In this paper,including some partial differential equations with a number of independent variables, which can he reduced by the infinitesimal form of the group, we obtain the theory of similarity transformation and it...In this paper,including some partial differential equations with a number of independent variables, which can he reduced by the infinitesimal form of the group, we obtain the theory of similarity transformation and its application of the second order nonlinear partial differential equations which have two independent variables and two dependent variables in mechanics.展开更多
In the context of globalization and rapid development of information technology,the transformation of industrial structure has become a major force driving China’s economic and social development.Under this situation...In the context of globalization and rapid development of information technology,the transformation of industrial structure has become a major force driving China’s economic and social development.Under this situation,as an important component of China’s higher vocational education,the information construction of the business and trade professional group is of great significance.The construction of informatization can not only improve the education quality of the business and trade professional group,but also closely connect with the needs of the industry,providing strong talent support for the transformation and upgrading of the industry.Aiming at the problems existing in China’s current economic and social development,this paper proposes a new economic and trade professional system based on information technology,and puts forward corresponding solutions.展开更多
The magnetohydrodynamics （MHD） convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the pres- ence of thermal stratification are examined. The pa...The magnetohydrodynamics （MHD） convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the pres- ence of thermal stratification are examined. The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gill- based shooting method. It is concluded that the flow field, temperature, and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.展开更多
Using a new symmetry group theory, the transformation groups and symmetries of the general Broer-Kaup system are obtained. The results are much simpler than those obtained via the standard approaches.
In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transf...In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.展开更多
The mutual relationships between four generating functions F-1(q, Q), F-2(q, P), F-3(p, P), F-4(p, Q) and four kinds of canonical variables q, p, Q, P concerned in Hamilton's canonical transformations, can be got ...The mutual relationships between four generating functions F-1(q, Q), F-2(q, P), F-3(p, P), F-4(p, Q) and four kinds of canonical variables q, p, Q, P concerned in Hamilton's canonical transformations, can be got with linear transformations from seven basic formulae. All of them are Legendre's transformation, which are implemented by 32 matrices of 8 x 8 which are homomorphic to D-4 point group of 8 elements with correspondence of 4:1. Transformations and relationships of four state functions G(P, T), H(P, S), U(V, S), F(V, T) and four variables P, V, T, S in thermodynamics, are just the same Lagendre's transformations with the relationships of canonical transformations. The state functions of thermodynamics are summarily founded on experimental results of macroscope measurements, and Hamilton's canonical transformations are theoretical generalization of classical mechanics. Both group represents are the same, and it is to say, their mathematical frames are the same. This generality indicates the thermodynamical transformation is an example of one-dimensional Hamilton's canonical transformation.展开更多
Sparse representation has been highly successful in various tasks related to image processing and computer vision.For ancient mural image inpainting,traditional group sparse representation models usually lead to struc...Sparse representation has been highly successful in various tasks related to image processing and computer vision.For ancient mural image inpainting,traditional group sparse representation models usually lead to structure blur and line discontinuity due to the construction of similarity group solely based on the Euclidean distance and the randomness of dictionary initialization.To address the aforementioned issues,an improved curvature Gabor transform and group sparse representation(CGabor-GSR)model for ancient Dunhuang mural inpainting is proposed.To begin with,mutual information is introduced to weight the Euclidean distance,and then the weighted Euclidean distance acts as a new standard of similarity group.Subsequently,to mitigate the randomness of dictionary initialization,a curvature Gabor wavelet transform is proposed to extract the features and initialize the feature dictionary with dimension reduction based on principal component analysis(PCA).Ultimately,singular value decomposition(SVD)and split Bregman iteration(SBI)can be used to resolve the CGabor-GSR model to reconstruct the mural images.Experimental results on Dunhuang mural inpainting demonstrate tha the proposed CGabor-GSR achieves a better performance than compared algorithms in both objective and visual evaluation.展开更多
In September 1965,the Xizang Autonomous Region was officially founded.A new page was turned in Xizang's history,one that saw people of all ethnic groups in Xizang forge ahead together in pursuit of shared progress...In September 1965,the Xizang Autonomous Region was officially founded.A new page was turned in Xizang's history,one that saw people of all ethnic groups in Xizang forge ahead together in pursuit of shared progress and prosperity.Over the past 60 years,under the leadership of the Communist Party of China(CPC)and with the strong support of the entire country.展开更多
As the first national exhibition with the theme of supply chain,China International Supply Chain Expo(hereinafter referred to as the CISCE)has already become a key spot to observe the establishment of the Chinese ente...As the first national exhibition with the theme of supply chain,China International Supply Chain Expo(hereinafter referred to as the CISCE)has already become a key spot to observe the establishment of the Chinese enterprise industry chain.During the evolution of three CISCE,the leading dairy enterprise,Yili Group(hereinafter referred to as Yili),takes the practice of the entire industry chain as a sample,clearly outlining the development trajectory of China's dairy industry from“following”to“leading”.Its explorations of indust r ial chain col laborat ion,green transformation,and global layout are prominent.Therefore,providing a good paradigm for the high-quality development of the real economy.展开更多
