A condition for the asymptotic stability of a linear homogeneous system whose principal part is a Jordan matrix

1970 ◽  
Vol 8 (6) ◽  
pp. 900-906
Author(s):  
V. A. Voblyi
Keyword(s):  
Asymptotic Stability ◽  
Principal Part ◽  
Homogeneous System ◽  
Linear Homogeneous System ◽  
Jordan Matrix

scholarly journals A Note on Sparse Supersaturation and Extremal Results for Linear Homogeneous Systems

10.37236/6730 ◽  
2017 ◽  
Vol 24 (3) ◽  
Author(s):  
Christoph Spiegel
Keyword(s):  
Homogeneous System ◽  
Random Sets ◽  
Type Result ◽  
Linear Homogeneous System ◽  
Homogeneous Systems ◽  
Class Of Matrices

We study the thresholds for the property of containing a solution to a linear homogeneous system in random sets. We expand a previous sparse Szémeredi-type result of Schacht to the broadest class of matrices possible. We also provide a shorter proof of a sparse Rado result of Friedgut, Rödl, Ruciński and Schacht based on a hypergraph container approach due to Nenadov and Steger. Lastly we further extend these results to include some solutions with repeated entries using a notion of non-trivial solutions due to Rúzsa as well as Rué et al.

scholarly journals Lyapunov-Type Inequality for a Class of Discrete Systems with Antiperiodic Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Xin-Ge Liu ◽  
Mei-Lan Tang
Keyword(s):  
Boundary Conditions ◽  
Positive Solution ◽  
Type Inequality ◽  
Discrete Systems ◽  
Homogeneous System ◽  
Higher Order ◽  
Linear Homogeneous System ◽  
3 Dimensional ◽  
Lyapunov Type Inequality

A class of higher-order 3-dimensional discrete systems with antiperiodic boundary conditions is investigated. Based on the existence of the positive solution of linear homogeneous system, several new Lyapunov-type inequalities are established.

scholarly journals Various Proofs of the Sylvester Criterion for Quadratic Forms

2017 ◽  
Vol 9 (6) ◽  
pp. 55
Author(s):  
Giorgi Giorgio
Keyword(s):  
Quadratic Forms ◽  
Homogeneous System ◽  
Algebraic Proof ◽  
Linear Homogeneous System

In the first part of the paper we present several proofs of the so-called Sylvester criterion for quadratic forms; some of the said proofs are short and easy. In the second part of the paper we give an algebraic proof of the Sylvester criterion for quadratic forms subject to a linear homogeneous system.

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