In this paper,a novel D-type iterative learning control(ILC)law is proposed for discrete-time antilinear systems.This D-type control law is different from the previous linear(nonlinear)D-type ILC law.The main feature ...In this paper,a novel D-type iterative learning control(ILC)law is proposed for discrete-time antilinear systems.This D-type control law is different from the previous linear(nonlinear)D-type ILC law.The main feature is that we take the conjugate of the(t+1)-th error to construct the proposed controller.The convergence proofs are given for their corresponding ILC schemes.展开更多
We study the Hopf ＊-algebra structures on the Hopf algebra H（1, q） over C. It is shown that H（1, q） is a Hopf ＊-algebra if and only if ｜q｜ = 1 or q is a real number. Then the Hopf ＊-algebra structures on H（1...We study the Hopf ＊-algebra structures on the Hopf algebra H（1, q） over C. It is shown that H（1, q） is a Hopf ＊-algebra if and only if ｜q｜ = 1 or q is a real number. Then the Hopf ＊-algebra structures on H（1, q） are classified up to the equivalence of Hopf ＊-algebra structures.展开更多
This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics.Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional com...This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics.Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional complex-linear spaces, the exposition becomes elementary in the functional analytic sense. Nevertheless it shows the amazing differences to the linear case. Basics of antilinearity is explained in sects. 2, 3, 4, 7 and in sect. 1.2: Spectrum, canonical Hermitian form, antilinear rank one and two operators,the Hermitian adjoint, classification of antilinear normal operators,(skew) conjugations, involutions, and acq-lines, the antilinear counterparts of 1-parameter operator groups. Applications include the representation of the Lagrangian Grassmannian by conjugations, its covering by acq-lines. As well as results on equivalence relations. After remembering elementary Tomita-Takesaki theory, antilinear maps, associated to a vector of a two-partite quantum system, are defined. By allowing to write modular objects as twisted products of pairs of them, they open some new ways to express EPR and teleportation tasks. The appendix presents a look onto the rich structure of antilinear operator spaces.展开更多
文摘In this paper,a novel D-type iterative learning control(ILC)law is proposed for discrete-time antilinear systems.This D-type control law is different from the previous linear(nonlinear)D-type ILC law.The main feature is that we take the conjugate of the(t+1)-th error to construct the proposed controller.The convergence proofs are given for their corresponding ILC schemes.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11171291）.
文摘We study the Hopf ＊-algebra structures on the Hopf algebra H（1, q） over C. It is shown that H（1, q） is a Hopf ＊-algebra if and only if ｜q｜ = 1 or q is a real number. Then the Hopf ＊-algebra structures on H（1, q） are classified up to the equivalence of Hopf ＊-algebra structures.
文摘This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics.Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional complex-linear spaces, the exposition becomes elementary in the functional analytic sense. Nevertheless it shows the amazing differences to the linear case. Basics of antilinearity is explained in sects. 2, 3, 4, 7 and in sect. 1.2: Spectrum, canonical Hermitian form, antilinear rank one and two operators,the Hermitian adjoint, classification of antilinear normal operators,(skew) conjugations, involutions, and acq-lines, the antilinear counterparts of 1-parameter operator groups. Applications include the representation of the Lagrangian Grassmannian by conjugations, its covering by acq-lines. As well as results on equivalence relations. After remembering elementary Tomita-Takesaki theory, antilinear maps, associated to a vector of a two-partite quantum system, are defined. By allowing to write modular objects as twisted products of pairs of them, they open some new ways to express EPR and teleportation tasks. The appendix presents a look onto the rich structure of antilinear operator spaces.