In this paper,a data consistency condition(DCC)in Radon domain is re-derived from the perspective of Lie transformation group and compared with other two derivations.By carefully observing the proof procedure on the b...In this paper,a data consistency condition(DCC)in Radon domain is re-derived from the perspective of Lie transformation group and compared with other two derivations.By carefully observing the proof procedure on the basis of Lie transformation group,we may have a deeper insight on the essence of this DCC.Moreover,it may help determine whether there are the corresponding counterparts in both image and Radon domains.Following this line of thought,more data consistency conditions will possibly be explored in the future.This is definitely critical as data consistency conditions would be applied to the construction of algorithms for next-generation CT imaging.展开更多
In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, ...In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.展开更多
In this paper, we introduce a practical method for obtaining the structure of thegroup of units for the ring of linear transformations of a vector space over an arbitrary field,and we give a further generalization of ...In this paper, we introduce a practical method for obtaining the structure of thegroup of units for the ring of linear transformations of a vector space over an arbitrary field,and we give a further generalization of the result in [3].展开更多
This paper examines transformational leadership theory and the relationship between transformational leadership and group performance as well. Transformational leadership asks leaders to understand the needs of follow...This paper examines transformational leadership theory and the relationship between transformational leadership and group performance as well. Transformational leadership asks leaders to understand the needs of followers and motivate followers for their overall development, which brings benefits to a group. It is hoped that this paper can contribute to comparative studies on Transformational leadership in the U.S. and China.展开更多
In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpote...In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpotent Lie groups.展开更多
For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,...For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.展开更多
Lie groups of bi-M<span style="white-space:nowrap;">öbius transformations are known and their actions on non orientable n-dimensional complex manifolds have been studied. In this paper, m-M<...Lie groups of bi-M<span style="white-space:nowrap;">öbius transformations are known and their actions on non orientable n-dimensional complex manifolds have been studied. In this paper, m-M<span style="white-space:nowrap;">öbius transformations are introduced and similar problems as those related to bi-M<span style="white-space:nowrap;">öbius transformations are tackled. In particular, it is shown that the subgroup generated by every m-M<span style="white-space:nowrap;">öbius transformation is a discrete group. Cyclic subgroups are exhibited. Vector valued m-M<span style="white-space:nowrap;">öbius transformations are also studied.展开更多
Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potenti...Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.展开更多
文摘In this paper,including some partial differential equations with a number of independent variables, which can he reduced by the infinitesimal form of the group, we obtain the theory of similarity transformation and its application of the second order nonlinear partial differential equations which have two independent variables and two dependent variables in mechanics.
基金Shandong Provincial Vocational Education Teaching Reform Research Project“Research and Practice on the Digital Upgrade of Business and Trade Professional Groups in Vocational Colleges from the Perspective of System Theory”(2023075)。
文摘In the context of globalization and rapid development of information technology,the transformation of industrial structure has become a major force driving China’s economic and social development.Under this situation,as an important component of China’s higher vocational education,the information construction of the business and trade professional group is of great significance.The construction of informatization can not only improve the education quality of the business and trade professional group,but also closely connect with the needs of the industry,providing strong talent support for the transformation and upgrading of the industry.Aiming at the problems existing in China’s current economic and social development,this paper proposes a new economic and trade professional system based on information technology,and puts forward corresponding solutions.
文摘The magnetohydrodynamics （MHD） convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the pres- ence of thermal stratification are examined. The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gill- based shooting method. It is concluded that the flow field, temperature, and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.
文摘Using a new symmetry group theory, the transformation groups and symmetries of the general Broer-Kaup system are obtained. The results are much simpler than those obtained via the standard approaches.
文摘In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.
文摘The mutual relationships between four generating functions F-1(q, Q), F-2(q, P), F-3(p, P), F-4(p, Q) and four kinds of canonical variables q, p, Q, P concerned in Hamilton's canonical transformations, can be got with linear transformations from seven basic formulae. All of them are Legendre's transformation, which are implemented by 32 matrices of 8 x 8 which are homomorphic to D-4 point group of 8 elements with correspondence of 4:1. Transformations and relationships of four state functions G(P, T), H(P, S), U(V, S), F(V, T) and four variables P, V, T, S in thermodynamics, are just the same Lagendre's transformations with the relationships of canonical transformations. The state functions of thermodynamics are summarily founded on experimental results of macroscope measurements, and Hamilton's canonical transformations are theoretical generalization of classical mechanics. Both group represents are the same, and it is to say, their mathematical frames are the same. This generality indicates the thermodynamical transformation is an example of one-dimensional Hamilton's canonical transformation.
