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1.
局部域有限阿贝尔扩张的导子与其判别式的应用   总被引:1,自引:0,他引:1  
在文献[1]的基础上,根据有限阿贝尔扩张的范数群及上限数分歧群的理论,进一步研究阿贝尔扩张k′/k的导子f(χ)与其判别式D(k′/k)之间的关系,从而得到局部域的有限阿贝尔扩张的又一个应用,即有限阿贝尔扩张k′/k的判别式D(k′/k)=∏χf(χ),其中上式右端是取遍Gal(k′/k)的所有特征标χ的导子之积.  相似文献   
2.
The purpose of this paper is to show that a first-order adaptive regulator globally stabilizes a class of infinite-dimensional systems having no right half plane zeros. Knowledge of the spectrum of the model's high-frequency gain is not required.  相似文献   
3.
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 Grabowski, P. 2003. Abstract Semigroup Model of Heavy Chain System with Application to a Motion Planning Problem. Proceedings of 9th IEEE International Conference: Methods and Models in Automation and Robotics. 25–28 August2003, Mi?dzyzdroje, Poland. pp.7786. (IS1-2-3.PDF) [Google Scholar]), ‘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 Grabowski, P. 2008. ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’. Opuscula Mathematica, 28: 481505. (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota) [Google Scholar]), ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’, Opuscula Mathematica, 28 (2008 Grabowski, P. 2008. ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’. Opuscula Mathematica, 28: 481505. (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota) [Google Scholar]) (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   
4.
定义了L-Fuzzy(内、左、右)正则半群,研究了它们与(内、左、右)正则半群的关系,并给出了判定定理,最后研究了L—Fuzzy(内、左、右)正则半群的结构。  相似文献   
5.
Development of intelligent decision-making systems which operate in complex environments like an automated factory, needs effective procedures for combining evidence from a variety of sources. Currently there are many ad-hoc evidence combination formulae as well as those based on specific methodologies such as the Bayesian, likelihood, etc. However, the limitations of these approaches have been well documented. In this paper, we begin with the testable and desirable properties required in a special problem. These properties are termed as axioms. We then systematically develop various families of combination rules obeying subsets of these axioms. The existing combination formulae form a subset of the rules mentioned here. We discuss the appropriateness of the different families of combination formulae.Partially supported by the Office of Naval Research under the grant N00014-85K-0611 and NSF under the grant IST 8405052.  相似文献   
6.
设T是交换格序群G的稳定等距。在这篇文章中,利用交换格序群可表为全序群的亚直积这特点.证得对×∈G.有T(x)=(T(x)1.T(x)2…7(x)i…)=(ε1x1.ε2x2…εixi…).其中T(x)i=εixi=±xi.进而得到交换格序群G等距的若干性质。  相似文献   
7.
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   
8.
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   
9.
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   
10.
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   
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