hausdorff meas\| ure of the Koch curve has been proved invalid.
文摘In this paper, we propose a novel method for finger-vein recognition. We extract the features of the vein patterns for recognition. Then, the minutiae features included bifurcation points and ending points are extracted from these vein patterns. These feature points are used as a geometric representation of the vein patterns shape. Finally, the modified Hausdorff distance algorithm is provided to evaluate the identifica-tion ability among all possible relative positions of the vein patterns shape. This algorithm has been widely used for comparing point sets or edge maps since it does not require point cor-respondence. Experimental results show these minutiae feature points can be used to perform personal verification tasks as a geometric rep-resentation of the vein patterns shape. Fur-thermore, in this developed method. we can achieve robust image matching under different lighting conditions.
基金Supported by the National Natural Science Foundation of China(10931001, 10871173 and 11026104)
文摘We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.
基金supported by NSF of China(Grant Nos.10931001,10871173)supported by NSF of China(Grant No.11026104)
文摘In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results are substantial extensions of some known results on Multilinear high dimensional Hardy operator.
文摘In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11271330 and 10931001)Education Foundation of Zhejiang Province(Grant No.Y201225707)Natural Science Foundation of Zhejiang Province of China(Grant No.Y604563)
文摘In this paper, we study certain Hausdorff operators in the high-dimensional product spaces. We obtain their power weighted boundedness from Lp to Lq and characterize the necessary and sufficient conditions for their boundedness on the power weighted Lp spaces. Moreover, in the case p = q, we obtain the sharp bound constants.
基金supported by the Aeronautical Science Foundation of China(20111052010)the Jiangsu Graduates Innovation Project (CXZZ120163)+1 种基金the "333" Project of Jiangsu Provincethe Qing Lan Project of Jiangsu Province
文摘With the development of global position system（GPS）,wireless technology and location aware services,it is possible to collect a large quantity of trajectory data.In the field of data mining for moving objects,the problem of anomaly detection is a hot topic.Based on the development of anomalous trajectory detection of moving objects,this paper introduces the classical trajectory outlier detection（TRAOD） algorithm,and then proposes a density-based trajectory outlier detection（DBTOD） algorithm,which compensates the disadvantages of the TRAOD algorithm that it is unable to detect anomalous defects when the trajectory is local and dense.The results of employing the proposed algorithm to Elk1993 and Deer1995 datasets are also presented,which show the effectiveness of the algorithm.
基金supported by Zhejiang Provincial Natural Science Foundation of China(Grant No. Y6100663)National Science Foundation of US (Grant No. DMS-1006903)
文摘Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, respectively. Existence of intersections of the sample paths of XH and XK is studied. More generally, let E1 R^N1, E2 R^N2 and F R^d be Borel sets. A necessary condition and a sufficient condition for P{（X^H（E1） ∩ X^K（E2）） ∩ F ≠ Ф} 〉 0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 x E2 x F in the metric space （R^N1＋N2＋d, ρ） are proved, whereρ is a metric defined in terms of H and K. These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.
文摘A spectral method is used to derive a series of equations for axisymmetric Couette-Taylor flow. A three-modes system, which is similar to the Lorenz systems, is obtained by a suitable three-modes truncation of the Navier-Stokes equations for the incompressible flow between two concentric rotating cylinders. The stability of the three-modes systems is discussed. Moreover, the existence of its attractor and the estimation of Hausdorff dimension are given.
基金This work is supported partially by the foundation of the National Education Ministry, National
文摘Let 0<A≤1/3 ,K(λ) be the attractor of an iterated function system {ψ1,ψ2} on the line, where 1(x)= AT, ψ1(x) = 1-λ+λx, x∈[0,1]. We call K(λ) the symmetry Cantor sets. In this paper, we obtained the exact Hausdorff Centred measure of K(λ).
文摘In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.