基金supported by National Natural Science Foundation of China(No.61963023)Humanities and Social Sciences Youth Foundation of Ministry of Education(No.19YJC760012)Lanzhou Jiaotong University Basic Top-Notch Personnel Project(No.2022JC36).
文摘Sparse representation has been highly successful in various tasks related to image processing and computer vision.For ancient mural image inpainting,traditional group sparse representation models usually lead to structure blur and line discontinuity due to the construction of similarity group solely based on the Euclidean distance and the randomness of dictionary initialization.To address the aforementioned issues,an improved curvature Gabor transform and group sparse representation(CGabor-GSR)model for ancient Dunhuang mural inpainting is proposed.To begin with,mutual information is introduced to weight the Euclidean distance,and then the weighted Euclidean distance acts as a new standard of similarity group.Subsequently,to mitigate the randomness of dictionary initialization,a curvature Gabor wavelet transform is proposed to extract the features and initialize the feature dictionary with dimension reduction based on principal component analysis(PCA).Ultimately,singular value decomposition(SVD)and split Bregman iteration(SBI)can be used to resolve the CGabor-GSR model to reconstruct the mural images.Experimental results on Dunhuang mural inpainting demonstrate tha the proposed CGabor-GSR achieves a better performance than compared algorithms in both objective and visual evaluation.
文摘In September 1965,the Xizang Autonomous Region was officially founded.A new page was turned in Xizang's history,one that saw people of all ethnic groups in Xizang forge ahead together in pursuit of shared progress and prosperity.Over the past 60 years,under the leadership of the Communist Party of China(CPC)and with the strong support of the entire country.
文摘As the first national exhibition with the theme of supply chain,China International Supply Chain Expo(hereinafter referred to as the CISCE)has already become a key spot to observe the establishment of the Chinese enterprise industry chain.During the evolution of three CISCE,the leading dairy enterprise,Yili Group(hereinafter referred to as Yili),takes the practice of the entire industry chain as a sample,clearly outlining the development trajectory of China's dairy industry from“following”to“leading”.Its explorations of indust r ial chain col laborat ion,green transformation,and global layout are prominent.Therefore,providing a good paradigm for the high-quality development of the real economy.
基金supported in partby Shaanxi Provincial Natural Science Foundation of China(No.2023-JC-YB-521)by National Natural Science Foundation of China(NSFC)(No.12475313)+1 种基金Excellent Youth Fund of Shandong Natural Science Foundation(ZR2024YQ066)by Xi'an Science and Technology Program of China(No.23GXFW0065).
文摘In this paper,a data consistency condition(DCC)in Radon domain is re-derived from the perspective of Lie transformation group and compared with other two derivations.By carefully observing the proof procedure on the basis of Lie transformation group,we may have a deeper insight on the essence of this DCC.Moreover,it may help determine whether there are the corresponding counterparts in both image and Radon domains.Following this line of thought,more data consistency conditions will possibly be explored in the future.This is definitely critical as data consistency conditions would be applied to the construction of algorithms for next-generation CT imaging.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11175092)the Scientific Research Fund of Education Department of Zhejiang Province of China (Grant No. Y201017148)K. C. Wong Magna Fund in Ningbo University
文摘In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.
基金Supported by the NSF of Educational Department of Henan Province(200510482001)
文摘In this paper, we introduce a practical method for obtaining the structure of thegroup of units for the ring of linear transformations of a vector space over an arbitrary field,and we give a further generalization of the result in [3].
文摘This paper examines transformational leadership theory and the relationship between transformational leadership and group performance as well. Transformational leadership asks leaders to understand the needs of followers and motivate followers for their overall development, which brings benefits to a group. It is hoped that this paper can contribute to comparative studies on Transformational leadership in the U.S. and China.
基金the National Nature Science Foundation of China(10261002)
文摘In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpotent Lie groups.
基金国家自然科学基金，湖南省自然科学基金，the Scientific Research Foundation of Education Burean of Hunan Province
文摘For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.
文摘Lie groups of bi-M<span style="white-space:nowrap;">öbius transformations are known and their actions on non orientable n-dimensional complex manifolds have been studied. In this paper, m-M<span style="white-space:nowrap;">öbius transformations are introduced and similar problems as those related to bi-M<span style="white-space:nowrap;">öbius transformations are tackled. In particular, it is shown that the subgroup generated by every m-M<span style="white-space:nowrap;">öbius transformation is a discrete group. Cyclic subgroups are exhibited. Vector valued m-M<span style="white-space:nowrap;">öbius transformations are also studied.
文摘Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.
