Optomechanical dynamics in two systems which are a transmission line resonator and Fabrya-Perot optical cavity via radiation-pressure are investigated by linearized quantum Langevin equation. We work in the resolved s...Optomechanical dynamics in two systems which are a transmission line resonator and Fabrya-Perot optical cavity via radiation-pressure are investigated by linearized quantum Langevin equation. We work in the resolved sideband regime where the oscillator resonance frequency exceeds the cavity linewidth. Normal mode splittings of the mechanical resonator as a pure result of the coupling interaction in the two optomechanical systems is studied, and we make a comparison of normal mode splitting of mechanical resonator between the two systems. In the optical cavity, the normal mode splitting of the movable mirror approaches the latest experiment very well. In addition, an approximation scheme is introduced to demonstrate the ground state cooling, and we make a comparison of cooling between the two systems dominated by two key factors, which are the initial bath temperature and the mechanical quality factor. Since both the normal mode splitting and cooling require working in the resolved sideband regime, whether the normal mode splitting influences the cooling of the mirror is considered. Considering the size of the mechanical resonator and precooling the system, the mechanical resonator in the transmission line resonator system is easier to achieve the ground state cooling than in optical cavity.展开更多
In this paper,a two-step semi-regularized Hermitian and skew-Hermitian splitting(SHSS)iteration method is constructed by introducing a regularization matrix in the(1,1)-block of the first iteration step,to solve the s...In this paper,a two-step semi-regularized Hermitian and skew-Hermitian splitting(SHSS)iteration method is constructed by introducing a regularization matrix in the(1,1)-block of the first iteration step,to solve the saddle-point linear system.By carefully selecting two different regularization matrices,two kinds of SHSS preconditioners are proposed to accelerate the convergence rates of the Krylov subspace iteration methods.Theoretical analysis about the eigenvalue distribution demonstrates that the proposed SHSS preconditioners can make the eigenvalues of the corresponding preconditioned matrices be clustered around 1 and uniformly bounded away from 0.The eigenvector distribution and the upper bound on the degree of the minimal polynomial of the SHSS-preconditioned matrices indicate that the SHSS-preconditioned Krylov subspace iterative methods can converge to the true solution within finite steps in exact arithmetic.In addition,the numerical example derived from the optimal control problem shows that the SHSS preconditioners can significantly improve the convergence speeds of the Krylov subspace iteration methods,and their convergence rates are independent of the discrete mesh size.展开更多
针对现有生成对抗网络的单图像超分辨率重建在大尺度因子下存在训练不稳定、特征提取不足和重建结果纹理细节严重缺失的问题,提出一种拆分注意力网络的单图超分辨率重建方法。首先,以拆分注意力残差模块作为基本残差块构造生成器,提高...针对现有生成对抗网络的单图像超分辨率重建在大尺度因子下存在训练不稳定、特征提取不足和重建结果纹理细节严重缺失的问题,提出一种拆分注意力网络的单图超分辨率重建方法。首先,以拆分注意力残差模块作为基本残差块构造生成器,提高生成器特征提取的能力。其次,在损失函数中引入鲁棒性更好的Charbonnier损失函数和Focal Frequency Loss损失函数代替均方差损失函数,同时加入正则化损失平滑训练结果,防止图像过于像素化。最后,在生成器和判别器中采用谱归一化处理,提高网络的稳定性。在4倍放大因子下,与其他方法在Set5、Set14、BSDS100、Urban100测试集上进行测试比较,本文方法的峰值信噪比比其他对比方法的平均值提升1.419 dB,结构相似性比其他对比方法的平均值提升0.051。实验数据和效果图表明,该方法主观上具有丰富的细节和更好的视觉效果,客观上具有较高的峰值信噪比值和结构相似度值。展开更多
In this paper, a generalized preconditioned Hermitian and skew-Hermitian splitting （GPHSS） iteration method for a non-Hermitian positive-definite matrix is studied, which covers standard Hermitian and skew-Hermitian...In this paper, a generalized preconditioned Hermitian and skew-Hermitian splitting （GPHSS） iteration method for a non-Hermitian positive-definite matrix is studied, which covers standard Hermitian and skew-Hermitian splitting （HSS） iteration and also many existing variants. Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix. From practical point of view, we have analyzed and implemented inexact generalized preconditioned Hermitian and skew-Hermitian splitting （IGPHSS） iteration, which employs Krylov subspace methods as its inner processes. Numerical experiments from three-dimensional convection-diffusion iterations are efficient and competitive with equation show that the GPHSS and IGPHSS standard HSS iteration and AHSS iteration.展开更多
Let G be a finite group of Lie type E6 over Fq (adjoint or simply connected) and W be the Weyl group of G. We describe maximal tori T such that T has a complement in its algebraic normalizer N(G, T). It is well known ...Let G be a finite group of Lie type E6 over Fq (adjoint or simply connected) and W be the Weyl group of G. We describe maximal tori T such that T has a complement in its algebraic normalizer N(G, T). It is well known that for each maximal torus T of G there exists an element w ∈ W such that N(G, T )/T ■ CW(w). When T does not have a complement isomorphic to CW(w), we show that w has a lift in N(G, T) of the same order.展开更多
