Counting shape and homotopy types among fundamental absolute neighborhood retracts: An elementary approach

1993 ◽  
Vol 79 (1) ◽  
pp. 411-414 ◽  
Author(s):  
M. A. Morón ◽  
F. R. Ruiz del Portal
Keyword(s):  
Elementary Approach ◽  
Homotopy Types ◽  
Absolute Neighborhood Retracts

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

scholarly journals Homotopy Types of Stabilizers and Orbits of Morse Functions on Surfaces

2006 ◽  
Vol 29 (3) ◽  
pp. 241-285 ◽  
Author(s):  
Sergiy Maksymenko
Keyword(s):  
Morse Functions ◽  
Homotopy Types

scholarly journals The Stable Homotopy Types of Stunted Lens Spaces mod 4

1998 ◽  
Vol 350 (12) ◽  
pp. 4775-4798 ◽  
Author(s):  
Huajian Yang
Keyword(s):  
Stable Homotopy ◽  
Lens Spaces ◽  
Homotopy Types

On Grothendieck's local duality theorem

1979 ◽  
Vol 85 (3) ◽  
pp. 431-437 ◽  
Author(s):  
M. H. Bijan-Zadeh ◽  
R. Y. Sharp
Keyword(s):  
Algebraic Geometry ◽  
Commutative Algebra ◽  
Noetherian Ring ◽  
Duality Theorem ◽  
Great Emphasis ◽  
Triangulated Category ◽  
Elementary Approach ◽  
Commutative Noetherian Ring ◽  
Local Duality ◽  
Dualizing Complexes

In (11) and (12), a comparatively elementary approach to the use of dualizing complexes in commutative algebra has been developed. Dualizing complexes were introduced by Grothendieck and Hartshorne in (2) for use in algebraic geometry; the approach to dualizing complexes in (11) and (12) differs from that of Grothendieck and Hartshorne in that it avoids use of the concepts of triangulated category, derived category, and localization of categories, and instead places great emphasis on the concept of quasi-isomorphism of complexes of modules over a commutative Noetherian ring.

scholarly journals Elementary approach to closed billiard trajectories in asymmetric normed spaces

2016 ◽  
Vol 144 (10) ◽  
pp. 4501-4513 ◽  
Author(s):  
Arseniy Akopyan ◽  
Alexey Balitskiy ◽  
Roman Karasev ◽  
Anastasia Sharipova
Keyword(s):  
Elementary Approach ◽  
Normed Spaces
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