scholarly journals New Stability Criterion for the Dissipative Linear System and Analysis of Bresse System

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 542 ◽  
Author(s):  
Yoshihiro Ueda
Keyword(s):  
Linear System ◽  
Eigenvalue Problem ◽  
Stability Condition ◽  
Dissipative Structure ◽  
Physical Models ◽  
System Of Differential Equations ◽  
New Approach ◽  
Relaxation Term ◽  
Classical Stability ◽  
Symmetric Property

In this article, we introduce a new approach to obtain the property of the dissipative structure for a system of differential equations. If the system has a viscosity or relaxation term which possesses symmetric property, Shizuta and Kawashima in 1985 introduced the suitable stability condition called in this article Classical Stability Condition for the corresponding eigenvalue problem of the system, and derived the detailed relation between the coefficient matrices of the system and the eigenvalues. However, there are some complicated physical models which possess a non-symmetric viscosity or relaxation term and we cannot apply Classical Stability Condition to these models. Under this situation, our purpose in this article is to extend Classical Stability Condition for complicated models and to make the relation between the coefficient matrices and the corresponding eigenvalues clear. Furthermore, we shall explain the new dissipative structure through the several concrete examples.

Characterization of the dissipative structure for the symmetric hyperbolic system with non-symmetric relaxation

2021 ◽  
Vol 18 (01) ◽  
pp. 195-219
Author(s):  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Stability Condition ◽  
Dissipative Structure ◽  
General System ◽  
Partial Result ◽  
Symmetric Hyperbolic System ◽  
Standard Type ◽  
Classical Stability ◽  
The Stability

This paper is concerned with the dissipative structure for the linear symmetric hyperbolic system with non-symmetric relaxation. If the relaxation matrix of the system has symmetric property, Shizuta and Kawashima in 1985 introduced the suitable stability condition called Classical Stability Condition in this paper, and Umeda, Kawashima and Shizuta in 1984 analyzed the dissipative structure of the standard type. On the other hand, Ueda, Duan and Kawashima in 2012 and 2018 focused on the system with non-symmetric relaxation, and got the partial result which is the extension of known results. Furthermore, they argued the new dissipative structure called the regularity-loss type. In this situation, our purpose of this paper is to extend the stability theory introduced by Shizuta and Kawashima in 1985 and Umeda, Kawashima and Shizuta in 1984 for our general system.

scholarly journals Outflowing Envelopes From Stars at Arbitrary Optical Depths a New Approach to the Problem

1998 ◽  
Vol 11 (1) ◽  
pp. 381-381
Author(s):  
A.V. Dorodnitsyn
Keyword(s):  
Differential Equations ◽  
Massive Star ◽  
System Of Differential Equations ◽  
Continuous Transition ◽  
Satisfactory Description ◽  
Sonic Point ◽  
New Approach ◽  
Star Evolution ◽  
Matter Flux ◽  
Massive Star Evolution

We have considered a stationary outflowing envelope accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with partially separated radiation at arbitrary optical depths. The obtained systemof differential equations provides a continuous transition of the solution between optically thin and optically thick regions. We analytically derivedapproximate representation of the solution at the vicinity of the sonic point. Using this representation we numerically integrate the system of equations from the critical point to the infinity. Matching the boundary conditions we obtain solutions describing the problem system of differential equations. The theoretical approach advanced in this work could be useful for self-consistent simulations of massive star evolution with mass loss.

A New Approach for Supervised Dimensionality Reduction

2018 ◽  
Vol 14 (4) ◽  
pp. 20-37 ◽  
Author(s):  
Yinglei Song ◽  
Yongzhong Li ◽  
Junfeng Qu
Keyword(s):  
Eigenvalue Problem ◽  
Dimensionality Reduction ◽  
Image Databases ◽  
Data Sets ◽  
Data Set ◽  
New Approach ◽  
Local Structures ◽  
Benchmark Data ◽  
Global And Local

This article develops a new approach for supervised dimensionality reduction. This approach considers both global and local structures of a labelled data set and maximizes a new objective that includes the effects from both of them. The objective can be approximately optimized by solving an eigenvalue problem. The approach is evaluated based on a few benchmark data sets and image databases. Its performance is also compared with a few other existing approaches for dimensionality reduction. Testing results show that, on average, this new approach can achieve more accurate results for dimensionality reduction than existing approaches.

scholarly journals A Method for Sensor Placement Taking into Account Diagnosability Criteria

2008 ◽  
Vol 18 (4) ◽  
pp. 497-512 ◽  
Author(s):  
Abed Yassine ◽  
Stéphane Ploix ◽  
Jean-Marie Flaus
Keyword(s):  
Linear System ◽  
Nonlinear Equations ◽  
Sensor Placement ◽  
New Approach ◽  
Analytical Redundancy ◽  
The Cost ◽  
Constraint Sets

A Method for Sensor Placement Taking into Account Diagnosability CriteriaThis paper presents a new approach to sensor placement based on diagnosability criteria. It is based on the study of structural matrices. Properties of structural matrices regarding detectability, discriminability and diagnosability are established in order to be used by sensor placement methods. The proposed approach manages any number of constraints modelled by linear or nonlinear equations and it does not require the design of analytical redundancy relations. Assuming that a constraint models a component and that the cost of the measurement of each variable is defined, a method determining sensor placements satisfying diagnosability specifications, where all the diagnosable, discriminable and detectable constraint sets are specified, is proposed. An application example dealing with a dynamical linear system is presented.

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