Convolutions onto an operator domain

1978 ◽  
Vol 12 (3) ◽  
pp. 230-231 ◽  
Author(s):  
É. L. Pekarev
Keyword(s):  
Operator Domain

Completely Indecomposable Modules

1949 ◽  
Vol 1 (2) ◽  
pp. 125-152 ◽  
Author(s):  
Ernst Snapper
Keyword(s):  
Abelian Group ◽  
Commutative Ring ◽  
Chain Condition ◽  
Indecomposable Module ◽  
Unit Element ◽  
Indecomposable Modules ◽  
Operator Domain ◽  
Unit Operator ◽  
Ascending Chain Condition

The purpose of this paper is to investigate completely indecomposable modules. A completely indecomposable module is an additive abelian group with a ring A as operator domain, where the following four conditions are satisfied.1-1. A is a commutative ring and has a unit element which is unit operator for .1-2. The submodules of satisfy the ascending chain condition. (Submodule will always mean invariant submodule.)

scholarly journals On Commutators of Fuzzy Multigroups

2020 ◽  
pp. 189-210
Author(s):  
P. A. Ejegwa ◽  
J. M. Agbetayo
Keyword(s):  
Group Theory ◽  
Operator Domain

Fuzzy multigroup is an application of fuzzy multiset to group theory. Although, a lots have been done on the theory of fuzzy multigroups, some group's theoretic notions could still be investigated in fuzzy multigroup context. Certainly, the idea of commutator is one of such group's theoretic notions yet to be studied in the environment of fuzzy multigroups. Hence, the aim of this article is to establish the notion of commutator in fuzzy multigroup setting. A number of some related results are obtained and characterized. Among several results that are obtained, it is established that, if $A$ and $B$ are fuzzy submultigroups of a fuzzy multigroup $C$, then $[A, B]\subseteq A\cup B$ holds. Some homomorphic properties of commutator in fuzzy multigroup context are discussed. The notion of admissible fuzzy submultisets $A$ and $B$ of $C\in FMG(X)$ under an operator domain $\mathcal{D}$ is explicated, and it is shown that $(A,B)$ and $[A,B]$ are $\mathcal{D}$-admissible.

Optimal State Feedback Control in Operator Domain for Multi-Rate Networked Control Systems with Long Time Delay

2012 ◽  
Vol 241-244 ◽  
pp. 1672-1676
Author(s):  
Yan Ping Wang ◽  
Qi Xin Zhu ◽  
Zhi Ping Li
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Control Systems ◽  
State Feedback ◽  
Networked Control Systems ◽  
State Feedback Control ◽  
Networked Control ◽  
Programming Approach ◽  
Operator Domain ◽  
Long Time

By multi-rate networked control systems (NCS), we mean the sampling periods of the sensor, the controller and the actuator in networked control systems are not the same, that is to say there are more than one sampling rate in networked control systems. For the long time delay multi-rate NCS with event-driven controller and actuator, a stochastic discrete model is established under operator. The state feedback control laws for the multi-rate NCS in operator domain are designed by using a dynamic programming approach. The derived optimal LQG controller can be used as a delay-compensator for multi-rate NCS with long time delays. An example is given to verify the theory results of this paper.

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