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.

Transient feedback and global instability in non-homogeneous systems

2005 ◽  
Vol 363 (1830) ◽  
pp. 1235-1245 ◽  
Author(s):  
S.N Timoshin ◽  
J.M Linkins
Keyword(s):  
Homogeneous System ◽  
Linear Wave ◽  
Transient Growth ◽  
Global Instability ◽  
Homogeneous Systems ◽  
Resonant Waves

Model examples of linear wave systems are considered to illustrate the origin of feedback instability in situations involving strong transients. Two mechanisms of transient growth are addressed. The first is a spatial amplification of resonant waves propagating in the same direction. The second form of transient growth is purely temporal. It is found that under certain conditions, both forms of transients can trigger global instability in a non-homogeneous system.

Performance of electrolyte measurements assessed by a trueness verification program

2016 ◽  
Vol 54 (8) ◽  
Author(s):  
Menglei Ge ◽  
Haijian Zhao ◽  
Ying Yan ◽  
Tianjiao Zhang ◽  
Jie Zeng ◽  
...  
Keyword(s):  
External Quality Assessment ◽  
Total Error ◽  
Homogeneous System ◽  
Serum Electrolyte ◽  
Sodium Potassium ◽  
Homogeneous Systems ◽  
Target Values ◽  
Fresh Frozen ◽  
Calcium And Magnesium ◽  
Sodium And Potassium

AbstractIn this study, we analyzed frozen sera with known commutabilities for standardization of serum electrolyte measurements in China.Fresh frozen sera were sent to 187 clinical laboratories in China for measurement of four electrolytes (sodium, potassium, calcium, and magnesium). Target values were assigned by two reference laboratories. Precision (CV), trueness (bias), and accuracy [total error (TEAbout half of the laboratories used a homogeneous system (same manufacturer for instrument, reagent and calibrator) for calcium and magnesium measurement, and more than 80% of laboratories used a homogeneous system for sodium and potassium measurement. More laboratories met the tolerance limit of imprecision (coefficient of variation [CVThe use of commutable proficiency testing/external quality assessment (PT/EQA) samples with values assigned by reference methods can monitor performance and provide reliable data for improving the performance of laboratory electrolyte measurement. The homogeneous systems were superior to the non homogeneous systems, whereas accuracy of assigned values of calibrators and assay stability remained challenges.

scholarly journals Growth and Decay Estimates near Non-Elementary Stationary Points

1970 ◽  
Vol 22 (6) ◽  
pp. 1156-1167 ◽  
Author(s):  
Courtney Coleman
Keyword(s):  
Stationary Point ◽  
Homogeneous System ◽  
Stationary Points ◽  
Vector System ◽  
Decay Estimates ◽  
Asymptotically Stable ◽  
Local Growth ◽  
Homogeneous Systems ◽  
First Approximation ◽  
Image Position

Local growth and decay estimates near the stationary point at the origin are derived in § 3 for solutions of the vector system,(1)where A(x) and B(y) are homogeneous of degree m > 1 in the components of x and y, respectively, and f* and g* are of order greater than m in ‖(x, y)‖ near the origin. It is assumed that x = 0 is asymptotically stable and y = 0 is asymptotically unstable for the homogeneous systems of first approximation,(2)In order to derive the estimates in § 3, various results are needed concerning solutions of a homogeneous system such as (2) (a). These are derived in § 2 and are based on work of Hahn [4; 5], Lefschetz [8], and Zubov [12].

scholarly journals Switched Convergence of Second-Order Switched Homogeneous Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Carmen Pérez ◽  
Francisco Benítez
Keyword(s):  
Sufficient Conditions ◽  
Homogeneous System ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Initial Condition ◽  
Numerical Examples ◽  
Switching Law ◽  
Homogeneous Systems ◽  
Switched Convergence ◽  
Necessary And Sufficient

This paper studies the stabilization of second-order switched homogeneous systems. We present results that solve the problem of stabilizing a switched homogeneous system; that is, we establish necessary and sufficient conditions under which the stabilization is assured. Moreover, given an initial condition, our method determines if there exists a switching law under which the solution converges to the origin and, if there exists this switching law, how it is constructed. Finally, two numerical examples are presented in order to illustrate the results.

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.

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