The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for tho...The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for those fractional order systems. The basic idea of the algorithm is to compute fractional derivatives and the filter simultaneously, i.e., the filtered fractional derivatives can be obtained by computing them in one step, and then system identification can be fulfilled by the least square method. The instrumental variable method is also used in the identification of fractional order systems. In this way, even if there is colored noise in the systems, the unbiased estimation of the parameters can still be obtained. Finally an example of identifying a viscoelastic system is given to show the effectiveness of the aforementioned method.展开更多
A class of generalization of Toda mechanics with long range interactions isconstructed in this paper. These systems are associated with the loop algebras L(B_r) in the sensethat their Lax matrices can be realized in t...A class of generalization of Toda mechanics with long range interactions isconstructed in this paper. These systems are associated with the loop algebras L(B_r) in the sensethat their Lax matrices can be realized in terms of the c = 0 representations of the affine Liealgebras B_r~((1)) . We adopt a pair of ordered integers (m, n) to describe the Toda mechanicssystem when we present the equations of motion and the Hamiltonian structure. We also extract theclassical r matrix which satisfy the classical Yang-Baxter relation. Such generalizations willbecome systems with noncommutative variables in the quantum case.展开更多
Diffusion curves can be used to generate vector graphics images with smooth variation by solving Poisson equations. However, using the classical diffusion curve model, it is difficult to ensure that the generated diff...Diffusion curves can be used to generate vector graphics images with smooth variation by solving Poisson equations. However, using the classical diffusion curve model, it is difficult to ensure that the generated diffusion image satisfies desired constraints. In this paper, we develop a model for producing a diffusion image by solving a diffusion equation with diffusion coefficients, in which color layers and coefficient layers are introduced to facilitate the generation of the diffusion image. Doing so allows us to impose various constraints on the diffusion image, such as diffusion strength, diffusion direction,diffusion points, etc., in a unified computational framework. Various examples are presented in this paper to illustrate the capabilities of our model.展开更多
文摘The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for those fractional order systems. The basic idea of the algorithm is to compute fractional derivatives and the filter simultaneously, i.e., the filtered fractional derivatives can be obtained by computing them in one step, and then system identification can be fulfilled by the least square method. The instrumental variable method is also used in the identification of fractional order systems. In this way, even if there is colored noise in the systems, the unbiased estimation of the parameters can still be obtained. Finally an example of identifying a viscoelastic system is given to show the effectiveness of the aforementioned method.
文摘A class of generalization of Toda mechanics with long range interactions isconstructed in this paper. These systems are associated with the loop algebras L(B_r) in the sensethat their Lax matrices can be realized in terms of the c = 0 representations of the affine Liealgebras B_r~((1)) . We adopt a pair of ordered integers (m, n) to describe the Toda mechanicssystem when we present the equations of motion and the Hamiltonian structure. We also extract theclassical r matrix which satisfy the classical Yang-Baxter relation. Such generalizations willbecome systems with noncommutative variables in the quantum case.
基金supported by the National Natural Science Foundation of China (No. 61379072)the National Key R&D Program of China (No. 2016YFB1001501)the Fundamental Research Funds for the Central Universities (No. 2017XZZX009-03)
文摘Diffusion curves can be used to generate vector graphics images with smooth variation by solving Poisson equations. However, using the classical diffusion curve model, it is difficult to ensure that the generated diffusion image satisfies desired constraints. In this paper, we develop a model for producing a diffusion image by solving a diffusion equation with diffusion coefficients, in which color layers and coefficient layers are introduced to facilitate the generation of the diffusion image. Doing so allows us to impose various constraints on the diffusion image, such as diffusion strength, diffusion direction,diffusion points, etc., in a unified computational framework. Various examples are presented in this paper to illustrate the capabilities of our model.