We generalize the accelerated Hermitian and skew-Hermitian splitting(AHSS)iteration methods for large sparse saddle-point problems.These methods involve four iteration parameters whose special choices can recover the ...We generalize the accelerated Hermitian and skew-Hermitian splitting(AHSS)iteration methods for large sparse saddle-point problems.These methods involve four iteration parameters whose special choices can recover the precondi-tioned HSS and accelerated HSS iteration methods.Also a new efficient case is in-troduced and we theoretically prove that this new method converges to the unique solution of the saddle-point problem.Numerical experiments are used to further examine the effectiveness and robustness of iterations.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 10647132 and 11104113)the Scientific Research Fund of Hunan Provincial Education Department of China (Grant No. 10A100)
文摘Optomechanical dynamics in two systems which are a transmission line resonator and Fabrya-Perot optical cavity via radiation-pressure are investigated by linearized quantum Langevin equation. We work in the resolved sideband regime where the oscillator resonance frequency exceeds the cavity linewidth. Normal mode splittings of the mechanical resonator as a pure result of the coupling interaction in the two optomechanical systems is studied, and we make a comparison of normal mode splitting of mechanical resonator between the two systems. In the optical cavity, the normal mode splitting of the movable mirror approaches the latest experiment very well. In addition, an approximation scheme is introduced to demonstrate the ground state cooling, and we make a comparison of cooling between the two systems dominated by two key factors, which are the initial bath temperature and the mechanical quality factor. Since both the normal mode splitting and cooling require working in the resolved sideband regime, whether the normal mode splitting influences the cooling of the mirror is considered. Considering the size of the mechanical resonator and precooling the system, the mechanical resonator in the transmission line resonator system is easier to achieve the ground state cooling than in optical cavity.
基金the National Natural Science Foundation of China(No.12001048)R&D Program of Beijing Municipal Education Commission(No.KM202011232019),China.
文摘In this paper,a two-step semi-regularized Hermitian and skew-Hermitian splitting(SHSS)iteration method is constructed by introducing a regularization matrix in the(1,1)-block of the first iteration step,to solve the saddle-point linear system.By carefully selecting two different regularization matrices,two kinds of SHSS preconditioners are proposed to accelerate the convergence rates of the Krylov subspace iteration methods.Theoretical analysis about the eigenvalue distribution demonstrates that the proposed SHSS preconditioners can make the eigenvalues of the corresponding preconditioned matrices be clustered around 1 and uniformly bounded away from 0.The eigenvector distribution and the upper bound on the degree of the minimal polynomial of the SHSS-preconditioned matrices indicate that the SHSS-preconditioned Krylov subspace iterative methods can converge to the true solution within finite steps in exact arithmetic.In addition,the numerical example derived from the optimal control problem shows that the SHSS preconditioners can significantly improve the convergence speeds of the Krylov subspace iteration methods,and their convergence rates are independent of the discrete mesh size.
文摘针对现有生成对抗网络的单图像超分辨率重建在大尺度因子下存在训练不稳定、特征提取不足和重建结果纹理细节严重缺失的问题,提出一种拆分注意力网络的单图超分辨率重建方法。首先,以拆分注意力残差模块作为基本残差块构造生成器,提高生成器特征提取的能力。其次,在损失函数中引入鲁棒性更好的Charbonnier损失函数和Focal Frequency Loss损失函数代替均方差损失函数,同时加入正则化损失平滑训练结果,防止图像过于像素化。最后,在生成器和判别器中采用谱归一化处理,提高网络的稳定性。在4倍放大因子下,与其他方法在Set5、Set14、BSDS100、Urban100测试集上进行测试比较,本文方法的峰值信噪比比其他对比方法的平均值提升1.419 dB,结构相似性比其他对比方法的平均值提升0.051。实验数据和效果图表明,该方法主观上具有丰富的细节和更好的视觉效果,客观上具有较高的峰值信噪比值和结构相似度值。
文摘In this paper, a generalized preconditioned Hermitian and skew-Hermitian splitting （GPHSS） iteration method for a non-Hermitian positive-definite matrix is studied, which covers standard Hermitian and skew-Hermitian splitting （HSS） iteration and also many existing variants. Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix. From practical point of view, we have analyzed and implemented inexact generalized preconditioned Hermitian and skew-Hermitian splitting （IGPHSS） iteration, which employs Krylov subspace methods as its inner processes. Numerical experiments from three-dimensional convection-diffusion iterations are efficient and competitive with equation show that the GPHSS and IGPHSS standard HSS iteration and AHSS iteration.
基金Russian Science Foundation (project no. 14-21-00065).
文摘Let G be a finite group of Lie type E6 over Fq (adjoint or simply connected) and W be the Weyl group of G. We describe maximal tori T such that T has a complement in its algebraic normalizer N(G, T). It is well known that for each maximal torus T of G there exists an element w ∈ W such that N(G, T )/T ■ CW(w). When T does not have a complement isomorphic to CW(w), we show that w has a lift in N(G, T) of the same order.
文摘We generalize the accelerated Hermitian and skew-Hermitian splitting(AHSS)iteration methods for large sparse saddle-point problems.These methods involve four iteration parameters whose special choices can recover the precondi-tioned HSS and accelerated HSS iteration methods.Also a new efficient case is in-troduced and we theoretically prove that this new method converges to the unique solution of the saddle-point problem.Numerical experiments are used to further examine the effectiveness and robustness of iterations.
