It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have ans...It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].展开更多
In this paper, square-integrable Octonion-valued function spaces on R3 and R7 are decomposed into the direct sum of Octonion Hardy and conjugate Hardy spaces, and square-integrable Octonion function spaces on the uppe...In this paper, square-integrable Octonion-valued function spaces on R3 and R7 are decomposed into the direct sum of Octonion Hardy and conjugate Hardy spaces, and square-integrable Octonion function spaces on the upper half spaces R + 4 and R + 8 are decomposed into infinity direct sum of subspaces in which the first components are just the Octonion Bergman spaces. The Octonion Hardy Spaces on R3 and R7 are characterized.展开更多
The concept of paraunitary two-scale similarity transform （PTST） is introduced. We discuss the property of PTST, and prove that PTST preserves the orthogonal, approximation order and smoothness of the given orthogon...The concept of paraunitary two-scale similarity transform （PTST） is introduced. We discuss the property of PTST, and prove that PTST preserves the orthogonal, approximation order and smoothness of the given orthogonal multiscaling functions. What is more, by applying PTST, we present an algorithm of constructing high order balanced multiscaling functions by balancing the already existing orthogonal nonbalanced multiscaling functions. The corresponding transform matrix is given explicitly. In addition, we also investigate the symmetry of the balanced multiscaling functions. Finally, construction examples are given.展开更多
Background modeling and subtraction is a fundamental problem in video analysis. Many algorithms have been developed to date, but there are still some challenges in complex environments, especially dynamic scenes in wh...Background modeling and subtraction is a fundamental problem in video analysis. Many algorithms have been developed to date, but there are still some challenges in complex environments, especially dynamic scenes in which backgrounds are themselves moving, such as rippling water and swaying trees. In this paper, a novel background modeling method is proposed for dynamic scenes by combining both tensor representation and swarm intelligence. We maintain several video patches, which are naturally represented as higher order tensors,to represent the patterns of background, and utilize tensor low-rank approximation to capture the dynamic nature. Furthermore, we introduce an ant colony algorithm to improve the performance. Experimental results show that the proposed method is robust and adaptive in dynamic environments, and moving objects can be perfectly separated from the complex dynamic background.展开更多
The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactne...The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactness on the Lp-spaces.展开更多
文摘It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].
文摘In this paper, square-integrable Octonion-valued function spaces on R3 and R7 are decomposed into the direct sum of Octonion Hardy and conjugate Hardy spaces, and square-integrable Octonion function spaces on the upper half spaces R + 4 and R + 8 are decomposed into infinity direct sum of subspaces in which the first components are just the Octonion Bergman spaces. The Octonion Hardy Spaces on R3 and R7 are characterized.
基金supported by the National Basic Research Program of China (Grant No. 1999075105)the National Natural Science Foundation of China (Grant No. 10471002)Research Foundation for Doctoral Programm (Grant No. 20050574002)
文摘The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved.
基金supported by the National Natural Science Foundation of China(Grant Nos.90104004 and 10471002)the 973 Project of China(Grant Nos.G1999075105)+1 种基金the Natural Science Foundation of Guangdong Province(Grant Nos.032038,05008289)the Doctoral Foundation of Guangdong Province(Grant No.04300917).
文摘The concept of paraunitary two-scale similarity transform （PTST） is introduced. We discuss the property of PTST, and prove that PTST preserves the orthogonal, approximation order and smoothness of the given orthogonal multiscaling functions. What is more, by applying PTST, we present an algorithm of constructing high order balanced multiscaling functions by balancing the already existing orthogonal nonbalanced multiscaling functions. The corresponding transform matrix is given explicitly. In addition, we also investigate the symmetry of the balanced multiscaling functions. Finally, construction examples are given.
基金supported by National Natural Science Foundation of China (Grant Nos. 11301137 and 11371036)the National Science Foundation of Hebei Province of China (Grant No. A2014205100
文摘Background modeling and subtraction is a fundamental problem in video analysis. Many algorithms have been developed to date, but there are still some challenges in complex environments, especially dynamic scenes in which backgrounds are themselves moving, such as rippling water and swaying trees. In this paper, a novel background modeling method is proposed for dynamic scenes by combining both tensor representation and swarm intelligence. We maintain several video patches, which are naturally represented as higher order tensors,to represent the patterns of background, and utilize tensor low-rank approximation to capture the dynamic nature. Furthermore, we introduce an ant colony algorithm to improve the performance. Experimental results show that the proposed method is robust and adaptive in dynamic environments, and moving objects can be perfectly separated from the complex dynamic background.
基金This work was supported by the National Natural Science Foundation of China(Grant No.90104004)973 Project of China(Grant No.G1999075105).
文摘The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactness on the Lp-spaces.
