scholarly journals A new variation of Weyl type theorems and perturbations

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1899-1906 ◽  
Author(s):  
Junli Shen ◽  
Alatancang Chen
Keyword(s):  
Finite Rank ◽  
Necessary Conditions ◽  
Finite Rank Operators ◽  
Weyl Type Theorems ◽  
Nilpotent Operators ◽  
Sufficient And Necessary Conditions ◽  
The Stability ◽  
Algebraic Operators

In this paper, we introduce the new property (aR), which extends property (R) introduced by Aiena and his collaborators. We investigate the property (aR) in connection with Weyl type theorems, and establish sufficient and necessary conditions for which property (aR) holds. We also study the stability of property (aR) under perturbations by finite rank operators, by nilpotent operators, by quasi-nilpotent operators and by algebraic operators commuting with T.

PROPERTY (Bgw) AND PERTURBATIONS

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
M.H.M. Rashid ◽  
T. Prasad
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Point Spectrum ◽  
Space Operator ◽  
Approximate Point Spectrum ◽  
Finite Rank Operators ◽  
Riesz Operators ◽  
Nilpotent Operators ◽  
The Stability ◽  
Isolated Eigenvalues

AbstractA Banach space operator T satisfies property (Bgw) if the complement in the approximate point spectrum σa(T) of the semi-B-essential approximate point spectrum σSHF+-(T) coincides with the set of isolated eigenvalues of T of Unite multiplicity E°(T). We find conditions for Banach Space operator tosatfafy the property (Bgw). We also study the stability of property (Bgw) under perturbations by nilpotent operators, by finite rank operators, by quasi-nilpotent operators and by Riesz operators commuting with T.

scholarly journals On strictly quasi-Fredholm linear relations and semi-B-Fredholm linear relation perturbations

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6337-6355 ◽  
Author(s):  
Bouaniza Hafsa ◽  
Maher Mnif
Keyword(s):  
Finite Rank ◽  
Linear Relation ◽  
Linear Relations ◽  
Finite Rank Operators ◽  
Lower Semi ◽  
The Stability

In this paper we introduce the set of strictly quasi-Fredholm linear relations and we give some of its properties. Furthermore, we study the connection between this set and some classes of linear relations related to the notions of ascent, essentially ascent, descent and essentially descent. The obtained results are used to study the stability of upper semi-B-Fredholm and lower semi-B-Fredholm linear relations under perturbation by finite rank operators.

scholarly journals A Note on Property(gb)and Perturbations

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Qingping Zeng ◽  
Huaijie Zhong
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Point Spectrum ◽  
Bounded Linear ◽  
Approximate Point Spectrum ◽  
Weyl Spectrum ◽  
Nilpotent Operators ◽  
The Stability ◽  
Quasinilpotent Operators ◽  
Study Property

An operatorT∈ℬ(X)defined on a Banach spaceXsatisfies property(gb)if the complement in the approximate point spectrumσa(T)of the upper semi-B-Weyl spectrumσSBF+-(T)coincides with the setΠ(T)of all poles of the resolvent ofT. In this paper, we continue to study property(gb)and the stability of it, for a bounded linear operatorTacting on a Banach space, under perturbations by nilpotent operators, by finite rank operators, and by quasinilpotent operators commuting withT. Two counterexamples show that property(gb)in general is not preserved under commuting quasi-nilpotent perturbations or commuting finite rank perturbations.

scholarly journals Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Awad A. Bakery ◽  
Afaf R. Abou Elmatty
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Finite Rank ◽  
Necessary Conditions ◽  
Operator Ideal ◽  
Approximation Numbers ◽  
Weighted Mean ◽  
Finite Rank Operators ◽  
Generalized Cesáro Sequence Space

Let E be a weighted Nakano sequence space or generalized Cesáro sequence space defined by weighted mean and by using s−numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SEX,Y≔T∈LX,Y:snTn=0∞∈E of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small, and finally, the pre-quasi Banach operator ideal constructed by s−numbers is simple Banach space.

Effects of aeroelasticity on coning motion of a spinning missile

2016 ◽  
Vol 230 (14) ◽  
pp. 2581-2595 ◽  
Author(s):  
Zhongjiao Shi ◽  
Liangyu Zhao
Keyword(s):  
Theoretical Analysis ◽  
Linear Equation ◽  
Vibration Mode ◽  
Necessary Conditions ◽  
Stable Region ◽  
Design Parameters ◽  
Governing Equations ◽  
First Order ◽  
Sufficient And Necessary Conditions ◽  
The Stability

