St. Frunza"3 laid the foundation of-duality theorem for decomposable operators. He proved that if y￡J?(X) is a 2-decomposable operator, then T* is also a 2-decomposable operator. His proof is fundamental, but it...St. Frunza"3 laid the foundation of-duality theorem for decomposable operators. He proved that if y￡J?(X) is a 2-decomposable operator, then T* is also a 2-decomposable operator. His proof is fundamental, but it is rather complicated. Here we give a very simple proof, using Dieudonn^’s duality theorem.Wang Shengwang proved that if T* is a decomposable operator, and F a closed set, then -STJ.^) is weak* closed. In this paper we prove if T* has the single-valued extension property, then xt*(f~) is weak* closed whenever it is closed in the strong topology.展开更多
The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (...The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (A) is decompcoable, moreover, in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released. Those results are partially answers to a question raised by K. B. Laursen and M. M. Neumann [5].展开更多
In this paper, a self-mode-locked Nd:YVO_4 picosecond vortex laser is demonstrated, which can operate on the different Laguerre-Gaussian(LG) modes at 1 064 nm. A π/2 mode converter is utilized to realize the picoseco...In this paper, a self-mode-locked Nd:YVO_4 picosecond vortex laser is demonstrated, which can operate on the different Laguerre-Gaussian(LG) modes at 1 064 nm. A π/2 mode converter is utilized to realize the picosecond vortex laser with LG mode transformed from the high-order Hermite-Gaussian(HG) mode. For the proposed laser, the mode-locked pulse repetition rate is 1.81 GHz. The average output powers of LG_(12) mode and LG_(02) mode are 1.241 W and 1.27 W, respectively, and their slope efficiencies are 23.2% and 24%, respectively.展开更多
Because of the fractional order derivatives, the identification of the fractional order system（FOS） is more complex than that of an integral order system（IOS）. In order to avoid high time consumption in the system...Because of the fractional order derivatives, the identification of the fractional order system（FOS） is more complex than that of an integral order system（IOS）. In order to avoid high time consumption in the system identification, the leastsquares method is used to find other parameters by fixing the fractional derivative order. Hereafter, the optimal parameters of a system will be found by varying the derivative order in an interval. In addition, the operational matrix of the fractional order integration combined with the multi-resolution nature of a wavelet is used to accelerate the FOS identification, which is achieved by discarding wavelet coefficients of high-frequency components of input and output signals. In the end, the identifications of some known fractional order systems and an elastic torsion system are used to verify the proposed method.展开更多
文摘St. Frunza"3 laid the foundation of-duality theorem for decomposable operators. He proved that if y￡J?(X) is a 2-decomposable operator, then T* is also a 2-decomposable operator. His proof is fundamental, but it is rather complicated. Here we give a very simple proof, using Dieudonn^’s duality theorem.Wang Shengwang proved that if T* is a decomposable operator, and F a closed set, then -STJ.^) is weak* closed. In this paper we prove if T* has the single-valued extension property, then xt*(f~) is weak* closed whenever it is closed in the strong topology.
文摘The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (A) is decompcoable, moreover, in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released. Those results are partially answers to a question raised by K. B. Laursen and M. M. Neumann [5].
基金supported by the National Natural Science Foundation of China(No.61108021)the Fundamental Research Funds for the Central Universities(Nos.2013JBM091 and S16JB00010)
文摘In this paper, a self-mode-locked Nd:YVO_4 picosecond vortex laser is demonstrated, which can operate on the different Laguerre-Gaussian(LG) modes at 1 064 nm. A π/2 mode converter is utilized to realize the picosecond vortex laser with LG mode transformed from the high-order Hermite-Gaussian(HG) mode. For the proposed laser, the mode-locked pulse repetition rate is 1.81 GHz. The average output powers of LG_(12) mode and LG_(02) mode are 1.241 W and 1.27 W, respectively, and their slope efficiencies are 23.2% and 24%, respectively.
基金Project supported by the National Natural Science Foundation of China(Grant No.61271395)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20161513)
文摘Because of the fractional order derivatives, the identification of the fractional order system（FOS） is more complex than that of an integral order system（IOS）. In order to avoid high time consumption in the system identification, the leastsquares method is used to find other parameters by fixing the fractional derivative order. Hereafter, the optimal parameters of a system will be found by varying the derivative order in an interval. In addition, the operational matrix of the fractional order integration combined with the multi-resolution nature of a wavelet is used to accelerate the FOS identification, which is achieved by discarding wavelet coefficients of high-frequency components of input and output signals. In the end, the identifications of some known fractional order systems and an elastic torsion system are used to verify the proposed method.
