scholarly journals The full separation of the countable linear homogeneous system of the differenial equations at the resonance case

2018 ◽  
Vol 23 (2(32)) ◽  
pp. 20-34
Author(s):  
В. В. Джашитова
10.37236/6730 ◽  
2017 ◽  
Vol 24 (3) ◽  
Author(s):  
Christoph Spiegel

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Xin-Ge Liu ◽  
Mei-Lan Tang

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.


2017 ◽  
Vol 9 (6) ◽  
pp. 55
Author(s):  
Giorgi Giorgio

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.


1974 ◽  
Vol 96 (1) ◽  
pp. 32-48 ◽  
Author(s):  
W. R. Wade ◽  
P. I. Shen ◽  
C. W. Owens ◽  
A. F. McLean

This first part, of a two part paper, reviews the NOx emission problem of the regenerative gas turbine engine for automotive application. It discusses the problem of fuel droplet burning, which causes heterogenous combustion with resulting high flame temperatures and high levels of oxides of nitrogen. The paper proposes means to achieve homogeneous combustion and shows that, even with this approach, flame temperatures need to be closely controlled to effect a compromise between NOx, CO, and HC emissions in order to meet the stringent numerical levels of emissions specified by the Federal standards for 1976 and subsequent model year automobiles. The paper shows that combustor inlet temperature of a homogeneous system has little effect, theoretically, on computed NOx emissions expressed as grams per mile, thereby strengthening the case for the regenerative turbine engine. A design concept for homogeneous combustion with controlled flame temperature is discussed.


2013 ◽  
Vol 129 (6) ◽  
pp. 3282-3289 ◽  
Author(s):  
Lu Li ◽  
Bing Yuan ◽  
Shiwei Liu ◽  
Shitao Yu ◽  
Congxia Xie ◽  
...  
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