By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent ...By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.展开更多
We use the method of discrete dipole approximation with surface interaction to construct a model in which a plurality of nanoparticles is arranged on the surface of BK7 glass. Nanoparticles are in air medium illuminat...We use the method of discrete dipole approximation with surface interaction to construct a model in which a plurality of nanoparticles is arranged on the surface of BK7 glass. Nanoparticles are in air medium illuminated by evanescent wave generated from total internal reflection. The effects of the wavelength, the polarization of the incident wave, the number of nanoparticles and the spacing of multiple nanoparticles on the field enhancement and extinction efficiency are calculated by our model. Our work could pave the way to improve the field enhancement of multiple nanoparticles systems.展开更多
In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a l...In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.12071491)Guangzhou Science and Technology Plan Project(Grant No.202102080177).
文摘By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.
基金supported by the Zhejiang Provincial Natural Science Foundation of China(No.LGF20C050001)the National Nature Science Foundation of China(No.61805213)。
文摘We use the method of discrete dipole approximation with surface interaction to construct a model in which a plurality of nanoparticles is arranged on the surface of BK7 glass. Nanoparticles are in air medium illuminated by evanescent wave generated from total internal reflection. The effects of the wavelength, the polarization of the incident wave, the number of nanoparticles and the spacing of multiple nanoparticles on the field enhancement and extinction efficiency are calculated by our model. Our work could pave the way to improve the field enhancement of multiple nanoparticles systems.
文摘In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.
