scholarly journals On Invertibility of an Interconnected System Composed of Two Dynamic Subsystems

2021 ◽  
Vol 11 (2) ◽  
pp. 596
Author(s):  
Mei Zhang ◽  
Boutaïeb Dahhou ◽  
Ze-tao Li
Keyword(s):  
Local Level ◽  
Sufficient Condition ◽  
Global Level ◽  
Necessary And Sufficient Condition ◽  
Initial State ◽  
Interconnected System ◽  
Global System ◽  
System A ◽  
Necessary And Sufficient ◽  
Local Input

In this paper, the invertibility of an interconnected system that consists of two dynamic subsystems was studied. It can be viewed as the distinguishability of the impacts of local input on the final global output, that is to say, whether the input at the local level can be recovered uniquely under a given output at the global level and initial state. The interconnected system constitutes two dynamic subsystems connected in a cascade manner. In order to guarantee the invertibility of the studied system, a necessary and sufficient condition was established. On the condition that both individual subsystems are invertible, the invertibility of the global system can be guaranteed. In order to recover the local input which generates a given global output, an algorithm was proposed for the studied interconnected system. Numerical examples were considered to confirm the effectiveness and robustness of the proposed algorithm.

Initial state estimation from limited observations of the heat equation in metric graphs

2022 ◽  
Author(s):  
Satoru Iwasaki
Keyword(s):  
Heat Equation ◽  
State Estimation ◽  
Observation Data ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Transition Matrices ◽  
Metric Graphs ◽  
Initial State ◽  
Estimation Problems ◽  
Necessary And Sufficient

Abstract This paper deals with initial state estimation problems of the heat equation in equilateral metric graphs being admitted to have cycles. Particularly, we are concerned with suitable placements of observation points in order to uniquely determine the initial state from observation data. We give a necessary and sufficient condition for suitable placements of observation points, and such suitable placements are determined from transition matrices of metric graphs. From numerical simulations, we confirm effectiveness of a necessary and sufficient condition.

Stochastic monotonicity of birth–death processes

1980 ◽  
Vol 12 (01) ◽  
pp. 59-80 ◽  
Author(s):  
Erik A. Van Doorn
Keyword(s):  
Initial Distribution ◽  
Unit Vector ◽  
Death Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Stochastic Monotonicity ◽  
Initial State ◽  
Distribution Vector ◽  
Necessary And Sufficient ◽  
Birth Death

A birth–death process {x(t): t ≥ 0} with state space the set of non-negative integers is said to be stochastically increasing (decreasing) on the interval (t 1, t 2) if Pr {x(t) > i} is increasing (decreasing) with t on (t 1, t 2) for all i = 0, 1, 2, ···. We study the problem of finding a necessary and sufficient condition for a birth–death process with general initial state probabilities to be stochastically monotone on an interval. Concrete results are obtained when the initial distribution vector of the process is a unit vector. Fundamental in the analysis, and of independent interest, is the concept of dual birth–death processes.

scholarly journals Stability Analysis ofθ-Methods for Neutral Multidelay Integrodifferential System

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Y. Xu ◽  
J. J. Zhao ◽  
Z. N. Sui
Keyword(s):  
Numerical Stability ◽  
Numerical Experiments ◽  
Analytic Solutions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Neutral Delay ◽  
Integrodifferential System ◽  
System A ◽  
The Stability ◽  
Necessary And Sufficient

This paper studies the stability of a class of neutral delay integrodifferential system. A necessary and sufficient condition of stability for its analytic solutions is considered. The improvedθ-methods are developed. Some numerical stability properties are obtained and numerical experiments are given.

scholarly journals Synchronization of a Generalized High-dimensional Kuramoto Model With Directed Graphs

2021 ◽  
Author(s):  
Jinxing Zhang ◽  
Jiandong Zhu ◽  
Xiaodi Li
Keyword(s):  
Directed Graph ◽  
Directed Graphs ◽  
Kuramoto Model ◽  
High Dimensional ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Initial State ◽  
Necessary And Sufficient ◽  
Theoretical Results

Abstract In this paper, a generalized high-dimensional Kuramoto model with directed graphs is investigated. A necessary and sufficient condition for equilibria is given and the synchronization is proved under weaker directed graph conditions and more general initial state constrains. Finally, an example is given to validate the theoretical results.

Stochastic monotonicity of birth–death processes

1980 ◽  
Vol 12 (1) ◽  
pp. 59-80 ◽  
Author(s):  
Erik A. Van Doorn
Keyword(s):  
Initial Distribution ◽  
Unit Vector ◽  
Death Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Stochastic Monotonicity ◽  
Initial State ◽  
Distribution Vector ◽  
Necessary And Sufficient ◽  
Birth Death

A birth–death process {x(t): t ≥ 0} with state space the set of non-negative integers is said to be stochastically increasing (decreasing) on the interval (t1, t2) if Pr {x(t) > i} is increasing (decreasing) with t on (t1, t2) for all i = 0, 1, 2, ···. We study the problem of finding a necessary and sufficient condition for a birth–death process with general initial state probabilities to be stochastically monotone on an interval. Concrete results are obtained when the initial distribution vector of the process is a unit vector. Fundamental in the analysis, and of independent interest, is the concept of dual birth–death processes.

scholarly journals Ο ρόλος των Συμβουλίων Ένταξης Μεταναστών στη συνύπαρξη ετερόθρησκων πληθυσμών σε τοπικό επίπεδο: Το παράδειγμα του Ισλάμ στην Ελλάδα

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
Νάσια Ιωάννου
Keyword(s):  
Religious Diversity ◽  
Local Level ◽  
Intercultural Dialogue ◽  
Potential Contribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Religious Groups ◽  
Necessary And Sufficient

The article examines the contribution of MICs in the coexistence of different religious groups at local level. It presents the basic problems encountered by Christians and Muslim migrants in Greece and proceeds by analysing the potential contribution of MICs in the harmonious coexistence of different religious groups. MICs are seen as providing a forum for intercultural dialogue and for acknowledging religious diversity as a necessary and sufficient condition for the inclusion of migrants.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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