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排序方式: 共有77条查询结果,搜索用时 15 毫秒
1.
We introduce general sequences of linear operators obtained from classical approximation processes which are useful in the
approximation of the resolvent operators of the generators of suitable C
0-semigroups. The main aim is the representation of the resolvent operators in terms of classical approximation operators.
Work performed under the auspices of PRIN 2006–07 “Kolmogorov equations” (coordinator G. Da Prato) 相似文献
2.
Pablo Irarrazaval Carlos Lizama Vicente Parot Carlos Sing-Long Cristian Tejos 《Computers & Mathematics with Applications》2011,62(3):1576-1590
The fractional Fourier transform (FrFT) is revisited in the framework of strongly continuous periodic semigroups to restate known results and to explore new properties of the FrFT. We then show how the FrFT can be used to reconstruct Magnetic Resonance (MR) images acquired under the presence of quadratic field inhomogeneity. Particularly, we prove that the order of the FrFT is a measure of the distortion in the reconstructed signal. Moreover, we give a dynamic interpretation to the order as time evolution of a function. We also introduce the notion of ρ-α space as an extension of the Fourier or k-space in MR, and we use it to study the distortions introduced in two common MR acquisition strategies. We formulate the reconstruction problem in the context of the FrFT and show how the semigroup theory allows us to find new reconstruction formulas for discrete sampled signals. Finally, the results are supplemented with numerical examples that show how it performs in a standard 1D MR signal reconstruction. 相似文献
3.
Analysis and synthesis of attractive quantum Markovian dynamics 总被引:1,自引:0,他引:1
We propose a general framework for investigating a large class of stabilization problems in Markovian quantum systems. Building on the notions of invariant and attractive quantum subsystem, we characterize attractive subspaces by exploring the structure of the invariant sets for the dynamics. Our general analysis results are exploited to assess the ability of open-loop Hamiltonian and output-feedback control strategies to synthesize Markovian generators which stabilize a target subsystem, subspace, or pure state. In particular, we provide an algebraic characterization of the manifold of stabilizable pure states in arbitrary finite-dimensional Markovian systems, that leads to a constructive strategy for designing the relevant controllers. Implications for stabilization of entangled pure states are addressed by example. 相似文献
4.
徐亚男 《湖南工业大学学报》2012,26(5):12-14
在不含单位元的情况下,通过半群S和T的子半群T~e={t~e|t∈T},给出了广义左Clifford半群的半直积的刻画,得到了2个半群的半直积为广义左Clifford半群的充要条件。 相似文献
5.
6.
给出了L^*-逆半群上的最小可消幺半群同余的一个刻划.在此基础上,研究了L^*-逆半群的一个子类,即强L^*-逆半群,借助于半群上自然偏序方法,证明了半群S为强L^*-逆半群,当且仅当关于任意的x∈S,存在惟一x°∈H1^*,使得x≤x°. 相似文献
7.
得到了生成元为闭算子的n次积分半群的表示定理,并根据积分半群的C半群的关系,进而得到了n次积分半群的谱映射定理。 相似文献
8.
揭示了无穷维线性反应扩散过程和偏微分方程这两种描述反应扩散现象的基本工具的关系,证明了无穷维线性反应扩散过程的大数定理,给出了无穷维线性反应扩散过程的极限状态.讨论了当无穷维线性反应扩散过程的无穷小算子中的参数随指标n变化时,反应扩散过程依概率收敛于一偏微分方程的解的条件,揭示了此偏微分方程的系数与过程的无穷小算子中的参数之间的关系. 相似文献
9.
把在群论中占有重要地位的同态基本定理和三个同构基本定理推广到幂等元唯一的扭半群中,建立了幂等元唯一的扭半群的同态基本定理和同构基本定理。 相似文献
10.
Piotr Grabowski 《International journal of control》2013,86(8):1539-1563
A model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations is interpreted as an abstract semigroup system on a Hilbert state space. Our aim is to solve the output motion planning problem of the same nature as in the case of an unloaded heavy chain (Grabowski, P. (2003), ‘Abstract Semigroup Model of Heavy Chain System with Application to a Motion Planning Problem’, in Proceedings of 9th IEEE International Conference: Methods and Models in Automation and Robotics, 25–28 August, Mi?dzyzdroje, Poland, pp. 77–86 (IS1-2-3.PDF)). In order to solve this problem we first analyse its well-posedness and some basic properties. Next, we solve the output motion planning problem using a substitute of the inverse of the input–output operator represented in terms of the Laplace transforms. A problem of exponential stabilisation is also formulated and solved using a stabiliser of the colocated type. The exponential stabilisation is proved using the method of Lyapunov functionals combined with some frequency-domain tools. The method of Lyapunov functionals can be replaced by the spectral or exact controllability approach as shown in the second part (Grabowski, P. (2008), ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’, Opuscula Mathematica, 28 (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota), 481–505) of the present article. A laboratory setup which allows verification of the results in practice is described in detail. Its dynamical model is used as an example to illustrate the theoretical results. 相似文献