The coning motion is a basic angular behavior of spinning missiles. Research on the stability of coning motion is always active. In this paper, the integrated nonlinear governing equations of rigid-elastic angular motion for a spinning missile with high fineness ratio are derived firstly following the Lagrangian approach. Secondly, a set of linear equation is obtained under some assumptions considering the first order vibration mode in the form of complex summation for theoretical analysis. Finally, the sufficient and necessary conditions of coning motion dynamic stability for spinning missile with and without an acceleration autopilot are analytically derived and verified by numerical simulations based on the linear equation. It is concluded that the aeroelasticity can shrink the stable region of the design parameters, even lead to a divergent coning motion.

scholarly journals On Stability of Multi-Valued Nonlinear Feedback Shift Registers

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Haiyan Wang ◽  
Qiuzhen Lin ◽  
Jianyong Chen ◽  
Jianqiang Li ◽  
Jianghua Zhong ◽  
...  
Keyword(s):  
Error Propagation ◽  
Necessary Conditions ◽  
Building Blocks ◽  
Nonlinear Feedback ◽  
Logic Network ◽  
Sufficient And Necessary Conditions ◽  
Nonlinear Feedback Shift Registers ◽  
Feedback Shift Registers ◽  
The Stability ◽  
Convolutional Decoders

Nonlinear feedback shift registers (NFSRs) are the main building blocks in many convolutional decoders, and a stable NFSR can limit decoding error propagation. Due to lack of efficient algebraic tools, the stability of multi-valued NFSRs has been much less studied. This paper studies the stability of multi-valued NFSRs using a logic network approach. A multi-valued NFSR can be viewed as a logic network. Based on its logic network representation, some sufficient and necessary conditions are provided for globally (locally) stable multi-valued NFSRs, explicit forms are given for the set of basins, and the algorithm for obtaining the set of basins is provided as well. Finally, a new method is presented for constructing stable n+1-stage NFSRs from stable n-stage NFSRs by the properties of D-morphism.

scholarly journals Economic Dynamics under Heterogeneous Adaptive Learning: General Criteria and Sufficient Conditions for Stability

2019 ◽  
Vol 19 (4) ◽  
pp. 87-103
Author(s):  
A. S. Bogomolova ◽  
D. V. Kolyuzhnov
Keyword(s):  
Adaptive Learning ◽  
Necessary Conditions ◽  
Learning Algorithm ◽  
Sufficient Conditions ◽  
Dsge Models ◽  
Shock Process ◽  
Sufficient And Necessary Conditions ◽  
Process Behavior ◽  
The Stability ◽  
Sign Conditions

The article extends the results of Honkapohja and Mitra (2006) and Kolyuzhnov (2011) and provides criteria and sufficient conditions for stability in a structurally heterogeneous economy under heterogeneous adaptive learning of agents. The criteria for stability under heterogeneous mixed RLS/SG learning for four classes of models – without lags and with lags of the endogenous variable and with t or t – 1 – dating of expectations – and sufficient conditions for stability for the cases of the diagonal structure of the shock process behavior or the heterogeneous RLS learning are presented in terms of the corresponding Jacobian matrices. In addition, the study presents a very useful criterion for the stability for all types of models under mixed RLS/SG learning with equal degrees of inertia for each type of learning algorithm in terms of stability of a suitably defined average economy with two agents. The derived criteria and sufficient conditions for stability are based on the results of the theory of stochastic approximation and are presented in terms of mixture of structural and learning heterogeneity, which are essential to get sufficient and necessary conditions for stability irrespective of heterogeneity in learning presented in terms of E-stability of suitably defined aggregate economies, the “same sign” conditions and the E-stability of a suitably defined average economy and its subeconomies. The fundamental nature of the approach adopted in the paper makes it possible to apply the results to a vast majority of the existing and prospective linear and linearized economic models (including estimated DSGE models) with adaptive learning of agents.

scholarly journals Stability Analysis of Distributed Order Fractional Chen System

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
H. Aminikhah ◽  
A. Refahi Sheikhani ◽  
H. Rezazadeh
Keyword(s):  
Stability Analysis ◽  
Numerical Solutions ◽  
Necessary Conditions ◽  
Chen System ◽  
Fractional Systems ◽  
Sufficient And Necessary Conditions ◽  
Fractional System ◽  
The Stability ◽  
Conditions Of Stability ◽  
Distributed Order

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.

Attractivity and Stability Analysis of Uncertain Differential Systems

2015 ◽  
Vol 25 (02) ◽  
pp. 1550022 ◽  
Author(s):  
Nana Tao ◽  
Yuanguo Zhu
Keyword(s):  
Stability Analysis ◽  
Differential System ◽  
Necessary Conditions ◽  
Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
The Stability

Uncertain differential system is a type of differential system involving uncertain processes. Stability analysis has been widely studied but no work has been dedicated to attractivity analysis of uncertain differential systems. In this paper, some concepts of attractivity for uncertain differential systems are presented. Then the corresponding sufficient and necessary conditions are given. Furthermore, the stability of the solutions and α-path of uncertain differential systems are studied.

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