Exposed 2-Homogeneous Polynomials on the two-Dimensional Real Predual of Lorentz Sequence Space

2015 ◽  
Vol 13 (5) ◽  
pp. 2827-2839 ◽  
Author(s):  
Sung Guen Kim
Keyword(s):  
Sequence Space ◽  
Two Dimensional ◽  
Homogeneous Polynomials ◽  
Lorentz Sequence Space

scholarly journals The weak cotype 2 and the Orlicz property of the Lorentz sequence space d(a, 1)

1992 ◽  
Vol 34 (3) ◽  
pp. 271-276
Author(s):  
J. Zhu
Keyword(s):  
Banach Space ◽  
Function Space ◽  
Sequence Space ◽  
Affirmative Answer ◽  
Sequence Spaces ◽  
Similar Question ◽  
Lorentz Sequence Space ◽  
Symmetric Basis ◽  
Orlicz Property

The question “Does a Banach space with a symmetric basis and weak cotype 2 (or Orlicz) property have cotype 2?” is being seriously considered but is still open though the similar question for the r.i. function space on [0, 1] has an affirmative answer. (If X is a r.i. function space on [0, 1] and has weak cotype 2 (or Orlicz) property then it must have cotype 2.) In this note we prove that for Lorentz sequence spaces d(a, 1) they both hold.

scholarly journals On boundaries on the predual of the Lorentz sequence space

2007 ◽  
Vol 336 (1) ◽  
pp. 470-479 ◽  
Author(s):  
María D. Acosta ◽  
Luiza A. Moraes ◽  
Luis Romero Grados
Keyword(s):  
Sequence Space ◽  
Lorentz Sequence Space

scholarly journals On the non existence of periodic orbits for a class of two dimensional Kolmogorov systems

2021 ◽  
Vol 2021 (1) ◽  
pp. 1-11
Author(s):  
Rachid Boukoucha
Keyword(s):  
Periodic Orbits ◽  
Limit Cycles ◽  
Two Dimensional ◽  
Homogeneous Polynomials

Abstract In this paper we characterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form x ′ = x ( B 1 ( x , y ) ln | A 3 ( x , y ) A 4 ( x , y ) | + B 3 ( x , y ) ln | A 1 ( x , y ) A 2 ( x , y ) | ) , y ′ = y ( B 2 ( x , y ) ln | A 5 ( x , y ) A 6 ( x , y ) | + B 3 ( x , y ) ln | A 1 ( x , y ) A 2 ( x , y ) | ) \matrix{{x' = x\left( {{B_1}\left( {x,y} \right)\ln \left| {{{{A_3}\left( {x,y} \right)} \over {{A_4}\left( {x,y} \right)}}} \right| + {B_3}\left( {x,y} \right)\ln \left| {{{{A_1}\left( {x,y} \right)} \over {{A_2}\left( {x,y} \right)}}} \right|} \right),} \hfill \cr {y' = y\left( {{B_2}\left( {x,y} \right)\ln \left| {{{{A_5}\left( {x,y} \right)} \over {{A_6}\left( {x,y} \right)}}} \right| + {B_3}\left( {x,y} \right)\ln \left| {{{{A_1}\left( {x,y} \right)} \over {{A_2}\left( {x,y} \right)}}} \right|} \right)} \hfill \cr } where A 1 (x, y), A 2 (x, y), A 3 (x, y), A 4 (x, y), A 5 (x, y), A 6 (x, y), B 1 (x, y), B 2 (x, y), B 3 (x, y) are homogeneous polynomials of degree a, a, b, b, c, c, n, n, m respectively. Concrete example exhibiting the applicability of our result is introduced.

scholarly journals On generalized Lorentz sequence space defined by modulus functions

Filomat ◽  
2016 ◽  
Vol 30 (2) ◽  
pp. 497-504 ◽  
Author(s):  
Oğuz Oğur ◽  
Cenap Duyar
Keyword(s):  
Sequence Space ◽  
Lorentz Sequence Space
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